%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC114-1 : 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 : n015.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 02:43:04 PM UTC 2026
% Result : Unsatisfiable 51.89s 8.07s
% Output : CNFRefutation 51.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 37
% Syntax : Number of clauses : 147 ( 42 unt; 21 nHn; 133 RR)
% Number of literals : 390 ( 84 equ; 242 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 193 ( 22 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(co1_7,negated_conjecture,
( nil != sk1
| nil != sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
cnf(clause98,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause98) ).
cnf(co1_10,negated_conjecture,
( nil = sk4
| cons(sk5,nil) = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
cnf(co1_6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
cnf(co1_5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
cnf(co1_13,negated_conjecture,
( nil = sk3
| cons(sk5,nil) = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
cnf(clause8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
cnf(co1_8,negated_conjecture,
( nil = sk4
| ssItem(sk5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
cnf(co1_9,negated_conjecture,
( nil = sk3
| ssItem(sk5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
cnf(clause143,axiom,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(X1,X2) != X3
| rearsegP(X3,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause143) ).
cnf(clause85,axiom,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause85) ).
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(co1_1,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
cnf(clause151,axiom,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(X1,X2) != app(X3,X2)
| X1 = X3 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause151) ).
cnf(clause131,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| app(skaf46(X1,X2),X2) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause131) ).
cnf(clause136,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ rearsegP(X1,X2)
| rearsegP(app(X3,X1),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause136) ).
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(clause137,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ frontsegP(X1,X2)
| frontsegP(app(X1,X3),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause137) ).
cnf(clause60,axiom,
( ~ ssList(X1)
| frontsegP(X1,nil) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause60) ).
cnf(clause50,axiom,
ssList(skaf46(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause50) ).
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(clause132,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| app(X2,skaf45(X1,X2)) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause132) ).
cnf(clause86,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).
cnf(clause74,axiom,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause74) ).
cnf(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(clause172,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ segmentP(X1,X2)
| segmentP(app(app(X4,X1),X3),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause172) ).
cnf(clause57,axiom,
( ~ ssList(X1)
| segmentP(X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause57) ).
cnf(clause51,axiom,
ssList(skaf45(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause51) ).
cnf(clause72,axiom,
( ~ ssList(X1)
| ssItem(X2)
| duplicatefreeP(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause72) ).
cnf(clause61,axiom,
( ~ ssList(X1)
| frontsegP(X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause61) ).
cnf(co1_14,negated_conjecture,
( nil = sk3
| memberP(sk4,sk5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
cnf(co1_2,negated_conjecture,
ssList(sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_2) ).
cnf(co1_16,negated_conjecture,
( ~ segmentP(sk2,sk1)
| ~ neq(sk1,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_16) ).
cnf(clause152,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ segmentP(X2,X3)
| ~ segmentP(X1,X2)
| segmentP(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause152) ).
cnf(clause100,axiom,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause100) ).
cnf(c_0_37,negated_conjecture,
( nil != sk1
| nil != sk2 ),
inference(fof_simplification,[status(thm)],[co1_7]) ).
cnf(c_0_38,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
inference(fof_simplification,[status(thm)],[clause98]) ).
cnf(c_0_39,negated_conjecture,
( nil = sk4
| cons(sk5,nil) = sk3 ),
co1_10 ).
cnf(c_0_40,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_41,negated_conjecture,
( nil != sk1
| nil != sk2 ),
c_0_37 ).
cnf(c_0_42,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_43,negated_conjecture,
( nil = sk3
| cons(sk5,nil) = sk3 ),
co1_13 ).
cnf(c_0_44,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
c_0_38 ).
cnf(c_0_45,negated_conjecture,
( nil = sk4
| cons(sk5,nil) = sk1 ),
inference(rw,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_46,axiom,
ssList(nil),
clause8 ).
cnf(c_0_47,negated_conjecture,
( nil = sk4
| ssItem(sk5) ),
co1_8 ).
cnf(c_0_48,negated_conjecture,
( nil != sk4
| nil != sk1 ),
inference(rw,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_49,negated_conjecture,
( nil = sk3
| ssItem(sk5) ),
co1_9 ).
cnf(c_0_50,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(X1,X2) != X3
| rearsegP(X3,X2) ),
inference(fof_simplification,[status(thm)],[clause143]) ).
cnf(c_0_51,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
inference(fof_simplification,[status(thm)],[clause85]) ).
cnf(c_0_52,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,nil),X2) = cons(X1,X2) ),
inference(fof_simplification,[status(thm)],[clause120]) ).
cnf(c_0_53,negated_conjecture,
( nil = sk1
| cons(sk5,nil) = sk1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_40]),c_0_40]) ).
cnf(c_0_54,negated_conjecture,
nil != sk1,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46])]),c_0_47]),c_0_48]) ).
cnf(c_0_55,negated_conjecture,
( ssItem(sk5)
| nil = sk1 ),
inference(rw,[status(thm)],[c_0_49,c_0_40]) ).
cnf(c_0_56,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(X1,X2) != X3
| rearsegP(X3,X2) ),
c_0_50 ).
cnf(c_0_57,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
c_0_51 ).
cnf(c_0_58,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,nil),X2) = cons(X1,X2) ),
c_0_52 ).
cnf(c_0_59,negated_conjecture,
cons(sk5,nil) = sk1,
inference(sr,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_60,negated_conjecture,
ssItem(sk5),
inference(sr,[status(thm)],[c_0_55,c_0_54]) ).
cnf(c_0_61,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| rearsegP(app(X1,X2),X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_56]),c_0_57]) ).
cnf(c_0_62,negated_conjecture,
( ~ ssList(X1)
| app(sk1,X1) = cons(sk5,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60])]) ).
cnf(c_0_63,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_64,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(X1,X2) != app(X3,X2)
| X1 = X3 ),
inference(fof_simplification,[status(thm)],[clause151]) ).
cnf(c_0_65,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| app(skaf46(X1,X2),X2) = X1 ),
inference(fof_simplification,[status(thm)],[clause131]) ).
cnf(c_0_66,negated_conjecture,
( ~ ssList(X1)
| rearsegP(cons(sk5,X1),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63])]) ).
cnf(c_0_67,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(X1,X2) != app(X3,X2)
| X1 = X3 ),
c_0_64 ).
cnf(c_0_68,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| app(skaf46(X1,X2),X2) = X1 ),
c_0_65 ).
cnf(c_0_69,negated_conjecture,
rearsegP(sk1,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_59]),c_0_46])]) ).
cnf(c_0_70,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ rearsegP(X1,X2)
| rearsegP(app(X3,X1),X2) ),
inference(fof_simplification,[status(thm)],[clause136]) ).
cnf(c_0_71,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| X1 != X2
| memberP(cons(X2,X3),X1) ),
inference(fof_simplification,[status(thm)],[clause138]) ).
cnf(c_0_72,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ frontsegP(X1,X2)
| frontsegP(app(X1,X3),X2) ),
inference(fof_simplification,[status(thm)],[clause137]) ).
cnf(c_0_73,plain,
( ~ ssList(X1)
| frontsegP(X1,nil) ),
inference(fof_simplification,[status(thm)],[clause60]) ).
cnf(c_0_74,negated_conjecture,
( ~ ssList(X2)
| ~ ssList(X1)
| app(X1,X2) != cons(sk5,X2)
| sk1 = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_62]),c_0_63])]) ).
cnf(c_0_75,negated_conjecture,
app(skaf46(sk1,nil),nil) = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_46]),c_0_63])]) ).
cnf(c_0_76,axiom,
ssList(skaf46(X1,X2)),
clause50 ).
cnf(c_0_77,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ rearsegP(X1,X2)
| rearsegP(app(X3,X1),X2) ),
c_0_70 ).
cnf(c_0_78,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| X1 != X2
| memberP(cons(X2,X3),X1) ),
c_0_71 ).
cnf(c_0_79,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ frontsegP(X1,X2)
| frontsegP(app(X1,X3),X2) ),
c_0_72 ).
cnf(c_0_80,plain,
( ~ ssList(X1)
| frontsegP(X1,nil) ),
c_0_73 ).
cnf(c_0_81,negated_conjecture,
skaf46(sk1,nil) = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_59]),c_0_76]),c_0_46])]) ).
cnf(c_0_82,negated_conjecture,
( ~ ssList(X1)
| rearsegP(app(X1,sk1),nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_69]),c_0_46]),c_0_63])]) ).
cnf(c_0_83,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_84,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_85,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| memberP(cons(X1,X2),X1) ),
inference(er,[status(thm)],[c_0_78]) ).
cnf(c_0_86,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| app(X2,skaf45(X1,X2)) = X1 ),
inference(fof_simplification,[status(thm)],[clause132]) ).
cnf(c_0_87,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| frontsegP(app(X1,X2),nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_46])]) ).
cnf(c_0_88,negated_conjecture,
app(sk1,nil) = sk1,
inference(rw,[status(thm)],[c_0_75,c_0_81]) ).
cnf(c_0_89,negated_conjecture,
rearsegP(cons(sk5,sk1),nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_62]),c_0_63])]) ).
cnf(c_0_90,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
inference(fof_simplification,[status(thm)],[clause86]) ).
cnf(c_0_91,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_83 ).
cnf(c_0_92,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| ~ memberP(X1,X2)
| app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1 ),
c_0_84 ).
cnf(c_0_93,negated_conjecture,
memberP(sk1,sk5),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_59]),c_0_60]),c_0_46])]) ).
cnf(c_0_94,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_simplification,[status(thm)],[clause74]) ).
cnf(c_0_95,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| app(X2,skaf45(X1,X2)) = X1 ),
c_0_86 ).
cnf(c_0_96,negated_conjecture,
frontsegP(sk1,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_46]),c_0_63])]) ).
cnf(c_0_97,negated_conjecture,
( ~ ssList(cons(sk5,sk1))
| app(skaf46(cons(sk5,sk1),nil),nil) = cons(sk5,sk1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_89]),c_0_46])]) ).
cnf(c_0_98,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
c_0_90 ).
cnf(c_0_99,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_91]) ).
cnf(c_0_100,negated_conjecture,
app(skaf42(sk1,sk5),cons(sk5,skaf43(sk5,sk1))) = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_60]),c_0_63])]) ).
cnf(c_0_101,axiom,
ssList(skaf43(X1,X2)),
clause52 ).
cnf(c_0_102,axiom,
ssList(skaf42(X1,X2)),
clause53 ).
cnf(c_0_103,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ segmentP(X1,X2)
| segmentP(app(app(X4,X1),X3),X2) ),
inference(fof_simplification,[status(thm)],[clause172]) ).
cnf(c_0_104,plain,
( ~ ssList(X1)
| segmentP(X1,X1) ),
inference(fof_simplification,[status(thm)],[clause57]) ).
cnf(c_0_105,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
c_0_94 ).
cnf(c_0_106,negated_conjecture,
app(nil,skaf45(sk1,nil)) = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_46]),c_0_63])]) ).
cnf(c_0_107,axiom,
ssList(skaf45(X1,X2)),
clause51 ).
cnf(c_0_108,plain,
( ~ ssList(X1)
| ssItem(X2)
| duplicatefreeP(X1) ),
inference(fof_simplification,[status(thm)],[clause72]) ).
cnf(c_0_109,negated_conjecture,
app(skaf46(cons(sk5,sk1),nil),nil) = cons(sk5,sk1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_60]),c_0_63])]) ).
cnf(c_0_110,negated_conjecture,
( ~ duplicatefreeP(app(sk1,cons(sk5,X1)))
| ~ ssList(X1)
| ~ ssList(app(sk1,cons(sk5,X1))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_60]),c_0_101]),c_0_102])]) ).
cnf(c_0_111,plain,
( ~ ssList(X1)
| frontsegP(X1,X1) ),
inference(fof_simplification,[status(thm)],[clause61]) ).
cnf(c_0_112,negated_conjecture,
( nil = sk3
| memberP(sk4,sk5) ),
co1_14 ).
cnf(c_0_113,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ segmentP(X1,X2)
| segmentP(app(app(X4,X1),X3),X2) ),
c_0_103 ).
cnf(c_0_114,plain,
( ~ ssList(X1)
| segmentP(X1,X1) ),
c_0_104 ).
cnf(c_0_115,negated_conjecture,
skaf45(sk1,nil) = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_107])]) ).
cnf(c_0_116,plain,
( ~ ssList(X1)
| ssItem(X2)
| duplicatefreeP(X1) ),
c_0_108 ).
cnf(c_0_117,negated_conjecture,
ssList(cons(sk5,sk1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_109]),c_0_76]),c_0_46])]) ).
cnf(c_0_118,negated_conjecture,
( ~ duplicatefreeP(app(sk1,sk1))
| ~ ssList(app(sk1,sk1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_59]),c_0_46])]) ).
cnf(c_0_119,plain,
( ~ ssList(X1)
| frontsegP(X1,X1) ),
c_0_111 ).
cnf(c_0_120,negated_conjecture,
( memberP(sk4,sk5)
| nil = sk1 ),
inference(rw,[status(thm)],[c_0_112,c_0_40]) ).
cnf(c_0_121,negated_conjecture,
ssList(sk2),
co1_2 ).
cnf(c_0_122,plain,
( ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| segmentP(app(app(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_123,negated_conjecture,
app(nil,sk1) = sk1,
inference(rw,[status(thm)],[c_0_106,c_0_115]) ).
cnf(c_0_124,negated_conjecture,
( duplicatefreeP(cons(sk5,sk1))
| ssItem(X1) ),
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_125,negated_conjecture,
~ duplicatefreeP(cons(sk5,sk1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_62]),c_0_117]),c_0_63])]) ).
cnf(c_0_126,plain,
( ~ ssList(X1)
| app(X1,skaf45(X1,X1)) = X1 ),
inference(spm,[status(thm)],[c_0_95,c_0_119]) ).
cnf(c_0_127,negated_conjecture,
memberP(sk4,sk5),
inference(sr,[status(thm)],[c_0_120,c_0_54]) ).
cnf(c_0_128,negated_conjecture,
ssList(sk4),
inference(rw,[status(thm)],[c_0_121,c_0_42]) ).
cnf(c_0_129,negated_conjecture,
( ~ segmentP(sk2,sk1)
| ~ neq(sk1,nil) ),
inference(fof_simplification,[status(thm)],[co1_16]) ).
cnf(c_0_130,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ segmentP(X2,X3)
| ~ segmentP(X1,X2)
| segmentP(X1,X3) ),
inference(fof_simplification,[status(thm)],[clause152]) ).
cnf(c_0_131,negated_conjecture,
( ~ ssList(X1)
| segmentP(app(sk1,X1),sk1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_46]),c_0_63])]) ).
cnf(c_0_132,negated_conjecture,
ssItem(X1),
inference(sr,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_133,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| segmentP(app(X1,X2),X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_126]),c_0_107])]),c_0_57]) ).
cnf(c_0_134,negated_conjecture,
app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))) = sk4,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_127]),c_0_60]),c_0_128])]) ).
cnf(c_0_135,negated_conjecture,
( ~ segmentP(sk2,sk1)
| ~ neq(sk1,nil) ),
c_0_129 ).
cnf(c_0_136,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
inference(fof_simplification,[status(thm)],[clause100]) ).
cnf(c_0_137,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ segmentP(X2,X3)
| ~ segmentP(X1,X2)
| segmentP(X1,X3) ),
c_0_130 ).
cnf(c_0_138,negated_conjecture,
( ~ ssList(X1)
| segmentP(cons(sk5,X1),sk1) ),
inference(spm,[status(thm)],[c_0_131,c_0_62]) ).
cnf(c_0_139,plain,
( ~ ssList(X2)
| ssList(cons(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_98,c_0_132])]) ).
cnf(c_0_140,negated_conjecture,
( ~ ssList(cons(sk5,skaf43(sk5,sk4)))
| segmentP(sk4,cons(sk5,skaf43(sk5,sk4))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_102])]) ).
cnf(c_0_141,negated_conjecture,
( ~ segmentP(sk4,sk1)
| ~ neq(sk1,nil) ),
inference(rw,[status(thm)],[c_0_135,c_0_42]) ).
cnf(c_0_142,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
c_0_136 ).
cnf(c_0_143,negated_conjecture,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ segmentP(X1,cons(sk5,X2))
| segmentP(X1,sk1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_63])]),c_0_139]) ).
cnf(c_0_144,negated_conjecture,
segmentP(sk4,cons(sk5,skaf43(sk5,sk4))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_139]),c_0_101])]) ).
cnf(c_0_145,negated_conjecture,
~ segmentP(sk4,sk1),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_142]),c_0_63]),c_0_46])]),c_0_54]) ).
cnf(c_0_146,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_144]),c_0_128]),c_0_101])]),c_0_145]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC114-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.35 % Computer : n015.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 07:59:37 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 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
% 51.89/8.07 % Version: 3.5.1
% 51.89/8.07 % Preprocessing class: FSLSSMSMSSSNFFN.
% 51.89/8.07 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 51.89/8.07 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 51.89/8.07 % Starting new_bool_3 with 300s (1) cores
% 51.89/8.07 % Starting new_bool_1 with 300s (1) cores
% 51.89/8.07 % Starting sh5l with 300s (1) cores
% 51.89/8.07 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 981833 completed with status 0
% 51.89/8.07 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 51.89/8.07 % Preprocessing class: FSLSSMSMSSSNFFN.
% 51.89/8.07 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 51.89/8.07 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 51.89/8.07 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 51.89/8.07 % No SInE strategy applied
% 51.89/8.07 % Search class: FGHSM-FSLM21-MFFFFFNN
% 51.89/8.07 % Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 51.89/8.07 % Starting SubtermCWHack with 136s (1) cores
% 51.89/8.07 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 51.89/8.07 % Starting G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y with 136s (1) cores
% 51.89/8.07 % Starting G-E--_200_B02_F1_SE_CS_SP_PI_S2k with 136s (1) cores
% 51.89/8.07 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 51.89/8.07 % G-E--_200_B02_F1_SE_CS_SP_PI_S2k with pid 981842 completed with status 0
% 51.89/8.07 % Result found by G-E--_200_B02_F1_SE_CS_SP_PI_S2k
% 51.89/8.07 % Preprocessing class: FSLSSMSMSSSNFFN.
% 51.89/8.07 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 51.89/8.07 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 51.89/8.07 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 51.89/8.07 % No SInE strategy applied
% 51.89/8.07 % Search class: FGHSM-FSLM21-MFFFFFNN
% 51.89/8.07 % Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 51.89/8.07 % Starting SubtermCWHack with 136s (1) cores
% 51.89/8.07 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 51.89/8.07 % Starting G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y with 136s (1) cores
% 51.89/8.07 % Starting G-E--_200_B02_F1_SE_CS_SP_PI_S2k with 136s (1) cores
% 51.89/8.07 % Preprocessing time : 0.004 s
% 51.89/8.07
% 51.89/8.07 % Proof found!
% 51.89/8.07 % SZS status Unsatisfiable
% 51.89/8.07 % SZS output start CNFRefutation
% See solution above
% 51.89/8.07 % Parsed axioms : 201
% 51.89/8.07 % Removed by relevancy pruning/SinE : 0
% 51.89/8.07 % Initial clauses : 201
% 51.89/8.07 % Removed in clause preprocessing : 0
% 51.89/8.07 % Initial clauses in saturation : 201
% 51.89/8.07 % Processed clauses : 21068
% 51.89/8.07 % ...of these trivial : 348
% 51.89/8.07 % ...subsumed : 15312
% 51.89/8.07 % ...remaining for further processing : 5408
% 51.89/8.07 % Other redundant clauses eliminated : 1573
% 51.89/8.07 % Clauses deleted for lack of memory : 0
% 51.89/8.07 % Backward-subsumed : 590
% 51.89/8.07 % Backward-rewritten : 702
% 51.89/8.07 % Generated clauses : 342703
% 51.89/8.07 % ...of the previous two non-redundant : 326936
% 51.89/8.07 % ...aggressively subsumed : 0
% 51.89/8.07 % Contextual simplify-reflections : 974
% 51.89/8.07 % Paramodulations : 340996
% 51.89/8.07 % Factorizations : 0
% 51.89/8.07 % NegExts : 0
% 51.89/8.07 % Equation resolutions : 1631
% 51.89/8.07 % Disequality decompositions : 0
% 51.89/8.07 % Total rewrite steps : 305606
% 51.89/8.07 % ...of those cached : 302225
% 51.89/8.07 % Propositional unsat checks : 0
% 51.89/8.07 % Propositional check models : 0
% 51.89/8.07 % Propositional check unsatisfiable : 0
% 51.89/8.07 % Propositional clauses : 0
% 51.89/8.07 % Propositional clauses after purity: 0
% 51.89/8.07 % Propositional unsat core size : 0
% 51.89/8.07 % Propositional preprocessing time : 0.000
% 51.89/8.07 % Propositional encoding time : 0.000
% 51.89/8.07 % Propositional solver time : 0.000
% 51.89/8.07 % Success case prop preproc time : 0.000
% 51.89/8.07 % Success case prop encoding time : 0.000
% 51.89/8.07 % Success case prop solver time : 0.000
% 51.89/8.07 % Current number of processed clauses : 4014
% 51.89/8.07 % Positive orientable unit clauses : 559
% 51.89/8.07 % Positive unorientable unit clauses: 0
% 51.89/8.07 % Negative unit clauses : 876
% 51.89/8.07 % Non-unit-clauses : 2579
% 51.89/8.07 % Current number of unprocessed clauses: 300692
% 51.89/8.07 % ...number of literals in the above : 1979036
% 51.89/8.07 % Current number of archived formulas : 0
% 51.89/8.07 % Current number of archived clauses : 1369
% 51.89/8.07 % Clause-clause subsumption calls (NU) : 1832451
% 51.89/8.07 % Rec. Clause-clause subsumption calls : 382649
% 51.89/8.07 % Non-unit clause-clause subsumptions : 6721
% 51.89/8.07 % Unit Clause-clause subsumption calls : 269475
% 51.89/8.07 % Rewrite failures with RHS unbound : 0
% 51.89/8.07 % BW rewrite match attempts : 1922
% 51.89/8.07 % BW rewrite match successes : 322
% 51.89/8.07 % Condensation attempts : 0
% 51.89/8.07 % Condensation successes : 0
% 51.89/8.07 % Termbank termtop insertions : 8612404
% 51.89/8.07 % Search garbage collected termcells : 547
% 51.89/8.07
% 51.89/8.07 % -------------------------------------------------
% 51.89/8.07 % User time : 6.907 s
% 51.89/8.07 % System time : 0.271 s
% 51.89/8.07 % Total time : 7.178 s
% 51.89/8.07 % Maximum resident set size: 4016 pages
% 51.89/8.07
% 51.89/8.07 % -------------------------------------------------
% 51.89/8.07 % User time : 35.277 s
% 51.89/8.07 % System time : 1.308 s
% 51.89/8.07 % Total time : 36.584 s
% 51.89/8.07 % Maximum resident set size: 4864 pages
% 51.89/8.07 % E exiting
%------------------------------------------------------------------------------