%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SWC073-1 : 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 : n011.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 02:44:48 PM UTC 2026
% Result : Unsatisfiable 0.16s 33.66s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 24
% Syntax : Number of clauses : 125 ( 27 unt; 28 nHn; 125 RR)
% Number of literals : 369 ( 126 equ; 230 neg)
% Maximal clause size : 12 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 136 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(co1_9,negated_conjecture,
( nil != sk1
| nil != sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
cnf(co1_8,negated_conjecture,
( nil != sk4
| nil = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
cnf(co1_6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
cnf(co1_5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
cnf(clause173,axiom,
( ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| app(app(X1,X2),X3) != X4
| segmentP(X4,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause173) ).
cnf(clause96,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| tl(cons(X1,X2)) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause96) ).
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(clause85,axiom,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause85) ).
cnf(clause73,axiom,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause73) ).
cnf(clause98,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause98) ).
cnf(clause104,axiom,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause104) ).
cnf(co1_2,negated_conjecture,
ssList(sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_2) ).
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(co1_1,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
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(clause8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
cnf(clause100,axiom,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause100) ).
cnf(co1_11,negated_conjecture,
( ~ neq(nil,sk3)
| ~ neq(nil,sk3)
| hd(sk3) != X4
| cons(X4,nil) != X3
| ~ ssItem(X4)
| app(X2,X3) != X1
| tl(sk3) != X2
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ neq(sk4,nil)
| sk4 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
cnf(co1_7,negated_conjecture,
( ~ segmentP(sk1,X1)
| ~ segmentP(sk2,X1)
| ~ neq(X1,nil)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
cnf(clause86,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).
cnf(clause74,axiom,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause74) ).
cnf(clause145,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| nil != X2
| nil != X1
| app(X1,X2) = nil ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause145) ).
cnf(co1_10,negated_conjecture,
( ~ neq(sk4,nil)
| neq(sk3,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
cnf(c_0_24,negated_conjecture,
( nil != sk1
| nil != sk2 ),
inference(fof_simplification,[status(thm)],[co1_9]) ).
cnf(c_0_25,negated_conjecture,
( nil != sk4
| nil = sk3 ),
inference(fof_simplification,[status(thm)],[co1_8]) ).
cnf(c_0_26,negated_conjecture,
( nil != sk1
| nil != sk2 ),
c_0_24 ).
cnf(c_0_27,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_28,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_29,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_30,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| tl(cons(X1,X2)) = X2 ),
inference(fof_simplification,[status(thm)],[clause96]) ).
cnf(c_0_31,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_32,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
inference(fof_simplification,[status(thm)],[clause85]) ).
cnf(c_0_33,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(fof_simplification,[status(thm)],[clause73]) ).
cnf(c_0_34,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
inference(fof_simplification,[status(thm)],[clause98]) ).
cnf(c_0_35,plain,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
inference(fof_simplification,[status(thm)],[clause104]) ).
cnf(c_0_36,negated_conjecture,
ssList(sk2),
co1_2 ).
cnf(c_0_37,negated_conjecture,
( nil != sk4
| nil = sk3 ),
c_0_25 ).
cnf(c_0_38,negated_conjecture,
( sk4 != nil
| sk3 != nil ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
cnf(c_0_39,plain,
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
inference(fof_simplification,[status(thm)],[clause76]) ).
cnf(c_0_40,plain,
( ~ ssList(X1)
| nil = X1
| ssList(tl(X1)) ),
inference(fof_simplification,[status(thm)],[clause75]) ).
cnf(c_0_41,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_42,plain,
( ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| app(app(X1,X2),X3) != X4
| segmentP(X4,X2) ),
c_0_29 ).
cnf(c_0_43,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| tl(cons(X1,X2)) = X2 ),
c_0_30 ).
cnf(c_0_44,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,app(X2,X3)) = app(cons(X1,X2),X3) ),
c_0_31 ).
cnf(c_0_45,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
c_0_32 ).
cnf(c_0_46,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,nil),X2) = cons(X1,X2) ),
inference(fof_simplification,[status(thm)],[clause120]) ).
cnf(c_0_47,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
c_0_33 ).
cnf(c_0_48,axiom,
ssList(nil),
clause8 ).
cnf(c_0_49,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
c_0_34 ).
cnf(c_0_50,plain,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
c_0_35 ).
cnf(c_0_51,negated_conjecture,
ssList(sk4),
inference(rw,[status(thm)],[c_0_36,c_0_28]) ).
cnf(c_0_52,negated_conjecture,
sk4 != nil,
inference(csr,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_53,plain,
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
c_0_39 ).
cnf(c_0_54,plain,
( ~ ssList(X1)
| nil = X1
| ssList(tl(X1)) ),
c_0_40 ).
cnf(c_0_55,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
inference(fof_simplification,[status(thm)],[clause100]) ).
cnf(c_0_56,negated_conjecture,
ssList(sk3),
inference(rw,[status(thm)],[c_0_41,c_0_27]) ).
cnf(c_0_57,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(app(app(X1,X2),X3))
| segmentP(app(app(X1,X2),X3),X2) ),
inference(er,[status(thm)],[c_0_42]) ).
cnf(c_0_58,negated_conjecture,
( ~ neq(nil,sk3)
| ~ neq(nil,sk3)
| hd(sk3) != X4
| cons(X4,nil) != X3
| ~ ssItem(X4)
| app(X2,X3) != X1
| tl(sk3) != X2
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ neq(sk4,nil)
| sk4 = X1 ),
inference(fof_simplification,[status(thm)],[co1_11]) ).
cnf(c_0_59,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_43,c_0_44]),c_0_45]) ).
cnf(c_0_60,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,nil),X2) = cons(X1,X2) ),
c_0_46 ).
cnf(c_0_61,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,X2),nil) = cons(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_47]),c_0_48])]) ).
cnf(c_0_62,plain,
( ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1)
| app(cons(X1,X2),X3) != nil ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_44]),c_0_45]) ).
cnf(c_0_63,negated_conjecture,
cons(hd(sk4),tl(sk4)) = sk4,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]) ).
cnf(c_0_64,negated_conjecture,
ssItem(hd(sk4)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_51]),c_0_52]) ).
cnf(c_0_65,negated_conjecture,
ssList(tl(sk4)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_51]),c_0_52]) ).
cnf(c_0_66,negated_conjecture,
( ~ segmentP(sk1,X1)
| ~ segmentP(sk2,X1)
| ~ neq(X1,nil)
| ~ ssList(X1) ),
inference(fof_simplification,[status(thm)],[co1_7]) ).
cnf(c_0_67,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
c_0_55 ).
cnf(c_0_68,negated_conjecture,
( ssList(tl(sk3))
| sk3 = nil ),
inference(spm,[status(thm)],[c_0_54,c_0_56]) ).
cnf(c_0_69,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| segmentP(app(X1,X2),X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_47]),c_0_48])]),c_0_45]) ).
cnf(c_0_70,negated_conjecture,
( ~ neq(nil,sk3)
| ~ neq(nil,sk3)
| hd(sk3) != X4
| cons(X4,nil) != X3
| ~ ssItem(X4)
| app(X2,X3) != X1
| tl(sk3) != X2
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ neq(sk4,nil)
| sk4 = X1 ),
c_0_58 ).
cnf(c_0_71,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| tl(cons(X1,X2)) = app(nil,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_48])]) ).
cnf(c_0_72,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| tl(cons(X1,X2)) = app(X2,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_61]),c_0_48])]) ).
cnf(c_0_73,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssItem(hd(app(X1,X2)))
| app(X1,X2) = nil ),
inference(spm,[status(thm)],[c_0_53,c_0_45]) ).
cnf(c_0_74,negated_conjecture,
( ~ ssList(X1)
| app(sk4,X1) != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]),c_0_65])]) ).
cnf(c_0_75,negated_conjecture,
( ~ segmentP(sk1,X1)
| ~ segmentP(sk2,X1)
| ~ neq(X1,nil)
| ~ ssList(X1) ),
c_0_66 ).
cnf(c_0_76,negated_conjecture,
( ~ ssList(X1)
| neq(tl(sk3),X1)
| sk3 = nil
| X1 = tl(sk3) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_77,plain,
( ~ ssList(X2)
| ~ ssList(cons(X1,nil))
| ~ ssItem(X1)
| segmentP(cons(X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_69,c_0_60]) ).
cnf(c_0_78,negated_conjecture,
( sk3 = nil
| cons(hd(sk3),tl(sk3)) = sk3 ),
inference(spm,[status(thm)],[c_0_50,c_0_56]) ).
cnf(c_0_79,negated_conjecture,
( ssItem(hd(sk3))
| sk3 = nil ),
inference(spm,[status(thm)],[c_0_53,c_0_56]) ).
cnf(c_0_80,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
inference(fof_simplification,[status(thm)],[clause86]) ).
cnf(c_0_81,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_simplification,[status(thm)],[clause74]) ).
cnf(c_0_82,negated_conjecture,
( ~ neq(sk4,nil)
| ~ neq(nil,sk3)
| ~ ssItem(X4)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| cons(X4,nil) != X3
| app(X2,X3) != X1
| hd(sk3) != X4
| tl(sk3) != X2
| sk4 = X1 ),
inference(cn,[status(thm)],[c_0_70]) ).
cnf(c_0_83,negated_conjecture,
( ~ ssList(X1)
| neq(sk4,X1)
| X1 = sk4 ),
inference(spm,[status(thm)],[c_0_67,c_0_51]) ).
cnf(c_0_84,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| app(X1,nil) = app(nil,X1) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_85,negated_conjecture,
( ~ ssList(X1)
| ssItem(hd(app(sk4,X1))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_51]),c_0_74]) ).
cnf(c_0_86,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| nil != X2
| nil != X1
| app(X1,X2) = nil ),
inference(fof_simplification,[status(thm)],[clause145]) ).
cnf(c_0_87,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(sk4,X1)
| ~ segmentP(sk3,X1)
| ~ neq(X1,nil) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_75,c_0_27]),c_0_28]) ).
cnf(c_0_88,negated_conjecture,
( neq(tl(sk3),nil)
| sk3 = nil
| tl(sk3) = nil ),
inference(spm,[status(thm)],[c_0_76,c_0_48]) ).
cnf(c_0_89,negated_conjecture,
( ~ ssList(cons(hd(sk3),nil))
| segmentP(sk3,tl(sk3))
| sk3 = nil ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_68]),c_0_79]) ).
cnf(c_0_90,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
c_0_80 ).
cnf(c_0_91,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
c_0_81 ).
cnf(c_0_92,negated_conjecture,
( ~ ssList(tl(sk3))
| ~ ssList(cons(hd(sk3),nil))
| ~ ssItem(hd(sk3))
| ~ neq(sk4,nil)
| ~ neq(nil,sk3)
| app(tl(sk3),cons(hd(sk3),nil)) = sk4 ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_82])])])]),c_0_45]) ).
cnf(c_0_93,negated_conjecture,
neq(sk4,nil),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_48]),c_0_52]) ).
cnf(c_0_94,negated_conjecture,
( ~ ssList(X2)
| ~ ssList(X1)
| app(X1,nil) = app(nil,X1) ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_95,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| nil != X2
| nil != X1
| app(X1,X2) = nil ),
c_0_86 ).
cnf(c_0_96,negated_conjecture,
( ~ segmentP(sk4,tl(sk3))
| ~ segmentP(sk3,tl(sk3))
| sk3 = nil
| tl(sk3) = nil ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_68]) ).
cnf(c_0_97,negated_conjecture,
( segmentP(sk3,tl(sk3))
| sk3 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_48])]),c_0_79]) ).
cnf(c_0_98,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| segmentP(app(X1,X2),X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_91]),c_0_48])]),c_0_45]) ).
cnf(c_0_99,negated_conjecture,
( ~ ssList(tl(sk3))
| ~ ssList(cons(hd(sk3),nil))
| ~ ssItem(hd(sk3))
| ~ neq(nil,sk3)
| app(tl(sk3),cons(hd(sk3),nil)) = sk4 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_92,c_0_93])]) ).
cnf(c_0_100,plain,
( ~ ssList(X1)
| neq(nil,X1)
| X1 = nil ),
inference(spm,[status(thm)],[c_0_67,c_0_48]) ).
cnf(c_0_101,negated_conjecture,
( ~ neq(sk4,nil)
| neq(sk3,nil) ),
inference(fof_simplification,[status(thm)],[co1_10]) ).
cnf(c_0_102,negated_conjecture,
( ~ ssList(X1)
| app(sk3,nil) = app(nil,sk3) ),
inference(spm,[status(thm)],[c_0_94,c_0_56]) ).
cnf(c_0_103,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_95])]),c_0_48])]) ).
cnf(c_0_104,negated_conjecture,
( ~ segmentP(sk4,tl(sk3))
| sk3 = nil
| tl(sk3) = nil ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_105,negated_conjecture,
( ~ ssList(tl(sk3))
| ~ ssList(cons(hd(sk3),nil))
| ~ ssItem(hd(sk3))
| ~ neq(nil,sk3)
| segmentP(sk4,tl(sk3)) ),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_106,negated_conjecture,
( neq(nil,sk3)
| sk3 = nil ),
inference(spm,[status(thm)],[c_0_100,c_0_56]) ).
cnf(c_0_107,negated_conjecture,
( ~ neq(sk4,nil)
| neq(sk3,nil) ),
c_0_101 ).
cnf(c_0_108,negated_conjecture,
app(sk3,nil) = app(nil,sk3),
inference(spm,[status(thm)],[c_0_102,c_0_51]) ).
cnf(c_0_109,plain,
( ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1)
| ssList(app(cons(X1,X2),X3)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_44]),c_0_45]) ).
cnf(c_0_110,plain,
( ~ ssItem(X1)
| app(cons(X1,nil),nil) = cons(X1,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_103]),c_0_48])]) ).
cnf(c_0_111,negated_conjecture,
( ~ ssList(cons(hd(sk3),nil))
| sk3 = nil
| tl(sk3) = nil ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_68]),c_0_79]),c_0_106]) ).
cnf(c_0_112,negated_conjecture,
neq(sk3,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_107,c_0_93])]) ).
cnf(c_0_113,negated_conjecture,
app(nil,sk3) = sk3,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_108]),c_0_56])]) ).
cnf(c_0_114,plain,
( ~ ssItem(X1)
| ssList(cons(X1,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_48])]) ).
cnf(c_0_115,negated_conjecture,
( sk3 = nil
| tl(sk3) = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_90]),c_0_48])]),c_0_79]) ).
cnf(c_0_116,negated_conjecture,
( ~ segmentP(sk4,sk3)
| ~ segmentP(sk3,sk3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_112]),c_0_56])]) ).
cnf(c_0_117,negated_conjecture,
segmentP(sk3,sk3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_113]),c_0_56]),c_0_48])]) ).
cnf(c_0_118,negated_conjecture,
( ~ ssList(tl(sk3))
| ~ ssItem(hd(sk3))
| ~ neq(nil,sk3)
| segmentP(sk4,cons(hd(sk3),nil)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_99]),c_0_114]) ).
cnf(c_0_119,negated_conjecture,
( sk3 = nil
| cons(hd(sk3),nil) = sk3 ),
inference(spm,[status(thm)],[c_0_78,c_0_115]) ).
cnf(c_0_120,negated_conjecture,
~ segmentP(sk4,sk3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_116,c_0_117])]) ).
cnf(c_0_121,negated_conjecture,
app(sk4,nil) = sk4,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_63]),c_0_64]),c_0_65])]) ).
cnf(c_0_122,negated_conjecture,
sk3 = nil,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_120]),c_0_68]),c_0_79]),c_0_106]) ).
cnf(c_0_123,negated_conjecture,
segmentP(sk4,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_121]),c_0_48]),c_0_51])]) ).
cnf(c_0_124,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_120,c_0_122]),c_0_123])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC073-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n011.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 07:53:26 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/33.66 % Version: 3.5.1
% 0.16/33.66 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.16/33.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/33.66 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.16/33.66 % Starting new_bool_3 with 300s (1) cores
% 0.16/33.66 % Starting new_bool_1 with 300s (1) cores
% 0.16/33.66 % Starting sh5l with 300s (1) cores
% 0.16/33.66 % new_bool_1 with pid 1394352 completed with status 0
% 0.16/33.66 % Result found by new_bool_1
% 0.16/33.66 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.16/33.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/33.66 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.16/33.66 % Starting new_bool_3 with 300s (1) cores
% 0.16/33.66 % Starting new_bool_1 with 300s (1) cores
% 0.16/33.66 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.16/33.66 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.16/33.66 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.16/33.66 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.16/33.66 % Starting SubtermCWHack with 31s (1) cores
% 0.16/33.66 % SubtermCWHack with pid 1394355 completed with status 8
% 0.16/33.66 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 0.16/33.66 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1394403 completed with status 0
% 0.16/33.66 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.16/33.66 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.16/33.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/33.66 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.16/33.66 % Starting new_bool_3 with 300s (1) cores
% 0.16/33.66 % Starting new_bool_1 with 300s (1) cores
% 0.16/33.66 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.16/33.66 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.16/33.66 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.16/33.66 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.16/33.66 % Starting SubtermCWHack with 31s (1) cores
% 0.16/33.66 % SubtermCWHack with pid 1394355 completed with status 8
% 0.16/33.66 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 0.16/33.66 % Preprocessing time : 0.004 s
% 0.16/33.66 % Presaturation interreduction done
% 0.16/33.66
% 0.16/33.66 % Proof found!
% 0.16/33.66 % SZS status Unsatisfiable
% 0.16/33.66 % SZS output start CNFRefutation
% See solution above
% 0.16/33.66 % Parsed axioms : 196
% 0.16/33.66 % Removed by relevancy pruning/SinE : 121
% 0.16/33.66 % Initial clauses : 75
% 0.16/33.66 % Removed in clause preprocessing : 0
% 0.16/33.66 % Initial clauses in saturation : 75
% 0.16/33.66 % Processed clauses : 3758
% 0.16/33.66 % ...of these trivial : 31
% 0.16/33.66 % ...subsumed : 2222
% 0.16/33.66 % ...remaining for further processing : 1505
% 0.16/33.66 % Other redundant clauses eliminated : 44
% 0.16/33.66 % Clauses deleted for lack of memory : 0
% 0.16/33.66 % Backward-subsumed : 102
% 0.16/33.66 % Backward-rewritten : 748
% 0.16/33.66 % Generated clauses : 31548
% 0.16/33.66 % ...of the previous two non-redundant : 30715
% 0.16/33.66 % ...aggressively subsumed : 0
% 0.16/33.66 % Contextual simplify-reflections : 377
% 0.16/33.66 % Paramodulations : 31474
% 0.16/33.66 % Factorizations : 0
% 0.16/33.66 % NegExts : 0
% 0.16/33.66 % Equation resolutions : 74
% 0.16/33.66 % Disequality decompositions : 0
% 0.16/33.66 % Total rewrite steps : 9089
% 0.16/33.66 % ...of those cached : 9057
% 0.16/33.66 % Propositional unsat checks : 0
% 0.16/33.66 % Propositional check models : 0
% 0.16/33.66 % Propositional check unsatisfiable : 0
% 0.16/33.66 % Propositional clauses : 0
% 0.16/33.66 % Propositional clauses after purity: 0
% 0.16/33.66 % Propositional unsat core size : 0
% 0.16/33.66 % Propositional preprocessing time : 0.000
% 0.16/33.66 % Propositional encoding time : 0.000
% 0.16/33.66 % Propositional solver time : 0.000
% 0.16/33.66 % Success case prop preproc time : 0.000
% 0.16/33.66 % Success case prop encoding time : 0.000
% 0.16/33.66 % Success case prop solver time : 0.000
% 0.16/33.66 % Current number of processed clauses : 574
% 0.16/33.66 % Positive orientable unit clauses : 27
% 0.16/33.66 % Positive unorientable unit clauses: 0
% 0.16/33.66 % Negative unit clauses : 18
% 0.16/33.66 % Non-unit-clauses : 529
% 0.16/33.66 % Current number of unprocessed clauses: 26664
% 0.16/33.66 % ...number of literals in the above : 115484
% 0.16/33.66 % Current number of archived formulas : 0
% 0.16/33.66 % Current number of archived clauses : 920
% 0.16/33.66 % Clause-clause subsumption calls (NU) : 250820
% 0.16/33.66 % Rec. Clause-clause subsumption calls : 98571
% 0.16/33.66 % Non-unit clause-clause subsumptions : 2431
% 0.16/33.66 % Unit Clause-clause subsumption calls : 7960
% 0.16/33.66 % Rewrite failures with RHS unbound : 0
% 0.16/33.66 % BW rewrite match attempts : 13
% 0.16/33.66 % BW rewrite match successes : 13
% 0.16/33.66 % Condensation attempts : 0
% 0.16/33.66 % Condensation successes : 0
% 0.16/33.66 % Termbank termtop insertions : 693856
% 0.16/33.66 % Search garbage collected termcells : 867
% 0.16/33.66
% 0.16/33.66 % -------------------------------------------------
% 0.16/33.66 % User time : 31.196 s
% 0.16/33.66 % System time : 1.222 s
% 0.16/33.66 % Total time : 32.418 s
% 0.16/33.66 % Maximum resident set size: 4016 pages
% 0.16/33.66
% 0.16/33.66 % -------------------------------------------------
% 0.16/33.66 % User time : 31.199 s
% 0.16/33.66 % System time : 1.227 s
% 0.16/33.66 % Total time : 32.426 s
% 0.16/33.66 % Maximum resident set size: 5120 pages
% 0.16/33.66 % E exiting
%------------------------------------------------------------------------------