TSTP Solution File: LCL384-10 by Twee---2.5.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.5.0
% Problem : LCL384-10 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee /export/starexec/sandbox/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 11:21:26 EDT 2024
% Result : Unsatisfiable 5.49s 1.07s
% Output : Proof 6.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : LCL384-10 : TPTP v8.2.0. Released v7.5.0.
% 0.04/0.12 % Command : parallel-twee /export/starexec/sandbox/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Jun 22 13:18:53 EDT 2024
% 0.12/0.33 % CPUTime :
% 5.49/1.07 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 5.49/1.07
% 5.49/1.07 % SZS status Unsatisfiable
% 5.49/1.07
% 5.79/1.11 % SZS output start Proof
% 5.79/1.11 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 5.79/1.11 Axiom 2 (cn_3): is_a_theorem(implies(X, implies(not(X), Y))) = true.
% 5.79/1.11 Axiom 3 (cn_2): is_a_theorem(implies(implies(not(X), X), X)) = true.
% 5.79/1.11 Axiom 4 (cn_1): is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))) = true.
% 5.79/1.11 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.
% 5.79/1.11
% 5.79/1.11 Lemma 6: ifeq(is_a_theorem(implies(implies(implies(not(X), X), X), Y)), true, is_a_theorem(Y), true) = true.
% 5.79/1.11 Proof:
% 5.79/1.11 ifeq(is_a_theorem(implies(implies(implies(not(X), X), X), Y)), true, is_a_theorem(Y), true)
% 5.79/1.11 = { by axiom 1 (ifeq_axiom) R->L }
% 5.79/1.11 ifeq(is_a_theorem(implies(implies(implies(not(X), X), X), Y)), true, ifeq(true, true, is_a_theorem(Y), true), true)
% 5.79/1.11 = { by axiom 3 (cn_2) R->L }
% 5.79/1.11 ifeq(is_a_theorem(implies(implies(implies(not(X), X), X), Y)), true, ifeq(is_a_theorem(implies(implies(not(X), X), X)), true, is_a_theorem(Y), true), true)
% 5.79/1.11 = { by axiom 5 (condensed_detachment) }
% 5.79/1.11 true
% 5.79/1.11
% 5.79/1.11 Lemma 7: ifeq(is_a_theorem(implies(X, Y)), true, is_a_theorem(implies(implies(Y, Z), implies(X, Z))), true) = true.
% 5.79/1.11 Proof:
% 5.79/1.11 ifeq(is_a_theorem(implies(X, Y)), true, is_a_theorem(implies(implies(Y, Z), implies(X, Z))), true)
% 5.79/1.11 = { by axiom 1 (ifeq_axiom) R->L }
% 5.79/1.11 ifeq(true, true, ifeq(is_a_theorem(implies(X, Y)), true, is_a_theorem(implies(implies(Y, Z), implies(X, Z))), true), true)
% 5.79/1.11 = { by axiom 4 (cn_1) R->L }
% 5.79/1.11 ifeq(is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))), true, ifeq(is_a_theorem(implies(X, Y)), true, is_a_theorem(implies(implies(Y, Z), implies(X, Z))), true), true)
% 5.79/1.11 = { by axiom 5 (condensed_detachment) }
% 5.79/1.11 true
% 5.79/1.11
% 5.79/1.11 Lemma 8: ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Z, Y)), W)), true, is_a_theorem(implies(implies(Z, X), W)), true) = true.
% 5.79/1.11 Proof:
% 5.79/1.11 ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Z, Y)), W)), true, is_a_theorem(implies(implies(Z, X), W)), true)
% 5.79/1.11 = { by axiom 1 (ifeq_axiom) R->L }
% 5.79/1.11 ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Z, Y)), W)), true, is_a_theorem(implies(implies(Z, X), W)), true), true)
% 5.79/1.11 = { by lemma 7 R->L }
% 5.79/1.11 ifeq(ifeq(is_a_theorem(implies(implies(Z, X), implies(implies(X, Y), implies(Z, Y)))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, Y)), W), implies(implies(Z, X), W))), true), true, ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Z, Y)), W)), true, is_a_theorem(implies(implies(Z, X), W)), true), true)
% 5.79/1.11 = { by axiom 4 (cn_1) }
% 5.79/1.11 ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, Y)), W), implies(implies(Z, X), W))), true), true, ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Z, Y)), W)), true, is_a_theorem(implies(implies(Z, X), W)), true), true)
% 5.79/1.11 = { by axiom 1 (ifeq_axiom) }
% 5.79/1.11 ifeq(is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, Y)), W), implies(implies(Z, X), W))), true, ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Z, Y)), W)), true, is_a_theorem(implies(implies(Z, X), W)), true), true)
% 5.79/1.11 = { by axiom 5 (condensed_detachment) }
% 5.79/1.11 true
% 5.79/1.11
% 5.79/1.11 Goal 1 (prove_cn_45): is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))) = true.
% 5.79/1.11 Proof:
% 5.79/1.11 is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z))))
% 5.79/1.11 = { by axiom 1 (ifeq_axiom) R->L }
% 5.79/1.11 ifeq(true, true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 5.79/1.11 = { by lemma 7 R->L }
% 5.79/1.11 ifeq(ifeq(is_a_theorem(implies(implies(not(z), y), implies(implies(y, z), z))), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 5.79/1.11 = { by axiom 1 (ifeq_axiom) R->L }
% 5.79/1.11 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(z), y), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 5.79/1.11 = { by lemma 6 R->L }
% 5.79/1.11 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 5.79/1.11 = { by axiom 1 (ifeq_axiom) R->L }
% 5.79/1.11 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 5.79/1.11 = { by lemma 8 R->L }
% 5.79/1.11 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 5.79/1.12 = { by axiom 1 (ifeq_axiom) R->L }
% 5.79/1.12 ifeq(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(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 5.79/1.12 = { by axiom 5 (condensed_detachment) R->L }
% 5.79/1.12 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(not(implies(implies(y, z), z)), implies(implies(not(z), z), z)))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(implies(not(z), z), z))), true, is_a_theorem(implies(not(implies(implies(y, z), z)), implies(implies(not(z), z), z))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 5.79/1.12 = { by axiom 1 (ifeq_axiom) R->L }
% 5.79/1.12 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(not(implies(implies(y, z), z)), implies(implies(not(z), z), z)))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(implies(not(z), z), z))), true, is_a_theorem(implies(not(implies(implies(y, z), z)), implies(implies(not(z), z), z))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 5.79/1.12 = { by axiom 4 (cn_1) R->L }
% 5.79/1.12 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(y, z), z)), implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z))), implies(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(not(implies(implies(y, z), z)), implies(implies(not(z), z), z))))), true, is_a_theorem(implies(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(not(implies(implies(y, z), z)), implies(implies(not(z), z), z)))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(implies(not(z), z), z))), true, is_a_theorem(implies(not(implies(implies(y, z), z)), implies(implies(not(z), z), z))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 5.79/1.12 = { by axiom 1 (ifeq_axiom) R->L }
% 5.79/1.12 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(y, z), z)), implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z))), implies(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(not(implies(implies(y, z), z)), implies(implies(not(z), z), z))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(not(implies(implies(y, z), z)), implies(implies(not(z), z), z)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(implies(not(z), z), z))), true, is_a_theorem(implies(not(implies(implies(y, z), z)), implies(implies(not(z), z), z))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 5.79/1.12 = { by axiom 2 (cn_3) R->L }
% 5.79/1.12 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(y, z), z)), implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z))), implies(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(not(implies(implies(y, z), z)), implies(implies(not(z), z), z))))), true, ifeq(is_a_theorem(implies(not(implies(implies(y, z), z)), implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)))), true, is_a_theorem(implies(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(not(implies(implies(y, z), z)), implies(implies(not(z), z), z)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(implies(not(z), z), z))), true, is_a_theorem(implies(not(implies(implies(y, z), z)), implies(implies(not(z), z), z))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 5.79/1.13 = { by axiom 5 (condensed_detachment) }
% 5.79/1.13 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(implies(not(z), z), z))), true, is_a_theorem(implies(not(implies(implies(y, z), z)), implies(implies(not(z), z), z))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 5.79/1.13 = { by axiom 1 (ifeq_axiom) }
% 5.79/1.13 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(implies(not(z), z), z))), true, is_a_theorem(implies(not(implies(implies(y, z), z)), implies(implies(not(z), z), z))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 5.79/1.13 = { by axiom 1 (ifeq_axiom) R->L }
% 5.79/1.13 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(implies(not(z), z), z))), true), true, is_a_theorem(implies(not(implies(implies(y, z), z)), implies(implies(not(z), z), z))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 5.79/1.13 = { by lemma 7 R->L }
% 5.79/1.13 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(implies(y, z), z))), 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(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true, is_a_theorem(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(implies(not(z), z), z))), true), true, is_a_theorem(implies(not(implies(implies(y, z), z)), implies(implies(not(z), z), z))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 5.79/1.13 = { by axiom 1 (ifeq_axiom) R->L }
% 5.79/1.13 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(implies(implies(y, z), z))), 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(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true, is_a_theorem(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(implies(not(z), z), z))), true), true, is_a_theorem(implies(not(implies(implies(y, z), z)), implies(implies(not(z), z), z))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 5.79/1.13 = { by axiom 5 (condensed_detachment) R->L }
% 5.79/1.14 ifeq(ifeq(ifeq(ifeq(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(not(implies(implies(y, z), z)))))), true, ifeq(is_a_theorem(implies(implies(not(z), z), z)), true, is_a_theorem(implies(not(implies(implies(not(z), z), z)), not(not(implies(implies(y, z), z))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(implies(y, z), z))), 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(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true, is_a_theorem(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(implies(not(z), z), z))), true), true, is_a_theorem(implies(not(implies(implies(y, z), z)), implies(implies(not(z), z), z))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 5.79/1.14 = { by axiom 2 (cn_3) }
% 5.79/1.14 ifeq(ifeq(ifeq(ifeq(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(not(implies(implies(y, z), z))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(implies(y, z), z))), 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(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true, is_a_theorem(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(implies(not(z), z), z))), true), true, is_a_theorem(implies(not(implies(implies(y, z), z)), implies(implies(not(z), z), z))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 6.30/1.14 = { by axiom 1 (ifeq_axiom) }
% 6.30/1.14 ifeq(ifeq(ifeq(ifeq(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(not(implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(not(not(implies(implies(y, z), z))), 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(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true, is_a_theorem(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(implies(not(z), z), z))), true), true, is_a_theorem(implies(not(implies(implies(y, z), z)), implies(implies(not(z), z), z))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 6.30/1.14 = { by axiom 3 (cn_2) }
% 6.30/1.14 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(implies(not(z), z), z)), not(not(implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(not(not(implies(implies(y, z), z))), 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(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true, is_a_theorem(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(implies(not(z), z), z))), true), true, is_a_theorem(implies(not(implies(implies(y, z), z)), implies(implies(not(z), z), z))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 6.30/1.14 = { by axiom 1 (ifeq_axiom) }
% 6.30/1.14 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(implies(not(z), z), z)), not(not(implies(implies(y, z), z))))), true, is_a_theorem(implies(implies(not(not(implies(implies(y, z), z))), 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(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true, is_a_theorem(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(implies(not(z), z), z))), true), true, is_a_theorem(implies(not(implies(implies(y, z), z)), implies(implies(not(z), z), z))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 6.30/1.14 = { by lemma 7 }
% 6.30/1.15 ifeq(ifeq(ifeq(ifeq(ifeq(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(not(z), z), z)), implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true, is_a_theorem(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(implies(not(z), z), z))), true), true, is_a_theorem(implies(not(implies(implies(y, z), z)), implies(implies(not(z), z), z))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 6.30/1.15 = { by axiom 1 (ifeq_axiom) }
% 6.30/1.15 ifeq(ifeq(ifeq(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(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true, is_a_theorem(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(implies(not(z), z), z))), true), true, is_a_theorem(implies(not(implies(implies(y, z), z)), implies(implies(not(z), z), z))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 6.30/1.15 = { by lemma 6 }
% 6.30/1.15 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(implies(y, z), z)), implies(implies(not(z), z), z))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 6.30/1.15 = { by axiom 1 (ifeq_axiom) }
% 6.30/1.15 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(implies(y, 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(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 6.30/1.15 = { by lemma 7 }
% 6.30/1.15 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 6.30/1.15 = { by axiom 1 (ifeq_axiom) }
% 6.30/1.15 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 6.30/1.15 = { by lemma 7 }
% 6.30/1.15 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 6.30/1.15 = { by axiom 1 (ifeq_axiom) }
% 6.30/1.15 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(y, z), z))), true, is_a_theorem(implies(implies(not(z), y), implies(implies(y, z), z))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 6.30/1.15 = { by lemma 8 }
% 6.30/1.15 ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 6.30/1.15 = { by axiom 1 (ifeq_axiom) }
% 6.30/1.15 ifeq(is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 6.30/1.15 = { by lemma 8 }
% 6.30/1.15 true
% 6.30/1.15 % SZS output end Proof
% 6.30/1.15
% 6.30/1.15 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------