TSTP Solution File: GRP011-4 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP011-4 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n017.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 01:13:34 EDT 2023
% Result : Unsatisfiable 0.56s 0.83s
% Output : CNFRefutation 0.56s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP011-4 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : toma --casc %s
% 0.12/0.34 % Computer : n017.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 00:16:28 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.56/0.83 % SZS status Unsatisfiable
% 0.56/0.83 % SZS output start Proof
% 0.56/0.83 original problem:
% 0.56/0.83 axioms:
% 0.56/0.83 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 0.56/0.83 multiply(identity(), X) = X
% 0.56/0.83 multiply(inverse(X), X) = identity()
% 0.56/0.83 multiply(b(), c()) = multiply(d(), c())
% 0.56/0.83 goal:
% 0.56/0.83 b() != d()
% 0.56/0.83 To show the unsatisfiability of the original goal,
% 0.56/0.83 it suffices to show that b() = d() (skolemized goal) is valid under the axioms.
% 0.56/0.83 Here is an equational proof:
% 0.56/0.83 0: multiply(multiply(X0, X1), X2) = multiply(X0, multiply(X1, X2)).
% 0.56/0.83 Proof: Axiom.
% 0.56/0.83
% 0.56/0.83 1: multiply(identity(), X0) = X0.
% 0.56/0.83 Proof: Axiom.
% 0.56/0.83
% 0.56/0.83 2: multiply(inverse(X0), X0) = identity().
% 0.56/0.83 Proof: Axiom.
% 0.56/0.83
% 0.56/0.83 3: multiply(b(), c()) = multiply(d(), c()).
% 0.56/0.83 Proof: Axiom.
% 0.56/0.83
% 0.56/0.83 4: multiply(inverse(X3), multiply(X3, X2)) = multiply(identity(), X2).
% 0.56/0.83 Proof: A critical pair between equations 0 and 2.
% 0.56/0.83
% 0.56/0.83 5: multiply(d(), multiply(c(), X2)) = multiply(multiply(b(), c()), X2).
% 0.56/0.83 Proof: A critical pair between equations 0 and 3.
% 0.56/0.83
% 0.56/0.83 6: multiply(d(), multiply(c(), X2)) = multiply(b(), multiply(c(), X2)).
% 0.56/0.83 Proof: Rewrite equation 5,
% 0.56/0.83 lhs with equations []
% 0.56/0.83 rhs with equations [0].
% 0.56/0.83
% 0.56/0.83 7: multiply(inverse(X3), multiply(X3, X2)) = X2.
% 0.56/0.83 Proof: Rewrite equation 4,
% 0.56/0.83 lhs with equations []
% 0.56/0.83 rhs with equations [1].
% 0.56/0.83
% 0.56/0.83 9: X4 = multiply(inverse(inverse(X4)), identity()).
% 0.56/0.83 Proof: A critical pair between equations 7 and 2.
% 0.56/0.83
% 0.56/0.83 11: multiply(X4, X5) = multiply(inverse(inverse(X4)), X5).
% 0.56/0.83 Proof: A critical pair between equations 7 and 7.
% 0.56/0.83
% 0.56/0.83 14: X4 = multiply(X4, identity()).
% 0.56/0.83 Proof: Rewrite equation 9,
% 0.56/0.83 lhs with equations []
% 0.56/0.83 rhs with equations [11].
% 0.56/0.83
% 0.56/0.83 16: multiply(X4, inverse(X4)) = identity().
% 0.56/0.83 Proof: A critical pair between equations 11 and 2.
% 0.56/0.83
% 0.56/0.83 40: multiply(b(), multiply(c(), inverse(c()))) = multiply(d(), identity()).
% 0.56/0.83 Proof: A critical pair between equations 6 and 16.
% 0.56/0.83
% 0.56/0.83 42: b() = d().
% 0.56/0.83 Proof: Rewrite equation 40,
% 0.56/0.83 lhs with equations [16,14]
% 0.56/0.83 rhs with equations [14].
% 0.56/0.83
% 0.56/0.83 43: b() = d().
% 0.56/0.83 Proof: Rewrite lhs with equations []
% 0.56/0.83 rhs with equations [42].
% 0.56/0.83
% 0.56/0.83 % SZS output end Proof
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