TSTP Solution File: LCL186-10 by Toma---0.4
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% File : Toma---0.4
% Problem : LCL186-10 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n003.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 08:14:06 EDT 2023
% Result : Unsatisfiable 0.19s 0.67s
% Output : CNFRefutation 0.19s
% 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 : LCL186-10 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13 % Command : toma --casc %s
% 0.12/0.34 % Computer : n003.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 : Fri Aug 25 04:27:38 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.67 % SZS status Unsatisfiable
% 0.19/0.67 % SZS output start Proof
% 0.19/0.67 original problem:
% 0.19/0.67 axioms:
% 0.19/0.67 ifeq(A, A, B, C) = B
% 0.19/0.67 axiom(or(not(or(A, A)), A)) = true()
% 0.19/0.67 axiom(or(not(A), or(B, A))) = true()
% 0.19/0.67 axiom(or(not(or(A, B)), or(B, A))) = true()
% 0.19/0.67 axiom(or(not(or(A, or(B, C))), or(B, or(A, C)))) = true()
% 0.19/0.67 axiom(or(not(or(not(A), B)), or(not(or(C, A)), or(C, B)))) = true()
% 0.19/0.67 ifeq(axiom(X), true(), theorem(X), true()) = true()
% 0.19/0.67 ifeq(theorem(Y), true(), ifeq(axiom(or(not(Y), X)), true(), theorem(X), true()), true()) = true()
% 0.19/0.67 ifeq(theorem(or(not(Y), Z)), true(), ifeq(axiom(or(not(X), Y)), true(), theorem(or(not(X), Z)), true()), true()) = true()
% 0.19/0.67 goal:
% 0.19/0.67 theorem(or(not(not(p())), or(not(p()), q()))) != true()
% 0.19/0.67 To show the unsatisfiability of the original goal,
% 0.19/0.67 it suffices to show that theorem(or(not(not(p())), or(not(p()), q()))) = true() (skolemized goal) is valid under the axioms.
% 0.19/0.67 Here is an equational proof:
% 0.19/0.67 0: ifeq(X0, X0, X1, X2) = X1.
% 0.19/0.67 Proof: Axiom.
% 0.19/0.67
% 0.19/0.67 2: axiom(or(not(X0), or(X1, X0))) = true().
% 0.19/0.67 Proof: Axiom.
% 0.19/0.67
% 0.19/0.67 3: axiom(or(not(or(X0, X1)), or(X1, X0))) = true().
% 0.19/0.67 Proof: Axiom.
% 0.19/0.67
% 0.19/0.67 6: ifeq(axiom(X3), true(), theorem(X3), true()) = true().
% 0.19/0.67 Proof: Axiom.
% 0.19/0.67
% 0.19/0.67 8: ifeq(theorem(or(not(X4), X5)), true(), ifeq(axiom(or(not(X3), X4)), true(), theorem(or(not(X3), X5)), true()), true()) = true().
% 0.19/0.67 Proof: Axiom.
% 0.19/0.67
% 0.19/0.67 12: true() = ifeq(true(), true(), theorem(or(not(or(X4, X5)), or(X5, X4))), true()).
% 0.19/0.67 Proof: A critical pair between equations 6 and 3.
% 0.19/0.67
% 0.19/0.67 20: true() = ifeq(theorem(or(not(or(X7, X6)), X5)), true(), ifeq(true(), true(), theorem(or(not(X6), X5)), true()), true()).
% 0.19/0.67 Proof: A critical pair between equations 8 and 2.
% 0.19/0.67
% 0.19/0.67 21: true() = ifeq(theorem(or(not(or(X7, X6)), X5)), true(), theorem(or(not(X6), X5)), true()).
% 0.19/0.67 Proof: Rewrite equation 20,
% 0.19/0.67 lhs with equations []
% 0.19/0.67 rhs with equations [0].
% 0.19/0.67
% 0.19/0.67 29: true() = theorem(or(not(or(X4, X5)), or(X5, X4))).
% 0.19/0.67 Proof: Rewrite equation 12,
% 0.19/0.67 lhs with equations []
% 0.19/0.67 rhs with equations [0].
% 0.19/0.67
% 0.19/0.67 36: true() = ifeq(true(), true(), theorem(or(not(X9), or(X9, X8))), true()).
% 0.19/0.67 Proof: A critical pair between equations 21 and 29.
% 0.19/0.67
% 0.19/0.67 47: true() = theorem(or(not(X9), or(X9, X8))).
% 0.19/0.67 Proof: Rewrite equation 36,
% 0.19/0.67 lhs with equations []
% 0.19/0.67 rhs with equations [0].
% 0.19/0.67
% 0.19/0.67 49: theorem(or(not(not(p())), or(not(p()), q()))) = true().
% 0.19/0.67 Proof: Rewrite lhs with equations [47]
% 0.19/0.67 rhs with equations [].
% 0.19/0.67
% 0.19/0.67 % SZS output end Proof
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