TSTP Solution File: LCL172-3 by Moca---0.1
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- Process Solution
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% File : Moca---0.1
% Problem : LCL172-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n011.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 : 600s
% DateTime : Sun Jul 17 12:58:41 EDT 2022
% Result : Unsatisfiable 0.19s 0.41s
% Output : Proof 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 : LCL172-3 : TPTP v8.1.0. Released v2.3.0.
% 0.13/0.13 % Command : moca.sh %s
% 0.13/0.34 % Computer : n011.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 : 600
% 0.13/0.34 % DateTime : Sun Jul 3 00:13:05 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.41 % SZS status Unsatisfiable
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 The input problem is unsatisfiable because
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% 0.19/0.41 [1] the following set of Horn clauses is unsatisfiable:
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% 0.19/0.41 axiom(implies(or(A, A), A))
% 0.19/0.41 axiom(implies(A, or(B, A)))
% 0.19/0.41 axiom(implies(or(A, B), or(B, A)))
% 0.19/0.41 axiom(implies(or(A, or(B, C)), or(B, or(A, C))))
% 0.19/0.41 axiom(implies(implies(A, B), implies(or(C, A), or(C, B))))
% 0.19/0.41 implies(X, Y) = or(not(X), Y)
% 0.19/0.41 axiom(X) ==> theorem(X)
% 0.19/0.41 theorem(implies(Y, X)) & theorem(Y) ==> theorem(X)
% 0.19/0.41 theorem(implies(implies(p, implies(q, r)), implies(q, implies(p, r)))) ==> \bottom
% 0.19/0.41
% 0.19/0.41 This holds because
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% 0.19/0.41 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
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% 0.19/0.41 E:
% 0.19/0.41 axiom(implies(A, or(B, A))) = true__
% 0.19/0.41 axiom(implies(implies(A, B), implies(or(C, A), or(C, B)))) = true__
% 0.19/0.41 axiom(implies(or(A, A), A)) = true__
% 0.19/0.41 axiom(implies(or(A, B), or(B, A))) = true__
% 0.19/0.41 axiom(implies(or(A, or(B, C)), or(B, or(A, C)))) = true__
% 0.19/0.41 f1(axiom(X), X) = true__
% 0.19/0.41 f1(true__, X) = theorem(X)
% 0.19/0.41 f2(true__, X) = theorem(X)
% 0.19/0.41 f3(theorem(Y), Y, X) = true__
% 0.19/0.41 f3(true__, Y, X) = f2(theorem(implies(Y, X)), X)
% 0.19/0.41 f4(theorem(implies(implies(p, implies(q, r)), implies(q, implies(p, r))))) = true__
% 0.19/0.41 f4(true__) = false__
% 0.19/0.41 implies(X, Y) = or(not(X), Y)
% 0.19/0.41 G:
% 0.19/0.41 true__ = false__
% 0.19/0.41
% 0.19/0.41 This holds because
% 0.19/0.41
% 0.19/0.41 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
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% 0.19/0.41
% 0.19/0.41 axiom(implies(A, or(B, A))) -> true__
% 0.19/0.41 axiom(implies(implies(A, B), implies(or(C, A), or(C, B)))) -> true__
% 0.19/0.41 axiom(implies(or(A, A), A)) -> true__
% 0.19/0.41 axiom(implies(or(A, B), or(B, A))) -> true__
% 0.19/0.41 axiom(implies(or(A, or(B, C)), or(B, or(A, C)))) -> true__
% 0.19/0.41 axiom(or(not(Y0), or(Y1, Y0))) -> true__
% 0.19/0.41 axiom(or(not(or(Y0, Y0)), Y0)) -> true__
% 0.19/0.41 axiom(or(not(or(Y0, Y1)), or(Y1, Y0))) -> true__
% 0.19/0.41 axiom(or(not(or(Y0, or(Y1, Y2))), or(Y1, or(Y0, Y2)))) -> true__
% 0.19/0.41 f1(axiom(X), X) -> true__
% 0.19/0.41 f1(true__, or(not(X0), or(X1, X0))) -> true__
% 0.19/0.41 f1(true__, or(not(or(X0, X0)), X0)) -> true__
% 0.19/0.41 f1(true__, or(not(or(X0, X1)), or(X1, X0))) -> true__
% 0.19/0.41 f1(true__, or(not(or(X0, or(X1, X2))), or(X1, or(X0, X2)))) -> true__
% 0.19/0.41 f1(true__, or(not(or(not(X0), X1)), or(not(or(X2, X0)), or(X2, X1)))) -> true__
% 0.19/0.41 f2(f1(true__, or(not(or(not(X0), or(X1, X0))), Y1)), Y1) -> true__
% 0.19/0.41 f2(f1(true__, or(not(or(not(or(X0, X0)), X0)), Y1)), Y1) -> true__
% 0.19/0.41 f2(f1(true__, or(not(or(not(or(X0, X1)), or(X1, X0))), Y1)), Y1) -> true__
% 0.19/0.41 f2(true__, X) -> theorem(X)
% 0.19/0.41 f3(f1(true__, Y0), Y0, Y1) -> true__
% 0.19/0.41 f3(theorem(Y), Y, X) -> true__
% 0.19/0.41 f3(true__, Y, X) -> f2(theorem(implies(Y, X)), X)
% 0.19/0.41 f4(theorem(implies(implies(p, implies(q, r)), implies(q, implies(p, r))))) -> true__
% 0.19/0.41 f4(true__) -> false__
% 0.19/0.41 false__ -> true__
% 0.19/0.41 implies(X, Y) -> or(not(X), Y)
% 0.19/0.41 theorem(X) -> f1(true__, X)
% 0.19/0.41 with the LPO induced by
% 0.19/0.41 r > q > p > f4 > f3 > f2 > theorem > f1 > axiom > implies > not > or > false__ > true__
% 0.19/0.41
% 0.19/0.41 % SZS output end Proof
% 0.19/0.41
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