TSTP Solution File: LCL161-1 by Moca---0.1
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- Process Solution
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% File : Moca---0.1
% Problem : LCL161-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n026.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 12:58:34 EDT 2022
% Result : Unsatisfiable 1.50s 1.60s
% Output : Proof 1.50s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : LCL161-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : moca.sh %s
% 0.14/0.34 % Computer : n026.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jul 4 13:50:22 EDT 2022
% 0.14/0.35 % CPUTime :
% 1.50/1.60 % SZS status Unsatisfiable
% 1.50/1.60 % SZS output start Proof
% 1.50/1.60 The input problem is unsatisfiable because
% 1.50/1.60
% 1.50/1.60 [1] the following set of Horn clauses is unsatisfiable:
% 1.50/1.60
% 1.50/1.60 not(X) = xor(X, truth)
% 1.50/1.60 xor(X, falsehood) = X
% 1.50/1.60 xor(X, X) = falsehood
% 1.50/1.60 and_star(X, truth) = X
% 1.50/1.60 and_star(X, falsehood) = falsehood
% 1.50/1.60 and_star(xor(truth, X), X) = falsehood
% 1.50/1.60 xor(X, xor(truth, Y)) = xor(xor(X, truth), Y)
% 1.50/1.60 and_star(xor(and_star(xor(truth, X), Y), truth), Y) = and_star(xor(and_star(xor(truth, Y), X), truth), X)
% 1.50/1.60 xor(X, Y) = xor(Y, X)
% 1.50/1.60 and_star(and_star(X, Y), Z) = and_star(X, and_star(Y, Z))
% 1.50/1.60 and_star(X, Y) = and_star(Y, X)
% 1.50/1.60 not(truth) = falsehood
% 1.50/1.60 implies(X, Y) = xor(truth, and_star(X, xor(truth, Y)))
% 1.50/1.60 implies(truth, x) = x ==> \bottom
% 1.50/1.60
% 1.50/1.60 This holds because
% 1.50/1.60
% 1.50/1.60 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 1.50/1.60
% 1.50/1.60 E:
% 1.50/1.60 and_star(X, Y) = and_star(Y, X)
% 1.50/1.60 and_star(X, falsehood) = falsehood
% 1.50/1.60 and_star(X, truth) = X
% 1.50/1.60 and_star(and_star(X, Y), Z) = and_star(X, and_star(Y, Z))
% 1.50/1.60 and_star(xor(and_star(xor(truth, X), Y), truth), Y) = and_star(xor(and_star(xor(truth, Y), X), truth), X)
% 1.50/1.60 and_star(xor(truth, X), X) = falsehood
% 1.50/1.60 f1(implies(truth, x)) = true__
% 1.50/1.60 f1(x) = false__
% 1.50/1.60 implies(X, Y) = xor(truth, and_star(X, xor(truth, Y)))
% 1.50/1.60 not(X) = xor(X, truth)
% 1.50/1.60 not(truth) = falsehood
% 1.50/1.60 xor(X, X) = falsehood
% 1.50/1.60 xor(X, Y) = xor(Y, X)
% 1.50/1.60 xor(X, falsehood) = X
% 1.50/1.60 xor(X, xor(truth, Y)) = xor(xor(X, truth), Y)
% 1.50/1.60 G:
% 1.50/1.60 true__ = false__
% 1.50/1.60
% 1.50/1.60 This holds because
% 1.50/1.60
% 1.50/1.60 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 1.50/1.60
% 1.50/1.60 and_star(X, Y) = and_star(Y, X)
% 1.50/1.60 and_star(X0, and_star(not(X0), Y0)) = and_star(false__, not(false__))
% 1.50/1.60 and_star(X0, not(X0)) = and_star(Y0, not(Y0))
% 1.50/1.60 and_star(X0, not(X0)) = and_star(false__, not(false__))
% 1.50/1.60 and_star(Y0, and_star(X0, not(X0))) = and_star(false__, not(false__))
% 1.50/1.60 and_star(Y0, and_star(Y1, not(Y0))) = and_star(false__, not(false__))
% 1.50/1.60 and_star(Y1, and_star(Y0, Y2)) = and_star(Y0, and_star(Y1, Y2))
% 1.50/1.60 and_star(Y1, not(Y1)) = not(truth)
% 1.50/1.60 and_star(Y1, not(and_star(not(Y0), Y1))) = and_star(Y0, not(and_star(not(Y1), Y0)))
% 1.50/1.60 and_star(Y1, not(not(truth))) = not(not(Y1))
% 1.50/1.60 and_star(Y2, and_star(Y0, Y1)) = and_star(Y0, and_star(Y1, Y2))
% 1.50/1.60 and_star(not(X0), and_star(X0, Y1)) = and_star(false__, not(false__))
% 1.50/1.60 and_star(xor(and_star(xor(truth, X), Y), truth), Y) = and_star(xor(and_star(xor(truth, Y), X), truth), X)
% 1.50/1.60 xor(X, Y) = xor(Y, X)
% 1.50/1.60 xor(Y1, not(Y0)) = xor(Y0, not(Y1))
% 1.50/1.60 and_star(X, falsehood) -> falsehood
% 1.50/1.60 and_star(X, truth) -> X
% 1.50/1.60 and_star(Y0, and_star(truth, Y2)) -> and_star(Y0, Y2)
% 1.50/1.60 and_star(Y0, not(truth)) -> not(truth)
% 1.50/1.60 and_star(and_star(X, Y), Z) -> and_star(X, and_star(Y, Z))
% 1.50/1.60 and_star(not(truth), Y0) -> not(truth)
% 1.50/1.60 and_star(truth, Y0) -> Y0
% 1.50/1.60 and_star(xor(truth, X), X) -> falsehood
% 1.50/1.60 f1(implies(truth, x)) -> true__
% 1.50/1.60 f1(x) -> false__
% 1.50/1.60 falsehood -> not(truth)
% 1.50/1.60 implies(X, Y) -> xor(truth, and_star(X, xor(truth, Y)))
% 1.50/1.60 not(and_star(X0, not(X0))) -> truth
% 1.50/1.60 not(not(Y1)) -> Y1
% 1.50/1.60 not(not(truth)) -> truth
% 1.50/1.60 true__ -> false__
% 1.50/1.60 xor(X, X) -> falsehood
% 1.50/1.60 xor(X, falsehood) -> X
% 1.50/1.60 xor(X, truth) -> not(X)
% 1.50/1.60 xor(Y0, and_star(X0, not(X0))) -> Y0
% 1.50/1.60 xor(Y0, not(not(Y0))) -> not(truth)
% 1.50/1.60 xor(Y0, not(not(truth))) -> not(Y0)
% 1.50/1.60 xor(Y0, not(truth)) -> Y0
% 1.50/1.60 xor(and_star(X0, not(X0)), Y0) -> Y0
% 1.50/1.60 xor(not(Y0), Y1) -> xor(Y0, not(Y1))
% 1.50/1.60 xor(not(truth), Y0) -> Y0
% 1.50/1.60 xor(truth, Y0) -> not(Y0)
% 1.50/1.60 xor(xor(X, truth), Y) -> xor(X, xor(truth, Y))
% 1.50/1.60 with the LPO induced by
% 1.50/1.60 x > f1 > implies > xor > falsehood > not > truth > and_star > true__ > false__
% 1.50/1.60
% 1.50/1.60 % SZS output end Proof
% 1.50/1.60
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