%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL029-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 11:48:52 AM UTC 2026
% Result : Unsatisfiable 11.56s 2.00s
% Output : Proof 14.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL029-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n017.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 15:13:20 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.56/2.00 Command-line arguments: --no-flatten-goal
% 11.56/2.00
% 11.56/2.00 % SZS status Unsatisfiable
% 11.56/2.00
% 13.66/2.20 % SZS output start Proof
% 13.66/2.20 Axiom 1 (c0_4): is_a_theorem(implies(falsehood, X)) = true.
% 13.66/2.20 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 13.66/2.20 Axiom 3 (c0_2): is_a_theorem(implies(X, implies(Y, X))) = true.
% 13.66/2.20 Axiom 4 (c0_3): is_a_theorem(implies(implies(implies(X, Y), X), X)) = true.
% 13.66/2.20 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.
% 13.66/2.20 Axiom 6 (c0_1): is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))) = true.
% 13.66/2.20
% 13.66/2.20 Goal 1 (prove_c0_5): is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)) = true.
% 13.66/2.20 Proof:
% 13.66/2.20 is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a))
% 13.66/2.20 = { by axiom 2 (ifeq_axiom) R->L }
% 13.66/2.20 ifeq(true, true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 13.83/2.20 = { by axiom 5 (condensed_detachment) R->L }
% 13.83/2.20 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a)), implies(implies(implies(implies(a, falsehood), a), a), implies(implies(implies(a, falsehood), falsehood), a)))), true, ifeq(is_a_theorem(implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a))), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), a), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 13.83/2.20 = { by axiom 6 (c0_1) }
% 13.83/2.20 ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a))), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), a), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 13.83/2.21 = { by axiom 2 (ifeq_axiom) }
% 13.83/2.21 ifeq(ifeq(is_a_theorem(implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a))), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), a), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 13.83/2.21 = { by axiom 2 (ifeq_axiom) R->L }
% 13.83/2.21 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), a), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 13.83/2.21 = { by axiom 5 (condensed_detachment) R->L }
% 13.83/2.21 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(falsehood, a), implies(implies(a, falsehood), a))), implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a))))), true, ifeq(is_a_theorem(implies(implies(implies(a, falsehood), falsehood), implies(implies(falsehood, a), implies(implies(a, falsehood), a)))), true, is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a)))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), a), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 13.83/2.21 = { by axiom 6 (c0_1) }
% 13.83/2.21 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, falsehood), falsehood), implies(implies(falsehood, a), implies(implies(a, falsehood), a)))), true, is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a)))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), a), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 13.83/2.21 = { by axiom 2 (ifeq_axiom) }
% 13.83/2.21 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, falsehood), falsehood), implies(implies(falsehood, a), implies(implies(a, falsehood), a)))), true, is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), a), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 13.83/2.22 = { by axiom 6 (c0_1) }
% 13.83/2.22 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), a), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 13.83/2.22 = { by axiom 2 (ifeq_axiom) }
% 13.83/2.22 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a)))), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), a), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 13.83/2.22 = { by axiom 2 (ifeq_axiom) R->L }
% 13.83/2.22 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a)))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), a), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 13.83/2.22 = { by axiom 5 (condensed_detachment) R->L }
% 13.83/2.23 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))), true, ifeq(is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), a), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 13.83/2.23 = { by axiom 2 (ifeq_axiom) R->L }
% 13.83/2.23 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a)))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), a), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 13.83/2.23 = { by axiom 5 (condensed_detachment) R->L }
% 13.83/2.24 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), implies(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))), implies(implies(implies(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), implies(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), a), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 13.83/2.24 = { by axiom 6 (c0_1) }
% 13.83/2.25 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a)))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), implies(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), a), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 13.83/2.25 = { by axiom 2 (ifeq_axiom) }
% 13.83/2.25 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), implies(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), a), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 13.83/2.25 = { by axiom 6 (c0_1) }
% 13.83/2.26 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a)))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), a), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 13.83/2.26 = { by axiom 2 (ifeq_axiom) }
% 13.83/2.26 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))))), true, is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), a), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 13.83/2.27 = { by axiom 2 (ifeq_axiom) R->L }
% 13.83/2.27 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), a), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 13.83/2.27 = { by axiom 4 (c0_3) R->L }
% 13.83/2.27 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))), true, is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), a), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 13.83/2.27 = { by axiom 5 (condensed_detachment) }
% 13.83/2.27 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a)))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), a), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 13.83/2.27 = { by axiom 2 (ifeq_axiom) }
% 13.83/2.27 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), a), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 13.83/2.28 = { by axiom 2 (ifeq_axiom) R->L }
% 13.83/2.28 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a)))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), a), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 13.83/2.28 = { by axiom 5 (condensed_detachment) R->L }
% 13.83/2.29 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(falsehood, a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))), implies(implies(falsehood, a), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(falsehood, a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))))), true, is_a_theorem(implies(implies(falsehood, a), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))))), true), true), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), a), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 13.83/2.29 = { by axiom 2 (ifeq_axiom) R->L }
% 13.83/2.29 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(falsehood, a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))), implies(implies(falsehood, a), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(falsehood, a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))))), true, is_a_theorem(implies(implies(falsehood, a), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))))), true), true), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), a), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 13.83/2.30 = { by axiom 6 (c0_1) R->L }
% 13.83/2.30 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(falsehood, a))), implies(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(falsehood, a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))), implies(implies(falsehood, a), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))))))), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(falsehood, a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))), implies(implies(falsehood, a), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(falsehood, a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))))), true, is_a_theorem(implies(implies(falsehood, a), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))))), true), true), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), a), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 13.83/2.30 = { by axiom 2 (ifeq_axiom) R->L }
% 13.83/2.30 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(falsehood, a))), implies(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(falsehood, a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))), implies(implies(falsehood, a), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(falsehood, a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))), implies(implies(falsehood, a), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(falsehood, a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))))), true, is_a_theorem(implies(implies(falsehood, a), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))))), true), true), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), a), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 14.59/2.30 = { by axiom 3 (c0_2) R->L }
% 14.59/2.31 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(falsehood, a))), implies(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(falsehood, a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))), implies(implies(falsehood, a), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))))))), true, ifeq(is_a_theorem(implies(implies(falsehood, a), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(falsehood, a)))), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(falsehood, a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))), implies(implies(falsehood, a), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(falsehood, a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))))), true, is_a_theorem(implies(implies(falsehood, a), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))))), true), true), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), a), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 14.59/2.31 = { by axiom 5 (condensed_detachment) }
% 14.59/2.31 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a)))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(falsehood, a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))))), true, is_a_theorem(implies(implies(falsehood, a), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))))), true), true), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), a), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 14.59/2.31 = { by axiom 2 (ifeq_axiom) }
% 14.59/2.31 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(falsehood, a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))))), true, is_a_theorem(implies(implies(falsehood, a), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), a), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 14.59/2.32 = { by axiom 6 (c0_1) }
% 14.59/2.32 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a)))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(falsehood, a), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), a), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 14.59/2.32 = { by axiom 2 (ifeq_axiom) }
% 14.59/2.32 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, a), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))))), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), a), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 14.59/2.32 = { by axiom 2 (ifeq_axiom) R->L }
% 14.59/2.32 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, a), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))), true), true), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), a), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 14.59/2.32 = { by axiom 1 (c0_4) R->L }
% 14.59/2.33 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, a), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))))), true, ifeq(is_a_theorem(implies(falsehood, a)), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)))), true), true), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), a), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 14.59/2.33 = { by axiom 5 (condensed_detachment) }
% 14.59/2.33 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a)))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), a), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 14.59/2.33 = { by axiom 2 (ifeq_axiom) }
% 14.59/2.33 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a)), implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a)))), true, ifeq(is_a_theorem(implies(implies(implies(falsehood, a), implies(implies(a, falsehood), a)), implies(implies(a, falsehood), a))), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), implies(implies(a, falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), a), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 14.59/2.33 = { by axiom 5 (condensed_detachment) }
% 14.59/2.33 ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, falsehood), a), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 14.59/2.33 = { by axiom 2 (ifeq_axiom) }
% 14.59/2.33 ifeq(is_a_theorem(implies(implies(implies(implies(a, falsehood), a), a), implies(implies(implies(a, falsehood), falsehood), a))), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 14.59/2.33 = { by axiom 2 (ifeq_axiom) R->L }
% 14.59/2.33 ifeq(is_a_theorem(implies(implies(implies(implies(a, falsehood), a), a), implies(implies(implies(a, falsehood), falsehood), a))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true), true)
% 14.59/2.33 = { by axiom 4 (c0_3) R->L }
% 14.59/2.33 ifeq(is_a_theorem(implies(implies(implies(implies(a, falsehood), a), a), implies(implies(implies(a, falsehood), falsehood), a))), true, ifeq(is_a_theorem(implies(implies(implies(a, falsehood), a), a)), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true), true)
% 14.59/2.33 = { by axiom 5 (condensed_detachment) }
% 14.59/2.33 true
% 14.59/2.33 % SZS output end Proof
% 14.59/2.33
% 14.59/2.33 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------