TSTP Solution File: LCL155-1 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : LCL155-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n004.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 115.60s 115.55s
% Output : Proof 115.60s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : LCL155-1 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.14 % Command : moca.sh %s
% 0.14/0.36 % Computer : n004.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Sun Jul 3 23:15:23 EDT 2022
% 0.14/0.36 % CPUTime :
% 115.60/115.55 % SZS status Unsatisfiable
% 115.60/115.55 % SZS output start Proof
% 115.60/115.55 The input problem is unsatisfiable because
% 115.60/115.55
% 115.60/115.55 [1] the following set of Horn clauses is unsatisfiable:
% 115.60/115.55
% 115.60/115.55 implies(truth, X) = X
% 115.60/115.55 implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))) = truth
% 115.60/115.55 implies(implies(X, Y), Y) = implies(implies(Y, X), X)
% 115.60/115.55 implies(implies(not(X), not(Y)), implies(Y, X)) = truth
% 115.60/115.55 or(X, Y) = implies(not(X), Y)
% 115.60/115.55 or(or(X, Y), Z) = or(X, or(Y, Z))
% 115.60/115.55 or(X, Y) = or(Y, X)
% 115.60/115.55 and(X, Y) = not(or(not(X), not(Y)))
% 115.60/115.55 and(and(X, Y), Z) = and(X, and(Y, Z))
% 115.60/115.55 and(X, Y) = and(Y, X)
% 115.60/115.55 xor(X, Y) = or(and(X, not(Y)), and(not(X), Y))
% 115.60/115.55 xor(X, Y) = xor(Y, X)
% 115.60/115.55 and_star(X, Y) = not(or(not(X), not(Y)))
% 115.60/115.55 and_star(and_star(X, Y), Z) = and_star(X, and_star(Y, Z))
% 115.60/115.55 and_star(X, Y) = and_star(Y, X)
% 115.60/115.55 not(truth) = falsehood
% 115.60/115.55 xor(x, x) = falsehood ==> \bottom
% 115.60/115.55
% 115.60/115.55 This holds because
% 115.60/115.55
% 115.60/115.55 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 115.60/115.55
% 115.60/115.55 E:
% 115.60/115.55 and(X, Y) = and(Y, X)
% 115.60/115.55 and(X, Y) = not(or(not(X), not(Y)))
% 115.60/115.55 and(and(X, Y), Z) = and(X, and(Y, Z))
% 115.60/115.55 and_star(X, Y) = and_star(Y, X)
% 115.60/115.55 and_star(X, Y) = not(or(not(X), not(Y)))
% 115.60/115.55 and_star(and_star(X, Y), Z) = and_star(X, and_star(Y, Z))
% 115.60/115.55 f1(falsehood) = false__
% 115.60/115.55 f1(xor(x, x)) = true__
% 115.60/115.55 implies(implies(X, Y), Y) = implies(implies(Y, X), X)
% 115.60/115.55 implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))) = truth
% 115.60/115.55 implies(implies(not(X), not(Y)), implies(Y, X)) = truth
% 115.60/115.55 implies(truth, X) = X
% 115.60/115.55 not(truth) = falsehood
% 115.60/115.55 or(X, Y) = implies(not(X), Y)
% 115.60/115.55 or(X, Y) = or(Y, X)
% 115.60/115.55 or(or(X, Y), Z) = or(X, or(Y, Z))
% 115.60/115.55 xor(X, Y) = or(and(X, not(Y)), and(not(X), Y))
% 115.60/115.55 xor(X, Y) = xor(Y, X)
% 115.60/115.55 G:
% 115.60/115.55 true__ = false__
% 115.60/115.55
% 115.60/115.55 This holds because
% 115.60/115.55
% 115.60/115.55 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 115.60/115.55
% 115.60/115.55 and(X, Y) = and(Y, X)
% 115.60/115.55 and_star(X, Y) = and_star(Y, X)
% 115.60/115.55 implies(X0, not(truth)) = not(X0)
% 115.60/115.55 implies(implies(X, Y), Y) = implies(implies(Y, X), X)
% 115.60/115.55 implies(implies(X0, X0), truth) = implies(implies(X0, truth), implies(X0, truth))
% 115.60/115.55 implies(implies(not(Y1), X0), Y1) = implies(implies(Y1, not(X0)), not(X0))
% 115.60/115.55 implies(not(Y1), Y0) = implies(not(Y0), Y1)
% 115.60/115.55 implies(not(Y1), implies(not(Y0), Y2)) = implies(not(Y0), implies(not(Y1), Y2))
% 115.60/115.55 implies(not(Y2), implies(not(Y0), Y1)) = implies(not(Y0), implies(not(Y1), Y2))
% 115.60/115.55 implies(not(not(implies(not(not(Y1)), not(not(Y0))))), not(implies(not(not(not(Y1))), not(Y0)))) = implies(not(not(implies(not(not(Y0)), not(not(Y1))))), not(implies(not(not(not(Y0))), not(Y1))))
% 115.60/115.55 not(implies(not(not(Y1)), not(Y0))) = not(implies(not(not(Y0)), not(Y1)))
% 115.60/115.55 not(implies(not(not(Y1)), not(not(implies(not(not(Y0)), not(Y2)))))) = not(implies(not(not(Y0)), not(not(implies(not(not(Y1)), not(Y2))))))
% 115.60/115.55 not(implies(not(not(Y2)), not(not(implies(not(not(Y0)), not(Y1)))))) = not(implies(not(not(Y0)), not(not(implies(not(not(Y1)), not(Y2))))))
% 115.60/115.55 or(X, Y) = or(Y, X)
% 115.60/115.55 xor(X, Y) = xor(Y, X)
% 115.60/115.55 and(X, Y) -> not(or(not(X), not(Y)))
% 115.60/115.55 and(and(X, Y), Z) -> and(X, and(Y, Z))
% 115.60/115.55 and_star(X, Y) -> not(or(not(X), not(Y)))
% 115.60/115.55 and_star(and_star(X, Y), Z) -> and_star(X, and_star(Y, Z))
% 115.60/115.55 f1(falsehood) -> false__
% 115.60/115.55 f1(not(truth)) -> false__
% 115.60/115.55 f1(xor(x, x)) -> true__
% 115.60/115.55 falsehood -> not(truth)
% 115.60/115.55 implies(Y0, implies(X1, not(not(Y0)))) -> truth
% 115.60/115.55 implies(Y0, implies(not(Y0), X0)) -> truth
% 115.60/115.55 implies(Y0, implies(not(not(not(Y0))), X1)) -> truth
% 115.60/115.55 implies(Y0, not(not(Y0))) -> truth
% 115.60/115.55 implies(Y0, not(not(not(not(Y0))))) -> truth
% 115.60/115.55 implies(Y0, truth) -> truth
% 115.60/115.55 implies(Y1, Y1) -> truth
% 115.60/115.55 implies(Y1, implies(Y0, Y1)) -> truth
% 115.60/115.55 implies(Y1, implies(implies(Y1, Y2), Y2)) -> truth
% 115.60/115.55 implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))) -> truth
% 115.60/115.55 implies(implies(X0, Y1), implies(implies(implies(Y1, X0), X0), Y1)) -> truth
% 115.60/115.55 implies(implies(Y0, not(truth)), implies(Y0, Y2)) -> truth
% 115.60/115.55 implies(implies(Y0, truth), implies(Y0, truth)) -> truth
% 115.60/115.55 implies(implies(Y0, truth), implies(Y2, implies(Y0, Y2))) -> truth
% 115.60/115.55 implies(implies(Y1, implies(not(Y1), not(truth))), implies(not(Y1), not(truth))) -> Y1
% 115.60/115.55 implies(implies(Y1, not(truth)), not(truth)) -> Y1
% 115.60/115.55 implies(implies(Y1, truth), truth) -> implies(Y1, Y1)
% 115.60/115.55 implies(implies(not(X), not(Y)), implies(Y, X)) -> truth
% 115.60/115.55 implies(implies(not(X0), truth), implies(not(truth), X0)) -> truth
% 115.60/115.55 implies(implies(not(Y0), not(not(X0))), implies(not(Y0), X0)) -> truth
% 115.60/115.55 implies(implies(not(Y0), not(truth)), Y0) -> truth
% 115.60/115.55 implies(implies(not(not(Y1)), Y0), implies(Y1, Y0)) -> truth
% 115.60/115.55 implies(implies(not(not(truth)), Y0), Y0) -> truth
% 115.60/115.55 implies(implies(not(truth), X0), implies(not(X0), truth)) -> truth
% 115.60/115.55 implies(implies(not(truth), X0), truth) -> truth
% 115.60/115.55 implies(implies(not(truth), not(truth)), implies(not(truth), not(truth))) -> truth
% 115.60/115.55 implies(not(X0), implies(implies(not(Y1), X0), Y1)) -> truth
% 115.60/115.55 implies(not(Y1), implies(Y1, not(truth))) -> truth
% 115.60/115.55 implies(not(Y1), not(truth)) -> Y1
% 115.60/115.55 implies(not(implies(not(Y0), Y1)), Y2) -> implies(not(Y0), implies(not(Y1), Y2))
% 115.60/115.55 implies(not(truth), Y0) -> truth
% 115.60/115.55 implies(truth, X) -> X
% 115.60/115.55 not(not(truth)) -> truth
% 115.60/115.55 or(X, Y) -> implies(not(X), Y)
% 115.60/115.55 or(or(X, Y), Z) -> or(X, or(Y, Z))
% 115.60/115.55 true__ -> false__
% 115.60/115.55 xor(X, Y) -> or(and(X, not(Y)), and(not(X), Y))
% 115.60/115.55 with the LPO induced by
% 115.60/115.55 xor > and > x > f1 > falsehood > and_star > or > not > implies > truth > true__ > false__
% 115.60/115.55
% 115.60/115.55 % SZS output end Proof
% 115.60/115.55
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