%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC382-1 : 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 : n014.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 02:44:10 PM UTC 2026
% Result : Unsatisfiable 1.86s 0.72s
% Output : CNFRefutation 1.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 29
% Syntax : Number of formulae : 123 ( 25 unt; 0 def)
% Number of atoms : 342 ( 123 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 418 ( 199 ~; 217 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 128 ( 7 sgn 2 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(clause98,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause98) ).
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(clause8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
cnf(co1_7,negated_conjecture,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
cnf(clause86,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).
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/sandbox/benchmark/theBenchmark.p',co1_11) ).
cnf(co1_5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
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(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_6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
cnf(clause100,axiom,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause100) ).
cnf(co1_2,negated_conjecture,
ssList(sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_2) ).
cnf(clause97,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| hd(cons(X1,X2)) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause97) ).
cnf(co1_1,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
cnf(clause76,axiom,
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause76) ).
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(clause109,axiom,
( ~ ssList(X1)
| nil = X1
| cons(skaf83(X1),skaf82(X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause109) ).
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_12,negated_conjecture,
( ~ neq(sk4,nil)
| ~ segmentP(sk2,sk1)
| ~ singletonP(sk1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
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(clause57,axiom,
( ~ ssList(X1)
| segmentP(X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause57) ).
cnf(clause115,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ neq(X1,X2)
| X1 != X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause115) ).
cnf(c_0_27,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
inference(fof_simplification,[status(thm)],[clause98]) ).
cnf(c_0_28,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(skaf44(X1),nil) = X1 ),
inference(fof_simplification,[status(thm)],[clause101]) ).
cnf(c_0_29,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,nil) != X2
| singletonP(X2) ),
inference(fof_simplification,[status(thm)],[clause116]) ).
cnf(c_0_30,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
c_0_27 ).
cnf(c_0_31,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(skaf44(X1),nil) = X1 ),
c_0_28 ).
cnf(c_0_32,axiom,
ssItem(skaf44(X1)),
clause47 ).
cnf(c_0_33,axiom,
ssList(nil),
clause8 ).
cnf(c_0_34,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,nil) != X2
| singletonP(X2) ),
c_0_29 ).
cnf(c_0_35,negated_conjecture,
neq(sk2,nil),
inference(fof_simplification,[status(thm)],[co1_7]) ).
cnf(c_0_36,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_30,c_0_31]),c_0_32]),c_0_33])]) ).
cnf(c_0_37,plain,
( ~ ssList(cons(X1,nil))
| ~ ssItem(X1)
| singletonP(cons(X1,nil)) ),
inference(er,[status(thm)],[c_0_34]) ).
cnf(c_0_38,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
inference(fof_simplification,[status(thm)],[clause86]) ).
cnf(c_0_39,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_40,negated_conjecture,
neq(sk2,nil),
c_0_35 ).
cnf(c_0_41,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_42,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| hd(app(X2,X1)) = hd(X2)
| nil = X2 ),
inference(fof_simplification,[status(thm)],[clause123]) ).
cnf(c_0_43,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,nil),X2) = cons(X1,X2) ),
inference(fof_simplification,[status(thm)],[clause120]) ).
cnf(c_0_44,plain,
( ~ ssList(cons(X1,nil))
| ~ ssItem(X1)
| cons(X1,nil) != nil ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_45,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
c_0_38 ).
cnf(c_0_46,negated_conjecture,
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| hd(sk4) != X2
| cons(X2,nil) != X1
| ~ ssItem(X2)
| ~ ssList(X1)
| sk3 = X1 ),
c_0_39 ).
cnf(c_0_47,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_48,negated_conjecture,
neq(sk4,nil),
inference(rw,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_49,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
inference(fof_simplification,[status(thm)],[clause100]) ).
cnf(c_0_50,negated_conjecture,
ssList(sk2),
co1_2 ).
cnf(c_0_51,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| hd(cons(X1,X2)) = X1 ),
inference(fof_simplification,[status(thm)],[clause97]) ).
cnf(c_0_52,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| hd(app(X2,X1)) = hd(X2)
| nil = X2 ),
c_0_42 ).
cnf(c_0_53,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,nil),X2) = cons(X1,X2) ),
c_0_43 ).
cnf(c_0_54,plain,
( ~ ssItem(X1)
| cons(X1,nil) != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_33])]) ).
fof(c_0_55,plain,
( ~ epred4_0
<=> ! [X2] : ~ ssList(X2) ),
introduced(definition) ).
cnf(c_0_56,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_46,c_0_47]),c_0_48])]) ).
cnf(c_0_57,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
c_0_49 ).
cnf(c_0_58,negated_conjecture,
ssList(sk4),
inference(rw,[status(thm)],[c_0_50,c_0_41]) ).
fof(c_0_59,plain,
( ~ epred3_0
<=> ! [X1] :
( ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| hd(cons(X1,nil)) = X1 ) ),
introduced(definition) ).
cnf(c_0_60,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| hd(cons(X1,X2)) = X1 ),
c_0_51 ).
cnf(c_0_61,plain,
( ~ ssList(X2)
| ~ ssList(cons(X1,nil))
| ~ ssItem(X1)
| hd(cons(X1,X2)) = hd(cons(X1,nil)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]) ).
cnf(c_0_62,plain,
( ~ ssList(X1)
| epred4_0 ),
inference(split_equiv,[status(thm)],[c_0_55]) ).
cnf(c_0_63,negated_conjecture,
( ~ ssList(X1)
| ~ ssItem(X2)
| hd(sk4) != X2
| cons(X2,nil) != X1
| sk1 = X1
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_33]),c_0_58])]) ).
cnf(c_0_64,plain,
( ~ epred3_0
| ~ epred4_0 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_59]),c_0_55]) ).
cnf(c_0_65,negated_conjecture,
epred4_0,
inference(spm,[status(thm)],[c_0_62,c_0_58]) ).
cnf(c_0_66,negated_conjecture,
( ~ ssList(cons(X1,nil))
| ~ ssItem(X1)
| hd(sk4) != X1
| sk4 = nil
| cons(X1,nil) = sk1 ),
inference(er,[status(thm)],[c_0_63]) ).
cnf(c_0_67,plain,
~ epred3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_65])]) ).
cnf(c_0_68,negated_conjecture,
( ~ ssItem(X1)
| hd(sk4) != X1
| sk4 = nil
| cons(X1,nil) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_45]),c_0_33])]) ).
cnf(c_0_69,plain,
( ~ ssList(cons(X1,nil))
| ~ ssItem(X1)
| hd(cons(X1,nil)) = X1 ),
inference(sr,[status(thm)],[inference(split_equiv,[status(thm)],[c_0_59]),c_0_67]) ).
cnf(c_0_70,negated_conjecture,
( ~ ssItem(hd(sk4))
| sk4 = nil
| cons(hd(sk4),nil) = sk1 ),
inference(er,[status(thm)],[c_0_68]) ).
cnf(c_0_71,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_72,plain,
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
inference(fof_simplification,[status(thm)],[clause76]) ).
cnf(c_0_73,plain,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
inference(fof_simplification,[status(thm)],[clause104]) ).
cnf(c_0_74,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| tl(cons(X1,X2)) = X2 ),
inference(fof_simplification,[status(thm)],[clause96]) ).
cnf(c_0_75,negated_conjecture,
( ~ ssItem(hd(sk4))
| sk4 = nil
| hd(sk1) = hd(sk4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71])]) ).
cnf(c_0_76,plain,
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
c_0_72 ).
cnf(c_0_77,negated_conjecture,
( ~ ssItem(hd(sk4))
| sk1 != nil
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_70]),c_0_33])]) ).
cnf(c_0_78,plain,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
c_0_73 ).
cnf(c_0_79,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| tl(cons(X1,X2)) = X2 ),
c_0_74 ).
cnf(c_0_80,negated_conjecture,
( sk4 = nil
| hd(sk1) = hd(sk4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_58])]) ).
cnf(c_0_81,negated_conjecture,
( sk1 != nil
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_76]),c_0_58])]) ).
cnf(c_0_82,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_78,c_0_79]),c_0_45]),c_0_30]) ).
cnf(c_0_83,negated_conjecture,
( ssItem(hd(sk4))
| sk4 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_80]),c_0_71])]),c_0_81]) ).
cnf(c_0_84,plain,
( ~ ssList(X1)
| nil = X1
| cons(skaf83(X1),skaf82(X1)) = X1 ),
inference(fof_simplification,[status(thm)],[clause109]) ).
cnf(c_0_85,negated_conjecture,
( sk4 = nil
| cons(hd(sk1),nil) = sk1 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_70]),c_0_33])]),c_0_83]) ).
cnf(c_0_86,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_78,c_0_60]),c_0_45]),c_0_30]) ).
cnf(c_0_87,plain,
( ~ ssList(X1)
| nil = X1
| cons(skaf83(X1),skaf82(X1)) = X1 ),
c_0_84 ).
cnf(c_0_88,axiom,
ssItem(skaf83(X1)),
clause12 ).
cnf(c_0_89,axiom,
ssList(skaf82(X1)),
clause13 ).
cnf(c_0_90,negated_conjecture,
( sk4 = nil
| cons(hd(sk4),nil) = sk1 ),
inference(spm,[status(thm)],[c_0_85,c_0_80]) ).
cnf(c_0_91,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_86,c_0_87]),c_0_88]),c_0_89])]) ).
cnf(c_0_92,negated_conjecture,
( sk4 = nil
| tl(sk1) = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_90]),c_0_33])]),c_0_83]) ).
cnf(c_0_93,negated_conjecture,
( 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_91,c_0_92]),c_0_71])]),c_0_81]) ).
cnf(c_0_94,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(skaf44(X1),tl(X1)) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_31]),c_0_32]),c_0_33])]) ).
cnf(c_0_95,negated_conjecture,
( singletonP(sk1)
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_93]),c_0_88]),c_0_71])]) ).
cnf(c_0_96,negated_conjecture,
( sk4 = nil
| cons(skaf44(sk1),nil) = sk1 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_92]),c_0_71])]),c_0_95]) ).
cnf(c_0_97,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ singletonP(X1)
| cons(skaf44(X1),X2) = app(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_31]),c_0_32])]) ).
cnf(c_0_98,negated_conjecture,
( sk4 = nil
| skaf44(sk1) = hd(sk1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_96]),c_0_32]),c_0_33])]) ).
cnf(c_0_99,negated_conjecture,
( ~ neq(sk4,nil)
| ~ segmentP(sk2,sk1)
| ~ singletonP(sk1) ),
inference(fof_simplification,[status(thm)],[co1_12]) ).
cnf(c_0_100,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_101,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_simplification,[status(thm)],[clause74]) ).
cnf(c_0_102,negated_conjecture,
( ~ ssList(X1)
| sk4 = nil
| cons(hd(sk1),X1) = app(sk1,X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_71])]),c_0_95]) ).
cnf(c_0_103,negated_conjecture,
( ~ neq(sk4,nil)
| ~ segmentP(sk2,sk1)
| ~ singletonP(sk1) ),
c_0_99 ).
cnf(c_0_104,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ segmentP(X1,X2)
| segmentP(app(app(X4,X1),X3),X2) ),
c_0_100 ).
cnf(c_0_105,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
c_0_101 ).
cnf(c_0_106,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_82,c_0_87]),c_0_88]),c_0_89])]) ).
cnf(c_0_107,negated_conjecture,
( ~ ssList(X1)
| sk4 = nil
| cons(hd(sk4),X1) = app(sk1,X1) ),
inference(spm,[status(thm)],[c_0_102,c_0_80]) ).
cnf(c_0_108,negated_conjecture,
( ~ singletonP(sk1)
| ~ segmentP(sk4,sk1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_103,c_0_41]),c_0_48])]) ).
cnf(c_0_109,negated_conjecture,
( ~ ssItem(hd(sk4))
| singletonP(sk1)
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_70]),c_0_71])]) ).
cnf(c_0_110,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_104,c_0_105]),c_0_33])]) ).
cnf(c_0_111,negated_conjecture,
( sk4 = nil
| app(sk1,skaf82(sk4)) = sk4 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_58]),c_0_89])]) ).
cnf(c_0_112,plain,
( ~ ssList(X1)
| segmentP(X1,X1) ),
inference(fof_simplification,[status(thm)],[clause57]) ).
cnf(c_0_113,negated_conjecture,
( ~ ssItem(hd(sk4))
| ~ segmentP(sk4,sk1)
| sk4 = nil ),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_114,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ neq(X1,X2)
| X1 != X2 ),
inference(fof_simplification,[status(thm)],[clause115]) ).
cnf(c_0_115,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(sk1,X1)
| segmentP(sk4,X1)
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_89]),c_0_71])]) ).
cnf(c_0_116,plain,
( ~ ssList(X1)
| segmentP(X1,X1) ),
c_0_112 ).
cnf(c_0_117,negated_conjecture,
( ~ segmentP(sk4,sk1)
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_76]),c_0_58])]) ).
cnf(c_0_118,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ neq(X1,X2)
| X1 != X2 ),
c_0_114 ).
cnf(c_0_119,negated_conjecture,
sk4 = nil,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_71])]),c_0_117]) ).
cnf(c_0_120,plain,
( ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(er,[status(thm)],[c_0_118]) ).
cnf(c_0_121,negated_conjecture,
neq(nil,nil),
inference(rw,[status(thm)],[c_0_48,c_0_119]) ).
cnf(c_0_122,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_33])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC382-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n014.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 21 08:20:06 UTC 2026
% 0.14/0.38 % CPUTime :
% 0.14/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.42 Running first-order theorem proving
% 0.14/0.42 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
% 1.86/0.72 % Version: 3.5.1
% 1.86/0.72 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.86/0.72 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.86/0.72 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.86/0.72 % Starting new_bool_3 with 300s (1) cores
% 1.86/0.72 % Starting new_bool_1 with 300s (1) cores
% 1.86/0.72 % Starting sh5l with 300s (1) cores
% 1.86/0.72 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 3626876 completed with status 0
% 1.86/0.72 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 1.86/0.72 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.86/0.72 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.86/0.72 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.86/0.72 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.86/0.72 % No SInE strategy applied
% 1.86/0.72 % Search class: FGHSM-FSLM21-MFFFFFNN
% 1.86/0.72 % Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 1.86/0.72 % Starting SubtermCWHack with 136s (1) cores
% 1.86/0.72 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 1.86/0.72 % Starting G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y with 136s (1) cores
% 1.86/0.72 % Starting G-E--_200_B02_F1_SE_CS_SP_PI_S2k with 136s (1) cores
% 1.86/0.72 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 1.86/0.72 % G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y with pid 3626884 completed with status 0
% 1.86/0.72 % Result found by G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y
% 1.86/0.72 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.86/0.72 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.86/0.72 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.86/0.72 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.86/0.72 % No SInE strategy applied
% 1.86/0.72 % Search class: FGHSM-FSLM21-MFFFFFNN
% 1.86/0.72 % Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 1.86/0.72 % Starting SubtermCWHack with 136s (1) cores
% 1.86/0.72 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 1.86/0.72 % Starting G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y with 136s (1) cores
% 1.86/0.72 % Preprocessing time : 0.004 s
% 1.86/0.72 % Presaturation interreduction done
% 1.86/0.72
% 1.86/0.72 % Proof found!
% 1.86/0.72 % SZS status Unsatisfiable
% 1.86/0.72 % SZS output start CNFRefutation
% See solution above
% 1.86/0.72 % Parsed axioms : 197
% 1.86/0.72 % Removed by relevancy pruning/SinE : 0
% 1.86/0.72 % Initial clauses : 197
% 1.86/0.72 % Removed in clause preprocessing : 0
% 1.86/0.72 % Initial clauses in saturation : 197
% 1.86/0.72 % Processed clauses : 1952
% 1.86/0.72 % ...of these trivial : 84
% 1.86/0.72 % ...subsumed : 1048
% 1.86/0.72 % ...remaining for further processing : 820
% 1.86/0.72 % Other redundant clauses eliminated : 179
% 1.86/0.72 % Clauses deleted for lack of memory : 0
% 1.86/0.72 % Backward-subsumed : 23
% 1.86/0.72 % Backward-rewritten : 208
% 1.86/0.72 % Generated clauses : 9300
% 1.86/0.72 % ...of the previous two non-redundant : 8480
% 1.86/0.72 % ...aggressively subsumed : 0
% 1.86/0.72 % Contextual simplify-reflections : 171
% 1.86/0.72 % Paramodulations : 9081
% 1.86/0.72 % Factorizations : 0
% 1.86/0.72 % NegExts : 0
% 1.86/0.72 % Equation resolutions : 213
% 1.86/0.72 % Disequality decompositions : 0
% 1.86/0.72 % Total rewrite steps : 7126
% 1.86/0.72 % ...of those cached : 6917
% 1.86/0.72 % Propositional unsat checks : 0
% 1.86/0.72 % Propositional check models : 0
% 1.86/0.72 % Propositional check unsatisfiable : 0
% 1.86/0.72 % Propositional clauses : 0
% 1.86/0.72 % Propositional clauses after purity: 0
% 1.86/0.72 % Propositional unsat core size : 0
% 1.86/0.72 % Propositional preprocessing time : 0.000
% 1.86/0.72 % Propositional encoding time : 0.000
% 1.86/0.72 % Propositional solver time : 0.000
% 1.86/0.72 % Success case prop preproc time : 0.000
% 1.86/0.72 % Success case prop encoding time : 0.000
% 1.86/0.72 % Success case prop solver time : 0.000
% 1.86/0.72 % Current number of processed clauses : 392
% 1.86/0.72 % Positive orientable unit clauses : 60
% 1.86/0.72 % Positive unorientable unit clauses: 0
% 1.86/0.72 % Negative unit clauses : 3
% 1.86/0.72 % Non-unit-clauses : 329
% 1.86/0.72 % Current number of unprocessed clauses: 6839
% 1.86/0.72 % ...number of literals in the above : 46409
% 1.86/0.72 % Current number of archived formulas : 0
% 1.86/0.72 % Current number of archived clauses : 421
% 1.86/0.72 % Clause-clause subsumption calls (NU) : 54766
% 1.86/0.72 % Rec. Clause-clause subsumption calls : 14749
% 1.86/0.72 % Non-unit clause-clause subsumptions : 1227
% 1.86/0.72 % Unit Clause-clause subsumption calls : 532
% 1.86/0.72 % Rewrite failures with RHS unbound : 0
% 1.86/0.72 % BW rewrite match attempts : 4
% 1.86/0.72 % BW rewrite match successes : 4
% 1.86/0.72 % Condensation attempts : 0
% 1.86/0.72 % Condensation successes : 0
% 1.86/0.72 % Termbank termtop insertions : 173513
% 1.86/0.72 % Search garbage collected termcells : 555
% 1.86/0.72
% 1.86/0.72 % -------------------------------------------------
% 1.86/0.72 % User time : 0.252 s
% 1.86/0.72 % System time : 0.018 s
% 1.86/0.72 % Total time : 0.270 s
% 1.86/0.72 % Maximum resident set size: 3812 pages
% 1.86/0.72
% 1.86/0.72 % -------------------------------------------------
% 1.86/0.72 % User time : 1.150 s
% 1.86/0.72 % System time : 0.076 s
% 1.86/0.72 % Total time : 1.226 s
% 1.86/0.72 % Maximum resident set size: 4864 pages
% 1.86/0.72 % E exiting
%------------------------------------------------------------------------------