TSTP Solution File: GRP196-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP196-1 : 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 : n019.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 01:17:44 EDT 2023
% Result : Unsatisfiable 179.21s 23.33s
% Output : Proof 179.21s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.16 % Problem : GRP196-1 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.17 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.17/0.39 % Computer : n019.cluster.edu
% 0.17/0.39 % Model : x86_64 x86_64
% 0.17/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.39 % Memory : 8042.1875MB
% 0.17/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.39 % CPULimit : 300
% 0.17/0.39 % WCLimit : 300
% 0.17/0.39 % DateTime : Mon Aug 28 19:52:58 EDT 2023
% 0.17/0.39 % CPUTime :
% 179.21/23.33 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 179.21/23.33
% 179.21/23.33 % SZS status Unsatisfiable
% 179.21/23.33
% 179.21/23.34 % SZS output start Proof
% 179.21/23.34 Axiom 1 (associativity_of_multiply): multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)).
% 179.21/23.34 Axiom 2 (condition): multiply(X, multiply(Y, multiply(Y, Y))) = multiply(Y, multiply(Y, multiply(Y, X))).
% 179.21/23.34
% 179.21/23.34 Lemma 3: multiply(Y, multiply(Y, multiply(Y, multiply(X, Z)))) = multiply(X, multiply(Y, multiply(Y, multiply(Y, Z)))).
% 179.21/23.34 Proof:
% 179.21/23.34 multiply(Y, multiply(Y, multiply(Y, multiply(X, Z))))
% 179.21/23.34 = { by axiom 2 (condition) R->L }
% 179.21/23.34 multiply(multiply(X, Z), multiply(Y, multiply(Y, Y)))
% 179.21/23.34 = { by axiom 1 (associativity_of_multiply) }
% 179.21/23.34 multiply(X, multiply(Z, multiply(Y, multiply(Y, Y))))
% 179.21/23.34 = { by axiom 2 (condition) }
% 179.21/23.34 multiply(X, multiply(Y, multiply(Y, multiply(Y, Z))))
% 179.21/23.34
% 179.21/23.34 Lemma 4: multiply(X, multiply(X, multiply(X, multiply(Y, multiply(Z, W))))) = multiply(Y, multiply(Z, multiply(X, multiply(X, multiply(X, W))))).
% 179.21/23.34 Proof:
% 179.21/23.34 multiply(X, multiply(X, multiply(X, multiply(Y, multiply(Z, W)))))
% 179.21/23.34 = { by lemma 3 }
% 179.21/23.34 multiply(Y, multiply(X, multiply(X, multiply(X, multiply(Z, W)))))
% 179.21/23.34 = { by lemma 3 }
% 179.21/23.34 multiply(Y, multiply(Z, multiply(X, multiply(X, multiply(X, W)))))
% 179.21/23.34
% 179.21/23.34 Lemma 5: multiply(X, multiply(X, multiply(X, multiply(Y, multiply(Z, multiply(W, multiply(V, U))))))) = multiply(Y, multiply(Z, multiply(W, multiply(V, multiply(X, multiply(X, multiply(X, U))))))).
% 179.21/23.34 Proof:
% 179.21/23.34 multiply(X, multiply(X, multiply(X, multiply(Y, multiply(Z, multiply(W, multiply(V, U)))))))
% 179.21/23.34 = { by lemma 4 }
% 179.21/23.34 multiply(Y, multiply(Z, multiply(X, multiply(X, multiply(X, multiply(W, multiply(V, U)))))))
% 179.21/23.34 = { by lemma 4 }
% 179.21/23.34 multiply(Y, multiply(Z, multiply(W, multiply(V, multiply(X, multiply(X, multiply(X, U)))))))
% 179.21/23.34
% 179.21/23.34 Lemma 6: multiply(Z, multiply(W, multiply(Z, multiply(W, multiply(Z, multiply(W, multiply(X, multiply(Y, V)))))))) = multiply(X, multiply(Y, multiply(Z, multiply(W, multiply(Z, multiply(W, multiply(Z, multiply(W, V)))))))).
% 179.21/23.34 Proof:
% 179.21/23.34 multiply(Z, multiply(W, multiply(Z, multiply(W, multiply(Z, multiply(W, multiply(X, multiply(Y, V))))))))
% 179.21/23.34 = { by axiom 1 (associativity_of_multiply) R->L }
% 179.21/23.34 multiply(Z, multiply(W, multiply(Z, multiply(W, multiply(multiply(Z, W), multiply(X, multiply(Y, V)))))))
% 179.21/23.34 = { by axiom 1 (associativity_of_multiply) R->L }
% 179.21/23.34 multiply(Z, multiply(W, multiply(multiply(Z, W), multiply(multiply(Z, W), multiply(X, multiply(Y, V))))))
% 179.21/23.34 = { by axiom 1 (associativity_of_multiply) R->L }
% 179.21/23.34 multiply(multiply(Z, W), multiply(multiply(Z, W), multiply(multiply(Z, W), multiply(X, multiply(Y, V)))))
% 179.21/23.34 = { by lemma 4 }
% 179.21/23.34 multiply(X, multiply(Y, multiply(multiply(Z, W), multiply(multiply(Z, W), multiply(multiply(Z, W), V)))))
% 179.21/23.34 = { by axiom 1 (associativity_of_multiply) }
% 179.21/23.34 multiply(X, multiply(Y, multiply(Z, multiply(W, multiply(multiply(Z, W), multiply(multiply(Z, W), V))))))
% 179.21/23.34 = { by axiom 1 (associativity_of_multiply) }
% 179.21/23.34 multiply(X, multiply(Y, multiply(Z, multiply(W, multiply(Z, multiply(W, multiply(multiply(Z, W), V)))))))
% 179.21/23.34 = { by axiom 1 (associativity_of_multiply) }
% 179.21/23.34 multiply(X, multiply(Y, multiply(Z, multiply(W, multiply(Z, multiply(W, multiply(Z, multiply(W, V))))))))
% 179.21/23.34
% 179.21/23.34 Lemma 7: multiply(Y, multiply(Z, multiply(W, multiply(Y, multiply(Z, multiply(W, multiply(Y, multiply(Z, multiply(W, multiply(X, V)))))))))) = multiply(X, multiply(Y, multiply(Z, multiply(W, multiply(Y, multiply(Z, multiply(W, multiply(Y, multiply(Z, multiply(W, V)))))))))).
% 179.21/23.34 Proof:
% 179.21/23.34 multiply(Y, multiply(Z, multiply(W, multiply(Y, multiply(Z, multiply(W, multiply(Y, multiply(Z, multiply(W, multiply(X, V))))))))))
% 179.21/23.34 = { by axiom 1 (associativity_of_multiply) R->L }
% 179.21/23.34 multiply(Y, multiply(Z, multiply(W, multiply(Y, multiply(Z, multiply(W, multiply(multiply(Y, Z), multiply(W, multiply(X, V)))))))))
% 179.21/23.34 = { by axiom 1 (associativity_of_multiply) R->L }
% 179.21/23.34 multiply(Y, multiply(Z, multiply(W, multiply(multiply(Y, Z), multiply(W, multiply(multiply(Y, Z), multiply(W, multiply(X, V))))))))
% 179.21/23.34 = { by axiom 1 (associativity_of_multiply) R->L }
% 179.21/23.34 multiply(multiply(Y, Z), multiply(W, multiply(multiply(Y, Z), multiply(W, multiply(multiply(Y, Z), multiply(W, multiply(X, V)))))))
% 179.21/23.34 = { by axiom 1 (associativity_of_multiply) R->L }
% 179.21/23.34 multiply(multiply(Y, Z), multiply(W, multiply(multiply(Y, Z), multiply(W, multiply(multiply(multiply(Y, Z), W), multiply(X, V))))))
% 179.21/23.34 = { by axiom 1 (associativity_of_multiply) R->L }
% 179.21/23.34 multiply(multiply(Y, Z), multiply(W, multiply(multiply(multiply(Y, Z), W), multiply(multiply(multiply(Y, Z), W), multiply(X, V)))))
% 179.21/23.34 = { by axiom 1 (associativity_of_multiply) R->L }
% 179.21/23.34 multiply(multiply(multiply(Y, Z), W), multiply(multiply(multiply(Y, Z), W), multiply(multiply(multiply(Y, Z), W), multiply(X, V))))
% 179.21/23.34 = { by lemma 3 }
% 179.21/23.34 multiply(X, multiply(multiply(multiply(Y, Z), W), multiply(multiply(multiply(Y, Z), W), multiply(multiply(multiply(Y, Z), W), V))))
% 179.21/23.34 = { by axiom 1 (associativity_of_multiply) }
% 179.21/23.34 multiply(X, multiply(multiply(Y, Z), multiply(W, multiply(multiply(multiply(Y, Z), W), multiply(multiply(multiply(Y, Z), W), V)))))
% 179.21/23.34 = { by axiom 1 (associativity_of_multiply) }
% 179.21/23.34 multiply(X, multiply(multiply(Y, Z), multiply(W, multiply(multiply(Y, Z), multiply(W, multiply(multiply(multiply(Y, Z), W), V))))))
% 179.21/23.34 = { by axiom 1 (associativity_of_multiply) }
% 179.21/23.34 multiply(X, multiply(multiply(Y, Z), multiply(W, multiply(multiply(Y, Z), multiply(W, multiply(multiply(Y, Z), multiply(W, V)))))))
% 179.21/23.34 = { by axiom 1 (associativity_of_multiply) }
% 179.21/23.34 multiply(X, multiply(Y, multiply(Z, multiply(W, multiply(multiply(Y, Z), multiply(W, multiply(multiply(Y, Z), multiply(W, V))))))))
% 179.21/23.34 = { by axiom 1 (associativity_of_multiply) }
% 179.21/23.35 multiply(X, multiply(Y, multiply(Z, multiply(W, multiply(Y, multiply(Z, multiply(W, multiply(multiply(Y, Z), multiply(W, V)))))))))
% 179.21/23.35 = { by axiom 1 (associativity_of_multiply) }
% 179.21/23.35 multiply(X, multiply(Y, multiply(Z, multiply(W, multiply(Y, multiply(Z, multiply(W, multiply(Y, multiply(Z, multiply(W, V))))))))))
% 179.21/23.35
% 179.21/23.35 Goal 1 (prove_this): multiply(a, multiply(b, multiply(a, multiply(b, multiply(a, multiply(b, multiply(a, multiply(b, multiply(a, multiply(b, multiply(a, multiply(b, multiply(a, multiply(b, multiply(a, multiply(b, multiply(a, b))))))))))))))))) = multiply(a, multiply(a, multiply(a, multiply(a, multiply(a, multiply(a, multiply(a, multiply(a, multiply(a, multiply(b, multiply(b, multiply(b, multiply(b, multiply(b, multiply(b, multiply(b, multiply(b, b))))))))))))))))).
% 179.21/23.35 Proof:
% 179.21/23.35 multiply(a, multiply(b, multiply(a, multiply(b, multiply(a, multiply(b, multiply(a, multiply(b, multiply(a, multiply(b, multiply(a, multiply(b, multiply(a, multiply(b, multiply(a, multiply(b, multiply(a, b)))))))))))))))))
% 179.21/23.35 = { by axiom 1 (associativity_of_multiply) R->L }
% 179.21/23.35 multiply(a, multiply(b, multiply(a, multiply(b, multiply(a, multiply(b, multiply(a, multiply(b, multiply(multiply(a, b), multiply(a, multiply(b, multiply(a, multiply(b, multiply(a, multiply(b, multiply(a, b))))))))))))))))
% 179.21/23.35 = { by axiom 1 (associativity_of_multiply) R->L }
% 179.21/23.35 multiply(a, multiply(b, multiply(a, multiply(b, multiply(a, multiply(b, multiply(multiply(a, b), multiply(multiply(a, b), multiply(a, multiply(b, multiply(a, multiply(b, multiply(a, multiply(b, multiply(a, b)))))))))))))))
% 179.21/23.35 = { by axiom 1 (associativity_of_multiply) R->L }
% 179.21/23.35 multiply(a, multiply(b, multiply(a, multiply(b, multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, b), multiply(a, multiply(b, multiply(a, multiply(b, multiply(a, multiply(b, multiply(a, b))))))))))))))
% 179.21/23.35 = { by lemma 4 R->L }
% 179.21/23.35 multiply(a, multiply(b, multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, b), multiply(a, multiply(b, multiply(a, multiply(b, multiply(a, multiply(b, multiply(a, multiply(b, multiply(a, b))))))))))))))
% 179.21/23.35 = { by lemma 3 R->L }
% 179.21/23.35 multiply(a, multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, b), multiply(b, multiply(a, multiply(b, multiply(a, multiply(b, multiply(a, multiply(b, multiply(a, multiply(b, multiply(a, b))))))))))))))
% 179.21/23.35 = { by axiom 1 (associativity_of_multiply) }
% 179.21/23.35 multiply(a, multiply(a, multiply(b, multiply(multiply(a, b), multiply(multiply(a, b), multiply(b, multiply(a, multiply(b, multiply(a, multiply(b, multiply(a, multiply(b, multiply(a, multiply(b, multiply(a, b)))))))))))))))
% 179.21/23.35 = { by axiom 1 (associativity_of_multiply) }
% 179.21/23.35 multiply(a, multiply(a, multiply(b, multiply(a, multiply(b, multiply(multiply(a, b), multiply(b, multiply(a, multiply(b, multiply(a, multiply(b, multiply(a, multiply(b, multiply(a, multiply(b, multiply(a, b))))))))))))))))
% 179.21/23.35 = { by axiom 1 (associativity_of_multiply) }
% 179.21/23.35 multiply(a, multiply(a, multiply(b, multiply(a, multiply(b, multiply(a, multiply(b, multiply(b, multiply(a, multiply(b, multiply(a, multiply(b, multiply(a, multiply(b, multiply(a, multiply(b, multiply(a, b)))))))))))))))))
% 179.21/23.35 = { by lemma 6 R->L }
% 179.21/23.35 multiply(a, multiply(a, multiply(b, multiply(a, multiply(b, multiply(a, multiply(a, multiply(b, multiply(a, multiply(b, multiply(a, multiply(b, multiply(b, multiply(b, multiply(a, multiply(b, multiply(a, b)))))))))))))))))
% 179.21/23.35 = { by lemma 6 R->L }
% 179.21/23.35 multiply(a, multiply(a, multiply(b, multiply(a, multiply(a, multiply(b, multiply(a, multiply(b, multiply(a, multiply(b, multiply(b, multiply(a, multiply(b, multiply(b, multiply(a, multiply(b, multiply(a, b)))))))))))))))))
% 179.21/23.35 = { by lemma 7 }
% 179.21/23.35 multiply(a, multiply(a, multiply(b, multiply(a, multiply(a, multiply(b, multiply(a, multiply(a, multiply(b, multiply(a, multiply(b, multiply(b, multiply(a, multiply(b, multiply(b, multiply(a, multiply(b, b)))))))))))))))))
% 179.21/23.35 = { by lemma 7 }
% 179.21/23.35 multiply(a, multiply(a, multiply(a, multiply(b, multiply(a, multiply(a, multiply(b, multiply(a, multiply(a, multiply(b, multiply(b, multiply(b, multiply(a, multiply(b, multiply(b, multiply(a, multiply(b, b)))))))))))))))))
% 179.21/23.35 = { by lemma 5 }
% 179.21/23.35 multiply(a, multiply(a, multiply(a, multiply(b, multiply(a, multiply(a, multiply(b, multiply(a, multiply(a, multiply(a, multiply(b, multiply(b, multiply(a, multiply(b, multiply(b, multiply(b, multiply(b, b)))))))))))))))))
% 179.21/23.35 = { by lemma 5 R->L }
% 179.21/23.35 multiply(a, multiply(a, multiply(a, multiply(a, multiply(a, multiply(a, multiply(b, multiply(a, multiply(a, multiply(b, multiply(b, multiply(b, multiply(a, multiply(b, multiply(b, multiply(b, multiply(b, b)))))))))))))))))
% 179.21/23.35 = { by lemma 4 }
% 179.21/23.35 multiply(a, multiply(a, multiply(a, multiply(a, multiply(a, multiply(a, multiply(b, multiply(a, multiply(a, multiply(a, multiply(b, multiply(b, multiply(b, multiply(b, multiply(b, multiply(b, multiply(b, b)))))))))))))))))
% 179.21/23.35 = { by lemma 3 R->L }
% 179.21/23.35 multiply(a, multiply(a, multiply(a, multiply(a, multiply(a, multiply(a, multiply(a, multiply(a, multiply(a, multiply(b, multiply(b, multiply(b, multiply(b, multiply(b, multiply(b, multiply(b, multiply(b, b)))))))))))))))))
% 179.21/23.35 % SZS output end Proof
% 179.21/23.35
% 179.21/23.35 RESULT: Unsatisfiable (the axioms are contradictory).
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