TSTP Solution File: LCL158-1 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : LCL158-1 : TPTP v8.1.0. Released v1.0.0.
% 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 12:58:33 EDT 2022
% Result : Unsatisfiable 128.08s 128.07s
% Output : Proof 128.08s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : LCL158-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.11 % Command : moca.sh %s
% 0.11/0.32 % Computer : n011.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Sat Jul 2 19:36:05 EDT 2022
% 0.11/0.32 % CPUTime :
% 128.08/128.07 % SZS status Unsatisfiable
% 128.08/128.07 % SZS output start Proof
% 128.08/128.07 The input problem is unsatisfiable because
% 128.08/128.07
% 128.08/128.07 [1] the following set of Horn clauses is unsatisfiable:
% 128.08/128.07
% 128.08/128.07 implies(truth, X) = X
% 128.08/128.07 implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))) = truth
% 128.08/128.07 implies(implies(X, Y), Y) = implies(implies(Y, X), X)
% 128.08/128.07 implies(implies(not(X), not(Y)), implies(Y, X)) = truth
% 128.08/128.07 or(X, Y) = implies(not(X), Y)
% 128.08/128.07 or(or(X, Y), Z) = or(X, or(Y, Z))
% 128.08/128.07 or(X, Y) = or(Y, X)
% 128.08/128.07 and(X, Y) = not(or(not(X), not(Y)))
% 128.08/128.07 and(and(X, Y), Z) = and(X, and(Y, Z))
% 128.08/128.07 and(X, Y) = and(Y, X)
% 128.08/128.07 xor(X, Y) = or(and(X, not(Y)), and(not(X), Y))
% 128.08/128.07 xor(X, Y) = xor(Y, X)
% 128.08/128.07 and_star(X, Y) = not(or(not(X), not(Y)))
% 128.08/128.07 and_star(and_star(X, Y), Z) = and_star(X, and_star(Y, Z))
% 128.08/128.07 and_star(X, Y) = and_star(Y, X)
% 128.08/128.07 not(truth) = falsehood
% 128.08/128.07 and_star(xor(truth, x), x) = falsehood ==> \bottom
% 128.08/128.07
% 128.08/128.07 This holds because
% 128.08/128.07
% 128.08/128.07 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 128.08/128.07
% 128.08/128.07 E:
% 128.08/128.07 and(X, Y) = and(Y, X)
% 128.08/128.07 and(X, Y) = not(or(not(X), not(Y)))
% 128.08/128.07 and(and(X, Y), Z) = and(X, and(Y, Z))
% 128.08/128.07 and_star(X, Y) = and_star(Y, X)
% 128.08/128.07 and_star(X, Y) = not(or(not(X), not(Y)))
% 128.08/128.07 and_star(and_star(X, Y), Z) = and_star(X, and_star(Y, Z))
% 128.08/128.07 f1(and_star(xor(truth, x), x)) = true__
% 128.08/128.07 f1(falsehood) = false__
% 128.08/128.07 implies(implies(X, Y), Y) = implies(implies(Y, X), X)
% 128.08/128.07 implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))) = truth
% 128.08/128.07 implies(implies(not(X), not(Y)), implies(Y, X)) = truth
% 128.08/128.07 implies(truth, X) = X
% 128.08/128.07 not(truth) = falsehood
% 128.08/128.07 or(X, Y) = implies(not(X), Y)
% 128.08/128.07 or(X, Y) = or(Y, X)
% 128.08/128.07 or(or(X, Y), Z) = or(X, or(Y, Z))
% 128.08/128.07 xor(X, Y) = or(and(X, not(Y)), and(not(X), Y))
% 128.08/128.07 xor(X, Y) = xor(Y, X)
% 128.08/128.07 G:
% 128.08/128.07 true__ = false__
% 128.08/128.07
% 128.08/128.07 This holds because
% 128.08/128.07
% 128.08/128.07 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 128.08/128.07
% 128.08/128.07 implies(X0, Y1) = implies(not(Y1), not(X0))
% 128.08/128.07 implies(X1, not(X0)) = implies(X0, not(X1))
% 128.08/128.07 implies(implies(X, Y), Y) = implies(implies(Y, X), X)
% 128.08/128.07 implies(implies(X, Y), not(implies(not(X), not(Y)))) = implies(implies(Y, X), not(implies(not(Y), not(X))))
% 128.08/128.07 implies(not(X), Y) = implies(not(Y), X)
% 128.08/128.07 not(implies(X, not(Y))) = not(implies(Y, not(X)))
% 128.08/128.07 not(implies(Y0, X0)) = not(implies(not(X0), not(Y0)))
% 128.08/128.07 and(X, Y) -> not(implies(X, not(Y)))
% 128.08/128.07 and(and(X, Y), Z) -> not(implies(X, implies(Y, not(Z))))
% 128.08/128.07 and_star(X, Y) -> not(implies(X, not(Y)))
% 128.08/128.07 and_star(and_star(X, Y), Z) -> not(implies(X, implies(Y, not(Z))))
% 128.08/128.07 f1(and_star(xor(truth, x), x)) -> true__
% 128.08/128.07 f1(not(truth)) -> false__
% 128.08/128.07 falsehood -> not(truth)
% 128.08/128.07 implies(X0, not(truth)) -> not(X0)
% 128.08/128.07 implies(Y0, implies(X1, not(implies(X1, not(Y0))))) -> truth
% 128.08/128.07 implies(Y0, implies(X1, not(implies(Y0, not(X1))))) -> truth
% 128.08/128.07 implies(Y0, implies(not(Y0), X0)) -> truth
% 128.08/128.07 implies(Y0, implies(not(Y1), not(implies(Y0, Y1)))) -> truth
% 128.08/128.07 implies(Y0, truth) -> truth
% 128.08/128.07 implies(Y1, Y1) -> truth
% 128.08/128.07 implies(Y1, implies(Y0, Y1)) -> truth
% 128.08/128.07 implies(Y1, implies(implies(Y1, Y2), Y2)) -> truth
% 128.08/128.07 implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))) -> truth
% 128.08/128.07 implies(implies(X0, Y1), implies(implies(implies(Y1, X0), X0), Y1)) -> truth
% 128.08/128.07 implies(implies(X0, not(Y1)), implies(Y1, not(X0))) -> truth
% 128.08/128.07 implies(implies(Y0, X0), implies(not(X0), not(Y0))) -> truth
% 128.08/128.07 implies(implies(not(X), not(Y)), implies(Y, X)) -> truth
% 128.08/128.07 implies(implies(not(Y1), X0), Y1) -> implies(implies(Y1, not(X0)), not(X0))
% 128.08/128.07 implies(not(X0), implies(X0, Y1)) -> truth
% 128.08/128.07 implies(not(X1), implies(X1, not(Y1))) -> truth
% 128.08/128.07 implies(not(truth), Y0) -> truth
% 128.08/128.07 implies(truth, X) -> X
% 128.08/128.07 not(not(Y0)) -> Y0
% 128.08/128.07 or(X, Y) -> implies(not(X), Y)
% 128.08/128.07 or(or(X, Y), Z) -> implies(not(X), implies(not(Y), Z))
% 128.08/128.07 true__ -> false__
% 128.08/128.07 xor(X, Y) -> implies(implies(X, Y), not(implies(not(X), not(Y))))
% 128.08/128.07 with the LPO induced by
% 128.08/128.07 x > xor > and_star > falsehood > and > or > implies > truth > f1 > not > true__ > false__
% 128.08/128.07
% 128.08/128.07 % SZS output end Proof
% 128.08/128.07
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