TSTP Solution File: LCL026-10 by Twee---2.5.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.5.0
% Problem : LCL026-10 : TPTP v8.2.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee /export/starexec/sandbox2/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% Computer : n029.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 11:20:06 EDT 2024
% Result : Unsatisfiable 33.18s 4.56s
% Output : Proof 33.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL026-10 : TPTP v8.2.0. Released v7.3.0.
% 0.06/0.12 % Command : parallel-twee /export/starexec/sandbox2/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% 0.12/0.33 % Computer : n029.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 17:26:09 EDT 2024
% 0.12/0.33 % CPUTime :
% 33.18/4.56 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 33.18/4.56
% 33.18/4.56 % SZS status Unsatisfiable
% 33.18/4.56
% 33.57/4.58 % SZS output start Proof
% 33.57/4.58 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 33.57/4.58 Axiom 2 (c0_2): is_a_theorem(implies(X, implies(Y, X))) = true.
% 33.57/4.58 Axiom 3 (c0_5): is_a_theorem(implies(implies(implies(X, falsehood), falsehood), X)) = true.
% 33.57/4.58 Axiom 4 (condensed_detachment): ifeq(is_a_theorem(implies(X, Y)), true, ifeq(is_a_theorem(X), true, is_a_theorem(Y), true), true) = true.
% 33.57/4.58 Axiom 5 (c0_6): is_a_theorem(implies(implies(X, implies(Y, Z)), implies(implies(X, Y), implies(X, Z)))) = true.
% 33.57/4.58
% 33.57/4.58 Lemma 6: ifeq(is_a_theorem(X), true, is_a_theorem(implies(Y, X)), true) = true.
% 33.57/4.58 Proof:
% 33.57/4.58 ifeq(is_a_theorem(X), true, is_a_theorem(implies(Y, X)), true)
% 33.57/4.58 = { by axiom 1 (ifeq_axiom) R->L }
% 33.57/4.58 ifeq(true, true, ifeq(is_a_theorem(X), true, is_a_theorem(implies(Y, X)), true), true)
% 33.57/4.58 = { by axiom 2 (c0_2) R->L }
% 33.57/4.58 ifeq(is_a_theorem(implies(X, implies(Y, X))), true, ifeq(is_a_theorem(X), true, is_a_theorem(implies(Y, X)), true), true)
% 33.57/4.58 = { by axiom 4 (condensed_detachment) }
% 33.57/4.58 true
% 33.57/4.58
% 33.57/4.58 Lemma 7: ifeq(is_a_theorem(implies(X, implies(Y, Z))), true, is_a_theorem(implies(implies(X, Y), implies(X, Z))), true) = true.
% 33.57/4.58 Proof:
% 33.57/4.58 ifeq(is_a_theorem(implies(X, implies(Y, Z))), true, is_a_theorem(implies(implies(X, Y), implies(X, Z))), true)
% 33.57/4.58 = { by axiom 1 (ifeq_axiom) R->L }
% 33.57/4.58 ifeq(true, true, ifeq(is_a_theorem(implies(X, implies(Y, Z))), true, is_a_theorem(implies(implies(X, Y), implies(X, Z))), true), true)
% 33.57/4.58 = { by axiom 5 (c0_6) R->L }
% 33.57/4.58 ifeq(is_a_theorem(implies(implies(X, implies(Y, Z)), implies(implies(X, Y), implies(X, Z)))), true, ifeq(is_a_theorem(implies(X, implies(Y, Z))), true, is_a_theorem(implies(implies(X, Y), implies(X, Z))), true), true)
% 33.57/4.58 = { by axiom 4 (condensed_detachment) }
% 33.57/4.58 true
% 33.57/4.58
% 33.57/4.58 Lemma 8: ifeq(is_a_theorem(implies(implies(X, implies(Y, X)), Z)), true, is_a_theorem(Z), true) = true.
% 33.57/4.58 Proof:
% 33.57/4.58 ifeq(is_a_theorem(implies(implies(X, implies(Y, X)), Z)), true, is_a_theorem(Z), true)
% 33.57/4.58 = { by axiom 1 (ifeq_axiom) R->L }
% 33.57/4.58 ifeq(is_a_theorem(implies(implies(X, implies(Y, X)), Z)), true, ifeq(true, true, is_a_theorem(Z), true), true)
% 33.57/4.58 = { by axiom 2 (c0_2) R->L }
% 33.57/4.58 ifeq(is_a_theorem(implies(implies(X, implies(Y, X)), Z)), true, ifeq(is_a_theorem(implies(X, implies(Y, X))), true, is_a_theorem(Z), true), true)
% 33.57/4.58 = { by axiom 4 (condensed_detachment) }
% 33.57/4.58 true
% 33.57/4.58
% 33.57/4.58 Lemma 9: is_a_theorem(implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y)))) = true.
% 33.57/4.58 Proof:
% 33.57/4.58 is_a_theorem(implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y))))
% 33.57/4.58 = { by axiom 1 (ifeq_axiom) R->L }
% 33.57/4.58 ifeq(true, true, is_a_theorem(implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y)))), true)
% 33.57/4.58 = { by lemma 7 R->L }
% 33.57/4.58 ifeq(ifeq(is_a_theorem(implies(implies(X, Y), implies(implies(Z, implies(X, Y)), implies(implies(Z, X), implies(Z, Y))))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Z, implies(X, Y))), implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y))))), true), true, is_a_theorem(implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y)))), true)
% 33.57/4.58 = { by axiom 1 (ifeq_axiom) R->L }
% 33.57/4.58 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(X, Y), implies(implies(Z, implies(X, Y)), implies(implies(Z, X), implies(Z, Y))))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Z, implies(X, Y))), implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y))))), true), true, is_a_theorem(implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y)))), true)
% 33.57/4.58 = { by axiom 5 (c0_6) R->L }
% 33.57/4.58 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(Z, implies(X, Y)), implies(implies(Z, X), implies(Z, Y)))), true, is_a_theorem(implies(implies(X, Y), implies(implies(Z, implies(X, Y)), implies(implies(Z, X), implies(Z, Y))))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Z, implies(X, Y))), implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y))))), true), true, is_a_theorem(implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y)))), true)
% 33.57/4.58 = { by lemma 6 }
% 33.57/4.58 ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(X, Y), implies(Z, implies(X, Y))), implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y))))), true), true, is_a_theorem(implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y)))), true)
% 33.57/4.58 = { by axiom 1 (ifeq_axiom) }
% 33.57/4.58 ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Z, implies(X, Y))), implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y))))), true, is_a_theorem(implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y)))), true)
% 33.57/4.58 = { by lemma 8 }
% 33.57/4.58 true
% 33.57/4.58
% 33.57/4.58 Lemma 10: is_a_theorem(implies(implies(X, implies(implies(Y, falsehood), falsehood)), implies(X, Y))) = true.
% 33.57/4.58 Proof:
% 33.57/4.58 is_a_theorem(implies(implies(X, implies(implies(Y, falsehood), falsehood)), implies(X, Y)))
% 33.57/4.58 = { by axiom 1 (ifeq_axiom) R->L }
% 33.57/4.58 ifeq(true, true, is_a_theorem(implies(implies(X, implies(implies(Y, falsehood), falsehood)), implies(X, Y))), true)
% 33.57/4.58 = { by lemma 6 R->L }
% 33.57/4.58 ifeq(ifeq(is_a_theorem(implies(implies(implies(Y, falsehood), falsehood), Y)), true, is_a_theorem(implies(X, implies(implies(implies(Y, falsehood), falsehood), Y))), true), true, is_a_theorem(implies(implies(X, implies(implies(Y, falsehood), falsehood)), implies(X, Y))), true)
% 33.57/4.58 = { by axiom 3 (c0_5) }
% 33.57/4.58 ifeq(ifeq(true, true, is_a_theorem(implies(X, implies(implies(implies(Y, falsehood), falsehood), Y))), true), true, is_a_theorem(implies(implies(X, implies(implies(Y, falsehood), falsehood)), implies(X, Y))), true)
% 33.57/4.58 = { by axiom 1 (ifeq_axiom) }
% 33.57/4.58 ifeq(is_a_theorem(implies(X, implies(implies(implies(Y, falsehood), falsehood), Y))), true, is_a_theorem(implies(implies(X, implies(implies(Y, falsehood), falsehood)), implies(X, Y))), true)
% 33.57/4.58 = { by lemma 7 }
% 33.57/4.58 true
% 33.57/4.58
% 33.57/4.58 Goal 1 (prove_c0_3): is_a_theorem(implies(implies(implies(a, b), a), a)) = true.
% 33.57/4.58 Proof:
% 33.57/4.58 is_a_theorem(implies(implies(implies(a, b), a), a))
% 33.57/4.58 = { by axiom 1 (ifeq_axiom) R->L }
% 33.57/4.58 ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 33.57/4.58 = { by axiom 4 (condensed_detachment) R->L }
% 33.57/4.58 ifeq(ifeq(is_a_theorem(implies(implies(implies(a, falsehood), implies(a, b)), implies(implies(implies(a, b), a), implies(implies(a, falsehood), a)))), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 33.57/4.59 = { by axiom 1 (ifeq_axiom) R->L }
% 33.57/4.59 ifeq(ifeq(is_a_theorem(implies(implies(implies(a, falsehood), implies(a, b)), implies(implies(implies(a, b), a), implies(implies(a, falsehood), a)))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(a, falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 33.57/4.59 = { by lemma 6 R->L }
% 33.57/4.59 ifeq(ifeq(is_a_theorem(implies(implies(implies(a, falsehood), implies(a, b)), implies(implies(implies(a, b), a), implies(implies(a, falsehood), a)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(falsehood, b)), true, is_a_theorem(implies(a, implies(falsehood, b))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 33.57/4.59 = { by axiom 1 (ifeq_axiom) R->L }
% 33.57/4.59 ifeq(ifeq(is_a_theorem(implies(implies(implies(a, falsehood), implies(a, b)), implies(implies(implies(a, b), a), implies(implies(a, falsehood), a)))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(falsehood, b)), true), true, is_a_theorem(implies(a, implies(falsehood, b))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 33.57/4.59 = { by lemma 10 R->L }
% 33.57/4.59 ifeq(ifeq(is_a_theorem(implies(implies(implies(a, falsehood), implies(a, b)), implies(implies(implies(a, b), a), implies(implies(a, falsehood), a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(implies(b, falsehood), falsehood)), implies(falsehood, b))), true, is_a_theorem(implies(falsehood, b)), true), true, is_a_theorem(implies(a, implies(falsehood, b))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 33.57/4.59 = { by lemma 8 }
% 33.57/4.59 ifeq(ifeq(is_a_theorem(implies(implies(implies(a, falsehood), implies(a, b)), implies(implies(implies(a, b), a), implies(implies(a, falsehood), a)))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(a, implies(falsehood, b))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 33.57/4.59 = { by axiom 1 (ifeq_axiom) }
% 33.57/4.59 ifeq(ifeq(is_a_theorem(implies(implies(implies(a, falsehood), implies(a, b)), implies(implies(implies(a, b), a), implies(implies(a, falsehood), a)))), true, ifeq(ifeq(is_a_theorem(implies(a, implies(falsehood, b))), true, is_a_theorem(implies(implies(a, falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 33.57/4.59 = { by lemma 7 }
% 33.57/4.59 ifeq(ifeq(is_a_theorem(implies(implies(implies(a, falsehood), implies(a, b)), implies(implies(implies(a, b), a), implies(implies(a, falsehood), a)))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 33.57/4.59 = { by axiom 1 (ifeq_axiom) }
% 33.57/4.59 ifeq(ifeq(is_a_theorem(implies(implies(implies(a, falsehood), implies(a, b)), implies(implies(implies(a, b), a), implies(implies(a, falsehood), a)))), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 33.57/4.59 = { by axiom 1 (ifeq_axiom) R->L }
% 33.57/4.59 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, falsehood), implies(a, b)), implies(implies(implies(a, b), a), implies(implies(a, falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 33.57/4.59 = { by axiom 4 (condensed_detachment) R->L }
% 33.57/4.59 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), implies(implies(a, falsehood), implies(a, b))), implies(implies(implies(a, b), a), implies(implies(a, falsehood), a))), implies(implies(implies(implies(a, falsehood), implies(a, b)), implies(implies(implies(a, b), a), implies(implies(a, falsehood), implies(a, b)))), implies(implies(implies(a, falsehood), implies(a, b)), implies(implies(implies(a, b), a), implies(implies(a, falsehood), a)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(a, falsehood), implies(a, b))), implies(implies(implies(a, b), a), implies(implies(a, falsehood), a)))), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(a, b)), implies(implies(implies(a, b), a), implies(implies(a, falsehood), implies(a, b)))), implies(implies(implies(a, falsehood), implies(a, b)), implies(implies(implies(a, b), a), implies(implies(a, falsehood), a))))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(a, b)), implies(implies(implies(a, b), a), implies(implies(a, falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 33.57/4.59 = { by lemma 9 }
% 33.57/4.59 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(a, falsehood), implies(a, b))), implies(implies(implies(a, b), a), implies(implies(a, falsehood), a)))), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(a, b)), implies(implies(implies(a, b), a), implies(implies(a, falsehood), implies(a, b)))), implies(implies(implies(a, falsehood), implies(a, b)), implies(implies(implies(a, b), a), implies(implies(a, falsehood), a))))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(a, b)), implies(implies(implies(a, b), a), implies(implies(a, falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 33.57/4.59 = { by axiom 1 (ifeq_axiom) }
% 33.57/4.59 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(a, falsehood), implies(a, b))), implies(implies(implies(a, b), a), implies(implies(a, falsehood), a)))), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(a, b)), implies(implies(implies(a, b), a), implies(implies(a, falsehood), implies(a, b)))), implies(implies(implies(a, falsehood), implies(a, b)), implies(implies(implies(a, b), a), implies(implies(a, falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(a, b)), implies(implies(implies(a, b), a), implies(implies(a, falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 33.57/4.59 = { by axiom 1 (ifeq_axiom) R->L }
% 33.57/4.59 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(a, falsehood), implies(a, b))), implies(implies(implies(a, b), a), implies(implies(a, falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(a, b)), implies(implies(implies(a, b), a), implies(implies(a, falsehood), implies(a, b)))), implies(implies(implies(a, falsehood), implies(a, b)), implies(implies(implies(a, b), a), implies(implies(a, falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(a, b)), implies(implies(implies(a, b), a), implies(implies(a, falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 33.57/4.59 = { by lemma 9 R->L }
% 33.57/4.59 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, falsehood), implies(a, b)), implies(implies(a, falsehood), a)))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(a, falsehood), implies(a, b))), implies(implies(implies(a, b), a), implies(implies(a, falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(a, b)), implies(implies(implies(a, b), a), implies(implies(a, falsehood), implies(a, b)))), implies(implies(implies(a, falsehood), implies(a, b)), implies(implies(implies(a, b), a), implies(implies(a, falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(a, b)), implies(implies(implies(a, b), a), implies(implies(a, falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 33.57/4.59 = { by lemma 7 }
% 33.57/4.59 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(a, b)), implies(implies(implies(a, b), a), implies(implies(a, falsehood), implies(a, b)))), implies(implies(implies(a, falsehood), implies(a, b)), implies(implies(implies(a, b), a), implies(implies(a, falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(a, b)), implies(implies(implies(a, b), a), implies(implies(a, falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 33.57/4.59 = { by axiom 1 (ifeq_axiom) }
% 33.57/4.59 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(a, b)), implies(implies(implies(a, b), a), implies(implies(a, falsehood), implies(a, b)))), implies(implies(implies(a, falsehood), implies(a, b)), implies(implies(implies(a, b), a), implies(implies(a, falsehood), a))))), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(a, b)), implies(implies(implies(a, b), a), implies(implies(a, falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 33.57/4.59 = { by lemma 8 }
% 33.57/4.59 ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 33.57/4.59 = { by axiom 1 (ifeq_axiom) }
% 33.57/4.59 ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 33.57/4.59 = { by axiom 1 (ifeq_axiom) R->L }
% 33.57/4.59 ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 33.57/4.59 = { by lemma 7 R->L }
% 33.57/4.59 ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, falsehood), a), a))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 33.57/4.59 = { by axiom 1 (ifeq_axiom) R->L }
% 33.57/4.59 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, falsehood), a), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 33.57/4.59 = { by axiom 4 (condensed_detachment) R->L }
% 33.57/4.59 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, falsehood), a), implies(implies(a, falsehood), falsehood)), implies(implies(implies(a, falsehood), a), a))), true, ifeq(is_a_theorem(implies(implies(implies(a, falsehood), a), implies(implies(a, falsehood), falsehood))), true, is_a_theorem(implies(implies(implies(a, falsehood), a), a)), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, falsehood), a), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 33.57/4.59 = { by lemma 10 }
% 33.57/4.59 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, falsehood), a), implies(implies(a, falsehood), falsehood))), true, is_a_theorem(implies(implies(implies(a, falsehood), a), a)), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, falsehood), a), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 33.57/4.59 = { by axiom 1 (ifeq_axiom) }
% 33.57/4.59 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, falsehood), a), implies(implies(a, falsehood), falsehood))), true, is_a_theorem(implies(implies(implies(a, falsehood), a), a)), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, falsehood), a), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 33.57/4.59 = { by axiom 1 (ifeq_axiom) R->L }
% 33.57/4.59 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, falsehood), a), implies(implies(a, falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), a), a)), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, falsehood), a), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 33.57/4.59 = { by axiom 5 (c0_6) R->L }
% 33.57/4.59 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, falsehood), implies(a, falsehood)), implies(implies(implies(a, falsehood), a), implies(implies(a, falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(a, falsehood), a), implies(implies(a, falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), a), a)), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, falsehood), a), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 33.57/4.59 = { by axiom 1 (ifeq_axiom) R->L }
% 33.57/4.59 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, falsehood), implies(a, falsehood)), implies(implies(implies(a, falsehood), a), implies(implies(a, falsehood), falsehood)))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(a, falsehood), a), implies(implies(a, falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), a), a)), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, falsehood), a), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 33.57/4.60 = { by lemma 8 R->L }
% 33.57/4.60 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, falsehood), implies(a, falsehood)), implies(implies(implies(a, falsehood), a), implies(implies(a, falsehood), falsehood)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(a, falsehood), implies(X, implies(a, falsehood))), implies(implies(a, falsehood), implies(a, falsehood)))), true, is_a_theorem(implies(implies(a, falsehood), implies(a, falsehood))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), a), implies(implies(a, falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), a), a)), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, falsehood), a), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 33.57/4.60 = { by axiom 1 (ifeq_axiom) R->L }
% 33.57/4.60 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, falsehood), implies(a, falsehood)), implies(implies(implies(a, falsehood), a), implies(implies(a, falsehood), falsehood)))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, falsehood), implies(X, implies(a, falsehood))), implies(implies(a, falsehood), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(a, falsehood))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), a), implies(implies(a, falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), a), a)), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, falsehood), a), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 33.57/4.60 = { by axiom 5 (c0_6) R->L }
% 33.57/4.60 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, falsehood), implies(a, falsehood)), implies(implies(implies(a, falsehood), a), implies(implies(a, falsehood), falsehood)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(X, implies(a, falsehood)), implies(a, falsehood))), implies(implies(implies(a, falsehood), implies(X, implies(a, falsehood))), implies(implies(a, falsehood), implies(a, falsehood))))), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(X, implies(a, falsehood))), implies(implies(a, falsehood), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(a, falsehood))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), a), implies(implies(a, falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), a), a)), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, falsehood), a), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 33.57/4.60 = { by lemma 8 }
% 33.57/4.60 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, falsehood), implies(a, falsehood)), implies(implies(implies(a, falsehood), a), implies(implies(a, falsehood), falsehood)))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(a, falsehood), implies(a, falsehood))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), a), implies(implies(a, falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), a), a)), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, falsehood), a), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 33.57/4.60 = { by axiom 1 (ifeq_axiom) }
% 33.57/4.60 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, falsehood), implies(a, falsehood)), implies(implies(implies(a, falsehood), a), implies(implies(a, falsehood), falsehood)))), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(a, falsehood))), true, is_a_theorem(implies(implies(implies(a, falsehood), a), implies(implies(a, falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), a), a)), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, falsehood), a), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 33.57/4.60 = { by axiom 4 (condensed_detachment) }
% 33.57/4.60 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, falsehood), a), a)), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, falsehood), a), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 33.57/4.60 = { by axiom 1 (ifeq_axiom) }
% 33.57/4.60 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, falsehood), a), a)), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, falsehood), a), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 33.57/4.60 = { by lemma 6 }
% 33.57/4.60 ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 33.57/4.60 = { by axiom 1 (ifeq_axiom) }
% 33.57/4.60 ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a)), implies(implies(implies(a, b), a), a))), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, falsehood), a))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 33.57/4.60 = { by axiom 4 (condensed_detachment) }
% 33.57/4.60 true
% 33.57/4.60 % SZS output end Proof
% 33.57/4.60
% 33.57/4.60 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------