TSTP Solution File: LCL135-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : LCL135-1 : TPTP v8.1.2. Released v1.0.0.
% 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 : n023.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 08:17:36 EDT 2023
% Result : Unsatisfiable 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LCL135-1 : TPTP v8.1.2. Released v1.0.0.
% 0.03/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n023.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 : Thu Aug 24 19:16:57 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.19/0.37 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
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% 0.19/0.37 % SZS status Unsatisfiable
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% 0.19/0.37 % SZS output start Proof
% 0.19/0.37 Axiom 1 (wajsberg_1): implies(truth, X) = X.
% 0.19/0.37 Axiom 2 (wajsberg_3): implies(implies(X, Y), Y) = implies(implies(Y, X), X).
% 0.19/0.37 Axiom 3 (wajsberg_2): implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))) = truth.
% 0.19/0.37
% 0.19/0.37 Lemma 4: implies(X, implies(implies(X, Y), Y)) = truth.
% 0.19/0.37 Proof:
% 0.19/0.37 implies(X, implies(implies(X, Y), Y))
% 0.19/0.37 = { by axiom 1 (wajsberg_1) R->L }
% 0.19/0.37 implies(X, implies(implies(X, Y), implies(truth, Y)))
% 0.19/0.37 = { by axiom 1 (wajsberg_1) R->L }
% 0.19/0.37 implies(implies(truth, X), implies(implies(X, Y), implies(truth, Y)))
% 0.19/0.37 = { by axiom 3 (wajsberg_2) }
% 0.19/0.37 truth
% 0.19/0.37
% 0.19/0.37 Goal 1 (prove_wajsberg_lemma): implies(x, implies(y, x)) = truth.
% 0.19/0.37 Proof:
% 0.19/0.37 implies(x, implies(y, x))
% 0.19/0.37 = { by axiom 1 (wajsberg_1) R->L }
% 0.19/0.37 implies(implies(truth, x), implies(y, x))
% 0.19/0.37 = { by axiom 1 (wajsberg_1) R->L }
% 0.19/0.37 implies(truth, implies(implies(truth, x), implies(y, x)))
% 0.19/0.37 = { by lemma 4 R->L }
% 0.19/0.37 implies(implies(y, implies(implies(y, truth), truth)), implies(implies(truth, x), implies(y, x)))
% 0.19/0.37 = { by axiom 2 (wajsberg_3) R->L }
% 0.19/0.37 implies(implies(y, implies(implies(truth, y), y)), implies(implies(truth, x), implies(y, x)))
% 0.19/0.37 = { by axiom 1 (wajsberg_1) R->L }
% 0.19/0.37 implies(implies(y, implies(truth, implies(implies(truth, y), y))), implies(implies(truth, x), implies(y, x)))
% 0.19/0.37 = { by lemma 4 }
% 0.19/0.37 implies(implies(y, truth), implies(implies(truth, x), implies(y, x)))
% 0.19/0.37 = { by axiom 3 (wajsberg_2) }
% 0.19/0.37 truth
% 0.19/0.37 % SZS output end Proof
% 0.19/0.37
% 0.19/0.37 RESULT: Unsatisfiable (the axioms are contradictory).
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