%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC299+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 : n005.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 0.23s 1.01s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 34
% Syntax : Number of formulae : 158 ( 18 unt; 25 def)
% Number of atoms : 665 ( 79 equ)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 828 ( 321 ~; 324 |; 111 &)
% ( 32 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 31 ( 29 usr; 24 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 11 con; 0-5 aty)
% Number of variables : 198 ( 154 !; 44 ?)
% 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(f33,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ( lt(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(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( nil != W
| nil != X )
& ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( ? [X8] :
( lt(X8,X4)
& memberP(X6,X8)
& ssItem(X8) )
| ? [X7] :
( lt(X4,X7)
& memberP(X5,X7)
& ssItem(X7) )
| app(app(X5,W),X6) != X
| 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] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( ? [X8] :
( lt(X8,X4)
& memberP(X6,X8)
& ssItem(X8) )
| ? [X7] :
( lt(X4,X7)
& memberP(X5,X7)
& ssItem(X7) )
| app(app(X5,W),X6) != X
| 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(f260,plain,
! [U] :
( ! [V] :
( ~ lt(V,U)
| ~ lt(U,V)
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f261,plain,
! [X0,X1] :
( ~ lt(X1,X0)
| ~ lt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f260]) ).
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 )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( ! [X8] :
( ~ lt(X8,X4)
| ~ memberP(X6,X8)
| ~ ssItem(X8) )
& ! [X7] :
( ~ lt(X4,X7)
| ~ memberP(X5,X7)
| ~ ssItem(X7) )
& app(app(X5,W),X6) = X
& cons(X4,nil) = W
& ssList(X6) )
& ssList(X5) )
& 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] :
( ? [X6] :
( ! [X8] :
( ~ lt(X8,X4)
| ~ memberP(X6,X8)
| ~ ssItem(X8) )
& ! [X7] :
( ~ lt(X4,X7)
| ~ memberP(X5,X7)
| ~ ssItem(X7) )
& app(app(X5,W),X6) = X
& cons(X4,nil) = W
& ssList(X6) )
& ssList(X5) )
& 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,definition,
! [X4,X5,X7] :
( sP1_prd(X7,X5,X4)
<=> ( ~ lt(X4,X7)
| ~ memberP(X5,X7)
| ~ ssItem(X7) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f435,plain,
! [W,X,X4] :
( sP0_prd(X4,X,W)
<=> ( ? [X5] :
( ? [X6] :
( ! [X8] :
( ~ lt(X8,X4)
| ~ memberP(X6,X8)
| ~ ssItem(X8) )
& ! [X7] : sP1_prd(X7,X5,X4)
& app(app(X5,W),X6) = X
& cons(X4,nil) = W
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) ) ),
inference(formula_renaming,[status(thm)],[f416,f434]) ).
fof(f436,plain,
! [W,X,X4] :
( ( ! [X5] :
( ! [X6] :
( ? [X8] :
( lt(X8,X4)
& memberP(X6,X8)
& ssItem(X8) )
| ? [X7] : ~ sP1_prd(X7,X5,X4)
| app(app(X5,W),X6) != X
| cons(X4,nil) != W
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4)
| sP0_prd(X4,X,W) )
& ( ( ? [X5] :
( ? [X6] :
( ! [X8] :
( ~ lt(X8,X4)
| ~ memberP(X6,X8)
| ~ ssItem(X8) )
& ! [X7] : sP1_prd(X7,X5,X4)
& app(app(X5,W),X6) = X
& cons(X4,nil) = W
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
| ~ sP0_prd(X4,X,W) ) ),
inference(NNF_transformation,[status(thm)],[f435]) ).
fof(f437,plain,
( ! [W,X,X4] :
( ! [X5] :
( ! [X6] :
( ? [X8] :
( lt(X8,X4)
& memberP(X6,X8)
& ssItem(X8) )
| ? [X7] : ~ sP1_prd(X7,X5,X4)
| app(app(X5,W),X6) != X
| cons(X4,nil) != W
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4)
| sP0_prd(X4,X,W) )
& ! [W,X,X4] :
( ( ? [X5] :
( ? [X6] :
( ! [X8] :
( ~ lt(X8,X4)
| ~ memberP(X6,X8)
| ~ ssItem(X8) )
& ! [X7] : sP1_prd(X7,X5,X4)
& app(app(X5,W),X6) = X
& cons(X4,nil) = W
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
| ~ sP0_prd(X4,X,W) ) ),
inference(miniscoping,[status(thm)],[f436]) ).
fof(f438,plain,
( ! [W,X,X4] :
( ! [X5] :
( ! [X6] :
( ( lt(sK60_skl(X6,X5,X4,X,W),X4)
& memberP(X6,sK60_skl(X6,X5,X4,X,W))
& ssItem(sK60_skl(X6,X5,X4,X,W)) )
| ~ sP1_prd(sK59_skl(X6,X5,X4,X,W),X5,X4)
| app(app(X5,W),X6) != X
| cons(X4,nil) != W
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4)
| sP0_prd(X4,X,W) )
& ! [W,X,X4] :
( ( ! [X8] :
( ~ lt(X8,X4)
| ~ memberP(sK58_skl(X4,X,W),X8)
| ~ ssItem(X8) )
& ! [X7] : sP1_prd(X7,sK57_skl(X4,X,W),X4)
& app(app(sK57_skl(X4,X,W),W),sK58_skl(X4,X,W)) = X
& cons(X4,nil) = W
& ssList(sK58_skl(X4,X,W))
& ssList(sK57_skl(X4,X,W))
& ssItem(X4) )
| ~ sP0_prd(X4,X,W) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK57_skl,sK58_skl,sK59_skl,sK60_skl]),skolemize(X5,sK57_skl(X4,X,W)),skolemize(X6,sK58_skl(X4,X,W)),skolemize(X7,sK59_skl(X6,X5,X4,X,W)),skolemize(X8,sK60_skl(X6,X5,X4,X,W))],[f437]) ).
fof(f439,plain,
! [X0,X1,X2] :
( ssItem(X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f438]) ).
fof(f442,plain,
! [X0,X1,X2] :
( cons(X0,nil) = X2
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f438]) ).
fof(f455,definition,
( sQ0_spl
<=> sP0_prd(sK56_skl,sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f456,plain,
( ~ sQ0_spl
| sP0_prd(sK56_skl,sK50_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f455]) ).
fof(f462,definition,
( sQ2_spl
<=> nil = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f463,plain,
( ~ sQ2_spl
| nil = sK49_skl ),
inference(component_clause,[status(thm)],[f462]) ).
fof(f465,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f433,f455,f462]) ).
fof(f468,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(f503,plain,
( ~ sQ0_spl
| sP0_prd(sK56_skl,sK48_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f423,f456]) ).
fof(f504,plain,
( ~ sQ0_spl
| sP0_prd(sK56_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f503]) ).
fof(f511,definition,
( sQ3_spl
<=> ssList(app(app(app(sK53_skl,cons(sK51_skl,nil)),sK54_skl),cons(sK52_skl,nil))) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f513,plain,
( sQ3_spl
| ~ ssList(app(app(app(sK53_skl,cons(sK51_skl,nil)),sK54_skl),cons(sK52_skl,nil))) ),
inference(component_clause,[status(thm)],[f511]) ).
fof(f514,definition,
( sQ4_spl
<=> ssList(sK55_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f516,plain,
( sQ4_spl
| ~ ssList(sK55_skl) ),
inference(component_clause,[status(thm)],[f514]) ).
fof(f521,plain,
( ~ lt(sK51_skl,sK52_skl)
| ~ ssItem(sK52_skl)
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f261,f431]) ).
fof(f522,definition,
( sQ6_spl
<=> ssItem(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f524,plain,
( sQ6_spl
| ~ ssItem(sK51_skl) ),
inference(component_clause,[status(thm)],[f522]) ).
fof(f525,definition,
( sQ7_spl
<=> ssItem(sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f527,plain,
( sQ7_spl
| ~ ssItem(sK52_skl) ),
inference(component_clause,[status(thm)],[f525]) ).
fof(f528,definition,
( sQ8_spl
<=> lt(sK51_skl,sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f530,plain,
( sQ8_spl
| ~ lt(sK51_skl,sK52_skl) ),
inference(component_clause,[status(thm)],[f528]) ).
fof(f531,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f521,f522,f525,f528]) ).
fof(f532,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f527,f426]) ).
fof(f533,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f532]) ).
fof(f534,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f524,f425]) ).
fof(f535,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f534]) ).
fof(f536,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(f537,definition,
! [X0] :
( sQ9_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,[sQ9_spl])],[split_symbol_definition]) ).
fof(f538,plain,
! [X0] :
( ~ sQ9_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)],[f537]) ).
fof(f540,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f536,f537,f511,f514]) ).
fof(f541,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f516,f429]) ).
fof(f542,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f541]) ).
fof(f571,plain,
( ~ sQ0_spl
| ssItem(sK56_skl) ),
inference(resolution,[status(thm)],[f504,f439]) ).
fof(f572,plain,
( ~ sQ0_spl
| cons(sK56_skl,nil) = sK47_skl ),
inference(resolution,[status(thm)],[f442,f504]) ).
fof(f575,definition,
( sQ13_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f577,plain,
( sQ13_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f575]) ).
fof(f578,definition,
( sQ14_spl
<=> ssItem(sK56_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f580,plain,
( sQ14_spl
| ~ ssItem(sK56_skl) ),
inference(component_clause,[status(thm)],[f578]) ).
fof(f585,plain,
( sQ3_spl
| ~ ssList(cons(sK52_skl,nil))
| ~ ssList(app(app(sK53_skl,cons(sK51_skl,nil)),sK54_skl)) ),
inference(resolution,[status(thm)],[f245,f513]) ).
fof(f587,definition,
( sQ16_spl
<=> ssList(app(app(sK53_skl,cons(sK51_skl,nil)),sK54_skl)) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f589,plain,
( sQ16_spl
| ~ ssList(app(app(sK53_skl,cons(sK51_skl,nil)),sK54_skl)) ),
inference(component_clause,[status(thm)],[f587]) ).
fof(f590,definition,
( sQ17_spl
<=> ssList(cons(sK52_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f592,plain,
( sQ17_spl
| ~ ssList(cons(sK52_skl,nil)) ),
inference(component_clause,[status(thm)],[f590]) ).
fof(f593,plain,
( sQ3_spl
| ~ sQ17_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f585,f587,f590,f511]) ).
fof(f597,plain,
( sQ17_spl
| ~ ssItem(sK52_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f222,f592]) ).
fof(f599,plain,
( sQ17_spl
| ~ sQ7_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f597,f575,f525,f590]) ).
fof(f601,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f577,f223]) ).
fof(f602,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f601]) ).
fof(f609,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ2_spl
| ~ memberP(app(app(app(sK53_skl,cons(sK51_skl,nil)),sK54_skl),cons(sK52_skl,nil)),X0)
| memberP(nil,X0)
| ~ ssItem(X0) ),
inference(backward_demodulation,[status(thm)],[f610,f538]) ).
fof(f610,plain,
( ~ sQ2_spl
| nil = sK47_skl ),
inference(forward_demodulation,[status(thm)],[f424,f463]) ).
fof(f614,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ2_spl
| ~ memberP(app(app(app(sK53_skl,cons(sK51_skl,nil)),sK54_skl),cons(sK52_skl,nil)),X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f609,f279]) ).
fof(f648,definition,
( sQ24_spl
<=> sK51_skl = sK52_skl ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f649,plain,
( ~ sQ24_spl
| sK51_skl = sK52_skl ),
inference(component_clause,[status(thm)],[f648]) ).
fof(f678,plain,
( sQ8_spl
| ~ sQ24_spl
| ~ lt(sK51_skl,sK51_skl) ),
inference(backward_demodulation,[status(thm)],[f649,f530]) ).
fof(f679,plain,
( ~ sQ24_spl
| lt(sK51_skl,sK51_skl) ),
inference(backward_demodulation,[status(thm)],[f649,f431]) ).
fof(f686,plain,
( ~ sQ24_spl
| sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f679,f678]) ).
fof(f687,plain,
( ~ sQ24_spl
| sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f686]) ).
fof(f715,plain,
( sQ16_spl
| ~ ssList(sK54_skl)
| ~ ssList(app(sK53_skl,cons(sK51_skl,nil))) ),
inference(resolution,[status(thm)],[f589,f245]) ).
fof(f716,definition,
( sQ29_spl
<=> ssList(app(sK53_skl,cons(sK51_skl,nil))) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f718,plain,
( sQ29_spl
| ~ ssList(app(sK53_skl,cons(sK51_skl,nil))) ),
inference(component_clause,[status(thm)],[f716]) ).
fof(f719,definition,
( sQ30_spl
<=> ssList(sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f721,plain,
( sQ30_spl
| ~ ssList(sK54_skl) ),
inference(component_clause,[status(thm)],[f719]) ).
fof(f722,plain,
( sQ16_spl
| ~ sQ30_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f715,f716,f719,f587]) ).
fof(f723,plain,
( sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f721,f428]) ).
fof(f724,plain,
sQ30_spl,
inference(contradiction_clause,[status(thm)],[f723]) ).
fof(f725,plain,
( sQ29_spl
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK53_skl) ),
inference(resolution,[status(thm)],[f718,f245]) ).
fof(f726,definition,
( sQ31_spl
<=> ssList(sK53_skl) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f728,plain,
( sQ31_spl
| ~ ssList(sK53_skl) ),
inference(component_clause,[status(thm)],[f726]) ).
fof(f729,definition,
( sQ32_spl
<=> ssList(cons(sK51_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f731,plain,
( sQ32_spl
| ~ ssList(cons(sK51_skl,nil)) ),
inference(component_clause,[status(thm)],[f729]) ).
fof(f732,plain,
( sQ29_spl
| ~ sQ32_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f725,f726,f729,f716]) ).
fof(f733,plain,
( sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f728,f427]) ).
fof(f734,plain,
sQ31_spl,
inference(contradiction_clause,[status(thm)],[f733]) ).
fof(f735,plain,
( sQ32_spl
| ~ ssItem(sK51_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f731,f222]) ).
fof(f736,plain,
( sQ32_spl
| ~ sQ6_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f735,f575,f522,f729]) ).
fof(f762,plain,
( ~ sQ9_spl
| ~ sQ2_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)))
| ~ ssItem(sK52_skl) ),
inference(resolution,[status(thm)],[f614,f468]) ).
fof(f765,plain,
( ~ sQ9_spl
| ~ sQ2_spl
| ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ3_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f762,f525,f511,f587,f575,f462,f537]) ).
fof(f775,plain,
( ~ sQ0_spl
| sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f571,f580]) ).
fof(f776,plain,
( ~ sQ0_spl
| sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f775]) ).
fof(f868,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)],[f572,f275]) ).
fof(f869,definition,
! [X0] :
( sQ48_spl
<=> ( memberP(nil,X0)
| X0 = sK56_skl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f870,plain,
! [X0] :
( ~ sQ48_spl
| memberP(nil,X0)
| X0 = sK56_skl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f869]) ).
fof(f872,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sQ48_spl ),
inference(split_clause,[status(thm)],[f868,f869,f578,f575,f455]) ).
fof(f873,plain,
! [X0] :
( ~ sQ48_spl
| X0 = sK56_skl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f870,f279]) ).
fof(f1050,plain,
( ~ sQ9_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)],[f538,f468]) ).
fof(f1052,plain,
! [X0] :
( ~ sQ9_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)],[f538,f271]) ).
fof(f1053,definition,
( sQ76_spl
<=> memberP(sK47_skl,sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f1054,plain,
( ~ sQ76_spl
| memberP(sK47_skl,sK52_skl) ),
inference(component_clause,[status(thm)],[f1053]) ).
fof(f1056,plain,
( ~ sQ9_spl
| ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ3_spl
| sQ76_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1050,f525,f1053,f511,f587,f575,f537]) ).
fof(f1061,definition,
! [X0] :
( sQ78_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,[sQ78_spl])],[split_symbol_definition]) ).
fof(f1062,plain,
! [X0] :
( ~ sQ78_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)],[f1061]) ).
fof(f1064,plain,
( ~ sQ9_spl
| ~ sQ17_spl
| ~ sQ16_spl
| sQ78_spl ),
inference(split_clause,[status(thm)],[f1052,f1061,f587,f590,f537]) ).
fof(f1066,plain,
! [X0] :
( ~ sQ78_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)],[f1062]) ).
fof(f1067,plain,
( ~ sQ48_spl
| ~ sQ76_spl
| sK52_skl = sK56_skl
| ~ ssItem(sK52_skl) ),
inference(resolution,[status(thm)],[f1054,f873]) ).
fof(f1068,definition,
( sQ79_spl
<=> sK52_skl = sK56_skl ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f1069,plain,
( ~ sQ79_spl
| sK52_skl = sK56_skl ),
inference(component_clause,[status(thm)],[f1068]) ).
fof(f1071,plain,
( ~ sQ48_spl
| ~ sQ76_spl
| sQ79_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1067,f525,f1068,f1053,f869]) ).
fof(f1072,plain,
! [X0] :
( ~ sQ48_spl
| ~ sQ79_spl
| X0 = sK52_skl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(backward_demodulation,[status(thm)],[f1069,f873]) ).
fof(f1292,plain,
! [X0] :
( ~ sQ78_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)],[f1066,f271]) ).
fof(f1297,definition,
! [X0] :
( sQ105_spl
<=> ( ~ memberP(app(sK53_skl,cons(sK51_skl,nil)),X0)
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ105_spl])],[split_symbol_definition]) ).
fof(f1298,plain,
! [X0] :
( ~ sQ105_spl
| ~ memberP(app(sK53_skl,cons(sK51_skl,nil)),X0)
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f1297]) ).
fof(f1300,plain,
( ~ sQ78_spl
| ~ sQ30_spl
| ~ sQ29_spl
| sQ105_spl ),
inference(split_clause,[status(thm)],[f1292,f1297,f716,f719,f1061]) ).
fof(f1302,plain,
! [X0] :
( ~ sQ105_spl
| ~ memberP(app(sK53_skl,cons(sK51_skl,nil)),X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1298]) ).
fof(f1303,plain,
( ~ sQ105_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)],[f1302,f468]) ).
fof(f1306,definition,
( sQ106_spl
<=> memberP(sK47_skl,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ106_spl])],[split_symbol_definition]) ).
fof(f1307,plain,
( ~ sQ106_spl
| memberP(sK47_skl,sK51_skl) ),
inference(component_clause,[status(thm)],[f1306]) ).
fof(f1309,plain,
( ~ sQ105_spl
| ~ sQ13_spl
| ~ sQ31_spl
| ~ sQ29_spl
| sQ106_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f1303,f522,f1306,f716,f726,f575,f1297]) ).
fof(f1320,plain,
( ~ sQ48_spl
| ~ sQ79_spl
| ~ sQ106_spl
| sK51_skl = sK52_skl
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f1307,f1072]) ).
fof(f1321,plain,
( ~ sQ48_spl
| ~ sQ79_spl
| ~ sQ106_spl
| sQ24_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f1320,f522,f648,f1306,f1068,f869]) ).
fof(f1322,plain,
$false,
inference(sat_refutation,[status(thm)],[f465,f531,f533,f535,f540,f542,f593,f599,f602,f687,f722,f724,f732,f734,f736,f765,f776,f872,f1056,f1064,f1071,f1300,f1309,f1321]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC299+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.46 % Computer : n005.cluster.edu
% 0.18/0.46 % Model : x86_64 x86_64
% 0.18/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.46 % Memory : 8046.5625MB
% 0.18/0.46 % OS : Linux 6.8.0-71-generic
% 0.18/0.46 % CPULimit : 300
% 0.18/0.47 % WCLimit : 300
% 0.18/0.47 % DateTime : Mon Sep 21 08:13:18 UTC 2026
% 0.18/0.47 % CPUTime :
% 0.18/0.52 % Drodi V4.1.1
% 0.23/1.01 % Refutation found
% 0.23/1.01 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.23/1.01 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.42/1.04 % Elapsed time: 0.544828 seconds
% 0.42/1.04 % CPU time: 3.789709 seconds
% 0.42/1.04 % Total memory used: 145.042 MB
% 0.42/1.04 % Net memory used: 142.881 MB
%------------------------------------------------------------------------------