TSTP Solution File: GRP577-1 by Toma---0.4
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%------------------------------------------------------------------------------
% File : Toma---0.4
% Problem : GRP577-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n012.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 01:15:24 EDT 2023
% Result : Unsatisfiable 9.29s 9.54s
% Output : CNFRefutation 9.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP577-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.14 % Command : toma --casc %s
% 0.14/0.35 % Computer : n012.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 19:59:54 EDT 2023
% 0.14/0.35 % CPUTime :
% 9.29/9.54 % SZS status Unsatisfiable
% 9.29/9.54 % SZS output start Proof
% 9.29/9.54 original problem:
% 9.29/9.54 axioms:
% 9.29/9.54 double_divide(double_divide(A, double_divide(double_divide(double_divide(B, A), C), double_divide(B, identity()))), double_divide(identity(), identity())) = C
% 9.29/9.54 multiply(A, B) = double_divide(double_divide(B, A), identity())
% 9.29/9.54 inverse(A) = double_divide(A, identity())
% 9.29/9.54 identity() = double_divide(A, inverse(A))
% 9.29/9.54 goal:
% 9.29/9.54 multiply(inverse(a1()), a1()) != identity()
% 9.29/9.54 To show the unsatisfiability of the original goal,
% 9.29/9.54 it suffices to show that multiply(inverse(a1()), a1()) = identity() (skolemized goal) is valid under the axioms.
% 9.29/9.54 Here is an equational proof:
% 9.29/9.54 0: double_divide(double_divide(X0, double_divide(double_divide(double_divide(X1, X0), X2), double_divide(X1, identity()))), double_divide(identity(), identity())) = X2.
% 9.29/9.54 Proof: Axiom.
% 9.29/9.54
% 9.29/9.54 1: multiply(X0, X1) = double_divide(double_divide(X1, X0), identity()).
% 9.29/9.54 Proof: Axiom.
% 9.29/9.54
% 9.29/9.54 2: inverse(X0) = double_divide(X0, identity()).
% 9.29/9.54 Proof: Axiom.
% 9.29/9.54
% 9.29/9.54 3: identity() = double_divide(X0, inverse(X0)).
% 9.29/9.54 Proof: Axiom.
% 9.29/9.54
% 9.29/9.54 4: double_divide(double_divide(X0, double_divide(double_divide(double_divide(X1, X0), X2), inverse(X1))), inverse(identity())) = X2.
% 9.29/9.54 Proof: Rewrite equation 0,
% 9.29/9.54 lhs with equations [2,2]
% 9.29/9.54 rhs with equations [].
% 9.29/9.54
% 9.29/9.54 5: multiply(X0, X1) = inverse(double_divide(X1, X0)).
% 9.29/9.54 Proof: Rewrite equation 1,
% 9.29/9.54 lhs with equations []
% 9.29/9.54 rhs with equations [2].
% 9.29/9.54
% 9.29/9.54 6: X2 = double_divide(double_divide(identity(), double_divide(double_divide(inverse(X3), X2), inverse(X3))), inverse(identity())).
% 9.29/9.54 Proof: A critical pair between equations 4 and 2.
% 9.29/9.54
% 9.29/9.54 7: identity() = double_divide(double_divide(X0, double_divide(inverse(double_divide(X1, X0)), inverse(X1))), inverse(identity())).
% 9.29/9.54 Proof: A critical pair between equations 4 and 2.
% 9.29/9.54
% 9.29/9.54 8: X2 = double_divide(double_divide(inverse(X3), double_divide(double_divide(identity(), X2), inverse(X3))), inverse(identity())).
% 9.29/9.54 Proof: A critical pair between equations 4 and 3.
% 9.29/9.54
% 9.29/9.54 9: inverse(double_divide(X1, X0)) = double_divide(double_divide(X0, double_divide(identity(), inverse(X1))), inverse(identity())).
% 9.29/9.54 Proof: A critical pair between equations 4 and 3.
% 9.29/9.54
% 9.29/9.54 10: double_divide(double_divide(double_divide(X4, double_divide(identity(), X0)), X5), inverse(X4)) = double_divide(double_divide(X0, X5), inverse(identity())).
% 9.29/9.54 Proof: A critical pair between equations 4 and 4.
% 9.29/9.54
% 9.29/9.54 15: double_divide(double_divide(X1, X0), identity()) = double_divide(double_divide(X0, double_divide(identity(), double_divide(X1, identity()))), double_divide(identity(), identity())).
% 9.29/9.54 Proof: Rewrite equation 9,
% 9.29/9.54 lhs with equations [2]
% 9.29/9.54 rhs with equations [2,2].
% 9.29/9.54
% 9.29/9.54 16: X2 = double_divide(double_divide(double_divide(X3, identity()), double_divide(double_divide(identity(), X2), double_divide(X3, identity()))), double_divide(identity(), identity())).
% 9.29/9.54 Proof: Rewrite equation 8,
% 9.29/9.54 lhs with equations []
% 9.29/9.54 rhs with equations [2,2,2].
% 9.29/9.54
% 9.29/9.54 17: identity() = double_divide(double_divide(X0, double_divide(double_divide(double_divide(X1, X0), identity()), double_divide(X1, identity()))), double_divide(identity(), identity())).
% 9.29/9.54 Proof: Rewrite equation 7,
% 9.29/9.54 lhs with equations []
% 9.29/9.54 rhs with equations [2,2,2].
% 9.29/9.54
% 9.29/9.54 18: X2 = double_divide(double_divide(identity(), double_divide(double_divide(double_divide(X3, identity()), X2), double_divide(X3, identity()))), double_divide(identity(), identity())).
% 9.29/9.54 Proof: Rewrite equation 6,
% 9.29/9.54 lhs with equations []
% 9.29/9.54 rhs with equations [2,2,2].
% 9.29/9.54
% 9.29/9.54 19: identity() = double_divide(X0, double_divide(X0, identity())).
% 9.29/9.54 Proof: Rewrite equation 3,
% 9.29/9.54 lhs with equations []
% 9.29/9.54 rhs with equations [2].
% 9.29/9.54
% 9.29/9.54 20: multiply(X0, X1) = double_divide(double_divide(X1, X0), identity()).
% 9.29/9.54 Proof: Rewrite equation 5,
% 9.29/9.54 lhs with equations []
% 9.29/9.54 rhs with equations [2].
% 9.29/9.54
% 9.29/9.54 22: double_divide(double_divide(double_divide(X4, double_divide(identity(), X0)), X5), double_divide(X4, identity())) = double_divide(double_divide(X0, X5), double_divide(identity(), identity())).
% 9.29/9.54 Proof: Rewrite equation 10,
% 9.29/9.54 lhs with equations [2]
% 9.29/9.54 rhs with equations [2].
% 9.29/9.54
% 9.29/9.54 23: double_divide(double_divide(identity(), X0), identity()) = double_divide(double_divide(X0, identity()), double_divide(identity(), identity())).
% 9.29/9.54 Proof: A critical pair between equations 15 and 19.
% 9.29/9.54
% 9.29/9.54 24: X2 = double_divide(double_divide(double_divide(double_divide(identity(), X2), identity()), identity()), double_divide(identity(), identity())).
% 9.29/9.54 Proof: A critical pair between equations 16 and 19.
% 9.29/9.54
% 9.29/9.54 26: identity() = double_divide(double_divide(double_divide(identity(), X7), double_divide(double_divide(X7, identity()), double_divide(identity(), identity()))), double_divide(identity(), identity())).
% 9.29/9.54 Proof: A critical pair between equations 17 and 22.
% 9.29/9.54
% 9.29/9.54 32: double_divide(double_divide(double_divide(X4, identity()), X5), double_divide(X4, identity())) = double_divide(double_divide(double_divide(identity(), identity()), X5), double_divide(identity(), identity())).
% 9.29/9.54 Proof: A critical pair between equations 16 and 18.
% 9.29/9.54
% 9.29/9.54 41: identity() = double_divide(double_divide(double_divide(identity(), X7), double_divide(inverse(X7), inverse(identity()))), inverse(identity())).
% 9.29/9.54 Proof: Rewrite equation 26,
% 9.29/9.54 lhs with equations []
% 9.29/9.54 rhs with equations [2,2,2].
% 9.29/9.54
% 9.29/9.54 43: X2 = double_divide(inverse(inverse(double_divide(identity(), X2))), inverse(identity())).
% 9.29/9.54 Proof: Rewrite equation 24,
% 9.29/9.54 lhs with equations []
% 9.29/9.54 rhs with equations [2,2,2].
% 9.29/9.54
% 9.29/9.54 44: double_divide(double_divide(double_divide(X4, double_divide(identity(), X0)), X5), inverse(X4)) = double_divide(double_divide(X0, X5), inverse(identity())).
% 9.29/9.54 Proof: Rewrite equation 22,
% 9.29/9.54 lhs with equations [2]
% 9.29/9.54 rhs with equations [2].
% 9.29/9.54
% 9.29/9.54 46: multiply(X0, X1) = inverse(double_divide(X1, X0)).
% 9.29/9.54 Proof: Rewrite equation 20,
% 9.29/9.54 lhs with equations []
% 9.29/9.54 rhs with equations [2].
% 9.29/9.54
% 9.29/9.54 47: identity() = double_divide(X0, inverse(X0)).
% 9.29/9.54 Proof: Rewrite equation 19,
% 9.29/9.54 lhs with equations []
% 9.29/9.54 rhs with equations [2].
% 9.29/9.54
% 9.29/9.54 53: double_divide(double_divide(inverse(X4), X5), inverse(X4)) = double_divide(double_divide(inverse(identity()), X5), inverse(identity())).
% 9.29/9.54 Proof: Rewrite equation 32,
% 9.29/9.54 lhs with equations [2,2]
% 9.29/9.54 rhs with equations [2,2].
% 9.29/9.54
% 9.29/9.54 55: inverse(double_divide(identity(), X0)) = double_divide(inverse(X0), inverse(identity())).
% 9.29/9.54 Proof: Rewrite equation 23,
% 9.29/9.54 lhs with equations [2]
% 9.29/9.54 rhs with equations [2,2].
% 9.29/9.54
% 9.29/9.54 56: inverse(double_divide(X1, X0)) = double_divide(double_divide(X0, double_divide(identity(), inverse(X1))), inverse(identity())).
% 9.29/9.54 Proof: Rewrite equation 15,
% 9.29/9.54 lhs with equations [2]
% 9.29/9.54 rhs with equations [2,2].
% 9.29/9.54
% 9.29/9.54 57: identity() = double_divide(inverse(inverse(inverse(identity()))), inverse(identity())).
% 9.29/9.54 Proof: A critical pair between equations 43 and 2.
% 9.29/9.54
% 9.29/9.54 68: double_divide(double_divide(inverse(X4), identity()), inverse(X4)) = double_divide(inverse(inverse(identity())), inverse(identity())).
% 9.29/9.54 Proof: A critical pair between equations 53 and 2.
% 9.29/9.54
% 9.29/9.54 78: identity() = double_divide(double_divide(double_divide(double_divide(identity(), identity()), double_divide(identity(), double_divide(double_divide(double_divide(identity(), double_divide(identity(), identity())), double_divide(identity(), double_divide(identity(), identity()))), double_divide(identity(), identity())))), double_divide(identity(), identity())), double_divide(identity(), identity())).
% 9.29/9.54 Proof: Rewrite equation 57,
% 9.29/9.54 lhs with equations []
% 9.29/9.54 rhs with equations [2,56,2,2,56,56,2,2,2,2].
% 9.29/9.54
% 9.29/9.54 80: double_divide(double_divide(identity(), X0), identity()) = double_divide(double_divide(X0, identity()), double_divide(identity(), identity())).
% 9.29/9.54 Proof: Rewrite equation 55,
% 9.29/9.54 lhs with equations [2]
% 9.29/9.54 rhs with equations [2,2].
% 9.29/9.54
% 9.29/9.54 86: identity() = double_divide(X0, double_divide(X0, identity())).
% 9.29/9.54 Proof: Rewrite equation 47,
% 9.29/9.54 lhs with equations []
% 9.29/9.54 rhs with equations [2].
% 9.29/9.54
% 9.29/9.54 87: multiply(X0, X1) = double_divide(double_divide(X1, X0), identity()).
% 9.29/9.54 Proof: Rewrite equation 46,
% 9.29/9.54 lhs with equations []
% 9.29/9.54 rhs with equations [2].
% 9.29/9.54
% 9.29/9.54 89: X2 = double_divide(double_divide(identity(), double_divide(double_divide(identity(), X2), identity())), identity()).
% 9.29/9.54 Proof: Rewrite equation 43,
% 9.29/9.54 lhs with equations []
% 9.29/9.54 rhs with equations [2,2,2,80].
% 9.29/9.54
% 9.29/9.54 91: identity() = double_divide(double_divide(double_divide(identity(), X7), double_divide(double_divide(X7, identity()), double_divide(identity(), identity()))), double_divide(identity(), identity())).
% 9.29/9.54 Proof: Rewrite equation 41,
% 9.29/9.54 lhs with equations []
% 9.29/9.54 rhs with equations [2,2,2].
% 9.29/9.54
% 9.29/9.54 98: double_divide(double_divide(double_divide(X4, identity()), identity()), double_divide(X4, identity())) = double_divide(identity(), identity()).
% 9.29/9.54 Proof: Rewrite equation 68,
% 9.29/9.54 lhs with equations [2,2]
% 9.29/9.54 rhs with equations [2,2,2,80,86].
% 9.29/9.54
% 9.29/9.54 99: double_divide(double_divide(double_divide(X4, double_divide(identity(), X0)), X5), double_divide(X4, identity())) = double_divide(double_divide(X0, X5), double_divide(identity(), identity())).
% 9.29/9.54 Proof: Rewrite equation 44,
% 9.29/9.54 lhs with equations [2]
% 9.29/9.54 rhs with equations [2].
% 9.29/9.54
% 9.29/9.54 102: identity() = double_divide(double_divide(identity(), X1), double_divide(double_divide(X1, identity()), double_divide(identity(), identity()))).
% 9.29/9.54 Proof: A critical pair between equations 86 and 80.
% 9.29/9.54
% 9.29/9.54 103: X3 = double_divide(double_divide(identity(), double_divide(double_divide(X3, identity()), double_divide(identity(), identity()))), identity()).
% 9.29/9.54 Proof: A critical pair between equations 89 and 80.
% 9.29/9.54
% 9.29/9.54 108: double_divide(double_divide(identity(), double_divide(identity(), double_divide(double_divide(identity(), X3), identity()))), identity()) = double_divide(X3, double_divide(identity(), identity())).
% 9.29/9.54 Proof: A critical pair between equations 80 and 89.
% 9.29/9.54
% 9.29/9.54 109: double_divide(double_divide(identity(), double_divide(identity(), double_divide(identity(), X7))), identity()) = double_divide(double_divide(X7, identity()), double_divide(identity(), identity())).
% 9.29/9.54 Proof: A critical pair between equations 80 and 99.
% 9.29/9.54
% 9.29/9.54 116: inverse(double_divide(identity(), double_divide(identity(), inverse(double_divide(identity(), X3))))) = double_divide(X3, inverse(identity())).
% 9.29/9.54 Proof: Rewrite equation 108,
% 9.29/9.54 lhs with equations [2,2]
% 9.29/9.54 rhs with equations [2].
% 9.29/9.54
% 9.29/9.54 121: X3 = inverse(double_divide(identity(), inverse(double_divide(identity(), double_divide(identity(), inverse(double_divide(identity(), inverse(X3)))))))).
% 9.29/9.54 Proof: Rewrite equation 103,
% 9.29/9.54 lhs with equations []
% 9.29/9.54 rhs with equations [2,2,116,2].
% 9.29/9.54
% 9.29/9.54 122: identity() = double_divide(double_divide(identity(), X1), inverse(double_divide(identity(), double_divide(identity(), inverse(double_divide(identity(), inverse(X1))))))).
% 9.29/9.54 Proof: Rewrite equation 102,
% 9.29/9.54 lhs with equations []
% 9.29/9.54 rhs with equations [2,2,116].
% 9.29/9.54
% 9.29/9.54 125: double_divide(inverse(inverse(X4)), inverse(X4)) = inverse(identity()).
% 9.29/9.54 Proof: Rewrite equation 98,
% 9.29/9.54 lhs with equations [2,2,2]
% 9.29/9.54 rhs with equations [2].
% 9.29/9.54
% 9.29/9.54 132: identity() = double_divide(identity(), inverse(identity())).
% 9.29/9.54 Proof: Rewrite equation 91,
% 9.29/9.54 lhs with equations []
% 9.29/9.54 rhs with equations [2,2,116,122,2].
% 9.29/9.54
% 9.29/9.54 134: X2 = inverse(double_divide(identity(), inverse(double_divide(identity(), X2)))).
% 9.29/9.54 Proof: Rewrite equation 89,
% 9.29/9.54 lhs with equations []
% 9.29/9.54 rhs with equations [2,2].
% 9.29/9.54
% 9.29/9.54 136: multiply(X0, X1) = inverse(double_divide(X1, X0)).
% 9.29/9.54 Proof: Rewrite equation 87,
% 9.29/9.54 lhs with equations []
% 9.29/9.54 rhs with equations [2].
% 9.29/9.54
% 9.29/9.54 137: identity() = double_divide(X0, inverse(X0)).
% 9.29/9.54 Proof: Rewrite equation 86,
% 9.29/9.54 lhs with equations []
% 9.29/9.54 rhs with equations [2].
% 9.29/9.54
% 9.29/9.54 143: identity() = inverse(double_divide(identity(), double_divide(identity(), double_divide(identity(), inverse(double_divide(identity(), double_divide(inverse(identity()), double_divide(identity(), inverse(inverse(identity())))))))))).
% 9.29/9.54 Proof: Rewrite equation 78,
% 9.29/9.54 lhs with equations []
% 9.29/9.54 rhs with equations [2,2,137,2,137,2,2,116,137,137,2,2,116,2,116,134].
% 9.29/9.54
% 9.29/9.54 151: inverse(double_divide(identity(), double_divide(identity(), double_divide(identity(), X7)))) = inverse(double_divide(identity(), double_divide(identity(), inverse(double_divide(identity(), inverse(X7)))))).
% 9.29/9.54 Proof: Rewrite equation 109,
% 9.29/9.54 lhs with equations [2]
% 9.29/9.54 rhs with equations [2,2,116].
% 9.29/9.54
% 9.29/9.54 153: inverse(double_divide(identity(), X0)) = inverse(double_divide(identity(), double_divide(identity(), double_divide(identity(), X0)))).
% 9.29/9.54 Proof: Rewrite equation 80,
% 9.29/9.54 lhs with equations [2]
% 9.29/9.54 rhs with equations [2,2,116,151].
% 9.29/9.54
% 9.29/9.54 160: identity() = inverse(double_divide(identity(), inverse(double_divide(identity(), double_divide(identity(), inverse(identity())))))).
% 9.29/9.54 Proof: A critical pair between equations 121 and 132.
% 9.29/9.54
% 9.29/9.54 166: inverse(identity()) = double_divide(inverse(inverse(double_divide(identity(), inverse(double_divide(identity(), X5))))), X5).
% 9.29/9.54 Proof: A critical pair between equations 125 and 134.
% 9.29/9.54
% 9.29/9.54 167: double_divide(identity(), identity()) = double_divide(double_divide(double_divide(double_divide(identity(), double_divide(double_divide(identity(), X5), identity())), identity()), identity()), X5).
% 9.29/9.54 Proof: Rewrite equation 166,
% 9.29/9.54 lhs with equations [2]
% 9.29/9.54 rhs with equations [2,2,2].
% 9.29/9.54
% 9.29/9.54 173: identity() = double_divide(double_divide(identity(), double_divide(double_divide(identity(), identity()), identity())), identity()).
% 9.29/9.54 Proof: Rewrite equation 160,
% 9.29/9.54 lhs with equations []
% 9.29/9.54 rhs with equations [2,153,2,2].
% 9.29/9.54
% 9.29/9.54 176: double_divide(double_divide(identity(), X0), identity()) = double_divide(double_divide(identity(), double_divide(identity(), double_divide(identity(), X0))), identity()).
% 9.29/9.54 Proof: Rewrite equation 153,
% 9.29/9.54 lhs with equations [2]
% 9.29/9.54 rhs with equations [2].
% 9.29/9.54
% 9.29/9.54 184: identity() = double_divide(double_divide(identity(), double_divide(double_divide(identity(), double_divide(double_divide(identity(), identity()), double_divide(identity(), double_divide(double_divide(identity(), identity()), identity())))), identity())), identity()).
% 9.29/9.54 Proof: Rewrite equation 143,
% 9.29/9.54 lhs with equations []
% 9.29/9.54 rhs with equations [2,2,2,2,2,176].
% 9.29/9.54
% 9.29/9.54 190: identity() = double_divide(X0, double_divide(X0, identity())).
% 9.29/9.54 Proof: Rewrite equation 137,
% 9.29/9.54 lhs with equations []
% 9.29/9.54 rhs with equations [2].
% 9.29/9.54
% 9.29/9.54 191: multiply(X0, X1) = double_divide(double_divide(X1, X0), identity()).
% 9.29/9.54 Proof: Rewrite equation 136,
% 9.29/9.54 lhs with equations []
% 9.29/9.54 rhs with equations [2].
% 9.29/9.54
% 9.29/9.54 211: double_divide(identity(), identity()) = double_divide(double_divide(identity(), identity()), identity()).
% 9.29/9.54 Proof: A critical pair between equations 167 and 173.
% 9.29/9.54
% 9.29/9.54 233: inverse(identity()) = inverse(inverse(identity())).
% 9.29/9.54 Proof: Rewrite equation 211,
% 9.29/9.54 lhs with equations [2]
% 9.29/9.54 rhs with equations [2,2].
% 9.29/9.54
% 9.29/9.54 251: multiply(X0, X1) = inverse(double_divide(X1, X0)).
% 9.29/9.54 Proof: Rewrite equation 191,
% 9.29/9.54 lhs with equations []
% 9.29/9.54 rhs with equations [2].
% 9.29/9.54
% 9.29/9.54 252: identity() = double_divide(X0, inverse(X0)).
% 9.29/9.54 Proof: Rewrite equation 190,
% 9.29/9.54 lhs with equations []
% 9.29/9.54 rhs with equations [2].
% 9.29/9.54
% 9.29/9.54 258: identity() = inverse(identity()).
% 9.29/9.54 Proof: Rewrite equation 184,
% 9.29/9.54 lhs with equations []
% 9.29/9.54 rhs with equations [2,2,2,233,252,2,233,252,2,252,2].
% 9.29/9.54
% 9.29/9.54 269: multiply(inverse(a1()), a1()) = identity().
% 9.29/9.54 Proof: Rewrite lhs with equations [251,252,258]
% 9.29/9.54 rhs with equations [].
% 9.29/9.54
% 9.29/9.54 % SZS output end Proof
%------------------------------------------------------------------------------