%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL364-1 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 11:49:40 AM UTC 2026
% Result : Unsatisfiable 18.39s 2.77s
% Output : Proof 19.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL364-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.33 % Computer : n012.cluster.edu
% 0.06/0.33 % Model : x86_64 x86_64
% 0.06/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.33 % Memory : 8046.5625MB
% 0.06/0.33 % OS : Linux 6.8.0-71-generic
% 0.06/0.33 % CPULimit : 300
% 0.06/0.33 % WCLimit : 300
% 0.06/0.33 % DateTime : Sun Sep 27 15:36:19 UTC 2026
% 0.06/0.33 % CPUTime :
% 0.06/0.33 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.39/2.77 Command-line arguments: --no-flatten-goal
% 18.39/2.77
% 18.39/2.77 % SZS status Unsatisfiable
% 18.39/2.77
% 19.11/2.86 % SZS output start Proof
% 19.11/2.86 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 19.11/2.86 Axiom 2 (cn_3): is_a_theorem(implies(X, implies(not(X), Y))) = true.
% 19.11/2.86 Axiom 3 (cn_2): is_a_theorem(implies(implies(not(X), X), X)) = true.
% 19.11/2.86 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.
% 19.11/2.87 Axiom 5 (cn_1): is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))) = true.
% 19.11/2.87
% 19.11/2.87 Goal 1 (prove_cn_13): is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))) = true.
% 19.11/2.87 Proof:
% 19.11/2.87 is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x))))
% 19.11/2.87 = { by axiom 1 (ifeq_axiom) R->L }
% 19.11/2.87 ifeq(true, true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.11/2.87 = { by axiom 4 (condensed_detachment) R->L }
% 19.11/2.87 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x))), implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.11/2.87 = { by axiom 1 (ifeq_axiom) R->L }
% 19.11/2.87 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x))), implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.11/2.87 = { by axiom 5 (cn_1) R->L }
% 19.11/2.87 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(implies(implies(not(x), x), x), implies(implies(y, x), x)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x))), implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.11/2.87 = { by axiom 1 (ifeq_axiom) R->L }
% 19.11/2.87 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(implies(implies(not(x), x), x), implies(implies(y, x), x)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x))), implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.11/2.87 = { by axiom 5 (cn_1) R->L }
% 19.11/2.87 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(y, x), implies(not(x), x)), implies(implies(implies(not(x), x), x), implies(implies(y, x), x))), implies(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x))), implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))))), true, ifeq(is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(implies(implies(not(x), x), x), implies(implies(y, x), x)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x))), implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.11/2.87 = { by axiom 4 (condensed_detachment) }
% 19.11/2.87 ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.11/2.87 = { by axiom 1 (ifeq_axiom) }
% 19.11/2.87 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.11/2.87 = { by axiom 1 (ifeq_axiom) R->L }
% 19.11/2.87 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.11/2.87 = { by axiom 4 (condensed_detachment) R->L }
% 19.11/2.87 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(x, x), implies(implies(not(x), x), x)), implies(z, implies(implies(not(x), x), x)))), true, ifeq(is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true, is_a_theorem(implies(z, implies(implies(not(x), x), x))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.11/2.87 = { by axiom 1 (ifeq_axiom) R->L }
% 19.11/2.87 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(x, x), implies(implies(not(x), x), x)), implies(z, implies(implies(not(x), x), x)))), true), true, ifeq(is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true, is_a_theorem(implies(z, implies(implies(not(x), x), x))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.11/2.87 = { by axiom 4 (condensed_detachment) R->L }
% 19.11/2.87 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(z, implies(x, x)))), true, ifeq(is_a_theorem(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x))), true, is_a_theorem(implies(z, implies(x, x))), true), true), true, is_a_theorem(implies(implies(implies(x, x), implies(implies(not(x), x), x)), implies(z, implies(implies(not(x), x), x)))), true), true, ifeq(is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true, is_a_theorem(implies(z, implies(implies(not(x), x), x))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.11/2.87 = { by axiom 3 (cn_2) }
% 19.11/2.88 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(z, implies(x, x)))), true, ifeq(true, true, is_a_theorem(implies(z, implies(x, x))), true), true), true, is_a_theorem(implies(implies(implies(x, x), implies(implies(not(x), x), x)), implies(z, implies(implies(not(x), x), x)))), true), true, ifeq(is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true, is_a_theorem(implies(z, implies(implies(not(x), x), x))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.11/2.88 = { by axiom 1 (ifeq_axiom) }
% 19.11/2.88 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(z, implies(x, x)))), true, is_a_theorem(implies(z, implies(x, x))), true), true, is_a_theorem(implies(implies(implies(x, x), implies(implies(not(x), x), x)), implies(z, implies(implies(not(x), x), x)))), true), true, ifeq(is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true, is_a_theorem(implies(z, implies(implies(not(x), x), x))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.11/2.88 = { by axiom 1 (ifeq_axiom) R->L }
% 19.11/2.88 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(z, implies(x, x)))), true), true, is_a_theorem(implies(z, implies(x, x))), true), true, is_a_theorem(implies(implies(implies(x, x), implies(implies(not(x), x), x)), implies(z, implies(implies(not(x), x), x)))), true), true, ifeq(is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true, is_a_theorem(implies(z, implies(implies(not(x), x), x))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.11/2.88 = { by axiom 4 (condensed_detachment) R->L }
% 19.11/2.88 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(z), implies(x, x)), implies(not(implies(x, x)), implies(x, x))), implies(z, implies(not(implies(x, x)), implies(x, x))))), true, ifeq(is_a_theorem(implies(implies(not(z), implies(x, x)), implies(not(implies(x, x)), implies(x, x)))), true, is_a_theorem(implies(z, implies(not(implies(x, x)), implies(x, x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(z, implies(x, x)))), true), true, is_a_theorem(implies(z, implies(x, x))), true), true, is_a_theorem(implies(implies(implies(x, x), implies(implies(not(x), x), x)), implies(z, implies(implies(not(x), x), x)))), true), true, ifeq(is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true, is_a_theorem(implies(z, implies(implies(not(x), x), x))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.11/2.88 = { by axiom 1 (ifeq_axiom) R->L }
% 19.11/2.88 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(z), implies(x, x)), implies(not(implies(x, x)), implies(x, x))), implies(z, implies(not(implies(x, x)), implies(x, x))))), true), true, ifeq(is_a_theorem(implies(implies(not(z), implies(x, x)), implies(not(implies(x, x)), implies(x, x)))), true, is_a_theorem(implies(z, implies(not(implies(x, x)), implies(x, x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(z, implies(x, x)))), true), true, is_a_theorem(implies(z, implies(x, x))), true), true, is_a_theorem(implies(implies(implies(x, x), implies(implies(not(x), x), x)), implies(z, implies(implies(not(x), x), x)))), true), true, ifeq(is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true, is_a_theorem(implies(z, implies(implies(not(x), x), x))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.11/2.89 = { by axiom 5 (cn_1) R->L }
% 19.11/2.89 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(z, implies(not(z), implies(x, x))), implies(implies(implies(not(z), implies(x, x)), implies(not(implies(x, x)), implies(x, x))), implies(z, implies(not(implies(x, x)), implies(x, x)))))), true, is_a_theorem(implies(implies(implies(not(z), implies(x, x)), implies(not(implies(x, x)), implies(x, x))), implies(z, implies(not(implies(x, x)), implies(x, x))))), true), true, ifeq(is_a_theorem(implies(implies(not(z), implies(x, x)), implies(not(implies(x, x)), implies(x, x)))), true, is_a_theorem(implies(z, implies(not(implies(x, x)), implies(x, x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(z, implies(x, x)))), true), true, is_a_theorem(implies(z, implies(x, x))), true), true, is_a_theorem(implies(implies(implies(x, x), implies(implies(not(x), x), x)), implies(z, implies(implies(not(x), x), x)))), true), true, ifeq(is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true, is_a_theorem(implies(z, implies(implies(not(x), x), x))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.11/2.89 = { by axiom 1 (ifeq_axiom) R->L }
% 19.11/2.89 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(z, implies(not(z), implies(x, x))), implies(implies(implies(not(z), implies(x, x)), implies(not(implies(x, x)), implies(x, x))), implies(z, implies(not(implies(x, x)), implies(x, x)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(z), implies(x, x)), implies(not(implies(x, x)), implies(x, x))), implies(z, implies(not(implies(x, x)), implies(x, x))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(z), implies(x, x)), implies(not(implies(x, x)), implies(x, x)))), true, is_a_theorem(implies(z, implies(not(implies(x, x)), implies(x, x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(z, implies(x, x)))), true), true, is_a_theorem(implies(z, implies(x, x))), true), true, is_a_theorem(implies(implies(implies(x, x), implies(implies(not(x), x), x)), implies(z, implies(implies(not(x), x), x)))), true), true, ifeq(is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true, is_a_theorem(implies(z, implies(implies(not(x), x), x))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.11/2.89 = { by axiom 2 (cn_3) R->L }
% 19.11/2.89 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(z, implies(not(z), implies(x, x))), implies(implies(implies(not(z), implies(x, x)), implies(not(implies(x, x)), implies(x, x))), implies(z, implies(not(implies(x, x)), implies(x, x)))))), true, ifeq(is_a_theorem(implies(z, implies(not(z), implies(x, x)))), true, is_a_theorem(implies(implies(implies(not(z), implies(x, x)), implies(not(implies(x, x)), implies(x, x))), implies(z, implies(not(implies(x, x)), implies(x, x))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(z), implies(x, x)), implies(not(implies(x, x)), implies(x, x)))), true, is_a_theorem(implies(z, implies(not(implies(x, x)), implies(x, x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(z, implies(x, x)))), true), true, is_a_theorem(implies(z, implies(x, x))), true), true, is_a_theorem(implies(implies(implies(x, x), implies(implies(not(x), x), x)), implies(z, implies(implies(not(x), x), x)))), true), true, ifeq(is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true, is_a_theorem(implies(z, implies(implies(not(x), x), x))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.11/2.89 = { by axiom 4 (condensed_detachment) }
% 19.11/2.89 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(z), implies(x, x)), implies(not(implies(x, x)), implies(x, x)))), true, is_a_theorem(implies(z, implies(not(implies(x, x)), implies(x, x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(z, implies(x, x)))), true), true, is_a_theorem(implies(z, implies(x, x))), true), true, is_a_theorem(implies(implies(implies(x, x), implies(implies(not(x), x), x)), implies(z, implies(implies(not(x), x), x)))), true), true, ifeq(is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true, is_a_theorem(implies(z, implies(implies(not(x), x), x))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.11/2.89 = { by axiom 1 (ifeq_axiom) }
% 19.11/2.89 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(z), implies(x, x)), implies(not(implies(x, x)), implies(x, x)))), true, is_a_theorem(implies(z, implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(z, implies(x, x)))), true), true, is_a_theorem(implies(z, implies(x, x))), true), true, is_a_theorem(implies(implies(implies(x, x), implies(implies(not(x), x), x)), implies(z, implies(implies(not(x), x), x)))), true), true, ifeq(is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true, is_a_theorem(implies(z, implies(implies(not(x), x), x))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.11/2.89 = { by axiom 1 (ifeq_axiom) R->L }
% 19.11/2.89 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(z), implies(x, x)), implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(z, implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(z, implies(x, x)))), true), true, is_a_theorem(implies(z, implies(x, x))), true), true, is_a_theorem(implies(implies(implies(x, x), implies(implies(not(x), x), x)), implies(z, implies(implies(not(x), x), x)))), true), true, ifeq(is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true, is_a_theorem(implies(z, implies(implies(not(x), x), x))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.11/2.89 = { by axiom 4 (condensed_detachment) R->L }
% 19.11/2.89 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(x, x), implies(not(implies(x, x)), not(z)))), true, ifeq(is_a_theorem(implies(x, x)), true, is_a_theorem(implies(not(implies(x, x)), not(z))), true), true), true, is_a_theorem(implies(implies(not(z), implies(x, x)), implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(z, implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(z, implies(x, x)))), true), true, is_a_theorem(implies(z, implies(x, x))), true), true, is_a_theorem(implies(implies(implies(x, x), implies(implies(not(x), x), x)), implies(z, implies(implies(not(x), x), x)))), true), true, ifeq(is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true, is_a_theorem(implies(z, implies(implies(not(x), x), x))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.11/2.89 = { by axiom 2 (cn_3) }
% 19.11/2.89 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(x, x)), true, is_a_theorem(implies(not(implies(x, x)), not(z))), true), true), true, is_a_theorem(implies(implies(not(z), implies(x, x)), implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(z, implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(z, implies(x, x)))), true), true, is_a_theorem(implies(z, implies(x, x))), true), true, is_a_theorem(implies(implies(implies(x, x), implies(implies(not(x), x), x)), implies(z, implies(implies(not(x), x), x)))), true), true, ifeq(is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true, is_a_theorem(implies(z, implies(implies(not(x), x), x))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.11/2.90 = { by axiom 1 (ifeq_axiom) }
% 19.11/2.90 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(x, x)), true, is_a_theorem(implies(not(implies(x, x)), not(z))), true), true, is_a_theorem(implies(implies(not(z), implies(x, x)), implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(z, implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(z, implies(x, x)))), true), true, is_a_theorem(implies(z, implies(x, x))), true), true, is_a_theorem(implies(implies(implies(x, x), implies(implies(not(x), x), x)), implies(z, implies(implies(not(x), x), x)))), true), true, ifeq(is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true, is_a_theorem(implies(z, implies(implies(not(x), x), x))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.11/2.90 = { by axiom 1 (ifeq_axiom) R->L }
% 19.11/2.90 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(x, x)), true), true, is_a_theorem(implies(not(implies(x, x)), not(z))), true), true, is_a_theorem(implies(implies(not(z), implies(x, x)), implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(z, implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(z, implies(x, x)))), true), true, is_a_theorem(implies(z, implies(x, x))), true), true, is_a_theorem(implies(implies(implies(x, x), implies(implies(not(x), x), x)), implies(z, implies(implies(not(x), x), x)))), true), true, ifeq(is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true, is_a_theorem(implies(z, implies(implies(not(x), x), x))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.11/2.90 = { by axiom 4 (condensed_detachment) R->L }
% 19.11/2.90 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(x), x)), implies(implies(implies(not(x), x), x), implies(x, x)))), true, ifeq(is_a_theorem(implies(x, implies(not(x), x))), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(x, x))), true), true), true, is_a_theorem(implies(x, x)), true), true, is_a_theorem(implies(not(implies(x, x)), not(z))), true), true, is_a_theorem(implies(implies(not(z), implies(x, x)), implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(z, implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(z, implies(x, x)))), true), true, is_a_theorem(implies(z, implies(x, x))), true), true, is_a_theorem(implies(implies(implies(x, x), implies(implies(not(x), x), x)), implies(z, implies(implies(not(x), x), x)))), true), true, ifeq(is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true, is_a_theorem(implies(z, implies(implies(not(x), x), x))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.11/2.90 = { by axiom 2 (cn_3) }
% 19.11/2.90 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(x), x)), implies(implies(implies(not(x), x), x), implies(x, x)))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(x, x))), true), true), true, is_a_theorem(implies(x, x)), true), true, is_a_theorem(implies(not(implies(x, x)), not(z))), true), true, is_a_theorem(implies(implies(not(z), implies(x, x)), implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(z, implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(z, implies(x, x)))), true), true, is_a_theorem(implies(z, implies(x, x))), true), true, is_a_theorem(implies(implies(implies(x, x), implies(implies(not(x), x), x)), implies(z, implies(implies(not(x), x), x)))), true), true, ifeq(is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true, is_a_theorem(implies(z, implies(implies(not(x), x), x))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.81/2.90 = { by axiom 1 (ifeq_axiom) }
% 19.81/2.90 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(x), x)), implies(implies(implies(not(x), x), x), implies(x, x)))), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(x, x))), true), true, is_a_theorem(implies(x, x)), true), true, is_a_theorem(implies(not(implies(x, x)), not(z))), true), true, is_a_theorem(implies(implies(not(z), implies(x, x)), implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(z, implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(z, implies(x, x)))), true), true, is_a_theorem(implies(z, implies(x, x))), true), true, is_a_theorem(implies(implies(implies(x, x), implies(implies(not(x), x), x)), implies(z, implies(implies(not(x), x), x)))), true), true, ifeq(is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true, is_a_theorem(implies(z, implies(implies(not(x), x), x))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.81/2.90 = { by axiom 5 (cn_1) }
% 19.81/2.90 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(x, x))), true), true, is_a_theorem(implies(x, x)), true), true, is_a_theorem(implies(not(implies(x, x)), not(z))), true), true, is_a_theorem(implies(implies(not(z), implies(x, x)), implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(z, implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(z, implies(x, x)))), true), true, is_a_theorem(implies(z, implies(x, x))), true), true, is_a_theorem(implies(implies(implies(x, x), implies(implies(not(x), x), x)), implies(z, implies(implies(not(x), x), x)))), true), true, ifeq(is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true, is_a_theorem(implies(z, implies(implies(not(x), x), x))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.81/2.90 = { by axiom 1 (ifeq_axiom) }
% 19.81/2.90 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(x), x), x), implies(x, x))), true, is_a_theorem(implies(x, x)), true), true, is_a_theorem(implies(not(implies(x, x)), not(z))), true), true, is_a_theorem(implies(implies(not(z), implies(x, x)), implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(z, implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(z, implies(x, x)))), true), true, is_a_theorem(implies(z, implies(x, x))), true), true, is_a_theorem(implies(implies(implies(x, x), implies(implies(not(x), x), x)), implies(z, implies(implies(not(x), x), x)))), true), true, ifeq(is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true, is_a_theorem(implies(z, implies(implies(not(x), x), x))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.81/2.90 = { by axiom 1 (ifeq_axiom) R->L }
% 19.81/2.90 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(x), x), x), implies(x, x))), true, ifeq(true, true, is_a_theorem(implies(x, x)), true), true), true, is_a_theorem(implies(not(implies(x, x)), not(z))), true), true, is_a_theorem(implies(implies(not(z), implies(x, x)), implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(z, implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(z, implies(x, x)))), true), true, is_a_theorem(implies(z, implies(x, x))), true), true, is_a_theorem(implies(implies(implies(x, x), implies(implies(not(x), x), x)), implies(z, implies(implies(not(x), x), x)))), true), true, ifeq(is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true, is_a_theorem(implies(z, implies(implies(not(x), x), x))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.81/2.90 = { by axiom 3 (cn_2) R->L }
% 19.81/2.91 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(x), x), x), implies(x, x))), true, ifeq(is_a_theorem(implies(implies(not(x), x), x)), true, is_a_theorem(implies(x, x)), true), true), true, is_a_theorem(implies(not(implies(x, x)), not(z))), true), true, is_a_theorem(implies(implies(not(z), implies(x, x)), implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(z, implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(z, implies(x, x)))), true), true, is_a_theorem(implies(z, implies(x, x))), true), true, is_a_theorem(implies(implies(implies(x, x), implies(implies(not(x), x), x)), implies(z, implies(implies(not(x), x), x)))), true), true, ifeq(is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true, is_a_theorem(implies(z, implies(implies(not(x), x), x))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.81/2.91 = { by axiom 4 (condensed_detachment) }
% 19.81/2.91 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(x, x)), not(z))), true), true, is_a_theorem(implies(implies(not(z), implies(x, x)), implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(z, implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(z, implies(x, x)))), true), true, is_a_theorem(implies(z, implies(x, x))), true), true, is_a_theorem(implies(implies(implies(x, x), implies(implies(not(x), x), x)), implies(z, implies(implies(not(x), x), x)))), true), true, ifeq(is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true, is_a_theorem(implies(z, implies(implies(not(x), x), x))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.81/2.91 = { by axiom 1 (ifeq_axiom) }
% 19.81/2.91 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(x, x)), not(z))), true, is_a_theorem(implies(implies(not(z), implies(x, x)), implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(z, implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(z, implies(x, x)))), true), true, is_a_theorem(implies(z, implies(x, x))), true), true, is_a_theorem(implies(implies(implies(x, x), implies(implies(not(x), x), x)), implies(z, implies(implies(not(x), x), x)))), true), true, ifeq(is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true, is_a_theorem(implies(z, implies(implies(not(x), x), x))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.81/2.91 = { by axiom 1 (ifeq_axiom) R->L }
% 19.81/2.91 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(x, x)), not(z))), true, is_a_theorem(implies(implies(not(z), implies(x, x)), implies(not(implies(x, x)), implies(x, x)))), true), true), true, is_a_theorem(implies(z, implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(z, implies(x, x)))), true), true, is_a_theorem(implies(z, implies(x, x))), true), true, is_a_theorem(implies(implies(implies(x, x), implies(implies(not(x), x), x)), implies(z, implies(implies(not(x), x), x)))), true), true, ifeq(is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true, is_a_theorem(implies(z, implies(implies(not(x), x), x))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.81/2.91 = { by axiom 5 (cn_1) R->L }
% 19.81/2.91 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, x)), not(z)), implies(implies(not(z), implies(x, x)), implies(not(implies(x, x)), implies(x, x))))), true, ifeq(is_a_theorem(implies(not(implies(x, x)), not(z))), true, is_a_theorem(implies(implies(not(z), implies(x, x)), implies(not(implies(x, x)), implies(x, x)))), true), true), true, is_a_theorem(implies(z, implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(z, implies(x, x)))), true), true, is_a_theorem(implies(z, implies(x, x))), true), true, is_a_theorem(implies(implies(implies(x, x), implies(implies(not(x), x), x)), implies(z, implies(implies(not(x), x), x)))), true), true, ifeq(is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true, is_a_theorem(implies(z, implies(implies(not(x), x), x))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.81/2.91 = { by axiom 4 (condensed_detachment) }
% 19.81/2.91 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(z, implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(z, implies(x, x)))), true), true, is_a_theorem(implies(z, implies(x, x))), true), true, is_a_theorem(implies(implies(implies(x, x), implies(implies(not(x), x), x)), implies(z, implies(implies(not(x), x), x)))), true), true, ifeq(is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true, is_a_theorem(implies(z, implies(implies(not(x), x), x))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.81/2.91 = { by axiom 1 (ifeq_axiom) }
% 19.81/2.91 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(z, implies(not(implies(x, x)), implies(x, x)))), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(z, implies(x, x)))), true), true, is_a_theorem(implies(z, implies(x, x))), true), true, is_a_theorem(implies(implies(implies(x, x), implies(implies(not(x), x), x)), implies(z, implies(implies(not(x), x), x)))), true), true, ifeq(is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true, is_a_theorem(implies(z, implies(implies(not(x), x), x))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.81/2.91 = { by axiom 1 (ifeq_axiom) R->L }
% 19.81/2.91 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(z, implies(not(implies(x, x)), implies(x, x)))), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(z, implies(x, x)))), true), true), true, is_a_theorem(implies(z, implies(x, x))), true), true, is_a_theorem(implies(implies(implies(x, x), implies(implies(not(x), x), x)), implies(z, implies(implies(not(x), x), x)))), true), true, ifeq(is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true, is_a_theorem(implies(z, implies(implies(not(x), x), x))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.81/2.91 = { by axiom 5 (cn_1) R->L }
% 19.81/2.91 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(z, implies(not(implies(x, x)), implies(x, x))), implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(z, implies(x, x))))), true, ifeq(is_a_theorem(implies(z, implies(not(implies(x, x)), implies(x, x)))), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(z, implies(x, x)))), true), true), true, is_a_theorem(implies(z, implies(x, x))), true), true, is_a_theorem(implies(implies(implies(x, x), implies(implies(not(x), x), x)), implies(z, implies(implies(not(x), x), x)))), true), true, ifeq(is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true, is_a_theorem(implies(z, implies(implies(not(x), x), x))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.81/2.91 = { by axiom 4 (condensed_detachment) }
% 19.81/2.91 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(z, implies(x, x))), true), true, is_a_theorem(implies(implies(implies(x, x), implies(implies(not(x), x), x)), implies(z, implies(implies(not(x), x), x)))), true), true, ifeq(is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true, is_a_theorem(implies(z, implies(implies(not(x), x), x))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.81/2.91 = { by axiom 1 (ifeq_axiom) }
% 19.81/2.91 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(z, implies(x, x))), true, is_a_theorem(implies(implies(implies(x, x), implies(implies(not(x), x), x)), implies(z, implies(implies(not(x), x), x)))), true), true, ifeq(is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true, is_a_theorem(implies(z, implies(implies(not(x), x), x))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.81/2.91 = { by axiom 1 (ifeq_axiom) R->L }
% 19.81/2.91 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(z, implies(x, x))), true, is_a_theorem(implies(implies(implies(x, x), implies(implies(not(x), x), x)), implies(z, implies(implies(not(x), x), x)))), true), true), true, ifeq(is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true, is_a_theorem(implies(z, implies(implies(not(x), x), x))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.81/2.91 = { by axiom 5 (cn_1) R->L }
% 19.81/2.91 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(z, implies(x, x)), implies(implies(implies(x, x), implies(implies(not(x), x), x)), implies(z, implies(implies(not(x), x), x))))), true, ifeq(is_a_theorem(implies(z, implies(x, x))), true, is_a_theorem(implies(implies(implies(x, x), implies(implies(not(x), x), x)), implies(z, implies(implies(not(x), x), x)))), true), true), true, ifeq(is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true, is_a_theorem(implies(z, implies(implies(not(x), x), x))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.81/2.91 = { by axiom 4 (condensed_detachment) }
% 19.81/2.91 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true, is_a_theorem(implies(z, implies(implies(not(x), x), x))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.81/2.91 = { by axiom 1 (ifeq_axiom) }
% 19.81/2.91 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true, is_a_theorem(implies(z, implies(implies(not(x), x), x))), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.81/2.91 = { by axiom 1 (ifeq_axiom) R->L }
% 19.81/2.91 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true), true, is_a_theorem(implies(z, implies(implies(not(x), x), x))), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.81/2.92 = { by axiom 5 (cn_1) R->L }
% 19.81/2.92 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(x, x), implies(implies(not(x), x), x)))), true, is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true), true, is_a_theorem(implies(z, implies(implies(not(x), x), x))), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.81/2.92 = { by axiom 1 (ifeq_axiom) R->L }
% 19.81/2.92 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(x, x), implies(implies(not(x), x), x)))), true, ifeq(true, true, is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true), true), true, is_a_theorem(implies(z, implies(implies(not(x), x), x))), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.81/2.92 = { by axiom 3 (cn_2) R->L }
% 19.81/2.92 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(x, x), implies(implies(not(x), x), x)))), true, ifeq(is_a_theorem(implies(implies(not(x), x), x)), true, is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true), true), true, is_a_theorem(implies(z, implies(implies(not(x), x), x))), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.81/2.92 = { by axiom 4 (condensed_detachment) }
% 19.81/2.92 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(z, implies(implies(not(x), x), x))), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.81/2.92 = { by axiom 1 (ifeq_axiom) }
% 19.81/2.92 ifeq(ifeq(ifeq(is_a_theorem(implies(z, implies(implies(not(x), x), x))), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.81/2.92 = { by axiom 1 (ifeq_axiom) R->L }
% 19.81/2.92 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(z, implies(implies(not(x), x), x))), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.81/2.92 = { by axiom 5 (cn_1) R->L }
% 19.81/2.92 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(z, implies(implies(not(x), x), x)), implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x))))), true, ifeq(is_a_theorem(implies(z, implies(implies(not(x), x), x))), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(implies(y, x), x)), implies(z, implies(implies(y, x), x)))), true), true), true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.81/2.92 = { by axiom 4 (condensed_detachment) }
% 19.81/2.92 ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.81/2.92 = { by axiom 1 (ifeq_axiom) }
% 19.81/2.92 ifeq(is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true)
% 19.81/2.92 = { by axiom 1 (ifeq_axiom) R->L }
% 19.81/2.92 ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true), true)
% 19.81/2.92 = { by axiom 4 (condensed_detachment) R->L }
% 19.81/2.92 ifeq(ifeq(is_a_theorem(implies(implies(implies(not(x), y), implies(implies(y, x), implies(not(x), x))), implies(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x))), implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))))), true, ifeq(is_a_theorem(implies(implies(not(x), y), implies(implies(y, x), implies(not(x), x)))), true, is_a_theorem(implies(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x))), implies(implies(not(x), y), implies(z, implies(implies(y, x), x))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true), true)
% 19.81/2.92 = { by axiom 5 (cn_1) }
% 19.81/2.92 ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(x), y), implies(implies(y, x), implies(not(x), x)))), true, is_a_theorem(implies(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x))), implies(implies(not(x), y), implies(z, implies(implies(y, x), x))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true), true)
% 19.81/2.92 = { by axiom 1 (ifeq_axiom) }
% 19.81/2.92 ifeq(ifeq(is_a_theorem(implies(implies(not(x), y), implies(implies(y, x), implies(not(x), x)))), true, is_a_theorem(implies(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x))), implies(implies(not(x), y), implies(z, implies(implies(y, x), x))))), true), true, ifeq(is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true), true)
% 19.81/2.92 = { by axiom 5 (cn_1) }
% 19.81/2.92 ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x))), implies(implies(not(x), y), implies(z, implies(implies(y, x), x))))), true), true, ifeq(is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true), true)
% 19.81/2.92 = { by axiom 1 (ifeq_axiom) }
% 19.81/2.92 ifeq(is_a_theorem(implies(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x))), implies(implies(not(x), y), implies(z, implies(implies(y, x), x))))), true, ifeq(is_a_theorem(implies(implies(implies(y, x), implies(not(x), x)), implies(z, implies(implies(y, x), x)))), true, is_a_theorem(implies(implies(not(x), y), implies(z, implies(implies(y, x), x)))), true), true)
% 19.81/2.92 = { by axiom 4 (condensed_detachment) }
% 19.81/2.92 true
% 19.81/2.92 % SZS output end Proof
% 19.81/2.92
% 19.81/2.92 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------