%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC090+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 : n001.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 02:42:57 PM UTC 2026
% Result : Theorem 1.57s 0.68s
% Output : CNFRefutation 1.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 86 ( 26 unt; 0 def)
% Number of atoms : 287 ( 87 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 337 ( 136 ~; 128 |; 25 &)
% ( 3 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 110 ( 0 sgn 65 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ( app(X7,X6) != X3
| app(X6,X7) != X4 ) ) )
| ? [X5] :
( segmentP(X1,X5)
& segmentP(X2,X5)
& neq(X5,nil)
& ssList(X5) )
| ~ neq(X2,nil)
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
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(ax56,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( segmentP(X1,X2)
=> segmentP(app(app(X3,X1),X4),X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax56) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
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(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax84) ).
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(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax55,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax55) ).
fof(ax53,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( segmentP(X2,X3)
& segmentP(X1,X2) )
=> segmentP(X1,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax53) ).
fof(c_0_12,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ( app(X7,X6) != X3
| app(X6,X7) != X4 ) ) )
| ? [X5] :
( segmentP(X1,X5)
& segmentP(X2,X5)
& neq(X5,nil)
& ssList(X5) )
| ~ neq(X2,nil)
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_13,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ( app(X7,X6) != X3
| app(X6,X7) != X4 ) ) )
| ? [X5] :
( segmentP(X1,X5)
& segmentP(X2,X5)
& neq(X5,nil)
& ssList(X5) )
| ~ neq(X2,nil)
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_14,negated_conjecture,
! [X12] :
( app(esk6_0,esk5_0) = esk3_0
& app(esk5_0,esk6_0) = esk4_0
& ssList(esk6_0)
& ssList(esk5_0)
& ( ~ segmentP(esk1_0,X12)
| ~ segmentP(esk2_0,X12)
| ~ neq(X12,nil)
| ~ ssList(X12) )
& neq(esk2_0,nil)
& esk1_0 = esk3_0
& esk2_0 = esk4_0
& ssList(esk4_0)
& ssList(esk3_0)
& ssList(esk2_0)
& ssList(esk1_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_13])])])])]) ).
fof(c_0_15,plain,
! [X32,X33] :
( ( ~ ssList(X32)
| ~ ssList(X33)
| nil = app(X32,X33)
| nil != X32
| nil != X33 )
& ( ~ ssList(X32)
| ~ ssList(X33)
| nil != app(X32,X33)
| nil = X32 )
& ( ~ ssList(X32)
| ~ ssList(X33)
| nil != app(X32,X33)
| nil = X33 ) ),
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_16,negated_conjecture,
app(esk5_0,esk6_0) = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_17,negated_conjecture,
esk2_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_18,plain,
! [X47,X48,X49,X50] :
( segmentP(app(app(X49,X47),X50),X48)
| ~ segmentP(X47,X48)
| ~ ssList(X50)
| ~ ssList(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)],[ax56])])])]) ).
fof(c_0_19,plain,
! [X20] :
( app(nil,X20) = X20
| ~ ssList(X20) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])]) ).
cnf(c_0_20,negated_conjecture,
app(esk6_0,esk5_0) = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,negated_conjecture,
esk1_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| nil != app(X2,X1)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,negated_conjecture,
app(esk5_0,esk6_0) = esk2_0,
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_24,negated_conjecture,
ssList(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_25,negated_conjecture,
ssList(esk6_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_26,plain,
! [X21,X22,X23] :
( X23 = X21
| app(X23,X22) != app(X21,X22)
| ~ ssList(X23)
| ~ ssList(X22)
| ~ ssList(X21) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax79])])])]) ).
fof(c_0_27,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
cnf(c_0_28,plain,
( ~ segmentP(X1,X2)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| segmentP(app(app(X3,X1),X4),X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_29,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_30,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
fof(c_0_31,plain,
! [X34] :
( app(X34,nil) = X34
| ~ ssList(X34) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])])]) ).
cnf(c_0_32,negated_conjecture,
app(esk6_0,esk5_0) = esk1_0,
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_33,negated_conjecture,
( esk2_0 != nil
| esk6_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25])]) ).
cnf(c_0_34,plain,
( app(X3,X2) != app(X1,X2)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| X3 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_35,plain,
! [X29,X30,X31] :
( app(app(X29,X30),X31) = app(X29,app(X30,X31))
| ~ ssList(X31)
| ~ ssList(X30)
| ~ ssList(X29) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])])]) ).
fof(c_0_36,plain,
! [X15,X16] :
( ssList(app(X15,X16))
| ~ ssList(X16)
| ~ ssList(X15) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).
fof(c_0_37,plain,
! [X55,X56] :
( ( ~ ssList(X55)
| ~ ssList(X56)
| neq(X55,X56)
| X55 = X56 )
& ( ~ ssList(X55)
| ~ ssList(X56)
| X55 != X56
| ~ neq(X55,X56) ) ),
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_38,plain,
( ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ segmentP(X1,X3)
| segmentP(app(X1,X2),X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]) ).
fof(c_0_39,plain,
! [X46] :
( segmentP(X46,X46)
| ~ ssList(X46) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax55])])]) ).
cnf(c_0_40,negated_conjecture,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ segmentP(esk6_0,X2)
| segmentP(app(esk2_0,X1),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_23]),c_0_24]),c_0_25])]) ).
cnf(c_0_41,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_42,negated_conjecture,
ssList(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_43,negated_conjecture,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ segmentP(esk5_0,X2)
| segmentP(app(esk1_0,X1),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_32]),c_0_25]),c_0_24])]) ).
cnf(c_0_44,negated_conjecture,
ssList(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_45,negated_conjecture,
( esk2_0 != nil
| app(esk5_0,nil) = esk2_0 ),
inference(spm,[status(thm)],[c_0_23,c_0_33]) ).
cnf(c_0_46,negated_conjecture,
( esk2_0 != nil
| app(nil,esk5_0) = esk1_0 ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_47,negated_conjecture,
( ~ ssList(X1)
| app(X1,esk6_0) != esk2_0
| X1 = esk5_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_23]),c_0_24]),c_0_25])]) ).
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_35]) ).
cnf(c_0_49,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_50,negated_conjecture,
( ~ segmentP(esk1_0,X1)
| ~ segmentP(esk2_0,X1)
| ~ neq(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_51,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_52,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(esk6_0,X1)
| segmentP(esk1_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_32]),c_0_24]),c_0_25])]) ).
cnf(c_0_53,plain,
( ~ ssList(X1)
| segmentP(X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_54,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(esk6_0,X1)
| segmentP(esk2_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_30]),c_0_42])]) ).
cnf(c_0_55,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(esk5_0,X1)
| segmentP(esk1_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_41]),c_0_30]),c_0_44])]) ).
fof(c_0_56,plain,
! [X41,X42,X43] :
( segmentP(X41,X43)
| ~ segmentP(X42,X43)
| ~ segmentP(X41,X42)
| ~ ssList(X43)
| ~ ssList(X42)
| ~ ssList(X41) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax53])])])]) ).
cnf(c_0_57,negated_conjecture,
neq(esk2_0,nil),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_58,negated_conjecture,
( esk2_0 != nil
| esk5_0 = esk2_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_45]),c_0_24])]) ).
cnf(c_0_59,negated_conjecture,
( esk2_0 != nil
| esk5_0 = esk1_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_46]),c_0_24])]) ).
cnf(c_0_60,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,app(X2,esk6_0)) != esk2_0
| app(X1,X2) = esk5_0 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_25])]),c_0_49]) ).
cnf(c_0_61,negated_conjecture,
( ~ ssList(X1)
| app(esk5_0,app(esk6_0,X1)) = app(esk2_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_23]),c_0_25]),c_0_24])]) ).
cnf(c_0_62,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(esk2_0,X1)
| ~ segmentP(esk1_0,X1)
| X1 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_30])]) ).
cnf(c_0_63,negated_conjecture,
segmentP(esk1_0,esk6_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_25])]) ).
cnf(c_0_64,negated_conjecture,
segmentP(esk2_0,esk6_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_53]),c_0_25])]) ).
cnf(c_0_65,negated_conjecture,
( ~ ssList(X1)
| app(esk6_0,app(esk5_0,X1)) = app(esk1_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_32]),c_0_24]),c_0_25])]) ).
cnf(c_0_66,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_48,c_0_29]),c_0_30])]) ).
cnf(c_0_67,negated_conjecture,
segmentP(esk1_0,esk5_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_53]),c_0_24])]) ).
cnf(c_0_68,plain,
( ~ segmentP(X2,X3)
| ~ segmentP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| segmentP(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_69,negated_conjecture,
( ~ segmentP(esk2_0,esk2_0)
| ~ segmentP(esk1_0,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_57]),c_0_42])]) ).
cnf(c_0_70,negated_conjecture,
( esk2_0 != nil
| esk1_0 = esk2_0 ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_71,negated_conjecture,
( app(esk2_0,esk6_0) != esk2_0
| esk5_0 = esk2_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_23]),c_0_25]),c_0_24])]) ).
cnf(c_0_72,negated_conjecture,
esk6_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]),c_0_25])]) ).
cnf(c_0_73,negated_conjecture,
app(esk2_0,nil) = esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_41]),c_0_23]),c_0_30]),c_0_25])]) ).
cnf(c_0_74,negated_conjecture,
app(esk6_0,esk2_0) = app(esk1_0,esk6_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_23]),c_0_25])]) ).
cnf(c_0_75,negated_conjecture,
app(nil,esk2_0) = esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_23]),c_0_25]),c_0_24])]) ).
cnf(c_0_76,negated_conjecture,
app(esk1_0,nil) = esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_41]),c_0_32]),c_0_30]),c_0_24])]) ).
cnf(c_0_77,negated_conjecture,
( ~ segmentP(esk2_0,esk5_0)
| esk5_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_67]),c_0_24])]) ).
cnf(c_0_78,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(X1,esk1_0)
| segmentP(X1,esk5_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_67]),c_0_24]),c_0_44])]) ).
cnf(c_0_79,negated_conjecture,
( ~ segmentP(esk2_0,esk2_0)
| esk2_0 != nil ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_80,negated_conjecture,
esk5_0 = esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_72]),c_0_73])]) ).
cnf(c_0_81,negated_conjecture,
esk1_0 = esk2_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_72]),c_0_75]),c_0_72]),c_0_76]) ).
cnf(c_0_82,negated_conjecture,
( ~ segmentP(esk2_0,esk1_0)
| esk5_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_42])]) ).
cnf(c_0_83,negated_conjecture,
esk2_0 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_53]),c_0_42])]) ).
cnf(c_0_84,negated_conjecture,
segmentP(esk2_0,esk2_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_80]),c_0_81]) ).
cnf(c_0_85,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_82,c_0_80]),c_0_83]),c_0_81]),c_0_84])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC090+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.35 % Computer : n001.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 08:00:29 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.43 Running first-order theorem proving
% 0.14/0.43 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
% 1.57/0.68 % Version: 3.5.1
% 1.57/0.68 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.57/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.57/0.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.57/0.68 % Starting new_bool_3 with 300s (1) cores
% 1.57/0.68 % Starting new_bool_1 with 300s (1) cores
% 1.57/0.68 % Starting sh5l with 300s (1) cores
% 1.57/0.68 % new_bool_1 with pid 2619480 completed with status 0
% 1.57/0.68 % Result found by new_bool_1
% 1.57/0.68 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.57/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.57/0.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.57/0.68 % Starting new_bool_3 with 300s (1) cores
% 1.57/0.68 % Starting new_bool_1 with 300s (1) cores
% 1.57/0.68 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 1.57/0.68 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.57/0.68 % Search class: FGHSF-FFMM21-MFFFFFNN
% 1.57/0.68 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 1.57/0.68 % Starting SubtermCWHack with 31s (1) cores
% 1.57/0.68 % SubtermCWHack with pid 2619482 completed with status 0
% 1.57/0.68 % Result found by SubtermCWHack
% 1.57/0.68 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.57/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.57/0.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.57/0.68 % Starting new_bool_3 with 300s (1) cores
% 1.57/0.68 % Starting new_bool_1 with 300s (1) cores
% 1.57/0.68 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 1.57/0.68 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.57/0.68 % Search class: FGHSF-FFMM21-MFFFFFNN
% 1.57/0.68 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 1.57/0.68 % Starting SubtermCWHack with 31s (1) cores
% 1.57/0.68 % Preprocessing time : 0.003 s
% 1.57/0.68
% 1.57/0.68 % Proof found!
% 1.57/0.68 % SZS status Theorem
% 1.57/0.68 % SZS output start CNFRefutation
% See solution above
% 1.57/0.68 % Parsed axioms : 96
% 1.57/0.68 % Removed by relevancy pruning/SinE : 70
% 1.57/0.68 % Initial clauses : 50
% 1.57/0.68 % Removed in clause preprocessing : 0
% 1.57/0.68 % Initial clauses in saturation : 50
% 1.57/0.68 % Processed clauses : 1647
% 1.57/0.68 % ...of these trivial : 58
% 1.57/0.68 % ...subsumed : 1091
% 1.57/0.68 % ...remaining for further processing : 497
% 1.57/0.68 % Other redundant clauses eliminated : 24
% 1.57/0.68 % Clauses deleted for lack of memory : 0
% 1.57/0.68 % Backward-subsumed : 42
% 1.57/0.68 % Backward-rewritten : 290
% 1.57/0.68 % Generated clauses : 6680
% 1.57/0.68 % ...of the previous two non-redundant : 6127
% 1.57/0.68 % ...aggressively subsumed : 0
% 1.57/0.68 % Contextual simplify-reflections : 32
% 1.57/0.68 % Paramodulations : 6652
% 1.57/0.68 % Factorizations : 0
% 1.57/0.68 % NegExts : 0
% 1.57/0.68 % Equation resolutions : 29
% 1.57/0.68 % Disequality decompositions : 0
% 1.57/0.68 % Total rewrite steps : 8529
% 1.57/0.68 % ...of those cached : 8484
% 1.57/0.68 % Propositional unsat checks : 0
% 1.57/0.68 % Propositional check models : 0
% 1.57/0.68 % Propositional check unsatisfiable : 0
% 1.57/0.68 % Propositional clauses : 0
% 1.57/0.68 % Propositional clauses after purity: 0
% 1.57/0.68 % Propositional unsat core size : 0
% 1.57/0.68 % Propositional preprocessing time : 0.000
% 1.57/0.68 % Propositional encoding time : 0.000
% 1.57/0.68 % Propositional solver time : 0.000
% 1.57/0.68 % Success case prop preproc time : 0.000
% 1.57/0.68 % Success case prop encoding time : 0.000
% 1.57/0.68 % Success case prop solver time : 0.000
% 1.57/0.68 % Current number of processed clauses : 160
% 1.57/0.68 % Positive orientable unit clauses : 28
% 1.57/0.68 % Positive unorientable unit clauses: 0
% 1.57/0.68 % Negative unit clauses : 7
% 1.57/0.68 % Non-unit-clauses : 125
% 1.57/0.68 % Current number of unprocessed clauses: 4473
% 1.57/0.68 % ...number of literals in the above : 20698
% 1.57/0.68 % Current number of archived formulas : 0
% 1.57/0.68 % Current number of archived clauses : 332
% 1.57/0.68 % Clause-clause subsumption calls (NU) : 28052
% 1.57/0.68 % Rec. Clause-clause subsumption calls : 16343
% 1.57/0.68 % Non-unit clause-clause subsumptions : 712
% 1.57/0.68 % Unit Clause-clause subsumption calls : 849
% 1.57/0.68 % Rewrite failures with RHS unbound : 0
% 1.57/0.68 % BW rewrite match attempts : 29
% 1.57/0.68 % BW rewrite match successes : 14
% 1.57/0.68 % Condensation attempts : 0
% 1.57/0.68 % Condensation successes : 0
% 1.57/0.68 % Termbank termtop insertions : 110530
% 1.57/0.68 % Search garbage collected termcells : 1535
% 1.57/0.68
% 1.57/0.68 % -------------------------------------------------
% 1.57/0.68 % User time : 0.205 s
% 1.57/0.68 % System time : 0.009 s
% 1.57/0.68 % Total time : 0.214 s
% 1.57/0.68 % Maximum resident set size: 3760 pages
% 1.57/0.68
% 1.57/0.68 % -------------------------------------------------
% 1.57/0.68 % User time : 0.214 s
% 1.57/0.68 % System time : 0.013 s
% 1.57/0.68 % Total time : 0.227 s
% 1.57/0.68 % Maximum resident set size: 4608 pages
% 1.57/0.68 % E exiting
%------------------------------------------------------------------------------