TSTP Solution File: ROB002-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : ROB002-1 : 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 14:09:05 EDT 2023
% Result : Unsatisfiable 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : ROB002-1 : TPTP v8.1.2. Released v1.0.0.
% 0.10/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 07:18:40 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.38 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.13/0.38
% 0.13/0.38 % SZS status Unsatisfiable
% 0.13/0.38
% 0.13/0.38 % SZS output start Proof
% 0.13/0.38 Axiom 1 (double_negation): negate(negate(X)) = X.
% 0.13/0.38 Axiom 2 (commutativity_of_add): add(X, Y) = add(Y, X).
% 0.13/0.38 Axiom 3 (robbins_axiom): negate(add(negate(add(X, Y)), negate(add(X, negate(Y))))) = X.
% 0.13/0.38
% 0.13/0.38 Goal 1 (prove_huntingtons_axiom): add(negate(add(a, negate(b))), negate(add(negate(a), negate(b)))) = b.
% 0.13/0.38 Proof:
% 0.13/0.38 add(negate(add(a, negate(b))), negate(add(negate(a), negate(b))))
% 0.13/0.38 = { by axiom 2 (commutativity_of_add) R->L }
% 0.13/0.38 add(negate(add(a, negate(b))), negate(add(negate(b), negate(a))))
% 0.13/0.38 = { by axiom 2 (commutativity_of_add) R->L }
% 0.13/0.38 add(negate(add(negate(b), a)), negate(add(negate(b), negate(a))))
% 0.13/0.38 = { by axiom 1 (double_negation) R->L }
% 0.13/0.38 negate(negate(add(negate(add(negate(b), a)), negate(add(negate(b), negate(a))))))
% 0.13/0.38 = { by axiom 3 (robbins_axiom) }
% 0.13/0.38 negate(negate(b))
% 0.13/0.38 = { by axiom 1 (double_negation) }
% 0.13/0.38 b
% 0.13/0.38 % SZS output end Proof
% 0.13/0.38
% 0.13/0.38 RESULT: Unsatisfiable (the axioms are contradictory).
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