TSTP Solution File: LCL156-1 by Moca---0.1
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- Process Solution
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% File : Moca---0.1
% Problem : LCL156-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n008.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 12:58:32 EDT 2022
% Result : Unsatisfiable 112.87s 112.80s
% Output : Proof 112.87s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL156-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13 % Command : moca.sh %s
% 0.12/0.34 % Computer : n008.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 : 600
% 0.12/0.34 % DateTime : Sun Jul 3 11:34:38 EDT 2022
% 0.12/0.34 % CPUTime :
% 112.87/112.80 % SZS status Unsatisfiable
% 112.87/112.80 % SZS output start Proof
% 112.87/112.80 The input problem is unsatisfiable because
% 112.87/112.80
% 112.87/112.80 [1] the following set of Horn clauses is unsatisfiable:
% 112.87/112.80
% 112.87/112.80 implies(truth, X) = X
% 112.87/112.80 implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))) = truth
% 112.87/112.80 implies(implies(X, Y), Y) = implies(implies(Y, X), X)
% 112.87/112.80 implies(implies(not(X), not(Y)), implies(Y, X)) = truth
% 112.87/112.80 or(X, Y) = implies(not(X), Y)
% 112.87/112.80 or(or(X, Y), Z) = or(X, or(Y, Z))
% 112.87/112.80 or(X, Y) = or(Y, X)
% 112.87/112.80 and(X, Y) = not(or(not(X), not(Y)))
% 112.87/112.80 and(and(X, Y), Z) = and(X, and(Y, Z))
% 112.87/112.80 and(X, Y) = and(Y, X)
% 112.87/112.80 xor(X, Y) = or(and(X, not(Y)), and(not(X), Y))
% 112.87/112.80 xor(X, Y) = xor(Y, X)
% 112.87/112.80 and_star(X, Y) = not(or(not(X), not(Y)))
% 112.87/112.80 and_star(and_star(X, Y), Z) = and_star(X, and_star(Y, Z))
% 112.87/112.80 and_star(X, Y) = and_star(Y, X)
% 112.87/112.80 not(truth) = falsehood
% 112.87/112.80 and_star(x, truth) = x ==> \bottom
% 112.87/112.80
% 112.87/112.80 This holds because
% 112.87/112.80
% 112.87/112.80 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 112.87/112.80
% 112.87/112.80 E:
% 112.87/112.80 and(X, Y) = and(Y, X)
% 112.87/112.80 and(X, Y) = not(or(not(X), not(Y)))
% 112.87/112.80 and(and(X, Y), Z) = and(X, and(Y, Z))
% 112.87/112.80 and_star(X, Y) = and_star(Y, X)
% 112.87/112.80 and_star(X, Y) = not(or(not(X), not(Y)))
% 112.87/112.80 and_star(and_star(X, Y), Z) = and_star(X, and_star(Y, Z))
% 112.87/112.80 f1(and_star(x, truth)) = true__
% 112.87/112.80 f1(x) = false__
% 112.87/112.80 implies(implies(X, Y), Y) = implies(implies(Y, X), X)
% 112.87/112.80 implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))) = truth
% 112.87/112.80 implies(implies(not(X), not(Y)), implies(Y, X)) = truth
% 112.87/112.80 implies(truth, X) = X
% 112.87/112.80 not(truth) = falsehood
% 112.87/112.80 or(X, Y) = implies(not(X), Y)
% 112.87/112.80 or(X, Y) = or(Y, X)
% 112.87/112.80 or(or(X, Y), Z) = or(X, or(Y, Z))
% 112.87/112.80 xor(X, Y) = or(and(X, not(Y)), and(not(X), Y))
% 112.87/112.80 xor(X, Y) = xor(Y, X)
% 112.87/112.80 G:
% 112.87/112.80 true__ = false__
% 112.87/112.80
% 112.87/112.80 This holds because
% 112.87/112.80
% 112.87/112.80 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 112.87/112.80
% 112.87/112.80 implies(X0, Y1) = implies(not(Y1), not(X0))
% 112.87/112.80 implies(X1, not(X0)) = implies(X0, not(X1))
% 112.87/112.80 implies(implies(X, Y), Y) = implies(implies(Y, X), X)
% 112.87/112.80 implies(implies(X, Y), not(implies(not(X), not(Y)))) = implies(implies(Y, X), not(implies(not(Y), not(X))))
% 112.87/112.80 implies(not(X), Y) = implies(not(Y), X)
% 112.87/112.80 not(implies(X, not(Y))) = not(implies(Y, not(X)))
% 112.87/112.80 not(implies(Y0, X0)) = not(implies(not(X0), not(Y0)))
% 112.87/112.80 and(X, Y) -> not(implies(X, not(Y)))
% 112.87/112.80 and(and(X, Y), Z) -> not(implies(X, implies(Y, not(Z))))
% 112.87/112.80 and_star(X, Y) -> not(implies(X, not(Y)))
% 112.87/112.80 and_star(and_star(X, Y), Z) -> not(implies(X, implies(Y, not(Z))))
% 112.87/112.80 f1(not(not(x))) -> true__
% 112.87/112.80 f1(x) -> false__
% 112.87/112.80 falsehood -> not(truth)
% 112.87/112.80 implies(X0, not(truth)) -> not(X0)
% 112.87/112.80 implies(Y0, implies(not(Y0), X0)) -> truth
% 112.87/112.80 implies(Y0, truth) -> truth
% 112.87/112.80 implies(Y1, Y1) -> truth
% 112.87/112.80 implies(Y1, implies(Y0, Y1)) -> truth
% 112.87/112.80 implies(Y1, implies(implies(Y1, Y2), Y2)) -> truth
% 112.87/112.80 implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))) -> truth
% 112.87/112.80 implies(implies(X0, Y1), implies(implies(implies(Y1, X0), X0), Y1)) -> truth
% 112.87/112.80 implies(implies(X0, not(X1)), implies(not(implies(X1, not(X0))), Y1)) -> truth
% 112.87/112.80 implies(implies(X0, not(Y1)), implies(Y1, not(X0))) -> truth
% 112.87/112.80 implies(implies(Y0, not(truth)), implies(Y0, Y2)) -> truth
% 112.87/112.80 implies(implies(not(X), not(Y)), implies(Y, X)) -> truth
% 112.87/112.80 implies(implies(not(Y1), X0), Y1) -> implies(implies(Y1, not(X0)), not(X0))
% 112.87/112.80 implies(not(X0), implies(X0, Y1)) -> truth
% 112.87/112.80 implies(not(truth), Y0) -> truth
% 112.87/112.80 implies(truth, X) -> X
% 112.87/112.80 not(not(Y0)) -> Y0
% 112.87/112.80 or(X, Y) -> implies(not(X), Y)
% 112.87/112.80 or(or(X, Y), Z) -> implies(not(X), implies(not(Y), Z))
% 112.87/112.80 true__ -> false__
% 112.87/112.80 xor(X, Y) -> implies(implies(X, Y), not(implies(not(X), not(Y))))
% 112.87/112.80 with the LPO induced by
% 112.87/112.80 xor > and_star > falsehood > and > or > implies > truth > x > f1 > not > true__ > false__
% 112.87/112.80
% 112.87/112.80 % SZS output end Proof
% 112.87/112.80
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