%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC397+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:41:04 PM UTC 2026
% Result : Theorem 0.16s 0.53s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 28
% Syntax : Number of formulae : 121 ( 16 unt; 19 def)
% Number of atoms : 419 ( 67 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 494 ( 196 ~; 197 |; 45 &)
% ( 27 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 25 ( 23 usr; 20 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 100 ( 87 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ( memberP(U,V)
<=> ? [W] :
( ? [X] :
( app(W,cons(V,X)) = U
& ssList(X) )
& ssList(W) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ssList(cons(V,U)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( memberP(app(V,W),U)
<=> ( memberP(W,U)
| memberP(V,U) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssList(W)
=> ( memberP(cons(V,W),U)
<=> ( memberP(W,U)
| U = V ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [U] :
( ssItem(U)
=> ~ memberP(nil,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f81,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> cons(V,U) = app(cons(V,nil),U) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( neq(X,nil)
& ! [Z] :
( ssItem(Z)
=> ! [X1] :
( ssList(X1)
=> ( app(X1,cons(Z,nil)) != X
| app(cons(Z,nil),X1) != W ) ) ) )
| ( nil = X
& nil != W )
| ! [Y] :
( ssItem(Y)
=> ( memberP(V,Y)
| ~ memberP(U,Y) ) )
| U != W
| V != X ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( neq(X,nil)
& ! [Z] :
( ssItem(Z)
=> ! [X1] :
( ssList(X1)
=> ( app(X1,cons(Z,nil)) != X
| app(cons(Z,nil),X1) != W ) ) ) )
| ( nil = X
& nil != W )
| ! [Y] :
( ssItem(Y)
=> ( memberP(V,Y)
| ~ memberP(U,Y) ) )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f106,plain,
! [U] :
( ! [V] :
( ( memberP(U,V)
<=> ? [W] :
( ? [X] :
( app(W,cons(V,X)) = U
& ssList(X) )
& ssList(W) ) )
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f107,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(W,cons(V,X)) != U
| ~ ssList(X) )
| ~ ssList(W) )
| memberP(U,V) )
& ( ? [W] :
( ? [X] :
( app(W,cons(V,X)) = U
& ssList(X) )
& ssList(W) )
| ~ memberP(U,V) ) )
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f106]) ).
fof(f108,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(W,cons(V,X)) != U
| ~ ssList(X) )
| ~ ssList(W) )
| memberP(U,V) )
& ( ( app(sK2_skl(V,U),cons(V,sK3_skl(V,U))) = U
& ssList(sK3_skl(V,U))
& ssList(sK2_skl(V,U)) )
| ~ memberP(U,V) ) )
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(W,sK2_skl(V,U)),skolemize(X,sK3_skl(V,U))],[f107]) ).
fof(f112,plain,
! [X0,X1,X2,X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f217,plain,
! [U] :
( ! [V] :
( ( neq(U,V)
<=> U != V )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f218,plain,
! [U] :
( ! [V] :
( ( ( U = V
| neq(U,V) )
& ( U != V
| ~ neq(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f217]) ).
fof(f220,plain,
! [X0,X1] :
( X0 = X1
| neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f218]) ).
fof(f221,plain,
! [U] :
( ! [V] :
( ssList(cons(V,U))
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f222,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f221]) ).
fof(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f268,plain,
! [U] :
( ! [V] :
( ! [W] :
( ( memberP(app(V,W),U)
<=> ( memberP(W,U)
| memberP(V,U) ) )
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f269,plain,
! [U] :
( ! [V] :
( ! [W] :
( ( ( ( ~ memberP(W,U)
& ~ memberP(V,U) )
| memberP(app(V,W),U) )
& ( memberP(W,U)
| memberP(V,U)
| ~ memberP(app(V,W),U) ) )
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssItem(U) ),
inference(NNF_transformation,[status(thm)],[f268]) ).
fof(f271,plain,
! [X0,X1,X2] :
( ~ memberP(X1,X0)
| memberP(app(X1,X2),X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f269]) ).
fof(f273,plain,
! [U] :
( ! [V] :
( ! [W] :
( ( memberP(cons(V,W),U)
<=> ( memberP(W,U)
| U = V ) )
| ~ ssList(W) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f274,plain,
! [U] :
( ! [V] :
( ! [W] :
( ( ( ( ~ memberP(W,U)
& U != V )
| memberP(cons(V,W),U) )
& ( memberP(W,U)
| U = V
| ~ memberP(cons(V,W),U) ) )
| ~ ssList(W) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(NNF_transformation,[status(thm)],[f273]) ).
fof(f275,plain,
! [X0,X1,X2] :
( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f274]) ).
fof(f278,plain,
! [U] :
( ~ memberP(nil,U)
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f279,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f278]) ).
fof(f379,plain,
! [U] :
( ! [V] :
( cons(V,U) = app(cons(V,nil),U)
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f81]) ).
fof(f380,plain,
! [X0,X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f379]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ~ neq(X,nil)
| ? [Z] :
( ? [X1] :
( app(X1,cons(Z,nil)) = X
& app(cons(Z,nil),X1) = W
& ssList(X1) )
& ssItem(Z) ) )
& ( nil != X
| nil = W )
& ? [Y] :
( ~ memberP(V,Y)
& memberP(U,Y)
& ssItem(Y) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,plain,
( ( ~ neq(sK50_skl,nil)
| ( app(sK53_skl,cons(sK52_skl,nil)) = sK50_skl
& app(cons(sK52_skl,nil),sK53_skl) = sK49_skl
& ssList(sK53_skl)
& ssItem(sK52_skl) ) )
& ( nil != sK50_skl
| nil = sK49_skl )
& ~ memberP(sK48_skl,sK51_skl)
& memberP(sK47_skl,sK51_skl)
& ssItem(sK51_skl)
& sK47_skl = sK49_skl
& sK48_skl = sK50_skl
& ssList(sK50_skl)
& ssList(sK49_skl)
& ssList(sK48_skl)
& ssList(sK47_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl,sK49_skl,sK50_skl,sK51_skl,sK52_skl,sK53_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Y,sK51_skl),skolemize(Z,sK52_skl),skolemize(X1,sK53_skl)],[f415]) ).
fof(f420,plain,
ssList(sK50_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f421,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f422,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f423,plain,
ssItem(sK51_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f424,plain,
memberP(sK47_skl,sK51_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f425,plain,
~ memberP(sK48_skl,sK51_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f426,plain,
( nil != sK50_skl
| nil = sK49_skl ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f427,plain,
( ~ neq(sK50_skl,nil)
| ssItem(sK52_skl) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f428,plain,
( ~ neq(sK50_skl,nil)
| ssList(sK53_skl) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f429,plain,
( ~ neq(sK50_skl,nil)
| app(cons(sK52_skl,nil),sK53_skl) = sK49_skl ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f430,plain,
( ~ neq(sK50_skl,nil)
| app(sK53_skl,cons(sK52_skl,nil)) = sK50_skl ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f431,definition,
( sQ0_spl
<=> nil = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f432,plain,
( ~ sQ0_spl
| nil = sK49_skl ),
inference(component_clause,[status(thm)],[f431]) ).
fof(f434,definition,
( sQ1_spl
<=> nil = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f437,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f426,f431,f434]) ).
fof(f438,definition,
( sQ2_spl
<=> ssItem(sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f441,definition,
( sQ3_spl
<=> neq(sK50_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f443,plain,
( sQ3_spl
| ~ neq(sK50_skl,nil) ),
inference(component_clause,[status(thm)],[f441]) ).
fof(f444,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f427,f438,f441]) ).
fof(f445,definition,
( sQ4_spl
<=> ssList(sK53_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f448,plain,
( ~ sQ3_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f428,f445,f441]) ).
fof(f449,definition,
( sQ5_spl
<=> app(cons(sK52_skl,nil),sK53_skl) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f450,plain,
( ~ sQ5_spl
| app(cons(sK52_skl,nil),sK53_skl) = sK49_skl ),
inference(component_clause,[status(thm)],[f449]) ).
fof(f452,plain,
( ~ sQ3_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f429,f449,f441]) ).
fof(f453,definition,
( sQ6_spl
<=> app(sK53_skl,cons(sK52_skl,nil)) = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f454,plain,
( ~ sQ6_spl
| app(sK53_skl,cons(sK52_skl,nil)) = sK50_skl ),
inference(component_clause,[status(thm)],[f453]) ).
fof(f456,plain,
( ~ sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f430,f453,f441]) ).
fof(f459,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| ~ ssList(X0)
| memberP(app(X0,cons(X1,X2)),X1)
| ~ ssItem(X1)
| ~ ssList(app(X0,cons(X1,X2))) ),
inference(destructive_equality_resolution,[status(thm)],[f112]) ).
fof(f490,plain,
memberP(sK49_skl,sK51_skl),
inference(forward_demodulation,[status(thm)],[f422,f424]) ).
fof(f491,plain,
~ memberP(sK50_skl,sK51_skl),
inference(forward_demodulation,[status(thm)],[f421,f425]) ).
fof(f493,plain,
! [X0] :
( ~ sQ0_spl
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f432,f279]) ).
fof(f494,plain,
( ~ sQ0_spl
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f493,f490]) ).
fof(f495,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f494,f423]) ).
fof(f496,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f495]) ).
fof(f507,plain,
( sQ3_spl
| sK50_skl = nil
| ~ ssList(nil)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f220,f443]) ).
fof(f510,definition,
( sQ9_spl
<=> ssList(sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f512,plain,
( sQ9_spl
| ~ ssList(sK50_skl) ),
inference(component_clause,[status(thm)],[f510]) ).
fof(f513,definition,
( sQ10_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f515,plain,
( sQ10_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f513]) ).
fof(f516,plain,
( sQ3_spl
| sQ1_spl
| ~ sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f507,f510,f513,f434,f441]) ).
fof(f517,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f512,f420]) ).
fof(f518,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f517]) ).
fof(f520,definition,
( sQ11_spl
<=> ssList(cons(sK52_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f522,plain,
( sQ11_spl
| ~ ssList(cons(sK52_skl,nil)) ),
inference(component_clause,[status(thm)],[f520]) ).
fof(f527,plain,
( sQ11_spl
| ~ ssItem(sK52_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f522,f222]) ).
fof(f528,plain,
( sQ11_spl
| ~ sQ2_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f527,f513,f438,f520]) ).
fof(f529,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f515,f223]) ).
fof(f530,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f529]) ).
fof(f622,plain,
! [X0] :
( ~ sQ6_spl
| ~ memberP(sK53_skl,X0)
| memberP(sK50_skl,X0)
| ~ ssList(cons(sK52_skl,nil))
| ~ ssList(sK53_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f454,f271]) ).
fof(f627,definition,
! [X0] :
( sQ29_spl
<=> ( ~ memberP(sK53_skl,X0)
| memberP(sK50_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f628,plain,
! [X0] :
( ~ sQ29_spl
| ~ memberP(sK53_skl,X0)
| memberP(sK50_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f627]) ).
fof(f630,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| ~ sQ4_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f622,f627,f445,f520,f453]) ).
fof(f667,plain,
( ~ sQ5_spl
| cons(sK52_skl,sK53_skl) = sK49_skl
| ~ ssItem(sK52_skl)
| ~ ssList(sK53_skl) ),
inference(paramodulation,[status(thm)],[f450,f380]) ).
fof(f668,definition,
( sQ35_spl
<=> cons(sK52_skl,sK53_skl) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f669,plain,
( ~ sQ35_spl
| cons(sK52_skl,sK53_skl) = sK49_skl ),
inference(component_clause,[status(thm)],[f668]) ).
fof(f671,plain,
( ~ sQ5_spl
| sQ35_spl
| ~ sQ2_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f667,f445,f438,f668,f449]) ).
fof(f754,plain,
! [X0] :
( ~ sQ35_spl
| memberP(sK53_skl,X0)
| X0 = sK52_skl
| ~ memberP(sK49_skl,X0)
| ~ ssList(sK53_skl)
| ~ ssItem(sK52_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f669,f275]) ).
fof(f755,definition,
! [X0] :
( sQ48_spl
<=> ( memberP(sK53_skl,X0)
| X0 = sK52_skl
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f756,plain,
! [X0] :
( ~ sQ48_spl
| memberP(sK53_skl,X0)
| X0 = sK52_skl
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f755]) ).
fof(f758,plain,
( ~ sQ35_spl
| ~ sQ4_spl
| ~ sQ2_spl
| sQ48_spl ),
inference(split_clause,[status(thm)],[f754,f755,f438,f445,f668]) ).
fof(f809,plain,
( ~ sQ48_spl
| memberP(sK53_skl,sK51_skl)
| sK51_skl = sK52_skl
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f756,f490]) ).
fof(f817,definition,
( sQ58_spl
<=> ssItem(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f819,plain,
( sQ58_spl
| ~ ssItem(sK51_skl) ),
inference(component_clause,[status(thm)],[f817]) ).
fof(f820,definition,
( sQ59_spl
<=> sK51_skl = sK52_skl ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f821,plain,
( ~ sQ59_spl
| sK51_skl = sK52_skl ),
inference(component_clause,[status(thm)],[f820]) ).
fof(f823,definition,
( sQ60_spl
<=> memberP(sK53_skl,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f824,plain,
( ~ sQ60_spl
| memberP(sK53_skl,sK51_skl) ),
inference(component_clause,[status(thm)],[f823]) ).
fof(f826,plain,
( ~ sQ48_spl
| sQ60_spl
| sQ59_spl
| ~ sQ58_spl ),
inference(split_clause,[status(thm)],[f809,f817,f820,f823,f755]) ).
fof(f898,plain,
( ~ sQ29_spl
| ~ sQ60_spl
| memberP(sK50_skl,sK51_skl)
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f824,f628]) ).
fof(f903,definition,
( sQ62_spl
<=> memberP(sK50_skl,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f904,plain,
( ~ sQ62_spl
| memberP(sK50_skl,sK51_skl) ),
inference(component_clause,[status(thm)],[f903]) ).
fof(f906,plain,
( ~ sQ29_spl
| ~ sQ60_spl
| sQ62_spl
| ~ sQ58_spl ),
inference(split_clause,[status(thm)],[f898,f817,f903,f823,f627]) ).
fof(f907,plain,
( sQ58_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f819,f423]) ).
fof(f908,plain,
sQ58_spl,
inference(contradiction_clause,[status(thm)],[f907]) ).
fof(f909,plain,
( ~ sQ62_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f904,f491]) ).
fof(f910,plain,
~ sQ62_spl,
inference(contradiction_clause,[status(thm)],[f909]) ).
fof(f911,plain,
( ~ sQ59_spl
| ~ memberP(sK50_skl,sK52_skl) ),
inference(backward_demodulation,[status(thm)],[f821,f491]) ).
fof(f994,plain,
( ~ sQ6_spl
| ~ ssList(nil)
| ~ ssList(sK53_skl)
| memberP(sK50_skl,sK52_skl)
| ~ ssItem(sK52_skl)
| ~ ssList(app(sK53_skl,cons(sK52_skl,nil))) ),
inference(paramodulation,[status(thm)],[f454,f459]) ).
fof(f1012,definition,
( sQ71_spl
<=> ssList(app(sK53_skl,cons(sK52_skl,nil))) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f1014,plain,
( sQ71_spl
| ~ ssList(app(sK53_skl,cons(sK52_skl,nil))) ),
inference(component_clause,[status(thm)],[f1012]) ).
fof(f1015,definition,
( sQ72_spl
<=> memberP(sK50_skl,sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f1016,plain,
( ~ sQ72_spl
| memberP(sK50_skl,sK52_skl) ),
inference(component_clause,[status(thm)],[f1015]) ).
fof(f1018,plain,
( ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ4_spl
| sQ72_spl
| ~ sQ2_spl
| ~ sQ71_spl ),
inference(split_clause,[status(thm)],[f994,f1012,f438,f1015,f445,f513,f453]) ).
fof(f1043,plain,
( sQ71_spl
| ~ sQ6_spl
| ~ ssList(sK50_skl) ),
inference(forward_demodulation,[status(thm)],[f454,f1014]) ).
fof(f1044,plain,
( sQ71_spl
| ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1043,f420]) ).
fof(f1045,plain,
( sQ71_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f1044]) ).
fof(f1046,plain,
( ~ sQ72_spl
| ~ sQ59_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1016,f911]) ).
fof(f1047,plain,
( ~ sQ72_spl
| ~ sQ59_spl ),
inference(contradiction_clause,[status(thm)],[f1046]) ).
fof(f1048,plain,
$false,
inference(sat_refutation,[status(thm)],[f437,f444,f448,f452,f456,f496,f516,f518,f528,f530,f630,f671,f758,f826,f906,f908,f910,f1018,f1045,f1047]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC397+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.46 % Computer : n018.cluster.edu
% 0.16/0.46 % Model : x86_64 x86_64
% 0.16/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.46 % Memory : 8046.5625MB
% 0.16/0.46 % OS : Linux 6.8.0-71-generic
% 0.16/0.46 % CPULimit : 300
% 0.16/0.46 % WCLimit : 300
% 0.16/0.46 % DateTime : Mon Sep 21 08:23:15 UTC 2026
% 0.16/0.47 % CPUTime :
% 0.16/0.50 % Drodi V4.1.1
% 0.16/0.53 % Refutation found
% 0.16/0.53 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.59 % Elapsed time: 0.104342 seconds
% 0.20/0.59 % CPU time: 0.225979 seconds
% 0.20/0.59 % Total memory used: 52.908 MB
% 0.20/0.59 % Net memory used: 52.833 MB
%------------------------------------------------------------------------------