TSTP Solution File: BOO071-1 by Toma---0.4
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% File : Toma---0.4
% Problem : BOO071-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n014.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 : Wed Aug 30 18:11:08 EDT 2023
% Result : Unsatisfiable 7.66s 8.01s
% Output : CNFRefutation 7.66s
% 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 : BOO071-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.12 % Command : toma --casc %s
% 0.10/0.32 % Computer : n014.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Sun Aug 27 08:03:46 EDT 2023
% 0.10/0.32 % CPUTime :
% 7.66/8.01 % SZS status Unsatisfiable
% 7.66/8.01 % SZS output start Proof
% 7.66/8.01 original problem:
% 7.66/8.01 axioms:
% 7.66/8.01 multiply(multiply(A, inverse(A), B), inverse(multiply(multiply(C, D, E), F, multiply(C, D, G))), multiply(D, multiply(G, F, E), C)) = B
% 7.66/8.01 goal:
% 7.66/8.01 multiply(inverse(b()), b(), a()) != a()
% 7.66/8.01 To show the unsatisfiability of the original goal,
% 7.66/8.01 it suffices to show that multiply(inverse(b()), b(), a()) = a() (skolemized goal) is valid under the axioms.
% 7.66/8.01 Here is an equational proof:
% 7.66/8.01 0: multiply(multiply(X0, inverse(X0), X1), inverse(multiply(multiply(X2, X3, X4), X5, multiply(X2, X3, X6))), multiply(X3, multiply(X6, X5, X4), X2)) = X1.
% 7.66/8.01 Proof: Axiom.
% 7.66/8.01
% 7.66/8.01 1: multiply(X10, multiply(X13, inverse(multiply(X9, X10, X11)), X11), X9) = multiply(multiply(X9, X10, X13), inverse(multiply(multiply(X2, X3, X4), X5, multiply(X2, X3, X6))), multiply(X3, multiply(X6, X5, X4), X2)).
% 7.66/8.01 Proof: A critical pair between equations 0 and 0.
% 7.66/8.01
% 7.66/8.01 2: X1 = multiply(multiply(X0, inverse(X0), X1), inverse(multiply(multiply(X2, X3, multiply(X10, multiply(X13, X12, X11), X9)), inverse(multiply(multiply(X9, X10, X11), X12, multiply(X9, X10, X13))), multiply(X2, X3, multiply(X7, inverse(X7), X8)))), multiply(X3, X8, X2)).
% 7.66/8.01 Proof: A critical pair between equations 0 and 0.
% 7.66/8.01
% 7.66/8.01 5: multiply(inverse(X14), multiply(X15, inverse(multiply(X14, inverse(X14), X11)), X11), X14) = X15.
% 7.66/8.01 Proof: A critical pair between equations 1 and 0.
% 7.66/8.01
% 7.66/8.01 8: X1 = multiply(multiply(X0, inverse(X0), X1), inverse(multiply(X17, multiply(multiply(X23, inverse(X23), inverse(X17)), inverse(multiply(multiply(X22, X18, X21), X20, multiply(X22, X18, X19))), multiply(X18, multiply(X19, X20, X21), X22)), multiply(X7, inverse(X7), X8))), multiply(inverse(X17), X8, X17)).
% 7.66/8.01 Proof: A critical pair between equations 2 and 2.
% 7.66/8.01
% 7.66/8.01 17: X1 = multiply(multiply(X0, inverse(X0), X1), inverse(multiply(X17, inverse(X17), multiply(X7, inverse(X7), X8))), multiply(inverse(X17), X8, X17)).
% 7.66/8.01 Proof: Rewrite equation 8,
% 7.66/8.01 lhs with equations []
% 7.66/8.01 rhs with equations [0].
% 7.66/8.01
% 7.66/8.01 21: multiply(inverse(X20), X22, X20) = multiply(multiply(X21, inverse(X21), X22), inverse(multiply(X17, inverse(X17), multiply(X7, inverse(X7), X8))), multiply(inverse(X17), X8, X17)).
% 7.66/8.01 Proof: A critical pair between equations 17 and 17.
% 7.66/8.01
% 7.66/8.01 23: multiply(inverse(X20), X22, X20) = multiply(multiply(X21, inverse(X21), X22), inverse(multiply(multiply(X2, X3, X4), X5, multiply(X2, X3, X6))), multiply(X3, multiply(X6, X5, X4), X2)).
% 7.66/8.01 Proof: A critical pair between equations 0 and 17.
% 7.66/8.01
% 7.66/8.01 30: multiply(inverse(X20), X22, X20) = X22.
% 7.66/8.01 Proof: Rewrite equation 23,
% 7.66/8.01 lhs with equations []
% 7.66/8.01 rhs with equations [0].
% 7.66/8.01
% 7.66/8.01 31: X22 = multiply(multiply(X21, inverse(X21), X22), inverse(multiply(X17, inverse(X17), multiply(X7, inverse(X7), X8))), X8).
% 7.66/8.01 Proof: Rewrite equation 21,
% 7.66/8.01 lhs with equations [30]
% 7.66/8.01 rhs with equations [30].
% 7.66/8.01
% 7.66/8.01 32: X15 = multiply(X15, inverse(multiply(X23, inverse(X23), X11)), X11).
% 7.66/8.01 Proof: A critical pair between equations 5 and 30.
% 7.66/8.01
% 7.66/8.01 33: inverse(X23) = multiply(inverse(X14), inverse(multiply(X14, inverse(X14), X23)), X14).
% 7.66/8.01 Proof: A critical pair between equations 5 and 30.
% 7.66/8.01
% 7.66/8.01 36: X22 = multiply(multiply(X21, inverse(X21), X22), inverse(multiply(X26, inverse(X26), inverse(inverse(X25)))), X25).
% 7.66/8.01 Proof: A critical pair between equations 31 and 17.
% 7.66/8.01
% 7.66/8.01 45: inverse(X23) = inverse(multiply(X14, inverse(X14), X23)).
% 7.66/8.01 Proof: Rewrite equation 33,
% 7.66/8.01 lhs with equations []
% 7.66/8.01 rhs with equations [30].
% 7.66/8.01
% 7.66/8.01 46: X15 = multiply(X15, inverse(X11), X11).
% 7.66/8.01 Proof: Rewrite equation 32,
% 7.66/8.01 lhs with equations []
% 7.66/8.01 rhs with equations [45].
% 7.66/8.01
% 7.66/8.01 47: X22 = multiply(X21, inverse(X21), X22).
% 7.66/8.01 Proof: Rewrite equation 31,
% 7.66/8.01 lhs with equations []
% 7.66/8.01 rhs with equations [45,45,46].
% 7.66/8.01
% 7.66/8.01 66: inverse(inverse(X28)) = X28.
% 7.66/8.01 Proof: A critical pair between equations 36 and 47.
% 7.66/8.01
% 7.66/8.01 83: X22 = multiply(inverse(X29), X29, X22).
% 7.66/8.01 Proof: A critical pair between equations 47 and 66.
% 7.66/8.01
% 7.66/8.01 103: multiply(inverse(b()), b(), a()) = a().
% 7.66/8.01 Proof: Rewrite lhs with equations [83]
% 7.66/8.01 rhs with equations [].
% 7.66/8.01
% 7.66/8.01 % SZS output end Proof
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