TSTP Solution File: LCL133-1 by Moca---0.1
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- Process Solution
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% File : Moca---0.1
% Problem : LCL133-1 : 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 12:58:22 EDT 2022
% Result : Unsatisfiable 0.79s 1.00s
% Output : Proof 0.79s
% 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 : LCL133-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : moca.sh %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jul 4 11:14:46 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.79/1.00 % SZS status Unsatisfiable
% 0.79/1.00 % SZS output start Proof
% 0.79/1.00 The input problem is unsatisfiable because
% 0.79/1.00
% 0.79/1.00 [1] the following set of Horn clauses is unsatisfiable:
% 0.79/1.00
% 0.79/1.00 implies(truth, X) = X
% 0.79/1.00 implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))) = truth
% 0.79/1.00 implies(implies(X, Y), Y) = implies(implies(Y, X), X)
% 0.79/1.00 implies(implies(not(X), not(Y)), implies(Y, X)) = truth
% 0.79/1.00 implies(X, Y) = implies(Y, X)
% 0.79/1.00 x = y ==> \bottom
% 0.79/1.00
% 0.79/1.00 This holds because
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% 0.79/1.00 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
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% 0.79/1.00 E:
% 0.79/1.00 f1(x) = true__
% 0.79/1.00 f1(y) = false__
% 0.79/1.00 implies(X, Y) = implies(Y, X)
% 0.79/1.00 implies(implies(X, Y), Y) = implies(implies(Y, X), X)
% 0.79/1.00 implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))) = truth
% 0.79/1.00 implies(implies(not(X), not(Y)), implies(Y, X)) = truth
% 0.79/1.00 implies(truth, X) = X
% 0.79/1.00 G:
% 0.79/1.00 true__ = false__
% 0.79/1.00
% 0.79/1.00 This holds because
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% 0.79/1.00 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
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% 0.79/1.00 X0 = Y0
% 0.79/1.00 Y0 = truth
% 0.79/1.00 false__ = Y0
% 0.79/1.00 implies(X, Y) = implies(Y, X)
% 0.79/1.00 implies(Y1, Y1) = implies(Y1, truth)
% 0.79/1.00 implies(Y1, implies(Y0, Y1)) = implies(Y0, implies(Y1, Y0))
% 0.79/1.00 implies(Y1, implies(Y1, Y0)) = implies(Y0, implies(Y1, Y0))
% 0.79/1.00 implies(implies(X, Y), Y) = implies(implies(Y, X), X)
% 0.79/1.00 f1(x) -> true__
% 0.79/1.00 f1(y) -> false__
% 0.79/1.00 implies(Y0, Y0) -> Y0
% 0.79/1.00 implies(Y0, Y2) -> truth
% 0.79/1.00 implies(Y0, implies(Y1, implies(Y1, Y0))) -> truth
% 0.79/1.00 implies(Y0, implies(not(Y0), not(truth))) -> truth
% 0.79/1.00 implies(Y0, implies(not(truth), not(Y0))) -> truth
% 0.79/1.00 implies(Y0, not(Y0)) -> truth
% 0.79/1.00 implies(Y1, Y1) -> truth
% 0.79/1.00 implies(Y1, implies(Y1, Y1)) -> implies(Y1, Y1)
% 0.79/1.00 implies(Y1, implies(Y1, Y1)) -> truth
% 0.79/1.00 implies(Y1, implies(Y2, implies(Y1, Y2))) -> truth
% 0.79/1.00 implies(Y1, truth) -> Y1
% 0.79/1.00 implies(Y2, implies(Y2, implies(Y0, Y2))) -> truth
% 0.79/1.00 implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))) -> truth
% 0.79/1.00 implies(implies(Y0, truth), implies(Y2, implies(Y0, Y2))) -> truth
% 0.79/1.00 implies(implies(Y1, Y0), implies(not(Y0), not(Y1))) -> truth
% 0.79/1.00 implies(implies(Y2, Y1), implies(Y2, implies(Y1, Y2))) -> truth
% 0.79/1.00 implies(implies(not(X), not(Y)), implies(Y, X)) -> truth
% 0.79/1.00 implies(truth, X) -> X
% 0.79/1.00 not(Y1) -> truth
% 0.79/1.00 not(truth) -> truth
% 0.79/1.00 true__ -> false__
% 0.79/1.00 with the LPO induced by
% 0.79/1.00 x > y > f1 > not > implies > truth > true__ > false__
% 0.79/1.00
% 0.79/1.00 % SZS output end Proof
% 0.79/1.00
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