%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC253-1 : 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 : n007.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 02:43:40 PM UTC 2026
% Result : Unsatisfiable 0.63s 0.56s
% Output : CNFRefutation 0.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 34
% Syntax : Number of clauses : 143 ( 24 unt; 48 nHn; 137 RR)
% Number of literals : 423 ( 173 equ; 237 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 176 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(co1_7,negated_conjecture,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
cnf(co1_11,negated_conjecture,
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| app(sk3,X2) != X1
| tl(sk4) != X2
| ~ ssList(X2)
| ~ ssList(X1)
| sk4 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
cnf(co1_5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
cnf(co1_6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
cnf(clause100,axiom,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause100) ).
cnf(co1_2,negated_conjecture,
ssList(sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_2) ).
cnf(clause8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
cnf(clause75,axiom,
( ~ ssList(X1)
| nil = X1
| ssList(tl(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause75) ).
cnf(clause85,axiom,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause85) ).
cnf(clause144,axiom,
( ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != X3
| frontsegP(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause144) ).
cnf(co1_1,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).
cnf(clause99,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause99) ).
cnf(clause104,axiom,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause104) ).
cnf(clause76,axiom,
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause76) ).
cnf(clause133,axiom,
( ~ ssList(X2)
| ~ ssList(X1)
| tl(app(X2,X1)) = app(tl(X2),X1)
| nil = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause133) ).
cnf(clause118,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause118) ).
cnf(clause96,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| tl(cons(X1,X2)) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause96) ).
cnf(clause86,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause86) ).
cnf(clause98,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause98) ).
cnf(clause132,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| app(X2,skaf45(X1,X2)) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause132) ).
cnf(clause73,axiom,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause73) ).
cnf(clause109,axiom,
( ~ ssList(X1)
| nil = X1
| cons(skaf83(X1),skaf82(X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause109) ).
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(clause12,axiom,
ssItem(skaf83(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause12) ).
cnf(clause13,axiom,
ssList(skaf82(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause13) ).
cnf(clause51,axiom,
ssList(skaf45(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause51) ).
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(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(clause151,axiom,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(X1,X2) != app(X3,X2)
| X1 = X3 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause151) ).
cnf(clause74,axiom,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause74) ).
cnf(clause116,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,nil) != X2
| singletonP(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause116) ).
cnf(clause97,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| hd(cons(X1,X2)) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause97) ).
cnf(co1_12,negated_conjecture,
( ~ neq(sk4,nil)
| ~ singletonP(sk1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
cnf(clause115,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ neq(X1,X2)
| X1 != X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause115) ).
cnf(c_0_34,negated_conjecture,
neq(sk2,nil),
inference(fof_simplification,[status(thm)],[co1_7]) ).
cnf(c_0_35,negated_conjecture,
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| app(sk3,X2) != X1
| tl(sk4) != X2
| ~ ssList(X2)
| ~ ssList(X1)
| sk4 = X1 ),
inference(fof_simplification,[status(thm)],[co1_11]) ).
cnf(c_0_36,negated_conjecture,
neq(sk2,nil),
c_0_34 ).
cnf(c_0_37,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_38,negated_conjecture,
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| app(sk3,X2) != X1
| tl(sk4) != X2
| ~ ssList(X2)
| ~ ssList(X1)
| sk4 = X1 ),
c_0_35 ).
cnf(c_0_39,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_40,negated_conjecture,
neq(sk4,nil),
inference(rw,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_41,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
inference(fof_simplification,[status(thm)],[clause100]) ).
cnf(c_0_42,negated_conjecture,
ssList(sk2),
co1_2 ).
cnf(c_0_43,negated_conjecture,
( ~ ssList(tl(sk4))
| ~ ssList(app(sk1,tl(sk4)))
| ~ neq(nil,sk4)
| app(sk1,tl(sk4)) = sk4 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39]),c_0_40])])])]) ).
cnf(c_0_44,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
c_0_41 ).
cnf(c_0_45,axiom,
ssList(nil),
clause8 ).
cnf(c_0_46,negated_conjecture,
ssList(sk4),
inference(rw,[status(thm)],[c_0_42,c_0_37]) ).
cnf(c_0_47,plain,
( ~ ssList(X1)
| nil = X1
| ssList(tl(X1)) ),
inference(fof_simplification,[status(thm)],[clause75]) ).
cnf(c_0_48,negated_conjecture,
( ~ ssList(tl(sk4))
| ~ ssList(app(sk1,tl(sk4)))
| sk4 = nil
| app(sk1,tl(sk4)) = sk4 ),
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(X1)
| nil = X1
| ssList(tl(X1)) ),
c_0_47 ).
cnf(c_0_50,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
inference(fof_simplification,[status(thm)],[clause85]) ).
cnf(c_0_51,plain,
( ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != X3
| frontsegP(X3,X1) ),
inference(fof_simplification,[status(thm)],[clause144]) ).
cnf(c_0_52,negated_conjecture,
( ~ ssList(app(sk1,tl(sk4)))
| sk4 = nil
| app(sk1,tl(sk4)) = sk4 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_46])]) ).
cnf(c_0_53,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
c_0_50 ).
cnf(c_0_54,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_55,plain,
( ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != X3
| frontsegP(X3,X1) ),
c_0_51 ).
cnf(c_0_56,negated_conjecture,
( ~ ssList(tl(sk4))
| sk4 = nil
| app(sk1,tl(sk4)) = sk4 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54])]) ).
cnf(c_0_57,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != X2 ),
inference(fof_simplification,[status(thm)],[clause99]) ).
cnf(c_0_58,plain,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
inference(fof_simplification,[status(thm)],[clause104]) ).
cnf(c_0_59,plain,
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
inference(fof_simplification,[status(thm)],[clause76]) ).
cnf(c_0_60,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| frontsegP(app(X1,X2),X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_55]),c_0_53]) ).
cnf(c_0_61,negated_conjecture,
( sk4 = nil
| app(sk1,tl(sk4)) = sk4 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_49]),c_0_46])]) ).
cnf(c_0_62,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != X2 ),
c_0_57 ).
cnf(c_0_63,plain,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
c_0_58 ).
cnf(c_0_64,plain,
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
c_0_59 ).
cnf(c_0_65,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| tl(app(X2,X1)) = app(tl(X2),X1)
| nil = X2 ),
inference(fof_simplification,[status(thm)],[clause133]) ).
cnf(c_0_66,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X1 ),
inference(fof_simplification,[status(thm)],[clause118]) ).
cnf(c_0_67,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| tl(cons(X1,X2)) = X2 ),
inference(fof_simplification,[status(thm)],[clause96]) ).
cnf(c_0_68,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
inference(fof_simplification,[status(thm)],[clause86]) ).
cnf(c_0_69,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
inference(fof_simplification,[status(thm)],[clause98]) ).
cnf(c_0_70,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| app(X2,skaf45(X1,X2)) = X1 ),
inference(fof_simplification,[status(thm)],[clause132]) ).
cnf(c_0_71,negated_conjecture,
( ~ ssList(tl(sk4))
| frontsegP(sk4,sk1)
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_54])]) ).
cnf(c_0_72,plain,
( ~ ssList(X1)
| tl(X1) != X1
| nil = X1 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_49]),c_0_64]) ).
cnf(c_0_73,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| tl(app(X2,X1)) = app(tl(X2),X1)
| nil = X2 ),
c_0_65 ).
cnf(c_0_74,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X1 ),
c_0_66 ).
cnf(c_0_75,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(fof_simplification,[status(thm)],[clause73]) ).
cnf(c_0_76,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| tl(cons(X1,X2)) = X2 ),
c_0_67 ).
cnf(c_0_77,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
c_0_68 ).
cnf(c_0_78,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
c_0_69 ).
cnf(c_0_79,plain,
( ~ ssList(X1)
| nil = X1
| cons(skaf83(X1),skaf82(X1)) = X1 ),
inference(fof_simplification,[status(thm)],[clause109]) ).
cnf(c_0_80,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| hd(app(X2,X1)) = hd(X2)
| nil = X2 ),
inference(fof_simplification,[status(thm)],[clause123]) ).
cnf(c_0_81,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| app(X2,skaf45(X1,X2)) = X1 ),
c_0_70 ).
cnf(c_0_82,negated_conjecture,
( frontsegP(sk4,sk1)
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_49]),c_0_46])]) ).
cnf(c_0_83,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| app(tl(X1),X2) != app(X1,X2)
| nil = X1 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_53]),c_0_74]) ).
cnf(c_0_84,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
c_0_75 ).
cnf(c_0_85,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_63,c_0_76]),c_0_77]),c_0_78]) ).
cnf(c_0_86,plain,
( ~ ssList(X1)
| nil = X1
| cons(skaf83(X1),skaf82(X1)) = X1 ),
c_0_79 ).
cnf(c_0_87,axiom,
ssItem(skaf83(X1)),
clause12 ).
cnf(c_0_88,axiom,
ssList(skaf82(X1)),
clause13 ).
cnf(c_0_89,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| hd(app(X2,X1)) = hd(X2)
| nil = X2 ),
c_0_80 ).
cnf(c_0_90,negated_conjecture,
( sk4 = nil
| app(sk1,skaf45(sk4,sk1)) = sk4 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_54]),c_0_46])]) ).
cnf(c_0_91,axiom,
ssList(skaf45(X1,X2)),
clause51 ).
cnf(c_0_92,plain,
( ~ ssList(X1)
| tl(X1) != app(X1,nil)
| nil = X1 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_45])]),c_0_49]) ).
cnf(c_0_93,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_94,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_85,c_0_86]),c_0_87]),c_0_88])]) ).
cnf(c_0_95,negated_conjecture,
( sk1 = nil
| sk4 = nil
| hd(sk1) = hd(sk4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_54]),c_0_91])]) ).
cnf(c_0_96,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,X2),nil) != X2 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_76]),c_0_77]),c_0_78]) ).
cnf(c_0_97,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,app(X2,X3)) = app(cons(X1,X2),X3) ),
c_0_93 ).
cnf(c_0_98,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_99,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(X1,X2) != app(X3,X2)
| X1 = X3 ),
inference(fof_simplification,[status(thm)],[clause151]) ).
cnf(c_0_100,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_simplification,[status(thm)],[clause74]) ).
cnf(c_0_101,negated_conjecture,
( sk1 = nil
| sk4 = nil
| cons(hd(sk4),skaf82(sk1)) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_54])]) ).
cnf(c_0_102,negated_conjecture,
( ssItem(hd(sk4))
| sk1 = nil
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_95]),c_0_54])]) ).
cnf(c_0_103,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,app(X2,nil)) != X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_45])]) ).
cnf(c_0_104,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X3,X2),X1) = app(X3,app(X2,X1)) ),
c_0_98 ).
cnf(c_0_105,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,nil) != X2
| singletonP(X2) ),
inference(fof_simplification,[status(thm)],[clause116]) ).
cnf(c_0_106,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(X1,X2) != app(X3,X2)
| X1 = X3 ),
c_0_99 ).
cnf(c_0_107,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
c_0_100 ).
cnf(c_0_108,negated_conjecture,
( ~ ssList(tl(sk4))
| sk1 = nil
| sk4 = nil
| app(tl(sk1),tl(sk4)) = tl(sk4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_61]),c_0_54])]) ).
cnf(c_0_109,negated_conjecture,
( sk4 = nil
| sk1 = nil
| skaf82(sk1) = tl(sk1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_101]),c_0_88])]),c_0_102]) ).
cnf(c_0_110,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(tl(X1),X2))
| nil = X1 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_73]),c_0_53]),c_0_74]) ).
cnf(c_0_111,negated_conjecture,
( sk1 = nil
| sk4 = nil
| app(tl(sk1),skaf45(sk4,sk1)) = tl(sk4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_90]),c_0_54]),c_0_91])]) ).
cnf(c_0_112,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| hd(cons(X1,X2)) = X1 ),
inference(fof_simplification,[status(thm)],[clause97]) ).
cnf(c_0_113,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,app(X2,app(X3,nil))) != app(X2,X3) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_45])]),c_0_53]) ).
cnf(c_0_114,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,nil) != X2
| singletonP(X2) ),
c_0_105 ).
cnf(c_0_115,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != X2
| X1 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_45])]) ).
cnf(c_0_116,negated_conjecture,
( sk4 = nil
| sk1 = nil
| app(tl(sk1),tl(sk4)) = tl(sk4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_49]),c_0_46])]) ).
cnf(c_0_117,negated_conjecture,
( ssList(tl(sk1))
| sk1 = nil
| sk4 = nil ),
inference(spm,[status(thm)],[c_0_88,c_0_109]) ).
cnf(c_0_118,negated_conjecture,
( ssList(tl(sk4))
| sk1 = nil
| 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_54]),c_0_91])]) ).
cnf(c_0_119,negated_conjecture,
( ~ neq(sk4,nil)
| ~ singletonP(sk1) ),
inference(fof_simplification,[status(thm)],[co1_12]) ).
cnf(c_0_120,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| hd(cons(X1,X2)) = X1 ),
c_0_112 ).
cnf(c_0_121,negated_conjecture,
( sk1 = nil
| sk4 = nil
| cons(skaf83(sk1),tl(sk1)) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_109]),c_0_54])]) ).
cnf(c_0_122,plain,
( ~ ssList(X2)
| ~ ssList(app(X2,nil))
| ~ ssItem(X1)
| cons(X1,app(X2,nil)) != app(nil,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_107]),c_0_45])]) ).
cnf(c_0_123,plain,
( ~ ssList(cons(X1,nil))
| ~ ssItem(X1)
| singletonP(cons(X1,nil)) ),
inference(er,[status(thm)],[c_0_114]) ).
cnf(c_0_124,negated_conjecture,
( sk1 = nil
| sk4 = nil
| tl(sk1) = nil ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_117]),c_0_118]) ).
cnf(c_0_125,negated_conjecture,
( ~ neq(sk4,nil)
| ~ singletonP(sk1) ),
c_0_119 ).
cnf(c_0_126,negated_conjecture,
( sk4 = nil
| sk1 = nil
| skaf83(sk1) = hd(sk1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_87])]),c_0_117]) ).
cnf(c_0_127,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != app(nil,X2) ),
inference(spm,[status(thm)],[c_0_122,c_0_84]) ).
cnf(c_0_128,plain,
( ~ ssItem(X1)
| singletonP(cons(X1,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_77]),c_0_45])]) ).
cnf(c_0_129,negated_conjecture,
( sk1 = nil
| sk4 = nil
| cons(hd(sk1),nil) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_124]),c_0_54])]) ).
cnf(c_0_130,negated_conjecture,
~ singletonP(sk1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_125,c_0_40])]) ).
cnf(c_0_131,negated_conjecture,
( ssItem(hd(sk1))
| sk1 = nil
| sk4 = nil ),
inference(spm,[status(thm)],[c_0_87,c_0_126]) ).
cnf(c_0_132,plain,
( ~ ssList(X1)
| app(nil,skaf82(X1)) != X1
| nil = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_86]),c_0_87]),c_0_88])]) ).
cnf(c_0_133,plain,
( ~ ssList(X1)
| nil = X1
| skaf82(X1) = tl(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_94]),c_0_88])]),c_0_64]) ).
cnf(c_0_134,negated_conjecture,
( sk4 = nil
| sk1 = nil ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_130]),c_0_131]) ).
cnf(c_0_135,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ neq(X1,X2)
| X1 != X2 ),
inference(fof_simplification,[status(thm)],[clause115]) ).
cnf(c_0_136,plain,
( ~ ssList(X1)
| app(nil,tl(X1)) != X1
| nil = X1 ),
inference(spm,[status(thm)],[c_0_132,c_0_133]) ).
cnf(c_0_137,negated_conjecture,
( sk4 = nil
| app(nil,tl(sk4)) = sk4 ),
inference(spm,[status(thm)],[c_0_61,c_0_134]) ).
cnf(c_0_138,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ neq(X1,X2)
| X1 != X2 ),
c_0_135 ).
cnf(c_0_139,negated_conjecture,
sk4 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_46])]) ).
cnf(c_0_140,plain,
( ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(er,[status(thm)],[c_0_138]) ).
cnf(c_0_141,negated_conjecture,
neq(nil,nil),
inference(rw,[status(thm)],[c_0_40,c_0_139]) ).
cnf(c_0_142,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_45])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC253-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.35 % Computer : n007.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 08:06:52 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 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
% 0.63/0.56 % Version: 3.5.1
% 0.63/0.56 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.63/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.63/0.56 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.63/0.56 % Starting new_bool_3 with 300s (1) cores
% 0.63/0.56 % Starting new_bool_1 with 300s (1) cores
% 0.63/0.56 % Starting sh5l with 300s (1) cores
% 0.63/0.56 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 608495 completed with status 0
% 0.63/0.56 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.63/0.56 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.63/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.63/0.56 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.63/0.56 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.63/0.56 % No SInE strategy applied
% 0.63/0.56 % Search class: FGHSM-FSLM21-MFFFFFNN
% 0.63/0.56 % Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 0.63/0.56 % Starting SubtermCWHack with 136s (1) cores
% 0.63/0.56 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.63/0.56 % Starting G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y with 136s (1) cores
% 0.63/0.56 % Starting G-E--_200_B02_F1_SE_CS_SP_PI_S2k with 136s (1) cores
% 0.63/0.56 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 0.63/0.56 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 608500 completed with status 0
% 0.63/0.56 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.63/0.56 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.63/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.63/0.56 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.63/0.56 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.63/0.56 % No SInE strategy applied
% 0.63/0.56 % Search class: FGHSM-FSLM21-MFFFFFNN
% 0.63/0.56 % Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 0.63/0.56 % Starting SubtermCWHack with 136s (1) cores
% 0.63/0.56 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.63/0.56 % Preprocessing time : 0.004 s
% 0.63/0.56 % Presaturation interreduction done
% 0.63/0.56
% 0.63/0.56 % Proof found!
% 0.63/0.56 % SZS status Unsatisfiable
% 0.63/0.56 % SZS output start CNFRefutation
% See solution above
% 0.63/0.56 % Parsed axioms : 197
% 0.63/0.56 % Removed by relevancy pruning/SinE : 0
% 0.63/0.56 % Initial clauses : 197
% 0.63/0.56 % Removed in clause preprocessing : 0
% 0.63/0.56 % Initial clauses in saturation : 197
% 0.63/0.56 % Processed clauses : 730
% 0.63/0.56 % ...of these trivial : 5
% 0.63/0.56 % ...subsumed : 150
% 0.63/0.56 % ...remaining for further processing : 575
% 0.63/0.56 % Other redundant clauses eliminated : 70
% 0.63/0.56 % Clauses deleted for lack of memory : 0
% 0.63/0.56 % Backward-subsumed : 100
% 0.63/0.56 % Backward-rewritten : 28
% 0.63/0.56 % Generated clauses : 1561
% 0.63/0.56 % ...of the previous two non-redundant : 1387
% 0.63/0.56 % ...aggressively subsumed : 0
% 0.63/0.56 % Contextual simplify-reflections : 42
% 0.63/0.56 % Paramodulations : 1488
% 0.63/0.56 % Factorizations : 0
% 0.63/0.56 % NegExts : 0
% 0.63/0.56 % Equation resolutions : 75
% 0.63/0.56 % Disequality decompositions : 0
% 0.63/0.56 % Total rewrite steps : 1285
% 0.63/0.56 % ...of those cached : 1205
% 0.63/0.56 % Propositional unsat checks : 0
% 0.63/0.56 % Propositional check models : 0
% 0.63/0.56 % Propositional check unsatisfiable : 0
% 0.63/0.56 % Propositional clauses : 0
% 0.63/0.56 % Propositional clauses after purity: 0
% 0.63/0.56 % Propositional unsat core size : 0
% 0.63/0.56 % Propositional preprocessing time : 0.000
% 0.63/0.56 % Propositional encoding time : 0.000
% 0.63/0.56 % Propositional solver time : 0.000
% 0.63/0.56 % Success case prop preproc time : 0.000
% 0.63/0.56 % Success case prop encoding time : 0.000
% 0.63/0.56 % Success case prop solver time : 0.000
% 0.63/0.56 % Current number of processed clauses : 237
% 0.63/0.56 % Positive orientable unit clauses : 63
% 0.63/0.56 % Positive unorientable unit clauses: 0
% 0.63/0.56 % Negative unit clauses : 3
% 0.63/0.56 % Non-unit-clauses : 171
% 0.63/0.56 % Current number of unprocessed clauses: 1034
% 0.63/0.56 % ...number of literals in the above : 6582
% 0.63/0.56 % Current number of archived formulas : 0
% 0.63/0.56 % Current number of archived clauses : 314
% 0.63/0.56 % Clause-clause subsumption calls (NU) : 20570
% 0.63/0.56 % Rec. Clause-clause subsumption calls : 3015
% 0.63/0.56 % Non-unit clause-clause subsumptions : 272
% 0.63/0.56 % Unit Clause-clause subsumption calls : 82
% 0.63/0.56 % Rewrite failures with RHS unbound : 0
% 0.63/0.56 % BW rewrite match attempts : 4
% 0.63/0.56 % BW rewrite match successes : 4
% 0.63/0.56 % Condensation attempts : 0
% 0.63/0.56 % Condensation successes : 0
% 0.63/0.56 % Termbank termtop insertions : 39863
% 0.63/0.56 % Search garbage collected termcells : 551
% 0.63/0.56
% 0.63/0.56 % -------------------------------------------------
% 0.63/0.56 % User time : 0.074 s
% 0.63/0.56 % System time : 0.009 s
% 0.63/0.56 % Total time : 0.083 s
% 0.63/0.56 % Maximum resident set size: 4024 pages
% 0.63/0.56
% 0.63/0.56 % -------------------------------------------------
% 0.63/0.56 % User time : 0.520 s
% 0.63/0.56 % System time : 0.049 s
% 0.63/0.56 % Total time : 0.569 s
% 0.63/0.56 % Maximum resident set size: 4864 pages
% 0.63/0.56 % E exiting
%------------------------------------------------------------------------------