%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC407+1 : TPTP v9.2.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n007.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 05:19:32 PM UTC 2026
% Result : Theorem 1.72s 1.84s
% Output : CNFRefutation 1.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 20
% Syntax : Number of formulae : 123 ( 20 unt; 0 def)
% Number of atoms : 425 ( 152 equ)
% Maximal formula atoms : 21 ( 3 avg)
% Number of connectives : 484 ( 182 ~; 215 |; 32 &)
% ( 7 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-2 aty)
% Number of variables : 137 ( 0 sgn 78 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax52,axiom,
! [X1] :
( ssList(X1)
=> ( rearsegP(nil,X1)
<=> nil = X1 ) ),
file('/export/starexec/sandbox2/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) ) )
& ( nil != X4
| nil != X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(ax50,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( rearsegP(X1,X2)
=> rearsegP(app(X3,X1),X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax50) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax6) ).
fof(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(ax23,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> hd(cons(X2,X1)) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax23) ).
fof(ax24,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax24) ).
fof(ax86,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> tl(app(X1,X2)) = app(tl(X1),X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax86) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax83,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(ax78,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax78) ).
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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax37) ).
fof(ax5,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X2,X3) = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax5) ).
fof(ax25,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> tl(cons(X2,X1)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax25) ).
fof(ax4,axiom,
! [X1] :
( ssList(X1)
=> ( singletonP(X1)
<=> ? [X2] :
( ssItem(X2)
& cons(X2,nil) = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax4) ).
fof(ax38,axiom,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax38) ).
fof(ax46,axiom,
! [X1] :
( ssList(X1)
=> ( frontsegP(nil,X1)
<=> nil = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax46) ).
fof(ax18,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax18) ).
fof(c_0_20,plain,
! [X392] :
( ( ~ rearsegP(nil,X392)
| nil = X392
| ~ ssList(X392) )
& ( nil != X392
| rearsegP(nil,X392)
| ~ ssList(X392) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax52])])]) ).
fof(c_0_21,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) ) )
& ( nil != X4
| nil != X3 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_22,plain,
! [X388,X389,X390] :
( ~ ssList(X388)
| ~ ssList(X389)
| ~ ssList(X390)
| ~ rearsegP(X388,X389)
| rearsegP(app(X390,X388),X389) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax50])])]) ).
cnf(c_0_23,plain,
( rearsegP(nil,X1)
| nil != X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
fof(c_0_25,plain,
! [X429,X430] :
( ~ ssList(X429)
| ~ ssItem(X430)
| cons(X430,X429) = app(cons(X430,nil),X429) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).
fof(c_0_26,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)
& 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) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])]) ).
cnf(c_0_27,plain,
( rearsegP(app(X3,X1),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ rearsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,plain,
rearsegP(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_23]),c_0_24])]) ).
cnf(c_0_29,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_30,negated_conjecture,
( nil = esk50_0
| cons(esk53_0,nil) = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,negated_conjecture,
( nil = esk50_0
| ssItem(esk53_0) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_34,plain,
( rearsegP(app(X1,nil),nil)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_24])]) ).
cnf(c_0_35,negated_conjecture,
( app(esk50_0,X1) = cons(esk53_0,X1)
| esk50_0 = nil
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
cnf(c_0_36,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_32,c_0_33]) ).
fof(c_0_37,plain,
! [X233,X234,X236] :
( ( ssList(esk7_2(X233,X234))
| ~ rearsegP(X233,X234)
| ~ ssList(X234)
| ~ ssList(X233) )
& ( app(esk7_2(X233,X234),X234) = X233
| ~ rearsegP(X233,X234)
| ~ ssList(X234)
| ~ ssList(X233) )
& ( ~ ssList(X236)
| app(X236,X234) != X233
| rearsegP(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)],[ax6])])])])]) ).
cnf(c_0_38,negated_conjecture,
( esk50_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_34,c_0_35]),c_0_36]),c_0_24])]) ).
fof(c_0_39,plain,
! [X436] :
( ~ ssList(X436)
| app(X436,nil) = X436 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).
cnf(c_0_40,plain,
( app(esk7_2(X1,X2),X2) = X1
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_41,negated_conjecture,
( esk50_0 = nil
| rearsegP(esk50_0,nil) ),
inference(spm,[status(thm)],[c_0_38,c_0_30]) ).
cnf(c_0_42,plain,
( ssList(esk7_2(X1,X2))
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_43,negated_conjecture,
( nil = esk51_0
| cons(esk53_0,nil) = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_44,negated_conjecture,
( nil = esk51_0
| ssItem(esk53_0) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_45,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_46,negated_conjecture,
( app(esk7_2(esk50_0,nil),nil) = esk50_0
| esk50_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_24]),c_0_36])]) ).
cnf(c_0_47,negated_conjecture,
( esk50_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_42,c_0_41]),c_0_24]),c_0_36])]) ).
cnf(c_0_48,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_29,c_0_43]),c_0_44]) ).
fof(c_0_49,plain,
! [X334,X335] :
( ~ ssList(X334)
| ~ ssItem(X335)
| hd(cons(X335,X334)) = X335 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])]) ).
fof(c_0_50,plain,
! [X336] :
( ~ ssList(X336)
| nil = X336
| ssList(tl(X336)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax24])]) ).
fof(c_0_51,plain,
! [X439,X440] :
( ~ ssList(X439)
| ~ ssList(X440)
| nil = X439
| tl(app(X439,X440)) = app(tl(X439),X440) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax86])])]) ).
fof(c_0_52,plain,
! [X339,X340] :
( ~ ssList(X339)
| ~ ssList(X340)
| ssList(app(X339,X340)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).
fof(c_0_53,plain,
! [X434,X435] :
( ( nil = X435
| nil != app(X434,X435)
| ~ ssList(X435)
| ~ ssList(X434) )
& ( nil = X434
| nil != app(X434,X435)
| ~ ssList(X435)
| ~ ssList(X434) )
& ( nil != X435
| nil != X434
| nil = app(X434,X435)
| ~ ssList(X435)
| ~ ssList(X434) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).
cnf(c_0_54,negated_conjecture,
( esk7_2(esk50_0,nil) = esk50_0
| esk50_0 = nil ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]) ).
cnf(c_0_55,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_34,c_0_48]),c_0_36]),c_0_24])]) ).
fof(c_0_56,plain,
! [X422] :
( ~ ssList(X422)
| nil = X422
| cons(hd(X422),tl(X422)) = X422 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax78])]) ).
cnf(c_0_57,plain,
( hd(cons(X2,X1)) = X2
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_58,plain,
( nil = X1
| ssList(tl(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_59,plain,
( nil = X1
| tl(app(X1,X2)) = app(tl(X1),X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_60,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_61,plain,
( nil = X1
| nil != app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_62,negated_conjecture,
( app(esk50_0,nil) = esk50_0
| esk50_0 = nil ),
inference(spm,[status(thm)],[c_0_46,c_0_54]) ).
cnf(c_0_63,negated_conjecture,
( esk51_0 = nil
| rearsegP(esk50_0,nil) ),
inference(spm,[status(thm)],[c_0_55,c_0_43]) ).
fof(c_0_64,plain,
! [X363,X364,X365] :
( ( ~ memberP(cons(X364,X365),X363)
| X363 = X364
| memberP(X365,X363)
| ~ ssList(X365)
| ~ ssItem(X364)
| ~ ssItem(X363) )
& ( X363 != X364
| memberP(cons(X364,X365),X363)
| ~ ssList(X365)
| ~ ssItem(X364)
| ~ ssItem(X363) )
& ( ~ memberP(X365,X363)
| memberP(cons(X364,X365),X363)
| ~ ssList(X365)
| ~ ssItem(X364)
| ~ ssItem(X363) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax37])])])]) ).
cnf(c_0_65,plain,
( nil = X1
| cons(hd(X1),tl(X1)) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_66,negated_conjecture,
( hd(esk50_0) = esk53_0
| esk50_0 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_30]),c_0_24])]),c_0_31]) ).
cnf(c_0_67,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_58,c_0_59]),c_0_60]),c_0_61]) ).
cnf(c_0_68,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_59,c_0_62]),c_0_24]),c_0_36])]) ).
fof(c_0_69,plain,
! [X229,X230,X232] :
( ( ssList(esk6_2(X229,X230))
| ~ frontsegP(X229,X230)
| ~ ssList(X230)
| ~ ssList(X229) )
& ( app(X230,esk6_2(X229,X230)) = X229
| ~ frontsegP(X229,X230)
| ~ ssList(X230)
| ~ ssList(X229) )
& ( ~ ssList(X232)
| app(X230,X232) != X229
| frontsegP(X229,X230)
| ~ ssList(X230)
| ~ ssList(X229) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax5])])])])]) ).
cnf(c_0_70,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_40,c_0_63]),c_0_24]),c_0_36])]) ).
cnf(c_0_71,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_42,c_0_63]),c_0_24]),c_0_36])]) ).
cnf(c_0_72,plain,
( X3 = X1
| memberP(X2,X3)
| ~ memberP(cons(X1,X2),X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_73,negated_conjecture,
( cons(esk53_0,tl(esk50_0)) = esk50_0
| esk50_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_36])]) ).
cnf(c_0_74,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_67,c_0_68]),c_0_24]),c_0_36])]) ).
cnf(c_0_75,negated_conjecture,
memberP(esk48_0,esk52_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_76,plain,
! [X337,X338] :
( ~ ssList(X337)
| ~ ssItem(X338)
| tl(cons(X338,X337)) = X337 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax25])])]) ).
fof(c_0_77,plain,
! [X226,X228] :
( ( ssItem(esk5_1(X226))
| ~ singletonP(X226)
| ~ ssList(X226) )
& ( cons(esk5_1(X226),nil) = X226
| ~ singletonP(X226)
| ~ ssList(X226) )
& ( ~ ssItem(X228)
| cons(X228,nil) != X226
| singletonP(X226)
| ~ ssList(X226) ) ),
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_78,plain,
( frontsegP(X3,X2)
| ~ ssList(X1)
| app(X2,X1) != X3
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_79,negated_conjecture,
( esk7_2(esk50_0,nil) = esk50_0
| esk51_0 = nil ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_70]),c_0_71]) ).
fof(c_0_80,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[ax38]) ).
cnf(c_0_81,negated_conjecture,
( esk50_0 = nil
| esk53_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_72,c_0_73]),c_0_31]),c_0_74]) ).
cnf(c_0_82,negated_conjecture,
memberP(esk50_0,esk52_0),
inference(rw,[status(thm)],[c_0_75,c_0_33]) ).
cnf(c_0_83,negated_conjecture,
ssItem(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_84,plain,
( tl(cons(X2,X1)) = X1
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
fof(c_0_85,plain,
! [X381] :
( ( ~ frontsegP(nil,X381)
| nil = X381
| ~ ssList(X381) )
& ( nil != X381
| frontsegP(nil,X381)
| ~ ssList(X381) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax46])])]) ).
fof(c_0_86,plain,
! [X322,X323] :
( ~ ssList(X322)
| ~ ssItem(X323)
| cons(X323,X322) != X322 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax18])])]) ).
cnf(c_0_87,plain,
( cons(esk5_1(X1),nil) = X1
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_88,plain,
( ssItem(esk5_1(X1))
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_89,plain,
( frontsegP(app(X1,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_78]),c_0_60]) ).
cnf(c_0_90,negated_conjecture,
( app(esk50_0,nil) = esk50_0
| esk51_0 = nil ),
inference(spm,[status(thm)],[c_0_70,c_0_79]) ).
cnf(c_0_91,plain,
( singletonP(X2)
| ~ ssItem(X1)
| cons(X1,nil) != X2
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
fof(c_0_92,plain,
! [X366] :
( ~ ssItem(X366)
| ~ memberP(nil,X366) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_80])]) ).
cnf(c_0_93,negated_conjecture,
( esk52_0 = esk53_0
| esk50_0 = nil
| memberP(tl(esk50_0),esk52_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_83])]) ).
cnf(c_0_94,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_84,c_0_30]),c_0_24])]),c_0_31]) ).
cnf(c_0_95,plain,
( frontsegP(nil,X1)
| nil != X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_96,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| cons(X2,X1) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_97,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_29,c_0_87]),c_0_88]) ).
cnf(c_0_98,plain,
( app(X1,esk6_2(X2,X1)) = X2
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_99,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_89,c_0_90]),c_0_36]),c_0_24])]) ).
cnf(c_0_100,plain,
( ssList(esk6_2(X1,X2))
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_101,plain,
( singletonP(cons(X1,nil))
| ~ ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(er,[status(thm)],[c_0_91]) ).
cnf(c_0_102,negated_conjecture,
~ memberP(esk49_0,esk52_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_103,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_104,plain,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_105,negated_conjecture,
( esk50_0 = nil
| esk52_0 = esk53_0
| memberP(nil,esk52_0) ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_106,plain,
frontsegP(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_95]),c_0_24])]) ).
cnf(c_0_107,plain,
( app(X1,X2) != X2
| ~ singletonP(X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_88]) ).
cnf(c_0_108,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_98,c_0_99]),c_0_36])]) ).
cnf(c_0_109,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_100,c_0_99]),c_0_36])]) ).
cnf(c_0_110,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_101,c_0_43]),c_0_36])]),c_0_44]) ).
cnf(c_0_111,negated_conjecture,
~ memberP(esk51_0,esk52_0),
inference(rw,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_112,negated_conjecture,
( esk52_0 = esk53_0
| esk50_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_83])]) ).
cnf(c_0_113,negated_conjecture,
( nil = esk50_0
| memberP(esk51_0,esk53_0) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_114,plain,
( nil = X1
| nil != app(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_115,plain,
app(nil,esk6_2(nil,nil)) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_106]),c_0_24])]) ).
cnf(c_0_116,plain,
ssList(esk6_2(nil,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_106]),c_0_24])]) ).
cnf(c_0_117,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_107,c_0_108]),c_0_36])]),c_0_109]),c_0_110]) ).
cnf(c_0_118,negated_conjecture,
esk50_0 = nil,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_113]) ).
cnf(c_0_119,plain,
esk6_2(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_24]),c_0_116])]) ).
cnf(c_0_120,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_117,c_0_118]),c_0_118]),c_0_119]),c_0_118])]) ).
cnf(c_0_121,negated_conjecture,
~ memberP(nil,esk52_0),
inference(rw,[status(thm)],[c_0_111,c_0_120]) ).
cnf(c_0_122,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_82,c_0_118]),c_0_121]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC407+1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.32 % Computer : n007.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Tue May 5 04:47:53 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.72/1.84 % Version : CSE_E---1.7
% 1.72/1.84 % Problem : theBenchmark.p
% 1.72/1.84 % SZS status Theorem for theBenchmark.p
% 1.72/1.84 % SZS output start CNFRefutation
% See solution above
% 1.72/1.84 % Total time : 1.373s
%------------------------------------------------------------------------------