%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC298+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 02:40:42 PM UTC 2026
% Result : Theorem 0.26s 0.69s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 36
% Syntax : Number of formulae : 168 ( 18 unt; 26 def)
% Number of atoms : 666 ( 81 equ)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 823 ( 325 ~; 334 |; 92 &)
% ( 34 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 34 ( 32 usr; 26 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 11 con; 0-3 aty)
% Number of variables : 170 ( 140 !; 30 ?)
% 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/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ssList(cons(V,U)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ssList(app(U,V)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ( gt(U,V)
<=> lt(V,U) ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [U] :
( ssItem(U)
=> ~ memberP(nil,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f94,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ( gt(U,V)
=> ~ gt(V,U) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( nil != W
| nil != X )
& ! [X4] :
( ssItem(X4)
=> ( ? [X5] :
( leq(X5,X4)
& memberP(X,X5)
& X4 != X5
& ssItem(X5) )
| ~ memberP(X,X4)
| cons(X4,nil) != W ) ) )
| ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssItem(Z)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ~ lt(Z,Y)
| app(app(app(app(X1,cons(Y,nil)),X2),cons(Z,nil)),X3) != U ) ) ) ) ) )
| U != W
| V != X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( nil != W
| nil != X )
& ! [X4] :
( ssItem(X4)
=> ( ? [X5] :
( leq(X5,X4)
& memberP(X,X5)
& X4 != X5
& ssItem(X5) )
| ~ memberP(X,X4)
| cons(X4,nil) != W ) ) )
| ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssItem(Z)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ~ lt(Z,Y)
| app(app(app(app(X1,cons(Y,nil)),X2),cons(Z,nil)),X3) != 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(f264,plain,
! [U] :
( ! [V] :
( ( gt(U,V)
<=> lt(V,U) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f35]) ).
fof(f265,plain,
! [U] :
( ! [V] :
( ( ( ~ lt(V,U)
| gt(U,V) )
& ( lt(V,U)
| ~ gt(U,V) ) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(NNF_transformation,[status(thm)],[f264]) ).
fof(f267,plain,
! [X0,X1] :
( ~ lt(X1,X0)
| gt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f265]) ).
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(f411,plain,
! [U] :
( ! [V] :
( ~ gt(V,U)
| ~ gt(U,V)
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f94]) ).
fof(f412,plain,
! [X0,X1] :
( ~ gt(X1,X0)
| ~ gt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f411]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil = W
& nil = X )
| ? [X4] :
( ! [X5] :
( ~ leq(X5,X4)
| ~ memberP(X,X5)
| X4 = X5
| ~ ssItem(X5) )
& memberP(X,X4)
& cons(X4,nil) = W
& ssItem(X4) ) )
& ? [Y] :
( ? [Z] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( lt(Z,Y)
& app(app(app(app(X1,cons(Y,nil)),X2),cons(Z,nil)),X3) = U
& ssList(X3) )
& 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,X4] :
( sP0_prd(X4,X,W)
<=> ( ! [X5] :
( ~ leq(X5,X4)
| ~ memberP(X,X5)
| X4 = X5
| ~ ssItem(X5) )
& memberP(X,X4)
& cons(X4,nil) = W
& ssItem(X4) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f417,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil = W
& nil = X )
| ? [X4] : sP0_prd(X4,X,W) )
& ? [Y] :
( ? [Z] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( lt(Z,Y)
& app(app(app(app(X1,cons(Y,nil)),X2),cons(Z,nil)),X3) = U
& ssList(X3) )
& 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(sK56_skl,sK50_skl,sK49_skl) )
& lt(sK52_skl,sK51_skl)
& app(app(app(app(sK53_skl,cons(sK51_skl,nil)),sK54_skl),cons(sK52_skl,nil)),sK55_skl) = sK47_skl
& ssList(sK55_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,sK56_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),skolemize(X4,sK56_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,
ssList(sK55_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f430,plain,
app(app(app(app(sK53_skl,cons(sK51_skl,nil)),sK54_skl),cons(sK52_skl,nil)),sK55_skl) = sK47_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f431,plain,
lt(sK52_skl,sK51_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f433,plain,
( nil = sK49_skl
| sP0_prd(sK56_skl,sK50_skl,sK49_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f434,plain,
! [W,X,X4] :
( ( ? [X5] :
( leq(X5,X4)
& memberP(X,X5)
& X4 != X5
& ssItem(X5) )
| ~ memberP(X,X4)
| cons(X4,nil) != W
| ~ ssItem(X4)
| sP0_prd(X4,X,W) )
& ( ( ! [X5] :
( ~ leq(X5,X4)
| ~ memberP(X,X5)
| X4 = X5
| ~ ssItem(X5) )
& memberP(X,X4)
& cons(X4,nil) = W
& ssItem(X4) )
| ~ sP0_prd(X4,X,W) ) ),
inference(NNF_transformation,[status(thm)],[f416]) ).
fof(f435,plain,
( ! [W,X,X4] :
( ? [X5] :
( leq(X5,X4)
& memberP(X,X5)
& X4 != X5
& ssItem(X5) )
| ~ memberP(X,X4)
| cons(X4,nil) != W
| ~ ssItem(X4)
| sP0_prd(X4,X,W) )
& ! [W,X,X4] :
( ( ! [X5] :
( ~ leq(X5,X4)
| ~ memberP(X,X5)
| X4 = X5
| ~ ssItem(X5) )
& memberP(X,X4)
& cons(X4,nil) = W
& ssItem(X4) )
| ~ sP0_prd(X4,X,W) ) ),
inference(miniscoping,[status(thm)],[f434]) ).
fof(f436,plain,
( ! [W,X,X4] :
( ( leq(sK57_skl(X4,X,W),X4)
& memberP(X,sK57_skl(X4,X,W))
& X4 != sK57_skl(X4,X,W)
& ssItem(sK57_skl(X4,X,W)) )
| ~ memberP(X,X4)
| cons(X4,nil) != W
| ~ ssItem(X4)
| sP0_prd(X4,X,W) )
& ! [W,X,X4] :
( ( ! [X5] :
( ~ leq(X5,X4)
| ~ memberP(X,X5)
| X4 = X5
| ~ ssItem(X5) )
& memberP(X,X4)
& cons(X4,nil) = W
& ssItem(X4) )
| ~ sP0_prd(X4,X,W) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK57_skl]),skolemize(X5,sK57_skl(X4,X,W))],[f435]) ).
fof(f437,plain,
! [X0,X1,X2] :
( ssItem(X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f436]) ).
fof(f438,plain,
! [X0,X1,X2] :
( cons(X0,nil) = X2
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f436]) ).
fof(f445,definition,
( sQ0_spl
<=> sP0_prd(sK56_skl,sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f446,plain,
( ~ sQ0_spl
| sP0_prd(sK56_skl,sK50_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f445]) ).
fof(f452,definition,
( sQ2_spl
<=> nil = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f453,plain,
( ~ sQ2_spl
| nil = sK49_skl ),
inference(component_clause,[status(thm)],[f452]) ).
fof(f455,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f433,f445,f452]) ).
fof(f458,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(f494,plain,
( ~ sQ0_spl
| sP0_prd(sK56_skl,sK48_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f423,f446]) ).
fof(f495,plain,
( ~ sQ0_spl
| sP0_prd(sK56_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f494]) ).
fof(f499,plain,
( ~ sQ0_spl
| ssItem(sK56_skl) ),
inference(resolution,[status(thm)],[f495,f437]) ).
fof(f500,plain,
( ~ sQ0_spl
| cons(sK56_skl,nil) = sK47_skl ),
inference(resolution,[status(thm)],[f438,f495]) ).
fof(f507,definition,
( sQ4_spl
<=> ssItem(sK56_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f509,plain,
( sQ4_spl
| ~ ssItem(sK56_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(f522,plain,
( sQ4_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f509,f499]) ).
fof(f523,plain,
( sQ4_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f522]) ).
fof(f530,plain,
( ~ sQ2_spl
| nil = sK47_skl ),
inference(forward_demodulation,[status(thm)],[f424,f453]) ).
fof(f546,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f513,f223]) ).
fof(f547,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f546]) ).
fof(f575,definition,
( sQ11_spl
<=> ssList(app(app(app(sK53_skl,cons(sK51_skl,nil)),sK54_skl),cons(sK52_skl,nil))) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f577,plain,
( sQ11_spl
| ~ ssList(app(app(app(sK53_skl,cons(sK51_skl,nil)),sK54_skl),cons(sK52_skl,nil))) ),
inference(component_clause,[status(thm)],[f575]) ).
fof(f578,definition,
( sQ12_spl
<=> ssList(sK55_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f580,plain,
( sQ12_spl
| ~ ssList(sK55_skl) ),
inference(component_clause,[status(thm)],[f578]) ).
fof(f592,definition,
( sQ14_spl
<=> ssItem(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f594,plain,
( sQ14_spl
| ~ ssItem(sK51_skl) ),
inference(component_clause,[status(thm)],[f592]) ).
fof(f595,definition,
( sQ15_spl
<=> ssItem(sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f597,plain,
( sQ15_spl
| ~ ssItem(sK52_skl) ),
inference(component_clause,[status(thm)],[f595]) ).
fof(f607,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f594,f425]) ).
fof(f608,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f607]) ).
fof(f609,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f597,f426]) ).
fof(f610,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f609]) ).
fof(f614,plain,
( gt(sK51_skl,sK52_skl)
| ~ ssItem(sK52_skl)
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f267,f431]) ).
fof(f615,definition,
( sQ18_spl
<=> gt(sK51_skl,sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f616,plain,
( ~ sQ18_spl
| gt(sK51_skl,sK52_skl) ),
inference(component_clause,[status(thm)],[f615]) ).
fof(f618,plain,
( sQ18_spl
| ~ sQ15_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f614,f592,f595,f615]) ).
fof(f643,definition,
( sQ24_spl
<=> sK51_skl = sK52_skl ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f644,plain,
( ~ sQ24_spl
| sK51_skl = sK52_skl ),
inference(component_clause,[status(thm)],[f643]) ).
fof(f649,plain,
( ~ sQ18_spl
| ~ gt(sK52_skl,sK51_skl)
| ~ ssItem(sK51_skl)
| ~ ssItem(sK52_skl) ),
inference(resolution,[status(thm)],[f412,f616]) ).
fof(f650,definition,
( sQ25_spl
<=> gt(sK52_skl,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f652,plain,
( sQ25_spl
| ~ gt(sK52_skl,sK51_skl) ),
inference(component_clause,[status(thm)],[f650]) ).
fof(f653,plain,
( ~ sQ18_spl
| ~ sQ25_spl
| ~ sQ14_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f649,f595,f592,f650,f615]) ).
fof(f681,plain,
( sQ25_spl
| ~ sQ24_spl
| ~ gt(sK51_skl,sK51_skl) ),
inference(backward_demodulation,[status(thm)],[f644,f652]) ).
fof(f684,plain,
( ~ sQ18_spl
| ~ sQ24_spl
| gt(sK51_skl,sK51_skl) ),
inference(backward_demodulation,[status(thm)],[f644,f616]) ).
fof(f691,plain,
( ~ sQ18_spl
| ~ sQ24_spl
| sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f684,f681]) ).
fof(f692,plain,
( ~ sQ18_spl
| ~ sQ24_spl
| sQ25_spl ),
inference(contradiction_clause,[status(thm)],[f691]) ).
fof(f803,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f580,f429]) ).
fof(f804,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f803]) ).
fof(f805,plain,
! [X0] :
( ~ memberP(app(app(app(sK53_skl,cons(sK51_skl,nil)),sK54_skl),cons(sK52_skl,nil)),X0)
| memberP(sK47_skl,X0)
| ~ ssList(sK55_skl)
| ~ ssList(app(app(app(sK53_skl,cons(sK51_skl,nil)),sK54_skl),cons(sK52_skl,nil)))
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f430,f271]) ).
fof(f806,definition,
! [X0] :
( sQ43_spl
<=> ( ~ memberP(app(app(app(sK53_skl,cons(sK51_skl,nil)),sK54_skl),cons(sK52_skl,nil)),X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f807,plain,
! [X0] :
( ~ sQ43_spl
| ~ memberP(app(app(app(sK53_skl,cons(sK51_skl,nil)),sK54_skl),cons(sK52_skl,nil)),X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f806]) ).
fof(f809,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| sQ43_spl ),
inference(split_clause,[status(thm)],[f805,f806,f575,f578]) ).
fof(f813,plain,
! [X0] :
( ~ sQ0_spl
| memberP(nil,X0)
| X0 = sK56_skl
| ~ memberP(sK47_skl,X0)
| ~ ssList(nil)
| ~ ssItem(sK56_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f500,f275]) ).
fof(f815,definition,
! [X0] :
( sQ44_spl
<=> ( memberP(nil,X0)
| X0 = sK56_skl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f816,plain,
! [X0] :
( ~ sQ44_spl
| memberP(nil,X0)
| X0 = sK56_skl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f815]) ).
fof(f818,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f813,f815,f507,f511,f445]) ).
fof(f819,plain,
! [X0] :
( ~ sQ44_spl
| X0 = sK56_skl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f816,f279]) ).
fof(f838,plain,
( sQ11_spl
| ~ ssList(cons(sK52_skl,nil))
| ~ ssList(app(app(sK53_skl,cons(sK51_skl,nil)),sK54_skl)) ),
inference(resolution,[status(thm)],[f577,f245]) ).
fof(f839,definition,
( sQ47_spl
<=> ssList(app(app(sK53_skl,cons(sK51_skl,nil)),sK54_skl)) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f841,plain,
( sQ47_spl
| ~ ssList(app(app(sK53_skl,cons(sK51_skl,nil)),sK54_skl)) ),
inference(component_clause,[status(thm)],[f839]) ).
fof(f842,definition,
( sQ48_spl
<=> ssList(cons(sK52_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f844,plain,
( sQ48_spl
| ~ ssList(cons(sK52_skl,nil)) ),
inference(component_clause,[status(thm)],[f842]) ).
fof(f845,plain,
( sQ11_spl
| ~ sQ48_spl
| ~ sQ47_spl ),
inference(split_clause,[status(thm)],[f838,f839,f842,f575]) ).
fof(f846,plain,
( sQ47_spl
| ~ ssList(sK54_skl)
| ~ ssList(app(sK53_skl,cons(sK51_skl,nil))) ),
inference(resolution,[status(thm)],[f841,f245]) ).
fof(f847,definition,
( sQ49_spl
<=> ssList(app(sK53_skl,cons(sK51_skl,nil))) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f849,plain,
( sQ49_spl
| ~ ssList(app(sK53_skl,cons(sK51_skl,nil))) ),
inference(component_clause,[status(thm)],[f847]) ).
fof(f850,definition,
( sQ50_spl
<=> ssList(sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f852,plain,
( sQ50_spl
| ~ ssList(sK54_skl) ),
inference(component_clause,[status(thm)],[f850]) ).
fof(f853,plain,
( sQ47_spl
| ~ sQ50_spl
| ~ sQ49_spl ),
inference(split_clause,[status(thm)],[f846,f847,f850,f839]) ).
fof(f854,plain,
( sQ50_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f852,f428]) ).
fof(f855,plain,
sQ50_spl,
inference(contradiction_clause,[status(thm)],[f854]) ).
fof(f877,plain,
( sQ48_spl
| ~ ssItem(sK52_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f844,f222]) ).
fof(f878,plain,
( sQ48_spl
| ~ sQ15_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f877,f511,f595,f842]) ).
fof(f879,plain,
( sQ49_spl
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK53_skl) ),
inference(resolution,[status(thm)],[f849,f245]) ).
fof(f880,definition,
( sQ53_spl
<=> ssList(sK53_skl) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f882,plain,
( sQ53_spl
| ~ ssList(sK53_skl) ),
inference(component_clause,[status(thm)],[f880]) ).
fof(f883,definition,
( sQ54_spl
<=> ssList(cons(sK51_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f885,plain,
( sQ54_spl
| ~ ssList(cons(sK51_skl,nil)) ),
inference(component_clause,[status(thm)],[f883]) ).
fof(f886,plain,
( sQ49_spl
| ~ sQ54_spl
| ~ sQ53_spl ),
inference(split_clause,[status(thm)],[f879,f880,f883,f847]) ).
fof(f887,plain,
( sQ53_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f882,f427]) ).
fof(f888,plain,
sQ53_spl,
inference(contradiction_clause,[status(thm)],[f887]) ).
fof(f889,plain,
( sQ54_spl
| ~ ssItem(sK51_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f885,f222]) ).
fof(f890,plain,
( sQ54_spl
| ~ sQ14_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f889,f511,f592,f883]) ).
fof(f928,plain,
( ~ sQ43_spl
| ~ ssList(nil)
| ~ ssList(app(app(sK53_skl,cons(sK51_skl,nil)),sK54_skl))
| ~ ssItem(sK52_skl)
| ~ ssList(app(app(app(sK53_skl,cons(sK51_skl,nil)),sK54_skl),cons(sK52_skl,nil)))
| memberP(sK47_skl,sK52_skl)
| ~ ssItem(sK52_skl) ),
inference(resolution,[status(thm)],[f807,f458]) ).
fof(f929,plain,
! [X0] :
( ~ sQ43_spl
| ~ memberP(app(app(sK53_skl,cons(sK51_skl,nil)),sK54_skl),X0)
| ~ ssList(cons(sK52_skl,nil))
| ~ ssList(app(app(sK53_skl,cons(sK51_skl,nil)),sK54_skl))
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f807,f271]) ).
fof(f932,definition,
( sQ61_spl
<=> memberP(sK47_skl,sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f933,plain,
( ~ sQ61_spl
| memberP(sK47_skl,sK52_skl) ),
inference(component_clause,[status(thm)],[f932]) ).
fof(f935,plain,
( ~ sQ43_spl
| ~ sQ5_spl
| ~ sQ47_spl
| ~ sQ11_spl
| sQ61_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f928,f595,f932,f575,f839,f511,f806]) ).
fof(f936,definition,
! [X0] :
( sQ62_spl
<=> ( ~ memberP(app(app(sK53_skl,cons(sK51_skl,nil)),sK54_skl),X0)
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f937,plain,
! [X0] :
( ~ sQ62_spl
| ~ memberP(app(app(sK53_skl,cons(sK51_skl,nil)),sK54_skl),X0)
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f936]) ).
fof(f939,plain,
( ~ sQ43_spl
| ~ sQ48_spl
| ~ sQ47_spl
| sQ62_spl ),
inference(split_clause,[status(thm)],[f929,f936,f839,f842,f806]) ).
fof(f945,plain,
! [X0] :
( ~ sQ62_spl
| ~ memberP(app(app(sK53_skl,cons(sK51_skl,nil)),sK54_skl),X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f937]) ).
fof(f947,plain,
( ~ sQ44_spl
| ~ sQ61_spl
| sK52_skl = sK56_skl
| ~ ssItem(sK52_skl) ),
inference(resolution,[status(thm)],[f933,f819]) ).
fof(f948,definition,
( sQ64_spl
<=> sK52_skl = sK56_skl ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f949,plain,
( ~ sQ64_spl
| sK52_skl = sK56_skl ),
inference(component_clause,[status(thm)],[f948]) ).
fof(f951,plain,
( ~ sQ44_spl
| ~ sQ61_spl
| sQ64_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f947,f595,f948,f932,f815]) ).
fof(f957,plain,
( ~ sQ0_spl
| ~ sQ64_spl
| cons(sK52_skl,nil) = sK47_skl ),
inference(backward_demodulation,[status(thm)],[f949,f500]) ).
fof(f1012,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ64_spl
| memberP(nil,X0)
| X0 = sK52_skl
| ~ memberP(sK47_skl,X0)
| ~ ssList(nil)
| ~ ssItem(sK52_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f957,f275]) ).
fof(f1056,definition,
! [X0] :
( sQ73_spl
<=> ( memberP(nil,X0)
| X0 = sK52_skl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f1057,plain,
! [X0] :
( ~ sQ73_spl
| memberP(nil,X0)
| X0 = sK52_skl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f1056]) ).
fof(f1059,plain,
( ~ sQ0_spl
| ~ sQ64_spl
| ~ sQ5_spl
| ~ sQ15_spl
| sQ73_spl ),
inference(split_clause,[status(thm)],[f1012,f1056,f595,f511,f948,f445]) ).
fof(f1074,plain,
( ~ sQ61_spl
| ~ sQ2_spl
| memberP(nil,sK52_skl) ),
inference(backward_demodulation,[status(thm)],[f530,f933]) ).
fof(f1097,plain,
( ~ sQ61_spl
| ~ sQ2_spl
| ~ ssItem(sK52_skl) ),
inference(resolution,[status(thm)],[f1074,f279]) ).
fof(f1098,plain,
( ~ sQ61_spl
| ~ sQ2_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f1097,f595,f452,f932]) ).
fof(f1134,plain,
! [X0] :
( ~ sQ73_spl
| X0 = sK52_skl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1057,f279]) ).
fof(f1292,plain,
! [X0] :
( ~ sQ62_spl
| ~ memberP(app(sK53_skl,cons(sK51_skl,nil)),X0)
| ~ ssList(sK54_skl)
| ~ ssList(app(sK53_skl,cons(sK51_skl,nil)))
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f945,f271]) ).
fof(f1295,definition,
! [X0] :
( sQ88_spl
<=> ( ~ memberP(app(sK53_skl,cons(sK51_skl,nil)),X0)
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f1296,plain,
! [X0] :
( ~ sQ88_spl
| ~ memberP(app(sK53_skl,cons(sK51_skl,nil)),X0)
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f1295]) ).
fof(f1298,plain,
( ~ sQ62_spl
| ~ sQ50_spl
| ~ sQ49_spl
| sQ88_spl ),
inference(split_clause,[status(thm)],[f1292,f1295,f847,f850,f936]) ).
fof(f1304,plain,
! [X0] :
( ~ sQ88_spl
| ~ memberP(app(sK53_skl,cons(sK51_skl,nil)),X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1296]) ).
fof(f1318,plain,
( ~ sQ88_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)],[f1304,f458]) ).
fof(f1322,definition,
( sQ90_spl
<=> memberP(sK47_skl,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f1323,plain,
( ~ sQ90_spl
| memberP(sK47_skl,sK51_skl) ),
inference(component_clause,[status(thm)],[f1322]) ).
fof(f1325,plain,
( ~ sQ88_spl
| ~ sQ5_spl
| ~ sQ53_spl
| ~ sQ49_spl
| sQ90_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f1318,f592,f1322,f847,f880,f511,f1295]) ).
fof(f1337,plain,
( ~ sQ73_spl
| ~ sQ90_spl
| sK51_skl = sK52_skl
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f1323,f1134]) ).
fof(f1338,plain,
( ~ sQ73_spl
| ~ sQ90_spl
| sQ24_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f1337,f592,f643,f1322,f1056]) ).
fof(f1339,plain,
$false,
inference(sat_refutation,[status(thm)],[f455,f523,f547,f608,f610,f618,f653,f692,f804,f809,f818,f845,f853,f855,f878,f886,f888,f890,f935,f939,f951,f1059,f1098,f1298,f1325,f1338]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC298+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n009.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 21 08:12:58 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.47 % Drodi V4.1.1
% 0.26/0.69 % Refutation found
% 0.26/0.69 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.26/0.69 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.51/0.73 % Elapsed time: 0.266009 seconds
% 0.51/0.73 % CPU time: 1.664982 seconds
% 0.51/0.73 % Total memory used: 126.268 MB
% 0.51/0.73 % Net memory used: 125.035 MB
%------------------------------------------------------------------------------