TSTP Solution File: ALG236-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ALG236-1 : TPTP v8.1.2. Released v4.0.0.
% 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 : n009.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 16:42:42 EDT 2023
% Result : Unsatisfiable 0.15s 0.45s
% Output : Proof 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : ALG236-1 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.11 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.11/0.31 % Computer : n009.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Mon Aug 28 04:20:35 EDT 2023
% 0.11/0.31 % CPUTime :
% 0.15/0.45 Command-line arguments: --flatten
% 0.15/0.45
% 0.15/0.45 % SZS status Unsatisfiable
% 0.15/0.45
% 0.15/0.49 % SZS output start Proof
% 0.15/0.49 Axiom 1 (c01): mult(X, mult(Y, mult(X, Y))) = mult(X, Y).
% 0.15/0.49 Axiom 2 (c02): mult(X, mult(Y, mult(Z, W))) = mult(Z, mult(Y, mult(X, W))).
% 0.15/0.49 Axiom 3 (c03): mult(mult(X, mult(Y, mult(Z, Y))), W) = mult(X, mult(W, mult(mult(Z, Y), W))).
% 0.15/0.49
% 0.15/0.49 Lemma 4: mult(mult(X, Y), mult(Z, mult(X, Z))) = mult(mult(X, Y), Z).
% 0.15/0.49 Proof:
% 0.15/0.49 mult(mult(X, Y), mult(Z, mult(X, Z)))
% 0.15/0.49 = { by axiom 2 (c02) }
% 0.15/0.49 mult(X, mult(Z, mult(mult(X, Y), Z)))
% 0.15/0.49 = { by axiom 3 (c03) R->L }
% 0.15/0.49 mult(mult(X, mult(Y, mult(X, Y))), Z)
% 0.15/0.49 = { by axiom 1 (c01) }
% 0.15/0.49 mult(mult(X, Y), Z)
% 0.15/0.49
% 0.15/0.49 Lemma 5: mult(X, mult(mult(Y, X), X)) = mult(X, mult(Y, X)).
% 0.15/0.49 Proof:
% 0.15/0.49 mult(X, mult(mult(Y, X), X))
% 0.15/0.49 = { by lemma 4 R->L }
% 0.15/0.49 mult(X, mult(mult(Y, X), mult(X, mult(Y, X))))
% 0.15/0.49 = { by axiom 1 (c01) }
% 0.15/0.49 mult(X, mult(Y, X))
% 0.15/0.49
% 0.15/0.49 Lemma 6: mult(mult(X, Y), Y) = mult(X, Y).
% 0.15/0.49 Proof:
% 0.15/0.49 mult(mult(X, Y), Y)
% 0.15/0.49 = { by lemma 4 R->L }
% 0.15/0.49 mult(mult(X, Y), mult(Y, mult(X, Y)))
% 0.15/0.49 = { by axiom 2 (c02) }
% 0.15/0.49 mult(X, mult(Y, mult(mult(X, Y), Y)))
% 0.15/0.49 = { by lemma 5 }
% 0.15/0.49 mult(X, mult(Y, mult(X, Y)))
% 0.15/0.49 = { by axiom 1 (c01) }
% 0.15/0.49 mult(X, Y)
% 0.15/0.49
% 0.15/0.49 Lemma 7: mult(X, mult(Y, mult(mult(X, Z), Y))) = mult(mult(X, Z), Y).
% 0.15/0.49 Proof:
% 0.15/0.49 mult(X, mult(Y, mult(mult(X, Z), Y)))
% 0.15/0.49 = { by axiom 2 (c02) }
% 0.15/0.49 mult(mult(X, Z), mult(Y, mult(X, Y)))
% 0.15/0.49 = { by lemma 4 }
% 0.15/0.49 mult(mult(X, Z), Y)
% 0.15/0.49
% 0.15/0.49 Lemma 8: mult(mult(Z, W), mult(Y, mult(X, W))) = mult(X, mult(Y, mult(Z, W))).
% 0.15/0.49 Proof:
% 0.15/0.49 mult(mult(Z, W), mult(Y, mult(X, W)))
% 0.15/0.49 = { by axiom 2 (c02) }
% 0.15/0.49 mult(X, mult(Y, mult(mult(Z, W), W)))
% 0.15/0.49 = { by lemma 6 }
% 0.15/0.49 mult(X, mult(Y, mult(Z, W)))
% 0.15/0.49
% 0.15/0.49 Lemma 9: mult(X, mult(Y, mult(Z, mult(W, mult(X, Y))))) = mult(Z, mult(W, mult(X, Y))).
% 0.15/0.49 Proof:
% 0.15/0.49 mult(X, mult(Y, mult(Z, mult(W, mult(X, Y)))))
% 0.15/0.49 = { by axiom 2 (c02) R->L }
% 0.15/0.49 mult(Z, mult(Y, mult(X, mult(W, mult(X, Y)))))
% 0.15/0.49 = { by axiom 2 (c02) R->L }
% 0.15/0.49 mult(Z, mult(W, mult(X, mult(Y, mult(X, Y)))))
% 0.15/0.49 = { by axiom 1 (c01) }
% 0.15/0.49 mult(Z, mult(W, mult(X, Y)))
% 0.15/0.49
% 0.15/0.49 Lemma 10: mult(mult(Z, mult(W, X)), mult(Y, mult(Z, mult(W, X)))) = mult(X, mult(Y, mult(Z, mult(W, X)))).
% 0.15/0.49 Proof:
% 0.15/0.49 mult(mult(Z, mult(W, X)), mult(Y, mult(Z, mult(W, X))))
% 0.15/0.49 = { by lemma 8 }
% 0.15/0.49 mult(Z, mult(Y, mult(Z, mult(W, X))))
% 0.15/0.49 = { by lemma 6 R->L }
% 0.15/0.49 mult(Z, mult(Y, mult(Z, mult(mult(W, X), X))))
% 0.15/0.49 = { by axiom 1 (c01) R->L }
% 0.15/0.49 mult(Z, mult(Y, mult(Z, mult(mult(W, X), mult(X, mult(mult(W, X), X))))))
% 0.15/0.49 = { by lemma 6 }
% 0.15/0.49 mult(Z, mult(Y, mult(Z, mult(mult(W, X), mult(X, mult(W, X))))))
% 0.15/0.49 = { by axiom 2 (c02) R->L }
% 0.15/0.49 mult(Z, mult(Y, mult(X, mult(mult(W, X), mult(Z, mult(W, X))))))
% 0.15/0.49 = { by axiom 2 (c02) R->L }
% 0.15/0.49 mult(Z, mult(mult(W, X), mult(X, mult(Y, mult(Z, mult(W, X))))))
% 0.15/0.49 = { by lemma 9 }
% 0.15/0.49 mult(X, mult(Y, mult(Z, mult(W, X))))
% 0.15/0.49
% 0.15/0.49 Lemma 11: mult(mult(X, Y), mult(Z, mult(mult(W, Y), V))) = mult(mult(X, Y), mult(Z, mult(W, V))).
% 0.15/0.49 Proof:
% 0.15/0.49 mult(mult(X, Y), mult(Z, mult(mult(W, Y), V)))
% 0.15/0.49 = { by lemma 4 R->L }
% 0.15/0.49 mult(mult(X, Y), mult(mult(Z, mult(mult(W, Y), V)), mult(X, mult(Z, mult(mult(W, Y), V)))))
% 0.15/0.49 = { by lemma 10 }
% 0.15/0.49 mult(mult(X, Y), mult(V, mult(X, mult(Z, mult(mult(W, Y), V)))))
% 0.15/0.49 = { by axiom 2 (c02) }
% 0.15/0.49 mult(X, mult(V, mult(mult(X, Y), mult(Z, mult(mult(W, Y), V)))))
% 0.15/0.49 = { by axiom 2 (c02) }
% 0.15/0.49 mult(X, mult(Z, mult(mult(X, Y), mult(V, mult(mult(W, Y), V)))))
% 0.15/0.49 = { by axiom 3 (c03) R->L }
% 0.15/0.49 mult(X, mult(Z, mult(mult(mult(X, Y), mult(Y, mult(W, Y))), V)))
% 0.15/0.49 = { by lemma 8 }
% 0.15/0.49 mult(X, mult(Z, mult(mult(W, mult(Y, mult(X, Y))), V)))
% 0.15/0.49 = { by axiom 3 (c03) }
% 0.15/0.49 mult(X, mult(Z, mult(W, mult(V, mult(mult(X, Y), V)))))
% 0.15/0.49 = { by axiom 2 (c02) R->L }
% 0.15/0.49 mult(X, mult(Z, mult(mult(X, Y), mult(V, mult(W, V)))))
% 0.15/0.49 = { by axiom 2 (c02) R->L }
% 0.15/0.49 mult(X, mult(V, mult(mult(X, Y), mult(Z, mult(W, V)))))
% 0.15/0.49 = { by lemma 10 R->L }
% 0.15/0.49 mult(X, mult(mult(Z, mult(W, V)), mult(mult(X, Y), mult(Z, mult(W, V)))))
% 0.15/0.49 = { by lemma 7 }
% 0.15/0.49 mult(mult(X, Y), mult(Z, mult(W, V)))
% 0.15/0.49
% 0.15/0.49 Goal 1 (goals): mult(mult(a, b), mult(c, mult(d, e))) = mult(a, mult(c, mult(mult(d, b), e))).
% 0.15/0.49 Proof:
% 0.15/0.49 mult(mult(a, b), mult(c, mult(d, e)))
% 0.15/0.49 = { by lemma 11 R->L }
% 0.15/0.49 mult(mult(a, b), mult(c, mult(mult(d, b), e)))
% 0.15/0.49 = { by axiom 1 (c01) R->L }
% 0.15/0.49 mult(mult(a, b), mult(mult(c, mult(mult(d, b), e)), mult(mult(a, b), mult(c, mult(mult(d, b), e)))))
% 0.15/0.49 = { by lemma 11 }
% 0.15/0.49 mult(mult(a, b), mult(mult(c, mult(mult(d, b), e)), mult(mult(a, b), mult(c, mult(d, e)))))
% 0.15/0.49 = { by lemma 8 R->L }
% 0.15/0.49 mult(mult(mult(a, b), mult(c, mult(d, e))), mult(mult(c, mult(mult(d, b), e)), mult(mult(a, b), mult(c, mult(d, e)))))
% 0.15/0.49 = { by lemma 11 R->L }
% 0.15/0.49 mult(mult(mult(a, b), mult(c, mult(d, e))), mult(mult(c, mult(mult(d, b), e)), mult(mult(a, b), mult(c, mult(mult(d, b), e)))))
% 0.15/0.49 = { by lemma 4 }
% 0.15/0.49 mult(mult(mult(a, b), mult(c, mult(d, e))), mult(c, mult(mult(d, b), e)))
% 0.15/0.49 = { by lemma 7 R->L }
% 0.15/0.49 mult(mult(a, mult(mult(c, mult(d, e)), mult(mult(a, b), mult(c, mult(d, e))))), mult(c, mult(mult(d, b), e)))
% 0.15/0.49 = { by axiom 3 (c03) }
% 0.15/0.49 mult(a, mult(mult(c, mult(mult(d, b), e)), mult(mult(mult(a, b), mult(c, mult(d, e))), mult(c, mult(mult(d, b), e)))))
% 0.15/0.49 = { by axiom 2 (c02) R->L }
% 0.15/0.49 mult(mult(mult(a, b), mult(c, mult(d, e))), mult(mult(c, mult(mult(d, b), e)), mult(a, mult(c, mult(mult(d, b), e)))))
% 0.15/0.49 = { by lemma 10 }
% 0.15/0.49 mult(mult(mult(a, b), mult(c, mult(d, e))), mult(e, mult(a, mult(c, mult(mult(d, b), e)))))
% 0.15/0.49 = { by lemma 11 R->L }
% 0.15/0.49 mult(mult(mult(a, b), mult(c, mult(mult(d, b), e))), mult(e, mult(a, mult(c, mult(mult(d, b), e)))))
% 0.15/0.49 = { by lemma 6 R->L }
% 0.15/0.49 mult(mult(mult(a, b), mult(c, mult(mult(mult(d, b), e), e))), mult(e, mult(a, mult(c, mult(mult(d, b), e)))))
% 0.15/0.50 = { by lemma 4 R->L }
% 0.15/0.50 mult(mult(mult(a, b), mult(c, mult(mult(mult(d, b), mult(e, mult(d, e))), e))), mult(e, mult(a, mult(c, mult(mult(d, b), e)))))
% 0.15/0.50 = { by axiom 2 (c02) }
% 0.15/0.50 mult(mult(mult(a, b), mult(c, mult(mult(d, mult(e, mult(mult(d, b), e))), e))), mult(e, mult(a, mult(c, mult(mult(d, b), e)))))
% 0.15/0.50 = { by axiom 3 (c03) }
% 0.15/0.50 mult(mult(mult(a, b), mult(c, mult(d, mult(e, mult(mult(mult(d, b), e), e))))), mult(e, mult(a, mult(c, mult(mult(d, b), e)))))
% 0.15/0.50 = { by axiom 2 (c02) R->L }
% 0.15/0.50 mult(mult(mult(a, b), mult(c, mult(mult(mult(d, b), e), mult(e, mult(d, e))))), mult(e, mult(a, mult(c, mult(mult(d, b), e)))))
% 0.15/0.50 = { by axiom 2 (c02) R->L }
% 0.15/0.50 mult(mult(mult(a, b), mult(e, mult(mult(mult(d, b), e), mult(c, mult(d, e))))), mult(e, mult(a, mult(c, mult(mult(d, b), e)))))
% 0.15/0.50 = { by axiom 2 (c02) R->L }
% 0.15/0.50 mult(mult(mult(mult(d, b), e), mult(e, mult(mult(a, b), mult(c, mult(d, e))))), mult(e, mult(a, mult(c, mult(mult(d, b), e)))))
% 0.15/0.50 = { by lemma 10 R->L }
% 0.15/0.50 mult(mult(mult(mult(d, b), e), mult(mult(c, mult(d, e)), mult(mult(a, b), mult(c, mult(d, e))))), mult(e, mult(a, mult(c, mult(mult(d, b), e)))))
% 0.15/0.50 = { by lemma 8 }
% 0.15/0.50 mult(mult(mult(mult(d, b), e), mult(c, mult(mult(a, b), mult(c, mult(d, e))))), mult(e, mult(a, mult(c, mult(mult(d, b), e)))))
% 0.15/0.50 = { by lemma 11 R->L }
% 0.15/0.50 mult(mult(mult(mult(d, b), e), mult(c, mult(mult(a, b), mult(c, mult(mult(d, b), e))))), mult(e, mult(a, mult(c, mult(mult(d, b), e)))))
% 0.15/0.50 = { by lemma 8 R->L }
% 0.15/0.50 mult(mult(mult(mult(d, b), e), mult(mult(c, mult(mult(d, b), e)), mult(mult(a, b), mult(c, mult(mult(d, b), e))))), mult(e, mult(a, mult(c, mult(mult(d, b), e)))))
% 0.15/0.50 = { by axiom 2 (c02) R->L }
% 0.15/0.50 mult(mult(mult(a, b), mult(mult(c, mult(mult(d, b), e)), mult(mult(mult(d, b), e), mult(c, mult(mult(d, b), e))))), mult(e, mult(a, mult(c, mult(mult(d, b), e)))))
% 0.15/0.50 = { by lemma 8 }
% 0.15/0.50 mult(mult(mult(a, b), mult(mult(c, mult(mult(d, b), e)), mult(mult(d, b), mult(c, mult(mult(d, b), e))))), mult(e, mult(a, mult(c, mult(mult(d, b), e)))))
% 0.15/0.50 = { by axiom 3 (c03) R->L }
% 0.15/0.50 mult(mult(mult(mult(a, b), mult(b, mult(d, b))), mult(c, mult(mult(d, b), e))), mult(e, mult(a, mult(c, mult(mult(d, b), e)))))
% 0.15/0.50 = { by axiom 2 (c02) }
% 0.15/0.50 mult(mult(mult(d, mult(b, mult(mult(a, b), b))), mult(c, mult(mult(d, b), e))), mult(e, mult(a, mult(c, mult(mult(d, b), e)))))
% 0.15/0.50 = { by lemma 5 }
% 0.15/0.50 mult(mult(mult(d, mult(b, mult(a, b))), mult(c, mult(mult(d, b), e))), mult(e, mult(a, mult(c, mult(mult(d, b), e)))))
% 0.15/0.50 = { by axiom 2 (c02) }
% 0.15/0.50 mult(mult(mult(a, mult(b, mult(d, b))), mult(c, mult(mult(d, b), e))), mult(e, mult(a, mult(c, mult(mult(d, b), e)))))
% 0.15/0.50 = { by axiom 3 (c03) }
% 0.15/0.50 mult(mult(a, mult(mult(c, mult(mult(d, b), e)), mult(mult(d, b), mult(c, mult(mult(d, b), e))))), mult(e, mult(a, mult(c, mult(mult(d, b), e)))))
% 0.15/0.50 = { by axiom 2 (c02) R->L }
% 0.15/0.50 mult(mult(mult(d, b), mult(mult(c, mult(mult(d, b), e)), mult(a, mult(c, mult(mult(d, b), e))))), mult(e, mult(a, mult(c, mult(mult(d, b), e)))))
% 0.15/0.50 = { by axiom 3 (c03) }
% 0.15/0.50 mult(mult(d, b), mult(mult(e, mult(a, mult(c, mult(mult(d, b), e)))), mult(mult(a, mult(c, mult(mult(d, b), e))), mult(e, mult(a, mult(c, mult(mult(d, b), e)))))))
% 0.15/0.50 = { by axiom 2 (c02) }
% 0.15/0.50 mult(mult(a, mult(c, mult(mult(d, b), e))), mult(mult(e, mult(a, mult(c, mult(mult(d, b), e)))), mult(mult(d, b), mult(e, mult(a, mult(c, mult(mult(d, b), e)))))))
% 0.15/0.50 = { by lemma 9 }
% 0.15/0.50 mult(mult(a, mult(c, mult(mult(d, b), e))), mult(mult(e, mult(a, mult(c, mult(mult(d, b), e)))), mult(a, mult(c, mult(mult(d, b), e)))))
% 0.15/0.50 = { by lemma 10 R->L }
% 0.15/0.50 mult(mult(a, mult(c, mult(mult(d, b), e))), mult(mult(mult(c, mult(mult(d, b), e)), mult(a, mult(c, mult(mult(d, b), e)))), mult(a, mult(c, mult(mult(d, b), e)))))
% 0.15/0.50 = { by lemma 6 }
% 0.15/0.50 mult(mult(a, mult(c, mult(mult(d, b), e))), mult(mult(c, mult(mult(d, b), e)), mult(a, mult(c, mult(mult(d, b), e)))))
% 0.15/0.50 = { by lemma 4 }
% 0.15/0.50 mult(mult(a, mult(c, mult(mult(d, b), e))), mult(c, mult(mult(d, b), e)))
% 0.15/0.50 = { by lemma 6 }
% 0.15/0.50 mult(a, mult(c, mult(mult(d, b), e)))
% 0.15/0.50 % SZS output end Proof
% 0.15/0.50
% 0.15/0.50 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------