TSTP Solution File: LAT090-1 by Toma---0.4
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% File : Toma---0.4
% Problem : LAT090-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n029.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 06:25:38 EDT 2023
% Result : Unsatisfiable 0.71s 1.07s
% Output : CNFRefutation 0.71s
% 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 : LAT090-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.14 % Command : toma --casc %s
% 0.12/0.34 % Computer : n029.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 : Thu Aug 24 09:52:23 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.71/1.07 % SZS status Unsatisfiable
% 0.71/1.07 % SZS output start Proof
% 0.71/1.07 original problem:
% 0.71/1.07 axioms:
% 0.71/1.07 join(meet(A, B), meet(A, join(A, B))) = A
% 0.71/1.07 join(meet(A, A), meet(B, join(A, A))) = A
% 0.71/1.07 join(meet(A, B), meet(B, join(A, B))) = B
% 0.71/1.07 meet(meet(join(A, B), join(C, A)), A) = A
% 0.71/1.07 join(join(meet(A, B), meet(C, A)), A) = A
% 0.71/1.07 goal:
% 0.71/1.07 join(a(), a()) != a()
% 0.71/1.07 To show the unsatisfiability of the original goal,
% 0.71/1.07 it suffices to show that join(a(), a()) = a() (skolemized goal) is valid under the axioms.
% 0.71/1.07 Here is an equational proof:
% 0.71/1.07 0: join(meet(X0, X1), meet(X0, join(X0, X1))) = X0.
% 0.71/1.07 Proof: Axiom.
% 0.71/1.07
% 0.71/1.07 1: join(meet(X0, X0), meet(X1, join(X0, X0))) = X0.
% 0.71/1.07 Proof: Axiom.
% 0.71/1.07
% 0.71/1.07 2: join(meet(X0, X1), meet(X1, join(X0, X1))) = X1.
% 0.71/1.07 Proof: Axiom.
% 0.71/1.07
% 0.71/1.07 3: meet(meet(join(X0, X1), join(X2, X0)), X0) = X0.
% 0.71/1.07 Proof: Axiom.
% 0.71/1.07
% 0.71/1.07 4: join(join(meet(X0, X1), meet(X2, X0)), X0) = X0.
% 0.71/1.07 Proof: Axiom.
% 0.71/1.07
% 0.71/1.07 6: X3 = meet(meet(join(X3, X1), X3), X3).
% 0.71/1.07 Proof: A critical pair between equations 3 and 4.
% 0.71/1.07
% 0.71/1.07 7: X3 = join(join(meet(X3, X1), X3), X3).
% 0.71/1.07 Proof: A critical pair between equations 4 and 3.
% 0.71/1.07
% 0.71/1.07 8: X3 = join(X3, meet(X3, join(meet(join(X3, X4), join(X5, X3)), X3))).
% 0.71/1.07 Proof: A critical pair between equations 2 and 3.
% 0.71/1.07
% 0.71/1.07 10: meet(X3, X4) = meet(meet(X3, join(X2, meet(X3, X4))), meet(X3, X4)).
% 0.71/1.07 Proof: A critical pair between equations 3 and 0.
% 0.71/1.07
% 0.71/1.07 14: meet(X2, X2) = join(meet(meet(X2, X2), meet(X3, join(X2, X2))), meet(meet(X2, X2), X2)).
% 0.71/1.07 Proof: A critical pair between equations 0 and 1.
% 0.71/1.07
% 0.71/1.07 17: X6 = meet(meet(X6, X6), X6).
% 0.71/1.07 Proof: A critical pair between equations 6 and 8.
% 0.71/1.07
% 0.71/1.07 28: meet(X6, join(X5, X5)) = meet(meet(X6, X5), meet(X6, join(X5, X5))).
% 0.71/1.07 Proof: A critical pair between equations 10 and 1.
% 0.71/1.07
% 0.71/1.07 29: meet(X2, X2) = join(meet(meet(X2, X2), meet(X3, join(X2, X2))), X2).
% 0.71/1.07 Proof: Rewrite equation 14,
% 0.71/1.07 lhs with equations []
% 0.71/1.07 rhs with equations [17].
% 0.71/1.07
% 0.71/1.07 33: meet(X8, X8) = join(meet(X8, join(X8, X8)), X8).
% 0.71/1.07 Proof: A critical pair between equations 29 and 28.
% 0.71/1.07
% 0.71/1.07 39: meet(X7, X7) = join(X7, meet(meet(X7, X7), join(meet(X7, X7), X7))).
% 0.71/1.07 Proof: A critical pair between equations 0 and 17.
% 0.71/1.07
% 0.71/1.07 43: X9 = join(meet(X9, X9), X9).
% 0.71/1.07 Proof: A critical pair between equations 7 and 33.
% 0.71/1.07
% 0.71/1.07 44: X8 = meet(meet(meet(X8, X8), X8), X8).
% 0.71/1.07 Proof: A critical pair between equations 6 and 39.
% 0.71/1.07
% 0.71/1.07 57: X8 = meet(X8, X8).
% 0.71/1.07 Proof: Rewrite equation 44,
% 0.71/1.07 lhs with equations []
% 0.71/1.07 rhs with equations [17].
% 0.71/1.07
% 0.71/1.07 58: X9 = join(X9, X9).
% 0.71/1.07 Proof: Rewrite equation 43,
% 0.71/1.07 lhs with equations []
% 0.71/1.07 rhs with equations [57].
% 0.71/1.07
% 0.71/1.07 65: join(a(), a()) = a().
% 0.71/1.07 Proof: Rewrite lhs with equations [58]
% 0.71/1.07 rhs with equations [].
% 0.71/1.07
% 0.71/1.07 % SZS output end Proof
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