TSTP Solution File: GRP547-1 by Toma---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Toma---0.4
% Problem : GRP547-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% 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 01:15:18 EDT 2023
% Result : Unsatisfiable 1.24s 1.51s
% Output : CNFRefutation 1.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP547-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.13 % Command : toma --casc %s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 21:45:23 EDT 2023
% 0.13/0.34 % CPUTime :
% 1.24/1.51 % SZS status Unsatisfiable
% 1.24/1.51 % SZS output start Proof
% 1.24/1.51 original problem:
% 1.24/1.51 axioms:
% 1.24/1.51 divide(divide(identity(), divide(A, B)), divide(divide(B, C), A)) = C
% 1.24/1.51 multiply(A, B) = divide(A, divide(identity(), B))
% 1.24/1.51 inverse(A) = divide(identity(), A)
% 1.24/1.51 identity() = divide(A, A)
% 1.24/1.51 goal:
% 1.24/1.51 multiply(multiply(a3(), b3()), c3()) != multiply(a3(), multiply(b3(), c3()))
% 1.24/1.51 To show the unsatisfiability of the original goal,
% 1.24/1.51 it suffices to show that multiply(multiply(a3(), b3()), c3()) = multiply(a3(), multiply(b3(), c3())) (skolemized goal) is valid under the axioms.
% 1.24/1.51 Here is an equational proof:
% 1.24/1.51 0: divide(divide(identity(), divide(X0, X1)), divide(divide(X1, X2), X0)) = X2.
% 1.24/1.51 Proof: Axiom.
% 1.24/1.51
% 1.24/1.51 1: multiply(X0, X1) = divide(X0, divide(identity(), X1)).
% 1.24/1.51 Proof: Axiom.
% 1.24/1.51
% 1.24/1.51 2: inverse(X0) = divide(identity(), X0).
% 1.24/1.51 Proof: Axiom.
% 1.24/1.51
% 1.24/1.51 3: identity() = divide(X0, X0).
% 1.24/1.51 Proof: Axiom.
% 1.24/1.51
% 1.24/1.51 4: divide(inverse(divide(X0, X1)), divide(divide(X1, X2), X0)) = X2.
% 1.24/1.51 Proof: Rewrite equation 0,
% 1.24/1.51 lhs with equations [2]
% 1.24/1.51 rhs with equations [].
% 1.24/1.51
% 1.24/1.51 5: multiply(X0, X1) = divide(X0, inverse(X1)).
% 1.24/1.51 Proof: Rewrite equation 1,
% 1.24/1.51 lhs with equations []
% 1.24/1.51 rhs with equations [2].
% 1.24/1.51
% 1.24/1.51 6: inverse(identity()) = identity().
% 1.24/1.51 Proof: A critical pair between equations 2 and 3.
% 1.24/1.51
% 1.24/1.51 7: X3 = divide(inverse(divide(X0, X3)), divide(identity(), X0)).
% 1.24/1.51 Proof: A critical pair between equations 4 and 3.
% 1.24/1.51
% 1.24/1.51 8: X2 = divide(inverse(divide(divide(X1, X2), X1)), identity()).
% 1.24/1.51 Proof: A critical pair between equations 4 and 3.
% 1.24/1.51
% 1.24/1.51 9: X2 = divide(inverse(identity()), divide(divide(X3, X2), X3)).
% 1.24/1.51 Proof: A critical pair between equations 4 and 3.
% 1.24/1.51
% 1.24/1.51 10: X3 = divide(inverse(divide(X0, identity())), divide(inverse(X3), X0)).
% 1.24/1.51 Proof: A critical pair between equations 4 and 2.
% 1.24/1.51
% 1.24/1.51 11: X2 = divide(inverse(inverse(X3)), divide(divide(X3, X2), identity())).
% 1.24/1.51 Proof: A critical pair between equations 4 and 2.
% 1.24/1.51
% 1.24/1.51 12: divide(divide(X4, X5), X3) = divide(inverse(divide(X0, inverse(divide(X3, X4)))), divide(X5, X0)).
% 1.24/1.51 Proof: A critical pair between equations 4 and 4.
% 1.24/1.51
% 1.24/1.51 15: X2 = divide(divide(identity(), divide(identity(), X3)), divide(divide(X3, X2), identity())).
% 1.24/1.51 Proof: Rewrite equation 11,
% 1.24/1.51 lhs with equations []
% 1.24/1.51 rhs with equations [2,2].
% 1.24/1.51
% 1.24/1.51 16: X3 = divide(divide(identity(), divide(X0, identity())), divide(divide(identity(), X3), X0)).
% 1.24/1.51 Proof: Rewrite equation 10,
% 1.24/1.51 lhs with equations []
% 1.24/1.51 rhs with equations [2,2].
% 1.24/1.51
% 1.24/1.51 17: X2 = divide(identity(), divide(divide(X3, X2), X3)).
% 1.24/1.51 Proof: Rewrite equation 9,
% 1.24/1.51 lhs with equations []
% 1.24/1.51 rhs with equations [6].
% 1.24/1.51
% 1.24/1.51 18: X2 = divide(X2, identity()).
% 1.24/1.51 Proof: Rewrite equation 8,
% 1.24/1.51 lhs with equations []
% 1.24/1.51 rhs with equations [2,17].
% 1.24/1.51
% 1.24/1.51 19: X3 = divide(divide(identity(), divide(X0, X3)), divide(identity(), X0)).
% 1.24/1.51 Proof: Rewrite equation 7,
% 1.24/1.51 lhs with equations []
% 1.24/1.51 rhs with equations [2].
% 1.24/1.51
% 1.24/1.51 20: multiply(X0, X1) = divide(X0, divide(identity(), X1)).
% 1.24/1.51 Proof: Rewrite equation 5,
% 1.24/1.51 lhs with equations []
% 1.24/1.51 rhs with equations [2].
% 1.24/1.51
% 1.24/1.51 21: divide(divide(identity(), divide(X0, X1)), divide(divide(X1, X2), X0)) = X2.
% 1.24/1.51 Proof: Rewrite equation 4,
% 1.24/1.51 lhs with equations [2]
% 1.24/1.51 rhs with equations [].
% 1.24/1.51
% 1.24/1.51 22: divide(divide(X4, X5), X3) = divide(divide(identity(), divide(X0, divide(identity(), divide(X3, X4)))), divide(X5, X0)).
% 1.24/1.51 Proof: Rewrite equation 12,
% 1.24/1.51 lhs with equations []
% 1.24/1.51 rhs with equations [2,2].
% 1.24/1.51
% 1.24/1.51 25: X3 = divide(divide(identity(), divide(identity(), X3)), identity()).
% 1.24/1.51 Proof: A critical pair between equations 19 and 18.
% 1.24/1.51
% 1.24/1.51 27: divide(divide(X4, identity()), X3) = divide(identity(), divide(X3, X4)).
% 1.24/1.51 Proof: A critical pair between equations 22 and 19.
% 1.24/1.51
% 1.24/1.51 32: X3 = divide(X5, divide(divide(identity(), X3), divide(identity(), X5))).
% 1.24/1.51 Proof: A critical pair between equations 16 and 17.
% 1.24/1.51
% 1.24/1.51 37: X3 = divide(X5, divide(inverse(X3), inverse(X5))).
% 1.24/1.51 Proof: Rewrite equation 32,
% 1.24/1.51 lhs with equations []
% 1.24/1.51 rhs with equations [2,2].
% 1.24/1.51
% 1.24/1.51 42: X3 = inverse(inverse(X3)).
% 1.24/1.51 Proof: Rewrite equation 25,
% 1.24/1.51 lhs with equations []
% 1.24/1.51 rhs with equations [2,2,18].
% 1.24/1.51
% 1.24/1.51 44: divide(inverse(divide(X0, X1)), divide(divide(X1, X2), X0)) = X2.
% 1.24/1.51 Proof: Rewrite equation 21,
% 1.24/1.51 lhs with equations [2]
% 1.24/1.51 rhs with equations [].
% 1.24/1.51
% 1.24/1.51 45: multiply(X0, X1) = divide(X0, inverse(X1)).
% 1.24/1.51 Proof: Rewrite equation 20,
% 1.24/1.51 lhs with equations []
% 1.24/1.51 rhs with equations [2].
% 1.24/1.51
% 1.24/1.51 46: X3 = divide(inverse(divide(X0, X3)), inverse(X0)).
% 1.24/1.51 Proof: Rewrite equation 19,
% 1.24/1.51 lhs with equations []
% 1.24/1.51 rhs with equations [2,2].
% 1.24/1.51
% 1.24/1.51 47: X2 = inverse(divide(divide(X3, X2), X3)).
% 1.24/1.51 Proof: Rewrite equation 17,
% 1.24/1.51 lhs with equations []
% 1.24/1.51 rhs with equations [2].
% 1.24/1.51
% 1.24/1.51 48: X2 = divide(X3, divide(X3, X2)).
% 1.24/1.51 Proof: Rewrite equation 15,
% 1.24/1.51 lhs with equations []
% 1.24/1.51 rhs with equations [2,2,42,18].
% 1.24/1.51
% 1.24/1.51 50: divide(X4, X3) = inverse(divide(X3, X4)).
% 1.24/1.51 Proof: Rewrite equation 27,
% 1.24/1.51 lhs with equations [18]
% 1.24/1.51 rhs with equations [2].
% 1.24/1.51
% 1.24/1.51 51: divide(divide(X4, X5), X3) = divide(inverse(divide(X0, inverse(divide(X3, X4)))), divide(X5, X0)).
% 1.24/1.51 Proof: Rewrite equation 22,
% 1.24/1.51 lhs with equations []
% 1.24/1.51 rhs with equations [2,2].
% 1.24/1.51
% 1.24/1.51 65: X2 = divide(identity(), divide(divide(X3, X2), X3)).
% 1.24/1.51 Proof: Rewrite equation 47,
% 1.24/1.51 lhs with equations []
% 1.24/1.51 rhs with equations [2].
% 1.24/1.51
% 1.24/1.51 66: X3 = divide(divide(identity(), divide(X0, X3)), divide(identity(), X0)).
% 1.24/1.51 Proof: Rewrite equation 46,
% 1.24/1.51 lhs with equations []
% 1.24/1.51 rhs with equations [2,2].
% 1.24/1.51
% 1.24/1.51 67: multiply(X0, X1) = divide(X0, divide(identity(), X1)).
% 1.24/1.51 Proof: Rewrite equation 45,
% 1.24/1.51 lhs with equations []
% 1.24/1.51 rhs with equations [2].
% 1.24/1.51
% 1.24/1.51 68: divide(divide(X1, X0), divide(divide(X1, X2), X0)) = X2.
% 1.24/1.51 Proof: Rewrite equation 44,
% 1.24/1.51 lhs with equations [50]
% 1.24/1.51 rhs with equations [].
% 1.24/1.51
% 1.24/1.51 69: X3 = divide(X5, divide(divide(identity(), X3), divide(identity(), X5))).
% 1.24/1.51 Proof: Rewrite equation 37,
% 1.24/1.51 lhs with equations []
% 1.24/1.51 rhs with equations [2,2].
% 1.24/1.51
% 1.24/1.51 70: divide(X4, X3) = divide(identity(), divide(X3, X4)).
% 1.24/1.51 Proof: Rewrite equation 50,
% 1.24/1.51 lhs with equations []
% 1.24/1.51 rhs with equations [2].
% 1.24/1.51
% 1.24/1.51 71: divide(divide(X4, X5), X3) = divide(divide(identity(), divide(X0, divide(identity(), divide(X3, X4)))), divide(X5, X0)).
% 1.24/1.51 Proof: Rewrite equation 51,
% 1.24/1.51 lhs with equations []
% 1.24/1.51 rhs with equations [2,2].
% 1.24/1.51
% 1.24/1.51 76: divide(divide(X4, X6), X5) = divide(divide(X4, X5), X6).
% 1.24/1.51 Proof: A critical pair between equations 48 and 68.
% 1.24/1.51
% 1.24/1.51 77: divide(divide(identity(), X7), divide(identity(), X6)) = divide(X6, X7).
% 1.24/1.51 Proof: A critical pair between equations 48 and 69.
% 1.24/1.51
% 1.24/1.51 78: divide(X5, X6) = divide(identity(), divide(divide(X6, X5), identity())).
% 1.24/1.51 Proof: A critical pair between equations 65 and 70.
% 1.24/1.51
% 1.24/1.51 87: divide(X5, X6) = inverse(divide(X6, X5)).
% 1.24/1.51 Proof: Rewrite equation 78,
% 1.24/1.51 lhs with equations []
% 1.24/1.51 rhs with equations [18,2].
% 1.24/1.51
% 1.24/1.51 92: multiply(X0, X1) = divide(X0, inverse(X1)).
% 1.24/1.51 Proof: Rewrite equation 67,
% 1.24/1.51 lhs with equations []
% 1.24/1.51 rhs with equations [2].
% 1.24/1.51
% 1.24/1.51 93: X3 = inverse(divide(inverse(X0), inverse(divide(X0, X3)))).
% 1.24/1.51 Proof: Rewrite equation 66,
% 1.24/1.51 lhs with equations []
% 1.24/1.51 rhs with equations [2,2,70,2].
% 1.24/1.51
% 1.24/1.51 94: X2 = inverse(inverse(X2)).
% 1.24/1.51 Proof: Rewrite equation 65,
% 1.24/1.51 lhs with equations []
% 1.24/1.51 rhs with equations [70,48,2,2].
% 1.24/1.51
% 1.24/1.51 96: divide(inverse(X7), inverse(X6)) = divide(X6, X7).
% 1.24/1.51 Proof: Rewrite equation 77,
% 1.24/1.51 lhs with equations [2,2]
% 1.24/1.51 rhs with equations [].
% 1.24/1.51
% 1.24/1.51 98: divide(divide(X4, X5), X3) = divide(inverse(divide(X0, inverse(divide(X3, X4)))), divide(X5, X0)).
% 1.24/1.51 Proof: Rewrite equation 71,
% 1.24/1.51 lhs with equations []
% 1.24/1.51 rhs with equations [2,2].
% 1.24/1.51
% 1.24/1.51 109: divide(X6, inverse(X8)) = divide(X8, inverse(X6)).
% 1.24/1.51 Proof: A critical pair between equations 96 and 94.
% 1.24/1.51
% 1.24/1.51 113: X3 = divide(identity(), divide(divide(identity(), X0), divide(identity(), divide(X0, X3)))).
% 1.24/1.51 Proof: Rewrite equation 93,
% 1.24/1.51 lhs with equations []
% 1.24/1.51 rhs with equations [2,2,2].
% 1.24/1.51
% 1.24/1.51 114: multiply(X0, X1) = divide(X0, divide(identity(), X1)).
% 1.24/1.51 Proof: Rewrite equation 92,
% 1.24/1.51 lhs with equations []
% 1.24/1.51 rhs with equations [2].
% 1.24/1.51
% 1.24/1.51 116: divide(X5, X6) = divide(identity(), divide(X6, X5)).
% 1.24/1.51 Proof: Rewrite equation 87,
% 1.24/1.51 lhs with equations []
% 1.24/1.51 rhs with equations [2].
% 1.24/1.51
% 1.24/1.51 117: divide(X6, divide(identity(), X8)) = divide(X8, divide(identity(), X6)).
% 1.24/1.51 Proof: Rewrite equation 109,
% 1.24/1.51 lhs with equations [2]
% 1.24/1.51 rhs with equations [2].
% 1.24/1.51
% 1.24/1.51 119: divide(divide(X4, X5), X3) = divide(divide(identity(), divide(X0, divide(identity(), divide(X3, X4)))), divide(X5, X0)).
% 1.24/1.51 Proof: Rewrite equation 98,
% 1.24/1.51 lhs with equations []
% 1.24/1.51 rhs with equations [2,2].
% 1.24/1.51
% 1.24/1.51 120: divide(divide(identity(), X7), divide(identity(), X6)) = divide(X6, X7).
% 1.24/1.51 Proof: Rewrite equation 96,
% 1.24/1.51 lhs with equations [2,2]
% 1.24/1.51 rhs with equations [].
% 1.24/1.51
% 1.24/1.51 121: X8 = divide(X7, divide(identity(), divide(X8, X7))).
% 1.24/1.51 Proof: A critical pair between equations 48 and 116.
% 1.24/1.51
% 1.24/1.51 127: divide(divide(identity(), X10), X9) = divide(identity(), divide(X10, divide(identity(), X9))).
% 1.24/1.51 Proof: A critical pair between equations 116 and 117.
% 1.24/1.51
% 1.24/1.51 130: divide(identity(), divide(X9, divide(X7, X8))) = divide(divide(X7, X9), X8).
% 1.24/1.51 Proof: A critical pair between equations 116 and 76.
% 1.24/1.51
% 1.24/1.51 131: divide(X9, X8) = divide(identity(), divide(divide(identity(), X9), divide(identity(), X8))).
% 1.24/1.51 Proof: A critical pair between equations 116 and 120.
% 1.24/1.51
% 1.24/1.51 132: divide(divide(identity(), X9), divide(identity(), X8)) = divide(identity(), divide(X9, X8)).
% 1.24/1.51 Proof: A critical pair between equations 116 and 120.
% 1.24/1.51
% 1.24/1.51 133: divide(inverse(X9), inverse(X8)) = inverse(divide(X9, X8)).
% 1.24/1.51 Proof: Rewrite equation 132,
% 1.24/1.51 lhs with equations [2,2]
% 1.24/1.51 rhs with equations [2].
% 1.24/1.51
% 1.24/1.51 134: divide(X9, X8) = inverse(inverse(divide(X9, X8))).
% 1.24/1.51 Proof: Rewrite equation 131,
% 1.24/1.51 lhs with equations []
% 1.24/1.51 rhs with equations [2,2,133,2].
% 1.24/1.51
% 1.24/1.51 135: inverse(divide(X9, divide(X7, X8))) = divide(divide(X7, X9), X8).
% 1.24/1.51 Proof: Rewrite equation 130,
% 1.24/1.51 lhs with equations [2]
% 1.24/1.51 rhs with equations [].
% 1.24/1.51
% 1.24/1.51 137: divide(inverse(X10), X9) = inverse(divide(X10, inverse(X9))).
% 1.24/1.51 Proof: Rewrite equation 127,
% 1.24/1.51 lhs with equations [2]
% 1.24/1.51 rhs with equations [2,2].
% 1.24/1.51
% 1.24/1.51 139: X8 = divide(X7, inverse(divide(X8, X7))).
% 1.24/1.51 Proof: Rewrite equation 121,
% 1.24/1.51 lhs with equations []
% 1.24/1.51 rhs with equations [2].
% 1.24/1.51
% 1.24/1.51 142: multiply(X0, X1) = divide(X0, inverse(X1)).
% 1.24/1.51 Proof: Rewrite equation 114,
% 1.24/1.51 lhs with equations []
% 1.24/1.51 rhs with equations [2].
% 1.24/1.51
% 1.24/1.51 143: X3 = inverse(inverse(X3)).
% 1.24/1.51 Proof: Rewrite equation 113,
% 1.24/1.51 lhs with equations []
% 1.24/1.51 rhs with equations [2,2,137,134,48,2].
% 1.24/1.51
% 1.24/1.51 146: inverse(divide(X7, X6)) = divide(X6, X7).
% 1.24/1.51 Proof: Rewrite equation 120,
% 1.24/1.51 lhs with equations [2,2,137,143]
% 1.24/1.51 rhs with equations [].
% 1.24/1.51
% 1.24/1.51 148: inverse(divide(X5, divide(X4, X3))) = divide(X4, divide(X3, inverse(X5))).
% 1.24/1.51 Proof: Rewrite equation 119,
% 1.24/1.51 lhs with equations [135]
% 1.24/1.51 rhs with equations [2,2,137,135,139,137,135,143,143].
% 1.24/1.51
% 1.24/1.51 164: multiply(X0, X1) = divide(X0, divide(identity(), X1)).
% 1.24/1.51 Proof: Rewrite equation 142,
% 1.24/1.51 lhs with equations []
% 1.24/1.51 rhs with equations [2].
% 1.24/1.51
% 1.24/1.51 168: divide(divide(X4, X3), X5) = divide(X4, divide(X3, divide(identity(), X5))).
% 1.24/1.51 Proof: Rewrite equation 148,
% 1.24/1.51 lhs with equations [146]
% 1.24/1.51 rhs with equations [2].
% 1.24/1.51
% 1.24/1.51 174: multiply(multiply(a3(), b3()), c3()) = multiply(a3(), multiply(b3(), c3())).
% 1.24/1.51 Proof: Rewrite lhs with equations [164,164,168,48,168]
% 1.24/1.51 rhs with equations [164,164].
% 1.24/1.51
% 1.24/1.51 % SZS output end Proof
%------------------------------------------------------------------------------