%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC354-1 : 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 : n016.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 02:44:03 PM UTC 2026
% Result : Unsatisfiable 3.56s 1.13s
% Output : CNFRefutation 3.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 33
% Syntax : Number of clauses : 137 ( 27 unt; 30 nHn; 120 RR)
% Number of literals : 414 ( 93 equ; 264 neg)
% Maximal clause size : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 198 ( 19 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(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(clause8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
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(clause101,axiom,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(skaf44(X1),nil) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause101) ).
cnf(clause47,axiom,
ssItem(skaf44(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause47) ).
cnf(clause72,axiom,
( ~ ssList(X1)
| ssItem(X2)
| duplicatefreeP(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause72) ).
cnf(clause116,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,nil) != X2
| singletonP(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause116) ).
cnf(co1_7,negated_conjecture,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
cnf(co1_11,negated_conjecture,
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| hd(sk4) != X2
| cons(X2,nil) != X1
| ~ ssItem(X2)
| ~ ssList(X1)
| sk3 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
cnf(co1_5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
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(clause178,axiom,
( ~ ssItem(X3)
| ~ ssItem(X4)
| ~ ssList(X1)
| ~ ssList(X2)
| X3 != X4
| ~ frontsegP(X1,X2)
| frontsegP(cons(X3,X1),cons(X4,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause178) ).
cnf(clause76,axiom,
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause76) ).
cnf(clause83,axiom,
( ~ ssList(X1)
| nil != X1
| frontsegP(nil,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause83) ).
cnf(clause137,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ frontsegP(X1,X2)
| frontsegP(app(X1,X3),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause137) ).
cnf(clause60,axiom,
( ~ ssList(X1)
| frontsegP(X1,nil) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause60) ).
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(co1_1,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).
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(clause51,axiom,
ssList(skaf45(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause51) ).
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(clause172,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ segmentP(X1,X2)
| segmentP(app(app(X4,X1),X3),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause172) ).
cnf(clause57,axiom,
( ~ ssList(X1)
| segmentP(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause57) ).
cnf(clause104,axiom,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause104) ).
cnf(clause75,axiom,
( ~ ssList(X1)
| nil = X1
| ssList(tl(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause75) ).
cnf(co1_12,negated_conjecture,
( ~ neq(sk4,nil)
| ~ segmentP(sk2,sk1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
cnf(clause50,axiom,
ssList(skaf46(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause50) ).
cnf(clause117,axiom,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ neq(X1,X2)
| X1 != X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause117) ).
cnf(c_0_33,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_34,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_33 ).
cnf(c_0_35,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_simplification,[status(thm)],[clause74]) ).
cnf(c_0_36,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
inference(fof_simplification,[status(thm)],[clause86]) ).
cnf(c_0_37,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_34]) ).
cnf(c_0_38,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
c_0_35 ).
cnf(c_0_39,axiom,
ssList(nil),
clause8 ).
cnf(c_0_40,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
c_0_36 ).
cnf(c_0_41,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,nil),X2) = cons(X1,X2) ),
inference(fof_simplification,[status(thm)],[clause120]) ).
cnf(c_0_42,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_37,c_0_38]),c_0_39])]),c_0_40]) ).
cnf(c_0_43,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,nil),X2) = cons(X1,X2) ),
c_0_41 ).
cnf(c_0_44,plain,
( ~ duplicatefreeP(cons(X1,cons(X1,X2)))
| ~ ssList(X2)
| ~ ssList(cons(X1,cons(X1,X2)))
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_39])]),c_0_40]) ).
cnf(c_0_45,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(skaf44(X1),nil) = X1 ),
inference(fof_simplification,[status(thm)],[clause101]) ).
cnf(c_0_46,plain,
( ~ duplicatefreeP(cons(X1,cons(X1,X2)))
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_40]),c_0_40]) ).
cnf(c_0_47,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(skaf44(X1),nil) = X1 ),
c_0_45 ).
cnf(c_0_48,axiom,
ssItem(skaf44(X1)),
clause47 ).
cnf(c_0_49,plain,
( ~ ssList(X1)
| ssItem(X2)
| duplicatefreeP(X1) ),
inference(fof_simplification,[status(thm)],[clause72]) ).
cnf(c_0_50,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,nil) != X2
| singletonP(X2) ),
inference(fof_simplification,[status(thm)],[clause116]) ).
cnf(c_0_51,plain,
( ~ duplicatefreeP(cons(skaf44(X1),X1))
| ~ ssList(X1)
| ~ singletonP(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]),c_0_39])]) ).
cnf(c_0_52,plain,
( ~ ssList(X1)
| ssItem(X2)
| duplicatefreeP(X1) ),
c_0_49 ).
cnf(c_0_53,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,nil) != X2
| singletonP(X2) ),
c_0_50 ).
cnf(c_0_54,negated_conjecture,
neq(sk2,nil),
inference(fof_simplification,[status(thm)],[co1_7]) ).
cnf(c_0_55,plain,
( ~ ssList(X2)
| ~ ssList(cons(skaf44(X2),X2))
| ~ singletonP(X2)
| ssItem(X1) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_56,plain,
( ~ ssList(cons(X1,nil))
| ~ ssItem(X1)
| singletonP(cons(X1,nil)) ),
inference(er,[status(thm)],[c_0_53]) ).
cnf(c_0_57,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_11]) ).
cnf(c_0_58,negated_conjecture,
neq(sk2,nil),
c_0_54 ).
cnf(c_0_59,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_60,plain,
( ~ ssList(X2)
| ~ singletonP(X2)
| ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_40]),c_0_48])]) ).
cnf(c_0_61,plain,
( ~ ssItem(X1)
| singletonP(cons(X1,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_40]),c_0_39])]) ).
cnf(c_0_62,negated_conjecture,
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| hd(sk4) != X2
| cons(X2,nil) != X1
| ~ ssItem(X2)
| ~ ssList(X1)
| sk3 = X1 ),
c_0_57 ).
cnf(c_0_63,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_64,negated_conjecture,
neq(sk4,nil),
inference(rw,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_65,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
inference(fof_simplification,[status(thm)],[clause100]) ).
cnf(c_0_66,negated_conjecture,
ssList(sk2),
co1_2 ).
cnf(c_0_67,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_68,plain,
( ~ ssList(cons(X2,nil))
| ~ ssItem(X2)
| ssItem(X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_69,negated_conjecture,
( ~ ssList(cons(hd(sk4),nil))
| ~ ssItem(hd(sk4))
| ~ neq(nil,sk4)
| cons(hd(sk4),nil) = sk1 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_63]),c_0_64])])])]) ).
cnf(c_0_70,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
c_0_65 ).
cnf(c_0_71,negated_conjecture,
ssList(sk4),
inference(rw,[status(thm)],[c_0_66,c_0_59]) ).
cnf(c_0_72,plain,
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
inference(fof_simplification,[status(thm)],[clause76]) ).
cnf(c_0_73,plain,
( ~ ssItem(X3)
| ~ ssItem(X4)
| ~ ssList(X1)
| ~ ssList(X2)
| X3 != X4
| ~ frontsegP(X1,X2)
| frontsegP(cons(X3,X1),cons(X4,X2)) ),
c_0_67 ).
cnf(c_0_74,plain,
( ~ ssItem(X2)
| ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_40]),c_0_39])]) ).
cnf(c_0_75,plain,
( ~ ssList(X1)
| nil != X1
| frontsegP(nil,X1) ),
inference(fof_simplification,[status(thm)],[clause83]) ).
cnf(c_0_76,negated_conjecture,
( ~ ssList(cons(hd(sk4),nil))
| ~ ssItem(hd(sk4))
| sk4 = nil
| cons(hd(sk4),nil) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_39]),c_0_71])]) ).
cnf(c_0_77,plain,
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
c_0_72 ).
cnf(c_0_78,plain,
( ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1)
| ~ frontsegP(X2,X3)
| frontsegP(cons(X1,X2),cons(X1,X3)) ),
inference(er,[status(thm)],[c_0_73]) ).
cnf(c_0_79,plain,
ssItem(X1),
inference(spm,[status(thm)],[c_0_74,c_0_48]) ).
cnf(c_0_80,plain,
( ~ ssList(X1)
| nil != X1
| frontsegP(nil,X1) ),
c_0_75 ).
cnf(c_0_81,negated_conjecture,
( ~ ssList(cons(hd(sk4),nil))
| sk4 = nil
| cons(hd(sk4),nil) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_71])]) ).
cnf(c_0_82,plain,
( ~ ssList(X2)
| ~ ssList(X3)
| ~ frontsegP(X2,X3)
| frontsegP(cons(X1,X2),cons(X1,X3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_79])]) ).
cnf(c_0_83,plain,
frontsegP(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_80]),c_0_39])]) ).
cnf(c_0_84,negated_conjecture,
( ~ ssItem(hd(sk4))
| sk4 = nil
| cons(hd(sk4),nil) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_40]),c_0_39])]) ).
cnf(c_0_85,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ frontsegP(X1,X2)
| frontsegP(app(X1,X3),X2) ),
inference(fof_simplification,[status(thm)],[clause137]) ).
cnf(c_0_86,plain,
( ~ ssList(X1)
| frontsegP(X1,nil) ),
inference(fof_simplification,[status(thm)],[clause60]) ).
cnf(c_0_87,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| app(X2,skaf45(X1,X2)) = X1 ),
inference(fof_simplification,[status(thm)],[clause132]) ).
cnf(c_0_88,plain,
frontsegP(cons(X1,nil),cons(X1,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_39])]) ).
cnf(c_0_89,negated_conjecture,
( sk4 = nil
| cons(hd(sk4),nil) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_77]),c_0_71])]) ).
cnf(c_0_90,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ frontsegP(X1,X2)
| frontsegP(app(X1,X3),X2) ),
c_0_85 ).
cnf(c_0_91,plain,
( ~ ssList(X1)
| frontsegP(X1,nil) ),
c_0_86 ).
cnf(c_0_92,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| app(X2,skaf45(X1,X2)) = X1 ),
c_0_87 ).
cnf(c_0_93,negated_conjecture,
( frontsegP(sk1,sk1)
| sk4 = nil ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_94,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_95,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(X1,X2) != X3
| rearsegP(X3,X2) ),
inference(fof_simplification,[status(thm)],[clause143]) ).
cnf(c_0_96,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
inference(fof_simplification,[status(thm)],[clause85]) ).
cnf(c_0_97,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| frontsegP(app(X1,X2),nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_39])]) ).
cnf(c_0_98,negated_conjecture,
( sk4 = nil
| app(sk1,skaf45(sk1,sk1)) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_94])]) ).
cnf(c_0_99,axiom,
ssList(skaf45(X1,X2)),
clause51 ).
cnf(c_0_100,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| app(skaf46(X1,X2),X2) = X1 ),
inference(fof_simplification,[status(thm)],[clause131]) ).
cnf(c_0_101,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(X1,X2) != X3
| rearsegP(X3,X2) ),
c_0_95 ).
cnf(c_0_102,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
c_0_96 ).
cnf(c_0_103,negated_conjecture,
( frontsegP(sk1,nil)
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_99]),c_0_94])]) ).
cnf(c_0_104,plain,
( ~ ssList(X1)
| app(nil,skaf45(X1,nil)) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_91]),c_0_39])]) ).
cnf(c_0_105,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_106,plain,
( ~ ssList(X1)
| segmentP(X1,X1) ),
inference(fof_simplification,[status(thm)],[clause57]) ).
cnf(c_0_107,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| app(skaf46(X1,X2),X2) = X1 ),
c_0_100 ).
cnf(c_0_108,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| rearsegP(app(X1,X2),X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_101]),c_0_102]) ).
cnf(c_0_109,negated_conjecture,
( sk4 = nil
| app(nil,skaf45(sk1,nil)) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_103]),c_0_39]),c_0_94])]) ).
cnf(c_0_110,plain,
( ~ ssList(X1)
| skaf45(X1,nil) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_104]),c_0_99])]) ).
cnf(c_0_111,plain,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
inference(fof_simplification,[status(thm)],[clause104]) ).
cnf(c_0_112,plain,
( ~ ssList(X2)
| app(cons(X1,nil),X2) = cons(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_79])]) ).
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_105 ).
cnf(c_0_114,plain,
( ~ ssList(X1)
| segmentP(X1,X1) ),
c_0_106 ).
cnf(c_0_115,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(skaf46(app(X1,X2),X2),X2) = app(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_102]) ).
cnf(c_0_116,negated_conjecture,
( sk4 = nil
| app(nil,sk1) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_94])]) ).
cnf(c_0_117,plain,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
c_0_111 ).
cnf(c_0_118,negated_conjecture,
( ~ ssList(X1)
| sk4 = nil
| cons(hd(sk4),X1) = app(sk1,X1) ),
inference(spm,[status(thm)],[c_0_112,c_0_89]) ).
cnf(c_0_119,plain,
( ~ ssList(X1)
| nil = X1
| ssList(tl(X1)) ),
inference(fof_simplification,[status(thm)],[clause75]) ).
cnf(c_0_120,negated_conjecture,
( ~ neq(sk4,nil)
| ~ segmentP(sk2,sk1) ),
inference(fof_simplification,[status(thm)],[co1_12]) ).
cnf(c_0_121,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_122,negated_conjecture,
( sk4 = nil
| app(skaf46(sk1,sk1),sk1) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_94]),c_0_39])]) ).
cnf(c_0_123,axiom,
ssList(skaf46(X1,X2)),
clause50 ).
cnf(c_0_124,negated_conjecture,
( ~ ssList(tl(sk4))
| sk4 = nil
| app(sk1,tl(sk4)) = sk4 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_71])]) ).
cnf(c_0_125,plain,
( ~ ssList(X1)
| nil = X1
| ssList(tl(X1)) ),
c_0_119 ).
cnf(c_0_126,negated_conjecture,
( ~ neq(sk4,nil)
| ~ segmentP(sk2,sk1) ),
c_0_120 ).
cnf(c_0_127,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ neq(X1,X2)
| X1 != X2 ),
inference(fof_simplification,[status(thm)],[clause117]) ).
cnf(c_0_128,negated_conjecture,
( ~ ssList(X1)
| segmentP(app(sk1,X1),sk1)
| 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_123]),c_0_94])]) ).
cnf(c_0_129,negated_conjecture,
( sk4 = nil
| app(sk1,tl(sk4)) = sk4 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_71])]) ).
cnf(c_0_130,negated_conjecture,
~ segmentP(sk4,sk1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_126,c_0_59]),c_0_64])]) ).
cnf(c_0_131,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ neq(X1,X2)
| X1 != X2 ),
c_0_127 ).
cnf(c_0_132,negated_conjecture,
( ~ ssList(tl(sk4))
| sk4 = nil ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_130]) ).
cnf(c_0_133,plain,
( ~ ssItem(X1)
| ~ neq(X1,X1) ),
inference(er,[status(thm)],[c_0_131]) ).
cnf(c_0_134,negated_conjecture,
sk4 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_125]),c_0_71])]) ).
cnf(c_0_135,plain,
~ neq(X1,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_133,c_0_79])]) ).
cnf(c_0_136,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_134]),c_0_135]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC354-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.36 % Computer : n016.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 08:23:07 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.44 Running first-order theorem proving
% 0.13/0.44 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.56/1.13 % Version: 3.5.1
% 3.56/1.13 % Preprocessing class: FSLSSMSSSSSNFFN.
% 3.56/1.13 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.56/1.13 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 3.56/1.13 % Starting new_bool_3 with 300s (1) cores
% 3.56/1.13 % Starting new_bool_1 with 300s (1) cores
% 3.56/1.13 % Starting sh5l with 300s (1) cores
% 3.56/1.13 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1999495 completed with status 0
% 3.56/1.13 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 3.56/1.13 % Preprocessing class: FSLSSMSSSSSNFFN.
% 3.56/1.13 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.56/1.13 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 3.56/1.13 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.56/1.13 % No SInE strategy applied
% 3.56/1.13 % Search class: FGHSM-FSLM21-MFFFFFNN
% 3.56/1.13 % Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 3.56/1.13 % Starting SubtermCWHack with 136s (1) cores
% 3.56/1.13 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 3.56/1.13 % Starting G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y with 136s (1) cores
% 3.56/1.13 % Starting G-E--_200_B02_F1_SE_CS_SP_PI_S2k with 136s (1) cores
% 3.56/1.13 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 3.56/1.13 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1999500 completed with status 0
% 3.56/1.13 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 3.56/1.13 % Preprocessing class: FSLSSMSSSSSNFFN.
% 3.56/1.13 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.56/1.13 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 3.56/1.13 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.56/1.13 % No SInE strategy applied
% 3.56/1.13 % Search class: FGHSM-FSLM21-MFFFFFNN
% 3.56/1.13 % Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 3.56/1.13 % Starting SubtermCWHack with 136s (1) cores
% 3.56/1.13 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 3.56/1.13 % Preprocessing time : 0.006 s
% 3.56/1.13 % Presaturation interreduction done
% 3.56/1.13
% 3.56/1.13 % Proof found!
% 3.56/1.13 % SZS status Unsatisfiable
% 3.56/1.13 % SZS output start CNFRefutation
% See solution above
% 3.56/1.13 % Parsed axioms : 197
% 3.56/1.13 % Removed by relevancy pruning/SinE : 0
% 3.56/1.13 % Initial clauses : 197
% 3.56/1.13 % Removed in clause preprocessing : 0
% 3.56/1.13 % Initial clauses in saturation : 197
% 3.56/1.13 % Processed clauses : 2704
% 3.56/1.13 % ...of these trivial : 12
% 3.56/1.13 % ...subsumed : 1624
% 3.56/1.13 % ...remaining for further processing : 1068
% 3.56/1.13 % Other redundant clauses eliminated : 115
% 3.56/1.13 % Clauses deleted for lack of memory : 0
% 3.56/1.13 % Backward-subsumed : 63
% 3.56/1.13 % Backward-rewritten : 424
% 3.56/1.13 % Generated clauses : 7252
% 3.56/1.13 % ...of the previous two non-redundant : 6765
% 3.56/1.13 % ...aggressively subsumed : 0
% 3.56/1.13 % Contextual simplify-reflections : 154
% 3.56/1.13 % Paramodulations : 7131
% 3.56/1.13 % Factorizations : 0
% 3.56/1.13 % NegExts : 0
% 3.56/1.13 % Equation resolutions : 123
% 3.56/1.13 % Disequality decompositions : 0
% 3.56/1.13 % Total rewrite steps : 6115
% 3.56/1.13 % ...of those cached : 5878
% 3.56/1.13 % Propositional unsat checks : 0
% 3.56/1.13 % Propositional check models : 0
% 3.56/1.13 % Propositional check unsatisfiable : 0
% 3.56/1.13 % Propositional clauses : 0
% 3.56/1.13 % Propositional clauses after purity: 0
% 3.56/1.13 % Propositional unsat core size : 0
% 3.56/1.13 % Propositional preprocessing time : 0.000
% 3.56/1.13 % Propositional encoding time : 0.000
% 3.56/1.13 % Propositional solver time : 0.000
% 3.56/1.13 % Success case prop preproc time : 0.000
% 3.56/1.13 % Success case prop encoding time : 0.000
% 3.56/1.13 % Success case prop solver time : 0.000
% 3.56/1.13 % Current number of processed clauses : 371
% 3.56/1.13 % Positive orientable unit clauses : 59
% 3.56/1.13 % Positive unorientable unit clauses: 0
% 3.56/1.13 % Negative unit clauses : 5
% 3.56/1.13 % Non-unit-clauses : 307
% 3.56/1.13 % Current number of unprocessed clauses: 3948
% 3.56/1.13 % ...number of literals in the above : 19446
% 3.56/1.13 % Current number of archived formulas : 0
% 3.56/1.13 % Current number of archived clauses : 673
% 3.56/1.13 % Clause-clause subsumption calls (NU) : 104204
% 3.56/1.13 % Rec. Clause-clause subsumption calls : 41250
% 3.56/1.13 % Non-unit clause-clause subsumptions : 1809
% 3.56/1.13 % Unit Clause-clause subsumption calls : 514
% 3.56/1.13 % Rewrite failures with RHS unbound : 0
% 3.56/1.13 % BW rewrite match attempts : 38
% 3.56/1.13 % BW rewrite match successes : 29
% 3.56/1.13 % Condensation attempts : 0
% 3.56/1.13 % Condensation successes : 0
% 3.56/1.13 % Termbank termtop insertions : 134038
% 3.56/1.13 % Search garbage collected termcells : 551
% 3.56/1.13
% 3.56/1.13 % -------------------------------------------------
% 3.56/1.13 % User time : 0.437 s
% 3.56/1.13 % System time : 0.015 s
% 3.56/1.13 % Total time : 0.453 s
% 3.56/1.13 % Maximum resident set size: 4068 pages
% 3.56/1.13
% 3.56/1.13 % -------------------------------------------------
% 3.56/1.13 % User time : 2.740 s
% 3.56/1.13 % System time : 0.141 s
% 3.56/1.13 % Total time : 2.880 s
% 3.56/1.13 % Maximum resident set size: 4864 pages
% 3.56/1.13 % E exiting
%------------------------------------------------------------------------------