%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC295-1 : 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 : n017.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 02:43:49 PM UTC 2026
% Result : Unsatisfiable 1.04s 0.69s
% Output : CNFRefutation 1.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 38
% Syntax : Number of clauses : 149 ( 35 unt; 31 nHn; 134 RR)
% Number of literals : 437 ( 123 equ; 269 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-2 aty)
% Number of variables : 214 ( 20 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(clause101,axiom,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(skaf44(X1),nil) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause101) ).
cnf(clause47,axiom,
ssItem(skaf44(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause47) ).
cnf(clause116,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,nil) != X2
| singletonP(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause116) ).
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(clause72,axiom,
( ~ ssList(X1)
| ssItem(X2)
| duplicatefreeP(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause72) ).
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(co1_10,negated_conjecture,
app(app(sk6,cons(sk5,nil)),sk7) = sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
cnf(co1_8,negated_conjecture,
ssList(sk6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
cnf(co1_9,negated_conjecture,
ssList(sk7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
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(clause85,axiom,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause85) ).
cnf(co1_7,negated_conjecture,
ssItem(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
cnf(clause143,axiom,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(X1,X2) != X3
| rearsegP(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause143) ).
cnf(clause161,axiom,
( ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ memberP(cons(X1,X2),X3)
| X3 = X1
| memberP(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause161) ).
cnf(co1_11,negated_conjecture,
ssItem(sk8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
cnf(clause71,axiom,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause71) ).
cnf(clause175,axiom,
( ~ ssList(X4)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| app(X1,cons(X2,X3)) != X4
| memberP(X4,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause175) ).
cnf(co1_21,negated_conjecture,
( nil = sk3
| cons(sk9,nil) = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_21) ).
cnf(co1_6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
cnf(clause119,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause119) ).
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(clause75,axiom,
( ~ ssList(X1)
| nil = X1
| ssList(tl(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause75) ).
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(co1_1,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).
cnf(clause96,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| tl(cons(X1,X2)) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause96) ).
cnf(co1_17,negated_conjecture,
( nil = sk3
| ssItem(sk9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_17) ).
cnf(clause118,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause118) ).
cnf(clause131,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| app(skaf46(X1,X2),X2) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause131) ).
cnf(clause138,axiom,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| X1 != X2
| memberP(cons(X2,X3),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause138) ).
cnf(clause51,axiom,
ssList(skaf45(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause51) ).
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(clause73,axiom,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause73) ).
cnf(clause50,axiom,
ssList(skaf46(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause50) ).
cnf(co1_12,negated_conjecture,
( memberP(sk7,sk8)
| memberP(sk6,sk8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
cnf(c_0_38,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_39,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_38 ).
cnf(c_0_40,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_simplification,[status(thm)],[clause74]) ).
cnf(c_0_41,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
inference(fof_simplification,[status(thm)],[clause86]) ).
cnf(c_0_42,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_39]) ).
cnf(c_0_43,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
c_0_40 ).
cnf(c_0_44,axiom,
ssList(nil),
clause8 ).
cnf(c_0_45,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
c_0_41 ).
cnf(c_0_46,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(skaf44(X1),nil) = X1 ),
inference(fof_simplification,[status(thm)],[clause101]) ).
cnf(c_0_47,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_42,c_0_43]),c_0_44])]),c_0_45]) ).
cnf(c_0_48,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(skaf44(X1),nil) = X1 ),
c_0_46 ).
cnf(c_0_49,axiom,
ssItem(skaf44(X1)),
clause47 ).
cnf(c_0_50,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,nil) != X2
| singletonP(X2) ),
inference(fof_simplification,[status(thm)],[clause116]) ).
cnf(c_0_51,plain,
( ~ duplicatefreeP(app(cons(skaf44(X1),X2),X1))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(app(cons(skaf44(X1),X2),X1))
| ~ singletonP(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]),c_0_44])]) ).
cnf(c_0_52,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,nil),X2) = cons(X1,X2) ),
inference(fof_simplification,[status(thm)],[clause120]) ).
cnf(c_0_53,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,nil) != X2
| singletonP(X2) ),
c_0_50 ).
cnf(c_0_54,plain,
( ~ ssList(X1)
| ssItem(X2)
| duplicatefreeP(X1) ),
inference(fof_simplification,[status(thm)],[clause72]) ).
cnf(c_0_55,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_56,plain,
( ~ duplicatefreeP(app(X1,X1))
| ~ ssList(X1)
| ~ ssList(app(X1,X1))
| ~ singletonP(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_48]),c_0_44])]) ).
cnf(c_0_57,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,nil),X2) = cons(X1,X2) ),
c_0_52 ).
cnf(c_0_58,plain,
( ~ ssList(cons(X1,nil))
| ~ ssItem(X1)
| singletonP(cons(X1,nil)) ),
inference(er,[status(thm)],[c_0_53]) ).
cnf(c_0_59,plain,
( ~ ssList(X1)
| ssItem(X2)
| duplicatefreeP(X1) ),
c_0_54 ).
cnf(c_0_60,negated_conjecture,
app(app(sk6,cons(sk5,nil)),sk7) = sk1,
co1_10 ).
cnf(c_0_61,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X3,X2),X1) = app(X3,app(X2,X1)) ),
c_0_55 ).
cnf(c_0_62,negated_conjecture,
ssList(sk6),
co1_8 ).
cnf(c_0_63,negated_conjecture,
ssList(sk7),
co1_9 ).
cnf(c_0_64,plain,
( ~ duplicatefreeP(cons(X1,cons(X1,nil)))
| ~ ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_45]),c_0_58]) ).
cnf(c_0_65,plain,
( ~ ssList(X3)
| ~ ssItem(X2)
| duplicatefreeP(cons(X2,X3))
| ssItem(X1) ),
inference(spm,[status(thm)],[c_0_59,c_0_45]) ).
cnf(c_0_66,plain,
( ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != X3
| frontsegP(X3,X1) ),
inference(fof_simplification,[status(thm)],[clause144]) ).
cnf(c_0_67,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
inference(fof_simplification,[status(thm)],[clause85]) ).
cnf(c_0_68,negated_conjecture,
( ~ ssList(cons(sk5,nil))
| app(sk6,app(cons(sk5,nil),sk7)) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]),c_0_63])]) ).
cnf(c_0_69,negated_conjecture,
ssItem(sk5),
co1_7 ).
cnf(c_0_70,plain,
( ~ ssList(cons(X2,nil))
| ~ ssItem(X2)
| ssItem(X1) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_71,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(X1,X2) != X3
| rearsegP(X3,X2) ),
inference(fof_simplification,[status(thm)],[clause143]) ).
cnf(c_0_72,plain,
( ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != X3
| frontsegP(X3,X1) ),
c_0_66 ).
cnf(c_0_73,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
c_0_67 ).
cnf(c_0_74,negated_conjecture,
app(sk6,app(cons(sk5,nil),sk7)) = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_45]),c_0_69]),c_0_44])]) ).
cnf(c_0_75,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_76,plain,
( ~ ssItem(X2)
| ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_45]),c_0_44])]) ).
cnf(c_0_77,negated_conjecture,
ssItem(sk8),
co1_11 ).
cnf(c_0_78,plain,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[clause71]) ).
cnf(c_0_79,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_80,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(X1,X2) != X3
| rearsegP(X3,X2) ),
c_0_71 ).
cnf(c_0_81,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| frontsegP(app(X1,X2),X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_72]),c_0_73]) ).
cnf(c_0_82,negated_conjecture,
app(sk6,cons(sk5,sk7)) = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_57]),c_0_69]),c_0_63])]) ).
cnf(c_0_83,plain,
( ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ memberP(cons(X1,X2),X3)
| X3 = X1
| memberP(X2,X3) ),
c_0_75 ).
cnf(c_0_84,negated_conjecture,
ssItem(X1),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_85,negated_conjecture,
( nil = sk3
| cons(sk9,nil) = sk3 ),
co1_21 ).
cnf(c_0_86,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_87,plain,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
c_0_78 ).
cnf(c_0_88,plain,
( ~ ssList(X4)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| app(X1,cons(X2,X3)) != X4
| memberP(X4,X2) ),
c_0_79 ).
cnf(c_0_89,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| rearsegP(app(X1,X2),X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_80]),c_0_73]) ).
cnf(c_0_90,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X2 ),
inference(fof_simplification,[status(thm)],[clause119]) ).
cnf(c_0_91,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| tl(app(X2,X1)) = app(tl(X2),X1)
| nil = X2 ),
inference(fof_simplification,[status(thm)],[clause133]) ).
cnf(c_0_92,plain,
( ~ ssList(X1)
| nil = X1
| ssList(tl(X1)) ),
inference(fof_simplification,[status(thm)],[clause75]) ).
cnf(c_0_93,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| app(X2,skaf45(X1,X2)) = X1 ),
inference(fof_simplification,[status(thm)],[clause132]) ).
cnf(c_0_94,negated_conjecture,
( ~ ssList(cons(sk5,sk7))
| frontsegP(sk1,sk6) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_62])]) ).
cnf(c_0_95,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_83,c_0_84]),c_0_84])]) ).
cnf(c_0_96,negated_conjecture,
( nil = sk1
| cons(sk9,nil) = sk1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_85,c_0_86]),c_0_86]) ).
cnf(c_0_97,plain,
~ memberP(nil,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_87,c_0_84])]) ).
cnf(c_0_98,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_88]) ).
cnf(c_0_99,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_100,negated_conjecture,
( ~ ssList(app(sk6,cons(sk5,nil)))
| rearsegP(sk1,sk7) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_60]),c_0_63])]) ).
cnf(c_0_101,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X2 ),
c_0_90 ).
cnf(c_0_102,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| tl(app(X2,X1)) = app(tl(X2),X1)
| nil = X2 ),
c_0_91 ).
cnf(c_0_103,plain,
( ~ ssList(X1)
| nil = X1
| ssList(tl(X1)) ),
c_0_92 ).
cnf(c_0_104,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| tl(cons(X1,X2)) = X2 ),
inference(fof_simplification,[status(thm)],[clause96]) ).
cnf(c_0_105,negated_conjecture,
( nil = sk3
| ssItem(sk9) ),
co1_17 ).
cnf(c_0_106,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X1 ),
inference(fof_simplification,[status(thm)],[clause118]) ).
cnf(c_0_107,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| app(X2,skaf45(X1,X2)) = X1 ),
c_0_93 ).
cnf(c_0_108,negated_conjecture,
frontsegP(sk1,sk6),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_45]),c_0_69]),c_0_63])]) ).
cnf(c_0_109,negated_conjecture,
( ~ memberP(sk1,X1)
| sk9 = X1
| nil = sk1 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_44])]),c_0_97]) ).
cnf(c_0_110,negated_conjecture,
memberP(sk1,sk5),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_82]),c_0_69]),c_0_99]),c_0_63]),c_0_62])]) ).
cnf(c_0_111,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| app(skaf46(X1,X2),X2) = X1 ),
inference(fof_simplification,[status(thm)],[clause131]) ).
cnf(c_0_112,negated_conjecture,
( ~ ssList(cons(sk5,nil))
| rearsegP(sk1,sk7) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_73]),c_0_62])]) ).
cnf(c_0_113,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| X1 != X2
| memberP(cons(X2,X3),X1) ),
inference(fof_simplification,[status(thm)],[clause138]) ).
cnf(c_0_114,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| tl(app(X1,X2)) != nil
| nil = X2
| nil = X1 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_103]) ).
cnf(c_0_115,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| tl(cons(X1,X2)) = X2 ),
c_0_104 ).
cnf(c_0_116,negated_conjecture,
( ssItem(sk9)
| nil = sk1 ),
inference(rw,[status(thm)],[c_0_105,c_0_86]) ).
cnf(c_0_117,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X1 ),
c_0_106 ).
cnf(c_0_118,negated_conjecture,
app(sk6,skaf45(sk1,sk6)) = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_62]),c_0_99])]) ).
cnf(c_0_119,axiom,
ssList(skaf45(X1,X2)),
clause51 ).
cnf(c_0_120,plain,
( ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != app(X1,X3)
| X2 = X3 ),
inference(fof_simplification,[status(thm)],[clause150]) ).
cnf(c_0_121,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(fof_simplification,[status(thm)],[clause73]) ).
cnf(c_0_122,negated_conjecture,
( nil = sk1
| sk9 = sk5 ),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_123,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| app(skaf46(X1,X2),X2) = X1 ),
c_0_111 ).
cnf(c_0_124,negated_conjecture,
rearsegP(sk1,sk7),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_45]),c_0_69]),c_0_44])]) ).
cnf(c_0_125,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| X1 != X2
| memberP(cons(X2,X3),X1) ),
c_0_113 ).
cnf(c_0_126,negated_conjecture,
( ~ ssList(cons(sk5,sk7))
| tl(sk1) != nil
| sk6 = nil
| cons(sk5,sk7) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_82]),c_0_62])]) ).
cnf(c_0_127,negated_conjecture,
( nil = sk1
| tl(sk1) = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_96]),c_0_44])]),c_0_116]) ).
cnf(c_0_128,negated_conjecture,
( nil != sk1
| sk6 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_119]),c_0_62])]) ).
cnf(c_0_129,plain,
( ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != app(X1,X3)
| X2 = X3 ),
c_0_120 ).
cnf(c_0_130,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
c_0_121 ).
cnf(c_0_131,negated_conjecture,
( nil = sk1
| cons(sk5,nil) = sk1 ),
inference(spm,[status(thm)],[c_0_96,c_0_122]) ).
cnf(c_0_132,negated_conjecture,
app(skaf46(sk1,sk7),sk7) = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_63]),c_0_99])]) ).
cnf(c_0_133,axiom,
ssList(skaf46(X1,X2)),
clause50 ).
cnf(c_0_134,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| memberP(cons(X1,X2),X1) ),
inference(er,[status(thm)],[c_0_125]) ).
cnf(c_0_135,negated_conjecture,
( ~ ssList(cons(sk5,sk7))
| sk6 = nil
| cons(sk5,sk7) = nil ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_128]) ).
cnf(c_0_136,plain,
( ~ ssList(X2)
| ssList(cons(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_84])]) ).
cnf(c_0_137,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| app(X2,X1) != X2
| X1 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_44])]) ).
cnf(c_0_138,negated_conjecture,
( nil = sk1
| app(app(sk6,sk1),sk7) = sk1 ),
inference(spm,[status(thm)],[c_0_60,c_0_131]) ).
cnf(c_0_139,negated_conjecture,
( nil != sk1
| sk7 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_132]),c_0_63]),c_0_133])]) ).
cnf(c_0_140,plain,
( ~ ssList(X2)
| memberP(cons(X1,X2),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_134,c_0_84])]) ).
cnf(c_0_141,negated_conjecture,
( sk6 = nil
| cons(sk5,sk7) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_63])]) ).
cnf(c_0_142,negated_conjecture,
( ~ ssList(app(sk6,sk1))
| app(sk6,sk1) != sk1
| sk7 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_63])]),c_0_139]) ).
cnf(c_0_143,negated_conjecture,
sk6 = nil,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_63])]),c_0_97]) ).
cnf(c_0_144,negated_conjecture,
( memberP(sk7,sk8)
| memberP(sk6,sk8) ),
co1_12 ).
cnf(c_0_145,negated_conjecture,
( ~ ssList(app(nil,sk1))
| app(nil,sk1) != sk1
| sk7 = nil ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_142,c_0_143]),c_0_143]) ).
cnf(c_0_146,negated_conjecture,
memberP(sk7,sk8),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_144,c_0_143]),c_0_97]) ).
cnf(c_0_147,negated_conjecture,
sk7 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_43]),c_0_99])]) ).
cnf(c_0_148,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_146,c_0_147]),c_0_97]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC295-1 : 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 : n017.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 08:08:27 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.45 Running first-order theorem proving
% 0.15/0.45 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
% 1.04/0.69 % Version: 3.5.1
% 1.04/0.69 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.04/0.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.04/0.69 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.04/0.69 % Starting new_bool_3 with 300s (1) cores
% 1.04/0.69 % Starting new_bool_1 with 300s (1) cores
% 1.04/0.69 % Starting sh5l with 300s (1) cores
% 1.04/0.69 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 1861480 completed with status 0
% 1.04/0.69 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 1.04/0.69 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.04/0.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.04/0.69 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.04/0.69 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.04/0.69 % No SInE strategy applied
% 1.04/0.69 % Search class: FGHSM-FSLM21-MFFFFFNN
% 1.04/0.69 % Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 1.04/0.69 % Starting SubtermCWHack with 136s (1) cores
% 1.04/0.69 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 1.04/0.69 % Starting G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y with 136s (1) cores
% 1.04/0.69 % Starting G-E--_200_B02_F1_SE_CS_SP_PI_S2k with 136s (1) cores
% 1.04/0.69 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 1.04/0.69 % G-E--_200_B02_F1_SE_CS_SP_PI_S2k with pid 1861489 completed with status 0
% 1.04/0.69 % Result found by G-E--_200_B02_F1_SE_CS_SP_PI_S2k
% 1.04/0.69 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.04/0.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.04/0.69 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.04/0.69 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.04/0.69 % No SInE strategy applied
% 1.04/0.69 % Search class: FGHSM-FSLM21-MFFFFFNN
% 1.04/0.69 % Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 1.04/0.69 % Starting SubtermCWHack with 136s (1) cores
% 1.04/0.69 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 1.04/0.69 % Starting G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y with 136s (1) cores
% 1.04/0.69 % Starting G-E--_200_B02_F1_SE_CS_SP_PI_S2k with 136s (1) cores
% 1.04/0.69 % Preprocessing time : 0.005 s
% 1.04/0.69
% 1.04/0.69 % Proof found!
% 1.04/0.69 % SZS status Unsatisfiable
% 1.04/0.69 % SZS output start CNFRefutation
% See solution above
% 1.04/0.69 % Parsed axioms : 208
% 1.04/0.69 % Removed by relevancy pruning/SinE : 0
% 1.04/0.69 % Initial clauses : 208
% 1.04/0.69 % Removed in clause preprocessing : 0
% 1.04/0.69 % Initial clauses in saturation : 208
% 1.04/0.69 % Processed clauses : 1410
% 1.04/0.69 % ...of these trivial : 7
% 1.04/0.69 % ...subsumed : 599
% 1.04/0.69 % ...remaining for further processing : 804
% 1.04/0.69 % Other redundant clauses eliminated : 90
% 1.04/0.69 % Clauses deleted for lack of memory : 0
% 1.04/0.69 % Backward-subsumed : 72
% 1.04/0.69 % Backward-rewritten : 265
% 1.04/0.69 % Generated clauses : 4819
% 1.04/0.69 % ...of the previous two non-redundant : 4556
% 1.04/0.69 % ...aggressively subsumed : 0
% 1.04/0.69 % Contextual simplify-reflections : 105
% 1.04/0.69 % Paramodulations : 4723
% 1.04/0.69 % Factorizations : 0
% 1.04/0.69 % NegExts : 0
% 1.04/0.69 % Equation resolutions : 97
% 1.04/0.69 % Disequality decompositions : 0
% 1.04/0.69 % Total rewrite steps : 4023
% 1.04/0.69 % ...of those cached : 3820
% 1.04/0.69 % Propositional unsat checks : 0
% 1.04/0.69 % Propositional check models : 0
% 1.04/0.69 % Propositional check unsatisfiable : 0
% 1.04/0.69 % Propositional clauses : 0
% 1.04/0.69 % Propositional clauses after purity: 0
% 1.04/0.69 % Propositional unsat core size : 0
% 1.04/0.69 % Propositional preprocessing time : 0.000
% 1.04/0.69 % Propositional encoding time : 0.000
% 1.04/0.69 % Propositional solver time : 0.000
% 1.04/0.69 % Success case prop preproc time : 0.000
% 1.04/0.69 % Success case prop encoding time : 0.000
% 1.04/0.69 % Success case prop solver time : 0.000
% 1.04/0.69 % Current number of processed clauses : 444
% 1.04/0.69 % Positive orientable unit clauses : 74
% 1.04/0.69 % Positive unorientable unit clauses: 0
% 1.04/0.69 % Negative unit clauses : 6
% 1.04/0.69 % Non-unit-clauses : 364
% 1.04/0.69 % Current number of unprocessed clauses: 3130
% 1.04/0.69 % ...number of literals in the above : 15929
% 1.04/0.69 % Current number of archived formulas : 0
% 1.04/0.69 % Current number of archived clauses : 337
% 1.04/0.69 % Clause-clause subsumption calls (NU) : 40362
% 1.04/0.69 % Rec. Clause-clause subsumption calls : 16446
% 1.04/0.69 % Non-unit clause-clause subsumptions : 724
% 1.04/0.69 % Unit Clause-clause subsumption calls : 538
% 1.04/0.69 % Rewrite failures with RHS unbound : 0
% 1.04/0.69 % BW rewrite match attempts : 55
% 1.04/0.69 % BW rewrite match successes : 50
% 1.04/0.69 % Condensation attempts : 0
% 1.04/0.69 % Condensation successes : 0
% 1.04/0.69 % Termbank termtop insertions : 89928
% 1.04/0.69 % Search garbage collected termcells : 544
% 1.04/0.69
% 1.04/0.69 % -------------------------------------------------
% 1.04/0.69 % User time : 0.149 s
% 1.04/0.69 % System time : 0.010 s
% 1.04/0.69 % Total time : 0.159 s
% 1.04/0.69 % Maximum resident set size: 3816 pages
% 1.04/0.69
% 1.04/0.69 % -------------------------------------------------
% 1.04/0.69 % User time : 0.670 s
% 1.04/0.69 % System time : 0.055 s
% 1.04/0.69 % Total time : 0.725 s
% 1.04/0.69 % Maximum resident set size: 5120 pages
% 1.04/0.69 % E exiting
%------------------------------------------------------------------------------