%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC409+1 : TPTP v9.2.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n015.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 5 05:19:33 PM UTC 2026
% Result : Theorem 41.68s 24.55s
% Output : CNFRefutation 41.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 29
% Syntax : Number of formulae : 202 ( 52 unt; 0 def)
% Number of atoms : 680 ( 174 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 796 ( 318 ~; 355 |; 46 &)
% ( 7 <=>; 70 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 6 con; 0-2 aty)
% Number of variables : 260 ( 0 sgn 121 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(X6,cons(X5,nil)) != X3
& app(cons(X5,nil),X6) = X4 ) )
| ! [X7] :
( ssItem(X7)
=> ( ~ memberP(X2,X7)
| memberP(X1,X7) ) )
| ( nil != X3
& nil = X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax5,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X2,X3) = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax5) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax3,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ( memberP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(X3,cons(X2,X4)) = X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax3) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
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(ax45,axiom,
! [X1] :
( ssList(X1)
=> frontsegP(X1,nil) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax45) ).
fof(ax83,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
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(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/sandbox/benchmark/Axioms/SWC001+0.ax',ax7) ).
fof(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(ax50,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( rearsegP(X1,X2)
=> rearsegP(app(X3,X1),X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax50) ).
fof(ax51,axiom,
! [X1] :
( ssList(X1)
=> rearsegP(X1,nil) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax51) ).
fof(ax6,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( rearsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X3,X2) = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax6) ).
fof(ax85,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> hd(app(X1,X2)) = hd(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax85) ).
fof(ax22,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
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(ax37,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(cons(X2,X3),X1)
<=> ( X1 = X2
| memberP(X3,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax37) ).
fof(ax20,axiom,
! [X1] :
( ssList(X1)
=> ( nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax20) ).
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(ax25,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> tl(cons(X2,X1)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax25) ).
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(ax47,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( rearsegP(X1,X2)
& rearsegP(X2,X3) )
=> rearsegP(X1,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax47) ).
fof(ax36,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(app(X2,X3),X1)
<=> ( memberP(X2,X1)
| memberP(X3,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax36) ).
fof(ax23,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> hd(cons(X2,X1)) = X2 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax23) ).
fof(ax38,axiom,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax38) ).
fof(c_0_29,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(X6,cons(X5,nil)) != X3
& app(cons(X5,nil),X6) = X4 ) )
| ! [X7] :
( ssItem(X7)
=> ( ~ memberP(X2,X7)
| memberP(X1,X7) ) )
| ( nil != X3
& nil = X4 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_30,negated_conjecture,
! [X466,X467] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& ( ~ ssItem(X466)
| ~ ssList(X467)
| app(X467,cons(X466,nil)) = esk50_0
| app(cons(X466,nil),X467) != esk51_0 )
& ssItem(esk52_0)
& memberP(esk49_0,esk52_0)
& ~ memberP(esk48_0,esk52_0)
& ( nil = esk50_0
| nil != esk51_0 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])])]) ).
fof(c_0_31,plain,
! [X231,X232,X234] :
( ( ssList(esk6_2(X231,X232))
| ~ frontsegP(X231,X232)
| ~ ssList(X232)
| ~ ssList(X231) )
& ( app(X232,esk6_2(X231,X232)) = X231
| ~ frontsegP(X231,X232)
| ~ ssList(X232)
| ~ ssList(X231) )
& ( ~ ssList(X234)
| app(X232,X234) != X231
| frontsegP(X231,X232)
| ~ ssList(X232)
| ~ ssList(X231) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax5])])])])]) ).
fof(c_0_32,plain,
! [X341,X342] :
( ~ ssList(X341)
| ~ ssList(X342)
| ssList(app(X341,X342)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).
fof(c_0_33,plain,
! [X222,X223,X226,X227] :
( ( ssList(esk3_2(X222,X223))
| ~ memberP(X222,X223)
| ~ ssItem(X223)
| ~ ssList(X222) )
& ( ssList(esk4_2(X222,X223))
| ~ memberP(X222,X223)
| ~ ssItem(X223)
| ~ ssList(X222) )
& ( app(esk3_2(X222,X223),cons(X223,esk4_2(X222,X223))) = X222
| ~ memberP(X222,X223)
| ~ ssItem(X223)
| ~ ssList(X222) )
& ( ~ ssList(X226)
| ~ ssList(X227)
| app(X226,cons(X223,X227)) != X222
| memberP(X222,X223)
| ~ ssItem(X223)
| ~ ssList(X222) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax3])])])])]) ).
cnf(c_0_34,negated_conjecture,
memberP(esk49_0,esk52_0),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_35,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_36,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_37,plain,
( frontsegP(X3,X2)
| ~ ssList(X1)
| app(X2,X1) != X3
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_38,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_39,plain,
( app(esk3_2(X1,X2),cons(X2,esk4_2(X1,X2))) = X1
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_40,negated_conjecture,
memberP(esk51_0,esk52_0),
inference(rw,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_36,c_0_35]) ).
cnf(c_0_42,negated_conjecture,
ssItem(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_43,plain,
( ssList(esk3_2(X1,X2))
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_44,plain,
( frontsegP(app(X1,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_37]),c_0_38]) ).
cnf(c_0_45,negated_conjecture,
app(esk3_2(esk51_0,esk52_0),cons(esk52_0,esk4_2(esk51_0,esk52_0))) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]),c_0_42])]) ).
cnf(c_0_46,negated_conjecture,
ssList(esk3_2(esk51_0,esk52_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_40]),c_0_41]),c_0_42])]) ).
fof(c_0_47,plain,
! [X322,X323] :
( ~ ssList(X322)
| ~ ssItem(X323)
| ssList(cons(X323,X322)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).
cnf(c_0_48,plain,
( ssList(esk4_2(X1,X2))
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_49,plain,
! [X375,X376,X377] :
( ~ ssList(X375)
| ~ ssList(X376)
| ~ ssList(X377)
| ~ frontsegP(X375,X376)
| frontsegP(app(X375,X377),X376) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax43])])]) ).
fof(c_0_50,plain,
! [X382] :
( ~ ssList(X382)
| frontsegP(X382,nil) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax45])]) ).
cnf(c_0_51,negated_conjecture,
( frontsegP(esk51_0,esk3_2(esk51_0,esk52_0))
| ~ ssList(cons(esk52_0,esk4_2(esk51_0,esk52_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46])]) ).
cnf(c_0_52,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_53,negated_conjecture,
ssList(esk4_2(esk51_0,esk52_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_40]),c_0_41]),c_0_42])]) ).
fof(c_0_54,plain,
! [X436,X437] :
( ( nil = X437
| nil != app(X436,X437)
| ~ ssList(X437)
| ~ ssList(X436) )
& ( nil = X436
| nil != app(X436,X437)
| ~ ssList(X437)
| ~ ssList(X436) )
& ( nil != X437
| nil != X436
| nil = app(X436,X437)
| ~ ssList(X437)
| ~ ssList(X436) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).
cnf(c_0_55,plain,
( frontsegP(app(X1,X3),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ frontsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_56,plain,
( frontsegP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_57,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_58,plain,
( app(X1,esk6_2(X2,X1)) = X2
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_59,negated_conjecture,
frontsegP(esk51_0,esk3_2(esk51_0,esk52_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]),c_0_42])]) ).
cnf(c_0_60,plain,
( ssList(esk6_2(X1,X2))
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_61,plain,
! [X433,X434,X435] :
( ~ ssList(X433)
| ~ ssList(X434)
| ~ ssList(X435)
| app(app(X433,X434),X435) = app(X433,app(X434,X435)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])]) ).
cnf(c_0_62,plain,
( nil = app(X2,X1)
| nil != X1
| nil != X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_63,plain,
( frontsegP(app(X1,X2),nil)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57])]) ).
cnf(c_0_64,negated_conjecture,
app(esk3_2(esk51_0,esk52_0),esk6_2(esk51_0,esk3_2(esk51_0,esk52_0))) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_41]),c_0_46])]) ).
cnf(c_0_65,negated_conjecture,
ssList(esk6_2(esk51_0,esk3_2(esk51_0,esk52_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_59]),c_0_46]),c_0_41])]) ).
fof(c_0_66,plain,
! [X239,X240,X243,X244] :
( ( ssList(esk8_2(X239,X240))
| ~ segmentP(X239,X240)
| ~ ssList(X240)
| ~ ssList(X239) )
& ( ssList(esk9_2(X239,X240))
| ~ segmentP(X239,X240)
| ~ ssList(X240)
| ~ ssList(X239) )
& ( app(app(esk8_2(X239,X240),X240),esk9_2(X239,X240)) = X239
| ~ segmentP(X239,X240)
| ~ ssList(X240)
| ~ ssList(X239) )
& ( ~ ssList(X243)
| ~ ssList(X244)
| app(app(X243,X240),X244) != X239
| segmentP(X239,X240)
| ~ ssList(X240)
| ~ ssList(X239) ) ),
inference(distribute,[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_67,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_68,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_62])]),c_0_57])]) ).
cnf(c_0_69,negated_conjecture,
frontsegP(esk51_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65]),c_0_46])]) ).
cnf(c_0_70,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_66]) ).
cnf(c_0_71,plain,
( app(nil,app(nil,X1)) = app(nil,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_57])]) ).
cnf(c_0_72,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_58,c_0_69]),c_0_41]),c_0_57])]) ).
cnf(c_0_73,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_60,c_0_69]),c_0_57]),c_0_41])]) ).
cnf(c_0_74,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_70]) ).
cnf(c_0_75,negated_conjecture,
app(nil,esk51_0) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73])]) ).
fof(c_0_76,plain,
! [X438] :
( ~ ssList(X438)
| app(X438,nil) = X438 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).
cnf(c_0_77,negated_conjecture,
( segmentP(app(esk51_0,X1),esk51_0)
| ~ ssList(app(esk51_0,X1))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_41]),c_0_57])]) ).
cnf(c_0_78,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_79,plain,
( app(app(esk8_2(X1,X2),X2),esk9_2(X1,X2)) = X1
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_80,negated_conjecture,
segmentP(esk51_0,esk51_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_41]),c_0_57])]) ).
cnf(c_0_81,plain,
( ssList(esk9_2(X1,X2))
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_82,plain,
( ssList(esk8_2(X1,X2))
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_83,negated_conjecture,
app(app(esk8_2(esk51_0,esk51_0),esk51_0),esk9_2(esk51_0,esk51_0)) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_41])]) ).
cnf(c_0_84,negated_conjecture,
ssList(esk9_2(esk51_0,esk51_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_80]),c_0_41])]) ).
cnf(c_0_85,negated_conjecture,
ssList(esk8_2(esk51_0,esk51_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_80]),c_0_41])]) ).
cnf(c_0_86,negated_conjecture,
app(esk8_2(esk51_0,esk51_0),app(esk51_0,esk9_2(esk51_0,esk51_0))) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_83]),c_0_84]),c_0_41]),c_0_85])]) ).
fof(c_0_87,plain,
! [X390,X391,X392] :
( ~ ssList(X390)
| ~ ssList(X391)
| ~ ssList(X392)
| ~ rearsegP(X390,X391)
| rearsegP(app(X392,X390),X391) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax50])])]) ).
fof(c_0_88,plain,
! [X393] :
( ~ ssList(X393)
| rearsegP(X393,nil) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax51])]) ).
cnf(c_0_89,negated_conjecture,
( frontsegP(esk51_0,esk8_2(esk51_0,esk51_0))
| ~ ssList(app(esk51_0,esk9_2(esk51_0,esk51_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_86]),c_0_85])]) ).
cnf(c_0_90,plain,
( rearsegP(app(X3,X1),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ rearsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_91,plain,
( rearsegP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_92,negated_conjecture,
frontsegP(esk51_0,esk8_2(esk51_0,esk51_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_38]),c_0_84]),c_0_41])]) ).
fof(c_0_93,plain,
! [X235,X236,X238] :
( ( ssList(esk7_2(X235,X236))
| ~ rearsegP(X235,X236)
| ~ ssList(X236)
| ~ ssList(X235) )
& ( app(esk7_2(X235,X236),X236) = X235
| ~ rearsegP(X235,X236)
| ~ ssList(X236)
| ~ ssList(X235) )
& ( ~ ssList(X238)
| app(X238,X236) != X235
| rearsegP(X235,X236)
| ~ ssList(X236)
| ~ ssList(X235) ) ),
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_94,plain,
( rearsegP(app(X1,X2),nil)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_57])]) ).
cnf(c_0_95,negated_conjecture,
app(esk8_2(esk51_0,esk51_0),esk6_2(esk51_0,esk8_2(esk51_0,esk51_0))) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_92]),c_0_41]),c_0_85])]) ).
cnf(c_0_96,negated_conjecture,
ssList(esk6_2(esk51_0,esk8_2(esk51_0,esk51_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_92]),c_0_85]),c_0_41])]) ).
cnf(c_0_97,plain,
( app(esk7_2(X1,X2),X2) = X1
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_98,plain,
( ssList(esk7_2(X1,X2))
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_99,negated_conjecture,
rearsegP(esk51_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_85]),c_0_96])]) ).
cnf(c_0_100,plain,
( app(esk7_2(X1,nil),nil) = X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_91]),c_0_57])]) ).
cnf(c_0_101,plain,
( ssList(esk7_2(X1,nil))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_91]),c_0_57])]) ).
cnf(c_0_102,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_97,c_0_99]),c_0_57]),c_0_41])]) ).
cnf(c_0_103,plain,
( esk7_2(X1,nil) = X1
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_100]),c_0_101]) ).
cnf(c_0_104,negated_conjecture,
app(esk51_0,nil) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_41])]) ).
fof(c_0_105,plain,
! [X439,X440] :
( ~ ssList(X439)
| ~ ssList(X440)
| nil = X439
| hd(app(X439,X440)) = hd(X439) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax85])])]) ).
cnf(c_0_106,negated_conjecture,
( app(esk51_0,app(nil,X1)) = app(esk51_0,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_104]),c_0_57]),c_0_41])]) ).
fof(c_0_107,plain,
! [X335] :
( ~ ssList(X335)
| nil = X335
| ssItem(hd(X335)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax22])]) ).
cnf(c_0_108,plain,
( nil = X1
| hd(app(X1,X2)) = hd(X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
cnf(c_0_109,negated_conjecture,
( rearsegP(app(esk51_0,X1),nil)
| ~ ssList(app(nil,X1))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_106]),c_0_41])]) ).
cnf(c_0_110,negated_conjecture,
( ssList(app(esk51_0,X1))
| ~ ssList(app(nil,X1))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_106]),c_0_41])]) ).
cnf(c_0_111,plain,
( nil = X1
| ssItem(hd(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
cnf(c_0_112,negated_conjecture,
( hd(esk3_2(esk51_0,esk52_0)) = hd(esk51_0)
| esk3_2(esk51_0,esk52_0) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_64]),c_0_65]),c_0_46])]) ).
cnf(c_0_113,negated_conjecture,
rearsegP(app(esk51_0,esk51_0),nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_75]),c_0_41])]) ).
cnf(c_0_114,negated_conjecture,
ssList(app(esk51_0,esk51_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_75]),c_0_41])]) ).
fof(c_0_115,plain,
! [X346] :
( ~ ssList(X346)
| app(nil,X346) = X346 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).
cnf(c_0_116,negated_conjecture,
( esk3_2(esk51_0,esk52_0) = nil
| ssItem(hd(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_46])]) ).
cnf(c_0_117,negated_conjecture,
app(esk7_2(app(esk51_0,esk51_0),nil),nil) = app(esk51_0,esk51_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_113]),c_0_57]),c_0_114])]) ).
cnf(c_0_118,negated_conjecture,
ssList(esk7_2(app(esk51_0,esk51_0),nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_113]),c_0_57]),c_0_114])]) ).
fof(c_0_119,plain,
! [X431,X432] :
( ~ ssList(X431)
| ~ ssItem(X432)
| cons(X432,X431) = app(cons(X432,nil),X431) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).
cnf(c_0_120,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_115]) ).
cnf(c_0_121,negated_conjecture,
( app(nil,cons(esk52_0,esk4_2(esk51_0,esk52_0))) = esk51_0
| ssItem(hd(esk51_0)) ),
inference(spm,[status(thm)],[c_0_45,c_0_116]) ).
cnf(c_0_122,plain,
( rearsegP(X3,X2)
| ~ ssList(X1)
| app(X1,X2) != X3
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_123,negated_conjecture,
frontsegP(app(esk51_0,esk51_0),nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_117]),c_0_57]),c_0_118])]) ).
fof(c_0_124,plain,
! [X365,X366,X367] :
( ( ~ memberP(cons(X366,X367),X365)
| X365 = X366
| memberP(X367,X365)
| ~ ssList(X367)
| ~ ssItem(X366)
| ~ ssItem(X365) )
& ( X365 != X366
| memberP(cons(X366,X367),X365)
| ~ ssList(X367)
| ~ ssItem(X366)
| ~ ssItem(X365) )
& ( ~ memberP(X367,X365)
| memberP(cons(X366,X367),X365)
| ~ ssList(X367)
| ~ ssItem(X366)
| ~ ssItem(X365) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax37])])])]) ).
fof(c_0_125,plain,
! [X330] :
( ( ssList(esk44_1(X330))
| nil = X330
| ~ ssList(X330) )
& ( ssItem(esk45_1(X330))
| nil = X330
| ~ ssList(X330) )
& ( cons(esk45_1(X330),esk44_1(X330)) = X330
| nil = X330
| ~ ssList(X330) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax20])])])]) ).
fof(c_0_126,plain,
! [X424] :
( ~ ssList(X424)
| nil = X424
| cons(hd(X424),tl(X424)) = X424 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax78])]) ).
cnf(c_0_127,negated_conjecture,
( app(X2,cons(X1,nil)) = esk50_0
| ~ ssItem(X1)
| ~ ssList(X2)
| app(cons(X1,nil),X2) != esk51_0 ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_128,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
cnf(c_0_129,negated_conjecture,
( cons(esk52_0,esk4_2(esk51_0,esk52_0)) = esk51_0
| ssItem(hd(esk51_0))
| ~ ssList(cons(esk52_0,esk4_2(esk51_0,esk52_0))) ),
inference(spm,[status(thm)],[c_0_120,c_0_121]) ).
cnf(c_0_130,plain,
( rearsegP(app(X1,X2),X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_122]),c_0_38]) ).
cnf(c_0_131,negated_conjecture,
app(nil,esk6_2(app(esk51_0,esk51_0),nil)) = app(esk51_0,esk51_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_123]),c_0_114]),c_0_57])]) ).
cnf(c_0_132,negated_conjecture,
ssList(esk6_2(app(esk51_0,esk51_0),nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_123]),c_0_57]),c_0_114])]) ).
cnf(c_0_133,plain,
( X3 = X1
| memberP(X2,X3)
| ~ memberP(cons(X1,X2),X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_124]) ).
cnf(c_0_134,plain,
( cons(esk45_1(X1),esk44_1(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_125]) ).
cnf(c_0_135,plain,
( ssItem(esk45_1(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_125]) ).
cnf(c_0_136,plain,
( ssList(esk44_1(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_125]) ).
fof(c_0_137,plain,
! [X339,X340] :
( ~ ssList(X339)
| ~ ssItem(X340)
| tl(cons(X340,X339)) = X339 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax25])])]) ).
fof(c_0_138,plain,
! [X338] :
( ~ ssList(X338)
| nil = X338
| ssList(tl(X338)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax24])]) ).
fof(c_0_139,plain,
! [X441,X442] :
( ~ ssList(X441)
| ~ ssList(X442)
| nil = X441
| tl(app(X441,X442)) = app(tl(X441),X442) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax86])])]) ).
cnf(c_0_140,plain,
( nil = X1
| cons(hd(X1),tl(X1)) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_126]) ).
cnf(c_0_141,plain,
( nil = X1
| nil != app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_142,plain,
( memberP(X4,X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X1,cons(X3,X2)) != X4
| ~ ssItem(X3)
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_143,negated_conjecture,
( app(X1,cons(X2,nil)) = esk50_0
| cons(X2,X1) != esk51_0
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(spm,[status(thm)],[c_0_127,c_0_128]) ).
cnf(c_0_144,negated_conjecture,
( cons(esk52_0,esk4_2(esk51_0,esk52_0)) = esk51_0
| ssItem(hd(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_52]),c_0_53]),c_0_42])]) ).
cnf(c_0_145,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_146,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_147,negated_conjecture,
~ memberP(esk48_0,esk52_0),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_148,plain,
! [X384,X385,X386] :
( ~ ssList(X384)
| ~ ssList(X385)
| ~ ssList(X386)
| ~ rearsegP(X384,X385)
| ~ rearsegP(X385,X386)
| rearsegP(X384,X386) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax47])])]) ).
cnf(c_0_149,plain,
( rearsegP(app(X1,app(X2,X3)),X3)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_130]),c_0_38]) ).
cnf(c_0_150,negated_conjecture,
app(nil,app(esk51_0,esk51_0)) = app(esk51_0,esk51_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_131]),c_0_132])]) ).
cnf(c_0_151,plain,
( esk45_1(X1) = X2
| nil = X1
| memberP(esk44_1(X1),X2)
| ~ memberP(X1,X2)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_135]),c_0_136]) ).
cnf(c_0_152,plain,
( tl(cons(X2,X1)) = X1
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_137]) ).
cnf(c_0_153,plain,
( nil = X1
| ssList(tl(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_138]) ).
cnf(c_0_154,plain,
( nil = X1
| tl(app(X1,X2)) = app(tl(X1),X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_139]) ).
cnf(c_0_155,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_140,c_0_108]),c_0_38]),c_0_141]) ).
cnf(c_0_156,plain,
( memberP(app(X1,cons(X2,X3)),X2)
| ~ ssList(app(X1,cons(X2,X3)))
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(er,[status(thm)],[c_0_142]) ).
cnf(c_0_157,negated_conjecture,
( app(esk4_2(esk51_0,esk52_0),cons(esk52_0,nil)) = esk50_0
| ssItem(hd(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_144]),c_0_53]),c_0_42])]) ).
cnf(c_0_158,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_145,c_0_146]) ).
cnf(c_0_159,negated_conjecture,
~ memberP(esk50_0,esk52_0),
inference(rw,[status(thm)],[c_0_147,c_0_146]) ).
cnf(c_0_160,plain,
( rearsegP(X1,X3)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_148]) ).
cnf(c_0_161,negated_conjecture,
rearsegP(app(esk51_0,esk51_0),esk51_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_150]),c_0_57]),c_0_41])]) ).
fof(c_0_162,plain,
! [X362,X363,X364] :
( ( ~ memberP(app(X363,X364),X362)
| memberP(X363,X362)
| memberP(X364,X362)
| ~ ssList(X364)
| ~ ssList(X363)
| ~ ssItem(X362) )
& ( ~ memberP(X363,X362)
| memberP(app(X363,X364),X362)
| ~ ssList(X364)
| ~ ssList(X363)
| ~ ssItem(X362) )
& ( ~ memberP(X364,X362)
| memberP(app(X363,X364),X362)
| ~ ssList(X364)
| ~ ssList(X363)
| ~ ssItem(X362) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax36])])])]) ).
cnf(c_0_163,negated_conjecture,
( esk45_1(esk51_0) = esk52_0
| esk51_0 = nil
| memberP(esk44_1(esk51_0),esk52_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_40]),c_0_41]),c_0_42])]) ).
cnf(c_0_164,plain,
( esk44_1(X1) = tl(X1)
| nil = X1
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_134]),c_0_135]),c_0_136]) ).
cnf(c_0_165,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_153,c_0_154]),c_0_38]),c_0_141]) ).
cnf(c_0_166,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_154,c_0_104]),c_0_57]),c_0_41])]) ).
cnf(c_0_167,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_155,c_0_104]),c_0_57]),c_0_41])]) ).
cnf(c_0_168,negated_conjecture,
ssItem(hd(esk51_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_157]),c_0_158]),c_0_57]),c_0_53]),c_0_42])]),c_0_159]) ).
cnf(c_0_169,negated_conjecture,
( rearsegP(X1,esk51_0)
| ~ rearsegP(X1,app(esk51_0,esk51_0))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_161]),c_0_41]),c_0_114])]) ).
cnf(c_0_170,negated_conjecture,
( rearsegP(app(esk51_0,X1),X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_106]),c_0_41]),c_0_57])]) ).
cnf(c_0_171,plain,
( memberP(app(X1,X3),X2)
| ~ memberP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_162]) ).
cnf(c_0_172,negated_conjecture,
( esk45_1(esk51_0) = esk52_0
| esk51_0 = nil
| memberP(tl(esk51_0),esk52_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_164]),c_0_41])]) ).
cnf(c_0_173,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_165,c_0_166]),c_0_57]),c_0_41])]) ).
cnf(c_0_174,negated_conjecture,
( app(tl(esk51_0),cons(hd(esk51_0),nil)) = esk50_0
| esk51_0 = nil
| ~ ssList(tl(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_167]),c_0_168])]) ).
cnf(c_0_175,negated_conjecture,
( rearsegP(app(esk51_0,app(esk51_0,esk51_0)),esk51_0)
| ~ ssList(app(esk51_0,app(esk51_0,esk51_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_170]),c_0_114])]) ).
fof(c_0_176,plain,
! [X336,X337] :
( ~ ssList(X336)
| ~ ssItem(X337)
| hd(cons(X337,X336)) = X337 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])]) ).
cnf(c_0_177,negated_conjecture,
( esk45_1(esk51_0) = esk52_0
| esk51_0 = nil
| memberP(app(tl(esk51_0),X1),esk52_0)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_172]),c_0_42])]),c_0_173]) ).
cnf(c_0_178,negated_conjecture,
( app(tl(esk51_0),cons(hd(esk51_0),nil)) = esk50_0
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_153]),c_0_41])]) ).
cnf(c_0_179,negated_conjecture,
( memberP(app(esk51_0,X1),esk52_0)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_40]),c_0_41]),c_0_42])]) ).
cnf(c_0_180,negated_conjecture,
( ssList(app(esk51_0,X1))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_110,c_0_120]) ).
cnf(c_0_181,negated_conjecture,
rearsegP(app(esk51_0,app(esk51_0,esk51_0)),esk51_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_38]),c_0_114]),c_0_41])]) ).
cnf(c_0_182,plain,
( hd(cons(X2,X1)) = X2
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_176]) ).
cnf(c_0_183,negated_conjecture,
( esk45_1(esk51_0) = esk52_0
| esk51_0 = nil
| ~ ssList(cons(hd(esk51_0),nil)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_178]),c_0_159]) ).
cnf(c_0_184,negated_conjecture,
( memberP(app(app(esk51_0,X1),X2),esk52_0)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_179]),c_0_42])]),c_0_180]) ).
cnf(c_0_185,negated_conjecture,
( app(esk7_2(app(esk51_0,app(esk51_0,esk51_0)),esk51_0),esk51_0) = app(esk51_0,app(esk51_0,esk51_0))
| ~ ssList(app(esk51_0,app(esk51_0,esk51_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_181]),c_0_41])]) ).
cnf(c_0_186,negated_conjecture,
( ssList(esk7_2(app(esk51_0,app(esk51_0,esk51_0)),esk51_0))
| ~ ssList(app(esk51_0,app(esk51_0,esk51_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_181]),c_0_41])]) ).
cnf(c_0_187,negated_conjecture,
( esk51_0 = nil
| memberP(esk50_0,hd(esk51_0))
| ~ ssList(tl(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_178]),c_0_158]),c_0_57]),c_0_168])]) ).
cnf(c_0_188,plain,
( esk45_1(X1) = hd(X1)
| nil = X1
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_134]),c_0_135]),c_0_136]) ).
cnf(c_0_189,negated_conjecture,
( esk45_1(esk51_0) = esk52_0
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_52]),c_0_57]),c_0_168])]) ).
fof(c_0_190,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[ax38]) ).
cnf(c_0_191,negated_conjecture,
( memberP(app(esk51_0,app(X1,X2)),esk52_0)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_67]),c_0_41])]) ).
cnf(c_0_192,negated_conjecture,
app(esk7_2(app(esk51_0,app(esk51_0,esk51_0)),esk51_0),esk51_0) = app(esk51_0,app(esk51_0,esk51_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_38]),c_0_114]),c_0_41])]) ).
cnf(c_0_193,negated_conjecture,
ssList(esk7_2(app(esk51_0,app(esk51_0,esk51_0)),esk51_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_186,c_0_38]),c_0_114]),c_0_41])]) ).
cnf(c_0_194,negated_conjecture,
( esk51_0 = nil
| memberP(esk50_0,hd(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_153]),c_0_41])]) ).
cnf(c_0_195,negated_conjecture,
( hd(esk51_0) = esk52_0
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_188,c_0_189]),c_0_41])]) ).
fof(c_0_196,plain,
! [X368] :
( ~ ssItem(X368)
| ~ memberP(nil,X368) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_190])]) ).
cnf(c_0_197,negated_conjecture,
memberP(app(esk51_0,app(esk51_0,app(esk51_0,esk51_0))),esk52_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_191,c_0_192]),c_0_41]),c_0_193])]) ).
cnf(c_0_198,negated_conjecture,
esk51_0 = nil,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_195]),c_0_159]) ).
cnf(c_0_199,plain,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
inference(split_conjunct,[status(thm)],[c_0_196]) ).
cnf(c_0_200,negated_conjecture,
memberP(nil,esk52_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_197,c_0_198]),c_0_198]),c_0_198]),c_0_198]),c_0_68]),c_0_68]),c_0_68]) ).
cnf(c_0_201,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_199,c_0_200]),c_0_42])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC409+1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n015.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 04:48:47 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 41.68/24.55 % Version : CSE_E---1.7
% 41.68/24.55 % Problem : theBenchmark.p
% 41.68/24.55 % SZS status Theorem for theBenchmark.p
% 41.68/24.55 % SZS output start CNFRefutation
% See solution above
% 41.88/24.71 % Total time : 18.405s
%------------------------------------------------------------------------------