%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SWC045+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 : n010.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 02:44:40 PM UTC 2026
% Result : Theorem 137.33s 20.82s
% Output : CNFRefutation 137.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of formulae : 80 ( 13 unt; 0 def)
% Number of atoms : 324 ( 93 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 414 ( 170 ~; 165 |; 32 &)
% ( 2 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 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; 0-2 aty)
% Number of variables : 144 ( 0 sgn 71 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ? [X5] :
( ( ( memberP(X3,X5)
& ! [X6] :
( ssList(X6)
=> ~ segmentP(X4,app(app(cons(X5,nil),X6),cons(X5,nil))) ) )
| ( ? [X6] :
( segmentP(X4,app(app(cons(X5,nil),X6),cons(X5,nil)))
& ssList(X6) )
& ~ memberP(X3,X5) ) )
& ssItem(X5) )
| nil = X1
| X1 != X3
| X2 != X4
| nil != X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
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(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(ax79,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X3,X2) = app(X1,X2)
=> X3 = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax79) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax21) ).
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(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
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(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
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(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(ax20,axiom,
! [X1] :
( ssList(X1)
=> ( ? [X2] :
( ? [X3] :
( cons(X3,X2) = X1
& ssItem(X3) )
& ssList(X2) )
| nil = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax20) ).
fof(c_0_15,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ? [X5] :
( ( ( memberP(X3,X5)
& ! [X6] :
( ssList(X6)
=> ~ segmentP(X4,app(app(cons(X5,nil),X6),cons(X5,nil))) ) )
| ( ? [X6] :
( segmentP(X4,app(app(cons(X5,nil),X6),cons(X5,nil)))
& ssList(X6) )
& ~ memberP(X3,X5) ) )
& ssItem(X5) )
| nil = X1
| X1 != X3
| X2 != X4
| nil != X2 ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_16,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])])])]) ).
fof(c_0_17,plain,
! [X227] :
( app(X227,nil) = X227
| ~ ssList(X227) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])])]) ).
fof(c_0_18,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ? [X5] :
( ( ( memberP(X3,X5)
& ! [X6] :
( ssList(X6)
=> ~ segmentP(X4,app(app(cons(X5,nil),X6),cons(X5,nil))) ) )
| ( ? [X6] :
( segmentP(X4,app(app(cons(X5,nil),X6),cons(X5,nil)))
& ssList(X6) )
& ~ memberP(X3,X5) ) )
& ssItem(X5) )
| nil = X1
| X1 != X3
| X2 != X4
| nil != X2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_19,plain,
! [X214,X215,X216] :
( X216 = X214
| app(X216,X215) != app(X214,X215)
| ~ ssList(X216)
| ~ ssList(X215)
| ~ ssList(X214) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax79])])])]) ).
fof(c_0_20,plain,
! [X135] :
( app(nil,X135) = X135
| ~ ssList(X135) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])]) ).
fof(c_0_21,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[ax21]) ).
fof(c_0_22,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_23,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X1,X2),X3) = app(X1,app(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
fof(c_0_26,negated_conjecture,
! [X255,X256] :
( ( ~ ssItem(X255)
| ~ memberP(esk50_0,X255)
| segmentP(esk51_0,app(app(cons(X255,nil),esk52_1(X255)),cons(X255,nil))) )
& ( ~ ssItem(X255)
| ~ memberP(esk50_0,X255)
| ssList(esk52_1(X255)) )
& ( ~ ssItem(X255)
| ~ segmentP(esk51_0,app(app(cons(X255,nil),X256),cons(X255,nil)))
| ~ ssList(X256)
| memberP(esk50_0,X255) )
& nil != esk48_0
& esk48_0 = esk50_0
& esk49_0 = esk51_0
& nil = esk49_0
& ssList(esk51_0)
& ssList(esk50_0)
& ssList(esk49_0)
& ssList(esk48_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_18])])])])])]) ).
cnf(c_0_27,plain,
( app(X3,X2) != app(X1,X2)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| X3 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_28,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_29,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])])])]) ).
fof(c_0_30,plain,
! [X111,X112] :
( ssList(cons(X112,X111))
| ~ ssItem(X112)
| ~ ssList(X111) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).
fof(c_0_31,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_21])])])]) ).
cnf(c_0_32,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| nil != app(X2,X1)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_33,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,app(nil,X2)) = app(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).
fof(c_0_34,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])])])]) ).
cnf(c_0_35,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_36,negated_conjecture,
nil = esk49_0,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_37,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != X2
| X1 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_25])]) ).
cnf(c_0_38,plain,
( ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_39,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ssList(cons(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_40,plain,
( nil != cons(X2,X1)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_41,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(app(nil,X1))
| app(X2,X1) != nil
| app(nil,X1) = nil ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_42,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_43,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| nil != X2
| nil != X1
| nil = app(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_44,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_45,negated_conjecture,
( ~ ssItem(X1)
| ~ memberP(esk50_0,X1)
| segmentP(esk51_0,app(app(cons(X1,nil),esk52_1(X1)),cons(X1,nil))) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_46,negated_conjecture,
esk51_0 = nil,
inference(rw,[status(thm)],[c_0_35,c_0_36]) ).
fof(c_0_47,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_48,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| cons(X1,app(X2,X3)) != X3 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]),c_0_40]) ).
cnf(c_0_49,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X2,X1) != nil
| app(nil,X1) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_25])]) ).
cnf(c_0_50,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_23,c_0_28]),c_0_25])]) ).
cnf(c_0_51,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ssList(cons(X1,app(X2,X3))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_38]),c_0_39]) ).
cnf(c_0_52,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_43])]),c_0_25])]) ).
cnf(c_0_53,plain,
( ~ segmentP(X2,X1)
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_54,negated_conjecture,
( ~ ssItem(X1)
| ~ memberP(esk50_0,X1)
| segmentP(nil,app(app(cons(X1,nil),esk52_1(X1)),cons(X1,nil))) ),
inference(rw,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_55,plain,
( ~ ssList(X1)
| segmentP(X1,nil) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_56,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| cons(X1,app(X2,app(X3,X4))) != X4 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_23]),c_0_42]) ).
cnf(c_0_57,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| app(nil,app(X1,X2)) = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_25])]),c_0_42]) ).
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_51,c_0_52]),c_0_25])]) ).
cnf(c_0_59,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(app(app(cons(X1,nil),esk52_1(X1)),cons(X1,nil)))
| ~ memberP(esk50_0,X1)
| app(app(cons(X1,nil),esk52_1(X1)),cons(X1,nil)) = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_25])]),c_0_55]) ).
fof(c_0_60,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_61,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| app(X1,cons(X2,nil)) != nil ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_25])])]),c_0_58]) ).
cnf(c_0_62,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(app(cons(X1,nil),esk52_1(X1)))
| ~ memberP(esk50_0,X1)
| app(app(cons(X1,nil),esk52_1(X1)),cons(X1,nil)) = nil ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_42]),c_0_58]) ).
cnf(c_0_63,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| X1 != X2
| memberP(cons(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
fof(c_0_64,plain,
! [X119] :
( ( ~ ssList(X119)
| nil = X119
| cons(esk45_1(X119),esk44_1(X119)) = X119 )
& ( ~ ssList(X119)
| nil = X119
| ssItem(esk45_1(X119)) )
& ( ~ ssList(X119)
| nil = X119
| ssList(esk44_1(X119)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax20])])])])]) ).
cnf(c_0_65,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(app(cons(X1,nil),esk52_1(X1)))
| ~ memberP(esk50_0,X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_66,negated_conjecture,
( ~ ssItem(X1)
| ~ memberP(esk50_0,X1)
| ssList(esk52_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_67,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| memberP(cons(X1,X2),X1) ),
inference(er,[status(thm)],[c_0_63]) ).
cnf(c_0_68,plain,
( ~ ssList(X1)
| nil = X1
| cons(esk45_1(X1),esk44_1(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_69,plain,
( ~ ssList(X1)
| nil = X1
| ssItem(esk45_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_70,plain,
( ~ ssList(X1)
| nil = X1
| ssList(esk44_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_71,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_72,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_73,negated_conjecture,
nil != esk48_0,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_74,negated_conjecture,
( ~ ssItem(X1)
| ~ memberP(esk50_0,X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_42]),c_0_66]),c_0_58]) ).
cnf(c_0_75,plain,
( ~ ssList(X1)
| memberP(X1,esk45_1(X1))
| nil = X1 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69]),c_0_70]) ).
cnf(c_0_76,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_77,negated_conjecture,
esk50_0 != nil,
inference(rw,[status(thm)],[c_0_73,c_0_72]) ).
cnf(c_0_78,negated_conjecture,
~ ssItem(esk45_1(esk50_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76])]),c_0_77]) ).
cnf(c_0_79,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_69]),c_0_76])]),c_0_77]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC045+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.42 % Computer : n010.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Mon Sep 21 07:51:56 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.53 Running first-order theorem proving
% 0.17/0.53 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
% 137.33/20.82 % Version: 3.5.1
% 137.33/20.82 % Preprocessing class: FSLSSMSSSSSNFFN.
% 137.33/20.82 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 137.33/20.82 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 137.33/20.82 % Starting new_bool_3 with 300s (1) cores
% 137.33/20.82 % Starting new_bool_1 with 300s (1) cores
% 137.33/20.82 % Starting sh5l with 300s (1) cores
% 137.33/20.82 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 408078 completed with status 0
% 137.33/20.82 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 137.33/20.82 % Preprocessing class: FSLSSMSSSSSNFFN.
% 137.33/20.82 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 137.33/20.82 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 137.33/20.82 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 137.33/20.82 % No SInE strategy applied
% 137.33/20.82 % Search class: FGHSF-FSLM21-MFFFFFNN
% 137.33/20.82 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 137.33/20.82 % Starting SubtermCWHack with 136s (1) cores
% 137.33/20.82 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 137.33/20.82 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 137.33/20.82 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 137.33/20.82 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 137.33/20.82 % G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with pid 408089 completed with status 0
% 137.33/20.82 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y
% 137.33/20.82 % Preprocessing class: FSLSSMSSSSSNFFN.
% 137.33/20.82 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 137.33/20.82 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 137.33/20.82 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 137.33/20.82 % No SInE strategy applied
% 137.33/20.82 % Search class: FGHSF-FSLM21-MFFFFFNN
% 137.33/20.82 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 137.33/20.82 % Starting SubtermCWHack with 136s (1) cores
% 137.33/20.82 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 137.33/20.82 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 137.33/20.82 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 137.33/20.82 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 137.33/20.82 % Preprocessing time : 0.003 s
% 137.33/20.82 % Presaturation interreduction done
% 137.33/20.82
% 137.33/20.82 % Proof found!
% 137.33/20.82 % SZS status Theorem
% 137.33/20.82 % SZS output start CNFRefutation
% See solution above
% 137.33/20.82 % Parsed axioms : 96
% 137.33/20.82 % Removed by relevancy pruning/SinE : 0
% 137.33/20.82 % Initial clauses : 201
% 137.33/20.82 % Removed in clause preprocessing : 2
% 137.33/20.82 % Initial clauses in saturation : 199
% 137.33/20.82 % Processed clauses : 46263
% 137.33/20.82 % ...of these trivial : 28
% 137.33/20.82 % ...subsumed : 41489
% 137.33/20.82 % ...remaining for further processing : 4746
% 137.33/20.82 % Other redundant clauses eliminated : 9207
% 137.33/20.82 % Clauses deleted for lack of memory : 0
% 137.33/20.82 % Backward-subsumed : 241
% 137.33/20.82 % Backward-rewritten : 8
% 137.33/20.82 % Generated clauses : 749292
% 137.33/20.82 % ...of the previous two non-redundant : 698149
% 137.33/20.82 % ...aggressively subsumed : 0
% 137.33/20.82 % Contextual simplify-reflections : 3476
% 137.33/20.82 % Paramodulations : 740026
% 137.33/20.82 % Factorizations : 0
% 137.33/20.82 % NegExts : 0
% 137.33/20.82 % Equation resolutions : 9268
% 137.33/20.82 % Disequality decompositions : 0
% 137.33/20.82 % Total rewrite steps : 374920
% 137.33/20.82 % ...of those cached : 374899
% 137.33/20.82 % Propositional unsat checks : 0
% 137.33/20.82 % Propositional check models : 0
% 137.33/20.82 % Propositional check unsatisfiable : 0
% 137.33/20.82 % Propositional clauses : 0
% 137.33/20.82 % Propositional clauses after purity: 0
% 137.33/20.82 % Propositional unsat core size : 0
% 137.33/20.82 % Propositional preprocessing time : 0.000
% 137.33/20.82 % Propositional encoding time : 0.000
% 137.33/20.82 % Propositional solver time : 0.000
% 137.33/20.82 % Success case prop preproc time : 0.000
% 137.33/20.82 % Success case prop encoding time : 0.000
% 137.33/20.82 % Success case prop solver time : 0.000
% 137.33/20.82 % Current number of processed clauses : 4282
% 137.33/20.82 % Positive orientable unit clauses : 22
% 137.33/20.82 % Positive unorientable unit clauses: 0
% 137.33/20.82 % Negative unit clauses : 4
% 137.33/20.82 % Non-unit-clauses : 4256
% 137.33/20.82 % Current number of unprocessed clauses: 651282
% 137.33/20.82 % ...number of literals in the above : 4958342
% 137.33/20.82 % Current number of archived formulas : 0
% 137.33/20.82 % Current number of archived clauses : 441
% 137.33/20.82 % Clause-clause subsumption calls (NU) : 5025356
% 137.33/20.82 % Rec. Clause-clause subsumption calls : 903404
% 137.33/20.82 % Non-unit clause-clause subsumptions : 34947
% 137.33/20.82 % Unit Clause-clause subsumption calls : 412
% 137.33/20.82 % Rewrite failures with RHS unbound : 0
% 137.33/20.82 % BW rewrite match attempts : 5
% 137.33/20.82 % BW rewrite match successes : 5
% 137.33/20.82 % Condensation attempts : 0
% 137.33/20.82 % Condensation successes : 0
% 137.33/20.82 % Termbank termtop insertions : 19805258
% 137.33/20.82 % Search garbage collected termcells : 4294
% 137.33/20.82
% 137.33/20.82 % -------------------------------------------------
% 137.33/20.82 % User time : 19.065 s
% 137.33/20.82 % System time : 0.621 s
% 137.33/20.82 % Total time : 19.687 s
% 137.33/20.82 % Maximum resident set size: 4272 pages
% 137.33/20.82
% 137.33/20.82 % -------------------------------------------------
% 137.33/20.82 % User time : 94.411 s
% 137.33/20.82 % System time : 2.770 s
% 137.33/20.82 % Total time : 97.181 s
% 137.33/20.82 % Maximum resident set size: 4864 pages
% 137.33/20.82 % E exiting
%------------------------------------------------------------------------------