TSTP Solution File: GRP683-11 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP683-11 : 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 : n029.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 01:19:41 EDT 2023
% Result : Unsatisfiable 0.19s 0.42s
% 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
% 0.07/0.12 % Problem : GRP683-11 : TPTP v8.1.2. Released v8.1.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.33 % Computer : n029.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 29 00:01:26 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.42 Command-line arguments: --flatten
% 0.19/0.42
% 0.19/0.42 % SZS status Unsatisfiable
% 0.19/0.42
% 0.19/0.45 % SZS output start Proof
% 0.19/0.45 Axiom 1 (f01): ld(X, mult(X, X)) = X.
% 0.19/0.45 Axiom 2 (f02): rd(mult(X, X), X) = X.
% 0.19/0.45 Axiom 3 (f03): mult(X, ld(X, Y)) = ld(X, mult(X, Y)).
% 0.19/0.45 Axiom 4 (f04): mult(rd(X, Y), Y) = rd(mult(X, Y), Y).
% 0.19/0.45 Axiom 5 (f07): ld(X, mult(X, ld(Y, Y))) = rd(mult(rd(X, X), Y), Y).
% 0.19/0.45 Axiom 6 (f05): ld(ld(X, Y), mult(ld(X, Y), mult(Z, W))) = mult(ld(X, mult(X, Z)), W).
% 0.19/0.45 Axiom 7 (f06): rd(mult(mult(X, Y), rd(Z, W)), rd(Z, W)) = mult(X, rd(mult(Y, W), W)).
% 0.19/0.45
% 0.19/0.45 Lemma 8: rd(X, X) = ld(X, X).
% 0.19/0.45 Proof:
% 0.19/0.45 rd(X, X)
% 0.19/0.45 = { by axiom 2 (f02) R->L }
% 0.19/0.45 rd(rd(mult(X, X), X), X)
% 0.19/0.45 = { by axiom 4 (f04) R->L }
% 0.19/0.45 rd(mult(rd(X, X), X), X)
% 0.19/0.45 = { by axiom 5 (f07) R->L }
% 0.19/0.45 ld(X, mult(X, ld(X, X)))
% 0.19/0.45 = { by axiom 3 (f03) }
% 0.19/0.45 ld(X, ld(X, mult(X, X)))
% 0.19/0.45 = { by axiom 1 (f01) }
% 0.19/0.45 ld(X, X)
% 0.19/0.45
% 0.19/0.45 Lemma 9: mult(ld(X, X), X) = X.
% 0.19/0.45 Proof:
% 0.19/0.45 mult(ld(X, X), X)
% 0.19/0.45 = { by lemma 8 R->L }
% 0.19/0.45 mult(rd(X, X), X)
% 0.19/0.45 = { by axiom 4 (f04) }
% 0.19/0.45 rd(mult(X, X), X)
% 0.19/0.45 = { by axiom 2 (f02) }
% 0.19/0.45 X
% 0.19/0.45
% 0.19/0.45 Lemma 10: mult(X, rd(mult(Y, Z), Z)) = rd(mult(mult(X, Y), Z), Z).
% 0.19/0.45 Proof:
% 0.19/0.45 mult(X, rd(mult(Y, Z), Z))
% 0.19/0.45 = { by axiom 7 (f06) R->L }
% 0.19/0.45 rd(mult(mult(X, Y), rd(mult(Z, Z), Z)), rd(mult(Z, Z), Z))
% 0.19/0.45 = { by axiom 2 (f02) }
% 0.19/0.45 rd(mult(mult(X, Y), Z), rd(mult(Z, Z), Z))
% 0.19/0.45 = { by axiom 2 (f02) }
% 0.19/0.45 rd(mult(mult(X, Y), Z), Z)
% 0.19/0.45
% 0.19/0.45 Lemma 11: rd(mult(mult(X, Y), Y), Y) = mult(X, Y).
% 0.19/0.45 Proof:
% 0.19/0.45 rd(mult(mult(X, Y), Y), Y)
% 0.19/0.45 = { by lemma 10 R->L }
% 0.19/0.45 mult(X, rd(mult(Y, Y), Y))
% 0.19/0.45 = { by axiom 2 (f02) }
% 0.19/0.45 mult(X, Y)
% 0.19/0.45
% 0.19/0.45 Lemma 12: mult(ld(X, X), Y) = ld(X, mult(X, Y)).
% 0.19/0.45 Proof:
% 0.19/0.45 mult(ld(X, X), Y)
% 0.19/0.45 = { by lemma 11 R->L }
% 0.19/0.45 rd(mult(mult(ld(X, X), Y), Y), Y)
% 0.19/0.45 = { by axiom 4 (f04) R->L }
% 0.19/0.45 mult(rd(mult(ld(X, X), Y), Y), Y)
% 0.19/0.45 = { by lemma 8 R->L }
% 0.19/0.45 mult(rd(mult(rd(X, X), Y), Y), Y)
% 0.19/0.45 = { by axiom 5 (f07) R->L }
% 0.19/0.45 mult(ld(X, mult(X, ld(Y, Y))), Y)
% 0.19/0.45 = { by axiom 6 (f05) R->L }
% 0.19/0.45 ld(ld(X, mult(X, X)), mult(ld(X, mult(X, X)), mult(ld(Y, Y), Y)))
% 0.19/0.45 = { by axiom 1 (f01) }
% 0.19/0.45 ld(X, mult(ld(X, mult(X, X)), mult(ld(Y, Y), Y)))
% 0.19/0.45 = { by axiom 1 (f01) }
% 0.19/0.45 ld(X, mult(X, mult(ld(Y, Y), Y)))
% 0.19/0.45 = { by lemma 9 }
% 0.19/0.45 ld(X, mult(X, Y))
% 0.19/0.45
% 0.19/0.45 Goal 1 (goal): mult(rd(mult(x3, x4), x4), x5) = mult(x3, x5).
% 0.19/0.45 Proof:
% 0.19/0.45 mult(rd(mult(x3, x4), x4), x5)
% 0.19/0.45 = { by lemma 11 R->L }
% 0.19/0.45 rd(mult(mult(rd(mult(x3, x4), x4), x5), x5), x5)
% 0.19/0.45 = { by axiom 4 (f04) R->L }
% 0.19/0.45 mult(rd(mult(rd(mult(x3, x4), x4), x5), x5), x5)
% 0.19/0.45 = { by lemma 9 R->L }
% 0.19/0.45 mult(rd(mult(rd(mult(mult(ld(x3, x3), x3), x4), x4), x5), x5), x5)
% 0.19/0.45 = { by lemma 10 R->L }
% 0.19/0.45 mult(rd(mult(mult(ld(x3, x3), rd(mult(x3, x4), x4)), x5), x5), x5)
% 0.19/0.45 = { by lemma 10 R->L }
% 0.19/0.45 mult(mult(ld(x3, x3), rd(mult(rd(mult(x3, x4), x4), x5), x5)), x5)
% 0.19/0.45 = { by lemma 12 }
% 0.19/0.45 mult(ld(x3, mult(x3, rd(mult(rd(mult(x3, x4), x4), x5), x5))), x5)
% 0.19/0.45 = { by axiom 7 (f06) R->L }
% 0.19/0.45 mult(ld(x3, rd(mult(mult(x3, rd(mult(x3, x4), x4)), rd(mult(rd(X, x4), x5), x5)), rd(mult(rd(X, x4), x5), x5))), x5)
% 0.19/0.45 = { by lemma 10 R->L }
% 0.19/0.45 mult(ld(x3, mult(x3, rd(mult(rd(mult(x3, x4), x4), rd(mult(rd(X, x4), x5), x5)), rd(mult(rd(X, x4), x5), x5)))), x5)
% 0.19/0.45 = { by lemma 10 }
% 0.19/0.45 mult(ld(x3, mult(x3, rd(rd(mult(mult(rd(mult(x3, x4), x4), rd(X, x4)), x5), x5), rd(mult(rd(X, x4), x5), x5)))), x5)
% 0.19/0.45 = { by lemma 9 R->L }
% 0.19/0.45 mult(ld(x3, mult(x3, rd(rd(mult(mult(rd(mult(mult(ld(x3, x3), x3), x4), x4), rd(X, x4)), x5), x5), rd(mult(rd(X, x4), x5), x5)))), x5)
% 0.19/0.45 = { by lemma 10 R->L }
% 0.19/0.45 mult(ld(x3, mult(x3, rd(rd(mult(mult(mult(ld(x3, x3), rd(mult(x3, x4), x4)), rd(X, x4)), x5), x5), rd(mult(rd(X, x4), x5), x5)))), x5)
% 0.19/0.45 = { by axiom 7 (f06) R->L }
% 0.19/0.45 mult(ld(x3, mult(x3, rd(rd(mult(mult(rd(mult(mult(ld(x3, x3), x3), rd(X, x4)), rd(X, x4)), rd(X, x4)), x5), x5), rd(mult(rd(X, x4), x5), x5)))), x5)
% 0.19/0.45 = { by lemma 9 }
% 0.19/0.45 mult(ld(x3, mult(x3, rd(rd(mult(mult(rd(mult(x3, rd(X, x4)), rd(X, x4)), rd(X, x4)), x5), x5), rd(mult(rd(X, x4), x5), x5)))), x5)
% 0.19/0.45 = { by axiom 4 (f04) }
% 0.19/0.45 mult(ld(x3, mult(x3, rd(rd(mult(rd(mult(mult(x3, rd(X, x4)), rd(X, x4)), rd(X, x4)), x5), x5), rd(mult(rd(X, x4), x5), x5)))), x5)
% 0.19/0.45 = { by lemma 11 }
% 0.19/0.45 mult(ld(x3, mult(x3, rd(rd(mult(mult(x3, rd(X, x4)), x5), x5), rd(mult(rd(X, x4), x5), x5)))), x5)
% 0.19/0.45 = { by lemma 10 R->L }
% 0.19/0.45 mult(ld(x3, mult(x3, rd(mult(x3, rd(mult(rd(X, x4), x5), x5)), rd(mult(rd(X, x4), x5), x5)))), x5)
% 0.19/0.45 = { by lemma 10 }
% 0.19/0.45 mult(ld(x3, rd(mult(mult(x3, x3), rd(mult(rd(X, x4), x5), x5)), rd(mult(rd(X, x4), x5), x5))), x5)
% 0.19/0.45 = { by axiom 7 (f06) }
% 0.19/0.45 mult(ld(x3, mult(x3, rd(mult(x3, x5), x5))), x5)
% 0.19/0.45 = { by lemma 12 R->L }
% 0.19/0.45 mult(mult(ld(x3, x3), rd(mult(x3, x5), x5)), x5)
% 0.19/0.45 = { by lemma 10 }
% 0.19/0.45 mult(rd(mult(mult(ld(x3, x3), x3), x5), x5), x5)
% 0.19/0.45 = { by lemma 9 }
% 0.19/0.45 mult(rd(mult(x3, x5), x5), x5)
% 0.19/0.45 = { by axiom 4 (f04) }
% 0.19/0.45 rd(mult(mult(x3, x5), x5), x5)
% 0.19/0.45 = { by lemma 11 }
% 0.19/0.45 mult(x3, x5)
% 0.19/0.45 % SZS output end Proof
% 0.19/0.45
% 0.19/0.45 RESULT: Unsatisfiable (the axioms are contradictory).
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