TSTP Solution File: LCL218-10 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : LCL218-10 : TPTP v8.1.2. Released v7.3.0.
% 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 : n008.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 08:18:04 EDT 2023
% Result : Unsatisfiable 4.34s 1.00s
% Output : Proof 4.34s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LCL218-10 : TPTP v8.1.2. Released v7.3.0.
% 0.13/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 06:31:32 EDT 2023
% 0.13/0.35 % CPUTime :
% 4.34/1.00 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 4.34/1.00
% 4.34/1.00 % SZS status Unsatisfiable
% 4.34/1.00
% 4.34/1.01 % SZS output start Proof
% 4.34/1.01 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 4.34/1.01 Axiom 2 (axiom_1_3): axiom(or(not(X), or(Y, X))) = true.
% 4.34/1.01 Axiom 3 (rule_1): ifeq(axiom(X), true, theorem(X), true) = true.
% 4.34/1.01 Axiom 4 (axiom_1_4): axiom(or(not(or(X, Y)), or(Y, X))) = true.
% 4.34/1.01 Axiom 5 (axiom_1_5): axiom(or(not(or(X, or(Y, Z))), or(Y, or(X, Z)))) = true.
% 4.34/1.01 Axiom 6 (rule_2): ifeq(theorem(X), true, ifeq(axiom(or(not(X), Y)), true, theorem(Y), true), true) = true.
% 4.34/1.01 Axiom 7 (rule_3): ifeq(theorem(or(not(X), Y)), true, ifeq(axiom(or(not(Z), X)), true, theorem(or(not(Z), Y)), true), true) = true.
% 4.34/1.01
% 4.34/1.01 Lemma 8: ifeq(theorem(or(X, or(Y, Z))), true, theorem(or(Y, or(X, Z))), true) = true.
% 4.34/1.01 Proof:
% 4.34/1.01 ifeq(theorem(or(X, or(Y, Z))), true, theorem(or(Y, or(X, Z))), true)
% 4.34/1.01 = { by axiom 1 (ifeq_axiom) R->L }
% 4.34/1.01 ifeq(theorem(or(X, or(Y, Z))), true, ifeq(true, true, theorem(or(Y, or(X, Z))), true), true)
% 4.34/1.01 = { by axiom 5 (axiom_1_5) R->L }
% 4.34/1.01 ifeq(theorem(or(X, or(Y, Z))), true, ifeq(axiom(or(not(or(X, or(Y, Z))), or(Y, or(X, Z)))), true, theorem(or(Y, or(X, Z))), true), true)
% 4.34/1.01 = { by axiom 6 (rule_2) }
% 4.34/1.01 true
% 4.34/1.01
% 4.34/1.01 Lemma 9: ifeq(theorem(or(not(or(X, Y)), Z)), true, theorem(or(not(or(Y, X)), Z)), true) = true.
% 4.34/1.01 Proof:
% 4.34/1.01 ifeq(theorem(or(not(or(X, Y)), Z)), true, theorem(or(not(or(Y, X)), Z)), true)
% 4.34/1.01 = { by axiom 1 (ifeq_axiom) R->L }
% 4.34/1.01 ifeq(theorem(or(not(or(X, Y)), Z)), true, ifeq(true, true, theorem(or(not(or(Y, X)), Z)), true), true)
% 4.34/1.01 = { by axiom 4 (axiom_1_4) R->L }
% 4.34/1.01 ifeq(theorem(or(not(or(X, Y)), Z)), true, ifeq(axiom(or(not(or(Y, X)), or(X, Y))), true, theorem(or(not(or(Y, X)), Z)), true), true)
% 4.34/1.01 = { by axiom 7 (rule_3) }
% 4.34/1.01 true
% 4.34/1.01
% 4.34/1.01 Goal 1 (prove_this): theorem(or(not(or(not(or(p, q)), q)), or(not(p), q))) = true.
% 4.34/1.01 Proof:
% 4.34/1.01 theorem(or(not(or(not(or(p, q)), q)), or(not(p), q)))
% 4.34/1.01 = { by axiom 1 (ifeq_axiom) R->L }
% 4.34/1.01 ifeq(true, true, theorem(or(not(or(not(or(p, q)), q)), or(not(p), q))), true)
% 4.34/1.01 = { by lemma 8 R->L }
% 4.34/1.01 ifeq(ifeq(theorem(or(not(p), or(not(or(q, not(or(p, q)))), q))), true, theorem(or(not(or(q, not(or(p, q)))), or(not(p), q))), true), true, theorem(or(not(or(not(or(p, q)), q)), or(not(p), q))), true)
% 4.34/1.01 = { by axiom 1 (ifeq_axiom) R->L }
% 4.34/1.01 ifeq(ifeq(ifeq(true, true, theorem(or(not(p), or(not(or(q, not(or(p, q)))), q))), true), true, theorem(or(not(or(q, not(or(p, q)))), or(not(p), q))), true), true, theorem(or(not(or(not(or(p, q)), q)), or(not(p), q))), true)
% 4.34/1.01 = { by lemma 9 R->L }
% 4.34/1.01 ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(p, q)), or(not(or(q, not(or(p, q)))), q))), true, theorem(or(not(or(q, p)), or(not(or(q, not(or(p, q)))), q))), true), true, theorem(or(not(p), or(not(or(q, not(or(p, q)))), q))), true), true, theorem(or(not(or(q, not(or(p, q)))), or(not(p), q))), true), true, theorem(or(not(or(not(or(p, q)), q)), or(not(p), q))), true)
% 4.34/1.01 = { by axiom 1 (ifeq_axiom) R->L }
% 4.34/1.01 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(or(p, q)), or(not(or(q, not(or(p, q)))), q))), true), true, theorem(or(not(or(q, p)), or(not(or(q, not(or(p, q)))), q))), true), true, theorem(or(not(p), or(not(or(q, not(or(p, q)))), q))), true), true, theorem(or(not(or(q, not(or(p, q)))), or(not(p), q))), true), true, theorem(or(not(or(not(or(p, q)), q)), or(not(p), q))), true)
% 4.34/1.01 = { by axiom 3 (rule_1) R->L }
% 4.34/1.01 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(or(not(or(q, not(or(p, q)))), or(not(or(p, q)), q))), true, theorem(or(not(or(q, not(or(p, q)))), or(not(or(p, q)), q))), true), true, theorem(or(not(or(p, q)), or(not(or(q, not(or(p, q)))), q))), true), true, theorem(or(not(or(q, p)), or(not(or(q, not(or(p, q)))), q))), true), true, theorem(or(not(p), or(not(or(q, not(or(p, q)))), q))), true), true, theorem(or(not(or(q, not(or(p, q)))), or(not(p), q))), true), true, theorem(or(not(or(not(or(p, q)), q)), or(not(p), q))), true)
% 4.34/1.01 = { by axiom 4 (axiom_1_4) }
% 4.34/1.01 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(or(q, not(or(p, q)))), or(not(or(p, q)), q))), true), true, theorem(or(not(or(p, q)), or(not(or(q, not(or(p, q)))), q))), true), true, theorem(or(not(or(q, p)), or(not(or(q, not(or(p, q)))), q))), true), true, theorem(or(not(p), or(not(or(q, not(or(p, q)))), q))), true), true, theorem(or(not(or(q, not(or(p, q)))), or(not(p), q))), true), true, theorem(or(not(or(not(or(p, q)), q)), or(not(p), q))), true)
% 4.34/1.01 = { by axiom 1 (ifeq_axiom) }
% 4.34/1.01 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(q, not(or(p, q)))), or(not(or(p, q)), q))), true, theorem(or(not(or(p, q)), or(not(or(q, not(or(p, q)))), q))), true), true, theorem(or(not(or(q, p)), or(not(or(q, not(or(p, q)))), q))), true), true, theorem(or(not(p), or(not(or(q, not(or(p, q)))), q))), true), true, theorem(or(not(or(q, not(or(p, q)))), or(not(p), q))), true), true, theorem(or(not(or(not(or(p, q)), q)), or(not(p), q))), true)
% 4.34/1.01 = { by lemma 8 }
% 4.34/1.01 ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(or(q, p)), or(not(or(q, not(or(p, q)))), q))), true), true, theorem(or(not(p), or(not(or(q, not(or(p, q)))), q))), true), true, theorem(or(not(or(q, not(or(p, q)))), or(not(p), q))), true), true, theorem(or(not(or(not(or(p, q)), q)), or(not(p), q))), true)
% 4.34/1.01 = { by axiom 1 (ifeq_axiom) }
% 4.34/1.01 ifeq(ifeq(ifeq(theorem(or(not(or(q, p)), or(not(or(q, not(or(p, q)))), q))), true, theorem(or(not(p), or(not(or(q, not(or(p, q)))), q))), true), true, theorem(or(not(or(q, not(or(p, q)))), or(not(p), q))), true), true, theorem(or(not(or(not(or(p, q)), q)), or(not(p), q))), true)
% 4.34/1.01 = { by axiom 1 (ifeq_axiom) R->L }
% 4.34/1.01 ifeq(ifeq(ifeq(theorem(or(not(or(q, p)), or(not(or(q, not(or(p, q)))), q))), true, ifeq(true, true, theorem(or(not(p), or(not(or(q, not(or(p, q)))), q))), true), true), true, theorem(or(not(or(q, not(or(p, q)))), or(not(p), q))), true), true, theorem(or(not(or(not(or(p, q)), q)), or(not(p), q))), true)
% 4.34/1.01 = { by axiom 2 (axiom_1_3) R->L }
% 4.34/1.01 ifeq(ifeq(ifeq(theorem(or(not(or(q, p)), or(not(or(q, not(or(p, q)))), q))), true, ifeq(axiom(or(not(p), or(q, p))), true, theorem(or(not(p), or(not(or(q, not(or(p, q)))), q))), true), true), true, theorem(or(not(or(q, not(or(p, q)))), or(not(p), q))), true), true, theorem(or(not(or(not(or(p, q)), q)), or(not(p), q))), true)
% 4.34/1.01 = { by axiom 7 (rule_3) }
% 4.34/1.01 ifeq(ifeq(true, true, theorem(or(not(or(q, not(or(p, q)))), or(not(p), q))), true), true, theorem(or(not(or(not(or(p, q)), q)), or(not(p), q))), true)
% 4.34/1.01 = { by axiom 1 (ifeq_axiom) }
% 4.34/1.01 ifeq(theorem(or(not(or(q, not(or(p, q)))), or(not(p), q))), true, theorem(or(not(or(not(or(p, q)), q)), or(not(p), q))), true)
% 4.34/1.01 = { by lemma 9 }
% 4.34/1.01 true
% 4.34/1.01 % SZS output end Proof
% 4.34/1.01
% 4.34/1.01 RESULT: Unsatisfiable (the axioms are contradictory).
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