TSTP Solution File: LAT008-1 by Toma---0.4
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% File : Toma---0.4
% Problem : LAT008-1 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n025.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 06:25:25 EDT 2023
% Result : Unsatisfiable 2.33s 2.86s
% Output : CNFRefutation 2.33s
% 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 : LAT008-1 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14 % Command : toma --casc %s
% 0.14/0.35 % Computer : n025.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 24 09:13:21 EDT 2023
% 0.14/0.35 % CPUTime :
% 2.33/2.86 % SZS status Unsatisfiable
% 2.33/2.86 % SZS output start Proof
% 2.33/2.86 original problem:
% 2.33/2.86 axioms:
% 2.33/2.86 meet(X, join(X, Y)) = X
% 2.33/2.86 meet(X, join(Y, Z)) = join(meet(Z, X), meet(Y, X))
% 2.33/2.86 goal:
% 2.33/2.86 join(a(), meet(a(), b())) != a()
% 2.33/2.86 To show the unsatisfiability of the original goal,
% 2.33/2.86 it suffices to show that join(a(), meet(a(), b())) = a() (skolemized goal) is valid under the axioms.
% 2.33/2.86 Here is an equational proof:
% 2.33/2.86 0: meet(X0, join(X0, X1)) = X0.
% 2.33/2.86 Proof: Axiom.
% 2.33/2.86
% 2.33/2.86 1: meet(X0, join(X1, X2)) = join(meet(X2, X0), meet(X1, X0)).
% 2.33/2.86 Proof: Axiom.
% 2.33/2.86
% 2.33/2.86 3: meet(X3, X4) = meet(meet(X3, X4), meet(X4, join(X5, X3))).
% 2.33/2.86 Proof: A critical pair between equations 0 and 1.
% 2.33/2.86
% 2.33/2.86 9: meet(X7, X6) = meet(meet(X7, X6), X6).
% 2.33/2.86 Proof: A critical pair between equations 3 and 0.
% 2.33/2.86
% 2.33/2.86 34: meet(X9, join(X1, meet(X8, X9))) = join(meet(X8, X9), meet(X1, X9)).
% 2.33/2.86 Proof: A critical pair between equations 1 and 9.
% 2.33/2.86
% 2.33/2.86 41: meet(X11, join(X12, meet(X10, X11))) = meet(X11, join(X12, X10)).
% 2.33/2.86 Proof: A critical pair between equations 34 and 1.
% 2.33/2.86
% 2.33/2.86 48: join(meet(X12, X11), meet(meet(X10, X11), X11)) = meet(X11, meet(X11, join(X12, X10))).
% 2.33/2.86 Proof: A critical pair between equations 34 and 1.
% 2.33/2.86
% 2.33/2.86 50: meet(X11, join(X1, meet(meet(X10, X11), X11))) = join(meet(X10, X11), meet(X1, X11)).
% 2.33/2.86 Proof: A critical pair between equations 34 and 9.
% 2.33/2.86
% 2.33/2.86 51: join(meet(X12, X11), meet(X10, X11)) = meet(X11, meet(X11, join(X12, X10))).
% 2.33/2.86 Proof: Rewrite equation 48,
% 2.33/2.86 lhs with equations [9]
% 2.33/2.86 rhs with equations [].
% 2.33/2.86
% 2.33/2.86 56: meet(X11, join(X1, X10)) = meet(X11, meet(X11, join(X10, X1))).
% 2.33/2.86 Proof: Rewrite equation 50,
% 2.33/2.86 lhs with equations [9,41]
% 2.33/2.86 rhs with equations [51].
% 2.33/2.86
% 2.33/2.86 66: meet(X12, join(X13, X12)) = meet(X12, X12).
% 2.33/2.86 Proof: A critical pair between equations 56 and 0.
% 2.33/2.86
% 2.33/2.86 84: join(meet(X12, X11), meet(X10, X11)) = meet(X11, join(X10, X12)).
% 2.33/2.86 Proof: Rewrite equation 51,
% 2.33/2.86 lhs with equations []
% 2.33/2.86 rhs with equations [56].
% 2.33/2.86
% 2.33/2.86 87: meet(X15, X15) = X15.
% 2.33/2.86 Proof: A critical pair between equations 66 and 0.
% 2.33/2.86
% 2.33/2.86 89: join(meet(X14, X14), meet(X15, X14)) = meet(X14, X14).
% 2.33/2.86 Proof: A critical pair between equations 84 and 66.
% 2.33/2.86
% 2.33/2.86 102: join(X14, meet(X15, X14)) = X14.
% 2.33/2.86 Proof: Rewrite equation 89,
% 2.33/2.86 lhs with equations [87]
% 2.33/2.86 rhs with equations [87].
% 2.33/2.86
% 2.33/2.86 111: X16 = join(X16, X16).
% 2.33/2.86 Proof: A critical pair between equations 102 and 87.
% 2.33/2.86
% 2.33/2.86 133: join(meet(X17, X11), meet(X17, X11)) = meet(X11, X17).
% 2.33/2.86 Proof: A critical pair between equations 84 and 111.
% 2.33/2.86
% 2.33/2.86 145: meet(X17, X11) = meet(X11, X17).
% 2.33/2.86 Proof: Rewrite equation 133,
% 2.33/2.86 lhs with equations [111]
% 2.33/2.86 rhs with equations [].
% 2.33/2.86
% 2.33/2.86 147: X19 = join(X19, meet(X19, X18)).
% 2.33/2.86 Proof: A critical pair between equations 102 and 145.
% 2.33/2.86
% 2.33/2.86 169: join(a(), meet(a(), b())) = a().
% 2.33/2.86 Proof: Rewrite lhs with equations [147]
% 2.33/2.86 rhs with equations [].
% 2.33/2.86
% 2.33/2.86 % SZS output end Proof
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