TSTP Solution File: GRP729-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP729-1 : 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 : n005.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 0.19s 0.65s
% Output : Proof 0.19s
% 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 : GRP729-1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n005.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 20:15:52 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.65 Command-line arguments: --no-flatten-goal
% 0.19/0.65
% 0.19/0.65 % SZS status Unsatisfiable
% 0.19/0.65
% 0.19/0.65 % SZS output start Proof
% 0.19/0.65 Axiom 1 (c02): mult(X, unit) = X.
% 0.19/0.65 Axiom 2 (c01): mult(unit, X) = X.
% 0.19/0.65 Axiom 3 (c03): mult(X, i(X)) = unit.
% 0.19/0.65 Axiom 4 (c04): mult(i(X), X) = unit.
% 0.19/0.65 Axiom 5 (c05): i(mult(X, Y)) = mult(i(X), i(Y)).
% 0.19/0.65 Axiom 6 (c06): mult(i(X), mult(X, Y)) = Y.
% 0.19/0.65 Axiom 7 (c22): asoc(X, Y, asoc(Z, W, V)) = unit.
% 0.19/0.65 Axiom 8 (c11): mult(X, Y) = mult(mult(Y, X), op_k(X, Y)).
% 0.19/0.65 Axiom 9 (c12): op_l(X, Y, Z) = mult(i(mult(Z, Y)), mult(Z, mult(Y, X))).
% 0.19/0.65 Axiom 10 (c10): mult(mult(X, Y), Z) = mult(mult(X, mult(Y, Z)), asoc(X, Y, Z)).
% 0.19/0.65
% 0.19/0.65 Lemma 11: i(i(X)) = X.
% 0.19/0.65 Proof:
% 0.19/0.65 i(i(X))
% 0.19/0.65 = { by axiom 1 (c02) R->L }
% 0.19/0.65 mult(i(i(X)), unit)
% 0.19/0.65 = { by axiom 4 (c04) R->L }
% 0.19/0.65 mult(i(i(X)), mult(i(X), X))
% 0.19/0.65 = { by axiom 6 (c06) }
% 0.19/0.65 X
% 0.19/0.65
% 0.19/0.65 Lemma 12: i(mult(X, i(Y))) = mult(i(X), Y).
% 0.19/0.65 Proof:
% 0.19/0.65 i(mult(X, i(Y)))
% 0.19/0.65 = { by axiom 5 (c05) }
% 0.19/0.65 mult(i(X), i(i(Y)))
% 0.19/0.65 = { by lemma 11 }
% 0.19/0.65 mult(i(X), Y)
% 0.19/0.65
% 0.19/0.65 Lemma 13: mult(i(mult(X, Y)), mult(Y, X)) = op_k(Y, X).
% 0.19/0.65 Proof:
% 0.19/0.65 mult(i(mult(X, Y)), mult(Y, X))
% 0.19/0.65 = { by axiom 8 (c11) }
% 0.19/0.65 mult(i(mult(X, Y)), mult(mult(X, Y), op_k(Y, X)))
% 0.19/0.65 = { by axiom 6 (c06) }
% 0.19/0.65 op_k(Y, X)
% 0.19/0.65
% 0.19/0.65 Lemma 14: mult(mult(X, Y), i(mult(Y, X))) = op_k(i(Y), i(X)).
% 0.19/0.65 Proof:
% 0.19/0.65 mult(mult(X, Y), i(mult(Y, X)))
% 0.19/0.65 = { by axiom 5 (c05) }
% 0.19/0.65 mult(mult(X, Y), mult(i(Y), i(X)))
% 0.19/0.65 = { by lemma 11 R->L }
% 0.19/0.65 mult(i(i(mult(X, Y))), mult(i(Y), i(X)))
% 0.19/0.65 = { by axiom 5 (c05) }
% 0.19/0.65 mult(i(mult(i(X), i(Y))), mult(i(Y), i(X)))
% 0.19/0.65 = { by lemma 13 }
% 0.19/0.65 op_k(i(Y), i(X))
% 0.19/0.65
% 0.19/0.65 Lemma 15: i(op_k(i(X), i(Y))) = op_k(X, Y).
% 0.19/0.65 Proof:
% 0.19/0.65 i(op_k(i(X), i(Y)))
% 0.19/0.65 = { by lemma 14 R->L }
% 0.19/0.65 i(mult(mult(Y, X), i(mult(X, Y))))
% 0.19/0.65 = { by lemma 12 }
% 0.19/0.65 mult(i(mult(Y, X)), mult(X, Y))
% 0.19/0.65 = { by lemma 13 }
% 0.19/0.65 op_k(X, Y)
% 0.19/0.65
% 0.19/0.65 Lemma 16: op_k(i(X), i(Y)) = i(op_k(X, Y)).
% 0.19/0.65 Proof:
% 0.19/0.65 op_k(i(X), i(Y))
% 0.19/0.65 = { by lemma 11 R->L }
% 0.19/0.65 i(i(op_k(i(X), i(Y))))
% 0.19/0.65 = { by lemma 15 }
% 0.19/0.65 i(op_k(X, Y))
% 0.19/0.65
% 0.19/0.65 Lemma 17: mult(X, i(mult(X, Y))) = i(Y).
% 0.19/0.65 Proof:
% 0.19/0.65 mult(X, i(mult(X, Y)))
% 0.19/0.65 = { by lemma 11 R->L }
% 0.19/0.65 mult(i(i(X)), i(mult(X, Y)))
% 0.19/0.65 = { by axiom 5 (c05) R->L }
% 0.19/0.65 i(mult(i(X), mult(X, Y)))
% 0.19/0.65 = { by axiom 6 (c06) }
% 0.19/0.65 i(Y)
% 0.19/0.65
% 0.19/0.65 Lemma 18: mult(i(mult(Y, X)), Y) = op_l(i(X), X, Y).
% 0.19/0.65 Proof:
% 0.19/0.65 mult(i(mult(Y, X)), Y)
% 0.19/0.65 = { by axiom 1 (c02) R->L }
% 0.19/0.65 mult(i(mult(Y, X)), mult(Y, unit))
% 0.19/0.65 = { by axiom 3 (c03) R->L }
% 0.19/0.65 mult(i(mult(Y, X)), mult(Y, mult(X, i(X))))
% 0.19/0.65 = { by axiom 9 (c12) R->L }
% 0.19/0.65 op_l(i(X), X, Y)
% 0.19/0.65
% 0.19/0.65 Goal 1 (goals): asoc(a, b, op_k(c, d)) = unit.
% 0.19/0.65 Proof:
% 0.19/0.65 asoc(a, b, op_k(c, d))
% 0.19/0.65 = { by lemma 15 R->L }
% 0.19/0.65 asoc(a, b, i(op_k(i(c), i(d))))
% 0.19/0.65 = { by lemma 16 R->L }
% 0.19/0.65 asoc(a, b, op_k(i(i(c)), i(i(d))))
% 0.19/0.65 = { by lemma 17 R->L }
% 0.19/0.65 asoc(a, b, op_k(i(i(c)), mult(i(c), i(mult(i(c), i(d))))))
% 0.19/0.65 = { by lemma 15 R->L }
% 0.19/0.65 asoc(a, b, i(op_k(i(i(i(c))), i(mult(i(c), i(mult(i(c), i(d))))))))
% 0.19/0.65 = { by lemma 11 }
% 0.19/0.65 asoc(a, b, i(op_k(i(c), i(mult(i(c), i(mult(i(c), i(d))))))))
% 0.19/0.65 = { by lemma 16 R->L }
% 0.19/0.66 asoc(a, b, op_k(i(i(c)), i(i(mult(i(c), i(mult(i(c), i(d))))))))
% 0.19/0.66 = { by lemma 14 R->L }
% 0.19/0.66 asoc(a, b, mult(mult(i(mult(i(c), i(mult(i(c), i(d))))), i(c)), i(mult(i(c), i(mult(i(c), i(mult(i(c), i(d)))))))))
% 0.19/0.66 = { by lemma 18 }
% 0.19/0.66 asoc(a, b, mult(op_l(i(i(mult(i(c), i(d)))), i(mult(i(c), i(d))), i(c)), i(mult(i(c), i(mult(i(c), i(mult(i(c), i(d)))))))))
% 0.19/0.66 = { by lemma 12 }
% 0.19/0.66 asoc(a, b, mult(op_l(i(i(mult(i(c), i(d)))), i(mult(i(c), i(d))), i(c)), mult(i(i(c)), mult(i(c), i(mult(i(c), i(d)))))))
% 0.19/0.66 = { by axiom 6 (c06) }
% 0.19/0.66 asoc(a, b, mult(op_l(i(i(mult(i(c), i(d)))), i(mult(i(c), i(d))), i(c)), i(mult(i(c), i(d)))))
% 0.19/0.66 = { by lemma 18 R->L }
% 0.19/0.66 asoc(a, b, mult(mult(i(mult(i(c), i(mult(i(c), i(d))))), i(c)), i(mult(i(c), i(d)))))
% 0.19/0.66 = { by axiom 10 (c10) }
% 0.19/0.66 asoc(a, b, mult(mult(i(mult(i(c), i(mult(i(c), i(d))))), mult(i(c), i(mult(i(c), i(d))))), asoc(i(mult(i(c), i(mult(i(c), i(d))))), i(c), i(mult(i(c), i(d))))))
% 0.19/0.66 = { by axiom 4 (c04) }
% 0.19/0.66 asoc(a, b, mult(unit, asoc(i(mult(i(c), i(mult(i(c), i(d))))), i(c), i(mult(i(c), i(d))))))
% 0.19/0.66 = { by axiom 2 (c01) }
% 0.19/0.66 asoc(a, b, asoc(i(mult(i(c), i(mult(i(c), i(d))))), i(c), i(mult(i(c), i(d)))))
% 0.19/0.66 = { by lemma 17 }
% 0.19/0.66 asoc(a, b, asoc(i(i(i(d))), i(c), i(mult(i(c), i(d)))))
% 0.19/0.66 = { by lemma 11 }
% 0.19/0.66 asoc(a, b, asoc(i(d), i(c), i(mult(i(c), i(d)))))
% 0.19/0.66 = { by axiom 7 (c22) }
% 0.19/0.66 unit
% 0.19/0.66 % SZS output end Proof
% 0.19/0.66
% 0.19/0.66 RESULT: Unsatisfiable (the axioms are contradictory).
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