TSTP Solution File: LCL153-1 by Moca---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : LCL153-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n028.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 12:58:31 EDT 2022
% Result : Unsatisfiable 114.07s 114.01s
% Output : Proof 114.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL153-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : moca.sh %s
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jul 3 21:24:04 EDT 2022
% 0.13/0.34 % CPUTime :
% 114.07/114.01 % SZS status Unsatisfiable
% 114.07/114.01 % SZS output start Proof
% 114.07/114.01 The input problem is unsatisfiable because
% 114.07/114.01
% 114.07/114.01 [1] the following set of Horn clauses is unsatisfiable:
% 114.07/114.01
% 114.07/114.01 implies(truth, X) = X
% 114.07/114.01 implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))) = truth
% 114.07/114.01 implies(implies(X, Y), Y) = implies(implies(Y, X), X)
% 114.07/114.01 implies(implies(not(X), not(Y)), implies(Y, X)) = truth
% 114.07/114.01 or(X, Y) = implies(not(X), Y)
% 114.07/114.01 or(or(X, Y), Z) = or(X, or(Y, Z))
% 114.07/114.01 or(X, Y) = or(Y, X)
% 114.07/114.01 and(X, Y) = not(or(not(X), not(Y)))
% 114.07/114.01 and(and(X, Y), Z) = and(X, and(Y, Z))
% 114.07/114.01 and(X, Y) = and(Y, X)
% 114.07/114.01 xor(X, Y) = or(and(X, not(Y)), and(not(X), Y))
% 114.07/114.01 xor(X, Y) = xor(Y, X)
% 114.07/114.01 and_star(X, Y) = not(or(not(X), not(Y)))
% 114.07/114.01 and_star(and_star(X, Y), Z) = and_star(X, and_star(Y, Z))
% 114.07/114.01 and_star(X, Y) = and_star(Y, X)
% 114.07/114.01 not(truth) = falsehood
% 114.07/114.01 not(x) = xor(x, truth) ==> \bottom
% 114.07/114.01
% 114.07/114.01 This holds because
% 114.07/114.01
% 114.07/114.01 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 114.07/114.01
% 114.07/114.01 E:
% 114.07/114.01 and(X, Y) = and(Y, X)
% 114.07/114.01 and(X, Y) = not(or(not(X), not(Y)))
% 114.07/114.01 and(and(X, Y), Z) = and(X, and(Y, Z))
% 114.07/114.01 and_star(X, Y) = and_star(Y, X)
% 114.07/114.01 and_star(X, Y) = not(or(not(X), not(Y)))
% 114.07/114.01 and_star(and_star(X, Y), Z) = and_star(X, and_star(Y, Z))
% 114.07/114.01 f1(not(x)) = true__
% 114.07/114.01 f1(xor(x, truth)) = false__
% 114.07/114.01 implies(implies(X, Y), Y) = implies(implies(Y, X), X)
% 114.07/114.01 implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))) = truth
% 114.07/114.01 implies(implies(not(X), not(Y)), implies(Y, X)) = truth
% 114.07/114.01 implies(truth, X) = X
% 114.07/114.01 not(truth) = falsehood
% 114.07/114.01 or(X, Y) = implies(not(X), Y)
% 114.07/114.01 or(X, Y) = or(Y, X)
% 114.07/114.01 or(or(X, Y), Z) = or(X, or(Y, Z))
% 114.07/114.01 xor(X, Y) = or(and(X, not(Y)), and(not(X), Y))
% 114.07/114.01 xor(X, Y) = xor(Y, X)
% 114.07/114.01 G:
% 114.07/114.01 true__ = false__
% 114.07/114.01
% 114.07/114.01 This holds because
% 114.07/114.01
% 114.07/114.01 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 114.07/114.01
% 114.07/114.01 and(X, Y) = and(Y, X)
% 114.07/114.01 and_star(X, Y) = and_star(Y, X)
% 114.07/114.01 implies(X0, not(truth)) = not(X0)
% 114.07/114.01 implies(implies(X, Y), Y) = implies(implies(Y, X), X)
% 114.07/114.01 implies(implies(X0, X0), truth) = implies(implies(X0, truth), implies(X0, truth))
% 114.07/114.01 implies(implies(Y0, not(truth)), Y1) = implies(not(Y1), Y0)
% 114.07/114.01 implies(implies(Y1, not(Y0)), not(truth)) = implies(implies(Y0, not(Y1)), not(truth))
% 114.07/114.01 implies(implies(not(Y1), X0), Y1) = implies(implies(Y1, not(X0)), not(X0))
% 114.07/114.01 implies(not(Y1), Y0) = implies(not(Y0), Y1)
% 114.07/114.01 implies(not(Y1), implies(not(Y0), Y2)) = implies(not(Y0), implies(not(Y1), Y2))
% 114.07/114.01 implies(not(Y2), implies(not(Y0), Y1)) = implies(not(Y0), implies(not(Y1), Y2))
% 114.07/114.01 not(implies(not(not(Y1)), not(Y0))) = not(implies(not(not(Y0)), not(Y1)))
% 114.07/114.01 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))))))
% 114.07/114.01 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))))))
% 114.07/114.01 or(X, Y) = or(Y, X)
% 114.07/114.01 xor(X, Y) = xor(Y, X)
% 114.07/114.01 and(X, Y) -> not(or(not(X), not(Y)))
% 114.07/114.01 and(and(X, Y), Z) -> and(X, and(Y, Z))
% 114.07/114.01 and_star(X, Y) -> not(or(not(X), not(Y)))
% 114.07/114.01 and_star(and_star(X, Y), Z) -> and_star(X, and_star(Y, Z))
% 114.07/114.01 f1(implies(not(not(implies(not(not(truth)), not(not(x))))), not(implies(not(not(not(truth))), not(x))))) -> false__
% 114.07/114.01 f1(implies(not(not(implies(not(truth), not(x)))), not(not(not(x))))) -> false__
% 114.07/114.01 f1(implies(x, not(truth))) -> false__
% 114.07/114.01 f1(implies(x, not(truth))) -> true__
% 114.07/114.01 f1(not(not(not(x)))) -> false__
% 114.07/114.01 f1(not(x)) -> true__
% 114.07/114.01 f1(xor(x, truth)) -> false__
% 114.07/114.01 falsehood -> not(truth)
% 114.07/114.01 implies(Y0, implies(X1, not(not(Y0)))) -> truth
% 114.07/114.01 implies(Y0, implies(implies(Y0, not(truth)), Y1)) -> truth
% 114.07/114.01 implies(Y0, implies(not(Y0), X0)) -> truth
% 114.07/114.01 implies(Y0, not(not(Y0))) -> truth
% 114.07/114.01 implies(Y0, not(not(not(not(Y0))))) -> truth
% 114.07/114.01 implies(Y0, truth) -> truth
% 114.07/114.01 implies(Y1, Y1) -> truth
% 114.07/114.01 implies(Y1, implies(Y0, Y1)) -> truth
% 114.07/114.01 implies(Y1, implies(implies(Y1, Y2), Y2)) -> truth
% 114.07/114.01 implies(Y1, implies(not(truth), Y1)) -> truth
% 114.07/114.01 implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))) -> truth
% 114.07/114.01 implies(implies(Y0, not(truth)), implies(Y0, Y2)) -> truth
% 114.07/114.01 implies(implies(Y0, truth), implies(Y0, truth)) -> truth
% 114.07/114.01 implies(implies(Y0, truth), implies(Y2, implies(Y0, Y2))) -> truth
% 114.07/114.01 implies(implies(Y1, not(truth)), not(Y1)) -> truth
% 114.07/114.01 implies(implies(Y1, not(truth)), not(truth)) -> Y1
% 114.07/114.01 implies(implies(Y1, truth), truth) -> implies(Y1, Y1)
% 114.07/114.01 implies(implies(not(X), not(Y)), implies(Y, X)) -> truth
% 114.07/114.01 implies(implies(not(X0), truth), implies(not(truth), X0)) -> truth
% 114.07/114.01 implies(implies(not(Y0), not(not(X0))), implies(not(Y0), X0)) -> truth
% 114.07/114.01 implies(implies(not(Y0), not(truth)), Y0) -> truth
% 114.07/114.01 implies(implies(not(not(Y1)), Y0), implies(Y1, Y0)) -> truth
% 114.07/114.01 implies(implies(not(not(truth)), Y0), Y0) -> truth
% 114.07/114.01 implies(implies(not(truth), X0), implies(not(X0), truth)) -> truth
% 114.07/114.01 implies(implies(not(truth), X0), truth) -> truth
% 114.07/114.01 implies(implies(not(truth), not(truth)), implies(not(truth), not(truth))) -> truth
% 114.07/114.01 implies(not(X0), implies(implies(not(Y1), X0), Y1)) -> truth
% 114.07/114.01 implies(not(Y1), implies(Y1, not(truth))) -> truth
% 114.07/114.01 implies(not(Y1), not(truth)) -> Y1
% 114.07/114.01 implies(not(implies(not(Y0), Y1)), Y2) -> implies(not(Y0), implies(not(Y1), Y2))
% 114.07/114.01 implies(not(truth), Y0) -> truth
% 114.07/114.01 implies(not(truth), not(Y0)) -> truth
% 114.07/114.01 implies(not(truth), truth) -> truth
% 114.07/114.01 implies(truth, X) -> X
% 114.07/114.01 not(not(truth)) -> truth
% 114.07/114.01 or(X, Y) -> implies(not(X), Y)
% 114.07/114.01 or(or(X, Y), Z) -> or(X, or(Y, Z))
% 114.07/114.01 true__ -> false__
% 114.07/114.01 xor(X, Y) -> or(and(X, not(Y)), and(not(X), Y))
% 114.07/114.01 with the LPO induced by
% 114.07/114.01 x > xor > and > falsehood > and_star > or > not > f1 > implies > truth > true__ > false__
% 114.07/114.01
% 114.07/114.01 % SZS output end Proof
% 114.07/114.01
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