TSTP Solution File: RNG008-7 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : RNG008-7 : 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 : 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 13:58:47 EDT 2023
% Result : Unsatisfiable 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG008-7 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Aug 27 02:09:47 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.42 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.42
% 0.20/0.42 % SZS status Unsatisfiable
% 0.20/0.42
% 0.20/0.43 % SZS output start Proof
% 0.20/0.43 Axiom 1 (commutativity_for_addition): add(X, Y) = add(Y, X).
% 0.20/0.43 Axiom 2 (right_additive_identity): add(X, additive_identity) = X.
% 0.20/0.43 Axiom 3 (left_additive_identity): add(additive_identity, X) = X.
% 0.20/0.43 Axiom 4 (boolean_ring): multiply(X, X) = X.
% 0.20/0.43 Axiom 5 (a_times_b_is_c): multiply(a, b) = c.
% 0.20/0.43 Axiom 6 (right_additive_inverse): add(X, additive_inverse(X)) = additive_identity.
% 0.20/0.43 Axiom 7 (associativity_for_addition): add(X, add(Y, Z)) = add(add(X, Y), Z).
% 0.20/0.43 Axiom 8 (distribute1): multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)).
% 0.20/0.43 Axiom 9 (distribute2): multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z)).
% 0.20/0.43
% 0.20/0.43 Lemma 10: add(X, add(additive_inverse(X), Y)) = Y.
% 0.20/0.43 Proof:
% 0.20/0.43 add(X, add(additive_inverse(X), Y))
% 0.20/0.43 = { by axiom 7 (associativity_for_addition) }
% 0.20/0.43 add(add(X, additive_inverse(X)), Y)
% 0.20/0.43 = { by axiom 6 (right_additive_inverse) }
% 0.20/0.43 add(additive_identity, Y)
% 0.20/0.43 = { by axiom 3 (left_additive_identity) }
% 0.20/0.43 Y
% 0.20/0.43
% 0.20/0.43 Lemma 11: additive_inverse(additive_inverse(X)) = X.
% 0.20/0.43 Proof:
% 0.20/0.43 additive_inverse(additive_inverse(X))
% 0.20/0.43 = { by lemma 10 R->L }
% 0.20/0.43 add(X, add(additive_inverse(X), additive_inverse(additive_inverse(X))))
% 0.20/0.43 = { by axiom 6 (right_additive_inverse) }
% 0.20/0.43 add(X, additive_identity)
% 0.20/0.43 = { by axiom 2 (right_additive_identity) }
% 0.20/0.43 X
% 0.20/0.43
% 0.20/0.43 Lemma 12: multiply(X, add(X, Y)) = add(X, multiply(X, Y)).
% 0.20/0.43 Proof:
% 0.20/0.43 multiply(X, add(X, Y))
% 0.20/0.43 = { by axiom 8 (distribute1) }
% 0.20/0.43 add(multiply(X, X), multiply(X, Y))
% 0.20/0.43 = { by axiom 4 (boolean_ring) }
% 0.20/0.43 add(X, multiply(X, Y))
% 0.20/0.43
% 0.20/0.43 Lemma 13: multiply(add(X, Y), X) = add(X, multiply(Y, X)).
% 0.20/0.43 Proof:
% 0.20/0.43 multiply(add(X, Y), X)
% 0.20/0.43 = { by axiom 9 (distribute2) }
% 0.20/0.43 add(multiply(X, X), multiply(Y, X))
% 0.20/0.43 = { by axiom 4 (boolean_ring) }
% 0.20/0.43 add(X, multiply(Y, X))
% 0.20/0.43
% 0.20/0.43 Lemma 14: add(X, add(X, Y)) = Y.
% 0.20/0.43 Proof:
% 0.20/0.43 add(X, add(X, Y))
% 0.20/0.43 = { by axiom 7 (associativity_for_addition) }
% 0.20/0.43 add(add(X, X), Y)
% 0.20/0.43 = { by axiom 2 (right_additive_identity) R->L }
% 0.20/0.43 add(add(X, add(X, additive_identity)), Y)
% 0.20/0.43 = { by axiom 6 (right_additive_inverse) R->L }
% 0.20/0.43 add(add(X, add(X, add(additive_inverse(additive_inverse(X)), additive_inverse(additive_inverse(additive_inverse(X)))))), Y)
% 0.20/0.43 = { by axiom 4 (boolean_ring) R->L }
% 0.20/0.43 add(add(X, add(X, add(additive_inverse(additive_inverse(X)), multiply(additive_inverse(additive_inverse(additive_inverse(X))), additive_inverse(additive_inverse(additive_inverse(X))))))), Y)
% 0.20/0.43 = { by axiom 2 (right_additive_identity) R->L }
% 0.20/0.43 add(add(X, add(X, add(additive_inverse(additive_inverse(X)), multiply(additive_inverse(additive_inverse(additive_inverse(X))), add(additive_inverse(additive_inverse(additive_inverse(X))), additive_identity))))), Y)
% 0.20/0.43 = { by lemma 12 }
% 0.20/0.43 add(add(X, add(X, add(additive_inverse(additive_inverse(X)), add(additive_inverse(additive_inverse(additive_inverse(X))), multiply(additive_inverse(additive_inverse(additive_inverse(X))), additive_identity))))), Y)
% 0.20/0.44 = { by lemma 10 }
% 0.20/0.44 add(add(X, add(X, multiply(additive_inverse(additive_inverse(additive_inverse(X))), additive_identity))), Y)
% 0.20/0.44 = { by lemma 11 }
% 0.20/0.44 add(add(X, add(X, multiply(additive_inverse(X), additive_identity))), Y)
% 0.20/0.44 = { by axiom 6 (right_additive_inverse) R->L }
% 0.20/0.44 add(add(X, add(X, multiply(additive_inverse(X), add(additive_inverse(X), additive_inverse(additive_inverse(X)))))), Y)
% 0.20/0.44 = { by lemma 12 }
% 0.20/0.44 add(add(X, add(X, add(additive_inverse(X), multiply(additive_inverse(X), additive_inverse(additive_inverse(X)))))), Y)
% 0.20/0.44 = { by lemma 10 }
% 0.20/0.44 add(add(X, multiply(additive_inverse(X), additive_inverse(additive_inverse(X)))), Y)
% 0.20/0.44 = { by lemma 11 }
% 0.20/0.44 add(add(X, multiply(additive_inverse(X), X)), Y)
% 0.20/0.44 = { by lemma 13 R->L }
% 0.20/0.44 add(multiply(add(X, additive_inverse(X)), X), Y)
% 0.20/0.44 = { by axiom 6 (right_additive_inverse) }
% 0.20/0.44 add(multiply(additive_identity, X), Y)
% 0.20/0.44 = { by lemma 11 R->L }
% 0.20/0.44 add(multiply(additive_identity, additive_inverse(additive_inverse(X))), Y)
% 0.20/0.44 = { by lemma 10 R->L }
% 0.20/0.44 add(add(additive_inverse(X), add(additive_inverse(additive_inverse(X)), multiply(additive_identity, additive_inverse(additive_inverse(X))))), Y)
% 0.20/0.44 = { by lemma 13 R->L }
% 0.20/0.44 add(add(additive_inverse(X), multiply(add(additive_inverse(additive_inverse(X)), additive_identity), additive_inverse(additive_inverse(X)))), Y)
% 0.20/0.44 = { by axiom 2 (right_additive_identity) }
% 0.20/0.44 add(add(additive_inverse(X), multiply(additive_inverse(additive_inverse(X)), additive_inverse(additive_inverse(X)))), Y)
% 0.20/0.44 = { by axiom 4 (boolean_ring) }
% 0.20/0.44 add(add(additive_inverse(X), additive_inverse(additive_inverse(X))), Y)
% 0.20/0.44 = { by axiom 6 (right_additive_inverse) }
% 0.20/0.44 add(additive_identity, Y)
% 0.20/0.44 = { by axiom 3 (left_additive_identity) }
% 0.20/0.44 Y
% 0.20/0.44
% 0.20/0.44 Goal 1 (prove_commutativity): multiply(b, a) = c.
% 0.20/0.44 Proof:
% 0.20/0.44 multiply(b, a)
% 0.20/0.44 = { by lemma 14 R->L }
% 0.20/0.44 add(a, add(a, multiply(b, a)))
% 0.20/0.44 = { by lemma 13 R->L }
% 0.20/0.44 add(a, multiply(add(a, b), a))
% 0.20/0.44 = { by lemma 13 R->L }
% 0.20/0.44 multiply(add(a, add(a, b)), a)
% 0.20/0.44 = { by lemma 14 R->L }
% 0.20/0.44 multiply(add(a, add(a, b)), add(add(a, b), add(add(a, b), a)))
% 0.20/0.44 = { by axiom 1 (commutativity_for_addition) }
% 0.20/0.44 multiply(add(a, add(a, b)), add(add(add(a, b), a), add(a, b)))
% 0.20/0.44 = { by axiom 7 (associativity_for_addition) R->L }
% 0.20/0.44 multiply(add(a, add(a, b)), add(add(a, b), add(a, add(a, b))))
% 0.20/0.44 = { by axiom 1 (commutativity_for_addition) R->L }
% 0.20/0.44 multiply(add(a, add(a, b)), add(add(a, add(a, b)), add(a, b)))
% 0.20/0.44 = { by lemma 12 }
% 0.20/0.44 add(add(a, add(a, b)), multiply(add(a, add(a, b)), add(a, b)))
% 0.20/0.44 = { by axiom 7 (associativity_for_addition) R->L }
% 0.20/0.44 add(a, add(add(a, b), multiply(add(a, add(a, b)), add(a, b))))
% 0.20/0.44 = { by axiom 1 (commutativity_for_addition) R->L }
% 0.20/0.44 add(a, add(add(a, b), multiply(add(add(a, b), a), add(a, b))))
% 0.20/0.44 = { by lemma 13 }
% 0.20/0.44 add(a, add(add(a, b), add(add(a, b), multiply(a, add(a, b)))))
% 0.20/0.44 = { by lemma 14 }
% 0.20/0.44 add(a, multiply(a, add(a, b)))
% 0.20/0.44 = { by lemma 12 }
% 0.20/0.44 add(a, add(a, multiply(a, b)))
% 0.20/0.44 = { by lemma 14 }
% 0.20/0.44 multiply(a, b)
% 0.20/0.44 = { by axiom 5 (a_times_b_is_c) }
% 0.20/0.44 c
% 0.20/0.44 % SZS output end Proof
% 0.20/0.44
% 0.20/0.44 RESULT: Unsatisfiable (the axioms are contradictory).
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