%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL365-1 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 176.11s 22.75s
% Output : Proof 177.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL365-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.07 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.45 % Computer : n009.cluster.edu
% 0.17/0.45 % Model : x86_64 x86_64
% 0.17/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.45 % Memory : 8046.5625MB
% 0.17/0.45 % OS : Linux 6.8.0-71-generic
% 0.17/0.45 % CPULimit : 300
% 0.17/0.45 % WCLimit : 300
% 0.17/0.45 % DateTime : Sun Sep 27 15:36:59 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 176.11/22.75 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-regeneralise
% 176.11/22.75
% 176.11/22.75 % SZS status Unsatisfiable
% 176.11/22.75
% 177.29/22.86 % SZS output start Proof
% 177.29/22.86 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 177.29/22.86 Axiom 2 (cn_3): is_a_theorem(implies(X, implies(not(X), Y))) = true.
% 177.29/22.86 Axiom 3 (cn_2): is_a_theorem(implies(implies(not(X), X), X)) = true.
% 177.29/22.86 Axiom 4 (cn_1): is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))) = true.
% 177.29/22.86 Axiom 5 (condensed_detachment): ifeq(is_a_theorem(implies(X, Y)), true, ifeq(is_a_theorem(X), true, is_a_theorem(Y), true), true) = true.
% 177.29/22.86
% 177.29/22.86 Goal 1 (prove_cn_14): is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))) = true.
% 177.29/22.86 Proof:
% 177.29/22.86 is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u)))
% 177.29/22.86 = { by axiom 1 (ifeq_axiom) R->L }
% 177.29/22.86 ifeq(true, true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.86 = { by axiom 5 (condensed_detachment) R->L }
% 177.29/22.86 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true, ifeq(is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.87 = { by axiom 1 (ifeq_axiom) R->L }
% 177.29/22.87 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.87 = { by axiom 4 (cn_1) R->L }
% 177.29/22.87 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(z), y), implies(implies(y, z), implies(not(z), z))), implies(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))))), true, is_a_theorem(implies(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.87 = { by axiom 1 (ifeq_axiom) R->L }
% 177.29/22.87 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(z), y), implies(implies(y, z), implies(not(z), z))), implies(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.87 = { by axiom 4 (cn_1) R->L }
% 177.29/22.87 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(z), y), implies(implies(y, z), implies(not(z), z))), implies(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))))), true, ifeq(is_a_theorem(implies(implies(not(z), y), implies(implies(y, z), implies(not(z), z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.87 = { by axiom 5 (condensed_detachment) }
% 177.29/22.87 ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.87 = { by axiom 1 (ifeq_axiom) }
% 177.29/22.87 ifeq(ifeq(is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.87 = { by axiom 1 (ifeq_axiom) R->L }
% 177.29/22.87 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.87 = { by axiom 5 (condensed_detachment) R->L }
% 177.29/22.87 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))))), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.87 = { by axiom 1 (ifeq_axiom) R->L }
% 177.29/22.88 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.88 = { by axiom 5 (condensed_detachment) R->L }
% 177.29/22.88 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z))))), true, ifeq(is_a_theorem(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(not(z), z), z))), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.88 = { by axiom 3 (cn_2) }
% 177.29/22.88 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.88 = { by axiom 1 (ifeq_axiom) }
% 177.29/22.88 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z))))), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.89 = { by axiom 4 (cn_1) }
% 177.29/22.89 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.89 = { by axiom 1 (ifeq_axiom) }
% 177.29/22.89 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.89 = { by axiom 1 (ifeq_axiom) R->L }
% 177.29/22.89 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.89 = { by axiom 4 (cn_1) R->L }
% 177.29/22.89 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.90 = { by axiom 5 (condensed_detachment) }
% 177.29/22.90 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.90 = { by axiom 1 (ifeq_axiom) }
% 177.29/22.90 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.90 = { by axiom 1 (ifeq_axiom) R->L }
% 177.29/22.90 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.90 = { by axiom 5 (condensed_detachment) R->L }
% 177.29/22.90 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(x), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z))), implies(x, implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z))))), true, ifeq(is_a_theorem(implies(implies(not(x), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true, is_a_theorem(implies(x, implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.90 = { by axiom 1 (ifeq_axiom) R->L }
% 177.29/22.90 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(x), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z))), implies(x, implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z))))), true), true, ifeq(is_a_theorem(implies(implies(not(x), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true, is_a_theorem(implies(x, implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.90 = { by axiom 4 (cn_1) R->L }
% 177.29/22.90 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(x), implies(implies(not(z), z), z))), implies(implies(implies(not(x), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z))), implies(x, implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))))), true, is_a_theorem(implies(implies(implies(not(x), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z))), implies(x, implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z))))), true), true, ifeq(is_a_theorem(implies(implies(not(x), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true, is_a_theorem(implies(x, implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.91 = { by axiom 1 (ifeq_axiom) R->L }
% 177.29/22.91 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(x), implies(implies(not(z), z), z))), implies(implies(implies(not(x), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z))), implies(x, implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(x), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z))), implies(x, implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(x), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true, is_a_theorem(implies(x, implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.91 = { by axiom 2 (cn_3) R->L }
% 177.29/22.91 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(x), implies(implies(not(z), z), z))), implies(implies(implies(not(x), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z))), implies(x, implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))))), true, ifeq(is_a_theorem(implies(x, implies(not(x), implies(implies(not(z), z), z)))), true, is_a_theorem(implies(implies(implies(not(x), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z))), implies(x, implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(x), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true, is_a_theorem(implies(x, implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.91 = { by axiom 5 (condensed_detachment) }
% 177.29/22.91 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(x), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true, is_a_theorem(implies(x, implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.91 = { by axiom 1 (ifeq_axiom) }
% 177.29/22.91 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(x), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true, is_a_theorem(implies(x, implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.91 = { by axiom 1 (ifeq_axiom) R->L }
% 177.29/22.91 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(x), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true, is_a_theorem(implies(x, implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.92 = { by axiom 5 (condensed_detachment) R->L }
% 177.29/22.92 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(z), z), z), implies(not(implies(implies(not(z), z), z)), not(x)))), true, ifeq(is_a_theorem(implies(implies(not(z), z), z)), true, is_a_theorem(implies(not(implies(implies(not(z), z), z)), not(x))), true), true), true, is_a_theorem(implies(implies(not(x), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true, is_a_theorem(implies(x, implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.92 = { by axiom 2 (cn_3) }
% 177.29/22.92 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(z), z), z)), true, is_a_theorem(implies(not(implies(implies(not(z), z), z)), not(x))), true), true), true, is_a_theorem(implies(implies(not(x), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true, is_a_theorem(implies(x, implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.92 = { by axiom 1 (ifeq_axiom) }
% 177.29/22.92 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(z), z), z)), true, is_a_theorem(implies(not(implies(implies(not(z), z), z)), not(x))), true), true, is_a_theorem(implies(implies(not(x), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true, is_a_theorem(implies(x, implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.92 = { by axiom 3 (cn_2) }
% 177.29/22.92 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(implies(not(z), z), z)), not(x))), true), true, is_a_theorem(implies(implies(not(x), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true, is_a_theorem(implies(x, implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.92 = { by axiom 1 (ifeq_axiom) }
% 177.29/22.92 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(implies(not(z), z), z)), not(x))), true, is_a_theorem(implies(implies(not(x), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true, is_a_theorem(implies(x, implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.92 = { by axiom 1 (ifeq_axiom) R->L }
% 177.29/22.93 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(implies(not(z), z), z)), not(x))), true, is_a_theorem(implies(implies(not(x), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true), true, is_a_theorem(implies(x, implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.93 = { by axiom 4 (cn_1) R->L }
% 177.29/22.93 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(not(z), z), z)), not(x)), implies(implies(not(x), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z))))), true, ifeq(is_a_theorem(implies(not(implies(implies(not(z), z), z)), not(x))), true, is_a_theorem(implies(implies(not(x), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true), true, is_a_theorem(implies(x, implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.93 = { by axiom 5 (condensed_detachment) }
% 177.29/22.93 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(x, implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.93 = { by axiom 1 (ifeq_axiom) }
% 177.29/22.93 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(x, implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.93 = { by axiom 1 (ifeq_axiom) R->L }
% 177.29/22.93 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(x, implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.93 = { by axiom 4 (cn_1) R->L }
% 177.29/22.93 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))))), true, ifeq(is_a_theorem(implies(x, implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.93 = { by axiom 5 (condensed_detachment) }
% 177.29/22.93 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.93 = { by axiom 1 (ifeq_axiom) }
% 177.29/22.93 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.93 = { by axiom 1 (ifeq_axiom) R->L }
% 177.29/22.94 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.94 = { by axiom 5 (condensed_detachment) R->L }
% 177.29/22.94 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(implies(not(z), z), z), implies(implies(y, z), z))), implies(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))))), true, ifeq(is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(implies(not(z), z), z), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.94 = { by axiom 4 (cn_1) }
% 177.29/22.94 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(implies(not(z), z), z), implies(implies(y, z), z))), implies(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.94 = { by axiom 1 (ifeq_axiom) }
% 177.29/22.94 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(implies(not(z), z), z), implies(implies(y, z), z))), implies(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.94 = { by axiom 4 (cn_1) }
% 177.29/22.94 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.94 = { by axiom 1 (ifeq_axiom) }
% 177.29/22.94 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.94 = { by axiom 5 (condensed_detachment) }
% 177.29/22.94 ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.94 = { by axiom 1 (ifeq_axiom) }
% 177.29/22.94 ifeq(is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 177.29/22.94 = { by axiom 1 (ifeq_axiom) R->L }
% 177.29/22.94 ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true), true)
% 177.29/22.94 = { by axiom 4 (cn_1) R->L }
% 177.29/22.94 ifeq(is_a_theorem(implies(implies(implies(not(z), y), implies(x, implies(implies(y, z), z))), implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u)))), true, ifeq(is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true), true)
% 177.29/22.94 = { by axiom 5 (condensed_detachment) }
% 177.29/22.94 true
% 177.29/22.94 % SZS output end Proof
% 177.29/22.94
% 177.29/22.94 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------