%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SWC307-1 : 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 02:45:48 PM UTC 2026
% Result : Unsatisfiable 1.88s 0.81s
% Output : CNFRefutation 1.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 42
% Syntax : Number of clauses : 156 ( 45 unt; 23 nHn; 148 RR)
% Number of literals : 456 ( 98 equ; 298 neg)
% Maximal clause size : 9 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 10 con; 0-2 aty)
% Number of variables : 218 ( 9 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(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(clause76,axiom,
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause76) ).
cnf(clause123,axiom,
( ~ ssList(X2)
| ~ ssList(X1)
| hd(app(X2,X1)) = hd(X2)
| nil = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause123) ).
cnf(clause85,axiom,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause85) ).
cnf(clause118,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause118) ).
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(clause97,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| hd(cons(X1,X2)) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause97) ).
cnf(clause98,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause98) ).
cnf(co1_13,negated_conjecture,
app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) = sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
cnf(co1_10,negated_conjecture,
ssList(sk7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
cnf(co1_11,negated_conjecture,
ssList(sk8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
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(clause145,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| nil != X2
| nil != X1
| app(X1,X2) = nil ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause145) ).
cnf(co1_8,negated_conjecture,
ssItem(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
cnf(clause72,axiom,
( ~ ssList(X1)
| ssItem(X2)
| duplicatefreeP(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause72) ).
cnf(co1_12,negated_conjecture,
ssList(sk9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
cnf(co1_9,negated_conjecture,
ssItem(sk6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
cnf(clause67,axiom,
( ~ ssItem(X1)
| totalorderedP(cons(X1,nil)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause67) ).
cnf(co1_15,negated_conjecture,
( ~ neq(sk4,nil)
| singletonP(sk3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
cnf(clause182,axiom,
( ~ ssList(X6)
| ~ totalorderedP(X6)
| ~ ssItem(X2)
| ~ ssItem(X4)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X5)
| app(app(X1,cons(X2,X3)),cons(X4,X5)) != X6
| leq(X2,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause182) ).
cnf(clause101,axiom,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(skaf44(X1),nil) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause101) ).
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(co1_5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
cnf(clause103,axiom,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ lt(X1,X2)
| leq(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause103) ).
cnf(clause130,axiom,
( ~ ssItem(X2)
| ~ ssItem(X1)
| ~ leq(X2,X1)
| ~ leq(X1,X2)
| X2 = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause130) ).
cnf(co1_14,negated_conjecture,
lt(sk6,sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
cnf(co1_1,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).
cnf(clause63,axiom,
( ~ ssItem(X1)
| ~ lt(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause63) ).
cnf(clause127,axiom,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ segmentP(X2,X1)
| ~ segmentP(X1,X2)
| X2 = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause127) ).
cnf(co1_7,negated_conjecture,
segmentP(sk4,sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
cnf(clause56,axiom,
( ~ ssList(X1)
| segmentP(X1,nil) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause56) ).
cnf(clause181,axiom,
( ~ ssList(X6)
| ~ strictorderedP(X6)
| ~ ssItem(X2)
| ~ ssItem(X4)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X5)
| app(app(X1,cons(X2,X3)),cons(X4,X5)) != X6
| lt(X2,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause181) ).
cnf(clause114,axiom,
( ~ ssItem(X2)
| ~ ssItem(X1)
| ~ lt(X2,X1)
| ~ lt(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause114) ).
cnf(clause3,axiom,
strictorderedP(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause3) ).
cnf(c_0_42,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_43,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_42 ).
cnf(c_0_44,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_simplification,[status(thm)],[clause74]) ).
cnf(c_0_45,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
inference(fof_simplification,[status(thm)],[clause86]) ).
cnf(c_0_46,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_43]) ).
cnf(c_0_47,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
c_0_44 ).
cnf(c_0_48,axiom,
ssList(nil),
clause8 ).
cnf(c_0_49,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
c_0_45 ).
cnf(c_0_50,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,nil),X2) = cons(X1,X2) ),
inference(fof_simplification,[status(thm)],[clause120]) ).
cnf(c_0_51,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_46,c_0_47]),c_0_48])]),c_0_49]) ).
cnf(c_0_52,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,nil),X2) = cons(X1,X2) ),
c_0_50 ).
cnf(c_0_53,plain,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
inference(fof_simplification,[status(thm)],[clause104]) ).
cnf(c_0_54,plain,
( ~ ssList(X1)
| nil = X1
| ssList(tl(X1)) ),
inference(fof_simplification,[status(thm)],[clause75]) ).
cnf(c_0_55,plain,
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
inference(fof_simplification,[status(thm)],[clause76]) ).
cnf(c_0_56,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_51,c_0_52]),c_0_48])]),c_0_49]) ).
cnf(c_0_57,plain,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
c_0_53 ).
cnf(c_0_58,plain,
( ~ ssList(X1)
| nil = X1
| ssList(tl(X1)) ),
c_0_54 ).
cnf(c_0_59,plain,
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
c_0_55 ).
cnf(c_0_60,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| hd(app(X2,X1)) = hd(X2)
| nil = X2 ),
inference(fof_simplification,[status(thm)],[clause123]) ).
cnf(c_0_61,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
inference(fof_simplification,[status(thm)],[clause85]) ).
cnf(c_0_62,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X1 ),
inference(fof_simplification,[status(thm)],[clause118]) ).
cnf(c_0_63,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_64,plain,
( ~ duplicatefreeP(cons(hd(X1),X1))
| ~ ssList(X1)
| nil = X1 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]),c_0_49]),c_0_59]) ).
cnf(c_0_65,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| hd(app(X2,X1)) = hd(X2)
| nil = X2 ),
c_0_60 ).
cnf(c_0_66,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
c_0_61 ).
cnf(c_0_67,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X1 ),
c_0_62 ).
cnf(c_0_68,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| hd(cons(X1,X2)) = X1 ),
inference(fof_simplification,[status(thm)],[clause97]) ).
cnf(c_0_69,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
inference(fof_simplification,[status(thm)],[clause98]) ).
cnf(c_0_70,negated_conjecture,
app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) = sk1,
co1_13 ).
cnf(c_0_71,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X3,X2),X1) = app(X3,app(X2,X1)) ),
c_0_63 ).
cnf(c_0_72,negated_conjecture,
ssList(sk7),
co1_10 ).
cnf(c_0_73,negated_conjecture,
ssList(sk8),
co1_11 ).
cnf(c_0_74,plain,
( ~ duplicatefreeP(cons(hd(X1),app(X1,X2)))
| ~ ssList(X2)
| ~ ssList(X1)
| nil = X1 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_66]),c_0_67]) ).
cnf(c_0_75,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| hd(cons(X1,X2)) = X1 ),
c_0_68 ).
cnf(c_0_76,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
c_0_69 ).
cnf(c_0_77,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_78,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| nil != X2
| nil != X1
| app(X1,X2) = nil ),
inference(fof_simplification,[status(thm)],[clause145]) ).
cnf(c_0_79,negated_conjecture,
( ~ ssList(cons(sk5,nil))
| app(app(app(sk7,app(cons(sk5,nil),sk8)),cons(sk6,nil)),sk9) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72]),c_0_73])]) ).
cnf(c_0_80,negated_conjecture,
ssItem(sk5),
co1_8 ).
cnf(c_0_81,plain,
( ~ duplicatefreeP(cons(X1,app(cons(X1,X3),X2)))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_49]),c_0_76]) ).
cnf(c_0_82,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,app(X2,X3)) = app(cons(X1,X2),X3) ),
c_0_77 ).
cnf(c_0_83,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| nil != X2
| nil != X1
| app(X1,X2) = nil ),
c_0_78 ).
cnf(c_0_84,plain,
( ~ ssList(X1)
| ssItem(X2)
| duplicatefreeP(X1) ),
inference(fof_simplification,[status(thm)],[clause72]) ).
cnf(c_0_85,negated_conjecture,
app(app(app(sk7,app(cons(sk5,nil),sk8)),cons(sk6,nil)),sk9) = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_49]),c_0_80]),c_0_48])]) ).
cnf(c_0_86,plain,
( ~ duplicatefreeP(cons(X1,cons(X1,app(X3,X2))))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_87,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_83])]),c_0_48])]) ).
cnf(c_0_88,plain,
( ~ ssList(X1)
| ssItem(X2)
| duplicatefreeP(X1) ),
c_0_84 ).
cnf(c_0_89,negated_conjecture,
app(app(app(sk7,cons(sk5,sk8)),cons(sk6,nil)),sk9) = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_52]),c_0_80]),c_0_73])]) ).
cnf(c_0_90,negated_conjecture,
ssList(sk9),
co1_12 ).
cnf(c_0_91,plain,
( ~ duplicatefreeP(cons(X1,cons(X1,nil)))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_48])]) ).
cnf(c_0_92,plain,
( ~ ssList(X3)
| ~ ssItem(X2)
| duplicatefreeP(cons(X2,X3))
| ssItem(X1) ),
inference(spm,[status(thm)],[c_0_88,c_0_49]) ).
cnf(c_0_93,negated_conjecture,
( ~ ssList(cons(sk6,nil))
| ~ ssList(app(sk7,cons(sk5,sk8)))
| app(app(sk7,cons(sk5,sk8)),app(cons(sk6,nil),sk9)) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_89]),c_0_90])]) ).
cnf(c_0_94,negated_conjecture,
ssItem(sk6),
co1_9 ).
cnf(c_0_95,plain,
( ~ ssList(cons(X2,nil))
| ~ ssItem(X2)
| ssItem(X1) ),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_96,negated_conjecture,
( ~ ssList(app(sk7,cons(sk5,sk8)))
| app(app(sk7,cons(sk5,sk8)),app(cons(sk6,nil),sk9)) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_49]),c_0_94]),c_0_48])]) ).
cnf(c_0_97,plain,
( ~ ssItem(X1)
| totalorderedP(cons(X1,nil)) ),
inference(fof_simplification,[status(thm)],[clause67]) ).
cnf(c_0_98,plain,
( ~ ssItem(X2)
| ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_49]),c_0_48])]) ).
cnf(c_0_99,negated_conjecture,
( ~ neq(sk4,nil)
| singletonP(sk3) ),
inference(fof_simplification,[status(thm)],[co1_15]) ).
cnf(c_0_100,plain,
( ~ ssList(X6)
| ~ totalorderedP(X6)
| ~ ssItem(X2)
| ~ ssItem(X4)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X5)
| app(app(X1,cons(X2,X3)),cons(X4,X5)) != X6
| leq(X2,X4) ),
inference(fof_simplification,[status(thm)],[clause182]) ).
cnf(c_0_101,negated_conjecture,
( ~ ssList(cons(sk5,sk8))
| app(app(sk7,cons(sk5,sk8)),app(cons(sk6,nil),sk9)) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_66]),c_0_72])]) ).
cnf(c_0_102,plain,
( ~ ssItem(X1)
| totalorderedP(cons(X1,nil)) ),
c_0_97 ).
cnf(c_0_103,negated_conjecture,
ssItem(X1),
inference(spm,[status(thm)],[c_0_98,c_0_94]) ).
cnf(c_0_104,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(skaf44(X1),nil) = X1 ),
inference(fof_simplification,[status(thm)],[clause101]) ).
cnf(c_0_105,negated_conjecture,
( ~ neq(sk4,nil)
| singletonP(sk3) ),
c_0_99 ).
cnf(c_0_106,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_107,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
inference(fof_simplification,[status(thm)],[clause100]) ).
cnf(c_0_108,negated_conjecture,
ssList(sk2),
co1_2 ).
cnf(c_0_109,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_110,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ lt(X1,X2)
| leq(X1,X2) ),
inference(fof_simplification,[status(thm)],[clause103]) ).
cnf(c_0_111,plain,
( ~ ssList(X6)
| ~ totalorderedP(X6)
| ~ ssItem(X2)
| ~ ssItem(X4)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X5)
| app(app(X1,cons(X2,X3)),cons(X4,X5)) != X6
| leq(X2,X4) ),
c_0_100 ).
cnf(c_0_112,negated_conjecture,
app(app(sk7,cons(sk5,sk8)),app(cons(sk6,nil),sk9)) = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_49]),c_0_80]),c_0_73])]) ).
cnf(c_0_113,plain,
totalorderedP(cons(X1,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_102,c_0_103])]) ).
cnf(c_0_114,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(skaf44(X1),nil) = X1 ),
c_0_104 ).
cnf(c_0_115,negated_conjecture,
( ~ neq(sk4,nil)
| singletonP(sk1) ),
inference(rw,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_116,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
c_0_107 ).
cnf(c_0_117,negated_conjecture,
ssList(sk4),
inference(rw,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_118,plain,
( ~ ssItem(X2)
| ~ ssItem(X1)
| ~ leq(X2,X1)
| ~ leq(X1,X2)
| X2 = X1 ),
inference(fof_simplification,[status(thm)],[clause130]) ).
cnf(c_0_119,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ lt(X1,X2)
| leq(X1,X2) ),
c_0_110 ).
cnf(c_0_120,negated_conjecture,
lt(sk6,sk5),
co1_14 ).
cnf(c_0_121,plain,
( ~ totalorderedP(app(app(X3,cons(X1,X4)),cons(X2,X5)))
| ~ ssList(X3)
| ~ ssList(X4)
| ~ ssList(X5)
| ~ ssList(app(app(X3,cons(X1,X4)),cons(X2,X5)))
| ~ ssItem(X1)
| ~ ssItem(X2)
| leq(X1,X2) ),
inference(er,[status(thm)],[c_0_111]) ).
cnf(c_0_122,negated_conjecture,
app(app(sk7,cons(sk5,sk8)),cons(sk6,sk9)) = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_52]),c_0_94]),c_0_90])]) ).
cnf(c_0_123,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_124,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| totalorderedP(X1) ),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_125,negated_conjecture,
( singletonP(sk1)
| nil = sk4 ),
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_48])]) ).
cnf(c_0_126,plain,
( ~ ssItem(X2)
| ~ ssItem(X1)
| ~ leq(X2,X1)
| ~ leq(X1,X2)
| X2 = X1 ),
c_0_118 ).
cnf(c_0_127,negated_conjecture,
leq(sk6,sk5),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_80]),c_0_94])]) ).
cnf(c_0_128,negated_conjecture,
( ~ totalorderedP(sk1)
| leq(sk5,sk6) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_94]),c_0_80]),c_0_123]),c_0_90]),c_0_73]),c_0_72])]) ).
cnf(c_0_129,negated_conjecture,
( totalorderedP(sk1)
| nil = sk4 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_123])]) ).
cnf(c_0_130,plain,
( ~ ssItem(X1)
| ~ lt(X1,X1) ),
inference(fof_simplification,[status(thm)],[clause63]) ).
cnf(c_0_131,negated_conjecture,
( ~ leq(sk5,sk6)
| sk6 = sk5 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_94]),c_0_80])]) ).
cnf(c_0_132,negated_conjecture,
( leq(sk5,sk6)
| nil = sk4 ),
inference(spm,[status(thm)],[c_0_128,c_0_129]) ).
cnf(c_0_133,plain,
( ~ ssItem(X1)
| ~ lt(X1,X1) ),
c_0_130 ).
cnf(c_0_134,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ segmentP(X2,X1)
| ~ segmentP(X1,X2)
| X2 = X1 ),
inference(fof_simplification,[status(thm)],[clause127]) ).
cnf(c_0_135,negated_conjecture,
segmentP(sk4,sk3),
co1_7 ).
cnf(c_0_136,plain,
( ~ ssList(X1)
| segmentP(X1,nil) ),
inference(fof_simplification,[status(thm)],[clause56]) ).
cnf(c_0_137,negated_conjecture,
( sk6 = sk5
| nil = sk4 ),
inference(spm,[status(thm)],[c_0_131,c_0_132]) ).
cnf(c_0_138,plain,
~ lt(X1,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_133,c_0_103])]) ).
cnf(c_0_139,plain,
( ~ ssList(X6)
| ~ strictorderedP(X6)
| ~ ssItem(X2)
| ~ ssItem(X4)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X5)
| app(app(X1,cons(X2,X3)),cons(X4,X5)) != X6
| lt(X2,X4) ),
inference(fof_simplification,[status(thm)],[clause181]) ).
cnf(c_0_140,plain,
( ~ ssItem(X2)
| ~ ssItem(X1)
| ~ lt(X2,X1)
| ~ lt(X1,X2) ),
inference(fof_simplification,[status(thm)],[clause114]) ).
cnf(c_0_141,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ segmentP(X2,X1)
| ~ segmentP(X1,X2)
| X2 = X1 ),
c_0_134 ).
cnf(c_0_142,negated_conjecture,
segmentP(sk4,sk1),
inference(rw,[status(thm)],[c_0_135,c_0_106]) ).
cnf(c_0_143,plain,
( ~ ssList(X1)
| segmentP(X1,nil) ),
c_0_136 ).
cnf(c_0_144,negated_conjecture,
nil = sk4,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_137]),c_0_138]) ).
cnf(c_0_145,plain,
( ~ ssList(X6)
| ~ strictorderedP(X6)
| ~ ssItem(X2)
| ~ ssItem(X4)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X5)
| app(app(X1,cons(X2,X3)),cons(X4,X5)) != X6
| lt(X2,X4) ),
c_0_139 ).
cnf(c_0_146,plain,
( ~ ssItem(X2)
| ~ ssItem(X1)
| ~ lt(X2,X1)
| ~ lt(X1,X2) ),
c_0_140 ).
cnf(c_0_147,axiom,
strictorderedP(nil),
clause3 ).
cnf(c_0_148,negated_conjecture,
( ~ segmentP(sk1,sk4)
| sk4 = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_142]),c_0_117]),c_0_123])]) ).
cnf(c_0_149,plain,
( ~ ssList(X1)
| segmentP(X1,sk4) ),
inference(rw,[status(thm)],[c_0_143,c_0_144]) ).
cnf(c_0_150,plain,
( ~ strictorderedP(app(app(X3,cons(X1,X4)),cons(X2,X5)))
| ~ ssList(X3)
| ~ ssList(X4)
| ~ ssList(X5)
| ~ ssList(app(app(X3,cons(X1,X4)),cons(X2,X5)))
| ~ ssItem(X1)
| ~ ssItem(X2)
| lt(X1,X2) ),
inference(er,[status(thm)],[c_0_145]) ).
cnf(c_0_151,negated_conjecture,
~ lt(sk5,sk6),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_120]),c_0_94]),c_0_80])]) ).
cnf(c_0_152,plain,
strictorderedP(sk4),
inference(rw,[status(thm)],[c_0_147,c_0_144]) ).
cnf(c_0_153,negated_conjecture,
sk4 = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_149]),c_0_123])]) ).
cnf(c_0_154,negated_conjecture,
~ strictorderedP(sk1),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_122]),c_0_94]),c_0_80]),c_0_123]),c_0_90]),c_0_73]),c_0_72])]),c_0_151]) ).
cnf(c_0_155,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_152,c_0_153]),c_0_154]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC307-1 : 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 : n016.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 08:18:52 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 1.88/0.81 % Version: 3.5.1
% 1.88/0.81 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.88/0.81 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.88/0.81 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.88/0.81 % Starting new_bool_3 with 300s (1) cores
% 1.88/0.81 % Starting new_bool_1 with 300s (1) cores
% 1.88/0.81 % Starting sh5l with 300s (1) cores
% 1.88/0.81 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 1991697 completed with status 0
% 1.88/0.81 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 1.88/0.81 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.88/0.81 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.88/0.81 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.88/0.81 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.88/0.81 % No SInE strategy applied
% 1.88/0.81 % Search class: FGHSM-FSLM21-MFFFFFNN
% 1.88/0.81 % Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 1.88/0.81 % Starting SubtermCWHack with 136s (1) cores
% 1.88/0.81 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 1.88/0.81 % Starting G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y with 136s (1) cores
% 1.88/0.81 % Starting G-E--_200_B02_F1_SE_CS_SP_PI_S2k with 136s (1) cores
% 1.88/0.81 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 1.88/0.81 % G-E--_200_B02_F1_SE_CS_SP_PI_S2k with pid 1991711 completed with status 0
% 1.88/0.81 % Result found by G-E--_200_B02_F1_SE_CS_SP_PI_S2k
% 1.88/0.81 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.88/0.81 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.88/0.81 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.88/0.81 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.88/0.81 % No SInE strategy applied
% 1.88/0.81 % Search class: FGHSM-FSLM21-MFFFFFNN
% 1.88/0.81 % Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 1.88/0.81 % Starting SubtermCWHack with 136s (1) cores
% 1.88/0.81 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 1.88/0.81 % Starting G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y with 136s (1) cores
% 1.88/0.81 % Starting G-E--_200_B02_F1_SE_CS_SP_PI_S2k with 136s (1) cores
% 1.88/0.81 % Preprocessing time : 0.005 s
% 1.88/0.81
% 1.88/0.81 % Proof found!
% 1.88/0.81 % SZS status Unsatisfiable
% 1.88/0.81 % SZS output start CNFRefutation
% See solution above
% 1.88/0.81 % Parsed axioms : 200
% 1.88/0.81 % Removed by relevancy pruning/SinE : 0
% 1.88/0.81 % Initial clauses : 200
% 1.88/0.81 % Removed in clause preprocessing : 0
% 1.88/0.81 % Initial clauses in saturation : 200
% 1.88/0.81 % Processed clauses : 663
% 1.88/0.81 % ...of these trivial : 17
% 1.88/0.81 % ...subsumed : 69
% 1.88/0.81 % ...remaining for further processing : 577
% 1.88/0.81 % Other redundant clauses eliminated : 66
% 1.88/0.81 % Clauses deleted for lack of memory : 0
% 1.88/0.81 % Backward-subsumed : 103
% 1.88/0.81 % Backward-rewritten : 261
% 1.88/0.81 % Generated clauses : 1751
% 1.88/0.81 % ...of the previous two non-redundant : 1716
% 1.88/0.81 % ...aggressively subsumed : 0
% 1.88/0.81 % Contextual simplify-reflections : 20
% 1.88/0.81 % Paramodulations : 1680
% 1.88/0.81 % Factorizations : 0
% 1.88/0.81 % NegExts : 0
% 1.88/0.81 % Equation resolutions : 72
% 1.88/0.81 % Disequality decompositions : 0
% 1.88/0.81 % Total rewrite steps : 2076
% 1.88/0.81 % ...of those cached : 1914
% 1.88/0.81 % Propositional unsat checks : 0
% 1.88/0.81 % Propositional check models : 0
% 1.88/0.81 % Propositional check unsatisfiable : 0
% 1.88/0.81 % Propositional clauses : 0
% 1.88/0.81 % Propositional clauses after purity: 0
% 1.88/0.81 % Propositional unsat core size : 0
% 1.88/0.81 % Propositional preprocessing time : 0.000
% 1.88/0.81 % Propositional encoding time : 0.000
% 1.88/0.81 % Propositional solver time : 0.000
% 1.88/0.81 % Success case prop preproc time : 0.000
% 1.88/0.81 % Success case prop encoding time : 0.000
% 1.88/0.81 % Success case prop solver time : 0.000
% 1.88/0.81 % Current number of processed clauses : 190
% 1.88/0.81 % Positive orientable unit clauses : 74
% 1.88/0.81 % Positive unorientable unit clauses: 0
% 1.88/0.81 % Negative unit clauses : 9
% 1.88/0.81 % Non-unit-clauses : 107
% 1.88/0.81 % Current number of unprocessed clauses: 1210
% 1.88/0.81 % ...number of literals in the above : 5756
% 1.88/0.81 % Current number of archived formulas : 0
% 1.88/0.81 % Current number of archived clauses : 364
% 1.88/0.81 % Clause-clause subsumption calls (NU) : 25070
% 1.88/0.81 % Rec. Clause-clause subsumption calls : 9398
% 1.88/0.81 % Non-unit clause-clause subsumptions : 131
% 1.88/0.81 % Unit Clause-clause subsumption calls : 1850
% 1.88/0.81 % Rewrite failures with RHS unbound : 0
% 1.88/0.81 % BW rewrite match attempts : 73
% 1.88/0.81 % BW rewrite match successes : 44
% 1.88/0.81 % Condensation attempts : 0
% 1.88/0.81 % Condensation successes : 0
% 1.88/0.81 % Termbank termtop insertions : 45752
% 1.88/0.81 % Search garbage collected termcells : 530
% 1.88/0.81
% 1.88/0.81 % -------------------------------------------------
% 1.88/0.81 % User time : 0.144 s
% 1.88/0.81 % System time : 0.012 s
% 1.88/0.81 % Total time : 0.157 s
% 1.88/0.81 % Maximum resident set size: 4068 pages
% 1.88/0.81
% 1.88/0.81 % -------------------------------------------------
% 1.88/0.81 % User time : 0.931 s
% 1.88/0.81 % System time : 0.064 s
% 1.88/0.81 % Total time : 0.995 s
% 1.88/0.81 % Maximum resident set size: 4864 pages
% 1.88/0.81 % E exiting
%------------------------------------------------------------------------------