TSTP Solution File: COL015-1 by Moca---0.1
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- Process Solution
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% File : Moca---0.1
% Problem : COL015-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n027.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 : Fri Jul 15 00:36:50 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 : COL015-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : moca.sh %s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue May 31 04:24:17 EDT 2022
% 0.13/0.34 % 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 apply(m, X) = apply(X, X)
% 0.67/0.84 apply(apply(apply(q, X), Y), Z) = apply(Y, apply(X, Z))
% 0.67/0.84 Y = apply(combinator, Y) ==> \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 apply(apply(apply(q, X), Y), Z) = apply(Y, apply(X, Z))
% 0.67/0.84 apply(m, X) = apply(X, X)
% 0.67/0.84 f1(Y, Y) = true__
% 0.67/0.84 f1(apply(combinator, Y), Y) = false__
% 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 apply(X1, apply(X0, apply(Y1, apply(apply(q, Y1), apply(apply(q, X0), X1))))) = apply(m, apply(apply(q, Y1), apply(apply(q, X0), X1)))
% 0.67/0.84 apply(Y0, apply(X1, apply(X0, apply(apply(q, apply(apply(q, X0), X1)), Y0)))) = apply(m, apply(apply(q, apply(apply(q, X0), X1)), Y0))
% 0.67/0.84 apply(Y0, apply(apply(q, X0), apply(X0, apply(apply(q, apply(m, apply(q, X0))), Y0)))) = apply(m, apply(apply(q, apply(m, apply(q, X0))), Y0))
% 0.67/0.84 apply(apply(m, apply(apply(q, X1), apply(q, Y0))), Y2) = apply(apply(X1, apply(apply(q, X1), apply(q, Y0))), apply(Y0, Y2))
% 0.67/0.84 apply(apply(m, apply(m, apply(apply(q, X1), q))), Y1) = apply(apply(q, apply(X1, apply(apply(q, X1), q))), apply(apply(X1, apply(apply(q, X1), q)), Y1))
% 0.67/0.84 apply(apply(q, X0), apply(X0, apply(Y1, apply(apply(q, Y1), apply(m, apply(q, X0)))))) = apply(m, apply(apply(q, Y1), apply(m, apply(q, X0))))
% 0.67/0.84 apply(apply(q, Y1), apply(Y1, apply(m, apply(q, Y1)))) = apply(m, apply(apply(q, Y1), apply(q, Y1)))
% 0.67/0.84 apply(m, X) = apply(X, X)
% 0.67/0.84 apply(m, apply(apply(q, Y0), Y1)) = apply(Y1, apply(Y0, apply(apply(q, Y0), Y1)))
% 0.67/0.84 apply(m, apply(m, apply(q, Y0))) = apply(apply(q, Y0), apply(Y0, apply(apply(q, Y0), apply(q, Y0))))
% 0.67/0.84 apply(m, apply(m, apply(q, Y0))) = apply(apply(q, Y0), apply(Y0, apply(m, apply(q, Y0))))
% 0.67/0.84 apply(apply(apply(m, apply(apply(q, X1), q)), Y1), Y2) -> apply(Y1, apply(apply(X1, apply(apply(q, X1), q)), Y2))
% 0.67/0.84 apply(apply(apply(q, X), Y), Z) -> apply(Y, apply(X, Z))
% 0.67/0.84 apply(apply(m, apply(apply(q, q), m)), Y1) -> apply(apply(q, apply(apply(q, q), m)), apply(m, apply(q, Y1)))
% 0.67/0.84 apply(apply(m, apply(q, Y0)), Y2) -> apply(apply(q, Y0), apply(Y0, Y2))
% 0.67/0.84 f1(Y, Y) -> true__
% 0.67/0.84 f1(apply(combinator, Y), Y) -> false__
% 0.67/0.84 f1(apply(m, apply(apply(q, X1), combinator)), apply(X1, apply(apply(q, X1), combinator))) -> false__
% 0.67/0.84 f1(apply(m, apply(apply(q, apply(apply(q, X0), X1)), combinator)), apply(X1, apply(X0, apply(apply(q, apply(apply(q, X0), X1)), combinator)))) -> false__
% 0.67/0.84 true__ -> false__
% 0.67/0.84 with the LPO induced by
% 0.67/0.84 m > f1 > apply > q > combinator > true__ > false__
% 0.67/0.84
% 0.67/0.84 % SZS output end Proof
% 0.67/0.84
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