%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC117+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 : n004.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 02:43:04 PM UTC 2026
% Result : Theorem 13.54s 2.28s
% Output : CNFRefutation 13.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 32
% Syntax : Number of formulae : 202 ( 53 unt; 0 def)
% Number of atoms : 666 ( 171 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 792 ( 328 ~; 319 |; 44 &)
% ( 7 <=>; 94 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 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 : 282 ( 1 sgn 140 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( segmentP(X2,X1)
& neq(X1,nil) )
| ( nil = X1
& nil = X2 )
| ? [X5] :
( equalelemsP(X5)
& segmentP(X5,X3)
& segmentP(X4,X5)
& neq(X3,X5)
& ssList(X5) )
| ~ equalelemsP(X3)
| ~ segmentP(X4,X3)
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
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(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(ax50,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( rearsegP(X1,X2)
=> rearsegP(app(X3,X1),X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax50) ).
fof(ax51,axiom,
! [X1] :
( ssList(X1)
=> rearsegP(X1,nil) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax51) ).
fof(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(ax43,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( frontsegP(X1,X2)
=> frontsegP(app(X1,X3),X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax43) ).
fof(ax45,axiom,
! [X1] :
( ssList(X1)
=> frontsegP(X1,nil) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax45) ).
fof(ax6,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( rearsegP(X1,X2)
<=> ? [X3] :
( app(X3,X2) = X1
& ssList(X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax6) ).
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(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax80,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X2,X3) = app(X2,X1)
=> X3 = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax80) ).
fof(ax42,axiom,
! [X1] :
( ssList(X1)
=> frontsegP(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax42) ).
fof(ax46,axiom,
! [X1] :
( ssList(X1)
=> ( frontsegP(nil,X1)
<=> nil = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax46) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax85,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> hd(app(X1,X2)) = hd(X1) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax83) ).
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(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(ax78,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax78) ).
fof(ax24,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax24) ).
fof(ax86,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> tl(app(X1,X2)) = app(tl(X1),X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax86) ).
fof(ax22,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(ax81,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax81) ).
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(ax55,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax55) ).
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(ax57,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,nil) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax57) ).
fof(ax21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax21) ).
fof(ax73,axiom,
! [X1] :
( ssItem(X1)
=> equalelemsP(cons(X1,nil)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax73) ).
fof(c_0_32,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( segmentP(X2,X1)
& neq(X1,nil) )
| ( nil = X1
& nil = X2 )
| ? [X5] :
( equalelemsP(X5)
& segmentP(X5,X3)
& segmentP(X4,X5)
& neq(X3,X5)
& ssList(X5) )
| ~ equalelemsP(X3)
| ~ segmentP(X4,X3)
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_33,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( segmentP(X2,X1)
& neq(X1,nil) )
| ( nil = X1
& nil = X2 )
| ? [X5] :
( equalelemsP(X5)
& segmentP(X5,X3)
& segmentP(X4,X5)
& neq(X3,X5)
& ssList(X5) )
| ~ equalelemsP(X3)
| ~ segmentP(X4,X3)
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_32]) ).
fof(c_0_34,negated_conjecture,
! [X255] :
( ( ~ segmentP(esk49_0,esk48_0)
| ~ neq(esk48_0,nil) )
& ( nil != esk48_0
| nil != esk49_0 )
& ( ~ equalelemsP(X255)
| ~ segmentP(X255,esk50_0)
| ~ segmentP(esk51_0,X255)
| ~ neq(esk50_0,X255)
| ~ ssList(X255) )
& equalelemsP(esk50_0)
& 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_33])])])])]) ).
fof(c_0_35,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
cnf(c_0_36,negated_conjecture,
( ~ segmentP(esk49_0,esk48_0)
| ~ neq(esk48_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_37,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_38,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_39,negated_conjecture,
segmentP(esk51_0,esk50_0),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_40,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_35])])])])]) ).
cnf(c_0_41,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_42,negated_conjecture,
~ neq(esk50_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37]),c_0_38]),c_0_37]),c_0_39])]) ).
cnf(c_0_43,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_44,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_45,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_41,c_0_37]) ).
fof(c_0_46,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_47,negated_conjecture,
esk50_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]),c_0_45])]) ).
cnf(c_0_48,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_49,plain,
! [X179,X180,X181] :
( rearsegP(app(X181,X179),X180)
| ~ rearsegP(X179,X180)
| ~ ssList(X181)
| ~ ssList(X180)
| ~ ssList(X179) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax50])])])]) ).
fof(c_0_50,plain,
! [X182] :
( rearsegP(X182,nil)
| ~ ssList(X182) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax51])])]) ).
cnf(c_0_51,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_46]) ).
cnf(c_0_52,negated_conjecture,
segmentP(esk51_0,nil),
inference(rw,[status(thm)],[c_0_39,c_0_47]) ).
cnf(c_0_53,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_48,c_0_38]) ).
fof(c_0_54,plain,
! [X227] :
( app(X227,nil) = X227
| ~ ssList(X227) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])])]) ).
cnf(c_0_55,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X1,X2)
| ssList(esk8_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
fof(c_0_56,plain,
! [X164,X165,X166] :
( frontsegP(app(X164,X166),X165)
| ~ frontsegP(X164,X165)
| ~ ssList(X166)
| ~ ssList(X165)
| ~ ssList(X164) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax43])])])]) ).
fof(c_0_57,plain,
! [X171] :
( frontsegP(X171,nil)
| ~ ssList(X171) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax45])])]) ).
cnf(c_0_58,plain,
( ~ rearsegP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| rearsegP(app(X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_59,plain,
( ~ ssList(X1)
| rearsegP(X1,nil) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_60,negated_conjecture,
app(app(esk8_2(esk51_0,nil),nil),esk9_2(esk51_0,nil)) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_44]),c_0_53])]) ).
cnf(c_0_61,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_62,negated_conjecture,
ssList(esk8_2(esk51_0,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_52]),c_0_44]),c_0_53])]) ).
cnf(c_0_63,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X1,X2)
| ssList(esk9_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_64,plain,
( ~ frontsegP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| frontsegP(app(X1,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_65,plain,
( ~ ssList(X1)
| frontsegP(X1,nil) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
fof(c_0_66,plain,
! [X24,X25,X27] :
( ( ~ ssList(X24)
| ~ ssList(X25)
| rearsegP(X24,X25)
| app(X27,X25) != X24
| ~ ssList(X27) )
& ( ~ ssList(X24)
| ~ ssList(X25)
| ~ rearsegP(X24,X25)
| app(esk7_2(X24,X25),X25) = X24 )
& ( ~ ssList(X24)
| ~ ssList(X25)
| ~ rearsegP(X24,X25)
| ssList(esk7_2(X24,X25)) ) ),
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)],[ax6])])])])])]) ).
cnf(c_0_67,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| rearsegP(app(X1,X2),nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_44])]) ).
cnf(c_0_68,negated_conjecture,
app(esk8_2(esk51_0,nil),esk9_2(esk51_0,nil)) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62])]) ).
cnf(c_0_69,negated_conjecture,
ssList(esk9_2(esk51_0,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_52]),c_0_44]),c_0_53])]) ).
fof(c_0_70,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_71,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| frontsegP(app(X1,X2),nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_44])]) ).
cnf(c_0_72,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| app(esk7_2(X1,X2),X2) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_73,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| ssList(esk7_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_74,negated_conjecture,
rearsegP(esk51_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_62]),c_0_69])]) ).
fof(c_0_75,plain,
! [X135] :
( app(nil,X135) = X135
| ~ ssList(X135) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])]) ).
cnf(c_0_76,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ frontsegP(X2,X1)
| app(X1,esk6_2(X2,X1)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_77,negated_conjecture,
frontsegP(esk51_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_68]),c_0_69]),c_0_62])]) ).
cnf(c_0_78,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| ssList(esk6_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_79,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| app(X2,X1) != X3
| ~ ssList(X1)
| frontsegP(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_80,plain,
( ~ ssList(X1)
| app(esk7_2(X1,nil),nil) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_59]),c_0_44])]) ).
cnf(c_0_81,plain,
( ~ ssList(X1)
| ssList(esk7_2(X1,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_59]),c_0_44])]) ).
cnf(c_0_82,negated_conjecture,
app(esk7_2(esk51_0,nil),nil) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_74]),c_0_44]),c_0_53])]) ).
cnf(c_0_83,negated_conjecture,
ssList(esk7_2(esk51_0,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_44]),c_0_53])]) ).
cnf(c_0_84,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_85,negated_conjecture,
app(nil,esk6_2(esk51_0,nil)) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_53]),c_0_44])]) ).
cnf(c_0_86,negated_conjecture,
ssList(esk6_2(esk51_0,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_77]),c_0_44]),c_0_53])]) ).
fof(c_0_87,plain,
! [X217,X218,X219] :
( X219 = X217
| app(X218,X219) != app(X218,X217)
| ~ ssList(X219)
| ~ ssList(X218)
| ~ ssList(X217) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax80])])])]) ).
cnf(c_0_88,plain,
( ~ ssList(X1)
| frontsegP(X1,esk7_2(X1,nil)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_44])])]),c_0_81]) ).
cnf(c_0_89,negated_conjecture,
esk7_2(esk51_0,nil) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_82]),c_0_83])]) ).
cnf(c_0_90,negated_conjecture,
esk6_2(esk51_0,nil) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_86])]) ).
fof(c_0_91,plain,
! [X163] :
( frontsegP(X163,X163)
| ~ ssList(X163) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax42])])]) ).
cnf(c_0_92,plain,
( app(X2,X3) != app(X2,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| X3 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_93,negated_conjecture,
frontsegP(esk51_0,esk51_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_53])]) ).
cnf(c_0_94,plain,
( ~ ssList(X1)
| ssList(esk6_2(X1,esk7_2(X1,nil))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_88]),c_0_81]) ).
cnf(c_0_95,plain,
( ~ ssList(X4)
| ~ ssList(X3)
| app(app(X1,X3),X2) != X4
| ~ ssList(X2)
| ~ ssList(X1)
| segmentP(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_96,negated_conjecture,
app(nil,esk51_0) = esk51_0,
inference(rw,[status(thm)],[c_0_85,c_0_90]) ).
cnf(c_0_97,plain,
( ~ ssList(X1)
| frontsegP(X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_98,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X2,X1) != X2
| X1 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_61]),c_0_44])]) ).
cnf(c_0_99,negated_conjecture,
app(esk51_0,esk6_2(esk51_0,esk51_0)) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_93]),c_0_53])]) ).
cnf(c_0_100,negated_conjecture,
ssList(esk6_2(esk51_0,esk51_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_89]),c_0_53])]) ).
cnf(c_0_101,negated_conjecture,
( ~ ssList(X2)
| ~ ssList(X1)
| app(esk51_0,X2) != X1
| segmentP(X1,esk51_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_53]),c_0_44])]) ).
cnf(c_0_102,plain,
( ~ ssList(X1)
| app(X1,esk6_2(X1,X1)) = X1 ),
inference(spm,[status(thm)],[c_0_76,c_0_97]) ).
cnf(c_0_103,negated_conjecture,
esk6_2(esk51_0,esk51_0) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_53]),c_0_100])]) ).
fof(c_0_104,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_105,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_106,negated_conjecture,
( ~ ssList(X1)
| esk51_0 != X1
| segmentP(X1,esk51_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_103]),c_0_44]),c_0_53])]) ).
cnf(c_0_107,plain,
( ~ ssList(X1)
| nil != X1
| frontsegP(nil,X1) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
fof(c_0_108,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> hd(app(X1,X2)) = hd(X1) ) ) ),
inference(fof_simplification,[status(thm)],[ax85]) ).
cnf(c_0_109,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
cnf(c_0_110,negated_conjecture,
segmentP(esk51_0,esk51_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_106]),c_0_53])]) ).
fof(c_0_111,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_112,plain,
frontsegP(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_107]),c_0_44])]) ).
fof(c_0_113,plain,
! [X228,X229] :
( hd(app(X228,X229)) = hd(X228)
| nil = X228
| ~ ssList(X229)
| ~ ssList(X228) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_108])])])]) ).
fof(c_0_114,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_115,negated_conjecture,
( nil != esk48_0
| nil != esk49_0 ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_116,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(X3,X2) != X1
| segmentP(X1,X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_61]),c_0_44])]),c_0_109]) ).
cnf(c_0_117,negated_conjecture,
app(app(esk8_2(esk51_0,esk51_0),esk51_0),esk9_2(esk51_0,esk51_0)) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_110]),c_0_53])]) ).
cnf(c_0_118,negated_conjecture,
ssList(esk9_2(esk51_0,esk51_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_110]),c_0_53])]) ).
fof(c_0_119,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_120,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])])])]) ).
cnf(c_0_121,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| nil != app(X2,X1)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_122,plain,
app(nil,esk6_2(nil,nil)) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_112]),c_0_44])]) ).
cnf(c_0_123,plain,
ssList(esk6_2(nil,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_112]),c_0_44])]) ).
fof(c_0_124,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
inference(fof_simplification,[status(thm)],[ax78]) ).
fof(c_0_125,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
inference(fof_simplification,[status(thm)],[ax24]) ).
fof(c_0_126,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> tl(app(X1,X2)) = app(tl(X1),X2) ) ) ),
inference(fof_simplification,[status(thm)],[ax86]) ).
fof(c_0_127,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
inference(fof_simplification,[status(thm)],[ax22]) ).
cnf(c_0_128,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| hd(app(X1,X2)) = hd(X1)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
cnf(c_0_129,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X1,X2),X3) = app(X1,app(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_130,negated_conjecture,
( esk51_0 != nil
| esk50_0 != nil ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_115,c_0_37]),c_0_38]) ).
cnf(c_0_131,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| nil != app(X1,X2)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_132,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(app(esk8_2(esk51_0,esk51_0),esk51_0))
| esk51_0 != X1
| segmentP(X1,esk9_2(esk51_0,esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_118])]) ).
cnf(c_0_133,plain,
( ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
cnf(c_0_134,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ssList(cons(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_120]) ).
cnf(c_0_135,plain,
esk6_2(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_44]),c_0_123])]) ).
fof(c_0_136,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_124])])]) ).
fof(c_0_137,plain,
! [X127] :
( ssList(tl(X127))
| nil = X127
| ~ ssList(X127) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_125])])]) ).
fof(c_0_138,plain,
! [X230,X231] :
( tl(app(X230,X231)) = app(tl(X230),X231)
| nil = X230
| ~ ssList(X231)
| ~ ssList(X230) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_126])])])]) ).
fof(c_0_139,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_127])])]) ).
cnf(c_0_140,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(X1,X2) = nil
| hd(app(X1,app(X2,X3))) = hd(app(X1,X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_109]) ).
cnf(c_0_141,negated_conjecture,
( ~ ssList(X1)
| app(nil,app(esk51_0,X1)) = app(esk51_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_96]),c_0_53]),c_0_44])]) ).
cnf(c_0_142,negated_conjecture,
esk51_0 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_130,c_0_47])]) ).
cnf(c_0_143,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ssList(app(X1,app(X2,X3))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_129]),c_0_109]) ).
cnf(c_0_144,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(X1,app(X2,X3)) != nil
| app(X1,X2) = nil ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_129]),c_0_109]) ).
cnf(c_0_145,negated_conjecture,
( ~ ssList(app(esk8_2(esk51_0,esk51_0),esk51_0))
| segmentP(esk51_0,esk9_2(esk51_0,esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_132]),c_0_53])]) ).
cnf(c_0_146,negated_conjecture,
ssList(esk8_2(esk51_0,esk51_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_110]),c_0_53])]) ).
cnf(c_0_147,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| app(X1,X2) != X3
| ~ ssList(X1)
| rearsegP(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
fof(c_0_148,plain,
! [X220,X221] :
( cons(X221,X220) = app(cons(X221,nil),X220)
| ~ ssItem(X221)
| ~ ssList(X220) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])])]) ).
cnf(c_0_149,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ssList(cons(X1,app(X2,X3))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_133]),c_0_134]) ).
cnf(c_0_150,plain,
app(nil,nil) = nil,
inference(rw,[status(thm)],[c_0_122,c_0_135]) ).
cnf(c_0_151,plain,
( ~ ssList(X1)
| cons(hd(X1),tl(X1)) = X1
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_136]) ).
cnf(c_0_152,plain,
( ~ ssList(X1)
| ssList(tl(X1))
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_137]) ).
cnf(c_0_153,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| tl(app(X1,X2)) = app(tl(X1),X2)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_138]) ).
cnf(c_0_154,negated_conjecture,
app(esk51_0,nil) = esk51_0,
inference(rw,[status(thm)],[c_0_82,c_0_89]) ).
cnf(c_0_155,plain,
( ~ ssList(X1)
| ssItem(hd(X1))
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_139]) ).
cnf(c_0_156,negated_conjecture,
( ~ ssList(X1)
| hd(app(esk51_0,X1)) = hd(esk51_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_96]),c_0_96]),c_0_53]),c_0_44])]),c_0_142]) ).
cnf(c_0_157,negated_conjecture,
( ~ ssList(X1)
| ssList(app(esk51_0,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_141]),c_0_53]),c_0_44])]) ).
cnf(c_0_158,negated_conjecture,
( ~ ssList(X1)
| app(esk51_0,X1) != nil ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_141]),c_0_96]),c_0_53]),c_0_44])]),c_0_142]) ).
cnf(c_0_159,negated_conjecture,
segmentP(esk51_0,esk9_2(esk51_0,esk51_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_109]),c_0_53]),c_0_146])]) ).
fof(c_0_160,plain,
! [X190,X191,X192,X193] :
( segmentP(app(app(X192,X190),X193),X191)
| ~ segmentP(X190,X191)
| ~ ssList(X193)
| ~ ssList(X192)
| ~ ssList(X191)
| ~ ssList(X190) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax56])])])]) ).
fof(c_0_161,plain,
! [X189] :
( segmentP(X189,X189)
| ~ ssList(X189) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax55])])]) ).
cnf(c_0_162,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| rearsegP(app(X1,X2),X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_147]),c_0_109]) ).
cnf(c_0_163,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) = app(cons(X2,nil),X1) ),
inference(split_conjunct,[status(thm)],[c_0_148]) ).
cnf(c_0_164,plain,
( ~ ssItem(X1)
| ssList(cons(X1,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_150]),c_0_44])]) ).
cnf(c_0_165,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_151,c_0_128]),c_0_109]),c_0_131]) ).
cnf(c_0_166,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_152,c_0_153]),c_0_109]),c_0_131]) ).
cnf(c_0_167,negated_conjecture,
app(tl(esk51_0),nil) = tl(esk51_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_154]),c_0_44]),c_0_53])]),c_0_142]) ).
cnf(c_0_168,negated_conjecture,
( ~ ssList(X1)
| ssItem(hd(esk51_0)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_156]),c_0_157]),c_0_158]) ).
cnf(c_0_169,negated_conjecture,
ssList(esk9_2(esk51_0,esk9_2(esk51_0,esk51_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_159]),c_0_118]),c_0_53])]) ).
fof(c_0_170,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_171,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_172,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_160]) ).
cnf(c_0_173,plain,
( ~ ssList(X1)
| segmentP(X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_161]) ).
cnf(c_0_174,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| rearsegP(cons(X1,X2),X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_163]),c_0_164]) ).
cnf(c_0_175,negated_conjecture,
cons(hd(esk51_0),tl(esk51_0)) = esk51_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_154]),c_0_44]),c_0_53])]),c_0_142]) ).
cnf(c_0_176,negated_conjecture,
ssList(tl(esk51_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_167]),c_0_44]),c_0_53])]),c_0_142]) ).
cnf(c_0_177,negated_conjecture,
ssItem(hd(esk51_0)),
inference(spm,[status(thm)],[c_0_168,c_0_169]) ).
cnf(c_0_178,plain,
( app(X3,X2) != app(X1,X2)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| X3 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_170]) ).
cnf(c_0_179,negated_conjecture,
( ~ equalelemsP(X1)
| ~ segmentP(X1,esk50_0)
| ~ segmentP(esk51_0,X1)
| ~ neq(esk50_0,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_180,plain,
( ~ ssList(X1)
| segmentP(X1,nil) ),
inference(split_conjunct,[status(thm)],[c_0_171]) ).
cnf(c_0_181,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| segmentP(app(app(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_172,c_0_173]) ).
cnf(c_0_182,negated_conjecture,
rearsegP(esk51_0,tl(esk51_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_175]),c_0_176]),c_0_177])]) ).
cnf(c_0_183,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(cons(X2,nil))
| app(X1,X3) != cons(X2,X3)
| X1 = cons(X2,nil) ),
inference(spm,[status(thm)],[c_0_178,c_0_163]) ).
cnf(c_0_184,negated_conjecture,
( ~ neq(nil,X1)
| ~ ssList(X1)
| ~ segmentP(esk51_0,X1)
| ~ equalelemsP(X1) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_179,c_0_47]),c_0_47]),c_0_180]) ).
cnf(c_0_185,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| segmentP(app(X1,X2),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_84]),c_0_44])]) ).
cnf(c_0_186,negated_conjecture,
app(esk7_2(esk51_0,tl(esk51_0)),tl(esk51_0)) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_182]),c_0_176]),c_0_53])]) ).
cnf(c_0_187,negated_conjecture,
ssList(esk7_2(esk51_0,tl(esk51_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_182]),c_0_176]),c_0_53])]) ).
cnf(c_0_188,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| app(X1,X3) != cons(X2,X3)
| X1 = cons(X2,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_134]),c_0_44])]) ).
cnf(c_0_189,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(esk51_0,X1)
| ~ equalelemsP(X1)
| nil = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_43]),c_0_44])]) ).
cnf(c_0_190,negated_conjecture,
segmentP(esk51_0,esk7_2(esk51_0,tl(esk51_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_186]),c_0_176]),c_0_187])]) ).
cnf(c_0_191,negated_conjecture,
( ~ ssList(X1)
| app(X1,tl(esk51_0)) != esk51_0
| X1 = cons(hd(esk51_0),nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_188,c_0_175]),c_0_176]),c_0_177])]) ).
fof(c_0_192,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[ax21]) ).
cnf(c_0_193,negated_conjecture,
( ~ equalelemsP(esk7_2(esk51_0,tl(esk51_0)))
| esk7_2(esk51_0,tl(esk51_0)) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_190]),c_0_187])]) ).
cnf(c_0_194,negated_conjecture,
esk7_2(esk51_0,tl(esk51_0)) = cons(hd(esk51_0),nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_191,c_0_186]),c_0_187])]) ).
fof(c_0_195,plain,
! [X206] :
( equalelemsP(cons(X206,nil))
| ~ ssItem(X206) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax73])])]) ).
fof(c_0_196,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_192])])])]) ).
cnf(c_0_197,negated_conjecture,
( ~ equalelemsP(cons(hd(esk51_0),nil))
| cons(hd(esk51_0),nil) = nil ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_193,c_0_194]),c_0_194]) ).
cnf(c_0_198,plain,
( ~ ssItem(X1)
| equalelemsP(cons(X1,nil)) ),
inference(split_conjunct,[status(thm)],[c_0_195]) ).
cnf(c_0_199,plain,
( nil != cons(X2,X1)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_196]) ).
cnf(c_0_200,negated_conjecture,
cons(hd(esk51_0),nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_197,c_0_198]),c_0_177])]) ).
cnf(c_0_201,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_199,c_0_200]),c_0_44]),c_0_177])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC117+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n004.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 07:56:34 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.45 Running first-order theorem proving
% 0.16/0.45 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
% 13.54/2.28 % Version: 3.5.1
% 13.54/2.28 % Preprocessing class: FSLSSMSSSSSNFFN.
% 13.54/2.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.54/2.28 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 13.54/2.28 % Starting new_bool_3 with 300s (1) cores
% 13.54/2.28 % Starting new_bool_1 with 300s (1) cores
% 13.54/2.28 % Starting sh5l with 300s (1) cores
% 13.54/2.28 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2650936 completed with status 0
% 13.54/2.28 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 13.54/2.28 % Preprocessing class: FSLSSMSSSSSNFFN.
% 13.54/2.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.54/2.28 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 13.54/2.28 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 13.54/2.28 % No SInE strategy applied
% 13.54/2.28 % Search class: FGHSF-FSLM21-MFFFFFNN
% 13.54/2.28 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 13.54/2.28 % Starting SubtermCWHack with 136s (1) cores
% 13.54/2.28 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 13.54/2.28 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 13.54/2.28 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 13.54/2.28 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 13.54/2.28 % G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with pid 2650945 completed with status 0
% 13.54/2.28 % Result found by G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d
% 13.54/2.28 % Preprocessing class: FSLSSMSSSSSNFFN.
% 13.54/2.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.54/2.28 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 13.54/2.28 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 13.54/2.28 % No SInE strategy applied
% 13.54/2.28 % Search class: FGHSF-FSLM21-MFFFFFNN
% 13.54/2.28 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 13.54/2.28 % Starting SubtermCWHack with 136s (1) cores
% 13.54/2.28 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 13.54/2.28 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 13.54/2.28 % Preprocessing time : 0.006 s
% 13.54/2.28
% 13.54/2.28 % Proof found!
% 13.54/2.28 % SZS status Theorem
% 13.54/2.28 % SZS output start CNFRefutation
% See solution above
% 13.54/2.28 % Parsed axioms : 96
% 13.54/2.28 % Removed by relevancy pruning/SinE : 0
% 13.54/2.28 % Initial clauses : 201
% 13.54/2.28 % Removed in clause preprocessing : 2
% 13.54/2.28 % Initial clauses in saturation : 199
% 13.54/2.28 % Processed clauses : 7435
% 13.54/2.28 % ...of these trivial : 81
% 13.54/2.28 % ...subsumed : 5117
% 13.54/2.28 % ...remaining for further processing : 2237
% 13.54/2.28 % Other redundant clauses eliminated : 615
% 13.54/2.28 % Clauses deleted for lack of memory : 0
% 13.54/2.28 % Backward-subsumed : 155
% 13.54/2.28 % Backward-rewritten : 430
% 13.54/2.28 % Generated clauses : 33003
% 13.54/2.28 % ...of the previous two non-redundant : 28837
% 13.54/2.28 % ...aggressively subsumed : 0
% 13.54/2.28 % Contextual simplify-reflections : 812
% 13.54/2.28 % Paramodulations : 32151
% 13.54/2.28 % Factorizations : 0
% 13.54/2.28 % NegExts : 0
% 13.54/2.28 % Equation resolutions : 852
% 13.54/2.28 % Disequality decompositions : 0
% 13.54/2.28 % Total rewrite steps : 27507
% 13.54/2.28 % ...of those cached : 27239
% 13.54/2.28 % Propositional unsat checks : 0
% 13.54/2.28 % Propositional check models : 0
% 13.54/2.28 % Propositional check unsatisfiable : 0
% 13.54/2.28 % Propositional clauses : 0
% 13.54/2.28 % Propositional clauses after purity: 0
% 13.54/2.28 % Propositional unsat core size : 0
% 13.54/2.28 % Propositional preprocessing time : 0.000
% 13.54/2.28 % Propositional encoding time : 0.000
% 13.54/2.28 % Propositional solver time : 0.000
% 13.54/2.28 % Success case prop preproc time : 0.000
% 13.54/2.28 % Success case prop encoding time : 0.000
% 13.54/2.28 % Success case prop solver time : 0.000
% 13.54/2.28 % Current number of processed clauses : 1646
% 13.54/2.28 % Positive orientable unit clauses : 251
% 13.54/2.28 % Positive unorientable unit clauses: 0
% 13.54/2.28 % Negative unit clauses : 20
% 13.54/2.28 % Non-unit-clauses : 1375
% 13.54/2.28 % Current number of unprocessed clauses: 20581
% 13.54/2.28 % ...number of literals in the above : 145526
% 13.54/2.28 % Current number of archived formulas : 0
% 13.54/2.28 % Current number of archived clauses : 585
% 13.54/2.28 % Clause-clause subsumption calls (NU) : 655666
% 13.54/2.28 % Rec. Clause-clause subsumption calls : 189822
% 13.54/2.28 % Non-unit clause-clause subsumptions : 4979
% 13.54/2.28 % Unit Clause-clause subsumption calls : 15712
% 13.54/2.28 % Rewrite failures with RHS unbound : 0
% 13.54/2.28 % BW rewrite match attempts : 313
% 13.54/2.28 % BW rewrite match successes : 157
% 13.54/2.28 % Condensation attempts : 0
% 13.54/2.28 % Condensation successes : 0
% 13.54/2.28 % Termbank termtop insertions : 710459
% 13.54/2.28 % Search garbage collected termcells : 4296
% 13.54/2.28
% 13.54/2.28 % -------------------------------------------------
% 13.54/2.28 % User time : 1.752 s
% 13.54/2.28 % System time : 0.038 s
% 13.54/2.28 % Total time : 1.790 s
% 13.54/2.28 % Maximum resident set size: 4016 pages
% 13.54/2.28
% 13.54/2.28 % -------------------------------------------------
% 13.54/2.28 % User time : 8.298 s
% 13.54/2.28 % System time : 0.216 s
% 13.54/2.28 % Total time : 8.514 s
% 13.54/2.28 % Maximum resident set size: 4608 pages
% 13.54/2.28 % E exiting
%------------------------------------------------------------------------------