TSTP Solution File: GRP536-1 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP536-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n026.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 01:15:16 EDT 2023
% Result : Unsatisfiable 0.65s 1.03s
% Output : CNFRefutation 0.65s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP536-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.00/0.12 % Command : toma --casc %s
% 0.11/0.32 % Computer : n026.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Aug 28 21:40:05 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.65/1.03 % SZS status Unsatisfiable
% 0.65/1.03 % SZS output start Proof
% 0.65/1.03 original problem:
% 0.65/1.03 axioms:
% 0.65/1.03 divide(divide(A, divide(divide(A, B), C)), B) = C
% 0.65/1.03 multiply(A, B) = divide(A, divide(divide(C, C), B))
% 0.65/1.03 inverse(A) = divide(divide(B, B), A)
% 0.65/1.03 identity() = divide(A, A)
% 0.65/1.03 goal:
% 0.65/1.03 multiply(a(), b()) != multiply(b(), a())
% 0.65/1.03 To show the unsatisfiability of the original goal,
% 0.65/1.03 it suffices to show that multiply(a(), b()) = multiply(b(), a()) (skolemized goal) is valid under the axioms.
% 0.65/1.03 Here is an equational proof:
% 0.65/1.03 0: divide(divide(X0, divide(divide(X0, X1), X2)), X1) = X2.
% 0.65/1.03 Proof: Axiom.
% 0.65/1.03
% 0.65/1.03 1: multiply(X0, X1) = divide(X0, divide(divide(X2, X2), X1)).
% 0.65/1.03 Proof: Axiom.
% 0.65/1.03
% 0.65/1.03 2: inverse(X0) = divide(divide(X1, X1), X0).
% 0.65/1.03 Proof: Axiom.
% 0.65/1.03
% 0.65/1.03 3: identity() = divide(X0, X0).
% 0.65/1.03 Proof: Axiom.
% 0.65/1.03
% 0.65/1.03 4: multiply(X0, X1) = divide(X0, divide(identity(), X1)).
% 0.65/1.03 Proof: Rewrite equation 1,
% 0.65/1.03 lhs with equations []
% 0.65/1.03 rhs with equations [3].
% 0.65/1.03
% 0.65/1.03 5: inverse(X0) = divide(identity(), X0).
% 0.65/1.03 Proof: Rewrite equation 2,
% 0.65/1.03 lhs with equations []
% 0.65/1.03 rhs with equations [3].
% 0.65/1.03
% 0.65/1.03 12: divide(X0, X1) = divide(divide(X0, identity()), X1).
% 0.65/1.03 Proof: A critical pair between equations 0 and 3.
% 0.65/1.03
% 0.65/1.03 15: X4 = divide(divide(X3, X5), divide(divide(X3, X4), X5)).
% 0.65/1.03 Proof: A critical pair between equations 0 and 0.
% 0.65/1.03
% 0.65/1.03 20: X4 = divide(X6, divide(divide(X6, X4), identity())).
% 0.65/1.03 Proof: A critical pair between equations 15 and 12.
% 0.65/1.03
% 0.65/1.03 21: X6 = divide(divide(X6, X5), divide(identity(), X5)).
% 0.65/1.03 Proof: A critical pair between equations 15 and 3.
% 0.65/1.03
% 0.65/1.03 22: X4 = divide(divide(X3, divide(X3, X4)), identity()).
% 0.65/1.03 Proof: A critical pair between equations 15 and 3.
% 0.65/1.03
% 0.65/1.03 29: divide(divide(X3, divide(divide(X3, identity()), X5)), X1) = divide(X5, X1).
% 0.65/1.03 Proof: A critical pair between equations 12 and 0.
% 0.65/1.03
% 0.65/1.03 30: divide(divide(X3, divide(X3, X5)), X1) = divide(X5, X1).
% 0.65/1.03 Proof: Rewrite equation 29,
% 0.65/1.03 lhs with equations [12]
% 0.65/1.03 rhs with equations [].
% 0.65/1.03
% 0.65/1.03 37: X4 = divide(X4, identity()).
% 0.65/1.03 Proof: Rewrite equation 22,
% 0.65/1.03 lhs with equations []
% 0.65/1.03 rhs with equations [30].
% 0.65/1.03
% 0.65/1.03 38: X6 = divide(divide(X6, X5), inverse(X5)).
% 0.65/1.03 Proof: Rewrite equation 21,
% 0.65/1.03 lhs with equations []
% 0.65/1.03 rhs with equations [5].
% 0.65/1.03
% 0.65/1.03 39: X4 = divide(X6, divide(X6, X4)).
% 0.65/1.03 Proof: Rewrite equation 20,
% 0.65/1.03 lhs with equations []
% 0.65/1.03 rhs with equations [37].
% 0.65/1.03
% 0.65/1.03 41: multiply(X0, X1) = divide(X0, inverse(X1)).
% 0.65/1.03 Proof: Rewrite equation 4,
% 0.65/1.03 lhs with equations []
% 0.65/1.03 rhs with equations [5].
% 0.65/1.03
% 0.65/1.03 46: divide(X5, inverse(divide(X7, X5))) = X7.
% 0.65/1.03 Proof: A critical pair between equations 30 and 38.
% 0.65/1.03
% 0.65/1.03 57: divide(X5, divide(identity(), divide(X7, X5))) = X7.
% 0.65/1.03 Proof: Rewrite equation 46,
% 0.65/1.03 lhs with equations [5]
% 0.65/1.03 rhs with equations [].
% 0.65/1.03
% 0.65/1.03 58: multiply(X0, X1) = divide(X0, divide(identity(), X1)).
% 0.65/1.03 Proof: Rewrite equation 41,
% 0.65/1.03 lhs with equations []
% 0.65/1.03 rhs with equations [5].
% 0.65/1.03
% 0.65/1.03 60: X6 = divide(divide(X6, X5), divide(identity(), X5)).
% 0.65/1.03 Proof: Rewrite equation 38,
% 0.65/1.03 lhs with equations []
% 0.65/1.03 rhs with equations [5].
% 0.65/1.03
% 0.65/1.03 73: divide(X8, X9) = divide(divide(identity(), X9), divide(identity(), X8)).
% 0.65/1.03 Proof: A critical pair between equations 57 and 60.
% 0.65/1.03
% 0.65/1.03 87: multiply(X0, X1) = divide(X0, inverse(X1)).
% 0.65/1.03 Proof: Rewrite equation 58,
% 0.65/1.03 lhs with equations []
% 0.65/1.03 rhs with equations [5].
% 0.65/1.03
% 0.65/1.03 90: divide(X8, X9) = divide(inverse(X9), inverse(X8)).
% 0.65/1.03 Proof: Rewrite equation 73,
% 0.65/1.03 lhs with equations []
% 0.65/1.03 rhs with equations [5,5].
% 0.65/1.03
% 0.65/1.03 107: multiply(X0, X1) = divide(X0, divide(identity(), X1)).
% 0.65/1.03 Proof: Rewrite equation 87,
% 0.65/1.03 lhs with equations []
% 0.65/1.03 rhs with equations [5].
% 0.65/1.03
% 0.65/1.03 115: divide(X8, X9) = divide(divide(identity(), X9), divide(identity(), X8)).
% 0.65/1.03 Proof: Rewrite equation 90,
% 0.65/1.03 lhs with equations []
% 0.65/1.03 rhs with equations [5,5].
% 0.65/1.03
% 0.65/1.03 116: multiply(a(), b()) = multiply(b(), a()).
% 0.65/1.03 Proof: Rewrite lhs with equations [107]
% 0.65/1.03 rhs with equations [107,115,39].
% 0.65/1.03
% 0.65/1.03 % SZS output end Proof
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