TSTP Solution File: RNG008-3 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : RNG008-3 : 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 13:58:46 EDT 2023
% Result : Unsatisfiable 0.21s 0.41s
% Output : Proof 0.21s
% 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 : RNG008-3 : 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
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 02:51:47 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.41 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.21/0.41
% 0.21/0.41 % SZS status Unsatisfiable
% 0.21/0.41
% 0.21/0.41 % SZS output start Proof
% 0.21/0.41 Axiom 1 (boolean_ring): multiply(X, X) = X.
% 0.21/0.41 Axiom 2 (a_times_b_is_c): multiply(a, b) = c.
% 0.21/0.41 Axiom 3 (commutative_addition): add(X, Y) = add(Y, X).
% 0.21/0.41 Axiom 4 (right_identity): add(X, additive_identity) = X.
% 0.21/0.41 Axiom 5 (left_identity): add(additive_identity, X) = X.
% 0.21/0.41 Axiom 6 (additive_inverse_additive_inverse): additive_inverse(additive_inverse(X)) = X.
% 0.21/0.41 Axiom 7 (right_inverse): add(X, additive_inverse(X)) = additive_identity.
% 0.21/0.41 Axiom 8 (multiply_additive_inverse1): multiply(X, additive_inverse(Y)) = additive_inverse(multiply(X, Y)).
% 0.21/0.42 Axiom 9 (multiply_additive_inverse2): multiply(additive_inverse(X), Y) = additive_inverse(multiply(X, Y)).
% 0.21/0.42 Axiom 10 (associative_addition): add(add(X, Y), Z) = add(X, add(Y, Z)).
% 0.21/0.42 Axiom 11 (distribute1): multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)).
% 0.21/0.42 Axiom 12 (distribute2): multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z)).
% 0.21/0.42
% 0.21/0.42 Lemma 13: add(X, X) = additive_identity.
% 0.21/0.42 Proof:
% 0.21/0.42 add(X, X)
% 0.21/0.42 = { by axiom 1 (boolean_ring) R->L }
% 0.21/0.42 add(X, multiply(X, X))
% 0.21/0.42 = { by axiom 6 (additive_inverse_additive_inverse) R->L }
% 0.21/0.42 add(X, multiply(X, additive_inverse(additive_inverse(X))))
% 0.21/0.42 = { by axiom 8 (multiply_additive_inverse1) }
% 0.21/0.42 add(X, additive_inverse(multiply(X, additive_inverse(X))))
% 0.21/0.42 = { by axiom 9 (multiply_additive_inverse2) R->L }
% 0.21/0.42 add(X, multiply(additive_inverse(X), additive_inverse(X)))
% 0.21/0.42 = { by axiom 1 (boolean_ring) }
% 0.21/0.42 add(X, additive_inverse(X))
% 0.21/0.42 = { by axiom 7 (right_inverse) }
% 0.21/0.42 additive_identity
% 0.21/0.42
% 0.21/0.42 Lemma 14: add(X, add(X, Y)) = Y.
% 0.21/0.42 Proof:
% 0.21/0.42 add(X, add(X, Y))
% 0.21/0.42 = { by axiom 10 (associative_addition) R->L }
% 0.21/0.42 add(add(X, X), Y)
% 0.21/0.42 = { by lemma 13 }
% 0.21/0.42 add(additive_identity, Y)
% 0.21/0.42 = { by axiom 5 (left_identity) }
% 0.21/0.42 Y
% 0.21/0.42
% 0.21/0.42 Lemma 15: add(X, multiply(X, Y)) = multiply(X, add(X, Y)).
% 0.21/0.42 Proof:
% 0.21/0.42 add(X, multiply(X, Y))
% 0.21/0.42 = { by axiom 1 (boolean_ring) R->L }
% 0.21/0.42 add(multiply(X, X), multiply(X, Y))
% 0.21/0.42 = { by axiom 11 (distribute1) R->L }
% 0.21/0.42 multiply(X, add(X, Y))
% 0.21/0.42
% 0.21/0.42 Goal 1 (prove_commutativity): multiply(b, a) = c.
% 0.21/0.42 Proof:
% 0.21/0.42 multiply(b, a)
% 0.21/0.42 = { by lemma 14 R->L }
% 0.21/0.42 add(a, add(a, multiply(b, a)))
% 0.21/0.42 = { by lemma 14 R->L }
% 0.21/0.42 add(a, add(a, add(b, add(b, multiply(b, a)))))
% 0.21/0.42 = { by axiom 10 (associative_addition) R->L }
% 0.21/0.42 add(a, add(add(a, b), add(b, multiply(b, a))))
% 0.21/0.42 = { by lemma 15 }
% 0.21/0.42 add(a, add(add(a, b), multiply(b, add(b, a))))
% 0.21/0.42 = { by axiom 3 (commutative_addition) }
% 0.21/0.42 add(a, add(add(a, b), multiply(b, add(a, b))))
% 0.21/0.42 = { by axiom 1 (boolean_ring) R->L }
% 0.21/0.42 add(a, add(multiply(add(a, b), add(a, b)), multiply(b, add(a, b))))
% 0.21/0.42 = { by axiom 12 (distribute2) R->L }
% 0.21/0.42 add(a, multiply(add(add(a, b), b), add(a, b)))
% 0.21/0.42 = { by axiom 10 (associative_addition) }
% 0.21/0.42 add(a, multiply(add(a, add(b, b)), add(a, b)))
% 0.21/0.42 = { by lemma 13 }
% 0.21/0.42 add(a, multiply(add(a, additive_identity), add(a, b)))
% 0.21/0.42 = { by axiom 4 (right_identity) }
% 0.21/0.42 add(a, multiply(a, add(a, b)))
% 0.21/0.42 = { by lemma 15 R->L }
% 0.21/0.42 add(a, add(a, multiply(a, b)))
% 0.21/0.42 = { by axiom 2 (a_times_b_is_c) }
% 0.21/0.42 add(a, add(a, c))
% 0.21/0.42 = { by lemma 14 }
% 0.21/0.42 c
% 0.21/0.42 % SZS output end Proof
% 0.21/0.42
% 0.21/0.42 RESULT: Unsatisfiable (the axioms are contradictory).
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