%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL402-1 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:49:46 AM UTC 2026
% Result : Unsatisfiable 58.88s 7.91s
% Output : Proof 140.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL402-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 15:38:09 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 58.88/7.91 Command-line arguments: --no-flatten-goal
% 58.88/7.91
% 58.88/7.91 % SZS status Unsatisfiable
% 58.88/7.91
% 119.08/17.51 % SZS output start Proof
% 119.08/17.51 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 119.08/17.51 Axiom 2 (cn_3): is_a_theorem(implies(X, implies(not(X), Y))) = true.
% 119.08/17.51 Axiom 3 (cn_2): is_a_theorem(implies(implies(not(X), X), X)) = true.
% 119.08/17.51 Axiom 4 (condensed_detachment): ifeq(is_a_theorem(implies(X, Y)), true, ifeq(is_a_theorem(X), true, is_a_theorem(Y), true), true) = true.
% 119.78/17.64 Axiom 5 (cn_1): is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))) = true.
% 119.78/17.64
% 119.78/17.64 Goal 1 (prove_cn_68): is_a_theorem(implies(not(implies(x, not(y))), y)) = true.
% 119.78/17.64 Proof:
% 119.78/17.64 is_a_theorem(implies(not(implies(x, not(y))), y))
% 119.78/17.64 = { by axiom 1 (ifeq_axiom) R->L }
% 119.78/17.64 ifeq(true, true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 119.78/17.64 = { by axiom 4 (condensed_detachment) R->L }
% 119.78/17.64 ifeq(ifeq(is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 119.78/17.64 = { by axiom 1 (ifeq_axiom) R->L }
% 119.78/17.64 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 119.78/17.64 = { by axiom 4 (condensed_detachment) R->L }
% 119.78/17.64 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y)))))))), true, ifeq(is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 119.78/17.64 = { by axiom 5 (cn_1) }
% 119.78/17.64 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 119.78/17.64 = { by axiom 1 (ifeq_axiom) }
% 119.78/17.64 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 119.78/17.64 = { by axiom 1 (ifeq_axiom) R->L }
% 119.78/17.64 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 119.78/17.65 = { by axiom 4 (condensed_detachment) R->L }
% 119.78/17.65 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 119.78/17.65 = { by axiom 1 (ifeq_axiom) R->L }
% 119.78/17.65 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 119.78/17.65 = { by axiom 5 (cn_1) R->L }
% 119.78/17.65 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 119.78/17.65 = { by axiom 1 (ifeq_axiom) R->L }
% 119.78/17.65 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 119.78/17.66 = { by axiom 5 (cn_1) R->L }
% 119.78/17.66 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y))))), implies(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))))), true, ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 119.78/17.66 = { by axiom 4 (condensed_detachment) }
% 119.78/17.66 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 119.78/17.66 = { by axiom 1 (ifeq_axiom) }
% 119.78/17.66 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 119.78/17.66 = { by axiom 1 (ifeq_axiom) R->L }
% 119.78/17.66 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 119.78/17.67 = { by axiom 4 (condensed_detachment) R->L }
% 119.78/17.67 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y)))))), true, ifeq(is_a_theorem(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 119.78/17.67 = { by axiom 1 (ifeq_axiom) R->L }
% 119.78/17.67 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 119.78/17.67 = { by axiom 4 (condensed_detachment) R->L }
% 119.78/17.67 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(x), not(y)), implies(not(not(y)), not(y))), implies(x, implies(not(not(y)), not(y)))), implies(not(y), implies(x, implies(not(not(y)), not(y)))))), true, ifeq(is_a_theorem(implies(implies(implies(not(x), not(y)), implies(not(not(y)), not(y))), implies(x, implies(not(not(y)), not(y))))), true, is_a_theorem(implies(not(y), implies(x, implies(not(not(y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 119.78/17.68 = { by axiom 1 (ifeq_axiom) R->L }
% 119.78/17.68 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(x), not(y)), implies(not(not(y)), not(y))), implies(x, implies(not(not(y)), not(y)))), implies(not(y), implies(x, implies(not(not(y)), not(y)))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(x), not(y)), implies(not(not(y)), not(y))), implies(x, implies(not(not(y)), not(y))))), true), true, is_a_theorem(implies(not(y), implies(x, implies(not(not(y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 119.78/17.68 = { by axiom 5 (cn_1) R->L }
% 119.78/17.68 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(x), not(y)), implies(not(not(y)), not(y))), implies(x, implies(not(not(y)), not(y)))), implies(not(y), implies(x, implies(not(not(y)), not(y)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(x), not(y))), implies(implies(implies(not(x), not(y)), implies(not(not(y)), not(y))), implies(x, implies(not(not(y)), not(y)))))), true, is_a_theorem(implies(implies(implies(not(x), not(y)), implies(not(not(y)), not(y))), implies(x, implies(not(not(y)), not(y))))), true), true, is_a_theorem(implies(not(y), implies(x, implies(not(not(y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 119.78/17.68 = { by axiom 1 (ifeq_axiom) R->L }
% 119.78/17.69 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(x), not(y)), implies(not(not(y)), not(y))), implies(x, implies(not(not(y)), not(y)))), implies(not(y), implies(x, implies(not(not(y)), not(y)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(x), not(y))), implies(implies(implies(not(x), not(y)), implies(not(not(y)), not(y))), implies(x, implies(not(not(y)), not(y)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(x), not(y)), implies(not(not(y)), not(y))), implies(x, implies(not(not(y)), not(y))))), true), true), true, is_a_theorem(implies(not(y), implies(x, implies(not(not(y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 119.78/17.69 = { by axiom 2 (cn_3) R->L }
% 119.78/17.69 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(x), not(y)), implies(not(not(y)), not(y))), implies(x, implies(not(not(y)), not(y)))), implies(not(y), implies(x, implies(not(not(y)), not(y)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(x), not(y))), implies(implies(implies(not(x), not(y)), implies(not(not(y)), not(y))), implies(x, implies(not(not(y)), not(y)))))), true, ifeq(is_a_theorem(implies(x, implies(not(x), not(y)))), true, is_a_theorem(implies(implies(implies(not(x), not(y)), implies(not(not(y)), not(y))), implies(x, implies(not(not(y)), not(y))))), true), true), true, is_a_theorem(implies(not(y), implies(x, implies(not(not(y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 119.78/17.69 = { by axiom 4 (condensed_detachment) }
% 119.78/17.69 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(x), not(y)), implies(not(not(y)), not(y))), implies(x, implies(not(not(y)), not(y)))), implies(not(y), implies(x, implies(not(not(y)), not(y)))))), true, ifeq(true, true, is_a_theorem(implies(not(y), implies(x, implies(not(not(y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 119.78/17.70 = { by axiom 1 (ifeq_axiom) }
% 119.78/17.70 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(x), not(y)), implies(not(not(y)), not(y))), implies(x, implies(not(not(y)), not(y)))), implies(not(y), implies(x, implies(not(not(y)), not(y)))))), true, is_a_theorem(implies(not(y), implies(x, implies(not(not(y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 120.49/17.70 = { by axiom 1 (ifeq_axiom) R->L }
% 120.49/17.70 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(x), not(y)), implies(not(not(y)), not(y))), implies(x, implies(not(not(y)), not(y)))), implies(not(y), implies(x, implies(not(not(y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(x, implies(not(not(y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 120.49/17.70 = { by axiom 4 (condensed_detachment) R->L }
% 120.49/17.71 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(y)), not(x)), implies(implies(not(x), not(y)), implies(not(not(y)), not(y)))), implies(not(y), implies(implies(not(x), not(y)), implies(not(not(y)), not(y)))))), true, ifeq(is_a_theorem(implies(implies(not(not(y)), not(x)), implies(implies(not(x), not(y)), implies(not(not(y)), not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(x), not(y)), implies(not(not(y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), not(y)), implies(not(not(y)), not(y))), implies(x, implies(not(not(y)), not(y)))), implies(not(y), implies(x, implies(not(not(y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(x, implies(not(not(y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 120.49/17.71 = { by axiom 1 (ifeq_axiom) R->L }
% 120.49/17.71 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(y)), not(x)), implies(implies(not(x), not(y)), implies(not(not(y)), not(y)))), implies(not(y), implies(implies(not(x), not(y)), implies(not(not(y)), not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(y)), not(x)), implies(implies(not(x), not(y)), implies(not(not(y)), not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(x), not(y)), implies(not(not(y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), not(y)), implies(not(not(y)), not(y))), implies(x, implies(not(not(y)), not(y)))), implies(not(y), implies(x, implies(not(not(y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(x, implies(not(not(y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 120.49/17.71 = { by axiom 5 (cn_1) R->L }
% 120.49/17.72 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(y), implies(not(not(y)), not(x))), implies(implies(implies(not(not(y)), not(x)), implies(implies(not(x), not(y)), implies(not(not(y)), not(y)))), implies(not(y), implies(implies(not(x), not(y)), implies(not(not(y)), not(y))))))), true, is_a_theorem(implies(implies(implies(not(not(y)), not(x)), implies(implies(not(x), not(y)), implies(not(not(y)), not(y)))), implies(not(y), implies(implies(not(x), not(y)), implies(not(not(y)), not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(y)), not(x)), implies(implies(not(x), not(y)), implies(not(not(y)), not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(x), not(y)), implies(not(not(y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), not(y)), implies(not(not(y)), not(y))), implies(x, implies(not(not(y)), not(y)))), implies(not(y), implies(x, implies(not(not(y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(x, implies(not(not(y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 120.49/17.72 = { by axiom 1 (ifeq_axiom) R->L }
% 120.49/17.72 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(y), implies(not(not(y)), not(x))), implies(implies(implies(not(not(y)), not(x)), implies(implies(not(x), not(y)), implies(not(not(y)), not(y)))), implies(not(y), implies(implies(not(x), not(y)), implies(not(not(y)), not(y))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(y)), not(x)), implies(implies(not(x), not(y)), implies(not(not(y)), not(y)))), implies(not(y), implies(implies(not(x), not(y)), implies(not(not(y)), not(y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(y)), not(x)), implies(implies(not(x), not(y)), implies(not(not(y)), not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(x), not(y)), implies(not(not(y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), not(y)), implies(not(not(y)), not(y))), implies(x, implies(not(not(y)), not(y)))), implies(not(y), implies(x, implies(not(not(y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(x, implies(not(not(y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 120.49/17.72 = { by axiom 2 (cn_3) R->L }
% 120.49/17.72 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(y), implies(not(not(y)), not(x))), implies(implies(implies(not(not(y)), not(x)), implies(implies(not(x), not(y)), implies(not(not(y)), not(y)))), implies(not(y), implies(implies(not(x), not(y)), implies(not(not(y)), not(y))))))), true, ifeq(is_a_theorem(implies(not(y), implies(not(not(y)), not(x)))), true, is_a_theorem(implies(implies(implies(not(not(y)), not(x)), implies(implies(not(x), not(y)), implies(not(not(y)), not(y)))), implies(not(y), implies(implies(not(x), not(y)), implies(not(not(y)), not(y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(y)), not(x)), implies(implies(not(x), not(y)), implies(not(not(y)), not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(x), not(y)), implies(not(not(y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), not(y)), implies(not(not(y)), not(y))), implies(x, implies(not(not(y)), not(y)))), implies(not(y), implies(x, implies(not(not(y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(x, implies(not(not(y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 120.49/17.73 = { by axiom 4 (condensed_detachment) }
% 120.49/17.73 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(y)), not(x)), implies(implies(not(x), not(y)), implies(not(not(y)), not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(x), not(y)), implies(not(not(y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), not(y)), implies(not(not(y)), not(y))), implies(x, implies(not(not(y)), not(y)))), implies(not(y), implies(x, implies(not(not(y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(x, implies(not(not(y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 120.49/17.73 = { by axiom 1 (ifeq_axiom) }
% 120.49/17.73 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(y)), not(x)), implies(implies(not(x), not(y)), implies(not(not(y)), not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(x), not(y)), implies(not(not(y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(x), not(y)), implies(not(not(y)), not(y))), implies(x, implies(not(not(y)), not(y)))), implies(not(y), implies(x, implies(not(not(y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(x, implies(not(not(y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 120.49/17.73 = { by axiom 5 (cn_1) }
% 120.49/17.74 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(y), implies(implies(not(x), not(y)), implies(not(not(y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(x), not(y)), implies(not(not(y)), not(y))), implies(x, implies(not(not(y)), not(y)))), implies(not(y), implies(x, implies(not(not(y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(x, implies(not(not(y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 120.49/17.74 = { by axiom 1 (ifeq_axiom) }
% 120.49/17.74 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(y), implies(implies(not(x), not(y)), implies(not(not(y)), not(y))))), true, is_a_theorem(implies(implies(implies(implies(not(x), not(y)), implies(not(not(y)), not(y))), implies(x, implies(not(not(y)), not(y)))), implies(not(y), implies(x, implies(not(not(y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(x, implies(not(not(y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 120.49/17.74 = { by axiom 1 (ifeq_axiom) R->L }
% 120.49/17.74 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(y), implies(implies(not(x), not(y)), implies(not(not(y)), not(y))))), true, is_a_theorem(implies(implies(implies(implies(not(x), not(y)), implies(not(not(y)), not(y))), implies(x, implies(not(not(y)), not(y)))), implies(not(y), implies(x, implies(not(not(y)), not(y)))))), true), true), true, is_a_theorem(implies(not(y), implies(x, implies(not(not(y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 120.49/17.74 = { by axiom 5 (cn_1) R->L }
% 120.49/17.75 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(y), implies(implies(not(x), not(y)), implies(not(not(y)), not(y)))), implies(implies(implies(implies(not(x), not(y)), implies(not(not(y)), not(y))), implies(x, implies(not(not(y)), not(y)))), implies(not(y), implies(x, implies(not(not(y)), not(y))))))), true, ifeq(is_a_theorem(implies(not(y), implies(implies(not(x), not(y)), implies(not(not(y)), not(y))))), true, is_a_theorem(implies(implies(implies(implies(not(x), not(y)), implies(not(not(y)), not(y))), implies(x, implies(not(not(y)), not(y)))), implies(not(y), implies(x, implies(not(not(y)), not(y)))))), true), true), true, is_a_theorem(implies(not(y), implies(x, implies(not(not(y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 120.49/17.75 = { by axiom 4 (condensed_detachment) }
% 120.49/17.75 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(y), implies(x, implies(not(not(y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 120.49/17.75 = { by axiom 1 (ifeq_axiom) }
% 120.49/17.75 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(y), implies(x, implies(not(not(y)), not(y))))), true, is_a_theorem(implies(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 120.49/17.75 = { by axiom 1 (ifeq_axiom) R->L }
% 120.49/17.75 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(y), implies(x, implies(not(not(y)), not(y))))), true, is_a_theorem(implies(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 120.49/17.75 = { by axiom 5 (cn_1) R->L }
% 120.49/17.76 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(y), implies(x, implies(not(not(y)), not(y)))), implies(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))))), true, ifeq(is_a_theorem(implies(not(y), implies(x, implies(not(not(y)), not(y))))), true, is_a_theorem(implies(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 120.49/17.76 = { by axiom 4 (condensed_detachment) }
% 120.49/17.76 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 120.49/17.76 = { by axiom 1 (ifeq_axiom) }
% 120.49/17.76 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 120.49/17.76 = { by axiom 1 (ifeq_axiom) R->L }
% 120.49/17.76 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 120.49/17.76 = { by axiom 4 (condensed_detachment) R->L }
% 120.49/17.77 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(y), not(y)), implies(implies(not(not(y)), not(y)), not(y))), implies(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(x, not(y))), implies(implies(not(y), not(y)), implies(x, not(y)))))), true, ifeq(is_a_theorem(implies(implies(not(y), not(y)), implies(implies(not(not(y)), not(y)), not(y)))), true, is_a_theorem(implies(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(x, not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 120.49/17.77 = { by axiom 5 (cn_1) }
% 120.49/17.77 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(y), not(y)), implies(implies(not(not(y)), not(y)), not(y)))), true, is_a_theorem(implies(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(x, not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 120.49/17.77 = { by axiom 1 (ifeq_axiom) }
% 120.49/17.77 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(y), not(y)), implies(implies(not(not(y)), not(y)), not(y)))), true, is_a_theorem(implies(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(x, not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 120.49/17.77 = { by axiom 1 (ifeq_axiom) R->L }
% 120.49/17.77 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(y), not(y)), implies(implies(not(not(y)), not(y)), not(y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(x, not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 120.49/17.78 = { by axiom 5 (cn_1) R->L }
% 120.49/17.78 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(implies(not(y), not(y)), implies(implies(not(not(y)), not(y)), not(y))))), true, is_a_theorem(implies(implies(not(y), not(y)), implies(implies(not(not(y)), not(y)), not(y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(x, not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 120.49/17.78 = { by axiom 1 (ifeq_axiom) R->L }
% 120.49/17.78 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(implies(not(y), not(y)), implies(implies(not(not(y)), not(y)), not(y))))), true, ifeq(true, true, is_a_theorem(implies(implies(not(y), not(y)), implies(implies(not(not(y)), not(y)), not(y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(x, not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 120.49/17.78 = { by axiom 3 (cn_2) R->L }
% 120.49/17.78 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(implies(not(y), not(y)), implies(implies(not(not(y)), not(y)), not(y))))), true, ifeq(is_a_theorem(implies(implies(not(not(y)), not(y)), not(y))), true, is_a_theorem(implies(implies(not(y), not(y)), implies(implies(not(not(y)), not(y)), not(y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(x, not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 120.49/17.78 = { by axiom 4 (condensed_detachment) }
% 120.49/17.79 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(x, not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 120.49/17.79 = { by axiom 1 (ifeq_axiom) }
% 120.49/17.79 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(x, not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true, is_a_theorem(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 120.49/17.79 = { by axiom 1 (ifeq_axiom) R->L }
% 120.49/17.79 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(x, not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true, is_a_theorem(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 120.49/17.79 = { by axiom 4 (condensed_detachment) R->L }
% 120.49/17.80 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(implies(not(not(y)), not(y)), not(y)), implies(x, not(y)))), implies(implies(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(x, not(y))), implies(implies(not(y), not(y)), implies(x, not(y)))), implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))))), true, ifeq(is_a_theorem(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(implies(not(not(y)), not(y)), not(y)), implies(x, not(y))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(x, not(y))), implies(implies(not(y), not(y)), implies(x, not(y)))), implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(x, not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true, is_a_theorem(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 120.49/17.80 = { by axiom 5 (cn_1) }
% 121.21/17.80 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(implies(not(not(y)), not(y)), not(y)), implies(x, not(y))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(x, not(y))), implies(implies(not(y), not(y)), implies(x, not(y)))), implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(x, not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true, is_a_theorem(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.21/17.80 = { by axiom 1 (ifeq_axiom) }
% 121.21/17.80 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(implies(not(not(y)), not(y)), not(y)), implies(x, not(y))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(x, not(y))), implies(implies(not(y), not(y)), implies(x, not(y)))), implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(x, not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true, is_a_theorem(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.21/17.80 = { by axiom 5 (cn_1) }
% 121.21/17.80 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(x, not(y))), implies(implies(not(y), not(y)), implies(x, not(y)))), implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(x, not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true, is_a_theorem(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.21/17.81 = { by axiom 1 (ifeq_axiom) }
% 121.21/17.81 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(x, not(y))), implies(implies(not(y), not(y)), implies(x, not(y)))), implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(x, not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true, is_a_theorem(implies(implies(x, implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.21/17.81 = { by axiom 4 (condensed_detachment) }
% 121.21/17.81 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.21/17.81 = { by axiom 1 (ifeq_axiom) }
% 121.21/17.81 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.21/17.81 = { by axiom 1 (ifeq_axiom) R->L }
% 121.21/17.81 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.21/17.81 = { by axiom 5 (cn_1) R->L }
% 121.21/17.81 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y)))), implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))))), true, ifeq(is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(x, not(y))))), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(x, not(y))), implies(not(implies(x, not(y))), implies(x, not(y)))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.21/17.81 = { by axiom 4 (condensed_detachment) }
% 121.21/17.82 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.21/17.82 = { by axiom 1 (ifeq_axiom) }
% 121.21/17.82 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.21/17.82 = { by axiom 1 (ifeq_axiom) R->L }
% 121.21/17.82 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true, ifeq(true, true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.21/17.82 = { by axiom 4 (condensed_detachment) R->L }
% 121.21/17.82 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(x, not(y))), implies(not(y), not(y))))), true, ifeq(is_a_theorem(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y)))), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(y), not(y)))), true), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.21/17.82 = { by axiom 3 (cn_2) }
% 121.21/17.82 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(x, not(y))), implies(not(y), not(y))))), true, ifeq(true, true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(y), not(y)))), true), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.21/17.82 = { by axiom 1 (ifeq_axiom) }
% 121.21/17.83 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(x, not(y))), implies(not(y), not(y))))), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.21/17.83 = { by axiom 1 (ifeq_axiom) R->L }
% 121.21/17.83 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(x, not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.21/17.83 = { by axiom 4 (condensed_detachment) R->L }
% 121.21/17.83 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y)))), implies(not(implies(x, not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y)))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(x, not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(x, not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.21/17.83 = { by axiom 1 (ifeq_axiom) R->L }
% 121.21/17.84 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y)))), implies(not(implies(x, not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(x, not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(x, not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.21/17.84 = { by axiom 5 (cn_1) R->L }
% 121.21/17.84 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(not(implies(x, not(y)))), implies(not(y), not(y)))), implies(implies(implies(not(not(implies(x, not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y)))), implies(not(implies(x, not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y)))), implies(not(implies(x, not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(x, not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(x, not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.21/17.84 = { by axiom 1 (ifeq_axiom) R->L }
% 121.21/17.84 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(not(implies(x, not(y)))), implies(not(y), not(y)))), implies(implies(implies(not(not(implies(x, not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y)))), implies(not(implies(x, not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y)))), implies(not(implies(x, not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(x, not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(x, not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.21/17.84 = { by axiom 2 (cn_3) R->L }
% 121.21/17.85 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(not(implies(x, not(y)))), implies(not(y), not(y)))), implies(implies(implies(not(not(implies(x, not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y)))), implies(not(implies(x, not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))))), true, ifeq(is_a_theorem(implies(not(implies(x, not(y))), implies(not(not(implies(x, not(y)))), implies(not(y), not(y))))), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y)))), implies(not(implies(x, not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(x, not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(x, not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.21/17.85 = { by axiom 4 (condensed_detachment) }
% 121.21/17.85 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(implies(x, not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(x, not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.21/17.85 = { by axiom 1 (ifeq_axiom) }
% 121.21/17.85 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(x, not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(x, not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.21/17.85 = { by axiom 1 (ifeq_axiom) R->L }
% 121.21/17.85 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(x, not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.21/17.86 = { by axiom 4 (condensed_detachment) R->L }
% 121.21/17.86 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(y), not(y)), implies(not(implies(not(y), not(y))), not(not(implies(x, not(y))))))), true, ifeq(is_a_theorem(implies(not(y), not(y))), true, is_a_theorem(implies(not(implies(not(y), not(y))), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(x, not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.21/17.86 = { by axiom 2 (cn_3) }
% 121.21/17.86 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(y), not(y))), true, is_a_theorem(implies(not(implies(not(y), not(y))), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(x, not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.21/17.86 = { by axiom 1 (ifeq_axiom) }
% 121.21/17.86 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(y), not(y))), true, is_a_theorem(implies(not(implies(not(y), not(y))), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(x, not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.21/17.87 = { by axiom 1 (ifeq_axiom) R->L }
% 121.21/17.87 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(y), not(y))), true), true, is_a_theorem(implies(not(implies(not(y), not(y))), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(x, not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.21/17.87 = { by axiom 4 (condensed_detachment) R->L }
% 121.21/17.87 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(y), implies(not(not(y)), not(y))), implies(implies(implies(not(not(y)), not(y)), not(y)), implies(not(y), not(y))))), true, ifeq(is_a_theorem(implies(not(y), implies(not(not(y)), not(y)))), true, is_a_theorem(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(not(y), not(y)))), true), true), true, is_a_theorem(implies(not(y), not(y))), true), true, is_a_theorem(implies(not(implies(not(y), not(y))), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(x, not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.21/17.89 = { by axiom 2 (cn_3) }
% 121.21/17.89 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(y), implies(not(not(y)), not(y))), implies(implies(implies(not(not(y)), not(y)), not(y)), implies(not(y), not(y))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(not(y), not(y)))), true), true), true, is_a_theorem(implies(not(y), not(y))), true), true, is_a_theorem(implies(not(implies(not(y), not(y))), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(x, not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.21/17.89 = { by axiom 1 (ifeq_axiom) }
% 121.21/17.89 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(y), implies(not(not(y)), not(y))), implies(implies(implies(not(not(y)), not(y)), not(y)), implies(not(y), not(y))))), true, is_a_theorem(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), not(y))), true), true, is_a_theorem(implies(not(implies(not(y), not(y))), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(x, not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.21/17.89 = { by axiom 5 (cn_1) }
% 121.21/17.89 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), not(y))), true), true, is_a_theorem(implies(not(implies(not(y), not(y))), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(x, not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.21/17.90 = { by axiom 1 (ifeq_axiom) }
% 121.21/17.90 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(not(y), not(y)))), true, is_a_theorem(implies(not(y), not(y))), true), true, is_a_theorem(implies(not(implies(not(y), not(y))), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(x, not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.90 = { by axiom 1 (ifeq_axiom) R->L }
% 121.91/17.90 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(not(y), not(y)))), true, ifeq(true, true, is_a_theorem(implies(not(y), not(y))), true), true), true, is_a_theorem(implies(not(implies(not(y), not(y))), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(x, not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.90 = { by axiom 3 (cn_2) R->L }
% 121.91/17.90 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(not(y), not(y)))), true, ifeq(is_a_theorem(implies(implies(not(not(y)), not(y)), not(y))), true, is_a_theorem(implies(not(y), not(y))), true), true), true, is_a_theorem(implies(not(implies(not(y), not(y))), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(x, not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.90 = { by axiom 4 (condensed_detachment) }
% 121.91/17.90 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(not(y), not(y))), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(x, not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.91 = { by axiom 1 (ifeq_axiom) }
% 121.91/17.91 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(not(y), not(y))), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(x, not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.91 = { by axiom 1 (ifeq_axiom) R->L }
% 121.91/17.91 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(not(y), not(y))), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(x, not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.91 = { by axiom 5 (cn_1) R->L }
% 121.91/17.91 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(y), not(y))), not(not(implies(x, not(y))))), implies(implies(not(not(implies(x, not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y)))))), true, ifeq(is_a_theorem(implies(not(implies(not(y), not(y))), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(x, not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.91 = { by axiom 4 (condensed_detachment) }
% 121.91/17.91 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(x, not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.91 = { by axiom 1 (ifeq_axiom) }
% 121.91/17.92 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(x, not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(x, not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.92 = { by axiom 1 (ifeq_axiom) R->L }
% 121.91/17.92 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(x, not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(x, not(y))), implies(not(y), not(y))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.92 = { by axiom 5 (cn_1) R->L }
% 121.91/17.92 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y)))), implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(x, not(y))), implies(not(y), not(y)))))), true, ifeq(is_a_theorem(implies(not(implies(x, not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(x, not(y))), implies(not(y), not(y))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.92 = { by axiom 4 (condensed_detachment) }
% 121.91/17.92 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(x, not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.92 = { by axiom 1 (ifeq_axiom) }
% 121.91/17.92 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y)))))), true, ifeq(is_a_theorem(implies(not(implies(x, not(y))), implies(not(y), not(y)))), true, is_a_theorem(implies(not(y), implies(not(implies(x, not(y))), implies(x, not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.92 = { by axiom 4 (condensed_detachment) }
% 121.91/17.92 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.92 = { by axiom 1 (ifeq_axiom) }
% 121.91/17.92 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.92 = { by axiom 1 (ifeq_axiom) R->L }
% 121.91/17.92 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.92 = { by axiom 4 (condensed_detachment) R->L }
% 121.91/17.92 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y)))))), implies(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y)))))), implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))))), true, ifeq(is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y)))))), implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.92 = { by axiom 5 (cn_1) }
% 121.91/17.93 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y)))))), implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.93 = { by axiom 1 (ifeq_axiom) }
% 121.91/17.93 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y)))))), implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.93 = { by axiom 1 (ifeq_axiom) R->L }
% 121.91/17.93 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y)))))), implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.93 = { by axiom 5 (cn_1) R->L }
% 121.91/17.93 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), implies(x, not(y))), implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y)))))))), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y)))))), implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.93 = { by axiom 1 (ifeq_axiom) R->L }
% 121.91/17.93 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), implies(x, not(y))), implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y)))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y)))))), implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.93 = { by axiom 3 (cn_2) R->L }
% 121.91/17.93 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), implies(x, not(y))), implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y)))))))), true, ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), implies(x, not(y))), implies(x, not(y)))), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y)))))), implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.93 = { by axiom 4 (condensed_detachment) }
% 121.91/17.93 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y)))))), implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.93 = { by axiom 1 (ifeq_axiom) }
% 121.91/17.93 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y)))))), implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y)))))))), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(x, not(y))), implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(implies(x, not(y)), not(not(implies(x, not(y))))), implies(not(y), not(not(implies(x, not(y))))))), true), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.93 = { by axiom 4 (condensed_detachment) }
% 121.91/17.93 ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.93 = { by axiom 1 (ifeq_axiom) }
% 121.91/17.93 ifeq(ifeq(is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.94 = { by axiom 1 (ifeq_axiom) R->L }
% 121.91/17.94 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.94 = { by axiom 4 (condensed_detachment) R->L }
% 121.91/17.94 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))))), true, ifeq(is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.94 = { by axiom 1 (ifeq_axiom) R->L }
% 121.91/17.94 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.94 = { by axiom 4 (condensed_detachment) R->L }
% 121.91/17.94 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))))), true), true), true, is_a_theorem(implies(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.94 = { by axiom 5 (cn_1) }
% 121.91/17.94 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))))), true), true), true, is_a_theorem(implies(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.95 = { by axiom 1 (ifeq_axiom) }
% 121.91/17.95 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.95 = { by axiom 1 (ifeq_axiom) R->L }
% 121.91/17.95 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.95 = { by axiom 5 (cn_1) R->L }
% 121.91/17.95 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))))), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.95 = { by axiom 1 (ifeq_axiom) R->L }
% 121.91/17.96 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))))), true, ifeq(true, true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.96 = { by axiom 3 (cn_2) R->L }
% 121.91/17.96 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))))), true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.96 = { by axiom 4 (condensed_detachment) }
% 121.91/17.96 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))))), true), true, is_a_theorem(implies(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.96 = { by axiom 1 (ifeq_axiom) }
% 121.91/17.96 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))))), true, is_a_theorem(implies(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.96 = { by axiom 1 (ifeq_axiom) R->L }
% 121.91/17.96 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))))), true, is_a_theorem(implies(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.97 = { by axiom 4 (condensed_detachment) R->L }
% 121.91/17.97 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), implies(implies(implies(implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), implies(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))))))), true, ifeq(is_a_theorem(implies(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), implies(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))))), true, is_a_theorem(implies(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.97 = { by axiom 5 (cn_1) }
% 121.91/17.97 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), implies(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))))), true, is_a_theorem(implies(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.97 = { by axiom 1 (ifeq_axiom) }
% 121.91/17.98 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), implies(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))))), true, is_a_theorem(implies(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.98 = { by axiom 5 (cn_1) }
% 121.91/17.98 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), implies(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))))), true, is_a_theorem(implies(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.98 = { by axiom 1 (ifeq_axiom) }
% 121.91/17.98 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), implies(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))))), true, is_a_theorem(implies(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.98 = { by axiom 4 (condensed_detachment) }
% 121.91/17.98 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.98 = { by axiom 1 (ifeq_axiom) }
% 121.91/17.98 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.98 = { by axiom 1 (ifeq_axiom) R->L }
% 121.91/17.98 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.99 = { by axiom 4 (condensed_detachment) R->L }
% 121.91/17.99 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))))), true, ifeq(is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.99 = { by axiom 1 (ifeq_axiom) R->L }
% 121.91/17.99 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.99 = { by axiom 4 (condensed_detachment) R->L }
% 121.91/17.99 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))), not(not(implies(x, not(y)))))), implies(implies(implies(implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))))), true, ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))))), true), true), true, is_a_theorem(implies(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/17.99 = { by axiom 5 (cn_1) }
% 121.91/18.00 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))))), true), true), true, is_a_theorem(implies(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/18.00 = { by axiom 1 (ifeq_axiom) }
% 121.91/18.00 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/18.00 = { by axiom 1 (ifeq_axiom) R->L }
% 121.91/18.00 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/18.01 = { by axiom 5 (cn_1) R->L }
% 121.91/18.01 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))), not(implies(x, not(y)))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))), not(not(implies(x, not(y)))))))), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/18.01 = { by axiom 1 (ifeq_axiom) R->L }
% 121.91/18.01 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))), not(implies(x, not(y)))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))), not(not(implies(x, not(y)))))))), true, ifeq(true, true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/18.01 = { by axiom 3 (cn_2) R->L }
% 121.91/18.01 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))), not(implies(x, not(y)))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))), not(not(implies(x, not(y)))))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))), not(implies(x, not(y))))), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/18.02 = { by axiom 4 (condensed_detachment) }
% 121.91/18.02 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/18.02 = { by axiom 1 (ifeq_axiom) }
% 121.91/18.02 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))))), true, is_a_theorem(implies(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/18.02 = { by axiom 1 (ifeq_axiom) R->L }
% 121.91/18.03 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))))), true, is_a_theorem(implies(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))))), true), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 121.91/18.03 = { by axiom 4 (condensed_detachment) R->L }
% 122.84/18.03 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), implies(implies(implies(implies(implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), implies(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))))))), true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), implies(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))))), true, is_a_theorem(implies(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))))), true), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 122.84/18.03 = { by axiom 5 (cn_1) }
% 122.84/18.04 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), implies(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))))), true, is_a_theorem(implies(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))))), true), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 122.84/18.04 = { by axiom 1 (ifeq_axiom) }
% 122.84/18.04 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), implies(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))))), true, is_a_theorem(implies(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))))), true), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 122.84/18.04 = { by axiom 5 (cn_1) }
% 122.84/18.04 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), implies(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))))), true, is_a_theorem(implies(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))))), true), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 122.84/18.04 = { by axiom 1 (ifeq_axiom) }
% 122.84/18.04 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), implies(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))))), true, is_a_theorem(implies(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))))), true), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 122.84/18.05 = { by axiom 4 (condensed_detachment) }
% 122.84/18.05 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 122.84/18.05 = { by axiom 1 (ifeq_axiom) }
% 122.84/18.05 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 122.84/18.05 = { by axiom 1 (ifeq_axiom) R->L }
% 122.84/18.05 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 122.84/18.06 = { by axiom 4 (condensed_detachment) R->L }
% 122.84/18.06 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))))), true, ifeq(is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 122.84/18.06 = { by axiom 1 (ifeq_axiom) R->L }
% 122.84/18.06 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 122.84/18.07 = { by axiom 4 (condensed_detachment) R->L }
% 122.84/18.07 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(x, not(y)))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), implies(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(x, not(y)))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(x, not(y)))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(x, not(y)))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 122.84/18.07 = { by axiom 5 (cn_1) }
% 122.84/18.07 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(x, not(y)))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(x, not(y)))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 122.84/18.08 = { by axiom 1 (ifeq_axiom) }
% 122.84/18.08 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(x, not(y)))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(x, not(y)))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 122.84/18.08 = { by axiom 5 (cn_1) }
% 122.84/18.09 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(x, not(y)))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 122.84/18.09 = { by axiom 1 (ifeq_axiom) }
% 122.84/18.09 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(x, not(y)))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))))), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 122.84/18.10 = { by axiom 1 (ifeq_axiom) R->L }
% 122.84/18.10 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(x, not(y)))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))))), true, ifeq(true, true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))))), true), true), true, ifeq(is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 122.84/18.11 = { by axiom 4 (condensed_detachment) R->L }
% 122.84/18.11 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(x, not(y)))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(x, not(y))))), implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(x, not(y)))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))))), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(x, not(y)))))), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(x, not(y)))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))))), true), true), true, ifeq(is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 122.84/18.12 = { by axiom 2 (cn_3) }
% 122.84/18.12 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(x, not(y)))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(x, not(y))))), implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(x, not(y)))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(x, not(y)))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))))), true), true), true, ifeq(is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 122.84/18.12 = { by axiom 1 (ifeq_axiom) }
% 122.84/18.12 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(x, not(y)))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(x, not(y))))), implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(x, not(y)))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))))), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(x, not(y)))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))))), true), true), true, ifeq(is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 122.84/18.13 = { by axiom 5 (cn_1) }
% 122.84/18.13 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(x, not(y)))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(x, not(y)))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))))), true), true), true, ifeq(is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 122.84/18.13 = { by axiom 1 (ifeq_axiom) }
% 123.54/18.13 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(x, not(y)))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), implies(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))))), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(x, not(y)))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))))), true), true), true, ifeq(is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 123.54/18.13 = { by axiom 4 (condensed_detachment) }
% 123.54/18.13 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 123.54/18.14 = { by axiom 1 (ifeq_axiom) }
% 123.54/18.14 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 123.54/18.14 = { by axiom 1 (ifeq_axiom) R->L }
% 123.54/18.14 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 123.54/18.15 = { by axiom 4 (condensed_detachment) R->L }
% 123.54/18.16 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, ifeq(is_a_theorem(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 123.54/18.16 = { by axiom 1 (ifeq_axiom) R->L }
% 123.54/18.17 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 123.54/18.17 = { by axiom 4 (condensed_detachment) R->L }
% 123.54/18.18 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true, ifeq(is_a_theorem(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, is_a_theorem(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 123.54/18.18 = { by axiom 2 (cn_3) }
% 123.54/18.19 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, is_a_theorem(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 123.54/18.19 = { by axiom 1 (ifeq_axiom) }
% 123.54/18.19 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 124.01/18.20 = { by axiom 5 (cn_1) }
% 124.01/18.20 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 124.01/18.21 = { by axiom 1 (ifeq_axiom) }
% 124.01/18.21 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 124.01/18.21 = { by axiom 1 (ifeq_axiom) R->L }
% 124.01/18.22 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, ifeq(true, true, is_a_theorem(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 124.01/18.22 = { by axiom 3 (cn_2) R->L }
% 124.01/18.22 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 124.01/18.23 = { by axiom 4 (condensed_detachment) }
% 124.01/18.23 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 124.01/18.23 = { by axiom 1 (ifeq_axiom) }
% 124.01/18.24 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 124.01/18.24 = { by axiom 1 (ifeq_axiom) R->L }
% 124.01/18.24 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 124.01/18.25 = { by axiom 4 (condensed_detachment) R->L }
% 124.01/18.26 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 124.01/18.27 = { by axiom 1 (ifeq_axiom) R->L }
% 124.01/18.27 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 124.01/18.28 = { by axiom 4 (condensed_detachment) R->L }
% 124.01/18.29 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true, ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 124.01/18.30 = { by axiom 3 (cn_2) }
% 124.73/18.30 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 124.73/18.31 = { by axiom 1 (ifeq_axiom) }
% 124.73/18.32 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 124.73/18.32 = { by axiom 5 (cn_1) }
% 124.73/18.33 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 124.73/18.34 = { by axiom 1 (ifeq_axiom) }
% 124.73/18.34 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 124.73/18.35 = { by axiom 1 (ifeq_axiom) R->L }
% 124.73/18.35 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 124.73/18.36 = { by axiom 5 (cn_1) R->L }
% 124.73/18.36 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 124.73/18.37 = { by axiom 4 (condensed_detachment) }
% 124.73/18.37 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 124.73/18.38 = { by axiom 1 (ifeq_axiom) }
% 124.73/18.38 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 124.73/18.39 = { by axiom 1 (ifeq_axiom) R->L }
% 124.73/18.39 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 125.43/18.41 = { by axiom 4 (condensed_detachment) R->L }
% 125.43/18.42 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 125.43/18.44 = { by axiom 1 (ifeq_axiom) R->L }
% 125.43/18.44 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 125.43/18.46 = { by axiom 4 (condensed_detachment) R->L }
% 125.43/18.47 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))))), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 125.43/18.49 = { by axiom 1 (ifeq_axiom) R->L }
% 126.14/18.50 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 126.14/18.52 = { by axiom 5 (cn_1) R->L }
% 126.14/18.53 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 126.14/18.55 = { by axiom 1 (ifeq_axiom) R->L }
% 126.14/18.56 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 126.14/18.57 = { by axiom 2 (cn_3) R->L }
% 126.14/18.58 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))))), true, ifeq(is_a_theorem(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 126.14/18.59 = { by axiom 4 (condensed_detachment) }
% 126.84/18.60 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))))), true, ifeq(true, true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 126.84/18.62 = { by axiom 1 (ifeq_axiom) }
% 126.84/18.63 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 126.84/18.65 = { by axiom 1 (ifeq_axiom) R->L }
% 126.84/18.66 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 126.84/18.69 = { by axiom 4 (condensed_detachment) R->L }
% 127.55/18.70 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))))), true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 127.55/18.75 = { by axiom 1 (ifeq_axiom) R->L }
% 127.55/18.76 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 127.55/18.78 = { by axiom 5 (cn_1) R->L }
% 127.55/18.80 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(not(not(implies(x, not(y))))))))), implies(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 128.25/18.81 = { by axiom 1 (ifeq_axiom) R->L }
% 128.25/18.82 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(not(not(implies(x, not(y))))))))), implies(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 128.25/18.84 = { by axiom 2 (cn_3) R->L }
% 128.25/18.86 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(not(not(implies(x, not(y))))))))), implies(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))))), true, ifeq(is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 128.25/18.87 = { by axiom 4 (condensed_detachment) }
% 128.25/18.88 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 128.25/18.90 = { by axiom 1 (ifeq_axiom) }
% 128.96/18.90 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 128.96/18.92 = { by axiom 5 (cn_1) }
% 128.96/18.93 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 128.96/18.95 = { by axiom 1 (ifeq_axiom) }
% 128.96/18.96 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 128.96/18.97 = { by axiom 1 (ifeq_axiom) R->L }
% 128.96/18.97 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 128.96/18.98 = { by axiom 5 (cn_1) R->L }
% 128.96/19.00 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), implies(implies(implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))))), true, ifeq(is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(not(implies(x, not(y))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 128.96/19.01 = { by axiom 4 (condensed_detachment) }
% 128.96/19.01 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 128.96/19.02 = { by axiom 1 (ifeq_axiom) }
% 128.96/19.03 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 129.88/19.03 = { by axiom 1 (ifeq_axiom) R->L }
% 129.88/19.04 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 129.88/19.04 = { by axiom 5 (cn_1) R->L }
% 129.88/19.05 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true, ifeq(is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 129.88/19.06 = { by axiom 4 (condensed_detachment) }
% 129.88/19.06 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 129.88/19.07 = { by axiom 1 (ifeq_axiom) }
% 129.88/19.08 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 129.88/19.08 = { by axiom 1 (ifeq_axiom) R->L }
% 129.88/19.09 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 129.88/19.10 = { by axiom 4 (condensed_detachment) R->L }
% 129.88/19.11 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y))))))), implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, ifeq(is_a_theorem(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 129.88/19.12 = { by axiom 5 (cn_1) }
% 129.88/19.12 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 130.59/19.13 = { by axiom 1 (ifeq_axiom) }
% 130.59/19.14 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 130.59/19.15 = { by axiom 1 (ifeq_axiom) R->L }
% 130.59/19.16 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 130.59/19.17 = { by axiom 4 (condensed_detachment) R->L }
% 130.59/19.18 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(not(not(implies(x, not(y)))))), implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y))))))))), true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(not(not(implies(x, not(y)))))), implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))))), true), true), true, is_a_theorem(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 130.59/19.19 = { by axiom 3 (cn_2) }
% 130.59/19.19 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(not(not(implies(x, not(y)))))), implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y))))))))), true, ifeq(true, true, is_a_theorem(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(not(not(implies(x, not(y)))))), implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))))), true), true), true, is_a_theorem(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 131.07/19.20 = { by axiom 1 (ifeq_axiom) }
% 131.07/19.21 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(not(not(implies(x, not(y)))))), implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(not(not(implies(x, not(y)))))), implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))))), true), true, is_a_theorem(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 131.07/19.22 = { by axiom 5 (cn_1) }
% 131.07/19.23 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(not(not(implies(x, not(y)))))), implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))))), true), true, is_a_theorem(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 131.07/19.25 = { by axiom 1 (ifeq_axiom) }
% 131.07/19.25 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(not(not(implies(x, not(y)))))), implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))))), true, is_a_theorem(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 131.07/19.27 = { by axiom 1 (ifeq_axiom) R->L }
% 131.07/19.28 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(not(not(implies(x, not(y)))))), implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))))), true, is_a_theorem(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 131.07/19.29 = { by axiom 4 (condensed_detachment) R->L }
% 131.78/19.30 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(not(not(implies(x, not(y))))))), implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(not(not(implies(x, not(y)))))), implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))))))), true, ifeq(is_a_theorem(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(not(not(implies(x, not(y)))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(not(not(implies(x, not(y)))))), implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(not(not(implies(x, not(y)))))), implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))))), true, is_a_theorem(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 131.78/19.31 = { by axiom 2 (cn_3) }
% 131.78/19.32 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(not(not(implies(x, not(y))))))), implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(not(not(implies(x, not(y)))))), implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(not(not(implies(x, not(y)))))), implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(not(not(implies(x, not(y)))))), implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))))), true, is_a_theorem(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 131.78/19.34 = { by axiom 1 (ifeq_axiom) }
% 131.78/19.35 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(not(not(implies(x, not(y))))))), implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(not(not(implies(x, not(y)))))), implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(not(not(implies(x, not(y)))))), implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(not(not(implies(x, not(y)))))), implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))))), true, is_a_theorem(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 131.78/19.36 = { by axiom 5 (cn_1) }
% 131.78/19.37 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(not(not(implies(x, not(y)))))), implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(not(not(implies(x, not(y)))))), implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))))), true, is_a_theorem(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 131.78/19.37 = { by axiom 1 (ifeq_axiom) }
% 131.78/19.38 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(not(not(implies(x, not(y)))))), implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y))))))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(not(not(implies(x, not(y)))))), implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))))), true, is_a_theorem(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 131.78/19.39 = { by axiom 4 (condensed_detachment) }
% 131.78/19.40 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 132.49/19.41 = { by axiom 1 (ifeq_axiom) }
% 132.49/19.42 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 132.49/19.43 = { by axiom 1 (ifeq_axiom) R->L }
% 132.49/19.43 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 132.49/19.44 = { by axiom 4 (condensed_detachment) R->L }
% 132.49/19.46 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 132.49/19.47 = { by axiom 5 (cn_1) }
% 132.49/19.47 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 132.49/19.48 = { by axiom 1 (ifeq_axiom) }
% 132.49/19.49 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 132.49/19.49 = { by axiom 5 (cn_1) }
% 133.19/19.50 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 133.19/19.51 = { by axiom 1 (ifeq_axiom) }
% 133.19/19.51 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(not(implies(x, not(y)))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), implies(not(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 133.19/19.52 = { by axiom 4 (condensed_detachment) }
% 133.19/19.52 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 133.19/19.53 = { by axiom 1 (ifeq_axiom) }
% 133.19/19.53 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 133.19/19.53 = { by axiom 1 (ifeq_axiom) R->L }
% 133.19/19.54 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 133.19/19.54 = { by axiom 5 (cn_1) R->L }
% 133.19/19.54 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true, ifeq(is_a_theorem(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 133.19/19.55 = { by axiom 4 (condensed_detachment) }
% 133.19/19.55 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 133.19/19.56 = { by axiom 1 (ifeq_axiom) }
% 133.19/19.57 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 133.19/19.58 = { by axiom 1 (ifeq_axiom) R->L }
% 133.19/19.58 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 133.19/19.60 = { by axiom 4 (condensed_detachment) R->L }
% 133.90/19.60 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 133.90/19.62 = { by axiom 1 (ifeq_axiom) R->L }
% 133.90/19.63 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 133.90/19.65 = { by axiom 5 (cn_1) R->L }
% 133.90/19.66 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 133.90/19.66 = { by axiom 1 (ifeq_axiom) R->L }
% 133.90/19.67 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 133.90/19.68 = { by axiom 5 (cn_1) R->L }
% 134.61/19.70 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(implies(implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), implies(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 134.61/19.71 = { by axiom 4 (condensed_detachment) }
% 134.61/19.71 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 134.61/19.73 = { by axiom 1 (ifeq_axiom) }
% 134.61/19.73 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 134.61/19.74 = { by axiom 1 (ifeq_axiom) R->L }
% 134.61/19.75 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 134.61/19.76 = { by axiom 4 (condensed_detachment) R->L }
% 134.61/19.77 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 134.61/19.77 = { by axiom 3 (cn_2) }
% 134.61/19.78 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true, ifeq(true, true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 134.61/19.79 = { by axiom 1 (ifeq_axiom) }
% 134.61/19.80 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 135.31/19.81 = { by axiom 5 (cn_1) }
% 135.31/19.81 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 135.31/19.82 = { by axiom 1 (ifeq_axiom) }
% 135.31/19.83 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 135.31/19.83 = { by axiom 1 (ifeq_axiom) R->L }
% 135.31/19.84 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 135.31/19.84 = { by axiom 5 (cn_1) R->L }
% 135.31/19.85 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true, ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 135.31/19.85 = { by axiom 4 (condensed_detachment) }
% 135.31/19.86 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 135.31/19.86 = { by axiom 1 (ifeq_axiom) }
% 135.31/19.86 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 135.31/19.86 = { by axiom 4 (condensed_detachment) }
% 135.31/19.86 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 135.31/19.87 = { by axiom 1 (ifeq_axiom) }
% 135.31/19.87 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 135.31/19.87 = { by axiom 1 (ifeq_axiom) R->L }
% 135.31/19.87 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 135.31/19.88 = { by axiom 4 (condensed_detachment) R->L }
% 135.31/19.88 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(x, not(y)))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true, ifeq(is_a_theorem(implies(not(not(implies(x, not(y)))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 135.31/19.88 = { by axiom 5 (cn_1) }
% 135.31/19.89 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(not(implies(x, not(y)))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 135.31/19.89 = { by axiom 1 (ifeq_axiom) }
% 135.31/19.89 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(not(implies(x, not(y)))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 136.01/19.91 = { by axiom 1 (ifeq_axiom) R->L }
% 136.01/19.91 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(not(implies(x, not(y)))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 136.01/19.91 = { by axiom 4 (condensed_detachment) R->L }
% 136.01/19.92 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(implies(not(not(not(implies(x, not(y))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(not(not(not(implies(x, not(y))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 136.01/19.92 = { by axiom 3 (cn_2) }
% 136.01/19.92 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(implies(not(not(not(implies(x, not(y))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true, ifeq(true, true, is_a_theorem(implies(implies(not(not(not(implies(x, not(y))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 136.01/19.93 = { by axiom 1 (ifeq_axiom) }
% 136.01/19.93 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(implies(not(not(not(implies(x, not(y))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true, is_a_theorem(implies(implies(not(not(not(implies(x, not(y))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 136.01/19.93 = { by axiom 5 (cn_1) }
% 136.01/19.94 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(not(implies(x, not(y))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 136.01/19.94 = { by axiom 1 (ifeq_axiom) }
% 136.01/19.94 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(implies(x, not(y))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(not(not(implies(x, not(y)))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 136.01/19.95 = { by axiom 1 (ifeq_axiom) R->L }
% 136.01/19.96 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(x, not(y))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(not(not(implies(x, not(y)))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 136.01/19.96 = { by axiom 4 (condensed_detachment) R->L }
% 136.01/19.97 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(x, not(y)))), implies(not(not(not(implies(x, not(y))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(implies(not(not(not(implies(x, not(y))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(implies(x, not(y)))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true, ifeq(is_a_theorem(implies(not(not(implies(x, not(y)))), implies(not(not(not(implies(x, not(y))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(implies(x, not(y))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(implies(x, not(y)))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(x, not(y))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(not(not(implies(x, not(y)))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 136.01/19.97 = { by axiom 2 (cn_3) }
% 136.01/19.97 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(x, not(y)))), implies(not(not(not(implies(x, not(y))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(implies(not(not(not(implies(x, not(y))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(implies(x, not(y)))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(not(implies(x, not(y))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(implies(x, not(y)))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(x, not(y))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(not(not(implies(x, not(y)))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 136.01/19.98 = { by axiom 1 (ifeq_axiom) }
% 136.01/19.98 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(x, not(y)))), implies(not(not(not(implies(x, not(y))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(implies(implies(not(not(not(implies(x, not(y))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(implies(x, not(y)))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(implies(x, not(y))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(implies(x, not(y)))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(x, not(y))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(not(not(implies(x, not(y)))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 136.01/19.99 = { by axiom 5 (cn_1) }
% 136.01/19.99 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(not(implies(x, not(y))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(implies(x, not(y)))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(x, not(y))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(not(not(implies(x, not(y)))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 136.01/19.99 = { by axiom 1 (ifeq_axiom) }
% 136.01/19.99 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(implies(x, not(y))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), implies(not(not(implies(x, not(y)))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))))), true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(x, not(y))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, is_a_theorem(implies(not(not(implies(x, not(y)))), implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 136.01/19.99 = { by axiom 4 (condensed_detachment) }
% 136.01/20.00 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 136.01/20.00 = { by axiom 1 (ifeq_axiom) }
% 136.01/20.00 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))))), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))))), true), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 136.01/20.00 = { by axiom 4 (condensed_detachment) }
% 136.01/20.01 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 136.01/20.01 = { by axiom 1 (ifeq_axiom) }
% 136.01/20.01 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 136.01/20.01 = { by axiom 1 (ifeq_axiom) R->L }
% 136.01/20.01 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 136.01/20.01 = { by axiom 4 (condensed_detachment) R->L }
% 136.01/20.01 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(implies(x, not(y))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))))), true, ifeq(is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))))), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 136.01/20.01 = { by axiom 2 (cn_3) }
% 136.01/20.02 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(implies(x, not(y))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 136.01/20.02 = { by axiom 1 (ifeq_axiom) }
% 136.01/20.02 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(implies(x, not(y))))), implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y))))))), implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))))), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 136.01/20.02 = { by axiom 5 (cn_1) }
% 136.01/20.02 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 136.01/20.02 = { by axiom 1 (ifeq_axiom) }
% 136.01/20.02 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y))))))), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(x, not(y)))))), not(not(not(implies(x, not(y)))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true, is_a_theorem(implies(not(not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 136.01/20.02 = { by axiom 4 (condensed_detachment) }
% 136.01/20.02 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 136.01/20.03 = { by axiom 1 (ifeq_axiom) }
% 136.01/20.03 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 136.01/20.03 = { by axiom 1 (ifeq_axiom) R->L }
% 136.01/20.03 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 136.01/20.03 = { by axiom 4 (condensed_detachment) R->L }
% 136.94/20.03 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(x, not(y)), implies(not(implies(x, not(y))), not(not(implies(x, not(y)))))), implies(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))))), true, ifeq(is_a_theorem(implies(implies(x, not(y)), implies(not(implies(x, not(y))), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 136.94/20.03 = { by axiom 2 (cn_3) }
% 136.94/20.03 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(x, not(y)), implies(not(implies(x, not(y))), not(not(implies(x, not(y)))))), implies(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 136.94/20.03 = { by axiom 1 (ifeq_axiom) }
% 136.94/20.04 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(x, not(y)), implies(not(implies(x, not(y))), not(not(implies(x, not(y)))))), implies(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))))), true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 136.94/20.04 = { by axiom 5 (cn_1) }
% 136.94/20.04 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 136.94/20.04 = { by axiom 1 (ifeq_axiom) }
% 136.94/20.04 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))))), true, ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), not(not(implies(x, not(y))))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(x, not(y)), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 136.94/20.04 = { by axiom 4 (condensed_detachment) }
% 136.94/20.04 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 136.94/20.04 = { by axiom 1 (ifeq_axiom) }
% 136.94/20.04 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 136.94/20.04 = { by axiom 1 (ifeq_axiom) R->L }
% 136.94/20.04 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true, ifeq(true, true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 136.94/20.04 = { by axiom 4 (condensed_detachment) R->L }
% 136.94/20.04 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))))), true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 136.94/20.04 = { by axiom 3 (cn_2) }
% 136.94/20.04 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))))), true, ifeq(true, true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 136.94/20.04 = { by axiom 1 (ifeq_axiom) }
% 136.94/20.05 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 136.94/20.05 = { by axiom 1 (ifeq_axiom) R->L }
% 136.94/20.05 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 136.94/20.05 = { by axiom 5 (cn_1) R->L }
% 136.94/20.05 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(x, not(y)))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y)))))))), true, is_a_theorem(implies(implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))))), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 136.94/20.05 = { by axiom 1 (ifeq_axiom) R->L }
% 136.94/20.05 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(x, not(y)))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y)))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 136.94/20.05 = { by axiom 2 (cn_3) R->L }
% 136.94/20.05 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(x, not(y)))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y)))))), implies(implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y)))))))), true, ifeq(is_a_theorem(implies(not(not(implies(x, not(y)))), implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))))), true, is_a_theorem(implies(implies(implies(not(not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), not(not(implies(x, not(y))))), implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))))), true), true), true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 136.94/20.05 = { by axiom 4 (condensed_detachment) }
% 136.94/20.05 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 136.94/20.05 = { by axiom 1 (ifeq_axiom) }
% 136.94/20.05 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y))))), implies(implies(x, not(y)), not(not(implies(x, not(y))))))), true, ifeq(is_a_theorem(implies(not(not(implies(x, not(y)))), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(implies(x, not(y)), not(not(implies(x, not(y)))))), true), true), true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 136.94/20.05 = { by axiom 4 (condensed_detachment) }
% 136.94/20.05 ifeq(ifeq(true, true, is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 136.94/20.05 = { by axiom 1 (ifeq_axiom) }
% 136.94/20.06 ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true)
% 136.94/20.06 = { by axiom 1 (ifeq_axiom) R->L }
% 136.94/20.06 ifeq(true, true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 136.94/20.06 = { by axiom 4 (condensed_detachment) R->L }
% 136.94/20.06 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)), implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y)))), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 136.94/20.06 = { by axiom 1 (ifeq_axiom) R->L }
% 136.94/20.06 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)), implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y)))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 136.94/20.06 = { by axiom 5 (cn_1) R->L }
% 136.94/20.06 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)), implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y)))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 136.94/20.06 = { by axiom 1 (ifeq_axiom) R->L }
% 136.94/20.06 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)), implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 136.94/20.06 = { by axiom 5 (cn_1) R->L }
% 136.94/20.06 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(y), not(not(implies(x, not(y))))), implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)), implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))))), true, ifeq(is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)), implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 136.94/20.06 = { by axiom 4 (condensed_detachment) }
% 136.94/20.06 ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 136.94/20.06 = { by axiom 1 (ifeq_axiom) }
% 136.94/20.06 ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 136.94/20.06 = { by axiom 1 (ifeq_axiom) R->L }
% 136.94/20.06 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 136.94/20.07 = { by axiom 4 (condensed_detachment) R->L }
% 136.94/20.07 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))))), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 136.94/20.07 = { by axiom 1 (ifeq_axiom) R->L }
% 136.94/20.07 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 136.94/20.07 = { by axiom 4 (condensed_detachment) R->L }
% 136.94/20.07 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(x, not(y))), y))), implies(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(x, not(y))), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 136.94/20.08 = { by axiom 5 (cn_1) }
% 136.94/20.08 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(x, not(y))), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 136.94/20.08 = { by axiom 1 (ifeq_axiom) }
% 136.94/20.08 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(x, not(y))), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 136.94/20.09 = { by axiom 1 (ifeq_axiom) R->L }
% 136.94/20.09 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 136.94/20.09 = { by axiom 5 (cn_1) R->L }
% 136.94/20.09 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(x, not(y))), y))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 136.94/20.10 = { by axiom 1 (ifeq_axiom) R->L }
% 136.94/20.10 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(x, not(y))), y))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(x, not(y))), y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 136.94/20.10 = { by axiom 3 (cn_2) R->L }
% 136.94/20.10 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(x, not(y))), y))))), true, ifeq(is_a_theorem(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(x, not(y))), y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 136.94/20.10 = { by axiom 4 (condensed_detachment) }
% 136.94/20.11 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 136.94/20.11 = { by axiom 1 (ifeq_axiom) }
% 136.94/20.11 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 136.94/20.12 = { by axiom 1 (ifeq_axiom) R->L }
% 136.94/20.12 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 136.94/20.12 = { by axiom 4 (condensed_detachment) R->L }
% 136.94/20.13 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), implies(implies(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 136.94/20.13 = { by axiom 5 (cn_1) }
% 137.65/20.13 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 137.65/20.13 = { by axiom 1 (ifeq_axiom) }
% 137.65/20.14 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 137.65/20.14 = { by axiom 5 (cn_1) }
% 137.65/20.14 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 137.65/20.14 = { by axiom 1 (ifeq_axiom) }
% 137.65/20.14 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 137.65/20.14 = { by axiom 4 (condensed_detachment) }
% 137.65/20.15 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 137.65/20.15 = { by axiom 1 (ifeq_axiom) }
% 137.65/20.15 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 137.65/20.16 = { by axiom 1 (ifeq_axiom) R->L }
% 137.65/20.16 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 137.65/20.16 = { by axiom 4 (condensed_detachment) R->L }
% 137.65/20.17 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 137.65/20.17 = { by axiom 1 (ifeq_axiom) R->L }
% 137.65/20.17 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 137.65/20.17 = { by axiom 4 (condensed_detachment) R->L }
% 137.65/20.18 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true, ifeq(is_a_theorem(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 137.65/20.18 = { by axiom 3 (cn_2) }
% 137.65/20.18 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 137.65/20.18 = { by axiom 1 (ifeq_axiom) }
% 137.65/20.19 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 137.65/20.19 = { by axiom 5 (cn_1) }
% 137.65/20.19 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 137.65/20.19 = { by axiom 1 (ifeq_axiom) }
% 137.65/20.19 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 137.65/20.20 = { by axiom 1 (ifeq_axiom) R->L }
% 138.15/20.20 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 138.15/20.20 = { by axiom 5 (cn_1) R->L }
% 138.15/20.20 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 138.15/20.21 = { by axiom 4 (condensed_detachment) }
% 138.15/20.21 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 138.15/20.21 = { by axiom 1 (ifeq_axiom) }
% 138.15/20.21 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 138.15/20.22 = { by axiom 1 (ifeq_axiom) R->L }
% 138.15/20.22 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 138.15/20.23 = { by axiom 4 (condensed_detachment) R->L }
% 138.15/20.23 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))))), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 138.15/20.23 = { by axiom 1 (ifeq_axiom) R->L }
% 138.15/20.24 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 138.15/20.24 = { by axiom 4 (condensed_detachment) R->L }
% 138.15/20.25 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), implies(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 138.15/20.26 = { by axiom 5 (cn_1) }
% 138.15/20.26 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 138.15/20.27 = { by axiom 1 (ifeq_axiom) }
% 138.15/20.27 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 138.15/20.28 = { by axiom 1 (ifeq_axiom) R->L }
% 138.15/20.29 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 138.15/20.29 = { by axiom 5 (cn_1) R->L }
% 138.84/20.30 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), 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% 138.84/20.31 = { by axiom 1 (ifeq_axiom) R->L }
% 138.84/20.31 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 138.84/20.32 = { by axiom 3 (cn_2) R->L }
% 138.84/20.33 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))))), true, ifeq(is_a_theorem(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 138.84/20.33 = { by axiom 4 (condensed_detachment) }
% 138.84/20.34 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 138.84/20.35 = { by axiom 1 (ifeq_axiom) }
% 138.84/20.36 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 138.84/20.37 = { by axiom 1 (ifeq_axiom) R->L }
% 138.84/20.37 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 138.84/20.38 = { by axiom 4 (condensed_detachment) R->L }
% 138.84/20.39 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), implies(implies(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 139.54/20.40 = { by axiom 5 (cn_1) }
% 139.54/20.41 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 139.54/20.42 = { by axiom 1 (ifeq_axiom) }
% 139.54/20.45 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 139.54/20.45 = { by axiom 5 (cn_1) }
% 139.54/20.45 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), 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true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 139.54/20.46 = { by axiom 1 (ifeq_axiom) }
% 139.54/20.46 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 139.54/20.47 = { by axiom 4 (condensed_detachment) }
% 139.54/20.47 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 139.54/20.47 = { by axiom 1 (ifeq_axiom) }
% 139.54/20.47 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 139.54/20.48 = { by axiom 1 (ifeq_axiom) R->L }
% 139.54/20.48 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 139.54/20.48 = { by axiom 4 (condensed_detachment) R->L }
% 139.54/20.49 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true, is_a_theorem(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 139.54/20.49 = { by axiom 1 (ifeq_axiom) R->L }
% 139.54/20.50 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true, is_a_theorem(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 140.24/20.50 = { by axiom 5 (cn_1) R->L }
% 140.24/20.50 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(not(implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(not(y), y), y))), implies(implies(implies(not(not(implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))))), true, is_a_theorem(implies(implies(implies(not(not(implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true, is_a_theorem(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 140.24/20.51 = { by axiom 1 (ifeq_axiom) R->L }
% 140.24/20.51 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(not(implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(not(y), y), y))), implies(implies(implies(not(not(implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true, is_a_theorem(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 140.24/20.51 = { by axiom 2 (cn_3) R->L }
% 140.24/20.52 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(not(implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(not(y), y), y))), implies(implies(implies(not(not(implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))))), true, ifeq(is_a_theorem(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(not(implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(not(y), y), y)))), true, is_a_theorem(implies(implies(implies(not(not(implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true, is_a_theorem(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 140.24/20.52 = { by axiom 4 (condensed_detachment) }
% 140.24/20.52 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true, is_a_theorem(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 140.24/20.53 = { by axiom 1 (ifeq_axiom) }
% 140.24/20.53 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true, is_a_theorem(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 140.24/20.53 = { by axiom 1 (ifeq_axiom) R->L }
% 140.24/20.53 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, is_a_theorem(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 140.24/20.54 = { by axiom 4 (condensed_detachment) R->L }
% 140.24/20.54 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(y), y), y), implies(not(implies(implies(not(y), y), y)), not(not(implies(implies(not(not(implies(x, not(y)))), y), y)))))), true, ifeq(is_a_theorem(implies(implies(not(y), y), y)), true, is_a_theorem(implies(not(implies(implies(not(y), y), y)), not(not(implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, is_a_theorem(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 140.24/20.54 = { by axiom 2 (cn_3) }
% 140.24/20.55 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(y), y), y)), true, is_a_theorem(implies(not(implies(implies(not(y), y), y)), not(not(implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, is_a_theorem(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 140.24/20.55 = { by axiom 1 (ifeq_axiom) }
% 140.24/20.55 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(y), y), y)), true, is_a_theorem(implies(not(implies(implies(not(y), y), y)), not(not(implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true, is_a_theorem(implies(implies(not(not(implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, is_a_theorem(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 140.24/20.56 = { by axiom 3 (cn_2) }
% 140.24/20.56 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(implies(not(y), y), y)), not(not(implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true, is_a_theorem(implies(implies(not(not(implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, is_a_theorem(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 140.24/20.56 = { by axiom 1 (ifeq_axiom) }
% 140.24/20.56 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(implies(not(y), y), y)), not(not(implies(implies(not(not(implies(x, not(y)))), y), y))))), true, is_a_theorem(implies(implies(not(not(implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, is_a_theorem(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 140.24/20.57 = { by axiom 1 (ifeq_axiom) R->L }
% 140.24/20.57 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(implies(not(y), y), y)), not(not(implies(implies(not(not(implies(x, not(y)))), y), y))))), true, is_a_theorem(implies(implies(not(not(implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true), true, is_a_theorem(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 140.24/20.57 = { by axiom 5 (cn_1) R->L }
% 140.24/20.57 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(not(y), y), y)), not(not(implies(implies(not(not(implies(x, not(y)))), y), y)))), implies(implies(not(not(implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y))))), true, ifeq(is_a_theorem(implies(not(implies(implies(not(y), y), y)), not(not(implies(implies(not(not(implies(x, not(y)))), y), y))))), true, is_a_theorem(implies(implies(not(not(implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true), true, is_a_theorem(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 140.24/20.58 = { by axiom 4 (condensed_detachment) }
% 140.24/20.58 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 140.24/20.58 = { by axiom 1 (ifeq_axiom) }
% 140.24/20.58 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 140.24/20.59 = { by axiom 1 (ifeq_axiom) R->L }
% 140.24/20.59 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 140.24/20.59 = { by axiom 5 (cn_1) R->L }
% 140.24/20.59 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true, ifeq(is_a_theorem(implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 140.95/20.60 = { by axiom 4 (condensed_detachment) }
% 140.95/20.60 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 140.95/20.60 = { by axiom 1 (ifeq_axiom) }
% 140.95/20.60 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 140.95/20.60 = { by axiom 1 (ifeq_axiom) R->L }
% 140.95/20.61 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 140.95/20.61 = { by axiom 2 (cn_3) R->L }
% 140.95/20.61 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 140.95/20.61 = { by axiom 4 (condensed_detachment) }
% 140.95/20.61 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 140.95/20.61 = { by axiom 1 (ifeq_axiom) }
% 140.95/20.61 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 140.95/20.62 = { by axiom 1 (ifeq_axiom) R->L }
% 140.95/20.62 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 140.95/20.62 = { by axiom 4 (condensed_detachment) R->L }
% 140.95/20.62 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))))), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 140.95/20.62 = { by axiom 5 (cn_1) }
% 140.95/20.62 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 140.95/20.62 = { by axiom 1 (ifeq_axiom) }
% 140.95/20.63 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 140.95/20.63 = { by axiom 5 (cn_1) }
% 140.95/20.63 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 140.95/20.63 = { by axiom 1 (ifeq_axiom) }
% 140.95/20.63 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(not(implies(x, not(y)))), y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(implies(not(not(implies(x, not(y)))), y), y)), implies(implies(not(not(implies(x, not(y)))), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 140.95/20.63 = { by axiom 4 (condensed_detachment) }
% 140.95/20.63 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 140.95/20.63 = { by axiom 1 (ifeq_axiom) }
% 140.95/20.63 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 140.95/20.63 = { by axiom 1 (ifeq_axiom) R->L }
% 140.95/20.63 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 140.95/20.63 = { by axiom 4 (condensed_detachment) R->L }
% 140.95/20.64 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true, ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(not(implies(x, not(y)))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)))), true, ifeq(is_a_theorem(implies(not(implies(x, not(y))), implies(not(not(implies(x, not(y)))), y))), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 140.95/20.64 = { by axiom 2 (cn_3) }
% 140.95/20.64 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true, ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(not(implies(x, not(y)))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 140.95/20.64 = { by axiom 1 (ifeq_axiom) }
% 140.95/20.64 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true, ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, not(y))), implies(not(not(implies(x, not(y)))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)))), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 140.95/20.64 = { by axiom 5 (cn_1) }
% 140.95/20.64 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 140.95/20.64 = { by axiom 1 (ifeq_axiom) }
% 140.95/20.64 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y)), implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y)))), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), y), implies(not(implies(x, not(y))), y))), true, is_a_theorem(implies(implies(implies(not(not(implies(x, not(y)))), y), implies(not(y), y)), implies(not(implies(x, not(y))), y))), true), true), true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 140.95/20.64 = { by axiom 4 (condensed_detachment) }
% 140.95/20.64 ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 140.95/20.64 = { by axiom 1 (ifeq_axiom) }
% 140.95/20.64 ifeq(is_a_theorem(implies(implies(not(y), not(not(implies(x, not(y))))), implies(not(implies(x, not(y))), y))), true, ifeq(is_a_theorem(implies(not(y), not(not(implies(x, not(y)))))), true, is_a_theorem(implies(not(implies(x, not(y))), y)), true), true)
% 140.95/20.64 = { by axiom 4 (condensed_detachment) }
% 140.95/20.64 true
% 140.95/20.64 % SZS output end Proof
% 140.95/20.64
% 140.95/20.64 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------