TSTP Solution File: ROB003-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : ROB003-1 : 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 : n031.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 14:09:06 EDT 2023
% Result : Unsatisfiable 0.22s 0.41s
% Output : Proof 0.22s
% 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 : ROB003-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.35 % Computer : n031.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon Aug 28 07:06:39 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.22/0.41 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.22/0.41
% 0.22/0.41 % SZS status Unsatisfiable
% 0.22/0.41
% 0.22/0.42 % SZS output start Proof
% 0.22/0.42 Axiom 1 (commutativity_of_add): add(X, Y) = add(Y, X).
% 0.22/0.42 Axiom 2 (there_exists_a_constant): add(X, c) = c.
% 0.22/0.42 Axiom 3 (associativity_of_add): add(add(X, Y), Z) = add(X, add(Y, Z)).
% 0.22/0.42 Axiom 4 (robbins_axiom): negate(add(negate(add(X, Y)), negate(add(X, negate(Y))))) = X.
% 0.22/0.42
% 0.22/0.42 Lemma 5: negate(add(negate(c), negate(add(X, negate(c))))) = X.
% 0.22/0.42 Proof:
% 0.22/0.42 negate(add(negate(c), negate(add(X, negate(c)))))
% 0.22/0.42 = { by axiom 2 (there_exists_a_constant) R->L }
% 0.22/0.42 negate(add(negate(add(X, c)), negate(add(X, negate(c)))))
% 0.22/0.42 = { by axiom 4 (robbins_axiom) }
% 0.22/0.42 X
% 0.22/0.42
% 0.22/0.42 Lemma 6: negate(add(negate(c), negate(add(negate(c), X)))) = X.
% 0.22/0.42 Proof:
% 0.22/0.42 negate(add(negate(c), negate(add(negate(c), X))))
% 0.22/0.42 = { by axiom 1 (commutativity_of_add) R->L }
% 0.22/0.42 negate(add(negate(c), negate(add(X, negate(c)))))
% 0.22/0.42 = { by lemma 5 }
% 0.22/0.42 X
% 0.22/0.42
% 0.22/0.42 Lemma 7: add(X, negate(c)) = X.
% 0.22/0.42 Proof:
% 0.22/0.42 add(X, negate(c))
% 0.22/0.42 = { by lemma 6 R->L }
% 0.22/0.42 negate(add(negate(c), negate(add(negate(c), add(X, negate(c))))))
% 0.22/0.42 = { by axiom 1 (commutativity_of_add) R->L }
% 0.22/0.42 negate(add(negate(c), negate(add(negate(c), add(negate(c), X)))))
% 0.22/0.42 = { by axiom 3 (associativity_of_add) R->L }
% 0.22/0.42 negate(add(negate(c), negate(add(add(negate(c), negate(c)), X))))
% 0.22/0.42 = { by lemma 6 R->L }
% 0.22/0.42 negate(add(negate(c), negate(add(negate(add(negate(c), negate(add(negate(c), add(negate(c), negate(c)))))), X))))
% 0.22/0.42 = { by axiom 1 (commutativity_of_add) R->L }
% 0.22/0.42 negate(add(negate(c), negate(add(negate(add(negate(add(negate(c), add(negate(c), negate(c)))), negate(c))), X))))
% 0.22/0.42 = { by lemma 5 R->L }
% 0.22/0.42 negate(add(negate(c), negate(add(negate(add(negate(add(negate(c), add(negate(c), negate(c)))), negate(add(negate(c), negate(add(negate(c), negate(c))))))), X))))
% 0.22/0.42 = { by axiom 4 (robbins_axiom) }
% 0.22/0.42 negate(add(negate(c), negate(add(negate(c), X))))
% 0.22/0.42 = { by axiom 1 (commutativity_of_add) }
% 0.22/0.42 negate(add(negate(c), negate(add(X, negate(c)))))
% 0.22/0.42 = { by lemma 5 }
% 0.22/0.42 X
% 0.22/0.42
% 0.22/0.42 Lemma 8: negate(negate(X)) = X.
% 0.22/0.42 Proof:
% 0.22/0.42 negate(negate(X))
% 0.22/0.42 = { by lemma 7 R->L }
% 0.22/0.42 negate(add(negate(X), negate(c)))
% 0.22/0.42 = { by axiom 1 (commutativity_of_add) }
% 0.22/0.42 negate(add(negate(c), negate(X)))
% 0.22/0.42 = { by axiom 2 (there_exists_a_constant) R->L }
% 0.22/0.42 negate(add(negate(add(X, c)), negate(X)))
% 0.22/0.42 = { by lemma 7 R->L }
% 0.22/0.42 negate(add(negate(add(X, c)), negate(add(X, negate(c)))))
% 0.22/0.42 = { by axiom 4 (robbins_axiom) }
% 0.22/0.42 X
% 0.22/0.42
% 0.22/0.42 Goal 1 (prove_huntingtons_axiom): add(negate(add(a, negate(b))), negate(add(negate(a), negate(b)))) = b.
% 0.22/0.42 Proof:
% 0.22/0.42 add(negate(add(a, negate(b))), negate(add(negate(a), negate(b))))
% 0.22/0.42 = { by axiom 1 (commutativity_of_add) R->L }
% 0.22/0.42 add(negate(add(a, negate(b))), negate(add(negate(b), negate(a))))
% 0.22/0.42 = { by axiom 1 (commutativity_of_add) R->L }
% 0.22/0.42 add(negate(add(negate(b), a)), negate(add(negate(b), negate(a))))
% 0.22/0.42 = { by lemma 8 R->L }
% 0.22/0.42 negate(negate(add(negate(add(negate(b), a)), negate(add(negate(b), negate(a))))))
% 0.22/0.42 = { by axiom 4 (robbins_axiom) }
% 0.22/0.42 negate(negate(b))
% 0.22/0.42 = { by lemma 8 }
% 0.22/0.42 b
% 0.22/0.42 % SZS output end Proof
% 0.22/0.42
% 0.22/0.42 RESULT: Unsatisfiable (the axioms are contradictory).
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