%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC392+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 05:19:28 PM UTC 2026
% Result : Theorem 1.70s 1.84s
% Output : CNFRefutation 1.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 92 ( 20 unt; 0 def)
% Number of atoms : 355 ( 110 equ)
% Maximal formula atoms : 31 ( 3 avg)
% Number of connectives : 428 ( 165 ~; 179 |; 40 &)
% ( 7 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 111 ( 0 sgn 63 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax52,axiom,
! [X1] :
( ssList(X1)
=> ( rearsegP(nil,X1)
<=> nil = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax52) ).
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ! [X5] :
( ssItem(X5)
=> ( ~ memberP(X1,X5)
| memberP(X2,X5) ) )
| ( ! [X6] :
( ssItem(X6)
=> ( cons(X6,nil) != X3
| ~ memberP(X4,X6)
| ? [X7] :
( ssItem(X7)
& X6 != X7
& memberP(X4,X7)
& leq(X7,X6) ) ) )
& ( nil != X4
| nil != X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SWC001+0.ax',ax50) ).
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(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(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
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(ax38,axiom,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax38) ).
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(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(ax46,axiom,
! [X1] :
( ssList(X1)
=> ( frontsegP(nil,X1)
<=> nil = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax46) ).
fof(ax18,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax18) ).
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(c_0_15,plain,
! [X394] :
( ( ~ rearsegP(nil,X394)
| nil = X394
| ~ ssList(X394) )
& ( nil != X394
| rearsegP(nil,X394)
| ~ ssList(X394) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax52])])]) ).
fof(c_0_16,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ! [X5] :
( ssItem(X5)
=> ( ~ memberP(X1,X5)
| memberP(X2,X5) ) )
| ( ! [X6] :
( ssItem(X6)
=> ( cons(X6,nil) != X3
| ~ memberP(X4,X6)
| ? [X7] :
( ssItem(X7)
& X6 != X7
& memberP(X4,X7)
& leq(X7,X6) ) ) )
& ( nil != X4
| nil != X3 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_17,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])])]) ).
cnf(c_0_18,plain,
( rearsegP(nil,X1)
| nil != X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
fof(c_0_20,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])])]) ).
fof(c_0_21,negated_conjecture,
! [X468] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& ssItem(esk52_0)
& memberP(esk48_0,esk52_0)
& ~ memberP(esk49_0,esk52_0)
& ( nil = esk51_0
| ssItem(esk53_0) )
& ( nil = esk50_0
| ssItem(esk53_0) )
& ( nil = esk51_0
| cons(esk53_0,nil) = esk50_0 )
& ( nil = esk50_0
| cons(esk53_0,nil) = esk50_0 )
& ( nil = esk51_0
| memberP(esk51_0,esk53_0) )
& ( nil = esk50_0
| memberP(esk51_0,esk53_0) )
& ( nil = esk51_0
| ~ ssItem(X468)
| esk53_0 = X468
| ~ memberP(esk51_0,X468)
| ~ leq(X468,esk53_0) )
& ( nil = esk50_0
| ~ ssItem(X468)
| esk53_0 = X468
| ~ memberP(esk51_0,X468)
| ~ leq(X468,esk53_0) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])])]) ).
cnf(c_0_22,plain,
( rearsegP(app(X3,X1),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ rearsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
rearsegP(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_18]),c_0_19])]) ).
cnf(c_0_24,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,negated_conjecture,
( nil = esk51_0
| cons(esk53_0,nil) = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_26,negated_conjecture,
( nil = esk51_0
| ssItem(esk53_0) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,plain,
( rearsegP(app(X1,nil),nil)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_19])]) ).
cnf(c_0_30,negated_conjecture,
( app(esk50_0,X1) = cons(esk53_0,X1)
| esk51_0 = nil
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_31,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
fof(c_0_32,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_33,negated_conjecture,
( esk51_0 = nil
| rearsegP(cons(esk53_0,nil),nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_19])]) ).
fof(c_0_34,plain,
! [X438] :
( ~ ssList(X438)
| app(X438,nil) = X438 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).
cnf(c_0_35,plain,
( app(esk7_2(X1,X2),X2) = X1
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_36,negated_conjecture,
( esk51_0 = nil
| rearsegP(esk50_0,nil) ),
inference(spm,[status(thm)],[c_0_33,c_0_25]) ).
cnf(c_0_37,plain,
( ssList(esk7_2(X1,X2))
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_38,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_39,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])])]) ).
cnf(c_0_40,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_41,negated_conjecture,
( app(esk7_2(esk50_0,nil),nil) = esk50_0
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_19]),c_0_31])]) ).
cnf(c_0_42,negated_conjecture,
( esk51_0 = nil
| ssList(esk7_2(esk50_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_36]),c_0_19]),c_0_31])]) ).
fof(c_0_43,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[ax38]) ).
fof(c_0_44,plain,
! [X228,X230] :
( ( ssItem(esk5_1(X228))
| ~ singletonP(X228)
| ~ ssList(X228) )
& ( cons(esk5_1(X228),nil) = X228
| ~ singletonP(X228)
| ~ ssList(X228) )
& ( ~ ssItem(X230)
| cons(X230,nil) != X228
| singletonP(X228)
| ~ ssList(X228) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax4])])])])]) ).
cnf(c_0_45,plain,
( frontsegP(X3,X2)
| ~ ssList(X1)
| app(X2,X1) != X3
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_46,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_47,negated_conjecture,
( esk7_2(esk50_0,nil) = esk50_0
| esk51_0 = nil ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
fof(c_0_48,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_49,plain,
! [X368] :
( ~ ssItem(X368)
| ~ memberP(nil,X368) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_43])]) ).
fof(c_0_50,plain,
! [X383] :
( ( ~ frontsegP(nil,X383)
| nil = X383
| ~ ssList(X383) )
& ( nil != X383
| frontsegP(nil,X383)
| ~ ssList(X383) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax46])])]) ).
fof(c_0_51,plain,
! [X324,X325] :
( ~ ssList(X324)
| ~ ssItem(X325)
| cons(X325,X324) != X324 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax18])])]) ).
cnf(c_0_52,plain,
( cons(esk5_1(X1),nil) = X1
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_53,plain,
( ssItem(esk5_1(X1))
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_54,plain,
( frontsegP(app(X1,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_45]),c_0_46]) ).
cnf(c_0_55,negated_conjecture,
( app(esk50_0,nil) = esk50_0
| esk51_0 = nil ),
inference(spm,[status(thm)],[c_0_41,c_0_47]) ).
cnf(c_0_56,plain,
( singletonP(X2)
| ~ ssItem(X1)
| cons(X1,nil) != X2
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_57,plain,
( X3 = X1
| memberP(X2,X3)
| ~ memberP(cons(X1,X2),X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_58,negated_conjecture,
( nil = esk50_0
| cons(esk53_0,nil) = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_59,negated_conjecture,
( nil = esk50_0
| ssItem(esk53_0) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_60,plain,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_61,negated_conjecture,
memberP(esk48_0,esk52_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_62,plain,
( frontsegP(nil,X1)
| nil != X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_63,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| cons(X2,X1) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_64,plain,
( cons(esk5_1(X1),X2) = app(X1,X2)
| ~ singletonP(X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_52]),c_0_53]) ).
cnf(c_0_65,plain,
( app(X1,esk6_2(X2,X1)) = X2
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_66,negated_conjecture,
( esk51_0 = nil
| frontsegP(esk50_0,esk50_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_31]),c_0_19])]) ).
cnf(c_0_67,plain,
( ssList(esk6_2(X1,X2))
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_68,plain,
( singletonP(cons(X1,nil))
| ~ ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(er,[status(thm)],[c_0_56]) ).
cnf(c_0_69,negated_conjecture,
~ memberP(esk49_0,esk52_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_70,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_71,negated_conjecture,
( esk50_0 = nil
| esk53_0 = X1
| ~ memberP(esk50_0,X1)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_19])]),c_0_59]),c_0_60]) ).
cnf(c_0_72,negated_conjecture,
memberP(esk50_0,esk52_0),
inference(rw,[status(thm)],[c_0_61,c_0_28]) ).
cnf(c_0_73,negated_conjecture,
ssItem(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_74,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_75,plain,
frontsegP(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_62]),c_0_19])]) ).
cnf(c_0_76,plain,
( app(X1,X2) != X2
| ~ singletonP(X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_53]) ).
cnf(c_0_77,negated_conjecture,
( app(esk50_0,esk6_2(esk50_0,esk50_0)) = esk50_0
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_31])]) ).
cnf(c_0_78,negated_conjecture,
( esk51_0 = nil
| ssList(esk6_2(esk50_0,esk50_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_66]),c_0_31])]) ).
cnf(c_0_79,negated_conjecture,
( esk51_0 = nil
| singletonP(esk50_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_25]),c_0_31])]),c_0_26]) ).
cnf(c_0_80,negated_conjecture,
~ memberP(esk51_0,esk52_0),
inference(rw,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_81,negated_conjecture,
( esk52_0 = esk53_0
| esk50_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73])]) ).
cnf(c_0_82,negated_conjecture,
( nil = esk50_0
| memberP(esk51_0,esk53_0) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_83,plain,
( nil = X1
| nil != app(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_84,plain,
app(nil,esk6_2(nil,nil)) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_75]),c_0_19])]) ).
cnf(c_0_85,plain,
ssList(esk6_2(nil,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_75]),c_0_19])]) ).
cnf(c_0_86,negated_conjecture,
( esk51_0 = nil
| esk6_2(esk50_0,esk50_0) != esk50_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_31])]),c_0_78]),c_0_79]) ).
cnf(c_0_87,negated_conjecture,
esk50_0 = nil,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82]) ).
cnf(c_0_88,plain,
esk6_2(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_19]),c_0_85])]) ).
cnf(c_0_89,negated_conjecture,
esk51_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_87]),c_0_87]),c_0_88]),c_0_87])]) ).
cnf(c_0_90,negated_conjecture,
~ memberP(nil,esk52_0),
inference(rw,[status(thm)],[c_0_80,c_0_89]) ).
cnf(c_0_91,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_87]),c_0_90]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC392+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 04:48:32 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.70/1.84 % Version : CSE_E---1.7
% 1.70/1.84 % Problem : theBenchmark.p
% 1.70/1.84 % SZS status Theorem for theBenchmark.p
% 1.70/1.84 % SZS output start CNFRefutation
% See solution above
% 1.70/1.84 % Total time : 1.372s
%------------------------------------------------------------------------------