%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC192+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 : n016.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 02:40:20 PM UTC 2026
% Result : Theorem 0.16s 5.63s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 28
% Syntax : Number of formulae : 133 ( 17 unt; 20 def)
% Number of atoms : 489 ( 73 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 584 ( 228 ~; 234 |; 65 &)
% ( 26 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 25 ( 23 usr; 20 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 10 con; 0-2 aty)
% Number of variables : 130 ( 106 !; 24 ?)
% 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(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(f26,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ssList(app(U,V)) ) ),
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(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( nil != W
| nil != X )
& ! [X3] :
( ssItem(X3)
=> ( ~ memberP(X,X3)
| cons(X3,nil) != W ) ) )
| ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssItem(Z)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( Y = Z
| app(app(app(X1,cons(Y,nil)),cons(Z,nil)),X2) != U ) ) ) ) )
| 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)
=> ( ( ( nil != W
| nil != X )
& ! [X3] :
( ssItem(X3)
=> ( ~ memberP(X,X3)
| cons(X3,nil) != W ) ) )
| ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssItem(Z)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( Y = Z
| app(app(app(X1,cons(Y,nil)),cons(Z,nil)),X2) != U ) ) ) ) )
| 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(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(f244,plain,
! [U] :
( ! [V] :
( ssList(app(U,V))
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f245,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f244]) ).
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(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil = W
& nil = X )
| ? [X3] :
( memberP(X,X3)
& cons(X3,nil) = W
& ssItem(X3) ) )
& ? [Y] :
( ? [Z] :
( ? [X1] :
( ? [X2] :
( Y != Z
& app(app(app(X1,cons(Y,nil)),cons(Z,nil)),X2) = U
& ssList(X2) )
& ssList(X1) )
& ssItem(Z) )
& ssItem(Y) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,definition,
! [W,X,X3] :
( sP0_prd(X3,X,W)
<=> ( memberP(X,X3)
& cons(X3,nil) = W
& ssItem(X3) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f417,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil = W
& nil = X )
| ? [X3] : sP0_prd(X3,X,W) )
& ? [Y] :
( ? [Z] :
( ? [X1] :
( ? [X2] :
( Y != Z
& app(app(app(X1,cons(Y,nil)),cons(Z,nil)),X2) = U
& ssList(X2) )
& ssList(X1) )
& ssItem(Z) )
& ssItem(Y) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(formula_renaming,[status(thm)],[f415,f416]) ).
fof(f418,plain,
( ( ( nil = sK49_skl
& nil = sK50_skl )
| sP0_prd(sK55_skl,sK50_skl,sK49_skl) )
& sK51_skl != sK52_skl
& app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK52_skl,nil)),sK54_skl) = sK47_skl
& ssList(sK54_skl)
& ssList(sK53_skl)
& ssItem(sK52_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,sK54_skl,sK55_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),skolemize(X2,sK54_skl),skolemize(X3,sK55_skl)],[f417]) ).
fof(f423,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f424,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f425,plain,
ssItem(sK51_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f426,plain,
ssItem(sK52_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f427,plain,
ssList(sK53_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f428,plain,
ssList(sK54_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f429,plain,
app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK52_skl,nil)),sK54_skl) = sK47_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f430,plain,
sK51_skl != sK52_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f432,plain,
( nil = sK49_skl
| sP0_prd(sK55_skl,sK50_skl,sK49_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f433,plain,
! [W,X,X3] :
( ( ~ memberP(X,X3)
| cons(X3,nil) != W
| ~ ssItem(X3)
| sP0_prd(X3,X,W) )
& ( ( memberP(X,X3)
& cons(X3,nil) = W
& ssItem(X3) )
| ~ sP0_prd(X3,X,W) ) ),
inference(NNF_transformation,[status(thm)],[f416]) ).
fof(f434,plain,
( ! [W,X,X3] :
( ~ memberP(X,X3)
| cons(X3,nil) != W
| ~ ssItem(X3)
| sP0_prd(X3,X,W) )
& ! [W,X,X3] :
( ( memberP(X,X3)
& cons(X3,nil) = W
& ssItem(X3) )
| ~ sP0_prd(X3,X,W) ) ),
inference(miniscoping,[status(thm)],[f433]) ).
fof(f435,plain,
! [X0,X1,X2] :
( ssItem(X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f434]) ).
fof(f436,plain,
! [X0,X1,X2] :
( cons(X0,nil) = X2
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f434]) ).
fof(f439,definition,
( sQ0_spl
<=> sP0_prd(sK55_skl,sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f440,plain,
( ~ sQ0_spl
| sP0_prd(sK55_skl,sK50_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f439]) ).
fof(f446,definition,
( sQ2_spl
<=> nil = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f447,plain,
( ~ sQ2_spl
| nil = sK49_skl ),
inference(component_clause,[status(thm)],[f446]) ).
fof(f449,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f432,f439,f446]) ).
fof(f452,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(f500,plain,
( ~ sQ0_spl
| sP0_prd(sK55_skl,sK48_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f423,f440]) ).
fof(f501,plain,
( ~ sQ0_spl
| sP0_prd(sK55_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f500]) ).
fof(f503,plain,
( ~ sQ0_spl
| ssItem(sK55_skl) ),
inference(resolution,[status(thm)],[f501,f435]) ).
fof(f504,plain,
( ~ sQ0_spl
| cons(sK55_skl,nil) = sK47_skl ),
inference(resolution,[status(thm)],[f436,f501]) ).
fof(f506,definition,
( sQ5_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f508,plain,
( sQ5_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f506]) ).
fof(f509,definition,
( sQ6_spl
<=> ssItem(sK55_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f511,plain,
( sQ6_spl
| ~ ssItem(sK55_skl) ),
inference(component_clause,[status(thm)],[f509]) ).
fof(f519,definition,
( sQ8_spl
<=> ssList(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK52_skl,nil))) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f521,plain,
( sQ8_spl
| ~ ssList(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK52_skl,nil))) ),
inference(component_clause,[status(thm)],[f519]) ).
fof(f522,definition,
( sQ9_spl
<=> ssList(sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f524,plain,
( sQ9_spl
| ~ ssList(sK54_skl) ),
inference(component_clause,[status(thm)],[f522]) ).
fof(f529,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f524,f428]) ).
fof(f530,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f529]) ).
fof(f534,plain,
( ~ sQ2_spl
| nil = sK47_skl ),
inference(forward_demodulation,[status(thm)],[f424,f447]) ).
fof(f535,plain,
! [X0] :
( ~ memberP(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK52_skl,nil)),X0)
| memberP(sK47_skl,X0)
| ~ ssList(sK54_skl)
| ~ ssList(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK52_skl,nil)))
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f429,f271]) ).
fof(f536,definition,
! [X0] :
( sQ11_spl
<=> ( ~ memberP(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK52_skl,nil)),X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f537,plain,
! [X0] :
( ~ sQ11_spl
| ~ memberP(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK52_skl,nil)),X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f536]) ).
fof(f539,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f535,f536,f519,f522]) ).
fof(f577,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f508,f223]) ).
fof(f578,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f577]) ).
fof(f584,plain,
( ~ sQ2_spl
| nil = sK49_skl ),
inference(backward_demodulation,[status(thm)],[f534,f424]) ).
fof(f632,plain,
( sQ8_spl
| ~ ssList(cons(sK52_skl,nil))
| ~ ssList(app(sK53_skl,cons(sK51_skl,nil))) ),
inference(resolution,[status(thm)],[f521,f245]) ).
fof(f633,definition,
( sQ25_spl
<=> ssList(app(sK53_skl,cons(sK51_skl,nil))) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f635,plain,
( sQ25_spl
| ~ ssList(app(sK53_skl,cons(sK51_skl,nil))) ),
inference(component_clause,[status(thm)],[f633]) ).
fof(f636,definition,
( sQ26_spl
<=> ssList(cons(sK52_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f638,plain,
( sQ26_spl
| ~ ssList(cons(sK52_skl,nil)) ),
inference(component_clause,[status(thm)],[f636]) ).
fof(f639,plain,
( sQ8_spl
| ~ sQ26_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f632,f633,f636,f519]) ).
fof(f640,plain,
( sQ25_spl
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK53_skl) ),
inference(resolution,[status(thm)],[f635,f245]) ).
fof(f641,definition,
( sQ27_spl
<=> ssList(sK53_skl) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f643,plain,
( sQ27_spl
| ~ ssList(sK53_skl) ),
inference(component_clause,[status(thm)],[f641]) ).
fof(f644,definition,
( sQ28_spl
<=> ssList(cons(sK51_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f646,plain,
( sQ28_spl
| ~ ssList(cons(sK51_skl,nil)) ),
inference(component_clause,[status(thm)],[f644]) ).
fof(f647,plain,
( sQ25_spl
| ~ sQ28_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f640,f641,f644,f633]) ).
fof(f650,plain,
( sQ26_spl
| ~ ssItem(sK52_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f638,f222]) ).
fof(f651,definition,
( sQ29_spl
<=> ssItem(sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f653,plain,
( sQ29_spl
| ~ ssItem(sK52_skl) ),
inference(component_clause,[status(thm)],[f651]) ).
fof(f654,plain,
( sQ26_spl
| ~ sQ29_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f650,f506,f651,f636]) ).
fof(f655,plain,
( sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f643,f427]) ).
fof(f656,plain,
sQ27_spl,
inference(contradiction_clause,[status(thm)],[f655]) ).
fof(f657,plain,
( sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f653,f426]) ).
fof(f658,plain,
sQ29_spl,
inference(contradiction_clause,[status(thm)],[f657]) ).
fof(f664,plain,
( sQ28_spl
| ~ ssItem(sK51_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f646,f222]) ).
fof(f665,definition,
( sQ30_spl
<=> ssItem(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f667,plain,
( sQ30_spl
| ~ ssItem(sK51_skl) ),
inference(component_clause,[status(thm)],[f665]) ).
fof(f668,plain,
( sQ28_spl
| ~ sQ30_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f664,f506,f665,f644]) ).
fof(f669,plain,
( sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f667,f425]) ).
fof(f670,plain,
sQ30_spl,
inference(contradiction_clause,[status(thm)],[f669]) ).
fof(f744,plain,
( ~ sQ0_spl
| sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f503,f511]) ).
fof(f745,plain,
( ~ sQ0_spl
| sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f744]) ).
fof(f749,plain,
! [X0] :
( ~ sQ0_spl
| memberP(nil,X0)
| X0 = sK55_skl
| ~ memberP(sK47_skl,X0)
| ~ ssList(nil)
| ~ ssItem(sK55_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f504,f275]) ).
fof(f773,definition,
! [X0] :
( sQ46_spl
<=> ( memberP(nil,X0)
| X0 = sK55_skl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f774,plain,
! [X0] :
( ~ sQ46_spl
| memberP(nil,X0)
| X0 = sK55_skl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f773]) ).
fof(f776,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sQ46_spl ),
inference(split_clause,[status(thm)],[f749,f773,f509,f506,f439]) ).
fof(f797,plain,
! [X0] :
( ~ sQ46_spl
| X0 = sK55_skl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f774,f279]) ).
fof(f851,plain,
( ~ sQ11_spl
| ~ ssList(nil)
| ~ ssList(app(sK53_skl,cons(sK51_skl,nil)))
| ~ ssItem(sK52_skl)
| ~ ssList(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK52_skl,nil)))
| memberP(sK47_skl,sK52_skl)
| ~ ssItem(sK52_skl) ),
inference(resolution,[status(thm)],[f537,f452]) ).
fof(f853,plain,
! [X0] :
( ~ sQ11_spl
| ~ memberP(app(sK53_skl,cons(sK51_skl,nil)),X0)
| ~ ssList(cons(sK52_skl,nil))
| ~ ssList(app(sK53_skl,cons(sK51_skl,nil)))
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f537,f271]) ).
fof(f854,definition,
( sQ57_spl
<=> memberP(sK47_skl,sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f855,plain,
( ~ sQ57_spl
| memberP(sK47_skl,sK52_skl) ),
inference(component_clause,[status(thm)],[f854]) ).
fof(f857,plain,
( ~ sQ11_spl
| ~ sQ5_spl
| ~ sQ25_spl
| ~ sQ8_spl
| sQ57_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f851,f651,f854,f519,f633,f506,f536]) ).
fof(f862,definition,
! [X0] :
( sQ59_spl
<=> ( ~ memberP(app(sK53_skl,cons(sK51_skl,nil)),X0)
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f863,plain,
! [X0] :
( ~ sQ59_spl
| ~ memberP(app(sK53_skl,cons(sK51_skl,nil)),X0)
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f862]) ).
fof(f865,plain,
( ~ sQ11_spl
| ~ sQ26_spl
| ~ sQ25_spl
| sQ59_spl ),
inference(split_clause,[status(thm)],[f853,f862,f633,f636,f536]) ).
fof(f867,plain,
! [X0] :
( ~ sQ59_spl
| ~ memberP(app(sK53_skl,cons(sK51_skl,nil)),X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f863]) ).
fof(f868,plain,
( ~ sQ46_spl
| ~ sQ57_spl
| sK52_skl = sK55_skl
| ~ ssItem(sK52_skl) ),
inference(resolution,[status(thm)],[f855,f797]) ).
fof(f869,definition,
( sQ60_spl
<=> sK52_skl = sK55_skl ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f870,plain,
( ~ sQ60_spl
| sK52_skl = sK55_skl ),
inference(component_clause,[status(thm)],[f869]) ).
fof(f872,plain,
( ~ sQ46_spl
| ~ sQ57_spl
| sQ60_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f868,f651,f869,f854,f773]) ).
fof(f873,plain,
! [X0] :
( ~ sQ46_spl
| ~ sQ60_spl
| X0 = sK52_skl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(backward_demodulation,[status(thm)],[f870,f797]) ).
fof(f978,plain,
( ~ sQ2_spl
| nil = sK47_skl ),
inference(forward_demodulation,[status(thm)],[f424,f584]) ).
fof(f992,plain,
( ~ sQ59_spl
| ~ ssList(nil)
| ~ ssList(sK53_skl)
| ~ ssItem(sK51_skl)
| ~ ssList(app(sK53_skl,cons(sK51_skl,nil)))
| memberP(sK47_skl,sK51_skl)
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f867,f452]) ).
fof(f995,definition,
( sQ74_spl
<=> memberP(sK47_skl,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f996,plain,
( ~ sQ74_spl
| memberP(sK47_skl,sK51_skl) ),
inference(component_clause,[status(thm)],[f995]) ).
fof(f998,plain,
( ~ sQ59_spl
| ~ sQ5_spl
| ~ sQ27_spl
| ~ sQ25_spl
| sQ74_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f992,f665,f995,f633,f641,f506,f862]) ).
fof(f1178,plain,
( ~ sQ74_spl
| ~ sQ2_spl
| memberP(nil,sK51_skl) ),
inference(backward_demodulation,[status(thm)],[f978,f996]) ).
fof(f1273,plain,
( ~ sQ74_spl
| ~ sQ2_spl
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f1178,f279]) ).
fof(f1274,plain,
( ~ sQ74_spl
| ~ sQ2_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f1273,f665,f446,f995]) ).
fof(f1339,plain,
( ~ sQ74_spl
| ~ sQ46_spl
| ~ sQ60_spl
| sK51_skl = sK52_skl
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f873,f996]) ).
fof(f1341,definition,
( sQ120_spl
<=> sK51_skl = sK52_skl ),
introduced(definition,[new_symbols(definition,[sQ120_spl])],[split_symbol_definition]) ).
fof(f1342,plain,
( ~ sQ120_spl
| sK51_skl = sK52_skl ),
inference(component_clause,[status(thm)],[f1341]) ).
fof(f1344,plain,
( ~ sQ74_spl
| ~ sQ46_spl
| ~ sQ60_spl
| sQ120_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f1339,f665,f1341,f869,f773,f995]) ).
fof(f1345,plain,
( ~ sQ120_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1342,f430]) ).
fof(f1346,plain,
~ sQ120_spl,
inference(contradiction_clause,[status(thm)],[f1345]) ).
fof(f1347,plain,
$false,
inference(sat_refutation,[status(thm)],[f449,f530,f539,f578,f639,f647,f654,f656,f658,f668,f670,f745,f776,f857,f865,f872,f998,f1274,f1344,f1346]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC192+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/5.40 % Computer : n016.cluster.edu
% 0.03/5.40 % Model : x86_64 x86_64
% 0.03/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/5.40 % Memory : 8046.5625MB
% 0.03/5.40 % OS : Linux 6.8.0-71-generic
% 0.03/5.40 % CPULimit : 300
% 0.03/5.40 % WCLimit : 300
% 0.03/5.40 % DateTime : Mon Sep 21 08:07:58 UTC 2026
% 0.03/5.40 % CPUTime :
% 0.03/5.43 % Drodi V4.1.1
% 0.16/5.63 % Refutation found
% 0.16/5.63 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/5.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/5.67 % Elapsed time: 0.247566 seconds
% 0.16/5.67 % CPU time: 1.521270 seconds
% 0.16/5.67 % Total memory used: 125.092 MB
% 0.16/5.67 % Net memory used: 123.897 MB
%------------------------------------------------------------------------------