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CSE_E---1.7.UNS-CRf.s

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%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : SWC420-1 : TPTP v9.2.1. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d

% Computer : n016.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  : 300s
% DateTime : Tue May  5 05:19:36 PM UTC 2026

% Result   : Unsatisfiable 4.60s 3.30s
% Output   : CNFRefutation 4.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   34
% Syntax   : Number of clauses     :  100 (  28 unt;  16 nHn;  82 RR)
%            Number of literals    :  301 (  74 equ; 202 neg)
%            Maximal clause size   :    7 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :   15 (  15 usr;   5 con; 0-2 aty)
%            Number of variables   :  160 (  24 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(co1_8,negated_conjecture,
    ( ~ ssItem(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | app(app(X2,cons(X1,nil)),X3) != sk2
    | app(app(X3,cons(X1,nil)),X2) != sk1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).

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

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

cnf(clause101,axiom,
    ( cons(skaf44(X1),nil) = X1
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause101) ).

cnf(clause47,axiom,
    ssItem(skaf44(X1)),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause47) ).

cnf(clause149,axiom,
    ( app(app(X3,X2),X1) = app(X3,app(X2,X1))
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause149) ).

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

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

cnf(clause179,axiom,
    ( app(app(X1,cons(X2,X3)),cons(X2,X4)) != X5
    | ~ ssList(X4)
    | ~ ssList(X3)
    | ~ ssList(X1)
    | ~ ssItem(X2)
    | ~ duplicatefreeP(X5)
    | ~ ssList(X5) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause179) ).

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

cnf(clause169,axiom,
    ( app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1
    | ~ memberP(X1,X2)
    | ~ ssItem(X2)
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause169) ).

cnf(clause52,axiom,
    ssList(skaf43(X1,X2)),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause52) ).

cnf(clause53,axiom,
    ssList(skaf42(X1,X2)),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause53) ).

cnf(clause138,axiom,
    ( memberP(cons(X2,X3),X1)
    | X1 != X2
    | ~ ssList(X3)
    | ~ ssItem(X2)
    | ~ ssItem(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause138) ).

cnf(clause72,axiom,
    ( duplicatefreeP(X1)
    | ssItem(X2)
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause72) ).

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

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

cnf(co1_9,negated_conjecture,
    ( app(X2,cons(X1,nil)) = sk3
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | app(cons(X1,nil),X2) != sk4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).

cnf(clause109,axiom,
    ( cons(skaf83(X1),skaf82(X1)) = X1
    | nil = X1
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause109) ).

cnf(clause12,axiom,
    ssItem(skaf83(X1)),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause12) ).

cnf(clause13,axiom,
    ssList(skaf82(X1)),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause13) ).

cnf(clause132,axiom,
    ( app(X2,skaf45(X1,X2)) = X1
    | ~ frontsegP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause132) ).

cnf(clause51,axiom,
    ssList(skaf45(X1,X2)),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause51) ).

cnf(clause116,axiom,
    ( singletonP(X2)
    | cons(X1,nil) != X2
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause116) ).

cnf(clause178,axiom,
    ( frontsegP(cons(X3,X1),cons(X4,X2))
    | ~ frontsegP(X1,X2)
    | X3 != X4
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssItem(X4)
    | ~ ssItem(X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause178) ).

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

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

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

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

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

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

cnf(clause60,axiom,
    ( frontsegP(X1,nil)
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause60) ).

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

cnf(clause115,axiom,
    ( X1 != X2
    | ~ neq(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause115) ).

cnf(c_0_34,negated_conjecture,
    ( ~ ssItem(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | app(app(X2,cons(X1,nil)),X3) != sk2
    | app(app(X3,cons(X1,nil)),X2) != sk1 ),
    co1_8 ).

cnf(c_0_35,negated_conjecture,
    sk1 = sk3,
    co1_6 ).

cnf(c_0_36,negated_conjecture,
    sk2 = sk4,
    co1_5 ).

cnf(c_0_37,negated_conjecture,
    ( app(app(X1,cons(X2,nil)),X3) != sk3
    | app(app(X3,cons(X2,nil)),X1) != sk4
    | ~ ssItem(X2)
    | ~ ssList(X1)
    | ~ ssList(X3) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).

cnf(c_0_38,axiom,
    ( cons(skaf44(X1),nil) = X1
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    clause101 ).

cnf(c_0_39,axiom,
    ssItem(skaf44(X1)),
    clause47 ).

cnf(c_0_40,negated_conjecture,
    ( app(app(X1,X2),X3) != sk3
    | app(app(X3,X2),X1) != sk4
    | ~ singletonP(X2)
    | ~ ssList(X1)
    | ~ ssList(X3)
    | ~ ssList(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39])]) ).

cnf(c_0_41,axiom,
    ( app(app(X3,X2),X1) = app(X3,app(X2,X1))
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    clause149 ).

cnf(c_0_42,negated_conjecture,
    ( app(X1,app(X2,X3)) != sk3
    | app(app(X3,X2),X1) != sk4
    | ~ singletonP(X2)
    | ~ ssList(X1)
    | ~ ssList(X3)
    | ~ ssList(X2) ),
    inference(spm,[status(thm)],[c_0_40,c_0_41]) ).

cnf(c_0_43,axiom,
    ( app(X1,nil) = X1
    | ~ ssList(X1) ),
    clause73 ).

cnf(c_0_44,axiom,
    ssList(nil),
    clause8 ).

cnf(c_0_45,axiom,
    ( app(app(X1,cons(X2,X3)),cons(X2,X4)) != X5
    | ~ ssList(X4)
    | ~ ssList(X3)
    | ~ ssList(X1)
    | ~ ssItem(X2)
    | ~ duplicatefreeP(X5)
    | ~ ssList(X5) ),
    clause179 ).

cnf(c_0_46,negated_conjecture,
    ( app(app(nil,X1),X2) != sk4
    | app(X2,X1) != sk3
    | ~ singletonP(X1)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44])]) ).

cnf(c_0_47,axiom,
    ( app(nil,X1) = X1
    | ~ ssList(X1) ),
    clause74 ).

cnf(c_0_48,plain,
    ( ~ ssItem(X1)
    | ~ ssList(app(app(X2,cons(X1,X3)),cons(X1,X4)))
    | ~ ssList(X4)
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ duplicatefreeP(app(app(X2,cons(X1,X3)),cons(X1,X4))) ),
    inference(er,[status(thm)],[c_0_45]) ).

cnf(c_0_49,axiom,
    ( app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1
    | ~ memberP(X1,X2)
    | ~ ssItem(X2)
    | ~ ssList(X1) ),
    clause169 ).

cnf(c_0_50,axiom,
    ssList(skaf43(X1,X2)),
    clause52 ).

cnf(c_0_51,axiom,
    ssList(skaf42(X1,X2)),
    clause53 ).

cnf(c_0_52,axiom,
    ( memberP(cons(X2,X3),X1)
    | X1 != X2
    | ~ ssList(X3)
    | ~ ssItem(X2)
    | ~ ssItem(X1) ),
    clause138 ).

cnf(c_0_53,axiom,
    ( duplicatefreeP(X1)
    | ssItem(X2)
    | ~ ssList(X1) ),
    clause72 ).

cnf(c_0_54,axiom,
    ( ssList(app(X2,X1))
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    clause85 ).

cnf(c_0_55,negated_conjecture,
    ssList(sk2),
    co1_2 ).

cnf(c_0_56,negated_conjecture,
    ( app(X2,cons(X1,nil)) = sk3
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | app(cons(X1,nil),X2) != sk4 ),
    co1_9 ).

cnf(c_0_57,negated_conjecture,
    ( app(X1,X2) != sk4
    | app(X2,X1) != sk3
    | ~ singletonP(X1)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[c_0_46,c_0_47]) ).

cnf(c_0_58,plain,
    ( ~ memberP(X1,X2)
    | ~ ssItem(X2)
    | ~ ssList(app(X1,cons(X2,X3)))
    | ~ ssList(X3)
    | ~ ssList(X1)
    | ~ duplicatefreeP(app(X1,cons(X2,X3))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]),c_0_51])]) ).

cnf(c_0_59,axiom,
    ( cons(skaf83(X1),skaf82(X1)) = X1
    | nil = X1
    | ~ ssList(X1) ),
    clause109 ).

cnf(c_0_60,axiom,
    ssItem(skaf83(X1)),
    clause12 ).

cnf(c_0_61,axiom,
    ssList(skaf82(X1)),
    clause13 ).

cnf(c_0_62,plain,
    ( memberP(cons(X1,X2),X1)
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    inference(er,[status(thm)],[c_0_52]) ).

cnf(c_0_63,plain,
    ( ssItem(X1)
    | duplicatefreeP(app(X2,X3))
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(spm,[status(thm)],[c_0_53,c_0_54]) ).

cnf(c_0_64,negated_conjecture,
    ssList(sk4),
    inference(rw,[status(thm)],[c_0_55,c_0_36]) ).

cnf(c_0_65,negated_conjecture,
    ( app(X1,X2) != sk4
    | ~ singletonP(X1)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_38]),c_0_39])]),c_0_57]) ).

cnf(c_0_66,axiom,
    ( app(X2,skaf45(X1,X2)) = X1
    | ~ frontsegP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    clause132 ).

cnf(c_0_67,axiom,
    ssList(skaf45(X1,X2)),
    clause51 ).

cnf(c_0_68,axiom,
    ( singletonP(X2)
    | cons(X1,nil) != X2
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    clause116 ).

cnf(c_0_69,axiom,
    ( frontsegP(cons(X3,X1),cons(X4,X2))
    | ~ frontsegP(X1,X2)
    | X3 != X4
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssItem(X4)
    | ~ ssItem(X3) ),
    clause178 ).

cnf(c_0_70,axiom,
    ( cons(X1,app(X2,X3)) = app(cons(X1,X2),X3)
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    clause157 ).

cnf(c_0_71,axiom,
    ( ssList(cons(X1,X2))
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    clause86 ).

cnf(c_0_72,axiom,
    ( app(X1,X2) = nil
    | nil != X1
    | nil != X2
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    clause145 ).

cnf(c_0_73,plain,
    ( nil = X1
    | ~ memberP(X2,skaf83(X1))
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ duplicatefreeP(app(X2,X1)) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60]),c_0_61])]),c_0_54]) ).

cnf(c_0_74,plain,
    ( nil = X1
    | memberP(X1,skaf83(X1))
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_59]),c_0_60]),c_0_61])]) ).

cnf(c_0_75,negated_conjecture,
    ( ssItem(X1)
    | duplicatefreeP(app(sk4,X2))
    | ~ ssList(X2) ),
    inference(spm,[status(thm)],[c_0_63,c_0_64]) ).

cnf(c_0_76,negated_conjecture,
    ( ~ frontsegP(sk4,X1)
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67])])]),c_0_64])]) ).

cnf(c_0_77,plain,
    ( singletonP(cons(X1,nil))
    | ~ ssItem(X1)
    | ~ ssList(cons(X1,nil)) ),
    inference(er,[status(thm)],[c_0_68]) ).

cnf(c_0_78,plain,
    ( frontsegP(cons(X1,X2),cons(X1,X3))
    | ~ frontsegP(X2,X3)
    | ~ ssItem(X1)
    | ~ ssList(X3)
    | ~ ssList(X2) ),
    inference(er,[status(thm)],[c_0_69]) ).

cnf(c_0_79,axiom,
    ( cons(hd(X1),tl(X1)) = X1
    | nil = X1
    | ~ ssList(X1) ),
    clause104 ).

cnf(c_0_80,axiom,
    ( ssList(tl(X1))
    | nil = X1
    | ~ ssList(X1) ),
    clause75 ).

cnf(c_0_81,axiom,
    ( ssItem(hd(X1))
    | nil = X1
    | ~ ssList(X1) ),
    clause76 ).

cnf(c_0_82,plain,
    ( ssList(cons(X1,app(X2,X3)))
    | ~ ssItem(X1)
    | ~ ssList(X3)
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_70]),c_0_71]) ).

cnf(c_0_83,plain,
    app(nil,nil) = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_72])]),c_0_44])]) ).

cnf(c_0_84,plain,
    ( nil = X1
    | ~ ssList(X1)
    | ~ duplicatefreeP(app(X1,X1)) ),
    inference(spm,[status(thm)],[c_0_73,c_0_74]) ).

cnf(c_0_85,negated_conjecture,
    ( ssItem(X1)
    | duplicatefreeP(app(sk4,sk4)) ),
    inference(spm,[status(thm)],[c_0_75,c_0_64]) ).

cnf(c_0_86,negated_conjecture,
    ( ~ frontsegP(sk4,cons(X1,nil))
    | ~ ssItem(X1)
    | ~ ssList(cons(X1,nil)) ),
    inference(spm,[status(thm)],[c_0_76,c_0_77]) ).

cnf(c_0_87,plain,
    ( nil = X1
    | frontsegP(X1,cons(hd(X1),X2))
    | ~ frontsegP(tl(X1),X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_80]),c_0_81]) ).

cnf(c_0_88,plain,
    ( ssList(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_44])]) ).

cnf(c_0_89,negated_conjecture,
    ( sk4 = nil
    | ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_64])]) ).

cnf(c_0_90,negated_conjecture,
    ( sk4 = nil
    | ~ frontsegP(tl(sk4),nil) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_44]),c_0_64])]),c_0_88]),c_0_89]) ).

cnf(c_0_91,axiom,
    ( frontsegP(X1,nil)
    | ~ ssList(X1) ),
    clause60 ).

cnf(c_0_92,negated_conjecture,
    neq(sk2,nil),
    co1_7 ).

cnf(c_0_93,negated_conjecture,
    ( sk4 = nil
    | ~ ssList(tl(sk4)) ),
    inference(spm,[status(thm)],[c_0_90,c_0_91]) ).

cnf(c_0_94,axiom,
    ( X1 != X2
    | ~ neq(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    clause115 ).

cnf(c_0_95,negated_conjecture,
    neq(sk4,nil),
    inference(rw,[status(thm)],[c_0_92,c_0_36]) ).

cnf(c_0_96,negated_conjecture,
    sk4 = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_80]),c_0_64])]) ).

cnf(c_0_97,plain,
    ( ~ neq(X1,X1)
    | ~ ssList(X1) ),
    inference(er,[status(thm)],[c_0_94]) ).

cnf(c_0_98,negated_conjecture,
    neq(nil,nil),
    inference(rw,[status(thm)],[c_0_95,c_0_96]) ).

cnf(c_0_99,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_44])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : SWC420-1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.11  % Command    : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32  % Computer : n016.cluster.edu
% 0.14/0.32  % Model    : x86_64 x86_64
% 0.14/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32  % Memory   : 8042.1875MB
% 0.14/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32  % CPULimit   : 300
% 0.14/0.32  % WCLimit    : 300
% 0.14/0.32  % DateTime   : Tue May  5 04:49:51 EDT 2026
% 0.14/0.32  % CPUTime    : 
% 0.14/0.33  % start to proof: theBenchmark
% 4.60/3.30  % Version  : CSE_E---1.7
% 4.60/3.30  % Problem  : theBenchmark.p
% 4.60/3.30  % SZS status Unsatisfiable for theBenchmark.p
% 4.60/3.30  % SZS output start CNFRefutation
% See solution above
% 4.60/3.31  % Total time : 2.370s
%------------------------------------------------------------------------------