TSTP Solution File: SYN058-1 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : SYN058-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n022.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 09:13:28 EDT 2022
% Result : Unsatisfiable 1.38s 1.52s
% Output : Proof 1.38s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SYN058-1 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.14 % Command : moca.sh %s
% 0.14/0.36 % Computer : n022.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Mon Jul 11 13:50:25 EDT 2022
% 0.14/0.36 % CPUTime :
% 1.38/1.52 % SZS status Unsatisfiable
% 1.38/1.52 % SZS output start Proof
% 1.38/1.52 The input problem is unsatisfiable because
% 1.38/1.52
% 1.38/1.52 [1] the following set of Horn clauses is unsatisfiable:
% 1.38/1.52
% 1.38/1.52 big_p(X) ==> big_q(Y)
% 1.38/1.52 big_q(b) ==> big_q(c)
% 1.38/1.52 big_q(b) ==> big_s(c)
% 1.38/1.52 big_r(b) ==> big_q(c)
% 1.38/1.52 big_r(b) ==> big_s(c)
% 1.38/1.52 big_s(Y) & big_f(X) ==> big_g(X)
% 1.38/1.52 big_p(d)
% 1.38/1.52 big_f(d)
% 1.38/1.52 big_g(d) ==> \bottom
% 1.38/1.52
% 1.38/1.52 This holds because
% 1.38/1.52
% 1.38/1.52 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 1.38/1.52
% 1.38/1.52 E:
% 1.38/1.52 big_f(d) = true__
% 1.38/1.52 big_p(d) = true__
% 1.38/1.52 f1(big_p(X), Y) = true__
% 1.38/1.52 f1(true__, Y) = big_q(Y)
% 1.38/1.52 f2(big_q(b)) = true__
% 1.38/1.52 f2(true__) = big_q(c)
% 1.38/1.52 f3(big_q(b)) = true__
% 1.38/1.52 f3(true__) = big_s(c)
% 1.38/1.52 f4(big_r(b)) = true__
% 1.38/1.52 f4(true__) = big_q(c)
% 1.38/1.52 f5(big_r(b)) = true__
% 1.38/1.52 f5(true__) = big_s(c)
% 1.38/1.52 f6(true__, X) = big_g(X)
% 1.38/1.52 f7(big_f(X), Y, X) = true__
% 1.38/1.52 f7(true__, Y, X) = f6(big_s(Y), X)
% 1.38/1.52 f8(big_g(d)) = true__
% 1.38/1.52 f8(true__) = false__
% 1.38/1.52 G:
% 1.38/1.52 true__ = false__
% 1.38/1.52
% 1.38/1.52 This holds because
% 1.38/1.52
% 1.38/1.52 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 1.38/1.52
% 1.38/1.52 f6(f3(true__), Y1) = f7(true__, c, Y1)
% 1.38/1.52 f6(true__, Y0) = f7(true__, c, Y0)
% 1.38/1.52 big_f(d) -> true__
% 1.38/1.52 big_g(X) -> f6(true__, X)
% 1.38/1.52 big_p(d) -> true__
% 1.38/1.52 big_q(Y) -> f1(true__, Y)
% 1.38/1.52 big_s(c) -> f3(true__)
% 1.38/1.52 f1(big_p(X), Y) -> true__
% 1.38/1.52 f1(true__, Y1) -> true__
% 1.38/1.52 f2(big_q(b)) -> true__
% 1.38/1.52 f2(f1(true__, b)) -> true__
% 1.38/1.52 f2(true__) -> big_q(c)
% 1.38/1.52 f3(big_q(b)) -> true__
% 1.38/1.52 f3(f1(true__, b)) -> true__
% 1.38/1.52 f3(true__) -> true__
% 1.38/1.52 f4(big_r(b)) -> true__
% 1.38/1.52 f4(true__) -> big_q(c)
% 1.38/1.52 f5(big_r(b)) -> true__
% 1.38/1.52 f5(true__) -> big_s(c)
% 1.38/1.52 f6(big_s(Y), X) -> f7(true__, Y, X)
% 1.38/1.52 f7(big_f(X), Y, X) -> true__
% 1.38/1.52 f7(true__, Y1, d) -> true__
% 1.38/1.52 f8(big_g(d)) -> true__
% 1.38/1.52 f8(f6(true__, d)) -> true__
% 1.38/1.52 f8(true__) -> false__
% 1.38/1.52 false__ -> true__
% 1.38/1.52 with the LPO induced by
% 1.38/1.52 d > f4 > f2 > f5 > c > f3 > big_f > f8 > big_g > f6 > f7 > big_s > big_q > f1 > big_r > b > big_p > false__ > true__
% 1.38/1.52
% 1.38/1.52 % SZS output end Proof
% 1.38/1.52
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