TSTP Solution File: BOO072-1 by Toma---0.4
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- Process Solution
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% File : Toma---0.4
% Problem : BOO072-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n009.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 18:11:09 EDT 2023
% Result : Unsatisfiable 10.32s 10.65s
% Output : CNFRefutation 10.32s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : BOO072-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.10 % Command : toma --casc %s
% 0.09/0.30 % Computer : n009.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Sun Aug 27 08:13:05 EDT 2023
% 0.09/0.30 % CPUTime :
% 10.32/10.65 % SZS status Unsatisfiable
% 10.32/10.65 % SZS output start Proof
% 10.32/10.65 original problem:
% 10.32/10.65 axioms:
% 10.32/10.65 inverse(add(inverse(add(inverse(add(A, B)), C)), inverse(add(A, inverse(add(inverse(C), inverse(add(C, D)))))))) = C
% 10.32/10.65 goal:
% 10.32/10.65 add(b(), a()) != add(a(), b())
% 10.32/10.65 To show the unsatisfiability of the original goal,
% 10.32/10.65 it suffices to show that add(b(), a()) = add(a(), b()) (skolemized goal) is valid under the axioms.
% 10.32/10.65 Here is an equational proof:
% 10.32/10.65 0: inverse(add(inverse(add(inverse(add(X0, X1)), X2)), inverse(add(X0, inverse(add(inverse(X2), inverse(add(X2, X3)))))))) = X2.
% 10.32/10.65 Proof: Axiom.
% 10.32/10.65
% 10.32/10.65 1: inverse(X6) = inverse(add(inverse(add(inverse(add(inverse(add(inverse(add(inverse(inverse(X6)), X5)), X6)), X1)), inverse(X6))), X6)).
% 10.32/10.65 Proof: A critical pair between equations 0 and 0.
% 10.32/10.65
% 10.32/10.65 2: X2 = inverse(add(inverse(add(X6, X2)), inverse(add(inverse(add(inverse(add(X4, X5)), X6)), inverse(add(inverse(X2), inverse(add(X2, X3)))))))).
% 10.32/10.65 Proof: A critical pair between equations 0 and 0.
% 10.32/10.65
% 10.32/10.65 4: inverse(add(X4, inverse(add(inverse(X6), inverse(add(X6, X7)))))) = inverse(add(X6, inverse(add(inverse(add(X4, X5)), inverse(add(inverse(inverse(add(X4, inverse(add(inverse(X6), inverse(add(X6, X7))))))), inverse(add(inverse(add(X4, inverse(add(inverse(X6), inverse(add(X6, X7)))))), X3)))))))).
% 10.32/10.65 Proof: A critical pair between equations 0 and 0.
% 10.32/10.65
% 10.32/10.65 8: X2 = inverse(add(inverse(add(X6, X2)), inverse(add(inverse(add(X8, X6)), inverse(add(inverse(X2), inverse(add(X2, X3)))))))).
% 10.32/10.65 Proof: A critical pair between equations 2 and 2.
% 10.32/10.65
% 10.32/10.65 12: X7 = inverse(add(inverse(X7), inverse(add(inverse(add(inverse(add(inverse(add(inverse(inverse(X7)), X8)), X7)), X9)), inverse(add(inverse(X7), inverse(add(X7, X3)))))))).
% 10.32/10.65 Proof: A critical pair between equations 0 and 1.
% 10.32/10.65
% 10.32/10.65 13: X2 = inverse(add(inverse(add(inverse(add(X7, inverse(add(inverse(X9), inverse(add(X9, X10)))))), X2)), inverse(add(X9, inverse(add(inverse(X2), inverse(add(X2, X3)))))))).
% 10.32/10.65 Proof: A critical pair between equations 2 and 0.
% 10.32/10.65
% 10.32/10.65 14: X8 = inverse(add(inverse(add(inverse(add(X0, X1)), X8)), inverse(add(X0, inverse(add(inverse(X8), inverse(add(X9, inverse(add(inverse(X8), inverse(add(X8, X11)))))))))))).
% 10.32/10.65 Proof: A critical pair between equations 0 and 4.
% 10.32/10.65
% 10.32/10.65 16: inverse(X6) = inverse(add(inverse(add(inverse(add(inverse(add(inverse(add(X9, inverse(add(inverse(inverse(inverse(X6))), inverse(add(inverse(inverse(X6)), X11)))))), X6)), X1)), inverse(X6))), X6)).
% 10.32/10.65 Proof: A critical pair between equations 1 and 4.
% 10.32/10.65
% 10.32/10.65 17: X8 = inverse(add(inverse(add(X6, X8)), inverse(add(inverse(add(inverse(add(X4, X5)), X6)), inverse(add(inverse(X8), inverse(add(X9, inverse(add(inverse(X8), inverse(add(X8, X11)))))))))))).
% 10.32/10.65 Proof: A critical pair between equations 2 and 4.
% 10.32/10.65
% 10.32/10.65 18: X8 = inverse(add(inverse(add(inverse(X8), X8)), inverse(X8))).
% 10.32/10.65 Proof: A critical pair between equations 17 and 13.
% 10.32/10.65
% 10.32/10.65 20: X12 = inverse(add(inverse(add(inverse(add(X0, X1)), X12)), inverse(add(X0, X12)))).
% 10.32/10.65 Proof: A critical pair between equations 14 and 12.
% 10.32/10.65
% 10.32/10.65 23: X12 = inverse(add(inverse(add(X6, X12)), inverse(add(inverse(add(inverse(add(X4, X5)), X6)), X12)))).
% 10.32/10.65 Proof: A critical pair between equations 17 and 12.
% 10.32/10.65
% 10.32/10.65 24: inverse(X6) = inverse(add(inverse(add(inverse(add(inverse(add(inverse(X6), X6)), X1)), inverse(X6))), X6)).
% 10.32/10.65 Proof: A critical pair between equations 16 and 14.
% 10.32/10.65
% 10.32/10.65 27: X8 = inverse(add(inverse(add(inverse(add(inverse(add(inverse(add(inverse(X8), X13)), inverse(X8))), X1)), X8)), inverse(X8))).
% 10.32/10.65 Proof: A critical pair between equations 14 and 0.
% 10.32/10.65
% 10.32/10.65 30: X14 = inverse(add(inverse(X14), inverse(X14))).
% 10.32/10.65 Proof: A critical pair between equations 27 and 24.
% 10.32/10.65
% 10.32/10.65 33: inverse(X13) = inverse(add(X13, inverse(add(inverse(X13), inverse(X13))))).
% 10.32/10.65 Proof: A critical pair between equations 20 and 18.
% 10.32/10.65
% 10.32/10.65 34: X14 = inverse(add(inverse(add(inverse(add(X14, X1)), X14)), inverse(X14))).
% 10.32/10.65 Proof: A critical pair between equations 27 and 18.
% 10.32/10.65
% 10.32/10.65 40: X12 = inverse(add(inverse(add(X6, X12)), inverse(add(inverse(add(X14, X6)), X12)))).
% 10.32/10.65 Proof: A critical pair between equations 23 and 27.
% 10.32/10.65
% 10.32/10.65 41: X12 = inverse(add(inverse(add(inverse(add(X13, X15)), X12)), inverse(add(X15, X12)))).
% 10.32/10.65 Proof: A critical pair between equations 23 and 20.
% 10.32/10.65
% 10.32/10.65 42: inverse(X13) = inverse(add(X13, X13)).
% 10.32/10.65 Proof: Rewrite equation 33,
% 10.32/10.65 lhs with equations []
% 10.32/10.65 rhs with equations [30].
% 10.32/10.65
% 10.32/10.65 43: X14 = inverse(inverse(X14)).
% 10.32/10.65 Proof: Rewrite equation 30,
% 10.32/10.65 lhs with equations []
% 10.32/10.65 rhs with equations [42].
% 10.32/10.65
% 10.32/10.65 50: inverse(add(X4, inverse(add(inverse(X6), inverse(add(X6, X7)))))) = inverse(add(X6, inverse(add(inverse(add(X4, X5)), inverse(add(add(X4, inverse(add(inverse(X6), inverse(add(X6, X7))))), inverse(add(inverse(add(X4, inverse(add(inverse(X6), inverse(add(X6, X7)))))), X3)))))))).
% 10.32/10.65 Proof: Rewrite equation 4,
% 10.32/10.65 lhs with equations []
% 10.32/10.65 rhs with equations [43].
% 10.32/10.65
% 10.32/10.65 73: add(inverse(add(inverse(add(X15, X16)), X15)), inverse(X15)) = inverse(X15).
% 10.32/10.65 Proof: A critical pair between equations 43 and 34.
% 10.32/10.65
% 10.32/10.65 83: inverse(inverse(X17)) = add(inverse(add(inverse(add(inverse(X17), X16)), inverse(X17))), X17).
% 10.32/10.65 Proof: A critical pair between equations 73 and 43.
% 10.32/10.65
% 10.32/10.65 87: inverse(add(X17, X18)) = inverse(add(inverse(add(X18, inverse(add(X17, X18)))), X18)).
% 10.32/10.65 Proof: A critical pair between equations 40 and 41.
% 10.32/10.65
% 10.32/10.65 90: add(inverse(add(inverse(add(X15, X16)), X17)), inverse(add(X15, X17))) = inverse(X17).
% 10.32/10.65 Proof: A critical pair between equations 43 and 20.
% 10.32/10.65
% 10.32/10.65 91: X2 = inverse(add(inverse(add(inverse(add(X2, X3)), X2)), inverse(add(X2, X3)))).
% 10.32/10.65 Proof: A critical pair between equations 8 and 41.
% 10.32/10.65
% 10.32/10.65 95: X17 = add(inverse(add(inverse(add(inverse(X17), X16)), inverse(X17))), X17).
% 10.32/10.65 Proof: Rewrite equation 83,
% 10.32/10.65 lhs with equations [43]
% 10.32/10.65 rhs with equations [].
% 10.32/10.65
% 10.32/10.65 99: X17 = add(inverse(add(X20, inverse(X17))), X17).
% 10.32/10.65 Proof: A critical pair between equations 95 and 87.
% 10.32/10.65
% 10.32/10.65 100: inverse(X19) = add(inverse(add(X20, X19)), inverse(X19)).
% 10.32/10.65 Proof: A critical pair between equations 73 and 87.
% 10.32/10.65
% 10.32/10.65 111: inverse(X22) = add(inverse(X22), inverse(add(X21, X22))).
% 10.32/10.65 Proof: A critical pair between equations 90 and 99.
% 10.32/10.65
% 10.32/10.65 116: inverse(inverse(X22)) = add(inverse(inverse(X22)), inverse(add(X21, inverse(X22)))).
% 10.32/10.65 Proof: A critical pair between equations 90 and 100.
% 10.32/10.65
% 10.32/10.65 127: X22 = add(X22, inverse(add(X21, inverse(X22)))).
% 10.32/10.65 Proof: Rewrite equation 116,
% 10.32/10.65 lhs with equations [43]
% 10.32/10.65 rhs with equations [43].
% 10.32/10.65
% 10.32/10.65 128: add(X23, X24) = add(add(X23, X24), X23).
% 10.32/10.65 Proof: A critical pair between equations 127 and 91.
% 10.32/10.65
% 10.32/10.65 148: X22 = add(X22, inverse(add(inverse(X22), X26))).
% 10.32/10.65 Proof: A critical pair between equations 127 and 128.
% 10.32/10.65
% 10.32/10.65 150: inverse(X25) = add(inverse(X25), inverse(add(X25, X26))).
% 10.32/10.65 Proof: A critical pair between equations 111 and 128.
% 10.32/10.65
% 10.32/10.65 161: inverse(add(X4, X6)) = inverse(add(X6, inverse(add(inverse(add(X4, X5)), inverse(add(X4, X6)))))).
% 10.32/10.65 Proof: Rewrite equation 50,
% 10.32/10.65 lhs with equations [150,43]
% 10.32/10.65 rhs with equations [150,43,150,43,148].
% 10.32/10.65
% 10.32/10.65 166: inverse(add(X27, X6)) = inverse(add(X6, inverse(add(inverse(X27), inverse(add(X27, X6)))))).
% 10.32/10.65 Proof: A critical pair between equations 161 and 148.
% 10.32/10.65
% 10.32/10.65 174: inverse(add(X27, X6)) = inverse(add(X6, X27)).
% 10.32/10.65 Proof: Rewrite equation 166,
% 10.32/10.65 lhs with equations []
% 10.32/10.65 rhs with equations [150,43].
% 10.32/10.65
% 10.32/10.65 175: add(X28, X29) = inverse(inverse(add(X29, X28))).
% 10.32/10.65 Proof: A critical pair between equations 43 and 174.
% 10.32/10.65
% 10.32/10.65 195: add(X28, X29) = add(X29, X28).
% 10.32/10.65 Proof: Rewrite equation 175,
% 10.32/10.65 lhs with equations []
% 10.32/10.65 rhs with equations [43].
% 10.32/10.65
% 10.32/10.65 196: add(b(), a()) = add(a(), b()).
% 10.32/10.65 Proof: Rewrite lhs with equations []
% 10.32/10.65 rhs with equations [195].
% 10.32/10.65
% 10.32/10.65 % SZS output end Proof
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