TSTP Solution File: BOO075-1 by Toma---0.4
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%------------------------------------------------------------------------------
% File : Toma---0.4
% Problem : BOO075-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n032.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 4.64s 4.97s
% Output : CNFRefutation 4.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : BOO075-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.11 % Command : toma --casc %s
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Sun Aug 27 08:21:29 EDT 2023
% 0.10/0.30 % CPUTime :
% 4.64/4.97 % SZS status Unsatisfiable
% 4.64/4.97 % SZS output start Proof
% 4.64/4.97 original problem:
% 4.64/4.97 axioms:
% 4.64/4.97 nand(nand(A, nand(nand(B, A), A)), nand(B, nand(C, A))) = B
% 4.64/4.97 goal:
% 4.64/4.97 nand(nand(a(), a()), nand(b(), a())) != a()
% 4.64/4.97 To show the unsatisfiability of the original goal,
% 4.64/4.97 it suffices to show that nand(nand(a(), a()), nand(b(), a())) = a() (skolemized goal) is valid under the axioms.
% 4.64/4.97 Here is an equational proof:
% 4.64/4.97 0: nand(nand(X0, nand(nand(X1, X0), X0)), nand(X1, nand(X2, X0))) = X1.
% 4.64/4.97 Proof: Axiom.
% 4.64/4.97
% 4.64/4.97 1: X1 = nand(nand(nand(X4, nand(X5, X3)), nand(nand(X1, nand(X4, nand(X5, X3))), nand(X4, nand(X5, X3)))), nand(X1, X4)).
% 4.64/4.97 Proof: A critical pair between equations 0 and 0.
% 4.64/4.97
% 4.64/4.97 2: nand(X3, nand(nand(X4, X3), X3)) = nand(nand(nand(X5, X3), nand(nand(nand(X3, nand(nand(X4, X3), X3)), nand(X5, X3)), nand(X5, X3))), X4).
% 4.64/4.97 Proof: A critical pair between equations 0 and 0.
% 4.64/4.97
% 4.64/4.97 3: nand(X3, nand(nand(X4, X3), X3)) = nand(nand(nand(X4, nand(X5, X3)), nand(X4, nand(X4, nand(X5, X3)))), nand(nand(X3, nand(nand(X4, X3), X3)), nand(X2, nand(X4, nand(X5, X3))))).
% 4.64/4.97 Proof: A critical pair between equations 0 and 0.
% 4.64/4.97
% 4.64/4.97 4: X1 = nand(nand(X8, nand(nand(X1, X8), X8)), nand(X1, nand(X7, nand(nand(X8, X7), X7)))).
% 4.64/4.97 Proof: A critical pair between equations 0 and 2.
% 4.64/4.97
% 4.64/4.97 5: X1 = nand(nand(nand(X9, X6), nand(nand(X1, nand(X9, X6)), nand(X9, X6))), nand(X1, X9)).
% 4.64/4.97 Proof: A critical pair between equations 0 and 1.
% 4.64/4.97
% 4.64/4.97 6: nand(X3, nand(nand(X9, X3), X3)) = nand(nand(nand(X9, nand(X5, X3)), nand(X9, nand(X9, nand(X5, X3)))), nand(nand(X3, nand(nand(X9, X3), X3)), X9)).
% 4.64/4.97 Proof: A critical pair between equations 3 and 1.
% 4.64/4.97
% 4.64/4.97 7: nand(X3, nand(nand(X4, X3), X3)) = nand(nand(nand(X4, nand(X5, X3)), nand(X4, nand(X4, nand(X5, X3)))), nand(nand(X3, nand(nand(X4, X3), X3)), nand(X7, nand(nand(nand(X4, nand(X5, X3)), X7), X7)))).
% 4.64/4.97 Proof: A critical pair between equations 3 and 2.
% 4.64/4.97
% 4.64/4.97 17: nand(X8, nand(nand(X8, X8), X8)) = nand(nand(nand(X8, nand(X5, X8)), nand(X8, nand(X8, nand(X5, X8)))), X8).
% 4.64/4.97 Proof: A critical pair between equations 7 and 0.
% 4.64/4.97
% 4.64/4.97 18: nand(X9, nand(nand(X9, X9), X9)) = nand(nand(X8, nand(nand(nand(X9, nand(nand(X9, X9), X9)), X8), X8)), X9).
% 4.64/4.97 Proof: A critical pair between equations 4 and 0.
% 4.64/4.97
% 4.64/4.97 19: nand(X11, nand(nand(X11, X11), X11)) = nand(nand(nand(X11, nand(nand(X11, X11), X11)), nand(X11, nand(X11, nand(nand(X11, X11), X11)))), X11).
% 4.64/4.97 Proof: A critical pair between equations 3 and 4.
% 4.64/4.97
% 4.64/4.97 20: nand(X11, nand(nand(X11, X11), X11)) = nand(X11, nand(nand(X11, nand(nand(X11, X11), X11)), nand(X2, nand(X11, nand(nand(X11, X11), X11))))).
% 4.64/4.97 Proof: A critical pair between equations 3 and 4.
% 4.64/4.97
% 4.64/4.97 22: nand(nand(X10, X11), nand(nand(X12, nand(X10, X11)), nand(X10, X11))) = nand(nand(X10, nand(nand(nand(nand(X10, X11), nand(nand(X12, nand(X10, X11)), nand(X10, X11))), X10), X10)), X12).
% 4.64/4.97 Proof: A critical pair between equations 0 and 5.
% 4.64/4.97
% 4.64/4.97 26: nand(nand(X10, nand(X11, X12)), nand(X10, nand(X10, nand(X11, X12)))) = nand(nand(X10, nand(nand(nand(nand(X10, nand(X11, X12)), nand(X10, nand(X10, nand(X11, X12)))), X10), X10)), nand(X12, nand(nand(X10, X12), X12))).
% 4.64/4.97 Proof: A critical pair between equations 0 and 6.
% 4.64/4.97
% 4.64/4.97 28: nand(X11, nand(nand(X11, X11), X11)) = nand(X11, X11).
% 4.64/4.97 Proof: Rewrite equation 19,
% 4.64/4.97 lhs with equations []
% 4.64/4.97 rhs with equations [4].
% 4.64/4.97
% 4.64/4.97 29: nand(X9, X9) = nand(nand(X8, nand(nand(nand(X9, X9), X8), X8)), X9).
% 4.64/4.97 Proof: Rewrite equation 18,
% 4.64/4.97 lhs with equations [28]
% 4.64/4.97 rhs with equations [28].
% 4.64/4.97
% 4.64/4.97 30: nand(X8, X8) = nand(nand(nand(X8, nand(X5, X8)), nand(X8, nand(X8, nand(X5, X8)))), X8).
% 4.64/4.97 Proof: Rewrite equation 17,
% 4.64/4.97 lhs with equations [28]
% 4.64/4.97 rhs with equations [].
% 4.64/4.97
% 4.64/4.97 31: X12 = nand(nand(X12, X12), nand(X12, nand(X2, X12))).
% 4.64/4.97 Proof: A critical pair between equations 0 and 28.
% 4.64/4.97
% 4.64/4.97 33: X12 = nand(nand(X12, nand(nand(X12, X12), X12)), nand(X12, X12)).
% 4.64/4.97 Proof: A critical pair between equations 0 and 28.
% 4.64/4.97
% 4.64/4.97 35: X12 = nand(nand(X8, nand(nand(X12, X8), X8)), nand(X12, nand(nand(X12, X12), X12))).
% 4.64/4.97 Proof: A critical pair between equations 4 and 20.
% 4.64/4.97
% 4.64/4.97 44: X12 = nand(nand(X8, nand(nand(X12, X8), X8)), nand(X12, X12)).
% 4.64/4.97 Proof: Rewrite equation 35,
% 4.64/4.97 lhs with equations []
% 4.64/4.97 rhs with equations [28].
% 4.64/4.97
% 4.64/4.97 45: X12 = nand(nand(X12, X12), nand(X12, X12)).
% 4.64/4.97 Proof: Rewrite equation 33,
% 4.64/4.97 lhs with equations []
% 4.64/4.97 rhs with equations [28].
% 4.64/4.97
% 4.64/4.97 54: nand(X13, nand(nand(X14, X13), X13)) = nand(nand(nand(X14, X14), nand(X14, nand(X14, X14))), nand(nand(X13, nand(nand(X14, X13), X13)), X14)).
% 4.64/4.97 Proof: A critical pair between equations 5 and 44.
% 4.64/4.97
% 4.64/4.97 59: nand(X13, nand(nand(X14, X13), X13)) = nand(X14, nand(nand(X13, nand(nand(X14, X13), X13)), X14)).
% 4.64/4.97 Proof: Rewrite equation 54,
% 4.64/4.97 lhs with equations []
% 4.64/4.97 rhs with equations [31].
% 4.64/4.97
% 4.64/4.97 60: X15 = nand(nand(X15, X15), nand(X16, nand(nand(X15, X16), X16))).
% 4.64/4.97 Proof: A critical pair between equations 31 and 59.
% 4.64/4.97
% 4.64/4.97 63: nand(nand(X14, X11), nand(nand(nand(X14, X14), nand(X14, X11)), nand(X14, X11))) = nand(nand(X14, nand(nand(X14, X14), X14)), nand(X14, X14)).
% 4.64/4.97 Proof: A critical pair between equations 22 and 29.
% 4.64/4.97
% 4.64/4.97 66: nand(nand(X13, nand(X14, X13)), nand(X13, nand(X13, nand(X14, X13)))) = nand(nand(X13, nand(nand(X13, X13), X13)), nand(X13, nand(nand(X13, X13), X13))).
% 4.64/4.97 Proof: A critical pair between equations 26 and 30.
% 4.64/4.97
% 4.64/4.97 75: nand(nand(X14, X11), nand(nand(nand(X14, X14), nand(X14, X11)), nand(X14, X11))) = X14.
% 4.64/4.97 Proof: Rewrite equation 63,
% 4.64/4.97 lhs with equations []
% 4.64/4.97 rhs with equations [28,45].
% 4.64/4.97
% 4.64/4.97 76: nand(nand(X13, nand(X14, X13)), nand(X13, nand(X13, nand(X14, X13)))) = X13.
% 4.64/4.97 Proof: Rewrite equation 66,
% 4.64/4.97 lhs with equations []
% 4.64/4.97 rhs with equations [28,28,45].
% 4.64/4.97
% 4.64/4.97 77: nand(X15, X16) = nand(nand(nand(X15, X16), nand(X15, X16)), X15).
% 4.64/4.97 Proof: A critical pair between equations 31 and 75.
% 4.64/4.97
% 4.64/4.97 78: nand(X15, X15) = nand(X15, nand(nand(X15, X15), nand(X2, nand(X15, X16)))).
% 4.64/4.97 Proof: A critical pair between equations 0 and 75.
% 4.64/4.97
% 4.64/4.97 91: nand(X18, X18) = nand(X18, nand(nand(X18, X18), X17)).
% 4.64/4.97 Proof: A critical pair between equations 78 and 60.
% 4.64/4.97
% 4.64/4.97 92: X17 = nand(nand(X17, X17), nand(X17, nand(X17, X18))).
% 4.64/4.97 Proof: A critical pair between equations 31 and 77.
% 4.64/4.97
% 4.64/4.97 97: X1 = nand(nand(X17, nand(nand(X1, X17), X17)), nand(X1, nand(X17, X18))).
% 4.64/4.97 Proof: A critical pair between equations 0 and 77.
% 4.64/4.97
% 4.64/4.97 111: nand(nand(X19, X19), nand(X19, X19)) = nand(nand(X19, X19), nand(X19, X17)).
% 4.64/4.97 Proof: A critical pair between equations 91 and 45.
% 4.64/4.97
% 4.64/4.97 112: X19 = nand(nand(X19, nand(X19, X20)), nand(X19, nand(X19, nand(X19, X20)))).
% 4.64/4.97 Proof: A critical pair between equations 75 and 92.
% 4.64/4.97
% 4.64/4.97 118: X19 = nand(nand(X19, X19), nand(X19, X17)).
% 4.64/4.97 Proof: Rewrite equation 111,
% 4.64/4.97 lhs with equations [45]
% 4.64/4.97 rhs with equations [].
% 4.64/4.97
% 4.64/4.97 119: X20 = nand(nand(X20, X21), nand(X20, nand(X20, X21))).
% 4.64/4.97 Proof: A critical pair between equations 75 and 118.
% 4.64/4.97
% 4.64/4.97 125: nand(X21, nand(X21, X22)) = nand(nand(X21, nand(nand(nand(X21, nand(X21, X22)), X21), X21)), X21).
% 4.64/4.97 Proof: A critical pair between equations 97 and 112.
% 4.64/4.97
% 4.64/4.97 126: nand(X19, nand(X20, X19)) = nand(nand(X19, nand(nand(nand(X19, nand(X20, X19)), X19), X19)), X19).
% 4.64/4.97 Proof: A critical pair between equations 97 and 76.
% 4.64/4.97
% 4.64/4.97 134: nand(X22, X23) = nand(nand(X22, nand(nand(nand(X22, X23), X22), X22)), X22).
% 4.64/4.97 Proof: A critical pair between equations 97 and 119.
% 4.64/4.97
% 4.64/4.97 137: nand(X21, nand(nand(nand(X21, nand(X22, X21)), X21), X21)) = nand(nand(X21, nand(nand(X21, nand(X22, X21)), X21)), X21).
% 4.64/4.97 Proof: A critical pair between equations 126 and 126.
% 4.64/4.97
% 4.64/4.97 138: nand(X23, nand(nand(nand(X23, nand(X23, X24)), X23), X23)) = nand(nand(X23, nand(nand(X23, nand(X23, X24)), X23)), X23).
% 4.64/4.97 Proof: A critical pair between equations 126 and 125.
% 4.64/4.97
% 4.64/4.97 140: nand(X22, X23) = nand(nand(nand(X22, nand(X22, X23)), nand(X22, nand(X22, nand(X22, X23)))), nand(nand(X22, X23), X22)).
% 4.64/4.97 Proof: A critical pair between equations 5 and 119.
% 4.64/4.97
% 4.64/4.97 149: nand(X22, X23) = nand(X22, nand(nand(X22, X23), X22)).
% 4.64/4.97 Proof: Rewrite equation 140,
% 4.64/4.97 lhs with equations []
% 4.64/4.97 rhs with equations [119].
% 4.64/4.97
% 4.64/4.97 151: nand(X23, nand(nand(nand(X23, nand(X23, X24)), X23), X23)) = nand(nand(X23, nand(X23, X24)), X23).
% 4.64/4.97 Proof: Rewrite equation 138,
% 4.64/4.97 lhs with equations []
% 4.64/4.97 rhs with equations [149].
% 4.64/4.97
% 4.64/4.97 152: nand(X21, nand(nand(nand(X21, nand(X22, X21)), X21), X21)) = nand(nand(X21, nand(X22, X21)), X21).
% 4.64/4.97 Proof: Rewrite equation 137,
% 4.64/4.97 lhs with equations []
% 4.64/4.97 rhs with equations [149].
% 4.64/4.97
% 4.64/4.97 153: nand(X21, nand(X21, X22)) = nand(nand(nand(X21, nand(X21, X22)), X21), X21).
% 4.64/4.97 Proof: Rewrite equation 125,
% 4.64/4.97 lhs with equations []
% 4.64/4.97 rhs with equations [151].
% 4.64/4.97
% 4.64/4.97 154: nand(X19, nand(X20, X19)) = nand(nand(nand(X19, nand(X20, X19)), X19), X19).
% 4.64/4.97 Proof: Rewrite equation 126,
% 4.64/4.97 lhs with equations []
% 4.64/4.97 rhs with equations [152].
% 4.64/4.97
% 4.64/4.97 158: nand(nand(X25, nand(X25, X26)), X25) = nand(X25, nand(X25, nand(X25, X26))).
% 4.64/4.97 Proof: A critical pair between equations 151 and 153.
% 4.64/4.97
% 4.64/4.97 162: nand(X24, nand(nand(X24, X25), X24)) = nand(nand(nand(X24, X25), X24), X24).
% 4.64/4.97 Proof: A critical pair between equations 154 and 149.
% 4.64/4.97
% 4.64/4.97 163: nand(X24, nand(nand(nand(X24, X25), X24), X24)) = nand(nand(X24, X25), X24).
% 4.64/4.97 Proof: A critical pair between equations 154 and 134.
% 4.64/4.97
% 4.64/4.97 166: nand(nand(X24, nand(nand(X24, X25), X24)), X24) = nand(X24, nand(nand(nand(X24, X25), X24), X24)).
% 4.64/4.97 Proof: A critical pair between equations 152 and 149.
% 4.64/4.97
% 4.64/4.97 167: nand(nand(X24, X25), X24) = nand(X24, nand(X24, X25)).
% 4.64/4.97 Proof: Rewrite equation 166,
% 4.64/4.97 lhs with equations [149]
% 4.64/4.97 rhs with equations [162,149].
% 4.64/4.97
% 4.64/4.97 168: nand(X24, nand(X24, nand(X24, nand(X24, X25)))) = nand(X24, nand(X24, X25)).
% 4.64/4.97 Proof: Rewrite equation 163,
% 4.64/4.97 lhs with equations [167,158]
% 4.64/4.97 rhs with equations [167].
% 4.64/4.97
% 4.64/4.97 171: nand(X22, X23) = nand(X22, nand(X22, nand(X22, X23))).
% 4.64/4.97 Proof: Rewrite equation 134,
% 4.64/4.97 lhs with equations []
% 4.64/4.97 rhs with equations [167,167,168,167].
% 4.64/4.97
% 4.64/4.97 183: X24 = nand(nand(nand(X24, nand(X24, X25)), nand(nand(X24, X25), nand(X24, nand(X24, X25)))), nand(X24, X24)).
% 4.64/4.97 Proof: A critical pair between equations 44 and 171.
% 4.64/4.97
% 4.64/4.97 184: X24 = nand(nand(X24, X25), nand(X24, X24)).
% 4.64/4.97 Proof: Rewrite equation 183,
% 4.64/4.97 lhs with equations []
% 4.64/4.97 rhs with equations [119,167,171].
% 4.64/4.97
% 4.64/4.97 194: nand(X26, nand(nand(X4, X26), X26)) = nand(nand(nand(X26, X26), nand(X26, nand(X26, X26))), X4).
% 4.64/4.97 Proof: A critical pair between equations 2 and 184.
% 4.64/4.97
% 4.64/4.97 205: nand(X26, nand(nand(X4, X26), X26)) = nand(X26, X4).
% 4.64/4.97 Proof: Rewrite equation 194,
% 4.64/4.97 lhs with equations []
% 4.64/4.97 rhs with equations [118].
% 4.64/4.97
% 4.64/4.97 220: nand(X13, X14) = nand(X14, X13).
% 4.64/4.97 Proof: Rewrite equation 59,
% 4.64/4.97 lhs with equations [205]
% 4.64/4.97 rhs with equations [205,205].
% 4.64/4.97
% 4.64/4.97 237: nand(nand(a(), a()), nand(b(), a())) = a().
% 4.64/4.97 Proof: Rewrite lhs with equations [220,118]
% 4.64/4.97 rhs with equations [].
% 4.64/4.97
% 4.64/4.97 % SZS output end Proof
%------------------------------------------------------------------------------