TSTP Solution File: GRP753-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP753-1 : 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 : n005.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 23.24s 3.34s
% Output : Proof 23.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP753-1 : 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
% 0.14/0.34 % Computer : n005.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 29 02:22:08 EDT 2023
% 0.14/0.34 % CPUTime :
% 23.24/3.34 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 23.24/3.34
% 23.24/3.34 % SZS status Unsatisfiable
% 23.24/3.34
% 23.24/3.36 % SZS output start Proof
% 23.24/3.36 Axiom 1 (f01): mult(X, ld(X, Y)) = Y.
% 23.24/3.36 Axiom 2 (f03): mult(rd(X, Y), Y) = X.
% 23.24/3.36 Axiom 3 (f02): ld(X, mult(X, Y)) = Y.
% 23.24/3.36 Axiom 4 (f04): rd(mult(X, Y), Y) = X.
% 23.24/3.36 Axiom 5 (f06): mult(mult(X, Y), Z) = mult(mult(X, Z), mult(Y, ld(Z, Z))).
% 23.24/3.36 Axiom 6 (f05): mult(X, mult(Y, Z)) = mult(mult(rd(X, X), Y), mult(X, Z)).
% 23.24/3.36
% 23.24/3.36 Lemma 7: ld(mult(X, Y), mult(mult(X, Z), Y)) = mult(Z, ld(Y, Y)).
% 23.24/3.36 Proof:
% 23.24/3.36 ld(mult(X, Y), mult(mult(X, Z), Y))
% 23.24/3.36 = { by axiom 5 (f06) }
% 23.24/3.36 ld(mult(X, Y), mult(mult(X, Y), mult(Z, ld(Y, Y))))
% 23.24/3.36 = { by axiom 3 (f02) }
% 23.24/3.36 mult(Z, ld(Y, Y))
% 23.24/3.36
% 23.24/3.36 Lemma 8: ld(mult(X, Z), mult(Y, Z)) = mult(ld(X, Y), ld(Z, Z)).
% 23.24/3.36 Proof:
% 23.24/3.36 ld(mult(X, Z), mult(Y, Z))
% 23.24/3.36 = { by axiom 1 (f01) R->L }
% 23.24/3.36 ld(mult(X, Z), mult(mult(X, ld(X, Y)), Z))
% 23.24/3.36 = { by lemma 7 }
% 23.24/3.36 mult(ld(X, Y), ld(Z, Z))
% 23.24/3.36
% 23.24/3.36 Lemma 9: mult(mult(rd(X, X), Y), Z) = mult(X, mult(Y, ld(X, Z))).
% 23.24/3.36 Proof:
% 23.24/3.36 mult(mult(rd(X, X), Y), Z)
% 23.24/3.36 = { by axiom 1 (f01) R->L }
% 23.24/3.36 mult(mult(rd(X, X), Y), mult(X, ld(X, Z)))
% 23.24/3.36 = { by axiom 6 (f05) R->L }
% 23.24/3.36 mult(X, mult(Y, ld(X, Z)))
% 23.24/3.36
% 23.24/3.36 Lemma 10: mult(mult(X, mult(Y, Z)), mult(X, mult(W, ld(Z, Z)))) = mult(mult(X, mult(Y, W)), mult(X, Z)).
% 23.24/3.36 Proof:
% 23.24/3.36 mult(mult(X, mult(Y, Z)), mult(X, mult(W, ld(Z, Z))))
% 23.24/3.36 = { by axiom 6 (f05) }
% 23.24/3.36 mult(mult(mult(rd(X, X), Y), mult(X, Z)), mult(X, mult(W, ld(Z, Z))))
% 23.24/3.36 = { by lemma 7 R->L }
% 23.24/3.36 mult(mult(mult(rd(X, X), Y), mult(X, Z)), mult(X, ld(mult(X, Z), mult(mult(X, W), Z))))
% 23.24/3.36 = { by axiom 3 (f02) R->L }
% 23.24/3.36 mult(mult(mult(rd(X, X), Y), mult(X, Z)), mult(X, ld(mult(X, Z), mult(mult(X, W), ld(X, mult(X, Z))))))
% 23.24/3.36 = { by axiom 3 (f02) R->L }
% 23.24/3.36 mult(mult(mult(rd(X, X), Y), mult(X, Z)), mult(X, ld(mult(X, Z), ld(X, mult(X, mult(mult(X, W), ld(X, mult(X, Z))))))))
% 23.24/3.36 = { by lemma 9 R->L }
% 23.24/3.36 mult(mult(mult(rd(X, X), Y), mult(X, Z)), mult(X, ld(mult(X, Z), ld(X, mult(mult(rd(X, X), mult(X, W)), mult(X, Z))))))
% 23.24/3.36 = { by axiom 5 (f06) }
% 23.24/3.36 mult(mult(mult(rd(X, X), Y), mult(X, Z)), mult(X, ld(mult(X, Z), ld(X, mult(mult(rd(X, X), mult(X, Z)), mult(mult(X, W), ld(mult(X, Z), mult(X, Z))))))))
% 23.24/3.36 = { by lemma 9 }
% 23.24/3.36 mult(mult(mult(rd(X, X), Y), mult(X, Z)), mult(X, ld(mult(X, Z), ld(X, mult(X, mult(mult(X, Z), ld(X, mult(mult(X, W), ld(mult(X, Z), mult(X, Z))))))))))
% 23.24/3.36 = { by axiom 3 (f02) }
% 23.24/3.36 mult(mult(mult(rd(X, X), Y), mult(X, Z)), mult(X, ld(mult(X, Z), mult(mult(X, Z), ld(X, mult(mult(X, W), ld(mult(X, Z), mult(X, Z))))))))
% 23.24/3.36 = { by axiom 3 (f02) }
% 23.24/3.36 mult(mult(mult(rd(X, X), Y), mult(X, Z)), mult(X, ld(X, mult(mult(X, W), ld(mult(X, Z), mult(X, Z))))))
% 23.24/3.36 = { by axiom 1 (f01) }
% 23.24/3.36 mult(mult(mult(rd(X, X), Y), mult(X, Z)), mult(mult(X, W), ld(mult(X, Z), mult(X, Z))))
% 23.24/3.36 = { by axiom 5 (f06) R->L }
% 23.24/3.36 mult(mult(mult(rd(X, X), Y), mult(X, W)), mult(X, Z))
% 23.24/3.36 = { by axiom 6 (f05) R->L }
% 23.24/3.36 mult(mult(X, mult(Y, W)), mult(X, Z))
% 23.24/3.36
% 23.24/3.36 Lemma 11: mult(mult(X, Y), mult(X, Z)) = mult(mult(X, X), mult(Y, Z)).
% 23.24/3.36 Proof:
% 23.24/3.36 mult(mult(X, Y), mult(X, Z))
% 23.24/3.36 = { by axiom 1 (f01) R->L }
% 23.24/3.36 mult(mult(X, mult(Y, ld(Y, Y))), mult(X, Z))
% 23.24/3.36 = { by lemma 10 R->L }
% 23.24/3.36 mult(mult(X, mult(Y, Z)), mult(X, mult(ld(Y, Y), ld(Z, Z))))
% 23.24/3.36 = { by lemma 8 R->L }
% 23.24/3.36 mult(mult(X, mult(Y, Z)), mult(X, ld(mult(Y, Z), mult(Y, Z))))
% 23.24/3.36 = { by axiom 5 (f06) R->L }
% 23.24/3.36 mult(mult(X, X), mult(Y, Z))
% 23.24/3.36
% 23.24/3.36 Lemma 12: rd(mult(X, Y), mult(X, Z)) = mult(rd(X, X), rd(Y, Z)).
% 23.24/3.36 Proof:
% 23.24/3.36 rd(mult(X, Y), mult(X, Z))
% 23.24/3.36 = { by axiom 2 (f03) R->L }
% 23.24/3.36 rd(mult(X, mult(rd(Y, Z), Z)), mult(X, Z))
% 23.24/3.36 = { by axiom 6 (f05) }
% 23.24/3.36 rd(mult(mult(rd(X, X), rd(Y, Z)), mult(X, Z)), mult(X, Z))
% 23.24/3.36 = { by axiom 4 (f04) }
% 23.24/3.36 mult(rd(X, X), rd(Y, Z))
% 23.24/3.36
% 23.24/3.36 Lemma 13: mult(mult(X, mult(rd(Y, Y), Z)), mult(mult(X, Y), W)) = mult(mult(X, Y), mult(mult(X, Z), W)).
% 23.24/3.36 Proof:
% 23.24/3.36 mult(mult(X, mult(rd(Y, Y), Z)), mult(mult(X, Y), W))
% 23.24/3.36 = { by axiom 6 (f05) }
% 23.24/3.36 mult(mult(mult(rd(X, X), rd(Y, Y)), mult(X, Z)), mult(mult(X, Y), W))
% 23.24/3.36 = { by lemma 12 R->L }
% 23.24/3.36 mult(mult(rd(mult(X, Y), mult(X, Y)), mult(X, Z)), mult(mult(X, Y), W))
% 23.24/3.36 = { by axiom 6 (f05) R->L }
% 23.24/3.36 mult(mult(X, Y), mult(mult(X, Z), W))
% 23.24/3.36
% 23.24/3.36 Lemma 14: mult(mult(mult(X, X), mult(Y, Z)), mult(W, mult(X, ld(Z, Z)))) = mult(mult(mult(X, Y), W), mult(mult(X, X), Z)).
% 23.24/3.36 Proof:
% 23.24/3.36 mult(mult(mult(X, X), mult(Y, Z)), mult(W, mult(X, ld(Z, Z))))
% 23.24/3.36 = { by axiom 1 (f01) R->L }
% 23.24/3.36 mult(mult(mult(X, X), mult(Y, Z)), mult(mult(X, ld(X, W)), mult(X, ld(Z, Z))))
% 23.24/3.36 = { by lemma 11 }
% 23.24/3.36 mult(mult(mult(X, X), mult(Y, Z)), mult(mult(X, X), mult(ld(X, W), ld(Z, Z))))
% 23.24/3.36 = { by lemma 11 }
% 23.24/3.36 mult(mult(mult(X, X), mult(X, X)), mult(mult(Y, Z), mult(ld(X, W), ld(Z, Z))))
% 23.24/3.36 = { by axiom 5 (f06) R->L }
% 23.24/3.36 mult(mult(mult(X, X), mult(X, X)), mult(mult(Y, ld(X, W)), Z))
% 23.24/3.36 = { by lemma 11 R->L }
% 23.24/3.36 mult(mult(mult(X, X), mult(Y, ld(X, W))), mult(mult(X, X), Z))
% 23.24/3.36 = { by lemma 11 R->L }
% 23.24/3.36 mult(mult(mult(X, Y), mult(X, ld(X, W))), mult(mult(X, X), Z))
% 23.24/3.36 = { by axiom 1 (f01) }
% 23.24/3.36 mult(mult(mult(X, Y), W), mult(mult(X, X), Z))
% 23.24/3.36
% 23.24/3.36 Goal 1 (goals): mult(mult(a, mult(a, a)), mult(b, c)) = mult(mult(a, b), mult(mult(a, a), c)).
% 23.24/3.36 Proof:
% 23.24/3.36 mult(mult(a, mult(a, a)), mult(b, c))
% 23.24/3.36 = { by axiom 4 (f04) R->L }
% 23.24/3.36 rd(mult(mult(mult(a, mult(a, a)), mult(b, c)), mult(mult(a, a), c)), mult(mult(a, a), c))
% 23.24/3.36 = { by axiom 1 (f01) R->L }
% 23.24/3.36 rd(mult(mult(mult(a, mult(a, a)), mult(mult(a, a), ld(mult(a, a), mult(b, c)))), mult(mult(a, a), c)), mult(mult(a, a), c))
% 23.24/3.36 = { by axiom 2 (f03) R->L }
% 23.24/3.36 rd(mult(mult(mult(a, mult(a, a)), mult(mult(a, a), mult(rd(ld(mult(a, a), mult(b, c)), ld(mult(a, a), mult(b, c))), ld(mult(a, a), mult(b, c))))), mult(mult(a, a), c)), mult(mult(a, a), c))
% 23.24/3.36 = { by lemma 11 R->L }
% 23.24/3.36 rd(mult(mult(mult(a, mult(a, a)), mult(mult(a, rd(ld(mult(a, a), mult(b, c)), ld(mult(a, a), mult(b, c)))), mult(a, ld(mult(a, a), mult(b, c))))), mult(mult(a, a), c)), mult(mult(a, a), c))
% 23.24/3.37 = { by lemma 13 R->L }
% 23.24/3.37 rd(mult(mult(mult(a, mult(rd(mult(a, a), mult(a, a)), rd(ld(mult(a, a), mult(b, c)), ld(mult(a, a), mult(b, c))))), mult(mult(a, mult(a, a)), mult(a, ld(mult(a, a), mult(b, c))))), mult(mult(a, a), c)), mult(mult(a, a), c))
% 23.24/3.37 = { by lemma 12 R->L }
% 23.24/3.37 rd(mult(mult(mult(a, rd(mult(mult(a, a), ld(mult(a, a), mult(b, c))), mult(mult(a, a), ld(mult(a, a), mult(b, c))))), mult(mult(a, mult(a, a)), mult(a, ld(mult(a, a), mult(b, c))))), mult(mult(a, a), c)), mult(mult(a, a), c))
% 23.24/3.37 = { by lemma 11 }
% 23.24/3.37 rd(mult(mult(mult(a, rd(mult(mult(a, a), ld(mult(a, a), mult(b, c))), mult(mult(a, a), ld(mult(a, a), mult(b, c))))), mult(mult(a, a), mult(mult(a, a), ld(mult(a, a), mult(b, c))))), mult(mult(a, a), c)), mult(mult(a, a), c))
% 23.24/3.37 = { by lemma 14 R->L }
% 23.24/3.37 rd(mult(mult(mult(a, a), mult(rd(mult(mult(a, a), ld(mult(a, a), mult(b, c))), mult(mult(a, a), ld(mult(a, a), mult(b, c)))), c)), mult(mult(mult(a, a), mult(mult(a, a), ld(mult(a, a), mult(b, c)))), mult(a, ld(c, c)))), mult(mult(a, a), c))
% 23.24/3.37 = { by lemma 13 }
% 23.24/3.37 rd(mult(mult(mult(a, a), mult(mult(a, a), ld(mult(a, a), mult(b, c)))), mult(mult(mult(a, a), c), mult(a, ld(c, c)))), mult(mult(a, a), c))
% 23.24/3.37 = { by axiom 5 (f06) R->L }
% 23.24/3.37 rd(mult(mult(mult(a, a), mult(mult(a, a), ld(mult(a, a), mult(b, c)))), mult(mult(mult(a, a), a), c)), mult(mult(a, a), c))
% 23.24/3.37 = { by lemma 11 R->L }
% 23.24/3.37 rd(mult(mult(mult(a, mult(a, a)), mult(a, ld(mult(a, a), mult(b, c)))), mult(mult(mult(a, a), a), c)), mult(mult(a, a), c))
% 23.24/3.37 = { by axiom 2 (f03) R->L }
% 23.24/3.37 rd(mult(mult(mult(a, mult(a, a)), mult(a, ld(mult(a, a), mult(rd(mult(b, c), a), a)))), mult(mult(mult(a, a), a), c)), mult(mult(a, a), c))
% 23.24/3.37 = { by lemma 8 }
% 23.24/3.37 rd(mult(mult(mult(a, mult(a, a)), mult(a, mult(ld(a, rd(mult(b, c), a)), ld(a, a)))), mult(mult(mult(a, a), a), c)), mult(mult(a, a), c))
% 23.24/3.37 = { by lemma 10 }
% 23.24/3.37 rd(mult(mult(mult(a, mult(a, ld(a, rd(mult(b, c), a)))), mult(a, a)), mult(mult(mult(a, a), a), c)), mult(mult(a, a), c))
% 23.24/3.37 = { by axiom 1 (f01) }
% 23.24/3.37 rd(mult(mult(mult(a, rd(mult(b, c), a)), mult(a, a)), mult(mult(mult(a, a), a), c)), mult(mult(a, a), c))
% 23.24/3.37 = { by lemma 11 }
% 23.24/3.37 rd(mult(mult(mult(a, a), mult(rd(mult(b, c), a), a)), mult(mult(mult(a, a), a), c)), mult(mult(a, a), c))
% 23.24/3.37 = { by axiom 2 (f03) }
% 23.24/3.37 rd(mult(mult(mult(a, a), mult(b, c)), mult(mult(mult(a, a), a), c)), mult(mult(a, a), c))
% 23.24/3.37 = { by axiom 5 (f06) }
% 23.24/3.37 rd(mult(mult(mult(a, a), mult(b, c)), mult(mult(mult(a, a), c), mult(a, ld(c, c)))), mult(mult(a, a), c))
% 23.24/3.37 = { by lemma 14 }
% 23.24/3.37 rd(mult(mult(mult(a, b), mult(mult(a, a), c)), mult(mult(a, a), c)), mult(mult(a, a), c))
% 23.24/3.37 = { by axiom 4 (f04) }
% 23.24/3.37 mult(mult(a, b), mult(mult(a, a), c))
% 23.24/3.37 % SZS output end Proof
% 23.24/3.37
% 23.24/3.37 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------