%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC377-1 : 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 : n005.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 02:44:09 PM UTC 2026
% Result : Unsatisfiable 1.59s 0.67s
% Output : CNFRefutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 36
% Syntax : Number of formulae : 168 ( 28 unt; 0 def)
% Number of atoms : 470 ( 121 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 571 ( 269 ~; 300 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 193 ( 10 sgn 2 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(co1_13,negated_conjecture,
( ~ neq(sk4,nil)
| app(cons(sk6,nil),sk7) = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
cnf(co1_14,negated_conjecture,
( ~ neq(sk4,nil)
| app(sk7,cons(sk6,nil)) = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
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(co1_12,negated_conjecture,
( ~ neq(sk4,nil)
| ssList(sk7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
cnf(co1_11,negated_conjecture,
( ~ neq(sk4,nil)
| ssItem(sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
cnf(co1_6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
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(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(co1_10,negated_conjecture,
( nil != sk4
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
cnf(co1_8,negated_conjecture,
( memberP(sk1,sk5)
| memberP(sk2,sk5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
cnf(clause85,axiom,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause85) ).
cnf(co1_1,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).
cnf(clause72,axiom,
( ~ ssList(X1)
| ssItem(X2)
| duplicatefreeP(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause72) ).
cnf(clause71,axiom,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause71) ).
cnf(co1_7,negated_conjecture,
ssItem(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
cnf(clause97,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| hd(cons(X1,X2)) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause97) ).
cnf(clause73,axiom,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause73) ).
cnf(clause149,axiom,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X3,X2),X1) = app(X3,app(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause149) ).
cnf(clause74,axiom,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause74) ).
cnf(clause96,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| tl(cons(X1,X2)) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause96) ).
cnf(clause104,axiom,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause104) ).
cnf(clause140,axiom,
( ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ memberP(X1,X2)
| memberP(app(X1,X3),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause140) ).
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(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(clause75,axiom,
( ~ ssList(X1)
| nil = X1
| ssList(tl(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause75) ).
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(clause158,axiom,
( ~ ssItem(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ memberP(app(X1,X2),X3)
| memberP(X1,X3)
| memberP(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause158) ).
cnf(clause139,axiom,
( ~ ssItem(X2)
| ~ ssItem(X3)
| ~ ssList(X1)
| ~ memberP(X1,X2)
| memberP(cons(X3,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause139) ).
cnf(co1_9,negated_conjecture,
( ~ memberP(sk1,sk5)
| ~ memberP(sk2,sk5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
cnf(clause86,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause86) ).
cnf(clause141,axiom,
( ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ memberP(X1,X2)
| memberP(app(X3,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause141) ).
cnf(c_0_34,negated_conjecture,
( ~ neq(sk4,nil)
| app(cons(sk6,nil),sk7) = sk3 ),
inference(fof_simplification,[status(thm)],[co1_13]) ).
cnf(c_0_35,negated_conjecture,
( ~ neq(sk4,nil)
| app(sk7,cons(sk6,nil)) = sk4 ),
inference(fof_simplification,[status(thm)],[co1_14]) ).
cnf(c_0_36,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
inference(fof_simplification,[status(thm)],[clause100]) ).
cnf(c_0_37,negated_conjecture,
ssList(sk2),
co1_2 ).
cnf(c_0_38,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_39,negated_conjecture,
( ~ neq(sk4,nil)
| ssList(sk7) ),
inference(fof_simplification,[status(thm)],[co1_12]) ).
cnf(c_0_40,negated_conjecture,
( ~ neq(sk4,nil)
| ssItem(sk6) ),
inference(fof_simplification,[status(thm)],[co1_11]) ).
cnf(c_0_41,negated_conjecture,
( ~ neq(sk4,nil)
| app(cons(sk6,nil),sk7) = sk3 ),
c_0_34 ).
cnf(c_0_42,negated_conjecture,
sk1 = sk3,
co1_6 ).
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 ),
inference(fof_simplification,[status(thm)],[clause179]) ).
cnf(c_0_44,negated_conjecture,
( ~ neq(sk4,nil)
| app(sk7,cons(sk6,nil)) = sk4 ),
c_0_35 ).
cnf(c_0_45,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
c_0_36 ).
cnf(c_0_46,negated_conjecture,
ssList(sk4),
inference(rw,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_47,axiom,
ssList(nil),
clause8 ).
cnf(c_0_48,negated_conjecture,
( ~ neq(sk4,nil)
| ssList(sk7) ),
c_0_39 ).
cnf(c_0_49,negated_conjecture,
( ~ neq(sk4,nil)
| ssItem(sk6) ),
c_0_40 ).
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,negated_conjecture,
( ~ neq(sk4,nil)
| app(cons(sk6,nil),sk7) = sk1 ),
inference(rw,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_52,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_43 ).
cnf(c_0_53,negated_conjecture,
( sk4 = nil
| app(sk7,cons(sk6,nil)) = sk4 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]),c_0_47])]) ).
cnf(c_0_54,negated_conjecture,
( ssList(sk7)
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_45]),c_0_46]),c_0_47])]) ).
cnf(c_0_55,negated_conjecture,
( ssItem(sk6)
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_45]),c_0_46]),c_0_47])]) ).
cnf(c_0_56,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,nil),X2) = cons(X1,X2) ),
c_0_50 ).
cnf(c_0_57,negated_conjecture,
( sk4 = nil
| app(cons(sk6,nil),sk7) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_45]),c_0_46]),c_0_47])]) ).
cnf(c_0_58,negated_conjecture,
( ~ duplicatefreeP(X2)
| ~ ssList(X1)
| ~ ssList(X2)
| app(sk4,cons(sk6,X1)) != X2
| sk4 = nil ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_47])]),c_0_54]),c_0_55]) ).
cnf(c_0_59,negated_conjecture,
( sk4 = nil
| cons(sk6,sk7) = sk1 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_54]),c_0_55]) ).
fof(c_0_60,plain,
( ~ epred2_0
<=> ! [X1] :
( ~ ssList(X1)
| duplicatefreeP(X1) ) ),
introduced(definition) ).
cnf(c_0_61,negated_conjecture,
( nil != sk4
| nil = sk3 ),
inference(fof_simplification,[status(thm)],[co1_10]) ).
cnf(c_0_62,negated_conjecture,
( ~ duplicatefreeP(X1)
| ~ ssList(X1)
| app(sk4,sk1) != X1
| sk4 = nil ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_54]) ).
cnf(c_0_63,plain,
( ~ ssList(X1)
| duplicatefreeP(X1)
| epred2_0 ),
inference(split_equiv,[status(thm)],[c_0_60]) ).
cnf(c_0_64,negated_conjecture,
( memberP(sk1,sk5)
| memberP(sk2,sk5) ),
co1_8 ).
cnf(c_0_65,negated_conjecture,
( nil != sk4
| nil = sk3 ),
c_0_61 ).
cnf(c_0_66,negated_conjecture,
( ~ ssList(X1)
| app(sk4,sk1) != X1
| epred2_0
| sk4 = nil ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
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,
( memberP(sk1,sk5)
| memberP(sk4,sk5) ),
inference(rw,[status(thm)],[c_0_64,c_0_38]) ).
cnf(c_0_69,negated_conjecture,
( sk4 != nil
| sk1 = nil ),
inference(rw,[status(thm)],[c_0_65,c_0_42]) ).
cnf(c_0_70,negated_conjecture,
( ~ ssList(app(sk4,sk1))
| epred2_0
| sk4 = nil ),
inference(er,[status(thm)],[c_0_66]) ).
cnf(c_0_71,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
c_0_67 ).
cnf(c_0_72,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_73,plain,
( ~ ssList(X1)
| ssItem(X2)
| duplicatefreeP(X1) ),
inference(fof_simplification,[status(thm)],[clause72]) ).
cnf(c_0_74,plain,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[clause71]) ).
cnf(c_0_75,negated_conjecture,
( sk4 != nil
| memberP(nil,sk5)
| memberP(sk4,sk5) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_76,negated_conjecture,
( epred2_0
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_46]),c_0_72])]) ).
fof(c_0_77,plain,
( ~ epred1_0
<=> ! [X2] : ssItem(X2) ),
introduced(definition) ).
cnf(c_0_78,plain,
( ~ ssList(X1)
| ssItem(X2)
| duplicatefreeP(X1) ),
c_0_73 ).
cnf(c_0_79,plain,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
c_0_74 ).
cnf(c_0_80,negated_conjecture,
( memberP(nil,sk5)
| epred2_0 ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_81,negated_conjecture,
ssItem(sk5),
co1_7 ).
cnf(c_0_82,plain,
( ~ epred1_0
| ~ epred2_0 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_78,c_0_77]),c_0_60]) ).
cnf(c_0_83,negated_conjecture,
epred2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81])]) ).
cnf(c_0_84,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| hd(cons(X1,X2)) = X1 ),
inference(fof_simplification,[status(thm)],[clause97]) ).
cnf(c_0_85,plain,
( ssItem(X1)
| epred1_0 ),
inference(split_equiv,[status(thm)],[c_0_77]) ).
cnf(c_0_86,plain,
~ epred1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_82,c_0_83])]) ).
cnf(c_0_87,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(fof_simplification,[status(thm)],[clause73]) ).
cnf(c_0_88,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_89,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_simplification,[status(thm)],[clause74]) ).
cnf(c_0_90,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| hd(cons(X1,X2)) = X1 ),
c_0_84 ).
cnf(c_0_91,plain,
ssItem(X1),
inference(sr,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_92,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
c_0_87 ).
cnf(c_0_93,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X3,X2),X1) = app(X3,app(X2,X1)) ),
c_0_88 ).
cnf(c_0_94,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
c_0_89 ).
cnf(c_0_95,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| tl(cons(X1,X2)) = X2 ),
inference(fof_simplification,[status(thm)],[clause96]) ).
cnf(c_0_96,plain,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
inference(fof_simplification,[status(thm)],[clause104]) ).
cnf(c_0_97,plain,
( ~ ssList(X2)
| hd(cons(X1,X2)) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_90,c_0_91])]) ).
cnf(c_0_98,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ memberP(X1,X2)
| memberP(app(X1,X3),X2) ),
inference(fof_simplification,[status(thm)],[clause140]) ).
cnf(c_0_99,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| nil != X2
| nil != X1
| app(X1,X2) = nil ),
inference(fof_simplification,[status(thm)],[clause145]) ).
cnf(c_0_100,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| app(X1,app(X2,nil)) = app(X1,X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_47])]),c_0_71]) ).
cnf(c_0_101,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| app(nil,app(X1,X2)) = app(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_47])]) ).
cnf(c_0_102,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| tl(cons(X1,X2)) = X2 ),
c_0_95 ).
cnf(c_0_103,plain,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
c_0_96 ).
cnf(c_0_104,negated_conjecture,
( sk4 = nil
| hd(sk1) = sk6 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_59]),c_0_54]) ).
cnf(c_0_105,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| X1 != X2
| memberP(cons(X2,X3),X1) ),
inference(fof_simplification,[status(thm)],[clause138]) ).
cnf(c_0_106,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ memberP(X1,X2)
| memberP(app(X1,X3),X2) ),
c_0_98 ).
cnf(c_0_107,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| nil != X2
| nil != X1
| app(X1,X2) = nil ),
c_0_99 ).
cnf(c_0_108,plain,
( ~ ssList(X1)
| app(X1,nil) = app(nil,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_47])]) ).
cnf(c_0_109,plain,
( ~ ssList(X2)
| tl(cons(X1,X2)) = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_102,c_0_91])]) ).
cnf(c_0_110,negated_conjecture,
( sk1 = nil
| cons(sk6,tl(sk1)) = sk1 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_72])]),c_0_69]) ).
cnf(c_0_111,plain,
( ~ ssList(X1)
| nil = X1
| ssList(tl(X1)) ),
inference(fof_simplification,[status(thm)],[clause75]) ).
cnf(c_0_112,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| X1 != X2
| memberP(cons(X2,X3),X1) ),
c_0_105 ).
cnf(c_0_113,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ memberP(X1,X3)
| memberP(app(X1,X2),X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_106,c_0_91])]) ).
cnf(c_0_114,plain,
( ~ ssList(X1)
| nil != X1
| app(X1,nil) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_47])]) ).
cnf(c_0_115,plain,
~ memberP(nil,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_91])]) ).
cnf(c_0_116,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_117,negated_conjecture,
( sk4 = nil
| tl(sk1) = sk7 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_59]),c_0_54]) ).
cnf(c_0_118,negated_conjecture,
( ~ ssList(tl(sk1))
| sk1 = nil
| hd(sk1) = sk6 ),
inference(spm,[status(thm)],[c_0_97,c_0_110]) ).
cnf(c_0_119,plain,
( ~ ssList(X1)
| nil = X1
| ssList(tl(X1)) ),
c_0_111 ).
cnf(c_0_120,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| memberP(cons(X1,X2),X1) ),
inference(er,[status(thm)],[c_0_112]) ).
cnf(c_0_121,plain,
( ~ ssList(X1)
| ~ memberP(X1,X2)
| nil != X1 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_47])]),c_0_115]) ).
cnf(c_0_122,plain,
( ~ ssItem(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ memberP(app(X1,X2),X3)
| memberP(X1,X3)
| memberP(X2,X3) ),
inference(fof_simplification,[status(thm)],[clause158]) ).
cnf(c_0_123,plain,
( ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ memberP(cons(X1,X2),X3)
| X3 = X1
| memberP(X2,X3) ),
c_0_116 ).
cnf(c_0_124,negated_conjecture,
( sk1 = nil
| cons(hd(sk1),sk7) = sk1 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_117]),c_0_72])]),c_0_69]) ).
cnf(c_0_125,negated_conjecture,
( sk1 = nil
| hd(sk1) = sk6 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_72])]) ).
cnf(c_0_126,negated_conjecture,
( memberP(sk1,sk6)
| sk4 = nil ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_59]),c_0_54]),c_0_55]) ).
cnf(c_0_127,negated_conjecture,
sk4 != nil,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_75]),c_0_46])]),c_0_115]) ).
cnf(c_0_128,plain,
( ~ ssItem(X2)
| ~ ssItem(X3)
| ~ ssList(X1)
| ~ memberP(X1,X2)
| memberP(cons(X3,X1),X2) ),
inference(fof_simplification,[status(thm)],[clause139]) ).
cnf(c_0_129,plain,
( ~ ssItem(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ memberP(app(X1,X2),X3)
| memberP(X1,X3)
| memberP(X2,X3) ),
c_0_122 ).
cnf(c_0_130,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_123,c_0_91]),c_0_91])]) ).
cnf(c_0_131,negated_conjecture,
( sk1 = nil
| cons(sk6,sk7) = sk1 ),
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_132,negated_conjecture,
memberP(sk1,sk6),
inference(sr,[status(thm)],[c_0_126,c_0_127]) ).
cnf(c_0_133,plain,
( ~ ssItem(X2)
| ~ ssItem(X3)
| ~ ssList(X1)
| ~ memberP(X1,X2)
| memberP(cons(X3,X1),X2) ),
c_0_128 ).
cnf(c_0_134,plain,
( ~ ssList(X1)
| ~ ssList(X3)
| ~ memberP(app(X1,X3),X2)
| memberP(X3,X2)
| memberP(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_129,c_0_91])]) ).
cnf(c_0_135,negated_conjecture,
app(sk7,cons(sk6,nil)) = sk4,
inference(sr,[status(thm)],[c_0_53,c_0_127]) ).
cnf(c_0_136,negated_conjecture,
ssList(sk7),
inference(sr,[status(thm)],[c_0_54,c_0_127]) ).
cnf(c_0_137,negated_conjecture,
( ~ ssList(sk7)
| ~ memberP(sk1,X1)
| memberP(sk7,X1)
| sk6 = X1
| sk1 = nil ),
inference(spm,[status(thm)],[c_0_130,c_0_131]) ).
cnf(c_0_138,negated_conjecture,
sk1 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_132]),c_0_72])]) ).
cnf(c_0_139,negated_conjecture,
( ~ memberP(sk1,sk5)
| ~ memberP(sk2,sk5) ),
inference(fof_simplification,[status(thm)],[co1_9]) ).
cnf(c_0_140,plain,
( ~ ssList(X2)
| ~ memberP(X2,X3)
| memberP(cons(X1,X2),X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_133,c_0_91]),c_0_91])]) ).
cnf(c_0_141,negated_conjecture,
cons(sk6,sk7) = sk1,
inference(sr,[status(thm)],[c_0_59,c_0_127]) ).
cnf(c_0_142,negated_conjecture,
( ~ ssList(cons(sk6,nil))
| ~ memberP(sk4,X1)
| memberP(sk7,X1)
| memberP(cons(sk6,nil),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_136])]) ).
cnf(c_0_143,negated_conjecture,
( ~ ssList(cons(sk6,nil))
| ~ memberP(sk7,X1)
| memberP(sk4,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_135]),c_0_136])]) ).
cnf(c_0_144,negated_conjecture,
( ~ memberP(sk1,X1)
| memberP(sk7,X1)
| sk6 = X1 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_137,c_0_136])]),c_0_138]) ).
cnf(c_0_145,negated_conjecture,
( ~ memberP(sk1,sk5)
| ~ memberP(sk2,sk5) ),
c_0_139 ).
cnf(c_0_146,negated_conjecture,
( ~ memberP(sk7,X1)
| memberP(sk1,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_136])]) ).
cnf(c_0_147,negated_conjecture,
( ~ ssList(cons(sk6,nil))
| ~ memberP(sk4,X1)
| memberP(sk7,X1)
| sk6 = X1 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_142]),c_0_47])]),c_0_115]) ).
cnf(c_0_148,negated_conjecture,
( ~ ssList(cons(sk6,nil))
| ~ memberP(sk1,X1)
| memberP(sk4,X1)
| sk6 = X1 ),
inference(spm,[status(thm)],[c_0_143,c_0_144]) ).
cnf(c_0_149,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
inference(fof_simplification,[status(thm)],[clause86]) ).
cnf(c_0_150,plain,
( ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ memberP(X1,X2)
| memberP(app(X3,X1),X2) ),
inference(fof_simplification,[status(thm)],[clause141]) ).
cnf(c_0_151,negated_conjecture,
( ~ memberP(sk4,sk5)
| ~ memberP(sk1,sk5) ),
inference(rw,[status(thm)],[c_0_145,c_0_38]) ).
cnf(c_0_152,negated_conjecture,
( ~ ssList(cons(sk6,nil))
| ~ memberP(sk4,X1)
| memberP(sk1,X1)
| sk6 = X1 ),
inference(spm,[status(thm)],[c_0_146,c_0_147]) ).
cnf(c_0_153,negated_conjecture,
( ~ ssList(cons(sk6,nil))
| memberP(sk4,sk5)
| sk6 = sk5 ),
inference(spm,[status(thm)],[c_0_148,c_0_68]) ).
cnf(c_0_154,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
c_0_149 ).
cnf(c_0_155,plain,
( ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ memberP(X1,X2)
| memberP(app(X3,X1),X2) ),
c_0_150 ).
cnf(c_0_156,negated_conjecture,
( ~ ssList(cons(sk6,nil))
| sk6 = sk5 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_152]),c_0_153]) ).
cnf(c_0_157,plain,
( ~ ssList(X2)
| ssList(cons(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_154,c_0_91])]) ).
cnf(c_0_158,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ memberP(X2,X3)
| memberP(app(X1,X2),X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_155,c_0_91])]) ).
cnf(c_0_159,negated_conjecture,
sk6 = sk5,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_157]),c_0_47])]) ).
cnf(c_0_160,negated_conjecture,
( ~ ssList(cons(sk6,nil))
| ~ memberP(cons(sk6,nil),X1)
| memberP(sk4,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_135]),c_0_136])]) ).
cnf(c_0_161,plain,
( ~ ssList(X2)
| memberP(cons(X1,X2),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_120,c_0_91])]) ).
cnf(c_0_162,negated_conjecture,
memberP(sk1,sk5),
inference(rw,[status(thm)],[c_0_132,c_0_159]) ).
cnf(c_0_163,negated_conjecture,
( ~ ssList(cons(sk6,nil))
| memberP(sk4,sk6) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_161]),c_0_47])]) ).
cnf(c_0_164,negated_conjecture,
~ memberP(sk4,sk5),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_151,c_0_162])]) ).
cnf(c_0_165,negated_conjecture,
( ~ ssList(cons(sk5,nil))
| memberP(sk4,sk5) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_163,c_0_159]),c_0_159]) ).
cnf(c_0_166,negated_conjecture,
~ ssList(cons(sk5,nil)),
inference(spm,[status(thm)],[c_0_164,c_0_165]) ).
cnf(c_0_167,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_157]),c_0_47])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC377-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.36 % Computer : n005.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % 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 08:19:32 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.41 Running first-order theorem proving
% 0.08/0.41 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
% 1.59/0.67 % Version: 3.5.1
% 1.59/0.67 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.59/0.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.59/0.67 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.59/0.67 % Starting new_bool_3 with 300s (1) cores
% 1.59/0.67 % Starting new_bool_1 with 300s (1) cores
% 1.59/0.67 % Starting sh5l with 300s (1) cores
% 1.59/0.67 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 3001817 completed with status 0
% 1.59/0.67 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 1.59/0.67 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.59/0.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.59/0.67 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.59/0.67 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.59/0.67 % No SInE strategy applied
% 1.59/0.67 % Search class: FGHSM-FSLM21-MFFFFFNN
% 1.59/0.67 % Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 1.59/0.67 % Starting SubtermCWHack with 136s (1) cores
% 1.59/0.67 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 1.59/0.67 % Starting G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y with 136s (1) cores
% 1.59/0.67 % Starting G-E--_200_B02_F1_SE_CS_SP_PI_S2k with 136s (1) cores
% 1.59/0.67 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 1.59/0.67 % G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y with pid 3001825 completed with status 0
% 1.59/0.67 % Result found by G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y
% 1.59/0.67 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.59/0.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.59/0.67 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.59/0.67 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.59/0.67 % No SInE strategy applied
% 1.59/0.67 % Search class: FGHSM-FSLM21-MFFFFFNN
% 1.59/0.67 % Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 1.59/0.67 % Starting SubtermCWHack with 136s (1) cores
% 1.59/0.67 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 1.59/0.67 % Starting G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y with 136s (1) cores
% 1.59/0.67 % Preprocessing time : 0.002 s
% 1.59/0.67 % Presaturation interreduction done
% 1.59/0.67
% 1.59/0.67 % Proof found!
% 1.59/0.67 % SZS status Unsatisfiable
% 1.59/0.67 % SZS output start CNFRefutation
% See solution above
% 1.59/0.67 % Parsed axioms : 199
% 1.59/0.67 % Removed by relevancy pruning/SinE : 0
% 1.59/0.67 % Initial clauses : 199
% 1.59/0.67 % Removed in clause preprocessing : 0
% 1.59/0.67 % Initial clauses in saturation : 199
% 1.59/0.67 % Processed clauses : 2515
% 1.59/0.67 % ...of these trivial : 87
% 1.59/0.67 % ...subsumed : 1179
% 1.59/0.67 % ...remaining for further processing : 1249
% 1.59/0.67 % Other redundant clauses eliminated : 329
% 1.59/0.67 % Clauses deleted for lack of memory : 0
% 1.59/0.67 % Backward-subsumed : 185
% 1.59/0.67 % Backward-rewritten : 160
% 1.59/0.67 % Generated clauses : 13163
% 1.59/0.67 % ...of the previous two non-redundant : 11308
% 1.59/0.67 % ...aggressively subsumed : 0
% 1.59/0.67 % Contextual simplify-reflections : 120
% 1.59/0.67 % Paramodulations : 12754
% 1.59/0.67 % Factorizations : 0
% 1.59/0.67 % NegExts : 0
% 1.59/0.67 % Equation resolutions : 376
% 1.59/0.67 % Disequality decompositions : 0
% 1.59/0.67 % Total rewrite steps : 11269
% 1.59/0.67 % ...of those cached : 10932
% 1.59/0.67 % Propositional unsat checks : 0
% 1.59/0.67 % Propositional check models : 0
% 1.59/0.67 % Propositional check unsatisfiable : 0
% 1.59/0.67 % Propositional clauses : 0
% 1.59/0.67 % Propositional clauses after purity: 0
% 1.59/0.67 % Propositional unsat core size : 0
% 1.59/0.67 % Propositional preprocessing time : 0.000
% 1.59/0.67 % Propositional encoding time : 0.000
% 1.59/0.67 % Propositional solver time : 0.000
% 1.59/0.67 % Success case prop preproc time : 0.000
% 1.59/0.67 % Success case prop encoding time : 0.000
% 1.59/0.67 % Success case prop solver time : 0.000
% 1.59/0.67 % Current number of processed clauses : 681
% 1.59/0.67 % Positive orientable unit clauses : 85
% 1.59/0.67 % Positive unorientable unit clauses: 0
% 1.59/0.67 % Negative unit clauses : 34
% 1.59/0.67 % Non-unit-clauses : 562
% 1.59/0.67 % Current number of unprocessed clauses: 8692
% 1.59/0.67 % ...number of literals in the above : 55987
% 1.59/0.67 % Current number of archived formulas : 0
% 1.59/0.67 % Current number of archived clauses : 555
% 1.59/0.67 % Clause-clause subsumption calls (NU) : 134378
% 1.59/0.67 % Rec. Clause-clause subsumption calls : 42785
% 1.59/0.67 % Non-unit clause-clause subsumptions : 895
% 1.59/0.67 % Unit Clause-clause subsumption calls : 4999
% 1.59/0.67 % Rewrite failures with RHS unbound : 0
% 1.59/0.67 % BW rewrite match attempts : 47
% 1.59/0.67 % BW rewrite match successes : 42
% 1.59/0.67 % Condensation attempts : 0
% 1.59/0.67 % Condensation successes : 0
% 1.59/0.67 % Termbank termtop insertions : 251945
% 1.59/0.67 % Search garbage collected termcells : 539
% 1.59/0.67
% 1.59/0.67 % -------------------------------------------------
% 1.59/0.67 % User time : 0.209 s
% 1.59/0.67 % System time : 0.009 s
% 1.59/0.67 % Total time : 0.217 s
% 1.59/0.67 % Maximum resident set size: 4068 pages
% 1.59/0.67
% 1.59/0.67 % -------------------------------------------------
% 1.59/0.67 % User time : 0.942 s
% 1.59/0.67 % System time : 0.058 s
% 1.59/0.67 % Total time : 1.000 s
% 1.59/0.67 % Maximum resident set size: 5120 pages
% 1.59/0.67 % E exiting
%------------------------------------------------------------------------------