TSTP Solution File: COL052-2 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : COL052-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n020.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 00:37:12 EDT 2022
% Result : Unsatisfiable 5.95s 5.94s
% Output : Proof 5.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : COL052-2 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : moca.sh %s
% 0.12/0.33 % Computer : n020.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 15:41:53 EDT 2022
% 0.12/0.33 % CPUTime :
% 5.95/5.94 % SZS status Unsatisfiable
% 5.95/5.94 % SZS output start Proof
% 5.95/5.94 The input problem is unsatisfiable because
% 5.95/5.94
% 5.95/5.94 [1] the following set of Horn clauses is unsatisfiable:
% 5.95/5.94
% 5.95/5.94 response(compose(X, Y), W) = response(X, response(Y, W))
% 5.95/5.94 agreeable(X) ==> response(X, common_bird(Y)) = response(Y, common_bird(Y))
% 5.95/5.94 response(X, Z) = response(compatible(X), Z) ==> agreeable(X)
% 5.95/5.94 agreeable(c)
% 5.95/5.94 agreeable(a) ==> \bottom
% 5.95/5.94 c = compose(a, b)
% 5.95/5.94
% 5.95/5.94 This holds because
% 5.95/5.94
% 5.95/5.94 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 5.95/5.94
% 5.95/5.94 E:
% 5.95/5.94 agreeable(c) = true__
% 5.95/5.94 c = compose(a, b)
% 5.95/5.94 f1(agreeable(X), X, Y) = response(Y, common_bird(Y))
% 5.95/5.94 f1(true__, X, Y) = response(X, common_bird(Y))
% 5.95/5.94 f2(response(X, Z), X, Z) = true__
% 5.95/5.94 f2(response(compatible(X), Z), X, Z) = agreeable(X)
% 5.95/5.94 f3(agreeable(a)) = true__
% 5.95/5.94 f3(true__) = false__
% 5.95/5.94 response(compose(X, Y), W) = response(X, response(Y, W))
% 5.95/5.94 G:
% 5.95/5.94 true__ = false__
% 5.95/5.94
% 5.95/5.94 This holds because
% 5.95/5.94
% 5.95/5.94 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 5.95/5.94
% 5.95/5.94 f1(agreeable(X), X, Y) = response(Y, common_bird(Y))
% 5.95/5.94 f1(agreeable(X1), X1, Y0) = f1(agreeable(Y1), Y1, Y0)
% 5.95/5.94 f1(true__, a, Y1) = f1(true__, Y1, Y1)
% 5.95/5.94 f1(true__, c, Y1) = f1(true__, Y1, Y1)
% 5.95/5.94 f1(true__, compose(Y0, Y2), Y2) = f1(true__, compose(Y0, c), Y2)
% 5.95/5.94 f1(true__, compose(Y0, compose(X0, c)), Y2) = f1(true__, compose(Y0, compose(X0, Y2)), Y2)
% 5.95/5.94 agreeable(a) -> true__
% 5.95/5.94 agreeable(c) -> true__
% 5.95/5.94 compose(a, b) -> c
% 5.95/5.94 f1(agreeable(Y1), Y1, Y0) -> f1(true__, Y0, Y0)
% 5.95/5.94 f1(true__, compose(Y0, compose(Y1, Y2)), compose(compose(Y0, Y1), Y2)) -> f1(true__, c, compose(compose(Y0, Y1), Y2))
% 5.95/5.94 f1(true__, compose(a, compose(b, Y0)), compose(c, Y0)) -> f1(true__, c, compose(c, Y0))
% 5.95/5.94 f1(true__, compose(c, Y1), Y2) -> f1(true__, compose(a, compose(b, Y1)), Y2)
% 5.95/5.94 f1(true__, compose(compose(X0, X1), Y1), Y2) -> f1(true__, compose(X0, compose(X1, Y1)), Y2)
% 5.95/5.94 f2(f1(agreeable(X1), X1, Y0), Y0, common_bird(Y0)) -> true__
% 5.95/5.94 f2(f1(true__, Y0, X1), Y0, common_bird(X1)) -> true__
% 5.95/5.94 f2(f1(true__, Y0, Y0), a, f1(true__, b, Y0)) -> true__
% 5.95/5.94 f2(f1(true__, Y1, Y1), c, common_bird(Y1)) -> true__
% 5.95/5.94 f2(f1(true__, a, Y1), Y1, common_bird(Y1)) -> true__
% 5.95/5.94 f2(f1(true__, b, b), a, f1(true__, b, b)) -> true__
% 5.95/5.94 f2(f1(true__, b, b), compose(a, c), common_bird(b)) -> true__
% 5.95/5.94 f2(f1(true__, c, Y1), Y1, common_bird(Y1)) -> true__
% 5.95/5.94 f2(f1(true__, c, Y2), a, f1(true__, b, Y2)) -> true__
% 5.95/5.94 f2(f1(true__, c, compatible(Y0)), Y0, common_bird(compatible(Y0))) -> agreeable(Y0)
% 5.95/5.94 f2(f1(true__, c, compose(Y0, Y1)), Y0, f1(true__, Y1, compose(Y0, Y1))) -> true__
% 5.95/5.94 f2(f1(true__, c, compose(Y0, c)), compose(Y0, a), f1(true__, b, compose(Y0, c))) -> true__
% 5.95/5.94 f2(f1(true__, c, compose(Y0, c)), compose(Y0, compose(Y0, c)), common_bird(compose(Y0, c))) -> true__
% 5.95/5.94 f2(f1(true__, c, compose(Y0, c)), compose(compose(Y0, a), b), common_bird(compose(Y0, c))) -> true__
% 5.95/5.94 f2(f1(true__, c, compose(a, compose(b, Y0))), c, f1(true__, Y0, compose(a, compose(b, Y0)))) -> true__
% 5.95/5.94 f2(f1(true__, c, compose(a, compose(b, Y0))), compose(c, Y0), common_bird(compose(a, compose(b, Y0)))) -> true__
% 5.95/5.94 f2(f1(true__, c, compose(compatible(Y0), Y1)), Y0, f1(true__, Y1, compose(compatible(Y0), Y1))) -> agreeable(Y0)
% 5.95/5.94 f2(f1(true__, compatible(Y0), X1), Y0, common_bird(X1)) -> agreeable(Y0)
% 5.95/5.94 f2(f1(true__, compose(X0, Y1), Y1), compose(X0, c), common_bird(Y1)) -> true__
% 5.95/5.94 f2(f1(true__, compose(X0, c), Y1), compose(X0, Y1), common_bird(Y1)) -> true__
% 5.95/5.94 f2(f1(true__, compose(Y0, X1), X2), Y0, f1(true__, X1, X2)) -> true__
% 5.95/5.94 f2(f1(true__, compose(Y0, Y2), Y2), Y0, f1(true__, c, Y2)) -> true__
% 5.95/5.94 f2(f1(true__, compose(Y0, c), Y2), Y0, f1(true__, Y2, Y2)) -> true__
% 5.95/5.94 f2(f1(true__, compose(Y0, c), Y3), compose(Y0, a), f1(true__, b, Y3)) -> true__
% 5.95/5.94 f2(f1(true__, compose(Y0, c), Y3), compose(compose(Y0, a), b), common_bird(Y3)) -> true__
% 5.95/5.94 f2(f1(true__, compose(Y0, compose(X0, Y2)), Y2), Y0, f1(true__, compose(X0, c), Y2)) -> true__
% 5.95/5.94 f2(f1(true__, compose(Y0, compose(X0, c)), Y2), Y0, f1(true__, compose(X0, Y2), Y2)) -> true__
% 5.95/5.94 f2(f1(true__, compose(Y0, compose(Y1, X1)), X2), compose(Y0, Y1), f1(true__, X1, X2)) -> true__
% 5.95/5.94 f2(f1(true__, compose(Y0, compose(Y1, Y2)), X1), compose(compose(Y0, Y1), Y2), common_bird(X1)) -> true__
% 5.95/5.94 f2(f1(true__, compose(Y0, compose(Y1, c)), Y3), compose(Y0, Y1), f1(true__, Y3, Y3)) -> true__
% 5.95/5.94 f2(f1(true__, compose(Y0, compose(a, compose(b, X1))), X2), compose(Y0, c), f1(true__, X1, X2)) -> true__
% 5.95/5.94 f2(f1(true__, compose(a, compose(b, X1)), X2), c, f1(true__, X1, X2)) -> true__
% 5.95/5.94 f2(f1(true__, compose(a, compose(b, Y0)), X1), compose(c, Y0), common_bird(X1)) -> true__
% 5.95/5.94 f2(f1(true__, compose(a, compose(b, Y1)), Y1), c, f1(true__, c, Y1)) -> true__
% 5.95/5.94 f2(f1(true__, compose(a, compose(b, c)), Y1), c, f1(true__, Y1, Y1)) -> true__
% 5.95/5.94 f2(f1(true__, compose(a, compose(b, compose(Y0, X1))), X2), compose(c, Y0), f1(true__, X1, X2)) -> true__
% 5.95/5.94 f2(f1(true__, compose(compatible(Y0), X1), X2), Y0, f1(true__, X1, X2)) -> agreeable(Y0)
% 5.95/5.94 f2(f1(true__, compose(compatible(Y0), Y2), Y2), Y0, f1(true__, c, Y2)) -> agreeable(Y0)
% 5.95/5.94 f2(f1(true__, compose(compatible(Y0), c), Y2), Y0, f1(true__, Y2, Y2)) -> agreeable(Y0)
% 5.95/5.94 f2(response(X, Z), X, Z) -> true__
% 5.95/5.94 f2(response(X0, response(X1, Y1)), compose(X0, X1), Y1) -> true__
% 5.95/5.94 f2(response(X0, response(X1, response(Y1, Y2))), compose(compose(X0, X1), Y1), Y2) -> true__
% 5.95/5.94 f2(response(X0, response(X1, response(Y1, response(Y2, Y3)))), compose(compose(compose(X0, X1), Y1), Y2), Y3) -> true__
% 5.95/5.94 f2(response(X0, response(X1, response(a, response(b, Y1)))), compose(compose(X0, X1), c), Y1) -> true__
% 5.95/5.94 f2(response(Y0, response(X0, response(X1, Y2))), compose(Y0, compose(X0, X1)), Y2) -> true__
% 5.95/5.94 f2(response(Y0, response(X0, response(X1, response(Y2, Y3)))), compose(compose(Y0, compose(X0, X1)), Y2), Y3) -> true__
% 5.95/5.94 f2(response(Y0, response(Y1, response(X0, response(X1, Y3)))), compose(compose(Y0, Y1), compose(X0, X1)), Y3) -> true__
% 5.95/5.94 f2(response(Y0, response(Y1, response(a, response(b, Y3)))), compose(Y0, compose(Y1, c)), Y3) -> true__
% 5.95/5.94 f2(response(Y0, response(a, response(b, Y2))), compose(Y0, c), Y2) -> true__
% 5.95/5.94 f2(response(Y0, response(a, response(b, response(Y2, Y3)))), compose(Y0, compose(c, Y2)), Y3) -> true__
% 5.95/5.94 f2(response(Y0, response(a, response(b, response(Y2, Y3)))), compose(compose(Y0, c), Y2), Y3) -> true__
% 5.95/5.94 f2(response(a, response(b, Y1)), c, Y1) -> true__
% 5.95/5.94 f2(response(a, response(b, response(X0, response(X1, Y1)))), compose(c, compose(X0, X1)), Y1) -> true__
% 5.95/5.94 f2(response(a, response(b, response(Y1, Y2))), compose(c, Y1), Y2) -> true__
% 5.95/5.94 f2(response(a, response(b, response(Y1, response(Y2, Y3)))), compose(compose(c, Y1), Y2), Y3) -> true__
% 5.95/5.94 f2(response(a, response(b, response(a, response(b, Y1)))), compose(c, c), Y1) -> true__
% 5.95/5.94 f2(response(compatible(X), Z), X, Z) -> agreeable(X)
% 5.95/5.94 f3(agreeable(a)) -> true__
% 5.95/5.94 f3(true__) -> false__
% 5.95/5.94 false__ -> true__
% 5.95/5.94 response(X, common_bird(Y)) -> f1(true__, X, Y)
% 5.95/5.94 response(Y0, f1(true__, Y1, X1)) -> f1(true__, compose(Y0, Y1), X1)
% 5.95/5.94 response(c, Y2) -> response(a, response(b, Y2))
% 5.95/5.94 response(compose(X, Y), W) -> response(X, response(Y, W))
% 5.95/5.94 with the LPO induced by
% 5.95/5.94 compatible > agreeable > response > f1 > common_bird > compose > c > a > b > f3 > f2 > false__ > true__
% 5.95/5.94
% 5.95/5.94 % SZS output end Proof
% 5.95/5.94
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