TSTP Solution File: LCL042-10 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL042-10 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n021.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 : Thu Aug 31 08:17:08 EDT 2023
% Result : Unsatisfiable 29.31s 4.34s
% Output : Proof 30.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL042-10 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 05:48:40 EDT 2023
% 0.14/0.35 % CPUTime :
% 29.31/4.34 Command-line arguments: --flatten
% 29.31/4.34
% 29.31/4.34 % SZS status Unsatisfiable
% 29.31/4.34
% 30.53/4.36 % SZS output start Proof
% 30.53/4.36 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 30.53/4.36 Axiom 2 (cn_18): is_a_theorem(implies(X, implies(Y, X))) = true.
% 30.53/4.36 Axiom 3 (cn_3): is_a_theorem(implies(X, implies(not(X), Y))) = true.
% 30.53/4.36 Axiom 4 (cn_54): is_a_theorem(implies(implies(X, Y), implies(implies(not(X), Y), Y))) = true.
% 30.53/4.36 Axiom 5 (cn_22): is_a_theorem(implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y)))) = true.
% 30.53/4.36 Axiom 6 (cn_21): is_a_theorem(implies(implies(X, implies(Y, Z)), implies(Y, implies(X, Z)))) = true.
% 30.53/4.36 Axiom 7 (condensed_detachment): ifeq(is_a_theorem(implies(X, Y)), true, ifeq(is_a_theorem(X), true, is_a_theorem(Y), true), true) = true.
% 30.53/4.36
% 30.53/4.36 Lemma 8: is_a_theorem(implies(implies(X, Y), implies(X, implies(Z, Y)))) = true.
% 30.53/4.36 Proof:
% 30.53/4.36 is_a_theorem(implies(implies(X, Y), implies(X, implies(Z, Y))))
% 30.53/4.36 = { by axiom 1 (ifeq_axiom) R->L }
% 30.53/4.36 ifeq(true, true, is_a_theorem(implies(implies(X, Y), implies(X, implies(Z, Y)))), true)
% 30.53/4.36 = { by axiom 5 (cn_22) R->L }
% 30.53/4.36 ifeq(is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(X, Y), implies(X, implies(Z, Y))))), true, is_a_theorem(implies(implies(X, Y), implies(X, implies(Z, Y)))), true)
% 30.53/4.36 = { by axiom 1 (ifeq_axiom) R->L }
% 30.53/4.36 ifeq(is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(X, Y), implies(X, implies(Z, Y))))), true, ifeq(true, true, is_a_theorem(implies(implies(X, Y), implies(X, implies(Z, Y)))), true), true)
% 30.53/4.36 = { by axiom 2 (cn_18) R->L }
% 30.53/4.36 ifeq(is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(X, Y), implies(X, implies(Z, Y))))), true, ifeq(is_a_theorem(implies(Y, implies(Z, Y))), true, is_a_theorem(implies(implies(X, Y), implies(X, implies(Z, Y)))), true), true)
% 30.53/4.36 = { by axiom 7 (condensed_detachment) }
% 30.53/4.36 true
% 30.53/4.36
% 30.53/4.36 Lemma 9: is_a_theorem(implies(not(X), implies(Y, implies(X, Z)))) = true.
% 30.53/4.36 Proof:
% 30.53/4.36 is_a_theorem(implies(not(X), implies(Y, implies(X, Z))))
% 30.53/4.36 = { by axiom 1 (ifeq_axiom) R->L }
% 30.53/4.36 ifeq(true, true, is_a_theorem(implies(not(X), implies(Y, implies(X, Z)))), true)
% 30.53/4.36 = { by lemma 8 R->L }
% 30.53/4.36 ifeq(is_a_theorem(implies(implies(not(X), implies(X, Z)), implies(not(X), implies(Y, implies(X, Z))))), true, is_a_theorem(implies(not(X), implies(Y, implies(X, Z)))), true)
% 30.53/4.36 = { by axiom 1 (ifeq_axiom) R->L }
% 30.53/4.36 ifeq(is_a_theorem(implies(implies(not(X), implies(X, Z)), implies(not(X), implies(Y, implies(X, Z))))), true, ifeq(true, true, is_a_theorem(implies(not(X), implies(Y, implies(X, Z)))), true), true)
% 30.53/4.36 = { by axiom 7 (condensed_detachment) R->L }
% 30.53/4.36 ifeq(is_a_theorem(implies(implies(not(X), implies(X, Z)), implies(not(X), implies(Y, implies(X, Z))))), true, ifeq(ifeq(is_a_theorem(implies(implies(X, implies(not(X), Z)), implies(not(X), implies(X, Z)))), true, ifeq(is_a_theorem(implies(X, implies(not(X), Z))), true, is_a_theorem(implies(not(X), implies(X, Z))), true), true), true, is_a_theorem(implies(not(X), implies(Y, implies(X, Z)))), true), true)
% 30.53/4.36 = { by axiom 3 (cn_3) }
% 30.53/4.36 ifeq(is_a_theorem(implies(implies(not(X), implies(X, Z)), implies(not(X), implies(Y, implies(X, Z))))), true, ifeq(ifeq(is_a_theorem(implies(implies(X, implies(not(X), Z)), implies(not(X), implies(X, Z)))), true, ifeq(true, true, is_a_theorem(implies(not(X), implies(X, Z))), true), true), true, is_a_theorem(implies(not(X), implies(Y, implies(X, Z)))), true), true)
% 30.53/4.36 = { by axiom 1 (ifeq_axiom) }
% 30.53/4.36 ifeq(is_a_theorem(implies(implies(not(X), implies(X, Z)), implies(not(X), implies(Y, implies(X, Z))))), true, ifeq(ifeq(is_a_theorem(implies(implies(X, implies(not(X), Z)), implies(not(X), implies(X, Z)))), true, is_a_theorem(implies(not(X), implies(X, Z))), true), true, is_a_theorem(implies(not(X), implies(Y, implies(X, Z)))), true), true)
% 30.53/4.36 = { by axiom 6 (cn_21) }
% 30.53/4.36 ifeq(is_a_theorem(implies(implies(not(X), implies(X, Z)), implies(not(X), implies(Y, implies(X, Z))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(not(X), implies(X, Z))), true), true, is_a_theorem(implies(not(X), implies(Y, implies(X, Z)))), true), true)
% 30.53/4.36 = { by axiom 1 (ifeq_axiom) }
% 30.53/4.36 ifeq(is_a_theorem(implies(implies(not(X), implies(X, Z)), implies(not(X), implies(Y, implies(X, Z))))), true, ifeq(is_a_theorem(implies(not(X), implies(X, Z))), true, is_a_theorem(implies(not(X), implies(Y, implies(X, Z)))), true), true)
% 30.53/4.36 = { by axiom 7 (condensed_detachment) }
% 30.53/4.36 true
% 30.53/4.36
% 30.53/4.36 Lemma 10: ifeq(is_a_theorem(implies(X, Y)), true, is_a_theorem(implies(implies(not(X), Y), Y)), true) = true.
% 30.53/4.36 Proof:
% 30.53/4.36 ifeq(is_a_theorem(implies(X, Y)), true, is_a_theorem(implies(implies(not(X), Y), Y)), true)
% 30.53/4.36 = { by axiom 1 (ifeq_axiom) R->L }
% 30.53/4.36 ifeq(true, true, ifeq(is_a_theorem(implies(X, Y)), true, is_a_theorem(implies(implies(not(X), Y), Y)), true), true)
% 30.53/4.36 = { by axiom 4 (cn_54) R->L }
% 30.53/4.36 ifeq(is_a_theorem(implies(implies(X, Y), implies(implies(not(X), Y), Y))), true, ifeq(is_a_theorem(implies(X, Y)), true, is_a_theorem(implies(implies(not(X), Y), Y)), true), true)
% 30.53/4.36 = { by axiom 7 (condensed_detachment) }
% 30.53/4.36 true
% 30.53/4.36
% 30.53/4.36 Goal 1 (prove_cn_35): is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))) = true.
% 30.53/4.36 Proof:
% 30.53/4.36 is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))
% 30.53/4.36 = { by axiom 1 (ifeq_axiom) R->L }
% 30.53/4.36 ifeq(true, true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true)
% 30.53/4.36 = { by axiom 7 (condensed_detachment) R->L }
% 30.53/4.36 ifeq(ifeq(is_a_theorem(implies(implies(not(a), implies(implies(a, b), implies(a, c))), implies(not(a), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))))), true, ifeq(is_a_theorem(implies(not(a), implies(implies(a, b), implies(a, c)))), true, is_a_theorem(implies(not(a), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true)
% 30.53/4.36 = { by lemma 8 }
% 30.53/4.36 ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(a), implies(implies(a, b), implies(a, c)))), true, is_a_theorem(implies(not(a), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true)
% 30.53/4.36 = { by axiom 1 (ifeq_axiom) }
% 30.53/4.36 ifeq(ifeq(is_a_theorem(implies(not(a), implies(implies(a, b), implies(a, c)))), true, is_a_theorem(implies(not(a), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true)
% 30.53/4.36 = { by lemma 9 }
% 30.53/4.36 ifeq(ifeq(true, true, is_a_theorem(implies(not(a), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true)
% 30.53/4.36 = { by axiom 1 (ifeq_axiom) }
% 30.53/4.36 ifeq(is_a_theorem(implies(not(a), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true)
% 30.53/4.37 = { by axiom 1 (ifeq_axiom) R->L }
% 30.53/4.37 ifeq(true, true, ifeq(is_a_theorem(implies(not(a), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 30.53/4.37 = { by lemma 10 R->L }
% 30.53/4.37 ifeq(ifeq(is_a_theorem(implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(not(a), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(not(a), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 30.53/4.37 = { by axiom 1 (ifeq_axiom) R->L }
% 30.53/4.37 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true, is_a_theorem(implies(implies(not(a), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(not(a), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 30.53/4.37 = { by lemma 9 R->L }
% 30.53/4.37 ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(a, implies(b, c))), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))))), true, is_a_theorem(implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true, is_a_theorem(implies(implies(not(a), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(not(a), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 30.53/4.37 = { by axiom 1 (ifeq_axiom) R->L }
% 30.53/4.37 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(a, implies(b, c))), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))))), true, is_a_theorem(implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(not(a), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(not(a), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 30.53/4.37 = { by lemma 10 R->L }
% 30.53/4.37 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(a, implies(b, c)), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))))), true, is_a_theorem(implies(implies(not(implies(a, implies(b, c))), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(not(implies(a, implies(b, c))), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))))), true, is_a_theorem(implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(not(a), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(not(a), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 30.53/4.37 = { by axiom 1 (ifeq_axiom) R->L }
% 30.53/4.37 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(a, implies(b, c)), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))))), true), true, is_a_theorem(implies(implies(not(implies(a, implies(b, c))), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(not(implies(a, implies(b, c))), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))))), true, is_a_theorem(implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(not(a), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(not(a), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 30.53/4.37 = { by axiom 5 (cn_22) R->L }
% 30.53/4.37 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(a, implies(b, c)), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))))), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))))), true), true, is_a_theorem(implies(implies(not(implies(a, implies(b, c))), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(not(implies(a, implies(b, c))), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))))), true, is_a_theorem(implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(not(a), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(not(a), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 30.53/4.38 = { by axiom 1 (ifeq_axiom) R->L }
% 30.53/4.38 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(a, implies(b, c)), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))))), true, ifeq(true, true, is_a_theorem(implies(implies(a, implies(b, c)), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(not(implies(a, implies(b, c))), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(not(implies(a, implies(b, c))), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))))), true, is_a_theorem(implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(not(a), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(not(a), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 30.53/4.38 = { by axiom 7 (condensed_detachment) R->L }
% 30.53/4.38 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(a, implies(b, c)), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))))), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(not(implies(a, implies(b, c))), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(not(implies(a, implies(b, c))), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))))), true, is_a_theorem(implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(not(a), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(not(a), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 30.53/4.38 = { by axiom 5 (cn_22) }
% 30.53/4.38 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(a, implies(b, c)), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))))), true, ifeq(true, true, is_a_theorem(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(not(implies(a, implies(b, c))), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(not(implies(a, implies(b, c))), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))))), true, is_a_theorem(implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(not(a), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(not(a), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 30.53/4.38 = { by axiom 1 (ifeq_axiom) }
% 30.53/4.38 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(a, implies(b, c)), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(not(implies(a, implies(b, c))), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(not(implies(a, implies(b, c))), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))))), true, is_a_theorem(implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(not(a), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(not(a), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 30.53/4.38 = { by lemma 8 }
% 30.53/4.39 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(a, implies(b, c)), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(not(implies(a, implies(b, c))), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(not(implies(a, implies(b, c))), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))))), true, is_a_theorem(implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(not(a), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(not(a), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 30.53/4.39 = { by axiom 1 (ifeq_axiom) }
% 30.53/4.39 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(a, implies(b, c)), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))))), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(not(implies(a, implies(b, c))), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(not(implies(a, implies(b, c))), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))))), true, is_a_theorem(implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(not(a), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(not(a), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 30.53/4.39 = { by axiom 7 (condensed_detachment) }
% 30.53/4.39 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(implies(a, implies(b, c))), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(not(implies(a, implies(b, c))), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))))), true, is_a_theorem(implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(not(a), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(not(a), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 30.53/4.39 = { by axiom 1 (ifeq_axiom) }
% 30.53/4.39 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, implies(b, c))), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))))), true, ifeq(is_a_theorem(implies(not(implies(a, implies(b, c))), implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))))), true, is_a_theorem(implies(a, implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(not(a), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(not(a), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 30.53/4.39 = { by axiom 7 (condensed_detachment) }
% 30.53/4.39 ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(a), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(not(a), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 30.53/4.39 = { by axiom 1 (ifeq_axiom) }
% 30.53/4.39 ifeq(is_a_theorem(implies(implies(not(a), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, ifeq(is_a_theorem(implies(not(a), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 30.53/4.39 = { by axiom 7 (condensed_detachment) }
% 30.53/4.39 true
% 30.53/4.39 % SZS output end Proof
% 30.53/4.39
% 30.53/4.39 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------