TSTP Solution File: GRP727-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP727-1 : 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 : n003.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 01:19:55 EDT 2023
% Result : Unsatisfiable 2.12s 0.67s
% Output : Proof 2.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GRP727-1 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.11/0.32 % Computer : n003.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Aug 28 23:28:25 EDT 2023
% 0.11/0.33 % CPUTime :
% 2.12/0.67 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 2.12/0.67
% 2.12/0.67 % SZS status Unsatisfiable
% 2.12/0.67
% 2.12/0.68 % SZS output start Proof
% 2.12/0.68 Axiom 1 (c02): mult(X, unit) = X.
% 2.12/0.68 Axiom 2 (c03): mult(X, i(X)) = unit.
% 2.12/0.68 Axiom 3 (c04): mult(i(X), X) = unit.
% 2.12/0.68 Axiom 4 (c05): i(mult(X, Y)) = mult(i(X), i(Y)).
% 2.12/0.68 Axiom 5 (c08): mult(rd(X, Y), Y) = X.
% 2.12/0.68 Axiom 6 (c07): rd(mult(X, Y), Y) = X.
% 2.12/0.68 Axiom 7 (c06): mult(i(X), mult(X, Y)) = Y.
% 2.12/0.68 Axiom 8 (c13): op_t(X, Y) = mult(i(Y), mult(X, Y)).
% 2.12/0.68 Axiom 9 (c20): asoc(asoc(X, Y, Z), W, V) = unit.
% 2.12/0.68 Axiom 10 (c10): mult(mult(X, Y), Z) = mult(mult(X, mult(Y, Z)), asoc(X, Y, Z)).
% 2.12/0.68
% 2.12/0.68 Lemma 11: i(i(X)) = X.
% 2.12/0.68 Proof:
% 2.12/0.68 i(i(X))
% 2.12/0.68 = { by axiom 1 (c02) R->L }
% 2.12/0.68 mult(i(i(X)), unit)
% 2.12/0.68 = { by axiom 3 (c04) R->L }
% 2.12/0.68 mult(i(i(X)), mult(i(X), X))
% 2.12/0.68 = { by axiom 7 (c06) }
% 2.12/0.68 X
% 2.12/0.68
% 2.12/0.68 Lemma 12: i(mult(i(X), Y)) = mult(X, i(Y)).
% 2.12/0.68 Proof:
% 2.12/0.68 i(mult(i(X), Y))
% 2.12/0.68 = { by axiom 4 (c05) }
% 2.12/0.68 mult(i(i(X)), i(Y))
% 2.12/0.68 = { by lemma 11 }
% 2.12/0.68 mult(X, i(Y))
% 2.12/0.68
% 2.12/0.68 Lemma 13: rd(X, mult(Y, X)) = i(Y).
% 2.12/0.68 Proof:
% 2.12/0.68 rd(X, mult(Y, X))
% 2.12/0.68 = { by axiom 7 (c06) R->L }
% 2.12/0.68 rd(mult(i(Y), mult(Y, X)), mult(Y, X))
% 2.12/0.68 = { by axiom 6 (c07) }
% 2.12/0.68 i(Y)
% 2.12/0.68
% 2.12/0.68 Lemma 14: mult(mult(asoc(X, Y, Z), W), V) = mult(asoc(X, Y, Z), mult(W, V)).
% 2.12/0.68 Proof:
% 2.12/0.68 mult(mult(asoc(X, Y, Z), W), V)
% 2.12/0.68 = { by axiom 10 (c10) }
% 2.12/0.68 mult(mult(asoc(X, Y, Z), mult(W, V)), asoc(asoc(X, Y, Z), W, V))
% 2.12/0.68 = { by axiom 9 (c20) }
% 2.12/0.68 mult(mult(asoc(X, Y, Z), mult(W, V)), unit)
% 2.12/0.68 = { by axiom 1 (c02) }
% 2.12/0.68 mult(asoc(X, Y, Z), mult(W, V))
% 2.12/0.68
% 2.12/0.68 Lemma 15: mult(asoc(X, Y, Z), W) = mult(W, asoc(X, Y, Z)).
% 2.12/0.68 Proof:
% 2.12/0.68 mult(asoc(X, Y, Z), W)
% 2.12/0.68 = { by axiom 7 (c06) R->L }
% 2.12/0.68 mult(i(i(W)), mult(i(W), mult(asoc(X, Y, Z), W)))
% 2.12/0.68 = { by lemma 11 }
% 2.12/0.68 mult(W, mult(i(W), mult(asoc(X, Y, Z), W)))
% 2.12/0.68 = { by axiom 8 (c13) R->L }
% 2.12/0.68 mult(W, op_t(asoc(X, Y, Z), W))
% 2.12/0.68 = { by lemma 11 R->L }
% 2.12/0.68 mult(W, op_t(asoc(X, Y, Z), i(i(W))))
% 2.12/0.68 = { by axiom 7 (c06) R->L }
% 2.12/0.68 mult(W, op_t(asoc(X, Y, Z), i(i(mult(i(asoc(X, Y, Z)), mult(asoc(X, Y, Z), W))))))
% 2.12/0.68 = { by lemma 12 }
% 2.12/0.68 mult(W, op_t(asoc(X, Y, Z), i(mult(asoc(X, Y, Z), i(mult(asoc(X, Y, Z), W))))))
% 2.12/0.68 = { by axiom 4 (c05) }
% 2.12/0.68 mult(W, op_t(asoc(X, Y, Z), mult(i(asoc(X, Y, Z)), i(i(mult(asoc(X, Y, Z), W))))))
% 2.12/0.68 = { by lemma 11 R->L }
% 2.12/0.68 mult(W, op_t(i(i(asoc(X, Y, Z))), mult(i(asoc(X, Y, Z)), i(i(mult(asoc(X, Y, Z), W))))))
% 2.12/0.68 = { by axiom 8 (c13) }
% 2.12/0.68 mult(W, mult(i(mult(i(asoc(X, Y, Z)), i(i(mult(asoc(X, Y, Z), W))))), mult(i(i(asoc(X, Y, Z))), mult(i(asoc(X, Y, Z)), i(i(mult(asoc(X, Y, Z), W)))))))
% 2.12/0.68 = { by axiom 7 (c06) }
% 2.12/0.68 mult(W, mult(i(mult(i(asoc(X, Y, Z)), i(i(mult(asoc(X, Y, Z), W))))), i(i(mult(asoc(X, Y, Z), W)))))
% 2.12/0.68 = { by axiom 4 (c05) R->L }
% 2.12/0.68 mult(W, mult(i(i(mult(asoc(X, Y, Z), i(mult(asoc(X, Y, Z), W))))), i(i(mult(asoc(X, Y, Z), W)))))
% 2.12/0.68 = { by axiom 4 (c05) R->L }
% 2.12/0.68 mult(W, i(mult(i(mult(asoc(X, Y, Z), i(mult(asoc(X, Y, Z), W)))), i(mult(asoc(X, Y, Z), W)))))
% 2.12/0.68 = { by lemma 12 }
% 2.12/0.68 mult(W, mult(mult(asoc(X, Y, Z), i(mult(asoc(X, Y, Z), W))), i(i(mult(asoc(X, Y, Z), W)))))
% 2.12/0.68 = { by lemma 14 }
% 2.12/0.68 mult(W, mult(asoc(X, Y, Z), mult(i(mult(asoc(X, Y, Z), W)), i(i(mult(asoc(X, Y, Z), W))))))
% 2.12/0.68 = { by axiom 2 (c03) }
% 2.12/0.68 mult(W, mult(asoc(X, Y, Z), unit))
% 2.12/0.68 = { by axiom 1 (c02) }
% 2.12/0.68 mult(W, asoc(X, Y, Z))
% 2.12/0.68
% 2.12/0.68 Lemma 16: rd(X, mult(asoc(Y, Z, W), mult(V, X))) = i(mult(V, asoc(Y, Z, W))).
% 2.12/0.68 Proof:
% 2.12/0.68 rd(X, mult(asoc(Y, Z, W), mult(V, X)))
% 2.12/0.68 = { by lemma 14 R->L }
% 2.12/0.68 rd(X, mult(mult(asoc(Y, Z, W), V), X))
% 2.12/0.68 = { by lemma 13 }
% 2.12/0.68 i(mult(asoc(Y, Z, W), V))
% 2.12/0.68 = { by lemma 15 }
% 2.12/0.68 i(mult(V, asoc(Y, Z, W)))
% 2.12/0.68
% 2.12/0.68 Goal 1 (goals): asoc(a, b, asoc(c, d, e)) = unit.
% 2.12/0.68 Proof:
% 2.12/0.68 asoc(a, b, asoc(c, d, e))
% 2.12/0.68 = { by axiom 1 (c02) R->L }
% 2.12/0.68 mult(asoc(a, b, asoc(c, d, e)), unit)
% 2.12/0.68 = { by axiom 2 (c03) R->L }
% 2.12/0.68 mult(asoc(a, b, asoc(c, d, e)), mult(a, i(a)))
% 2.12/0.68 = { by lemma 14 R->L }
% 2.12/0.68 mult(mult(asoc(a, b, asoc(c, d, e)), a), i(a))
% 2.12/0.68 = { by lemma 15 }
% 2.12/0.68 mult(mult(a, asoc(a, b, asoc(c, d, e))), i(a))
% 2.12/0.68 = { by lemma 13 R->L }
% 2.12/0.68 mult(mult(a, asoc(a, b, asoc(c, d, e))), rd(asoc(c, d, e), mult(a, asoc(c, d, e))))
% 2.12/0.68 = { by axiom 5 (c08) R->L }
% 2.12/0.68 mult(mult(a, asoc(a, b, asoc(c, d, e))), rd(asoc(c, d, e), mult(rd(mult(a, asoc(c, d, e)), asoc(c, d, e)), asoc(c, d, e))))
% 2.12/0.68 = { by lemma 13 }
% 2.12/0.68 mult(mult(a, asoc(a, b, asoc(c, d, e))), i(rd(mult(a, asoc(c, d, e)), asoc(c, d, e))))
% 2.12/0.68 = { by axiom 7 (c06) R->L }
% 2.12/0.68 mult(mult(a, asoc(a, b, asoc(c, d, e))), i(mult(i(asoc(c, d, e)), mult(asoc(c, d, e), rd(mult(a, asoc(c, d, e)), asoc(c, d, e))))))
% 2.12/0.68 = { by lemma 15 }
% 2.12/0.68 mult(mult(a, asoc(a, b, asoc(c, d, e))), i(mult(i(asoc(c, d, e)), mult(rd(mult(a, asoc(c, d, e)), asoc(c, d, e)), asoc(c, d, e)))))
% 2.12/0.68 = { by axiom 5 (c08) }
% 2.12/0.68 mult(mult(a, asoc(a, b, asoc(c, d, e))), i(mult(i(asoc(c, d, e)), mult(a, asoc(c, d, e)))))
% 2.12/0.68 = { by lemma 12 }
% 2.12/0.68 mult(mult(a, asoc(a, b, asoc(c, d, e))), mult(asoc(c, d, e), i(mult(a, asoc(c, d, e)))))
% 2.12/0.68 = { by lemma 16 R->L }
% 2.12/0.68 mult(mult(a, asoc(a, b, asoc(c, d, e))), mult(asoc(c, d, e), rd(b, mult(asoc(c, d, e), mult(a, b)))))
% 2.12/0.68 = { by axiom 6 (c07) R->L }
% 2.12/0.68 mult(mult(a, asoc(a, b, asoc(c, d, e))), rd(mult(mult(asoc(c, d, e), rd(b, mult(asoc(c, d, e), mult(a, b)))), mult(asoc(c, d, e), mult(a, b))), mult(asoc(c, d, e), mult(a, b))))
% 2.12/0.68 = { by lemma 14 }
% 2.12/0.68 mult(mult(a, asoc(a, b, asoc(c, d, e))), rd(mult(asoc(c, d, e), mult(rd(b, mult(asoc(c, d, e), mult(a, b))), mult(asoc(c, d, e), mult(a, b)))), mult(asoc(c, d, e), mult(a, b))))
% 2.12/0.68 = { by axiom 5 (c08) }
% 2.12/0.68 mult(mult(a, asoc(a, b, asoc(c, d, e))), rd(mult(asoc(c, d, e), b), mult(asoc(c, d, e), mult(a, b))))
% 2.12/0.68 = { by lemma 15 }
% 2.12/0.68 mult(mult(a, asoc(a, b, asoc(c, d, e))), rd(mult(b, asoc(c, d, e)), mult(asoc(c, d, e), mult(a, b))))
% 2.12/0.69 = { by lemma 15 }
% 2.12/0.69 mult(mult(a, asoc(a, b, asoc(c, d, e))), rd(mult(b, asoc(c, d, e)), mult(mult(a, b), asoc(c, d, e))))
% 2.12/0.69 = { by axiom 10 (c10) }
% 2.12/0.69 mult(mult(a, asoc(a, b, asoc(c, d, e))), rd(mult(b, asoc(c, d, e)), mult(mult(a, mult(b, asoc(c, d, e))), asoc(a, b, asoc(c, d, e)))))
% 2.12/0.69 = { by lemma 15 R->L }
% 2.12/0.69 mult(mult(a, asoc(a, b, asoc(c, d, e))), rd(mult(b, asoc(c, d, e)), mult(asoc(a, b, asoc(c, d, e)), mult(a, mult(b, asoc(c, d, e))))))
% 2.12/0.69 = { by lemma 16 }
% 2.12/0.69 mult(mult(a, asoc(a, b, asoc(c, d, e))), i(mult(a, asoc(a, b, asoc(c, d, e)))))
% 2.12/0.69 = { by axiom 2 (c03) }
% 2.12/0.69 unit
% 2.12/0.69 % SZS output end Proof
% 2.12/0.69
% 2.12/0.69 RESULT: Unsatisfiable (the axioms are contradictory).
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