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E---3.5.1.UNS-CRf.s

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%------------------------------------------------------------------------------
% File     : E---3.5.1
% Problem  : SWC089-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM

% Computer : n019.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Sep 24 02:42:57 PM UTC 2026

% Result   : Unsatisfiable 233.57s 34.10s
% Output   : CNFRefutation 233.57s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   23
% Syntax   : Number of clauses     :  102 (  21 unt;  28 nHn; 102 RR)
%            Number of literals    :  309 (  95 equ; 183 neg)
%            Maximal clause size   :   12 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-2 aty)
%            Number of variables   :  110 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(clause173,axiom,
    ( ~ ssList(X4)
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssList(X3)
    | app(app(X1,X2),X3) != X4
    | segmentP(X4,X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause173) ).

cnf(clause75,axiom,
    ( ~ ssList(X1)
    | nil = X1
    | ssList(tl(X1)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause75) ).

cnf(co1_1,negated_conjecture,
    ssList(sk1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).

cnf(co1_6,negated_conjecture,
    sk1 = sk3,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).

cnf(clause73,axiom,
    ( ~ ssList(X1)
    | app(X1,nil) = X1 ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause73) ).

cnf(clause85,axiom,
    ( ~ ssList(X2)
    | ~ ssList(X1)
    | ssList(app(X2,X1)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause85) ).

cnf(clause100,axiom,
    ( ~ ssList(X2)
    | ~ ssList(X1)
    | X2 = X1
    | neq(X2,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause100) ).

cnf(clause8,axiom,
    ssList(nil),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).

cnf(clause120,axiom,
    ( ~ ssList(X2)
    | ~ ssItem(X1)
    | app(cons(X1,nil),X2) = cons(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause120) ).

cnf(clause104,axiom,
    ( ~ ssList(X1)
    | nil = X1
    | cons(hd(X1),tl(X1)) = X1 ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause104) ).

cnf(clause76,axiom,
    ( ~ ssList(X1)
    | nil = X1
    | ssItem(hd(X1)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause76) ).

cnf(clause145,axiom,
    ( ~ ssList(X1)
    | ~ ssList(X2)
    | nil != X2
    | nil != X1
    | app(X1,X2) = nil ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause145) ).

cnf(co1_8,negated_conjecture,
    ( ~ segmentP(sk1,X1)
    | ~ segmentP(sk2,X1)
    | ~ neq(X1,nil)
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).

cnf(co1_11,negated_conjecture,
    ( ~ neq(nil,sk3)
    | ~ neq(nil,sk3)
    | hd(sk3) != X4
    | cons(X4,nil) != X3
    | ~ ssItem(X4)
    | app(X2,X3) != X1
    | tl(sk3) != X2
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ neq(sk4,nil)
    | sk4 = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).

cnf(clause86,axiom,
    ( ~ ssList(X2)
    | ~ ssItem(X1)
    | ssList(cons(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).

cnf(clause157,axiom,
    ( ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssItem(X1)
    | cons(X1,app(X2,X3)) = app(cons(X1,X2),X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause157) ).

cnf(co1_5,negated_conjecture,
    sk2 = sk4,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).

cnf(clause74,axiom,
    ( ~ ssList(X1)
    | app(nil,X1) = X1 ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause74) ).

cnf(co1_7,negated_conjecture,
    neq(sk2,nil),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).

cnf(co1_10,negated_conjecture,
    ( ~ neq(sk4,nil)
    | neq(sk3,nil) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).

cnf(clause79,axiom,
    ( ~ ssList(X1)
    | nil != X1
    | segmentP(nil,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause79) ).

cnf(clause56,axiom,
    ( ~ ssList(X1)
    | segmentP(X1,nil) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause56) ).

cnf(co1_2,negated_conjecture,
    ssList(sk2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_2) ).

cnf(c_0_23,plain,
    ( ~ ssList(X4)
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssList(X3)
    | app(app(X1,X2),X3) != X4
    | segmentP(X4,X2) ),
    inference(fof_simplification,[status(thm)],[clause173]) ).

cnf(c_0_24,plain,
    ( ~ ssList(X1)
    | nil = X1
    | ssList(tl(X1)) ),
    inference(fof_simplification,[status(thm)],[clause75]) ).

cnf(c_0_25,negated_conjecture,
    ssList(sk1),
    co1_1 ).

cnf(c_0_26,negated_conjecture,
    sk1 = sk3,
    co1_6 ).

cnf(c_0_27,plain,
    ( ~ ssList(X4)
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssList(X3)
    | app(app(X1,X2),X3) != X4
    | segmentP(X4,X2) ),
    c_0_23 ).

cnf(c_0_28,plain,
    ( ~ ssList(X1)
    | app(X1,nil) = X1 ),
    inference(fof_simplification,[status(thm)],[clause73]) ).

cnf(c_0_29,plain,
    ( ~ ssList(X2)
    | ~ ssList(X1)
    | ssList(app(X2,X1)) ),
    inference(fof_simplification,[status(thm)],[clause85]) ).

cnf(c_0_30,plain,
    ( ~ ssList(X2)
    | ~ ssList(X1)
    | X2 = X1
    | neq(X2,X1) ),
    inference(fof_simplification,[status(thm)],[clause100]) ).

cnf(c_0_31,plain,
    ( ~ ssList(X1)
    | nil = X1
    | ssList(tl(X1)) ),
    c_0_24 ).

cnf(c_0_32,negated_conjecture,
    ssList(sk3),
    inference(rw,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_33,plain,
    ( ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | ~ ssList(app(app(X1,X2),X3))
    | segmentP(app(app(X1,X2),X3),X2) ),
    inference(er,[status(thm)],[c_0_27]) ).

cnf(c_0_34,plain,
    ( ~ ssList(X1)
    | app(X1,nil) = X1 ),
    c_0_28 ).

cnf(c_0_35,axiom,
    ssList(nil),
    clause8 ).

cnf(c_0_36,plain,
    ( ~ ssList(X2)
    | ~ ssList(X1)
    | ssList(app(X2,X1)) ),
    c_0_29 ).

cnf(c_0_37,plain,
    ( ~ ssList(X2)
    | ~ ssItem(X1)
    | app(cons(X1,nil),X2) = cons(X1,X2) ),
    inference(fof_simplification,[status(thm)],[clause120]) ).

cnf(c_0_38,plain,
    ( ~ ssList(X1)
    | nil = X1
    | cons(hd(X1),tl(X1)) = X1 ),
    inference(fof_simplification,[status(thm)],[clause104]) ).

cnf(c_0_39,plain,
    ( ~ ssList(X1)
    | nil = X1
    | ssItem(hd(X1)) ),
    inference(fof_simplification,[status(thm)],[clause76]) ).

cnf(c_0_40,plain,
    ( ~ ssList(X1)
    | ~ ssList(X2)
    | nil != X2
    | nil != X1
    | app(X1,X2) = nil ),
    inference(fof_simplification,[status(thm)],[clause145]) ).

cnf(c_0_41,negated_conjecture,
    ( ~ segmentP(sk1,X1)
    | ~ segmentP(sk2,X1)
    | ~ neq(X1,nil)
    | ~ ssList(X1) ),
    inference(fof_simplification,[status(thm)],[co1_8]) ).

cnf(c_0_42,plain,
    ( ~ ssList(X2)
    | ~ ssList(X1)
    | X2 = X1
    | neq(X2,X1) ),
    c_0_30 ).

cnf(c_0_43,negated_conjecture,
    ( ssList(tl(sk3))
    | sk3 = nil ),
    inference(spm,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_44,plain,
    ( ~ ssList(X1)
    | ~ ssList(X2)
    | segmentP(app(X1,X2),X2) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35])]),c_0_36]) ).

cnf(c_0_45,plain,
    ( ~ ssList(X2)
    | ~ ssItem(X1)
    | app(cons(X1,nil),X2) = cons(X1,X2) ),
    c_0_37 ).

cnf(c_0_46,plain,
    ( ~ ssList(X1)
    | nil = X1
    | cons(hd(X1),tl(X1)) = X1 ),
    c_0_38 ).

cnf(c_0_47,plain,
    ( ~ ssList(X1)
    | nil = X1
    | ssItem(hd(X1)) ),
    c_0_39 ).

cnf(c_0_48,negated_conjecture,
    ( ~ neq(nil,sk3)
    | ~ neq(nil,sk3)
    | hd(sk3) != X4
    | cons(X4,nil) != X3
    | ~ ssItem(X4)
    | app(X2,X3) != X1
    | tl(sk3) != X2
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ neq(sk4,nil)
    | sk4 = X1 ),
    inference(fof_simplification,[status(thm)],[co1_11]) ).

cnf(c_0_49,plain,
    ( ~ ssList(X2)
    | ~ ssItem(X1)
    | ssList(cons(X1,X2)) ),
    inference(fof_simplification,[status(thm)],[clause86]) ).

cnf(c_0_50,plain,
    ( ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssItem(X1)
    | cons(X1,app(X2,X3)) = app(cons(X1,X2),X3) ),
    inference(fof_simplification,[status(thm)],[clause157]) ).

cnf(c_0_51,plain,
    ( ~ ssList(X1)
    | ~ ssList(X2)
    | nil != X2
    | nil != X1
    | app(X1,X2) = nil ),
    c_0_40 ).

cnf(c_0_52,negated_conjecture,
    ( ~ segmentP(sk1,X1)
    | ~ segmentP(sk2,X1)
    | ~ neq(X1,nil)
    | ~ ssList(X1) ),
    c_0_41 ).

cnf(c_0_53,negated_conjecture,
    sk2 = sk4,
    co1_5 ).

cnf(c_0_54,negated_conjecture,
    ( ~ ssList(X1)
    | neq(tl(sk3),X1)
    | sk3 = nil
    | X1 = tl(sk3) ),
    inference(spm,[status(thm)],[c_0_42,c_0_43]) ).

cnf(c_0_55,plain,
    ( ~ ssList(X2)
    | ~ ssList(cons(X1,nil))
    | ~ ssItem(X1)
    | segmentP(cons(X1,X2),X2) ),
    inference(spm,[status(thm)],[c_0_44,c_0_45]) ).

cnf(c_0_56,negated_conjecture,
    ( sk3 = nil
    | cons(hd(sk3),tl(sk3)) = sk3 ),
    inference(spm,[status(thm)],[c_0_46,c_0_32]) ).

cnf(c_0_57,negated_conjecture,
    ( ssItem(hd(sk3))
    | sk3 = nil ),
    inference(spm,[status(thm)],[c_0_47,c_0_32]) ).

cnf(c_0_58,plain,
    ( ~ ssList(X1)
    | app(nil,X1) = X1 ),
    inference(fof_simplification,[status(thm)],[clause74]) ).

cnf(c_0_59,negated_conjecture,
    ( ~ neq(nil,sk3)
    | ~ neq(nil,sk3)
    | hd(sk3) != X4
    | cons(X4,nil) != X3
    | ~ ssItem(X4)
    | app(X2,X3) != X1
    | tl(sk3) != X2
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ neq(sk4,nil)
    | sk4 = X1 ),
    c_0_48 ).

cnf(c_0_60,negated_conjecture,
    neq(sk2,nil),
    co1_7 ).

cnf(c_0_61,plain,
    ( ~ ssList(X2)
    | ~ ssItem(X1)
    | ssList(cons(X1,X2)) ),
    c_0_49 ).

cnf(c_0_62,plain,
    ( ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssItem(X1)
    | cons(X1,app(X2,X3)) = app(cons(X1,X2),X3) ),
    c_0_50 ).

cnf(c_0_63,plain,
    app(nil,nil) = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_51])]),c_0_35])]) ).

cnf(c_0_64,negated_conjecture,
    ( ~ ssList(X1)
    | ~ segmentP(sk4,X1)
    | ~ segmentP(sk3,X1)
    | ~ neq(X1,nil) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_26]),c_0_53]) ).

cnf(c_0_65,negated_conjecture,
    ( neq(tl(sk3),nil)
    | sk3 = nil
    | tl(sk3) = nil ),
    inference(spm,[status(thm)],[c_0_54,c_0_35]) ).

cnf(c_0_66,negated_conjecture,
    ( ~ ssList(cons(hd(sk3),nil))
    | segmentP(sk3,tl(sk3))
    | sk3 = nil ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_43]),c_0_57]) ).

cnf(c_0_67,plain,
    ( ~ ssList(X1)
    | app(nil,X1) = X1 ),
    c_0_58 ).

cnf(c_0_68,negated_conjecture,
    ( ~ neq(sk4,nil)
    | ~ neq(nil,sk3)
    | ~ ssItem(X4)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | cons(X4,nil) != X3
    | app(X2,X3) != X1
    | hd(sk3) != X4
    | tl(sk3) != X2
    | sk4 = X1 ),
    inference(cn,[status(thm)],[c_0_59]) ).

cnf(c_0_69,negated_conjecture,
    neq(sk4,nil),
    inference(rw,[status(thm)],[c_0_60,c_0_53]) ).

cnf(c_0_70,plain,
    ( ~ ssList(X2)
    | ~ ssList(X3)
    | ~ ssItem(X1)
    | ssList(app(cons(X1,X2),X3)) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_36]) ).

cnf(c_0_71,plain,
    ( ~ ssItem(X1)
    | app(cons(X1,nil),nil) = cons(X1,nil) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_35])]) ).

cnf(c_0_72,negated_conjecture,
    ( ~ segmentP(sk4,tl(sk3))
    | ~ segmentP(sk3,tl(sk3))
    | sk3 = nil
    | tl(sk3) = nil ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_43]) ).

cnf(c_0_73,negated_conjecture,
    ( segmentP(sk3,tl(sk3))
    | sk3 = nil ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_61]),c_0_35])]),c_0_57]) ).

cnf(c_0_74,plain,
    ( ~ ssList(X1)
    | ~ ssList(X2)
    | segmentP(app(X1,X2),X1) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_67]),c_0_35])]),c_0_36]) ).

cnf(c_0_75,negated_conjecture,
    ( ~ ssList(tl(sk3))
    | ~ ssList(cons(hd(sk3),nil))
    | ~ ssItem(hd(sk3))
    | ~ neq(nil,sk3)
    | app(tl(sk3),cons(hd(sk3),nil)) = sk4 ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_69])])])])])]),c_0_36]) ).

cnf(c_0_76,plain,
    ( ~ ssItem(X1)
    | ssList(cons(X1,nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_35])]) ).

cnf(c_0_77,plain,
    ( ~ ssList(X1)
    | neq(nil,X1)
    | X1 = nil ),
    inference(spm,[status(thm)],[c_0_42,c_0_35]) ).

cnf(c_0_78,negated_conjecture,
    ( ~ neq(sk4,nil)
    | neq(sk3,nil) ),
    inference(fof_simplification,[status(thm)],[co1_10]) ).

cnf(c_0_79,negated_conjecture,
    ( ~ segmentP(sk4,tl(sk3))
    | sk3 = nil
    | tl(sk3) = nil ),
    inference(spm,[status(thm)],[c_0_72,c_0_73]) ).

cnf(c_0_80,negated_conjecture,
    ( ~ ssList(tl(sk3))
    | ~ ssItem(hd(sk3))
    | ~ neq(nil,sk3)
    | segmentP(sk4,tl(sk3)) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]) ).

cnf(c_0_81,negated_conjecture,
    ( neq(nil,sk3)
    | sk3 = nil ),
    inference(spm,[status(thm)],[c_0_77,c_0_32]) ).

cnf(c_0_82,negated_conjecture,
    ( ~ neq(sk4,nil)
    | neq(sk3,nil) ),
    c_0_78 ).

cnf(c_0_83,negated_conjecture,
    ( sk3 = nil
    | tl(sk3) = nil ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_43]),c_0_57]),c_0_81]) ).

cnf(c_0_84,plain,
    ( ~ ssList(X2)
    | ~ ssItem(X1)
    | app(cons(X1,X2),nil) = cons(X1,X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_34]),c_0_35])]) ).

cnf(c_0_85,negated_conjecture,
    neq(sk3,nil),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_82,c_0_69])]) ).

cnf(c_0_86,negated_conjecture,
    ( ~ ssList(tl(sk3))
    | ~ ssItem(hd(sk3))
    | ~ neq(nil,sk3)
    | segmentP(sk4,cons(hd(sk3),nil)) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_75]),c_0_76]) ).

cnf(c_0_87,negated_conjecture,
    ( sk3 = nil
    | cons(hd(sk3),nil) = sk3 ),
    inference(spm,[status(thm)],[c_0_56,c_0_83]) ).

cnf(c_0_88,negated_conjecture,
    ( sk3 = nil
    | app(sk3,nil) = sk3 ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_56]),c_0_43]),c_0_57]) ).

cnf(c_0_89,plain,
    ( ~ ssList(X1)
    | nil != X1
    | segmentP(nil,X1) ),
    inference(fof_simplification,[status(thm)],[clause79]) ).

cnf(c_0_90,negated_conjecture,
    ( ~ segmentP(sk4,sk3)
    | ~ segmentP(sk3,sk3) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_85]),c_0_32])]) ).

cnf(c_0_91,negated_conjecture,
    ( segmentP(sk4,sk3)
    | sk3 = nil ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_43]),c_0_57]),c_0_81]) ).

cnf(c_0_92,negated_conjecture,
    ( segmentP(sk3,sk3)
    | sk3 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_88]),c_0_35]),c_0_32])]) ).

cnf(c_0_93,plain,
    ( ~ ssList(X1)
    | nil != X1
    | segmentP(nil,X1) ),
    c_0_89 ).

cnf(c_0_94,negated_conjecture,
    sk3 = nil,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_92]) ).

cnf(c_0_95,plain,
    segmentP(nil,nil),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_93]),c_0_35])]) ).

cnf(c_0_96,plain,
    ( ~ ssList(X1)
    | segmentP(X1,nil) ),
    inference(fof_simplification,[status(thm)],[clause56]) ).

cnf(c_0_97,negated_conjecture,
    ssList(sk2),
    co1_2 ).

cnf(c_0_98,negated_conjecture,
    ~ segmentP(sk4,nil),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_90,c_0_94]),c_0_94]),c_0_95]),c_0_94])]) ).

cnf(c_0_99,plain,
    ( ~ ssList(X1)
    | segmentP(X1,nil) ),
    c_0_96 ).

cnf(c_0_100,negated_conjecture,
    ssList(sk4),
    inference(rw,[status(thm)],[c_0_97,c_0_53]) ).

cnf(c_0_101,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_100])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWC089-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05  % Command  : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37  % Computer : n019.cluster.edu
% 0.11/0.37  % Model    : x86_64 x86_64
% 0.11/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37  % Memory   : 8046.5625MB
% 0.11/0.37  % OS       : Linux 6.8.0-71-generic
% 0.11/0.37  % CPULimit : 300
% 0.11/0.37  % WCLimit  : 300
% 0.11/0.37  % DateTime : Mon Sep 21 07:55:04 UTC 2026
% 0.11/0.38  % CPUTime  : 
% 0.11/0.38  Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42  Running first-order theorem proving
% 0.11/0.42  Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 233.57/34.10  % Version: 3.5.1
% 233.57/34.10  % Preprocessing class: FSLSSMSSSSSNFFN.
% 233.57/34.10  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 233.57/34.10  % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 233.57/34.10  % Starting new_bool_3 with 300s (1) cores
% 233.57/34.10  % Starting new_bool_1 with 300s (1) cores
% 233.57/34.10  % Starting sh5l with 300s (1) cores
% 233.57/34.10  % new_bool_1 with pid 2078668 completed with status 0
% 233.57/34.10  % Result found by new_bool_1
% 233.57/34.10  % Preprocessing class: FSLSSMSSSSSNFFN.
% 233.57/34.10  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 233.57/34.10  % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 233.57/34.10  % Starting new_bool_3 with 300s (1) cores
% 233.57/34.10  % Starting new_bool_1 with 300s (1) cores
% 233.57/34.10  % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 233.57/34.10  % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 233.57/34.10  % Search class: FGHSF-FFMM21-MFFFFFNN
% 233.57/34.10  % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 233.57/34.10  % Starting SubtermCWHack with 31s (1) cores
% 233.57/34.10  % SubtermCWHack with pid 2078672 completed with status 8
% 233.57/34.10  % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 233.57/34.10  % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2078706 completed with status 0
% 233.57/34.10  % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 233.57/34.10  % Preprocessing class: FSLSSMSSSSSNFFN.
% 233.57/34.10  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 233.57/34.10  % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 233.57/34.10  % Starting new_bool_3 with 300s (1) cores
% 233.57/34.10  % Starting new_bool_1 with 300s (1) cores
% 233.57/34.10  % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 233.57/34.10  % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 233.57/34.10  % Search class: FGHSF-FFMM21-MFFFFFNN
% 233.57/34.10  % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 233.57/34.10  % Starting SubtermCWHack with 31s (1) cores
% 233.57/34.10  % SubtermCWHack with pid 2078672 completed with status 8
% 233.57/34.10  % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 233.57/34.10  % Preprocessing time       : 0.004 s
% 233.57/34.10  % Presaturation interreduction done
% 233.57/34.10  
% 233.57/34.10  % Proof found!
% 233.57/34.10  % SZS status Unsatisfiable
% 233.57/34.10  % SZS output start CNFRefutation
% See solution above
% 233.57/34.10  % Parsed axioms                        : 196
% 233.57/34.10  % Removed by relevancy pruning/SinE    : 121
% 233.57/34.10  % Initial clauses                      : 75
% 233.57/34.10  % Removed in clause preprocessing      : 0
% 233.57/34.10  % Initial clauses in saturation        : 75
% 233.57/34.10  % Processed clauses                    : 6048
% 233.57/34.10  % ...of these trivial                  : 9
% 233.57/34.10  % ...subsumed                          : 4079
% 233.57/34.10  % ...remaining for further processing  : 1960
% 233.57/34.10  % Other redundant clauses eliminated   : 52
% 233.57/34.10  % Clauses deleted for lack of memory   : 0
% 233.57/34.10  % Backward-subsumed                    : 189
% 233.57/34.10  % Backward-rewritten                   : 802
% 233.57/34.10  % Generated clauses                    : 64203
% 233.57/34.10  % ...of the previous two non-redundant : 63118
% 233.57/34.10  % ...aggressively subsumed             : 0
% 233.57/34.10  % Contextual simplify-reflections      : 614
% 233.57/34.10  % Paramodulations                      : 64120
% 233.57/34.10  % Factorizations                       : 0
% 233.57/34.10  % NegExts                              : 0
% 233.57/34.10  % Equation resolutions                 : 86
% 233.57/34.10  % Disequality decompositions           : 0
% 233.57/34.10  % Total rewrite steps                  : 11833
% 233.57/34.10  % ...of those cached                   : 11821
% 233.57/34.10  % Propositional unsat checks           : 0
% 233.57/34.10  %    Propositional check models        : 0
% 233.57/34.10  %    Propositional check unsatisfiable : 0
% 233.57/34.10  %    Propositional clauses             : 0
% 233.57/34.10  %    Propositional clauses after purity: 0
% 233.57/34.10  %    Propositional unsat core size     : 0
% 233.57/34.10  %    Propositional preprocessing time  : 0.000
% 233.57/34.10  %    Propositional encoding time       : 0.000
% 233.57/34.10  %    Propositional solver time         : 0.000
% 233.57/34.10  %    Success case prop preproc time    : 0.000
% 233.57/34.10  %    Success case prop encoding time   : 0.000
% 233.57/34.10  %    Success case prop solver time     : 0.000
% 233.57/34.10  % Current number of processed clauses  : 890
% 233.57/34.10  %    Positive orientable unit clauses  : 9
% 233.57/34.10  %    Positive unorientable unit clauses: 0
% 233.57/34.10  %    Negative unit clauses             : 2
% 233.57/34.10  %    Non-unit-clauses                  : 879
% 233.57/34.10  % Current number of unprocessed clauses: 56989
% 233.57/34.10  % ...number of literals in the above   : 260494
% 233.57/34.10  % Current number of archived formulas  : 0
% 233.57/34.10  % Current number of archived clauses   : 1059
% 233.57/34.10  % Clause-clause subsumption calls (NU) : 811382
% 233.57/34.10  % Rec. Clause-clause subsumption calls : 298721
% 233.57/34.10  % Non-unit clause-clause subsumptions  : 4878
% 233.57/34.10  % Unit Clause-clause subsumption calls : 732
% 233.57/34.10  % Rewrite failures with RHS unbound    : 0
% 233.57/34.10  % BW rewrite match attempts            : 1
% 233.57/34.10  % BW rewrite match successes           : 1
% 233.57/34.10  % Condensation attempts                : 0
% 233.57/34.10  % Condensation successes               : 0
% 233.57/34.10  % Termbank termtop insertions          : 1467809
% 233.57/34.10  % Search garbage collected termcells   : 862
% 233.57/34.10  
% 233.57/34.10  % -------------------------------------------------
% 233.57/34.10  % User time                : 32.035 s
% 233.57/34.10  % System time              : 1.173 s
% 233.57/34.10  % Total time               : 33.209 s
% 233.57/34.10  % Maximum resident set size: 4068 pages
% 233.57/34.10  
% 233.57/34.10  % -------------------------------------------------
% 233.57/34.10  % User time                : 32.041 s
% 233.57/34.10  % System time              : 1.180 s
% 233.57/34.10  % Total time               : 33.221 s
% 233.57/34.10  % Maximum resident set size: 5120 pages
% 233.57/34.10  % E exiting
%------------------------------------------------------------------------------