%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC252+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 : n017.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 02:40:31 PM UTC 2026
% Result : Theorem 0.17s 0.55s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 21
% Syntax : Number of formulae : 98 ( 10 unt; 15 def)
% Number of atoms : 431 ( 72 equ)
% Maximal formula atoms : 21 ( 4 avg)
% Number of connectives : 566 ( 233 ~; 222 |; 73 &)
% ( 19 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 15 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 134 ( 110 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( segmentP(U,V)
<=> ? [W] :
( ? [X] :
( app(app(W,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(f55,axiom,
! [U] :
( ssList(U)
=> segmentP(U,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f93,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ( lt(U,V)
<=> ( leq(U,V)
& U != V ) ) ) ),
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] :
( ? [Z] :
( ? [X1] :
( ! [X2] :
( ssItem(X2)
=> ( leq(Y,X2)
| ~ lt(Y,X2)
| ~ memberP(X1,X2)
| ~ memberP(Z,X2) ) )
& app(app(Z,cons(Y,nil)),X1) = U
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) )
| nil = 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] :
( ? [Z] :
( ? [X1] :
( ! [X2] :
( ssItem(X2)
=> ( leq(Y,X2)
| ~ lt(Y,X2)
| ~ memberP(X1,X2)
| ~ memberP(Z,X2) ) )
& app(app(Z,cons(Y,nil)),X1) = U
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) )
| nil = U
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f131,plain,
! [U] :
( ! [V] :
( ( segmentP(U,V)
<=> ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f132,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(app(W,V),X) != U
| ~ ssList(X) )
| ~ ssList(W) )
| segmentP(U,V) )
& ( ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) )
| ~ segmentP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f131]) ).
fof(f133,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(app(W,V),X) != U
| ~ ssList(X) )
| ~ ssList(W) )
| segmentP(U,V) )
& ( ( app(app(sK7_skl(V,U),V),sK8_skl(V,U)) = U
& ssList(sK8_skl(V,U))
& ssList(sK7_skl(V,U)) )
| ~ segmentP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl]),skolemize(W,sK7_skl(V,U)),skolemize(X,sK8_skl(V,U))],[f132]) ).
fof(f134,plain,
! [X0,X1] :
( ssList(sK7_skl(X1,X0))
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f135,plain,
! [X0,X1] :
( ssList(sK8_skl(X1,X0))
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f136,plain,
! [X0,X1] :
( app(app(sK7_skl(X1,X0),X1),sK8_skl(X1,X0)) = X0
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
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(f318,plain,
! [U] :
( segmentP(U,U)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f55]) ).
fof(f319,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f318]) ).
fof(f406,plain,
! [U] :
( ! [V] :
( ( lt(U,V)
<=> ( leq(U,V)
& U != V ) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f93]) ).
fof(f407,plain,
! [U] :
( ! [V] :
( ( ( ~ leq(U,V)
| U = V
| lt(U,V) )
& ( ( leq(U,V)
& U != V )
| ~ lt(U,V) ) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(NNF_transformation,[status(thm)],[f406]) ).
fof(f409,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ lt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f407]) ).
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] :
( ~ leq(Y,X2)
& lt(Y,X2)
& memberP(X1,X2)
& memberP(Z,X2)
& ssItem(X2) )
| app(app(Z,cons(Y,nil)),X1) != U
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssItem(Y) )
& nil != U
& 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] :
( ~ leq(Y,X2)
& lt(Y,X2)
& memberP(X1,X2)
& memberP(Z,X2)
& ssItem(X2) )
| app(app(Z,cons(Y,nil)),X1) != U
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssItem(Y) )
& nil != U
& 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(sK52_skl,sK50_skl,sK49_skl) )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( ( ~ leq(Y,sK51_skl(X1,Z,Y))
& lt(Y,sK51_skl(X1,Z,Y))
& memberP(X1,sK51_skl(X1,Z,Y))
& memberP(Z,sK51_skl(X1,Z,Y))
& ssItem(sK51_skl(X1,Z,Y)) )
| app(app(Z,cons(Y,nil)),X1) != sK47_skl
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssItem(Y) )
& nil != sK47_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]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(X2,sK51_skl(X1,Z,Y)),skolemize(X3,sK52_skl)],[f417]) ).
fof(f421,plain,
ssList(sK49_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f424,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f425,plain,
nil != sK47_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f426,plain,
! [X0,X1,X2] :
( ssItem(sK51_skl(X2,X1,X0))
| app(app(X1,cons(X0,nil)),X2) != sK47_skl
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f429,plain,
! [X0,X1,X2] :
( lt(X0,sK51_skl(X2,X1,X0))
| app(app(X1,cons(X0,nil)),X2) != sK47_skl
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f430,plain,
! [X0,X1,X2] :
( ~ leq(X0,sK51_skl(X2,X1,X0))
| app(app(X1,cons(X0,nil)),X2) != sK47_skl
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f432,plain,
( nil = sK49_skl
| sP0_prd(sK52_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(sK52_skl,sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f440,plain,
( ~ sQ0_spl
| sP0_prd(sK52_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(f483,plain,
nil != sK49_skl,
inference(forward_demodulation,[status(thm)],[f424,f425]) ).
fof(f484,plain,
( ~ sQ0_spl
| ssItem(sK52_skl) ),
inference(resolution,[status(thm)],[f440,f435]) ).
fof(f488,plain,
( ~ sQ0_spl
| cons(sK52_skl,nil) = sK49_skl ),
inference(resolution,[status(thm)],[f436,f440]) ).
fof(f489,plain,
( ~ sQ0_spl
| ssList(sK49_skl)
| ~ ssItem(sK52_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f488,f222]) ).
fof(f491,definition,
( sQ3_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f493,plain,
( sQ3_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f491]) ).
fof(f494,definition,
( sQ4_spl
<=> ssItem(sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f496,plain,
( sQ4_spl
| ~ ssItem(sK52_skl) ),
inference(component_clause,[status(thm)],[f494]) ).
fof(f497,definition,
( sQ5_spl
<=> ssList(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f500,plain,
( ~ sQ0_spl
| sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f489,f491,f494,f497,f439]) ).
fof(f505,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f493,f223]) ).
fof(f506,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f505]) ).
fof(f507,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f447,f483]) ).
fof(f508,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f507]) ).
fof(f509,plain,
! [X0,X1,X2] :
( ssItem(sK51_skl(X2,X1,X0))
| app(app(X1,cons(X0,nil)),X2) != sK49_skl
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f424,f426]) ).
fof(f510,plain,
( ~ sQ0_spl
| sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f484,f496]) ).
fof(f511,plain,
( ~ sQ0_spl
| sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f510]) ).
fof(f515,plain,
! [X0,X1] :
( ~ sQ0_spl
| ssItem(sK51_skl(X1,X0,sK52_skl))
| app(app(X0,sK49_skl),X1) != sK49_skl
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(sK52_skl) ),
inference(paramodulation,[status(thm)],[f488,f509]) ).
fof(f518,definition,
! [X0,X1] :
( sQ7_spl
<=> ( ssItem(sK51_skl(X1,X0,sK52_skl))
| app(app(X0,sK49_skl),X1) != sK49_skl
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f519,plain,
! [X0,X1] :
( ~ sQ7_spl
| ssItem(sK51_skl(X1,X0,sK52_skl))
| app(app(X0,sK49_skl),X1) != sK49_skl
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f518]) ).
fof(f521,plain,
( ~ sQ0_spl
| sQ7_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f515,f494,f518,f439]) ).
fof(f808,plain,
! [X0,X1,X2] :
( lt(X0,sK51_skl(X2,X1,X0))
| app(app(X1,cons(X0,nil)),X2) != sK49_skl
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f424,f429]) ).
fof(f810,plain,
! [X0,X1] :
( ~ sQ0_spl
| lt(sK52_skl,sK51_skl(X1,X0,sK52_skl))
| app(app(X0,sK49_skl),X1) != sK49_skl
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(sK52_skl) ),
inference(paramodulation,[status(thm)],[f488,f808]) ).
fof(f815,definition,
! [X0,X1] :
( sQ52_spl
<=> ( lt(sK52_skl,sK51_skl(X1,X0,sK52_skl))
| app(app(X0,sK49_skl),X1) != sK49_skl
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f816,plain,
! [X0,X1] :
( ~ sQ52_spl
| lt(sK52_skl,sK51_skl(X1,X0,sK52_skl))
| app(app(X0,sK49_skl),X1) != sK49_skl
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f815]) ).
fof(f818,plain,
( ~ sQ0_spl
| sQ52_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f810,f494,f815,f439]) ).
fof(f928,plain,
! [X0,X1,X2] :
( ~ leq(X0,sK51_skl(X2,X1,X0))
| app(app(X1,cons(X0,nil)),X2) != sK49_skl
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f424,f430]) ).
fof(f930,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ leq(sK52_skl,sK51_skl(X1,X0,sK52_skl))
| app(app(X0,sK49_skl),X1) != sK49_skl
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(sK52_skl) ),
inference(paramodulation,[status(thm)],[f488,f928]) ).
fof(f935,definition,
! [X0,X1] :
( sQ68_spl
<=> ( ~ leq(sK52_skl,sK51_skl(X1,X0,sK52_skl))
| app(app(X0,sK49_skl),X1) != sK49_skl
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f936,plain,
! [X0,X1] :
( ~ sQ68_spl
| ~ leq(sK52_skl,sK51_skl(X1,X0,sK52_skl))
| app(app(X0,sK49_skl),X1) != sK49_skl
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f935]) ).
fof(f938,plain,
( ~ sQ0_spl
| sQ68_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f930,f494,f935,f439]) ).
fof(f1042,plain,
( ~ sQ68_spl
| ~ leq(sK52_skl,sK51_skl(sK8_skl(sK49_skl,sK49_skl),sK7_skl(sK49_skl,sK49_skl),sK52_skl))
| ~ ssList(sK8_skl(sK49_skl,sK49_skl))
| ~ ssList(sK7_skl(sK49_skl,sK49_skl))
| ~ segmentP(sK49_skl,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f136,f936]) ).
fof(f1043,plain,
( ~ sQ52_spl
| lt(sK52_skl,sK51_skl(sK8_skl(sK49_skl,sK49_skl),sK7_skl(sK49_skl,sK49_skl),sK52_skl))
| ~ ssList(sK8_skl(sK49_skl,sK49_skl))
| ~ ssList(sK7_skl(sK49_skl,sK49_skl))
| ~ segmentP(sK49_skl,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f136,f816]) ).
fof(f1046,plain,
( ~ sQ7_spl
| ssItem(sK51_skl(sK8_skl(sK49_skl,sK49_skl),sK7_skl(sK49_skl,sK49_skl),sK52_skl))
| ~ ssList(sK8_skl(sK49_skl,sK49_skl))
| ~ ssList(sK7_skl(sK49_skl,sK49_skl))
| ~ segmentP(sK49_skl,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f136,f519]) ).
fof(f1054,definition,
( sQ80_spl
<=> segmentP(sK49_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f1056,plain,
( sQ80_spl
| ~ segmentP(sK49_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f1054]) ).
fof(f1057,definition,
( sQ81_spl
<=> ssList(sK7_skl(sK49_skl,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f1059,plain,
( sQ81_spl
| ~ ssList(sK7_skl(sK49_skl,sK49_skl)) ),
inference(component_clause,[status(thm)],[f1057]) ).
fof(f1060,definition,
( sQ82_spl
<=> ssList(sK8_skl(sK49_skl,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f1062,plain,
( sQ82_spl
| ~ ssList(sK8_skl(sK49_skl,sK49_skl)) ),
inference(component_clause,[status(thm)],[f1060]) ).
fof(f1063,definition,
( sQ83_spl
<=> leq(sK52_skl,sK51_skl(sK8_skl(sK49_skl,sK49_skl),sK7_skl(sK49_skl,sK49_skl),sK52_skl)) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f1066,plain,
( ~ sQ68_spl
| ~ sQ83_spl
| ~ sQ82_spl
| ~ sQ81_spl
| ~ sQ80_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1042,f497,f1054,f1057,f1060,f1063,f935]) ).
fof(f1067,definition,
( sQ84_spl
<=> lt(sK52_skl,sK51_skl(sK8_skl(sK49_skl,sK49_skl),sK7_skl(sK49_skl,sK49_skl),sK52_skl)) ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f1068,plain,
( ~ sQ84_spl
| lt(sK52_skl,sK51_skl(sK8_skl(sK49_skl,sK49_skl),sK7_skl(sK49_skl,sK49_skl),sK52_skl)) ),
inference(component_clause,[status(thm)],[f1067]) ).
fof(f1070,plain,
( ~ sQ52_spl
| sQ84_spl
| ~ sQ82_spl
| ~ sQ81_spl
| ~ sQ80_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1043,f497,f1054,f1057,f1060,f1067,f815]) ).
fof(f1079,definition,
( sQ87_spl
<=> ssItem(sK51_skl(sK8_skl(sK49_skl,sK49_skl),sK7_skl(sK49_skl,sK49_skl),sK52_skl)) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f1082,plain,
( ~ sQ7_spl
| sQ87_spl
| ~ sQ82_spl
| ~ sQ81_spl
| ~ sQ80_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1046,f497,f1054,f1057,f1060,f1079,f518]) ).
fof(f1131,plain,
( sQ82_spl
| ~ segmentP(sK49_skl,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f1062,f135]) ).
fof(f1132,plain,
( sQ82_spl
| ~ sQ80_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1131,f497,f1054,f1060]) ).
fof(f1133,plain,
( sQ80_spl
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f1056,f319]) ).
fof(f1134,plain,
( sQ80_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1133,f421]) ).
fof(f1135,plain,
sQ80_spl,
inference(contradiction_clause,[status(thm)],[f1134]) ).
fof(f1136,plain,
( sQ81_spl
| ~ segmentP(sK49_skl,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f1059,f134]) ).
fof(f1137,plain,
( sQ81_spl
| ~ sQ80_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1136,f497,f1054,f1057]) ).
fof(f1165,plain,
( ~ sQ84_spl
| leq(sK52_skl,sK51_skl(sK8_skl(sK49_skl,sK49_skl),sK7_skl(sK49_skl,sK49_skl),sK52_skl))
| ~ ssItem(sK51_skl(sK8_skl(sK49_skl,sK49_skl),sK7_skl(sK49_skl,sK49_skl),sK52_skl))
| ~ ssItem(sK52_skl) ),
inference(resolution,[status(thm)],[f1068,f409]) ).
fof(f1171,plain,
( ~ sQ84_spl
| sQ83_spl
| ~ sQ87_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1165,f494,f1079,f1063,f1067]) ).
fof(f1176,plain,
$false,
inference(sat_refutation,[status(thm)],[f449,f500,f506,f508,f511,f521,f818,f938,f1066,f1070,f1082,f1132,f1135,f1137,f1171]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC252+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.45 % Computer : n017.cluster.edu
% 0.17/0.45 % Model : x86_64 x86_64
% 0.17/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.45 % Memory : 8046.5625MB
% 0.17/0.45 % OS : Linux 6.8.0-71-generic
% 0.17/0.45 % CPULimit : 300
% 0.17/0.45 % WCLimit : 300
% 0.17/0.45 % DateTime : Mon Sep 21 08:04:13 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.50 % Drodi V4.1.1
% 0.17/0.55 % Refutation found
% 0.17/0.55 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.26/0.61 % Elapsed time: 0.145737 seconds
% 0.26/0.61 % CPU time: 0.370205 seconds
% 0.26/0.61 % Total memory used: 51.293 MB
% 0.26/0.61 % Net memory used: 51.007 MB
%------------------------------------------------------------------------------