TSTP Solution File: GRP682-10 by Toma---0.4
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%------------------------------------------------------------------------------
% File : Toma---0.4
% Problem : GRP682-10 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% 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 01:16:01 EDT 2023
% Result : Unsatisfiable 1.48s 1.81s
% Output : CNFRefutation 1.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP682-10 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.14 % Command : toma --casc %s
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 22:04:52 EDT 2023
% 0.21/0.35 % CPUTime :
% 1.48/1.81 % SZS status Unsatisfiable
% 1.48/1.81 % SZS output start Proof
% 1.48/1.81 original problem:
% 1.48/1.81 axioms:
% 1.48/1.81 ld(A, mult(A, A)) = A
% 1.48/1.81 rd(mult(A, A), A) = A
% 1.48/1.81 mult(A, ld(A, B)) = ld(A, mult(A, B))
% 1.48/1.81 mult(rd(A, B), B) = rd(mult(A, B), B)
% 1.48/1.81 ld(ld(A, B), mult(ld(A, B), mult(C, D))) = mult(ld(A, mult(A, C)), D)
% 1.48/1.81 rd(mult(mult(A, B), rd(C, D)), rd(C, D)) = mult(A, rd(mult(B, D), D))
% 1.48/1.81 ld(A, mult(A, ld(B, B))) = rd(mult(rd(A, A), B), B)
% 1.48/1.81 goal:
% 1.48/1.81 ld(ld(x0(), x1()), mult(ld(x0(), x1()), x2())) != ld(x0(), mult(x0(), x2()))
% 1.48/1.81 To show the unsatisfiability of the original goal,
% 1.48/1.81 it suffices to show that ld(ld(x0(), x1()), mult(ld(x0(), x1()), x2())) = ld(x0(), mult(x0(), x2())) (skolemized goal) is valid under the axioms.
% 1.48/1.81 Here is an equational proof:
% 1.48/1.81 0: ld(X0, mult(X0, X0)) = X0.
% 1.48/1.81 Proof: Axiom.
% 1.48/1.81
% 1.48/1.81 1: rd(mult(X0, X0), X0) = X0.
% 1.48/1.81 Proof: Axiom.
% 1.48/1.81
% 1.48/1.81 2: mult(X0, ld(X0, X1)) = ld(X0, mult(X0, X1)).
% 1.48/1.81 Proof: Axiom.
% 1.48/1.81
% 1.48/1.81 3: mult(rd(X0, X1), X1) = rd(mult(X0, X1), X1).
% 1.48/1.81 Proof: Axiom.
% 1.48/1.81
% 1.48/1.81 4: ld(ld(X0, X1), mult(ld(X0, X1), mult(X2, X3))) = mult(ld(X0, mult(X0, X2)), X3).
% 1.48/1.81 Proof: Axiom.
% 1.48/1.81
% 1.48/1.81 5: rd(mult(mult(X0, X1), rd(X2, X3)), rd(X2, X3)) = mult(X0, rd(mult(X1, X3), X3)).
% 1.48/1.81 Proof: Axiom.
% 1.48/1.81
% 1.48/1.81 6: ld(X0, mult(X0, ld(X1, X1))) = rd(mult(rd(X0, X0), X1), X1).
% 1.48/1.81 Proof: Axiom.
% 1.48/1.81
% 1.48/1.81 7: mult(X0, ld(X0, X0)) = X0.
% 1.48/1.81 Proof: Rewrite equation 0,
% 1.48/1.81 lhs with equations [2]
% 1.48/1.81 rhs with equations [].
% 1.48/1.81
% 1.48/1.81 8: mult(rd(X0, X0), X0) = X0.
% 1.48/1.81 Proof: Rewrite equation 1,
% 1.48/1.81 lhs with equations [3]
% 1.48/1.81 rhs with equations [].
% 1.48/1.81
% 1.48/1.81 9: mult(ld(X0, X1), ld(ld(X0, X1), mult(X2, X3))) = mult(mult(X0, ld(X0, X2)), X3).
% 1.48/1.81 Proof: Rewrite equation 4,
% 1.48/1.81 lhs with equations [2]
% 1.48/1.81 rhs with equations [2].
% 1.48/1.81
% 1.48/1.81 10: mult(rd(mult(X0, X1), rd(X2, X3)), rd(X2, X3)) = mult(X0, mult(rd(X1, X3), X3)).
% 1.48/1.81 Proof: Rewrite equation 5,
% 1.48/1.81 lhs with equations [3]
% 1.48/1.81 rhs with equations [3].
% 1.48/1.81
% 1.48/1.81 11: mult(X0, ld(X0, ld(X1, X1))) = mult(rd(rd(X0, X0), X1), X1).
% 1.48/1.81 Proof: Rewrite equation 6,
% 1.48/1.81 lhs with equations [2]
% 1.48/1.81 rhs with equations [3].
% 1.48/1.81
% 1.48/1.81 12: mult(X2, ld(X2, ld(X2, X2))) = ld(X2, X2).
% 1.48/1.81 Proof: A critical pair between equations 2 and 7.
% 1.48/1.81
% 1.48/1.81 13: mult(rd(rd(X2, X2), X2), X2) = rd(X2, X2).
% 1.48/1.81 Proof: A critical pair between equations 3 and 8.
% 1.48/1.81
% 1.48/1.81 18: mult(mult(X0, ld(X0, X4)), ld(X4, X4)) = mult(ld(X0, X1), ld(ld(X0, X1), X4)).
% 1.48/1.81 Proof: A critical pair between equations 9 and 7.
% 1.48/1.81
% 1.48/1.81 19: mult(mult(X0, ld(X0, rd(X4, X4))), X4) = mult(ld(X0, X1), ld(ld(X0, X1), X4)).
% 1.48/1.81 Proof: A critical pair between equations 9 and 8.
% 1.48/1.81
% 1.48/1.81 20: mult(X4, mult(rd(ld(X4, X4), X3), X3)) = mult(rd(X4, rd(X2, X3)), rd(X2, X3)).
% 1.48/1.81 Proof: A critical pair between equations 10 and 7.
% 1.48/1.81
% 1.48/1.81 21: mult(rd(X4, X4), mult(rd(X4, X3), X3)) = mult(rd(X4, rd(X2, X3)), rd(X2, X3)).
% 1.48/1.81 Proof: A critical pair between equations 10 and 8.
% 1.48/1.81
% 1.48/1.81 28: ld(X2, X2) = rd(X2, X2).
% 1.48/1.81 Proof: Rewrite equation 13,
% 1.48/1.81 lhs with equations [11,12]
% 1.48/1.81 rhs with equations [].
% 1.48/1.81
% 1.48/1.81 29: ld(X2, mult(X2, rd(X2, X2))) = rd(X2, X2).
% 1.48/1.81 Proof: Rewrite equation 12,
% 1.48/1.81 lhs with equations [28,2]
% 1.48/1.81 rhs with equations [28].
% 1.48/1.81
% 1.48/1.81 30: ld(X0, mult(X0, rd(X1, X1))) = rd(mult(rd(X0, X0), X1), X1).
% 1.48/1.81 Proof: Rewrite equation 11,
% 1.48/1.81 lhs with equations [28,2]
% 1.48/1.81 rhs with equations [3].
% 1.48/1.81
% 1.48/1.81 31: rd(mult(mult(X0, X1), rd(X2, X3)), rd(X2, X3)) = mult(X0, rd(mult(X1, X3), X3)).
% 1.48/1.81 Proof: Rewrite equation 10,
% 1.48/1.81 lhs with equations [3]
% 1.48/1.81 rhs with equations [3].
% 1.48/1.81
% 1.48/1.81 32: rd(mult(X0, X0), X0) = X0.
% 1.48/1.81 Proof: Rewrite equation 8,
% 1.48/1.81 lhs with equations [3]
% 1.48/1.81 rhs with equations [].
% 1.48/1.81
% 1.48/1.81 33: mult(X0, rd(X0, X0)) = X0.
% 1.48/1.81 Proof: Rewrite equation 7,
% 1.48/1.81 lhs with equations [28]
% 1.48/1.81 rhs with equations [].
% 1.48/1.81
% 1.48/1.81 35: mult(rd(X4, X4), rd(mult(X4, X3), X3)) = rd(mult(X4, rd(X2, X3)), rd(X2, X3)).
% 1.48/1.81 Proof: Rewrite equation 21,
% 1.48/1.81 lhs with equations [3]
% 1.48/1.81 rhs with equations [3].
% 1.48/1.81
% 1.48/1.81 36: ld(X4, mult(X4, mult(X4, rd(X3, X3)))) = rd(mult(X4, rd(X2, X3)), rd(X2, X3)).
% 1.48/1.81 Proof: Rewrite equation 20,
% 1.48/1.81 lhs with equations [28,3,30,2]
% 1.48/1.81 rhs with equations [3].
% 1.48/1.81
% 1.48/1.81 37: mult(ld(X0, mult(X0, rd(X4, X4))), X4) = ld(ld(X0, X1), mult(ld(X0, X1), X4)).
% 1.48/1.81 Proof: Rewrite equation 19,
% 1.48/1.81 lhs with equations [2]
% 1.48/1.81 rhs with equations [2].
% 1.48/1.81
% 1.48/1.81 38: mult(ld(X0, mult(X0, X4)), rd(X4, X4)) = ld(ld(X0, X1), mult(ld(X0, X1), X4)).
% 1.48/1.81 Proof: Rewrite equation 18,
% 1.48/1.81 lhs with equations [2,28]
% 1.48/1.81 rhs with equations [2].
% 1.48/1.81
% 1.48/1.81 39: ld(ld(X0, X1), mult(ld(X0, X1), mult(X2, X3))) = mult(ld(X0, mult(X0, X2)), X3).
% 1.48/1.81 Proof: Rewrite equation 9,
% 1.48/1.81 lhs with equations [2]
% 1.48/1.81 rhs with equations [2].
% 1.48/1.81
% 1.48/1.81 44: ld(ld(X5, X1), mult(ld(X5, X1), X5)) = mult(rd(X5, X5), X5).
% 1.48/1.81 Proof: A critical pair between equations 37 and 29.
% 1.48/1.81
% 1.48/1.81 49: mult(rd(X5, X5), rd(mult(X5, X7), X7)) = ld(X5, mult(X5, mult(X5, rd(X7, X7)))).
% 1.48/1.81 Proof: A critical pair between equations 35 and 36.
% 1.48/1.81
% 1.48/1.81 51: mult(rd(X4, X4), rd(mult(X4, X5), X5)) = rd(mult(X4, X5), rd(mult(X5, X5), X5)).
% 1.48/1.81 Proof: A critical pair between equations 35 and 32.
% 1.48/1.81
% 1.48/1.81 52: mult(rd(X4, X4), mult(rd(X4, X5), X5)) = mult(rd(X4, X5), X5).
% 1.48/1.81 Proof: Rewrite equation 51,
% 1.48/1.81 lhs with equations [3]
% 1.48/1.81 rhs with equations [32,3].
% 1.48/1.81
% 1.48/1.81 53: mult(rd(X5, X7), X7) = mult(X5, mult(X5, ld(X5, rd(X7, X7)))).
% 1.48/1.81 Proof: Rewrite equation 49,
% 1.48/1.81 lhs with equations [3,52]
% 1.48/1.81 rhs with equations [2,2].
% 1.48/1.81
% 1.48/1.81 55: mult(ld(X5, X1), ld(ld(X5, X1), X5)) = mult(rd(X5, X5), X5).
% 1.48/1.81 Proof: Rewrite equation 44,
% 1.48/1.81 lhs with equations [2]
% 1.48/1.81 rhs with equations [].
% 1.48/1.81
% 1.48/1.81 57: mult(rd(X0, X0), X0) = X0.
% 1.48/1.81 Proof: Rewrite equation 32,
% 1.48/1.81 lhs with equations [3]
% 1.48/1.81 rhs with equations [].
% 1.48/1.81
% 1.48/1.81 58: mult(rd(mult(X0, X1), X3), X3) = mult(X0, mult(rd(X1, X3), X3)).
% 1.48/1.81 Proof: Rewrite equation 31,
% 1.48/1.81 lhs with equations [35,3,52]
% 1.48/1.81 rhs with equations [3].
% 1.48/1.81
% 1.48/1.81 59: mult(X0, ld(X0, rd(X1, X1))) = mult(rd(rd(X0, X0), X1), X1).
% 1.48/1.81 Proof: Rewrite equation 30,
% 1.48/1.81 lhs with equations [2]
% 1.48/1.81 rhs with equations [3].
% 1.48/1.81
% 1.48/1.81 60: mult(mult(X0, ld(X0, mult(X2, X3))), rd(mult(X2, X3), mult(X2, X3))) = mult(mult(X0, ld(X0, X2)), X3).
% 1.48/1.81 Proof: Rewrite equation 39,
% 1.48/1.81 lhs with equations [38,2]
% 1.48/1.81 rhs with equations [2].
% 1.48/1.81
% 1.48/1.81 61: mult(mult(X0, ld(X0, X4)), rd(X4, X4)) = mult(mult(rd(rd(X0, X0), X4), X4), X4).
% 1.48/1.81 Proof: Rewrite equation 38,
% 1.48/1.81 lhs with equations [2]
% 1.48/1.81 rhs with equations [37,2,59].
% 1.48/1.81
% 1.48/1.81 62: mult(mult(rd(rd(X0, X0), X4), X4), X4) = mult(ld(X0, X1), ld(ld(X0, X1), X4)).
% 1.48/1.81 Proof: Rewrite equation 37,
% 1.48/1.81 lhs with equations [2,59]
% 1.48/1.81 rhs with equations [2].
% 1.48/1.81
% 1.48/1.81 71: mult(rd(X6, X6), X6) = mult(rd(X6, X6), ld(ld(X6, X6), X6)).
% 1.48/1.81 Proof: A critical pair between equations 55 and 28.
% 1.48/1.81
% 1.48/1.81 74: mult(rd(X2, X2), ld(rd(X2, X2), X2)) = ld(rd(X2, X2), X2).
% 1.48/1.81 Proof: A critical pair between equations 2 and 57.
% 1.48/1.81
% 1.48/1.81 80: ld(ld(X2, X2), mult(ld(X2, X2), X2)) = ld(ld(X2, X2), X2).
% 1.48/1.81 Proof: Rewrite equation 74,
% 1.48/1.81 lhs with equations [28,28,2]
% 1.48/1.81 rhs with equations [28].
% 1.48/1.81
% 1.48/1.81 83: mult(ld(X6, X6), X6) = ld(ld(X6, X6), X6).
% 1.48/1.81 Proof: Rewrite equation 71,
% 1.48/1.81 lhs with equations [28]
% 1.48/1.81 rhs with equations [28,2,80].
% 1.48/1.81
% 1.48/1.81 91: mult(ld(X0, mult(X0, X4)), ld(X4, X4)) = mult(ld(X0, X0), ld(ld(X4, X4), X4)).
% 1.48/1.81 Proof: Rewrite equation 61,
% 1.48/1.81 lhs with equations [2,28]
% 1.48/1.81 rhs with equations [28,3,58,28,83].
% 1.48/1.81
% 1.48/1.81 92: mult(ld(X0, X0), ld(ld(mult(X2, X3), mult(X2, X3)), mult(X2, X3))) = mult(ld(X0, mult(X0, X2)), X3).
% 1.48/1.81 Proof: Rewrite equation 60,
% 1.48/1.81 lhs with equations [2,28,91]
% 1.48/1.81 rhs with equations [2].
% 1.48/1.81
% 1.48/1.81 93: ld(X0, mult(X0, ld(X1, X1))) = rd(mult(ld(X0, X0), X1), X1).
% 1.48/1.81 Proof: Rewrite equation 59,
% 1.48/1.81 lhs with equations [28,2]
% 1.48/1.81 rhs with equations [28,3].
% 1.48/1.81
% 1.48/1.81 95: ld(X0, mult(X0, mult(X0, ld(X1, X1)))) = rd(mult(X0, X1), X1).
% 1.48/1.81 Proof: Rewrite equation 3,
% 1.48/1.81 lhs with equations [53,28,2,2]
% 1.48/1.81 rhs with equations [].
% 1.48/1.81
% 1.48/1.81 96: ld(ld(X0, X0), X0) = X0.
% 1.48/1.81 Proof: Rewrite equation 57,
% 1.48/1.81 lhs with equations [28,83]
% 1.48/1.81 rhs with equations [].
% 1.48/1.81
% 1.48/1.81 97: ld(X0, mult(X0, X0)) = X0.
% 1.48/1.81 Proof: Rewrite equation 33,
% 1.48/1.81 lhs with equations [28,2]
% 1.48/1.81 rhs with equations [].
% 1.48/1.81
% 1.48/1.81 100: mult(rd(X5, X7), X7) = rd(mult(X5, X7), X7).
% 1.48/1.81 Proof: Rewrite equation 53,
% 1.48/1.81 lhs with equations []
% 1.48/1.81 rhs with equations [28,2,2,95].
% 1.48/1.81
% 1.48/1.81 103: mult(ld(X0, X0), X4) = ld(ld(X0, X1), mult(ld(X0, X1), X4)).
% 1.48/1.81 Proof: Rewrite equation 62,
% 1.48/1.81 lhs with equations [28,100,93,92,83,96,83,96,83,96,96]
% 1.48/1.81 rhs with equations [2].
% 1.48/1.81
% 1.48/1.81 108: mult(ld(X5, X5), X4) = ld(X5, mult(ld(X5, mult(X5, X5)), X4)).
% 1.48/1.81 Proof: A critical pair between equations 103 and 97.
% 1.48/1.81
% 1.48/1.81 123: mult(rd(X5, X5), X4) = mult(X5, ld(X5, X4)).
% 1.48/1.81 Proof: Rewrite equation 108,
% 1.48/1.81 lhs with equations [28]
% 1.48/1.81 rhs with equations [97,2].
% 1.48/1.81
% 1.48/1.81 131: mult(rd(X0, X0), X1) = ld(X0, mult(X0, X1)).
% 1.48/1.81 Proof: Rewrite equation 2,
% 1.48/1.81 lhs with equations [123]
% 1.48/1.81 rhs with equations [].
% 1.48/1.81
% 1.48/1.81 140: mult(rd(X0, X0), X4) = mult(rd(ld(X0, X1), ld(X0, X1)), X4).
% 1.48/1.81 Proof: Rewrite equation 103,
% 1.48/1.81 lhs with equations [28]
% 1.48/1.81 rhs with equations [131].
% 1.48/1.81
% 1.48/1.81 143: ld(ld(x0(), x1()), mult(ld(x0(), x1()), x2())) = ld(x0(), mult(x0(), x2())).
% 1.48/1.81 Proof: Rewrite lhs with equations [131,140]
% 1.48/1.81 rhs with equations [131].
% 1.48/1.81
% 1.48/1.81 % SZS output end Proof
%------------------------------------------------------------------------------