%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC091-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 14.58s 2.49s
% Output : CNFRefutation 14.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 54
% Syntax : Number of formulae : 235 ( 38 unt; 0 def)
% Number of atoms : 750 ( 168 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 1030 ( 515 ~; 513 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 3 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-2 aty)
% Number of variables : 371 ( 27 sgn 2 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(clause179,axiom,
( ~ ssList(X5)
| ~ duplicatefreeP(X5)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X4)
| app(app(X1,cons(X2,X3)),cons(X2,X4)) != X5 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause179) ).
cnf(clause169,axiom,
( ~ ssList(X1)
| ~ ssItem(X2)
| ~ memberP(X1,X2)
| app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause169) ).
cnf(clause138,axiom,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| X1 != X2
| memberP(cons(X2,X3),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause138) ).
cnf(clause52,axiom,
ssList(skaf43(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause52) ).
cnf(clause53,axiom,
ssList(skaf42(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause53) ).
cnf(clause109,axiom,
( ~ ssList(X1)
| nil = X1
| cons(skaf83(X1),skaf82(X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause109) ).
cnf(clause12,axiom,
ssItem(skaf83(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause12) ).
cnf(clause13,axiom,
ssList(skaf82(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause13) ).
cnf(clause85,axiom,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause85) ).
cnf(co1_2,negated_conjecture,
ssList(sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_2) ).
cnf(co1_5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
cnf(clause115,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ neq(X1,X2)
| X1 != X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause115) ).
cnf(co1_7,negated_conjecture,
neq(sk2,nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
cnf(clause72,axiom,
( ~ ssList(X1)
| ssItem(X2)
| duplicatefreeP(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause72) ).
cnf(clause8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
cnf(co1_10,negated_conjecture,
( ~ segmentP(sk1,X1)
| ~ segmentP(sk2,X1)
| ~ neq(X1,nil)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
cnf(clause173,axiom,
( ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| app(app(X1,X2),X3) != X4
| segmentP(X4,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause173) ).
cnf(clause74,axiom,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause74) ).
cnf(clause154,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ frontsegP(X2,X3)
| ~ frontsegP(X1,X2)
| frontsegP(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause154) ).
cnf(co1_1,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).
cnf(co1_6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
cnf(clause100,axiom,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause100) ).
cnf(clause132,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| app(X2,skaf45(X1,X2)) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause132) ).
cnf(clause73,axiom,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause73) ).
cnf(clause149,axiom,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X3,X2),X1) = app(X3,app(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause149) ).
cnf(clause120,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,nil),X2) = cons(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause120) ).
cnf(clause157,axiom,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,app(X2,X3)) = app(cons(X1,X2),X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause157) ).
cnf(clause99,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause99) ).
cnf(clause104,axiom,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause104) ).
cnf(clause75,axiom,
( ~ ssList(X1)
| nil = X1
| ssList(tl(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause75) ).
cnf(clause76,axiom,
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause76) ).
cnf(clause119,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause119) ).
cnf(co1_8,negated_conjecture,
frontsegP(sk4,sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
cnf(clause83,axiom,
( ~ ssList(X1)
| nil != X1
| frontsegP(nil,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause83) ).
cnf(clause51,axiom,
ssList(skaf45(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause51) ).
cnf(clause144,axiom,
( ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != X3
| frontsegP(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause144) ).
cnf(clause133,axiom,
( ~ ssList(X2)
| ~ ssList(X1)
| tl(app(X2,X1)) = app(tl(X2),X1)
| nil = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause133) ).
cnf(clause118,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause118) ).
cnf(clause60,axiom,
( ~ ssList(X1)
| frontsegP(X1,nil) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause60) ).
cnf(clause172,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ segmentP(X1,X2)
| segmentP(app(app(X4,X1),X3),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause172) ).
cnf(clause57,axiom,
( ~ ssList(X1)
| segmentP(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause57) ).
cnf(clause96,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| tl(cons(X1,X2)) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause96) ).
cnf(clause84,axiom,
( ~ ssList(X1)
| ~ frontsegP(nil,X1)
| nil = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause84) ).
cnf(co1_11,negated_conjecture,
( ~ totalorderedP(X1)
| ~ segmentP(X1,sk3)
| ~ frontsegP(sk4,X1)
| ~ neq(sk3,X1)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
cnf(clause86,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause86) ).
cnf(clause98,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause98) ).
cnf(clause127,axiom,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ segmentP(X2,X1)
| ~ segmentP(X1,X2)
| X2 = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause127) ).
cnf(clause67,axiom,
( ~ ssItem(X1)
| totalorderedP(cons(X1,nil)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause67) ).
cnf(clause178,axiom,
( ~ ssItem(X3)
| ~ ssItem(X4)
| ~ ssList(X1)
| ~ ssList(X2)
| X3 != X4
| ~ frontsegP(X1,X2)
| frontsegP(cons(X3,X1),cons(X4,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause178) ).
cnf(clause79,axiom,
( ~ ssList(X1)
| nil != X1
| segmentP(nil,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause79) ).
cnf(clause56,axiom,
( ~ ssList(X1)
| segmentP(X1,nil) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause56) ).
cnf(clause137,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ frontsegP(X1,X2)
| frontsegP(app(X1,X3),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause137) ).
cnf(c_0_52,plain,
( ~ ssList(X5)
| ~ duplicatefreeP(X5)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X4)
| app(app(X1,cons(X2,X3)),cons(X2,X4)) != X5 ),
inference(fof_simplification,[status(thm)],[clause179]) ).
cnf(c_0_53,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| ~ memberP(X1,X2)
| app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1 ),
inference(fof_simplification,[status(thm)],[clause169]) ).
cnf(c_0_54,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| X1 != X2
| memberP(cons(X2,X3),X1) ),
inference(fof_simplification,[status(thm)],[clause138]) ).
cnf(c_0_55,plain,
( ~ ssList(X5)
| ~ duplicatefreeP(X5)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X4)
| app(app(X1,cons(X2,X3)),cons(X2,X4)) != X5 ),
c_0_52 ).
cnf(c_0_56,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| ~ memberP(X1,X2)
| app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1 ),
c_0_53 ).
cnf(c_0_57,axiom,
ssList(skaf43(X1,X2)),
clause52 ).
cnf(c_0_58,axiom,
ssList(skaf42(X1,X2)),
clause53 ).
cnf(c_0_59,plain,
( ~ ssList(X1)
| nil = X1
| cons(skaf83(X1),skaf82(X1)) = X1 ),
inference(fof_simplification,[status(thm)],[clause109]) ).
cnf(c_0_60,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| X1 != X2
| memberP(cons(X2,X3),X1) ),
c_0_54 ).
cnf(c_0_61,plain,
( ~ duplicatefreeP(X4)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X4)
| ~ ssItem(X2)
| ~ memberP(X1,X2)
| app(X1,cons(X2,X3)) != X4 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57]),c_0_58])]) ).
cnf(c_0_62,plain,
( ~ ssList(X1)
| nil = X1
| cons(skaf83(X1),skaf82(X1)) = X1 ),
c_0_59 ).
cnf(c_0_63,axiom,
ssItem(skaf83(X1)),
clause12 ).
cnf(c_0_64,axiom,
ssList(skaf82(X1)),
clause13 ).
cnf(c_0_65,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| memberP(cons(X1,X2),X1) ),
inference(er,[status(thm)],[c_0_60]) ).
cnf(c_0_66,plain,
( ~ duplicatefreeP(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ memberP(X2,skaf83(X1))
| app(X2,X1) != X3
| nil = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63]),c_0_64])]) ).
cnf(c_0_67,plain,
( ~ ssList(X1)
| memberP(X1,skaf83(X1))
| nil = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_62]),c_0_63]),c_0_64])]) ).
cnf(c_0_68,plain,
( ~ duplicatefreeP(X2)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X1) != X2
| nil = X1 ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
fof(c_0_69,plain,
( ~ epred2_0
<=> ! [X1] :
( ~ ssList(X1)
| duplicatefreeP(X1) ) ),
introduced(definition) ).
cnf(c_0_70,plain,
( ~ duplicatefreeP(app(X1,X1))
| ~ ssList(X1)
| ~ ssList(app(X1,X1))
| nil = X1 ),
inference(er,[status(thm)],[c_0_68]) ).
cnf(c_0_71,plain,
( ~ ssList(X1)
| duplicatefreeP(X1)
| epred2_0 ),
inference(split_equiv,[status(thm)],[c_0_69]) ).
cnf(c_0_72,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
inference(fof_simplification,[status(thm)],[clause85]) ).
cnf(c_0_73,plain,
( ~ ssList(X1)
| ~ ssList(app(X1,X1))
| epred2_0
| nil = X1 ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_74,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
c_0_72 ).
cnf(c_0_75,negated_conjecture,
ssList(sk2),
co1_2 ).
cnf(c_0_76,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_77,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ neq(X1,X2)
| X1 != X2 ),
inference(fof_simplification,[status(thm)],[clause115]) ).
cnf(c_0_78,negated_conjecture,
neq(sk2,nil),
co1_7 ).
cnf(c_0_79,plain,
( ~ ssList(X1)
| epred2_0
| nil = X1 ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_80,negated_conjecture,
ssList(sk4),
inference(rw,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_81,plain,
( ~ ssList(X1)
| ssItem(X2)
| duplicatefreeP(X1) ),
inference(fof_simplification,[status(thm)],[clause72]) ).
cnf(c_0_82,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ neq(X1,X2)
| X1 != X2 ),
c_0_77 ).
cnf(c_0_83,negated_conjecture,
neq(sk4,nil),
inference(rw,[status(thm)],[c_0_78,c_0_76]) ).
cnf(c_0_84,negated_conjecture,
( epred2_0
| sk4 = nil ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
fof(c_0_85,plain,
( ~ epred1_0
<=> ! [X2] : ssItem(X2) ),
introduced(definition) ).
cnf(c_0_86,plain,
( ~ ssList(X1)
| ssItem(X2)
| duplicatefreeP(X1) ),
c_0_81 ).
cnf(c_0_87,plain,
( ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(er,[status(thm)],[c_0_82]) ).
cnf(c_0_88,negated_conjecture,
( neq(nil,nil)
| epred2_0 ),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_89,axiom,
ssList(nil),
clause8 ).
cnf(c_0_90,negated_conjecture,
( ~ segmentP(sk1,X1)
| ~ segmentP(sk2,X1)
| ~ neq(X1,nil)
| ~ ssList(X1) ),
inference(fof_simplification,[status(thm)],[co1_10]) ).
cnf(c_0_91,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_92,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_simplification,[status(thm)],[clause74]) ).
cnf(c_0_93,plain,
( ~ epred1_0
| ~ epred2_0 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_86,c_0_85]),c_0_69]) ).
cnf(c_0_94,negated_conjecture,
epred2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_89])]) ).
cnf(c_0_95,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ frontsegP(X2,X3)
| ~ frontsegP(X1,X2)
| frontsegP(X1,X3) ),
inference(fof_simplification,[status(thm)],[clause154]) ).
cnf(c_0_96,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_97,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_98,negated_conjecture,
( ~ segmentP(sk1,X1)
| ~ segmentP(sk2,X1)
| ~ neq(X1,nil)
| ~ ssList(X1) ),
c_0_90 ).
cnf(c_0_99,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
inference(fof_simplification,[status(thm)],[clause100]) ).
cnf(c_0_100,plain,
( ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| app(app(X1,X2),X3) != X4
| segmentP(X4,X2) ),
c_0_91 ).
cnf(c_0_101,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
c_0_92 ).
cnf(c_0_102,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| app(X2,skaf45(X1,X2)) = X1 ),
inference(fof_simplification,[status(thm)],[clause132]) ).
cnf(c_0_103,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(fof_simplification,[status(thm)],[clause73]) ).
cnf(c_0_104,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X3,X2),X1) = app(X3,app(X2,X1)) ),
inference(fof_simplification,[status(thm)],[clause149]) ).
cnf(c_0_105,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,nil),X2) = cons(X1,X2) ),
inference(fof_simplification,[status(thm)],[clause120]) ).
cnf(c_0_106,plain,
( ssItem(X1)
| epred1_0 ),
inference(split_equiv,[status(thm)],[c_0_85]) ).
cnf(c_0_107,plain,
~ epred1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_94])]) ).
cnf(c_0_108,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_109,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != X2 ),
inference(fof_simplification,[status(thm)],[clause99]) ).
cnf(c_0_110,plain,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
inference(fof_simplification,[status(thm)],[clause104]) ).
cnf(c_0_111,plain,
( ~ ssList(X1)
| nil = X1
| ssList(tl(X1)) ),
inference(fof_simplification,[status(thm)],[clause75]) ).
cnf(c_0_112,plain,
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
inference(fof_simplification,[status(thm)],[clause76]) ).
cnf(c_0_113,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X2 ),
inference(fof_simplification,[status(thm)],[clause119]) ).
cnf(c_0_114,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ frontsegP(X2,X3)
| ~ frontsegP(X1,X2)
| frontsegP(X1,X3) ),
c_0_95 ).
cnf(c_0_115,negated_conjecture,
frontsegP(sk4,sk3),
co1_8 ).
cnf(c_0_116,negated_conjecture,
ssList(sk3),
inference(rw,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_117,plain,
( ~ ssList(X1)
| nil != X1
| frontsegP(nil,X1) ),
inference(fof_simplification,[status(thm)],[clause83]) ).
cnf(c_0_118,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(sk4,X1)
| ~ segmentP(sk3,X1)
| ~ neq(X1,nil) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_98,c_0_97]),c_0_76]) ).
cnf(c_0_119,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
c_0_99 ).
cnf(c_0_120,plain,
( ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| app(X2,X3) != X1
| segmentP(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_89])]) ).
cnf(c_0_121,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| app(X2,skaf45(X1,X2)) = X1 ),
c_0_102 ).
cnf(c_0_122,axiom,
ssList(skaf45(X1,X2)),
clause51 ).
cnf(c_0_123,plain,
( ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != X3
| frontsegP(X3,X1) ),
inference(fof_simplification,[status(thm)],[clause144]) ).
cnf(c_0_124,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
c_0_103 ).
cnf(c_0_125,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X3,X2),X1) = app(X3,app(X2,X1)) ),
c_0_104 ).
cnf(c_0_126,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,nil),X2) = cons(X1,X2) ),
c_0_105 ).
cnf(c_0_127,plain,
ssItem(X1),
inference(sr,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_128,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,app(X2,X3)) = app(cons(X1,X2),X3) ),
c_0_108 ).
cnf(c_0_129,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != X2 ),
c_0_109 ).
cnf(c_0_130,plain,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
c_0_110 ).
cnf(c_0_131,plain,
( ~ ssList(X1)
| nil = X1
| ssList(tl(X1)) ),
c_0_111 ).
cnf(c_0_132,plain,
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
c_0_112 ).
cnf(c_0_133,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| tl(app(X2,X1)) = app(tl(X2),X1)
| nil = X2 ),
inference(fof_simplification,[status(thm)],[clause133]) ).
cnf(c_0_134,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X1 ),
inference(fof_simplification,[status(thm)],[clause118]) ).
cnf(c_0_135,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X2 ),
c_0_113 ).
cnf(c_0_136,negated_conjecture,
( ~ ssList(X1)
| ~ frontsegP(X1,sk4)
| frontsegP(X1,sk3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_116]),c_0_80])]) ).
cnf(c_0_137,plain,
( ~ ssList(X1)
| nil != X1
| frontsegP(nil,X1) ),
c_0_117 ).
cnf(c_0_138,plain,
( ~ ssList(X1)
| frontsegP(X1,nil) ),
inference(fof_simplification,[status(thm)],[clause60]) ).
cnf(c_0_139,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ segmentP(X1,X2)
| segmentP(app(app(X4,X1),X3),X2) ),
inference(fof_simplification,[status(thm)],[clause172]) ).
cnf(c_0_140,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(sk4,X1)
| ~ segmentP(sk3,X1)
| nil = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_89])]) ).
cnf(c_0_141,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ frontsegP(X1,X2)
| segmentP(X1,X2) ),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_122])])]) ).
cnf(c_0_142,plain,
( ~ ssList(X1)
| segmentP(X1,X1) ),
inference(fof_simplification,[status(thm)],[clause57]) ).
cnf(c_0_143,plain,
( ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != X3
| frontsegP(X3,X1) ),
c_0_123 ).
cnf(c_0_144,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| app(X1,app(X2,nil)) = app(X1,X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_89])]),c_0_74]) ).
cnf(c_0_145,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| app(nil,app(X1,X2)) = app(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_101]),c_0_89])]) ).
cnf(c_0_146,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| tl(cons(X1,X2)) = X2 ),
inference(fof_simplification,[status(thm)],[clause96]) ).
cnf(c_0_147,plain,
( ~ ssList(X2)
| app(cons(X1,nil),X2) = cons(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_126,c_0_127])]) ).
cnf(c_0_148,plain,
( ~ ssList(X2)
| ~ ssList(X3)
| app(cons(X1,X2),X3) = cons(X1,app(X2,X3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_128,c_0_127])]) ).
cnf(c_0_149,plain,
( ~ ssList(X1)
| tl(X1) != X1
| nil = X1 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_131]),c_0_132]) ).
cnf(c_0_150,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| tl(app(X2,X1)) = app(tl(X2),X1)
| nil = X2 ),
c_0_133 ).
cnf(c_0_151,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X1 ),
c_0_134 ).
cnf(c_0_152,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| X1 != nil
| skaf45(X1,X2) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_121]),c_0_122])]) ).
cnf(c_0_153,negated_conjecture,
( sk4 != nil
| frontsegP(nil,sk3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_89]),c_0_80])]) ).
cnf(c_0_154,plain,
( ~ ssList(X1)
| frontsegP(X1,nil) ),
c_0_138 ).
cnf(c_0_155,plain,
( ~ ssList(X1)
| ~ frontsegP(nil,X1)
| nil = X1 ),
inference(fof_simplification,[status(thm)],[clause84]) ).
cnf(c_0_156,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ segmentP(X1,X2)
| segmentP(app(app(X4,X1),X3),X2) ),
c_0_139 ).
cnf(c_0_157,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(sk3,X1)
| ~ frontsegP(sk4,X1)
| nil = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_80])]) ).
cnf(c_0_158,plain,
( ~ ssList(X1)
| segmentP(X1,X1) ),
c_0_142 ).
cnf(c_0_159,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| frontsegP(app(X1,X2),X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_143]),c_0_74]) ).
cnf(c_0_160,plain,
( ~ ssList(X1)
| app(X1,nil) = app(nil,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_145]),c_0_89])]) ).
cnf(c_0_161,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| tl(cons(X1,X2)) = X2 ),
c_0_146 ).
cnf(c_0_162,plain,
( ~ ssList(X2)
| cons(X1,app(nil,X2)) = cons(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_148]),c_0_89])]) ).
cnf(c_0_163,negated_conjecture,
( ~ totalorderedP(X1)
| ~ segmentP(X1,sk3)
| ~ frontsegP(sk4,X1)
| ~ neq(sk3,X1)
| ~ ssList(X1) ),
inference(fof_simplification,[status(thm)],[co1_11]) ).
cnf(c_0_164,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| app(tl(X1),X2) != app(X1,X2)
| nil = X1 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_150]),c_0_74]),c_0_151]) ).
cnf(c_0_165,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
inference(fof_simplification,[status(thm)],[clause86]) ).
cnf(c_0_166,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
inference(fof_simplification,[status(thm)],[clause98]) ).
cnf(c_0_167,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ frontsegP(X2,X1)
| X2 != nil
| app(X1,nil) = X2 ),
inference(spm,[status(thm)],[c_0_121,c_0_152]) ).
cnf(c_0_168,negated_conjecture,
( ~ ssList(X1)
| sk4 != nil
| frontsegP(X1,sk3) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_153]),c_0_116]),c_0_89])]),c_0_154]) ).
cnf(c_0_169,plain,
( ~ ssList(X1)
| ~ frontsegP(nil,X1)
| nil = X1 ),
c_0_155 ).
cnf(c_0_170,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ segmentP(X2,X1)
| ~ segmentP(X1,X2)
| X2 = X1 ),
inference(fof_simplification,[status(thm)],[clause127]) ).
cnf(c_0_171,plain,
( ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ segmentP(X1,X3)
| segmentP(app(X1,X2),X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_101]),c_0_89])]) ).
cnf(c_0_172,negated_conjecture,
sk3 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_158]),c_0_115]),c_0_116])]) ).
cnf(c_0_173,plain,
( ~ ssList(X1)
| frontsegP(app(nil,X1),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_160]),c_0_89])]) ).
cnf(c_0_174,plain,
( ~ ssList(X2)
| tl(cons(X1,X2)) = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_161,c_0_127])]) ).
cnf(c_0_175,plain,
( ~ ssList(X2)
| cons(X1,skaf45(X2,nil)) = cons(X1,X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_121]),c_0_122]),c_0_89])]),c_0_154]) ).
cnf(c_0_176,negated_conjecture,
( ~ totalorderedP(X1)
| ~ segmentP(X1,sk3)
| ~ frontsegP(sk4,X1)
| ~ neq(sk3,X1)
| ~ ssList(X1) ),
c_0_163 ).
cnf(c_0_177,plain,
( ~ ssItem(X1)
| totalorderedP(cons(X1,nil)) ),
inference(fof_simplification,[status(thm)],[clause67]) ).
cnf(c_0_178,plain,
( ~ ssList(X1)
| tl(X1) != app(X1,nil)
| nil = X1 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_124]),c_0_89])]),c_0_131]) ).
cnf(c_0_179,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
c_0_165 ).
cnf(c_0_180,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
c_0_166 ).
cnf(c_0_181,plain,
( ~ ssItem(X3)
| ~ ssItem(X4)
| ~ ssList(X1)
| ~ ssList(X2)
| X3 != X4
| ~ frontsegP(X1,X2)
| frontsegP(cons(X3,X1),cons(X4,X2)) ),
inference(fof_simplification,[status(thm)],[clause178]) ).
cnf(c_0_182,negated_conjecture,
( ~ ssList(X1)
| X1 != nil
| sk4 != nil
| app(sk3,nil) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_168]),c_0_116])]) ).
cnf(c_0_183,negated_conjecture,
( sk4 != nil
| sk3 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_153]),c_0_116])]) ).
cnf(c_0_184,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ segmentP(X2,X1)
| ~ segmentP(X1,X2)
| X2 = X1 ),
c_0_170 ).
cnf(c_0_185,plain,
( ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ segmentP(X3,X2)
| ~ frontsegP(X1,X3)
| segmentP(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_121]),c_0_122])]) ).
cnf(c_0_186,negated_conjecture,
frontsegP(sk4,nil),
inference(rw,[status(thm)],[c_0_115,c_0_172]) ).
cnf(c_0_187,plain,
( ~ ssList(X1)
| nil != X1
| segmentP(nil,X1) ),
inference(fof_simplification,[status(thm)],[clause79]) ).
cnf(c_0_188,plain,
( ~ ssList(X1)
| frontsegP(X1,skaf45(X1,nil)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_121]),c_0_122]),c_0_89])]),c_0_154]) ).
cnf(c_0_189,plain,
( ~ ssList(X2)
| tl(cons(X1,X2)) = skaf45(X2,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_175]),c_0_122])]) ).
cnf(c_0_190,negated_conjecture,
( ~ totalorderedP(X1)
| ~ ssList(X1)
| ~ segmentP(X1,sk3)
| ~ frontsegP(sk4,X1)
| X1 = sk3 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_119]),c_0_116])]) ).
cnf(c_0_191,plain,
( ~ ssItem(X1)
| totalorderedP(cons(X1,nil)) ),
c_0_177 ).
cnf(c_0_192,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,X2),nil) != X2 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_178,c_0_161]),c_0_179]),c_0_180]) ).
cnf(c_0_193,plain,
( ~ ssItem(X3)
| ~ ssItem(X4)
| ~ ssList(X1)
| ~ ssList(X2)
| X3 != X4
| ~ frontsegP(X1,X2)
| frontsegP(cons(X3,X1),cons(X4,X2)) ),
c_0_181 ).
cnf(c_0_194,negated_conjecture,
( ~ segmentP(sk4,sk4)
| ~ segmentP(sk3,sk4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_83]),c_0_80])]) ).
cnf(c_0_195,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ segmentP(nil,X3)
| segmentP(app(X1,X2),X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_124]),c_0_89])]) ).
cnf(c_0_196,negated_conjecture,
( sk4 != nil
| app(sk3,nil) = sk3 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_116]),c_0_183]) ).
cnf(c_0_197,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X1,X2)
| ~ frontsegP(X2,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_184,c_0_141]) ).
cnf(c_0_198,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(nil,X1)
| segmentP(sk4,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_186]),c_0_89]),c_0_80])]) ).
cnf(c_0_199,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ segmentP(nil,X2)
| segmentP(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_101]),c_0_89])]) ).
cnf(c_0_200,plain,
( ~ ssList(X1)
| nil != X1
| segmentP(nil,X1) ),
c_0_187 ).
cnf(c_0_201,plain,
( ~ ssList(X1)
| frontsegP(X1,tl(cons(X2,X1))) ),
inference(spm,[status(thm)],[c_0_188,c_0_189]) ).
cnf(c_0_202,negated_conjecture,
( ~ ssList(cons(X1,nil))
| ~ ssItem(X1)
| ~ segmentP(cons(X1,nil),sk3)
| ~ frontsegP(sk4,cons(X1,nil))
| cons(X1,nil) = sk3 ),
inference(spm,[status(thm)],[c_0_190,c_0_191]) ).
cnf(c_0_203,plain,
( ~ ssItem(X1)
| cons(X1,nil) != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_192,c_0_126]),c_0_89])]) ).
cnf(c_0_204,plain,
( ~ ssList(X1)
| segmentP(X1,nil) ),
inference(fof_simplification,[status(thm)],[clause56]) ).
cnf(c_0_205,plain,
( ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1)
| ~ frontsegP(X2,X3)
| frontsegP(cons(X1,X2),cons(X1,X3)) ),
inference(er,[status(thm)],[c_0_193]) ).
cnf(c_0_206,negated_conjecture,
~ segmentP(sk3,sk4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_158]),c_0_80])]) ).
cnf(c_0_207,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(nil,X1)
| sk4 != nil
| segmentP(sk3,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_195,c_0_196]),c_0_116]),c_0_89])]) ).
cnf(c_0_208,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ frontsegP(X1,X2)
| frontsegP(app(X1,X3),X2) ),
inference(fof_simplification,[status(thm)],[clause137]) ).
cnf(c_0_209,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(nil,X1)
| ~ frontsegP(X1,sk4)
| sk4 = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_197,c_0_198]),c_0_80])]) ).
cnf(c_0_210,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| nil != X2
| segmentP(X1,X2) ),
inference(spm,[status(thm)],[c_0_199,c_0_200]) ).
cnf(c_0_211,plain,
( ~ ssList(X1)
| frontsegP(skaf45(X1,nil),tl(cons(X2,X1))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_175]),c_0_122])]) ).
cnf(c_0_212,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(tl(X1),X2))
| nil = X1 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_150]),c_0_74]),c_0_151]) ).
cnf(c_0_213,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ frontsegP(X2,X1)
| nil = X1
| app(tl(X1),skaf45(X2,X1)) = tl(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_121]),c_0_122])]) ).
cnf(c_0_214,negated_conjecture,
( ~ ssList(cons(X1,nil))
| ~ segmentP(cons(X1,nil),sk3)
| ~ frontsegP(sk4,cons(X1,nil))
| cons(X1,nil) = sk3 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_202,c_0_127])]) ).
cnf(c_0_215,plain,
cons(X1,nil) != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_203,c_0_127])]) ).
cnf(c_0_216,plain,
( ~ ssList(X1)
| segmentP(X1,nil) ),
c_0_204 ).
cnf(c_0_217,plain,
( ~ ssList(X2)
| ~ ssList(X3)
| ~ frontsegP(X2,X3)
| frontsegP(cons(X1,X2),cons(X1,X3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_205,c_0_127])]) ).
cnf(c_0_218,negated_conjecture,
( ~ segmentP(nil,sk4)
| sk4 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_206,c_0_207]),c_0_80])]) ).
cnf(c_0_219,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ frontsegP(X1,X2)
| frontsegP(app(X1,X3),X2) ),
c_0_208 ).
cnf(c_0_220,negated_conjecture,
( ~ ssList(X1)
| ~ frontsegP(X1,sk4)
| nil != X1
| sk4 = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_209,c_0_210]),c_0_89])]) ).
cnf(c_0_221,plain,
( ~ ssList(X1)
| frontsegP(skaf45(X1,nil),X1) ),
inference(spm,[status(thm)],[c_0_211,c_0_174]) ).
cnf(c_0_222,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ frontsegP(X2,X1)
| ssList(tl(X2))
| nil = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_212,c_0_213]),c_0_122])]) ).
cnf(c_0_223,negated_conjecture,
( ~ ssList(cons(X1,nil))
| ~ frontsegP(sk4,cons(X1,nil)) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_214,c_0_172]),c_0_172]),c_0_215]),c_0_216]) ).
cnf(c_0_224,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(tl(X1),X2)
| frontsegP(X1,cons(hd(X1),X2))
| nil = X1 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_217,c_0_130]),c_0_131]) ).
cnf(c_0_225,negated_conjecture,
sk4 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_218,c_0_200]),c_0_80])]) ).
cnf(c_0_226,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ frontsegP(nil,X2)
| frontsegP(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_219,c_0_101]),c_0_89])]) ).
cnf(c_0_227,negated_conjecture,
( skaf45(sk4,nil) != nil
| skaf45(sk4,nil) = sk4 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_220,c_0_221]),c_0_122]),c_0_80])]) ).
cnf(c_0_228,plain,
( ~ ssList(X1)
| ssList(tl(X1))
| skaf45(X1,nil) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_222,c_0_188]),c_0_122])]) ).
cnf(c_0_229,negated_conjecture,
( ~ ssList(cons(hd(sk4),nil))
| ~ frontsegP(tl(sk4),nil) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_223,c_0_224]),c_0_89]),c_0_80])]),c_0_225]) ).
cnf(c_0_230,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| nil != X2
| frontsegP(X1,X2) ),
inference(spm,[status(thm)],[c_0_226,c_0_137]) ).
cnf(c_0_231,negated_conjecture,
ssList(tl(sk4)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_227,c_0_228]),c_0_80])]),c_0_225]) ).
cnf(c_0_232,negated_conjecture,
~ ssList(cons(hd(sk4),nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_229,c_0_230]),c_0_231]),c_0_89])]) ).
cnf(c_0_233,plain,
( ~ ssList(X2)
| ssList(cons(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_179,c_0_127])]) ).
cnf(c_0_234,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_232,c_0_233]),c_0_89])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC091-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n017.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 07:49:56 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.45 Running first-order theorem proving
% 0.16/0.45 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 14.58/2.49 % Version: 3.5.1
% 14.58/2.49 % Preprocessing class: FSLSSMSSSSSNFFN.
% 14.58/2.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 14.58/2.49 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 14.58/2.49 % Starting new_bool_3 with 300s (1) cores
% 14.58/2.49 % Starting new_bool_1 with 300s (1) cores
% 14.58/2.49 % Starting sh5l with 300s (1) cores
% 14.58/2.49 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1824245 completed with status 0
% 14.58/2.49 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 14.58/2.49 % Preprocessing class: FSLSSMSSSSSNFFN.
% 14.58/2.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 14.58/2.49 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 14.58/2.49 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 14.58/2.49 % No SInE strategy applied
% 14.58/2.49 % Search class: FGHSM-FSLM21-MFFFFFNN
% 14.58/2.49 % Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 14.58/2.49 % Starting SubtermCWHack with 136s (1) cores
% 14.58/2.49 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 14.58/2.49 % Starting G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y with 136s (1) cores
% 14.58/2.49 % Starting G-E--_200_B02_F1_SE_CS_SP_PI_S2k with 136s (1) cores
% 14.58/2.49 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 14.58/2.49 % G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y with pid 1824254 completed with status 0
% 14.58/2.49 % Result found by G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y
% 14.58/2.49 % Preprocessing class: FSLSSMSSSSSNFFN.
% 14.58/2.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 14.58/2.49 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 14.58/2.49 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 14.58/2.49 % No SInE strategy applied
% 14.58/2.49 % Search class: FGHSM-FSLM21-MFFFFFNN
% 14.58/2.49 % Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 14.58/2.49 % Starting SubtermCWHack with 136s (1) cores
% 14.58/2.49 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 14.58/2.49 % Starting G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y with 136s (1) cores
% 14.58/2.49 % Preprocessing time : 0.006 s
% 14.58/2.49 % Presaturation interreduction done
% 14.58/2.49
% 14.58/2.49 % Proof found!
% 14.58/2.49 % SZS status Unsatisfiable
% 14.58/2.49 % SZS output start CNFRefutation
% See solution above
% 14.58/2.49 % Parsed axioms : 196
% 14.58/2.49 % Removed by relevancy pruning/SinE : 0
% 14.58/2.49 % Initial clauses : 196
% 14.58/2.49 % Removed in clause preprocessing : 0
% 14.58/2.49 % Initial clauses in saturation : 196
% 14.58/2.49 % Processed clauses : 5537
% 14.58/2.49 % ...of these trivial : 99
% 14.58/2.49 % ...subsumed : 3429
% 14.58/2.49 % ...remaining for further processing : 2009
% 14.58/2.49 % Other redundant clauses eliminated : 771
% 14.58/2.49 % Clauses deleted for lack of memory : 0
% 14.58/2.49 % Backward-subsumed : 105
% 14.58/2.49 % Backward-rewritten : 163
% 14.58/2.49 % Generated clauses : 38349
% 14.58/2.49 % ...of the previous two non-redundant : 35004
% 14.58/2.49 % ...aggressively subsumed : 0
% 14.58/2.49 % Contextual simplify-reflections : 202
% 14.58/2.49 % Paramodulations : 37434
% 14.58/2.49 % Factorizations : 0
% 14.58/2.49 % NegExts : 0
% 14.58/2.49 % Equation resolutions : 879
% 14.58/2.49 % Disequality decompositions : 0
% 14.58/2.49 % Total rewrite steps : 26669
% 14.58/2.49 % ...of those cached : 26163
% 14.58/2.49 % Propositional unsat checks : 0
% 14.58/2.49 % Propositional check models : 0
% 14.58/2.49 % Propositional check unsatisfiable : 0
% 14.58/2.49 % Propositional clauses : 0
% 14.58/2.49 % Propositional clauses after purity: 0
% 14.58/2.49 % Propositional unsat core size : 0
% 14.58/2.49 % Propositional preprocessing time : 0.000
% 14.58/2.49 % Propositional encoding time : 0.000
% 14.58/2.49 % Propositional solver time : 0.000
% 14.58/2.49 % Success case prop preproc time : 0.000
% 14.58/2.49 % Success case prop encoding time : 0.000
% 14.58/2.49 % Success case prop solver time : 0.000
% 14.58/2.49 % Current number of processed clauses : 1527
% 14.58/2.49 % Positive orientable unit clauses : 70
% 14.58/2.49 % Positive unorientable unit clauses: 0
% 14.58/2.49 % Negative unit clauses : 38
% 14.58/2.49 % Non-unit-clauses : 1419
% 14.58/2.49 % Current number of unprocessed clauses: 29104
% 14.58/2.49 % ...number of literals in the above : 168357
% 14.58/2.49 % Current number of archived formulas : 0
% 14.58/2.49 % Current number of archived clauses : 461
% 14.58/2.49 % Clause-clause subsumption calls (NU) : 450742
% 14.58/2.49 % Rec. Clause-clause subsumption calls : 95749
% 14.58/2.49 % Non-unit clause-clause subsumptions : 2736
% 14.58/2.49 % Unit Clause-clause subsumption calls : 10192
% 14.58/2.49 % Rewrite failures with RHS unbound : 0
% 14.58/2.49 % BW rewrite match attempts : 42
% 14.58/2.49 % BW rewrite match successes : 35
% 14.58/2.49 % Condensation attempts : 0
% 14.58/2.49 % Condensation successes : 0
% 14.58/2.49 % Termbank termtop insertions : 784558
% 14.58/2.49 % Search garbage collected termcells : 547
% 14.58/2.49
% 14.58/2.49 % -------------------------------------------------
% 14.58/2.49 % User time : 1.726 s
% 14.58/2.49 % System time : 0.051 s
% 14.58/2.49 % Total time : 1.777 s
% 14.58/2.49 % Maximum resident set size: 4068 pages
% 14.58/2.49
% 14.58/2.49 % -------------------------------------------------
% 14.58/2.49 % User time : 8.754 s
% 14.58/2.49 % System time : 0.335 s
% 14.58/2.49 % Total time : 9.089 s
% 14.58/2.49 % Maximum resident set size: 4864 pages
% 14.58/2.49 % E exiting
%------------------------------------------------------------------------------