TSTP Solution File: LAT089-1 by Toma---0.4
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%------------------------------------------------------------------------------
% File : Toma---0.4
% Problem : LAT089-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n013.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 : Thu Aug 31 06:25:37 EDT 2023
% Result : Unsatisfiable 1.59s 1.94s
% Output : CNFRefutation 1.59s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT089-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.13 % Command : toma --casc %s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 08:20:47 EDT 2023
% 0.13/0.34 % CPUTime :
% 1.59/1.94 % SZS status Unsatisfiable
% 1.59/1.94 % SZS output start Proof
% 1.59/1.94 original problem:
% 1.59/1.94 axioms:
% 1.59/1.94 join(meet(A, B), meet(A, join(A, B))) = A
% 1.59/1.94 join(meet(A, A), meet(B, join(A, A))) = A
% 1.59/1.94 join(meet(A, B), meet(B, join(A, B))) = B
% 1.59/1.94 meet(meet(join(A, B), join(C, A)), A) = A
% 1.59/1.94 join(join(meet(A, B), meet(C, A)), A) = A
% 1.59/1.94 goal:
% 1.59/1.94 meet(b(), a()) != meet(a(), b())
% 1.59/1.94 To show the unsatisfiability of the original goal,
% 1.59/1.94 it suffices to show that meet(b(), a()) = meet(a(), b()) (skolemized goal) is valid under the axioms.
% 1.59/1.94 Here is an equational proof:
% 1.59/1.94 0: join(meet(X0, X1), meet(X0, join(X0, X1))) = X0.
% 1.59/1.94 Proof: Axiom.
% 1.59/1.94
% 1.59/1.94 1: join(meet(X0, X0), meet(X1, join(X0, X0))) = X0.
% 1.59/1.94 Proof: Axiom.
% 1.59/1.94
% 1.59/1.94 2: join(meet(X0, X1), meet(X1, join(X0, X1))) = X1.
% 1.59/1.94 Proof: Axiom.
% 1.59/1.94
% 1.59/1.94 3: meet(meet(join(X0, X1), join(X2, X0)), X0) = X0.
% 1.59/1.94 Proof: Axiom.
% 1.59/1.94
% 1.59/1.94 4: join(join(meet(X0, X1), meet(X2, X0)), X0) = X0.
% 1.59/1.94 Proof: Axiom.
% 1.59/1.94
% 1.59/1.94 6: X3 = meet(meet(join(X3, X1), X3), X3).
% 1.59/1.94 Proof: A critical pair between equations 3 and 4.
% 1.59/1.94
% 1.59/1.94 7: X3 = join(join(meet(X3, X1), X3), X3).
% 1.59/1.94 Proof: A critical pair between equations 4 and 3.
% 1.59/1.94
% 1.59/1.94 8: X3 = join(X3, meet(X3, join(meet(join(X3, X4), join(X5, X3)), X3))).
% 1.59/1.94 Proof: A critical pair between equations 2 and 3.
% 1.59/1.94
% 1.59/1.94 10: meet(X3, X4) = meet(meet(X3, join(X2, meet(X3, X4))), meet(X3, X4)).
% 1.59/1.94 Proof: A critical pair between equations 3 and 0.
% 1.59/1.94
% 1.59/1.94 12: meet(X3, X4) = meet(meet(X4, join(X2, meet(X3, X4))), meet(X3, X4)).
% 1.59/1.94 Proof: A critical pair between equations 3 and 2.
% 1.59/1.94
% 1.59/1.94 14: meet(X2, X2) = join(meet(meet(X2, X2), meet(X3, join(X2, X2))), meet(meet(X2, X2), X2)).
% 1.59/1.94 Proof: A critical pair between equations 0 and 1.
% 1.59/1.94
% 1.59/1.94 17: X6 = meet(meet(X6, X6), X6).
% 1.59/1.94 Proof: A critical pair between equations 6 and 8.
% 1.59/1.94
% 1.59/1.94 18: X6 = meet(meet(X6, join(X2, X6)), X6).
% 1.59/1.94 Proof: A critical pair between equations 3 and 8.
% 1.59/1.94
% 1.59/1.94 28: meet(X6, join(X5, X5)) = meet(meet(X6, X5), meet(X6, join(X5, X5))).
% 1.59/1.94 Proof: A critical pair between equations 10 and 1.
% 1.59/1.94
% 1.59/1.94 29: meet(X2, X2) = join(meet(meet(X2, X2), meet(X3, join(X2, X2))), X2).
% 1.59/1.94 Proof: Rewrite equation 14,
% 1.59/1.94 lhs with equations []
% 1.59/1.94 rhs with equations [17].
% 1.59/1.94
% 1.59/1.94 33: meet(X8, X8) = join(meet(X8, join(X8, X8)), X8).
% 1.59/1.94 Proof: A critical pair between equations 29 and 28.
% 1.59/1.94
% 1.59/1.94 39: meet(X7, X7) = join(X7, meet(meet(X7, X7), join(meet(X7, X7), X7))).
% 1.59/1.94 Proof: A critical pair between equations 0 and 17.
% 1.59/1.94
% 1.59/1.94 43: X9 = join(meet(X9, X9), X9).
% 1.59/1.94 Proof: A critical pair between equations 7 and 33.
% 1.59/1.94
% 1.59/1.94 44: X8 = meet(meet(meet(X8, X8), X8), X8).
% 1.59/1.94 Proof: A critical pair between equations 6 and 39.
% 1.59/1.94
% 1.59/1.94 57: X8 = meet(X8, X8).
% 1.59/1.94 Proof: Rewrite equation 44,
% 1.59/1.94 lhs with equations []
% 1.59/1.94 rhs with equations [17].
% 1.59/1.94
% 1.59/1.94 58: X9 = join(X9, X9).
% 1.59/1.94 Proof: Rewrite equation 43,
% 1.59/1.94 lhs with equations []
% 1.59/1.94 rhs with equations [57].
% 1.59/1.94
% 1.59/1.94 62: join(X0, meet(X1, X0)) = X0.
% 1.59/1.94 Proof: Rewrite equation 1,
% 1.59/1.94 lhs with equations [57,58]
% 1.59/1.94 rhs with equations [].
% 1.59/1.94
% 1.59/1.94 64: X2 = join(meet(X2, meet(X3, X2)), X2).
% 1.59/1.94 Proof: Rewrite equation 29,
% 1.59/1.94 lhs with equations [57]
% 1.59/1.94 rhs with equations [57,58].
% 1.59/1.94
% 1.59/1.94 65: meet(X6, X5) = meet(meet(X5, X5), meet(X6, X5)).
% 1.59/1.94 Proof: A critical pair between equations 12 and 62.
% 1.59/1.94
% 1.59/1.94 69: meet(X3, X2) = join(meet(X2, meet(X3, X2)), meet(meet(X3, X2), X2)).
% 1.59/1.94 Proof: A critical pair between equations 2 and 62.
% 1.59/1.94
% 1.59/1.94 82: meet(X6, X5) = meet(X5, meet(X6, X5)).
% 1.59/1.94 Proof: Rewrite equation 65,
% 1.59/1.94 lhs with equations []
% 1.59/1.94 rhs with equations [57].
% 1.59/1.94
% 1.59/1.94 83: X2 = join(meet(X3, X2), X2).
% 1.59/1.94 Proof: Rewrite equation 64,
% 1.59/1.94 lhs with equations []
% 1.59/1.94 rhs with equations [82].
% 1.59/1.94
% 1.59/1.94 86: meet(join(X4, X5), X4) = join(meet(X4, meet(join(X4, X5), X4)), X4).
% 1.59/1.94 Proof: A critical pair between equations 69 and 6.
% 1.59/1.94
% 1.59/1.94 99: meet(join(X4, X5), X4) = X4.
% 1.59/1.94 Proof: Rewrite equation 86,
% 1.59/1.94 lhs with equations []
% 1.59/1.94 rhs with equations [82,83].
% 1.59/1.94
% 1.59/1.94 101: X6 = join(X6, meet(X6, join(join(X6, X7), X6))).
% 1.59/1.94 Proof: A critical pair between equations 2 and 99.
% 1.59/1.94
% 1.59/1.94 102: join(meet(X6, X7), X6) = meet(X6, join(meet(X6, X7), X6)).
% 1.59/1.94 Proof: A critical pair between equations 99 and 7.
% 1.59/1.94
% 1.59/1.94 104: join(X6, X7) = join(join(X6, join(X6, X7)), join(X6, X7)).
% 1.59/1.94 Proof: A critical pair between equations 7 and 99.
% 1.59/1.94
% 1.59/1.94 110: meet(X7, join(X8, X7)) = join(join(X7, meet(X7, join(X8, X7))), meet(X7, join(X8, X7))).
% 1.59/1.94 Proof: A critical pair between equations 7 and 18.
% 1.59/1.94
% 1.59/1.94 112: meet(X7, join(X8, X7)) = join(X7, meet(meet(X7, join(X8, X7)), join(meet(X7, join(X8, X7)), X7))).
% 1.59/1.94 Proof: A critical pair between equations 0 and 18.
% 1.59/1.94
% 1.59/1.94 125: join(X8, join(X8, X9)) = meet(join(X8, X9), join(X8, join(X8, X9))).
% 1.59/1.94 Proof: A critical pair between equations 99 and 104.
% 1.59/1.94
% 1.59/1.94 136: meet(X9, join(join(X9, X10), X9)) = join(X9, meet(X9, join(join(X9, X10), X9))).
% 1.59/1.94 Proof: A critical pair between equations 110 and 101.
% 1.59/1.94
% 1.59/1.94 139: meet(X9, join(join(X9, X10), X9)) = X9.
% 1.59/1.94 Proof: Rewrite equation 136,
% 1.59/1.94 lhs with equations []
% 1.59/1.94 rhs with equations [101].
% 1.59/1.94
% 1.59/1.94 140: X11 = meet(X11, join(meet(X11, join(X12, X11)), X11)).
% 1.59/1.94 Proof: A critical pair between equations 139 and 112.
% 1.59/1.94
% 1.59/1.94 153: X11 = join(meet(X11, join(X12, X11)), X11).
% 1.59/1.94 Proof: Rewrite equation 140,
% 1.59/1.94 lhs with equations []
% 1.59/1.94 rhs with equations [102].
% 1.59/1.94
% 1.59/1.94 154: meet(X7, join(X8, X7)) = X7.
% 1.59/1.94 Proof: Rewrite equation 112,
% 1.59/1.94 lhs with equations []
% 1.59/1.94 rhs with equations [153,18,58].
% 1.59/1.94
% 1.59/1.94 155: join(meet(X9, X7), X9) = X9.
% 1.59/1.94 Proof: A critical pair between equations 102 and 154.
% 1.59/1.94
% 1.59/1.94 156: join(X11, join(X11, X9)) = join(X11, X9).
% 1.59/1.94 Proof: A critical pair between equations 125 and 154.
% 1.59/1.94
% 1.59/1.94 160: meet(X9, join(X10, X9)) = meet(join(X10, X9), X9).
% 1.59/1.94 Proof: A critical pair between equations 82 and 154.
% 1.59/1.94
% 1.59/1.94 167: X9 = meet(join(X10, X9), X9).
% 1.59/1.94 Proof: Rewrite equation 160,
% 1.59/1.94 lhs with equations [154]
% 1.59/1.94 rhs with equations [].
% 1.59/1.94
% 1.59/1.94 172: X12 = join(meet(X12, join(X12, X13)), meet(X12, join(X12, X13))).
% 1.59/1.94 Proof: A critical pair between equations 0 and 156.
% 1.59/1.94
% 1.59/1.94 176: join(X11, X12) = join(join(X12, meet(X2, join(X11, X12))), join(X11, X12)).
% 1.59/1.94 Proof: A critical pair between equations 4 and 167.
% 1.59/1.94
% 1.59/1.94 178: meet(X10, X11) = join(meet(meet(X10, X11), X10), meet(meet(X10, X11), X10)).
% 1.59/1.94 Proof: A critical pair between equations 0 and 155.
% 1.59/1.94
% 1.59/1.94 180: meet(X10, X11) = meet(meet(X10, X11), X10).
% 1.59/1.94 Proof: Rewrite equation 178,
% 1.59/1.94 lhs with equations []
% 1.59/1.94 rhs with equations [58].
% 1.59/1.94
% 1.59/1.94 181: X12 = meet(X12, join(X12, X13)).
% 1.59/1.94 Proof: Rewrite equation 172,
% 1.59/1.94 lhs with equations []
% 1.59/1.94 rhs with equations [58].
% 1.59/1.94
% 1.59/1.94 182: X12 = join(X12, meet(X12, X13)).
% 1.59/1.94 Proof: A critical pair between equations 62 and 180.
% 1.59/1.94
% 1.59/1.94 184: join(X14, X15) = join(join(X15, X14), join(X14, X15)).
% 1.59/1.94 Proof: A critical pair between equations 176 and 181.
% 1.59/1.94
% 1.59/1.94 196: meet(X14, X15) = meet(meet(X15, X14), meet(X14, X15)).
% 1.59/1.94 Proof: A critical pair between equations 12 and 182.
% 1.59/1.94
% 1.59/1.94 198: join(X16, X17) = meet(join(X17, X16), join(X16, X17)).
% 1.59/1.94 Proof: A critical pair between equations 99 and 184.
% 1.59/1.94
% 1.59/1.94 200: join(X16, X17) = meet(join(X16, X17), join(X17, X16)).
% 1.59/1.94 Proof: A critical pair between equations 181 and 184.
% 1.59/1.94
% 1.59/1.94 206: join(X16, X17) = join(X17, X16).
% 1.59/1.94 Proof: Rewrite equation 200,
% 1.59/1.94 lhs with equations []
% 1.59/1.94 rhs with equations [198].
% 1.59/1.94
% 1.59/1.94 225: meet(X16, X17) = join(meet(X16, X17), meet(X17, X16)).
% 1.59/1.94 Proof: A critical pair between equations 182 and 196.
% 1.59/1.94
% 1.59/1.94 226: join(X18, X19) = join(join(X19, X18), join(X19, X18)).
% 1.59/1.94 Proof: A critical pair between equations 184 and 206.
% 1.59/1.94
% 1.59/1.94 232: join(X18, X19) = join(X19, X18).
% 1.59/1.94 Proof: Rewrite equation 226,
% 1.59/1.94 lhs with equations []
% 1.59/1.94 rhs with equations [58].
% 1.59/1.94
% 1.59/1.94 241: join(meet(X21, X20), meet(X20, X21)) = meet(X20, X21).
% 1.59/1.94 Proof: A critical pair between equations 232 and 225.
% 1.59/1.94
% 1.59/1.94 257: meet(X21, X20) = meet(X20, X21).
% 1.59/1.94 Proof: Rewrite equation 241,
% 1.59/1.94 lhs with equations [225]
% 1.59/1.94 rhs with equations [].
% 1.59/1.94
% 1.59/1.94 267: meet(b(), a()) = meet(a(), b()).
% 1.59/1.94 Proof: Rewrite lhs with equations []
% 1.59/1.94 rhs with equations [257].
% 1.59/1.94
% 1.59/1.94 % SZS output end Proof
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