TSTP Solution File: LCL157-1 by Moca---0.1
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- Process Solution
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% File : Moca---0.1
% Problem : LCL157-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n013.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 12:58:33 EDT 2022
% Result : Unsatisfiable 50.76s 50.91s
% Output : Proof 50.76s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL157-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : moca.sh %s
% 0.12/0.34 % Computer : n013.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 : Tue Jul 5 00:10:29 EDT 2022
% 0.12/0.34 % CPUTime :
% 50.76/50.91 % SZS status Unsatisfiable
% 50.76/50.91 % SZS output start Proof
% 50.76/50.91 The input problem is unsatisfiable because
% 50.76/50.91
% 50.76/50.91 [1] the following set of Horn clauses is unsatisfiable:
% 50.76/50.91
% 50.76/50.91 implies(truth, X) = X
% 50.76/50.91 implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))) = truth
% 50.76/50.91 implies(implies(X, Y), Y) = implies(implies(Y, X), X)
% 50.76/50.91 implies(implies(not(X), not(Y)), implies(Y, X)) = truth
% 50.76/50.91 or(X, Y) = implies(not(X), Y)
% 50.76/50.91 or(or(X, Y), Z) = or(X, or(Y, Z))
% 50.76/50.91 or(X, Y) = or(Y, X)
% 50.76/50.91 and(X, Y) = not(or(not(X), not(Y)))
% 50.76/50.91 and(and(X, Y), Z) = and(X, and(Y, Z))
% 50.76/50.91 and(X, Y) = and(Y, X)
% 50.76/50.91 xor(X, Y) = or(and(X, not(Y)), and(not(X), Y))
% 50.76/50.91 xor(X, Y) = xor(Y, X)
% 50.76/50.91 and_star(X, Y) = not(or(not(X), not(Y)))
% 50.76/50.91 and_star(and_star(X, Y), Z) = and_star(X, and_star(Y, Z))
% 50.76/50.91 and_star(X, Y) = and_star(Y, X)
% 50.76/50.91 not(truth) = falsehood
% 50.76/50.91 and_star(x, falsehood) = falsehood ==> \bottom
% 50.76/50.91
% 50.76/50.91 This holds because
% 50.76/50.91
% 50.76/50.91 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 50.76/50.91
% 50.76/50.91 E:
% 50.76/50.91 and(X, Y) = and(Y, X)
% 50.76/50.91 and(X, Y) = not(or(not(X), not(Y)))
% 50.76/50.91 and(and(X, Y), Z) = and(X, and(Y, Z))
% 50.76/50.91 and_star(X, Y) = and_star(Y, X)
% 50.76/50.91 and_star(X, Y) = not(or(not(X), not(Y)))
% 50.76/50.91 and_star(and_star(X, Y), Z) = and_star(X, and_star(Y, Z))
% 50.76/50.91 f1(and_star(x, falsehood)) = true__
% 50.76/50.91 f1(falsehood) = false__
% 50.76/50.91 implies(implies(X, Y), Y) = implies(implies(Y, X), X)
% 50.76/50.91 implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))) = truth
% 50.76/50.91 implies(implies(not(X), not(Y)), implies(Y, X)) = truth
% 50.76/50.91 implies(truth, X) = X
% 50.76/50.91 not(truth) = falsehood
% 50.76/50.91 or(X, Y) = implies(not(X), Y)
% 50.76/50.91 or(X, Y) = or(Y, X)
% 50.76/50.91 or(or(X, Y), Z) = or(X, or(Y, Z))
% 50.76/50.91 xor(X, Y) = or(and(X, not(Y)), and(not(X), Y))
% 50.76/50.91 xor(X, Y) = xor(Y, X)
% 50.76/50.91 G:
% 50.76/50.91 true__ = false__
% 50.76/50.91
% 50.76/50.91 This holds because
% 50.76/50.91
% 50.76/50.91 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 50.76/50.91
% 50.76/50.91 implies(implies(X, Y), Y) = implies(implies(Y, X), X)
% 50.76/50.91 implies(not(X), Y) = implies(not(Y), X)
% 50.76/50.91 implies(not(not(implies(not(not(X)), not(not(Y))))), not(implies(not(not(not(X))), not(Y)))) = implies(not(not(implies(not(not(Y)), not(not(X))))), not(implies(not(not(not(Y))), not(X))))
% 50.76/50.91 not(implies(not(not(X)), not(Y))) = not(implies(not(not(Y)), not(X)))
% 50.76/50.91 and(X, Y) -> not(implies(not(not(X)), not(Y)))
% 50.76/50.91 and(and(X, Y), Z) -> not(implies(not(not(X)), not(not(implies(not(not(Y)), not(Z))))))
% 50.76/50.91 and_star(X, Y) -> not(implies(not(not(X)), not(Y)))
% 50.76/50.91 and_star(and_star(X, Y), Z) -> not(implies(not(not(X)), not(not(implies(not(not(Y)), not(Z))))))
% 50.76/50.91 f1(not(implies(not(not(not(truth))), not(x)))) -> true__
% 50.76/50.91 f1(not(implies(not(not(x)), not(not(truth))))) -> true__
% 50.76/50.91 f1(not(implies(not(truth), not(x)))) -> true__
% 50.76/50.91 f1(not(truth)) -> false__
% 50.76/50.91 falsehood -> not(truth)
% 50.76/50.91 implies(Y0, implies(implies(Y1, Y0), Y0)) -> truth
% 50.76/50.91 implies(Y0, implies(implies(implies(Y0, X0), X0), Y0)) -> truth
% 50.76/50.91 implies(Y0, truth) -> truth
% 50.76/50.91 implies(Y1, Y1) -> truth
% 50.76/50.91 implies(Y1, implies(Y0, Y1)) -> truth
% 50.76/50.91 implies(Y1, implies(implies(Y1, Y2), Y2)) -> truth
% 50.76/50.91 implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))) -> truth
% 50.76/50.91 implies(implies(X0, Y1), implies(implies(implies(Y1, X0), X0), Y1)) -> truth
% 50.76/50.91 implies(implies(Y0, truth), implies(Y2, implies(Y0, Y2))) -> truth
% 50.76/50.91 implies(implies(not(X), not(Y)), implies(Y, X)) -> truth
% 50.76/50.91 implies(implies(not(Y1), X0), Y1) -> implies(implies(Y1, not(X0)), not(X0))
% 50.76/50.91 implies(not(Y1), implies(Y1, not(truth))) -> truth
% 50.76/50.91 implies(not(Y1), not(truth)) -> Y1
% 50.76/50.91 implies(not(truth), Y0) -> truth
% 50.76/50.91 implies(truth, X) -> X
% 50.76/50.91 not(not(truth)) -> truth
% 50.76/50.91 or(X, Y) -> implies(not(X), Y)
% 50.76/50.91 or(or(X, Y), Z) -> implies(not(X), implies(not(Y), Z))
% 50.76/50.91 true__ -> false__
% 50.76/50.91 xor(X, Y) -> implies(not(not(implies(not(not(X)), not(not(Y))))), not(implies(not(not(not(X))), not(Y))))
% 50.76/50.91 with the LPO induced by
% 50.76/50.91 xor > and_star > and > or > implies > x > falsehood > truth > not > f1 > true__ > false__
% 50.76/50.91
% 50.76/50.91 % SZS output end Proof
% 50.76/50.91
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