TSTP Solution File: GRP754-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP754-1 : 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 : n027.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 7.39s 1.31s
% Output : Proof 7.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.14 % Problem : GRP754-1 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.14 % 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 : n027.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 : Tue Aug 29 02:06:22 EDT 2023
% 0.12/0.34 % CPUTime :
% 7.39/1.31 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 7.39/1.31
% 7.39/1.31 % SZS status Unsatisfiable
% 7.39/1.31
% 7.39/1.32 % SZS output start Proof
% 7.39/1.32 Axiom 1 (f01): mult(X, ld(X, Y)) = Y.
% 7.39/1.32 Axiom 2 (f03): mult(rd(X, Y), Y) = X.
% 7.39/1.32 Axiom 3 (f02): ld(X, mult(X, Y)) = Y.
% 7.39/1.32 Axiom 4 (f04): rd(mult(X, Y), Y) = X.
% 7.39/1.32 Axiom 5 (f06): mult(mult(X, Y), Z) = mult(mult(X, Z), mult(Y, ld(Z, Z))).
% 7.39/1.32 Axiom 6 (f05): mult(X, mult(Y, Z)) = mult(mult(rd(X, X), Y), mult(X, Z)).
% 7.39/1.32
% 7.39/1.32 Lemma 7: ld(rd(X, Y), X) = Y.
% 7.39/1.32 Proof:
% 7.39/1.32 ld(rd(X, Y), X)
% 7.39/1.32 = { by axiom 2 (f03) R->L }
% 7.39/1.32 ld(rd(X, Y), mult(rd(X, Y), Y))
% 7.39/1.32 = { by axiom 3 (f02) }
% 7.39/1.32 Y
% 7.39/1.32
% 7.39/1.32 Lemma 8: rd(X, ld(Y, X)) = Y.
% 7.39/1.32 Proof:
% 7.39/1.32 rd(X, ld(Y, X))
% 7.39/1.32 = { by axiom 1 (f01) R->L }
% 7.39/1.32 rd(mult(Y, ld(Y, X)), ld(Y, X))
% 7.39/1.32 = { by axiom 4 (f04) }
% 7.39/1.32 Y
% 7.39/1.32
% 7.39/1.32 Lemma 9: ld(mult(X, Y), mult(Z, Y)) = mult(ld(X, Z), ld(Y, Y)).
% 7.39/1.32 Proof:
% 7.39/1.32 ld(mult(X, Y), mult(Z, Y))
% 7.39/1.32 = { by axiom 1 (f01) R->L }
% 7.39/1.33 ld(mult(X, Y), mult(mult(X, ld(X, Z)), Y))
% 7.39/1.33 = { by axiom 5 (f06) }
% 7.39/1.33 ld(mult(X, Y), mult(mult(X, Y), mult(ld(X, Z), ld(Y, Y))))
% 7.39/1.33 = { by axiom 3 (f02) }
% 7.39/1.33 mult(ld(X, Z), ld(Y, Y))
% 7.39/1.33
% 7.39/1.33 Lemma 10: rd(mult(X, Y), mult(X, Z)) = mult(rd(X, X), rd(Y, Z)).
% 7.39/1.33 Proof:
% 7.39/1.33 rd(mult(X, Y), mult(X, Z))
% 7.39/1.33 = { by axiom 2 (f03) R->L }
% 7.39/1.33 rd(mult(X, mult(rd(Y, Z), Z)), mult(X, Z))
% 7.39/1.33 = { by axiom 6 (f05) }
% 7.39/1.33 rd(mult(mult(rd(X, X), rd(Y, Z)), mult(X, Z)), mult(X, Z))
% 7.39/1.33 = { by axiom 4 (f04) }
% 7.39/1.33 mult(rd(X, X), rd(Y, Z))
% 7.39/1.33
% 7.39/1.33 Goal 1 (goals): mult(mult(a, a), mult(b, c)) = mult(mult(a, b), mult(a, c)).
% 7.39/1.33 Proof:
% 7.39/1.33 mult(mult(a, a), mult(b, c))
% 7.39/1.33 = { by axiom 1 (f01) R->L }
% 7.39/1.33 mult(mult(a, a), mult(a, ld(a, mult(b, c))))
% 7.39/1.33 = { by axiom 3 (f02) R->L }
% 7.39/1.33 mult(mult(a, a), mult(a, ld(mult(a, c), mult(mult(a, c), ld(a, mult(b, c))))))
% 7.39/1.33 = { by axiom 3 (f02) R->L }
% 7.39/1.33 mult(mult(a, a), mult(a, ld(mult(a, c), ld(a, mult(a, mult(mult(a, c), ld(a, mult(b, c))))))))
% 7.39/1.33 = { by lemma 7 R->L }
% 7.39/1.33 mult(mult(a, a), ld(rd(mult(a, mult(mult(a, c), ld(a, mult(b, c)))), mult(a, ld(mult(a, c), ld(a, mult(a, mult(mult(a, c), ld(a, mult(b, c)))))))), mult(a, mult(mult(a, c), ld(a, mult(b, c))))))
% 7.39/1.33 = { by axiom 1 (f01) R->L }
% 7.39/1.33 mult(mult(a, a), ld(rd(mult(a, ld(a, mult(a, mult(mult(a, c), ld(a, mult(b, c)))))), mult(a, ld(mult(a, c), ld(a, mult(a, mult(mult(a, c), ld(a, mult(b, c)))))))), mult(a, mult(mult(a, c), ld(a, mult(b, c))))))
% 7.39/1.33 = { by lemma 10 }
% 7.39/1.33 mult(mult(a, a), ld(mult(rd(a, a), rd(ld(a, mult(a, mult(mult(a, c), ld(a, mult(b, c))))), ld(mult(a, c), ld(a, mult(a, mult(mult(a, c), ld(a, mult(b, c)))))))), mult(a, mult(mult(a, c), ld(a, mult(b, c))))))
% 7.39/1.33 = { by lemma 8 }
% 7.39/1.33 mult(mult(a, a), ld(mult(rd(a, a), mult(a, c)), mult(a, mult(mult(a, c), ld(a, mult(b, c))))))
% 7.39/1.33 = { by axiom 4 (f04) R->L }
% 7.39/1.33 mult(mult(a, a), ld(mult(rd(mult(rd(a, a), rd(mult(mult(a, c), ld(a, mult(b, c))), c)), rd(mult(mult(a, c), ld(a, mult(b, c))), c)), mult(a, c)), mult(a, mult(mult(a, c), ld(a, mult(b, c))))))
% 7.39/1.33 = { by lemma 10 R->L }
% 7.39/1.33 mult(mult(a, a), ld(mult(rd(rd(mult(a, mult(mult(a, c), ld(a, mult(b, c)))), mult(a, c)), rd(mult(mult(a, c), ld(a, mult(b, c))), c)), mult(a, c)), mult(a, mult(mult(a, c), ld(a, mult(b, c))))))
% 7.39/1.33 = { by axiom 2 (f03) R->L }
% 7.39/1.33 mult(mult(a, a), ld(mult(rd(rd(mult(a, mult(mult(a, c), ld(a, mult(b, c)))), mult(a, c)), rd(mult(mult(a, c), ld(a, mult(b, c))), c)), mult(a, c)), mult(rd(mult(a, mult(mult(a, c), ld(a, mult(b, c)))), mult(a, c)), mult(a, c))))
% 7.39/1.33 = { by lemma 9 }
% 7.39/1.33 mult(mult(a, a), mult(ld(rd(rd(mult(a, mult(mult(a, c), ld(a, mult(b, c)))), mult(a, c)), rd(mult(mult(a, c), ld(a, mult(b, c))), c)), rd(mult(a, mult(mult(a, c), ld(a, mult(b, c)))), mult(a, c))), ld(mult(a, c), mult(a, c))))
% 7.39/1.33 = { by lemma 7 }
% 7.39/1.33 mult(mult(a, a), mult(rd(mult(mult(a, c), ld(a, mult(b, c))), c), ld(mult(a, c), mult(a, c))))
% 7.39/1.33 = { by axiom 2 (f03) R->L }
% 7.39/1.33 mult(mult(a, a), mult(rd(mult(mult(a, c), ld(mult(rd(a, c), c), mult(b, c))), c), ld(mult(a, c), mult(a, c))))
% 7.39/1.33 = { by lemma 9 }
% 7.39/1.33 mult(mult(a, a), mult(rd(mult(mult(a, c), mult(ld(rd(a, c), b), ld(c, c))), c), ld(mult(a, c), mult(a, c))))
% 7.39/1.33 = { by axiom 5 (f06) R->L }
% 7.39/1.33 mult(mult(a, a), mult(rd(mult(mult(a, ld(rd(a, c), b)), c), c), ld(mult(a, c), mult(a, c))))
% 7.39/1.33 = { by lemma 7 R->L }
% 7.39/1.33 mult(mult(a, a), mult(rd(mult(ld(rd(mult(a, b), mult(a, ld(rd(a, c), b))), mult(a, b)), c), c), ld(mult(a, c), mult(a, c))))
% 7.39/1.33 = { by lemma 10 }
% 7.39/1.33 mult(mult(a, a), mult(rd(mult(ld(mult(rd(a, a), rd(b, ld(rd(a, c), b))), mult(a, b)), c), c), ld(mult(a, c), mult(a, c))))
% 7.39/1.33 = { by lemma 8 }
% 7.39/1.33 mult(mult(a, a), mult(rd(mult(ld(mult(rd(a, a), rd(a, c)), mult(a, b)), c), c), ld(mult(a, c), mult(a, c))))
% 7.39/1.33 = { by lemma 10 R->L }
% 7.39/1.33 mult(mult(a, a), mult(rd(mult(ld(rd(mult(a, a), mult(a, c)), mult(a, b)), c), c), ld(mult(a, c), mult(a, c))))
% 7.39/1.33 = { by axiom 4 (f04) }
% 7.39/1.33 mult(mult(a, a), mult(ld(rd(mult(a, a), mult(a, c)), mult(a, b)), ld(mult(a, c), mult(a, c))))
% 7.39/1.33 = { by lemma 9 R->L }
% 7.39/1.33 mult(mult(a, a), ld(mult(rd(mult(a, a), mult(a, c)), mult(a, c)), mult(mult(a, b), mult(a, c))))
% 7.39/1.33 = { by axiom 2 (f03) }
% 7.39/1.33 mult(mult(a, a), ld(mult(a, a), mult(mult(a, b), mult(a, c))))
% 7.39/1.33 = { by axiom 1 (f01) }
% 7.39/1.33 mult(mult(a, b), mult(a, c))
% 7.39/1.33 % SZS output end Proof
% 7.39/1.33
% 7.39/1.33 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------