%------------------------------------------------------------------------------
% 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 : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:43:39 PM UTC 2026
% Result : Theorem 6.23s 1.54s
% Output : CNFRefutation 6.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 19
% Syntax : Number of formulae : 111 ( 22 unt; 0 def)
% Number of atoms : 455 ( 163 equ)
% Maximal formula atoms : 44 ( 4 avg)
% Number of connectives : 561 ( 217 ~; 223 |; 60 &)
% ( 3 <=>; 58 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-3 aty)
% Number of variables : 187 ( 0 sgn 94 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ( nil = X3
& nil != X4 )
| ! [X9] :
( ? [X10] :
( ? [X11] :
( ? [X12] :
( ? [X13] :
( lt(X12,X10)
& app(X13,cons(X12,nil)) = X3
& ssList(X13) )
& ssItem(X12) )
& app(cons(X10,nil),X11) = X9
& ssList(X11) )
& ssItem(X10) )
| ~ strictorderedP(X3)
| app(X3,X9) != X4
| ~ ssList(X9) )
| ? [X5] :
( ? [X6] :
( ? [X7] :
( ! [X8] :
( leq(X5,X8)
| ~ lt(X5,X8)
| ~ memberP(X7,X8)
| ~ memberP(X6,X8)
| ~ ssItem(X8) )
& app(app(X6,cons(X5,nil)),X7) = X1
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
| nil = X1
| X1 != X3
| X2 != X4
| ~ ssList(X4) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax23,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> hd(cons(X2,X1)) = X2 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax23) ).
fof(ax20,axiom,
! [X1] :
( ssList(X1)
=> ( ? [X2] :
( ? [X3] :
( cons(X3,X2) = X1
& ssItem(X3) )
& ssList(X2) )
| nil = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax20) ).
fof(ax85,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> hd(app(X1,X2)) = hd(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax85) ).
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(ax22,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(ax86,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> tl(app(X1,X2)) = app(tl(X1),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax86) ).
fof(ax25,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> tl(cons(X2,X1)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax25) ).
fof(ax27,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax27) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(ax93,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( lt(X1,X2)
<=> ( leq(X1,X2)
& X1 != X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax93) ).
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(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax24,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax24) ).
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(ax78,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax78) ).
fof(c_0_19,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ( nil = X3
& nil != X4 )
| ! [X9] :
( ? [X10] :
( ? [X11] :
( ? [X12] :
( ? [X13] :
( lt(X12,X10)
& app(X13,cons(X12,nil)) = X3
& ssList(X13) )
& ssItem(X12) )
& app(cons(X10,nil),X11) = X9
& ssList(X11) )
& ssItem(X10) )
| ~ strictorderedP(X3)
| app(X3,X9) != X4
| ~ ssList(X9) )
| ? [X5] :
( ? [X6] :
( ? [X7] :
( ! [X8] :
( leq(X5,X8)
| ~ lt(X5,X8)
| ~ memberP(X7,X8)
| ~ memberP(X6,X8)
| ~ ssItem(X8) )
& app(app(X6,cons(X5,nil)),X7) = X1
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
| nil = X1
| X1 != X3
| X2 != X4
| ~ ssList(X4) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_20,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ( nil = X3
& nil != X4 )
| ! [X9] :
( ? [X10] :
( ? [X11] :
( ? [X12] :
( ? [X13] :
( lt(X12,X10)
& app(X13,cons(X12,nil)) = X3
& ssList(X13) )
& ssItem(X12) )
& app(cons(X10,nil),X11) = X9
& ssList(X11) )
& ssItem(X10) )
| ~ strictorderedP(X3)
| app(X3,X9) != X4
| ~ ssList(X9) )
| ? [X5] :
( ? [X6] :
( ? [X7] :
( ! [X8] :
( leq(X5,X8)
| ~ lt(X5,X8)
| ~ memberP(X7,X8)
| ~ memberP(X6,X8)
| ~ ssItem(X8) )
& app(app(X6,cons(X5,nil)),X7) = X1
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
| nil = X1
| X1 != X3
| X2 != X4
| ~ ssList(X4) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_21,plain,
! [X109,X110] :
( hd(cons(X110,X109)) = X110
| ~ ssItem(X110)
| ~ ssList(X109) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])])]) ).
fof(c_0_22,plain,
! [X27] :
( ( ~ ssList(X27)
| nil = X27
| cons(esk8_1(X27),esk7_1(X27)) = X27 )
& ( ~ ssList(X27)
| nil = X27
| ssItem(esk8_1(X27)) )
& ( ~ ssList(X27)
| nil = X27
| ssList(esk7_1(X27)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax20])])])])]) ).
fof(c_0_23,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> hd(app(X1,X2)) = hd(X1) ) ) ),
inference(fof_simplification,[status(thm)],[ax85]) ).
fof(c_0_24,negated_conjecture,
! [X18,X19,X20,X23,X24,X25,X26] :
( ( nil != esk3_0
| nil = esk4_0 )
& ( ~ lt(X25,X23)
| app(X26,cons(X25,nil)) != esk3_0
| ~ ssList(X26)
| ~ ssItem(X25)
| app(cons(X23,nil),X24) != esk6_0
| ~ ssList(X24)
| ~ ssItem(X23) )
& strictorderedP(esk3_0)
& app(esk3_0,esk6_0) = esk4_0
& ssList(esk6_0)
& ( ~ ssItem(X18)
| ~ ssList(X19)
| app(app(X19,cons(X18,nil)),X20) != esk1_0
| ~ ssList(X20)
| ~ leq(X18,esk5_3(X18,X19,X20)) )
& ( ~ ssItem(X18)
| ~ ssList(X19)
| app(app(X19,cons(X18,nil)),X20) != esk1_0
| ~ ssList(X20)
| lt(X18,esk5_3(X18,X19,X20)) )
& ( ~ ssItem(X18)
| ~ ssList(X19)
| app(app(X19,cons(X18,nil)),X20) != esk1_0
| ~ ssList(X20)
| memberP(X20,esk5_3(X18,X19,X20)) )
& ( ~ ssItem(X18)
| ~ ssList(X19)
| app(app(X19,cons(X18,nil)),X20) != esk1_0
| ~ ssList(X20)
| memberP(X19,esk5_3(X18,X19,X20)) )
& ( ~ ssItem(X18)
| ~ ssList(X19)
| app(app(X19,cons(X18,nil)),X20) != esk1_0
| ~ ssList(X20)
| ssItem(esk5_3(X18,X19,X20)) )
& nil != esk1_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(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])])])]) ).
cnf(c_0_25,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| hd(cons(X2,X1)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_26,plain,
( ~ ssList(X1)
| nil = X1
| cons(esk8_1(X1),esk7_1(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
( ~ ssList(X1)
| nil = X1
| ssItem(esk8_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,plain,
( ~ ssList(X1)
| nil = X1
| ssList(esk7_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_29,plain,
! [X116,X117] :
( hd(app(X116,X117)) = hd(X116)
| nil = X116
| ~ ssList(X117)
| ~ ssList(X116) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])])]) ).
cnf(c_0_30,negated_conjecture,
app(esk3_0,esk6_0) = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,negated_conjecture,
esk1_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_32,plain,
! [X62,X63] :
( ( ~ ssList(X62)
| ~ ssList(X63)
| nil = app(X62,X63)
| nil != X62
| nil != X63 )
& ( ~ ssList(X62)
| ~ ssList(X63)
| nil != app(X62,X63)
| nil = X62 )
& ( ~ ssList(X62)
| ~ ssList(X63)
| nil != app(X62,X63)
| nil = X63 ) ),
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])])])])]) ).
fof(c_0_33,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
inference(fof_simplification,[status(thm)],[ax22]) ).
fof(c_0_34,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> tl(app(X1,X2)) = app(tl(X1),X2) ) ) ),
inference(fof_simplification,[status(thm)],[ax86]) ).
cnf(c_0_35,plain,
( ~ ssList(X1)
| nil = X1
| esk8_1(X1) = hd(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_28]) ).
cnf(c_0_36,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| hd(app(X1,X2)) = hd(X1)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_37,negated_conjecture,
app(esk1_0,esk6_0) = esk4_0,
inference(rw,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_38,negated_conjecture,
ssList(esk6_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_39,negated_conjecture,
ssList(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_40,negated_conjecture,
nil != esk1_0,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_41,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| nil != app(X1,X2)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_42,plain,
! [X108] :
( ssItem(hd(X108))
| nil = X108
| ~ ssList(X108) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])])]) ).
fof(c_0_43,plain,
! [X123,X124] :
( tl(app(X123,X124)) = app(tl(X123),X124)
| nil = X123
| ~ ssList(X124)
| ~ ssList(X123) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_34])])])]) ).
fof(c_0_44,plain,
! [X119,X120] :
( tl(cons(X120,X119)) = X119
| ~ ssItem(X120)
| ~ ssList(X119) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax25])])])]) ).
cnf(c_0_45,plain,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),esk7_1(X1)) = X1 ),
inference(spm,[status(thm)],[c_0_26,c_0_35]) ).
cnf(c_0_46,negated_conjecture,
hd(esk4_0) = hd(esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),c_0_39])]),c_0_40]) ).
cnf(c_0_47,negated_conjecture,
ssList(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_48,negated_conjecture,
esk4_0 != nil,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_37]),c_0_38]),c_0_39])]),c_0_40]) ).
cnf(c_0_49,plain,
( ~ ssList(X1)
| ssItem(hd(X1))
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
fof(c_0_50,plain,
! [X47,X48,X49] :
( cons(X49,app(X48,X47)) = app(cons(X49,X48),X47)
| ~ ssItem(X49)
| ~ ssList(X48)
| ~ ssList(X47) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])])]) ).
cnf(c_0_51,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| tl(app(X1,X2)) = app(tl(X1),X2)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_52,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| tl(cons(X2,X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_53,negated_conjecture,
cons(hd(esk1_0),esk7_1(esk4_0)) = esk4_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47])]),c_0_48]) ).
cnf(c_0_54,negated_conjecture,
ssItem(hd(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_46]),c_0_47])]),c_0_48]) ).
cnf(c_0_55,plain,
( ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_56,negated_conjecture,
app(tl(esk1_0),esk6_0) = tl(esk4_0),
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_37]),c_0_38]),c_0_39])]),c_0_40]) ).
cnf(c_0_57,plain,
( ~ ssList(X1)
| nil = X1
| esk7_1(X1) = tl(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_26]),c_0_27]),c_0_28]) ).
cnf(c_0_58,negated_conjecture,
( ~ ssList(esk7_1(esk4_0))
| esk7_1(esk4_0) = tl(esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54])]) ).
cnf(c_0_59,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(tl(esk1_0))
| app(cons(X1,tl(esk1_0)),esk6_0) = cons(X1,tl(esk4_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_38])]) ).
cnf(c_0_60,plain,
( ~ ssList(X1)
| nil = X1
| cons(esk8_1(X1),tl(X1)) = X1 ),
inference(spm,[status(thm)],[c_0_26,c_0_57]) ).
cnf(c_0_61,negated_conjecture,
esk7_1(esk4_0) = tl(esk4_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_28]),c_0_47])]),c_0_48]) ).
cnf(c_0_62,negated_conjecture,
( ~ ssItem(esk8_1(esk1_0))
| ~ ssList(tl(esk1_0))
| cons(esk8_1(esk1_0),tl(esk4_0)) = esk4_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_37]),c_0_39])]),c_0_40]) ).
cnf(c_0_63,negated_conjecture,
ssList(tl(esk4_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_61]),c_0_47])]),c_0_48]) ).
fof(c_0_64,plain,
! [X65,X66] :
( ssList(cons(X66,X65))
| ~ ssItem(X66)
| ~ ssList(X65) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).
fof(c_0_65,plain,
! [X45,X46] :
( ssList(app(X45,X46))
| ~ ssList(X46)
| ~ ssList(X45) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).
cnf(c_0_66,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| nil != X2
| nil != X1
| nil = app(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_67,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
fof(c_0_68,plain,
! [X64] :
( app(X64,nil) = X64
| ~ ssList(X64) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])])]) ).
cnf(c_0_69,negated_conjecture,
( ~ ssItem(esk8_1(esk1_0))
| ~ ssList(tl(esk1_0))
| esk8_1(esk1_0) = hd(esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_62]),c_0_46]),c_0_63])]) ).
fof(c_0_70,plain,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( lt(X1,X2)
<=> ( leq(X1,X2)
& X1 != X2 ) ) ) ),
inference(fof_simplification,[status(thm)],[ax93]) ).
fof(c_0_71,plain,
! [X59,X60,X61] :
( app(app(X59,X60),X61) = app(X59,app(X60,X61))
| ~ ssList(X61)
| ~ ssList(X60)
| ~ ssList(X59) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])])]) ).
fof(c_0_72,plain,
! [X50] :
( app(nil,X50) = X50
| ~ ssList(X50) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])]) ).
cnf(c_0_73,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ssList(cons(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_74,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_75,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_66])]),c_0_67])]) ).
cnf(c_0_76,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_77,negated_conjecture,
( ~ ssList(tl(esk1_0))
| esk8_1(esk1_0) = hd(esk1_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_27]),c_0_39])]),c_0_40]) ).
fof(c_0_78,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
inference(fof_simplification,[status(thm)],[ax24]) ).
fof(c_0_79,plain,
! [X43,X44] :
( ( ~ ssItem(X43)
| ~ ssItem(X44)
| lt(X43,X44)
| ~ leq(X43,X44)
| X43 = X44 )
& ( ~ ssItem(X43)
| ~ ssItem(X44)
| ~ lt(X43,X44)
| leq(X43,X44) )
& ( ~ ssItem(X43)
| ~ ssItem(X44)
| ~ lt(X43,X44)
| X43 != X44 ) ),
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_70])])])])]) ).
cnf(c_0_80,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X1,X2),X3) = app(X1,app(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_81,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
fof(c_0_82,plain,
! [X57,X58] :
( cons(X58,X57) = app(cons(X58,nil),X57)
| ~ ssItem(X58)
| ~ ssList(X57) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])])]) ).
cnf(c_0_83,plain,
( ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ssList(app(cons(X1,X2),X3)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_55]),c_0_74]) ).
cnf(c_0_84,plain,
( ~ ssItem(X1)
| app(cons(X1,nil),nil) = cons(X1,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_75]),c_0_67])]) ).
fof(c_0_85,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
inference(fof_simplification,[status(thm)],[ax78]) ).
cnf(c_0_86,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| app(cons(X1,X2),nil) = cons(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_76]),c_0_67])]) ).
cnf(c_0_87,negated_conjecture,
( ~ ssList(tl(esk1_0))
| cons(hd(esk1_0),tl(esk1_0)) = esk1_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_77]),c_0_39])]),c_0_40]) ).
fof(c_0_88,plain,
! [X118] :
( ssList(tl(X118))
| nil = X118
| ~ ssList(X118) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_78])])]) ).
cnf(c_0_89,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(X2)
| app(app(X2,cons(X1,nil)),X3) != esk1_0
| ~ ssList(X3)
| ~ leq(X1,esk5_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_90,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ lt(X1,X2)
| leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_91,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(X2)
| app(app(X2,cons(X1,nil)),X3) != esk1_0
| ~ ssList(X3)
| ssItem(esk5_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_92,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(X2)
| app(app(X2,cons(X1,nil)),X3) != esk1_0
| ~ ssList(X3)
| lt(X1,esk5_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_93,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(nil,app(X1,X2)) = app(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_67])]) ).
cnf(c_0_94,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) = app(cons(X2,nil),X1) ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_95,plain,
( ~ ssItem(X1)
| ssList(cons(X1,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_67])]) ).
fof(c_0_96,plain,
! [X115] :
( cons(hd(X115),tl(X115)) = X115
| nil = X115
| ~ ssList(X115) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_85])])]) ).
cnf(c_0_97,negated_conjecture,
( ~ ssList(tl(esk1_0))
| app(esk1_0,nil) = esk1_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_54])]) ).
cnf(c_0_98,plain,
( ~ ssList(X1)
| ssList(tl(X1))
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_99,negated_conjecture,
( ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| app(app(X1,cons(X2,nil)),X3) != esk1_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_91]),c_0_92]) ).
cnf(c_0_100,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| app(nil,cons(X1,X2)) = cons(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_95]) ).
cnf(c_0_101,plain,
( ~ ssList(X1)
| cons(hd(X1),tl(X1)) = X1
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_102,negated_conjecture,
app(esk1_0,nil) = esk1_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_39])]),c_0_40]) ).
cnf(c_0_103,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(X2)
| app(cons(X1,nil),X2) != esk1_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_67])]) ).
cnf(c_0_104,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| 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_101,c_0_36]),c_0_74]),c_0_41]) ).
cnf(c_0_105,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ssList(app(tl(X1),X2))
| nil = X1 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_51]),c_0_74]),c_0_41]) ).
cnf(c_0_106,negated_conjecture,
app(tl(esk1_0),nil) = tl(esk1_0),
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_102]),c_0_67]),c_0_39])]),c_0_40]) ).
cnf(c_0_107,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(X2)
| cons(X1,X2) != esk1_0 ),
inference(spm,[status(thm)],[c_0_103,c_0_94]) ).
cnf(c_0_108,negated_conjecture,
cons(hd(esk1_0),tl(esk1_0)) = esk1_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_102]),c_0_67]),c_0_39])]),c_0_40]) ).
cnf(c_0_109,negated_conjecture,
ssList(tl(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_67]),c_0_39])]),c_0_40]) ).
cnf(c_0_110,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_109]),c_0_54])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % 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
% 0.18/0.50 % Computer : n007.cluster.edu
% 0.18/0.50 % Model : x86_64 x86_64
% 0.18/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.50 % Memory : 8046.5625MB
% 0.18/0.50 % OS : Linux 6.8.0-71-generic
% 0.18/0.50 % CPULimit : 300
% 0.18/0.50 % WCLimit : 300
% 0.18/0.50 % DateTime : Mon Sep 21 08:06:20 UTC 2026
% 0.18/0.50 % CPUTime :
% 0.18/0.50 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.58 Running first-order theorem proving
% 0.23/0.58 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
% 6.23/1.54 % Version: 3.5.1
% 6.23/1.54 % Preprocessing class: FSLSSMSSSSSNFFN.
% 6.23/1.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.23/1.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 6.23/1.54 % Starting new_bool_3 with 300s (1) cores
% 6.23/1.54 % Starting new_bool_1 with 300s (1) cores
% 6.23/1.54 % Starting sh5l with 300s (1) cores
% 6.23/1.54 % new_bool_1 with pid 607278 completed with status 0
% 6.23/1.54 % Result found by new_bool_1
% 6.23/1.54 % Preprocessing class: FSLSSMSSSSSNFFN.
% 6.23/1.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.23/1.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 6.23/1.54 % Starting new_bool_3 with 300s (1) cores
% 6.23/1.54 % Starting new_bool_1 with 300s (1) cores
% 6.23/1.54 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 6.23/1.54 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 6.23/1.54 % Search class: FGHSF-FFMM31-MFFFFFNN
% 6.23/1.54 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 6.23/1.54 % Starting SubtermCWHack with 31s (1) cores
% 6.23/1.54 % SubtermCWHack with pid 607285 completed with status 0
% 6.23/1.54 % Result found by SubtermCWHack
% 6.23/1.54 % Preprocessing class: FSLSSMSSSSSNFFN.
% 6.23/1.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.23/1.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 6.23/1.54 % Starting new_bool_3 with 300s (1) cores
% 6.23/1.54 % Starting new_bool_1 with 300s (1) cores
% 6.23/1.54 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 6.23/1.54 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 6.23/1.54 % Search class: FGHSF-FFMM31-MFFFFFNN
% 6.23/1.54 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 6.23/1.54 % Starting SubtermCWHack with 31s (1) cores
% 6.23/1.54 % Preprocessing time : 0.002 s
% 6.23/1.54
% 6.23/1.54 % Proof found!
% 6.23/1.54 % SZS status Theorem
% 6.23/1.54 % SZS output start CNFRefutation
% See solution above
% 6.23/1.55 % Parsed axioms : 96
% 6.23/1.55 % Removed by relevancy pruning/SinE : 52
% 6.23/1.55 % Initial clauses : 89
% 6.23/1.55 % Removed in clause preprocessing : 1
% 6.23/1.55 % Initial clauses in saturation : 88
% 6.23/1.55 % Processed clauses : 4266
% 6.23/1.55 % ...of these trivial : 202
% 6.23/1.55 % ...subsumed : 2857
% 6.23/1.55 % ...remaining for further processing : 1207
% 6.23/1.55 % Other redundant clauses eliminated : 110
% 6.23/1.55 % Clauses deleted for lack of memory : 0
% 6.23/1.55 % Backward-subsumed : 158
% 6.23/1.55 % Backward-rewritten : 62
% 6.23/1.55 % Generated clauses : 23954
% 6.23/1.55 % ...of the previous two non-redundant : 19956
% 6.23/1.55 % ...aggressively subsumed : 0
% 6.23/1.55 % Contextual simplify-reflections : 270
% 6.23/1.55 % Paramodulations : 23829
% 6.23/1.55 % Factorizations : 0
% 6.23/1.55 % NegExts : 0
% 6.23/1.55 % Equation resolutions : 126
% 6.23/1.55 % Disequality decompositions : 0
% 6.23/1.55 % Total rewrite steps : 26633
% 6.23/1.55 % ...of those cached : 26523
% 6.23/1.55 % Propositional unsat checks : 0
% 6.23/1.55 % Propositional check models : 0
% 6.23/1.55 % Propositional check unsatisfiable : 0
% 6.23/1.55 % Propositional clauses : 0
% 6.23/1.55 % Propositional clauses after purity: 0
% 6.23/1.55 % Propositional unsat core size : 0
% 6.23/1.55 % Propositional preprocessing time : 0.000
% 6.23/1.55 % Propositional encoding time : 0.000
% 6.23/1.55 % Propositional solver time : 0.000
% 6.23/1.55 % Success case prop preproc time : 0.000
% 6.23/1.55 % Success case prop encoding time : 0.000
% 6.23/1.55 % Success case prop solver time : 0.000
% 6.23/1.55 % Current number of processed clauses : 981
% 6.23/1.55 % Positive orientable unit clauses : 116
% 6.23/1.55 % Positive unorientable unit clauses: 0
% 6.23/1.55 % Negative unit clauses : 144
% 6.23/1.55 % Non-unit-clauses : 721
% 6.23/1.55 % Current number of unprocessed clauses: 15637
% 6.23/1.55 % ...number of literals in the above : 79542
% 6.23/1.55 % Current number of archived formulas : 0
% 6.23/1.55 % Current number of archived clauses : 220
% 6.23/1.55 % Clause-clause subsumption calls (NU) : 79769
% 6.23/1.55 % Rec. Clause-clause subsumption calls : 25541
% 6.23/1.55 % Non-unit clause-clause subsumptions : 2092
% 6.23/1.55 % Unit Clause-clause subsumption calls : 4080
% 6.23/1.55 % Rewrite failures with RHS unbound : 0
% 6.23/1.55 % BW rewrite match attempts : 152
% 6.23/1.55 % BW rewrite match successes : 30
% 6.23/1.55 % Condensation attempts : 0
% 6.23/1.55 % Condensation successes : 0
% 6.23/1.55 % Termbank termtop insertions : 451973
% 6.23/1.55 % Search garbage collected termcells : 2337
% 6.23/1.55
% 6.23/1.55 % -------------------------------------------------
% 6.23/1.55 % User time : 0.431 s
% 6.23/1.55 % System time : 0.020 s
% 6.23/1.55 % Total time : 0.451 s
% 6.23/1.55 % Maximum resident set size: 4024 pages
% 6.23/1.55
% 6.23/1.55 % -------------------------------------------------
% 6.23/1.55 % User time : 0.436 s
% 6.23/1.55 % System time : 0.027 s
% 6.23/1.55 % Total time : 0.463 s
% 6.23/1.55 % Maximum resident set size: 4864 pages
% 6.23/1.55 % E exiting
%------------------------------------------------------------------------------