TSTP Solution File: SYN068-1 by Moca---0.1
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- Process Solution
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% File : Moca---0.1
% Problem : SYN068-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n025.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 : Thu Jul 21 09:13:36 EDT 2022
% Result : Unsatisfiable 0.91s 1.06s
% Output : Proof 0.91s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SYN068-1 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.12 % Command : moca.sh %s
% 0.11/0.33 % Computer : n025.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Mon Jul 11 22:36:47 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.91/1.06 % SZS status Unsatisfiable
% 0.91/1.06 % SZS output start Proof
% 0.91/1.06 The input problem is unsatisfiable because
% 0.91/1.06
% 0.91/1.06 [1] the following set of Horn clauses is unsatisfiable:
% 0.91/1.06
% 0.91/1.06 big_f(X) ==> big_g(f(X))
% 0.91/1.06 big_f(X) ==> big_h(X, f(X))
% 0.91/1.06 big_f(X) ==> big_g(g(X))
% 0.91/1.06 big_f(X) & big_h(X, g(X)) ==> \bottom
% 0.91/1.06 big_j(a)
% 0.91/1.06 big_g(X) ==> big_h(a, X)
% 0.91/1.06 big_j(X) ==> big_f(X)
% 0.91/1.06
% 0.91/1.06 This holds because
% 0.91/1.06
% 0.91/1.06 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 0.91/1.06
% 0.91/1.06 E:
% 0.91/1.06 big_j(a) = true__
% 0.91/1.06 f1(big_f(X), X) = true__
% 0.91/1.06 f1(true__, X) = big_g(f(X))
% 0.91/1.06 f2(big_f(X), X) = true__
% 0.91/1.06 f2(true__, X) = big_h(X, f(X))
% 0.91/1.06 f3(big_f(X), X) = true__
% 0.91/1.06 f3(true__, X) = big_g(g(X))
% 0.91/1.06 f4(true__) = false__
% 0.91/1.06 f5(big_h(X, g(X)), X) = true__
% 0.91/1.06 f5(true__, X) = f4(big_f(X))
% 0.91/1.06 f6(big_g(X), X) = true__
% 0.91/1.06 f6(true__, X) = big_h(a, X)
% 0.91/1.06 f7(big_j(X), X) = true__
% 0.91/1.06 f7(true__, X) = big_f(X)
% 0.91/1.06 G:
% 0.91/1.06 true__ = false__
% 0.91/1.06
% 0.91/1.06 This holds because
% 0.91/1.06
% 0.91/1.06 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.91/1.06
% 0.91/1.06
% 0.91/1.06 big_f(X) -> f7(true__, X)
% 0.91/1.06 big_g(f(X)) -> f1(true__, X)
% 0.91/1.06 big_g(g(X)) -> f3(true__, X)
% 0.91/1.06 big_h(X, f(X)) -> f2(true__, X)
% 0.91/1.06 big_h(a, g(a)) -> true__
% 0.91/1.06 big_j(a) -> true__
% 0.91/1.06 f1(big_f(X), X) -> true__
% 0.91/1.06 f1(f7(true__, Y0), Y0) -> true__
% 0.91/1.06 f1(true__, a) -> true__
% 0.91/1.06 f2(big_f(X), X) -> true__
% 0.91/1.06 f2(f7(true__, Y0), Y0) -> true__
% 0.91/1.06 f2(true__, a) -> true__
% 0.91/1.06 f3(big_f(X), X) -> true__
% 0.91/1.06 f3(f7(true__, Y0), Y0) -> true__
% 0.91/1.06 f3(true__, a) -> true__
% 0.91/1.06 f4(true__) -> false__
% 0.91/1.06 f5(big_h(X, g(X)), X) -> true__
% 0.91/1.06 f5(true__, X) -> f4(big_f(X))
% 0.91/1.06 f6(big_g(X), X) -> true__
% 0.91/1.06 f6(f1(true__, X0), f(X0)) -> true__
% 0.91/1.06 f6(f3(true__, X0), g(X0)) -> true__
% 0.91/1.06 f6(true__, X) -> big_h(a, X)
% 0.91/1.06 f7(big_j(X), X) -> true__
% 0.91/1.06 f7(true__, a) -> true__
% 0.91/1.06 false__ -> true__
% 0.91/1.06 with the LPO induced by
% 0.91/1.06 f5 > f4 > big_f > f7 > f6 > a > big_h > big_g > f3 > f1 > g > f2 > big_j > f > false__ > true__
% 0.91/1.06
% 0.91/1.06 % SZS output end Proof
% 0.91/1.06
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