%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC239+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 : n006.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 02:40:29 PM UTC 2026
% Result : Theorem 7.51s 1.39s
% Output : CNFRefutation 7.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 21
% Syntax : Number of formulae : 97 ( 8 unt; 15 def)
% Number of atoms : 468 ( 82 equ)
% Maximal formula atoms : 25 ( 4 avg)
% Number of connectives : 618 ( 247 ~; 237 |; 96 &)
% ( 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 : 12 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 140 ( 112 !; 28 ?)
% 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)
=> ( ? [X4] :
( leq(X3,X4)
& memberP(X,X4)
& X3 != X4
& ssItem(X4) )
| ~ 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)
=> ( ? [X4] :
( leq(X3,X4)
& memberP(X,X4)
& X3 != X4
& ssItem(X4) )
| ~ 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] :
( ! [X4] :
( ~ leq(X3,X4)
| ~ memberP(X,X4)
| X3 = X4
| ~ ssItem(X4) )
& 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)
<=> ( ! [X4] :
( ~ leq(X3,X4)
| ~ 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] :
( ~ 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(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,
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] :
( ( ? [X4] :
( leq(X3,X4)
& memberP(X,X4)
& X3 != X4
& ssItem(X4) )
| ~ memberP(X,X3)
| cons(X3,nil) != W
| ~ ssItem(X3)
| sP0_prd(X3,X,W) )
& ( ( ! [X4] :
( ~ leq(X3,X4)
| ~ 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(X3,X4)
& 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(X3,X4)
| ~ 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(X3,sK53_skl(X3,X,W))
& memberP(X,sK53_skl(X3,X,W))
& X3 != sK53_skl(X3,X,W)
& ssItem(sK53_skl(X3,X,W)) )
| ~ memberP(X,X3)
| cons(X3,nil) != W
| ~ ssItem(X3)
| sP0_prd(X3,X,W) )
& ! [W,X,X3] :
( ( ! [X4] :
( ~ leq(X3,X4)
| ~ 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,[sK53_skl]),skolemize(X4,sK53_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(sK52_skl,sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f445,plain,
( ~ sQ0_spl
| sP0_prd(sK52_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(f493,plain,
( ~ sQ0_spl
| sP0_prd(sK52_skl,sK48_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f423,f445]) ).
fof(f494,plain,
( ~ sQ0_spl
| sP0_prd(sK52_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f493]) ).
fof(f528,definition,
( sQ5_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f530,plain,
( sQ5_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f528]) ).
fof(f544,plain,
( ~ sQ0_spl
| cons(sK52_skl,nil) = sK47_skl ),
inference(resolution,[status(thm)],[f494,f437]) ).
fof(f546,plain,
( ~ sQ0_spl
| ssItem(sK52_skl) ),
inference(resolution,[status(thm)],[f494,f436]) ).
fof(f553,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ leq(sK52_skl,sK51_skl(X1,X0,sK52_skl))
| app(app(X0,sK47_skl),X1) != sK47_skl
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(sK52_skl) ),
inference(paramodulation,[status(thm)],[f544,f430]) ).
fof(f559,plain,
! [X0,X1] :
( ~ sQ0_spl
| lt(sK52_skl,sK51_skl(X1,X0,sK52_skl))
| app(app(X0,sK47_skl),X1) != sK47_skl
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(sK52_skl) ),
inference(paramodulation,[status(thm)],[f544,f429]) ).
fof(f560,plain,
! [X0,X1] :
( ~ sQ0_spl
| ssItem(sK51_skl(X1,X0,sK52_skl))
| app(app(X0,sK47_skl),X1) != sK47_skl
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(sK52_skl) ),
inference(paramodulation,[status(thm)],[f544,f426]) ).
fof(f565,plain,
( ~ sQ0_spl
| ssList(sK47_skl)
| ~ ssItem(sK52_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f544,f222]) ).
fof(f571,definition,
( sQ9_spl
<=> ssItem(sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f573,plain,
( sQ9_spl
| ~ ssItem(sK52_skl) ),
inference(component_clause,[status(thm)],[f571]) ).
fof(f575,definition,
! [X0,X1] :
( sQ10_spl
<=> ( ~ leq(sK52_skl,sK51_skl(X1,X0,sK52_skl))
| app(app(X0,sK47_skl),X1) != sK47_skl
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f576,plain,
! [X0,X1] :
( ~ sQ10_spl
| ~ leq(sK52_skl,sK51_skl(X1,X0,sK52_skl))
| app(app(X0,sK47_skl),X1) != sK47_skl
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f575]) ).
fof(f578,plain,
( ~ sQ0_spl
| sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f553,f571,f575,f444]) ).
fof(f599,definition,
! [X0,X1] :
( sQ16_spl
<=> ( lt(sK52_skl,sK51_skl(X1,X0,sK52_skl))
| app(app(X0,sK47_skl),X1) != sK47_skl
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f600,plain,
! [X0,X1] :
( ~ sQ16_spl
| lt(sK52_skl,sK51_skl(X1,X0,sK52_skl))
| app(app(X0,sK47_skl),X1) != sK47_skl
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f599]) ).
fof(f602,plain,
( ~ sQ0_spl
| sQ16_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f559,f571,f599,f444]) ).
fof(f603,definition,
! [X0,X1] :
( sQ17_spl
<=> ( ssItem(sK51_skl(X1,X0,sK52_skl))
| app(app(X0,sK47_skl),X1) != sK47_skl
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f604,plain,
! [X0,X1] :
( ~ sQ17_spl
| ssItem(sK51_skl(X1,X0,sK52_skl))
| app(app(X0,sK47_skl),X1) != sK47_skl
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f603]) ).
fof(f606,plain,
( ~ sQ0_spl
| sQ17_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f560,f571,f603,f444]) ).
fof(f623,definition,
( sQ22_spl
<=> ssList(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f626,plain,
( ~ sQ0_spl
| sQ22_spl
| ~ sQ9_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f565,f528,f571,f623,f444]) ).
fof(f632,plain,
( sQ9_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f573,f546]) ).
fof(f633,plain,
( sQ9_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f632]) ).
fof(f634,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f530,f223]) ).
fof(f635,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f634]) ).
fof(f777,plain,
( ~ sQ2_spl
| nil = sK47_skl ),
inference(forward_demodulation,[status(thm)],[f424,f452]) ).
fof(f778,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f777,f425]) ).
fof(f779,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f778]) ).
fof(f1841,plain,
( ~ sQ17_spl
| ~ segmentP(sK47_skl,sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl)
| ssItem(sK51_skl(sK8_skl(sK47_skl,sK47_skl),sK7_skl(sK47_skl,sK47_skl),sK52_skl))
| ~ ssList(sK8_skl(sK47_skl,sK47_skl))
| ~ ssList(sK7_skl(sK47_skl,sK47_skl)) ),
inference(resolution,[status(thm)],[f604,f136]) ).
fof(f1843,definition,
( sQ172_spl
<=> ssList(sK7_skl(sK47_skl,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ172_spl])],[split_symbol_definition]) ).
fof(f1845,plain,
( sQ172_spl
| ~ ssList(sK7_skl(sK47_skl,sK47_skl)) ),
inference(component_clause,[status(thm)],[f1843]) ).
fof(f1846,definition,
( sQ173_spl
<=> ssList(sK8_skl(sK47_skl,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ173_spl])],[split_symbol_definition]) ).
fof(f1848,plain,
( sQ173_spl
| ~ ssList(sK8_skl(sK47_skl,sK47_skl)) ),
inference(component_clause,[status(thm)],[f1846]) ).
fof(f1849,definition,
( sQ174_spl
<=> ssItem(sK51_skl(sK8_skl(sK47_skl,sK47_skl),sK7_skl(sK47_skl,sK47_skl),sK52_skl)) ),
introduced(definition,[new_symbols(definition,[sQ174_spl])],[split_symbol_definition]) ).
fof(f1852,definition,
( sQ175_spl
<=> segmentP(sK47_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ175_spl])],[split_symbol_definition]) ).
fof(f1854,plain,
( sQ175_spl
| ~ segmentP(sK47_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f1852]) ).
fof(f1855,plain,
( ~ sQ17_spl
| ~ sQ175_spl
| ~ sQ22_spl
| sQ174_spl
| ~ sQ173_spl
| ~ sQ172_spl ),
inference(split_clause,[status(thm)],[f1841,f1843,f1846,f1849,f623,f1852,f603]) ).
fof(f1860,plain,
( sQ175_spl
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f1854,f319]) ).
fof(f1861,plain,
( sQ175_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f1860,f623,f1852]) ).
fof(f1883,plain,
( sQ173_spl
| ~ segmentP(sK47_skl,sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f1848,f135]) ).
fof(f1884,plain,
( sQ173_spl
| ~ sQ175_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f1883,f623,f1852,f1846]) ).
fof(f1885,plain,
( sQ172_spl
| ~ segmentP(sK47_skl,sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f1845,f134]) ).
fof(f1886,plain,
( sQ172_spl
| ~ sQ175_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f1885,f623,f1852,f1843]) ).
fof(f2236,plain,
( ~ sQ10_spl
| ~ segmentP(sK47_skl,sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl)
| ~ leq(sK52_skl,sK51_skl(sK8_skl(sK47_skl,sK47_skl),sK7_skl(sK47_skl,sK47_skl),sK52_skl))
| ~ ssList(sK8_skl(sK47_skl,sK47_skl))
| ~ ssList(sK7_skl(sK47_skl,sK47_skl)) ),
inference(resolution,[status(thm)],[f576,f136]) ).
fof(f2238,definition,
( sQ205_spl
<=> leq(sK52_skl,sK51_skl(sK8_skl(sK47_skl,sK47_skl),sK7_skl(sK47_skl,sK47_skl),sK52_skl)) ),
introduced(definition,[new_symbols(definition,[sQ205_spl])],[split_symbol_definition]) ).
fof(f2241,plain,
( ~ sQ10_spl
| ~ sQ175_spl
| ~ sQ22_spl
| ~ sQ205_spl
| ~ sQ173_spl
| ~ sQ172_spl ),
inference(split_clause,[status(thm)],[f2236,f1843,f1846,f2238,f623,f1852,f575]) ).
fof(f2246,plain,
( ~ sQ16_spl
| ~ segmentP(sK47_skl,sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl)
| lt(sK52_skl,sK51_skl(sK8_skl(sK47_skl,sK47_skl),sK7_skl(sK47_skl,sK47_skl),sK52_skl))
| ~ ssList(sK8_skl(sK47_skl,sK47_skl))
| ~ ssList(sK7_skl(sK47_skl,sK47_skl)) ),
inference(resolution,[status(thm)],[f600,f136]) ).
fof(f2248,definition,
( sQ207_spl
<=> lt(sK52_skl,sK51_skl(sK8_skl(sK47_skl,sK47_skl),sK7_skl(sK47_skl,sK47_skl),sK52_skl)) ),
introduced(definition,[new_symbols(definition,[sQ207_spl])],[split_symbol_definition]) ).
fof(f2249,plain,
( ~ sQ207_spl
| lt(sK52_skl,sK51_skl(sK8_skl(sK47_skl,sK47_skl),sK7_skl(sK47_skl,sK47_skl),sK52_skl)) ),
inference(component_clause,[status(thm)],[f2248]) ).
fof(f2251,plain,
( ~ sQ16_spl
| ~ sQ175_spl
| ~ sQ22_spl
| sQ207_spl
| ~ sQ173_spl
| ~ sQ172_spl ),
inference(split_clause,[status(thm)],[f2246,f1843,f1846,f2248,f623,f1852,f599]) ).
fof(f2259,plain,
( ~ sQ207_spl
| leq(sK52_skl,sK51_skl(sK8_skl(sK47_skl,sK47_skl),sK7_skl(sK47_skl,sK47_skl),sK52_skl))
| ~ ssItem(sK51_skl(sK8_skl(sK47_skl,sK47_skl),sK7_skl(sK47_skl,sK47_skl),sK52_skl))
| ~ ssItem(sK52_skl) ),
inference(resolution,[status(thm)],[f2249,f409]) ).
fof(f2273,plain,
( ~ sQ207_spl
| sQ205_spl
| ~ sQ174_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f2259,f571,f1849,f2238,f2248]) ).
fof(f2278,plain,
$false,
inference(sat_refutation,[status(thm)],[f454,f578,f602,f606,f626,f633,f635,f779,f1855,f1861,f1884,f1886,f2241,f2251,f2273]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC239+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n006.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 08:07:27 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 7.51/1.39 % Refutation found
% 7.51/1.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 7.51/1.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.51/1.41 % Elapsed time: 1.043950 seconds
% 7.51/1.41 % CPU time: 7.918523 seconds
% 7.51/1.41 % Total memory used: 184.102 MB
% 7.51/1.41 % Net memory used: 177.470 MB
%------------------------------------------------------------------------------