%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC197-1 : 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 : n020.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 02:43:25 PM UTC 2026
% Result : Unsatisfiable 2.07s 0.70s
% Output : CNFRefutation 2.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 37
% Syntax : Number of clauses : 160 ( 49 unt; 26 nHn; 153 RR)
% Number of literals : 417 ( 116 equ; 252 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 10 con; 0-2 aty)
% Number of variables : 180 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(clause149,axiom,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X3,X2),X1) = app(X3,app(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause149) ).
cnf(co1_13,negated_conjecture,
app(app(app(app(sk7,cons(sk5,nil)),sk9),cons(sk6,nil)),sk8) = sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
cnf(co1_10,negated_conjecture,
ssList(sk7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
cnf(co1_12,negated_conjecture,
ssList(sk9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
cnf(clause86,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).
cnf(co1_8,negated_conjecture,
ssItem(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
cnf(clause8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
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_9,negated_conjecture,
ssItem(sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
cnf(co1_11,negated_conjecture,
ssList(sk8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
cnf(clause85,axiom,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause85) ).
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/sandbox/benchmark/Axioms/SWC001-0.ax',clause179) ).
cnf(clause74,axiom,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause74) ).
cnf(clause157,axiom,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,app(X2,X3)) = app(cons(X1,X2),X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause157) ).
cnf(clause104,axiom,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause104) ).
cnf(clause75,axiom,
( ~ ssList(X1)
| nil = X1
| ssList(tl(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause75) ).
cnf(clause76,axiom,
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause76) ).
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(clause118,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause118) ).
cnf(clause97,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| hd(cons(X1,X2)) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause97) ).
cnf(clause98,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause98) ).
cnf(clause145,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| nil != X2
| nil != X1
| app(X1,X2) = nil ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause145) ).
cnf(clause72,axiom,
( ~ ssList(X1)
| ssItem(X2)
| duplicatefreeP(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause72) ).
cnf(clause175,axiom,
( ~ ssList(X4)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| app(X1,cons(X2,X3)) != X4
| memberP(X4,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause175) ).
cnf(clause161,axiom,
( ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ memberP(cons(X1,X2),X3)
| X3 = X1
| memberP(X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause161) ).
cnf(clause71,axiom,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause71) ).
cnf(co1_1,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
cnf(clause101,axiom,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(skaf44(X1),nil) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause101) ).
cnf(co1_15,negated_conjecture,
( ~ neq(sk4,nil)
| singletonP(sk3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_15) ).
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(co1_5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
cnf(co1_14,negated_conjecture,
sk5 != sk6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
cnf(clause127,axiom,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ segmentP(X2,X1)
| ~ segmentP(X1,X2)
| X2 = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause127) ).
cnf(co1_7,negated_conjecture,
segmentP(sk4,sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
cnf(clause56,axiom,
( ~ ssList(X1)
| segmentP(X1,nil) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause56) ).
cnf(c_0_37,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_38,negated_conjecture,
app(app(app(app(sk7,cons(sk5,nil)),sk9),cons(sk6,nil)),sk8) = sk1,
co1_13 ).
cnf(c_0_39,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X3,X2),X1) = app(X3,app(X2,X1)) ),
c_0_37 ).
cnf(c_0_40,negated_conjecture,
ssList(sk7),
co1_10 ).
cnf(c_0_41,negated_conjecture,
ssList(sk9),
co1_12 ).
cnf(c_0_42,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
inference(fof_simplification,[status(thm)],[clause86]) ).
cnf(c_0_43,negated_conjecture,
( ~ ssList(cons(sk5,nil))
| app(app(app(sk7,app(cons(sk5,nil),sk9)),cons(sk6,nil)),sk8) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_41])]) ).
cnf(c_0_44,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
c_0_42 ).
cnf(c_0_45,negated_conjecture,
ssItem(sk5),
co1_8 ).
cnf(c_0_46,axiom,
ssList(nil),
clause8 ).
cnf(c_0_47,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,nil),X2) = cons(X1,X2) ),
inference(fof_simplification,[status(thm)],[clause120]) ).
cnf(c_0_48,negated_conjecture,
app(app(app(sk7,app(cons(sk5,nil),sk9)),cons(sk6,nil)),sk8) = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),c_0_46])]) ).
cnf(c_0_49,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,nil),X2) = cons(X1,X2) ),
c_0_47 ).
cnf(c_0_50,negated_conjecture,
app(app(app(sk7,cons(sk5,sk9)),cons(sk6,nil)),sk8) = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_45]),c_0_41])]) ).
cnf(c_0_51,negated_conjecture,
( ~ ssList(cons(sk6,nil))
| ~ ssList(cons(sk5,sk9))
| app(app(sk7,app(cons(sk5,sk9),cons(sk6,nil))),sk8) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_39]),c_0_40])]) ).
cnf(c_0_52,negated_conjecture,
( ~ ssList(cons(sk6,nil))
| app(app(sk7,app(cons(sk5,sk9),cons(sk6,nil))),sk8) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_44]),c_0_45]),c_0_41])]) ).
cnf(c_0_53,negated_conjecture,
ssItem(sk6),
co1_9 ).
cnf(c_0_54,negated_conjecture,
app(app(sk7,app(cons(sk5,sk9),cons(sk6,nil))),sk8) = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_44]),c_0_53]),c_0_46])]) ).
cnf(c_0_55,negated_conjecture,
ssList(sk8),
co1_11 ).
cnf(c_0_56,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
inference(fof_simplification,[status(thm)],[clause85]) ).
cnf(c_0_57,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_58,negated_conjecture,
( ~ ssList(app(cons(sk5,sk9),cons(sk6,nil)))
| app(sk7,app(app(cons(sk5,sk9),cons(sk6,nil)),sk8)) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_54]),c_0_40]),c_0_55])]) ).
cnf(c_0_59,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
c_0_56 ).
cnf(c_0_60,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_57 ).
cnf(c_0_61,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_simplification,[status(thm)],[clause74]) ).
cnf(c_0_62,negated_conjecture,
( ~ ssList(cons(sk6,nil))
| ~ ssList(cons(sk5,sk9))
| app(sk7,app(app(cons(sk5,sk9),cons(sk6,nil)),sk8)) = sk1 ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_63,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_60]) ).
cnf(c_0_64,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
c_0_61 ).
cnf(c_0_65,negated_conjecture,
( ~ ssList(cons(sk6,nil))
| app(sk7,app(app(cons(sk5,sk9),cons(sk6,nil)),sk8)) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_44]),c_0_45]),c_0_41])]) ).
cnf(c_0_66,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_67,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_63,c_0_64]),c_0_46])]),c_0_44]) ).
cnf(c_0_68,plain,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
inference(fof_simplification,[status(thm)],[clause104]) ).
cnf(c_0_69,plain,
( ~ ssList(X1)
| nil = X1
| ssList(tl(X1)) ),
inference(fof_simplification,[status(thm)],[clause75]) ).
cnf(c_0_70,plain,
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
inference(fof_simplification,[status(thm)],[clause76]) ).
cnf(c_0_71,negated_conjecture,
app(sk7,app(app(cons(sk5,sk9),cons(sk6,nil)),sk8)) = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_44]),c_0_53]),c_0_46])]) ).
cnf(c_0_72,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,app(X2,X3)) = app(cons(X1,X2),X3) ),
c_0_66 ).
cnf(c_0_73,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_67,c_0_49]),c_0_46])]),c_0_44]) ).
cnf(c_0_74,plain,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
c_0_68 ).
cnf(c_0_75,plain,
( ~ ssList(X1)
| nil = X1
| ssList(tl(X1)) ),
c_0_69 ).
cnf(c_0_76,plain,
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
c_0_70 ).
cnf(c_0_77,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| hd(app(X2,X1)) = hd(X2)
| nil = X2 ),
inference(fof_simplification,[status(thm)],[clause123]) ).
cnf(c_0_78,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X1 ),
inference(fof_simplification,[status(thm)],[clause118]) ).
cnf(c_0_79,negated_conjecture,
( ~ ssList(cons(sk6,nil))
| app(sk7,app(cons(sk5,app(sk9,cons(sk6,nil))),sk8)) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_45]),c_0_41])]) ).
cnf(c_0_80,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_73,c_0_74]),c_0_75]),c_0_44]),c_0_76]) ).
cnf(c_0_81,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| hd(app(X2,X1)) = hd(X2)
| nil = X2 ),
c_0_77 ).
cnf(c_0_82,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X1 ),
c_0_78 ).
cnf(c_0_83,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| hd(cons(X1,X2)) = X1 ),
inference(fof_simplification,[status(thm)],[clause97]) ).
cnf(c_0_84,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
inference(fof_simplification,[status(thm)],[clause98]) ).
cnf(c_0_85,negated_conjecture,
app(sk7,app(cons(sk5,app(sk9,cons(sk6,nil))),sk8)) = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_44]),c_0_53]),c_0_46])]) ).
cnf(c_0_86,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_80,c_0_81]),c_0_59]),c_0_82]) ).
cnf(c_0_87,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| hd(cons(X1,X2)) = X1 ),
c_0_83 ).
cnf(c_0_88,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
c_0_84 ).
cnf(c_0_89,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| nil != X2
| nil != X1
| app(X1,X2) = nil ),
inference(fof_simplification,[status(thm)],[clause145]) ).
cnf(c_0_90,negated_conjecture,
( ~ ssList(app(sk9,cons(sk6,nil)))
| app(sk7,cons(sk5,app(app(sk9,cons(sk6,nil)),sk8))) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_72]),c_0_45]),c_0_55])]) ).
cnf(c_0_91,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_86,c_0_87]),c_0_44]),c_0_88]) ).
cnf(c_0_92,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| nil != X2
| nil != X1
| app(X1,X2) = nil ),
c_0_89 ).
cnf(c_0_93,plain,
( ~ ssList(X1)
| ssItem(X2)
| duplicatefreeP(X1) ),
inference(fof_simplification,[status(thm)],[clause72]) ).
cnf(c_0_94,negated_conjecture,
( ~ ssList(cons(sk6,nil))
| ~ ssList(app(sk7,cons(sk5,sk9)))
| app(app(sk7,cons(sk5,sk9)),app(cons(sk6,nil),sk8)) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_50]),c_0_55])]) ).
cnf(c_0_95,negated_conjecture,
( ~ ssList(cons(sk6,nil))
| app(sk7,cons(sk5,app(app(sk9,cons(sk6,nil)),sk8))) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_59]),c_0_41])]) ).
cnf(c_0_96,plain,
( ~ duplicatefreeP(cons(X1,cons(X1,app(X3,X2))))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[c_0_91,c_0_72]) ).
cnf(c_0_97,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_92])]),c_0_46])]) ).
cnf(c_0_98,plain,
( ~ ssList(X1)
| ssItem(X2)
| duplicatefreeP(X1) ),
c_0_93 ).
cnf(c_0_99,negated_conjecture,
( ~ ssList(app(sk7,cons(sk5,sk9)))
| app(app(sk7,cons(sk5,sk9)),app(cons(sk6,nil),sk8)) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_44]),c_0_53]),c_0_46])]) ).
cnf(c_0_100,negated_conjecture,
app(sk7,cons(sk5,app(app(sk9,cons(sk6,nil)),sk8))) = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_44]),c_0_53]),c_0_46])]) ).
cnf(c_0_101,plain,
( ~ duplicatefreeP(cons(X1,cons(X1,nil)))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_46])]) ).
cnf(c_0_102,plain,
( ~ ssList(X3)
| ~ ssItem(X2)
| duplicatefreeP(cons(X2,X3))
| ssItem(X1) ),
inference(spm,[status(thm)],[c_0_98,c_0_44]) ).
cnf(c_0_103,plain,
( ~ ssList(X4)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| app(X1,cons(X2,X3)) != X4
| memberP(X4,X2) ),
inference(fof_simplification,[status(thm)],[clause175]) ).
cnf(c_0_104,negated_conjecture,
( ~ ssList(cons(sk5,sk9))
| app(app(sk7,cons(sk5,sk9)),app(cons(sk6,nil),sk8)) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_59]),c_0_40])]) ).
cnf(c_0_105,negated_conjecture,
( ~ ssList(cons(sk6,nil))
| app(sk7,cons(sk5,app(sk9,app(cons(sk6,nil),sk8)))) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_39]),c_0_41]),c_0_55])]) ).
cnf(c_0_106,plain,
( ~ ssList(cons(X2,nil))
| ~ ssItem(X2)
| ssItem(X1) ),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_107,plain,
( ~ ssList(X4)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| app(X1,cons(X2,X3)) != X4
| memberP(X4,X2) ),
c_0_103 ).
cnf(c_0_108,negated_conjecture,
app(app(sk7,cons(sk5,sk9)),app(cons(sk6,nil),sk8)) = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_44]),c_0_45]),c_0_41])]) ).
cnf(c_0_109,negated_conjecture,
app(sk7,cons(sk5,app(sk9,app(cons(sk6,nil),sk8)))) = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_44]),c_0_53]),c_0_46])]) ).
cnf(c_0_110,plain,
( ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ memberP(cons(X1,X2),X3)
| X3 = X1
| memberP(X2,X3) ),
inference(fof_simplification,[status(thm)],[clause161]) ).
cnf(c_0_111,plain,
( ~ ssItem(X2)
| ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_44]),c_0_46])]) ).
cnf(c_0_112,plain,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[clause71]) ).
cnf(c_0_113,plain,
( ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(app(X1,cons(X2,X3)))
| ~ ssItem(X2)
| memberP(app(X1,cons(X2,X3)),X2) ),
inference(er,[status(thm)],[c_0_107]) ).
cnf(c_0_114,negated_conjecture,
app(app(sk7,cons(sk5,sk9)),cons(sk6,sk8)) = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_49]),c_0_53]),c_0_55])]) ).
cnf(c_0_115,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_116,negated_conjecture,
app(sk7,cons(sk5,app(sk9,cons(sk6,sk8)))) = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_49]),c_0_53]),c_0_55])]) ).
cnf(c_0_117,plain,
( ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ memberP(cons(X1,X2),X3)
| X3 = X1
| memberP(X2,X3) ),
c_0_110 ).
cnf(c_0_118,negated_conjecture,
ssItem(X1),
inference(spm,[status(thm)],[c_0_111,c_0_53]) ).
cnf(c_0_119,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(skaf44(X1),nil) = X1 ),
inference(fof_simplification,[status(thm)],[clause101]) ).
cnf(c_0_120,plain,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
c_0_112 ).
cnf(c_0_121,negated_conjecture,
( ~ ssList(app(sk7,cons(sk5,sk9)))
| memberP(sk1,sk6) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_53]),c_0_115]),c_0_55])]) ).
cnf(c_0_122,negated_conjecture,
( ~ neq(sk4,nil)
| singletonP(sk3) ),
inference(fof_simplification,[status(thm)],[co1_15]) ).
cnf(c_0_123,negated_conjecture,
( ~ ssList(app(sk9,cons(sk6,sk8)))
| memberP(sk1,sk5) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_116]),c_0_45]),c_0_115]),c_0_40])]) ).
cnf(c_0_124,plain,
( ~ ssList(X3)
| ~ memberP(cons(X1,X3),X2)
| memberP(X3,X2)
| X1 = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_117,c_0_118]),c_0_118])]) ).
cnf(c_0_125,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(skaf44(X1),nil) = X1 ),
c_0_119 ).
cnf(c_0_126,plain,
~ memberP(nil,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_120,c_0_118])]) ).
cnf(c_0_127,negated_conjecture,
( ~ ssList(cons(sk5,sk9))
| memberP(sk1,sk6) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_59]),c_0_40])]) ).
cnf(c_0_128,negated_conjecture,
( ~ neq(sk4,nil)
| singletonP(sk3) ),
c_0_122 ).
cnf(c_0_129,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_130,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
inference(fof_simplification,[status(thm)],[clause100]) ).
cnf(c_0_131,negated_conjecture,
ssList(sk2),
co1_2 ).
cnf(c_0_132,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_133,negated_conjecture,
( ~ ssList(cons(sk6,sk8))
| memberP(sk1,sk5) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_59]),c_0_41])]) ).
cnf(c_0_134,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| ~ memberP(X1,X2)
| skaf44(X1) = X2 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_46])]),c_0_126]) ).
cnf(c_0_135,negated_conjecture,
memberP(sk1,sk6),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_44]),c_0_45]),c_0_41])]) ).
cnf(c_0_136,negated_conjecture,
( ~ neq(sk4,nil)
| singletonP(sk1) ),
inference(rw,[status(thm)],[c_0_128,c_0_129]) ).
cnf(c_0_137,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
c_0_130 ).
cnf(c_0_138,negated_conjecture,
ssList(sk4),
inference(rw,[status(thm)],[c_0_131,c_0_132]) ).
cnf(c_0_139,negated_conjecture,
memberP(sk1,sk5),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_44]),c_0_53]),c_0_55])]) ).
cnf(c_0_140,negated_conjecture,
( ~ singletonP(sk1)
| skaf44(sk1) = sk6 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_115])]) ).
cnf(c_0_141,negated_conjecture,
( singletonP(sk1)
| nil = sk4 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_138]),c_0_46])]) ).
cnf(c_0_142,negated_conjecture,
( ~ singletonP(sk1)
| skaf44(sk1) = sk5 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_139]),c_0_115])]) ).
cnf(c_0_143,negated_conjecture,
sk5 != sk6,
inference(fof_simplification,[status(thm)],[co1_14]) ).
cnf(c_0_144,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ segmentP(X2,X1)
| ~ segmentP(X1,X2)
| X2 = X1 ),
inference(fof_simplification,[status(thm)],[clause127]) ).
cnf(c_0_145,negated_conjecture,
segmentP(sk4,sk3),
co1_7 ).
cnf(c_0_146,plain,
( ~ ssList(X1)
| segmentP(X1,nil) ),
inference(fof_simplification,[status(thm)],[clause56]) ).
cnf(c_0_147,negated_conjecture,
( nil = sk4
| skaf44(sk1) = sk6 ),
inference(spm,[status(thm)],[c_0_140,c_0_141]) ).
cnf(c_0_148,negated_conjecture,
( nil = sk4
| skaf44(sk1) = sk5 ),
inference(spm,[status(thm)],[c_0_142,c_0_141]) ).
cnf(c_0_149,negated_conjecture,
sk5 != sk6,
c_0_143 ).
cnf(c_0_150,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ segmentP(X2,X1)
| ~ segmentP(X1,X2)
| X2 = X1 ),
c_0_144 ).
cnf(c_0_151,negated_conjecture,
segmentP(sk4,sk1),
inference(rw,[status(thm)],[c_0_145,c_0_129]) ).
cnf(c_0_152,plain,
( ~ ssList(X1)
| segmentP(X1,nil) ),
c_0_146 ).
cnf(c_0_153,negated_conjecture,
nil = sk4,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_148]),c_0_149]) ).
cnf(c_0_154,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_150,c_0_151]),c_0_138]),c_0_115])]) ).
cnf(c_0_155,plain,
( ~ ssList(X1)
| segmentP(X1,sk4) ),
inference(rw,[status(thm)],[c_0_152,c_0_153]) ).
cnf(c_0_156,plain,
~ memberP(sk4,X1),
inference(rw,[status(thm)],[c_0_126,c_0_153]) ).
cnf(c_0_157,negated_conjecture,
sk4 = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_155]),c_0_115])]) ).
cnf(c_0_158,plain,
~ memberP(sk1,X1),
inference(rw,[status(thm)],[c_0_156,c_0_157]) ).
cnf(c_0_159,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_139,c_0_158]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC197-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n020.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 08:04:32 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 2.07/0.70 % Version: 3.5.1
% 2.07/0.70 % Preprocessing class: FSLSSMSMSSSNFFN.
% 2.07/0.70 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.07/0.70 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 2.07/0.70 % Starting new_bool_3 with 300s (1) cores
% 2.07/0.70 % Starting new_bool_1 with 300s (1) cores
% 2.07/0.70 % Starting sh5l with 300s (1) cores
% 2.07/0.70 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 2443657 completed with status 0
% 2.07/0.70 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 2.07/0.70 % Preprocessing class: FSLSSMSMSSSNFFN.
% 2.07/0.70 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.07/0.70 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 2.07/0.70 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.07/0.70 % No SInE strategy applied
% 2.07/0.70 % Search class: FGHSM-FSLM21-MFFFFFNN
% 2.07/0.70 % Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 2.07/0.70 % Starting SubtermCWHack with 136s (1) cores
% 2.07/0.70 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 2.07/0.70 % Starting G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y with 136s (1) cores
% 2.07/0.70 % Starting G-E--_200_B02_F1_SE_CS_SP_PI_S2k with 136s (1) cores
% 2.07/0.70 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 2.07/0.70 % G-E--_200_B02_F1_SE_CS_SP_PI_S2k with pid 2443666 completed with status 0
% 2.07/0.70 % Result found by G-E--_200_B02_F1_SE_CS_SP_PI_S2k
% 2.07/0.70 % Preprocessing class: FSLSSMSMSSSNFFN.
% 2.07/0.70 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.07/0.70 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 2.07/0.70 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.07/0.70 % No SInE strategy applied
% 2.07/0.70 % Search class: FGHSM-FSLM21-MFFFFFNN
% 2.07/0.70 % Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 2.07/0.70 % Starting SubtermCWHack with 136s (1) cores
% 2.07/0.70 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 2.07/0.70 % Starting G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y with 136s (1) cores
% 2.07/0.70 % Starting G-E--_200_B02_F1_SE_CS_SP_PI_S2k with 136s (1) cores
% 2.07/0.70 % Preprocessing time : 0.003 s
% 2.07/0.70
% 2.07/0.70 % Proof found!
% 2.07/0.70 % SZS status Unsatisfiable
% 2.07/0.70 % SZS output start CNFRefutation
% See solution above
% 2.07/0.70 % Parsed axioms : 200
% 2.07/0.70 % Removed by relevancy pruning/SinE : 0
% 2.07/0.70 % Initial clauses : 200
% 2.07/0.70 % Removed in clause preprocessing : 0
% 2.07/0.70 % Initial clauses in saturation : 200
% 2.07/0.70 % Processed clauses : 1037
% 2.07/0.70 % ...of these trivial : 27
% 2.07/0.70 % ...subsumed : 141
% 2.07/0.70 % ...remaining for further processing : 869
% 2.07/0.70 % Other redundant clauses eliminated : 85
% 2.07/0.70 % Clauses deleted for lack of memory : 0
% 2.07/0.70 % Backward-subsumed : 146
% 2.07/0.70 % Backward-rewritten : 415
% 2.07/0.70 % Generated clauses : 3333
% 2.07/0.70 % ...of the previous two non-redundant : 3239
% 2.07/0.70 % ...aggressively subsumed : 0
% 2.07/0.70 % Contextual simplify-reflections : 21
% 2.07/0.70 % Paramodulations : 3240
% 2.07/0.70 % Factorizations : 0
% 2.07/0.70 % NegExts : 0
% 2.07/0.70 % Equation resolutions : 92
% 2.07/0.70 % Disequality decompositions : 0
% 2.07/0.70 % Total rewrite steps : 4168
% 2.07/0.70 % ...of those cached : 3950
% 2.07/0.70 % Propositional unsat checks : 0
% 2.07/0.70 % Propositional check models : 0
% 2.07/0.70 % Propositional check unsatisfiable : 0
% 2.07/0.70 % Propositional clauses : 0
% 2.07/0.70 % Propositional clauses after purity: 0
% 2.07/0.70 % Propositional unsat core size : 0
% 2.07/0.70 % Propositional preprocessing time : 0.000
% 2.07/0.70 % Propositional encoding time : 0.000
% 2.07/0.70 % Propositional solver time : 0.000
% 2.07/0.70 % Success case prop preproc time : 0.000
% 2.07/0.70 % Success case prop encoding time : 0.000
% 2.07/0.70 % Success case prop solver time : 0.000
% 2.07/0.70 % Current number of processed clauses : 283
% 2.07/0.70 % Positive orientable unit clauses : 78
% 2.07/0.70 % Positive unorientable unit clauses: 0
% 2.07/0.70 % Negative unit clauses : 9
% 2.07/0.70 % Non-unit-clauses : 196
% 2.07/0.70 % Current number of unprocessed clauses: 2294
% 2.07/0.70 % ...number of literals in the above : 10069
% 2.07/0.70 % Current number of archived formulas : 0
% 2.07/0.70 % Current number of archived clauses : 563
% 2.07/0.70 % Clause-clause subsumption calls (NU) : 46431
% 2.07/0.70 % Rec. Clause-clause subsumption calls : 24115
% 2.07/0.70 % Non-unit clause-clause subsumptions : 241
% 2.07/0.70 % Unit Clause-clause subsumption calls : 3030
% 2.07/0.70 % Rewrite failures with RHS unbound : 0
% 2.07/0.70 % BW rewrite match attempts : 109
% 2.07/0.70 % BW rewrite match successes : 67
% 2.07/0.70 % Condensation attempts : 0
% 2.07/0.70 % Condensation successes : 0
% 2.07/0.70 % Termbank termtop insertions : 78057
% 2.07/0.70 % Search garbage collected termcells : 532
% 2.07/0.70
% 2.07/0.70 % -------------------------------------------------
% 2.07/0.70 % User time : 0.158 s
% 2.07/0.70 % System time : 0.011 s
% 2.07/0.70 % Total time : 0.169 s
% 2.07/0.70 % Maximum resident set size: 4068 pages
% 2.07/0.70
% 2.07/0.70 % -------------------------------------------------
% 2.07/0.70 % User time : 1.040 s
% 2.07/0.70 % System time : 0.057 s
% 2.07/0.70 % Total time : 1.097 s
% 2.07/0.70 % Maximum resident set size: 4864 pages
% 2.07/0.70 % E exiting
%------------------------------------------------------------------------------