%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL399-1 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 14.41s 2.36s
% Output : Proof 17.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL399-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n010.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 15:40:31 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.41/2.36 Command-line arguments: --no-flatten-goal
% 14.41/2.36
% 14.41/2.36 % SZS status Unsatisfiable
% 14.41/2.36
% 16.82/2.62 % SZS output start Proof
% 16.82/2.62 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 16.82/2.62 Axiom 2 (cn_3): is_a_theorem(implies(X, implies(not(X), Y))) = true.
% 16.82/2.62 Axiom 3 (cn_2): is_a_theorem(implies(implies(not(X), X), X)) = true.
% 16.82/2.62 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.
% 16.82/2.62 Axiom 5 (cn_1): is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))) = true.
% 16.82/2.62
% 16.82/2.62 Goal 1 (prove_cn_65): is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)) = true.
% 16.82/2.62 Proof:
% 16.82/2.62 is_a_theorem(implies(implies(not(x), not(implies(y, y))), x))
% 16.82/2.62 = { by axiom 1 (ifeq_axiom) R->L }
% 16.82/2.62 ifeq(true, true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 16.82/2.62 = { by axiom 4 (condensed_detachment) R->L }
% 16.82/2.62 ifeq(ifeq(is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true, ifeq(is_a_theorem(implies(implies(not(x), x), x)), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 16.82/2.62 = { by axiom 3 (cn_2) }
% 16.82/2.62 ifeq(ifeq(is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 16.82/2.62 = { by axiom 1 (ifeq_axiom) }
% 16.82/2.62 ifeq(ifeq(is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 16.82/2.62 = { by axiom 1 (ifeq_axiom) R->L }
% 16.82/2.62 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 16.82/2.63 = { by axiom 4 (condensed_detachment) R->L }
% 16.82/2.63 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true, is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 16.82/2.63 = { by axiom 1 (ifeq_axiom) R->L }
% 16.82/2.63 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true, is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 16.82/2.63 = { by axiom 5 (cn_1) R->L }
% 16.82/2.63 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true, is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 16.82/2.63 = { by axiom 1 (ifeq_axiom) R->L }
% 16.82/2.64 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true, is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 16.82/2.64 = { by axiom 5 (cn_1) R->L }
% 16.82/2.64 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x)))), implies(implies(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))))), true, ifeq(is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true, is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 16.82/2.64 = { by axiom 4 (condensed_detachment) }
% 16.82/2.64 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true, is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 16.82/2.64 = { by axiom 1 (ifeq_axiom) }
% 16.82/2.64 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true, is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 16.82/2.64 = { by axiom 1 (ifeq_axiom) R->L }
% 16.82/2.64 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true, is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 16.82/2.65 = { by axiom 4 (condensed_detachment) R->L }
% 16.82/2.65 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(not(implies(not(x), x)), implies(not(x), x)), x)), implies(implies(implies(implies(not(implies(not(x), x)), implies(not(x), x)), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))))), true, ifeq(is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(not(implies(not(x), x)), implies(not(x), x)), x))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(x), x)), implies(not(x), x)), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true, is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 16.82/2.65 = { by axiom 5 (cn_1) }
% 16.82/2.65 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(not(implies(not(x), x)), implies(not(x), x)), x))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(x), x)), implies(not(x), x)), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true, is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 16.82/2.65 = { by axiom 1 (ifeq_axiom) }
% 16.82/2.65 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(not(implies(not(x), x)), implies(not(x), x)), x))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(x), x)), implies(not(x), x)), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true, is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 16.82/2.65 = { by axiom 1 (ifeq_axiom) R->L }
% 16.82/2.65 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(not(implies(not(x), x)), implies(not(x), x)), x))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(x), x)), implies(not(x), x)), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true, is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 16.82/2.66 = { by axiom 5 (cn_1) R->L }
% 16.82/2.66 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(x), x)), implies(not(x), x)), implies(not(x), x)), implies(implies(implies(not(x), x), x), implies(implies(not(implies(not(x), x)), implies(not(x), x)), x)))), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(not(implies(not(x), x)), implies(not(x), x)), x))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(x), x)), implies(not(x), x)), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true, is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 16.82/2.66 = { by axiom 1 (ifeq_axiom) R->L }
% 16.82/2.66 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(x), x)), implies(not(x), x)), implies(not(x), x)), implies(implies(implies(not(x), x), x), implies(implies(not(implies(not(x), x)), implies(not(x), x)), x)))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(not(implies(not(x), x)), implies(not(x), x)), x))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(x), x)), implies(not(x), x)), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true, is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 16.82/2.66 = { by axiom 3 (cn_2) R->L }
% 16.82/2.66 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(x), x)), implies(not(x), x)), implies(not(x), x)), implies(implies(implies(not(x), x), x), implies(implies(not(implies(not(x), x)), implies(not(x), x)), x)))), true, ifeq(is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(x), x)), implies(not(x), x))), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(not(implies(not(x), x)), implies(not(x), x)), x))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(x), x)), implies(not(x), x)), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true, is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 16.82/2.66 = { by axiom 4 (condensed_detachment) }
% 16.82/2.66 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(not(x), x)), implies(not(x), x)), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true, is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 16.82/2.67 = { by axiom 1 (ifeq_axiom) }
% 16.82/2.67 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(x), x)), implies(not(x), x)), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true, is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 16.82/2.67 = { by axiom 1 (ifeq_axiom) R->L }
% 16.82/2.67 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(x), x)), implies(not(x), x)), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true), true, is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 16.82/2.67 = { by axiom 4 (condensed_detachment) R->L }
% 16.82/2.67 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(implies(not(x), x)), implies(not(x), x)), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), implies(implies(implies(implies(implies(not(implies(not(x), x)), implies(not(x), x)), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), implies(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(implies(not(x), x)), implies(not(x), x)), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(x), x)), implies(not(x), x)), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), implies(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(x), x)), implies(not(x), x)), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true), true, is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 16.82/2.68 = { by axiom 5 (cn_1) }
% 16.82/2.68 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(implies(not(x), x)), implies(not(x), x)), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(x), x)), implies(not(x), x)), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), implies(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(x), x)), implies(not(x), x)), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true), true, is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 16.82/2.68 = { by axiom 1 (ifeq_axiom) }
% 16.82/2.68 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(implies(not(x), x)), implies(not(x), x)), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(x), x)), implies(not(x), x)), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), implies(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(x), x)), implies(not(x), x)), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true), true, is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 16.82/2.68 = { by axiom 5 (cn_1) }
% 16.82/2.68 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(x), x)), implies(not(x), x)), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), implies(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(x), x)), implies(not(x), x)), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true), true, is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 16.82/2.68 = { by axiom 1 (ifeq_axiom) }
% 16.82/2.69 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(x), x)), implies(not(x), x)), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), implies(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(x), x)), implies(not(x), x)), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true), true, is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 16.82/2.69 = { by axiom 4 (condensed_detachment) }
% 16.82/2.69 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 16.82/2.69 = { by axiom 1 (ifeq_axiom) }
% 16.82/2.69 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 16.82/2.69 = { by axiom 1 (ifeq_axiom) R->L }
% 16.82/2.69 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 16.82/2.69 = { by axiom 4 (condensed_detachment) R->L }
% 16.82/2.70 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(x), x))), x), implies(not(implies(y, y)), x)), implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(x), x))), x), implies(not(implies(y, y)), x))), true, is_a_theorem(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x))), true), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 16.82/2.70 = { by axiom 1 (ifeq_axiom) R->L }
% 16.82/2.70 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(x), x))), x), implies(not(implies(y, y)), x)), implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(x), x))), x), implies(not(implies(y, y)), x))), true, is_a_theorem(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x))), true), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 16.82/2.70 = { by axiom 5 (cn_1) R->L }
% 16.82/2.70 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(not(implies(not(x), x))), x)), implies(implies(implies(not(not(implies(not(x), x))), x), implies(not(implies(y, y)), x)), implies(not(implies(not(x), x)), implies(not(implies(y, y)), x))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(x), x))), x), implies(not(implies(y, y)), x)), implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(x), x))), x), implies(not(implies(y, y)), x))), true, is_a_theorem(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x))), true), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 16.82/2.70 = { by axiom 1 (ifeq_axiom) R->L }
% 16.82/2.70 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(not(implies(not(x), x))), x)), implies(implies(implies(not(not(implies(not(x), x))), x), implies(not(implies(y, y)), x)), implies(not(implies(not(x), x)), implies(not(implies(y, y)), x))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(x), x))), x), implies(not(implies(y, y)), x)), implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(x), x))), x), implies(not(implies(y, y)), x))), true, is_a_theorem(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x))), true), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 16.82/2.71 = { by axiom 2 (cn_3) R->L }
% 17.63/2.71 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(not(implies(not(x), x))), x)), implies(implies(implies(not(not(implies(not(x), x))), x), implies(not(implies(y, y)), x)), implies(not(implies(not(x), x)), implies(not(implies(y, y)), x))))), true, ifeq(is_a_theorem(implies(not(implies(not(x), x)), implies(not(not(implies(not(x), x))), x))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(x), x))), x), implies(not(implies(y, y)), x)), implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(x), x))), x), implies(not(implies(y, y)), x))), true, is_a_theorem(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x))), true), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 17.63/2.71 = { by axiom 4 (condensed_detachment) }
% 17.63/2.71 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(x), x))), x), implies(not(implies(y, y)), x))), true, is_a_theorem(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x))), true), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 17.63/2.71 = { by axiom 1 (ifeq_axiom) }
% 17.63/2.71 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true, ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(x), x))), x), implies(not(implies(y, y)), x))), true, is_a_theorem(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x))), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 17.63/2.71 = { by axiom 1 (ifeq_axiom) R->L }
% 17.63/2.71 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(implies(not(x), x))), x), implies(not(implies(y, y)), x))), true), true, is_a_theorem(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x))), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 17.63/2.71 = { by axiom 4 (condensed_detachment) R->L }
% 17.63/2.72 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(y, y), implies(not(implies(y, y)), not(not(implies(not(x), x)))))), true, ifeq(is_a_theorem(implies(y, y)), true, is_a_theorem(implies(not(implies(y, y)), not(not(implies(not(x), x))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(x), x))), x), implies(not(implies(y, y)), x))), true), true, is_a_theorem(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x))), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 17.63/2.72 = { by axiom 2 (cn_3) }
% 17.63/2.72 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(y, y)), true, is_a_theorem(implies(not(implies(y, y)), not(not(implies(not(x), x))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(x), x))), x), implies(not(implies(y, y)), x))), true), true, is_a_theorem(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x))), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 17.63/2.72 = { by axiom 1 (ifeq_axiom) }
% 17.63/2.72 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(y, y)), true, is_a_theorem(implies(not(implies(y, y)), not(not(implies(not(x), x))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(x), x))), x), implies(not(implies(y, y)), x))), true), true, is_a_theorem(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x))), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 17.63/2.73 = { by axiom 1 (ifeq_axiom) R->L }
% 17.63/2.73 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(y, y)), true), true, is_a_theorem(implies(not(implies(y, y)), not(not(implies(not(x), x))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(x), x))), x), implies(not(implies(y, y)), x))), true), true, is_a_theorem(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x))), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 17.63/2.73 = { by axiom 4 (condensed_detachment) R->L }
% 17.63/2.73 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(y, implies(not(y), y)), implies(implies(implies(not(y), y), y), implies(y, y)))), true, ifeq(is_a_theorem(implies(y, implies(not(y), y))), true, is_a_theorem(implies(implies(implies(not(y), y), y), implies(y, y))), true), true), true, is_a_theorem(implies(y, y)), true), true, is_a_theorem(implies(not(implies(y, y)), not(not(implies(not(x), x))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(x), x))), x), implies(not(implies(y, y)), x))), true), true, is_a_theorem(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x))), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 17.63/2.73 = { by axiom 2 (cn_3) }
% 17.63/2.73 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(y, implies(not(y), y)), implies(implies(implies(not(y), y), y), implies(y, y)))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(y), y), y), implies(y, y))), true), true), true, is_a_theorem(implies(y, y)), true), true, is_a_theorem(implies(not(implies(y, y)), not(not(implies(not(x), x))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(x), x))), x), implies(not(implies(y, y)), x))), true), true, is_a_theorem(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x))), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 17.63/2.73 = { by axiom 1 (ifeq_axiom) }
% 17.63/2.73 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(y, implies(not(y), y)), implies(implies(implies(not(y), y), y), implies(y, y)))), true, is_a_theorem(implies(implies(implies(not(y), y), y), implies(y, y))), true), true, is_a_theorem(implies(y, y)), true), true, is_a_theorem(implies(not(implies(y, y)), not(not(implies(not(x), x))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(x), x))), x), implies(not(implies(y, y)), x))), true), true, is_a_theorem(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x))), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 17.63/2.73 = { by axiom 5 (cn_1) }
% 17.63/2.73 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(y), y), y), implies(y, y))), true), true, is_a_theorem(implies(y, y)), true), true, is_a_theorem(implies(not(implies(y, y)), not(not(implies(not(x), x))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(x), x))), x), implies(not(implies(y, y)), x))), true), true, is_a_theorem(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x))), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 17.63/2.74 = { by axiom 1 (ifeq_axiom) }
% 17.63/2.74 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(y), y), y), implies(y, y))), true, is_a_theorem(implies(y, y)), true), true, is_a_theorem(implies(not(implies(y, y)), not(not(implies(not(x), x))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(x), x))), x), implies(not(implies(y, y)), x))), true), true, is_a_theorem(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x))), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 17.63/2.74 = { by axiom 1 (ifeq_axiom) R->L }
% 17.63/2.74 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(y), y), y), implies(y, y))), true, ifeq(true, true, is_a_theorem(implies(y, y)), true), true), true, is_a_theorem(implies(not(implies(y, y)), not(not(implies(not(x), x))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(x), x))), x), implies(not(implies(y, y)), x))), true), true, is_a_theorem(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x))), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 17.63/2.74 = { by axiom 3 (cn_2) R->L }
% 17.63/2.74 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(y), y), y), implies(y, y))), true, ifeq(is_a_theorem(implies(implies(not(y), y), y)), true, is_a_theorem(implies(y, y)), true), true), true, is_a_theorem(implies(not(implies(y, y)), not(not(implies(not(x), x))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(x), x))), x), implies(not(implies(y, y)), x))), true), true, is_a_theorem(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x))), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 17.63/2.74 = { by axiom 4 (condensed_detachment) }
% 17.63/2.74 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(y, y)), not(not(implies(not(x), x))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(x), x))), x), implies(not(implies(y, y)), x))), true), true, is_a_theorem(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x))), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 17.63/2.74 = { by axiom 1 (ifeq_axiom) }
% 17.63/2.75 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(y, y)), not(not(implies(not(x), x))))), true, is_a_theorem(implies(implies(not(not(implies(not(x), x))), x), implies(not(implies(y, y)), x))), true), true, is_a_theorem(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x))), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 17.63/2.75 = { by axiom 1 (ifeq_axiom) R->L }
% 17.63/2.75 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(y, y)), not(not(implies(not(x), x))))), true, is_a_theorem(implies(implies(not(not(implies(not(x), x))), x), implies(not(implies(y, y)), x))), true), true), true, is_a_theorem(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x))), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 17.63/2.75 = { by axiom 5 (cn_1) R->L }
% 17.63/2.75 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(y, y)), not(not(implies(not(x), x)))), implies(implies(not(not(implies(not(x), x))), x), implies(not(implies(y, y)), x)))), true, ifeq(is_a_theorem(implies(not(implies(y, y)), not(not(implies(not(x), x))))), true, is_a_theorem(implies(implies(not(not(implies(not(x), x))), x), implies(not(implies(y, y)), x))), true), true), true, is_a_theorem(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x))), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 17.63/2.75 = { by axiom 4 (condensed_detachment) }
% 17.63/2.75 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true, ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x))), true), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 17.63/2.75 = { by axiom 1 (ifeq_axiom) }
% 17.63/2.75 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x)), implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)))), true, ifeq(is_a_theorem(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x))), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 17.63/2.75 = { by axiom 4 (condensed_detachment) }
% 17.63/2.75 ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 17.63/2.75 = { by axiom 1 (ifeq_axiom) }
% 17.63/2.75 ifeq(is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true)
% 17.63/2.75 = { by axiom 1 (ifeq_axiom) R->L }
% 17.63/2.75 ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true), true)
% 17.63/2.75 = { by axiom 4 (condensed_detachment) R->L }
% 17.63/2.75 ifeq(ifeq(is_a_theorem(implies(implies(implies(not(x), not(implies(y, y))), implies(implies(not(implies(y, y)), x), implies(not(x), x))), implies(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x), implies(implies(not(x), not(implies(y, y))), x)))), true, ifeq(is_a_theorem(implies(implies(not(x), not(implies(y, y))), implies(implies(not(implies(y, y)), x), implies(not(x), x)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x), implies(implies(not(x), not(implies(y, y))), x))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true), true)
% 17.63/2.75 = { by axiom 5 (cn_1) }
% 17.63/2.75 ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(x), not(implies(y, y))), implies(implies(not(implies(y, y)), x), implies(not(x), x)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x), implies(implies(not(x), not(implies(y, y))), x))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true), true)
% 17.63/2.75 = { by axiom 1 (ifeq_axiom) }
% 17.63/2.75 ifeq(ifeq(is_a_theorem(implies(implies(not(x), not(implies(y, y))), implies(implies(not(implies(y, y)), x), implies(not(x), x)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x), implies(implies(not(x), not(implies(y, y))), x))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true), true)
% 17.63/2.75 = { by axiom 5 (cn_1) }
% 17.63/2.75 ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x), implies(implies(not(x), not(implies(y, y))), x))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true), true)
% 17.63/2.76 = { by axiom 1 (ifeq_axiom) }
% 17.63/2.76 ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x), implies(implies(not(x), not(implies(y, y))), x))), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), x)), true, is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)), true), true)
% 17.63/2.76 = { by axiom 4 (condensed_detachment) }
% 17.63/2.76 true
% 17.63/2.76 % SZS output end Proof
% 17.63/2.76
% 17.63/2.76 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------