%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC066+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:42:50 PM UTC 2026
% Result : Theorem 229.72s 34.08s
% Output : CNFRefutation 229.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 34
% Syntax : Number of formulae : 231 ( 15 unt; 0 def)
% Number of atoms : 969 ( 208 equ)
% Maximal formula atoms : 27 ( 4 avg)
% Number of connectives : 1304 ( 566 ~; 561 |; 66 &)
% ( 8 <=>; 103 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 5 con; 0-2 aty)
% Number of variables : 400 ( 1 sgn 156 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax18,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax18) ).
fof(ax78,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax78) ).
fof(ax22,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(ax24,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SWC001+0.ax',ax86) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax83,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X1
& nil = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(ax21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax21) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax25,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> tl(cons(X2,X1)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax25) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( ? [X6] :
( segmentP(X1,X6)
& segmentP(X2,X6)
& neq(X6,nil)
& ssList(X6) )
| ~ neq(X2,nil) )
& ( nil = X1
| nil != X2 ) )
| ? [X5] :
( totalorderedP(X5)
& segmentP(X5,X3)
& segmentP(X4,X5)
& neq(X3,X5)
& ssList(X5) )
| ~ totalorderedP(X3)
| ~ segmentP(X4,X3)
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax81,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax81) ).
fof(ax53,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( segmentP(X2,X3)
& segmentP(X1,X2) )
=> segmentP(X1,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax53) ).
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/sandbox/benchmark/Axioms/SWC001+0.ax',ax7) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax75,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ? [X2] :
( hd(X1) = X2
& ssItem(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax75) ).
fof(ax82,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> app(app(X1,X2),X3) = app(X1,app(X2,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax82) ).
fof(ax55,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax55) ).
fof(ax54,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( segmentP(X2,X1)
& segmentP(X1,X2) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax54) ).
fof(ax6,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( rearsegP(X1,X2)
<=> ? [X3] :
( app(X3,X2) = X1
& ssList(X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax6) ).
fof(ax57,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,nil) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax57) ).
fof(ax47,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( rearsegP(X2,X3)
& rearsegP(X1,X2) )
=> rearsegP(X1,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax47) ).
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/sandbox/benchmark/Axioms/SWC001+0.ax',ax56) ).
fof(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(ax58,axiom,
! [X1] :
( ssList(X1)
=> ( segmentP(nil,X1)
<=> nil = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax58) ).
fof(ax5,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X1,X2)
<=> ? [X3] :
( app(X2,X3) = X1
& ssList(X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax5) ).
fof(ax44,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( frontsegP(cons(X1,X3),cons(X2,X4))
<=> ( frontsegP(X3,X4)
& X1 = X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax44) ).
fof(ax20,axiom,
! [X1] :
( ssList(X1)
=> ( ? [X2] :
( ? [X3] :
( cons(X3,X2) = X1
& ssItem(X3) )
& ssList(X2) )
| nil = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax20) ).
fof(ax27,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax27) ).
fof(ax40,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( frontsegP(X2,X3)
& frontsegP(X1,X2) )
=> frontsegP(X1,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax40) ).
fof(ax65,axiom,
! [X1] :
( ssItem(X1)
=> totalorderedP(cons(X1,nil)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax65) ).
fof(ax43,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( frontsegP(X1,X2)
=> frontsegP(app(X1,X3),X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax43) ).
fof(c_0_34,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
inference(fof_simplification,[status(thm)],[ax18]) ).
fof(c_0_35,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
inference(fof_simplification,[status(thm)],[ax78]) ).
fof(c_0_36,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
inference(fof_simplification,[status(thm)],[ax22]) ).
fof(c_0_37,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
inference(fof_simplification,[status(thm)],[ax24]) ).
fof(c_0_38,plain,
! [X48,X49] :
( cons(X49,X48) != X48
| ~ ssItem(X49)
| ~ ssList(X48) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_34])])])]) ).
fof(c_0_39,plain,
! [X116] :
( cons(hd(X116),tl(X116)) = X116
| nil = X116
| ~ ssList(X116) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])])]) ).
fof(c_0_40,plain,
! [X148] :
( ssItem(hd(X148))
| nil = X148
| ~ ssList(X148) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])])]) ).
fof(c_0_41,plain,
! [X171] :
( ssList(tl(X171))
| nil = X171
| ~ ssList(X171) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])])]) ).
fof(c_0_42,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> tl(app(X1,X2)) = app(tl(X1),X2) ) ) ),
inference(fof_simplification,[status(thm)],[ax86]) ).
cnf(c_0_43,plain,
( cons(X2,X1) != X1
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_44,plain,
( ~ ssList(X1)
| cons(hd(X1),tl(X1)) = X1
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_45,plain,
( ~ ssList(X1)
| ssItem(hd(X1))
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_46,plain,
( ~ ssList(X1)
| ssList(tl(X1))
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
fof(c_0_47,plain,
! [X98,X99] :
( tl(app(X98,X99)) = app(tl(X98),X99)
| nil = X98
| ~ ssList(X99)
| ~ ssList(X98) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])])])]) ).
fof(c_0_48,plain,
! [X54,X55] :
( ssList(app(X54,X55))
| ~ ssList(X55)
| ~ ssList(X54) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).
fof(c_0_49,plain,
! [X43,X44] :
( ( ~ ssList(X43)
| ~ ssList(X44)
| nil = app(X43,X44)
| nil != X43
| nil != X44 )
& ( ~ ssList(X43)
| ~ ssList(X44)
| nil != app(X43,X44)
| nil = X43 )
& ( ~ ssList(X43)
| ~ ssList(X44)
| nil != app(X43,X44)
| nil = X44 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])])]) ).
cnf(c_0_50,plain,
( ~ ssList(X1)
| tl(X1) != X1
| nil = X1 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),c_0_46]) ).
cnf(c_0_51,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| tl(app(X1,X2)) = app(tl(X1),X2)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_52,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_53,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| nil != app(X1,X2)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
fof(c_0_54,plain,
! [X45] :
( app(X45,nil) = X45
| ~ ssList(X45) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])])]) ).
fof(c_0_55,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[ax21]) ).
cnf(c_0_56,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(tl(X1),X2) != app(X1,X2)
| nil = X1 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]),c_0_53]) ).
cnf(c_0_57,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_58,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
fof(c_0_59,plain,
! [X110,X111] :
( tl(cons(X111,X110)) = X110
| ~ ssItem(X111)
| ~ ssList(X110) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax25])])])]) ).
fof(c_0_60,plain,
! [X46,X47] :
( ssList(cons(X47,X46))
| ~ ssItem(X47)
| ~ ssList(X46) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).
fof(c_0_61,plain,
! [X38,X39] :
( nil != cons(X39,X38)
| ~ ssItem(X39)
| ~ ssList(X38) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_55])])])]) ).
fof(c_0_62,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( ? [X6] :
( segmentP(X1,X6)
& segmentP(X2,X6)
& neq(X6,nil)
& ssList(X6) )
| ~ neq(X2,nil) )
& ( nil = X1
| nil != X2 ) )
| ? [X5] :
( totalorderedP(X5)
& segmentP(X5,X3)
& segmentP(X4,X5)
& neq(X3,X5)
& ssList(X5) )
| ~ totalorderedP(X3)
| ~ segmentP(X4,X3)
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
cnf(c_0_63,plain,
( ~ ssList(X1)
| tl(X1) != app(X1,nil)
| nil = X1 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58])]),c_0_46]) ).
cnf(c_0_64,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| tl(cons(X2,X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_65,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ssList(cons(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_66,plain,
( nil != cons(X2,X1)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
fof(c_0_67,plain,
! [X41,X42] :
( cons(X42,X41) = app(cons(X42,nil),X41)
| ~ ssItem(X42)
| ~ ssList(X41) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])])]) ).
fof(c_0_68,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( ? [X6] :
( segmentP(X1,X6)
& segmentP(X2,X6)
& neq(X6,nil)
& ssList(X6) )
| ~ neq(X2,nil) )
& ( nil = X1
| nil != X2 ) )
| ? [X5] :
( totalorderedP(X5)
& segmentP(X5,X3)
& segmentP(X4,X5)
& neq(X3,X5)
& ssList(X5) )
| ~ totalorderedP(X3)
| ~ segmentP(X4,X3)
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_62]) ).
cnf(c_0_69,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| app(cons(X1,X2),nil) != X2 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65]),c_0_66]) ).
cnf(c_0_70,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) = app(cons(X2,nil),X1) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
fof(c_0_71,negated_conjecture,
! [X11,X12] :
( ( nil != esk1_0
| ~ segmentP(esk1_0,X12)
| ~ segmentP(esk2_0,X12)
| ~ neq(X12,nil)
| ~ ssList(X12) )
& ( nil != esk1_0
| neq(esk2_0,nil) )
& ( nil = esk2_0
| ~ segmentP(esk1_0,X12)
| ~ segmentP(esk2_0,X12)
| ~ neq(X12,nil)
| ~ ssList(X12) )
& ( nil = esk2_0
| neq(esk2_0,nil) )
& ( ~ totalorderedP(X11)
| ~ segmentP(X11,esk3_0)
| ~ segmentP(esk4_0,X11)
| ~ neq(esk3_0,X11)
| ~ ssList(X11) )
& totalorderedP(esk3_0)
& segmentP(esk4_0,esk3_0)
& esk1_0 = esk3_0
& esk2_0 = esk4_0
& ssList(esk4_0)
& ssList(esk3_0)
& ssList(esk2_0)
& ssList(esk1_0) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_68])])])])])]) ).
cnf(c_0_72,plain,
( ~ ssItem(X1)
| cons(X1,nil) != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_58])]) ).
fof(c_0_73,plain,
! [X19,X20,X21] :
( segmentP(X19,X21)
| ~ segmentP(X20,X21)
| ~ segmentP(X19,X20)
| ~ ssList(X21)
| ~ ssList(X20)
| ~ ssList(X19) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax53])])])]) ).
cnf(c_0_74,negated_conjecture,
segmentP(esk4_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_75,negated_conjecture,
esk2_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_76,negated_conjecture,
esk1_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_71]) ).
fof(c_0_77,plain,
! [X13,X14,X17,X18] :
( ( ~ ssList(X13)
| ~ ssList(X14)
| segmentP(X13,X14)
| app(app(X17,X14),X18) != X13
| ~ ssList(X18)
| ~ ssList(X17) )
& ( ~ ssList(X13)
| ~ ssList(X14)
| ~ segmentP(X13,X14)
| app(app(esk5_2(X13,X14),X14),esk6_2(X13,X14)) = X13 )
& ( ~ ssList(X13)
| ~ ssList(X14)
| ~ segmentP(X13,X14)
| ssList(esk6_2(X13,X14)) )
& ( ~ ssList(X13)
| ~ ssList(X14)
| ~ segmentP(X13,X14)
| ssList(esk5_2(X13,X14)) ) ),
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_78,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_46,c_0_51]),c_0_52]),c_0_53]) ).
cnf(c_0_79,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(cons(X1,nil))
| app(tl(cons(X1,nil)),X2) = tl(cons(X1,X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_70]),c_0_72]) ).
cnf(c_0_80,plain,
( ~ segmentP(X2,X3)
| ~ segmentP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| segmentP(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_81,negated_conjecture,
segmentP(esk2_0,esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_75]),c_0_76]) ).
cnf(c_0_82,negated_conjecture,
ssList(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_83,negated_conjecture,
ssList(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_84,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_77]) ).
fof(c_0_85,plain,
! [X40] :
( app(nil,X40) = X40
| ~ ssList(X40) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])]) ).
cnf(c_0_86,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(cons(X1,nil))
| ssList(tl(cons(X1,X2))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_72]) ).
cnf(c_0_87,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(cons(X1,nil))
| tl(cons(X1,X2)) = app(nil,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_64]),c_0_58])]) ).
fof(c_0_88,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ? [X2] :
( hd(X1) = X2
& ssItem(X2) ) ) ),
inference(fof_simplification,[status(thm)],[ax75]) ).
cnf(c_0_89,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(X1,esk2_0)
| segmentP(X1,esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82]),c_0_83])]) ).
cnf(c_0_90,plain,
( ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(app(app(X1,X2),X3))
| segmentP(app(app(X1,X2),X3),X2) ),
inference(er,[status(thm)],[c_0_84]) ).
cnf(c_0_91,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
fof(c_0_92,plain,
! [X65,X66,X67] :
( app(app(X65,X66),X67) = app(X65,app(X66,X67))
| ~ ssList(X67)
| ~ ssList(X66)
| ~ ssList(X65) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])])]) ).
cnf(c_0_93,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(cons(X2,nil))
| ssList(app(nil,X1)) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
fof(c_0_94,plain,
! [X151] :
( ( ~ ssList(X151)
| nil = X151
| hd(X151) = esk28_1(X151) )
& ( ~ ssList(X151)
| nil = X151
| ssItem(esk28_1(X151)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_88])])])])]) ).
cnf(c_0_95,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X2,esk2_0)
| segmentP(X1,esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_89]),c_0_82])]) ).
cnf(c_0_96,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| segmentP(app(X1,X2),X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_58])]),c_0_52]) ).
fof(c_0_97,plain,
! [X24] :
( segmentP(X24,X24)
| ~ ssList(X24) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax55])])]) ).
cnf(c_0_98,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| nil != app(X2,X1)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_99,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X1,X2)
| app(app(esk5_2(X1,X2),X2),esk6_2(X1,X2)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_100,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X1,X2),X3) = app(X1,app(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_101,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ssList(app(nil,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_65]),c_0_58])]) ).
cnf(c_0_102,plain,
( ~ ssList(X1)
| nil = X1
| ssItem(esk28_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
fof(c_0_103,plain,
! [X22,X23] :
( X22 = X23
| ~ segmentP(X23,X22)
| ~ segmentP(X22,X23)
| ~ ssList(X23)
| ~ ssList(X22) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax54])])])]) ).
cnf(c_0_104,negated_conjecture,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(esk2_0,X2))
| ~ segmentP(X1,app(esk2_0,X2))
| segmentP(X1,esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_83])]) ).
cnf(c_0_105,plain,
( ~ ssList(X1)
| segmentP(X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_106,plain,
( ~ ssList(X1)
| ~ ssList(esk6_2(nil,X1))
| ~ ssList(app(esk5_2(nil,X1),X1))
| ~ segmentP(nil,X1)
| esk6_2(nil,X1) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99])]),c_0_58])]) ).
cnf(c_0_107,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_100,c_0_57]),c_0_58])]) ).
cnf(c_0_108,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| nil != X2
| nil != X1
| nil = app(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_109,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ssList(app(nil,X2))
| nil = X1 ),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_110,plain,
( ~ segmentP(X2,X1)
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_111,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(app(esk2_0,X1))
| segmentP(app(esk2_0,X1),esk1_0) ),
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_112,plain,
( ~ ssList(X1)
| ~ ssList(esk5_2(nil,X1))
| ~ ssList(esk6_2(nil,X1))
| ~ segmentP(nil,X1)
| esk6_2(nil,X1) = nil ),
inference(spm,[status(thm)],[c_0_106,c_0_52]) ).
cnf(c_0_113,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X1,X2)
| ssList(esk6_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
fof(c_0_114,plain,
! [X86,X87,X89] :
( ( ~ ssList(X86)
| ~ ssList(X87)
| rearsegP(X86,X87)
| app(X89,X87) != X86
| ~ ssList(X89) )
& ( ~ ssList(X86)
| ~ ssList(X87)
| ~ rearsegP(X86,X87)
| app(esk15_2(X86,X87),X87) = X86 )
& ( ~ ssList(X86)
| ~ ssList(X87)
| ~ rearsegP(X86,X87)
| ssList(esk15_2(X86,X87)) ) ),
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_115,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(app(nil,X1))
| app(X2,X1) != nil
| app(nil,X1) = nil ),
inference(spm,[status(thm)],[c_0_98,c_0_107]) ).
cnf(c_0_116,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_108])]),c_0_58])]) ).
cnf(c_0_117,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ssList(app(nil,X3))
| app(X1,X2) = nil ),
inference(spm,[status(thm)],[c_0_109,c_0_52]) ).
fof(c_0_118,plain,
! [X29] :
( segmentP(X29,nil)
| ~ ssList(X29) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax57])])]) ).
cnf(c_0_119,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(app(esk2_0,X1))
| ~ segmentP(esk1_0,app(esk2_0,X1))
| app(esk2_0,X1) = esk1_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_82])]) ).
cnf(c_0_120,plain,
( ~ ssList(X1)
| ~ ssList(esk5_2(nil,X1))
| ~ segmentP(nil,X1)
| esk6_2(nil,X1) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_58])]) ).
cnf(c_0_121,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X1,X2)
| ssList(esk5_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
fof(c_0_122,plain,
! [X163,X164,X165] :
( rearsegP(X163,X165)
| ~ rearsegP(X164,X165)
| ~ rearsegP(X163,X164)
| ~ ssList(X165)
| ~ ssList(X164)
| ~ ssList(X163) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax47])])])]) ).
cnf(c_0_123,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| app(X1,X2) != X3
| ~ ssList(X1)
| rearsegP(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_124,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_115,c_0_52]),c_0_58])]) ).
cnf(c_0_125,plain,
( ~ ssList(X1)
| app(nil,app(nil,X1)) = app(nil,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_116]),c_0_58])]) ).
cnf(c_0_126,negated_conjecture,
( nil != esk1_0
| ~ segmentP(esk1_0,X1)
| ~ segmentP(esk2_0,X1)
| ~ neq(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_127,negated_conjecture,
( nil != esk1_0
| neq(esk2_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_128,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(nil,X2))
| segmentP(nil,X1) ),
inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_117])]) ).
cnf(c_0_129,plain,
( ~ ssList(X1)
| segmentP(X1,nil) ),
inference(split_conjunct,[status(thm)],[c_0_118]) ).
cnf(c_0_130,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(esk1_0,nil)
| ssList(app(nil,X1))
| esk1_0 = nil ),
inference(condense,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_117]),c_0_58]),c_0_83])])]) ).
fof(c_0_131,plain,
! [X25,X26,X27,X28] :
( segmentP(app(app(X27,X25),X28),X26)
| ~ segmentP(X25,X26)
| ~ ssList(X28)
| ~ ssList(X27)
| ~ ssList(X26)
| ~ ssList(X25) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax56])])])]) ).
cnf(c_0_132,plain,
( ~ ssList(X1)
| ~ segmentP(nil,X1)
| esk6_2(nil,X1) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_58])]) ).
cnf(c_0_133,plain,
( ~ rearsegP(X2,X3)
| ~ rearsegP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| rearsegP(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_134,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| rearsegP(app(X1,X2),X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_123]),c_0_52]) ).
cnf(c_0_135,plain,
( ~ ssList(X1)
| ~ ssList(app(nil,X1))
| app(nil,X1) != nil
| app(nil,app(nil,X1)) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_58])]) ).
cnf(c_0_136,negated_conjecture,
( ~ segmentP(esk2_0,esk2_0)
| ~ segmentP(esk1_0,esk2_0)
| esk1_0 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_83])]) ).
cnf(c_0_137,plain,
( ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| ssList(app(nil,X3))
| segmentP(X1,X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_128]),c_0_58])]),c_0_129]) ).
cnf(c_0_138,negated_conjecture,
( ~ ssList(X1)
| ssList(app(nil,X1))
| esk1_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_129]),c_0_82])]) ).
cnf(c_0_139,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_131]) ).
cnf(c_0_140,plain,
( ~ ssList(X1)
| ~ segmentP(nil,X1)
| app(app(esk5_2(nil,X1),X1),nil) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_132]),c_0_58])]) ).
cnf(c_0_141,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| segmentP(app(X1,X2),X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_57]),c_0_58])]),c_0_52]) ).
cnf(c_0_142,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| app(esk15_2(X1,X2),X2) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_143,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| ssList(esk15_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_144,plain,
( ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,app(X3,X2))
| rearsegP(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_52]) ).
cnf(c_0_145,plain,
( ~ ssList(X1)
| ~ ssList(app(nil,X1))
| app(nil,X1) != nil
| rearsegP(nil,app(nil,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_58])]) ).
cnf(c_0_146,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(esk2_0,esk2_0)
| ssList(app(nil,X1)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_83]),c_0_82])]),c_0_138]) ).
cnf(c_0_147,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(esk5_2(nil,X2))
| ~ segmentP(X2,X1)
| ~ segmentP(nil,X2)
| segmentP(nil,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_58])]) ).
cnf(c_0_148,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| segmentP(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_142]),c_0_143]) ).
cnf(c_0_149,plain,
( ~ ssList(X1)
| ~ ssList(app(nil,X1))
| app(nil,X1) != nil
| rearsegP(nil,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_145]),c_0_58])]) ).
cnf(c_0_150,negated_conjecture,
( ~ ssList(X1)
| ssList(app(nil,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_105]),c_0_83])]) ).
cnf(c_0_151,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ segmentP(X2,X1)
| ~ segmentP(nil,X2)
| segmentP(nil,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_121]),c_0_58])]) ).
cnf(c_0_152,plain,
( ~ ssList(X1)
| app(nil,X1) != nil
| segmentP(nil,X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_149]),c_0_58])]),c_0_150]) ).
cnf(c_0_153,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ segmentP(X2,X1)
| app(nil,X2) != nil
| segmentP(nil,X1) ),
inference(spm,[status(thm)],[c_0_151,c_0_152]) ).
cnf(c_0_154,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| app(nil,app(X2,X1)) != nil
| segmentP(nil,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_141]),c_0_52]) ).
cnf(c_0_155,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_100,c_0_91]),c_0_58])]) ).
cnf(c_0_156,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| app(X2,X1) != nil
| segmentP(nil,X1) ),
inference(spm,[status(thm)],[c_0_154,c_0_155]) ).
fof(c_0_157,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
cnf(c_0_158,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ segmentP(nil,X2)
| segmentP(app(nil,X1),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_116]),c_0_58])]) ).
cnf(c_0_159,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X2,X1) != nil
| segmentP(nil,app(nil,X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_107]),c_0_150]) ).
cnf(c_0_160,plain,
( ~ ssList(X1)
| ~ ssList(esk15_2(nil,X1))
| ~ rearsegP(nil,X1)
| esk15_2(nil,X1) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_142])]),c_0_58])]) ).
fof(c_0_161,plain,
! [X33,X34] :
( ( ~ ssList(X33)
| ~ ssList(X34)
| neq(X33,X34)
| X33 = X34 )
& ( ~ ssList(X33)
| ~ ssList(X34)
| X33 != X34
| ~ neq(X33,X34) ) ),
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_157])])])])]) ).
cnf(c_0_162,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ segmentP(nil,X2)
| segmentP(X1,X2) ),
inference(spm,[status(thm)],[c_0_158,c_0_91]) ).
cnf(c_0_163,plain,
( ~ ssList(X1)
| ~ ssList(esk15_2(nil,X1))
| ~ rearsegP(nil,X1)
| segmentP(nil,app(nil,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_142])]),c_0_58])]) ).
cnf(c_0_164,plain,
( ~ ssList(X1)
| ~ rearsegP(nil,X1)
| esk15_2(nil,X1) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_143]),c_0_58])]) ).
cnf(c_0_165,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,app(X2,nil)) = app(X1,X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_100]),c_0_58])]),c_0_52]) ).
fof(c_0_166,plain,
! [X30] :
( ( ~ ssList(X30)
| segmentP(nil,X30)
| nil != X30 )
& ( ~ ssList(X30)
| nil = X30
| ~ segmentP(nil,X30) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax58])])])]) ).
cnf(c_0_167,negated_conjecture,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X2,esk2_0))
| ~ segmentP(X1,app(X2,esk2_0))
| segmentP(X1,esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_141]),c_0_83])]) ).
cnf(c_0_168,plain,
( ~ ssList(X1)
| app(nil,X1) != nil
| segmentP(nil,app(nil,X1)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_135]),c_0_58])]),c_0_150]) ).
cnf(c_0_169,negated_conjecture,
( ~ segmentP(esk1_0,X1)
| ~ segmentP(esk2_0,X1)
| ~ neq(X1,nil)
| ~ ssList(X1)
| nil = esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_170,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_161]) ).
cnf(c_0_171,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| app(nil,X2) != nil
| segmentP(X1,X2) ),
inference(spm,[status(thm)],[c_0_162,c_0_152]) ).
cnf(c_0_172,plain,
( ~ ssList(X1)
| ~ rearsegP(nil,X1)
| segmentP(nil,app(nil,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_164]),c_0_58])]) ).
cnf(c_0_173,plain,
( ~ ssList(X1)
| app(nil,X1) = app(X1,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_165]),c_0_58])]) ).
cnf(c_0_174,plain,
( ~ ssList(X1)
| ~ segmentP(nil,X1)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_166]) ).
cnf(c_0_175,negated_conjecture,
( ~ ssList(app(nil,esk2_0))
| app(nil,esk2_0) != nil
| segmentP(nil,esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_168]),c_0_58]),c_0_83])]) ).
cnf(c_0_176,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(esk2_0,X1)
| ~ segmentP(esk1_0,X1)
| X1 = nil
| esk2_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_170]),c_0_58])]) ).
fof(c_0_177,plain,
! [X82,X83,X85] :
( ( ~ ssList(X82)
| ~ ssList(X83)
| frontsegP(X82,X83)
| app(X83,X85) != X82
| ~ ssList(X85) )
& ( ~ ssList(X82)
| ~ ssList(X83)
| ~ frontsegP(X82,X83)
| app(X83,esk14_2(X82,X83)) = X82 )
& ( ~ ssList(X82)
| ~ ssList(X83)
| ~ frontsegP(X82,X83)
| ssList(esk14_2(X82,X83)) ) ),
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_178,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X1,X2)
| app(nil,X1) != nil
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_110,c_0_171]) ).
cnf(c_0_179,plain,
( ~ ssList(X1)
| ~ rearsegP(nil,X1)
| segmentP(nil,app(X1,nil)) ),
inference(spm,[status(thm)],[c_0_172,c_0_173]) ).
cnf(c_0_180,negated_conjecture,
( ~ ssList(X1)
| ssList(app(X1,nil)) ),
inference(spm,[status(thm)],[c_0_150,c_0_173]) ).
cnf(c_0_181,negated_conjecture,
( ~ ssList(app(nil,esk2_0))
| app(nil,esk2_0) != nil
| esk1_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_175]),c_0_82])]) ).
cnf(c_0_182,negated_conjecture,
( esk2_0 = nil
| esk1_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_105]),c_0_81]),c_0_82])]) ).
cnf(c_0_183,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| app(X2,X1) != X3
| ~ ssList(X1)
| frontsegP(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_177]) ).
cnf(c_0_184,plain,
( ~ ssList(X1)
| ~ rearsegP(nil,X1)
| app(X1,nil) = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_178,c_0_179]),c_0_116]),c_0_58])]),c_0_180]) ).
cnf(c_0_185,negated_conjecture,
( ~ totalorderedP(X1)
| ~ segmentP(X1,esk3_0)
| ~ segmentP(esk4_0,X1)
| ~ neq(esk3_0,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
fof(c_0_186,plain,
! [X112,X113,X114,X115] :
( ( ~ ssItem(X112)
| ~ ssItem(X113)
| ~ ssList(X114)
| ~ ssList(X115)
| frontsegP(cons(X112,X114),cons(X113,X115))
| ~ frontsegP(X114,X115)
| X112 != X113 )
& ( ~ ssItem(X112)
| ~ ssItem(X113)
| ~ ssList(X114)
| ~ ssList(X115)
| ~ frontsegP(cons(X112,X114),cons(X113,X115))
| frontsegP(X114,X115) )
& ( ~ ssItem(X112)
| ~ ssItem(X113)
| ~ ssList(X114)
| ~ ssList(X115)
| ~ frontsegP(cons(X112,X114),cons(X113,X115))
| X112 = X113 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax44])])])])]) ).
cnf(c_0_187,negated_conjecture,
esk1_0 = nil,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_91]),c_0_83])]),c_0_182]) ).
cnf(c_0_188,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| frontsegP(app(X1,X2),X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_183]),c_0_52]) ).
cnf(c_0_189,plain,
( ~ ssList(X1)
| app(nil,X1) != nil
| app(app(nil,X1),nil) = nil ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_145]),c_0_150]) ).
cnf(c_0_190,negated_conjecture,
( ~ neq(esk1_0,X1)
| ~ ssList(X1)
| ~ segmentP(esk2_0,X1)
| ~ segmentP(X1,esk1_0)
| ~ totalorderedP(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_185,c_0_76]),c_0_76]),c_0_75]) ).
cnf(c_0_191,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| ~ frontsegP(X3,X4)
| X1 != X2
| frontsegP(cons(X1,X3),cons(X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_186]) ).
fof(c_0_192,plain,
! [X35] :
( ( ~ ssList(X35)
| nil = X35
| cons(esk8_1(X35),esk7_1(X35)) = X35 )
& ( ~ ssList(X35)
| nil = X35
| ssItem(esk8_1(X35)) )
& ( ~ ssList(X35)
| nil = X35
| ssList(esk7_1(X35)) ) ),
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_193,negated_conjecture,
( ~ segmentP(esk2_0,esk2_0)
| ~ segmentP(nil,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_136,c_0_187]),c_0_187])]) ).
fof(c_0_194,plain,
! [X56,X57,X58] :
( cons(X58,app(X57,X56)) = app(cons(X58,X57),X56)
| ~ ssItem(X58)
| ~ ssList(X57)
| ~ ssList(X56) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])])]) ).
fof(c_0_195,plain,
! [X155,X156,X157] :
( frontsegP(X155,X157)
| ~ frontsegP(X156,X157)
| ~ frontsegP(X155,X156)
| ~ ssList(X157)
| ~ ssList(X156)
| ~ ssList(X155) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax40])])])]) ).
cnf(c_0_196,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| frontsegP(app(X1,app(X2,X3)),app(X1,X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_188,c_0_100]),c_0_52]) ).
cnf(c_0_197,plain,
( ~ ssList(X1)
| app(nil,X1) != nil
| app(nil,app(X1,nil)) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_189]),c_0_58])]) ).
cnf(c_0_198,negated_conjecture,
( ~ neq(nil,X1)
| ~ ssList(X1)
| ~ segmentP(esk2_0,X1)
| ~ totalorderedP(X1) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_190,c_0_187]),c_0_187]),c_0_129]) ).
fof(c_0_199,plain,
! [X79] :
( totalorderedP(cons(X79,nil))
| ~ ssItem(X79) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax65])])]) ).
cnf(c_0_200,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ frontsegP(X2,X1)
| app(X1,esk14_2(X2,X1)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_177]) ).
cnf(c_0_201,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| ssList(esk14_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_177]) ).
cnf(c_0_202,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ frontsegP(X2,X3)
| frontsegP(cons(X1,X2),cons(X1,X3)) ),
inference(er,[status(thm)],[c_0_191]) ).
cnf(c_0_203,plain,
( ~ ssList(X1)
| nil = X1
| cons(esk8_1(X1),esk7_1(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_192]) ).
cnf(c_0_204,plain,
( ~ ssList(X1)
| nil = X1
| ssItem(esk8_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_192]) ).
cnf(c_0_205,plain,
( ~ ssList(X1)
| nil = X1
| ssList(esk7_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_192]) ).
cnf(c_0_206,negated_conjecture,
~ segmentP(nil,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_193,c_0_105]),c_0_83])]) ).
cnf(c_0_207,plain,
( ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_194]) ).
fof(c_0_208,plain,
! [X90,X91,X92] :
( frontsegP(app(X90,X92),X91)
| ~ frontsegP(X90,X91)
| ~ ssList(X92)
| ~ ssList(X91)
| ~ ssList(X90) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax43])])])]) ).
cnf(c_0_209,plain,
( ~ frontsegP(X2,X3)
| ~ frontsegP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| frontsegP(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_195]) ).
cnf(c_0_210,plain,
( ~ ssList(X1)
| app(nil,X1) != nil
| frontsegP(nil,app(nil,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_196,c_0_197]),c_0_58])]) ).
cnf(c_0_211,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(esk2_0,X1)
| ~ totalorderedP(X1)
| nil = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_198,c_0_170]),c_0_58])]) ).
cnf(c_0_212,plain,
( ~ ssItem(X1)
| totalorderedP(cons(X1,nil)) ),
inference(split_conjunct,[status(thm)],[c_0_199]) ).
cnf(c_0_213,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| segmentP(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_200]),c_0_201]) ).
cnf(c_0_214,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(esk7_1(X1),X2)
| frontsegP(X1,cons(esk8_1(X1),X2))
| nil = X1 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_202,c_0_203]),c_0_204]),c_0_205]) ).
cnf(c_0_215,negated_conjecture,
app(nil,esk2_0) != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_206,c_0_152]),c_0_83])]) ).
cnf(c_0_216,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ssList(cons(X1,app(X2,X3))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_207]),c_0_65]) ).
cnf(c_0_217,plain,
( ~ frontsegP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| frontsegP(app(X1,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_208]) ).
cnf(c_0_218,plain,
( ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,app(X2,X3))
| frontsegP(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_209,c_0_188]),c_0_52]) ).
cnf(c_0_219,plain,
( ~ ssList(X1)
| app(X1,nil) != nil
| frontsegP(nil,app(X1,nil)) ),
inference(spm,[status(thm)],[c_0_210,c_0_173]) ).
cnf(c_0_220,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| ~ segmentP(esk2_0,cons(X1,nil)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_211,c_0_212]),c_0_72]) ).
cnf(c_0_221,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(cons(esk8_1(X1),X2))
| ~ frontsegP(esk7_1(X1),X2)
| segmentP(X1,cons(esk8_1(X1),X2))
| nil = X1 ),
inference(spm,[status(thm)],[c_0_213,c_0_214]) ).
cnf(c_0_222,negated_conjecture,
esk2_0 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_215,c_0_91]),c_0_83])]) ).
cnf(c_0_223,plain,
( ~ ssItem(X1)
| ssList(cons(X1,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_216,c_0_116]),c_0_58])]) ).
cnf(c_0_224,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ frontsegP(nil,X2)
| frontsegP(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_217,c_0_91]),c_0_58])]) ).
cnf(c_0_225,plain,
( ~ ssList(X1)
| app(X1,nil) != nil
| frontsegP(nil,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_218,c_0_219]),c_0_58])]) ).
cnf(c_0_226,negated_conjecture,
( ~ ssItem(esk8_1(esk2_0))
| ~ frontsegP(esk7_1(esk2_0),nil) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_220,c_0_221]),c_0_83]),c_0_58])]),c_0_222]),c_0_223]) ).
cnf(c_0_227,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| app(X2,nil) != nil
| frontsegP(X1,X2) ),
inference(spm,[status(thm)],[c_0_224,c_0_225]) ).
cnf(c_0_228,negated_conjecture,
( ~ ssItem(esk8_1(esk2_0))
| ~ ssList(esk7_1(esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_226,c_0_227]),c_0_116]),c_0_58])]) ).
cnf(c_0_229,negated_conjecture,
~ ssList(esk7_1(esk2_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_228,c_0_204]),c_0_83])]),c_0_222]) ).
cnf(c_0_230,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_229,c_0_205]),c_0_83])]),c_0_222]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC066+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.43 % Computer : n007.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 07:50:20 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.51 Running first-order theorem proving
% 0.25/0.51 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 229.72/34.08 % Version: 3.5.1
% 229.72/34.08 % Preprocessing class: FSLSSMSSSSSNFFN.
% 229.72/34.08 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 229.72/34.08 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 229.72/34.08 % Starting new_bool_3 with 300s (1) cores
% 229.72/34.08 % Starting new_bool_1 with 300s (1) cores
% 229.72/34.08 % Starting sh5l with 300s (1) cores
% 229.72/34.08 % sh5l with pid 574840 completed with status 0
% 229.72/34.08 % Result found by sh5l
% 229.72/34.08 % Preprocessing class: FSLSSMSSSSSNFFN.
% 229.72/34.08 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 229.72/34.08 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 229.72/34.08 % Starting new_bool_3 with 300s (1) cores
% 229.72/34.08 % Starting new_bool_1 with 300s (1) cores
% 229.72/34.08 % Starting sh5l with 300s (1) cores
% 229.72/34.08 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 229.72/34.08 % SinE strategy is gf500_gu_R04_F100_L20000
% 229.72/34.08 % Search class: FGHSF-FSLM21-MFFFFFNN
% 229.72/34.08 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 229.72/34.08 % Starting SubtermCWHack with 28s (1) cores
% 229.72/34.08 % SubtermCWHack with pid 574843 completed with status 8
% 229.72/34.08 % Starting sh5l with 31s (1) cores
% 229.72/34.08 % sh5l with pid 575009 completed with status 0
% 229.72/34.08 % Result found by sh5l
% 229.72/34.08 % Preprocessing class: FSLSSMSSSSSNFFN.
% 229.72/34.08 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 229.72/34.08 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 229.72/34.08 % Starting new_bool_3 with 300s (1) cores
% 229.72/34.08 % Starting new_bool_1 with 300s (1) cores
% 229.72/34.08 % Starting sh5l with 300s (1) cores
% 229.72/34.08 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 229.72/34.08 % SinE strategy is gf500_gu_R04_F100_L20000
% 229.72/34.08 % Search class: FGHSF-FSLM21-MFFFFFNN
% 229.72/34.08 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 229.72/34.08 % Starting SubtermCWHack with 28s (1) cores
% 229.72/34.08 % SubtermCWHack with pid 574843 completed with status 8
% 229.72/34.08 % Starting sh5l with 31s (1) cores
% 229.72/34.08 % Preprocessing time : 0.002 s
% 229.72/34.08 % Presaturation interreduction done
% 229.72/34.08
% 229.72/34.08 % Proof found!
% 229.72/34.08 % SZS status Theorem
% 229.72/34.08 % SZS output start CNFRefutation
% See solution above
% 229.72/34.08 % Parsed axioms : 96
% 229.72/34.08 % Removed by relevancy pruning/SinE : 12
% 229.72/34.08 % Initial clauses : 169
% 229.72/34.08 % Removed in clause preprocessing : 2
% 229.72/34.08 % Initial clauses in saturation : 167
% 229.72/34.08 % Processed clauses : 26905
% 229.72/34.08 % ...of these trivial : 21
% 229.72/34.08 % ...subsumed : 23512
% 229.72/34.08 % ...remaining for further processing : 3372
% 229.72/34.08 % Other redundant clauses eliminated : 3631
% 229.72/34.08 % Clauses deleted for lack of memory : 0
% 229.72/34.08 % Backward-subsumed : 247
% 229.72/34.08 % Backward-rewritten : 43
% 229.72/34.08 % Generated clauses : 278815
% 229.72/34.08 % ...of the previous two non-redundant : 254355
% 229.72/34.08 % ...aggressively subsumed : 0
% 229.72/34.08 % Contextual simplify-reflections : 2258
% 229.72/34.08 % Paramodulations : 275155
% 229.72/34.08 % Factorizations : 0
% 229.72/34.08 % NegExts : 0
% 229.72/34.08 % Equation resolutions : 3661
% 229.72/34.08 % Disequality decompositions : 0
% 229.72/34.08 % Total rewrite steps : 159664
% 229.72/34.08 % ...of those cached : 159642
% 229.72/34.08 % Propositional unsat checks : 0
% 229.72/34.08 % Propositional check models : 0
% 229.72/34.08 % Propositional check unsatisfiable : 0
% 229.72/34.08 % Propositional clauses : 0
% 229.72/34.08 % Propositional clauses after purity: 0
% 229.72/34.08 % Propositional unsat core size : 0
% 229.72/34.08 % Propositional preprocessing time : 0.000
% 229.72/34.08 % Propositional encoding time : 0.000
% 229.72/34.08 % Propositional solver time : 0.000
% 229.72/34.08 % Success case prop preproc time : 0.000
% 229.72/34.08 % Success case prop encoding time : 0.000
% 229.72/34.08 % Success case prop solver time : 0.000
% 229.72/34.08 % Current number of processed clauses : 2903
% 229.72/34.08 % Positive orientable unit clauses : 23
% 229.72/34.08 % Positive unorientable unit clauses: 0
% 229.72/34.08 % Negative unit clauses : 6
% 229.72/34.08 % Non-unit-clauses : 2874
% 229.72/34.08 % Current number of unprocessed clauses: 227079
% 229.72/34.08 % ...number of literals in the above : 1761557
% 229.72/34.08 % Current number of archived formulas : 0
% 229.72/34.08 % Current number of archived clauses : 451
% 229.72/34.08 % Clause-clause subsumption calls (NU) : 2187260
% 229.72/34.08 % Rec. Clause-clause subsumption calls : 289726
% 229.72/34.08 % Non-unit clause-clause subsumptions : 26096
% 229.72/34.08 % Unit Clause-clause subsumption calls : 3313
% 229.72/34.08 % Rewrite failures with RHS unbound : 0
% 229.72/34.08 % BW rewrite match attempts : 7
% 229.72/34.08 % BW rewrite match successes : 7
% 229.72/34.08 % Condensation attempts : 26905
% 229.72/34.08 % Condensation successes : 94
% 229.72/34.08 % Termbank termtop insertions : 7391392
% 229.72/34.08 % Search garbage collected termcells : 3700
% 229.72/34.08
% 229.72/34.08 % -------------------------------------------------
% 229.72/34.08 % User time : 31.635 s
% 229.72/34.08 % System time : 1.142 s
% 229.72/34.08 % Total time : 32.776 s
% 229.72/34.08 % Maximum resident set size: 4272 pages
% 229.72/34.08
% 229.72/34.08 % -------------------------------------------------
% 229.72/34.08 % User time : 31.642 s
% 229.72/34.08 % System time : 1.149 s
% 229.72/34.08 % Total time : 32.791 s
% 229.72/34.08 % Maximum resident set size: 4608 pages
% 229.72/34.08 % E exiting
%------------------------------------------------------------------------------