%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC234-1 : 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 : n026.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 02:43:35 PM UTC 2026
% Result : Unsatisfiable 110.34s 17.01s
% Output : CNFRefutation 110.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 37
% Syntax : Number of clauses : 140 ( 40 unt; 26 nHn; 127 RR)
% Number of literals : 422 ( 107 equ; 279 neg)
% Maximal clause size : 7 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 228 ( 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(co1_12,negated_conjecture,
( ~ lt(X1,sk5(X3,X2,X1))
| app(app(X2,cons(X1,nil)),X3) != sk1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
cnf(clause121,axiom,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ leq(X1,X2)
| X1 = X2
| lt(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause121) ).
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(co1_11,negated_conjecture,
( app(app(X2,cons(X1,nil)),X3) != sk1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| leq(X1,sk5(X3,X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
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(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_37,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_38,negated_conjecture,
app(sk3,sk6) = sk4,
co1_14 ).
cnf(c_0_39,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_40,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| hd(app(X2,X1)) = hd(X2)
| nil = X2 ),
inference(fof_simplification,[status(thm)],[clause123]) ).
cnf(c_0_41,negated_conjecture,
nil != sk1,
inference(fof_simplification,[status(thm)],[co1_7]) ).
cnf(c_0_42,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X1 ),
inference(fof_simplification,[status(thm)],[clause118]) ).
cnf(c_0_43,plain,
( ~ ssList(X1)
| nil = X1
| ssList(tl(X1)) ),
inference(fof_simplification,[status(thm)],[clause75]) ).
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)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
inference(fof_simplification,[status(thm)],[clause85]) ).
cnf(c_0_46,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X3,X2),X1) = app(X3,app(X2,X1)) ),
c_0_37 ).
cnf(c_0_47,negated_conjecture,
app(sk1,sk6) = sk4,
inference(rw,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_48,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_49,negated_conjecture,
ssList(sk6),
co1_13 ).
cnf(c_0_50,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_51,plain,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
inference(fof_simplification,[status(thm)],[clause104]) ).
cnf(c_0_52,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| hd(app(X2,X1)) = hd(X2)
| nil = X2 ),
c_0_40 ).
cnf(c_0_53,negated_conjecture,
nil != sk1,
c_0_41 ).
cnf(c_0_54,negated_conjecture,
ssList(sk2),
co1_2 ).
cnf(c_0_55,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_56,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X1 ),
c_0_42 ).
cnf(c_0_57,plain,
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
inference(fof_simplification,[status(thm)],[clause76]) ).
cnf(c_0_58,plain,
( ~ ssList(X1)
| nil = X1
| ssList(tl(X1)) ),
c_0_43 ).
cnf(c_0_59,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| tl(app(X2,X1)) = app(tl(X2),X1)
| nil = X2 ),
c_0_44 ).
cnf(c_0_60,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
c_0_45 ).
cnf(c_0_61,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(fof_simplification,[status(thm)],[clause73]) ).
cnf(c_0_62,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_46,c_0_47]),c_0_48]),c_0_49])]) ).
cnf(c_0_63,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| X1 != X2
| memberP(cons(X2,X3),X1) ),
inference(fof_simplification,[status(thm)],[clause138]) ).
cnf(c_0_64,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_50 ).
cnf(c_0_65,plain,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
c_0_51 ).
cnf(c_0_66,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_52,c_0_47]),c_0_48]),c_0_49])]),c_0_53]) ).
cnf(c_0_67,negated_conjecture,
ssList(sk4),
inference(rw,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_68,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_56,c_0_47]),c_0_49]),c_0_48])]),c_0_53]) ).
cnf(c_0_69,plain,
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
c_0_57 ).
cnf(c_0_70,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_58,c_0_59]),c_0_60]),c_0_56]) ).
cnf(c_0_71,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_59,c_0_47]),c_0_48]),c_0_49])]),c_0_53]) ).
cnf(c_0_72,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
c_0_61 ).
cnf(c_0_73,axiom,
ssList(nil),
clause8 ).
cnf(c_0_74,plain,
( ~ ssList(X1)
| ssItem(X2)
| duplicatefreeP(X1) ),
inference(fof_simplification,[status(thm)],[clause72]) ).
cnf(c_0_75,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_60,c_0_62]),c_0_48])]) ).
cnf(c_0_76,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| X1 != X2
| memberP(cons(X2,X3),X1) ),
c_0_63 ).
cnf(c_0_77,plain,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[clause71]) ).
cnf(c_0_78,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_79,negated_conjecture,
( ~ lt(X1,sk5(X3,X2,X1))
| app(app(X2,cons(X1,nil)),X3) != sk1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(fof_simplification,[status(thm)],[co1_12]) ).
cnf(c_0_80,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ leq(X1,X2)
| X1 = X2
| lt(X1,X2) ),
inference(fof_simplification,[status(thm)],[clause121]) ).
cnf(c_0_81,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_82,negated_conjecture,
( app(app(X2,cons(X1,nil)),X3) != sk1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| leq(X1,sk5(X3,X2,X1)) ),
inference(fof_simplification,[status(thm)],[co1_11]) ).
cnf(c_0_83,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_64]) ).
cnf(c_0_84,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_65,c_0_66]),c_0_67])]),c_0_68]) ).
cnf(c_0_85,negated_conjecture,
ssItem(hd(sk1)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_66]),c_0_67])]),c_0_68]) ).
cnf(c_0_86,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_70,c_0_71]),c_0_48]),c_0_49])]),c_0_53]) ).
cnf(c_0_87,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_88,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ssList(app(X1,app(X2,X3))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_46]),c_0_60]) ).
cnf(c_0_89,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_62,c_0_72]),c_0_47]),c_0_73]),c_0_49])]) ).
cnf(c_0_90,plain,
( ~ ssList(X1)
| ssItem(X2)
| duplicatefreeP(X1) ),
c_0_74 ).
cnf(c_0_91,negated_conjecture,
( ~ ssList(X1)
| ssList(app(sk4,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_60]),c_0_49])]) ).
cnf(c_0_92,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| memberP(cons(X1,X2),X1) ),
inference(er,[status(thm)],[c_0_76]) ).
cnf(c_0_93,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_94,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
inference(fof_simplification,[status(thm)],[clause86]) ).
cnf(c_0_95,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| nil != X2
| nil != X1
| app(X1,X2) = nil ),
inference(fof_simplification,[status(thm)],[clause145]) ).
cnf(c_0_96,plain,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
c_0_77 ).
cnf(c_0_97,negated_conjecture,
( app(app(X2,cons(X1,nil)),X3) != sk1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| memberP(X2,sk5(X3,X2,X1)) ),
c_0_78 ).
cnf(c_0_98,negated_conjecture,
( ~ lt(X1,sk5(X3,X2,X1))
| app(app(X2,cons(X1,nil)),X3) != sk1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1) ),
c_0_79 ).
cnf(c_0_99,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ leq(X1,X2)
| X1 = X2
| lt(X1,X2) ),
c_0_80 ).
cnf(c_0_100,negated_conjecture,
( app(app(X2,cons(X1,nil)),X3) != sk1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ssItem(sk5(X3,X2,X1)) ),
c_0_81 ).
cnf(c_0_101,negated_conjecture,
( app(app(X2,cons(X1,nil)),X3) != sk1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| leq(X1,sk5(X3,X2,X1)) ),
c_0_82 ).
cnf(c_0_102,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_83,c_0_84]),c_0_85])]),c_0_86])]) ).
cnf(c_0_103,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| ~ memberP(X1,X2)
| app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1 ),
c_0_87 ).
cnf(c_0_104,axiom,
ssList(skaf43(X1,X2)),
clause52 ).
cnf(c_0_105,axiom,
ssList(skaf42(X1,X2)),
clause53 ).
cnf(c_0_106,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_88,c_0_89]),c_0_73]),c_0_67])]) ).
cnf(c_0_107,negated_conjecture,
( ~ ssList(X2)
| duplicatefreeP(app(sk4,X2))
| ssItem(X1) ),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_108,plain,
( ~ ssList(X1)
| memberP(X1,hd(X1))
| nil = X1 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_65]),c_0_58]),c_0_69]) ).
cnf(c_0_109,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,app(X2,X3)) = app(cons(X1,X2),X3) ),
c_0_93 ).
cnf(c_0_110,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
c_0_94 ).
cnf(c_0_111,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| nil != X2
| nil != X1
| app(X1,X2) = nil ),
c_0_95 ).
cnf(c_0_112,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_96,c_0_97]),c_0_73])]) ).
cnf(c_0_113,negated_conjecture,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X3)
| app(app(X2,cons(X3,nil)),X1) != sk1
| sk5(X1,X2,X3) = X3 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_100]),c_0_101]) ).
cnf(c_0_114,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_102,c_0_103]),c_0_104]),c_0_105]),c_0_85])]),c_0_106]) ).
cnf(c_0_115,negated_conjecture,
( duplicatefreeP(app(sk4,sk4))
| ssItem(X1) ),
inference(spm,[status(thm)],[c_0_107,c_0_67]) ).
cnf(c_0_116,negated_conjecture,
memberP(sk4,hd(sk1)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_66]),c_0_67])]),c_0_68]) ).
cnf(c_0_117,plain,
( ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1)
| ssList(cons(X1,app(X2,X3))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_109]),c_0_110]) ).
cnf(c_0_118,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_111])]),c_0_73])]) ).
cnf(c_0_119,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_112,c_0_113]),c_0_73])]) ).
cnf(c_0_120,negated_conjecture,
ssItem(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_116]),c_0_67])]) ).
cnf(c_0_121,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_simplification,[status(thm)],[clause74]) ).
cnf(c_0_122,plain,
( ~ ssItem(X1)
| ssList(cons(X1,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_73])]) ).
cnf(c_0_123,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_124,negated_conjecture,
( ~ ssList(X2)
| app(app(nil,cons(X1,nil)),X2) != sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_119,c_0_120])]) ).
cnf(c_0_125,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
c_0_121 ).
cnf(c_0_126,plain,
ssList(cons(X1,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_122,c_0_120])]) ).
cnf(c_0_127,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| app(X2,skaf45(X1,X2)) = X1 ),
inference(fof_simplification,[status(thm)],[clause132]) ).
cnf(c_0_128,plain,
( ~ ssItem(X3)
| ~ ssItem(X4)
| ~ ssList(X1)
| ~ ssList(X2)
| X3 != X4
| ~ frontsegP(X1,X2)
| frontsegP(cons(X3,X1),cons(X4,X2)) ),
c_0_123 ).
cnf(c_0_129,negated_conjecture,
( ~ ssList(X2)
| app(cons(X1,nil),X2) != sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_126])]) ).
cnf(c_0_130,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| app(X2,skaf45(X1,X2)) = X1 ),
c_0_127 ).
cnf(c_0_131,axiom,
ssList(skaf45(X1,X2)),
clause51 ).
cnf(c_0_132,plain,
( ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1)
| ~ frontsegP(X2,X3)
| frontsegP(cons(X1,X2),cons(X1,X3)) ),
inference(er,[status(thm)],[c_0_128]) ).
cnf(c_0_133,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_129,c_0_130]),c_0_131]),c_0_126])])]),c_0_48])]) ).
cnf(c_0_134,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_132,c_0_65]),c_0_58]),c_0_69]) ).
cnf(c_0_135,plain,
( ~ ssList(X1)
| frontsegP(X1,nil) ),
inference(fof_simplification,[status(thm)],[clause60]) ).
cnf(c_0_136,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_133,c_0_134]),c_0_73]),c_0_48])]),c_0_53]) ).
cnf(c_0_137,plain,
( ~ ssList(X1)
| frontsegP(X1,nil) ),
c_0_135 ).
cnf(c_0_138,negated_conjecture,
~ ssList(tl(sk1)),
inference(spm,[status(thm)],[c_0_136,c_0_137]) ).
cnf(c_0_139,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_58]),c_0_48])]),c_0_53]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC234-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 08:09:37 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.44 Running first-order theorem proving
% 0.14/0.44 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
% 110.34/17.01 % Version: 3.5.1
% 110.34/17.01 % Preprocessing class: FSLSSMSMSSSNFFN.
% 110.34/17.01 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 110.34/17.01 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 110.34/17.01 % Starting new_bool_3 with 300s (1) cores
% 110.34/17.01 % Starting new_bool_1 with 300s (1) cores
% 110.34/17.01 % Starting sh5l with 300s (1) cores
% 110.34/17.01 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 1802207 completed with status 0
% 110.34/17.01 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 110.34/17.01 % Preprocessing class: FSLSSMSMSSSNFFN.
% 110.34/17.01 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 110.34/17.01 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 110.34/17.01 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 110.34/17.01 % No SInE strategy applied
% 110.34/17.01 % Search class: FGHSM-FSLM31-MFFFFFNN
% 110.34/17.01 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 110.34/17.01 % Starting SubtermCWHack with 136s (1) cores
% 110.34/17.01 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 110.34/17.01 % Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_S04BN with 136s (1) cores
% 110.34/17.01 % Starting G-E--_207_B07_F1_AE_CS_SP_PI_PS_S0Y with 136s (1) cores
% 110.34/17.01 % Starting U----_116Y_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 110.34/17.01 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 1802215 completed with status 0
% 110.34/17.01 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 110.34/17.01 % Preprocessing class: FSLSSMSMSSSNFFN.
% 110.34/17.01 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 110.34/17.01 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 110.34/17.01 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 110.34/17.01 % No SInE strategy applied
% 110.34/17.01 % Search class: FGHSM-FSLM31-MFFFFFNN
% 110.34/17.01 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 110.34/17.01 % Starting SubtermCWHack with 136s (1) cores
% 110.34/17.01 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 110.34/17.01 % Preprocessing time : 0.005 s
% 110.34/17.01 % Presaturation interreduction done
% 110.34/17.01
% 110.34/17.01 % Proof found!
% 110.34/17.01 % SZS status Unsatisfiable
% 110.34/17.01 % SZS output start CNFRefutation
% See solution above
% 110.34/17.01 % Parsed axioms : 202
% 110.34/17.01 % Removed by relevancy pruning/SinE : 0
% 110.34/17.01 % Initial clauses : 202
% 110.34/17.01 % Removed in clause preprocessing : 0
% 110.34/17.01 % Initial clauses in saturation : 202
% 110.34/17.01 % Processed clauses : 51951
% 110.34/17.01 % ...of these trivial : 844
% 110.34/17.01 % ...subsumed : 43070
% 110.34/17.01 % ...remaining for further processing : 8037
% 110.34/17.01 % Other redundant clauses eliminated : 855
% 110.34/17.01 % Clauses deleted for lack of memory : 0
% 110.34/17.01 % Backward-subsumed : 3336
% 110.34/17.01 % Backward-rewritten : 1646
% 110.34/17.01 % Generated clauses : 320215
% 110.34/17.01 % ...of the previous two non-redundant : 312986
% 110.34/17.01 % ...aggressively subsumed : 0
% 110.34/17.01 % Contextual simplify-reflections : 1045
% 110.34/17.01 % Paramodulations : 319349
% 110.34/17.01 % Factorizations : 0
% 110.34/17.01 % NegExts : 0
% 110.34/17.01 % Equation resolutions : 867
% 110.34/17.01 % Disequality decompositions : 0
% 110.34/17.01 % Total rewrite steps : 164962
% 110.34/17.01 % ...of those cached : 164295
% 110.34/17.01 % Propositional unsat checks : 1
% 110.34/17.01 % Propositional check models : 0
% 110.34/17.01 % Propositional check unsatisfiable : 0
% 110.34/17.01 % Propositional clauses : 0
% 110.34/17.01 % Propositional clauses after purity: 0
% 110.34/17.01 % Propositional unsat core size : 0
% 110.34/17.01 % Propositional preprocessing time : 0.000
% 110.34/17.01 % Propositional encoding time : 0.391
% 110.34/17.01 % Propositional solver time : 0.240
% 110.34/17.01 % Success case prop preproc time : 0.000
% 110.34/17.01 % Success case prop encoding time : 0.000
% 110.34/17.01 % Success case prop solver time : 0.000
% 110.34/17.01 % Current number of processed clauses : 2839
% 110.34/17.01 % Positive orientable unit clauses : 130
% 110.34/17.01 % Positive unorientable unit clauses: 0
% 110.34/17.01 % Negative unit clauses : 80
% 110.34/17.01 % Non-unit-clauses : 2629
% 110.34/17.01 % Current number of unprocessed clauses: 260098
% 110.34/17.01 % ...number of literals in the above : 1178455
% 110.34/17.01 % Current number of archived formulas : 0
% 110.34/17.01 % Current number of archived clauses : 5175
% 110.34/17.01 % Clause-clause subsumption calls (NU) : 10272147
% 110.34/17.01 % Rec. Clause-clause subsumption calls : 3475720
% 110.34/17.01 % Non-unit clause-clause subsumptions : 34835
% 110.34/17.01 % Unit Clause-clause subsumption calls : 61277
% 110.34/17.01 % Rewrite failures with RHS unbound : 0
% 110.34/17.01 % BW rewrite match attempts : 78
% 110.34/17.01 % BW rewrite match successes : 64
% 110.34/17.01 % Condensation attempts : 0
% 110.34/17.01 % Condensation successes : 0
% 110.34/17.01 % Termbank termtop insertions : 6500857
% 110.34/17.01 % Search garbage collected termcells : 563
% 110.34/17.01
% 110.34/17.01 % -------------------------------------------------
% 110.34/17.01 % User time : 15.619 s
% 110.34/17.01 % System time : 0.352 s
% 110.34/17.01 % Total time : 15.972 s
% 110.34/17.01 % Maximum resident set size: 3560 pages
% 110.34/17.01
% 110.34/17.01 % -------------------------------------------------
% 110.34/17.01 % User time : 76.250 s
% 110.34/17.01 % System time : 2.218 s
% 110.34/17.01 % Total time : 78.467 s
% 110.34/17.01 % Maximum resident set size: 5120 pages
% 110.34/17.01 % E exiting
%------------------------------------------------------------------------------