TSTP Solution File: GRP685-11 by Toma---0.4
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%------------------------------------------------------------------------------
% File : Toma---0.4
% Problem : GRP685-11 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n022.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 01:16:02 EDT 2023
% Result : Unsatisfiable 1.93s 2.27s
% Output : CNFRefutation 1.93s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : GRP685-11 : TPTP v8.1.2. Released v8.1.0.
% 0.11/0.13 % Command : toma --casc %s
% 0.12/0.34 % Computer : n022.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 02:13:38 EDT 2023
% 0.12/0.34 % CPUTime :
% 1.93/2.27 % SZS status Unsatisfiable
% 1.93/2.27 % SZS output start Proof
% 1.93/2.27 original problem:
% 1.93/2.27 axioms:
% 1.93/2.27 ld(A, mult(A, A)) = A
% 1.93/2.27 rd(mult(A, A), A) = A
% 1.93/2.27 mult(A, ld(A, B)) = ld(A, mult(A, B))
% 1.93/2.27 mult(rd(A, B), B) = rd(mult(A, B), B)
% 1.93/2.27 ld(ld(A, B), mult(ld(A, B), mult(C, D))) = mult(ld(A, mult(A, C)), D)
% 1.93/2.27 rd(mult(mult(A, B), rd(C, D)), rd(C, D)) = mult(A, rd(mult(B, D), D))
% 1.93/2.27 ld(A, mult(A, ld(B, B))) = rd(mult(rd(A, A), B), B)
% 1.93/2.27 goal:
% 1.93/2.27 rd(mult(x6(), rd(x7(), x8())), rd(x7(), x8())) != rd(mult(x6(), x8()), x8())
% 1.93/2.27 To show the unsatisfiability of the original goal,
% 1.93/2.27 it suffices to show that rd(mult(x6(), rd(x7(), x8())), rd(x7(), x8())) = rd(mult(x6(), x8()), x8()) (skolemized goal) is valid under the axioms.
% 1.93/2.27 Here is an equational proof:
% 1.93/2.27 0: ld(X0, mult(X0, X0)) = X0.
% 1.93/2.27 Proof: Axiom.
% 1.93/2.27
% 1.93/2.27 1: rd(mult(X0, X0), X0) = X0.
% 1.93/2.27 Proof: Axiom.
% 1.93/2.27
% 1.93/2.27 2: mult(X0, ld(X0, X1)) = ld(X0, mult(X0, X1)).
% 1.93/2.27 Proof: Axiom.
% 1.93/2.27
% 1.93/2.27 3: mult(rd(X0, X1), X1) = rd(mult(X0, X1), X1).
% 1.93/2.27 Proof: Axiom.
% 1.93/2.27
% 1.93/2.27 4: ld(ld(X0, X1), mult(ld(X0, X1), mult(X2, X3))) = mult(ld(X0, mult(X0, X2)), X3).
% 1.93/2.27 Proof: Axiom.
% 1.93/2.27
% 1.93/2.27 5: rd(mult(mult(X0, X1), rd(X2, X3)), rd(X2, X3)) = mult(X0, rd(mult(X1, X3), X3)).
% 1.93/2.27 Proof: Axiom.
% 1.93/2.27
% 1.93/2.27 6: ld(X0, mult(X0, ld(X1, X1))) = rd(mult(rd(X0, X0), X1), X1).
% 1.93/2.27 Proof: Axiom.
% 1.93/2.27
% 1.93/2.27 7: mult(X0, ld(X0, X0)) = X0.
% 1.93/2.27 Proof: Rewrite equation 0,
% 1.93/2.27 lhs with equations [2]
% 1.93/2.27 rhs with equations [].
% 1.93/2.27
% 1.93/2.27 8: mult(rd(X0, X0), X0) = X0.
% 1.93/2.27 Proof: Rewrite equation 1,
% 1.93/2.27 lhs with equations [3]
% 1.93/2.27 rhs with equations [].
% 1.93/2.27
% 1.93/2.27 9: mult(ld(X0, X1), ld(ld(X0, X1), mult(X2, X3))) = mult(mult(X0, ld(X0, X2)), X3).
% 1.93/2.27 Proof: Rewrite equation 4,
% 1.93/2.27 lhs with equations [2]
% 1.93/2.27 rhs with equations [2].
% 1.93/2.27
% 1.93/2.27 10: mult(rd(mult(X0, X1), rd(X2, X3)), rd(X2, X3)) = mult(X0, mult(rd(X1, X3), X3)).
% 1.93/2.27 Proof: Rewrite equation 5,
% 1.93/2.27 lhs with equations [3]
% 1.93/2.27 rhs with equations [3].
% 1.93/2.27
% 1.93/2.27 11: mult(X0, ld(X0, ld(X1, X1))) = mult(rd(rd(X0, X0), X1), X1).
% 1.93/2.27 Proof: Rewrite equation 6,
% 1.93/2.27 lhs with equations [2]
% 1.93/2.27 rhs with equations [3].
% 1.93/2.27
% 1.93/2.27 12: mult(X2, ld(X2, ld(X2, X2))) = ld(X2, X2).
% 1.93/2.27 Proof: A critical pair between equations 2 and 7.
% 1.93/2.27
% 1.93/2.27 13: mult(rd(rd(X2, X2), X2), X2) = rd(X2, X2).
% 1.93/2.27 Proof: A critical pair between equations 3 and 8.
% 1.93/2.27
% 1.93/2.27 20: mult(X4, mult(rd(ld(X4, X4), X3), X3)) = mult(rd(X4, rd(X2, X3)), rd(X2, X3)).
% 1.93/2.27 Proof: A critical pair between equations 10 and 7.
% 1.93/2.27
% 1.93/2.27 21: mult(rd(X4, X4), mult(rd(X4, X3), X3)) = mult(rd(X4, rd(X2, X3)), rd(X2, X3)).
% 1.93/2.27 Proof: A critical pair between equations 10 and 8.
% 1.93/2.27
% 1.93/2.27 22: mult(mult(X4, ld(X4, X2)), X3) = mult(ld(X4, mult(X4, X5)), ld(mult(X4, ld(X4, X5)), mult(X2, X3))).
% 1.93/2.27 Proof: A critical pair between equations 9 and 2.
% 1.93/2.27
% 1.93/2.27 28: ld(X2, X2) = rd(X2, X2).
% 1.93/2.27 Proof: Rewrite equation 13,
% 1.93/2.27 lhs with equations [11,12]
% 1.93/2.27 rhs with equations [].
% 1.93/2.27
% 1.93/2.27 30: ld(X0, mult(X0, ld(X1, X1))) = rd(mult(ld(X0, X0), X1), X1).
% 1.93/2.27 Proof: Rewrite equation 11,
% 1.93/2.27 lhs with equations [2]
% 1.93/2.27 rhs with equations [28,3].
% 1.93/2.27
% 1.93/2.27 32: mult(ld(X0, X0), X0) = X0.
% 1.93/2.27 Proof: Rewrite equation 8,
% 1.93/2.27 lhs with equations [28]
% 1.93/2.27 rhs with equations [].
% 1.93/2.27
% 1.93/2.27 33: ld(X0, mult(X0, X0)) = X0.
% 1.93/2.27 Proof: Rewrite equation 7,
% 1.93/2.27 lhs with equations [2]
% 1.93/2.27 rhs with equations [].
% 1.93/2.27
% 1.93/2.27 34: mult(ld(X4, mult(X4, X2)), X3) = ld(ld(X4, mult(X4, X5)), mult(ld(X4, mult(X4, X5)), mult(X2, X3))).
% 1.93/2.27 Proof: Rewrite equation 22,
% 1.93/2.27 lhs with equations [2]
% 1.93/2.27 rhs with equations [2,2].
% 1.93/2.27
% 1.93/2.27 35: mult(ld(X4, X4), rd(mult(X4, X3), X3)) = rd(mult(X4, rd(X2, X3)), rd(X2, X3)).
% 1.93/2.27 Proof: Rewrite equation 21,
% 1.93/2.27 lhs with equations [28,3]
% 1.93/2.27 rhs with equations [3].
% 1.93/2.27
% 1.93/2.27 36: ld(X4, mult(X4, mult(X4, ld(X3, X3)))) = rd(mult(X4, rd(X2, X3)), rd(X2, X3)).
% 1.93/2.27 Proof: Rewrite equation 20,
% 1.93/2.27 lhs with equations [3,30,2]
% 1.93/2.27 rhs with equations [3].
% 1.93/2.27
% 1.93/2.27 49: ld(ld(X6, mult(X6, X5)), mult(ld(X6, mult(X6, X5)), mult(X6, X3))) = mult(X6, X3).
% 1.93/2.27 Proof: A critical pair between equations 34 and 33.
% 1.93/2.27
% 1.93/2.27 50: mult(ld(X5, X5), rd(mult(X5, X7), X7)) = ld(X5, mult(X5, mult(X5, ld(X7, X7)))).
% 1.93/2.27 Proof: A critical pair between equations 35 and 36.
% 1.93/2.27
% 1.93/2.27 51: rd(mult(X6, rd(X2, X6)), rd(X2, X6)) = ld(X6, mult(X6, ld(X6, mult(X6, X6)))).
% 1.93/2.27 Proof: A critical pair between equations 36 and 2.
% 1.93/2.27
% 1.93/2.27 52: mult(rd(X6, rd(X2, X6)), rd(X2, X6)) = X6.
% 1.93/2.27 Proof: Rewrite equation 51,
% 1.93/2.27 lhs with equations [3]
% 1.93/2.27 rhs with equations [33,33].
% 1.93/2.27
% 1.93/2.27 53: mult(ld(X5, X5), mult(rd(X5, X7), X7)) = mult(X5, mult(X5, ld(X5, ld(X7, X7)))).
% 1.93/2.27 Proof: Rewrite equation 50,
% 1.93/2.27 lhs with equations [3]
% 1.93/2.27 rhs with equations [2,2].
% 1.93/2.27
% 1.93/2.27 54: mult(mult(X6, ld(X6, X5)), ld(mult(X6, ld(X6, X5)), mult(X6, X3))) = mult(X6, X3).
% 1.93/2.27 Proof: Rewrite equation 49,
% 1.93/2.27 lhs with equations [2,2,2]
% 1.93/2.27 rhs with equations [].
% 1.93/2.27
% 1.93/2.27 59: mult(X0, ld(X0, X0)) = X0.
% 1.93/2.27 Proof: Rewrite equation 33,
% 1.93/2.27 lhs with equations [2]
% 1.93/2.27 rhs with equations [].
% 1.93/2.27
% 1.93/2.27 63: mult(X4, mult(X4, ld(X4, ld(X3, X3)))) = mult(rd(X4, rd(X2, X3)), rd(X2, X3)).
% 1.93/2.27 Proof: Rewrite equation 35,
% 1.93/2.27 lhs with equations [3,53]
% 1.93/2.27 rhs with equations [3].
% 1.93/2.27
% 1.93/2.27 69: X9 = mult(X9, mult(X9, ld(X9, ld(X9, X9)))).
% 1.93/2.27 Proof: A critical pair between equations 52 and 63.
% 1.93/2.27
% 1.93/2.27 70: mult(X2, ld(X2, ld(X2, X2))) = ld(X2, X2).
% 1.93/2.27 Proof: A critical pair between equations 2 and 59.
% 1.93/2.27
% 1.93/2.27 76: mult(X7, X3) = mult(X7, ld(mult(X7, ld(X7, X7)), mult(X7, X3))).
% 1.93/2.27 Proof: A critical pair between equations 54 and 59.
% 1.93/2.27
% 1.93/2.27 81: mult(X7, X3) = mult(X7, ld(mult(X7, rd(X7, X7)), mult(X7, X3))).
% 1.93/2.27 Proof: Rewrite equation 76,
% 1.93/2.27 lhs with equations []
% 1.93/2.27 rhs with equations [28].
% 1.93/2.27
% 1.93/2.27 86: ld(X2, mult(X2, rd(X2, X2))) = rd(X2, X2).
% 1.93/2.27 Proof: Rewrite equation 70,
% 1.93/2.27 lhs with equations [28,2]
% 1.93/2.27 rhs with equations [28].
% 1.93/2.27
% 1.93/2.27 87: X9 = mult(X9, rd(X9, X9)).
% 1.93/2.27 Proof: Rewrite equation 69,
% 1.93/2.27 lhs with equations []
% 1.93/2.27 rhs with equations [28,2,86].
% 1.93/2.27
% 1.93/2.27 89: ld(X4, mult(X4, mult(X4, rd(X3, X3)))) = rd(mult(X4, rd(X2, X3)), rd(X2, X3)).
% 1.93/2.27 Proof: Rewrite equation 63,
% 1.93/2.27 lhs with equations [28,2,2]
% 1.93/2.27 rhs with equations [3].
% 1.93/2.27
% 1.93/2.27 92: rd(mult(X0, X0), X0) = X0.
% 1.93/2.27 Proof: Rewrite equation 32,
% 1.93/2.27 lhs with equations [28,3]
% 1.93/2.27 rhs with equations [].
% 1.93/2.27
% 1.93/2.27 103: mult(X10, X3) = mult(X10, ld(X10, mult(X10, X3))).
% 1.93/2.27 Proof: A critical pair between equations 81 and 87.
% 1.93/2.27
% 1.93/2.27 115: mult(X10, X3) = mult(X10, mult(X10, ld(X10, X3))).
% 1.93/2.27 Proof: Rewrite equation 103,
% 1.93/2.27 lhs with equations []
% 1.93/2.27 rhs with equations [2].
% 1.93/2.27
% 1.93/2.27 123: mult(ld(X0, X0), X0) = X0.
% 1.93/2.27 Proof: Rewrite equation 92,
% 1.93/2.27 lhs with equations [3,28]
% 1.93/2.27 rhs with equations [].
% 1.93/2.27
% 1.93/2.27 128: mult(X4, ld(X3, X3)) = mult(rd(X4, rd(X2, X3)), rd(X2, X3)).
% 1.93/2.27 Proof: Rewrite equation 89,
% 1.93/2.27 lhs with equations [28,2,2,115]
% 1.93/2.27 rhs with equations [3].
% 1.93/2.27
% 1.93/2.27 152: mult(X4, rd(X3, X3)) = rd(mult(X4, rd(X2, X3)), rd(X2, X3)).
% 1.93/2.27 Proof: Rewrite equation 128,
% 1.93/2.27 lhs with equations [28]
% 1.93/2.27 rhs with equations [3].
% 1.93/2.27
% 1.93/2.27 157: rd(mult(X0, X0), X0) = X0.
% 1.93/2.27 Proof: Rewrite equation 123,
% 1.93/2.27 lhs with equations [28,3]
% 1.93/2.27 rhs with equations [].
% 1.93/2.27
% 1.93/2.27 171: mult(X4, rd(X5, X5)) = rd(mult(X4, X5), rd(mult(X5, X5), X5)).
% 1.93/2.27 Proof: A critical pair between equations 152 and 157.
% 1.93/2.27
% 1.93/2.27 183: mult(X4, ld(X5, X5)) = mult(rd(X4, X5), X5).
% 1.93/2.27 Proof: Rewrite equation 171,
% 1.93/2.27 lhs with equations [28]
% 1.93/2.27 rhs with equations [157,3].
% 1.93/2.27
% 1.93/2.27 194: mult(X0, ld(X1, X1)) = rd(mult(X0, X1), X1).
% 1.93/2.27 Proof: Rewrite equation 3,
% 1.93/2.27 lhs with equations [183]
% 1.93/2.27 rhs with equations [].
% 1.93/2.27
% 1.93/2.27 206: mult(X4, ld(X3, X3)) = mult(X4, ld(rd(X2, X3), rd(X2, X3))).
% 1.93/2.27 Proof: Rewrite equation 152,
% 1.93/2.27 lhs with equations [28]
% 1.93/2.27 rhs with equations [194].
% 1.93/2.27
% 1.93/2.27 208: rd(mult(x6(), rd(x7(), x8())), rd(x7(), x8())) = rd(mult(x6(), x8()), x8()).
% 1.93/2.27 Proof: Rewrite lhs with equations [194,206]
% 1.93/2.27 rhs with equations [194].
% 1.93/2.27
% 1.93/2.27 % SZS output end Proof
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