TSTP Solution File: BOO074-1 by Toma---0.4
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%------------------------------------------------------------------------------
% File : Toma---0.4
% Problem : BOO074-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n011.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 6.67s 7.01s
% Output : CNFRefutation 6.67s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : BOO074-1 : TPTP v8.1.2. Released v2.6.0.
% 0.07/0.13 % Command : toma --casc %s
% 0.12/0.34 % Computer : n011.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 : Sun Aug 27 08:33:09 EDT 2023
% 0.12/0.34 % CPUTime :
% 6.67/7.01 % SZS status Unsatisfiable
% 6.67/7.01 % SZS output start Proof
% 6.67/7.01 original problem:
% 6.67/7.01 axioms:
% 6.67/7.01 inverse(add(inverse(add(inverse(add(A, B)), C)), inverse(add(A, inverse(add(inverse(C), inverse(add(C, D)))))))) = C
% 6.67/7.01 goal:
% 6.67/7.01 add(inverse(add(inverse(a()), b())), inverse(add(inverse(a()), inverse(b())))) != a()
% 6.67/7.01 To show the unsatisfiability of the original goal,
% 6.67/7.01 it suffices to show that add(inverse(add(inverse(a()), b())), inverse(add(inverse(a()), inverse(b())))) = a() (skolemized goal) is valid under the axioms.
% 6.67/7.01 Here is an equational proof:
% 6.67/7.01 0: inverse(add(inverse(add(inverse(add(X0, X1)), X2)), inverse(add(X0, inverse(add(inverse(X2), inverse(add(X2, X3)))))))) = X2.
% 6.67/7.01 Proof: Axiom.
% 6.67/7.01
% 6.67/7.01 1: inverse(X6) = inverse(add(inverse(add(inverse(add(inverse(add(inverse(add(inverse(inverse(X6)), X5)), X6)), X1)), inverse(X6))), X6)).
% 6.67/7.01 Proof: A critical pair between equations 0 and 0.
% 6.67/7.01
% 6.67/7.01 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)))))))).
% 6.67/7.01 Proof: A critical pair between equations 0 and 0.
% 6.67/7.01
% 6.67/7.01 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)))))))).
% 6.67/7.01 Proof: A critical pair between equations 0 and 0.
% 6.67/7.01
% 6.67/7.01 7: X2 = inverse(add(inverse(add(X7, X2)), inverse(add(inverse(X7), inverse(add(inverse(X2), inverse(add(X2, X3)))))))).
% 6.67/7.01 Proof: A critical pair between equations 2 and 1.
% 6.67/7.01
% 6.67/7.01 8: X2 = inverse(add(inverse(add(X6, X2)), inverse(add(inverse(add(X8, X6)), inverse(add(inverse(X2), inverse(add(X2, X3)))))))).
% 6.67/7.01 Proof: A critical pair between equations 2 and 2.
% 6.67/7.01
% 6.67/7.01 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)))))))).
% 6.67/7.01 Proof: A critical pair between equations 0 and 1.
% 6.67/7.01
% 6.67/7.01 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)))))))).
% 6.67/7.01 Proof: A critical pair between equations 2 and 0.
% 6.67/7.01
% 6.67/7.01 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)))))))))))).
% 6.67/7.01 Proof: A critical pair between equations 0 and 4.
% 6.67/7.01
% 6.67/7.01 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)).
% 6.67/7.01 Proof: A critical pair between equations 1 and 4.
% 6.67/7.01
% 6.67/7.01 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)))))))))))).
% 6.67/7.01 Proof: A critical pair between equations 2 and 4.
% 6.67/7.01
% 6.67/7.01 18: X8 = inverse(add(inverse(add(inverse(X8), X8)), inverse(X8))).
% 6.67/7.01 Proof: A critical pair between equations 17 and 13.
% 6.67/7.01
% 6.67/7.01 20: X12 = inverse(add(inverse(add(inverse(add(X0, X1)), X12)), inverse(add(X0, X12)))).
% 6.67/7.01 Proof: A critical pair between equations 14 and 12.
% 6.67/7.01
% 6.67/7.01 23: X12 = inverse(add(inverse(add(X6, X12)), inverse(add(inverse(add(inverse(add(X4, X5)), X6)), X12)))).
% 6.67/7.01 Proof: A critical pair between equations 17 and 12.
% 6.67/7.01
% 6.67/7.01 24: inverse(X6) = inverse(add(inverse(add(inverse(add(inverse(add(inverse(X6), X6)), X1)), inverse(X6))), X6)).
% 6.67/7.01 Proof: A critical pair between equations 16 and 14.
% 6.67/7.01
% 6.67/7.01 25: inverse(X14) = inverse(add(inverse(add(add(inverse(add(inverse(inverse(X14)), X13)), X14), inverse(X14))), X14)).
% 6.67/7.01 Proof: A critical pair between equations 7 and 14.
% 6.67/7.01
% 6.67/7.01 27: X8 = inverse(add(inverse(add(inverse(add(inverse(add(inverse(add(inverse(X8), X13)), inverse(X8))), X1)), X8)), inverse(X8))).
% 6.67/7.01 Proof: A critical pair between equations 14 and 0.
% 6.67/7.01
% 6.67/7.01 30: X14 = inverse(add(inverse(X14), inverse(X14))).
% 6.67/7.01 Proof: A critical pair between equations 27 and 24.
% 6.67/7.01
% 6.67/7.01 33: inverse(X13) = inverse(add(X13, inverse(add(inverse(X13), inverse(X13))))).
% 6.67/7.01 Proof: A critical pair between equations 20 and 18.
% 6.67/7.01
% 6.67/7.01 34: X14 = inverse(add(inverse(add(inverse(add(X14, X1)), X14)), inverse(X14))).
% 6.67/7.01 Proof: A critical pair between equations 27 and 18.
% 6.67/7.01
% 6.67/7.01 36: X12 = inverse(add(inverse(add(X15, X12)), inverse(add(inverse(X15), X12)))).
% 6.67/7.01 Proof: A critical pair between equations 23 and 25.
% 6.67/7.01
% 6.67/7.01 40: X12 = inverse(add(inverse(add(X6, X12)), inverse(add(inverse(add(X14, X6)), X12)))).
% 6.67/7.01 Proof: A critical pair between equations 23 and 27.
% 6.67/7.01
% 6.67/7.01 41: X12 = inverse(add(inverse(add(inverse(add(X13, X15)), X12)), inverse(add(X15, X12)))).
% 6.67/7.01 Proof: A critical pair between equations 23 and 20.
% 6.67/7.01
% 6.67/7.01 42: inverse(X13) = inverse(add(X13, X13)).
% 6.67/7.01 Proof: Rewrite equation 33,
% 6.67/7.01 lhs with equations []
% 6.67/7.01 rhs with equations [30].
% 6.67/7.01
% 6.67/7.01 43: X14 = inverse(inverse(X14)).
% 6.67/7.01 Proof: Rewrite equation 30,
% 6.67/7.01 lhs with equations []
% 6.67/7.01 rhs with equations [42].
% 6.67/7.01
% 6.67/7.01 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)))))))).
% 6.67/7.01 Proof: Rewrite equation 4,
% 6.67/7.01 lhs with equations []
% 6.67/7.01 rhs with equations [43].
% 6.67/7.01
% 6.67/7.01 73: add(inverse(add(inverse(add(X15, X16)), X15)), inverse(X15)) = inverse(X15).
% 6.67/7.01 Proof: A critical pair between equations 43 and 34.
% 6.67/7.01
% 6.67/7.01 75: add(inverse(add(X16, X17)), inverse(add(inverse(X16), X17))) = inverse(X17).
% 6.67/7.01 Proof: A critical pair between equations 43 and 36.
% 6.67/7.01
% 6.67/7.01 83: inverse(inverse(X17)) = add(inverse(add(inverse(add(inverse(X17), X16)), inverse(X17))), X17).
% 6.67/7.01 Proof: A critical pair between equations 73 and 43.
% 6.67/7.01
% 6.67/7.01 86: inverse(add(X17, X18)) = inverse(add(X18, inverse(add(X18, inverse(add(X17, X18)))))).
% 6.67/7.01 Proof: A critical pair between equations 41 and 41.
% 6.67/7.01
% 6.67/7.01 87: inverse(add(X17, X18)) = inverse(add(inverse(add(X18, inverse(add(X17, X18)))), X18)).
% 6.67/7.01 Proof: A critical pair between equations 40 and 41.
% 6.67/7.01
% 6.67/7.01 90: add(inverse(add(inverse(add(X15, X16)), X17)), inverse(add(X15, X17))) = inverse(X17).
% 6.67/7.01 Proof: A critical pair between equations 43 and 20.
% 6.67/7.01
% 6.67/7.01 91: X2 = inverse(add(inverse(add(inverse(add(X2, X3)), X2)), inverse(add(X2, X3)))).
% 6.67/7.01 Proof: A critical pair between equations 8 and 41.
% 6.67/7.01
% 6.67/7.01 95: X17 = add(inverse(add(inverse(add(inverse(X17), X16)), inverse(X17))), X17).
% 6.67/7.01 Proof: Rewrite equation 83,
% 6.67/7.01 lhs with equations [43]
% 6.67/7.01 rhs with equations [].
% 6.67/7.01
% 6.67/7.01 99: X17 = add(inverse(add(X20, inverse(X17))), X17).
% 6.67/7.01 Proof: A critical pair between equations 95 and 87.
% 6.67/7.01
% 6.67/7.01 100: inverse(X19) = add(inverse(add(X20, X19)), inverse(X19)).
% 6.67/7.01 Proof: A critical pair between equations 73 and 87.
% 6.67/7.01
% 6.67/7.01 108: inverse(add(X4, X5)) = inverse(add(X4, inverse(add(inverse(add(X4, X5)), X4)))).
% 6.67/7.01 Proof: A critical pair between equations 91 and 91.
% 6.67/7.01
% 6.67/7.01 111: inverse(X22) = add(inverse(X22), inverse(add(X21, X22))).
% 6.67/7.01 Proof: A critical pair between equations 90 and 99.
% 6.67/7.01
% 6.67/7.01 116: inverse(inverse(X22)) = add(inverse(inverse(X22)), inverse(add(X21, inverse(X22)))).
% 6.67/7.01 Proof: A critical pair between equations 90 and 100.
% 6.67/7.01
% 6.67/7.01 120: add(X15, inverse(add(inverse(add(X15, X16)), X15))) = inverse(inverse(add(X15, X16))).
% 6.67/7.01 Proof: A critical pair between equations 43 and 108.
% 6.67/7.01
% 6.67/7.01 121: add(X19, inverse(add(X19, inverse(add(X20, X19))))) = inverse(inverse(add(X20, X19))).
% 6.67/7.01 Proof: A critical pair between equations 43 and 86.
% 6.67/7.01
% 6.67/7.01 124: add(X19, inverse(add(X19, inverse(add(X20, X19))))) = add(X20, X19).
% 6.67/7.01 Proof: Rewrite equation 121,
% 6.67/7.01 lhs with equations []
% 6.67/7.01 rhs with equations [43].
% 6.67/7.01
% 6.67/7.01 125: add(X15, inverse(add(inverse(add(X15, X16)), X15))) = add(X15, X16).
% 6.67/7.01 Proof: Rewrite equation 120,
% 6.67/7.01 lhs with equations []
% 6.67/7.01 rhs with equations [43].
% 6.67/7.01
% 6.67/7.01 127: X22 = add(X22, inverse(add(X21, inverse(X22)))).
% 6.67/7.01 Proof: Rewrite equation 116,
% 6.67/7.01 lhs with equations [43]
% 6.67/7.01 rhs with equations [43].
% 6.67/7.01
% 6.67/7.01 128: add(X23, X24) = add(add(X23, X24), X23).
% 6.67/7.01 Proof: A critical pair between equations 127 and 91.
% 6.67/7.01
% 6.67/7.01 136: add(inverse(add(X21, X22)), X21) = add(X21, inverse(add(X21, X22))).
% 6.67/7.01 Proof: A critical pair between equations 124 and 125.
% 6.67/7.01
% 6.67/7.01 146: add(X15, inverse(add(X15, inverse(add(X15, X16))))) = add(X15, X16).
% 6.67/7.01 Proof: Rewrite equation 125,
% 6.67/7.01 lhs with equations [136]
% 6.67/7.01 rhs with equations [].
% 6.67/7.01
% 6.67/7.01 148: X22 = add(X22, inverse(add(inverse(X22), X26))).
% 6.67/7.01 Proof: A critical pair between equations 127 and 128.
% 6.67/7.01
% 6.67/7.01 150: inverse(X25) = add(inverse(X25), inverse(add(X25, X26))).
% 6.67/7.01 Proof: A critical pair between equations 111 and 128.
% 6.67/7.01
% 6.67/7.01 161: inverse(add(X4, X6)) = inverse(add(X6, inverse(add(inverse(add(X4, X5)), inverse(add(X4, X6)))))).
% 6.67/7.01 Proof: Rewrite equation 50,
% 6.67/7.01 lhs with equations [150,43]
% 6.67/7.01 rhs with equations [150,43,150,43,148].
% 6.67/7.01
% 6.67/7.01 166: inverse(add(X27, X6)) = inverse(add(X6, inverse(add(inverse(X27), inverse(add(X27, X6)))))).
% 6.67/7.01 Proof: A critical pair between equations 161 and 148.
% 6.67/7.01
% 6.67/7.01 174: inverse(add(X27, X6)) = inverse(add(X6, X27)).
% 6.67/7.01 Proof: Rewrite equation 166,
% 6.67/7.01 lhs with equations []
% 6.67/7.01 rhs with equations [150,43].
% 6.67/7.01
% 6.67/7.01 178: inverse(X29) = add(inverse(add(X29, X28)), inverse(add(inverse(X28), X29))).
% 6.67/7.01 Proof: A critical pair between equations 75 and 174.
% 6.67/7.01
% 6.67/7.01 181: add(X28, X29) = add(X28, inverse(add(X28, inverse(add(X29, X28))))).
% 6.67/7.01 Proof: A critical pair between equations 146 and 174.
% 6.67/7.01
% 6.67/7.01 188: add(X28, X29) = add(X29, X28).
% 6.67/7.01 Proof: Rewrite equation 181,
% 6.67/7.01 lhs with equations []
% 6.67/7.01 rhs with equations [124].
% 6.67/7.01
% 6.67/7.01 201: inverse(X31) = add(inverse(add(X31, X28)), inverse(add(X31, inverse(X28)))).
% 6.67/7.01 Proof: A critical pair between equations 178 and 188.
% 6.67/7.01
% 6.67/7.01 215: add(inverse(add(inverse(a()), b())), inverse(add(inverse(a()), inverse(b())))) = a().
% 6.67/7.01 Proof: Rewrite lhs with equations [201,43]
% 6.67/7.01 rhs with equations [].
% 6.67/7.01
% 6.67/7.01 % SZS output end Proof
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