TSTP Solution File: LCL110-2 by Moca---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : LCL110-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n021.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 12:58:11 EDT 2022
% Result : Unsatisfiable 4.78s 4.87s
% Output : Proof 4.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL110-2 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : moca.sh %s
% 0.11/0.33 % Computer : n021.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Mon Jul 4 19:39:32 EDT 2022
% 0.11/0.33 % CPUTime :
% 4.78/4.87 % SZS status Unsatisfiable
% 4.78/4.87 % SZS output start Proof
% 4.78/4.87 The input problem is unsatisfiable because
% 4.78/4.87
% 4.78/4.87 [1] the following set of Horn clauses is unsatisfiable:
% 4.78/4.87
% 4.78/4.87 implies(truth, X) = X
% 4.78/4.87 implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))) = truth
% 4.78/4.87 implies(implies(X, Y), Y) = implies(implies(Y, X), X)
% 4.78/4.87 implies(implies(not(X), not(Y)), implies(Y, X)) = truth
% 4.78/4.87 implies(not(not(x)), x) = truth ==> \bottom
% 4.78/4.87
% 4.78/4.87 This holds because
% 4.78/4.87
% 4.78/4.87 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 4.78/4.87
% 4.78/4.87 E:
% 4.78/4.87 f1(implies(not(not(x)), x)) = true__
% 4.78/4.87 f1(truth) = false__
% 4.78/4.87 implies(implies(X, Y), Y) = implies(implies(Y, X), X)
% 4.78/4.87 implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))) = truth
% 4.78/4.87 implies(implies(not(X), not(Y)), implies(Y, X)) = truth
% 4.78/4.87 implies(truth, X) = X
% 4.78/4.87 G:
% 4.78/4.87 true__ = false__
% 4.78/4.87
% 4.78/4.87 This holds because
% 4.78/4.87
% 4.78/4.87 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 4.78/4.87
% 4.78/4.87 implies(implies(X, Y), Y) = implies(implies(Y, X), X)
% 4.78/4.87 implies(implies(X0, X0), truth) = implies(implies(X0, truth), implies(X0, truth))
% 4.78/4.87 f1(implies(not(not(x)), x)) -> true__
% 4.78/4.87 f1(truth) -> false__
% 4.78/4.87 implies(X0, implies(implies(X0, not(truth)), Y1)) -> truth
% 4.78/4.87 implies(X0, implies(implies(X0, not(truth)), implies(Y2, not(truth)))) -> truth
% 4.78/4.87 implies(Y0, implies(X1, implies(implies(Y0, Y1), Y1))) -> truth
% 4.78/4.87 implies(Y0, implies(Y0, Y0)) -> truth
% 4.78/4.87 implies(Y0, implies(Y2, implies(implies(Y0, not(truth)), X1))) -> truth
% 4.78/4.87 implies(Y0, implies(Y2, implies(not(Y0), not(truth)))) -> truth
% 4.78/4.87 implies(Y0, implies(implies(Y1, Y0), Y0)) -> truth
% 4.78/4.87 implies(Y0, implies(implies(implies(implies(Y0, Y2), Y2), X0), X0)) -> truth
% 4.78/4.87 implies(Y0, truth) -> truth
% 4.78/4.87 implies(Y1, Y1) -> truth
% 4.78/4.87 implies(Y1, implies(X1, implies(X2, implies(Y0, Y1)))) -> truth
% 4.78/4.87 implies(Y1, implies(X1, implies(Y0, Y1))) -> truth
% 4.78/4.87 implies(Y1, implies(Y0, Y1)) -> truth
% 4.78/4.87 implies(Y1, implies(implies(Y1, Y2), Y2)) -> truth
% 4.78/4.87 implies(Y1, implies(implies(implies(Y0, Y1), X1), X1)) -> truth
% 4.78/4.87 implies(Y1, implies(implies(implies(Y0, Y1), not(truth)), X1)) -> truth
% 4.78/4.87 implies(Y1, implies(implies(not(truth), not(X0)), Y1)) -> truth
% 4.78/4.87 implies(Y1, implies(not(Y1), not(truth))) -> truth
% 4.78/4.87 implies(Y1, implies(not(implies(Y0, Y1)), not(truth))) -> truth
% 4.78/4.87 implies(Y1, implies(not(not(truth)), Y1)) -> truth
% 4.78/4.87 implies(Y1, implies(not(not(truth)), implies(Y0, Y1))) -> truth
% 4.78/4.87 implies(Y1, not(not(Y1))) -> truth
% 4.78/4.87 implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))) -> truth
% 4.78/4.87 implies(implies(X0, Y1), implies(implies(Y1, implies(X0, Y1)), implies(X0, Y1))) -> truth
% 4.78/4.87 implies(implies(X0, not(truth)), implies(Y2, implies(X0, X1))) -> truth
% 4.78/4.87 implies(implies(X0, truth), implies(implies(X0, X0), truth)) -> truth
% 4.78/4.87 implies(implies(Y0, Y1), implies(Y0, implies(X1, Y1))) -> truth
% 4.78/4.87 implies(implies(Y0, Y1), implies(Y0, implies(implies(Y1, X1), X1))) -> truth
% 4.78/4.87 implies(implies(Y0, implies(not(Y2), not(truth))), implies(Y0, Y2)) -> truth
% 4.78/4.87 implies(implies(Y0, not(X0)), implies(Y0, implies(X0, X1))) -> truth
% 4.78/4.87 implies(implies(Y0, not(truth)), implies(Y0, Y2)) -> truth
% 4.78/4.87 implies(implies(Y0, truth), implies(Y0, truth)) -> truth
% 4.78/4.87 implies(implies(Y0, truth), implies(Y2, implies(Y0, Y2))) -> truth
% 4.78/4.87 implies(implies(Y1, Y2), implies(implies(not(Y1), not(truth)), Y2)) -> truth
% 4.78/4.87 implies(implies(Y1, implies(not(Y1), not(truth))), implies(not(Y1), not(truth))) -> Y1
% 4.78/4.87 implies(implies(Y1, not(implies(Y1, not(truth)))), not(implies(Y1, not(truth)))) -> Y1
% 4.78/4.87 implies(implies(Y1, not(not(Y1))), not(not(Y1))) -> Y1
% 4.78/4.87 implies(implies(Y1, not(truth)), not(truth)) -> Y1
% 4.78/4.87 implies(implies(Y1, truth), truth) -> implies(Y1, Y1)
% 4.78/4.87 implies(implies(implies(X0, X1), Y2), implies(not(X0), Y2)) -> truth
% 4.78/4.87 implies(implies(implies(X0, X1), implies(X0, not(truth))), implies(X0, not(truth))) -> implies(X0, X1)
% 4.78/4.87 implies(implies(implies(X0, X1), not(X0)), not(X0)) -> implies(X0, X1)
% 4.78/4.87 implies(implies(implies(X0, Y1), not(truth)), implies(implies(Y1, X0), X0)) -> truth
% 4.78/4.87 implies(implies(implies(X0, implies(Y2, Y1)), Y1), implies(implies(implies(Y2, Y1), X0), X0)) -> truth
% 4.78/4.87 implies(implies(implies(X0, not(truth)), not(X0)), not(X0)) -> implies(X0, not(truth))
% 4.78/4.87 implies(implies(implies(X1, X0), implies(not(X0), not(X1))), implies(not(X0), not(X1))) -> implies(X1, X0)
% 4.78/4.87 implies(implies(implies(X1, X0), implies(not(X0), not(truth))), implies(not(X0), not(truth))) -> implies(X1, X0)
% 4.78/4.87 implies(implies(implies(X1, X2), implies(implies(X0, X1), X2)), implies(implies(X0, X1), X2)) -> implies(X1, X2)
% 4.78/4.87 implies(implies(implies(X1, Y0), Y2), implies(Y0, Y2)) -> truth
% 4.78/4.87 implies(implies(implies(X1, implies(X0, X2)), not(X0)), not(X0)) -> implies(X1, implies(X0, X2))
% 4.78/4.87 implies(implies(implies(Y0, implies(X0, Y2)), Y2), implies(implies(Y2, X0), X0)) -> truth
% 4.78/4.87 implies(implies(implies(Y0, implies(X0, not(truth))), not(truth)), X0) -> truth
% 4.78/4.87 implies(implies(implies(Y1, X0), X0), Y1) -> implies(implies(Y1, implies(X0, Y1)), implies(X0, Y1))
% 4.78/4.87 implies(implies(implies(Y1, X0), X0), implies(implies(X0, Y1), implies(Y2, Y1))) -> truth
% 4.78/4.87 implies(implies(implies(implies(Y0, X1), X1), Y2), implies(Y0, Y2)) -> truth
% 4.78/4.87 implies(implies(not(X), not(Y)), implies(Y, X)) -> truth
% 4.78/4.87 implies(implies(not(X0), not(X1)), implies(Y2, implies(X1, X0))) -> truth
% 4.78/4.87 implies(implies(not(Y0), not(implies(X0, Y0))), implies(implies(Y0, X0), X0)) -> truth
% 4.78/4.87 implies(implies(not(Y0), not(implies(implies(X1, Y0), Y0))), implies(X1, Y0)) -> truth
% 4.78/4.87 implies(implies(not(Y0), not(truth)), Y0) -> truth
% 4.78/4.87 implies(implies(not(Y0), not(truth)), implies(X1, Y0)) -> truth
% 4.78/4.87 implies(implies(not(Y0), not(truth)), implies(implies(Y0, X0), X0)) -> truth
% 4.78/4.87 implies(implies(not(implies(not(Y1), not(truth))), not(truth)), Y1) -> truth
% 4.78/4.87 implies(implies(not(not(X0)), not(truth)), implies(X0, X1)) -> truth
% 4.78/4.87 implies(implies(not(not(truth)), not(truth)), Y1) -> truth
% 4.78/4.87 implies(implies(not(truth), not(Y1)), truth) -> truth
% 4.78/4.87 implies(implies(not(truth), not(implies(X0, truth))), truth) -> truth
% 4.78/4.87 implies(implies(not(truth), not(not(not(truth)))), truth) -> truth
% 4.78/4.87 implies(implies(not(truth), not(not(truth))), not(not(truth))) -> truth
% 4.78/4.87 implies(implies(not(truth), not(truth)), implies(not(truth), not(truth))) -> truth
% 4.78/4.87 implies(not(X0), implies(Y2, implies(X0, X1))) -> truth
% 4.78/4.87 implies(not(X0), implies(Y2, implies(X0, not(truth)))) -> truth
% 4.78/4.87 implies(not(X1), implies(X1, X0)) -> truth
% 4.78/4.87 implies(not(Y0), implies(implies(implies(Y0, Y2), X0), X0)) -> truth
% 4.78/4.87 implies(not(Y1), implies(Y1, not(truth))) -> truth
% 4.78/4.87 implies(not(implies(X0, Y1)), implies(implies(Y1, X0), X0)) -> truth
% 4.78/4.87 implies(not(implies(X0, Y2)), implies(Y1, implies(implies(Y2, X0), X0))) -> truth
% 4.78/4.87 implies(not(implies(X0, not(truth))), X0) -> truth
% 4.78/4.87 implies(not(implies(Y1, not(truth))), implies(Y2, Y1)) -> truth
% 4.78/4.87 implies(not(not(Y1)), Y1) -> truth
% 4.78/4.87 implies(not(not(Y1)), implies(Y2, Y1)) -> truth
% 4.78/4.87 implies(not(not(truth)), truth) -> truth
% 4.78/4.87 implies(not(truth), Y1) -> truth
% 4.78/4.87 implies(truth, X) -> X
% 4.78/4.87 not(not(truth)) -> truth
% 4.78/4.87 true__ -> false__
% 4.78/4.87 with the LPO induced by
% 4.78/4.87 x > f1 > not > implies > truth > true__ > false__
% 4.78/4.87
% 4.78/4.87 % SZS output end Proof
% 4.78/4.87
%------------------------------------------------------------------------------