%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC388+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 : n018.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 02:44:12 PM UTC 2026
% Result : Theorem 31.48s 5.84s
% Output : CNFRefutation 31.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 20
% Syntax : Number of formulae : 115 ( 21 unt; 0 def)
% Number of atoms : 451 ( 129 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 555 ( 219 ~; 227 |; 42 &)
% ( 9 <=>; 58 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-2 aty)
% Number of variables : 161 ( 0 sgn 93 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( nil = X1
& nil = X2 )
| ( neq(X4,nil)
& ~ singletonP(X3) )
| ? [X5] :
( memberP(X2,X5)
& cons(X5,nil) = X1
& ssItem(X5) )
| ~ segmentP(X4,X3)
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(ax46,axiom,
! [X1] :
( ssList(X1)
=> ( frontsegP(nil,X1)
<=> nil = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax46) ).
fof(ax5,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X1,X2)
<=> ? [X3] :
( app(X2,X3) = X1
& ssList(X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax5) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(ax83,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X1
& nil = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(ax25,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> tl(cons(X2,X1)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax25) ).
fof(ax4,axiom,
! [X1] :
( ssList(X1)
=> ( singletonP(X1)
<=> ? [X2] :
( cons(X2,nil) = X1
& ssItem(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax4) ).
fof(ax78,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax78) ).
fof(ax23,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> hd(cons(X2,X1)) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax23) ).
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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax27) ).
fof(ax22,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(ax21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax21) ).
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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax37) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax82) ).
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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax36) ).
fof(ax7,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( segmentP(X1,X2)
<=> ? [X3] :
( ? [X4] :
( app(app(X3,X2),X4) = X1
& ssList(X4) )
& ssList(X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax7) ).
fof(ax54,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( segmentP(X2,X1)
& segmentP(X1,X2) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax54) ).
fof(ax57,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,nil) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax57) ).
fof(c_0_20,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( nil = X1
& nil = X2 )
| ( neq(X4,nil)
& ~ singletonP(X3) )
| ? [X5] :
( memberP(X2,X5)
& cons(X5,nil) = X1
& ssItem(X5) )
| ~ segmentP(X4,X3)
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_21,plain,
! [X172] :
( ( ~ ssList(X172)
| frontsegP(nil,X172)
| nil != X172 )
& ( ~ ssList(X172)
| nil = X172
| ~ frontsegP(nil,X172) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax46])])])]) ).
fof(c_0_22,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( nil = X1
& nil = X2 )
| ( neq(X4,nil)
& ~ singletonP(X3) )
| ? [X5] :
( memberP(X2,X5)
& cons(X5,nil) = X1
& ssItem(X5) )
| ~ segmentP(X4,X3)
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_20]) ).
fof(c_0_23,plain,
! [X20,X21,X23] :
( ( ~ ssList(X20)
| ~ ssList(X21)
| frontsegP(X20,X21)
| app(X21,X23) != X20
| ~ ssList(X23) )
& ( ~ ssList(X20)
| ~ ssList(X21)
| ~ frontsegP(X20,X21)
| app(X21,esk6_2(X20,X21)) = X20 )
& ( ~ ssList(X20)
| ~ ssList(X21)
| ~ frontsegP(X20,X21)
| ssList(esk6_2(X20,X21)) ) ),
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)],[ax5])])])])])]) ).
cnf(c_0_24,plain,
( ~ ssList(X1)
| nil != X1
| frontsegP(nil,X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_25,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
fof(c_0_26,negated_conjecture,
! [X255] :
( ( nil != esk48_0
| nil != esk49_0 )
& ( ~ neq(esk51_0,nil)
| singletonP(esk50_0) )
& ( ~ memberP(esk49_0,X255)
| cons(X255,nil) != esk48_0
| ~ ssItem(X255) )
& segmentP(esk51_0,esk50_0)
& esk48_0 = esk50_0
& esk49_0 = esk51_0
& ssList(esk51_0)
& ssList(esk50_0)
& ssList(esk49_0)
& ssList(esk48_0) ),
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_22])])])])]) ).
fof(c_0_27,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
fof(c_0_28,plain,
! [X225,X226] :
( ( ~ ssList(X225)
| ~ ssList(X226)
| nil = app(X225,X226)
| nil != X225
| nil != X226 )
& ( ~ ssList(X225)
| ~ ssList(X226)
| nil != app(X225,X226)
| nil = X225 )
& ( ~ ssList(X225)
| ~ ssList(X226)
| nil != app(X225,X226)
| nil = X226 ) ),
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_29,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ frontsegP(X2,X1)
| app(X1,esk6_2(X2,X1)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
frontsegP(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_24]),c_0_25])]) ).
cnf(c_0_31,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| ssList(esk6_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_32,plain,
! [X128,X129] :
( tl(cons(X129,X128)) = X128
| ~ ssItem(X129)
| ~ ssList(X128) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax25])])])]) ).
fof(c_0_33,plain,
! [X17,X19] :
( ( ~ ssList(X17)
| singletonP(X17)
| cons(X19,nil) != X17
| ~ ssItem(X19) )
& ( ~ ssList(X17)
| ~ singletonP(X17)
| cons(esk5_1(X17),nil) = X17 )
& ( ~ ssList(X17)
| ~ singletonP(X17)
| ssItem(esk5_1(X17)) ) ),
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)],[ax4])])])])])]) ).
cnf(c_0_34,negated_conjecture,
( ~ neq(esk51_0,nil)
| singletonP(esk50_0) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_35,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_36,plain,
! [X109,X110] :
( ( ~ ssList(X109)
| ~ ssList(X110)
| neq(X109,X110)
| X109 = X110 )
& ( ~ ssList(X109)
| ~ ssList(X110)
| X109 != X110
| ~ neq(X109,X110) ) ),
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_27])])])])]) ).
cnf(c_0_37,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_38,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_39,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| nil != app(X2,X1)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_40,plain,
app(nil,esk6_2(nil,nil)) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_25])]) ).
cnf(c_0_41,plain,
ssList(esk6_2(nil,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_30]),c_0_25])]) ).
fof(c_0_42,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
inference(fof_simplification,[status(thm)],[ax78]) ).
cnf(c_0_43,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| tl(cons(X2,X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_44,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(esk5_1(X1),nil) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_45,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| ssItem(esk5_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_46,negated_conjecture,
( ~ neq(esk51_0,nil)
| singletonP(esk48_0) ),
inference(rw,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_47,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_48,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_37,c_0_38]) ).
fof(c_0_49,plain,
! [X125,X126] :
( hd(cons(X126,X125)) = X126
| ~ ssItem(X126)
| ~ ssList(X125) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])])]) ).
fof(c_0_50,plain,
! [X132,X133,X134] :
( cons(X134,app(X133,X132)) = app(cons(X134,X133),X132)
| ~ ssItem(X134)
| ~ ssList(X133)
| ~ ssList(X132) ),
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,
esk6_2(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_25]),c_0_41])]) ).
fof(c_0_52,plain,
! [X213] :
( cons(hd(X213),tl(X213)) = X213
| nil = X213
| ~ ssList(X213) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])])]) ).
cnf(c_0_53,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| tl(X1) = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_25])]),c_0_45]) ).
cnf(c_0_54,negated_conjecture,
( singletonP(esk48_0)
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_25]),c_0_48])]) ).
cnf(c_0_55,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_56,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| hd(cons(X2,X1)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_57,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_58,plain,
app(nil,nil) = nil,
inference(rw,[status(thm)],[c_0_40,c_0_51]) ).
cnf(c_0_59,plain,
( ~ ssList(X1)
| cons(hd(X1),tl(X1)) = X1
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_60,negated_conjecture,
( esk51_0 = nil
| tl(esk48_0) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55])]) ).
fof(c_0_61,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
inference(fof_simplification,[status(thm)],[ax22]) ).
fof(c_0_62,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[ax21]) ).
cnf(c_0_63,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| esk5_1(X1) = hd(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_44]),c_0_25])]),c_0_45]) ).
fof(c_0_64,plain,
! [X154,X155,X156] :
( ( ~ ssItem(X154)
| ~ ssItem(X155)
| ~ ssList(X156)
| memberP(cons(X155,X156),X154)
| ~ memberP(X156,X154) )
& ( ~ ssItem(X154)
| ~ ssItem(X155)
| ~ ssList(X156)
| memberP(cons(X155,X156),X154)
| X154 != X155 )
& ( ~ ssItem(X154)
| ~ ssItem(X155)
| ~ ssList(X156)
| memberP(X156,X154)
| X154 = X155
| ~ memberP(cons(X155,X156),X154) ) ),
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_65,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_57,c_0_58]),c_0_25])]) ).
cnf(c_0_66,negated_conjecture,
( esk48_0 = nil
| esk51_0 = nil
| cons(hd(esk48_0),nil) = esk48_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_55])]) ).
fof(c_0_67,plain,
! [X124] :
( ssItem(hd(X124))
| nil = X124
| ~ ssList(X124) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_61])])]) ).
fof(c_0_68,plain,
! [X122,X123] :
( nil != cons(X123,X122)
| ~ ssItem(X123)
| ~ ssList(X122) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_62])])])]) ).
cnf(c_0_69,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(hd(X1),nil) = X1 ),
inference(spm,[status(thm)],[c_0_44,c_0_63]) ).
cnf(c_0_70,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| ssItem(hd(X1)) ),
inference(spm,[status(thm)],[c_0_45,c_0_63]) ).
cnf(c_0_71,negated_conjecture,
( nil != esk48_0
| nil != esk49_0 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_72,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| X1 != X2
| memberP(cons(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
fof(c_0_73,plain,
! [X130,X131] :
( ssList(app(X130,X131))
| ~ ssList(X131)
| ~ ssList(X130) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).
fof(c_0_74,plain,
! [X222,X223,X224] :
( app(app(X222,X223),X224) = app(X222,app(X223,X224))
| ~ ssList(X224)
| ~ ssList(X223)
| ~ ssList(X222) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])])]) ).
cnf(c_0_75,negated_conjecture,
( ~ ssItem(hd(esk48_0))
| esk51_0 = nil
| esk48_0 = nil
| app(esk48_0,nil) = esk48_0 ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_76,plain,
( ~ ssList(X1)
| ssItem(hd(X1))
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_77,plain,
( nil != cons(X2,X1)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_78,negated_conjecture,
( esk51_0 = nil
| cons(hd(esk48_0),nil) = esk48_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_54]),c_0_55])]) ).
cnf(c_0_79,negated_conjecture,
( ssItem(hd(esk48_0))
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_54]),c_0_55])]) ).
cnf(c_0_80,negated_conjecture,
( esk51_0 != nil
| esk48_0 != nil ),
inference(rw,[status(thm)],[c_0_71,c_0_38]) ).
fof(c_0_81,plain,
! [X151,X152,X153] :
( ( ~ ssItem(X151)
| ~ ssList(X152)
| ~ ssList(X153)
| memberP(app(X152,X153),X151)
| ~ memberP(X153,X151) )
& ( ~ ssItem(X151)
| ~ ssList(X152)
| ~ ssList(X153)
| memberP(app(X152,X153),X151)
| ~ memberP(X152,X151) )
& ( ~ ssItem(X151)
| ~ ssList(X152)
| ~ ssList(X153)
| memberP(X153,X151)
| memberP(X152,X151)
| ~ memberP(app(X152,X153),X151) ) ),
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_82,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| memberP(cons(X1,X2),X1) ),
inference(er,[status(thm)],[c_0_72]) ).
cnf(c_0_83,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_84,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X1,X2),X3) = app(X1,app(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_85,negated_conjecture,
( esk48_0 = nil
| esk51_0 = nil
| app(esk48_0,nil) = esk48_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_55])]) ).
cnf(c_0_86,negated_conjecture,
esk48_0 != nil,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_25])]),c_0_79]),c_0_80]) ).
cnf(c_0_87,plain,
( ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ memberP(X1,X2)
| memberP(app(X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_88,negated_conjecture,
( memberP(esk48_0,hd(esk48_0))
| esk51_0 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_78]),c_0_25])]),c_0_79]) ).
cnf(c_0_89,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ssList(app(X1,app(X2,X3))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_83]) ).
cnf(c_0_90,negated_conjecture,
( esk51_0 = nil
| app(esk48_0,nil) = esk48_0 ),
inference(sr,[status(thm)],[c_0_85,c_0_86]) ).
fof(c_0_91,plain,
! [X28,X29,X32,X33] :
( ( ~ ssList(X28)
| ~ ssList(X29)
| segmentP(X28,X29)
| app(app(X32,X29),X33) != X28
| ~ ssList(X33)
| ~ ssList(X32) )
& ( ~ ssList(X28)
| ~ ssList(X29)
| ~ segmentP(X28,X29)
| app(app(esk8_2(X28,X29),X29),esk9_2(X28,X29)) = X28 )
& ( ~ ssList(X28)
| ~ ssList(X29)
| ~ segmentP(X28,X29)
| ssList(esk9_2(X28,X29)) )
& ( ~ ssList(X28)
| ~ ssList(X29)
| ~ segmentP(X28,X29)
| ssList(esk8_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)],[ax7])])])])])]) ).
cnf(c_0_92,negated_conjecture,
segmentP(esk51_0,esk50_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_93,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ memberP(X1,X2)
| memberP(app(X1,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_94,negated_conjecture,
( ~ ssList(X1)
| memberP(app(X1,esk48_0),hd(esk48_0))
| esk51_0 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_55])]),c_0_79]) ).
cnf(c_0_95,negated_conjecture,
( ~ ssList(X1)
| ssList(app(X1,esk48_0))
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_25]),c_0_55])]) ).
cnf(c_0_96,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X1,X2)
| app(app(esk8_2(X1,X2),X2),esk9_2(X1,X2)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_97,negated_conjecture,
segmentP(esk51_0,esk48_0),
inference(rw,[status(thm)],[c_0_92,c_0_35]) ).
cnf(c_0_98,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X1,X2)
| ssList(esk9_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_99,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X1,X2)
| ssList(esk8_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
fof(c_0_100,plain,
! [X187,X188] :
( X187 = X188
| ~ segmentP(X188,X187)
| ~ segmentP(X187,X188)
| ~ ssList(X188)
| ~ ssList(X187) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax54])])])]) ).
cnf(c_0_101,negated_conjecture,
( ~ memberP(esk49_0,X1)
| cons(X1,nil) != esk48_0
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_102,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(X2)
| memberP(app(app(X1,esk48_0),X2),hd(esk48_0))
| esk51_0 = nil ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_79]),c_0_95]) ).
cnf(c_0_103,negated_conjecture,
app(app(esk8_2(esk51_0,esk48_0),esk48_0),esk9_2(esk51_0,esk48_0)) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_55]),c_0_48])]) ).
cnf(c_0_104,negated_conjecture,
ssList(esk9_2(esk51_0,esk48_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_97]),c_0_55]),c_0_48])]) ).
cnf(c_0_105,negated_conjecture,
ssList(esk8_2(esk51_0,esk48_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_97]),c_0_55]),c_0_48])]) ).
cnf(c_0_106,plain,
( ~ segmentP(X2,X1)
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_107,negated_conjecture,
( ~ ssItem(X1)
| ~ memberP(esk51_0,X1)
| cons(X1,nil) != esk48_0 ),
inference(rw,[status(thm)],[c_0_101,c_0_38]) ).
cnf(c_0_108,negated_conjecture,
( memberP(esk51_0,hd(esk48_0))
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_104]),c_0_105])]) ).
cnf(c_0_109,negated_conjecture,
( ~ segmentP(esk48_0,esk51_0)
| esk51_0 = esk48_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_97]),c_0_48]),c_0_55])]) ).
cnf(c_0_110,negated_conjecture,
esk51_0 = nil,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_79]),c_0_78]) ).
fof(c_0_111,plain,
! [X194] :
( segmentP(X194,nil)
| ~ ssList(X194) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax57])])]) ).
cnf(c_0_112,negated_conjecture,
~ segmentP(esk48_0,nil),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_109,c_0_110]),c_0_110]),c_0_86]) ).
cnf(c_0_113,plain,
( ~ ssList(X1)
| segmentP(X1,nil) ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_114,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_55])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC388+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n018.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 21 08:22:44 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.48 Running first-order theorem proving
% 0.18/0.48 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
% 31.48/5.84 % Version: 3.5.1
% 31.48/5.84 % Preprocessing class: FSLSSMSSSSSNFFN.
% 31.48/5.84 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 31.48/5.84 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 31.48/5.84 % Starting new_bool_3 with 300s (1) cores
% 31.48/5.84 % Starting new_bool_1 with 300s (1) cores
% 31.48/5.84 % Starting sh5l with 300s (1) cores
% 31.48/5.84 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1436899 completed with status 0
% 31.48/5.84 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 31.48/5.84 % Preprocessing class: FSLSSMSSSSSNFFN.
% 31.48/5.84 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 31.48/5.84 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 31.48/5.84 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 31.48/5.84 % No SInE strategy applied
% 31.48/5.84 % Search class: FGHSF-FSLM21-MFFFFFNN
% 31.48/5.84 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 31.48/5.84 % Starting SubtermCWHack with 136s (1) cores
% 31.48/5.84 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 31.48/5.84 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 31.48/5.84 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 31.48/5.84 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 31.48/5.84 % G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with pid 1436908 completed with status 0
% 31.48/5.84 % Result found by G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d
% 31.48/5.84 % Preprocessing class: FSLSSMSSSSSNFFN.
% 31.48/5.84 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 31.48/5.84 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 31.48/5.84 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 31.48/5.84 % No SInE strategy applied
% 31.48/5.84 % Search class: FGHSF-FSLM21-MFFFFFNN
% 31.48/5.84 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 31.48/5.84 % Starting SubtermCWHack with 136s (1) cores
% 31.48/5.84 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 31.48/5.84 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 31.48/5.84 % Preprocessing time : 0.006 s
% 31.48/5.84
% 31.48/5.84 % Proof found!
% 31.48/5.84 % SZS status Theorem
% 31.48/5.84 % SZS output start CNFRefutation
% See solution above
% 31.48/5.84 % Parsed axioms : 96
% 31.48/5.84 % Removed by relevancy pruning/SinE : 0
% 31.48/5.84 % Initial clauses : 200
% 31.48/5.84 % Removed in clause preprocessing : 2
% 31.48/5.84 % Initial clauses in saturation : 198
% 31.48/5.84 % Processed clauses : 8267
% 31.48/5.84 % ...of these trivial : 18
% 31.48/5.84 % ...subsumed : 6314
% 31.48/5.84 % ...remaining for further processing : 1935
% 31.48/5.84 % Other redundant clauses eliminated : 478
% 31.48/5.84 % Clauses deleted for lack of memory : 0
% 31.48/5.84 % Backward-subsumed : 90
% 31.48/5.84 % Backward-rewritten : 1103
% 31.48/5.84 % Generated clauses : 50750
% 31.48/5.84 % ...of the previous two non-redundant : 48981
% 31.48/5.84 % ...aggressively subsumed : 0
% 31.48/5.84 % Contextual simplify-reflections : 1154
% 31.48/5.84 % Paramodulations : 50054
% 31.48/5.84 % Factorizations : 0
% 31.48/5.84 % NegExts : 0
% 31.48/5.84 % Equation resolutions : 685
% 31.48/5.84 % Disequality decompositions : 0
% 31.48/5.84 % Total rewrite steps : 30322
% 31.48/5.84 % ...of those cached : 30275
% 31.48/5.84 % Propositional unsat checks : 0
% 31.48/5.84 % Propositional check models : 0
% 31.48/5.84 % Propositional check unsatisfiable : 0
% 31.48/5.84 % Propositional clauses : 0
% 31.48/5.84 % Propositional clauses after purity: 0
% 31.48/5.84 % Propositional unsat core size : 0
% 31.48/5.84 % Propositional preprocessing time : 0.000
% 31.48/5.84 % Propositional encoding time : 0.000
% 31.48/5.84 % Propositional solver time : 0.000
% 31.48/5.84 % Success case prop preproc time : 0.000
% 31.48/5.84 % Success case prop encoding time : 0.000
% 31.48/5.84 % Success case prop solver time : 0.000
% 31.48/5.84 % Current number of processed clauses : 725
% 31.48/5.84 % Positive orientable unit clauses : 29
% 31.48/5.84 % Positive unorientable unit clauses: 0
% 31.48/5.84 % Negative unit clauses : 4
% 31.48/5.84 % Non-unit-clauses : 692
% 31.48/5.84 % Current number of unprocessed clauses: 40600
% 31.48/5.84 % ...number of literals in the above : 306279
% 31.48/5.84 % Current number of archived formulas : 0
% 31.48/5.84 % Current number of archived clauses : 1204
% 31.48/5.84 % Clause-clause subsumption calls (NU) : 516926
% 31.48/5.84 % Rec. Clause-clause subsumption calls : 190434
% 31.48/5.84 % Non-unit clause-clause subsumptions : 7241
% 31.48/5.84 % Unit Clause-clause subsumption calls : 5144
% 31.48/5.84 % Rewrite failures with RHS unbound : 0
% 31.48/5.84 % BW rewrite match attempts : 11
% 31.48/5.84 % BW rewrite match successes : 11
% 31.48/5.84 % Condensation attempts : 0
% 31.48/5.84 % Condensation successes : 0
% 31.48/5.84 % Termbank termtop insertions : 1214904
% 31.48/5.84 % Search garbage collected termcells : 4264
% 31.48/5.84
% 31.48/5.84 % -------------------------------------------------
% 31.48/5.84 % User time : 2.735 s
% 31.48/5.84 % System time : 0.063 s
% 31.48/5.84 % Total time : 2.798 s
% 31.48/5.84 % Maximum resident set size: 4268 pages
% 31.48/5.84
% 31.48/5.84 % -------------------------------------------------
% 31.48/5.84 % User time : 20.574 s
% 31.48/5.84 % System time : 0.606 s
% 31.48/5.84 % Total time : 21.181 s
% 31.48/5.84 % Maximum resident set size: 4608 pages
% 31.48/5.84 % E exiting
%------------------------------------------------------------------------------