TSTP Solution File: COL045-1 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : COL045-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n029.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 00:37:09 EDT 2022
% Result : Unsatisfiable 16.95s 17.12s
% Output : Proof 16.95s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : COL045-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : moca.sh %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue May 31 14:41:00 EDT 2022
% 0.12/0.33 % CPUTime :
% 16.95/17.12 % SZS status Unsatisfiable
% 16.95/17.12 % SZS output start Proof
% 16.95/17.12 The input problem is unsatisfiable because
% 16.95/17.12
% 16.95/17.12 [1] the following set of Horn clauses is unsatisfiable:
% 16.95/17.12
% 16.95/17.12 apply(apply(apply(s, X), Y), Z) = apply(apply(X, Z), apply(Y, Z))
% 16.95/17.12 apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z))
% 16.95/17.12 apply(m, X) = apply(X, X)
% 16.95/17.12 Y = apply(combinator, Y) ==> \bottom
% 16.95/17.12
% 16.95/17.12 This holds because
% 16.95/17.12
% 16.95/17.12 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 16.95/17.12
% 16.95/17.12 E:
% 16.95/17.12 apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z))
% 16.95/17.12 apply(apply(apply(s, X), Y), Z) = apply(apply(X, Z), apply(Y, Z))
% 16.95/17.12 apply(m, X) = apply(X, X)
% 16.95/17.12 f1(Y, Y) = true__
% 16.95/17.12 f1(apply(combinator, Y), Y) = false__
% 16.95/17.12 G:
% 16.95/17.12 true__ = false__
% 16.95/17.12
% 16.95/17.12 This holds because
% 16.95/17.12
% 16.95/17.12 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 16.95/17.12
% 16.95/17.12 apply(X0, apply(Y1, apply(Y1, Y1))) = apply(apply(apply(s, apply(b, X0)), m), Y1)
% 16.95/17.12 apply(X0, apply(Y1, apply(Y2, Y1))) = apply(apply(apply(s, apply(b, X0)), Y2), Y1)
% 16.95/17.12 apply(Y0, apply(Y1, apply(m, Y1))) = apply(apply(apply(s, apply(b, Y0)), m), Y1)
% 16.95/17.12 apply(Y0, apply(apply(m, Y0), Y2)) = apply(Y0, apply(apply(Y0, Y0), Y2))
% 16.95/17.12 apply(apply(Y0, Y1), apply(Y1, Y1)) = apply(apply(apply(s, Y0), m), Y1)
% 16.95/17.12 apply(apply(Y1, Y1), apply(Y2, Y1)) = apply(apply(apply(s, m), Y2), Y1)
% 16.95/17.12 apply(apply(apply(apply(m, s), X2), Y0), Y2) = apply(apply(Y0, Y2), apply(apply(X2, Y0), Y2))
% 16.95/17.12 apply(apply(apply(apply(m, s), m), Y0), Y2) = apply(apply(Y0, Y2), apply(apply(Y0, Y0), Y2))
% 16.95/17.12 apply(apply(apply(m, s), Y1), Y2) = apply(apply(s, Y2), apply(Y1, Y2))
% 16.95/17.12 apply(apply(apply(s, X), Y), Z) = apply(apply(X, Z), apply(Y, Z))
% 16.95/17.12 apply(apply(m, Y1), apply(apply(Y1, Y1), Y1)) = apply(apply(apply(apply(m, s), m), Y1), Y1)
% 16.95/17.12 apply(apply(m, apply(s, Y0)), Y2) = apply(apply(Y0, Y2), apply(apply(s, Y0), Y2))
% 16.95/17.12 apply(apply(m, apply(s, m)), Y1) = apply(apply(Y1, Y1), apply(apply(s, m), Y1))
% 16.95/17.12 apply(apply(s, Y0), apply(Y0, Y0)) = apply(apply(apply(m, s), m), Y0)
% 16.95/17.12 apply(b, apply(Y1, apply(Y1, Y1))) = apply(apply(apply(s, apply(m, b)), m), Y1)
% 16.95/17.12 apply(b, apply(Y1, apply(Y2, Y1))) = apply(apply(apply(s, apply(m, b)), Y2), Y1)
% 16.95/17.12 apply(m, X) = apply(X, X)
% 16.95/17.12 apply(m, apply(apply(b, Y0), Y1)) = apply(Y0, apply(Y1, apply(apply(b, Y0), Y1)))
% 16.95/17.12 apply(X0, apply(apply(b, X0), apply(m, apply(b, X0)))) -> apply(m, apply(m, apply(b, X0)))
% 16.95/17.12 apply(apply(Y0, Y0), apply(Y0, Y0)) -> apply(m, apply(m, Y0))
% 16.95/17.12 apply(apply(Y0, Y0), apply(m, Y0)) -> apply(m, apply(Y0, Y0))
% 16.95/17.12 apply(apply(Y0, Y0), apply(m, Y0)) -> apply(m, apply(m, Y0))
% 16.95/17.12 apply(apply(apply(apply(m, s), Y2), Y1), Y1) -> apply(apply(m, Y1), apply(apply(Y2, Y1), Y1))
% 16.95/17.12 apply(apply(apply(apply(s, b), X2), Y0), Y2) -> apply(Y0, apply(apply(X2, Y0), Y2))
% 16.95/17.12 apply(apply(apply(b, X), Y), Z) -> apply(X, apply(Y, Z))
% 16.95/17.12 apply(apply(apply(m, apply(s, b)), Y0), Y2) -> apply(Y0, apply(apply(apply(s, b), Y0), Y2))
% 16.95/17.12 apply(apply(apply(m, b), Y1), Y2) -> apply(b, apply(Y1, Y2))
% 16.95/17.12 apply(apply(apply(m, s), s), Y1) -> apply(m, apply(s, Y1))
% 16.95/17.12 apply(apply(apply(s, Y2), Y2), Y1) -> apply(m, apply(Y2, Y1))
% 16.95/17.12 apply(apply(apply(s, m), apply(m, X0)), apply(X0, X0)) -> apply(m, apply(m, apply(m, X0)))
% 16.95/17.12 apply(apply(m, Y1), apply(Y1, Y1)) -> apply(m, apply(Y1, Y1))
% 16.95/17.12 apply(apply(m, apply(X0, X0)), apply(m, apply(m, X0))) -> apply(m, apply(m, apply(m, X0)))
% 16.95/17.12 apply(apply(m, apply(b, Y0)), Y2) -> apply(Y0, apply(apply(b, Y0), Y2))
% 16.95/17.12 apply(apply(m, apply(m, X0)), apply(m, apply(X0, X0))) -> apply(m, apply(m, apply(X0, X0)))
% 16.95/17.12 apply(apply(m, apply(m, X0)), apply(m, apply(X0, X0))) -> apply(m, apply(m, apply(m, X0)))
% 16.95/17.12 apply(apply(m, apply(m, b)), Y1) -> apply(b, apply(apply(m, b), Y1))
% 16.95/17.12 apply(apply(m, apply(m, s)), s) -> apply(apply(m, s), apply(apply(m, s), s))
% 16.95/17.12 apply(apply(m, apply(s, Y1)), Y1) -> apply(apply(m, Y1), apply(apply(s, Y1), Y1))
% 16.95/17.12 apply(apply(m, apply(s, m)), apply(s, m)) -> apply(m, apply(m, apply(s, m)))
% 16.95/17.12 apply(apply(s, Y1), apply(apply(m, s), Y1)) -> apply(apply(m, apply(m, s)), Y1)
% 16.95/17.12 apply(b, apply(Y0, apply(apply(m, b), Y0))) -> apply(m, apply(apply(m, b), Y0))
% 16.95/17.12 apply(b, apply(apply(m, b), apply(m, apply(m, b)))) -> apply(m, apply(m, apply(m, b)))
% 16.95/17.12 apply(m, apply(Y0, apply(apply(s, Y0), Y0))) -> apply(m, apply(apply(s, Y0), Y0))
% 16.95/17.12 apply(m, apply(s, apply(apply(m, s), s))) -> apply(m, apply(apply(m, s), s))
% 16.95/17.12 f1(Y, Y) -> true__
% 16.95/17.12 f1(apply(apply(apply(s, apply(b, combinator)), X2), X1), apply(X1, apply(X2, X1))) -> false__
% 16.95/17.12 f1(apply(apply(apply(s, apply(b, combinator)), m), X1), apply(X1, apply(X1, X1))) -> false__
% 16.95/17.12 f1(apply(combinator, Y), Y) -> false__
% 16.95/17.12 f1(apply(combinator, apply(Y1, apply(Y1, Y1))), apply(Y1, apply(m, Y1))) -> false__
% 16.95/17.12 f1(apply(m, apply(apply(b, combinator), X1)), apply(X1, apply(apply(b, combinator), X1))) -> false__
% 16.95/17.12 f1(apply(m, apply(m, apply(b, combinator))), apply(apply(b, combinator), apply(m, apply(b, combinator)))) -> false__
% 16.95/17.12 f1(apply(m, combinator), combinator) -> false__
% 16.95/17.12 false__ -> true__
% 16.95/17.12 with the LPO induced by
% 16.95/17.12 apply > s > b > m > combinator > f1 > false__ > true__
% 16.95/17.12
% 16.95/17.12 % SZS output end Proof
% 16.95/17.12
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