TSTP Solution File: LCL239-10 by Toma---0.4
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%------------------------------------------------------------------------------
% File : Toma---0.4
% Problem : LCL239-10 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n024.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 08:14:21 EDT 2023
% Result : Unsatisfiable 1.51s 1.97s
% Output : CNFRefutation 1.51s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : LCL239-10 : TPTP v8.1.2. Released v7.5.0.
% 0.11/0.13 % Command : toma --casc %s
% 0.13/0.35 % Computer : n024.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 06:05:54 EDT 2023
% 0.13/0.35 % CPUTime :
% 1.51/1.97 % SZS status Unsatisfiable
% 1.51/1.97 % SZS output start Proof
% 1.51/1.97 original problem:
% 1.51/1.97 axioms:
% 1.51/1.97 ifeq(A, A, B, C) = B
% 1.51/1.97 axiom(implies(or(A, A), A)) = true()
% 1.51/1.97 axiom(implies(A, or(B, A))) = true()
% 1.51/1.97 axiom(implies(or(A, B), or(B, A))) = true()
% 1.51/1.97 axiom(implies(or(A, or(B, C)), or(B, or(A, C)))) = true()
% 1.51/1.97 axiom(implies(implies(A, B), implies(or(C, A), or(C, B)))) = true()
% 1.51/1.97 implies(X, Y) = or(not(X), Y)
% 1.51/1.97 ifeq(axiom(X), true(), theorem(X), true()) = true()
% 1.51/1.97 ifeq(theorem(implies(Y, X)), true(), ifeq(theorem(Y), true(), theorem(X), true()), true()) = true()
% 1.51/1.97 and(P, Q) = not(or(not(P), not(Q)))
% 1.51/1.97 goal:
% 1.51/1.97 theorem(not(and(p(), not(p())))) != true()
% 1.51/1.97 To show the unsatisfiability of the original goal,
% 1.51/1.97 it suffices to show that theorem(not(and(p(), not(p())))) = true() (skolemized goal) is valid under the axioms.
% 1.51/1.97 Here is an equational proof:
% 1.51/1.97 0: ifeq(X0, X0, X1, X2) = X1.
% 1.51/1.97 Proof: Axiom.
% 1.51/1.97
% 1.51/1.97 1: axiom(implies(or(X0, X0), X0)) = true().
% 1.51/1.97 Proof: Axiom.
% 1.51/1.97
% 1.51/1.97 2: axiom(implies(X0, or(X1, X0))) = true().
% 1.51/1.97 Proof: Axiom.
% 1.51/1.97
% 1.51/1.97 3: axiom(implies(or(X0, X1), or(X1, X0))) = true().
% 1.51/1.97 Proof: Axiom.
% 1.51/1.97
% 1.51/1.97 4: axiom(implies(or(X0, or(X1, X2)), or(X1, or(X0, X2)))) = true().
% 1.51/1.97 Proof: Axiom.
% 1.51/1.97
% 1.51/1.97 6: implies(X3, X4) = or(not(X3), X4).
% 1.51/1.97 Proof: Axiom.
% 1.51/1.97
% 1.51/1.97 7: ifeq(axiom(X3), true(), theorem(X3), true()) = true().
% 1.51/1.97 Proof: Axiom.
% 1.51/1.97
% 1.51/1.97 8: ifeq(theorem(implies(X4, X3)), true(), ifeq(theorem(X4), true(), theorem(X3), true()), true()) = true().
% 1.51/1.97 Proof: Axiom.
% 1.51/1.97
% 1.51/1.97 9: and(X5, X6) = not(or(not(X5), not(X6))).
% 1.51/1.97 Proof: Axiom.
% 1.51/1.97
% 1.51/1.97 10: and(X5, X6) = not(implies(X5, not(X6))).
% 1.51/1.97 Proof: Rewrite equation 9,
% 1.51/1.97 lhs with equations []
% 1.51/1.97 rhs with equations [6].
% 1.51/1.97
% 1.51/1.97 15: true() = ifeq(true(), true(), theorem(implies(or(X4, X4), X4)), true()).
% 1.51/1.97 Proof: A critical pair between equations 7 and 1.
% 1.51/1.97
% 1.51/1.97 16: true() = ifeq(true(), true(), theorem(implies(X4, or(X5, X4))), true()).
% 1.51/1.97 Proof: A critical pair between equations 7 and 2.
% 1.51/1.97
% 1.51/1.97 17: true() = ifeq(true(), true(), theorem(implies(or(X4, X5), or(X5, X4))), true()).
% 1.51/1.97 Proof: A critical pair between equations 7 and 3.
% 1.51/1.97
% 1.51/1.97 21: true() = axiom(implies(implies(X5, or(X1, X2)), or(X1, or(not(X5), X2)))).
% 1.51/1.97 Proof: A critical pair between equations 4 and 6.
% 1.51/1.97
% 1.51/1.97 24: true() = axiom(or(not(or(not(X5), or(X1, X2))), or(X1, or(not(X5), X2)))).
% 1.51/1.97 Proof: Rewrite equation 21,
% 1.51/1.97 lhs with equations []
% 1.51/1.97 rhs with equations [6,6].
% 1.51/1.97
% 1.51/1.97 26: true() = theorem(or(not(or(X4, X5)), or(X5, X4))).
% 1.51/1.97 Proof: Rewrite equation 17,
% 1.51/1.97 lhs with equations []
% 1.51/1.97 rhs with equations [6,0].
% 1.51/1.97
% 1.51/1.97 27: true() = theorem(or(not(X4), or(X5, X4))).
% 1.51/1.97 Proof: Rewrite equation 16,
% 1.51/1.97 lhs with equations []
% 1.51/1.97 rhs with equations [6,0].
% 1.51/1.97
% 1.51/1.97 28: true() = theorem(or(not(or(X4, X4)), X4)).
% 1.51/1.97 Proof: Rewrite equation 15,
% 1.51/1.97 lhs with equations []
% 1.51/1.97 rhs with equations [6,0].
% 1.51/1.97
% 1.51/1.97 33: and(X5, X6) = not(or(not(X5), not(X6))).
% 1.51/1.97 Proof: Rewrite equation 10,
% 1.51/1.97 lhs with equations []
% 1.51/1.97 rhs with equations [6].
% 1.51/1.97
% 1.51/1.97 34: ifeq(theorem(or(not(X4), X3)), true(), ifeq(theorem(X4), true(), theorem(X3), true()), true()) = true().
% 1.51/1.97 Proof: Rewrite equation 8,
% 1.51/1.97 lhs with equations [6]
% 1.51/1.97 rhs with equations [].
% 1.51/1.97
% 1.51/1.97 41: true() = ifeq(true(), true(), ifeq(theorem(or(X5, X5)), true(), theorem(X5), true()), true()).
% 1.51/1.97 Proof: A critical pair between equations 34 and 28.
% 1.51/1.97
% 1.51/1.97 42: true() = ifeq(true(), true(), ifeq(theorem(or(X6, X7)), true(), theorem(or(X7, X6)), true()), true()).
% 1.51/1.97 Proof: A critical pair between equations 34 and 26.
% 1.51/1.97
% 1.51/1.97 45: true() = ifeq(theorem(or(not(or(not(X6), or(X7, X6))), X3)), true(), ifeq(true(), true(), theorem(X3), true()), true()).
% 1.51/1.97 Proof: A critical pair between equations 34 and 27.
% 1.51/1.97
% 1.51/1.97 48: true() = ifeq(true(), true(), theorem(or(not(or(not(X6), or(X7, X8))), or(X7, or(not(X6), X8)))), true()).
% 1.51/1.97 Proof: A critical pair between equations 7 and 24.
% 1.51/1.97
% 1.51/1.97 55: true() = theorem(implies(implies(X6, or(X7, X8)), or(X7, implies(X6, X8)))).
% 1.51/1.97 Proof: Rewrite equation 48,
% 1.51/1.97 lhs with equations []
% 1.51/1.97 rhs with equations [6,6,6,0].
% 1.51/1.97
% 1.51/1.97 58: true() = ifeq(theorem(implies(implies(X6, or(X7, X6)), X3)), true(), theorem(X3), true()).
% 1.51/1.97 Proof: Rewrite equation 45,
% 1.51/1.97 lhs with equations []
% 1.51/1.97 rhs with equations [6,6,0].
% 1.51/1.97
% 1.51/1.97 61: true() = ifeq(theorem(or(X6, X7)), true(), theorem(or(X7, X6)), true()).
% 1.51/1.97 Proof: Rewrite equation 42,
% 1.51/1.97 lhs with equations []
% 1.51/1.97 rhs with equations [0].
% 1.51/1.97
% 1.51/1.97 62: true() = ifeq(theorem(or(X5, X5)), true(), theorem(X5), true()).
% 1.51/1.97 Proof: Rewrite equation 41,
% 1.51/1.97 lhs with equations []
% 1.51/1.97 rhs with equations [0].
% 1.51/1.97
% 1.51/1.97 69: ifeq(theorem(implies(X4, X3)), true(), ifeq(theorem(X4), true(), theorem(X3), true()), true()) = true().
% 1.51/1.97 Proof: Rewrite equation 34,
% 1.51/1.97 lhs with equations [6]
% 1.51/1.97 rhs with equations [].
% 1.51/1.97
% 1.51/1.97 70: and(X5, X6) = not(implies(X5, not(X6))).
% 1.51/1.97 Proof: Rewrite equation 33,
% 1.51/1.97 lhs with equations []
% 1.51/1.97 rhs with equations [6].
% 1.51/1.97
% 1.51/1.97 86: true() = ifeq(true(), true(), theorem(or(X10, implies(X11, X11))), true()).
% 1.51/1.97 Proof: A critical pair between equations 58 and 55.
% 1.51/1.97
% 1.51/1.97 98: true() = theorem(or(X10, or(not(X11), X11))).
% 1.51/1.97 Proof: Rewrite equation 86,
% 1.51/1.97 lhs with equations []
% 1.51/1.97 rhs with equations [6,0].
% 1.51/1.97
% 1.51/1.97 112: and(X5, X6) = not(or(not(X5), not(X6))).
% 1.51/1.97 Proof: Rewrite equation 70,
% 1.51/1.97 lhs with equations []
% 1.51/1.97 rhs with equations [6].
% 1.51/1.97
% 1.51/1.97 113: ifeq(theorem(or(not(X4), X3)), true(), ifeq(theorem(X4), true(), theorem(X3), true()), true()) = true().
% 1.51/1.97 Proof: Rewrite equation 69,
% 1.51/1.97 lhs with equations [6]
% 1.51/1.97 rhs with equations [].
% 1.51/1.97
% 1.51/1.97 124: true() = ifeq(true(), true(), theorem(or(not(X13), X13)), true()).
% 1.51/1.97 Proof: A critical pair between equations 62 and 98.
% 1.51/1.97
% 1.51/1.97 147: true() = theorem(implies(X13, X13)).
% 1.51/1.97 Proof: Rewrite equation 124,
% 1.51/1.97 lhs with equations []
% 1.51/1.97 rhs with equations [6,0].
% 1.51/1.97
% 1.51/1.97 157: ifeq(theorem(implies(X4, X3)), true(), ifeq(theorem(X4), true(), theorem(X3), true()), true()) = true().
% 1.51/1.97 Proof: Rewrite equation 113,
% 1.51/1.97 lhs with equations [6]
% 1.51/1.97 rhs with equations [].
% 1.51/1.97
% 1.51/1.97 158: and(X5, X6) = not(implies(X5, not(X6))).
% 1.51/1.97 Proof: Rewrite equation 112,
% 1.51/1.97 lhs with equations []
% 1.51/1.97 rhs with equations [6].
% 1.51/1.97
% 1.51/1.97 215: and(X5, X6) = not(or(not(X5), not(X6))).
% 1.51/1.97 Proof: Rewrite equation 158,
% 1.51/1.97 lhs with equations []
% 1.51/1.97 rhs with equations [6].
% 1.51/1.97
% 1.51/1.97 216: ifeq(theorem(or(not(X4), X3)), true(), ifeq(theorem(X4), true(), theorem(X3), true()), true()) = true().
% 1.51/1.97 Proof: Rewrite equation 157,
% 1.51/1.97 lhs with equations [6]
% 1.51/1.97 rhs with equations [].
% 1.51/1.97
% 1.51/1.97 226: true() = theorem(or(not(X13), X13)).
% 1.51/1.97 Proof: Rewrite equation 147,
% 1.51/1.97 lhs with equations []
% 1.51/1.97 rhs with equations [6].
% 1.51/1.97
% 1.51/1.97 234: true() = ifeq(true(), true(), theorem(or(X14, not(X14))), true()).
% 1.51/1.97 Proof: A critical pair between equations 61 and 226.
% 1.51/1.97
% 1.51/1.97 254: true() = theorem(or(X14, not(X14))).
% 1.51/1.97 Proof: Rewrite equation 234,
% 1.51/1.97 lhs with equations []
% 1.51/1.97 rhs with equations [0].
% 1.51/1.97
% 1.51/1.97 272: ifeq(theorem(implies(X4, X3)), true(), ifeq(theorem(X4), true(), theorem(X3), true()), true()) = true().
% 1.51/1.97 Proof: Rewrite equation 216,
% 1.51/1.97 lhs with equations [6]
% 1.51/1.97 rhs with equations [].
% 1.51/1.97
% 1.51/1.97 273: and(X5, X6) = not(implies(X5, not(X6))).
% 1.51/1.97 Proof: Rewrite equation 215,
% 1.51/1.97 lhs with equations []
% 1.51/1.97 rhs with equations [6].
% 1.51/1.97
% 1.51/1.97 341: and(X5, X6) = not(or(not(X5), not(X6))).
% 1.51/1.97 Proof: Rewrite equation 273,
% 1.51/1.97 lhs with equations []
% 1.51/1.97 rhs with equations [6].
% 1.51/1.97
% 1.51/1.97 342: ifeq(theorem(or(not(X4), X3)), true(), ifeq(theorem(X4), true(), theorem(X3), true()), true()) = true().
% 1.51/1.97 Proof: Rewrite equation 272,
% 1.51/1.97 lhs with equations [6]
% 1.51/1.97 rhs with equations [].
% 1.51/1.97
% 1.51/1.97 366: true() = ifeq(true(), true(), ifeq(theorem(X4), true(), theorem(not(not(X4))), true()), true()).
% 1.51/1.97 Proof: A critical pair between equations 342 and 254.
% 1.51/1.97
% 1.51/1.97 383: true() = ifeq(theorem(X4), true(), theorem(not(not(X4))), true()).
% 1.51/1.97 Proof: Rewrite equation 366,
% 1.51/1.97 lhs with equations []
% 1.51/1.97 rhs with equations [0].
% 1.51/1.97
% 1.51/1.97 385: true() = ifeq(true(), true(), theorem(not(not(or(X15, not(X15))))), true()).
% 1.51/1.97 Proof: A critical pair between equations 383 and 254.
% 1.51/1.97
% 1.51/1.97 405: true() = theorem(not(not(or(X15, not(X15))))).
% 1.51/1.97 Proof: Rewrite equation 385,
% 1.51/1.97 lhs with equations []
% 1.51/1.97 rhs with equations [0].
% 1.51/1.97
% 1.51/1.97 406: theorem(not(and(p(), not(p())))) = true().
% 1.51/1.97 Proof: Rewrite lhs with equations [341,405]
% 1.51/1.97 rhs with equations [].
% 1.51/1.97
% 1.51/1.97 % SZS output end Proof
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