TSTP Solution File: SWC091+1 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SWC091+1 : TPTP v8.2.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 04:23:14 EDT 2024
% Result : Theorem 1.41s 0.63s
% Output : CNFRefutation 1.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 30
% Syntax : Number of formulae : 196 ( 45 unt; 0 def)
% Number of atoms : 668 ( 177 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 794 ( 322 ~; 333 |; 48 &)
% ( 7 <=>; 84 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-2 aty)
% Number of variables : 243 ( 0 sgn 131 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| ~ frontsegP(X4,X3)
| ~ totalorderedP(X3)
| ? [X5] :
( ssList(X5)
& neq(X5,nil)
& segmentP(X2,X5)
& segmentP(X1,X5) )
| ? [X6] :
( ssList(X6)
& neq(X3,X6)
& frontsegP(X4,X6)
& segmentP(X6,X3)
& totalorderedP(X6) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
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(ax5,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X2,X3) = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax5) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax7,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( segmentP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(app(X3,X2),X4) = X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax7) ).
fof(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax82,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> app(app(X1,X2),X3) = app(X1,app(X2,X3)) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax82) ).
fof(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(ax55,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax55) ).
fof(ax6,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( rearsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X3,X2) = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax6) ).
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(ax78,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax78) ).
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(ax21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax21) ).
fof(ax83,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(ax19,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssItem(X4)
=> ( cons(X3,X1) = cons(X4,X2)
=> ( X3 = X4
& X2 = X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax19) ).
fof(ax20,axiom,
! [X1] :
( ssList(X1)
=> ( nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax20) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax24,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax24) ).
fof(ax22,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax22) ).
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(ax23,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> hd(cons(X2,X1)) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax23) ).
fof(ax44,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( frontsegP(cons(X1,X3),cons(X2,X4))
<=> ( X1 = X2
& frontsegP(X3,X4) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax44) ).
fof(ax57,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,nil) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax57) ).
fof(ax65,axiom,
! [X1] :
( ssItem(X1)
=> totalorderedP(cons(X1,nil)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax65) ).
fof(ax18,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax18) ).
fof(c_0_30,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| ~ frontsegP(X4,X3)
| ~ totalorderedP(X3)
| ? [X5] :
( ssList(X5)
& neq(X5,nil)
& segmentP(X2,X5)
& segmentP(X1,X5) )
| ? [X6] :
( ssList(X6)
& neq(X3,X6)
& frontsegP(X4,X6)
& segmentP(X6,X3)
& totalorderedP(X6) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_31,negated_conjecture,
! [X11,X12] :
( ssList(esk1_0)
& ssList(esk2_0)
& ssList(esk3_0)
& ssList(esk4_0)
& esk2_0 = esk4_0
& esk1_0 = esk3_0
& neq(esk2_0,nil)
& frontsegP(esk4_0,esk3_0)
& totalorderedP(esk3_0)
& ( ~ ssList(X11)
| ~ neq(X11,nil)
| ~ segmentP(esk2_0,X11)
| ~ segmentP(esk1_0,X11) )
& ( ~ ssList(X12)
| ~ neq(esk3_0,X12)
| ~ frontsegP(esk4_0,X12)
| ~ segmentP(X12,esk3_0)
| ~ totalorderedP(X12) ) ),
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_30])])])])]) ).
fof(c_0_32,plain,
! [X55,X56,X57] :
( ~ ssList(X55)
| ~ ssList(X56)
| ~ ssList(X57)
| ~ frontsegP(X55,X56)
| frontsegP(app(X55,X57),X56) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax43])])])]) ).
fof(c_0_33,plain,
! [X62] :
( ~ ssList(X62)
| frontsegP(X62,nil) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax45])])]) ).
fof(c_0_34,plain,
! [X45,X46,X48] :
( ( ssList(esk12_2(X45,X46))
| ~ frontsegP(X45,X46)
| ~ ssList(X46)
| ~ ssList(X45) )
& ( app(X46,esk12_2(X45,X46)) = X45
| ~ frontsegP(X45,X46)
| ~ ssList(X46)
| ~ ssList(X45) )
& ( ~ ssList(X48)
| app(X46,X48) != X45
| frontsegP(X45,X46)
| ~ ssList(X46)
| ~ ssList(X45) ) ),
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_35,negated_conjecture,
ssList(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_36,negated_conjecture,
esk2_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_37,negated_conjecture,
ssList(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_38,negated_conjecture,
esk1_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_39,plain,
( frontsegP(app(X1,X3),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ frontsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_40,plain,
( frontsegP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_41,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_42,plain,
( app(X1,esk12_2(X2,X1)) = X2
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_43,negated_conjecture,
frontsegP(esk4_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_44,negated_conjecture,
ssList(esk4_0),
inference(rw,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_45,negated_conjecture,
ssList(esk3_0),
inference(rw,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_46,plain,
( ssList(esk12_2(X1,X2))
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_47,plain,
( frontsegP(app(X1,X2),nil)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41])]) ).
cnf(c_0_48,negated_conjecture,
app(esk3_0,esk12_2(esk4_0,esk3_0)) = esk4_0,
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_49,negated_conjecture,
ssList(esk12_2(esk4_0,esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_43]),c_0_45]),c_0_44])]) ).
fof(c_0_50,plain,
! [X86] :
( ~ ssList(X86)
| app(nil,X86) = X86 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])]) ).
cnf(c_0_51,negated_conjecture,
frontsegP(esk4_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]),c_0_45])]) ).
fof(c_0_52,plain,
! [X27,X28,X31,X32] :
( ( ssList(esk10_2(X27,X28))
| ~ segmentP(X27,X28)
| ~ ssList(X28)
| ~ ssList(X27) )
& ( ssList(esk11_2(X27,X28))
| ~ segmentP(X27,X28)
| ~ ssList(X28)
| ~ ssList(X27) )
& ( app(app(esk10_2(X27,X28),X28),esk11_2(X27,X28)) = X27
| ~ segmentP(X27,X28)
| ~ ssList(X28)
| ~ ssList(X27) )
& ( ~ ssList(X31)
| ~ ssList(X32)
| app(app(X31,X28),X32) != X27
| segmentP(X27,X28)
| ~ ssList(X28)
| ~ ssList(X27) ) ),
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_53,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_54,negated_conjecture,
app(nil,esk12_2(esk4_0,nil)) = esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_51]),c_0_44]),c_0_41])]) ).
cnf(c_0_55,negated_conjecture,
ssList(esk12_2(esk4_0,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_51]),c_0_41]),c_0_44])]) ).
cnf(c_0_56,plain,
( segmentP(X4,X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(app(X1,X3),X2) != X4
| ~ ssList(X3)
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_57,negated_conjecture,
esk12_2(esk4_0,nil) = esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55])]) ).
cnf(c_0_58,plain,
( segmentP(app(app(X1,X2),X3),X2)
| ~ ssList(app(app(X1,X2),X3))
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1) ),
inference(er,[status(thm)],[c_0_56]) ).
cnf(c_0_59,negated_conjecture,
app(nil,esk4_0) = esk4_0,
inference(rw,[status(thm)],[c_0_54,c_0_57]) ).
fof(c_0_60,plain,
! [X100] :
( ~ ssList(X100)
| app(X100,nil) = X100 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])])]) ).
cnf(c_0_61,negated_conjecture,
( segmentP(app(esk4_0,X1),esk4_0)
| ~ ssList(app(esk4_0,X1))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_44]),c_0_41])]) ).
cnf(c_0_62,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
fof(c_0_63,plain,
! [X81,X82] :
( ~ ssList(X81)
| ~ ssList(X82)
| ssList(app(X81,X82)) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).
fof(c_0_64,plain,
! [X95,X96,X97] :
( ~ ssList(X95)
| ~ ssList(X96)
| ~ ssList(X97)
| app(app(X95,X96),X97) = app(X95,app(X96,X97)) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])])]) ).
cnf(c_0_65,plain,
( app(app(esk10_2(X1,X2),X2),esk11_2(X1,X2)) = X1
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_66,negated_conjecture,
segmentP(esk4_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_44]),c_0_41])]) ).
cnf(c_0_67,plain,
( ssList(esk11_2(X1,X2))
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_68,plain,
( ssList(esk10_2(X1,X2))
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_69,plain,
( frontsegP(X3,X2)
| ~ ssList(X1)
| app(X2,X1) != X3
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_70,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_71,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_72,negated_conjecture,
app(app(esk10_2(esk4_0,esk4_0),esk4_0),esk11_2(esk4_0,esk4_0)) = esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_44])]) ).
cnf(c_0_73,negated_conjecture,
ssList(esk11_2(esk4_0,esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_66]),c_0_44])]) ).
cnf(c_0_74,negated_conjecture,
ssList(esk10_2(esk4_0,esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_66]),c_0_44])]) ).
cnf(c_0_75,plain,
( frontsegP(app(X1,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_69]),c_0_70]) ).
cnf(c_0_76,negated_conjecture,
app(esk10_2(esk4_0,esk4_0),app(esk4_0,esk11_2(esk4_0,esk4_0))) = esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]),c_0_44]),c_0_74])]) ).
fof(c_0_77,plain,
! [X142,X143,X144] :
( ~ ssList(X142)
| ~ ssList(X143)
| ~ ssList(X144)
| ~ rearsegP(X142,X143)
| rearsegP(app(X144,X142),X143) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax50])])])]) ).
fof(c_0_78,plain,
! [X207] :
( ~ ssList(X207)
| rearsegP(X207,nil) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax51])])]) ).
cnf(c_0_79,negated_conjecture,
( frontsegP(esk4_0,esk10_2(esk4_0,esk4_0))
| ~ ssList(app(esk4_0,esk11_2(esk4_0,esk4_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_74])]) ).
cnf(c_0_80,plain,
( rearsegP(app(X3,X1),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ rearsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_81,plain,
( rearsegP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_82,negated_conjecture,
frontsegP(esk4_0,esk10_2(esk4_0,esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_70]),c_0_73]),c_0_44])]) ).
cnf(c_0_83,negated_conjecture,
( ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(esk2_0,X1)
| ~ segmentP(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_84,plain,
! [X38] :
( ~ ssList(X38)
| segmentP(X38,X38) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax55])])]) ).
fof(c_0_85,plain,
! [X138,X139,X141] :
( ( ssList(esk25_2(X138,X139))
| ~ rearsegP(X138,X139)
| ~ ssList(X139)
| ~ ssList(X138) )
& ( app(esk25_2(X138,X139),X139) = X138
| ~ rearsegP(X138,X139)
| ~ ssList(X139)
| ~ ssList(X138) )
& ( ~ ssList(X141)
| app(X141,X139) != X138
| rearsegP(X138,X139)
| ~ ssList(X139)
| ~ ssList(X138) ) ),
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_86,plain,
( rearsegP(app(X1,X2),nil)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_41])]) ).
cnf(c_0_87,negated_conjecture,
app(esk10_2(esk4_0,esk4_0),esk12_2(esk4_0,esk10_2(esk4_0,esk4_0))) = esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_82]),c_0_44]),c_0_74])]) ).
cnf(c_0_88,negated_conjecture,
ssList(esk12_2(esk4_0,esk10_2(esk4_0,esk4_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_82]),c_0_74]),c_0_44])]) ).
cnf(c_0_89,negated_conjecture,
( ~ segmentP(esk3_0,X1)
| ~ segmentP(esk4_0,X1)
| ~ ssList(X1)
| ~ neq(X1,nil) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_83,c_0_38]),c_0_36]) ).
cnf(c_0_90,plain,
( segmentP(X1,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_91,plain,
( segmentP(app(X1,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_53]),c_0_41])]),c_0_70]) ).
fof(c_0_92,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
fof(c_0_93,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
inference(fof_simplification,[status(thm)],[ax78]) ).
fof(c_0_94,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> hd(app(X1,X2)) = hd(X1) ) ) ),
inference(fof_simplification,[status(thm)],[ax85]) ).
cnf(c_0_95,plain,
( app(esk25_2(X1,X2),X2) = X1
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_96,negated_conjecture,
rearsegP(esk4_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_74]),c_0_88])]) ).
cnf(c_0_97,plain,
( ssList(esk25_2(X1,X2))
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_98,negated_conjecture,
( ~ segmentP(esk4_0,esk3_0)
| ~ neq(esk3_0,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_45])]) ).
cnf(c_0_99,negated_conjecture,
segmentP(esk4_0,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_48]),c_0_45]),c_0_49])]) ).
fof(c_0_100,plain,
! [X66,X67] :
( ( ~ neq(X66,X67)
| X66 != X67
| ~ ssList(X67)
| ~ ssList(X66) )
& ( X66 = X67
| neq(X66,X67)
| ~ ssList(X67)
| ~ ssList(X66) ) ),
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_92])])])])]) ).
fof(c_0_101,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[ax21]) ).
fof(c_0_102,plain,
! [X153] :
( ~ ssList(X153)
| nil = X153
| cons(hd(X153),tl(X153)) = X153 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_93])])]) ).
fof(c_0_103,plain,
! [X145,X146] :
( ~ ssList(X145)
| ~ ssList(X146)
| nil = X145
| hd(app(X145,X146)) = hd(X145) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_94])])])]) ).
fof(c_0_104,plain,
! [X98,X99] :
( ( nil = X99
| nil != app(X98,X99)
| ~ ssList(X99)
| ~ ssList(X98) )
& ( nil = X98
| nil != app(X98,X99)
| ~ ssList(X99)
| ~ ssList(X98) )
& ( nil != X99
| nil != X98
| nil = app(X98,X99)
| ~ ssList(X99)
| ~ ssList(X98) ) ),
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_105,negated_conjecture,
app(esk25_2(esk4_0,nil),nil) = esk4_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_41]),c_0_44])]) ).
cnf(c_0_106,negated_conjecture,
ssList(esk25_2(esk4_0,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_96]),c_0_41]),c_0_44])]) ).
cnf(c_0_107,negated_conjecture,
~ neq(esk3_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_98,c_0_99])]) ).
cnf(c_0_108,plain,
( X1 = X2
| neq(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
fof(c_0_109,plain,
! [X72,X73,X74,X75] :
( ( X74 = X75
| cons(X74,X72) != cons(X75,X73)
| ~ ssItem(X75)
| ~ ssItem(X74)
| ~ ssList(X73)
| ~ ssList(X72) )
& ( X73 = X72
| cons(X74,X72) != cons(X75,X73)
| ~ ssItem(X75)
| ~ ssItem(X74)
| ~ ssList(X73)
| ~ ssList(X72) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax19])])])])]) ).
fof(c_0_110,plain,
! [X76] :
( ( ssList(esk13_1(X76))
| nil = X76
| ~ ssList(X76) )
& ( ssItem(esk14_1(X76))
| nil = X76
| ~ ssList(X76) )
& ( cons(esk14_1(X76),esk13_1(X76)) = X76
| nil = X76
| ~ ssList(X76) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax20])])])])]) ).
fof(c_0_111,plain,
! [X68,X69] :
( ~ ssList(X68)
| ~ ssItem(X69)
| ssList(cons(X69,X68)) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).
fof(c_0_112,plain,
! [X79,X80] :
( ~ ssList(X79)
| ~ ssItem(X80)
| nil != cons(X80,X79) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_101])])])]) ).
cnf(c_0_113,plain,
( nil = X1
| cons(hd(X1),tl(X1)) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_114,plain,
( nil = X1
| hd(app(X1,X2)) = hd(X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_115,plain,
( nil = X1
| nil != app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_116,negated_conjecture,
esk25_2(esk4_0,nil) = esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_105]),c_0_106])]) ).
cnf(c_0_117,negated_conjecture,
esk3_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_41]),c_0_45])]) ).
cnf(c_0_118,plain,
( X1 = X2
| cons(X3,X2) != cons(X4,X1)
| ~ ssItem(X4)
| ~ ssItem(X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_119,plain,
( cons(esk14_1(X1),esk13_1(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_120,plain,
( ssItem(esk14_1(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_121,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_122,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| nil != cons(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
cnf(c_0_123,plain,
( cons(hd(X1),tl(app(X1,X2))) = app(X1,X2)
| nil = X1
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_70]),c_0_115]) ).
cnf(c_0_124,negated_conjecture,
app(esk4_0,nil) = esk4_0,
inference(rw,[status(thm)],[c_0_105,c_0_116]) ).
cnf(c_0_125,negated_conjecture,
segmentP(esk4_0,nil),
inference(rw,[status(thm)],[c_0_99,c_0_117]) ).
cnf(c_0_126,plain,
( esk13_1(cons(X1,X2)) = X2
| ~ ssList(esk13_1(cons(X1,X2)))
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119])]),c_0_120]),c_0_121]),c_0_122]) ).
cnf(c_0_127,negated_conjecture,
( cons(hd(esk4_0),tl(esk4_0)) = esk4_0
| esk4_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_41]),c_0_44])]) ).
fof(c_0_128,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
inference(fof_simplification,[status(thm)],[ax24]) ).
fof(c_0_129,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
inference(fof_simplification,[status(thm)],[ax22]) ).
cnf(c_0_130,negated_conjecture,
app(app(esk10_2(esk4_0,nil),nil),esk11_2(esk4_0,nil)) = esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_125]),c_0_41]),c_0_44])]) ).
cnf(c_0_131,negated_conjecture,
ssList(esk10_2(esk4_0,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_125]),c_0_41]),c_0_44])]) ).
cnf(c_0_132,negated_conjecture,
( esk13_1(esk4_0) = tl(esk4_0)
| esk4_0 = nil
| ~ ssList(esk13_1(esk4_0))
| ~ ssList(tl(esk4_0))
| ~ ssItem(hd(esk4_0)) ),
inference(spm,[status(thm)],[c_0_126,c_0_127]) ).
cnf(c_0_133,plain,
( ssList(esk13_1(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
fof(c_0_134,plain,
! [X209] :
( ~ ssList(X209)
| nil = X209
| ssList(tl(X209)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_128])])]) ).
fof(c_0_135,plain,
! [X87,X88,X89] :
( ~ ssList(X87)
| ~ ssList(X88)
| ~ ssList(X89)
| app(X89,X88) != app(X87,X88)
| X89 = X87 ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax79])])])]) ).
fof(c_0_136,plain,
! [X156] :
( ~ ssList(X156)
| nil = X156
| ssItem(hd(X156)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_129])])]) ).
cnf(c_0_137,negated_conjecture,
app(esk10_2(esk4_0,nil),esk11_2(esk4_0,nil)) = esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_62]),c_0_131])]) ).
cnf(c_0_138,negated_conjecture,
ssList(esk11_2(esk4_0,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_125]),c_0_41]),c_0_44])]) ).
cnf(c_0_139,negated_conjecture,
( esk13_1(esk4_0) = tl(esk4_0)
| esk4_0 = nil
| ~ ssList(tl(esk4_0))
| ~ ssItem(hd(esk4_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_133]),c_0_44])]) ).
cnf(c_0_140,plain,
( nil = X1
| ssList(tl(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_134]) ).
cnf(c_0_141,plain,
( X3 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(X3,X2) != app(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_135]) ).
cnf(c_0_142,plain,
( nil = X1
| ssItem(hd(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_136]) ).
cnf(c_0_143,negated_conjecture,
( hd(esk10_2(esk4_0,nil)) = hd(esk4_0)
| esk10_2(esk4_0,nil) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_137]),c_0_138]),c_0_131])]) ).
cnf(c_0_144,plain,
( nil = app(X2,X1)
| nil != X1
| nil != X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_145,negated_conjecture,
( esk13_1(esk4_0) = tl(esk4_0)
| esk4_0 = nil
| ~ ssItem(hd(esk4_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_44])]) ).
cnf(c_0_146,plain,
( X1 = nil
| app(X1,X2) != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_53]),c_0_41])]) ).
cnf(c_0_147,negated_conjecture,
( esk10_2(esk4_0,nil) = nil
| ssItem(hd(esk4_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_143]),c_0_131])]) ).
cnf(c_0_148,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_144])]),c_0_41])]) ).
fof(c_0_149,plain,
! [X149,X150] :
( ~ ssList(X149)
| ~ ssItem(X150)
| hd(cons(X150,X149)) = X150 ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])])]) ).
cnf(c_0_150,negated_conjecture,
( esk13_1(esk4_0) = tl(esk4_0)
| esk4_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_142]),c_0_44])]) ).
cnf(c_0_151,negated_conjecture,
( app(esk10_2(esk4_0,nil),nil) = nil
| esk11_2(esk4_0,nil) != esk4_0
| ~ ssList(app(esk10_2(esk4_0,nil),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_130]),c_0_138])]) ).
cnf(c_0_152,negated_conjecture,
( app(nil,esk11_2(esk4_0,nil)) = esk4_0
| ssItem(hd(esk4_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_147]),c_0_148]) ).
cnf(c_0_153,plain,
( hd(cons(X2,X1)) = X2
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_149]) ).
cnf(c_0_154,negated_conjecture,
( cons(esk14_1(esk4_0),tl(esk4_0)) = esk4_0
| esk4_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_150]),c_0_44])]) ).
cnf(c_0_155,negated_conjecture,
( esk4_0 = nil
| ssList(tl(esk4_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_150]),c_0_44])]) ).
fof(c_0_156,plain,
! [X58,X59,X60,X61] :
( ( X58 = X59
| ~ frontsegP(cons(X58,X60),cons(X59,X61))
| ~ ssList(X61)
| ~ ssList(X60)
| ~ ssItem(X59)
| ~ ssItem(X58) )
& ( frontsegP(X60,X61)
| ~ frontsegP(cons(X58,X60),cons(X59,X61))
| ~ ssList(X61)
| ~ ssList(X60)
| ~ ssItem(X59)
| ~ ssItem(X58) )
& ( X58 != X59
| ~ frontsegP(X60,X61)
| frontsegP(cons(X58,X60),cons(X59,X61))
| ~ ssList(X61)
| ~ ssList(X60)
| ~ ssItem(X59)
| ~ ssItem(X58) ) ),
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_157,negated_conjecture,
( app(esk10_2(esk4_0,nil),nil) = nil
| esk11_2(esk4_0,nil) != esk4_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_70]),c_0_41]),c_0_131])]) ).
cnf(c_0_158,negated_conjecture,
( esk11_2(esk4_0,nil) = esk4_0
| ssItem(hd(esk4_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_152]),c_0_138])]) ).
cnf(c_0_159,negated_conjecture,
( esk14_1(esk4_0) = hd(esk4_0)
| esk4_0 = nil
| ~ ssItem(esk14_1(esk4_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_154]),c_0_155]) ).
cnf(c_0_160,plain,
( frontsegP(cons(X1,X3),cons(X2,X4))
| X1 != X2
| ~ frontsegP(X3,X4)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_156]) ).
cnf(c_0_161,negated_conjecture,
( app(esk10_2(esk4_0,nil),nil) = nil
| ssItem(hd(esk4_0)) ),
inference(spm,[status(thm)],[c_0_157,c_0_158]) ).
cnf(c_0_162,negated_conjecture,
( esk14_1(esk4_0) = hd(esk4_0)
| esk4_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_120]),c_0_44])]) ).
cnf(c_0_163,plain,
( frontsegP(cons(X1,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(er,[status(thm)],[c_0_160]) ).
cnf(c_0_164,negated_conjecture,
( ~ segmentP(nil,X1)
| ~ segmentP(esk4_0,X1)
| ~ ssList(X1)
| ~ neq(X1,nil) ),
inference(rw,[status(thm)],[c_0_89,c_0_117]) ).
cnf(c_0_165,negated_conjecture,
( segmentP(nil,esk10_2(esk4_0,nil))
| ssItem(hd(esk4_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_161]),c_0_131]),c_0_41])]) ).
cnf(c_0_166,negated_conjecture,
segmentP(esk4_0,esk10_2(esk4_0,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_137]),c_0_131]),c_0_138])]) ).
cnf(c_0_167,negated_conjecture,
( X1 = esk4_0
| app(X1,nil) != esk4_0
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_124]),c_0_44]),c_0_41])]) ).
cnf(c_0_168,negated_conjecture,
( esk4_0 = nil
| ssItem(hd(esk4_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_162]),c_0_44])]) ).
cnf(c_0_169,negated_conjecture,
neq(esk2_0,nil),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_170,plain,
! [X43] :
( ~ ssList(X43)
| segmentP(X43,nil) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax57])])]) ).
cnf(c_0_171,plain,
( frontsegP(cons(X1,X2),cons(X1,nil))
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_40]),c_0_41])]) ).
cnf(c_0_172,negated_conjecture,
( ssItem(hd(esk4_0))
| ~ neq(esk10_2(esk4_0,nil),nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_165]),c_0_166]),c_0_131])]) ).
cnf(c_0_173,negated_conjecture,
( esk10_2(esk4_0,nil) = esk4_0
| ssItem(hd(esk4_0)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_161]),c_0_131])]),c_0_168]) ).
cnf(c_0_174,negated_conjecture,
neq(esk4_0,nil),
inference(rw,[status(thm)],[c_0_169,c_0_36]) ).
cnf(c_0_175,negated_conjecture,
( ~ ssList(X1)
| ~ neq(esk3_0,X1)
| ~ frontsegP(esk4_0,X1)
| ~ segmentP(X1,esk3_0)
| ~ totalorderedP(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_176,plain,
( segmentP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_170]) ).
cnf(c_0_177,negated_conjecture,
( esk4_0 = nil
| frontsegP(esk4_0,cons(esk14_1(esk4_0),nil))
| ~ ssItem(esk14_1(esk4_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_154]),c_0_155]) ).
cnf(c_0_178,plain,
( esk14_1(X1) = hd(X1)
| nil = X1
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_119]),c_0_120]),c_0_133]) ).
cnf(c_0_179,negated_conjecture,
ssItem(hd(esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_173]),c_0_174])]) ).
cnf(c_0_180,negated_conjecture,
( ~ totalorderedP(X1)
| ~ frontsegP(esk4_0,X1)
| ~ ssList(X1)
| ~ neq(nil,X1) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_175,c_0_117]),c_0_117]),c_0_176]) ).
cnf(c_0_181,negated_conjecture,
( esk4_0 = nil
| frontsegP(esk4_0,cons(hd(esk4_0),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_178]),c_0_179]),c_0_44])]) ).
cnf(c_0_182,negated_conjecture,
( esk4_0 = nil
| ~ totalorderedP(cons(hd(esk4_0),nil))
| ~ ssList(cons(hd(esk4_0),nil))
| ~ neq(nil,cons(hd(esk4_0),nil)) ),
inference(spm,[status(thm)],[c_0_180,c_0_181]) ).
fof(c_0_183,plain,
! [X24] :
( ~ ssItem(X24)
| totalorderedP(cons(X24,nil)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax65])])]) ).
cnf(c_0_184,negated_conjecture,
( esk4_0 = nil
| ~ totalorderedP(cons(hd(esk4_0),nil))
| ~ neq(nil,cons(hd(esk4_0),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_121]),c_0_41]),c_0_179])]) ).
cnf(c_0_185,plain,
( totalorderedP(cons(X1,nil))
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_183]) ).
fof(c_0_186,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
inference(fof_simplification,[status(thm)],[ax18]) ).
cnf(c_0_187,negated_conjecture,
( esk4_0 = nil
| ~ neq(nil,cons(hd(esk4_0),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_185]),c_0_179])]) ).
fof(c_0_188,plain,
! [X70,X71] :
( ~ ssList(X70)
| ~ ssItem(X71)
| cons(X71,X70) != X70 ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_186])])])]) ).
cnf(c_0_189,negated_conjecture,
( cons(hd(esk4_0),nil) = nil
| esk4_0 = nil
| ~ ssList(cons(hd(esk4_0),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_108]),c_0_41])]) ).
cnf(c_0_190,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| cons(X2,X1) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_188]) ).
cnf(c_0_191,negated_conjecture,
( cons(hd(esk4_0),nil) = nil
| esk4_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_121]),c_0_41]),c_0_179])]) ).
cnf(c_0_192,negated_conjecture,
( ~ segmentP(esk4_0,nil)
| ~ neq(nil,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_176]),c_0_41]),c_0_45])]) ).
cnf(c_0_193,negated_conjecture,
esk4_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_191]),c_0_41]),c_0_179])]) ).
cnf(c_0_194,negated_conjecture,
~ neq(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_192,c_0_176]),c_0_44])]) ).
cnf(c_0_195,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_174,c_0_193]),c_0_194]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC091+1 : TPTP v8.2.0. Released v2.4.0.
% 0.13/0.13 % Command : run_E %s %d THM
% 0.14/0.34 % Computer : n027.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun May 19 03:14:38 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.41/0.63 # Version: 3.1.0
% 1.41/0.63 # Preprocessing class: FSLSSMSSSSSNFFN.
% 1.41/0.63 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.41/0.63 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.41/0.63 # Starting new_bool_3 with 300s (1) cores
% 1.41/0.63 # Starting new_bool_1 with 300s (1) cores
% 1.41/0.63 # Starting sh5l with 300s (1) cores
% 1.41/0.63 # sh5l with pid 22242 completed with status 0
% 1.41/0.63 # Result found by sh5l
% 1.41/0.63 # Preprocessing class: FSLSSMSSSSSNFFN.
% 1.41/0.63 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.41/0.63 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.41/0.63 # Starting new_bool_3 with 300s (1) cores
% 1.41/0.63 # Starting new_bool_1 with 300s (1) cores
% 1.41/0.63 # Starting sh5l with 300s (1) cores
% 1.41/0.63 # SinE strategy is gf500_gu_R04_F100_L20000
% 1.41/0.63 # Search class: FGHSF-FSLM21-MFFFFFNN
% 1.41/0.63 # Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 1.41/0.63 # Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 28s (1) cores
% 1.41/0.63 # G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with pid 22245 completed with status 0
% 1.41/0.63 # Result found by G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c
% 1.41/0.63 # Preprocessing class: FSLSSMSSSSSNFFN.
% 1.41/0.63 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.41/0.63 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.41/0.63 # Starting new_bool_3 with 300s (1) cores
% 1.41/0.63 # Starting new_bool_1 with 300s (1) cores
% 1.41/0.63 # Starting sh5l with 300s (1) cores
% 1.41/0.63 # SinE strategy is gf500_gu_R04_F100_L20000
% 1.41/0.63 # Search class: FGHSF-FSLM21-MFFFFFNN
% 1.41/0.63 # Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 1.41/0.63 # Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 28s (1) cores
% 1.41/0.63 # Preprocessing time : 0.003 s
% 1.41/0.63 # Presaturation interreduction done
% 1.41/0.63
% 1.41/0.63 # Proof found!
% 1.41/0.63 # SZS status Theorem
% 1.41/0.63 # SZS output start CNFRefutation
% See solution above
% 1.41/0.63 # Parsed axioms : 96
% 1.41/0.63 # Removed by relevancy pruning/SinE : 12
% 1.41/0.63 # Initial clauses : 167
% 1.41/0.63 # Removed in clause preprocessing : 2
% 1.41/0.63 # Initial clauses in saturation : 165
% 1.41/0.63 # Processed clauses : 1334
% 1.41/0.63 # ...of these trivial : 21
% 1.41/0.63 # ...subsumed : 501
% 1.41/0.63 # ...remaining for further processing : 812
% 1.41/0.63 # Other redundant clauses eliminated : 63
% 1.41/0.63 # Clauses deleted for lack of memory : 0
% 1.41/0.63 # Backward-subsumed : 76
% 1.41/0.63 # Backward-rewritten : 241
% 1.41/0.63 # Generated clauses : 3882
% 1.41/0.63 # ...of the previous two non-redundant : 3209
% 1.41/0.63 # ...aggressively subsumed : 0
% 1.41/0.63 # Contextual simplify-reflections : 182
% 1.41/0.63 # Paramodulations : 3814
% 1.41/0.63 # Factorizations : 0
% 1.41/0.63 # NegExts : 0
% 1.41/0.63 # Equation resolutions : 69
% 1.41/0.63 # Disequality decompositions : 0
% 1.41/0.63 # Total rewrite steps : 4283
% 1.41/0.63 # ...of those cached : 4204
% 1.41/0.63 # Propositional unsat checks : 0
% 1.41/0.63 # Propositional check models : 0
% 1.41/0.63 # Propositional check unsatisfiable : 0
% 1.41/0.63 # Propositional clauses : 0
% 1.41/0.63 # Propositional clauses after purity: 0
% 1.41/0.63 # Propositional unsat core size : 0
% 1.41/0.63 # Propositional preprocessing time : 0.000
% 1.41/0.63 # Propositional encoding time : 0.000
% 1.41/0.63 # Propositional solver time : 0.000
% 1.41/0.63 # Success case prop preproc time : 0.000
% 1.41/0.63 # Success case prop encoding time : 0.000
% 1.41/0.63 # Success case prop solver time : 0.000
% 1.41/0.63 # Current number of processed clauses : 318
% 1.41/0.63 # Positive orientable unit clauses : 43
% 1.41/0.63 # Positive unorientable unit clauses: 0
% 1.41/0.63 # Negative unit clauses : 2
% 1.41/0.63 # Non-unit-clauses : 273
% 1.41/0.63 # Current number of unprocessed clauses: 2038
% 1.41/0.63 # ...number of literals in the above : 11405
% 1.41/0.63 # Current number of archived formulas : 0
% 1.41/0.63 # Current number of archived clauses : 476
% 1.41/0.63 # Clause-clause subsumption calls (NU) : 50521
% 1.41/0.63 # Rec. Clause-clause subsumption calls : 17433
% 1.41/0.63 # Non-unit clause-clause subsumptions : 737
% 1.41/0.63 # Unit Clause-clause subsumption calls : 3332
% 1.41/0.63 # Rewrite failures with RHS unbound : 0
% 1.41/0.63 # BW rewrite match attempts : 28
% 1.41/0.63 # BW rewrite match successes : 22
% 1.41/0.63 # Condensation attempts : 0
% 1.41/0.63 # Condensation successes : 0
% 1.41/0.63 # Termbank termtop insertions : 85029
% 1.41/0.63 # Search garbage collected termcells : 3681
% 1.41/0.63
% 1.41/0.63 # -------------------------------------------------
% 1.41/0.63 # User time : 0.137 s
% 1.41/0.63 # System time : 0.004 s
% 1.41/0.63 # Total time : 0.141 s
% 1.41/0.63 # Maximum resident set size: 2452 pages
% 1.41/0.63
% 1.41/0.63 # -------------------------------------------------
% 1.41/0.63 # User time : 0.140 s
% 1.41/0.63 # System time : 0.007 s
% 1.41/0.63 # Total time : 0.147 s
% 1.41/0.63 # Maximum resident set size: 1820 pages
% 1.41/0.63 % E---3.1 exiting
% 1.41/0.63 % E exiting
%------------------------------------------------------------------------------