%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC418+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 : n017.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 05:19:35 PM UTC 2026
% Result : Theorem 1.69s 1.82s
% Output : CNFRefutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 15
% Syntax : Number of formulae : 92 ( 13 unt; 0 def)
% Number of atoms : 358 ( 160 equ)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 438 ( 172 ~; 185 |; 45 &)
% ( 2 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 113 ( 0 sgn 57 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X6,cons(X5,nil)),X7) = X2
& app(app(X7,cons(X5,nil)),X6) = X1 ) ) )
| ( nil != X3
& nil = X4 )
| ( ? [X8] :
( ssList(X8)
& X3 != X8
& ? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& tl(X4) = X9
& app(X9,X10) = X8
& ? [X11] :
( ssItem(X11)
& cons(X11,nil) = X10
& hd(X4) = X11
& neq(nil,X4) )
& neq(nil,X4) ) ) )
& neq(X4,nil) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax24,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax24) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax22,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax22) ).
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(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(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(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(ax85,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> hd(app(X1,X2)) = hd(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax85) ).
fof(ax21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax21) ).
fof(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax81) ).
fof(c_0_15,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X6,cons(X5,nil)),X7) = X2
& app(app(X7,cons(X5,nil)),X6) = X1 ) ) )
| ( nil != X3
& nil = X4 )
| ( ? [X8] :
( ssList(X8)
& X3 != X8
& ? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& tl(X4) = X9
& app(X9,X10) = X8
& ? [X11] :
( ssItem(X11)
& cons(X11,nil) = X10
& hd(X4) = X11
& neq(nil,X4) )
& neq(nil,X4) ) ) )
& neq(X4,nil) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_16,negated_conjecture,
! [X474,X475,X476,X477,X478,X479,X480] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& neq(esk49_0,nil)
& ( ~ ssItem(X474)
| ~ ssList(X475)
| ~ ssList(X476)
| app(app(X475,cons(X474,nil)),X476) != esk49_0
| app(app(X476,cons(X474,nil)),X475) != esk48_0 )
& ( nil = esk50_0
| nil != esk51_0 )
& ( ~ ssList(X477)
| esk50_0 = X477
| ~ ssList(X478)
| ~ ssList(X479)
| tl(esk51_0) != X478
| app(X478,X479) != X477
| ~ ssItem(X480)
| cons(X480,nil) != X479
| hd(esk51_0) != X480
| ~ neq(nil,esk51_0)
| ~ neq(nil,esk51_0)
| ~ neq(esk51_0,nil) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])]) ).
cnf(c_0_17,negated_conjecture,
( esk50_0 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| tl(esk51_0) != X2
| app(X2,X3) != X1
| ~ ssItem(X4)
| cons(X4,nil) != X3
| hd(esk51_0) != X4
| ~ neq(nil,esk51_0)
| ~ neq(nil,esk51_0)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_18,negated_conjecture,
neq(esk49_0,nil),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_19,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_20,plain,
! [X349,X350] :
( ~ ssList(X349)
| ~ ssList(X350)
| ssList(app(X349,X350)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).
cnf(c_0_21,negated_conjecture,
( esk50_0 = X1
| hd(esk51_0) != X4
| tl(esk51_0) != X2
| app(X2,X3) != X1
| cons(X4,nil) != X3
| ~ ssItem(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ neq(nil,esk51_0)
| ~ neq(esk51_0,nil) ),
inference(cn,[status(thm)],[c_0_17]) ).
cnf(c_0_22,negated_conjecture,
neq(esk51_0,nil),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_24,plain,
! [X346] :
( ~ ssList(X346)
| nil = X346
| ssList(tl(X346)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax24])]) ).
cnf(c_0_25,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_26,negated_conjecture,
( app(tl(esk51_0),cons(hd(esk51_0),nil)) = esk50_0
| ~ ssList(cons(hd(esk51_0),nil))
| ~ ssList(tl(esk51_0))
| ~ neq(nil,esk51_0)
| ~ ssItem(hd(esk51_0)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22])])])])])]),c_0_23]) ).
cnf(c_0_27,plain,
( nil = X1
| ssList(tl(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_28,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_25,c_0_19]) ).
fof(c_0_29,plain,
! [X330,X331] :
( ~ ssList(X330)
| ~ ssItem(X331)
| ssList(cons(X331,X330)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).
cnf(c_0_30,negated_conjecture,
( app(tl(esk51_0),cons(hd(esk51_0),nil)) = esk50_0
| esk51_0 = nil
| ~ ssList(cons(hd(esk51_0),nil))
| ~ neq(nil,esk51_0)
| ~ ssItem(hd(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]) ).
cnf(c_0_31,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_32,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
fof(c_0_33,plain,
! [X343] :
( ~ ssList(X343)
| nil = X343
| ssItem(hd(X343)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax22])]) ).
fof(c_0_34,plain,
! [X432] :
( ~ ssList(X432)
| nil = X432
| cons(hd(X432),tl(X432)) = X432 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax78])]) ).
fof(c_0_35,plain,
! [X449,X450] :
( ~ ssList(X449)
| ~ ssList(X450)
| nil = X449
| tl(app(X449,X450)) = app(tl(X449),X450) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax86])])]) ).
fof(c_0_36,plain,
! [X444,X445] :
( ( nil = X445
| nil != app(X444,X445)
| ~ ssList(X445)
| ~ ssList(X444) )
& ( nil = X444
| nil != app(X444,X445)
| ~ ssList(X445)
| ~ ssList(X444) )
& ( nil != X445
| nil != X444
| nil = app(X444,X445)
| ~ ssList(X445)
| ~ ssList(X444) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).
cnf(c_0_37,negated_conjecture,
( app(tl(esk51_0),cons(hd(esk51_0),nil)) = esk50_0
| esk51_0 = nil
| ~ neq(nil,esk51_0)
| ~ ssItem(hd(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]) ).
cnf(c_0_38,plain,
( nil = X1
| ssItem(hd(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_39,plain,
! [X328,X329] :
( ( ~ neq(X328,X329)
| X328 != X329
| ~ ssList(X329)
| ~ ssList(X328) )
& ( X328 = X329
| neq(X328,X329)
| ~ ssList(X329)
| ~ ssList(X328) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])])]) ).
cnf(c_0_40,plain,
( nil = X1
| cons(hd(X1),tl(X1)) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_41,plain,
( nil = X1
| tl(app(X1,X2)) = app(tl(X1),X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_42,plain,
( nil = X1
| nil != app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_43,negated_conjecture,
( app(tl(esk51_0),cons(hd(esk51_0),nil)) = esk50_0
| esk51_0 = nil
| ~ neq(nil,esk51_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_28])]) ).
cnf(c_0_44,plain,
( X1 = X2
| neq(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_45,plain,
( cons(hd(app(X1,X2)),app(tl(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_40,c_0_41]),c_0_23]),c_0_42]) ).
cnf(c_0_46,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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_28]),c_0_32])]) ).
cnf(c_0_47,negated_conjecture,
( cons(hd(app(esk51_0,cons(hd(esk51_0),nil))),esk50_0) = app(esk51_0,cons(hd(esk51_0),nil))
| esk51_0 = nil
| ~ ssList(cons(hd(esk51_0),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_28])]) ).
cnf(c_0_48,negated_conjecture,
( cons(hd(app(esk51_0,cons(hd(esk51_0),nil))),esk50_0) = app(esk51_0,cons(hd(esk51_0),nil))
| esk51_0 = nil
| ~ ssItem(hd(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_31]),c_0_32])]) ).
fof(c_0_49,plain,
! [X447,X448] :
( ~ ssList(X447)
| ~ ssList(X448)
| nil = X447
| hd(app(X447,X448)) = hd(X447) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax85])])]) ).
cnf(c_0_50,negated_conjecture,
( cons(hd(app(esk51_0,cons(hd(esk51_0),nil))),esk50_0) = app(esk51_0,cons(hd(esk51_0),nil))
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_38]),c_0_28])]) ).
cnf(c_0_51,plain,
( nil = X1
| hd(app(X1,X2)) = hd(X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
fof(c_0_52,plain,
! [X341,X342] :
( ~ ssList(X341)
| ~ ssItem(X342)
| nil != cons(X342,X341) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax21])])]) ).
cnf(c_0_53,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_54,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_55,negated_conjecture,
( app(esk51_0,cons(hd(esk51_0),nil)) = cons(hd(esk51_0),esk50_0)
| esk51_0 = nil
| ~ ssList(cons(hd(esk51_0),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_28])]) ).
cnf(c_0_56,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| nil != cons(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_57,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_58,negated_conjecture,
( app(esk51_0,cons(hd(esk51_0),nil)) = cons(hd(esk51_0),esk50_0)
| esk51_0 = nil
| ~ ssItem(hd(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_31]),c_0_32])]) ).
cnf(c_0_59,negated_conjecture,
( esk51_0 = nil
| app(esk51_0,cons(hd(esk51_0),nil)) != nil
| ~ ssItem(hd(app(esk51_0,cons(hd(esk51_0),nil)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_50]),c_0_57])]) ).
cnf(c_0_60,negated_conjecture,
( app(esk51_0,cons(hd(esk51_0),nil)) = cons(hd(esk51_0),esk50_0)
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_38]),c_0_28])]) ).
cnf(c_0_61,negated_conjecture,
( esk51_0 = nil
| app(esk51_0,cons(hd(esk51_0),nil)) != nil
| ~ ssList(cons(hd(esk51_0),nil))
| ~ ssItem(hd(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_51]),c_0_28])]) ).
cnf(c_0_62,negated_conjecture,
( hd(cons(hd(esk51_0),esk50_0)) = hd(esk51_0)
| esk51_0 = nil
| ~ ssList(cons(hd(esk51_0),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_60]),c_0_28])]) ).
cnf(c_0_63,negated_conjecture,
( esk51_0 = nil
| ssList(cons(hd(esk51_0),esk50_0))
| ~ ssList(cons(hd(esk51_0),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_60]),c_0_28])]) ).
cnf(c_0_64,negated_conjecture,
( esk51_0 = nil
| app(esk51_0,cons(hd(esk51_0),nil)) != nil
| ~ ssItem(hd(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_31]),c_0_32])]) ).
cnf(c_0_65,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X2,cons(X1,nil)),X3) != esk49_0
| app(app(X3,cons(X1,nil)),X2) != esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_66,plain,
! [X446] :
( ~ ssList(X446)
| app(X446,nil) = X446 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).
cnf(c_0_67,negated_conjecture,
( hd(cons(hd(esk51_0),esk50_0)) = hd(esk51_0)
| esk51_0 = nil
| ~ ssItem(hd(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_31]),c_0_32])]) ).
cnf(c_0_68,negated_conjecture,
( esk51_0 = nil
| ssList(cons(hd(esk51_0),esk50_0))
| ~ ssItem(hd(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_31]),c_0_32])]) ).
cnf(c_0_69,negated_conjecture,
( esk51_0 = nil
| app(esk51_0,cons(hd(esk51_0),nil)) != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_38]),c_0_28])]) ).
cnf(c_0_70,negated_conjecture,
( app(app(X1,cons(X2,nil)),X3) != esk50_0
| app(app(X3,cons(X2,nil)),X1) != esk51_0
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssItem(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_54]),c_0_19]) ).
cnf(c_0_71,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_72,negated_conjecture,
( hd(cons(hd(esk51_0),esk50_0)) = hd(esk51_0)
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_38]),c_0_28])]) ).
cnf(c_0_73,negated_conjecture,
( esk51_0 = nil
| ssList(cons(hd(esk51_0),esk50_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_38]),c_0_28])]) ).
cnf(c_0_74,negated_conjecture,
( esk51_0 = nil
| cons(hd(esk51_0),esk50_0) != nil ),
inference(spm,[status(thm)],[c_0_69,c_0_60]) ).
cnf(c_0_75,negated_conjecture,
( app(app(nil,cons(X1,nil)),X2) != esk51_0
| app(X2,cons(X1,nil)) != esk50_0
| ~ ssList(app(X2,cons(X1,nil)))
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_32])]) ).
cnf(c_0_76,negated_conjecture,
( esk51_0 = nil
| ssItem(hd(esk51_0)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_72]),c_0_73]),c_0_74]) ).
cnf(c_0_77,negated_conjecture,
( esk51_0 = nil
| app(app(nil,cons(hd(esk51_0),nil)),tl(esk51_0)) != esk51_0
| ~ ssList(tl(esk51_0)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_46]),c_0_57])]),c_0_76]) ).
fof(c_0_78,plain,
! [X354] :
( ~ ssList(X354)
| app(nil,X354) = X354 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).
cnf(c_0_79,negated_conjecture,
( esk51_0 = nil
| app(app(nil,cons(hd(esk51_0),nil)),tl(esk51_0)) != esk51_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_27]),c_0_28])]) ).
cnf(c_0_80,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_81,negated_conjecture,
( esk51_0 = nil
| app(cons(hd(esk51_0),nil),tl(esk51_0)) != esk51_0
| ~ ssList(cons(hd(esk51_0),nil)) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
fof(c_0_82,plain,
! [X439,X440] :
( ~ ssList(X439)
| ~ ssItem(X440)
| cons(X440,X439) = app(cons(X440,nil),X439) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).
cnf(c_0_83,negated_conjecture,
( esk51_0 = nil
| app(cons(hd(esk51_0),nil),tl(esk51_0)) != esk51_0 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_31]),c_0_32])]),c_0_76]) ).
cnf(c_0_84,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_85,negated_conjecture,
( esk51_0 = nil
| cons(hd(esk51_0),tl(esk51_0)) != esk51_0
| ~ ssList(tl(esk51_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_76]) ).
cnf(c_0_86,negated_conjecture,
( esk51_0 = nil
| cons(hd(esk51_0),tl(esk51_0)) != esk51_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_27]),c_0_28])]) ).
cnf(c_0_87,plain,
( ~ neq(X1,X2)
| X1 != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_88,negated_conjecture,
esk51_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_40]),c_0_28])]) ).
cnf(c_0_89,plain,
( ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(er,[status(thm)],[c_0_87]) ).
cnf(c_0_90,negated_conjecture,
neq(nil,nil),
inference(rw,[status(thm)],[c_0_22,c_0_88]) ).
cnf(c_0_91,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC418+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
% 0.16/0.33 % Computer : n017.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 04:47:58 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.69/1.82 % Version : CSE_E---1.7
% 1.69/1.82 % Problem : theBenchmark.p
% 1.69/1.82 % SZS status Theorem for theBenchmark.p
% 1.69/1.82 % SZS output start CNFRefutation
% See solution above
% 1.69/1.82 % Total time : 1.374s
%------------------------------------------------------------------------------