%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC285-1 : 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 : n010.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 02:43:47 PM UTC 2026
% Result : Unsatisfiable 0.62s 0.52s
% Output : CNFRefutation 0.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 41
% Syntax : Number of clauses : 160 ( 45 unt; 20 nHn; 148 RR)
% Number of literals : 448 ( 91 equ; 289 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-2 aty)
% Number of variables : 219 ( 17 sgn)
% 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/sandbox2/benchmark/Axioms/SWC001-0.ax',clause179) ).
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(clause143,axiom,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(X1,X2) != X3
| rearsegP(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause143) ).
cnf(clause85,axiom,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause85) ).
cnf(clause74,axiom,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause74) ).
cnf(clause86,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause86) ).
cnf(co1_11,negated_conjecture,
app(app(sk6,cons(sk5,nil)),sk7) = sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
cnf(co1_9,negated_conjecture,
ssList(sk6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
cnf(co1_10,negated_conjecture,
ssList(sk7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
cnf(clause8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
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(co1_8,negated_conjecture,
ssItem(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
cnf(clause120,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,nil),X2) = cons(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause120) ).
cnf(clause72,axiom,
( ~ ssList(X1)
| ssItem(X2)
| duplicatefreeP(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause72) ).
cnf(clause144,axiom,
( ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != X3
| frontsegP(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause144) ).
cnf(clause141,axiom,
( ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ memberP(X1,X2)
| memberP(app(X3,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause141) ).
cnf(clause131,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| app(skaf46(X1,X2),X2) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause131) ).
cnf(co1_1,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).
cnf(co1_13,negated_conjecture,
( memberP(sk7,sk8)
| memberP(sk6,sk8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
cnf(co1_12,negated_conjecture,
ssItem(sk8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
cnf(clause161,axiom,
( ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ memberP(cons(X1,X2),X3)
| X3 = X1
| memberP(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause161) ).
cnf(clause71,axiom,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause71) ).
cnf(clause140,axiom,
( ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ memberP(X1,X2)
| memberP(app(X1,X3),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause140) ).
cnf(clause50,axiom,
ssList(skaf46(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause50) ).
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(clause175,axiom,
( ~ ssList(X4)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| app(X1,cons(X2,X3)) != X4
| memberP(X4,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause175) ).
cnf(clause101,axiom,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(skaf44(X1),nil) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause101) ).
cnf(co1_17,negated_conjecture,
( ~ neq(sk4,nil)
| singletonP(sk3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_17) ).
cnf(clause150,axiom,
( ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != app(X1,X3)
| X2 = X3 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause150) ).
cnf(clause51,axiom,
ssList(skaf45(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause51) ).
cnf(co1_6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
cnf(clause100,axiom,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause100) ).
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(clause98,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause98) ).
cnf(clause62,axiom,
( ~ ssItem(X1)
| leq(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause62) ).
cnf(clause119,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause119) ).
cnf(co1_16,negated_conjecture,
( ~ leq(sk5,sk8)
| ~ leq(sk8,sk5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_16) ).
cnf(clause127,axiom,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ segmentP(X2,X1)
| ~ segmentP(X1,X2)
| X2 = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause127) ).
cnf(co1_7,negated_conjecture,
segmentP(sk4,sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
cnf(clause56,axiom,
( ~ ssList(X1)
| segmentP(X1,nil) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause56) ).
cnf(c_0_41,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_42,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_43,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(X1,X2) != X3
| rearsegP(X3,X2) ),
inference(fof_simplification,[status(thm)],[clause143]) ).
cnf(c_0_44,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
inference(fof_simplification,[status(thm)],[clause85]) ).
cnf(c_0_45,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_41 ).
cnf(c_0_46,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_simplification,[status(thm)],[clause74]) ).
cnf(c_0_47,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
inference(fof_simplification,[status(thm)],[clause86]) ).
cnf(c_0_48,negated_conjecture,
app(app(sk6,cons(sk5,nil)),sk7) = sk1,
co1_11 ).
cnf(c_0_49,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X3,X2),X1) = app(X3,app(X2,X1)) ),
c_0_42 ).
cnf(c_0_50,negated_conjecture,
ssList(sk6),
co1_9 ).
cnf(c_0_51,negated_conjecture,
ssList(sk7),
co1_10 ).
cnf(c_0_52,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(X1,X2) != X3
| rearsegP(X3,X2) ),
c_0_43 ).
cnf(c_0_53,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
c_0_44 ).
cnf(c_0_54,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_45]) ).
cnf(c_0_55,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
c_0_46 ).
cnf(c_0_56,axiom,
ssList(nil),
clause8 ).
cnf(c_0_57,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
c_0_47 ).
cnf(c_0_58,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_59,negated_conjecture,
( ~ ssList(cons(sk5,nil))
| app(sk6,app(cons(sk5,nil),sk7)) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]),c_0_51])]) ).
cnf(c_0_60,negated_conjecture,
ssItem(sk5),
co1_8 ).
cnf(c_0_61,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,nil),X2) = cons(X1,X2) ),
inference(fof_simplification,[status(thm)],[clause120]) ).
cnf(c_0_62,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| rearsegP(app(X1,X2),X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_52]),c_0_53]) ).
cnf(c_0_63,plain,
( ~ duplicatefreeP(app(cons(X1,X2),cons(X1,X3)))
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(app(cons(X1,X2),cons(X1,X3)))
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56])]),c_0_57]) ).
cnf(c_0_64,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,app(X2,X3)) = app(cons(X1,X2),X3) ),
c_0_58 ).
cnf(c_0_65,negated_conjecture,
app(sk6,app(cons(sk5,nil),sk7)) = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_57]),c_0_60]),c_0_56])]) ).
cnf(c_0_66,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,nil),X2) = cons(X1,X2) ),
c_0_61 ).
cnf(c_0_67,plain,
( ~ ssList(X1)
| ssItem(X2)
| duplicatefreeP(X1) ),
inference(fof_simplification,[status(thm)],[clause72]) ).
cnf(c_0_68,negated_conjecture,
( ~ ssList(app(sk6,cons(sk5,nil)))
| rearsegP(sk1,sk7) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_48]),c_0_51])]) ).
cnf(c_0_69,plain,
( ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != X3
| frontsegP(X3,X1) ),
inference(fof_simplification,[status(thm)],[clause144]) ).
cnf(c_0_70,plain,
( ~ duplicatefreeP(cons(X1,app(X2,cons(X1,X3))))
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(cons(X1,app(X2,cons(X1,X3))))
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_57]) ).
cnf(c_0_71,negated_conjecture,
app(sk6,cons(sk5,sk7)) = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_60]),c_0_51])]) ).
cnf(c_0_72,plain,
( ~ ssList(X1)
| ssItem(X2)
| duplicatefreeP(X1) ),
c_0_67 ).
cnf(c_0_73,plain,
( ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ memberP(X1,X2)
| memberP(app(X3,X1),X2) ),
inference(fof_simplification,[status(thm)],[clause141]) ).
cnf(c_0_74,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| app(skaf46(X1,X2),X2) = X1 ),
inference(fof_simplification,[status(thm)],[clause131]) ).
cnf(c_0_75,negated_conjecture,
( ~ ssList(cons(sk5,nil))
| rearsegP(sk1,sk7) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_53]),c_0_50])]) ).
cnf(c_0_76,plain,
( ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != X3
| frontsegP(X3,X1) ),
c_0_69 ).
cnf(c_0_77,negated_conjecture,
( ~ duplicatefreeP(cons(sk5,sk1))
| ~ ssList(cons(sk5,sk1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_60]),c_0_51]),c_0_50])]) ).
cnf(c_0_78,plain,
( ~ ssList(X3)
| ~ ssItem(X2)
| duplicatefreeP(cons(X2,X3))
| ssItem(X1) ),
inference(spm,[status(thm)],[c_0_72,c_0_57]) ).
cnf(c_0_79,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_80,plain,
( ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ memberP(X1,X2)
| memberP(app(X3,X1),X2) ),
c_0_73 ).
cnf(c_0_81,negated_conjecture,
( memberP(sk7,sk8)
| memberP(sk6,sk8) ),
co1_13 ).
cnf(c_0_82,negated_conjecture,
ssItem(sk8),
co1_12 ).
cnf(c_0_83,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| app(skaf46(X1,X2),X2) = X1 ),
c_0_74 ).
cnf(c_0_84,negated_conjecture,
rearsegP(sk1,sk7),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_57]),c_0_60]),c_0_56])]) ).
cnf(c_0_85,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| frontsegP(app(X1,X2),X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_76]),c_0_53]) ).
cnf(c_0_86,plain,
( ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ memberP(cons(X1,X2),X3)
| X3 = X1
| memberP(X2,X3) ),
inference(fof_simplification,[status(thm)],[clause161]) ).
cnf(c_0_87,negated_conjecture,
( ~ ssList(cons(sk5,sk1))
| ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_60]),c_0_79])]) ).
cnf(c_0_88,plain,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[clause71]) ).
cnf(c_0_89,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ memberP(X1,X2)
| memberP(app(X1,X3),X2) ),
inference(fof_simplification,[status(thm)],[clause140]) ).
cnf(c_0_90,negated_conjecture,
( ~ ssList(X1)
| memberP(sk6,sk8)
| memberP(app(X1,sk7),sk8) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82]),c_0_51])]) ).
cnf(c_0_91,negated_conjecture,
app(skaf46(sk1,sk7),sk7) = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_51]),c_0_79])]) ).
cnf(c_0_92,axiom,
ssList(skaf46(X1,X2)),
clause50 ).
cnf(c_0_93,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| app(X2,skaf45(X1,X2)) = X1 ),
inference(fof_simplification,[status(thm)],[clause132]) ).
cnf(c_0_94,negated_conjecture,
( ~ ssList(cons(sk5,sk7))
| frontsegP(sk1,sk6) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_71]),c_0_50])]) ).
cnf(c_0_95,plain,
( ~ ssList(X4)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| app(X1,cons(X2,X3)) != X4
| memberP(X4,X2) ),
inference(fof_simplification,[status(thm)],[clause175]) ).
cnf(c_0_96,plain,
( ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ memberP(cons(X1,X2),X3)
| X3 = X1
| memberP(X2,X3) ),
c_0_86 ).
cnf(c_0_97,negated_conjecture,
ssItem(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_57]),c_0_60]),c_0_79])]) ).
cnf(c_0_98,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(skaf44(X1),nil) = X1 ),
inference(fof_simplification,[status(thm)],[clause101]) ).
cnf(c_0_99,plain,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
c_0_88 ).
cnf(c_0_100,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ memberP(X1,X2)
| memberP(app(X1,X3),X2) ),
c_0_89 ).
cnf(c_0_101,negated_conjecture,
( memberP(sk1,sk8)
| memberP(sk6,sk8) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_92])]) ).
cnf(c_0_102,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| app(X2,skaf45(X1,X2)) = X1 ),
c_0_93 ).
cnf(c_0_103,negated_conjecture,
frontsegP(sk1,sk6),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_57]),c_0_60]),c_0_51])]) ).
cnf(c_0_104,negated_conjecture,
( ~ neq(sk4,nil)
| singletonP(sk3) ),
inference(fof_simplification,[status(thm)],[co1_17]) ).
cnf(c_0_105,plain,
( ~ ssList(X4)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| app(X1,cons(X2,X3)) != X4
| memberP(X4,X2) ),
c_0_95 ).
cnf(c_0_106,plain,
( ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != app(X1,X3)
| X2 = X3 ),
inference(fof_simplification,[status(thm)],[clause150]) ).
cnf(c_0_107,plain,
( ~ ssList(X3)
| ~ memberP(cons(X1,X3),X2)
| memberP(X3,X2)
| X1 = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_96,c_0_97]),c_0_97])]) ).
cnf(c_0_108,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(skaf44(X1),nil) = X1 ),
c_0_98 ).
cnf(c_0_109,plain,
~ memberP(nil,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_97])]) ).
cnf(c_0_110,negated_conjecture,
( ~ ssList(X1)
| memberP(sk1,sk8)
| memberP(app(sk6,X1),sk8) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_82]),c_0_50])]) ).
cnf(c_0_111,negated_conjecture,
app(sk6,skaf45(sk1,sk6)) = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_50]),c_0_79])]) ).
cnf(c_0_112,axiom,
ssList(skaf45(X1,X2)),
clause51 ).
cnf(c_0_113,negated_conjecture,
( ~ neq(sk4,nil)
| singletonP(sk3) ),
c_0_104 ).
cnf(c_0_114,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_115,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
inference(fof_simplification,[status(thm)],[clause100]) ).
cnf(c_0_116,negated_conjecture,
ssList(sk2),
co1_2 ).
cnf(c_0_117,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_118,plain,
( ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(app(X1,cons(X2,X3)))
| ~ ssItem(X2)
| memberP(app(X1,cons(X2,X3)),X2) ),
inference(er,[status(thm)],[c_0_105]) ).
cnf(c_0_119,plain,
( ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != app(X1,X3)
| X2 = X3 ),
c_0_106 ).
cnf(c_0_120,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| ~ memberP(X1,X2)
| skaf44(X1) = X2 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_56])]),c_0_109]) ).
cnf(c_0_121,negated_conjecture,
memberP(sk1,sk8),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_112])]) ).
cnf(c_0_122,negated_conjecture,
( ~ neq(sk4,nil)
| singletonP(sk1) ),
inference(rw,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_123,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
c_0_115 ).
cnf(c_0_124,negated_conjecture,
ssList(sk4),
inference(rw,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_125,negated_conjecture,
memberP(sk1,sk5),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_71]),c_0_60]),c_0_79]),c_0_51]),c_0_50])]) ).
cnf(c_0_126,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
inference(fof_simplification,[status(thm)],[clause98]) ).
cnf(c_0_127,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(cons(sk5,sk7))
| app(sk6,X1) != sk1
| cons(sk5,sk7) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_71]),c_0_50])]) ).
cnf(c_0_128,negated_conjecture,
( ~ singletonP(sk1)
| skaf44(sk1) = sk8 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_79])]) ).
cnf(c_0_129,negated_conjecture,
( singletonP(sk1)
| nil = sk4 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_124]),c_0_56])]) ).
cnf(c_0_130,negated_conjecture,
( ~ singletonP(sk1)
| skaf44(sk1) = sk5 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_125]),c_0_79])]) ).
cnf(c_0_131,plain,
( ~ ssItem(X1)
| leq(X1,X1) ),
inference(fof_simplification,[status(thm)],[clause62]) ).
cnf(c_0_132,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X2 ),
inference(fof_simplification,[status(thm)],[clause119]) ).
cnf(c_0_133,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
c_0_126 ).
cnf(c_0_134,negated_conjecture,
( ~ ssList(cons(sk5,sk7))
| cons(sk5,sk7) = skaf45(sk1,sk6) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_111]),c_0_112])]) ).
cnf(c_0_135,plain,
( ~ ssList(X2)
| ssList(cons(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_97])]) ).
cnf(c_0_136,negated_conjecture,
( ~ leq(sk5,sk8)
| ~ leq(sk8,sk5) ),
inference(fof_simplification,[status(thm)],[co1_16]) ).
cnf(c_0_137,negated_conjecture,
( nil = sk4
| skaf44(sk1) = sk8 ),
inference(spm,[status(thm)],[c_0_128,c_0_129]) ).
cnf(c_0_138,negated_conjecture,
( nil = sk4
| skaf44(sk1) = sk5 ),
inference(spm,[status(thm)],[c_0_130,c_0_129]) ).
cnf(c_0_139,plain,
( ~ ssItem(X1)
| leq(X1,X1) ),
c_0_131 ).
cnf(c_0_140,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X2 ),
c_0_132 ).
cnf(c_0_141,plain,
( ~ ssList(X2)
| cons(X1,X2) != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_133,c_0_97])]) ).
cnf(c_0_142,negated_conjecture,
cons(sk5,sk7) = skaf45(sk1,sk6),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_51])]) ).
cnf(c_0_143,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ segmentP(X2,X1)
| ~ segmentP(X1,X2)
| X2 = X1 ),
inference(fof_simplification,[status(thm)],[clause127]) ).
cnf(c_0_144,negated_conjecture,
segmentP(sk4,sk3),
co1_7 ).
cnf(c_0_145,plain,
( ~ ssList(X1)
| segmentP(X1,nil) ),
inference(fof_simplification,[status(thm)],[clause56]) ).
cnf(c_0_146,negated_conjecture,
( ~ leq(sk5,sk8)
| ~ leq(sk8,sk5) ),
c_0_136 ).
cnf(c_0_147,negated_conjecture,
( sk8 = sk5
| nil = sk4 ),
inference(spm,[status(thm)],[c_0_137,c_0_138]) ).
cnf(c_0_148,plain,
leq(X1,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_139,c_0_97])]) ).
cnf(c_0_149,negated_conjecture,
( ~ ssList(cons(sk5,sk7))
| nil != sk1
| cons(sk5,sk7) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_71]),c_0_50])]) ).
cnf(c_0_150,negated_conjecture,
skaf45(sk1,sk6) != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_142]),c_0_51])]) ).
cnf(c_0_151,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ segmentP(X2,X1)
| ~ segmentP(X1,X2)
| X2 = X1 ),
c_0_143 ).
cnf(c_0_152,negated_conjecture,
segmentP(sk4,sk1),
inference(rw,[status(thm)],[c_0_144,c_0_114]) ).
cnf(c_0_153,plain,
( ~ ssList(X1)
| segmentP(X1,nil) ),
c_0_145 ).
cnf(c_0_154,negated_conjecture,
nil = sk4,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_148])]) ).
cnf(c_0_155,negated_conjecture,
nil != sk1,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_149,c_0_142]),c_0_142]),c_0_112])]),c_0_150]) ).
cnf(c_0_156,negated_conjecture,
( ~ segmentP(sk1,sk4)
| sk4 = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_152]),c_0_124]),c_0_79])]) ).
cnf(c_0_157,plain,
( ~ ssList(X1)
| segmentP(X1,sk4) ),
inference(rw,[status(thm)],[c_0_153,c_0_154]) ).
cnf(c_0_158,negated_conjecture,
sk4 != sk1,
inference(rw,[status(thm)],[c_0_155,c_0_154]) ).
cnf(c_0_159,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_157]),c_0_79])]),c_0_158]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC285-1 : 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 : n010.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 08:12:41 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 0.62/0.52 % Version: 3.5.1
% 0.62/0.52 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.62/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.62/0.52 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.62/0.52 % Starting new_bool_3 with 300s (1) cores
% 0.62/0.52 % Starting new_bool_1 with 300s (1) cores
% 0.62/0.52 % Starting sh5l with 300s (1) cores
% 0.62/0.52 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 441201 completed with status 0
% 0.62/0.52 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.62/0.52 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.62/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.62/0.52 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.62/0.52 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.62/0.52 % No SInE strategy applied
% 0.62/0.52 % Search class: FGHSM-FSLM21-MFFFFFNN
% 0.62/0.52 % Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 0.62/0.52 % Starting SubtermCWHack with 136s (1) cores
% 0.62/0.52 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.62/0.52 % Starting G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y with 136s (1) cores
% 0.62/0.52 % Starting G-E--_200_B02_F1_SE_CS_SP_PI_S2k with 136s (1) cores
% 0.62/0.52 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 0.62/0.52 % G-E--_200_B02_F1_SE_CS_SP_PI_S2k with pid 441210 completed with status 0
% 0.62/0.52 % Result found by G-E--_200_B02_F1_SE_CS_SP_PI_S2k
% 0.62/0.52 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.62/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.62/0.52 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.62/0.52 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.62/0.52 % No SInE strategy applied
% 0.62/0.52 % Search class: FGHSM-FSLM21-MFFFFFNN
% 0.62/0.52 % Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 0.62/0.52 % Starting SubtermCWHack with 136s (1) cores
% 0.62/0.52 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.62/0.52 % Starting G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y with 136s (1) cores
% 0.62/0.52 % Starting G-E--_200_B02_F1_SE_CS_SP_PI_S2k with 136s (1) cores
% 0.62/0.52 % Preprocessing time : 0.002 s
% 0.62/0.52
% 0.62/0.52 % Proof found!
% 0.62/0.52 % SZS status Unsatisfiable
% 0.62/0.52 % SZS output start CNFRefutation
% See solution above
% 0.62/0.52 % Parsed axioms : 202
% 0.62/0.52 % Removed by relevancy pruning/SinE : 0
% 0.62/0.52 % Initial clauses : 202
% 0.62/0.52 % Removed in clause preprocessing : 0
% 0.62/0.52 % Initial clauses in saturation : 202
% 0.62/0.52 % Processed clauses : 1133
% 0.62/0.52 % ...of these trivial : 18
% 0.62/0.52 % ...subsumed : 315
% 0.62/0.52 % ...remaining for further processing : 800
% 0.62/0.52 % Other redundant clauses eliminated : 80
% 0.62/0.52 % Clauses deleted for lack of memory : 0
% 0.62/0.52 % Backward-subsumed : 67
% 0.62/0.52 % Backward-rewritten : 333
% 0.62/0.52 % Generated clauses : 3471
% 0.62/0.52 % ...of the previous two non-redundant : 3288
% 0.62/0.52 % ...aggressively subsumed : 0
% 0.62/0.52 % Contextual simplify-reflections : 34
% 0.62/0.52 % Paramodulations : 3385
% 0.62/0.52 % Factorizations : 0
% 0.62/0.52 % NegExts : 0
% 0.62/0.52 % Equation resolutions : 87
% 0.62/0.52 % Disequality decompositions : 0
% 0.62/0.52 % Total rewrite steps : 3820
% 0.62/0.52 % ...of those cached : 3603
% 0.62/0.52 % Propositional unsat checks : 0
% 0.62/0.52 % Propositional check models : 0
% 0.62/0.52 % Propositional check unsatisfiable : 0
% 0.62/0.52 % Propositional clauses : 0
% 0.62/0.52 % Propositional clauses after purity: 0
% 0.62/0.52 % Propositional unsat core size : 0
% 0.62/0.52 % Propositional preprocessing time : 0.000
% 0.62/0.52 % Propositional encoding time : 0.000
% 0.62/0.52 % Propositional solver time : 0.000
% 0.62/0.52 % Success case prop preproc time : 0.000
% 0.62/0.52 % Success case prop encoding time : 0.000
% 0.62/0.52 % Success case prop solver time : 0.000
% 0.62/0.52 % Current number of processed clauses : 377
% 0.62/0.52 % Positive orientable unit clauses : 103
% 0.62/0.52 % Positive unorientable unit clauses: 0
% 0.62/0.52 % Negative unit clauses : 18
% 0.62/0.52 % Non-unit-clauses : 256
% 0.62/0.52 % Current number of unprocessed clauses: 2221
% 0.62/0.52 % ...number of literals in the above : 11021
% 0.62/0.52 % Current number of archived formulas : 0
% 0.62/0.52 % Current number of archived clauses : 400
% 0.62/0.52 % Clause-clause subsumption calls (NU) : 39066
% 0.62/0.52 % Rec. Clause-clause subsumption calls : 15786
% 0.62/0.52 % Non-unit clause-clause subsumptions : 274
% 0.62/0.52 % Unit Clause-clause subsumption calls : 3105
% 0.62/0.52 % Rewrite failures with RHS unbound : 0
% 0.62/0.52 % BW rewrite match attempts : 65
% 0.62/0.52 % BW rewrite match successes : 56
% 0.62/0.52 % Condensation attempts : 0
% 0.62/0.52 % Condensation successes : 0
% 0.62/0.52 % Termbank termtop insertions : 75837
% 0.62/0.52 % Search garbage collected termcells : 537
% 0.62/0.52
% 0.62/0.52 % -------------------------------------------------
% 0.62/0.52 % User time : 0.084 s
% 0.62/0.52 % System time : 0.008 s
% 0.62/0.52 % Total time : 0.092 s
% 0.62/0.52 % Maximum resident set size: 4068 pages
% 0.62/0.52
% 0.62/0.52 % -------------------------------------------------
% 0.62/0.52 % User time : 0.383 s
% 0.62/0.52 % System time : 0.045 s
% 0.62/0.52 % Total time : 0.429 s
% 0.62/0.52 % Maximum resident set size: 5120 pages
% 0.62/0.52 % E exiting
%------------------------------------------------------------------------------