TSTP Solution File: SYN095-1.002 by Moca---0.1
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% File : Moca---0.1
% Problem : SYN095-1.002 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n012.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 09:13:51 EDT 2022
% Result : Unsatisfiable 1.78s 1.93s
% Output : Proof 1.78s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SYN095-1.002 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.11/0.12 % Command : moca.sh %s
% 0.11/0.33 % Computer : n012.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 : Tue Jul 12 05:38:57 EDT 2022
% 0.11/0.33 % CPUTime :
% 1.78/1.93 % SZS status Unsatisfiable
% 1.78/1.93 % SZS output start Proof
% 1.78/1.93 The input problem is unsatisfiable because
% 1.78/1.93
% 1.78/1.93 [1] the following set of Horn clauses is unsatisfiable:
% 1.78/1.93
% 1.78/1.93 p_1_2(X) ==> \bottom
% 1.78/1.93 p_2_2(X) & p_1_1(X) ==> p_1_2(X)
% 1.78/1.93 q_2_2(X) & q_1_1(X) ==> p_1_2(X)
% 1.78/1.93 p_2_2(X) & q_1_1(X) ==> q_1_2(X)
% 1.78/1.93 q_2_2(X) & p_1_1(X) ==> q_1_2(X)
% 1.78/1.93 p_1_2(X) ==> p_1_1(X)
% 1.78/1.93 q_1_2(X) ==> q_1_1(X)
% 1.78/1.93 p_1_2(X) ==> p_2_2(X)
% 1.78/1.93 q_1_2(X) ==> q_2_2(X)
% 1.78/1.93 p_1_1(a)
% 1.78/1.93 q_1_1(a)
% 1.78/1.93 p_2_2(a)
% 1.78/1.93 q_2_2(a)
% 1.78/1.93
% 1.78/1.93 This holds because
% 1.78/1.93
% 1.78/1.93 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 1.78/1.93
% 1.78/1.93 E:
% 1.78/1.93 f1(p_1_2(X)) = true__
% 1.78/1.93 f1(true__) = false__
% 1.78/1.93 f10(p_1_2(X), X) = true__
% 1.78/1.93 f10(true__, X) = p_1_1(X)
% 1.78/1.93 f11(q_1_2(X), X) = true__
% 1.78/1.93 f11(true__, X) = q_1_1(X)
% 1.78/1.93 f12(p_1_2(X), X) = true__
% 1.78/1.93 f12(true__, X) = p_2_2(X)
% 1.78/1.93 f13(q_1_2(X), X) = true__
% 1.78/1.93 f13(true__, X) = q_2_2(X)
% 1.78/1.93 f2(true__, X) = p_1_2(X)
% 1.78/1.93 f3(p_1_1(X), X) = true__
% 1.78/1.93 f3(true__, X) = f2(p_2_2(X), X)
% 1.78/1.93 f4(true__, X) = p_1_2(X)
% 1.78/1.93 f5(q_1_1(X), X) = true__
% 1.78/1.93 f5(true__, X) = f4(q_2_2(X), X)
% 1.78/1.93 f6(true__, X) = q_1_2(X)
% 1.78/1.93 f7(q_1_1(X), X) = true__
% 1.78/1.93 f7(true__, X) = f6(p_2_2(X), X)
% 1.78/1.93 f8(true__, X) = q_1_2(X)
% 1.78/1.93 f9(p_1_1(X), X) = true__
% 1.78/1.93 f9(true__, X) = f8(q_2_2(X), X)
% 1.78/1.93 p_1_1(a) = true__
% 1.78/1.93 p_2_2(a) = true__
% 1.78/1.93 q_1_1(a) = true__
% 1.78/1.93 q_2_2(a) = true__
% 1.78/1.93 G:
% 1.78/1.93 true__ = false__
% 1.78/1.93
% 1.78/1.93 This holds because
% 1.78/1.93
% 1.78/1.93 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 1.78/1.93
% 1.78/1.93
% 1.78/1.93 f1(f2(true__, Y0)) -> true__
% 1.78/1.93 f1(p_1_2(X)) -> true__
% 1.78/1.93 f1(true__) -> false__
% 1.78/1.93 f10(f2(true__, Y0), Y0) -> true__
% 1.78/1.93 f10(p_1_2(X), X) -> true__
% 1.78/1.93 f10(true__, a) -> true__
% 1.78/1.93 f11(f6(true__, Y0), Y0) -> true__
% 1.78/1.93 f11(q_1_2(X), X) -> true__
% 1.78/1.93 f11(true__, X) -> q_1_1(X)
% 1.78/1.93 f12(f2(true__, Y0), Y0) -> true__
% 1.78/1.93 f12(p_1_2(X), X) -> true__
% 1.78/1.93 f12(true__, a) -> true__
% 1.78/1.93 f13(f6(true__, Y0), Y0) -> true__
% 1.78/1.93 f13(q_1_2(X), X) -> true__
% 1.78/1.93 f13(true__, a) -> true__
% 1.78/1.93 f2(f12(true__, a), a) -> true__
% 1.78/1.93 f2(true__, a) -> true__
% 1.78/1.93 f3(f10(true__, Y0), Y0) -> true__
% 1.78/1.93 f3(p_1_1(X), X) -> true__
% 1.78/1.93 f3(true__, X) -> f2(p_2_2(X), X)
% 1.78/1.93 f4(f13(true__, a), a) -> true__
% 1.78/1.93 f4(true__, X) -> p_1_2(X)
% 1.78/1.93 f5(q_1_1(X), X) -> true__
% 1.78/1.93 f5(true__, X) -> f4(q_2_2(X), X)
% 1.78/1.93 f6(f12(true__, a), a) -> true__
% 1.78/1.93 f6(true__, a) -> true__
% 1.78/1.93 f7(q_1_1(X), X) -> true__
% 1.78/1.93 f7(true__, X) -> f6(p_2_2(X), X)
% 1.78/1.93 f8(f13(true__, a), a) -> true__
% 1.78/1.93 f8(true__, X) -> q_1_2(X)
% 1.78/1.93 f9(f10(true__, Y0), Y0) -> true__
% 1.78/1.93 f9(p_1_1(X), X) -> true__
% 1.78/1.93 f9(true__, X) -> f8(q_2_2(X), X)
% 1.78/1.93 false__ -> true__
% 1.78/1.93 p_1_1(X) -> f10(true__, X)
% 1.78/1.93 p_1_1(a) -> true__
% 1.78/1.93 p_1_2(X) -> f2(true__, X)
% 1.78/1.93 p_2_2(X) -> f12(true__, X)
% 1.78/1.93 p_2_2(a) -> true__
% 1.78/1.93 q_1_1(a) -> true__
% 1.78/1.93 q_1_2(X) -> f6(true__, X)
% 1.78/1.93 q_2_2(X) -> f13(true__, X)
% 1.78/1.93 q_2_2(a) -> true__
% 1.78/1.93 with the LPO induced by
% 1.78/1.93 a > f9 > p_1_1 > f10 > f5 > q_2_2 > f13 > f7 > f3 > f4 > p_1_2 > f2 > p_2_2 > f12 > f11 > f8 > q_1_2 > f6 > q_1_1 > f1 > false__ > true__
% 1.78/1.93
% 1.78/1.93 % SZS output end Proof
% 1.78/1.93
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