TSTP Solution File: SYN065-1 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : SYN065-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n007.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 09:13:33 EDT 2022
% Result : Unsatisfiable 1.12s 1.28s
% Output : Proof 1.12s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN065-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : moca.sh %s
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jul 11 22:16:03 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.12/1.28 % SZS status Unsatisfiable
% 1.12/1.28 % SZS output start Proof
% 1.12/1.28 The input problem is unsatisfiable because
% 1.12/1.28
% 1.12/1.28 [1] the following set of Horn clauses is unsatisfiable:
% 1.12/1.28
% 1.12/1.28 big_f(X, f(X))
% 1.12/1.28 big_g(X, g(X))
% 1.12/1.28 big_f(X, Y) & big_f(Y, Z) ==> big_h(X, Z)
% 1.12/1.28 big_f(X, Y) & big_g(Y, Z) ==> big_h(X, Z)
% 1.12/1.28 big_g(X, Y) & big_f(Y, Z) ==> big_h(X, Z)
% 1.12/1.28 big_g(X, Y) & big_g(Y, Z) ==> big_h(X, Z)
% 1.12/1.28 big_h(a, X) ==> \bottom
% 1.12/1.28
% 1.12/1.28 This holds because
% 1.12/1.28
% 1.12/1.28 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 1.12/1.28
% 1.12/1.28 E:
% 1.12/1.28 big_f(X, f(X)) = true__
% 1.12/1.28 big_g(X, g(X)) = true__
% 1.12/1.28 f1(true__, X, Z) = big_h(X, Z)
% 1.12/1.28 f2(big_f(Y, Z), X, Y, Z) = true__
% 1.12/1.28 f2(true__, X, Y, Z) = f1(big_f(X, Y), X, Z)
% 1.12/1.28 f3(true__, X, Z) = big_h(X, Z)
% 1.12/1.28 f4(big_g(Y, Z), X, Y, Z) = true__
% 1.12/1.28 f4(true__, X, Y, Z) = f3(big_f(X, Y), X, Z)
% 1.12/1.28 f5(true__, X, Z) = big_h(X, Z)
% 1.12/1.28 f6(big_f(Y, Z), X, Y, Z) = true__
% 1.12/1.28 f6(true__, X, Y, Z) = f5(big_g(X, Y), X, Z)
% 1.12/1.28 f7(true__, X, Z) = big_h(X, Z)
% 1.12/1.28 f8(big_g(Y, Z), X, Y, Z) = true__
% 1.12/1.28 f8(true__, X, Y, Z) = f7(big_g(X, Y), X, Z)
% 1.12/1.28 f9(big_h(a, X)) = true__
% 1.12/1.28 f9(true__) = false__
% 1.12/1.28 G:
% 1.12/1.28 true__ = false__
% 1.12/1.28
% 1.12/1.28 This holds because
% 1.12/1.28
% 1.12/1.28 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 1.12/1.28
% 1.12/1.28
% 1.12/1.28 big_f(X, f(X)) -> true__
% 1.12/1.28 big_g(X, g(X)) -> true__
% 1.12/1.28 big_h(X, Z) -> f5(true__, X, Z)
% 1.12/1.28 f1(big_f(Y2, Y0), Y2, f(Y0)) -> true__
% 1.12/1.28 f1(true__, X, Z) -> big_h(X, Z)
% 1.12/1.28 f2(big_f(Y, Z), X, Y, Z) -> true__
% 1.12/1.28 f2(true__, X, Y, Z) -> f1(big_f(X, Y), X, Z)
% 1.12/1.28 f3(big_f(Y2, Y0), Y2, g(Y0)) -> true__
% 1.12/1.28 f3(true__, X, Z) -> big_h(X, Z)
% 1.12/1.28 f4(big_g(Y, Z), X, Y, Z) -> true__
% 1.12/1.28 f4(true__, X, Y, Z) -> f3(big_f(X, Y), X, Z)
% 1.12/1.28 f5(big_g(Y2, Y0), Y2, f(Y0)) -> true__
% 1.12/1.28 f5(true__, Y0, f(f(Y0))) -> true__
% 1.12/1.28 f5(true__, Y0, f(g(Y0))) -> true__
% 1.12/1.28 f5(true__, Y0, g(f(Y0))) -> true__
% 1.12/1.28 f5(true__, Y0, g(g(Y0))) -> true__
% 1.12/1.28 f6(big_f(Y, Z), X, Y, Z) -> true__
% 1.12/1.28 f6(true__, X, Y, Z) -> f5(big_g(X, Y), X, Z)
% 1.12/1.28 f7(big_g(Y2, Y0), Y2, g(Y0)) -> true__
% 1.12/1.28 f7(true__, X, Z) -> big_h(X, Z)
% 1.12/1.28 f8(big_g(Y, Z), X, Y, Z) -> true__
% 1.12/1.28 f8(true__, X, Y, Z) -> f7(big_g(X, Y), X, Z)
% 1.12/1.28 f9(big_h(a, X)) -> true__
% 1.12/1.28 f9(f5(true__, a, Y0)) -> true__
% 1.12/1.28 f9(true__) -> false__
% 1.12/1.28 false__ -> true__
% 1.12/1.28 with the LPO induced by
% 1.12/1.28 a > f9 > f8 > f6 > big_g > f4 > f2 > big_f > f7 > f3 > f1 > big_h > f5 > g > f > false__ > true__
% 1.12/1.28
% 1.12/1.28 % SZS output end Proof
% 1.12/1.28
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