TSTP Solution File: GRP685-10 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP685-10 : 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 : n021.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 01:19:42 EDT 2023
% Result : Unsatisfiable 0.21s 0.58s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : GRP685-10 : TPTP v8.1.2. Released v8.1.0.
% 0.07/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.37 % Computer : n021.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Tue Aug 29 01:18:13 EDT 2023
% 0.14/0.37 % CPUTime :
% 0.21/0.58 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.21/0.58
% 0.21/0.58 % SZS status Unsatisfiable
% 0.21/0.58
% 0.21/0.59 % SZS output start Proof
% 0.21/0.59 Axiom 1 (f01): ld(X, mult(X, X)) = X.
% 0.21/0.59 Axiom 2 (f03): mult(X, ld(X, Y)) = ld(X, mult(X, Y)).
% 0.21/0.59 Axiom 3 (f02): rd(mult(X, X), X) = X.
% 0.21/0.59 Axiom 4 (f04): mult(rd(X, Y), Y) = rd(mult(X, Y), Y).
% 0.21/0.59 Axiom 5 (f05): ld(ld(X, Y), mult(ld(X, Y), mult(Z, W))) = mult(ld(X, mult(X, Z)), W).
% 0.21/0.59 Axiom 6 (f06): rd(mult(mult(X, Y), rd(Z, W)), rd(Z, W)) = mult(X, rd(mult(Y, W), W)).
% 0.21/0.59
% 0.21/0.59 Lemma 7: mult(X, ld(X, X)) = X.
% 0.21/0.59 Proof:
% 0.21/0.59 mult(X, ld(X, X))
% 0.21/0.59 = { by axiom 2 (f03) }
% 0.21/0.59 ld(X, mult(X, X))
% 0.21/0.59 = { by axiom 1 (f01) }
% 0.21/0.59 X
% 0.21/0.59
% 0.21/0.59 Lemma 8: mult(rd(X, X), X) = X.
% 0.21/0.59 Proof:
% 0.21/0.59 mult(rd(X, X), X)
% 0.21/0.59 = { by axiom 4 (f04) }
% 0.21/0.59 rd(mult(X, X), X)
% 0.21/0.59 = { by axiom 3 (f02) }
% 0.21/0.59 X
% 0.21/0.59
% 0.21/0.59 Lemma 9: mult(X, mult(X, ld(X, Y))) = mult(X, Y).
% 0.21/0.59 Proof:
% 0.21/0.59 mult(X, mult(X, ld(X, Y)))
% 0.21/0.59 = { by axiom 2 (f03) }
% 0.21/0.59 mult(X, ld(X, mult(X, Y)))
% 0.21/0.59 = { by axiom 1 (f01) R->L }
% 0.21/0.59 mult(X, ld(ld(X, mult(X, X)), mult(X, Y)))
% 0.21/0.59 = { by axiom 1 (f01) R->L }
% 0.21/0.59 mult(ld(X, mult(X, X)), ld(ld(X, mult(X, X)), mult(X, Y)))
% 0.21/0.59 = { by axiom 2 (f03) }
% 0.21/0.59 ld(ld(X, mult(X, X)), mult(ld(X, mult(X, X)), mult(X, Y)))
% 0.21/0.59 = { by axiom 5 (f05) }
% 0.21/0.59 mult(ld(X, mult(X, X)), Y)
% 0.21/0.59 = { by axiom 2 (f03) R->L }
% 0.21/0.59 mult(mult(X, ld(X, X)), Y)
% 0.21/0.59 = { by lemma 7 }
% 0.21/0.59 mult(X, Y)
% 0.21/0.59
% 0.21/0.59 Lemma 10: mult(rd(mult(X, Y), rd(Z, W)), rd(Z, W)) = mult(X, mult(rd(Y, W), W)).
% 0.21/0.59 Proof:
% 0.21/0.59 mult(rd(mult(X, Y), rd(Z, W)), rd(Z, W))
% 0.21/0.59 = { by axiom 4 (f04) }
% 0.21/0.59 rd(mult(mult(X, Y), rd(Z, W)), rd(Z, W))
% 0.21/0.59 = { by axiom 6 (f06) }
% 0.21/0.59 mult(X, rd(mult(Y, W), W))
% 0.21/0.59 = { by axiom 4 (f04) R->L }
% 0.21/0.59 mult(X, mult(rd(Y, W), W))
% 0.21/0.59
% 0.21/0.59 Lemma 11: mult(rd(mult(X, Y), Z), Z) = mult(X, mult(rd(Y, Z), Z)).
% 0.21/0.59 Proof:
% 0.21/0.59 mult(rd(mult(X, Y), Z), Z)
% 0.21/0.59 = { by axiom 3 (f02) R->L }
% 0.21/0.59 mult(rd(mult(X, Y), Z), rd(mult(Z, Z), Z))
% 0.21/0.59 = { by axiom 3 (f02) R->L }
% 0.21/0.59 mult(rd(mult(X, Y), rd(mult(Z, Z), Z)), rd(mult(Z, Z), Z))
% 0.21/0.59 = { by lemma 10 }
% 0.21/0.59 mult(X, mult(rd(Y, Z), Z))
% 0.21/0.59
% 0.21/0.59 Lemma 12: mult(X, mult(rd(ld(X, X), Y), Y)) = mult(rd(X, Y), Y).
% 0.21/0.59 Proof:
% 0.21/0.59 mult(X, mult(rd(ld(X, X), Y), Y))
% 0.21/0.59 = { by lemma 11 R->L }
% 0.21/0.59 mult(rd(mult(X, ld(X, X)), Y), Y)
% 0.21/0.59 = { by lemma 7 }
% 0.21/0.59 mult(rd(X, Y), Y)
% 0.21/0.59
% 0.21/0.59 Lemma 13: mult(rd(X, mult(Y, Z)), mult(Y, Z)) = mult(rd(X, Z), Z).
% 0.21/0.59 Proof:
% 0.21/0.59 mult(rd(X, mult(Y, Z)), mult(Y, Z))
% 0.21/0.59 = { by lemma 12 R->L }
% 0.21/0.59 mult(X, mult(rd(ld(X, X), mult(Y, Z)), mult(Y, Z)))
% 0.21/0.59 = { by lemma 8 R->L }
% 0.21/0.59 mult(X, mult(rd(ld(X, X), mult(Y, Z)), mult(Y, mult(rd(Z, Z), Z))))
% 0.21/0.59 = { by lemma 11 R->L }
% 0.21/0.59 mult(X, mult(rd(ld(X, X), mult(Y, Z)), mult(rd(mult(Y, Z), Z), Z)))
% 0.21/0.59 = { by lemma 8 R->L }
% 0.21/0.59 mult(X, mult(rd(ld(X, X), mult(Y, mult(rd(Z, Z), Z))), mult(rd(mult(Y, Z), Z), Z)))
% 0.21/0.59 = { by lemma 11 R->L }
% 0.21/0.59 mult(X, mult(rd(ld(X, X), mult(rd(mult(Y, Z), Z), Z)), mult(rd(mult(Y, Z), Z), Z)))
% 0.21/0.59 = { by lemma 11 R->L }
% 0.21/0.59 mult(rd(mult(X, ld(X, X)), mult(rd(mult(Y, Z), Z), Z)), mult(rd(mult(Y, Z), Z), Z))
% 0.21/0.59 = { by axiom 4 (f04) }
% 0.21/0.59 mult(rd(mult(X, ld(X, X)), mult(rd(mult(Y, Z), Z), Z)), rd(mult(mult(Y, Z), Z), Z))
% 0.21/0.59 = { by axiom 4 (f04) }
% 0.21/0.59 mult(rd(mult(X, ld(X, X)), rd(mult(mult(Y, Z), Z), Z)), rd(mult(mult(Y, Z), Z), Z))
% 0.21/0.59 = { by lemma 10 }
% 0.21/0.59 mult(X, mult(rd(ld(X, X), Z), Z))
% 0.21/0.59 = { by lemma 12 }
% 0.21/0.59 mult(rd(X, Z), Z)
% 0.21/0.59
% 0.21/0.59 Goal 1 (goal): rd(mult(x6, ld(x7, x8)), ld(x7, x8)) = rd(mult(x6, x8), x8).
% 0.21/0.59 Proof:
% 0.21/0.59 rd(mult(x6, ld(x7, x8)), ld(x7, x8))
% 0.21/0.59 = { by axiom 4 (f04) R->L }
% 0.21/0.59 mult(rd(x6, ld(x7, x8)), ld(x7, x8))
% 0.21/0.59 = { by lemma 13 R->L }
% 0.21/0.59 mult(rd(x6, mult(x7, ld(x7, x8))), mult(x7, ld(x7, x8)))
% 0.21/0.59 = { by lemma 13 R->L }
% 0.21/0.59 mult(rd(x6, mult(x7, mult(x7, ld(x7, x8)))), mult(x7, mult(x7, ld(x7, x8))))
% 0.21/0.59 = { by lemma 9 }
% 0.21/0.59 mult(rd(x6, mult(x7, x8)), mult(x7, mult(x7, ld(x7, x8))))
% 0.21/0.59 = { by lemma 9 }
% 0.21/0.59 mult(rd(x6, mult(x7, x8)), mult(x7, x8))
% 0.21/0.59 = { by lemma 13 }
% 0.21/0.59 mult(rd(x6, x8), x8)
% 0.21/0.59 = { by axiom 4 (f04) }
% 0.21/0.59 rd(mult(x6, x8), x8)
% 0.21/0.59 % SZS output end Proof
% 0.21/0.59
% 0.21/0.59 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------