%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC126-1 : 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 02:43:07 PM UTC 2026
% Result : Unsatisfiable 170.20s 25.76s
% Output : CNFRefutation 170.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 35
% Syntax : Number of formulae : 143 ( 36 unt; 0 def)
% Number of atoms : 398 ( 95 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 510 ( 255 ~; 253 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 3 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 199 ( 15 sgn 2 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(co1_14,negated_conjecture,
( ~ neq(sk4,nil)
| cons(sk5,nil) = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
cnf(co1_7,negated_conjecture,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
cnf(co1_13,negated_conjecture,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
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(co1_6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
cnf(co1_5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
cnf(clause96,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| tl(cons(X1,X2)) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause96) ).
cnf(clause98,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause98) ).
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(clause8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
cnf(co1_1,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).
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(clause85,axiom,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause85) ).
cnf(clause104,axiom,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause104) ).
cnf(clause97,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| hd(cons(X1,X2)) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause97) ).
cnf(clause86,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause86) ).
cnf(clause145,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| nil != X2
| nil != X1
| app(X1,X2) = nil ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause145) ).
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(clause74,axiom,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause74) ).
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(clause101,axiom,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(skaf44(X1),nil) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause101) ).
cnf(clause116,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,nil) != X2
| singletonP(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause116) ).
cnf(clause47,axiom,
ssItem(skaf44(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause47) ).
cnf(clause72,axiom,
( ~ ssList(X1)
| ssItem(X2)
| duplicatefreeP(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause72) ).
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(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(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(co1_16,negated_conjecture,
( ~ neq(sk4,nil)
| ~ segmentP(sk2,sk1)
| ~ neq(sk1,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_16) ).
cnf(clause53,axiom,
ssList(skaf42(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause53) ).
cnf(clause52,axiom,
ssList(skaf43(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause52) ).
cnf(co1_15,negated_conjecture,
( ~ neq(sk4,nil)
| memberP(sk4,sk5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
cnf(clause102,axiom,
( ~ ssItem(X2)
| ~ ssItem(X1)
| X2 = X1
| neq(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause102) ).
cnf(co1_2,negated_conjecture,
ssList(sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_2) ).
cnf(c_0_33,negated_conjecture,
( ~ neq(sk4,nil)
| cons(sk5,nil) = sk3 ),
inference(fof_simplification,[status(thm)],[co1_14]) ).
cnf(c_0_34,negated_conjecture,
neq(sk2,nil),
inference(fof_simplification,[status(thm)],[co1_7]) ).
cnf(c_0_35,negated_conjecture,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
inference(fof_simplification,[status(thm)],[co1_13]) ).
cnf(c_0_36,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,nil),X2) = cons(X1,X2) ),
inference(fof_simplification,[status(thm)],[clause120]) ).
cnf(c_0_37,negated_conjecture,
( ~ neq(sk4,nil)
| cons(sk5,nil) = sk3 ),
c_0_33 ).
cnf(c_0_38,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_39,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_40,negated_conjecture,
neq(sk2,nil),
c_0_34 ).
cnf(c_0_41,negated_conjecture,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
c_0_35 ).
cnf(c_0_42,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| tl(cons(X1,X2)) = X2 ),
inference(fof_simplification,[status(thm)],[clause96]) ).
cnf(c_0_43,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
inference(fof_simplification,[status(thm)],[clause98]) ).
cnf(c_0_44,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| tl(app(X2,X1)) = app(tl(X2),X1)
| nil = X2 ),
inference(fof_simplification,[status(thm)],[clause133]) ).
cnf(c_0_45,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,nil),X2) = cons(X1,X2) ),
c_0_36 ).
cnf(c_0_46,negated_conjecture,
cons(sk5,nil) = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38]),c_0_39]),c_0_40])]) ).
cnf(c_0_47,negated_conjecture,
ssItem(sk5),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_39]),c_0_40])]) ).
cnf(c_0_48,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| tl(cons(X1,X2)) = X2 ),
c_0_42 ).
cnf(c_0_49,axiom,
ssList(nil),
clause8 ).
cnf(c_0_50,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
c_0_43 ).
cnf(c_0_51,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| tl(app(X2,X1)) = app(tl(X2),X1)
| nil = X2 ),
c_0_44 ).
cnf(c_0_52,negated_conjecture,
( ~ ssList(X1)
| app(sk1,X1) = cons(sk5,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47])]) ).
cnf(c_0_53,negated_conjecture,
tl(sk1) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_46]),c_0_47]),c_0_49])]) ).
cnf(c_0_54,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_55,negated_conjecture,
sk1 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_46]),c_0_47]),c_0_49])]) ).
cnf(c_0_56,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_57,negated_conjecture,
( ~ ssList(X1)
| tl(cons(sk5,X1)) = app(nil,X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]),c_0_54])]),c_0_55]) ).
cnf(c_0_58,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,app(X2,X3)) = app(cons(X1,X2),X3) ),
c_0_56 ).
cnf(c_0_59,negated_conjecture,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_46]),c_0_53]),c_0_49])]) ).
cnf(c_0_60,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
inference(fof_simplification,[status(thm)],[clause85]) ).
cnf(c_0_61,negated_conjecture,
( ~ ssItem(X1)
| app(cons(X1,nil),nil) = cons(X1,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_49])]) ).
cnf(c_0_62,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
c_0_60 ).
cnf(c_0_63,negated_conjecture,
app(sk1,nil) = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_46]),c_0_47])]) ).
cnf(c_0_64,plain,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
inference(fof_simplification,[status(thm)],[clause104]) ).
cnf(c_0_65,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| hd(cons(X1,X2)) = X1 ),
inference(fof_simplification,[status(thm)],[clause97]) ).
cnf(c_0_66,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
inference(fof_simplification,[status(thm)],[clause86]) ).
cnf(c_0_67,plain,
( ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1)
| tl(app(cons(X1,X2),X3)) = app(X2,X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_58]),c_0_62]) ).
cnf(c_0_68,negated_conjecture,
( ~ ssItem(X1)
| app(cons(X1,sk1),nil) = cons(X1,sk1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_63]),c_0_49]),c_0_54])]) ).
cnf(c_0_69,plain,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
c_0_64 ).
cnf(c_0_70,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| hd(cons(X1,X2)) = X1 ),
c_0_65 ).
cnf(c_0_71,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
c_0_66 ).
cnf(c_0_72,negated_conjecture,
( ~ ssItem(X1)
| tl(cons(X1,sk1)) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_63]),c_0_49]),c_0_54])]) ).
cnf(c_0_73,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_69,c_0_70]),c_0_71]),c_0_50]) ).
cnf(c_0_74,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| nil != X2
| nil != X1
| app(X1,X2) = nil ),
inference(fof_simplification,[status(thm)],[clause145]) ).
cnf(c_0_75,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_76,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_simplification,[status(thm)],[clause74]) ).
cnf(c_0_77,negated_conjecture,
app(nil,sk1) = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_72]),c_0_54]),c_0_47])]) ).
cnf(c_0_78,negated_conjecture,
( ~ ssList(X1)
| cons(sk5,app(nil,X1)) = cons(sk5,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_57]),c_0_47])]) ).
cnf(c_0_79,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| nil != X2
| nil != X1
| app(X1,X2) = nil ),
c_0_74 ).
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 ),
inference(fof_simplification,[status(thm)],[clause179]) ).
cnf(c_0_81,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X3,X2),X1) = app(X3,app(X2,X1)) ),
c_0_75 ).
cnf(c_0_82,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
c_0_76 ).
cnf(c_0_83,negated_conjecture,
( ~ ssItem(X1)
| app(cons(X1,nil),sk1) = cons(X1,sk1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_77]),c_0_54]),c_0_49])]) ).
cnf(c_0_84,negated_conjecture,
( ~ ssList(X1)
| nil != X1
| cons(sk5,X1) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_46]),c_0_49])]) ).
cnf(c_0_85,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(skaf44(X1),nil) = X1 ),
inference(fof_simplification,[status(thm)],[clause101]) ).
cnf(c_0_86,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,nil) != X2
| singletonP(X2) ),
inference(fof_simplification,[status(thm)],[clause116]) ).
cnf(c_0_87,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_80 ).
cnf(c_0_88,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_81,c_0_82]),c_0_49])]) ).
cnf(c_0_89,negated_conjecture,
app(sk1,sk1) = cons(sk5,sk1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_47]),c_0_49])]) ).
cnf(c_0_90,plain,
( ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1)
| ssList(app(cons(X1,X2),X3)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_58]),c_0_62]) ).
cnf(c_0_91,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(skaf44(X1),nil) = X1 ),
c_0_85 ).
cnf(c_0_92,axiom,
ssItem(skaf44(X1)),
clause47 ).
cnf(c_0_93,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,nil) != X2
| singletonP(X2) ),
c_0_86 ).
cnf(c_0_94,negated_conjecture,
( ~ duplicatefreeP(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X1,cons(sk5,X2)),sk1) != X3 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_46]),c_0_47]),c_0_49])]) ).
cnf(c_0_95,negated_conjecture,
app(nil,cons(sk5,sk1)) = cons(sk5,sk1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_54])]) ).
fof(c_0_96,plain,
( ~ epred2_0
<=> ! [X1] :
( ~ ssList(X1)
| duplicatefreeP(X1) ) ),
introduced(definition) ).
cnf(c_0_97,negated_conjecture,
( ~ ssItem(X1)
| ssList(cons(X1,sk1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_68]),c_0_49]),c_0_54])]) ).
cnf(c_0_98,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ singletonP(X1)
| cons(skaf44(X1),X2) = app(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_91]),c_0_92])]) ).
cnf(c_0_99,plain,
( ~ ssList(cons(X1,nil))
| ~ ssItem(X1)
| singletonP(cons(X1,nil)) ),
inference(er,[status(thm)],[c_0_93]) ).
cnf(c_0_100,negated_conjecture,
( ~ duplicatefreeP(X1)
| ~ ssList(X1)
| app(cons(sk5,sk1),sk1) != X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_54]),c_0_49])]) ).
cnf(c_0_101,plain,
( ~ ssList(X1)
| duplicatefreeP(X1)
| epred2_0 ),
inference(split_equiv,[status(thm)],[c_0_96]) ).
cnf(c_0_102,negated_conjecture,
( ~ ssList(X1)
| ~ singletonP(X1)
| ssList(app(X1,sk1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_92]),c_0_54])]) ).
cnf(c_0_103,negated_conjecture,
singletonP(sk1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_46]),c_0_47]),c_0_54])]) ).
cnf(c_0_104,plain,
( ~ ssList(X1)
| ssItem(X2)
| duplicatefreeP(X1) ),
inference(fof_simplification,[status(thm)],[clause72]) ).
cnf(c_0_105,negated_conjecture,
( ~ ssList(X1)
| app(cons(sk5,sk1),sk1) != X1
| epred2_0 ),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_106,negated_conjecture,
ssList(app(sk1,sk1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_54])]) ).
fof(c_0_107,plain,
( ~ epred1_0
<=> ! [X2] : ssItem(X2) ),
introduced(definition) ).
cnf(c_0_108,plain,
( ~ ssList(X1)
| ssItem(X2)
| duplicatefreeP(X1) ),
c_0_104 ).
cnf(c_0_109,negated_conjecture,
( ~ ssList(app(cons(sk5,sk1),sk1))
| epred2_0 ),
inference(er,[status(thm)],[c_0_105]) ).
cnf(c_0_110,negated_conjecture,
ssList(cons(sk5,sk1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_52]),c_0_54])]) ).
cnf(c_0_111,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_112,plain,
( ~ epred1_0
| ~ epred2_0 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_108,c_0_107]),c_0_96]) ).
cnf(c_0_113,negated_conjecture,
epred2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_62]),c_0_110]),c_0_54])]) ).
cnf(c_0_114,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ segmentP(X1,X2)
| segmentP(app(app(X4,X1),X3),X2) ),
c_0_111 ).
cnf(c_0_115,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_116,plain,
( ssItem(X1)
| epred1_0 ),
inference(split_equiv,[status(thm)],[c_0_107]) ).
cnf(c_0_117,plain,
~ epred1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_112,c_0_113])]) ).
cnf(c_0_118,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_119,plain,
( ~ ssList(X2)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ segmentP(X2,X4)
| segmentP(app(X1,app(X2,X3)),X4) ),
inference(spm,[status(thm)],[c_0_114,c_0_81]) ).
cnf(c_0_120,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| ~ memberP(X1,X2)
| app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1 ),
c_0_115 ).
cnf(c_0_121,plain,
ssItem(X1),
inference(sr,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_122,plain,
( ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| app(app(X1,X2),X3) != X4
| segmentP(X4,X2) ),
c_0_118 ).
cnf(c_0_123,negated_conjecture,
( ~ neq(sk4,nil)
| ~ segmentP(sk2,sk1)
| ~ neq(sk1,nil) ),
inference(fof_simplification,[status(thm)],[co1_16]) ).
cnf(c_0_124,negated_conjecture,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ segmentP(sk1,X3)
| segmentP(app(X1,cons(sk5,X2)),X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_52]),c_0_54])]) ).
cnf(c_0_125,plain,
( ~ ssList(X1)
| ~ memberP(X1,X2)
| app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_120,c_0_121])]) ).
cnf(c_0_126,axiom,
ssList(skaf42(X1,X2)),
clause53 ).
cnf(c_0_127,axiom,
ssList(skaf43(X1,X2)),
clause52 ).
cnf(c_0_128,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_122,c_0_82]),c_0_49])]) ).
cnf(c_0_129,negated_conjecture,
( ~ neq(sk4,nil)
| memberP(sk4,sk5) ),
inference(fof_simplification,[status(thm)],[co1_15]) ).
cnf(c_0_130,negated_conjecture,
( ~ neq(sk4,nil)
| ~ segmentP(sk2,sk1)
| ~ neq(sk1,nil) ),
c_0_123 ).
cnf(c_0_131,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(sk1,X2)
| ~ memberP(X1,sk5)
| segmentP(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_126]),c_0_127])]) ).
cnf(c_0_132,negated_conjecture,
( ~ ssList(X1)
| sk1 != X1
| segmentP(X1,sk1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_63]),c_0_49]),c_0_54])]) ).
cnf(c_0_133,negated_conjecture,
( ~ neq(sk4,nil)
| memberP(sk4,sk5) ),
c_0_129 ).
cnf(c_0_134,plain,
( ~ ssItem(X2)
| ~ ssItem(X1)
| X2 = X1
| neq(X2,X1) ),
inference(fof_simplification,[status(thm)],[clause102]) ).
cnf(c_0_135,negated_conjecture,
( ~ segmentP(sk2,sk1)
| ~ neq(sk1,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_130,c_0_39]),c_0_40])]) ).
cnf(c_0_136,negated_conjecture,
( ~ ssList(X1)
| ~ memberP(X1,sk5)
| segmentP(X1,sk1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_54])]) ).
cnf(c_0_137,negated_conjecture,
memberP(sk2,sk5),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_133,c_0_39]),c_0_39]),c_0_40])]) ).
cnf(c_0_138,negated_conjecture,
ssList(sk2),
co1_2 ).
cnf(c_0_139,plain,
( ~ ssItem(X2)
| ~ ssItem(X1)
| X2 = X1
| neq(X2,X1) ),
c_0_134 ).
cnf(c_0_140,negated_conjecture,
~ neq(sk1,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_137]),c_0_138])]) ).
cnf(c_0_141,plain,
( neq(X2,X1)
| X1 = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_139,c_0_121]),c_0_121])]) ).
cnf(c_0_142,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_55]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC126-1 : 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 07:52:56 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 170.20/25.76 % Version: 3.5.1
% 170.20/25.76 % Preprocessing class: FSLSSMSMSSSNFFN.
% 170.20/25.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 170.20/25.76 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 170.20/25.76 % Starting new_bool_3 with 300s (1) cores
% 170.20/25.76 % Starting new_bool_1 with 300s (1) cores
% 170.20/25.76 % Starting sh5l with 300s (1) cores
% 170.20/25.76 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 1831634 completed with status 0
% 170.20/25.76 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 170.20/25.76 % Preprocessing class: FSLSSMSMSSSNFFN.
% 170.20/25.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 170.20/25.76 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 170.20/25.76 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 170.20/25.76 % No SInE strategy applied
% 170.20/25.76 % Search class: FGHSM-FSLM21-MFFFFFNN
% 170.20/25.76 % Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 170.20/25.76 % Starting SubtermCWHack with 136s (1) cores
% 170.20/25.76 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 170.20/25.76 % Starting G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y with 136s (1) cores
% 170.20/25.76 % Starting G-E--_200_B02_F1_SE_CS_SP_PI_S2k with 136s (1) cores
% 170.20/25.76 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 170.20/25.76 % G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y with pid 1831642 completed with status 0
% 170.20/25.76 % Result found by G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y
% 170.20/25.76 % Preprocessing class: FSLSSMSMSSSNFFN.
% 170.20/25.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 170.20/25.76 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 170.20/25.76 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 170.20/25.76 % No SInE strategy applied
% 170.20/25.76 % Search class: FGHSM-FSLM21-MFFFFFNN
% 170.20/25.76 % Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 170.20/25.76 % Starting SubtermCWHack with 136s (1) cores
% 170.20/25.76 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 170.20/25.76 % Starting G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y with 136s (1) cores
% 170.20/25.76 % Preprocessing time : 0.005 s
% 170.20/25.76 % Presaturation interreduction done
% 170.20/25.76
% 170.20/25.76 % Proof found!
% 170.20/25.76 % SZS status Unsatisfiable
% 170.20/25.76 % SZS output start CNFRefutation
% See solution above
% 170.20/25.76 % Parsed axioms : 201
% 170.20/25.76 % Removed by relevancy pruning/SinE : 0
% 170.20/25.76 % Initial clauses : 201
% 170.20/25.76 % Removed in clause preprocessing : 0
% 170.20/25.76 % Initial clauses in saturation : 201
% 170.20/25.76 % Processed clauses : 27974
% 170.20/25.76 % ...of these trivial : 610
% 170.20/25.76 % ...subsumed : 22310
% 170.20/25.76 % ...remaining for further processing : 5054
% 170.20/25.76 % Other redundant clauses eliminated : 7817
% 170.20/25.76 % Clauses deleted for lack of memory : 0
% 170.20/25.76 % Backward-subsumed : 461
% 170.20/25.76 % Backward-rewritten : 437
% 170.20/25.76 % Generated clauses : 751422
% 170.20/25.76 % ...of the previous two non-redundant : 716505
% 170.20/25.76 % ...aggressively subsumed : 0
% 170.20/25.76 % Contextual simplify-reflections : 1343
% 170.20/25.76 % Paramodulations : 743031
% 170.20/25.76 % Factorizations : 0
% 170.20/25.76 % NegExts : 0
% 170.20/25.76 % Equation resolutions : 8232
% 170.20/25.76 % Disequality decompositions : 0
% 170.20/25.76 % Total rewrite steps : 520740
% 170.20/25.76 % ...of those cached : 512245
% 170.20/25.76 % Propositional unsat checks : 0
% 170.20/25.76 % Propositional check models : 0
% 170.20/25.76 % Propositional check unsatisfiable : 0
% 170.20/25.76 % Propositional clauses : 0
% 170.20/25.76 % Propositional clauses after purity: 0
% 170.20/25.76 % Propositional unsat core size : 0
% 170.20/25.76 % Propositional preprocessing time : 0.000
% 170.20/25.76 % Propositional encoding time : 0.000
% 170.20/25.76 % Propositional solver time : 0.000
% 170.20/25.76 % Success case prop preproc time : 0.000
% 170.20/25.76 % Success case prop encoding time : 0.000
% 170.20/25.76 % Success case prop solver time : 0.000
% 170.20/25.76 % Current number of processed clauses : 3883
% 170.20/25.76 % Positive orientable unit clauses : 253
% 170.20/25.76 % Positive unorientable unit clauses: 0
% 170.20/25.76 % Negative unit clauses : 205
% 170.20/25.76 % Non-unit-clauses : 3425
% 170.20/25.76 % Current number of unprocessed clauses: 682118
% 170.20/25.76 % ...number of literals in the above : 6256312
% 170.20/25.76 % Current number of archived formulas : 0
% 170.20/25.76 % Current number of archived clauses : 1091
% 170.20/25.76 % Clause-clause subsumption calls (NU) : 3445138
% 170.20/25.76 % Rec. Clause-clause subsumption calls : 369518
% 170.20/25.76 % Non-unit clause-clause subsumptions : 12791
% 170.20/25.76 % Unit Clause-clause subsumption calls : 172081
% 170.20/25.76 % Rewrite failures with RHS unbound : 0
% 170.20/25.76 % BW rewrite match attempts : 253
% 170.20/25.76 % BW rewrite match successes : 94
% 170.20/25.76 % Condensation attempts : 0
% 170.20/25.76 % Condensation successes : 0
% 170.20/25.76 % Termbank termtop insertions : 21262899
% 170.20/25.76 % Search garbage collected termcells : 541
% 170.20/25.76
% 170.20/25.76 % -------------------------------------------------
% 170.20/25.76 % User time : 23.620 s
% 170.20/25.76 % System time : 0.730 s
% 170.20/25.76 % Total time : 24.349 s
% 170.20/25.76 % Maximum resident set size: 4068 pages
% 170.20/25.76
% 170.20/25.76 % -------------------------------------------------
% 170.20/25.76 % User time : 117.190 s
% 170.20/25.76 % System time : 3.933 s
% 170.20/25.76 % Total time : 121.122 s
% 170.20/25.76 % Maximum resident set size: 4864 pages
% 170.20/25.76 % E exiting
%------------------------------------------------------------------------------