%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC045-1 : 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 : n009.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 02:42:45 PM UTC 2026
% Result : Unsatisfiable 231.12s 30.21s
% Output : CNFRefutation 231.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 37
% Syntax : Number of formulae : 154 ( 42 unt; 0 def)
% Number of atoms : 436 ( 99 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 573 ( 291 ~; 280 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 3 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 5 con; 0-2 aty)
% Number of variables : 251 ( 43 sgn 2 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(clause179,axiom,
( ~ ssList(X5)
| ~ duplicatefreeP(X5)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X4)
| app(app(X1,cons(X2,X3)),cons(X2,X4)) != X5 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause179) ).
cnf(clause169,axiom,
( ~ ssList(X1)
| ~ ssItem(X2)
| ~ memberP(X1,X2)
| app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause169) ).
cnf(clause138,axiom,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| X1 != X2
| memberP(cons(X2,X3),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause138) ).
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(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(clause8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
cnf(clause85,axiom,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause85) ).
cnf(clause116,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,nil) != X2
| singletonP(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause116) ).
cnf(clause86,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).
cnf(clause72,axiom,
( ~ ssList(X1)
| ssItem(X2)
| duplicatefreeP(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause72) ).
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(clause73,axiom,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause73) ).
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(clause97,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| hd(cons(X1,X2)) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause97) ).
cnf(clause171,axiom,
( ~ ssList(X2)
| ~ ssList(X4)
| ~ ssItem(X1)
| ~ ssItem(X3)
| cons(X1,X2) != cons(X3,X4)
| X4 = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause171) ).
cnf(clause98,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause98) ).
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(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(clause109,axiom,
( ~ ssList(X1)
| nil = X1
| cons(skaf83(X1),skaf82(X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause109) ).
cnf(co1_11,negated_conjecture,
( ~ memberP(sk3,X1)
| ~ ssItem(X1)
| segmentP(sk4,app(app(cons(X1,nil),sk5(X1)),cons(X1,nil))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
cnf(co1_6,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
cnf(co1_5,negated_conjecture,
nil = sk2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
cnf(clause13,axiom,
ssList(skaf82(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause13) ).
cnf(co1_10,negated_conjecture,
( ~ memberP(sk3,X1)
| ~ ssItem(X1)
| ssList(sk5(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
cnf(clause168,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X1,X2)
| app(app(skaf47(X1,X2),X2),skaf48(X2,X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause168) ).
cnf(clause127,axiom,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ segmentP(X2,X1)
| ~ segmentP(X1,X2)
| X2 = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause127) ).
cnf(clause48,axiom,
ssList(skaf48(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause48) ).
cnf(clause49,axiom,
ssList(skaf47(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause49) ).
cnf(clause12,axiom,
ssItem(skaf83(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause12) ).
cnf(co1_8,negated_conjecture,
nil != sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
cnf(co1_1,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
cnf(co1_7,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
cnf(c_0_35,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_36,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_37,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| X1 != X2
| memberP(cons(X2,X3),X1) ),
inference(fof_simplification,[status(thm)],[clause138]) ).
cnf(c_0_38,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_35 ).
cnf(c_0_39,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| ~ memberP(X1,X2)
| app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1 ),
c_0_36 ).
cnf(c_0_40,axiom,
ssList(skaf43(X1,X2)),
clause52 ).
cnf(c_0_41,axiom,
ssList(skaf42(X1,X2)),
clause53 ).
cnf(c_0_42,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(skaf44(X1),nil) = X1 ),
inference(fof_simplification,[status(thm)],[clause101]) ).
cnf(c_0_43,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| X1 != X2
| memberP(cons(X2,X3),X1) ),
c_0_37 ).
cnf(c_0_44,plain,
( ~ duplicatefreeP(X4)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X4)
| ~ ssItem(X2)
| ~ memberP(X1,X2)
| app(X1,cons(X2,X3)) != X4 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_41])]) ).
cnf(c_0_45,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(skaf44(X1),nil) = X1 ),
c_0_42 ).
cnf(c_0_46,axiom,
ssItem(skaf44(X1)),
clause47 ).
cnf(c_0_47,axiom,
ssList(nil),
clause8 ).
cnf(c_0_48,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| memberP(cons(X1,X2),X1) ),
inference(er,[status(thm)],[c_0_43]) ).
cnf(c_0_49,plain,
( ~ duplicatefreeP(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ singletonP(X2)
| ~ memberP(X1,skaf44(X2))
| app(X1,X2) != X3 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]),c_0_47])]) ).
cnf(c_0_50,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_48,c_0_45]),c_0_46]),c_0_47])]) ).
cnf(c_0_51,plain,
( ~ duplicatefreeP(X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ singletonP(X1)
| app(X1,X1) != X2 ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
fof(c_0_52,plain,
( ~ epred2_0
<=> ! [X1] :
( ~ ssList(X1)
| duplicatefreeP(X1) ) ),
introduced(definition) ).
cnf(c_0_53,plain,
( ~ duplicatefreeP(app(X1,X1))
| ~ ssList(X1)
| ~ ssList(app(X1,X1))
| ~ singletonP(X1) ),
inference(er,[status(thm)],[c_0_51]) ).
cnf(c_0_54,plain,
( ~ ssList(X1)
| duplicatefreeP(X1)
| epred2_0 ),
inference(split_equiv,[status(thm)],[c_0_52]) ).
cnf(c_0_55,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
inference(fof_simplification,[status(thm)],[clause85]) ).
cnf(c_0_56,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,nil) != X2
| singletonP(X2) ),
inference(fof_simplification,[status(thm)],[clause116]) ).
cnf(c_0_57,plain,
( ~ ssList(X1)
| ~ ssList(app(X1,X1))
| ~ singletonP(X1)
| epred2_0 ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_58,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
c_0_55 ).
cnf(c_0_59,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,nil) != X2
| singletonP(X2) ),
c_0_56 ).
cnf(c_0_60,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| epred2_0 ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_61,plain,
( ~ ssList(cons(X1,nil))
| ~ ssItem(X1)
| singletonP(cons(X1,nil)) ),
inference(er,[status(thm)],[c_0_59]) ).
cnf(c_0_62,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
inference(fof_simplification,[status(thm)],[clause86]) ).
cnf(c_0_63,plain,
( ~ ssList(X1)
| ssItem(X2)
| duplicatefreeP(X1) ),
inference(fof_simplification,[status(thm)],[clause72]) ).
cnf(c_0_64,plain,
( ~ ssList(cons(X1,nil))
| ~ ssItem(X1)
| epred2_0 ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_65,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
c_0_62 ).
cnf(c_0_66,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_67,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_simplification,[status(thm)],[clause74]) ).
cnf(c_0_68,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(fof_simplification,[status(thm)],[clause73]) ).
fof(c_0_69,plain,
( ~ epred1_0
<=> ! [X2] : ssItem(X2) ),
introduced(definition) ).
cnf(c_0_70,plain,
( ~ ssList(X1)
| ssItem(X2)
| duplicatefreeP(X1) ),
c_0_63 ).
cnf(c_0_71,plain,
( ~ ssItem(X1)
| epred2_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_47])]) ).
cnf(c_0_72,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X3,X2),X1) = app(X3,app(X2,X1)) ),
c_0_66 ).
cnf(c_0_73,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
c_0_67 ).
cnf(c_0_74,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
c_0_68 ).
cnf(c_0_75,plain,
( ~ epred1_0
| ~ epred2_0 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_70,c_0_69]),c_0_52]) ).
cnf(c_0_76,plain,
epred2_0,
inference(spm,[status(thm)],[c_0_71,c_0_46]) ).
cnf(c_0_77,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_72,c_0_73]),c_0_47])]) ).
cnf(c_0_78,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_74,c_0_72]),c_0_47])]),c_0_58]) ).
cnf(c_0_79,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_80,plain,
( ssItem(X1)
| epred1_0 ),
inference(split_equiv,[status(thm)],[c_0_69]) ).
cnf(c_0_81,plain,
~ epred1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_75,c_0_76])]) ).
cnf(c_0_82,plain,
( ~ ssList(X1)
| app(nil,X1) = app(X1,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_47])]) ).
cnf(c_0_83,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,app(X2,X3)) = app(cons(X1,X2),X3) ),
c_0_79 ).
cnf(c_0_84,plain,
ssItem(X1),
inference(sr,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_85,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| hd(cons(X1,X2)) = X1 ),
inference(fof_simplification,[status(thm)],[clause97]) ).
cnf(c_0_86,plain,
( ~ ssList(X1)
| ssList(app(X1,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_82]),c_0_47])]) ).
cnf(c_0_87,plain,
( ~ ssList(X2)
| ~ ssList(X3)
| app(cons(X1,X2),X3) = cons(X1,app(X2,X3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_83,c_0_84])]) ).
cnf(c_0_88,plain,
( ~ ssList(X2)
| ssList(cons(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_84])]) ).
cnf(c_0_89,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| hd(cons(X1,X2)) = X1 ),
c_0_85 ).
cnf(c_0_90,plain,
( ~ ssList(X2)
| ssList(cons(X1,app(X2,nil))) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_47])]),c_0_88]) ).
cnf(c_0_91,plain,
( ~ ssList(X2)
| ~ ssList(X4)
| ~ ssItem(X1)
| ~ ssItem(X3)
| cons(X1,X2) != cons(X3,X4)
| X4 = X2 ),
inference(fof_simplification,[status(thm)],[clause171]) ).
cnf(c_0_92,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| skaf44(X1) = hd(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_45]),c_0_46]),c_0_47])]) ).
cnf(c_0_93,plain,
( ~ ssList(cons(X1,nil))
| singletonP(cons(X1,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_84])]) ).
cnf(c_0_94,plain,
ssList(cons(X1,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_73]),c_0_47])]) ).
cnf(c_0_95,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
inference(fof_simplification,[status(thm)],[clause98]) ).
cnf(c_0_96,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_97,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,nil),X2) = cons(X1,X2) ),
inference(fof_simplification,[status(thm)],[clause120]) ).
cnf(c_0_98,plain,
( ~ ssList(X2)
| ~ ssList(X4)
| ~ ssItem(X1)
| ~ ssItem(X3)
| cons(X1,X2) != cons(X3,X4)
| X4 = X2 ),
c_0_91 ).
cnf(c_0_99,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(hd(X1),nil) = X1 ),
inference(spm,[status(thm)],[c_0_45,c_0_92]) ).
cnf(c_0_100,plain,
singletonP(cons(X1,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_94])]) ).
cnf(c_0_101,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
c_0_95 ).
cnf(c_0_102,plain,
( ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| app(app(X1,X2),X3) != X4
| segmentP(X4,X2) ),
c_0_96 ).
cnf(c_0_103,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,nil),X2) = cons(X1,X2) ),
c_0_97 ).
cnf(c_0_104,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| cons(X3,X1) != cons(X4,X2)
| X1 = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_98,c_0_84]),c_0_84])]) ).
cnf(c_0_105,plain,
cons(hd(cons(X1,nil)),nil) = cons(X1,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_94])]) ).
cnf(c_0_106,plain,
( ~ ssList(X1)
| nil = X1
| cons(skaf83(X1),skaf82(X1)) = X1 ),
inference(fof_simplification,[status(thm)],[clause109]) ).
cnf(c_0_107,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| X1 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_45]),c_0_46]),c_0_47])]) ).
cnf(c_0_108,negated_conjecture,
( ~ memberP(sk3,X1)
| ~ ssItem(X1)
| segmentP(sk4,app(app(cons(X1,nil),sk5(X1)),cons(X1,nil))) ),
inference(fof_simplification,[status(thm)],[co1_11]) ).
cnf(c_0_109,negated_conjecture,
sk2 = sk4,
co1_6 ).
cnf(c_0_110,negated_conjecture,
nil = sk2,
co1_5 ).
cnf(c_0_111,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(X3,X2) != X1
| segmentP(X1,X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_74]),c_0_47])]),c_0_58]) ).
cnf(c_0_112,plain,
( ~ ssList(X2)
| app(cons(X1,nil),X2) = cons(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_103,c_0_84])]) ).
cnf(c_0_113,plain,
( ~ ssList(X1)
| cons(X2,nil) != cons(X3,X1)
| nil = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_47])]) ).
cnf(c_0_114,plain,
( ~ ssList(X1)
| nil = X1
| cons(skaf83(X1),skaf82(X1)) = X1 ),
c_0_106 ).
cnf(c_0_115,axiom,
ssList(skaf82(X1)),
clause13 ).
cnf(c_0_116,plain,
( ~ ssList(cons(X1,nil))
| cons(X1,nil) != nil ),
inference(spm,[status(thm)],[c_0_107,c_0_93]) ).
cnf(c_0_117,negated_conjecture,
( ~ memberP(sk3,X1)
| ~ ssItem(X1)
| segmentP(sk4,app(app(cons(X1,nil),sk5(X1)),cons(X1,nil))) ),
c_0_108 ).
cnf(c_0_118,negated_conjecture,
sk4 = nil,
inference(rw,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_119,negated_conjecture,
( ~ memberP(sk3,X1)
| ~ ssItem(X1)
| ssList(sk5(X1)) ),
inference(fof_simplification,[status(thm)],[co1_10]) ).
cnf(c_0_120,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| cons(X3,X2) != X1
| segmentP(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_94])]) ).
cnf(c_0_121,plain,
( ~ ssList(X1)
| cons(X2,nil) != X1
| nil = X1
| skaf82(X1) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_115])]) ).
cnf(c_0_122,plain,
cons(X1,nil) != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_88]),c_0_47])]) ).
cnf(c_0_123,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X1,X2)
| app(app(skaf47(X1,X2),X2),skaf48(X2,X1)) = X1 ),
inference(fof_simplification,[status(thm)],[clause168]) ).
cnf(c_0_124,negated_conjecture,
( ~ ssItem(X1)
| ~ memberP(sk3,X1)
| segmentP(nil,app(app(cons(X1,nil),sk5(X1)),cons(X1,nil))) ),
inference(rw,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_125,negated_conjecture,
( ~ memberP(sk3,X1)
| ~ ssItem(X1)
| ssList(sk5(X1)) ),
c_0_119 ).
cnf(c_0_126,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ segmentP(X2,X1)
| ~ segmentP(X1,X2)
| X2 = X1 ),
inference(fof_simplification,[status(thm)],[clause127]) ).
cnf(c_0_127,plain,
( ~ ssList(X1)
| segmentP(X1,skaf82(X1))
| nil = X1 ),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_114]),c_0_115])])]) ).
cnf(c_0_128,plain,
skaf82(cons(X1,nil)) = nil,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_121]),c_0_94])]),c_0_122]) ).
cnf(c_0_129,plain,
( ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X5)
| ~ ssList(X1)
| app(app(X3,app(X4,X2)),X5) != X1
| segmentP(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_72]),c_0_58]) ).
cnf(c_0_130,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X1,X2)
| app(app(skaf47(X1,X2),X2),skaf48(X2,X1)) = X1 ),
c_0_123 ).
cnf(c_0_131,axiom,
ssList(skaf48(X1,X2)),
clause48 ).
cnf(c_0_132,axiom,
ssList(skaf47(X1,X2)),
clause49 ).
cnf(c_0_133,negated_conjecture,
( ~ memberP(sk3,X1)
| segmentP(nil,app(app(cons(X1,nil),sk5(X1)),cons(X1,nil))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_124,c_0_84])]) ).
cnf(c_0_134,negated_conjecture,
( ~ memberP(sk3,X1)
| ssList(sk5(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_125,c_0_84])]) ).
cnf(c_0_135,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ segmentP(X2,X1)
| ~ segmentP(X1,X2)
| X2 = X1 ),
c_0_126 ).
cnf(c_0_136,plain,
segmentP(cons(X1,nil),nil),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_128]),c_0_94])]),c_0_122]) ).
cnf(c_0_137,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ segmentP(X1,app(X3,X2))
| segmentP(X1,X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_131]),c_0_132])])]),c_0_58]) ).
cnf(c_0_138,negated_conjecture,
( ~ memberP(sk3,X1)
| segmentP(nil,app(cons(X1,sk5(X1)),cons(X1,nil))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_112]),c_0_134]) ).
cnf(c_0_139,plain,
~ segmentP(nil,cons(X1,nil)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_94]),c_0_47])]),c_0_122]) ).
cnf(c_0_140,axiom,
ssItem(skaf83(X1)),
clause12 ).
cnf(c_0_141,plain,
( ~ ssList(X2)
| hd(cons(X1,X2)) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_89,c_0_84])]) ).
cnf(c_0_142,negated_conjecture,
nil != sk1,
inference(fof_simplification,[status(thm)],[co1_8]) ).
cnf(c_0_143,negated_conjecture,
( ~ ssList(cons(X1,sk5(X1)))
| ~ memberP(sk3,X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_47]),c_0_94])]),c_0_139]) ).
cnf(c_0_144,plain,
( ~ ssList(X1)
| memberP(X1,skaf83(X1))
| nil = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_114]),c_0_140]),c_0_115])]) ).
cnf(c_0_145,plain,
( ~ ssList(X1)
| nil = X1
| skaf83(X1) = hd(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_114]),c_0_115])]) ).
cnf(c_0_146,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_147,negated_conjecture,
sk1 = sk3,
co1_7 ).
cnf(c_0_148,negated_conjecture,
nil != sk1,
c_0_142 ).
cnf(c_0_149,negated_conjecture,
~ memberP(sk3,X1),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_88]),c_0_134]) ).
cnf(c_0_150,plain,
( ~ ssList(X1)
| memberP(X1,hd(X1))
| nil = X1 ),
inference(spm,[status(thm)],[c_0_144,c_0_145]) ).
cnf(c_0_151,negated_conjecture,
ssList(sk3),
inference(rw,[status(thm)],[c_0_146,c_0_147]) ).
cnf(c_0_152,negated_conjecture,
sk3 != nil,
inference(rw,[status(thm)],[c_0_148,c_0_147]) ).
cnf(c_0_153,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_150]),c_0_151])]),c_0_152]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC045-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.38 % Computer : n009.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Mon Sep 21 07:51:28 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 231.12/30.21 % Version: 3.5.1
% 231.12/30.21 % Preprocessing class: FSLSSMSSSSSNFFN.
% 231.12/30.21 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 231.12/30.21 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 231.12/30.21 % Starting new_bool_3 with 300s (1) cores
% 231.12/30.21 % Starting new_bool_1 with 300s (1) cores
% 231.12/30.21 % Starting sh5l with 300s (1) cores
% 231.12/30.21 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1245880 completed with status 0
% 231.12/30.21 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 231.12/30.21 % Preprocessing class: FSLSSMSSSSSNFFN.
% 231.12/30.21 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 231.12/30.21 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 231.12/30.21 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 231.12/30.21 % No SInE strategy applied
% 231.12/30.21 % Search class: FGHSM-FSLM21-MFFFFFNN
% 231.12/30.21 % Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 231.12/30.21 % Starting SubtermCWHack with 136s (1) cores
% 231.12/30.21 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 231.12/30.21 % Starting G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y with 136s (1) cores
% 231.12/30.21 % Starting G-E--_200_B02_F1_SE_CS_SP_PI_S2k with 136s (1) cores
% 231.12/30.21 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 231.12/30.21 % G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y with pid 1245888 completed with status 0
% 231.12/30.21 % Result found by G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y
% 231.12/30.21 % Preprocessing class: FSLSSMSSSSSNFFN.
% 231.12/30.21 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 231.12/30.21 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 231.12/30.21 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 231.12/30.21 % No SInE strategy applied
% 231.12/30.21 % Search class: FGHSM-FSLM21-MFFFFFNN
% 231.12/30.21 % Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 231.12/30.21 % Starting SubtermCWHack with 136s (1) cores
% 231.12/30.21 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 231.12/30.21 % Starting G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y with 136s (1) cores
% 231.12/30.21 % Preprocessing time : 0.004 s
% 231.12/30.21 % Presaturation interreduction done
% 231.12/30.21
% 231.12/30.21 % Proof found!
% 231.12/30.21 % SZS status Unsatisfiable
% 231.12/30.21 % SZS output start CNFRefutation
% See solution above
% 231.12/30.21 % Parsed axioms : 196
% 231.12/30.21 % Removed by relevancy pruning/SinE : 0
% 231.12/30.21 % Initial clauses : 196
% 231.12/30.21 % Removed in clause preprocessing : 0
% 231.12/30.21 % Initial clauses in saturation : 196
% 231.12/30.21 % Processed clauses : 35770
% 231.12/30.21 % ...of these trivial : 394
% 231.12/30.21 % ...subsumed : 30480
% 231.12/30.21 % ...remaining for further processing : 4896
% 231.12/30.21 % Other redundant clauses eliminated : 11628
% 231.12/30.21 % Clauses deleted for lack of memory : 0
% 231.12/30.21 % Backward-subsumed : 119
% 231.12/30.21 % Backward-rewritten : 152
% 231.12/30.21 % Generated clauses : 1280593
% 231.12/30.21 % ...of the previous two non-redundant : 1214221
% 231.12/30.21 % ...aggressively subsumed : 0
% 231.12/30.21 % Contextual simplify-reflections : 1860
% 231.12/30.21 % Paramodulations : 1268350
% 231.12/30.21 % Factorizations : 0
% 231.12/30.21 % NegExts : 0
% 231.12/30.21 % Equation resolutions : 12116
% 231.12/30.21 % Disequality decompositions : 0
% 231.12/30.21 % Total rewrite steps : 862092
% 231.12/30.21 % ...of those cached : 849745
% 231.12/30.21 % Propositional unsat checks : 0
% 231.12/30.21 % Propositional check models : 0
% 231.12/30.21 % Propositional check unsatisfiable : 0
% 231.12/30.21 % Propositional clauses : 0
% 231.12/30.21 % Propositional clauses after purity: 0
% 231.12/30.21 % Propositional unsat core size : 0
% 231.12/30.21 % Propositional preprocessing time : 0.000
% 231.12/30.21 % Propositional encoding time : 0.000
% 231.12/30.21 % Propositional solver time : 0.000
% 231.12/30.21 % Success case prop preproc time : 0.000
% 231.12/30.21 % Success case prop encoding time : 0.000
% 231.12/30.21 % Success case prop solver time : 0.000
% 231.12/30.21 % Current number of processed clauses : 4366
% 231.12/30.21 % Positive orientable unit clauses : 107
% 231.12/30.21 % Positive unorientable unit clauses: 0
% 231.12/30.21 % Negative unit clauses : 108
% 231.12/30.21 % Non-unit-clauses : 4151
% 231.12/30.21 % Current number of unprocessed clauses: 1177940
% 231.12/30.21 % ...number of literals in the above : 10421050
% 231.12/30.21 % Current number of archived formulas : 0
% 231.12/30.21 % Current number of archived clauses : 463
% 231.12/30.21 % Clause-clause subsumption calls (NU) : 6110991
% 231.12/30.21 % Rec. Clause-clause subsumption calls : 1214386
% 231.12/30.21 % Non-unit clause-clause subsumptions : 27080
% 231.12/30.21 % Unit Clause-clause subsumption calls : 150357
% 231.12/30.21 % Rewrite failures with RHS unbound : 0
% 231.12/30.21 % BW rewrite match attempts : 79
% 231.12/30.21 % BW rewrite match successes : 38
% 231.12/30.21 % Condensation attempts : 0
% 231.12/30.21 % Condensation successes : 0
% 231.12/30.21 % Termbank termtop insertions : 35452474
% 231.12/30.21 % Search garbage collected termcells : 539
% 231.12/30.21
% 231.12/30.21 % -------------------------------------------------
% 231.12/30.21 % User time : 28.052 s
% 231.12/30.21 % System time : 0.926 s
% 231.12/30.21 % Total time : 28.977 s
% 231.12/30.21 % Maximum resident set size: 4068 pages
% 231.12/30.21
% 231.12/30.21 % -------------------------------------------------
% 231.12/30.21 % User time : 139.079 s
% 231.12/30.21 % System time : 5.156 s
% 231.12/30.21 % Total time : 144.235 s
% 231.12/30.21 % Maximum resident set size: 5120 pages
% 231.12/30.21 % E exiting
%------------------------------------------------------------------------------