%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC284+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 : 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 02:43:46 PM UTC 2026
% Result : Theorem 0.16s 0.54s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 13
% Syntax : Number of formulae : 93 ( 23 unt; 0 def)
% Number of atoms : 382 ( 93 equ)
% Maximal formula atoms : 27 ( 4 avg)
% Number of connectives : 489 ( 200 ~; 199 |; 40 &)
% ( 6 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 10 con; 0-2 aty)
% Number of variables : 124 ( 0 sgn 78 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ( neq(X4,nil)
& ! [X9] :
( ~ memberP(X4,X9)
| cons(X9,nil) != X3
| ~ ssItem(X9) ) )
| ( nil = X4
& nil != X3 )
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ! [X8] :
( ssItem(X8)
=> ( ( leq(X5,X8)
| ~ memberP(X7,X8) )
& ( leq(X8,X5)
| ~ memberP(X6,X8) ) ) )
| app(app(X6,cons(X5,nil)),X7) != X1
| ~ ssList(X7) ) ) )
| X1 != X3
| X2 != X4
| ~ ssList(X4) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax83,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X1
& nil = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax38,axiom,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax38) ).
fof(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(ax82,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> app(app(X1,X2),X3) = app(X1,app(X2,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax82) ).
fof(ax3,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ( memberP(X1,X2)
<=> ? [X3] :
( ? [X4] :
( app(X3,cons(X2,X4)) = X1
& ssList(X4) )
& ssList(X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax3) ).
fof(ax81,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax81) ).
fof(ax37,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(cons(X2,X3),X1)
<=> ( memberP(X3,X1)
| X1 = X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax37) ).
fof(ax36,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(app(X2,X3),X1)
<=> ( memberP(X3,X1)
| memberP(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax36) ).
fof(ax31,axiom,
! [X1] :
( ssItem(X1)
=> leq(X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax31) ).
fof(c_0_13,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ( neq(X4,nil)
& ! [X9] :
( ~ memberP(X4,X9)
| cons(X9,nil) != X3
| ~ ssItem(X9) ) )
| ( nil = X4
& nil != X3 )
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ! [X8] :
( ssItem(X8)
=> ( ( leq(X5,X8)
| ~ memberP(X7,X8) )
& ( leq(X8,X5)
| ~ memberP(X6,X8) ) ) )
| app(app(X6,cons(X5,nil)),X7) != X1
| ~ ssList(X7) ) ) )
| X1 != X3
| X2 != X4
| ~ ssList(X4) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_14,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ( neq(X4,nil)
& ! [X9] :
( ~ memberP(X4,X9)
| cons(X9,nil) != X3
| ~ ssItem(X9) ) )
| ( nil = X4
& nil != X3 )
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ! [X8] :
( ssItem(X8)
=> ( ( leq(X5,X8)
| ~ memberP(X7,X8) )
& ( leq(X8,X5)
| ~ memberP(X6,X8) ) ) )
| app(app(X6,cons(X5,nil)),X7) != X1
| ~ ssList(X7) ) ) )
| X1 != X3
| X2 != X4
| ~ ssList(X4) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_15,negated_conjecture,
( ( ~ neq(esk4_0,nil)
| memberP(esk4_0,esk9_0) )
& ( ~ neq(esk4_0,nil)
| cons(esk9_0,nil) = esk3_0 )
& ( ~ neq(esk4_0,nil)
| ssItem(esk9_0) )
& ( nil != esk4_0
| nil = esk3_0 )
& ( ~ leq(esk8_0,esk5_0)
| ~ leq(esk5_0,esk8_0) )
& ( ~ leq(esk8_0,esk5_0)
| memberP(esk7_0,esk8_0) )
& ( memberP(esk6_0,esk8_0)
| ~ leq(esk5_0,esk8_0) )
& ( memberP(esk6_0,esk8_0)
| memberP(esk7_0,esk8_0) )
& ssItem(esk8_0)
& app(app(esk6_0,cons(esk5_0,nil)),esk7_0) = esk1_0
& ssList(esk7_0)
& ssList(esk6_0)
& ssItem(esk5_0)
& esk1_0 = esk3_0
& esk2_0 = esk4_0
& ssList(esk4_0)
& ssList(esk3_0)
& ssList(esk2_0)
& ssList(esk1_0) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])])]) ).
fof(c_0_16,plain,
! [X81,X82] :
( ( ~ ssList(X81)
| ~ ssList(X82)
| nil = app(X81,X82)
| nil != X81
| nil != X82 )
& ( ~ ssList(X81)
| ~ ssList(X82)
| nil != app(X81,X82)
| nil = X81 )
& ( ~ ssList(X81)
| ~ ssList(X82)
| nil != app(X81,X82)
| nil = X82 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])])]) ).
cnf(c_0_17,negated_conjecture,
app(app(esk6_0,cons(esk5_0,nil)),esk7_0) = esk1_0,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_18,negated_conjecture,
esk1_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| nil != app(X2,X1)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,negated_conjecture,
app(app(esk6_0,cons(esk5_0,nil)),esk7_0) = esk3_0,
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
ssList(esk7_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_22,plain,
! [X69,X70] :
( ssList(app(X69,X70))
| ~ ssList(X70)
| ~ ssList(X69) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).
cnf(c_0_23,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| nil != app(X1,X2)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,negated_conjecture,
( ~ ssList(app(esk6_0,cons(esk5_0,nil)))
| esk3_0 != nil
| esk7_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).
cnf(c_0_25,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,negated_conjecture,
ssList(esk6_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_27,plain,
! [X41,X42] :
( ssList(cons(X42,X41))
| ~ ssItem(X42)
| ~ ssList(X41) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).
cnf(c_0_28,negated_conjecture,
( ~ ssList(app(esk6_0,cons(esk5_0,nil)))
| esk3_0 != nil
| app(esk6_0,cons(esk5_0,nil)) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_20]),c_0_21])]) ).
cnf(c_0_29,negated_conjecture,
( ~ ssList(cons(esk5_0,nil))
| esk3_0 != nil
| esk7_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_30,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ssList(cons(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_31,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_32,negated_conjecture,
ssItem(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_33,negated_conjecture,
( ~ ssList(cons(esk5_0,nil))
| esk3_0 != nil
| app(esk6_0,cons(esk5_0,nil)) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_25]),c_0_26])]) ).
fof(c_0_34,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[ax38]) ).
cnf(c_0_35,negated_conjecture,
( memberP(esk6_0,esk8_0)
| memberP(esk7_0,esk8_0) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_36,negated_conjecture,
( esk3_0 != nil
| esk7_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_32])]) ).
cnf(c_0_37,negated_conjecture,
( ~ ssList(cons(esk5_0,nil))
| esk3_0 != nil
| esk6_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_33]),c_0_26])]) ).
fof(c_0_38,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
fof(c_0_39,plain,
! [X40] :
( ~ memberP(nil,X40)
| ~ ssItem(X40) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_34])])]) ).
cnf(c_0_40,negated_conjecture,
( esk3_0 != nil
| memberP(nil,esk8_0)
| memberP(esk6_0,esk8_0) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,negated_conjecture,
( esk3_0 != nil
| esk6_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_30]),c_0_31]),c_0_32])]) ).
fof(c_0_42,plain,
! [X78,X79,X80] :
( app(app(X78,X79),X80) = app(X78,app(X79,X80))
| ~ ssList(X80)
| ~ ssList(X79)
| ~ ssList(X78) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])])]) ).
fof(c_0_43,plain,
! [X21,X22] :
( ( ~ ssList(X21)
| ~ ssList(X22)
| neq(X21,X22)
| X21 = X22 )
& ( ~ ssList(X21)
| ~ ssList(X22)
| X21 != X22
| ~ neq(X21,X22) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])])])])]) ).
cnf(c_0_44,plain,
( ~ memberP(nil,X1)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_45,negated_conjecture,
( esk3_0 != nil
| memberP(nil,esk8_0) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_46,negated_conjecture,
ssItem(esk8_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_47,plain,
! [X28,X29,X32,X33] :
( ( ~ ssList(X28)
| ~ ssItem(X29)
| memberP(X28,X29)
| app(X32,cons(X29,X33)) != X28
| ~ ssList(X33)
| ~ ssList(X32) )
& ( ~ ssList(X28)
| ~ ssItem(X29)
| ~ memberP(X28,X29)
| app(esk12_2(X28,X29),cons(X29,esk13_2(X28,X29))) = X28 )
& ( ~ ssList(X28)
| ~ ssItem(X29)
| ~ memberP(X28,X29)
| ssList(esk13_2(X28,X29)) )
& ( ~ ssList(X28)
| ~ ssItem(X29)
| ~ memberP(X28,X29)
| ssList(esk12_2(X28,X29)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax3])])])])])]) ).
cnf(c_0_48,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X1,X2),X3) = app(X1,app(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
fof(c_0_49,plain,
! [X52,X53] :
( cons(X53,X52) = app(cons(X53,nil),X52)
| ~ ssItem(X53)
| ~ ssList(X52) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])])]) ).
cnf(c_0_50,negated_conjecture,
( ~ neq(esk4_0,nil)
| cons(esk9_0,nil) = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_51,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_52,negated_conjecture,
ssList(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_53,negated_conjecture,
esk3_0 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46])]) ).
cnf(c_0_54,negated_conjecture,
( nil != esk4_0
| nil = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_55,negated_conjecture,
( ~ neq(esk4_0,nil)
| ssItem(esk9_0) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_56,plain,
( ~ ssList(X4)
| ~ ssItem(X3)
| app(X1,cons(X3,X2)) != X4
| ~ ssList(X2)
| ~ ssList(X1)
| memberP(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_57,negated_conjecture,
( ~ ssList(cons(esk5_0,nil))
| app(esk6_0,app(cons(esk5_0,nil),esk7_0)) = esk3_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_48]),c_0_21]),c_0_26])]) ).
cnf(c_0_58,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) = app(cons(X2,nil),X1) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
fof(c_0_59,plain,
! [X37,X38,X39] :
( ( ~ ssItem(X37)
| ~ ssItem(X38)
| ~ ssList(X39)
| memberP(cons(X38,X39),X37)
| ~ memberP(X39,X37) )
& ( ~ ssItem(X37)
| ~ ssItem(X38)
| ~ ssList(X39)
| memberP(cons(X38,X39),X37)
| X37 != X38 )
& ( ~ ssItem(X37)
| ~ ssItem(X38)
| ~ ssList(X39)
| memberP(X39,X37)
| X37 = X38
| ~ memberP(cons(X38,X39),X37) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax37])])])])]) ).
cnf(c_0_60,negated_conjecture,
( esk4_0 = nil
| cons(esk9_0,nil) = esk3_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_31]),c_0_52])]) ).
cnf(c_0_61,negated_conjecture,
esk4_0 != nil,
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_62,negated_conjecture,
( ssItem(esk9_0)
| esk4_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_51]),c_0_31]),c_0_52])]) ).
cnf(c_0_63,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(app(X1,cons(X2,X3)))
| memberP(app(X1,cons(X2,X3)),X2) ),
inference(er,[status(thm)],[c_0_56]) ).
cnf(c_0_64,negated_conjecture,
( ~ ssList(cons(esk5_0,nil))
| app(esk6_0,cons(esk5_0,esk7_0)) = esk3_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_21]),c_0_32])]) ).
cnf(c_0_65,negated_conjecture,
ssList(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_66,plain,
( ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ memberP(cons(X1,X2),X3)
| memberP(X2,X3)
| X3 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_67,negated_conjecture,
cons(esk9_0,nil) = esk3_0,
inference(sr,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_68,negated_conjecture,
ssItem(esk9_0),
inference(sr,[status(thm)],[c_0_62,c_0_61]) ).
cnf(c_0_69,negated_conjecture,
( ~ ssList(cons(esk5_0,nil))
| memberP(esk3_0,esk5_0) ),
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_63,c_0_64]),c_0_65]),c_0_21]),c_0_26]),c_0_32])]) ).
cnf(c_0_70,negated_conjecture,
( ~ ssItem(X1)
| ~ memberP(esk3_0,X1)
| esk9_0 = X1 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_31]),c_0_68])]),c_0_44]) ).
cnf(c_0_71,negated_conjecture,
memberP(esk3_0,esk5_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_30]),c_0_31]),c_0_32])]) ).
fof(c_0_72,plain,
! [X34,X35,X36] :
( ( ~ ssItem(X34)
| ~ ssList(X35)
| ~ ssList(X36)
| memberP(app(X35,X36),X34)
| ~ memberP(X36,X34) )
& ( ~ ssItem(X34)
| ~ ssList(X35)
| ~ ssList(X36)
| memberP(app(X35,X36),X34)
| ~ memberP(X35,X34) )
& ( ~ ssItem(X34)
| ~ ssList(X35)
| ~ ssList(X36)
| memberP(X36,X34)
| memberP(X35,X34)
| ~ memberP(app(X35,X36),X34) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax36])])])])]) ).
cnf(c_0_73,negated_conjecture,
esk9_0 = esk5_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_32])]) ).
cnf(c_0_74,plain,
( ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ memberP(X1,X2)
| memberP(app(X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_75,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ memberP(X1,X2)
| memberP(app(X1,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_76,negated_conjecture,
cons(esk5_0,nil) = esk3_0,
inference(rw,[status(thm)],[c_0_67,c_0_73]) ).
cnf(c_0_77,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(app(esk6_0,cons(esk5_0,nil)))
| ~ memberP(esk7_0,X1)
| memberP(esk3_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_20]),c_0_21])]) ).
cnf(c_0_78,plain,
( ~ ssItem(X4)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ memberP(app(X1,X2),X4)
| memberP(app(X1,app(X2,X3)),X4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_48]),c_0_25]) ).
cnf(c_0_79,negated_conjecture,
app(esk6_0,app(esk3_0,esk7_0)) = esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_76]),c_0_76]),c_0_65])]) ).
cnf(c_0_80,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(cons(esk5_0,nil))
| ~ memberP(esk7_0,X1)
| memberP(esk3_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_25]),c_0_26])]) ).
cnf(c_0_81,negated_conjecture,
( ~ ssItem(X1)
| ~ memberP(app(esk6_0,esk3_0),X1)
| memberP(esk3_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_21]),c_0_65]),c_0_26])]) ).
cnf(c_0_82,negated_conjecture,
( ~ ssItem(X1)
| ~ memberP(esk7_0,X1)
| memberP(esk3_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_30]),c_0_31]),c_0_32])]) ).
cnf(c_0_83,negated_conjecture,
( ~ ssItem(X1)
| ~ memberP(esk6_0,X1)
| memberP(esk3_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_75]),c_0_65]),c_0_26])]) ).
cnf(c_0_84,negated_conjecture,
( memberP(esk3_0,esk8_0)
| memberP(esk6_0,esk8_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_35]),c_0_46])]) ).
cnf(c_0_85,negated_conjecture,
( ~ ssItem(X1)
| ~ memberP(esk3_0,X1)
| esk5_0 = X1 ),
inference(rw,[status(thm)],[c_0_70,c_0_73]) ).
cnf(c_0_86,negated_conjecture,
memberP(esk3_0,esk8_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_46])]) ).
cnf(c_0_87,negated_conjecture,
( ~ leq(esk8_0,esk5_0)
| ~ leq(esk5_0,esk8_0) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_88,negated_conjecture,
esk5_0 = esk8_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_46])]) ).
fof(c_0_89,plain,
! [X61] :
( leq(X61,X61)
| ~ ssItem(X61) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax31])])]) ).
cnf(c_0_90,negated_conjecture,
~ leq(esk8_0,esk8_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_87,c_0_88]),c_0_88])]) ).
cnf(c_0_91,plain,
( ~ ssItem(X1)
| leq(X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_92,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_46])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC284+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n005.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 08:12:02 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.42 Running first-order theorem proving
% 0.09/0.42 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.54 % Version: 3.5.1
% 0.16/0.54 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.16/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.16/0.54 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.54 % Starting new_bool_1 with 300s (1) cores
% 0.16/0.54 % Starting sh5l with 300s (1) cores
% 0.16/0.54 % new_bool_1 with pid 2984888 completed with status 0
% 0.16/0.54 % Result found by new_bool_1
% 0.16/0.54 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.16/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.16/0.54 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.54 % Starting new_bool_1 with 300s (1) cores
% 0.16/0.54 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.16/0.54 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.16/0.54 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.16/0.54 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.54 % Starting SubtermCWHack with 31s (1) cores
% 0.16/0.54 % SubtermCWHack with pid 2984891 completed with status 0
% 0.16/0.54 % Result found by SubtermCWHack
% 0.16/0.54 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.16/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.16/0.54 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.54 % Starting new_bool_1 with 300s (1) cores
% 0.16/0.54 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.16/0.54 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.16/0.54 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.16/0.54 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.54 % Starting SubtermCWHack with 31s (1) cores
% 0.16/0.54 % Preprocessing time : 0.002 s
% 0.16/0.54
% 0.16/0.54 % Proof found!
% 0.16/0.54 % SZS status Theorem
% 0.16/0.54 % SZS output start CNFRefutation
% See solution above
% 0.16/0.54 % Parsed axioms : 96
% 0.16/0.54 % Removed by relevancy pruning/SinE : 64
% 0.16/0.54 % Initial clauses : 68
% 0.16/0.54 % Removed in clause preprocessing : 0
% 0.16/0.54 % Initial clauses in saturation : 68
% 0.16/0.54 % Processed clauses : 985
% 0.16/0.54 % ...of these trivial : 10
% 0.16/0.54 % ...subsumed : 585
% 0.16/0.54 % ...remaining for further processing : 390
% 0.16/0.54 % Other redundant clauses eliminated : 27
% 0.16/0.54 % Clauses deleted for lack of memory : 0
% 0.16/0.54 % Backward-subsumed : 56
% 0.16/0.54 % Backward-rewritten : 76
% 0.16/0.54 % Generated clauses : 3937
% 0.16/0.54 % ...of the previous two non-redundant : 3281
% 0.16/0.54 % ...aggressively subsumed : 0
% 0.16/0.54 % Contextual simplify-reflections : 54
% 0.16/0.54 % Paramodulations : 3896
% 0.16/0.54 % Factorizations : 0
% 0.16/0.54 % NegExts : 0
% 0.16/0.54 % Equation resolutions : 37
% 0.16/0.54 % Disequality decompositions : 0
% 0.16/0.54 % Total rewrite steps : 4394
% 0.16/0.54 % ...of those cached : 4358
% 0.16/0.54 % Propositional unsat checks : 0
% 0.16/0.54 % Propositional check models : 0
% 0.16/0.54 % Propositional check unsatisfiable : 0
% 0.16/0.54 % Propositional clauses : 0
% 0.16/0.54 % Propositional clauses after purity: 0
% 0.16/0.54 % Propositional unsat core size : 0
% 0.16/0.54 % Propositional preprocessing time : 0.000
% 0.16/0.54 % Propositional encoding time : 0.000
% 0.16/0.54 % Propositional solver time : 0.000
% 0.16/0.54 % Success case prop preproc time : 0.000
% 0.16/0.54 % Success case prop encoding time : 0.000
% 0.16/0.54 % Success case prop solver time : 0.000
% 0.16/0.54 % Current number of processed clauses : 247
% 0.16/0.54 % Positive orientable unit clauses : 27
% 0.16/0.54 % Positive unorientable unit clauses: 0
% 0.16/0.54 % Negative unit clauses : 9
% 0.16/0.54 % Non-unit-clauses : 211
% 0.16/0.54 % Current number of unprocessed clauses: 2273
% 0.16/0.54 % ...number of literals in the above : 11371
% 0.16/0.54 % Current number of archived formulas : 0
% 0.16/0.54 % Current number of archived clauses : 137
% 0.16/0.54 % Clause-clause subsumption calls (NU) : 12188
% 0.16/0.54 % Rec. Clause-clause subsumption calls : 5116
% 0.16/0.54 % Non-unit clause-clause subsumptions : 548
% 0.16/0.54 % Unit Clause-clause subsumption calls : 944
% 0.16/0.54 % Rewrite failures with RHS unbound : 0
% 0.16/0.54 % BW rewrite match attempts : 16
% 0.16/0.54 % BW rewrite match successes : 14
% 0.16/0.54 % Condensation attempts : 0
% 0.16/0.54 % Condensation successes : 0
% 0.16/0.54 % Termbank termtop insertions : 70102
% 0.16/0.54 % Search garbage collected termcells : 1871
% 0.16/0.54
% 0.16/0.54 % -------------------------------------------------
% 0.16/0.54 % User time : 0.087 s
% 0.16/0.54 % System time : 0.006 s
% 0.16/0.54 % Total time : 0.093 s
% 0.16/0.54 % Maximum resident set size: 3764 pages
% 0.16/0.54
% 0.16/0.54 % -------------------------------------------------
% 0.16/0.54 % User time : 0.091 s
% 0.16/0.54 % System time : 0.011 s
% 0.16/0.54 % Total time : 0.102 s
% 0.16/0.54 % Maximum resident set size: 4608 pages
% 0.16/0.54 % E exiting
%------------------------------------------------------------------------------