%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC079-1 : 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 : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:42:54 PM UTC 2026
% Result : Unsatisfiable 5.36s 1.17s
% Output : CNFRefutation 5.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 47
% Syntax : Number of clauses : 226 ( 35 unt; 39 nHn; 216 RR)
% Number of literals : 745 ( 228 equ; 502 neg)
% Maximal clause size : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-2 aty)
% Number of variables : 322 ( 14 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(co1_7,negated_conjecture,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
cnf(co1_12,negated_conjecture,
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| hd(sk4) != X2
| cons(X2,nil) != X1
| ~ ssItem(X2)
| ~ ssList(X1)
| sk3 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
cnf(co1_5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
cnf(co1_6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
cnf(clause86,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).
cnf(clause8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
cnf(clause98,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause98) ).
cnf(clause171,axiom,
( ~ ssList(X2)
| ~ ssList(X4)
| ~ ssItem(X1)
| ~ ssItem(X3)
| cons(X1,X2) != cons(X3,X4)
| X4 = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause171) ).
cnf(clause104,axiom,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause104) ).
cnf(clause96,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| tl(cons(X1,X2)) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause96) ).
cnf(clause97,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| hd(cons(X1,X2)) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause97) ).
cnf(clause76,axiom,
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause76) ).
cnf(co1_2,negated_conjecture,
ssList(sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_2) ).
cnf(clause109,axiom,
( ~ ssList(X1)
| nil = X1
| cons(skaf83(X1),skaf82(X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause109) ).
cnf(clause100,axiom,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause100) ).
cnf(clause12,axiom,
ssItem(skaf83(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause12) ).
cnf(clause13,axiom,
ssList(skaf82(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause13) ).
cnf(co1_1,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
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(clause74,axiom,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause74) ).
cnf(clause157,axiom,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,app(X2,X3)) = app(cons(X1,X2),X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause157) ).
cnf(clause73,axiom,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause73) ).
cnf(co1_11,negated_conjecture,
( ~ neq(sk4,nil)
| ~ segmentP(sk1,X1)
| ~ segmentP(sk2,X1)
| ~ neq(X1,nil)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
cnf(clause79,axiom,
( ~ ssList(X1)
| nil != X1
| segmentP(nil,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause79) ).
cnf(clause123,axiom,
( ~ ssList(X2)
| ~ ssList(X1)
| hd(app(X2,X1)) = hd(X2)
| nil = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause123) ).
cnf(clause85,axiom,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause85) ).
cnf(clause118,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause118) ).
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(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(clause57,axiom,
( ~ ssList(X1)
| segmentP(X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause57) ).
cnf(clause144,axiom,
( ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != X3
| frontsegP(X3,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause144) ).
cnf(clause82,axiom,
( ~ ssList(X1)
| ~ rearsegP(nil,X1)
| nil = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause82) ).
cnf(clause51,axiom,
ssList(skaf45(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause51) ).
cnf(clause75,axiom,
( ~ ssList(X1)
| nil = X1
| ssList(tl(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause75) ).
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(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(clause101,axiom,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(skaf44(X1),nil) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause101) ).
cnf(clause116,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,nil) != X2
| singletonP(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause116) ).
cnf(clause47,axiom,
ssItem(skaf44(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause47) ).
cnf(clause170,axiom,
( ~ ssList(X2)
| ~ ssList(X4)
| ~ ssItem(X1)
| ~ ssItem(X3)
| cons(X1,X2) != cons(X3,X4)
| X1 = X3 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause170) ).
cnf(clause173,axiom,
( ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| app(app(X1,X2),X3) != X4
| segmentP(X4,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause173) ).
cnf(clause149,axiom,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X3,X2),X1) = app(X3,app(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause149) ).
cnf(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/sandbox/benchmark/Axioms/SWC001-0.ax',clause178) ).
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(clause83,axiom,
( ~ ssList(X1)
| nil != X1
| frontsegP(nil,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause83) ).
cnf(c_0_47,negated_conjecture,
neq(sk2,nil),
inference(fof_simplification,[status(thm)],[co1_7]) ).
cnf(c_0_48,negated_conjecture,
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| hd(sk4) != X2
| cons(X2,nil) != X1
| ~ ssItem(X2)
| ~ ssList(X1)
| sk3 = X1 ),
inference(fof_simplification,[status(thm)],[co1_12]) ).
cnf(c_0_49,negated_conjecture,
neq(sk2,nil),
c_0_47 ).
cnf(c_0_50,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_51,negated_conjecture,
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| hd(sk4) != X2
| cons(X2,nil) != X1
| ~ ssItem(X2)
| ~ ssList(X1)
| sk3 = X1 ),
c_0_48 ).
cnf(c_0_52,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_53,negated_conjecture,
neq(sk4,nil),
inference(rw,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_54,negated_conjecture,
( ~ ssList(X1)
| ~ ssItem(X2)
| ~ neq(nil,sk4)
| hd(sk4) != X2
| cons(X2,nil) != X1
| sk1 = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52]),c_0_53])]) ).
cnf(c_0_55,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
inference(fof_simplification,[status(thm)],[clause86]) ).
cnf(c_0_56,negated_conjecture,
( ~ ssList(cons(X1,nil))
| ~ ssItem(X1)
| ~ neq(nil,sk4)
| hd(sk4) != X1
| cons(X1,nil) = sk1 ),
inference(er,[status(thm)],[c_0_54]) ).
cnf(c_0_57,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
c_0_55 ).
cnf(c_0_58,axiom,
ssList(nil),
clause8 ).
cnf(c_0_59,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
inference(fof_simplification,[status(thm)],[clause98]) ).
cnf(c_0_60,negated_conjecture,
( ~ ssItem(X1)
| ~ neq(nil,sk4)
| hd(sk4) != X1
| cons(X1,nil) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58])]) ).
cnf(c_0_61,plain,
( ~ ssList(X2)
| ~ ssList(X4)
| ~ ssItem(X1)
| ~ ssItem(X3)
| cons(X1,X2) != cons(X3,X4)
| X4 = X2 ),
inference(fof_simplification,[status(thm)],[clause171]) ).
cnf(c_0_62,plain,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
inference(fof_simplification,[status(thm)],[clause104]) ).
cnf(c_0_63,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| tl(cons(X1,X2)) = X2 ),
inference(fof_simplification,[status(thm)],[clause96]) ).
cnf(c_0_64,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| hd(cons(X1,X2)) = X1 ),
inference(fof_simplification,[status(thm)],[clause97]) ).
cnf(c_0_65,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
c_0_59 ).
cnf(c_0_66,negated_conjecture,
( ~ ssItem(hd(sk4))
| ~ neq(nil,sk4)
| cons(hd(sk4),nil) = sk1 ),
inference(er,[status(thm)],[c_0_60]) ).
cnf(c_0_67,plain,
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
inference(fof_simplification,[status(thm)],[clause76]) ).
cnf(c_0_68,negated_conjecture,
ssList(sk2),
co1_2 ).
cnf(c_0_69,plain,
( ~ ssList(X2)
| ~ ssList(X4)
| ~ ssItem(X1)
| ~ ssItem(X3)
| cons(X1,X2) != cons(X3,X4)
| X4 = X2 ),
c_0_61 ).
cnf(c_0_70,plain,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
c_0_62 ).
cnf(c_0_71,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| tl(cons(X1,X2)) = X2 ),
c_0_63 ).
cnf(c_0_72,plain,
( ~ ssList(X1)
| nil = X1
| cons(skaf83(X1),skaf82(X1)) = X1 ),
inference(fof_simplification,[status(thm)],[clause109]) ).
cnf(c_0_73,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| hd(cons(X1,X2)) = X1 ),
c_0_64 ).
cnf(c_0_74,negated_conjecture,
( ~ ssItem(hd(sk4))
| ~ neq(nil,sk4)
| sk1 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_58])]) ).
cnf(c_0_75,plain,
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
c_0_67 ).
cnf(c_0_76,negated_conjecture,
ssList(sk4),
inference(rw,[status(thm)],[c_0_68,c_0_50]) ).
cnf(c_0_77,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
inference(fof_simplification,[status(thm)],[clause100]) ).
cnf(c_0_78,negated_conjecture,
( ~ ssList(X1)
| ~ ssItem(X2)
| ~ ssItem(hd(sk4))
| ~ neq(nil,sk4)
| cons(X2,X1) != sk1
| nil = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_66]),c_0_58])]) ).
cnf(c_0_79,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(hd(cons(X1,X2)),X2) = cons(X1,X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_57]),c_0_65]) ).
cnf(c_0_80,plain,
( ~ ssList(X1)
| nil = X1
| cons(skaf83(X1),skaf82(X1)) = X1 ),
c_0_72 ).
cnf(c_0_81,axiom,
ssItem(skaf83(X1)),
clause12 ).
cnf(c_0_82,axiom,
ssList(skaf82(X1)),
clause13 ).
cnf(c_0_83,negated_conjecture,
( ~ ssItem(hd(sk4))
| ~ neq(nil,sk4)
| hd(sk1) = hd(sk4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_66]),c_0_58])]) ).
cnf(c_0_84,negated_conjecture,
( ~ neq(nil,sk4)
| sk1 != nil
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76])]) ).
cnf(c_0_85,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
c_0_77 ).
cnf(c_0_86,negated_conjecture,
( ~ ssList(X1)
| ~ ssItem(X2)
| ~ neq(nil,sk4)
| cons(X2,X1) != sk1
| nil = X1
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_75]),c_0_76])]) ).
cnf(c_0_87,plain,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),skaf82(X1)) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81]),c_0_82])]) ).
cnf(c_0_88,negated_conjecture,
( ~ neq(nil,sk4)
| sk4 = nil
| hd(sk1) = hd(sk4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_75]),c_0_76])]) ).
cnf(c_0_89,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_90,negated_conjecture,
( sk1 != nil
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_58]),c_0_76])]) ).
cnf(c_0_91,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_92,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_simplification,[status(thm)],[clause74]) ).
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(X1)
| app(X1,nil) = X1 ),
inference(fof_simplification,[status(thm)],[clause73]) ).
cnf(c_0_95,negated_conjecture,
( ~ ssList(X1)
| ~ ssItem(X2)
| cons(X2,X1) != sk1
| nil = X1
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_85]),c_0_58]),c_0_76])]) ).
cnf(c_0_96,negated_conjecture,
( ~ neq(nil,sk4)
| sk4 = nil
| cons(hd(sk4),skaf82(sk1)) = sk1 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_89])]),c_0_90]) ).
cnf(c_0_97,negated_conjecture,
( ~ neq(nil,sk4)
| ssItem(hd(sk4))
| sk4 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_88]),c_0_89])]),c_0_90]) ).
cnf(c_0_98,negated_conjecture,
( ~ neq(sk4,nil)
| ~ segmentP(sk1,X1)
| ~ segmentP(sk2,X1)
| ~ neq(X1,nil)
| ~ ssList(X1) ),
inference(fof_simplification,[status(thm)],[co1_11]) ).
cnf(c_0_99,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ segmentP(X1,X2)
| segmentP(app(app(X4,X1),X3),X2) ),
c_0_91 ).
cnf(c_0_100,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
c_0_92 ).
cnf(c_0_101,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,app(X2,X3)) = app(cons(X1,X2),X3) ),
c_0_93 ).
cnf(c_0_102,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
c_0_94 ).
cnf(c_0_103,negated_conjecture,
( ~ neq(nil,sk4)
| sk4 = nil
| skaf82(sk1) = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_82])]),c_0_97]) ).
cnf(c_0_104,negated_conjecture,
( ~ neq(sk4,nil)
| ~ segmentP(sk1,X1)
| ~ segmentP(sk2,X1)
| ~ neq(X1,nil)
| ~ ssList(X1) ),
c_0_98 ).
cnf(c_0_105,plain,
( ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ segmentP(X1,X3)
| segmentP(app(X1,X2),X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_58])]) ).
cnf(c_0_106,plain,
( ~ ssList(X1)
| nil != X1
| segmentP(nil,X1) ),
inference(fof_simplification,[status(thm)],[clause79]) ).
cnf(c_0_107,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| hd(app(X2,X1)) = hd(X2)
| nil = X2 ),
inference(fof_simplification,[status(thm)],[clause123]) ).
cnf(c_0_108,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
inference(fof_simplification,[status(thm)],[clause85]) ).
cnf(c_0_109,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X1 ),
inference(fof_simplification,[status(thm)],[clause118]) ).
cnf(c_0_110,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,X2),nil) = cons(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_58])]) ).
cnf(c_0_111,negated_conjecture,
( ~ neq(nil,sk4)
| sk4 = nil
| cons(skaf83(sk1),nil) = sk1 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_103]),c_0_89])]),c_0_90]) ).
cnf(c_0_112,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(sk4,X1)
| ~ segmentP(sk1,X1)
| ~ neq(X1,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_104,c_0_50]),c_0_53])]) ).
cnf(c_0_113,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ segmentP(nil,X2)
| segmentP(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_100]),c_0_58])]) ).
cnf(c_0_114,plain,
( ~ ssList(X1)
| nil != X1
| segmentP(nil,X1) ),
c_0_106 ).
cnf(c_0_115,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| hd(app(X2,X1)) = hd(X2)
| nil = X2 ),
c_0_107 ).
cnf(c_0_116,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
c_0_108 ).
cnf(c_0_117,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X1 ),
c_0_109 ).
cnf(c_0_118,negated_conjecture,
( ~ neq(nil,sk4)
| sk4 = nil
| app(sk1,nil) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_81]),c_0_58])]) ).
cnf(c_0_119,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(X1,X2) != X3
| rearsegP(X3,X2) ),
inference(fof_simplification,[status(thm)],[clause143]) ).
cnf(c_0_120,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| app(X2,skaf45(X1,X2)) = X1 ),
inference(fof_simplification,[status(thm)],[clause132]) ).
cnf(c_0_121,negated_conjecture,
( ~ segmentP(sk4,sk4)
| ~ segmentP(sk1,sk4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_53]),c_0_76])]) ).
cnf(c_0_122,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| nil != X2
| segmentP(X1,X2) ),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_123,plain,
( ~ ssList(X1)
| segmentP(X1,X1) ),
inference(fof_simplification,[status(thm)],[clause57]) ).
cnf(c_0_124,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(app(X1,X2))) = app(X1,X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_115]),c_0_116]),c_0_117]) ).
cnf(c_0_125,negated_conjecture,
( sk4 = nil
| app(sk1,nil) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_85]),c_0_58]),c_0_76])]) ).
cnf(c_0_126,plain,
( ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != X3
| frontsegP(X3,X1) ),
inference(fof_simplification,[status(thm)],[clause144]) ).
cnf(c_0_127,plain,
( ~ ssList(X1)
| ~ rearsegP(nil,X1)
| nil = X1 ),
inference(fof_simplification,[status(thm)],[clause82]) ).
cnf(c_0_128,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(X1,X2) != X3
| rearsegP(X3,X2) ),
c_0_119 ).
cnf(c_0_129,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| app(X2,skaf45(X1,X2)) = X1 ),
c_0_120 ).
cnf(c_0_130,axiom,
ssList(skaf45(X1,X2)),
clause51 ).
cnf(c_0_131,negated_conjecture,
( ~ segmentP(sk4,sk4)
| sk4 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_89]),c_0_76])]) ).
cnf(c_0_132,plain,
( ~ ssList(X1)
| segmentP(X1,X1) ),
c_0_123 ).
cnf(c_0_133,negated_conjecture,
( sk4 = nil
| cons(hd(sk1),tl(sk1)) = sk1 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_89]),c_0_58])]),c_0_90]) ).
cnf(c_0_134,plain,
( ~ ssList(X1)
| nil = X1
| ssList(tl(X1)) ),
inference(fof_simplification,[status(thm)],[clause75]) ).
cnf(c_0_135,plain,
( ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1)
| app(cons(X1,X2),X3) != nil ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_101]),c_0_116]) ).
cnf(c_0_136,plain,
( ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != X3
| frontsegP(X3,X1) ),
c_0_126 ).
cnf(c_0_137,plain,
( ~ ssList(X1)
| ~ rearsegP(nil,X1)
| nil = X1 ),
c_0_127 ).
cnf(c_0_138,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ frontsegP(X1,X2)
| rearsegP(X1,skaf45(X1,X2)) ),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_130])])]) ).
cnf(c_0_139,negated_conjecture,
sk4 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_76])]) ).
cnf(c_0_140,negated_conjecture,
( ~ ssList(tl(sk1))
| ~ ssItem(hd(sk1))
| sk4 = nil
| tl(sk1) = nil ),
inference(spm,[status(thm)],[c_0_95,c_0_133]) ).
cnf(c_0_141,plain,
( ~ ssList(X1)
| nil = X1
| ssList(tl(X1)) ),
c_0_134 ).
cnf(c_0_142,negated_conjecture,
( ~ ssList(X1)
| ~ neq(nil,sk4)
| app(sk1,X1) != nil
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_111]),c_0_81]),c_0_58])]) ).
cnf(c_0_143,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| frontsegP(app(X1,X2),X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_136]),c_0_116]) ).
cnf(c_0_144,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(X1,X2) != app(X3,X2)
| X1 = X3 ),
inference(fof_simplification,[status(thm)],[clause151]) ).
cnf(c_0_145,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| app(skaf46(X1,X2),X2) = X1 ),
inference(fof_simplification,[status(thm)],[clause131]) ).
cnf(c_0_146,plain,
( ~ ssList(X1)
| ~ frontsegP(nil,X1)
| skaf45(nil,X1) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_130]),c_0_58])]) ).
cnf(c_0_147,plain,
( ~ ssList(X1)
| frontsegP(X1,nil) ),
inference(fof_simplification,[status(thm)],[clause60]) ).
cnf(c_0_148,negated_conjecture,
cons(hd(sk1),tl(sk1)) = sk1,
inference(sr,[status(thm)],[c_0_133,c_0_139]) ).
cnf(c_0_149,negated_conjecture,
( ~ ssItem(hd(sk1))
| sk4 = nil
| tl(sk1) = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_89])]),c_0_90]) ).
cnf(c_0_150,negated_conjecture,
( ~ ssList(X1)
| app(sk1,X1) != nil
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_85]),c_0_58]),c_0_76])]) ).
cnf(c_0_151,negated_conjecture,
( frontsegP(sk1,sk1)
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_125]),c_0_58]),c_0_89])]) ).
cnf(c_0_152,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(X1,X2) != app(X3,X2)
| X1 = X3 ),
c_0_144 ).
cnf(c_0_153,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| app(skaf46(X1,X2),X2) = X1 ),
c_0_145 ).
cnf(c_0_154,axiom,
ssList(skaf46(X1,X2)),
clause50 ).
cnf(c_0_155,plain,
( ~ ssList(X1)
| ~ frontsegP(nil,X1)
| app(X1,nil) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_146]),c_0_58])]) ).
cnf(c_0_156,plain,
( ~ ssList(X1)
| frontsegP(X1,nil) ),
c_0_147 ).
cnf(c_0_157,negated_conjecture,
( ~ ssItem(hd(sk1))
| cons(hd(sk1),nil) = sk1 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_149]),c_0_139]) ).
cnf(c_0_158,negated_conjecture,
( ~ ssList(X1)
| ~ frontsegP(X1,sk1)
| X1 != nil
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_129]),c_0_130]),c_0_89])]) ).
cnf(c_0_159,negated_conjecture,
frontsegP(sk1,sk1),
inference(sr,[status(thm)],[c_0_151,c_0_139]) ).
cnf(c_0_160,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| app(X1,X3) != X2
| X1 = skaf46(X2,X3) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_153]),c_0_154])]),c_0_128]) ).
cnf(c_0_161,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_156]),c_0_58])]) ).
cnf(c_0_162,negated_conjecture,
app(sk1,nil) = sk1,
inference(sr,[status(thm)],[c_0_125,c_0_139]) ).
cnf(c_0_163,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,tl(cons(X1,X2))) = cons(X1,X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_73]),c_0_57]),c_0_65]) ).
cnf(c_0_164,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(skaf44(X1),nil) = X1 ),
inference(fof_simplification,[status(thm)],[clause101]) ).
cnf(c_0_165,negated_conjecture,
( ~ ssList(X1)
| ~ ssItem(X2)
| ~ ssItem(hd(sk1))
| cons(X2,X1) != sk1
| nil = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_157]),c_0_58])]) ).
cnf(c_0_166,negated_conjecture,
sk1 != nil,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_159]),c_0_89])]),c_0_139]) ).
cnf(c_0_167,plain,
( ~ ssList(X1)
| nil != X1
| skaf46(X1,nil) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_161]),c_0_58])]) ).
cnf(c_0_168,negated_conjecture,
( ~ ssList(X1)
| sk1 != X1
| skaf46(X1,nil) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_162]),c_0_58]),c_0_89])]) ).
cnf(c_0_169,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,nil) != X2
| singletonP(X2) ),
inference(fof_simplification,[status(thm)],[clause116]) ).
cnf(c_0_170,plain,
( ~ ssList(X1)
| nil = X1
| cons(skaf83(X1),tl(X1)) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_80]),c_0_81]),c_0_82])]) ).
cnf(c_0_171,negated_conjecture,
( ~ ssItem(hd(sk4))
| ~ neq(nil,sk4)
| tl(sk1) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_66]),c_0_58])]) ).
cnf(c_0_172,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(skaf44(X1),nil) = X1 ),
c_0_164 ).
cnf(c_0_173,axiom,
ssItem(skaf44(X1)),
clause47 ).
cnf(c_0_174,negated_conjecture,
( ~ ssList(X1)
| ~ ssItem(X2)
| cons(X2,X1) != sk1
| nil = X1 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_75]),c_0_89])]),c_0_166]) ).
cnf(c_0_175,negated_conjecture,
( ~ ssList(X1)
| sk1 != X1
| nil != X1 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_168]),c_0_166]) ).
cnf(c_0_176,plain,
( ~ ssList(X2)
| ~ ssList(X4)
| ~ ssItem(X1)
| ~ ssItem(X3)
| cons(X1,X2) != cons(X3,X4)
| X1 = X3 ),
inference(fof_simplification,[status(thm)],[clause170]) ).
cnf(c_0_177,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,nil) != X2
| singletonP(X2) ),
c_0_169 ).
cnf(c_0_178,negated_conjecture,
( ~ ssItem(hd(sk4))
| ~ neq(nil,sk4)
| cons(skaf83(sk1),nil) = sk1 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_171]),c_0_89])]),c_0_74]) ).
cnf(c_0_179,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| skaf44(X1) = hd(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_172]),c_0_173]),c_0_58])]) ).
cnf(c_0_180,negated_conjecture,
( ~ neq(nil,sk4)
| sk4 = nil
| skaf82(sk1) = tl(sk1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_96]),c_0_82])]),c_0_97]) ).
cnf(c_0_181,negated_conjecture,
( ~ ssList(X1)
| X1 != sk1
| skaf82(X1) = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_80]),c_0_81]),c_0_82])]),c_0_175]) ).
cnf(c_0_182,plain,
( ~ ssList(X2)
| ~ ssList(X4)
| ~ ssItem(X1)
| ~ ssItem(X3)
| cons(X1,X2) != cons(X3,X4)
| X1 = X3 ),
c_0_176 ).
cnf(c_0_183,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| X1 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_172]),c_0_173]),c_0_58])]) ).
cnf(c_0_184,negated_conjecture,
( ~ ssList(X1)
| ~ ssItem(hd(sk4))
| ~ neq(nil,sk4)
| sk1 != X1
| singletonP(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_178]),c_0_81])]) ).
cnf(c_0_185,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| ssItem(hd(X1)) ),
inference(spm,[status(thm)],[c_0_173,c_0_179]) ).
cnf(c_0_186,plain,
( ~ ssList(cons(X1,nil))
| ~ ssItem(X1)
| singletonP(cons(X1,nil)) ),
inference(er,[status(thm)],[c_0_177]) ).
cnf(c_0_187,negated_conjecture,
( ~ neq(nil,sk4)
| tl(sk1) = nil ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_181]),c_0_89])]),c_0_139]) ).
cnf(c_0_188,plain,
( ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1)
| cons(X1,X3) != X2
| nil = X2
| X1 = hd(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_70]),c_0_141]),c_0_75]) ).
cnf(c_0_189,negated_conjecture,
( ~ ssList(X1)
| ~ ssItem(hd(sk4))
| ~ neq(nil,sk4)
| sk1 != X1
| X1 != nil ),
inference(spm,[status(thm)],[c_0_183,c_0_184]) ).
cnf(c_0_190,plain,
( ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| app(app(X1,X2),X3) != X4
| segmentP(X4,X2) ),
inference(fof_simplification,[status(thm)],[clause173]) ).
cnf(c_0_191,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_192,plain,
( ~ ssList(cons(X1,nil))
| ~ ssItem(X1)
| ssItem(hd(cons(X1,nil))) ),
inference(spm,[status(thm)],[c_0_185,c_0_186]) ).
cnf(c_0_193,negated_conjecture,
( ~ neq(nil,sk4)
| cons(skaf83(sk1),nil) = sk1 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_187]),c_0_89])]),c_0_166]) ).
cnf(c_0_194,negated_conjecture,
( ~ ssList(X1)
| ~ ssItem(hd(sk4))
| ~ neq(nil,sk4)
| sk1 != X1
| hd(sk4) = hd(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_188,c_0_66]),c_0_58])]),c_0_189]) ).
cnf(c_0_195,plain,
( ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| app(app(X1,X2),X3) != X4
| segmentP(X4,X2) ),
c_0_190 ).
cnf(c_0_196,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X3,X2),X1) = app(X3,app(X2,X1)) ),
c_0_191 ).
cnf(c_0_197,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_198,negated_conjecture,
( ~ neq(nil,sk4)
| ssItem(hd(sk1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_192,c_0_193]),c_0_81]),c_0_89])]) ).
cnf(c_0_199,negated_conjecture,
( ~ ssList(X1)
| ~ neq(nil,sk4)
| sk1 != X1
| sk4 = nil
| hd(sk4) = hd(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_75]),c_0_76])]) ).
cnf(c_0_200,plain,
( ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| app(X2,X3) != X1
| segmentP(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_195,c_0_100]),c_0_58])]) ).
cnf(c_0_201,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| app(nil,app(X1,X2)) = app(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_196,c_0_100]),c_0_58])]) ).
cnf(c_0_202,plain,
( ~ ssItem(X3)
| ~ ssItem(X4)
| ~ ssList(X1)
| ~ ssList(X2)
| X3 != X4
| ~ frontsegP(X1,X2)
| frontsegP(cons(X3,X1),cons(X4,X2)) ),
c_0_197 ).
cnf(c_0_203,negated_conjecture,
( ~ neq(nil,sk4)
| ssItem(hd(sk4)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_198,c_0_199]),c_0_89])]),c_0_139]) ).
cnf(c_0_204,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(sk4,X1)
| ~ segmentP(sk1,X1)
| nil = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_85]),c_0_58])]) ).
cnf(c_0_205,negated_conjecture,
( ~ ssList(X1)
| sk1 != X1
| segmentP(X1,sk1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_200,c_0_162]),c_0_58]),c_0_89])]) ).
cnf(c_0_206,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ frontsegP(X1,app(X3,X2))
| segmentP(X1,X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_195,c_0_129]),c_0_130])])]),c_0_116]) ).
cnf(c_0_207,negated_conjecture,
app(nil,sk1) = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_162]),c_0_89]),c_0_58])]) ).
cnf(c_0_208,plain,
( ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1)
| ~ frontsegP(X2,X3)
| frontsegP(cons(X1,X2),cons(X1,X3)) ),
inference(er,[status(thm)],[c_0_202]) ).
cnf(c_0_209,negated_conjecture,
( ~ neq(nil,sk4)
| hd(sk1) = hd(sk4) ),
inference(spm,[status(thm)],[c_0_83,c_0_203]) ).
cnf(c_0_210,negated_conjecture,
~ segmentP(sk4,sk1),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_204,c_0_205]),c_0_89])]),c_0_166]) ).
cnf(c_0_211,negated_conjecture,
( ~ ssList(X1)
| ~ frontsegP(X1,sk1)
| segmentP(X1,sk1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_206,c_0_207]),c_0_89]),c_0_58])]) ).
cnf(c_0_212,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ frontsegP(X1,X2)
| frontsegP(app(X1,X3),X2) ),
inference(fof_simplification,[status(thm)],[clause137]) ).
cnf(c_0_213,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_208,c_0_70]),c_0_141]),c_0_75]) ).
cnf(c_0_214,negated_conjecture,
( ~ neq(nil,sk4)
| cons(hd(sk4),skaf82(sk1)) = sk1 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_209]),c_0_89])]),c_0_166]) ).
cnf(c_0_215,negated_conjecture,
~ frontsegP(sk4,sk1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_210,c_0_211]),c_0_76])]) ).
cnf(c_0_216,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ frontsegP(X1,X2)
| frontsegP(app(X1,X3),X2) ),
c_0_212 ).
cnf(c_0_217,plain,
( ~ ssList(X1)
| nil != X1
| frontsegP(nil,X1) ),
inference(fof_simplification,[status(thm)],[clause83]) ).
cnf(c_0_218,negated_conjecture,
( ~ frontsegP(tl(sk4),skaf82(sk1))
| ~ neq(nil,sk4) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_213,c_0_214]),c_0_82]),c_0_76])]),c_0_139]),c_0_215]) ).
cnf(c_0_219,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ frontsegP(nil,X2)
| frontsegP(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_216,c_0_100]),c_0_58])]) ).
cnf(c_0_220,plain,
( ~ ssList(X1)
| nil != X1
| frontsegP(nil,X1) ),
c_0_217 ).
cnf(c_0_221,negated_conjecture,
( ~ frontsegP(tl(sk4),nil)
| ~ neq(nil,sk4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_218,c_0_181]),c_0_89])]) ).
cnf(c_0_222,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| nil != X2
| frontsegP(X1,X2) ),
inference(spm,[status(thm)],[c_0_219,c_0_220]) ).
cnf(c_0_223,negated_conjecture,
( ~ ssList(tl(sk4))
| ~ neq(nil,sk4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_221,c_0_222]),c_0_58])]) ).
cnf(c_0_224,negated_conjecture,
~ neq(nil,sk4),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_223,c_0_141]),c_0_76])]),c_0_139]) ).
cnf(c_0_225,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_224,c_0_85]),c_0_58]),c_0_76])]),c_0_139]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC079-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n002.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 07:56:31 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.36/1.17 % Version: 3.5.1
% 5.36/1.17 % Preprocessing class: FSLSSMSSSSSNFFN.
% 5.36/1.17 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.36/1.17 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 5.36/1.17 % Starting new_bool_3 with 300s (1) cores
% 5.36/1.17 % Starting new_bool_1 with 300s (1) cores
% 5.36/1.17 % Starting sh5l with 300s (1) cores
% 5.36/1.17 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2812673 completed with status 0
% 5.36/1.17 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 5.36/1.17 % Preprocessing class: FSLSSMSSSSSNFFN.
% 5.36/1.17 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.36/1.17 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 5.36/1.17 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 5.36/1.17 % No SInE strategy applied
% 5.36/1.17 % Search class: FGHSM-FSLM21-MFFFFFNN
% 5.36/1.17 % Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 5.36/1.17 % Starting SubtermCWHack with 136s (1) cores
% 5.36/1.17 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 5.36/1.17 % Starting G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y with 136s (1) cores
% 5.36/1.17 % Starting G-E--_200_B02_F1_SE_CS_SP_PI_S2k with 136s (1) cores
% 5.36/1.17 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 5.36/1.17 % G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y with pid 2812681 completed with status 0
% 5.36/1.17 % Result found by G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y
% 5.36/1.17 % Preprocessing class: FSLSSMSSSSSNFFN.
% 5.36/1.17 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.36/1.17 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 5.36/1.17 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 5.36/1.17 % No SInE strategy applied
% 5.36/1.17 % Search class: FGHSM-FSLM21-MFFFFFNN
% 5.36/1.17 % Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 5.36/1.17 % Starting SubtermCWHack with 136s (1) cores
% 5.36/1.17 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 5.36/1.17 % Starting G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y with 136s (1) cores
% 5.36/1.17 % Preprocessing time : 0.004 s
% 5.36/1.17 % Presaturation interreduction done
% 5.36/1.17
% 5.36/1.17 % Proof found!
% 5.36/1.17 % SZS status Unsatisfiable
% 5.36/1.17 % SZS output start CNFRefutation
% See solution above
% 5.36/1.17 % Parsed axioms : 197
% 5.36/1.17 % Removed by relevancy pruning/SinE : 0
% 5.36/1.17 % Initial clauses : 197
% 5.36/1.17 % Removed in clause preprocessing : 0
% 5.36/1.17 % Initial clauses in saturation : 197
% 5.36/1.17 % Processed clauses : 2791
% 5.36/1.17 % ...of these trivial : 80
% 5.36/1.17 % ...subsumed : 1552
% 5.36/1.17 % ...remaining for further processing : 1159
% 5.36/1.17 % Other redundant clauses eliminated : 298
% 5.36/1.17 % Clauses deleted for lack of memory : 0
% 5.36/1.17 % Backward-subsumed : 320
% 5.36/1.17 % Backward-rewritten : 22
% 5.36/1.17 % Generated clauses : 16868
% 5.36/1.17 % ...of the previous two non-redundant : 15295
% 5.36/1.17 % ...aggressively subsumed : 0
% 5.36/1.17 % Contextual simplify-reflections : 212
% 5.36/1.17 % Paramodulations : 16503
% 5.36/1.17 % Factorizations : 0
% 5.36/1.17 % NegExts : 0
% 5.36/1.17 % Equation resolutions : 345
% 5.36/1.17 % Disequality decompositions : 0
% 5.36/1.17 % Total rewrite steps : 11999
% 5.36/1.17 % ...of those cached : 11720
% 5.36/1.17 % Propositional unsat checks : 0
% 5.36/1.17 % Propositional check models : 0
% 5.36/1.17 % Propositional check unsatisfiable : 0
% 5.36/1.17 % Propositional clauses : 0
% 5.36/1.17 % Propositional clauses after purity: 0
% 5.36/1.17 % Propositional unsat core size : 0
% 5.36/1.17 % Propositional preprocessing time : 0.000
% 5.36/1.17 % Propositional encoding time : 0.000
% 5.36/1.17 % Propositional solver time : 0.000
% 5.36/1.17 % Success case prop preproc time : 0.000
% 5.36/1.17 % Success case prop encoding time : 0.000
% 5.36/1.17 % Success case prop solver time : 0.000
% 5.36/1.17 % Current number of processed clauses : 610
% 5.36/1.17 % Positive orientable unit clauses : 72
% 5.36/1.17 % Positive unorientable unit clauses: 0
% 5.36/1.17 % Negative unit clauses : 16
% 5.36/1.17 % Non-unit-clauses : 522
% 5.36/1.17 % Current number of unprocessed clauses: 12713
% 5.36/1.17 % ...number of literals in the above : 89242
% 5.36/1.17 % Current number of archived formulas : 0
% 5.36/1.17 % Current number of archived clauses : 539
% 5.36/1.17 % Clause-clause subsumption calls (NU) : 105008
% 5.36/1.17 % Rec. Clause-clause subsumption calls : 25131
% 5.36/1.17 % Non-unit clause-clause subsumptions : 1763
% 5.36/1.17 % Unit Clause-clause subsumption calls : 3463
% 5.36/1.17 % Rewrite failures with RHS unbound : 0
% 5.36/1.17 % BW rewrite match attempts : 9
% 5.36/1.17 % BW rewrite match successes : 9
% 5.36/1.17 % Condensation attempts : 0
% 5.36/1.17 % Condensation successes : 0
% 5.36/1.17 % Termbank termtop insertions : 313566
% 5.36/1.17 % Search garbage collected termcells : 561
% 5.36/1.17
% 5.36/1.17 % -------------------------------------------------
% 5.36/1.17 % User time : 0.681 s
% 5.36/1.17 % System time : 0.029 s
% 5.36/1.17 % Total time : 0.710 s
% 5.36/1.17 % Maximum resident set size: 4068 pages
% 5.36/1.17
% 5.36/1.17 % -------------------------------------------------
% 5.36/1.17 % User time : 3.293 s
% 5.36/1.17 % System time : 0.139 s
% 5.36/1.17 % Total time : 3.433 s
% 5.36/1.17 % Maximum resident set size: 5120 pages
% 5.36/1.17 % E exiting
%------------------------------------------------------------------------------