TSTP Solution File: GRP562-1 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP562-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n003.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 01:15:21 EDT 2023
% Result : Unsatisfiable 0.75s 1.16s
% Output : CNFRefutation 0.75s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP562-1 : TPTP v8.1.2. Released v2.6.0.
% 0.12/0.13 % Command : toma --casc %s
% 0.12/0.34 % Computer : n003.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 : Mon Aug 28 20:51:25 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.75/1.16 % SZS status Unsatisfiable
% 0.75/1.16 % SZS output start Proof
% 0.75/1.16 original problem:
% 0.75/1.16 axioms:
% 0.75/1.16 divide(divide(divide(A, inverse(B)), C), divide(A, C)) = B
% 0.75/1.16 multiply(A, B) = divide(A, inverse(B))
% 0.75/1.16 goal:
% 0.75/1.16 multiply(multiply(inverse(b2()), b2()), a2()) != a2()
% 0.75/1.16 To show the unsatisfiability of the original goal,
% 0.75/1.16 it suffices to show that multiply(multiply(inverse(b2()), b2()), a2()) = a2() (skolemized goal) is valid under the axioms.
% 0.75/1.16 Here is an equational proof:
% 0.75/1.16 0: divide(divide(divide(X0, inverse(X1)), X2), divide(X0, X2)) = X1.
% 0.75/1.16 Proof: Axiom.
% 0.75/1.16
% 0.75/1.16 1: multiply(X0, X1) = divide(X0, inverse(X1)).
% 0.75/1.16 Proof: Axiom.
% 0.75/1.16
% 0.75/1.16 2: X1 = divide(X4, divide(divide(X3, inverse(X4)), divide(X3, inverse(X1)))).
% 0.75/1.16 Proof: A critical pair between equations 0 and 0.
% 0.75/1.16
% 0.75/1.16 3: X1 = divide(divide(divide(divide(divide(X3, inverse(X4)), X5), inverse(X1)), divide(X3, X5)), X4).
% 0.75/1.16 Proof: A critical pair between equations 0 and 0.
% 0.75/1.16
% 0.75/1.16 4: X1 = divide(divide(X9, divide(divide(divide(X6, inverse(inverse(X1))), X8), divide(X6, X8))), X9).
% 0.75/1.16 Proof: A critical pair between equations 3 and 3.
% 0.75/1.16
% 0.75/1.16 12: X1 = divide(X4, divide(X9, divide(divide(divide(divide(divide(X6, inverse(inverse(X4))), X8), inverse(X9)), divide(X6, X8)), inverse(X1)))).
% 0.75/1.16 Proof: A critical pair between equations 2 and 3.
% 0.75/1.16
% 0.75/1.16 14: X1 = divide(divide(divide(divide(X9, X5), inverse(X1)), divide(divide(divide(divide(divide(X6, inverse(inverse(X4))), X8), inverse(X9)), divide(X6, X8)), X5)), X4).
% 0.75/1.16 Proof: A critical pair between equations 3 and 3.
% 0.75/1.16
% 0.75/1.16 15: X1 = divide(divide(X9, inverse(X1)), X9).
% 0.75/1.16 Proof: Rewrite equation 4,
% 0.75/1.16 lhs with equations []
% 0.75/1.16 rhs with equations [0].
% 0.75/1.16
% 0.75/1.16 16: X4 = divide(X4, divide(X13, X13)).
% 0.75/1.16 Proof: A critical pair between equations 12 and 3.
% 0.75/1.16
% 0.75/1.16 17: X1 = divide(X11, divide(inverse(X1), inverse(X11))).
% 0.75/1.16 Proof: A critical pair between equations 15 and 15.
% 0.75/1.16
% 0.75/1.16 19: X1 = divide(divide(divide(divide(X13, inverse(X4)), inverse(X1)), X13), X4).
% 0.75/1.16 Proof: A critical pair between equations 14 and 3.
% 0.75/1.16
% 0.75/1.16 28: divide(divide(X13, X13), inverse(X15)) = X15.
% 0.75/1.16 Proof: A critical pair between equations 16 and 15.
% 0.75/1.16
% 0.75/1.16 29: divide(inverse(X13), inverse(X4)) = divide(X4, X13).
% 0.75/1.16 Proof: A critical pair between equations 2 and 17.
% 0.75/1.16
% 0.75/1.16 30: X1 = divide(divide(divide(divide(X15, X15), inverse(X4)), inverse(X1)), X4).
% 0.75/1.16 Proof: A critical pair between equations 19 and 16.
% 0.75/1.16
% 0.75/1.16 49: X1 = multiply(inverse(X4), multiply(X4, X1)).
% 0.75/1.16 Proof: Rewrite equation 30,
% 0.75/1.16 lhs with equations []
% 0.75/1.16 rhs with equations [28,1,29,1].
% 0.75/1.16
% 0.75/1.16 65: X1 = multiply(inverse(X4), multiply(inverse(X13), multiply(multiply(X13, X4), X1))).
% 0.75/1.16 Proof: Rewrite equation 19,
% 0.75/1.16 lhs with equations []
% 0.75/1.16 rhs with equations [1,1,29,1,29,1].
% 0.75/1.16
% 0.75/1.16 70: multiply(inverse(X13), X4) = divide(X4, X13).
% 0.75/1.16 Proof: Rewrite equation 29,
% 0.75/1.16 lhs with equations [1]
% 0.75/1.16 rhs with equations [].
% 0.75/1.16
% 0.75/1.16 77: multiply(multiply(X15, inverse(X15)), X16) = X16.
% 0.75/1.16 Proof: A critical pair between equations 49 and 65.
% 0.75/1.16
% 0.75/1.16 79: multiply(X5, X6) = multiply(inverse(inverse(X5)), X6).
% 0.75/1.16 Proof: A critical pair between equations 49 and 49.
% 0.75/1.16
% 0.75/1.16 80: multiply(X14, X1) = multiply(inverse(inverse(X1)), X14).
% 0.75/1.16 Proof: A critical pair between equations 1 and 70.
% 0.75/1.16
% 0.75/1.16 114: multiply(X14, X1) = multiply(X1, X14).
% 0.75/1.16 Proof: Rewrite equation 80,
% 0.75/1.16 lhs with equations []
% 0.75/1.16 rhs with equations [79].
% 0.75/1.16
% 0.75/1.16 116: multiply(multiply(inverse(b2()), b2()), a2()) = a2().
% 0.75/1.16 Proof: Rewrite lhs with equations [114,77]
% 0.75/1.16 rhs with equations [].
% 0.75/1.16
% 0.75/1.16 % SZS output end Proof
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