%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC063-1 : 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 : n004.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 02:42:50 PM UTC 2026
% Result : Unsatisfiable 0.19s 0.57s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 26
% Syntax : Number of clauses : 129 ( 31 unt; 9 nHn; 129 RR)
% Number of literals : 331 ( 98 equ; 201 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 126 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(co1_10,negated_conjecture,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk6) = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
cnf(co1_6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
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(co1_9,negated_conjecture,
( ~ neq(sk4,nil)
| ssList(sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
cnf(co1_8,negated_conjecture,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
cnf(co1_14,negated_conjecture,
( nil != sk1
| neq(sk2,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
cnf(co1_5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
cnf(clause98,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause98) ).
cnf(co1_7,negated_conjecture,
( nil != sk4
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
cnf(co1_12,negated_conjecture,
( neq(sk2,nil)
| nil = sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
cnf(clause150,axiom,
( ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != app(X1,X3)
| X2 = X3 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause150) ).
cnf(clause149,axiom,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X3,X2),X1) = app(X3,app(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause149) ).
cnf(clause74,axiom,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause74) ).
cnf(co1_11,negated_conjecture,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
cnf(clause8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
cnf(clause86,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause86) ).
cnf(clause157,axiom,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,app(X2,X3)) = app(cons(X1,X2),X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause157) ).
cnf(clause85,axiom,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause85) ).
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(clause100,axiom,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause100) ).
cnf(clause73,axiom,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause73) ).
cnf(clause173,axiom,
( ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| app(app(X1,X2),X3) != X4
| segmentP(X4,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause173) ).
cnf(co1_4,negated_conjecture,
ssList(sk4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_4) ).
cnf(co1_13,negated_conjecture,
( ~ segmentP(sk1,X1)
| ~ segmentP(sk2,X1)
| ~ neq(X1,nil)
| ~ ssList(X1)
| nil = sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
cnf(co1_1,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).
cnf(clause57,axiom,
( ~ ssList(X1)
| segmentP(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause57) ).
cnf(c_0_26,negated_conjecture,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk6) = sk3 ),
inference(fof_simplification,[status(thm)],[co1_10]) ).
cnf(c_0_27,negated_conjecture,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk6) = sk3 ),
c_0_26 ).
cnf(c_0_28,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_29,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,nil),X2) = cons(X1,X2) ),
inference(fof_simplification,[status(thm)],[clause120]) ).
cnf(c_0_30,negated_conjecture,
( ~ neq(sk4,nil)
| ssList(sk6) ),
inference(fof_simplification,[status(thm)],[co1_9]) ).
cnf(c_0_31,negated_conjecture,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
inference(fof_simplification,[status(thm)],[co1_8]) ).
cnf(c_0_32,negated_conjecture,
( nil != sk1
| neq(sk2,nil) ),
inference(fof_simplification,[status(thm)],[co1_14]) ).
cnf(c_0_33,negated_conjecture,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk6) = sk1 ),
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,nil),X2) = cons(X1,X2) ),
c_0_29 ).
cnf(c_0_35,negated_conjecture,
( ~ neq(sk4,nil)
| ssList(sk6) ),
c_0_30 ).
cnf(c_0_36,negated_conjecture,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
c_0_31 ).
cnf(c_0_37,negated_conjecture,
( nil != sk1
| neq(sk2,nil) ),
c_0_32 ).
cnf(c_0_38,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_39,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
inference(fof_simplification,[status(thm)],[clause98]) ).
cnf(c_0_40,negated_conjecture,
( ~ neq(sk4,nil)
| cons(sk5,sk6) = sk1 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]),c_0_36]) ).
cnf(c_0_41,negated_conjecture,
( sk1 != nil
| neq(sk4,nil) ),
inference(rw,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,negated_conjecture,
( nil != sk4
| nil = sk3 ),
inference(fof_simplification,[status(thm)],[co1_7]) ).
cnf(c_0_43,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
c_0_39 ).
cnf(c_0_44,negated_conjecture,
( sk1 != nil
| cons(sk5,sk6) = sk1 ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_45,negated_conjecture,
( sk1 != nil
| ssList(sk6) ),
inference(spm,[status(thm)],[c_0_35,c_0_41]) ).
cnf(c_0_46,negated_conjecture,
( sk1 != nil
| ssItem(sk5) ),
inference(spm,[status(thm)],[c_0_36,c_0_41]) ).
cnf(c_0_47,negated_conjecture,
( nil != sk4
| nil = sk3 ),
c_0_42 ).
cnf(c_0_48,negated_conjecture,
( neq(sk2,nil)
| nil = sk2 ),
co1_12 ).
cnf(c_0_49,negated_conjecture,
sk1 != nil,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),c_0_46]) ).
cnf(c_0_50,negated_conjecture,
( sk4 != nil
| sk1 = nil ),
inference(rw,[status(thm)],[c_0_47,c_0_28]) ).
cnf(c_0_51,negated_conjecture,
( neq(sk4,nil)
| sk4 = nil ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_38]),c_0_38]) ).
cnf(c_0_52,negated_conjecture,
sk4 != nil,
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_53,plain,
( ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != app(X1,X3)
| X2 = X3 ),
inference(fof_simplification,[status(thm)],[clause150]) ).
cnf(c_0_54,negated_conjecture,
neq(sk4,nil),
inference(sr,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_55,negated_conjecture,
( ssList(sk6)
| sk4 = nil ),
inference(spm,[status(thm)],[c_0_35,c_0_51]) ).
cnf(c_0_56,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_57,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_simplification,[status(thm)],[clause74]) ).
cnf(c_0_58,negated_conjecture,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = sk4 ),
inference(fof_simplification,[status(thm)],[co1_11]) ).
cnf(c_0_59,plain,
( ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != app(X1,X3)
| X2 = X3 ),
c_0_53 ).
cnf(c_0_60,negated_conjecture,
app(cons(sk5,nil),sk6) = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_54])]) ).
cnf(c_0_61,negated_conjecture,
ssList(sk6),
inference(sr,[status(thm)],[c_0_55,c_0_52]) ).
cnf(c_0_62,negated_conjecture,
( ssItem(sk5)
| sk4 = nil ),
inference(spm,[status(thm)],[c_0_36,c_0_51]) ).
cnf(c_0_63,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X3,X2),X1) = app(X3,app(X2,X1)) ),
c_0_56 ).
cnf(c_0_64,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
c_0_57 ).
cnf(c_0_65,axiom,
ssList(nil),
clause8 ).
cnf(c_0_66,negated_conjecture,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = sk4 ),
c_0_58 ).
cnf(c_0_67,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(cons(sk5,nil))
| app(cons(sk5,nil),X1) != sk1
| sk6 = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61])]) ).
cnf(c_0_68,negated_conjecture,
ssItem(sk5),
inference(sr,[status(thm)],[c_0_62,c_0_52]) ).
cnf(c_0_69,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
inference(fof_simplification,[status(thm)],[clause86]) ).
cnf(c_0_70,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_63,c_0_64]),c_0_65])]) ).
cnf(c_0_71,negated_conjecture,
app(sk6,cons(sk5,nil)) = sk4,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_54])]) ).
cnf(c_0_72,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(cons(sk5,nil))
| cons(sk5,X1) != sk1
| sk6 = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_34]),c_0_68])]) ).
cnf(c_0_73,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
c_0_69 ).
cnf(c_0_74,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_75,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
inference(fof_simplification,[status(thm)],[clause85]) ).
cnf(c_0_76,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_77,negated_conjecture,
( ~ ssList(cons(sk5,nil))
| app(nil,sk4) = sk4 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_61])]) ).
cnf(c_0_78,negated_conjecture,
( ~ ssList(X1)
| cons(sk5,X1) != sk1
| sk6 = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_68]),c_0_65])]) ).
cnf(c_0_79,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,app(X2,X3)) = app(cons(X1,X2),X3) ),
c_0_74 ).
cnf(c_0_80,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
c_0_75 ).
cnf(c_0_81,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
inference(fof_simplification,[status(thm)],[clause100]) ).
cnf(c_0_82,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ segmentP(X1,X2)
| segmentP(app(app(X4,X1),X3),X2) ),
c_0_76 ).
cnf(c_0_83,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(fof_simplification,[status(thm)],[clause73]) ).
cnf(c_0_84,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_85,negated_conjecture,
app(nil,sk4) = sk4,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_73]),c_0_68]),c_0_65])]) ).
cnf(c_0_86,negated_conjecture,
ssList(sk4),
co1_4 ).
cnf(c_0_87,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(X2)
| app(cons(sk5,X1),X2) != sk1
| app(X1,X2) = sk6 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_68])]),c_0_80]) ).
cnf(c_0_88,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
c_0_81 ).
cnf(c_0_89,negated_conjecture,
( ~ segmentP(sk1,X1)
| ~ segmentP(sk2,X1)
| ~ neq(X1,nil)
| ~ ssList(X1)
| nil = sk2 ),
inference(fof_simplification,[status(thm)],[co1_13]) ).
cnf(c_0_90,negated_conjecture,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(cons(sk5,nil))
| ~ segmentP(sk6,X2)
| segmentP(app(sk1,X1),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_60]),c_0_61])]) ).
cnf(c_0_91,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
c_0_83 ).
cnf(c_0_92,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_93,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_82,c_0_64]),c_0_65])]) ).
cnf(c_0_94,plain,
( ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| app(app(X1,X2),X3) != X4
| segmentP(X4,X2) ),
c_0_84 ).
cnf(c_0_95,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ssList(app(X1,app(X2,X3))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_63]),c_0_80]) ).
cnf(c_0_96,negated_conjecture,
( ~ ssList(X1)
| app(nil,app(sk4,X1)) = app(sk4,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_85]),c_0_65]),c_0_86])]) ).
cnf(c_0_97,negated_conjecture,
app(nil,sk6) = sk6,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_60]),c_0_61]),c_0_65])]) ).
cnf(c_0_98,negated_conjecture,
( sk4 = nil
| cons(sk5,sk6) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_88]),c_0_86]),c_0_65])]) ).
cnf(c_0_99,negated_conjecture,
( ~ segmentP(sk1,X1)
| ~ segmentP(sk2,X1)
| ~ neq(X1,nil)
| ~ ssList(X1)
| nil = sk2 ),
c_0_89 ).
cnf(c_0_100,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(cons(sk5,nil))
| ~ segmentP(sk6,X1)
| segmentP(sk1,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_65]),c_0_92])]) ).
cnf(c_0_101,plain,
( ~ ssList(X1)
| segmentP(X1,X1) ),
inference(fof_simplification,[status(thm)],[clause57]) ).
cnf(c_0_102,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(cons(sk5,nil))
| ~ segmentP(sk6,X1)
| segmentP(sk4,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_71]),c_0_61])]) ).
cnf(c_0_103,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(app(app(X1,X2),X3))
| segmentP(app(app(X1,X2),X3),X2) ),
inference(er,[status(thm)],[c_0_94]) ).
cnf(c_0_104,negated_conjecture,
( ~ ssList(X1)
| ssList(app(sk4,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_65]),c_0_86])]) ).
cnf(c_0_105,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(cons(sk5,nil))
| app(sk6,app(cons(sk5,nil),X1)) = app(sk4,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_71]),c_0_61])]) ).
cnf(c_0_106,negated_conjecture,
( ~ ssItem(X1)
| app(cons(X1,nil),sk6) = cons(X1,sk6) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_97]),c_0_61]),c_0_65])]) ).
cnf(c_0_107,negated_conjecture,
cons(sk5,sk6) = sk1,
inference(sr,[status(thm)],[c_0_98,c_0_52]) ).
cnf(c_0_108,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(sk4,X1)
| ~ segmentP(sk1,X1)
| ~ neq(X1,nil) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_38]),c_0_38]),c_0_52]) ).
cnf(c_0_109,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(sk6,X1)
| segmentP(sk1,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_73]),c_0_68]),c_0_65])]) ).
cnf(c_0_110,plain,
( ~ ssList(X1)
| segmentP(X1,X1) ),
c_0_101 ).
cnf(c_0_111,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(sk6,X1)
| segmentP(sk4,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_73]),c_0_68]),c_0_65])]) ).
cnf(c_0_112,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_79,c_0_91]),c_0_65])]) ).
cnf(c_0_113,negated_conjecture,
( ~ ssList(X1)
| segmentP(app(sk4,X1),sk4) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_85]),c_0_86]),c_0_65])]),c_0_104]) ).
cnf(c_0_114,negated_conjecture,
( ~ ssList(cons(sk5,nil))
| app(sk6,sk1) = app(sk4,sk6) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_107]),c_0_61]),c_0_68])]) ).
cnf(c_0_115,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_108,c_0_88]),c_0_65])]) ).
cnf(c_0_116,negated_conjecture,
segmentP(sk1,sk6),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_61])]) ).
cnf(c_0_117,negated_conjecture,
segmentP(sk4,sk6),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_110]),c_0_61])]) ).
cnf(c_0_118,negated_conjecture,
app(sk1,nil) = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_107]),c_0_68]),c_0_61])]) ).
cnf(c_0_119,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| app(X1,app(X2,nil)) = app(X1,X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_63]),c_0_65])]),c_0_80]) ).
cnf(c_0_120,negated_conjecture,
( ~ segmentP(sk4,sk4)
| ~ segmentP(sk1,sk4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_54]),c_0_86])]) ).
cnf(c_0_121,negated_conjecture,
segmentP(sk4,sk4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_91]),c_0_65]),c_0_86])]) ).
cnf(c_0_122,negated_conjecture,
app(sk6,sk1) = app(sk4,sk6),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_73]),c_0_68]),c_0_65])]) ).
cnf(c_0_123,negated_conjecture,
sk6 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_117]),c_0_61])]) ).
cnf(c_0_124,negated_conjecture,
app(nil,sk1) = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_118]),c_0_92]),c_0_65])]) ).
cnf(c_0_125,negated_conjecture,
app(sk4,nil) = sk4,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_119]),c_0_85]),c_0_65]),c_0_86])]) ).
cnf(c_0_126,negated_conjecture,
~ segmentP(sk1,sk4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_120,c_0_121])]) ).
cnf(c_0_127,negated_conjecture,
sk1 = sk4,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_122,c_0_123]),c_0_124]),c_0_123]),c_0_125]) ).
cnf(c_0_128,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_126,c_0_127]),c_0_121])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC063-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n004.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 07:52:19 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.44 Running first-order theorem proving
% 0.14/0.44 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
% 0.19/0.57 % Version: 3.5.1
% 0.19/0.57 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.19/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.57 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.19/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.19/0.57 % Starting new_bool_1 with 300s (1) cores
% 0.19/0.57 % Starting sh5l with 300s (1) cores
% 0.19/0.57 % new_bool_3 with pid 2643975 completed with status 0
% 0.19/0.57 % Result found by new_bool_3
% 0.19/0.57 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.19/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.57 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.19/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.19/0.57 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.19/0.57 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.19/0.57 % Search class: FGHSF-FFMM22-SFFFFFNN
% 0.19/0.57 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.57 % Starting SubtermCWHack with 31s (1) cores
% 0.19/0.57 % SubtermCWHack with pid 2643978 completed with status 0
% 0.19/0.57 % Result found by SubtermCWHack
% 0.19/0.57 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.19/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.57 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.19/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.19/0.57 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.19/0.57 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.19/0.57 % Search class: FGHSF-FFMM22-SFFFFFNN
% 0.19/0.57 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.57 % Starting SubtermCWHack with 31s (1) cores
% 0.19/0.57 % Preprocessing time : 0.002 s
% 0.19/0.57
% 0.19/0.57 % Proof found!
% 0.19/0.57 % SZS status Unsatisfiable
% 0.19/0.57 % SZS output start CNFRefutation
% See solution above
% 0.19/0.58 % Parsed axioms : 200
% 0.19/0.58 % Removed by relevancy pruning/SinE : 156
% 0.19/0.58 % Initial clauses : 44
% 0.19/0.58 % Removed in clause preprocessing : 0
% 0.19/0.58 % Initial clauses in saturation : 44
% 0.19/0.58 % Processed clauses : 1235
% 0.19/0.58 % ...of these trivial : 18
% 0.19/0.58 % ...subsumed : 795
% 0.19/0.58 % ...remaining for further processing : 422
% 0.19/0.58 % Other redundant clauses eliminated : 18
% 0.19/0.58 % Clauses deleted for lack of memory : 0
% 0.19/0.58 % Backward-subsumed : 40
% 0.19/0.58 % Backward-rewritten : 214
% 0.19/0.58 % Generated clauses : 5000
% 0.19/0.58 % ...of the previous two non-redundant : 4359
% 0.19/0.58 % ...aggressively subsumed : 0
% 0.19/0.58 % Contextual simplify-reflections : 50
% 0.19/0.58 % Paramodulations : 4969
% 0.19/0.58 % Factorizations : 0
% 0.19/0.58 % NegExts : 0
% 0.19/0.58 % Equation resolutions : 28
% 0.19/0.58 % Disequality decompositions : 0
% 0.19/0.58 % Total rewrite steps : 5861
% 0.19/0.58 % ...of those cached : 5825
% 0.19/0.58 % Propositional unsat checks : 0
% 0.19/0.58 % Propositional check models : 0
% 0.19/0.58 % Propositional check unsatisfiable : 0
% 0.19/0.58 % Propositional clauses : 0
% 0.19/0.58 % Propositional clauses after purity: 0
% 0.19/0.58 % Propositional unsat core size : 0
% 0.19/0.58 % Propositional preprocessing time : 0.000
% 0.19/0.58 % Propositional encoding time : 0.000
% 0.19/0.58 % Propositional solver time : 0.000
% 0.19/0.58 % Success case prop preproc time : 0.000
% 0.19/0.58 % Success case prop encoding time : 0.000
% 0.19/0.58 % Success case prop solver time : 0.000
% 0.19/0.58 % Current number of processed clauses : 159
% 0.19/0.58 % Positive orientable unit clauses : 18
% 0.19/0.58 % Positive unorientable unit clauses: 0
% 0.19/0.58 % Negative unit clauses : 5
% 0.19/0.58 % Non-unit-clauses : 136
% 0.19/0.58 % Current number of unprocessed clauses: 3144
% 0.19/0.58 % ...number of literals in the above : 16479
% 0.19/0.58 % Current number of archived formulas : 0
% 0.19/0.58 % Current number of archived clauses : 258
% 0.19/0.58 % Clause-clause subsumption calls (NU) : 11702
% 0.19/0.58 % Rec. Clause-clause subsumption calls : 5057
% 0.19/0.58 % Non-unit clause-clause subsumptions : 619
% 0.19/0.58 % Unit Clause-clause subsumption calls : 433
% 0.19/0.58 % Rewrite failures with RHS unbound : 0
% 0.19/0.58 % BW rewrite match attempts : 18
% 0.19/0.58 % BW rewrite match successes : 16
% 0.19/0.58 % Condensation attempts : 0
% 0.19/0.58 % Condensation successes : 0
% 0.19/0.58 % Termbank termtop insertions : 86552
% 0.19/0.58 % Search garbage collected termcells : 928
% 0.19/0.58
% 0.19/0.58 % -------------------------------------------------
% 0.19/0.58 % User time : 0.086 s
% 0.19/0.58 % System time : 0.011 s
% 0.19/0.58 % Total time : 0.097 s
% 0.19/0.58 % Maximum resident set size: 3812 pages
% 0.19/0.58
% 0.19/0.58 % -------------------------------------------------
% 0.19/0.58 % User time : 0.094 s
% 0.19/0.58 % System time : 0.018 s
% 0.19/0.58 % Total time : 0.112 s
% 0.19/0.58 % Maximum resident set size: 4864 pages
% 0.19/0.58 % E exiting
%------------------------------------------------------------------------------