%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC187+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 : n025.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 05:18:39 PM UTC 2026
% Result : Theorem 2.33s 2.01s
% Output : CNFRefutation 2.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 31
% Syntax : Number of formulae : 206 ( 53 unt; 0 def)
% Number of atoms : 675 ( 210 equ)
% Maximal formula atoms : 24 ( 3 avg)
% Number of connectives : 783 ( 314 ~; 336 |; 45 &)
% ( 7 <=>; 81 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 9 con; 0-2 aty)
% Number of variables : 253 ( 0 sgn 136 !; 7 ?)
% 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)
=> ! [X7] :
( ssList(X7)
=> ( app(app(X6,cons(X5,nil)),X7) != X1
| ( ~ memberP(X6,X5)
& ~ memberP(X7,X5) ) ) ) ) )
| ( ! [X8] :
( ssItem(X8)
=> ( cons(X8,nil) != X3
| ~ memberP(X4,X8) ) )
& ( nil != X4
| nil != X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
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(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
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(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
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(ax80,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X2,X3) = app(X2,X1)
=> X3 = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax80) ).
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(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(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(ax38,axiom,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax38) ).
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(ax23,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> hd(cons(X2,X1)) = X2 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax23) ).
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(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(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
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(ax4,axiom,
! [X1] :
( ssList(X1)
=> ( singletonP(X1)
<=> ? [X2] :
( ssItem(X2)
& cons(X2,nil) = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax4) ).
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(ax27,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax27) ).
fof(ax21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax21) ).
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(ax79,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X3,X2) = app(X1,X2)
=> X3 = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax79) ).
fof(ax49,axiom,
! [X1] :
( ssList(X1)
=> rearsegP(X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax49) ).
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(ax54,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( segmentP(X1,X2)
& segmentP(X2,X1) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax54) ).
fof(c_0_31,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ( app(app(X6,cons(X5,nil)),X7) != X1
| ( ~ memberP(X6,X5)
& ~ memberP(X7,X5) ) ) ) ) )
| ( ! [X8] :
( ssItem(X8)
=> ( cons(X8,nil) != X3
| ~ memberP(X4,X8) ) )
& ( nil != X4
| nil != X3 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_32,negated_conjecture,
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& ssItem(esk52_0)
& ssList(esk53_0)
& ssList(esk54_0)
& app(app(esk53_0,cons(esk52_0,nil)),esk54_0) = esk48_0
& ( memberP(esk53_0,esk52_0)
| memberP(esk54_0,esk52_0) )
& ( nil = esk51_0
| ssItem(esk55_0) )
& ( nil = esk50_0
| ssItem(esk55_0) )
& ( nil = esk51_0
| cons(esk55_0,nil) = esk50_0 )
& ( nil = esk50_0
| cons(esk55_0,nil) = esk50_0 )
& ( nil = esk51_0
| memberP(esk51_0,esk55_0) )
& ( nil = esk50_0
| memberP(esk51_0,esk55_0) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])])]) ).
cnf(c_0_33,negated_conjecture,
app(app(esk53_0,cons(esk52_0,nil)),esk54_0) = esk48_0,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_34,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_35,plain,
! [X435,X436,X437] :
( ~ ssList(X435)
| ~ ssList(X436)
| ~ ssList(X437)
| app(app(X435,X436),X437) = app(X435,app(X436,X437)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])]) ).
cnf(c_0_36,negated_conjecture,
app(app(esk53_0,cons(esk52_0,nil)),esk54_0) = esk50_0,
inference(rw,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_38,negated_conjecture,
ssList(esk54_0),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_39,negated_conjecture,
ssList(esk53_0),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_40,plain,
! [X324,X325] :
( ~ ssList(X324)
| ~ ssItem(X325)
| ssList(cons(X325,X324)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).
fof(c_0_41,plain,
! [X233,X234,X236] :
( ( ssList(esk6_2(X233,X234))
| ~ frontsegP(X233,X234)
| ~ ssList(X234)
| ~ ssList(X233) )
& ( app(X234,esk6_2(X233,X234)) = X233
| ~ frontsegP(X233,X234)
| ~ ssList(X234)
| ~ ssList(X233) )
& ( ~ ssList(X236)
| app(X234,X236) != X233
| frontsegP(X233,X234)
| ~ ssList(X234)
| ~ ssList(X233) ) ),
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_42,plain,
! [X343,X344] :
( ~ ssList(X343)
| ~ ssList(X344)
| ssList(app(X343,X344)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).
cnf(c_0_43,negated_conjecture,
( app(esk53_0,app(cons(esk52_0,nil),esk54_0)) = esk50_0
| ~ ssList(cons(esk52_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),c_0_39])]) ).
cnf(c_0_44,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_45,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_46,negated_conjecture,
ssItem(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_47,plain,
! [X433,X434] :
( ~ ssList(X433)
| ~ ssItem(X434)
| cons(X434,X433) = app(cons(X434,nil),X433) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).
cnf(c_0_48,plain,
( frontsegP(X3,X2)
| ~ ssList(X1)
| app(X2,X1) != X3
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_49,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_50,negated_conjecture,
app(esk53_0,app(cons(esk52_0,nil),esk54_0)) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),c_0_46])]) ).
cnf(c_0_51,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_52,plain,
( frontsegP(app(X1,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_48]),c_0_49]) ).
cnf(c_0_53,negated_conjecture,
app(esk53_0,cons(esk52_0,esk54_0)) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_38]),c_0_46])]) ).
cnf(c_0_54,negated_conjecture,
( frontsegP(esk50_0,esk53_0)
| ~ ssList(cons(esk52_0,esk54_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_39])]) ).
cnf(c_0_55,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_56,plain,
! [X430,X431,X432] :
( ~ ssList(X430)
| ~ ssList(X431)
| ~ ssList(X432)
| app(X431,X432) != app(X431,X430)
| X432 = X430 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax80])])]) ).
cnf(c_0_57,plain,
( app(X1,esk6_2(X2,X1)) = X2
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_58,negated_conjecture,
frontsegP(esk50_0,esk53_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_44]),c_0_38]),c_0_46])]) ).
cnf(c_0_59,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_55,c_0_34]) ).
cnf(c_0_60,plain,
( ssList(esk6_2(X1,X2))
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_61,plain,
( X3 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(X2,X3) != app(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_62,negated_conjecture,
app(esk53_0,esk6_2(esk50_0,esk53_0)) = esk50_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_59]),c_0_39])]) ).
cnf(c_0_63,negated_conjecture,
ssList(esk6_2(esk50_0,esk53_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_58]),c_0_39]),c_0_59])]) ).
cnf(c_0_64,negated_conjecture,
( X1 = esk6_2(esk50_0,esk53_0)
| app(esk53_0,X1) != esk50_0
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63]),c_0_39])]) ).
fof(c_0_65,plain,
! [X392,X393,X394] :
( ~ ssList(X392)
| ~ ssList(X393)
| ~ ssList(X394)
| ~ rearsegP(X392,X393)
| rearsegP(app(X394,X392),X393) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax50])])]) ).
fof(c_0_66,plain,
! [X395] :
( ~ ssList(X395)
| rearsegP(X395,nil) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax51])]) ).
cnf(c_0_67,negated_conjecture,
( esk6_2(esk50_0,esk53_0) = cons(esk52_0,esk54_0)
| ~ ssList(cons(esk52_0,esk54_0)) ),
inference(spm,[status(thm)],[c_0_64,c_0_53]) ).
cnf(c_0_68,plain,
( rearsegP(app(X3,X1),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ rearsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_69,plain,
( rearsegP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_70,negated_conjecture,
esk6_2(esk50_0,esk53_0) = cons(esk52_0,esk54_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_44]),c_0_38]),c_0_46])]) ).
fof(c_0_71,plain,
! [X237,X238,X240] :
( ( ssList(esk7_2(X237,X238))
| ~ rearsegP(X237,X238)
| ~ ssList(X238)
| ~ ssList(X237) )
& ( app(esk7_2(X237,X238),X238) = X237
| ~ rearsegP(X237,X238)
| ~ ssList(X238)
| ~ ssList(X237) )
& ( ~ ssList(X240)
| app(X240,X238) != X237
| rearsegP(X237,X238)
| ~ ssList(X238)
| ~ ssList(X237) ) ),
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_72,plain,
( rearsegP(app(X1,X2),nil)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_45])]) ).
cnf(c_0_73,negated_conjecture,
ssList(cons(esk52_0,esk54_0)),
inference(rw,[status(thm)],[c_0_63,c_0_70]) ).
fof(c_0_74,plain,
! [X377,X378,X379] :
( ~ ssList(X377)
| ~ ssList(X378)
| ~ ssList(X379)
| ~ frontsegP(X377,X378)
| frontsegP(app(X377,X379),X378) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax43])])]) ).
fof(c_0_75,plain,
! [X384] :
( ~ ssList(X384)
| frontsegP(X384,nil) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax45])]) ).
fof(c_0_76,plain,
! [X440] :
( ~ ssList(X440)
| app(X440,nil) = X440 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).
cnf(c_0_77,plain,
( app(esk7_2(X1,X2),X2) = X1
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_78,negated_conjecture,
rearsegP(esk50_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_53]),c_0_39]),c_0_73])]) ).
cnf(c_0_79,plain,
( ssList(esk7_2(X1,X2))
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_80,plain,
( frontsegP(app(X1,X3),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ frontsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_81,plain,
( frontsegP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_82,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_83,negated_conjecture,
app(esk7_2(esk50_0,nil),nil) = esk50_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_45]),c_0_59])]) ).
cnf(c_0_84,negated_conjecture,
ssList(esk7_2(esk50_0,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_78]),c_0_45]),c_0_59])]) ).
cnf(c_0_85,negated_conjecture,
( X1 = cons(esk52_0,esk54_0)
| app(esk53_0,X1) != esk50_0
| ~ ssList(X1) ),
inference(rw,[status(thm)],[c_0_64,c_0_70]) ).
cnf(c_0_86,plain,
( frontsegP(app(X1,X2),nil)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_45])]) ).
fof(c_0_87,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[ax38]) ).
fof(c_0_88,plain,
! [X224,X225,X228,X229] :
( ( ssList(esk3_2(X224,X225))
| ~ memberP(X224,X225)
| ~ ssItem(X225)
| ~ ssList(X224) )
& ( ssList(esk4_2(X224,X225))
| ~ memberP(X224,X225)
| ~ ssItem(X225)
| ~ ssList(X224) )
& ( app(esk3_2(X224,X225),cons(X225,esk4_2(X224,X225))) = X224
| ~ memberP(X224,X225)
| ~ ssItem(X225)
| ~ ssList(X224) )
& ( ~ ssList(X228)
| ~ ssList(X229)
| app(X228,cons(X225,X229)) != X224
| memberP(X224,X225)
| ~ ssItem(X225)
| ~ ssList(X224) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax3])])])])]) ).
fof(c_0_89,plain,
! [X338,X339] :
( ~ ssList(X338)
| ~ ssItem(X339)
| hd(cons(X339,X338)) = X339 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])]) ).
fof(c_0_90,plain,
! [X340] :
( ~ ssList(X340)
| nil = X340
| ssList(tl(X340)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax24])]) ).
fof(c_0_91,plain,
! [X443,X444] :
( ~ ssList(X443)
| ~ ssList(X444)
| nil = X443
| tl(app(X443,X444)) = app(tl(X443),X444) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax86])])]) ).
fof(c_0_92,plain,
! [X438,X439] :
( ( nil = X439
| nil != app(X438,X439)
| ~ ssList(X439)
| ~ ssList(X438) )
& ( nil = X438
| nil != app(X438,X439)
| ~ ssList(X439)
| ~ ssList(X438) )
& ( nil != X439
| nil != X438
| nil = app(X438,X439)
| ~ ssList(X439)
| ~ ssList(X438) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).
cnf(c_0_93,negated_conjecture,
esk7_2(esk50_0,nil) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_84])]) ).
cnf(c_0_94,negated_conjecture,
( app(cons(esk52_0,nil),esk54_0) = cons(esk52_0,esk54_0)
| ~ ssList(app(cons(esk52_0,nil),esk54_0)) ),
inference(spm,[status(thm)],[c_0_85,c_0_50]) ).
fof(c_0_95,plain,
! [X348] :
( ~ ssList(X348)
| app(nil,X348) = X348 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).
cnf(c_0_96,negated_conjecture,
frontsegP(esk50_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_53]),c_0_73]),c_0_39])]) ).
fof(c_0_97,plain,
! [X367,X368,X369] :
( ( ~ memberP(cons(X368,X369),X367)
| X367 = X368
| memberP(X369,X367)
| ~ ssList(X369)
| ~ ssItem(X368)
| ~ ssItem(X367) )
& ( X367 != X368
| memberP(cons(X368,X369),X367)
| ~ ssList(X369)
| ~ ssItem(X368)
| ~ ssItem(X367) )
& ( ~ memberP(X369,X367)
| memberP(cons(X368,X369),X367)
| ~ ssList(X369)
| ~ ssItem(X368)
| ~ ssItem(X367) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax37])])])]) ).
fof(c_0_98,plain,
! [X230,X232] :
( ( ssItem(esk5_1(X230))
| ~ singletonP(X230)
| ~ ssList(X230) )
& ( cons(esk5_1(X230),nil) = X230
| ~ singletonP(X230)
| ~ ssList(X230) )
& ( ~ ssItem(X232)
| cons(X232,nil) != X230
| singletonP(X230)
| ~ ssList(X230) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax4])])])])]) ).
fof(c_0_99,plain,
! [X370] :
( ~ ssItem(X370)
| ~ memberP(nil,X370) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_87])]) ).
cnf(c_0_100,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_88]) ).
fof(c_0_101,plain,
! [X426] :
( ~ ssList(X426)
| nil = X426
| cons(hd(X426),tl(X426)) = X426 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax78])]) ).
cnf(c_0_102,plain,
( hd(cons(X2,X1)) = X2
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_103,negated_conjecture,
( nil = esk50_0
| cons(esk55_0,nil) = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_104,negated_conjecture,
( nil = esk50_0
| ssItem(esk55_0) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_105,plain,
( nil = X1
| ssList(tl(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_106,plain,
( nil = X1
| tl(app(X1,X2)) = app(tl(X1),X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_107,plain,
( nil = X1
| nil != app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_108,negated_conjecture,
app(esk50_0,nil) = esk50_0,
inference(rw,[status(thm)],[c_0_83,c_0_93]) ).
fof(c_0_109,plain,
! [X345,X346,X347] :
( ~ ssList(X345)
| ~ ssList(X346)
| ~ ssItem(X347)
| cons(X347,app(X346,X345)) = app(cons(X347,X346),X345) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])]) ).
cnf(c_0_110,negated_conjecture,
( app(cons(esk52_0,nil),esk54_0) = cons(esk52_0,esk54_0)
| ~ ssList(cons(esk52_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_49]),c_0_38])]) ).
cnf(c_0_111,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_112,negated_conjecture,
app(nil,esk6_2(esk50_0,nil)) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_96]),c_0_59]),c_0_45])]) ).
cnf(c_0_113,negated_conjecture,
ssList(esk6_2(esk50_0,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_96]),c_0_45]),c_0_59])]) ).
cnf(c_0_114,plain,
( X3 = X1
| memberP(X2,X3)
| ~ memberP(cons(X1,X2),X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_115,plain,
( cons(esk5_1(X1),nil) = X1
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_116,plain,
( ssItem(esk5_1(X1))
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_117,plain,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_118,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_100]) ).
cnf(c_0_119,plain,
( singletonP(X2)
| ~ ssItem(X1)
| cons(X1,nil) != X2
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_120,plain,
( nil = X1
| cons(hd(X1),tl(X1)) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_121,negated_conjecture,
( hd(esk50_0) = esk55_0
| esk50_0 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_45])]),c_0_104]) ).
cnf(c_0_122,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_105,c_0_106]),c_0_49]),c_0_107]) ).
cnf(c_0_123,negated_conjecture,
( app(tl(esk50_0),nil) = tl(esk50_0)
| esk50_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_108]),c_0_45]),c_0_59])]) ).
fof(c_0_124,plain,
! [X335,X336] :
( ~ ssList(X335)
| ~ ssItem(X336)
| nil != cons(X336,X335) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax21])])]) ).
cnf(c_0_125,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_126,negated_conjecture,
app(cons(esk52_0,nil),esk54_0) = cons(esk52_0,esk54_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_44]),c_0_45]),c_0_46])]) ).
cnf(c_0_127,plain,
( rearsegP(X3,X2)
| ~ ssList(X1)
| app(X1,X2) != X3
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_128,negated_conjecture,
esk6_2(esk50_0,nil) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_113])]) ).
fof(c_0_129,plain,
! [X341,X342] :
( ~ ssList(X341)
| ~ ssItem(X342)
| tl(cons(X342,X341)) = X341 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax25])])]) ).
cnf(c_0_130,plain,
( esk5_1(X1) = X2
| ~ singletonP(X1)
| ~ memberP(X1,X2)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_45])]),c_0_116]),c_0_117]) ).
cnf(c_0_131,negated_conjecture,
memberP(esk50_0,esk52_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_118,c_0_53]),c_0_59]),c_0_38]),c_0_39]),c_0_46])]) ).
cnf(c_0_132,plain,
( singletonP(cons(X1,nil))
| ~ ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(er,[status(thm)],[c_0_119]) ).
cnf(c_0_133,negated_conjecture,
( cons(esk55_0,tl(esk50_0)) = esk50_0
| esk50_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_59])]) ).
cnf(c_0_134,negated_conjecture,
( esk50_0 = nil
| ssList(tl(esk50_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_45]),c_0_59])]) ).
cnf(c_0_135,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| nil != cons(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_124]) ).
cnf(c_0_136,negated_conjecture,
cons(esk52_0,app(nil,esk54_0)) = cons(esk52_0,esk54_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_45]),c_0_38]),c_0_46])]) ).
fof(c_0_137,plain,
! [X427,X428,X429] :
( ~ ssList(X427)
| ~ ssList(X428)
| ~ ssList(X429)
| app(X429,X428) != app(X427,X428)
| X429 = X427 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax79])])]) ).
fof(c_0_138,plain,
! [X391] :
( ~ ssList(X391)
| rearsegP(X391,X391) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax49])]) ).
cnf(c_0_139,plain,
( rearsegP(app(X1,X2),X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_127]),c_0_49]) ).
cnf(c_0_140,negated_conjecture,
app(nil,esk50_0) = esk50_0,
inference(rw,[status(thm)],[c_0_112,c_0_128]) ).
fof(c_0_141,plain,
! [X241,X242,X245,X246] :
( ( ssList(esk8_2(X241,X242))
| ~ segmentP(X241,X242)
| ~ ssList(X242)
| ~ ssList(X241) )
& ( ssList(esk9_2(X241,X242))
| ~ segmentP(X241,X242)
| ~ ssList(X242)
| ~ ssList(X241) )
& ( app(app(esk8_2(X241,X242),X242),esk9_2(X241,X242)) = X241
| ~ segmentP(X241,X242)
| ~ ssList(X242)
| ~ ssList(X241) )
& ( ~ ssList(X245)
| ~ ssList(X246)
| app(app(X245,X242),X246) != X241
| segmentP(X241,X242)
| ~ ssList(X242)
| ~ ssList(X241) ) ),
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_142,plain,
( tl(cons(X2,X1)) = X1
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
cnf(c_0_143,negated_conjecture,
( esk5_1(esk50_0) = esk52_0
| ~ singletonP(esk50_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_59]),c_0_46])]) ).
cnf(c_0_144,negated_conjecture,
( esk50_0 = nil
| singletonP(esk50_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_103]),c_0_59])]),c_0_104]) ).
cnf(c_0_145,negated_conjecture,
( esk50_0 = nil
| esk55_0 = X1
| memberP(tl(esk50_0),X1)
| ~ memberP(esk50_0,X1)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_133]),c_0_104]),c_0_134]) ).
cnf(c_0_146,plain,
( nil = X1
| nil != app(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_147,negated_conjecture,
( cons(esk52_0,esk54_0) != nil
| ~ ssList(app(nil,esk54_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_46])]) ).
cnf(c_0_148,plain,
( X3 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(X3,X2) != app(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_137]) ).
cnf(c_0_149,plain,
( rearsegP(X1,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_138]) ).
cnf(c_0_150,negated_conjecture,
rearsegP(esk50_0,esk50_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_59]),c_0_45])]) ).
cnf(c_0_151,negated_conjecture,
( rearsegP(esk50_0,cons(esk52_0,esk54_0))
| ~ ssList(cons(esk52_0,esk54_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_53]),c_0_39])]) ).
cnf(c_0_152,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_141]) ).
cnf(c_0_153,negated_conjecture,
( tl(esk50_0) = nil
| esk50_0 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_103]),c_0_45])]),c_0_104]) ).
cnf(c_0_154,plain,
( esk5_1(X1) = hd(X1)
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_115]),c_0_45])]),c_0_116]) ).
cnf(c_0_155,negated_conjecture,
( esk5_1(esk50_0) = esk52_0
| esk50_0 = nil ),
inference(spm,[status(thm)],[c_0_143,c_0_144]) ).
cnf(c_0_156,negated_conjecture,
( esk52_0 = esk55_0
| esk50_0 = nil
| memberP(tl(esk50_0),esk52_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_131]),c_0_46])]) ).
cnf(c_0_157,plain,
( nil = X1
| app(X2,app(X3,X1)) != nil
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_37]),c_0_49]) ).
cnf(c_0_158,negated_conjecture,
cons(esk52_0,esk54_0) != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_111]),c_0_38])]) ).
cnf(c_0_159,negated_conjecture,
( X1 = nil
| app(X1,esk50_0) != esk50_0
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_140]),c_0_45]),c_0_59])]) ).
cnf(c_0_160,plain,
( app(esk7_2(X1,X1),X1) = X1
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_77,c_0_149]) ).
cnf(c_0_161,negated_conjecture,
ssList(esk7_2(esk50_0,esk50_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_150]),c_0_59])]) ).
cnf(c_0_162,negated_conjecture,
rearsegP(esk50_0,cons(esk52_0,esk54_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_44]),c_0_38]),c_0_46])]) ).
cnf(c_0_163,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_152]) ).
cnf(c_0_164,negated_conjecture,
( cons(hd(esk50_0),nil) = esk50_0
| esk50_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_153]),c_0_59])]) ).
cnf(c_0_165,negated_conjecture,
( hd(esk50_0) = esk52_0
| esk50_0 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_155]),c_0_59])]),c_0_144]) ).
cnf(c_0_166,negated_conjecture,
( esk50_0 = nil
| esk52_0 = esk55_0
| memberP(nil,esk52_0) ),
inference(spm,[status(thm)],[c_0_156,c_0_153]) ).
cnf(c_0_167,negated_conjecture,
( app(X1,esk50_0) != nil
| ~ ssList(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_53]),c_0_73]),c_0_39])]),c_0_158]) ).
cnf(c_0_168,negated_conjecture,
esk7_2(esk50_0,esk50_0) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_160]),c_0_161]),c_0_59])]) ).
cnf(c_0_169,negated_conjecture,
( X1 = esk53_0
| app(X1,esk6_2(esk50_0,esk53_0)) != esk50_0
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_62]),c_0_39]),c_0_63])]) ).
cnf(c_0_170,negated_conjecture,
( app(esk7_2(esk50_0,cons(esk52_0,esk54_0)),cons(esk52_0,esk54_0)) = esk50_0
| ~ ssList(cons(esk52_0,esk54_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_162]),c_0_59])]) ).
cnf(c_0_171,negated_conjecture,
( ssList(esk7_2(esk50_0,cons(esk52_0,esk54_0)))
| ~ ssList(cons(esk52_0,esk54_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_162]),c_0_59])]) ).
fof(c_0_172,plain,
! [X400,X401] :
( ~ ssList(X400)
| ~ ssList(X401)
| ~ segmentP(X400,X401)
| ~ segmentP(X401,X400)
| X400 = X401 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax54])])]) ).
cnf(c_0_173,plain,
( segmentP(app(X1,X2),X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_82]),c_0_45])]),c_0_49]) ).
cnf(c_0_174,negated_conjecture,
( cons(esk52_0,nil) = esk50_0
| esk50_0 = nil ),
inference(spm,[status(thm)],[c_0_164,c_0_165]) ).
cnf(c_0_175,negated_conjecture,
( esk52_0 = esk55_0
| esk50_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_166]),c_0_46])]) ).
cnf(c_0_176,negated_conjecture,
esk50_0 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_160]),c_0_168]),c_0_45]),c_0_59])]) ).
cnf(c_0_177,negated_conjecture,
( X1 = esk53_0
| app(X1,cons(esk52_0,esk54_0)) != esk50_0
| ~ ssList(X1) ),
inference(rw,[status(thm)],[c_0_169,c_0_70]) ).
cnf(c_0_178,negated_conjecture,
app(esk7_2(esk50_0,cons(esk52_0,esk54_0)),cons(esk52_0,esk54_0)) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_170,c_0_73])]) ).
cnf(c_0_179,negated_conjecture,
ssList(esk7_2(esk50_0,cons(esk52_0,esk54_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_44]),c_0_38]),c_0_46])]) ).
cnf(c_0_180,plain,
( X1 = X2
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_172]) ).
cnf(c_0_181,negated_conjecture,
segmentP(esk50_0,cons(esk52_0,esk54_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_53]),c_0_73]),c_0_39])]) ).
cnf(c_0_182,negated_conjecture,
( app(esk50_0,esk54_0) = cons(esk52_0,esk54_0)
| esk50_0 = nil ),
inference(spm,[status(thm)],[c_0_126,c_0_174]) ).
cnf(c_0_183,negated_conjecture,
esk52_0 = esk55_0,
inference(sr,[status(thm)],[c_0_175,c_0_176]) ).
cnf(c_0_184,negated_conjecture,
( tl(cons(esk52_0,esk54_0)) = app(nil,esk54_0)
| ~ ssList(app(nil,esk54_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_136]),c_0_46])]) ).
cnf(c_0_185,negated_conjecture,
esk7_2(esk50_0,cons(esk52_0,esk54_0)) = esk53_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_178]),c_0_179])]) ).
cnf(c_0_186,negated_conjecture,
( cons(esk52_0,esk54_0) = esk50_0
| ~ segmentP(cons(esk52_0,esk54_0),esk50_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_181]),c_0_59]),c_0_73])]) ).
cnf(c_0_187,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_163,c_0_111]),c_0_45])]),c_0_49]) ).
cnf(c_0_188,negated_conjecture,
app(esk50_0,esk54_0) = cons(esk55_0,esk54_0),
inference(rw,[status(thm)],[inference(sr,[status(thm)],[c_0_182,c_0_176]),c_0_183]) ).
cnf(c_0_189,negated_conjecture,
tl(cons(esk52_0,esk54_0)) = esk54_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_111]),c_0_38])]) ).
cnf(c_0_190,negated_conjecture,
( memberP(esk53_0,esk52_0)
| memberP(esk54_0,esk52_0) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_191,negated_conjecture,
( esk7_2(esk50_0,cons(esk55_0,esk54_0)) = esk53_0
| esk50_0 = nil ),
inference(spm,[status(thm)],[c_0_185,c_0_175]) ).
cnf(c_0_192,negated_conjecture,
( cons(esk55_0,esk54_0) = esk50_0
| ~ segmentP(cons(esk55_0,esk54_0),esk50_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_186,c_0_183]),c_0_183]) ).
cnf(c_0_193,negated_conjecture,
segmentP(cons(esk55_0,esk54_0),esk50_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_188]),c_0_59]),c_0_38])]) ).
cnf(c_0_194,negated_conjecture,
( tl(cons(esk55_0,esk54_0)) = esk54_0
| esk50_0 = nil ),
inference(spm,[status(thm)],[c_0_189,c_0_175]) ).
cnf(c_0_195,negated_conjecture,
( esk50_0 = nil
| memberP(esk54_0,esk55_0)
| memberP(esk53_0,esk55_0) ),
inference(spm,[status(thm)],[c_0_190,c_0_175]) ).
cnf(c_0_196,negated_conjecture,
esk7_2(esk50_0,cons(esk55_0,esk54_0)) = esk53_0,
inference(sr,[status(thm)],[c_0_191,c_0_176]) ).
cnf(c_0_197,negated_conjecture,
cons(esk55_0,esk54_0) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_192,c_0_193])]) ).
cnf(c_0_198,negated_conjecture,
tl(cons(esk55_0,esk54_0)) = esk54_0,
inference(sr,[status(thm)],[c_0_194,c_0_176]) ).
cnf(c_0_199,negated_conjecture,
tl(esk50_0) = nil,
inference(sr,[status(thm)],[c_0_153,c_0_176]) ).
cnf(c_0_200,negated_conjecture,
( memberP(esk53_0,esk55_0)
| memberP(esk54_0,esk55_0) ),
inference(sr,[status(thm)],[c_0_195,c_0_176]) ).
cnf(c_0_201,negated_conjecture,
esk53_0 = nil,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_196,c_0_197]),c_0_168]) ).
cnf(c_0_202,negated_conjecture,
esk54_0 = nil,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_198,c_0_197]),c_0_199]) ).
cnf(c_0_203,negated_conjecture,
memberP(nil,esk55_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_200,c_0_201]),c_0_202])]) ).
cnf(c_0_204,negated_conjecture,
ssItem(esk55_0),
inference(sr,[status(thm)],[c_0_104,c_0_176]) ).
cnf(c_0_205,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_203]),c_0_204])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC187+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 : n025.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 04:39:28 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 2.33/2.01 % Version : CSE_E---1.7
% 2.33/2.01 % Problem : theBenchmark.p
% 2.33/2.01 % SZS status Theorem for theBenchmark.p
% 2.33/2.01 % SZS output start CNFRefutation
% See solution above
% 2.33/2.02 % Total time : 1.373s
%------------------------------------------------------------------------------