TSTP Solution File: GRP658-10 by Twee---2.4.2
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- Process Solution
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% File : Twee---2.4.2
% Problem : GRP658-10 : TPTP v8.1.2. Released v8.1.0.
% 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 01:19:30 EDT 2023
% Result : Unsatisfiable 0.19s 0.40s
% 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 : GRP658-10 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.34 % Computer : n019.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Aug 29 00:07:13 EDT 2023
% 0.15/0.34 % CPUTime :
% 0.19/0.40 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.19/0.40
% 0.19/0.40 % SZS status Unsatisfiable
% 0.19/0.40
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 Axiom 1 (f02): ld(X, mult(X, Y)) = Y.
% 0.19/0.41 Axiom 2 (f04): rd(mult(X, Y), Y) = X.
% 0.19/0.41 Axiom 3 (f03): mult(rd(X, Y), Y) = X.
% 0.19/0.41 Axiom 4 (f05): mult(mult(X, mult(Y, Y)), Z) = mult(mult(X, Y), mult(Y, Z)).
% 0.19/0.41
% 0.19/0.41 Lemma 5: ld(rd(X, Y), X) = Y.
% 0.19/0.41 Proof:
% 0.19/0.41 ld(rd(X, Y), X)
% 0.19/0.41 = { by axiom 3 (f03) R->L }
% 0.19/0.41 ld(rd(X, Y), mult(rd(X, Y), Y))
% 0.19/0.41 = { by axiom 1 (f02) }
% 0.19/0.41 Y
% 0.19/0.41
% 0.19/0.41 Lemma 6: mult(mult(rd(X, mult(Y, Y)), Y), mult(Y, Z)) = mult(X, Z).
% 0.19/0.41 Proof:
% 0.19/0.41 mult(mult(rd(X, mult(Y, Y)), Y), mult(Y, Z))
% 0.19/0.41 = { by axiom 4 (f05) R->L }
% 0.19/0.41 mult(mult(rd(X, mult(Y, Y)), mult(Y, Y)), Z)
% 0.19/0.41 = { by axiom 3 (f03) }
% 0.19/0.41 mult(X, Z)
% 0.19/0.41
% 0.19/0.41 Lemma 7: rd(mult(X, W), mult(Z, W)) = rd(mult(X, Y), mult(Z, Y)).
% 0.19/0.41 Proof:
% 0.19/0.41 rd(mult(X, W), mult(Z, W))
% 0.19/0.41 = { by lemma 6 R->L }
% 0.19/0.42 rd(mult(mult(rd(X, mult(Z, Z)), Z), mult(Z, W)), mult(Z, W))
% 0.19/0.42 = { by axiom 2 (f04) }
% 0.19/0.42 mult(rd(X, mult(Z, Z)), Z)
% 0.19/0.42 = { by axiom 2 (f04) R->L }
% 0.19/0.42 rd(mult(mult(rd(X, mult(Z, Z)), Z), mult(Z, Y)), mult(Z, Y))
% 0.19/0.42 = { by lemma 6 }
% 0.19/0.42 rd(mult(X, Y), mult(Z, Y))
% 0.19/0.42
% 0.19/0.42 Lemma 8: rd(mult(rd(X, Y), Z), mult(W, Z)) = rd(X, mult(W, Y)).
% 0.19/0.42 Proof:
% 0.19/0.42 rd(mult(rd(X, Y), Z), mult(W, Z))
% 0.19/0.42 = { by lemma 7 }
% 0.19/0.42 rd(mult(rd(X, Y), Y), mult(W, Y))
% 0.19/0.42 = { by axiom 3 (f03) }
% 0.19/0.42 rd(X, mult(W, Y))
% 0.19/0.42
% 0.19/0.42 Lemma 9: rd(mult(rd(X, Y), Z), W) = rd(X, mult(rd(W, Z), Y)).
% 0.19/0.42 Proof:
% 0.19/0.42 rd(mult(rd(X, Y), Z), W)
% 0.19/0.42 = { by axiom 3 (f03) R->L }
% 0.19/0.42 rd(mult(rd(X, Y), Z), mult(rd(W, Z), Z))
% 0.19/0.42 = { by lemma 7 R->L }
% 0.19/0.42 rd(mult(rd(X, Y), V), mult(rd(W, Z), V))
% 0.19/0.42 = { by lemma 8 }
% 0.19/0.42 rd(X, mult(rd(W, Z), Y))
% 0.19/0.42
% 0.19/0.42 Lemma 10: mult(rd(X, X), Y) = Y.
% 0.19/0.42 Proof:
% 0.19/0.42 mult(rd(X, X), Y)
% 0.19/0.42 = { by lemma 5 R->L }
% 0.19/0.42 ld(rd(Z, mult(rd(X, X), Y)), Z)
% 0.19/0.42 = { by lemma 9 R->L }
% 0.19/0.42 ld(rd(mult(rd(Z, Y), X), X), Z)
% 0.19/0.42 = { by axiom 2 (f04) }
% 0.19/0.42 ld(rd(Z, Y), Z)
% 0.19/0.42 = { by lemma 5 }
% 0.19/0.42 Y
% 0.19/0.42
% 0.19/0.42 Lemma 11: rd(X, mult(rd(Y, Z), X)) = rd(Z, Y).
% 0.19/0.42 Proof:
% 0.19/0.42 rd(X, mult(rd(Y, Z), X))
% 0.19/0.42 = { by lemma 9 R->L }
% 0.19/0.42 rd(mult(rd(X, X), Z), Y)
% 0.19/0.42 = { by lemma 10 }
% 0.19/0.42 rd(Z, Y)
% 0.19/0.42
% 0.19/0.42 Goal 1 (goal): tuple(mult(X, x1(X)), mult(x1_2(X), X)) = tuple(x1(X), x1_2(X)).
% 0.19/0.42 The goal is true when:
% 0.19/0.42 X = rd(X, X)
% 0.19/0.42
% 0.19/0.42 Proof:
% 0.19/0.42 tuple(mult(rd(X, X), x1(rd(X, X))), mult(x1_2(rd(X, X)), rd(X, X)))
% 0.19/0.42 = { by axiom 2 (f04) R->L }
% 0.19/0.42 tuple(mult(rd(X, X), x1(rd(X, X))), rd(mult(mult(x1_2(rd(X, X)), rd(X, X)), Y), Y))
% 0.19/0.42 = { by lemma 11 R->L }
% 0.19/0.42 tuple(mult(rd(X, X), x1(rd(X, X))), rd(rd(mult(mult(x1_2(rd(X, X)), rd(X, X)), Y), Y), mult(rd(Y, mult(mult(x1_2(rd(X, X)), rd(X, X)), Y)), rd(mult(mult(x1_2(rd(X, X)), rd(X, X)), Y), Y))))
% 0.19/0.42 = { by lemma 11 R->L }
% 0.19/0.42 tuple(mult(rd(X, X), x1(rd(X, X))), rd(rd(mult(mult(x1_2(rd(X, X)), rd(X, X)), Y), Y), mult(rd(rd(mult(mult(x1_2(rd(X, X)), rd(X, X)), Y), Y), mult(rd(mult(mult(x1_2(rd(X, X)), rd(X, X)), Y), Y), rd(mult(mult(x1_2(rd(X, X)), rd(X, X)), Y), Y))), rd(mult(mult(x1_2(rd(X, X)), rd(X, X)), Y), Y))))
% 0.19/0.42 = { by axiom 2 (f04) R->L }
% 0.19/0.42 tuple(mult(rd(X, X), x1(rd(X, X))), rd(rd(mult(mult(x1_2(rd(X, X)), rd(X, X)), Y), Y), rd(mult(mult(rd(rd(mult(mult(x1_2(rd(X, X)), rd(X, X)), Y), Y), mult(rd(mult(mult(x1_2(rd(X, X)), rd(X, X)), Y), Y), rd(mult(mult(x1_2(rd(X, X)), rd(X, X)), Y), Y))), rd(mult(mult(x1_2(rd(X, X)), rd(X, X)), Y), Y)), mult(rd(mult(mult(x1_2(rd(X, X)), rd(X, X)), Y), Y), Z)), mult(rd(mult(mult(x1_2(rd(X, X)), rd(X, X)), Y), Y), Z))))
% 0.19/0.42 = { by lemma 6 }
% 0.19/0.42 tuple(mult(rd(X, X), x1(rd(X, X))), rd(rd(mult(mult(x1_2(rd(X, X)), rd(X, X)), Y), Y), rd(mult(rd(mult(mult(x1_2(rd(X, X)), rd(X, X)), Y), Y), Z), mult(rd(mult(mult(x1_2(rd(X, X)), rd(X, X)), Y), Y), Z))))
% 0.19/0.42 = { by lemma 8 }
% 0.19/0.42 tuple(mult(rd(X, X), x1(rd(X, X))), rd(rd(mult(mult(x1_2(rd(X, X)), rd(X, X)), Y), Y), rd(mult(mult(x1_2(rd(X, X)), rd(X, X)), Y), mult(rd(mult(mult(x1_2(rd(X, X)), rd(X, X)), Y), Y), Y))))
% 0.19/0.42 = { by axiom 3 (f03) }
% 0.19/0.42 tuple(mult(rd(X, X), x1(rd(X, X))), rd(rd(mult(mult(x1_2(rd(X, X)), rd(X, X)), Y), Y), rd(mult(mult(x1_2(rd(X, X)), rd(X, X)), Y), mult(mult(x1_2(rd(X, X)), rd(X, X)), Y))))
% 0.19/0.42 = { by axiom 2 (f04) R->L }
% 0.19/0.42 tuple(mult(rd(X, X), x1(rd(X, X))), rd(rd(mult(mult(x1_2(rd(X, X)), rd(X, X)), Y), Y), rd(mult(rd(mult(mult(x1_2(rd(X, X)), rd(X, X)), Y), mult(mult(x1_2(rd(X, X)), rd(X, X)), Y)), X), X)))
% 0.19/0.42 = { by lemma 10 }
% 0.19/0.42 tuple(mult(rd(X, X), x1(rd(X, X))), rd(rd(mult(mult(x1_2(rd(X, X)), rd(X, X)), Y), Y), rd(X, X)))
% 0.19/0.42 = { by axiom 2 (f04) }
% 0.19/0.42 tuple(mult(rd(X, X), x1(rd(X, X))), rd(mult(x1_2(rd(X, X)), rd(X, X)), rd(X, X)))
% 0.19/0.42 = { by axiom 2 (f04) }
% 0.19/0.42 tuple(mult(rd(X, X), x1(rd(X, X))), x1_2(rd(X, X)))
% 0.19/0.42 = { by lemma 10 }
% 0.19/0.42 tuple(x1(rd(X, X)), x1_2(rd(X, X)))
% 0.19/0.42 % SZS output end Proof
% 0.19/0.42
% 0.19/0.42 RESULT: Unsatisfiable (the axioms are contradictory).
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