TSTP Solution File: BOO022-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : BOO022-1 : TPTP v8.1.2. Released v2.2.0.
% 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 : n013.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 : Wed Aug 30 18:11:28 EDT 2023
% Result : Unsatisfiable 0.20s 0.56s
% 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 : BOO022-1 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n013.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Aug 27 08:31:17 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.56 Command-line arguments: --flatten
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% 0.20/0.56 % SZS status Unsatisfiable
% 0.20/0.56
% 0.20/0.57 % SZS output start Proof
% 0.20/0.57 Axiom 1 (add_multiply): add(multiply(X, Y), Y) = Y.
% 0.20/0.57 Axiom 2 (multiply_add): multiply(add(X, Y), Y) = Y.
% 0.20/0.57 Axiom 3 (multiply_add_property): multiply(X, add(Y, Z)) = add(multiply(Y, X), multiply(Z, X)).
% 0.20/0.57 Axiom 4 (add_multiply_property): add(X, multiply(Y, Z)) = multiply(add(Y, X), add(Z, X)).
% 0.20/0.57
% 0.20/0.57 Lemma 5: add(X, X) = X.
% 0.20/0.57 Proof:
% 0.20/0.57 add(X, X)
% 0.20/0.57 = { by axiom 2 (multiply_add) R->L }
% 0.20/0.57 add(multiply(add(Y, X), X), X)
% 0.20/0.57 = { by axiom 1 (add_multiply) }
% 0.20/0.57 X
% 0.20/0.57
% 0.20/0.57 Lemma 6: multiply(X, X) = X.
% 0.20/0.57 Proof:
% 0.20/0.57 multiply(X, X)
% 0.20/0.57 = { by axiom 1 (add_multiply) R->L }
% 0.20/0.57 multiply(add(multiply(Y, X), X), X)
% 0.20/0.57 = { by axiom 2 (multiply_add) }
% 0.20/0.57 X
% 0.20/0.57
% 0.20/0.57 Lemma 7: add(Y, X) = add(X, Y).
% 0.20/0.57 Proof:
% 0.20/0.57 add(Y, X)
% 0.20/0.57 = { by lemma 6 R->L }
% 0.20/0.57 multiply(add(Y, X), add(Y, X))
% 0.20/0.57 = { by axiom 4 (add_multiply_property) R->L }
% 0.20/0.57 add(X, multiply(Y, Y))
% 0.20/0.57 = { by lemma 6 }
% 0.20/0.57 add(X, Y)
% 0.20/0.57
% 0.20/0.57 Lemma 8: multiply(Y, X) = multiply(X, Y).
% 0.20/0.57 Proof:
% 0.20/0.57 multiply(Y, X)
% 0.20/0.57 = { by lemma 5 R->L }
% 0.20/0.57 add(multiply(Y, X), multiply(Y, X))
% 0.20/0.57 = { by axiom 3 (multiply_add_property) R->L }
% 0.20/0.57 multiply(X, add(Y, Y))
% 0.20/0.57 = { by lemma 5 }
% 0.20/0.57 multiply(X, Y)
% 0.20/0.57
% 0.20/0.57 Lemma 9: add(multiply(X, Y), X) = X.
% 0.20/0.57 Proof:
% 0.20/0.57 add(multiply(X, Y), X)
% 0.20/0.57 = { by lemma 7 }
% 0.20/0.57 add(X, multiply(X, Y))
% 0.20/0.57 = { by lemma 8 }
% 0.20/0.57 add(X, multiply(Y, X))
% 0.20/0.57 = { by axiom 4 (add_multiply_property) }
% 0.20/0.57 multiply(add(Y, X), add(X, X))
% 0.20/0.57 = { by lemma 5 }
% 0.20/0.57 multiply(add(Y, X), X)
% 0.20/0.57 = { by axiom 2 (multiply_add) }
% 0.20/0.57 X
% 0.20/0.57
% 0.20/0.57 Lemma 10: multiply(X, add(X, Y)) = X.
% 0.20/0.57 Proof:
% 0.20/0.57 multiply(X, add(X, Y))
% 0.20/0.57 = { by lemma 7 }
% 0.20/0.57 multiply(X, add(Y, X))
% 0.20/0.57 = { by axiom 3 (multiply_add_property) }
% 0.20/0.57 add(multiply(Y, X), multiply(X, X))
% 0.20/0.57 = { by lemma 6 }
% 0.20/0.57 add(multiply(Y, X), X)
% 0.20/0.57 = { by axiom 1 (add_multiply) }
% 0.20/0.57 X
% 0.20/0.57
% 0.20/0.57 Lemma 11: add(multiply(Z, X), multiply(Y, X)) = multiply(X, add(Y, Z)).
% 0.20/0.57 Proof:
% 0.20/0.57 add(multiply(Z, X), multiply(Y, X))
% 0.20/0.57 = { by axiom 3 (multiply_add_property) R->L }
% 0.20/0.57 multiply(X, add(Z, Y))
% 0.20/0.57 = { by lemma 7 R->L }
% 0.20/0.57 multiply(X, add(Y, Z))
% 0.20/0.57
% 0.20/0.57 Goal 1 (prove_associativity_of_multiply): multiply(multiply(a, b), c) = multiply(a, multiply(b, c)).
% 0.20/0.57 Proof:
% 0.20/0.57 multiply(multiply(a, b), c)
% 0.20/0.57 = { by lemma 8 }
% 0.20/0.57 multiply(c, multiply(a, b))
% 0.20/0.57 = { by lemma 8 }
% 0.20/0.57 multiply(c, multiply(b, a))
% 0.20/0.57 = { by lemma 9 R->L }
% 0.20/0.57 multiply(c, multiply(b, add(multiply(a, multiply(b, c)), a)))
% 0.20/0.57 = { by lemma 11 R->L }
% 0.20/0.57 multiply(c, add(multiply(a, b), multiply(multiply(a, multiply(b, c)), b)))
% 0.20/0.57 = { by lemma 9 R->L }
% 0.20/0.57 multiply(c, add(multiply(a, b), multiply(multiply(a, multiply(b, c)), add(multiply(b, c), b))))
% 0.20/0.57 = { by lemma 7 }
% 0.20/0.57 multiply(c, add(multiply(a, b), multiply(multiply(a, multiply(b, c)), add(b, multiply(b, c)))))
% 0.20/0.57 = { by axiom 1 (add_multiply) R->L }
% 0.20/0.57 multiply(c, add(multiply(a, b), multiply(multiply(a, multiply(b, c)), add(b, add(multiply(a, multiply(b, c)), multiply(b, c))))))
% 0.20/0.57 = { by lemma 7 }
% 0.20/0.57 multiply(c, add(multiply(a, b), multiply(multiply(a, multiply(b, c)), add(b, add(multiply(b, c), multiply(a, multiply(b, c)))))))
% 0.20/0.57 = { by axiom 3 (multiply_add_property) }
% 0.20/0.57 multiply(c, add(multiply(a, b), add(multiply(b, multiply(a, multiply(b, c))), multiply(add(multiply(b, c), multiply(a, multiply(b, c))), multiply(a, multiply(b, c))))))
% 0.20/0.57 = { by axiom 2 (multiply_add) }
% 0.20/0.57 multiply(c, add(multiply(a, b), add(multiply(b, multiply(a, multiply(b, c))), multiply(a, multiply(b, c)))))
% 0.20/0.57 = { by axiom 1 (add_multiply) }
% 0.20/0.57 multiply(c, add(multiply(a, b), multiply(a, multiply(b, c))))
% 0.20/0.57 = { by lemma 7 R->L }
% 0.20/0.57 multiply(c, add(multiply(a, multiply(b, c)), multiply(a, b)))
% 0.20/0.57 = { by lemma 11 R->L }
% 0.20/0.57 add(multiply(multiply(a, b), c), multiply(multiply(a, multiply(b, c)), c))
% 0.20/0.57 = { by axiom 2 (multiply_add) R->L }
% 0.20/0.57 add(multiply(multiply(a, b), c), multiply(multiply(a, multiply(b, c)), multiply(add(a, c), c)))
% 0.20/0.57 = { by axiom 1 (add_multiply) R->L }
% 0.20/0.57 add(multiply(multiply(a, b), c), multiply(multiply(a, multiply(b, c)), multiply(add(a, c), add(multiply(b, c), c))))
% 0.20/0.57 = { by axiom 4 (add_multiply_property) R->L }
% 0.20/0.57 add(multiply(multiply(a, b), c), multiply(multiply(a, multiply(b, c)), add(c, multiply(a, multiply(b, c)))))
% 0.20/0.57 = { by lemma 7 R->L }
% 0.20/0.57 add(multiply(multiply(a, b), c), multiply(multiply(a, multiply(b, c)), add(multiply(a, multiply(b, c)), c)))
% 0.20/0.57 = { by lemma 10 }
% 0.20/0.57 add(multiply(multiply(a, b), c), multiply(a, multiply(b, c)))
% 0.20/0.57 = { by lemma 7 }
% 0.20/0.57 add(multiply(a, multiply(b, c)), multiply(multiply(a, b), c))
% 0.20/0.57 = { by lemma 10 R->L }
% 0.20/0.57 add(multiply(a, multiply(b, c)), multiply(multiply(multiply(a, b), c), add(multiply(multiply(a, b), c), multiply(b, c))))
% 0.20/0.57 = { by lemma 7 }
% 0.20/0.57 add(multiply(a, multiply(b, c)), multiply(multiply(multiply(a, b), c), add(multiply(b, c), multiply(multiply(a, b), c))))
% 0.20/0.57 = { by lemma 11 }
% 0.20/0.57 add(multiply(a, multiply(b, c)), multiply(multiply(multiply(a, b), c), multiply(c, add(multiply(a, b), b))))
% 0.20/0.57 = { by axiom 1 (add_multiply) }
% 0.20/0.57 add(multiply(a, multiply(b, c)), multiply(multiply(multiply(a, b), c), multiply(c, b)))
% 0.20/0.57 = { by lemma 8 }
% 0.20/0.57 add(multiply(a, multiply(b, c)), multiply(multiply(multiply(a, b), c), multiply(b, c)))
% 0.20/0.57 = { by lemma 11 }
% 0.20/0.57 multiply(multiply(b, c), add(multiply(multiply(a, b), c), a))
% 0.20/0.57 = { by lemma 7 }
% 0.20/0.57 multiply(multiply(b, c), add(a, multiply(multiply(a, b), c)))
% 0.20/0.57 = { by lemma 10 R->L }
% 0.20/0.57 multiply(multiply(b, c), add(a, multiply(multiply(multiply(a, b), c), add(multiply(multiply(a, b), c), multiply(a, b)))))
% 0.20/0.57 = { by lemma 9 }
% 0.20/0.57 multiply(multiply(b, c), add(a, multiply(multiply(multiply(a, b), c), multiply(a, b))))
% 0.20/0.57 = { by lemma 8 }
% 0.20/0.57 multiply(multiply(b, c), add(a, multiply(multiply(multiply(a, b), c), multiply(b, a))))
% 0.20/0.57 = { by axiom 4 (add_multiply_property) }
% 0.20/0.57 multiply(multiply(b, c), multiply(add(multiply(multiply(a, b), c), a), add(multiply(b, a), a)))
% 0.20/0.57 = { by axiom 1 (add_multiply) }
% 0.20/0.57 multiply(multiply(b, c), multiply(add(multiply(multiply(a, b), c), a), a))
% 0.20/0.57 = { by axiom 2 (multiply_add) }
% 0.20/0.57 multiply(multiply(b, c), a)
% 0.20/0.57 = { by lemma 8 }
% 0.20/0.57 multiply(a, multiply(b, c))
% 0.20/0.57 % SZS output end Proof
% 0.20/0.57
% 0.20/0.57 RESULT: Unsatisfiable (the axioms are contradictory).
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