TSTP Solution File: GRP751-1 by Twee---2.4.2
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- Process Solution
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% File : Twee---2.4.2
% Problem : GRP751-1 : 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 : n028.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 01:19:59 EDT 2023
% Result : Unsatisfiable 0.20s 0.56s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP751-1 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.33 % Computer : n028.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Aug 28 21:23:40 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.56 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
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% 0.20/0.56 % SZS status Unsatisfiable
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% 0.20/0.56 % SZS output start Proof
% 0.20/0.56 Axiom 1 (f04): rd(mult(X, Y), Y) = X.
% 0.20/0.56 Axiom 2 (f03): mult(rd(X, Y), Y) = X.
% 0.20/0.56 Axiom 3 (f07): mult(mult(X, Y), mult(Z, Z)) = mult(mult(X, Z), mult(Y, Z)).
% 0.20/0.56 Axiom 4 (f05): mult(mult(X, mult(X, X)), mult(Y, Z)) = mult(mult(X, Y), mult(mult(X, X), Z)).
% 0.20/0.56
% 0.20/0.56 Lemma 5: rd(mult(mult(X, Y), mult(Z, Y)), mult(Y, Y)) = mult(X, Z).
% 0.20/0.56 Proof:
% 0.20/0.56 rd(mult(mult(X, Y), mult(Z, Y)), mult(Y, Y))
% 0.20/0.56 = { by axiom 3 (f07) R->L }
% 0.20/0.56 rd(mult(mult(X, Z), mult(Y, Y)), mult(Y, Y))
% 0.20/0.56 = { by axiom 1 (f04) }
% 0.20/0.56 mult(X, Z)
% 0.20/0.56
% 0.20/0.56 Lemma 6: rd(mult(X, mult(Y, Z)), mult(Z, Z)) = mult(rd(X, Z), Y).
% 0.20/0.56 Proof:
% 0.20/0.56 rd(mult(X, mult(Y, Z)), mult(Z, Z))
% 0.20/0.56 = { by axiom 2 (f03) R->L }
% 0.20/0.56 rd(mult(mult(rd(X, Z), Z), mult(Y, Z)), mult(Z, Z))
% 0.20/0.56 = { by lemma 5 }
% 0.20/0.56 mult(rd(X, Z), Y)
% 0.20/0.56
% 0.20/0.56 Lemma 7: rd(mult(X, mult(Y, Y)), mult(Z, Y)) = mult(rd(X, Z), Y).
% 0.20/0.56 Proof:
% 0.20/0.56 rd(mult(X, mult(Y, Y)), mult(Z, Y))
% 0.20/0.56 = { by axiom 2 (f03) R->L }
% 0.20/0.57 rd(mult(mult(rd(X, Z), Z), mult(Y, Y)), mult(Z, Y))
% 0.20/0.57 = { by axiom 3 (f07) }
% 0.20/0.57 rd(mult(mult(rd(X, Z), Y), mult(Z, Y)), mult(Z, Y))
% 0.20/0.57 = { by axiom 1 (f04) }
% 0.20/0.57 mult(rd(X, Z), Y)
% 0.20/0.57
% 0.20/0.57 Lemma 8: rd(mult(X, mult(Y, X)), mult(Z, X)) = mult(rd(X, Z), Y).
% 0.20/0.57 Proof:
% 0.20/0.57 rd(mult(X, mult(Y, X)), mult(Z, X))
% 0.20/0.57 = { by axiom 1 (f04) R->L }
% 0.20/0.57 rd(mult(rd(mult(X, mult(Y, X)), mult(Z, X)), mult(X, X)), mult(X, X))
% 0.20/0.57 = { by lemma 6 R->L }
% 0.20/0.57 rd(rd(mult(mult(X, mult(Y, X)), mult(mult(X, X), mult(Z, X))), mult(mult(Z, X), mult(Z, X))), mult(X, X))
% 0.20/0.57 = { by axiom 4 (f05) R->L }
% 0.20/0.57 rd(rd(mult(mult(X, mult(X, X)), mult(mult(Y, X), mult(Z, X))), mult(mult(Z, X), mult(Z, X))), mult(X, X))
% 0.20/0.57 = { by lemma 6 }
% 0.20/0.57 rd(mult(rd(mult(X, mult(X, X)), mult(Z, X)), mult(Y, X)), mult(X, X))
% 0.20/0.57 = { by lemma 7 }
% 0.20/0.57 rd(mult(mult(rd(X, Z), X), mult(Y, X)), mult(X, X))
% 0.20/0.57 = { by axiom 2 (f03) R->L }
% 0.20/0.57 rd(mult(mult(rd(X, Z), X), mult(rd(mult(Y, X), X), X)), mult(X, X))
% 0.20/0.57 = { by lemma 5 }
% 0.20/0.57 mult(rd(X, Z), rd(mult(Y, X), X))
% 0.20/0.57 = { by axiom 1 (f04) }
% 0.20/0.57 mult(rd(X, Z), Y)
% 0.20/0.57
% 0.20/0.57 Goal 1 (goals): mult(a, mult(b, c)) = mult(mult(rd(a, a), b), mult(a, c)).
% 0.20/0.57 Proof:
% 0.20/0.57 mult(a, mult(b, c))
% 0.20/0.57 = { by axiom 2 (f03) R->L }
% 0.20/0.57 mult(rd(mult(a, mult(b, c)), mult(a, c)), mult(a, c))
% 0.20/0.57 = { by axiom 2 (f03) R->L }
% 0.20/0.57 mult(rd(mult(mult(rd(a, c), c), mult(b, c)), mult(a, c)), mult(a, c))
% 0.20/0.57 = { by axiom 3 (f07) R->L }
% 0.20/0.57 mult(rd(mult(mult(rd(a, c), b), mult(c, c)), mult(a, c)), mult(a, c))
% 0.20/0.57 = { by lemma 7 }
% 0.20/0.57 mult(mult(rd(mult(rd(a, c), b), a), c), mult(a, c))
% 0.20/0.57 = { by lemma 6 R->L }
% 0.20/0.57 mult(rd(mult(mult(rd(a, c), b), mult(c, a)), mult(a, a)), mult(a, c))
% 0.20/0.57 = { by lemma 8 R->L }
% 0.20/0.57 mult(rd(mult(rd(mult(a, mult(b, a)), mult(c, a)), mult(c, a)), mult(a, a)), mult(a, c))
% 0.20/0.57 = { by axiom 2 (f03) }
% 0.20/0.57 mult(rd(mult(a, mult(b, a)), mult(a, a)), mult(a, c))
% 0.20/0.57 = { by lemma 8 }
% 0.20/0.57 mult(mult(rd(a, a), b), mult(a, c))
% 0.20/0.57 % SZS output end Proof
% 0.20/0.57
% 0.20/0.57 RESULT: Unsatisfiable (the axioms are contradictory).
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