TSTP Solution File: BOO068-1 by Toma---0.4
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% File : Toma---0.4
% Problem : BOO068-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n010.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 4.97s 5.32s
% Output : CNFRefutation 4.97s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : BOO068-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.13 % Command : toma --casc %s
% 0.15/0.34 % Computer : n010.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Sun Aug 27 07:43:04 EDT 2023
% 0.15/0.35 % CPUTime :
% 4.97/5.32 % SZS status Unsatisfiable
% 4.97/5.32 % SZS output start Proof
% 4.97/5.32 original problem:
% 4.97/5.32 axioms:
% 4.97/5.32 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
% 4.97/5.32 goal:
% 4.97/5.32 multiply(b(), a(), a()) != a()
% 4.97/5.32 To show the unsatisfiability of the original goal,
% 4.97/5.32 it suffices to show that multiply(b(), a(), a()) = a() (skolemized goal) is valid under the axioms.
% 4.97/5.32 Here is an equational proof:
% 4.97/5.32 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.
% 4.97/5.32 Proof: Axiom.
% 4.97/5.32
% 4.97/5.32 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)).
% 4.97/5.32 Proof: A critical pair between equations 0 and 0.
% 4.97/5.32
% 4.97/5.32 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)).
% 4.97/5.32 Proof: A critical pair between equations 0 and 0.
% 4.97/5.32
% 4.97/5.32 5: multiply(inverse(X14), multiply(X15, inverse(multiply(X14, inverse(X14), X11)), X11), X14) = X15.
% 4.97/5.32 Proof: A critical pair between equations 1 and 0.
% 4.97/5.32
% 4.97/5.32 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)).
% 4.97/5.32 Proof: A critical pair between equations 2 and 2.
% 4.97/5.32
% 4.97/5.32 13: multiply(X10, multiply(X13, inverse(multiply(X9, X10, X11)), X11), X9) = multiply(multiply(X9, X10, X13), inverse(multiply(multiply(X2, X3, multiply(X17, multiply(X20, X19, X18), X16)), inverse(multiply(multiply(X16, X17, X18), X19, multiply(X16, X17, X20))), multiply(X2, X3, multiply(X14, inverse(X14), X15)))), multiply(X3, X15, X2)).
% 4.97/5.32 Proof: A critical pair between equations 1 and 0.
% 4.97/5.32
% 4.97/5.32 15: multiply(X17, multiply(X20, inverse(multiply(X16, X17, X18)), X18), X16) = multiply(multiply(X16, X17, X20), 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)).
% 4.97/5.32 Proof: A critical pair between equations 2 and 0.
% 4.97/5.32
% 4.97/5.32 17: X1 = multiply(multiply(X0, inverse(X0), X1), inverse(multiply(X17, inverse(X17), multiply(X7, inverse(X7), X8))), multiply(inverse(X17), X8, X17)).
% 4.97/5.32 Proof: Rewrite equation 8,
% 4.97/5.32 lhs with equations []
% 4.97/5.32 rhs with equations [0].
% 4.97/5.32
% 4.97/5.32 18: multiply(X22, multiply(X23, inverse(multiply(X21, X22, X18)), X18), X21) = multiply(X22, multiply(X23, inverse(multiply(X21, X22, X33)), X33), X21).
% 4.97/5.32 Proof: A critical pair between equations 15 and 13.
% 4.97/5.32
% 4.97/5.32 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)).
% 4.97/5.32 Proof: A critical pair between equations 17 and 17.
% 4.97/5.32
% 4.97/5.32 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)).
% 4.97/5.32 Proof: A critical pair between equations 0 and 17.
% 4.97/5.32
% 4.97/5.32 30: multiply(inverse(X20), X22, X20) = X22.
% 4.97/5.32 Proof: Rewrite equation 23,
% 4.97/5.32 lhs with equations []
% 4.97/5.32 rhs with equations [0].
% 4.97/5.32
% 4.97/5.32 31: X22 = multiply(multiply(X21, inverse(X21), X22), inverse(multiply(X17, inverse(X17), multiply(X7, inverse(X7), X8))), X8).
% 4.97/5.32 Proof: Rewrite equation 21,
% 4.97/5.32 lhs with equations [30]
% 4.97/5.32 rhs with equations [30].
% 4.97/5.32
% 4.97/5.32 32: X15 = multiply(X15, inverse(multiply(X23, inverse(X23), X11)), X11).
% 4.97/5.32 Proof: A critical pair between equations 5 and 30.
% 4.97/5.32
% 4.97/5.32 33: inverse(X23) = multiply(inverse(X14), inverse(multiply(X14, inverse(X14), X23)), X14).
% 4.97/5.32 Proof: A critical pair between equations 5 and 30.
% 4.97/5.32
% 4.97/5.32 36: X22 = multiply(multiply(X21, inverse(X21), X22), inverse(multiply(X26, inverse(X26), inverse(inverse(X25)))), X25).
% 4.97/5.32 Proof: A critical pair between equations 31 and 17.
% 4.97/5.32
% 4.97/5.32 42: multiply(X35, multiply(X23, inverse(multiply(inverse(X34), X35, X18)), X18), inverse(X34)) = multiply(X35, multiply(X23, inverse(X35), X34), inverse(X34)).
% 4.97/5.32 Proof: A critical pair between equations 18 and 30.
% 4.97/5.32
% 4.97/5.32 45: inverse(X23) = inverse(multiply(X14, inverse(X14), X23)).
% 4.97/5.32 Proof: Rewrite equation 33,
% 4.97/5.32 lhs with equations []
% 4.97/5.32 rhs with equations [30].
% 4.97/5.32
% 4.97/5.32 46: X15 = multiply(X15, inverse(X11), X11).
% 4.97/5.32 Proof: Rewrite equation 32,
% 4.97/5.32 lhs with equations []
% 4.97/5.32 rhs with equations [45].
% 4.97/5.32
% 4.97/5.32 47: X22 = multiply(X21, inverse(X21), X22).
% 4.97/5.32 Proof: Rewrite equation 31,
% 4.97/5.32 lhs with equations []
% 4.97/5.32 rhs with equations [45,45,46].
% 4.97/5.32
% 4.97/5.32 56: X1 = multiply(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, X8))), multiply(X3, X8, X2)).
% 4.97/5.32 Proof: Rewrite equation 2,
% 4.97/5.32 lhs with equations []
% 4.97/5.32 rhs with equations [47,47].
% 4.97/5.32
% 4.97/5.32 62: multiply(X17, multiply(X20, inverse(multiply(X16, X17, X18)), X18), X16) = multiply(X16, X17, X20).
% 4.97/5.32 Proof: Rewrite equation 15,
% 4.97/5.32 lhs with equations []
% 4.97/5.32 rhs with equations [47,56].
% 4.97/5.32
% 4.97/5.32 66: inverse(inverse(X28)) = X28.
% 4.97/5.32 Proof: A critical pair between equations 36 and 47.
% 4.97/5.32
% 4.97/5.32 71: multiply(X16, X17, multiply(X16, X17, X24)) = multiply(X17, X24, X16).
% 4.97/5.32 Proof: A critical pair between equations 62 and 47.
% 4.97/5.32
% 4.97/5.32 75: multiply(inverse(X38), X36, X37) = multiply(X36, multiply(X37, inverse(X36), X38), inverse(X38)).
% 4.97/5.32 Proof: A critical pair between equations 62 and 42.
% 4.97/5.32
% 4.97/5.32 83: X22 = multiply(inverse(X29), X29, X22).
% 4.97/5.32 Proof: A critical pair between equations 47 and 66.
% 4.97/5.32
% 4.97/5.32 86: multiply(X26, X25, multiply(X26, X25, inverse(X26))) = X25.
% 4.97/5.32 Proof: A critical pair between equations 71 and 46.
% 4.97/5.32
% 4.97/5.32 90: multiply(inverse(X40), X40, X39) = multiply(X40, X39, inverse(X40)).
% 4.97/5.32 Proof: A critical pair between equations 75 and 46.
% 4.97/5.32
% 4.97/5.32 97: X39 = multiply(X40, X39, inverse(X40)).
% 4.97/5.32 Proof: Rewrite equation 90,
% 4.97/5.32 lhs with equations [83]
% 4.97/5.32 rhs with equations [].
% 4.97/5.32
% 4.97/5.32 98: multiply(X26, X25, X25) = X25.
% 4.97/5.32 Proof: Rewrite equation 86,
% 4.97/5.32 lhs with equations [97]
% 4.97/5.32 rhs with equations [].
% 4.97/5.32
% 4.97/5.32 103: multiply(b(), a(), a()) = a().
% 4.97/5.32 Proof: Rewrite lhs with equations [98]
% 4.97/5.32 rhs with equations [].
% 4.97/5.32
% 4.97/5.32 % SZS output end Proof
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