TSTP Solution File: SWC123+1 by Enigma---0.5.1
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%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : SWC123+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% Computer : n005.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 : 600s
% DateTime : Tue Jul 19 20:13:46 EDT 2022
% Result : Theorem 13.78s 3.13s
% Output : CNFRefutation 13.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 33
% Syntax : Number of formulae : 184 ( 35 unt; 0 def)
% Number of atoms : 621 ( 168 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 741 ( 304 ~; 319 |; 37 &)
% ( 5 <=>; 76 =>; 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 : 13 ( 13 usr; 5 con; 0-2 aty)
% Number of variables : 253 ( 0 sgn 129 !; 6 ?)
% 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)
| ~ equalelemsP(X3)
| ? [X5] :
( ssList(X5)
& neq(X3,X5)
& frontsegP(X4,X5)
& segmentP(X5,X3)
& equalelemsP(X5) )
| ( neq(X1,nil)
& segmentP(X2,X1) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
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(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(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(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(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax84) ).
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(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(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
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(ax24,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax24) ).
fof(ax86,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> tl(app(X1,X2)) = app(tl(X1),X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax86) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax79,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X3,X2) = app(X1,X2)
=> X3 = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax79) ).
fof(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(ax22,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax22) ).
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(ax49,axiom,
! [X1] :
( ssList(X1)
=> rearsegP(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax49) ).
fof(ax56,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( segmentP(X1,X2)
=> segmentP(app(app(X3,X1),X4),X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax56) ).
fof(ax55,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax55) ).
fof(ax25,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> tl(cons(X2,X1)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax25) ).
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(ax57,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,nil) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax57) ).
fof(ax27,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax27) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax18,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax18) ).
fof(ax73,axiom,
! [X1] :
( ssItem(X1)
=> equalelemsP(cons(X1,nil)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax73) ).
fof(ax21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax21) ).
fof(ax81,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax81) ).
fof(c_0_33,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| ~ frontsegP(X4,X3)
| ~ equalelemsP(X3)
| ? [X5] :
( ssList(X5)
& neq(X3,X5)
& frontsegP(X4,X5)
& segmentP(X5,X3)
& equalelemsP(X5) )
| ( neq(X1,nil)
& segmentP(X2,X1) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_34,negated_conjecture,
! [X255] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& neq(esk49_0,nil)
& frontsegP(esk51_0,esk50_0)
& equalelemsP(esk50_0)
& ( ~ ssList(X255)
| ~ neq(esk50_0,X255)
| ~ frontsegP(esk51_0,X255)
| ~ segmentP(X255,esk50_0)
| ~ equalelemsP(X255) )
& ( ~ neq(esk48_0,nil)
| ~ segmentP(esk49_0,esk48_0) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_33])])])])]) ).
fof(c_0_35,plain,
! [X179,X180,X181] :
( ~ ssList(X179)
| ~ ssList(X180)
| ~ ssList(X181)
| ~ rearsegP(X179,X180)
| rearsegP(app(X181,X179),X180) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax50])])]) ).
fof(c_0_36,plain,
! [X182] :
( ~ ssList(X182)
| rearsegP(X182,nil) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax51])]) ).
fof(c_0_37,plain,
! [X20,X21,X23] :
( ( ssList(esk6_2(X20,X21))
| ~ frontsegP(X20,X21)
| ~ ssList(X21)
| ~ ssList(X20) )
& ( app(X21,esk6_2(X20,X21)) = X20
| ~ frontsegP(X20,X21)
| ~ ssList(X21)
| ~ ssList(X20) )
& ( ~ ssList(X23)
| app(X21,X23) != X20
| frontsegP(X20,X21)
| ~ ssList(X21)
| ~ ssList(X20) ) ),
inference(distribute,[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_38,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_39,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_40,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_41,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_42,plain,
( rearsegP(app(X3,X1),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ rearsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_43,plain,
( rearsegP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_44,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_45,plain,
( app(X1,esk6_2(X2,X1)) = X2
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_46,negated_conjecture,
frontsegP(esk51_0,esk50_0),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_47,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_48,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_49,plain,
( ssList(esk6_2(X1,X2))
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
fof(c_0_50,plain,
! [X24,X25,X27] :
( ( ssList(esk7_2(X24,X25))
| ~ rearsegP(X24,X25)
| ~ ssList(X25)
| ~ ssList(X24) )
& ( app(esk7_2(X24,X25),X25) = X24
| ~ rearsegP(X24,X25)
| ~ ssList(X25)
| ~ ssList(X24) )
& ( ~ ssList(X27)
| app(X27,X25) != X24
| rearsegP(X24,X25)
| ~ ssList(X25)
| ~ ssList(X24) ) ),
inference(distribute,[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_51,plain,
( rearsegP(app(X1,X2),nil)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44])]) ).
cnf(c_0_52,negated_conjecture,
app(esk50_0,esk6_2(esk51_0,esk50_0)) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]),c_0_48])]) ).
cnf(c_0_53,negated_conjecture,
ssList(esk6_2(esk51_0,esk50_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_46]),c_0_48]),c_0_47])]) ).
fof(c_0_54,plain,
! [X164,X165,X166] :
( ~ ssList(X164)
| ~ ssList(X165)
| ~ ssList(X166)
| ~ frontsegP(X164,X165)
| frontsegP(app(X164,X166),X165) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax43])])]) ).
fof(c_0_55,plain,
! [X171] :
( ~ ssList(X171)
| frontsegP(X171,nil) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax45])]) ).
fof(c_0_56,plain,
! [X227] :
( ~ ssList(X227)
| app(X227,nil) = X227 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).
cnf(c_0_57,plain,
( app(esk7_2(X1,X2),X2) = X1
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_58,negated_conjecture,
rearsegP(esk51_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_48]),c_0_53])]) ).
cnf(c_0_59,plain,
( ssList(esk7_2(X1,X2))
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_60,plain,
( frontsegP(app(X1,X3),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ frontsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_61,plain,
( frontsegP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_62,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_63,negated_conjecture,
app(esk7_2(esk51_0,nil),nil) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_44]),c_0_47])]) ).
cnf(c_0_64,negated_conjecture,
ssList(esk7_2(esk51_0,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_58]),c_0_44]),c_0_47])]) ).
cnf(c_0_65,plain,
( frontsegP(app(X1,X2),nil)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_44])]) ).
fof(c_0_66,plain,
! [X167,X168,X169,X170] :
( ( X167 = X168
| ~ frontsegP(cons(X167,X169),cons(X168,X170))
| ~ ssList(X170)
| ~ ssList(X169)
| ~ ssItem(X168)
| ~ ssItem(X167) )
& ( frontsegP(X169,X170)
| ~ frontsegP(cons(X167,X169),cons(X168,X170))
| ~ ssList(X170)
| ~ ssList(X169)
| ~ ssItem(X168)
| ~ ssItem(X167) )
& ( X167 != X168
| ~ frontsegP(X169,X170)
| frontsegP(cons(X167,X169),cons(X168,X170))
| ~ ssList(X170)
| ~ ssList(X169)
| ~ ssItem(X168)
| ~ ssItem(X167) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax44])])])]) ).
fof(c_0_67,plain,
! [X213] :
( ~ ssList(X213)
| nil = X213
| cons(hd(X213),tl(X213)) = X213 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax78])]) ).
fof(c_0_68,plain,
! [X228,X229] :
( ~ ssList(X228)
| ~ ssList(X229)
| nil = X228
| hd(app(X228,X229)) = hd(X228) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax85])])]) ).
fof(c_0_69,plain,
! [X130,X131] :
( ~ ssList(X130)
| ~ ssList(X131)
| ssList(app(X130,X131)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).
fof(c_0_70,plain,
! [X225,X226] :
( ( nil = X226
| nil != app(X225,X226)
| ~ ssList(X226)
| ~ ssList(X225) )
& ( nil = X225
| nil != app(X225,X226)
| ~ ssList(X226)
| ~ ssList(X225) )
& ( nil != X226
| nil != X225
| nil = app(X225,X226)
| ~ ssList(X226)
| ~ ssList(X225) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).
fof(c_0_71,plain,
! [X127] :
( ~ ssList(X127)
| nil = X127
| ssList(tl(X127)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax24])]) ).
fof(c_0_72,plain,
! [X230,X231] :
( ~ ssList(X230)
| ~ ssList(X231)
| nil = X230
| tl(app(X230,X231)) = app(tl(X230),X231) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax86])])]) ).
cnf(c_0_73,negated_conjecture,
esk7_2(esk51_0,nil) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64])]) ).
fof(c_0_74,plain,
! [X135] :
( ~ ssList(X135)
| app(nil,X135) = X135 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).
cnf(c_0_75,negated_conjecture,
frontsegP(esk51_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_52]),c_0_53]),c_0_48])]) ).
cnf(c_0_76,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_66]) ).
cnf(c_0_77,plain,
( nil = X1
| cons(hd(X1),tl(X1)) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_78,plain,
( nil = X1
| hd(app(X1,X2)) = hd(X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_79,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_80,plain,
( nil = X1
| nil != app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_81,plain,
( nil = X1
| ssList(tl(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_82,plain,
( nil = X1
| tl(app(X1,X2)) = app(tl(X1),X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_83,negated_conjecture,
app(esk51_0,nil) = esk51_0,
inference(rw,[status(thm)],[c_0_63,c_0_73]) ).
cnf(c_0_84,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_85,negated_conjecture,
app(nil,esk6_2(esk51_0,nil)) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_75]),c_0_47]),c_0_44])]) ).
cnf(c_0_86,negated_conjecture,
ssList(esk6_2(esk51_0,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_75]),c_0_44]),c_0_47])]) ).
cnf(c_0_87,plain,
( frontsegP(cons(X1,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(er,[status(thm)],[c_0_76]) ).
cnf(c_0_88,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_77,c_0_78]),c_0_79]),c_0_80]) ).
cnf(c_0_89,plain,
( nil = X1
| ssList(app(tl(X1),X2))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_79]),c_0_80]) ).
cnf(c_0_90,negated_conjecture,
( app(tl(esk51_0),nil) = tl(esk51_0)
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_44]),c_0_47])]) ).
fof(c_0_91,plain,
! [X214,X215,X216] :
( ~ ssList(X214)
| ~ ssList(X215)
| ~ ssList(X216)
| app(X216,X215) != app(X214,X215)
| X216 = X214 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax79])])]) ).
cnf(c_0_92,plain,
( rearsegP(X3,X2)
| ~ ssList(X1)
| app(X1,X2) != X3
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_93,negated_conjecture,
esk6_2(esk51_0,nil) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_86])]) ).
fof(c_0_94,plain,
! [X119] :
( ( ssList(esk44_1(X119))
| nil = X119
| ~ ssList(X119) )
& ( ssItem(esk45_1(X119))
| nil = X119
| ~ ssList(X119) )
& ( cons(esk45_1(X119),esk44_1(X119)) = X119
| nil = X119
| ~ ssList(X119) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax20])])])]) ).
cnf(c_0_95,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_87,c_0_61]),c_0_44])]) ).
cnf(c_0_96,negated_conjecture,
( cons(hd(esk51_0),tl(esk51_0)) = esk51_0
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_83]),c_0_44]),c_0_47])]) ).
cnf(c_0_97,negated_conjecture,
( esk51_0 = nil
| ssList(tl(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_44]),c_0_47])]) ).
fof(c_0_98,plain,
! [X124] :
( ~ ssList(X124)
| nil = X124
| ssItem(hd(X124)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax22])]) ).
cnf(c_0_99,plain,
( X3 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(X3,X2) != app(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
fof(c_0_100,plain,
! [X222,X223,X224] :
( ~ ssList(X222)
| ~ ssList(X223)
| ~ ssList(X224)
| app(app(X222,X223),X224) = app(X222,app(X223,X224)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])]) ).
cnf(c_0_101,plain,
( rearsegP(app(X1,X2),X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_92]),c_0_79]) ).
cnf(c_0_102,negated_conjecture,
app(nil,esk51_0) = esk51_0,
inference(rw,[status(thm)],[c_0_85,c_0_93]) ).
cnf(c_0_103,plain,
( X1 = X2
| ~ frontsegP(cons(X1,X3),cons(X2,X4))
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_104,plain,
( cons(esk45_1(X1),esk44_1(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_105,plain,
( ssItem(esk45_1(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_106,plain,
( ssList(esk44_1(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_107,negated_conjecture,
( esk51_0 = nil
| frontsegP(esk51_0,cons(hd(esk51_0),nil))
| ~ ssItem(hd(esk51_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_97]) ).
cnf(c_0_108,plain,
( nil = X1
| ssItem(hd(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_109,negated_conjecture,
( X1 = esk50_0
| app(X1,esk6_2(esk51_0,esk50_0)) != esk51_0
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_52]),c_0_48]),c_0_53])]) ).
cnf(c_0_110,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
fof(c_0_111,plain,
! [X178] :
( ~ ssList(X178)
| rearsegP(X178,X178) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax49])]) ).
cnf(c_0_112,negated_conjecture,
rearsegP(esk51_0,esk51_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_47]),c_0_44])]) ).
cnf(c_0_113,plain,
( ssList(esk7_2(app(X1,X2),X2))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_101]),c_0_79]) ).
cnf(c_0_114,plain,
( esk45_1(X1) = X2
| nil = X1
| ~ frontsegP(X1,cons(X2,X3))
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_105]),c_0_106]) ).
cnf(c_0_115,negated_conjecture,
( esk51_0 = nil
| frontsegP(esk51_0,cons(hd(esk51_0),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_47])]) ).
fof(c_0_116,plain,
! [X190,X191,X192,X193] :
( ~ ssList(X190)
| ~ ssList(X191)
| ~ ssList(X192)
| ~ ssList(X193)
| ~ segmentP(X190,X191)
| segmentP(app(app(X192,X190),X193),X191) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax56])])]) ).
fof(c_0_117,plain,
! [X189] :
( ~ ssList(X189)
| segmentP(X189,X189) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax55])]) ).
cnf(c_0_118,negated_conjecture,
( app(X1,X2) = esk50_0
| app(X1,app(X2,esk6_2(esk51_0,esk50_0))) != esk51_0
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_53])]),c_0_79]) ).
cnf(c_0_119,plain,
( rearsegP(X1,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_120,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_99,c_0_84]),c_0_44])]) ).
cnf(c_0_121,negated_conjecture,
app(esk7_2(esk51_0,esk51_0),esk51_0) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_112]),c_0_47])]) ).
cnf(c_0_122,negated_conjecture,
ssList(esk7_2(esk51_0,esk51_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_102]),c_0_47]),c_0_44])]) ).
cnf(c_0_123,negated_conjecture,
( esk45_1(esk51_0) = hd(esk51_0)
| esk51_0 = nil
| ~ ssItem(hd(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_44]),c_0_47])]) ).
cnf(c_0_124,plain,
( segmentP(app(app(X3,X1),X4),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| ~ segmentP(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_125,plain,
( segmentP(X1,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_117]) ).
cnf(c_0_126,negated_conjecture,
( app(X1,esk50_0) = esk50_0
| app(X1,esk51_0) != esk51_0
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_52]),c_0_48])]) ).
cnf(c_0_127,plain,
( app(esk7_2(X1,X1),X1) = X1
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_57,c_0_119]) ).
cnf(c_0_128,negated_conjecture,
esk7_2(esk51_0,esk51_0) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_47]),c_0_122])]) ).
fof(c_0_129,plain,
! [X128,X129] :
( ~ ssList(X128)
| ~ ssItem(X129)
| tl(cons(X129,X128)) = X128 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax25])])]) ).
cnf(c_0_130,negated_conjecture,
( esk45_1(esk51_0) = hd(esk51_0)
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_108]),c_0_47])]) ).
cnf(c_0_131,plain,
( segmentP(app(app(X1,X2),X3),X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_132,negated_conjecture,
app(nil,esk50_0) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_128]),c_0_128]),c_0_44]),c_0_47])]) ).
cnf(c_0_133,plain,
( tl(cons(X2,X1)) = X1
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
cnf(c_0_134,negated_conjecture,
( cons(hd(esk51_0),esk44_1(esk51_0)) = esk51_0
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_130]),c_0_47])]) ).
cnf(c_0_135,negated_conjecture,
( esk51_0 = nil
| ssItem(hd(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_130]),c_0_47])]) ).
cnf(c_0_136,negated_conjecture,
( ~ neq(esk48_0,nil)
| ~ segmentP(esk49_0,esk48_0) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_137,negated_conjecture,
( segmentP(app(esk50_0,X1),esk50_0)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_44]),c_0_48])]) ).
cnf(c_0_138,negated_conjecture,
( esk44_1(esk51_0) = tl(esk51_0)
| esk51_0 = nil
| ~ ssList(esk44_1(esk51_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_135]) ).
cnf(c_0_139,negated_conjecture,
( ~ segmentP(esk51_0,esk50_0)
| ~ neq(esk50_0,nil) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_136,c_0_41]),c_0_39]),c_0_41]) ).
cnf(c_0_140,negated_conjecture,
segmentP(esk51_0,esk50_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_52]),c_0_53])]) ).
fof(c_0_141,plain,
! [X109,X110] :
( ( ~ neq(X109,X110)
| X109 != X110
| ~ ssList(X110)
| ~ ssList(X109) )
& ( X109 = X110
| neq(X109,X110)
| ~ ssList(X110)
| ~ ssList(X109) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])])]) ).
cnf(c_0_142,negated_conjecture,
( esk44_1(esk51_0) = tl(esk51_0)
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_106]),c_0_47])]) ).
cnf(c_0_143,negated_conjecture,
~ neq(esk50_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_139,c_0_140])]) ).
cnf(c_0_144,plain,
( X1 = X2
| neq(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_141]) ).
fof(c_0_145,plain,
! [X194] :
( ~ ssList(X194)
| segmentP(X194,nil) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax57])]) ).
cnf(c_0_146,negated_conjecture,
( cons(esk45_1(esk51_0),tl(esk51_0)) = esk51_0
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_142]),c_0_47])]) ).
fof(c_0_147,plain,
! [X132,X133,X134] :
( ~ ssList(X132)
| ~ ssList(X133)
| ~ ssItem(X134)
| cons(X134,app(X133,X132)) = app(cons(X134,X133),X132) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])]) ).
fof(c_0_148,plain,
! [X111,X112] :
( ~ ssList(X111)
| ~ ssItem(X112)
| ssList(cons(X112,X111)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).
fof(c_0_149,plain,
! [X113,X114] :
( ~ ssList(X113)
| ~ ssItem(X114)
| cons(X114,X113) != X113 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax18])])]) ).
cnf(c_0_150,negated_conjecture,
( ~ ssList(X1)
| ~ neq(esk50_0,X1)
| ~ frontsegP(esk51_0,X1)
| ~ segmentP(X1,esk50_0)
| ~ equalelemsP(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_151,negated_conjecture,
esk50_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_144]),c_0_44]),c_0_48])]) ).
cnf(c_0_152,plain,
( segmentP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_145]) ).
cnf(c_0_153,negated_conjecture,
( esk51_0 = nil
| frontsegP(esk51_0,cons(esk45_1(esk51_0),nil))
| ~ ssItem(esk45_1(esk51_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_146]),c_0_97]) ).
cnf(c_0_154,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_147]) ).
cnf(c_0_155,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_148]) ).
cnf(c_0_156,plain,
( nil = app(X2,X1)
| nil != X1
| nil != X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_157,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| cons(X2,X1) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_149]) ).
cnf(c_0_158,negated_conjecture,
( ~ equalelemsP(X1)
| ~ frontsegP(esk51_0,X1)
| ~ ssList(X1)
| ~ neq(nil,X1) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_150,c_0_151]),c_0_151]),c_0_152]) ).
cnf(c_0_159,negated_conjecture,
( esk51_0 = nil
| frontsegP(esk51_0,cons(esk45_1(esk51_0),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_105]),c_0_47])]) ).
fof(c_0_160,plain,
! [X206] :
( ~ ssItem(X206)
| equalelemsP(cons(X206,nil)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax73])]) ).
cnf(c_0_161,plain,
( ssList(cons(X1,app(X2,X3)))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_154]),c_0_155]) ).
cnf(c_0_162,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_156])]),c_0_44])]) ).
cnf(c_0_163,plain,
( nil = X1
| tl(X1) != X1
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_77]),c_0_108]),c_0_81]) ).
cnf(c_0_164,negated_conjecture,
( esk51_0 = nil
| ~ equalelemsP(cons(esk45_1(esk51_0),nil))
| ~ ssList(cons(esk45_1(esk51_0),nil))
| ~ neq(nil,cons(esk45_1(esk51_0),nil)) ),
inference(spm,[status(thm)],[c_0_158,c_0_159]) ).
cnf(c_0_165,plain,
( equalelemsP(cons(X1,nil))
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_160]) ).
cnf(c_0_166,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_162]),c_0_44])]) ).
cnf(c_0_167,plain,
( nil = X1
| app(tl(X1),X2) != app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_82]),c_0_79]),c_0_80]) ).
fof(c_0_168,plain,
! [X122,X123] :
( ~ ssList(X122)
| ~ ssItem(X123)
| nil != cons(X123,X122) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax21])])]) ).
cnf(c_0_169,negated_conjecture,
( esk51_0 = nil
| ~ neq(nil,cons(esk45_1(esk51_0),nil))
| ~ ssItem(esk45_1(esk51_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_165]),c_0_166]) ).
cnf(c_0_170,plain,
( nil = X1
| tl(X1) != app(X1,nil)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_62]),c_0_44])]),c_0_81]) ).
cnf(c_0_171,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| nil != cons(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_168]) ).
fof(c_0_172,plain,
! [X220,X221] :
( ~ ssList(X220)
| ~ ssItem(X221)
| cons(X221,X220) = app(cons(X221,nil),X220) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).
cnf(c_0_173,negated_conjecture,
( esk51_0 = nil
| ~ neq(nil,cons(esk45_1(esk51_0),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_105]),c_0_47])]) ).
cnf(c_0_174,plain,
( app(cons(X1,X2),nil) != X2
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_133]),c_0_155]),c_0_171]) ).
cnf(c_0_175,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_172]) ).
cnf(c_0_176,negated_conjecture,
( cons(esk45_1(esk51_0),nil) = nil
| esk51_0 = nil
| ~ ssList(cons(esk45_1(esk51_0),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_144]),c_0_44])]) ).
cnf(c_0_177,plain,
( cons(X1,nil) != nil
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_175]),c_0_44])]) ).
cnf(c_0_178,negated_conjecture,
neq(esk49_0,nil),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_179,negated_conjecture,
( esk51_0 = nil
| ~ ssItem(esk45_1(esk51_0)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_155]),c_0_44])]),c_0_177]) ).
cnf(c_0_180,negated_conjecture,
neq(esk51_0,nil),
inference(rw,[status(thm)],[c_0_178,c_0_39]) ).
cnf(c_0_181,negated_conjecture,
esk51_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_179,c_0_105]),c_0_47])]) ).
cnf(c_0_182,negated_conjecture,
~ neq(nil,nil),
inference(rw,[status(thm)],[c_0_143,c_0_151]) ).
cnf(c_0_183,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_180,c_0_181]),c_0_182]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC123+1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.12 % Command : enigmatic-eprover.py %s %d 1
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 12 12:44:25 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.43 # ENIGMATIC: Selected SinE mode:
% 0.18/0.44 # Parsing /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 # Filter: axfilter_auto 0 goes into file theBenchmark_axfilter_auto 0.p
% 0.18/0.44 # Filter: axfilter_auto 1 goes into file theBenchmark_axfilter_auto 1.p
% 0.18/0.44 # Filter: axfilter_auto 2 goes into file theBenchmark_axfilter_auto 2.p
% 13.78/3.13 # ENIGMATIC: Solved by autoschedule:
% 13.78/3.13 # No SInE strategy applied
% 13.78/3.13 # Trying AutoSched0 for 150 seconds
% 13.78/3.13 # AutoSched0-Mode selected heuristic G_E___207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 13.78/3.13 # and selection function SelectNewComplexAHP.
% 13.78/3.13 #
% 13.78/3.13 # Preprocessing time : 0.034 s
% 13.78/3.13 # Presaturation interreduction done
% 13.78/3.13
% 13.78/3.13 # Proof found!
% 13.78/3.13 # SZS status Theorem
% 13.78/3.13 # SZS output start CNFRefutation
% See solution above
% 13.78/3.13 # Training examples: 0 positive, 0 negative
% 13.78/3.13
% 13.78/3.13 # -------------------------------------------------
% 13.78/3.13 # User time : 0.680 s
% 13.78/3.13 # System time : 0.031 s
% 13.78/3.13 # Total time : 0.712 s
% 13.78/3.13 # Maximum resident set size: 7120 pages
% 13.78/3.13
%------------------------------------------------------------------------------