TSTP Solution File: LCL134-1 by Moca---0.1
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- Process Solution
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% File : Moca---0.1
% Problem : LCL134-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n018.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 12:58:23 EDT 2022
% Result : Unsatisfiable 0.67s 0.84s
% Output : Proof 0.67s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL134-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : moca.sh %s
% 0.14/0.34 % Computer : n018.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sun Jul 3 04:33:04 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.67/0.84 % SZS status Unsatisfiable
% 0.67/0.84 % SZS output start Proof
% 0.67/0.84 The input problem is unsatisfiable because
% 0.67/0.84
% 0.67/0.84 [1] the following set of Horn clauses is unsatisfiable:
% 0.67/0.84
% 0.67/0.84 implies(truth, X) = X
% 0.67/0.84 implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))) = truth
% 0.67/0.84 implies(implies(X, Y), Y) = implies(implies(Y, X), X)
% 0.67/0.84 implies(implies(not(X), not(Y)), implies(Y, X)) = truth
% 0.67/0.84 implies(x, truth) = truth ==> \bottom
% 0.67/0.84
% 0.67/0.84 This holds because
% 0.67/0.84
% 0.67/0.84 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 0.67/0.84
% 0.67/0.84 E:
% 0.67/0.84 f1(implies(x, truth)) = true__
% 0.67/0.84 f1(truth) = false__
% 0.67/0.84 implies(implies(X, Y), Y) = implies(implies(Y, X), X)
% 0.67/0.84 implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))) = truth
% 0.67/0.84 implies(implies(not(X), not(Y)), implies(Y, X)) = truth
% 0.67/0.84 implies(truth, X) = X
% 0.67/0.84 G:
% 0.67/0.84 true__ = false__
% 0.67/0.84
% 0.67/0.84 This holds because
% 0.67/0.84
% 0.67/0.84 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.67/0.84
% 0.67/0.84 implies(implies(X, Y), Y) = implies(implies(Y, X), X)
% 0.67/0.84 implies(implies(X0, X0), truth) = implies(implies(X0, truth), implies(X0, truth))
% 0.67/0.84 f1(implies(x, truth)) -> true__
% 0.67/0.84 f1(truth) -> false__
% 0.67/0.84 implies(Y0, implies(Y0, Y0)) -> truth
% 0.67/0.84 implies(Y0, implies(implies(Y1, Y0), Y0)) -> truth
% 0.67/0.84 implies(Y0, truth) -> truth
% 0.67/0.84 implies(Y1, Y1) -> truth
% 0.67/0.84 implies(Y1, implies(Y0, Y1)) -> truth
% 0.67/0.84 implies(Y1, implies(implies(Y1, Y2), Y2)) -> truth
% 0.67/0.84 implies(Y1, implies(implies(not(truth), not(X0)), Y1)) -> truth
% 0.67/0.84 implies(Y1, implies(not(not(truth)), Y1)) -> truth
% 0.67/0.84 implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))) -> truth
% 0.67/0.84 implies(implies(X0, Y1), implies(implies(Y1, implies(X0, Y1)), implies(X0, Y1))) -> truth
% 0.67/0.84 implies(implies(X0, truth), implies(implies(X0, X0), truth)) -> truth
% 0.67/0.84 implies(implies(Y0, implies(not(Y2), not(truth))), implies(Y0, Y2)) -> truth
% 0.67/0.84 implies(implies(Y0, truth), implies(Y0, truth)) -> truth
% 0.67/0.84 implies(implies(Y0, truth), implies(Y2, implies(Y0, Y2))) -> truth
% 0.67/0.84 implies(implies(Y1, Y2), implies(implies(not(Y1), not(truth)), Y2)) -> truth
% 0.67/0.84 implies(implies(Y1, implies(not(Y1), not(truth))), implies(not(Y1), not(truth))) -> Y1
% 0.67/0.84 implies(implies(Y1, truth), truth) -> implies(Y1, Y1)
% 0.67/0.84 implies(implies(implies(X1, X0), implies(not(X0), not(X1))), implies(not(X0), not(X1))) -> implies(X1, X0)
% 0.67/0.84 implies(implies(implies(Y1, X0), X0), Y1) -> implies(implies(Y1, implies(X0, Y1)), implies(X0, Y1))
% 0.67/0.84 implies(implies(not(X), not(Y)), implies(Y, X)) -> truth
% 0.67/0.84 implies(implies(not(Y0), not(implies(X0, Y0))), implies(implies(Y0, X0), X0)) -> truth
% 0.67/0.84 implies(implies(not(Y0), not(truth)), Y0) -> truth
% 0.67/0.84 implies(implies(not(truth), not(Y1)), truth) -> truth
% 0.67/0.84 implies(implies(not(truth), not(implies(X0, truth))), truth) -> truth
% 0.67/0.84 implies(implies(not(truth), not(not(not(truth)))), truth) -> truth
% 0.67/0.84 implies(implies(not(truth), not(not(truth))), not(not(truth))) -> truth
% 0.67/0.84 implies(implies(not(truth), not(truth)), implies(not(truth), not(truth))) -> truth
% 0.67/0.84 implies(not(not(truth)), truth) -> truth
% 0.67/0.84 implies(truth, X) -> X
% 0.67/0.84 true__ -> false__
% 0.67/0.84 with the LPO induced by
% 0.67/0.84 x > f1 > not > implies > truth > true__ > false__
% 0.67/0.84
% 0.67/0.84 % SZS output end Proof
% 0.67/0.84
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