TSTP Solution File: GRP731-1 by Twee---2.4.2
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- Process Solution
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% File : Twee---2.4.2
% Problem : GRP731-1 : 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 : Thu Aug 31 01:19:55 EDT 2023
% Result : Unsatisfiable 0.19s 0.44s
% 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
% 0.03/0.12 % Problem : GRP731-1 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 28 21:04:50 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.44 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.19/0.44
% 0.19/0.44 % SZS status Unsatisfiable
% 0.19/0.44
% 0.19/0.45 % SZS output start Proof
% 0.19/0.45 Axiom 1 (c02): mult(X, unit) = X.
% 0.19/0.45 Axiom 2 (c01): mult(unit, X) = X.
% 0.19/0.45 Axiom 3 (c03): mult(X, i(X)) = unit.
% 0.19/0.45 Axiom 4 (c04): mult(i(X), X) = unit.
% 0.19/0.45 Axiom 5 (c05): i(mult(X, Y)) = mult(i(X), i(Y)).
% 0.19/0.45 Axiom 6 (c08): mult(rd(X, Y), Y) = X.
% 0.19/0.45 Axiom 7 (c07): rd(mult(X, Y), Y) = X.
% 0.19/0.45 Axiom 8 (c06): mult(i(X), mult(X, Y)) = Y.
% 0.19/0.45 Axiom 9 (c14): op_t(X, Y) = mult(i(Y), mult(X, Y)).
% 0.19/0.45 Axiom 10 (c11): mult(X, Y) = mult(mult(Y, X), op_k(X, Y)).
% 0.19/0.45 Axiom 11 (c22): asoc(X, Y, asoc(Z, W, V)) = unit.
% 0.19/0.45 Axiom 12 (c21): asoc(asoc(X, Y, Z), W, V) = unit.
% 0.19/0.45 Axiom 13 (c12): op_l(X, Y, Z) = mult(i(mult(Z, Y)), mult(Z, mult(Y, X))).
% 0.19/0.45 Axiom 14 (c10): mult(mult(X, Y), Z) = mult(mult(X, mult(Y, Z)), asoc(X, Y, Z)).
% 0.19/0.45
% 0.19/0.45 Lemma 15: i(i(X)) = X.
% 0.19/0.45 Proof:
% 0.19/0.45 i(i(X))
% 0.19/0.45 = { by axiom 1 (c02) R->L }
% 0.19/0.45 mult(i(i(X)), unit)
% 0.19/0.45 = { by axiom 4 (c04) R->L }
% 0.19/0.45 mult(i(i(X)), mult(i(X), X))
% 0.19/0.45 = { by axiom 8 (c06) }
% 0.19/0.45 X
% 0.19/0.45
% 0.19/0.45 Lemma 16: mult(mult(X, Y), asoc(Z, W, V)) = mult(X, mult(Y, asoc(Z, W, V))).
% 0.19/0.45 Proof:
% 0.19/0.45 mult(mult(X, Y), asoc(Z, W, V))
% 0.19/0.45 = { by axiom 14 (c10) }
% 0.19/0.45 mult(mult(X, mult(Y, asoc(Z, W, V))), asoc(X, Y, asoc(Z, W, V)))
% 0.19/0.45 = { by axiom 11 (c22) }
% 0.19/0.45 mult(mult(X, mult(Y, asoc(Z, W, V))), unit)
% 0.19/0.45 = { by axiom 1 (c02) }
% 0.19/0.45 mult(X, mult(Y, asoc(Z, W, V)))
% 0.19/0.45
% 0.19/0.45 Lemma 17: op_t(X, asoc(Y, Z, W)) = X.
% 0.19/0.45 Proof:
% 0.19/0.45 op_t(X, asoc(Y, Z, W))
% 0.19/0.45 = { by axiom 9 (c14) }
% 0.19/0.45 mult(i(asoc(Y, Z, W)), mult(X, asoc(Y, Z, W)))
% 0.19/0.45 = { by lemma 16 R->L }
% 0.19/0.45 mult(mult(i(asoc(Y, Z, W)), X), asoc(Y, Z, W))
% 0.19/0.45 = { by lemma 15 R->L }
% 0.19/0.45 mult(mult(i(asoc(Y, Z, W)), i(i(X))), asoc(Y, Z, W))
% 0.19/0.45 = { by axiom 5 (c05) R->L }
% 0.19/0.45 mult(i(mult(asoc(Y, Z, W), i(X))), asoc(Y, Z, W))
% 0.19/0.45 = { by axiom 1 (c02) R->L }
% 0.19/0.45 mult(i(mult(asoc(Y, Z, W), i(X))), mult(asoc(Y, Z, W), unit))
% 0.19/0.45 = { by axiom 3 (c03) R->L }
% 0.19/0.45 mult(i(mult(asoc(Y, Z, W), i(X))), mult(asoc(Y, Z, W), mult(i(X), i(i(X)))))
% 0.19/0.45 = { by axiom 13 (c12) R->L }
% 0.19/0.45 op_l(i(i(X)), i(X), asoc(Y, Z, W))
% 0.19/0.46 = { by lemma 15 }
% 0.19/0.46 op_l(X, i(X), asoc(Y, Z, W))
% 0.19/0.46 = { by axiom 13 (c12) }
% 0.19/0.46 mult(i(mult(asoc(Y, Z, W), i(X))), mult(asoc(Y, Z, W), mult(i(X), X)))
% 0.19/0.46 = { by axiom 1 (c02) R->L }
% 0.19/0.46 mult(i(mult(asoc(Y, Z, W), i(X))), mult(mult(asoc(Y, Z, W), mult(i(X), X)), unit))
% 0.19/0.46 = { by axiom 12 (c21) R->L }
% 0.19/0.46 mult(i(mult(asoc(Y, Z, W), i(X))), mult(mult(asoc(Y, Z, W), mult(i(X), X)), asoc(asoc(Y, Z, W), i(X), X)))
% 0.19/0.46 = { by axiom 14 (c10) R->L }
% 0.19/0.46 mult(i(mult(asoc(Y, Z, W), i(X))), mult(mult(asoc(Y, Z, W), i(X)), X))
% 0.19/0.46 = { by axiom 8 (c06) }
% 0.19/0.46 X
% 0.19/0.46
% 0.19/0.46 Lemma 18: mult(asoc(Y, Z, W), X) = mult(X, asoc(Y, Z, W)).
% 0.19/0.46 Proof:
% 0.19/0.46 mult(asoc(Y, Z, W), X)
% 0.19/0.46 = { by lemma 17 R->L }
% 0.19/0.46 mult(asoc(Y, Z, W), op_t(X, asoc(Y, Z, W)))
% 0.19/0.46 = { by axiom 9 (c14) }
% 0.19/0.46 mult(asoc(Y, Z, W), mult(i(asoc(Y, Z, W)), mult(X, asoc(Y, Z, W))))
% 0.19/0.46 = { by lemma 15 R->L }
% 0.19/0.46 mult(i(i(asoc(Y, Z, W))), mult(i(asoc(Y, Z, W)), mult(X, asoc(Y, Z, W))))
% 0.19/0.46 = { by axiom 8 (c06) }
% 0.19/0.46 mult(X, asoc(Y, Z, W))
% 0.19/0.46
% 0.19/0.46 Goal 1 (goals): op_k(asoc(a, b, c), d) = unit.
% 0.19/0.46 Proof:
% 0.19/0.46 op_k(asoc(a, b, c), d)
% 0.19/0.46 = { by axiom 8 (c06) R->L }
% 0.19/0.46 mult(i(asoc(a, b, c)), mult(asoc(a, b, c), op_k(asoc(a, b, c), d)))
% 0.19/0.46 = { by axiom 8 (c06) R->L }
% 0.19/0.46 mult(i(asoc(a, b, c)), mult(i(d), mult(d, mult(asoc(a, b, c), op_k(asoc(a, b, c), d)))))
% 0.19/0.46 = { by lemma 18 }
% 0.19/0.46 mult(i(asoc(a, b, c)), mult(i(d), mult(d, mult(op_k(asoc(a, b, c), d), asoc(a, b, c)))))
% 0.19/0.46 = { by axiom 1 (c02) R->L }
% 0.19/0.46 mult(i(asoc(a, b, c)), mult(i(d), mult(mult(d, mult(op_k(asoc(a, b, c), d), asoc(a, b, c))), unit)))
% 0.19/0.46 = { by axiom 12 (c21) R->L }
% 0.19/0.46 mult(i(asoc(a, b, c)), mult(i(d), mult(mult(d, mult(op_k(asoc(a, b, c), d), asoc(a, b, c))), asoc(asoc(a, b, c), d, op_k(asoc(a, b, c), d)))))
% 0.19/0.46 = { by lemma 16 R->L }
% 0.19/0.46 mult(i(asoc(a, b, c)), mult(i(d), mult(mult(mult(d, op_k(asoc(a, b, c), d)), asoc(a, b, c)), asoc(asoc(a, b, c), d, op_k(asoc(a, b, c), d)))))
% 0.19/0.46 = { by lemma 18 R->L }
% 0.19/0.46 mult(i(asoc(a, b, c)), mult(i(d), mult(mult(asoc(a, b, c), mult(d, op_k(asoc(a, b, c), d))), asoc(asoc(a, b, c), d, op_k(asoc(a, b, c), d)))))
% 0.19/0.46 = { by axiom 14 (c10) R->L }
% 0.19/0.46 mult(i(asoc(a, b, c)), mult(i(d), mult(mult(asoc(a, b, c), d), op_k(asoc(a, b, c), d))))
% 0.19/0.46 = { by lemma 18 }
% 0.19/0.46 mult(i(asoc(a, b, c)), mult(i(d), mult(mult(d, asoc(a, b, c)), op_k(asoc(a, b, c), d))))
% 0.19/0.46 = { by axiom 10 (c11) R->L }
% 0.19/0.46 mult(i(asoc(a, b, c)), mult(i(d), mult(asoc(a, b, c), d)))
% 0.19/0.46 = { by lemma 18 }
% 0.19/0.46 mult(i(asoc(a, b, c)), mult(i(d), mult(d, asoc(a, b, c))))
% 0.19/0.46 = { by axiom 8 (c06) }
% 0.19/0.46 mult(i(asoc(a, b, c)), asoc(a, b, c))
% 0.19/0.46 = { by axiom 6 (c08) R->L }
% 0.19/0.46 mult(i(asoc(a, b, c)), mult(rd(asoc(a, b, c), asoc(a, b, c)), asoc(a, b, c)))
% 0.19/0.46 = { by axiom 9 (c14) R->L }
% 0.19/0.46 op_t(rd(asoc(a, b, c), asoc(a, b, c)), asoc(a, b, c))
% 0.19/0.46 = { by lemma 17 }
% 0.19/0.46 rd(asoc(a, b, c), asoc(a, b, c))
% 0.19/0.46 = { by axiom 2 (c01) R->L }
% 0.19/0.46 rd(mult(unit, asoc(a, b, c)), asoc(a, b, c))
% 0.19/0.46 = { by axiom 7 (c07) }
% 0.19/0.46 unit
% 0.19/0.46 % SZS output end Proof
% 0.19/0.46
% 0.19/0.46 RESULT: Unsatisfiable (the axioms are contradictory).
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