%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC087-1 : 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 : n018.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 02:42:56 PM UTC 2026
% Result : Unsatisfiable 279.14s 38.62s
% Output : CNFRefutation 279.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 52
% Syntax : Number of clauses : 246 ( 34 unt; 69 nHn; 221 RR)
% Number of literals : 785 ( 234 equ; 495 neg)
% Maximal clause size : 12 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 5 con; 0-2 aty)
% Number of variables : 371 ( 34 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(co1_12,negated_conjecture,
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| ~ neq(nil,sk4)
| hd(sk4) != X4
| cons(X4,nil) != X3
| ~ ssItem(X4)
| app(X2,X3) != X1
| tl(sk4) != X2
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| sk3 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
cnf(co1_7,negated_conjecture,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
cnf(co1_5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
cnf(clause85,axiom,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause85) ).
cnf(co1_6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
cnf(clause100,axiom,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause100) ).
cnf(co1_2,negated_conjecture,
ssList(sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_2) ).
cnf(clause8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
cnf(clause76,axiom,
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause76) ).
cnf(clause75,axiom,
( ~ ssList(X1)
| nil = X1
| ssList(tl(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause75) ).
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/sandbox/benchmark/Axioms/SWC001-0.ax',clause179) ).
cnf(clause86,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).
cnf(clause104,axiom,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause104) ).
cnf(clause96,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| tl(cons(X1,X2)) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause96) ).
cnf(clause98,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause98) ).
cnf(clause116,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,nil) != X2
| singletonP(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause116) ).
cnf(clause101,axiom,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(skaf44(X1),nil) = 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(clause144,axiom,
( ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != X3
| frontsegP(X3,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause144) ).
cnf(co1_1,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
cnf(clause72,axiom,
( ~ ssList(X1)
| ssItem(X2)
| duplicatefreeP(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause72) ).
cnf(clause97,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| hd(cons(X1,X2)) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause97) ).
cnf(clause138,axiom,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| X1 != X2
| memberP(cons(X2,X3),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause138) ).
cnf(clause132,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| app(X2,skaf45(X1,X2)) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause132) ).
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(clause169,axiom,
( ~ ssList(X1)
| ~ ssItem(X2)
| ~ memberP(X1,X2)
| app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause169) ).
cnf(clause176,axiom,
( ~ ssItem(X1)
| ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X4)
| ~ frontsegP(cons(X1,X2),cons(X3,X4))
| X1 = X3 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause176) ).
cnf(clause109,axiom,
( ~ ssList(X1)
| nil = X1
| cons(skaf83(X1),skaf82(X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause109) ).
cnf(clause51,axiom,
ssList(skaf45(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause51) ).
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(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/sandbox/benchmark/Axioms/SWC001-0.ax',clause178) ).
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(clause61,axiom,
( ~ ssList(X1)
| frontsegP(X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause61) ).
cnf(clause150,axiom,
( ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != app(X1,X3)
| X2 = X3 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause150) ).
cnf(clause73,axiom,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause73) ).
cnf(clause143,axiom,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(X1,X2) != X3
| rearsegP(X3,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause143) ).
cnf(clause133,axiom,
( ~ ssList(X2)
| ~ ssList(X1)
| tl(app(X2,X1)) = app(tl(X2),X1)
| nil = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause133) ).
cnf(clause118,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause118) ).
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(clause172,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ segmentP(X1,X2)
| segmentP(app(app(X4,X1),X3),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause172) ).
cnf(clause57,axiom,
( ~ ssList(X1)
| segmentP(X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause57) ).
cnf(clause131,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| app(skaf46(X1,X2),X2) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause131) ).
cnf(clause59,axiom,
( ~ ssList(X1)
| rearsegP(X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause59) ).
cnf(co1_11,negated_conjecture,
( ~ neq(sk4,nil)
| ~ segmentP(sk1,X1)
| ~ segmentP(sk2,X1)
| ~ neq(X1,nil)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
cnf(clause123,axiom,
( ~ ssList(X2)
| ~ ssList(X1)
| hd(app(X2,X1)) = hd(X2)
| nil = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause123) ).
cnf(clause99,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause99) ).
cnf(clause50,axiom,
ssList(skaf46(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause50) ).
cnf(clause149,axiom,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X3,X2),X1) = app(X3,app(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause149) ).
cnf(clause74,axiom,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause74) ).
cnf(clause117,axiom,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ neq(X1,X2)
| X1 != X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause117) ).
cnf(c_0_52,negated_conjecture,
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| ~ neq(nil,sk4)
| hd(sk4) != X4
| cons(X4,nil) != X3
| ~ ssItem(X4)
| app(X2,X3) != X1
| tl(sk4) != X2
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| sk3 = X1 ),
inference(fof_simplification,[status(thm)],[co1_12]) ).
cnf(c_0_53,negated_conjecture,
neq(sk2,nil),
inference(fof_simplification,[status(thm)],[co1_7]) ).
cnf(c_0_54,negated_conjecture,
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| ~ neq(nil,sk4)
| hd(sk4) != X4
| cons(X4,nil) != X3
| ~ ssItem(X4)
| app(X2,X3) != X1
| tl(sk4) != X2
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| sk3 = X1 ),
c_0_52 ).
cnf(c_0_55,negated_conjecture,
neq(sk2,nil),
c_0_53 ).
cnf(c_0_56,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_57,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
inference(fof_simplification,[status(thm)],[clause85]) ).
cnf(c_0_58,negated_conjecture,
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| ~ ssItem(X4)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| cons(X4,nil) != X3
| app(X2,X3) != X1
| hd(sk4) != X4
| tl(sk4) != X2
| sk3 = X1 ),
inference(cn,[status(thm)],[c_0_54]) ).
cnf(c_0_59,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_60,negated_conjecture,
neq(sk4,nil),
inference(rw,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_61,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
c_0_57 ).
cnf(c_0_62,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
inference(fof_simplification,[status(thm)],[clause100]) ).
cnf(c_0_63,negated_conjecture,
ssList(sk2),
co1_2 ).
cnf(c_0_64,negated_conjecture,
( ~ ssList(tl(sk4))
| ~ ssList(cons(hd(sk4),nil))
| ~ ssItem(hd(sk4))
| ~ neq(nil,sk4)
| app(tl(sk4),cons(hd(sk4),nil)) = sk1 ),
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)],[inference(rw,[status(thm)],[c_0_58,c_0_59]),c_0_60])])])])])]),c_0_61]) ).
cnf(c_0_65,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
c_0_62 ).
cnf(c_0_66,axiom,
ssList(nil),
clause8 ).
cnf(c_0_67,negated_conjecture,
ssList(sk4),
inference(rw,[status(thm)],[c_0_63,c_0_56]) ).
cnf(c_0_68,plain,
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
inference(fof_simplification,[status(thm)],[clause76]) ).
cnf(c_0_69,negated_conjecture,
( ~ ssList(tl(sk4))
| ~ ssList(cons(hd(sk4),nil))
| ~ ssItem(hd(sk4))
| sk4 = nil
| app(tl(sk4),cons(hd(sk4),nil)) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_66]),c_0_67])]) ).
cnf(c_0_70,plain,
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
c_0_68 ).
cnf(c_0_71,plain,
( ~ ssList(X1)
| nil = X1
| ssList(tl(X1)) ),
inference(fof_simplification,[status(thm)],[clause75]) ).
cnf(c_0_72,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_73,negated_conjecture,
( ~ ssList(tl(sk4))
| ~ ssList(cons(hd(sk4),nil))
| sk4 = nil
| app(tl(sk4),cons(hd(sk4),nil)) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_67])]) ).
cnf(c_0_74,plain,
( ~ ssList(X1)
| nil = X1
| ssList(tl(X1)) ),
c_0_71 ).
cnf(c_0_75,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
inference(fof_simplification,[status(thm)],[clause86]) ).
cnf(c_0_76,plain,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
inference(fof_simplification,[status(thm)],[clause104]) ).
cnf(c_0_77,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| tl(cons(X1,X2)) = X2 ),
inference(fof_simplification,[status(thm)],[clause96]) ).
cnf(c_0_78,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
inference(fof_simplification,[status(thm)],[clause98]) ).
cnf(c_0_79,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,nil) != X2
| singletonP(X2) ),
inference(fof_simplification,[status(thm)],[clause116]) ).
cnf(c_0_80,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_72 ).
cnf(c_0_81,negated_conjecture,
( ~ ssList(cons(hd(sk4),nil))
| sk4 = nil
| app(tl(sk4),cons(hd(sk4),nil)) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_67])]) ).
cnf(c_0_82,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
c_0_75 ).
cnf(c_0_83,plain,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
c_0_76 ).
cnf(c_0_84,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| tl(cons(X1,X2)) = X2 ),
c_0_77 ).
cnf(c_0_85,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
c_0_78 ).
cnf(c_0_86,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(skaf44(X1),nil) = X1 ),
inference(fof_simplification,[status(thm)],[clause101]) ).
cnf(c_0_87,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,nil) != X2
| singletonP(X2) ),
c_0_79 ).
cnf(c_0_88,plain,
( ~ duplicatefreeP(app(app(X2,cons(X1,X3)),cons(X1,X4)))
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| ~ ssList(app(app(X2,cons(X1,X3)),cons(X1,X4)))
| ~ ssItem(X1) ),
inference(er,[status(thm)],[c_0_80]) ).
cnf(c_0_89,negated_conjecture,
( ~ ssItem(hd(sk4))
| sk4 = nil
| app(tl(sk4),cons(hd(sk4),nil)) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_66])]) ).
cnf(c_0_90,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(hd(cons(X1,X2)),X2) = cons(X1,X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_82]),c_0_85]) ).
cnf(c_0_91,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(skaf44(X1),nil) = X1 ),
c_0_86 ).
cnf(c_0_92,axiom,
ssItem(skaf44(X1)),
clause47 ).
cnf(c_0_93,plain,
( ~ ssList(cons(X1,nil))
| ~ ssItem(X1)
| singletonP(cons(X1,nil)) ),
inference(er,[status(thm)],[c_0_87]) ).
cnf(c_0_94,plain,
( ~ duplicatefreeP(app(app(X2,cons(hd(X1),X3)),X1))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(app(app(X2,cons(hd(X1),X3)),X1))
| nil = X1 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_83]),c_0_74]),c_0_70]) ).
cnf(c_0_95,negated_conjecture,
( sk4 = nil
| app(tl(sk4),cons(hd(sk4),nil)) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_70]),c_0_67])]) ).
cnf(c_0_96,plain,
( ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != X3
| frontsegP(X3,X1) ),
inference(fof_simplification,[status(thm)],[clause144]) ).
cnf(c_0_97,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(hd(X1),nil) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_92]),c_0_66])]) ).
cnf(c_0_98,plain,
( ~ ssItem(X1)
| singletonP(cons(X1,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_82]),c_0_66])]) ).
cnf(c_0_99,negated_conjecture,
( ~ duplicatefreeP(app(sk1,sk4))
| ~ ssList(tl(sk4))
| ~ ssList(app(sk1,sk4))
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_66]),c_0_67])]) ).
cnf(c_0_100,plain,
( ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != X3
| frontsegP(X3,X1) ),
c_0_96 ).
cnf(c_0_101,plain,
( ~ ssList(cons(X1,nil))
| ~ ssItem(X1)
| cons(hd(cons(X1,nil)),nil) = cons(X1,nil) ),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_102,negated_conjecture,
( ~ duplicatefreeP(app(sk1,sk4))
| ~ ssList(app(sk1,sk4))
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_74]),c_0_67])]) ).
cnf(c_0_103,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_104,plain,
( ~ ssList(X1)
| ssItem(X2)
| duplicatefreeP(X1) ),
inference(fof_simplification,[status(thm)],[clause72]) ).
cnf(c_0_105,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| frontsegP(app(X1,X2),X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_100]),c_0_61]) ).
cnf(c_0_106,plain,
( ~ ssItem(X1)
| cons(hd(cons(X1,nil)),nil) = cons(X1,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_82]),c_0_66])]) ).
cnf(c_0_107,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| hd(cons(X1,X2)) = X1 ),
inference(fof_simplification,[status(thm)],[clause97]) ).
cnf(c_0_108,negated_conjecture,
( ~ duplicatefreeP(app(sk1,sk4))
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_61]),c_0_103]),c_0_67])]) ).
cnf(c_0_109,plain,
( ~ ssList(X1)
| ssItem(X2)
| duplicatefreeP(X1) ),
c_0_104 ).
cnf(c_0_110,negated_conjecture,
( ~ ssList(tl(sk4))
| ~ ssList(cons(hd(sk4),nil))
| frontsegP(sk1,tl(sk4))
| sk4 = nil ),
inference(spm,[status(thm)],[c_0_105,c_0_95]) ).
cnf(c_0_111,plain,
( ~ ssItem(X1)
| ~ ssItem(hd(cons(X1,nil)))
| ssList(cons(X1,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_106]),c_0_66])]) ).
cnf(c_0_112,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| hd(cons(X1,X2)) = X1 ),
c_0_107 ).
cnf(c_0_113,negated_conjecture,
( ~ ssList(app(sk1,sk4))
| ssItem(X1)
| sk4 = nil ),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_114,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| X1 != X2
| memberP(cons(X2,X3),X1) ),
inference(fof_simplification,[status(thm)],[clause138]) ).
cnf(c_0_115,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| app(X2,skaf45(X1,X2)) = X1 ),
inference(fof_simplification,[status(thm)],[clause132]) ).
cnf(c_0_116,negated_conjecture,
( ~ ssList(cons(hd(sk4),nil))
| frontsegP(sk1,tl(sk4))
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_74]),c_0_67])]) ).
cnf(c_0_117,plain,
( ~ ssItem(X1)
| ssList(cons(X1,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_66])]) ).
cnf(c_0_118,negated_conjecture,
( ssItem(X1)
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_61]),c_0_103]),c_0_67])]) ).
cnf(c_0_119,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| X1 != X2
| memberP(cons(X2,X3),X1) ),
c_0_114 ).
cnf(c_0_120,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_121,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| app(X2,skaf45(X1,X2)) = X1 ),
c_0_115 ).
cnf(c_0_122,negated_conjecture,
( frontsegP(sk1,tl(sk4))
| sk4 = nil ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_118]) ).
cnf(c_0_123,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_124,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| memberP(cons(X1,X2),X1) ),
inference(er,[status(thm)],[c_0_119]) ).
cnf(c_0_125,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,app(X2,X3)) = app(cons(X1,X2),X3) ),
c_0_120 ).
cnf(c_0_126,negated_conjecture,
( ~ ssList(tl(sk4))
| sk4 = nil
| app(tl(sk4),skaf45(sk1,tl(sk4))) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_103])]) ).
cnf(c_0_127,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| ~ memberP(X1,X2)
| app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1 ),
c_0_123 ).
cnf(c_0_128,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| memberP(X1,skaf44(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_91]),c_0_92]),c_0_66])]) ).
cnf(c_0_129,plain,
( ~ ssItem(X1)
| ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X4)
| ~ frontsegP(cons(X1,X2),cons(X3,X4))
| X1 = X3 ),
inference(fof_simplification,[status(thm)],[clause176]) ).
cnf(c_0_130,plain,
( ~ ssList(X1)
| nil = X1
| cons(skaf83(X1),skaf82(X1)) = X1 ),
inference(fof_simplification,[status(thm)],[clause109]) ).
cnf(c_0_131,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| nil = X1
| cons(hd(X1),app(tl(X1),X2)) = app(X1,X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_83]),c_0_74]),c_0_70]) ).
cnf(c_0_132,negated_conjecture,
( sk4 = nil
| app(tl(sk4),skaf45(sk1,tl(sk4))) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_74]),c_0_67])]) ).
cnf(c_0_133,axiom,
ssList(skaf45(X1,X2)),
clause51 ).
cnf(c_0_134,plain,
( ~ duplicatefreeP(app(app(X2,cons(skaf44(X1),X3)),X1))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(app(app(X2,cons(skaf44(X1),X3)),X1))
| ~ singletonP(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_91]),c_0_92]),c_0_66])]) ).
cnf(c_0_135,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| app(skaf42(X1,skaf44(X1)),cons(skaf44(X1),skaf43(skaf44(X1),X1))) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_128]),c_0_92])]) ).
cnf(c_0_136,axiom,
ssList(skaf43(X1,X2)),
clause52 ).
cnf(c_0_137,axiom,
ssList(skaf42(X1,X2)),
clause53 ).
cnf(c_0_138,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_139,plain,
( ~ ssItem(X1)
| ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X4)
| ~ frontsegP(cons(X1,X2),cons(X3,X4))
| X1 = X3 ),
c_0_129 ).
cnf(c_0_140,plain,
( ~ ssList(X1)
| nil = X1
| cons(skaf83(X1),skaf82(X1)) = X1 ),
c_0_130 ).
cnf(c_0_141,axiom,
ssItem(skaf83(X1)),
clause12 ).
cnf(c_0_142,axiom,
ssList(skaf82(X1)),
clause13 ).
cnf(c_0_143,negated_conjecture,
( sk4 = nil
| app(sk4,skaf45(sk1,tl(sk4))) = cons(hd(sk4),sk1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_133]),c_0_67])]) ).
cnf(c_0_144,plain,
( ~ duplicatefreeP(app(X1,X1))
| ~ ssList(X1)
| ~ ssList(app(X1,X1))
| ~ singletonP(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_136]),c_0_137])]) ).
cnf(c_0_145,plain,
( ~ ssItem(X3)
| ~ ssItem(X4)
| ~ ssList(X1)
| ~ ssList(X2)
| X3 != X4
| ~ frontsegP(X1,X2)
| frontsegP(cons(X3,X1),cons(X4,X2)) ),
c_0_138 ).
cnf(c_0_146,plain,
( ~ ssList(X1)
| frontsegP(X1,X1) ),
inference(fof_simplification,[status(thm)],[clause61]) ).
cnf(c_0_147,plain,
( ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1)
| ~ frontsegP(cons(X1,X3),X2)
| nil = X2
| X1 = skaf83(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_141]),c_0_142])]) ).
cnf(c_0_148,negated_conjecture,
( frontsegP(cons(hd(sk4),sk1),sk4)
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_143]),c_0_133]),c_0_67])]) ).
cnf(c_0_149,plain,
( ~ duplicatefreeP(app(X1,X1))
| ~ ssList(X1)
| ~ singletonP(X1) ),
inference(spm,[status(thm)],[c_0_144,c_0_61]) ).
cnf(c_0_150,plain,
( ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1)
| ~ frontsegP(X2,X3)
| frontsegP(cons(X1,X2),cons(X1,X3)) ),
inference(er,[status(thm)],[c_0_145]) ).
cnf(c_0_151,plain,
( ~ ssList(X1)
| frontsegP(X1,X1) ),
c_0_146 ).
cnf(c_0_152,negated_conjecture,
( sk4 = nil
| skaf83(sk4) = hd(sk4) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_148]),c_0_103]),c_0_67])]),c_0_118]) ).
cnf(c_0_153,plain,
( ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != app(X1,X3)
| X2 = X3 ),
inference(fof_simplification,[status(thm)],[clause150]) ).
cnf(c_0_154,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(fof_simplification,[status(thm)],[clause73]) ).
cnf(c_0_155,plain,
( ~ ssList(X2)
| ~ ssList(app(X2,X2))
| ~ singletonP(X2)
| ssItem(X1) ),
inference(spm,[status(thm)],[c_0_149,c_0_109]) ).
cnf(c_0_156,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| frontsegP(cons(X1,X2),cons(X1,X2)) ),
inference(spm,[status(thm)],[c_0_150,c_0_151]) ).
cnf(c_0_157,negated_conjecture,
( sk4 = nil
| cons(hd(sk4),skaf82(sk4)) = sk4 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_152]),c_0_67])]) ).
cnf(c_0_158,plain,
( ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != app(X1,X3)
| X2 = X3 ),
c_0_153 ).
cnf(c_0_159,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
c_0_154 ).
cnf(c_0_160,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(X1,X2) != X3
| rearsegP(X3,X2) ),
inference(fof_simplification,[status(thm)],[clause143]) ).
cnf(c_0_161,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| tl(app(X2,X1)) = app(tl(X2),X1)
| nil = X2 ),
inference(fof_simplification,[status(thm)],[clause133]) ).
cnf(c_0_162,plain,
( ~ ssList(X2)
| ~ singletonP(X2)
| ssItem(X1) ),
inference(spm,[status(thm)],[c_0_155,c_0_61]) ).
cnf(c_0_163,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X1 ),
inference(fof_simplification,[status(thm)],[clause118]) ).
cnf(c_0_164,negated_conjecture,
( frontsegP(sk4,sk4)
| sk4 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_157]),c_0_142])]),c_0_118]) ).
cnf(c_0_165,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| app(X2,X1) != X2
| X1 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_159]),c_0_66])]) ).
cnf(c_0_166,plain,
( ~ ssList(X1)
| app(X1,skaf45(X1,X1)) = X1 ),
inference(spm,[status(thm)],[c_0_121,c_0_151]) ).
cnf(c_0_167,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(X1,X2) != X3
| rearsegP(X3,X2) ),
c_0_160 ).
cnf(c_0_168,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,nil),X2) = cons(X1,X2) ),
inference(fof_simplification,[status(thm)],[clause120]) ).
cnf(c_0_169,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| tl(app(X2,X1)) = app(tl(X2),X1)
| nil = X2 ),
c_0_161 ).
cnf(c_0_170,plain,
( ~ ssItem(X2)
| ssItem(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_98]),c_0_117]) ).
cnf(c_0_171,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X1 ),
c_0_163 ).
cnf(c_0_172,negated_conjecture,
( sk4 = nil
| app(sk4,skaf45(sk4,sk4)) = sk4 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_164]),c_0_67])]) ).
cnf(c_0_173,plain,
( ~ ssList(X1)
| skaf45(X1,X1) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_166]),c_0_133])]) ).
cnf(c_0_174,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_175,plain,
( ~ ssList(X1)
| segmentP(X1,X1) ),
inference(fof_simplification,[status(thm)],[clause57]) ).
cnf(c_0_176,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| app(skaf46(X1,X2),X2) = X1 ),
inference(fof_simplification,[status(thm)],[clause131]) ).
cnf(c_0_177,plain,
( ~ ssList(X1)
| rearsegP(X1,X1) ),
inference(fof_simplification,[status(thm)],[clause59]) ).
cnf(c_0_178,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| rearsegP(app(X1,X2),X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_167]),c_0_61]) ).
cnf(c_0_179,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,nil),X2) = cons(X1,X2) ),
c_0_168 ).
cnf(c_0_180,plain,
( ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1)
| tl(cons(X1,app(X2,X3))) = app(tl(cons(X1,X2)),X3) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_125]),c_0_82]),c_0_85]) ).
cnf(c_0_181,plain,
ssItem(X1),
inference(spm,[status(thm)],[c_0_170,c_0_92]) ).
cnf(c_0_182,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| nil = X1
| cons(hd(app(X1,X2)),app(tl(X1),X2)) = app(X1,X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_169]),c_0_61]),c_0_171]) ).
cnf(c_0_183,negated_conjecture,
( sk4 = nil
| app(sk4,nil) = sk4 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_173]),c_0_67])]) ).
cnf(c_0_184,negated_conjecture,
( sk4 = nil
| skaf82(sk4) = tl(sk4) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_157]),c_0_142])]),c_0_118]) ).
cnf(c_0_185,negated_conjecture,
( ~ neq(sk4,nil)
| ~ segmentP(sk1,X1)
| ~ segmentP(sk2,X1)
| ~ neq(X1,nil)
| ~ ssList(X1) ),
inference(fof_simplification,[status(thm)],[co1_11]) ).
cnf(c_0_186,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ segmentP(X1,X2)
| segmentP(app(app(X4,X1),X3),X2) ),
c_0_174 ).
cnf(c_0_187,plain,
( ~ ssList(X1)
| segmentP(X1,X1) ),
c_0_175 ).
cnf(c_0_188,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| app(skaf46(X1,X2),X2) = X1 ),
c_0_176 ).
cnf(c_0_189,plain,
( ~ ssList(X1)
| rearsegP(X1,X1) ),
c_0_177 ).
cnf(c_0_190,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| rearsegP(cons(X1,X2),X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_178,c_0_179]),c_0_117]) ).
cnf(c_0_191,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| hd(app(X2,X1)) = hd(X2)
| nil = X2 ),
inference(fof_simplification,[status(thm)],[clause123]) ).
cnf(c_0_192,plain,
( ~ ssList(X2)
| ~ ssList(X3)
| tl(cons(X1,app(X2,X3))) = app(tl(cons(X1,X2)),X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_180,c_0_181])]) ).
cnf(c_0_193,negated_conjecture,
( sk4 = nil
| cons(hd(sk4),app(tl(sk4),nil)) = sk4 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_183]),c_0_67]),c_0_66])]) ).
cnf(c_0_194,negated_conjecture,
( ssList(tl(sk4))
| sk4 = nil ),
inference(spm,[status(thm)],[c_0_142,c_0_184]) ).
cnf(c_0_195,negated_conjecture,
( sk4 = nil
| app(tl(sk4),nil) = tl(sk4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_183]),c_0_67]),c_0_66])]) ).
cnf(c_0_196,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != X2 ),
inference(fof_simplification,[status(thm)],[clause99]) ).
cnf(c_0_197,negated_conjecture,
( ~ neq(sk4,nil)
| ~ segmentP(sk1,X1)
| ~ segmentP(sk2,X1)
| ~ neq(X1,nil)
| ~ ssList(X1) ),
c_0_185 ).
cnf(c_0_198,plain,
( ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| segmentP(app(app(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_186,c_0_187]) ).
cnf(c_0_199,plain,
( ~ ssList(X1)
| app(skaf46(X1,X1),X1) = X1 ),
inference(spm,[status(thm)],[c_0_188,c_0_189]) ).
cnf(c_0_200,axiom,
ssList(skaf46(X1,X2)),
clause50 ).
cnf(c_0_201,plain,
( ~ ssList(X1)
| rearsegP(X1,skaf82(X1))
| nil = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_140]),c_0_141]),c_0_142])]) ).
cnf(c_0_202,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| hd(app(X2,X1)) = hd(X2)
| nil = X2 ),
c_0_191 ).
cnf(c_0_203,negated_conjecture,
( sk4 = nil
| app(tl(cons(hd(sk4),tl(sk4))),nil) = tl(sk4) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_192,c_0_193]),c_0_66])]),c_0_194]) ).
cnf(c_0_204,negated_conjecture,
( sk4 = nil
| cons(hd(sk4),tl(sk4)) = app(sk4,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_195]),c_0_66]),c_0_67])]) ).
cnf(c_0_205,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_206,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_simplification,[status(thm)],[clause74]) ).
cnf(c_0_207,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != X2 ),
c_0_196 ).
cnf(c_0_208,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,tl(cons(X1,X2))) = cons(X1,X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_112]),c_0_82]),c_0_85]) ).
cnf(c_0_209,plain,
( ~ ssItem(X1)
| ~ ssItem(hd(cons(X1,nil)))
| tl(cons(X1,nil)) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_106]),c_0_66])]) ).
cnf(c_0_210,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(sk4,X1)
| ~ segmentP(sk1,X1)
| ~ neq(X1,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_197,c_0_56]),c_0_60])]) ).
cnf(c_0_211,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| segmentP(app(X1,X2),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_198,c_0_199]),c_0_200])]) ).
cnf(c_0_212,plain,
ssList(cons(X1,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_117,c_0_181])]) ).
cnf(c_0_213,negated_conjecture,
( rearsegP(sk4,tl(sk4))
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_184]),c_0_67])]) ).
cnf(c_0_214,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| nil = X1
| cons(hd(X1),app(tl(app(X1,X2)),X3)) = app(app(X1,X2),X3) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_202]),c_0_61]),c_0_171]) ).
cnf(c_0_215,negated_conjecture,
( sk4 = nil
| app(tl(app(sk4,nil)),nil) = tl(sk4) ),
inference(spm,[status(thm)],[c_0_203,c_0_204]) ).
cnf(c_0_216,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X3,X2),X1) = app(X3,app(X2,X1)) ),
c_0_205 ).
cnf(c_0_217,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
c_0_206 ).
cnf(c_0_218,plain,
( ~ ssList(X2)
| ~ ssList(tl(cons(X1,X2)))
| ~ ssItem(X1)
| tl(cons(X1,X2)) != cons(X1,X2) ),
inference(spm,[status(thm)],[c_0_207,c_0_208]) ).
cnf(c_0_219,plain,
( ~ ssItem(X1)
| tl(cons(X1,nil)) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_209,c_0_112]),c_0_66])]) ).
cnf(c_0_220,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(sk4,X1)
| ~ segmentP(sk1,X1)
| nil = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_210,c_0_65]),c_0_66])]) ).
cnf(c_0_221,negated_conjecture,
( segmentP(sk1,tl(sk4))
| sk4 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_211,c_0_95]),c_0_212])]),c_0_194]) ).
cnf(c_0_222,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| segmentP(app(X1,X2),X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_198,c_0_166]),c_0_133])]),c_0_61]) ).
cnf(c_0_223,negated_conjecture,
( sk4 = nil
| app(skaf46(sk4,tl(sk4)),tl(sk4)) = sk4 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_188,c_0_213]),c_0_67])]),c_0_194]) ).
cnf(c_0_224,negated_conjecture,
( sk4 = nil
| cons(hd(sk4),tl(sk4)) = app(app(sk4,nil),nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_214,c_0_215]),c_0_66]),c_0_67])]) ).
cnf(c_0_225,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_159,c_0_216]),c_0_66])]),c_0_61]) ).
cnf(c_0_226,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_216,c_0_217]),c_0_66])]) ).
cnf(c_0_227,negated_conjecture,
( ~ ssList(X1)
| segmentP(app(sk1,X1),cons(hd(sk4),nil))
| sk4 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_198,c_0_95]),c_0_212])]),c_0_194]) ).
cnf(c_0_228,plain,
( ~ ssItem(X1)
| cons(X1,nil) != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_218,c_0_219]),c_0_66])]) ).
cnf(c_0_229,negated_conjecture,
( ~ segmentP(sk4,tl(sk4))
| sk4 = nil
| tl(sk4) = nil ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_220,c_0_221]),c_0_194]) ).
cnf(c_0_230,negated_conjecture,
( segmentP(sk4,tl(sk4))
| sk4 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_222,c_0_223]),c_0_200])]),c_0_194]) ).
cnf(c_0_231,negated_conjecture,
( sk4 = nil
| app(app(sk4,nil),nil) = sk4 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_224]),c_0_67])]) ).
cnf(c_0_232,plain,
( ~ ssList(X1)
| app(X1,nil) = app(nil,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_225,c_0_226]),c_0_66])]) ).
cnf(c_0_233,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ neq(X1,X2)
| X1 != X2 ),
inference(fof_simplification,[status(thm)],[clause117]) ).
cnf(c_0_234,negated_conjecture,
( segmentP(sk1,cons(hd(sk4),nil))
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_227,c_0_166]),c_0_133]),c_0_103])]) ).
cnf(c_0_235,plain,
cons(X1,nil) != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_228,c_0_181])]) ).
cnf(c_0_236,negated_conjecture,
( sk4 = nil
| tl(sk4) = nil ),
inference(spm,[status(thm)],[c_0_229,c_0_230]) ).
cnf(c_0_237,negated_conjecture,
( sk4 = nil
| app(app(nil,sk4),nil) = sk4 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_231,c_0_232]),c_0_67])]) ).
cnf(c_0_238,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ neq(X1,X2)
| X1 != X2 ),
c_0_233 ).
cnf(c_0_239,negated_conjecture,
( ~ segmentP(sk4,cons(hd(sk4),nil))
| sk4 = nil ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_220,c_0_234]),c_0_212])]),c_0_235]) ).
cnf(c_0_240,negated_conjecture,
( sk4 = nil
| cons(hd(sk4),nil) = sk4 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_236]),c_0_67])]) ).
cnf(c_0_241,negated_conjecture,
( segmentP(sk4,sk4)
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_198,c_0_237]),c_0_66]),c_0_67])]) ).
cnf(c_0_242,plain,
( ~ ssItem(X1)
| ~ neq(X1,X1) ),
inference(er,[status(thm)],[c_0_238]) ).
cnf(c_0_243,negated_conjecture,
sk4 = nil,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_239,c_0_240]),c_0_241]) ).
cnf(c_0_244,plain,
~ neq(X1,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_242,c_0_181])]) ).
cnf(c_0_245,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_243]),c_0_244]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC087-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.50 % Computer : n018.cluster.edu
% 0.11/0.50 % Model : x86_64 x86_64
% 0.11/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.50 % Memory : 8046.5625MB
% 0.11/0.50 % OS : Linux 6.8.0-71-generic
% 0.11/0.50 % CPULimit : 300
% 0.11/0.50 % WCLimit : 300
% 0.11/0.50 % DateTime : Mon Sep 21 07:56:28 UTC 2026
% 0.11/0.50 % CPUTime :
% 0.11/0.50 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.55 Running first-order theorem proving
% 0.11/0.55 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
% 279.14/38.61 % Version: 3.5.1
% 279.14/38.61 % Preprocessing class: FSLSSMSSSSSNFFN.
% 279.14/38.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 279.14/38.61 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 279.14/38.61 % Starting new_bool_3 with 300s (1) cores
% 279.14/38.61 % Starting new_bool_1 with 300s (1) cores
% 279.14/38.61 % Starting sh5l with 300s (1) cores
% 279.14/38.61 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1388557 completed with status 0
% 279.14/38.61 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 279.14/38.61 % Preprocessing class: FSLSSMSSSSSNFFN.
% 279.14/38.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 279.14/38.61 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 279.14/38.61 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 279.14/38.61 % No SInE strategy applied
% 279.14/38.61 % Search class: FGHSM-FSLM21-MFFFFFNN
% 279.14/38.61 % Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 279.14/38.61 % Starting SubtermCWHack with 136s (1) cores
% 279.14/38.61 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 279.14/38.61 % Starting G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y with 136s (1) cores
% 279.14/38.62 % Starting G-E--_200_B02_F1_SE_CS_SP_PI_S2k with 136s (1) cores
% 279.14/38.62 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 279.14/38.62 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1388564 completed with status 0
% 279.14/38.62 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 279.14/38.62 % Preprocessing class: FSLSSMSSSSSNFFN.
% 279.14/38.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 279.14/38.62 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 279.14/38.62 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 279.14/38.62 % No SInE strategy applied
% 279.14/38.62 % Search class: FGHSM-FSLM21-MFFFFFNN
% 279.14/38.62 % Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 279.14/38.62 % Starting SubtermCWHack with 136s (1) cores
% 279.14/38.62 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 279.14/38.62 % Preprocessing time : 0.002 s
% 279.14/38.62 % Presaturation interreduction done
% 279.14/38.62
% 279.14/38.62 % Proof found!
% 279.14/38.62 % SZS status Unsatisfiable
% 279.14/38.62 % SZS output start CNFRefutation
% See solution above
% 279.14/38.62 % Parsed axioms : 197
% 279.14/38.62 % Removed by relevancy pruning/SinE : 0
% 279.14/38.62 % Initial clauses : 197
% 279.14/38.62 % Removed in clause preprocessing : 0
% 279.14/38.62 % Initial clauses in saturation : 197
% 279.14/38.62 % Processed clauses : 43218
% 279.14/38.62 % ...of these trivial : 56
% 279.14/38.62 % ...subsumed : 36131
% 279.14/38.62 % ...remaining for further processing : 7031
% 279.14/38.62 % Other redundant clauses eliminated : 2233
% 279.14/38.62 % Clauses deleted for lack of memory : 0
% 279.14/38.62 % Backward-subsumed : 1073
% 279.14/38.62 % Backward-rewritten : 3217
% 279.14/38.62 % Generated clauses : 630182
% 279.14/38.62 % ...of the previous two non-redundant : 616011
% 279.14/38.62 % ...aggressively subsumed : 0
% 279.14/38.62 % Contextual simplify-reflections : 2597
% 279.14/38.62 % Paramodulations : 627886
% 279.14/38.62 % Factorizations : 2
% 279.14/38.62 % NegExts : 0
% 279.14/38.62 % Equation resolutions : 2298
% 279.14/38.62 % Disequality decompositions : 0
% 279.14/38.62 % Total rewrite steps : 547425
% 279.14/38.62 % ...of those cached : 543800
% 279.14/38.62 % Propositional unsat checks : 1
% 279.14/38.62 % Propositional check models : 0
% 279.14/38.62 % Propositional check unsatisfiable : 0
% 279.14/38.62 % Propositional clauses : 0
% 279.14/38.62 % Propositional clauses after purity: 0
% 279.14/38.62 % Propositional unsat core size : 0
% 279.14/38.62 % Propositional preprocessing time : 0.000
% 279.14/38.62 % Propositional encoding time : 1.545
% 279.14/38.62 % Propositional solver time : 0.820
% 279.14/38.62 % Success case prop preproc time : 0.000
% 279.14/38.62 % Success case prop encoding time : 0.000
% 279.14/38.62 % Success case prop solver time : 0.000
% 279.14/38.62 % Current number of processed clauses : 2531
% 279.14/38.62 % Positive orientable unit clauses : 72
% 279.14/38.62 % Positive unorientable unit clauses: 0
% 279.14/38.62 % Negative unit clauses : 53
% 279.14/38.62 % Non-unit-clauses : 2406
% 279.14/38.62 % Current number of unprocessed clauses: 553030
% 279.14/38.62 % ...number of literals in the above : 3456440
% 279.14/38.62 % Current number of archived formulas : 0
% 279.14/38.62 % Current number of archived clauses : 4476
% 279.14/38.62 % Clause-clause subsumption calls (NU) : 6766991
% 279.14/38.62 % Rec. Clause-clause subsumption calls : 3002166
% 279.14/38.62 % Non-unit clause-clause subsumptions : 33129
% 279.14/38.62 % Unit Clause-clause subsumption calls : 6706
% 279.14/38.62 % Rewrite failures with RHS unbound : 0
% 279.14/38.62 % BW rewrite match attempts : 100
% 279.14/38.62 % BW rewrite match successes : 74
% 279.14/38.62 % Condensation attempts : 0
% 279.14/38.62 % Condensation successes : 0
% 279.14/38.62 % Termbank termtop insertions : 21657397
% 279.14/38.62 % Search garbage collected termcells : 575
% 279.14/38.62
% 279.14/38.62 % -------------------------------------------------
% 279.14/38.62 % User time : 30.827 s
% 279.14/38.62 % System time : 0.821 s
% 279.14/38.62 % Total time : 31.648 s
% 279.14/38.62 % Maximum resident set size: 3816 pages
% 279.14/38.62
% 279.14/38.62 % -------------------------------------------------
% 279.14/38.62 % User time : 169.352 s
% 279.14/38.62 % System time : 5.524 s
% 279.14/38.62 % Total time : 174.876 s
% 279.14/38.62 % Maximum resident set size: 4864 pages
% 279.14/38.62 % E exiting
%------------------------------------------------------------------------------