%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC224-1 : 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 02:43:32 PM UTC 2026
% Result : Unsatisfiable 90.91s 13.77s
% Output : CNFRefutation 90.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 34
% Syntax : Number of clauses : 130 ( 40 unt; 23 nHn; 117 RR)
% Number of literals : 372 ( 96 equ; 239 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 201 ( 22 sgn)
% Comments :
%------------------------------------------------------------------------------
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(co1_14,negated_conjecture,
app(sk3,sk6) = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
cnf(co1_6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
cnf(clause123,axiom,
( ~ ssList(X2)
| ~ ssList(X1)
| hd(app(X2,X1)) = hd(X2)
| nil = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause123) ).
cnf(co1_7,negated_conjecture,
nil != sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
cnf(clause118,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause118) ).
cnf(clause75,axiom,
( ~ ssList(X1)
| nil = X1
| ssList(tl(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause75) ).
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(clause85,axiom,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause85) ).
cnf(co1_1,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).
cnf(co1_13,negated_conjecture,
ssList(sk6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
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(clause104,axiom,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause104) ).
cnf(co1_2,negated_conjecture,
ssList(sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_2) ).
cnf(co1_5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
cnf(clause76,axiom,
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause76) ).
cnf(clause73,axiom,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause73) ).
cnf(clause138,axiom,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| X1 != X2
| memberP(cons(X2,X3),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause138) ).
cnf(clause8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
cnf(clause72,axiom,
( ~ ssList(X1)
| ssItem(X2)
| duplicatefreeP(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause72) ).
cnf(clause71,axiom,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause71) ).
cnf(co1_9,negated_conjecture,
( app(app(X2,cons(X1,nil)),X3) != sk1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| memberP(X2,sk5(X3,X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
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(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(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(co1_8,negated_conjecture,
( app(app(X2,cons(X1,nil)),X3) != sk1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ssItem(sk5(X3,X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
cnf(clause52,axiom,
ssList(skaf43(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause52) ).
cnf(clause53,axiom,
ssList(skaf42(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause53) ).
cnf(clause74,axiom,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause74) ).
cnf(clause178,axiom,
( ~ ssItem(X3)
| ~ ssItem(X4)
| ~ ssList(X1)
| ~ ssList(X2)
| X3 != X4
| ~ frontsegP(X1,X2)
| frontsegP(cons(X3,X1),cons(X4,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause178) ).
cnf(clause132,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| app(X2,skaf45(X1,X2)) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause132) ).
cnf(clause51,axiom,
ssList(skaf45(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause51) ).
cnf(clause60,axiom,
( ~ ssList(X1)
| frontsegP(X1,nil) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause60) ).
cnf(c_0_34,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_35,negated_conjecture,
app(sk3,sk6) = sk4,
co1_14 ).
cnf(c_0_36,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_37,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| hd(app(X2,X1)) = hd(X2)
| nil = X2 ),
inference(fof_simplification,[status(thm)],[clause123]) ).
cnf(c_0_38,negated_conjecture,
nil != sk1,
inference(fof_simplification,[status(thm)],[co1_7]) ).
cnf(c_0_39,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X1 ),
inference(fof_simplification,[status(thm)],[clause118]) ).
cnf(c_0_40,plain,
( ~ ssList(X1)
| nil = X1
| ssList(tl(X1)) ),
inference(fof_simplification,[status(thm)],[clause75]) ).
cnf(c_0_41,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| tl(app(X2,X1)) = app(tl(X2),X1)
| nil = X2 ),
inference(fof_simplification,[status(thm)],[clause133]) ).
cnf(c_0_42,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
inference(fof_simplification,[status(thm)],[clause85]) ).
cnf(c_0_43,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X3,X2),X1) = app(X3,app(X2,X1)) ),
c_0_34 ).
cnf(c_0_44,negated_conjecture,
app(sk1,sk6) = sk4,
inference(rw,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_45,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_46,negated_conjecture,
ssList(sk6),
co1_13 ).
cnf(c_0_47,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_48,plain,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
inference(fof_simplification,[status(thm)],[clause104]) ).
cnf(c_0_49,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| hd(app(X2,X1)) = hd(X2)
| nil = X2 ),
c_0_37 ).
cnf(c_0_50,negated_conjecture,
nil != sk1,
c_0_38 ).
cnf(c_0_51,negated_conjecture,
ssList(sk2),
co1_2 ).
cnf(c_0_52,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_53,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X1 ),
c_0_39 ).
cnf(c_0_54,plain,
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
inference(fof_simplification,[status(thm)],[clause76]) ).
cnf(c_0_55,plain,
( ~ ssList(X1)
| nil = X1
| ssList(tl(X1)) ),
c_0_40 ).
cnf(c_0_56,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| tl(app(X2,X1)) = app(tl(X2),X1)
| nil = X2 ),
c_0_41 ).
cnf(c_0_57,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
c_0_42 ).
cnf(c_0_58,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(fof_simplification,[status(thm)],[clause73]) ).
cnf(c_0_59,negated_conjecture,
( ~ ssList(X1)
| app(sk1,app(sk6,X1)) = app(sk4,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),c_0_46])]) ).
cnf(c_0_60,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| X1 != X2
| memberP(cons(X2,X3),X1) ),
inference(fof_simplification,[status(thm)],[clause138]) ).
cnf(c_0_61,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_47 ).
cnf(c_0_62,plain,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
c_0_48 ).
cnf(c_0_63,negated_conjecture,
hd(sk4) = hd(sk1),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_44]),c_0_45]),c_0_46])]),c_0_50]) ).
cnf(c_0_64,negated_conjecture,
ssList(sk4),
inference(rw,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_65,negated_conjecture,
sk4 != nil,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_44]),c_0_46]),c_0_45])]),c_0_50]) ).
cnf(c_0_66,plain,
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
c_0_54 ).
cnf(c_0_67,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(tl(X1),X2))
| nil = X1 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57]),c_0_53]) ).
cnf(c_0_68,negated_conjecture,
app(tl(sk1),sk6) = tl(sk4),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_44]),c_0_45]),c_0_46])]),c_0_50]) ).
cnf(c_0_69,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
c_0_58 ).
cnf(c_0_70,axiom,
ssList(nil),
clause8 ).
cnf(c_0_71,plain,
( ~ ssList(X1)
| ssItem(X2)
| duplicatefreeP(X1) ),
inference(fof_simplification,[status(thm)],[clause72]) ).
cnf(c_0_72,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(app(sk6,X1))
| ssList(app(sk4,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_59]),c_0_45])]) ).
cnf(c_0_73,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| X1 != X2
| memberP(cons(X2,X3),X1) ),
c_0_60 ).
cnf(c_0_74,plain,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[clause71]) ).
cnf(c_0_75,negated_conjecture,
( app(app(X2,cons(X1,nil)),X3) != sk1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| memberP(X2,sk5(X3,X2,X1)) ),
inference(fof_simplification,[status(thm)],[co1_9]) ).
cnf(c_0_76,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_61]) ).
cnf(c_0_77,negated_conjecture,
cons(hd(sk1),tl(sk4)) = sk4,
inference(sr,[status(thm)],[inference(cn,[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_78,negated_conjecture,
ssItem(hd(sk1)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_63]),c_0_64])]),c_0_65]) ).
cnf(c_0_79,negated_conjecture,
ssList(tl(sk4)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_45]),c_0_46])]),c_0_50]) ).
cnf(c_0_80,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_81,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ssList(app(X1,app(X2,X3))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_43]),c_0_57]) ).
cnf(c_0_82,negated_conjecture,
app(sk4,nil) = sk4,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_69]),c_0_44]),c_0_70]),c_0_46])]) ).
cnf(c_0_83,plain,
( ~ ssList(X1)
| ssItem(X2)
| duplicatefreeP(X1) ),
c_0_71 ).
cnf(c_0_84,negated_conjecture,
( ~ ssList(X1)
| ssList(app(sk4,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_57]),c_0_46])]) ).
cnf(c_0_85,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| memberP(cons(X1,X2),X1) ),
inference(er,[status(thm)],[c_0_73]) ).
cnf(c_0_86,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_87,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
inference(fof_simplification,[status(thm)],[clause86]) ).
cnf(c_0_88,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| nil != X2
| nil != X1
| app(X1,X2) = nil ),
inference(fof_simplification,[status(thm)],[clause145]) ).
cnf(c_0_89,plain,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
c_0_74 ).
cnf(c_0_90,negated_conjecture,
( app(app(X2,cons(X1,nil)),X3) != sk1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| memberP(X2,sk5(X3,X2,X1)) ),
c_0_75 ).
cnf(c_0_91,negated_conjecture,
( app(app(X2,cons(X1,nil)),X3) != sk1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ssItem(sk5(X3,X2,X1)) ),
inference(fof_simplification,[status(thm)],[co1_8]) ).
cnf(c_0_92,negated_conjecture,
( ~ duplicatefreeP(app(app(X1,cons(hd(sk1),X2)),sk4))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(app(app(X1,cons(hd(sk1),X2)),sk4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_78])]),c_0_79])]) ).
cnf(c_0_93,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| ~ memberP(X1,X2)
| app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1 ),
c_0_80 ).
cnf(c_0_94,axiom,
ssList(skaf43(X1,X2)),
clause52 ).
cnf(c_0_95,axiom,
ssList(skaf42(X1,X2)),
clause53 ).
cnf(c_0_96,negated_conjecture,
( ~ ssList(X1)
| ssList(app(X1,sk4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_70]),c_0_64])]) ).
cnf(c_0_97,negated_conjecture,
( ~ ssList(X2)
| duplicatefreeP(app(sk4,X2))
| ssItem(X1) ),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_98,plain,
( ~ ssList(X1)
| memberP(X1,hd(X1))
| nil = X1 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_62]),c_0_55]),c_0_66]) ).
cnf(c_0_99,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,app(X2,X3)) = app(cons(X1,X2),X3) ),
c_0_86 ).
cnf(c_0_100,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
c_0_87 ).
cnf(c_0_101,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| nil != X2
| nil != X1
| app(X1,X2) = nil ),
c_0_88 ).
cnf(c_0_102,negated_conjecture,
( ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(sk5(X2,nil,X1))
| app(app(nil,cons(X1,nil)),X2) != sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_70])]) ).
cnf(c_0_103,negated_conjecture,
( app(app(X2,cons(X1,nil)),X3) != sk1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ssItem(sk5(X3,X2,X1)) ),
c_0_91 ).
cnf(c_0_104,negated_conjecture,
( ~ duplicatefreeP(app(X1,sk4))
| ~ ssList(X1)
| ~ memberP(X1,hd(sk1)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_94]),c_0_95]),c_0_78])]),c_0_96]) ).
cnf(c_0_105,negated_conjecture,
( duplicatefreeP(app(sk4,sk4))
| ssItem(X1) ),
inference(spm,[status(thm)],[c_0_97,c_0_64]) ).
cnf(c_0_106,negated_conjecture,
memberP(sk4,hd(sk1)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_63]),c_0_64])]),c_0_65]) ).
cnf(c_0_107,plain,
( ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1)
| ssList(cons(X1,app(X2,X3))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_99]),c_0_100]) ).
cnf(c_0_108,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_101])]),c_0_70])]) ).
cnf(c_0_109,negated_conjecture,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(app(nil,cons(X1,nil)),X2) != sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_70])]) ).
cnf(c_0_110,negated_conjecture,
ssItem(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_106]),c_0_64])]) ).
cnf(c_0_111,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_simplification,[status(thm)],[clause74]) ).
cnf(c_0_112,plain,
( ~ ssItem(X1)
| ssList(cons(X1,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_70])]) ).
cnf(c_0_113,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_114,negated_conjecture,
( ~ ssList(X2)
| app(app(nil,cons(X1,nil)),X2) != sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_109,c_0_110])]) ).
cnf(c_0_115,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
c_0_111 ).
cnf(c_0_116,plain,
ssList(cons(X1,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_112,c_0_110])]) ).
cnf(c_0_117,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| app(X2,skaf45(X1,X2)) = X1 ),
inference(fof_simplification,[status(thm)],[clause132]) ).
cnf(c_0_118,plain,
( ~ ssItem(X3)
| ~ ssItem(X4)
| ~ ssList(X1)
| ~ ssList(X2)
| X3 != X4
| ~ frontsegP(X1,X2)
| frontsegP(cons(X3,X1),cons(X4,X2)) ),
c_0_113 ).
cnf(c_0_119,negated_conjecture,
( ~ ssList(X2)
| app(cons(X1,nil),X2) != sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_116])]) ).
cnf(c_0_120,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| app(X2,skaf45(X1,X2)) = X1 ),
c_0_117 ).
cnf(c_0_121,axiom,
ssList(skaf45(X1,X2)),
clause51 ).
cnf(c_0_122,plain,
( ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1)
| ~ frontsegP(X2,X3)
| frontsegP(cons(X1,X2),cons(X1,X3)) ),
inference(er,[status(thm)],[c_0_118]) ).
cnf(c_0_123,negated_conjecture,
~ frontsegP(sk1,cons(X1,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_121]),c_0_116])])]),c_0_45])]) ).
cnf(c_0_124,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(tl(X1),X2)
| frontsegP(X1,cons(hd(X1),X2))
| nil = X1 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_62]),c_0_55]),c_0_66]) ).
cnf(c_0_125,plain,
( ~ ssList(X1)
| frontsegP(X1,nil) ),
inference(fof_simplification,[status(thm)],[clause60]) ).
cnf(c_0_126,negated_conjecture,
~ frontsegP(tl(sk1),nil),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_70]),c_0_45])]),c_0_50]) ).
cnf(c_0_127,plain,
( ~ ssList(X1)
| frontsegP(X1,nil) ),
c_0_125 ).
cnf(c_0_128,negated_conjecture,
~ ssList(tl(sk1)),
inference(spm,[status(thm)],[c_0_126,c_0_127]) ).
cnf(c_0_129,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_55]),c_0_45])]),c_0_50]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC224-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n017.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 08:01:27 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.43 Running first-order theorem proving
% 0.14/0.43 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
% 90.91/13.77 % Version: 3.5.1
% 90.91/13.77 % Preprocessing class: FSLSSMSMSSSNFFN.
% 90.91/13.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 90.91/13.77 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 90.91/13.77 % Starting new_bool_3 with 300s (1) cores
% 90.91/13.77 % Starting new_bool_1 with 300s (1) cores
% 90.91/13.77 % Starting sh5l with 300s (1) cores
% 90.91/13.77 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 1848758 completed with status 0
% 90.91/13.77 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 90.91/13.77 % Preprocessing class: FSLSSMSMSSSNFFN.
% 90.91/13.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 90.91/13.77 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 90.91/13.77 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 90.91/13.77 % No SInE strategy applied
% 90.91/13.77 % Search class: FGHSM-FSLM31-MFFFFFNN
% 90.91/13.77 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 90.91/13.77 % Starting SubtermCWHack with 136s (1) cores
% 90.91/13.77 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 90.91/13.77 % Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_S04BN with 136s (1) cores
% 90.91/13.77 % Starting G-E--_207_B07_F1_AE_CS_SP_PI_PS_S0Y with 136s (1) cores
% 90.91/13.77 % Starting U----_116Y_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 90.91/13.77 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 1848763 completed with status 0
% 90.91/13.77 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 90.91/13.77 % Preprocessing class: FSLSSMSMSSSNFFN.
% 90.91/13.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 90.91/13.77 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 90.91/13.77 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 90.91/13.77 % No SInE strategy applied
% 90.91/13.77 % Search class: FGHSM-FSLM31-MFFFFFNN
% 90.91/13.77 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 90.91/13.77 % Starting SubtermCWHack with 136s (1) cores
% 90.91/13.77 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 90.91/13.77 % Preprocessing time : 0.006 s
% 90.91/13.77 % Presaturation interreduction done
% 90.91/13.77
% 90.91/13.77 % Proof found!
% 90.91/13.77 % SZS status Unsatisfiable
% 90.91/13.77 % SZS output start CNFRefutation
% See solution above
% 90.91/13.77 % Parsed axioms : 202
% 90.91/13.77 % Removed by relevancy pruning/SinE : 0
% 90.91/13.77 % Initial clauses : 202
% 90.91/13.77 % Removed in clause preprocessing : 0
% 90.91/13.77 % Initial clauses in saturation : 202
% 90.91/13.77 % Processed clauses : 52138
% 90.91/13.77 % ...of these trivial : 842
% 90.91/13.77 % ...subsumed : 43236
% 90.91/13.77 % ...remaining for further processing : 8060
% 90.91/13.77 % Other redundant clauses eliminated : 855
% 90.91/13.77 % Clauses deleted for lack of memory : 0
% 90.91/13.77 % Backward-subsumed : 3343
% 90.91/13.77 % Backward-rewritten : 1645
% 90.91/13.77 % Generated clauses : 319425
% 90.91/13.77 % ...of the previous two non-redundant : 312300
% 90.91/13.77 % ...aggressively subsumed : 0
% 90.91/13.77 % Contextual simplify-reflections : 1076
% 90.91/13.77 % Paramodulations : 318559
% 90.91/13.77 % Factorizations : 0
% 90.91/13.77 % NegExts : 0
% 90.91/13.77 % Equation resolutions : 867
% 90.91/13.77 % Disequality decompositions : 0
% 90.91/13.77 % Total rewrite steps : 163566
% 90.91/13.77 % ...of those cached : 162898
% 90.91/13.77 % Propositional unsat checks : 1
% 90.91/13.77 % Propositional check models : 0
% 90.91/13.77 % Propositional check unsatisfiable : 0
% 90.91/13.77 % Propositional clauses : 0
% 90.91/13.77 % Propositional clauses after purity: 0
% 90.91/13.77 % Propositional unsat core size : 0
% 90.91/13.77 % Propositional preprocessing time : 0.000
% 90.91/13.77 % Propositional encoding time : 0.390
% 90.91/13.77 % Propositional solver time : 0.243
% 90.91/13.77 % Success case prop preproc time : 0.000
% 90.91/13.77 % Success case prop encoding time : 0.000
% 90.91/13.77 % Success case prop solver time : 0.000
% 90.91/13.77 % Current number of processed clauses : 2856
% 90.91/13.77 % Positive orientable unit clauses : 130
% 90.91/13.77 % Positive unorientable unit clauses: 0
% 90.91/13.77 % Negative unit clauses : 80
% 90.91/13.77 % Non-unit-clauses : 2646
% 90.91/13.77 % Current number of unprocessed clauses: 258513
% 90.91/13.77 % ...number of literals in the above : 1171693
% 90.91/13.77 % Current number of archived formulas : 0
% 90.91/13.77 % Current number of archived clauses : 5181
% 90.91/13.77 % Clause-clause subsumption calls (NU) : 10460209
% 90.91/13.77 % Rec. Clause-clause subsumption calls : 3534254
% 90.91/13.77 % Non-unit clause-clause subsumptions : 35068
% 90.91/13.77 % Unit Clause-clause subsumption calls : 61036
% 90.91/13.77 % Rewrite failures with RHS unbound : 0
% 90.91/13.77 % BW rewrite match attempts : 79
% 90.91/13.77 % BW rewrite match successes : 65
% 90.91/13.77 % Condensation attempts : 0
% 90.91/13.77 % Condensation successes : 0
% 90.91/13.77 % Termbank termtop insertions : 6487034
% 90.91/13.77 % Search garbage collected termcells : 563
% 90.91/13.77
% 90.91/13.77 % -------------------------------------------------
% 90.91/13.77 % User time : 12.744 s
% 90.91/13.77 % System time : 0.312 s
% 90.91/13.77 % Total time : 13.055 s
% 90.91/13.77 % Maximum resident set size: 4064 pages
% 90.91/13.77
% 90.91/13.77 % -------------------------------------------------
% 90.91/13.77 % User time : 63.178 s
% 90.91/13.77 % System time : 1.999 s
% 90.91/13.77 % Total time : 65.177 s
% 90.91/13.77 % Maximum resident set size: 4864 pages
% 90.91/13.77 % E exiting
%------------------------------------------------------------------------------