%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC188+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 : n007.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 02:40:19 PM UTC 2026
% Result : Theorem 1.33s 0.81s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 28
% Syntax : Number of formulae : 132 ( 16 unt; 20 def)
% Number of atoms : 531 ( 83 equ)
% Maximal formula atoms : 21 ( 4 avg)
% Number of connectives : 647 ( 248 ~; 254 |; 88 &)
% ( 26 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 26 ( 24 usr; 20 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 10 con; 0-3 aty)
% Number of variables : 144 ( 116 !; 28 ?)
% 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)
=> ( ? [X4] :
( leq(X4,X3)
& memberP(X,X4)
& X3 != X4
& ssItem(X4) )
| ~ 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)
=> ( ? [X4] :
( leq(X4,X3)
& memberP(X,X4)
& X3 != X4
& ssItem(X4) )
| ~ 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] :
( ! [X4] :
( ~ leq(X4,X3)
| ~ memberP(X,X4)
| X3 = X4
| ~ ssItem(X4) )
& 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)
<=> ( ! [X4] :
( ~ leq(X4,X3)
| ~ memberP(X,X4)
| X3 = X4
| ~ ssItem(X4) )
& 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] :
( ( ? [X4] :
( leq(X4,X3)
& memberP(X,X4)
& X3 != X4
& ssItem(X4) )
| ~ memberP(X,X3)
| cons(X3,nil) != W
| ~ ssItem(X3)
| sP0_prd(X3,X,W) )
& ( ( ! [X4] :
( ~ leq(X4,X3)
| ~ memberP(X,X4)
| X3 = X4
| ~ ssItem(X4) )
& 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] :
( ? [X4] :
( leq(X4,X3)
& memberP(X,X4)
& X3 != X4
& ssItem(X4) )
| ~ memberP(X,X3)
| cons(X3,nil) != W
| ~ ssItem(X3)
| sP0_prd(X3,X,W) )
& ! [W,X,X3] :
( ( ! [X4] :
( ~ leq(X4,X3)
| ~ memberP(X,X4)
| X3 = X4
| ~ ssItem(X4) )
& memberP(X,X3)
& cons(X3,nil) = W
& ssItem(X3) )
| ~ sP0_prd(X3,X,W) ) ),
inference(miniscoping,[status(thm)],[f433]) ).
fof(f435,plain,
( ! [W,X,X3] :
( ( leq(sK56_skl(X3,X,W),X3)
& memberP(X,sK56_skl(X3,X,W))
& X3 != sK56_skl(X3,X,W)
& ssItem(sK56_skl(X3,X,W)) )
| ~ memberP(X,X3)
| cons(X3,nil) != W
| ~ ssItem(X3)
| sP0_prd(X3,X,W) )
& ! [W,X,X3] :
( ( ! [X4] :
( ~ leq(X4,X3)
| ~ memberP(X,X4)
| X3 = X4
| ~ ssItem(X4) )
& memberP(X,X3)
& cons(X3,nil) = W
& ssItem(X3) )
| ~ sP0_prd(X3,X,W) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56_skl]),skolemize(X4,sK56_skl(X3,X,W))],[f434]) ).
fof(f436,plain,
! [X0,X1,X2] :
( ssItem(X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f435]) ).
fof(f437,plain,
! [X0,X1,X2] :
( cons(X0,nil) = X2
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f435]) ).
fof(f444,definition,
( sQ0_spl
<=> sP0_prd(sK55_skl,sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f445,plain,
( ~ sQ0_spl
| sP0_prd(sK55_skl,sK50_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f444]) ).
fof(f451,definition,
( sQ2_spl
<=> nil = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f452,plain,
( ~ sQ2_spl
| nil = sK49_skl ),
inference(component_clause,[status(thm)],[f451]) ).
fof(f454,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f432,f444,f451]) ).
fof(f457,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(f493,plain,
( ~ sQ0_spl
| sP0_prd(sK55_skl,sK48_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f423,f445]) ).
fof(f494,plain,
( ~ sQ0_spl
| sP0_prd(sK55_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f493]) ).
fof(f498,plain,
( ~ sQ0_spl
| ssItem(sK55_skl) ),
inference(resolution,[status(thm)],[f494,f436]) ).
fof(f499,plain,
( ~ sQ0_spl
| cons(sK55_skl,nil) = sK47_skl ),
inference(resolution,[status(thm)],[f437,f494]) ).
fof(f507,definition,
( sQ4_spl
<=> ssItem(sK55_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f509,plain,
( sQ4_spl
| ~ ssItem(sK55_skl) ),
inference(component_clause,[status(thm)],[f507]) ).
fof(f511,definition,
( sQ5_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f513,plain,
( sQ5_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f511]) ).
fof(f526,plain,
( sQ4_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f509,f498]) ).
fof(f527,plain,
( sQ4_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f526]) ).
fof(f534,plain,
( ~ sQ2_spl
| nil = sK47_skl ),
inference(forward_demodulation,[status(thm)],[f424,f452]) ).
fof(f550,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f513,f223]) ).
fof(f551,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f550]) ).
fof(f575,definition,
( sQ11_spl
<=> ssList(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK52_skl,nil))) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f577,plain,
( sQ11_spl
| ~ ssList(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK52_skl,nil))) ),
inference(component_clause,[status(thm)],[f575]) ).
fof(f578,definition,
( sQ12_spl
<=> ssList(sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f580,plain,
( sQ12_spl
| ~ ssList(sK54_skl) ),
inference(component_clause,[status(thm)],[f578]) ).
fof(f683,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f580,f428]) ).
fof(f684,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f683]) ).
fof(f685,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(f686,definition,
! [X0] :
( sQ28_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,[sQ28_spl])],[split_symbol_definition]) ).
fof(f687,plain,
! [X0] :
( ~ sQ28_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)],[f686]) ).
fof(f689,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f685,f686,f575,f578]) ).
fof(f690,plain,
( sQ11_spl
| ~ ssList(cons(sK52_skl,nil))
| ~ ssList(app(sK53_skl,cons(sK51_skl,nil))) ),
inference(resolution,[status(thm)],[f577,f245]) ).
fof(f691,definition,
( sQ29_spl
<=> ssList(app(sK53_skl,cons(sK51_skl,nil))) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f693,plain,
( sQ29_spl
| ~ ssList(app(sK53_skl,cons(sK51_skl,nil))) ),
inference(component_clause,[status(thm)],[f691]) ).
fof(f694,definition,
( sQ30_spl
<=> ssList(cons(sK52_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f696,plain,
( sQ30_spl
| ~ ssList(cons(sK52_skl,nil)) ),
inference(component_clause,[status(thm)],[f694]) ).
fof(f697,plain,
( sQ11_spl
| ~ sQ30_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f690,f691,f694,f575]) ).
fof(f698,plain,
( sQ29_spl
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK53_skl) ),
inference(resolution,[status(thm)],[f693,f245]) ).
fof(f699,definition,
( sQ31_spl
<=> ssList(sK53_skl) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f701,plain,
( sQ31_spl
| ~ ssList(sK53_skl) ),
inference(component_clause,[status(thm)],[f699]) ).
fof(f702,definition,
( sQ32_spl
<=> ssList(cons(sK51_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f704,plain,
( sQ32_spl
| ~ ssList(cons(sK51_skl,nil)) ),
inference(component_clause,[status(thm)],[f702]) ).
fof(f705,plain,
( sQ29_spl
| ~ sQ32_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f698,f699,f702,f691]) ).
fof(f706,plain,
( sQ30_spl
| ~ ssItem(sK52_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f696,f222]) ).
fof(f707,definition,
( sQ33_spl
<=> ssItem(sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f709,plain,
( sQ33_spl
| ~ ssItem(sK52_skl) ),
inference(component_clause,[status(thm)],[f707]) ).
fof(f710,plain,
( sQ30_spl
| ~ sQ33_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f706,f511,f707,f694]) ).
fof(f711,plain,
( sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f709,f426]) ).
fof(f712,plain,
sQ33_spl,
inference(contradiction_clause,[status(thm)],[f711]) ).
fof(f713,plain,
( sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f701,f427]) ).
fof(f714,plain,
sQ31_spl,
inference(contradiction_clause,[status(thm)],[f713]) ).
fof(f734,plain,
( sQ32_spl
| ~ ssItem(sK51_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f704,f222]) ).
fof(f735,definition,
( sQ36_spl
<=> ssItem(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f737,plain,
( sQ36_spl
| ~ ssItem(sK51_skl) ),
inference(component_clause,[status(thm)],[f735]) ).
fof(f738,plain,
( sQ32_spl
| ~ sQ36_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f734,f511,f735,f702]) ).
fof(f739,plain,
( sQ36_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f737,f425]) ).
fof(f740,plain,
sQ36_spl,
inference(contradiction_clause,[status(thm)],[f739]) ).
fof(f782,plain,
( ~ sQ28_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)],[f687,f457]) ).
fof(f783,plain,
! [X0] :
( ~ sQ28_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)],[f687,f271]) ).
fof(f787,definition,
( sQ45_spl
<=> memberP(sK47_skl,sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f788,plain,
( ~ sQ45_spl
| memberP(sK47_skl,sK52_skl) ),
inference(component_clause,[status(thm)],[f787]) ).
fof(f790,plain,
( ~ sQ28_spl
| ~ sQ5_spl
| ~ sQ29_spl
| ~ sQ11_spl
| sQ45_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f782,f707,f787,f575,f691,f511,f686]) ).
fof(f791,definition,
! [X0] :
( sQ46_spl
<=> ( ~ memberP(app(sK53_skl,cons(sK51_skl,nil)),X0)
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f792,plain,
! [X0] :
( ~ sQ46_spl
| ~ memberP(app(sK53_skl,cons(sK51_skl,nil)),X0)
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f791]) ).
fof(f794,plain,
( ~ sQ28_spl
| ~ sQ30_spl
| ~ sQ29_spl
| sQ46_spl ),
inference(split_clause,[status(thm)],[f783,f791,f691,f694,f686]) ).
fof(f813,plain,
! [X0] :
( ~ sQ46_spl
| ~ memberP(app(sK53_skl,cons(sK51_skl,nil)),X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f792]) ).
fof(f862,plain,
( ~ sQ46_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)],[f813,f457]) ).
fof(f867,definition,
( sQ58_spl
<=> memberP(sK47_skl,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f868,plain,
( ~ sQ58_spl
| memberP(sK47_skl,sK51_skl) ),
inference(component_clause,[status(thm)],[f867]) ).
fof(f870,plain,
( ~ sQ46_spl
| ~ sQ5_spl
| ~ sQ31_spl
| ~ sQ29_spl
| sQ58_spl
| ~ sQ36_spl ),
inference(split_clause,[status(thm)],[f862,f735,f867,f691,f699,f511,f791]) ).
fof(f1021,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)],[f499,f275]) ).
fof(f1024,definition,
! [X0] :
( sQ79_spl
<=> ( memberP(nil,X0)
| X0 = sK55_skl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f1025,plain,
! [X0] :
( ~ sQ79_spl
| memberP(nil,X0)
| X0 = sK55_skl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f1024]) ).
fof(f1027,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sQ79_spl ),
inference(split_clause,[status(thm)],[f1021,f1024,f507,f511,f444]) ).
fof(f1028,plain,
! [X0] :
( ~ sQ79_spl
| X0 = sK55_skl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1025,f279]) ).
fof(f1029,plain,
( ~ sQ58_spl
| ~ sQ79_spl
| sK51_skl = sK55_skl
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f1028,f868]) ).
fof(f1033,plain,
( ~ sQ45_spl
| ~ sQ79_spl
| sK52_skl = sK55_skl
| ~ ssItem(sK52_skl) ),
inference(resolution,[status(thm)],[f1028,f788]) ).
fof(f1037,definition,
( sQ80_spl
<=> sK51_skl = sK55_skl ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f1038,plain,
( ~ sQ80_spl
| sK51_skl = sK55_skl ),
inference(component_clause,[status(thm)],[f1037]) ).
fof(f1040,plain,
( ~ sQ58_spl
| ~ sQ79_spl
| sQ80_spl
| ~ sQ36_spl ),
inference(split_clause,[status(thm)],[f1029,f735,f1037,f1024,f867]) ).
fof(f1053,definition,
( sQ84_spl
<=> sK52_skl = sK55_skl ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f1054,plain,
( ~ sQ84_spl
| sK52_skl = sK55_skl ),
inference(component_clause,[status(thm)],[f1053]) ).
fof(f1056,plain,
( ~ sQ45_spl
| ~ sQ79_spl
| sQ84_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f1033,f707,f1053,f1024,f787]) ).
fof(f1099,plain,
( ~ sQ80_spl
| ~ sQ84_spl
| sK51_skl = sK52_skl ),
inference(forward_demodulation,[status(thm)],[f1054,f1038]) ).
fof(f1100,plain,
( ~ sQ80_spl
| ~ sQ84_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1099,f430]) ).
fof(f1101,plain,
( ~ sQ80_spl
| ~ sQ84_spl ),
inference(contradiction_clause,[status(thm)],[f1100]) ).
fof(f1111,plain,
( ~ sQ58_spl
| ~ sQ2_spl
| memberP(nil,sK51_skl) ),
inference(backward_demodulation,[status(thm)],[f534,f868]) ).
fof(f1208,plain,
( ~ sQ58_spl
| ~ sQ2_spl
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f1111,f279]) ).
fof(f1209,plain,
( ~ sQ58_spl
| ~ sQ2_spl
| ~ sQ36_spl ),
inference(split_clause,[status(thm)],[f1208,f735,f451,f867]) ).
fof(f1210,plain,
$false,
inference(sat_refutation,[status(thm)],[f454,f527,f551,f684,f689,f697,f705,f710,f712,f714,f738,f740,f790,f794,f870,f1027,f1040,f1056,f1101,f1209]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC188+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n007.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 08:00:50 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.39 % Drodi V4.1.1
% 1.33/0.81 % Refutation found
% 1.33/0.81 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.33/0.81 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.33/0.85 % Elapsed time: 0.465724 seconds
% 1.33/0.85 % CPU time: 2.984311 seconds
% 1.33/0.85 % Total memory used: 135.080 MB
% 1.33/0.85 % Net memory used: 133.185 MB
%------------------------------------------------------------------------------