%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC250-1 : 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 : 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 02:43:39 PM UTC 2026
% Result : Unsatisfiable 4.75s 6.47s
% Output : CNFRefutation 4.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 26
% Syntax : Number of clauses : 107 ( 28 unt; 19 nHn; 107 RR)
% Number of literals : 301 ( 105 equ; 190 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 149 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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(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(clause85,axiom,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause85) ).
cnf(clause86,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).
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(clause99,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause99) ).
cnf(clause8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
cnf(clause73,axiom,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause73) ).
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(co1_14,negated_conjecture,
app(sk3,sk6) = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
cnf(co1_6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
cnf(co1_7,negated_conjecture,
nil != sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
cnf(clause118,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause118) ).
cnf(clause104,axiom,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause104) ).
cnf(co1_1,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
cnf(co1_13,negated_conjecture,
ssList(sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
cnf(clause76,axiom,
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause76) ).
cnf(co1_4,negated_conjecture,
ssList(sk4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_4) ).
cnf(clause75,axiom,
( ~ ssList(X1)
| nil = X1
| ssList(tl(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause75) ).
cnf(clause133,axiom,
( ~ ssList(X2)
| ~ ssList(X1)
| tl(app(X2,X1)) = app(tl(X2),X1)
| nil = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause133) ).
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(clause74,axiom,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause74) ).
cnf(clause103,axiom,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ lt(X1,X2)
| leq(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause103) ).
cnf(co1_11,negated_conjecture,
( app(app(X2,cons(X1,nil)),X3) != sk1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| lt(X1,sk5(X3,X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
cnf(co1_8,negated_conjecture,
( app(app(X2,cons(X1,nil)),X3) != sk1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ssItem(sk5(X3,X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
cnf(co1_12,negated_conjecture,
( ~ leq(X1,sk5(X3,X2,X1))
| app(app(X2,cons(X1,nil)),X3) != sk1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
cnf(c_0_26,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,nil),X2) = cons(X1,X2) ),
inference(fof_simplification,[status(thm)],[clause120]) ).
cnf(c_0_27,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_28,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
inference(fof_simplification,[status(thm)],[clause85]) ).
cnf(c_0_29,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
inference(fof_simplification,[status(thm)],[clause86]) ).
cnf(c_0_30,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| nil != X2
| nil != X1
| app(X1,X2) = nil ),
inference(fof_simplification,[status(thm)],[clause145]) ).
cnf(c_0_31,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != X2 ),
inference(fof_simplification,[status(thm)],[clause99]) ).
cnf(c_0_32,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,nil),X2) = cons(X1,X2) ),
c_0_26 ).
cnf(c_0_33,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,app(X2,X3)) = app(cons(X1,X2),X3) ),
c_0_27 ).
cnf(c_0_34,axiom,
ssList(nil),
clause8 ).
cnf(c_0_35,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
c_0_28 ).
cnf(c_0_36,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
c_0_29 ).
cnf(c_0_37,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| nil != X2
| nil != X1
| app(X1,X2) = nil ),
c_0_30 ).
cnf(c_0_38,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != X2 ),
c_0_31 ).
cnf(c_0_39,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,app(nil,X2)) = cons(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]) ).
cnf(c_0_40,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(fof_simplification,[status(thm)],[clause73]) ).
cnf(c_0_41,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| hd(app(X2,X1)) = hd(X2)
| nil = X2 ),
inference(fof_simplification,[status(thm)],[clause123]) ).
cnf(c_0_42,negated_conjecture,
app(sk3,sk6) = sk4,
co1_14 ).
cnf(c_0_43,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_44,negated_conjecture,
nil != sk1,
inference(fof_simplification,[status(thm)],[co1_7]) ).
cnf(c_0_45,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X1 ),
inference(fof_simplification,[status(thm)],[clause118]) ).
cnf(c_0_46,plain,
( ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1)
| ssList(cons(X1,app(X2,X3))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_33]),c_0_36]) ).
cnf(c_0_47,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_37])]),c_0_34])]) ).
cnf(c_0_48,plain,
( ~ ssList(X2)
| ~ ssList(app(nil,X2))
| ~ ssItem(X1)
| cons(X1,X2) != app(nil,X2) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_49,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
c_0_40 ).
cnf(c_0_50,plain,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
inference(fof_simplification,[status(thm)],[clause104]) ).
cnf(c_0_51,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| hd(app(X2,X1)) = hd(X2)
| nil = X2 ),
c_0_41 ).
cnf(c_0_52,negated_conjecture,
app(sk1,sk6) = sk4,
inference(rw,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_53,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_54,negated_conjecture,
ssList(sk6),
co1_13 ).
cnf(c_0_55,negated_conjecture,
nil != sk1,
c_0_44 ).
cnf(c_0_56,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X1 ),
c_0_45 ).
cnf(c_0_57,plain,
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
inference(fof_simplification,[status(thm)],[clause76]) ).
cnf(c_0_58,plain,
( ~ ssItem(X1)
| ssList(cons(X1,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_34])]) ).
cnf(c_0_59,plain,
( ~ ssItem(X1)
| cons(X1,nil) != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_34])]) ).
cnf(c_0_60,plain,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
c_0_50 ).
cnf(c_0_61,negated_conjecture,
hd(sk4) = hd(sk1),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]),c_0_54])]),c_0_55]) ).
cnf(c_0_62,negated_conjecture,
ssList(sk4),
co1_4 ).
cnf(c_0_63,negated_conjecture,
sk4 != nil,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_52]),c_0_54]),c_0_53])]),c_0_55]) ).
cnf(c_0_64,plain,
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
c_0_57 ).
cnf(c_0_65,plain,
( ~ ssList(X1)
| nil = X1
| ssList(tl(X1)) ),
inference(fof_simplification,[status(thm)],[clause75]) ).
cnf(c_0_66,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| tl(app(X2,X1)) = app(tl(X2),X1)
| nil = X2 ),
inference(fof_simplification,[status(thm)],[clause133]) ).
cnf(c_0_67,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| hd(cons(X1,X2)) = hd(cons(X1,nil)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_32]),c_0_58]),c_0_59]) ).
cnf(c_0_68,negated_conjecture,
cons(hd(sk1),tl(sk4)) = sk4,
inference(sr,[status(thm)],[inference(cn,[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(hd(sk1)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_61]),c_0_62])]),c_0_63]) ).
cnf(c_0_70,plain,
( ~ ssList(X1)
| nil = X1
| ssList(tl(X1)) ),
c_0_65 ).
cnf(c_0_71,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| tl(app(X2,X1)) = app(tl(X2),X1)
| nil = X2 ),
c_0_66 ).
cnf(c_0_72,negated_conjecture,
( ~ ssList(tl(sk4))
| hd(cons(hd(sk1),nil)) = hd(sk1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_61]),c_0_69])]) ).
cnf(c_0_73,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_70,c_0_71]),c_0_35]),c_0_56]) ).
cnf(c_0_74,negated_conjecture,
app(tl(sk1),sk6) = tl(sk4),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_52]),c_0_53]),c_0_54])]),c_0_55]) ).
cnf(c_0_75,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(tl(sk4))
| hd(cons(hd(sk1),X1)) = hd(sk1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_72]),c_0_69])]) ).
cnf(c_0_76,negated_conjecture,
ssList(tl(sk4)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_53]),c_0_54])]),c_0_55]) ).
cnf(c_0_77,negated_conjecture,
( ~ ssList(X1)
| hd(cons(hd(sk1),X1)) = hd(sk1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_75,c_0_76])]) ).
cnf(c_0_78,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(app(X1,X2))) = app(X1,X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_51]),c_0_35]),c_0_56]) ).
cnf(c_0_79,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(tl(app(sk1,X1)))
| hd(app(sk1,X1)) = hd(sk1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_53])]),c_0_55]) ).
cnf(c_0_80,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_81,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_simplification,[status(thm)],[clause74]) ).
cnf(c_0_82,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(app(tl(sk1),X1))
| hd(app(sk1,X1)) = hd(sk1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_71]),c_0_53])]),c_0_55]) ).
cnf(c_0_83,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ lt(X1,X2)
| leq(X1,X2) ),
inference(fof_simplification,[status(thm)],[clause103]) ).
cnf(c_0_84,negated_conjecture,
( app(app(X2,cons(X1,nil)),X3) != sk1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| lt(X1,sk5(X3,X2,X1)) ),
inference(fof_simplification,[status(thm)],[co1_11]) ).
cnf(c_0_85,negated_conjecture,
( app(app(X2,cons(X1,nil)),X3) != sk1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ssItem(sk5(X3,X2,X1)) ),
inference(fof_simplification,[status(thm)],[co1_8]) ).
cnf(c_0_86,negated_conjecture,
( ~ leq(X1,sk5(X3,X2,X1))
| app(app(X2,cons(X1,nil)),X3) != sk1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(fof_simplification,[status(thm)],[co1_12]) ).
cnf(c_0_87,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X3,X2),X1) = app(X3,app(X2,X1)) ),
c_0_80 ).
cnf(c_0_88,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
c_0_81 ).
cnf(c_0_89,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| nil = X1
| cons(hd(app(X1,X2)),app(tl(X1),X2)) = app(X1,X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_71]),c_0_35]),c_0_56]) ).
cnf(c_0_90,negated_conjecture,
( ~ ssList(X1)
| hd(app(sk1,X1)) = hd(sk1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_73]),c_0_53])]),c_0_55]) ).
cnf(c_0_91,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ lt(X1,X2)
| leq(X1,X2) ),
c_0_83 ).
cnf(c_0_92,negated_conjecture,
( app(app(X2,cons(X1,nil)),X3) != sk1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| lt(X1,sk5(X3,X2,X1)) ),
c_0_84 ).
cnf(c_0_93,negated_conjecture,
( app(app(X2,cons(X1,nil)),X3) != sk1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ssItem(sk5(X3,X2,X1)) ),
c_0_85 ).
cnf(c_0_94,negated_conjecture,
( ~ leq(X1,sk5(X3,X2,X1))
| app(app(X2,cons(X1,nil)),X3) != sk1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1) ),
c_0_86 ).
cnf(c_0_95,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_87,c_0_88]),c_0_34])]) ).
cnf(c_0_96,plain,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),app(tl(X1),nil)) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_49]),c_0_34])]) ).
cnf(c_0_97,negated_conjecture,
( ~ ssList(X1)
| cons(hd(sk1),app(tl(sk1),X1)) = app(sk1,X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_53])]),c_0_55]) ).
cnf(c_0_98,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(X3)
| ~ ssItem(X2)
| app(app(X1,cons(X2,nil)),X3) != sk1 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_93]),c_0_94]) ).
cnf(c_0_99,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(nil,cons(X1,X2)) = cons(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_32]),c_0_58]) ).
cnf(c_0_100,negated_conjecture,
app(sk1,nil) = sk1,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_53]),c_0_34])]),c_0_55]) ).
cnf(c_0_101,negated_conjecture,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,nil),X2) != sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_34])]) ).
cnf(c_0_102,negated_conjecture,
app(tl(sk1),nil) = tl(sk1),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_100]),c_0_53]),c_0_34])]),c_0_55]) ).
cnf(c_0_103,negated_conjecture,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != sk1 ),
inference(spm,[status(thm)],[c_0_101,c_0_32]) ).
cnf(c_0_104,negated_conjecture,
cons(hd(sk1),tl(sk1)) = sk1,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_100]),c_0_53]),c_0_34])]),c_0_55]) ).
cnf(c_0_105,negated_conjecture,
ssList(tl(sk1)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_102]),c_0_53]),c_0_34])]),c_0_55]) ).
cnf(c_0_106,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_69]),c_0_105])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC250-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/5.60 % Computer : n017.cluster.edu
% 0.16/5.60 % Model : x86_64 x86_64
% 0.16/5.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.60 % Memory : 8046.5625MB
% 0.16/5.60 % OS : Linux 6.8.0-71-generic
% 0.16/5.60 % CPULimit : 300
% 0.16/5.60 % WCLimit : 300
% 0.16/5.60 % DateTime : Mon Sep 21 08:03:47 UTC 2026
% 0.16/5.60 % CPUTime :
% 0.16/5.60 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/5.66 Running first-order theorem proving
% 0.16/5.66 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
% 4.75/6.47 % Version: 3.5.1
% 4.75/6.47 % Preprocessing class: FSLSSMSMSSSNFFN.
% 4.75/6.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.75/6.47 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 4.75/6.47 % Starting new_bool_3 with 300s (1) cores
% 4.75/6.47 % Starting new_bool_1 with 300s (1) cores
% 4.75/6.47 % Starting sh5l with 300s (1) cores
% 4.75/6.47 % sh5l with pid 1852845 completed with status 0
% 4.75/6.47 % Result found by sh5l
% 4.75/6.47 % Preprocessing class: FSLSSMSMSSSNFFN.
% 4.75/6.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.75/6.47 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 4.75/6.47 % Starting new_bool_3 with 300s (1) cores
% 4.75/6.47 % Starting new_bool_1 with 300s (1) cores
% 4.75/6.47 % Starting sh5l with 300s (1) cores
% 4.75/6.47 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 4.75/6.47 % SinE strategy is gf500_gu_R04_F100_L20000
% 4.75/6.47 % Search class: FGHSM-FSLM31-MFFFFFNN
% 4.75/6.47 % Scheduled 8 strats onto 1 cores with 300 seconds (300 total)
% 4.75/6.47 % Starting SubtermCWHack with 28s (1) cores
% 4.75/6.47 % SubtermCWHack with pid 1852853 completed with status 0
% 4.75/6.47 % Result found by SubtermCWHack
% 4.75/6.47 % Preprocessing class: FSLSSMSMSSSNFFN.
% 4.75/6.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.75/6.47 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 4.75/6.47 % Starting new_bool_3 with 300s (1) cores
% 4.75/6.47 % Starting new_bool_1 with 300s (1) cores
% 4.75/6.47 % Starting sh5l with 300s (1) cores
% 4.75/6.47 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 4.75/6.47 % SinE strategy is gf500_gu_R04_F100_L20000
% 4.75/6.47 % Search class: FGHSM-FSLM31-MFFFFFNN
% 4.75/6.47 % Scheduled 8 strats onto 1 cores with 300 seconds (300 total)
% 4.75/6.47 % Starting SubtermCWHack with 28s (1) cores
% 4.75/6.47 % Preprocessing time : 0.004 s
% 4.75/6.47
% 4.75/6.47 % Proof found!
% 4.75/6.47 % SZS status Unsatisfiable
% 4.75/6.47 % SZS output start CNFRefutation
% See solution above
% 4.75/6.47 % Parsed axioms : 202
% 4.75/6.47 % Removed by relevancy pruning/SinE : 58
% 4.75/6.47 % Initial clauses : 144
% 4.75/6.47 % Removed in clause preprocessing : 0
% 4.75/6.47 % Initial clauses in saturation : 144
% 4.75/6.47 % Processed clauses : 5844
% 4.75/6.47 % ...of these trivial : 368
% 4.75/6.47 % ...subsumed : 3596
% 4.75/6.47 % ...remaining for further processing : 1880
% 4.75/6.47 % Other redundant clauses eliminated : 115
% 4.75/6.47 % Clauses deleted for lack of memory : 0
% 4.75/6.47 % Backward-subsumed : 103
% 4.75/6.47 % Backward-rewritten : 85
% 4.75/6.47 % Generated clauses : 37654
% 4.75/6.47 % ...of the previous two non-redundant : 31948
% 4.75/6.47 % ...aggressively subsumed : 0
% 4.75/6.47 % Contextual simplify-reflections : 265
% 4.75/6.47 % Paramodulations : 37528
% 4.75/6.47 % Factorizations : 0
% 4.75/6.47 % NegExts : 0
% 4.75/6.47 % Equation resolutions : 127
% 4.75/6.47 % Disequality decompositions : 0
% 4.75/6.47 % Total rewrite steps : 40758
% 4.75/6.47 % ...of those cached : 40453
% 4.75/6.47 % Propositional unsat checks : 0
% 4.75/6.47 % Propositional check models : 0
% 4.75/6.47 % Propositional check unsatisfiable : 0
% 4.75/6.47 % Propositional clauses : 0
% 4.75/6.47 % Propositional clauses after purity: 0
% 4.75/6.47 % Propositional unsat core size : 0
% 4.75/6.47 % Propositional preprocessing time : 0.000
% 4.75/6.47 % Propositional encoding time : 0.000
% 4.75/6.47 % Propositional solver time : 0.000
% 4.75/6.47 % Success case prop preproc time : 0.000
% 4.75/6.47 % Success case prop encoding time : 0.000
% 4.75/6.47 % Success case prop solver time : 0.000
% 4.75/6.47 % Current number of processed clauses : 1678
% 4.75/6.47 % Positive orientable unit clauses : 285
% 4.75/6.47 % Positive unorientable unit clauses: 0
% 4.75/6.47 % Negative unit clauses : 71
% 4.75/6.47 % Non-unit-clauses : 1322
% 4.75/6.47 % Current number of unprocessed clauses: 25945
% 4.75/6.47 % ...number of literals in the above : 132747
% 4.75/6.47 % Current number of archived formulas : 0
% 4.75/6.47 % Current number of archived clauses : 188
% 4.75/6.47 % Clause-clause subsumption calls (NU) : 286817
% 4.75/6.47 % Rec. Clause-clause subsumption calls : 93066
% 4.75/6.47 % Non-unit clause-clause subsumptions : 3101
% 4.75/6.47 % Unit Clause-clause subsumption calls : 22340
% 4.75/6.47 % Rewrite failures with RHS unbound : 0
% 4.75/6.47 % BW rewrite match attempts : 417
% 4.75/6.47 % BW rewrite match successes : 37
% 4.75/6.47 % Condensation attempts : 0
% 4.75/6.47 % Condensation successes : 0
% 4.75/6.47 % Termbank termtop insertions : 766097
% 4.75/6.47 % Search garbage collected termcells : 696
% 4.75/6.47
% 4.75/6.47 % -------------------------------------------------
% 4.75/6.47 % User time : 0.703 s
% 4.75/6.47 % System time : 0.019 s
% 4.75/6.47 % Total time : 0.721 s
% 4.75/6.47 % Maximum resident set size: 4072 pages
% 4.75/6.47
% 4.75/6.47 % -------------------------------------------------
% 4.75/6.47 % User time : 0.710 s
% 4.75/6.47 % System time : 0.025 s
% 4.75/6.47 % Total time : 0.735 s
% 4.75/6.47 % Maximum resident set size: 5120 pages
% 4.75/6.47 % E exiting
%------------------------------------------------------------------------------