%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC270+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 : n011.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 02:40:35 PM UTC 2026
% Result : Theorem 13.71s 2.29s
% Output : CNFRefutation 13.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 27
% Syntax : Number of formulae : 130 ( 25 unt; 18 def)
% Number of atoms : 429 ( 56 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 500 ( 201 ~; 187 |; 60 &)
% ( 24 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 27 ( 25 usr; 19 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 7 con; 0-2 aty)
% Number of variables : 125 ( 105 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
? [U] :
( ? [V] :
( U != V
& ssItem(V) )
& ssItem(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [U] :
( ssList(U)
=> ( totalorderedP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> leq(V,W) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [U] :
( ssList(U)
=> ( strictorderedP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> lt(V,W) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> cons(V,U) != U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> nil != cons(V,U) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ssList(app(U,V)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(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] :
( totalorderedP(U)
| ~ strictorderedP(W)
| ~ segmentP(X,W)
| U != W
| V != X
| ~ ssList(X) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( totalorderedP(U)
| ~ strictorderedP(W)
| ~ segmentP(X,W)
| U != W
| V != X
| ~ ssList(X) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f102,plain,
( sK0_skl != sK1_skl
& ssItem(sK1_skl)
& ssItem(sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(U,sK0_skl),skolemize(V,sK1_skl)],[f2]) ).
fof(f103,plain,
ssItem(sK0_skl),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f104,plain,
ssItem(sK1_skl),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f174,plain,
! [U] :
( ( totalorderedP(U)
<=> ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( leq(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) ) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f175,plain,
! [U] :
( ( ( ? [V] :
( ? [W] :
( ? [X] :
( ? [Y] :
( ? [Z] :
( ~ leq(V,W)
& app(app(X,cons(V,Y)),cons(W,Z)) = U
& ssList(Z) )
& ssList(Y) )
& ssList(X) )
& ssItem(W) )
& ssItem(V) )
| totalorderedP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( leq(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ totalorderedP(U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f174]) ).
fof(f176,plain,
! [U] :
( ( ( ( ~ leq(sK24_skl(U),sK25_skl(U))
& app(app(sK26_skl(U),cons(sK24_skl(U),sK27_skl(U))),cons(sK25_skl(U),sK28_skl(U))) = U
& ssList(sK28_skl(U))
& ssList(sK27_skl(U))
& ssList(sK26_skl(U))
& ssItem(sK25_skl(U))
& ssItem(sK24_skl(U)) )
| totalorderedP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( leq(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ totalorderedP(U) ) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24_skl,sK25_skl,sK26_skl,sK27_skl,sK28_skl]),skolemize(V,sK24_skl(U)),skolemize(W,sK25_skl(U)),skolemize(X,sK26_skl(U)),skolemize(Y,sK27_skl(U)),skolemize(Z,sK28_skl(U))],[f175]) ).
fof(f178,plain,
! [X0] :
( ssItem(sK24_skl(X0))
| totalorderedP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f176]) ).
fof(f179,plain,
! [X0] :
( ssItem(sK25_skl(X0))
| totalorderedP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f176]) ).
fof(f180,plain,
! [X0] :
( ssList(sK26_skl(X0))
| totalorderedP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f176]) ).
fof(f181,plain,
! [X0] :
( ssList(sK27_skl(X0))
| totalorderedP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f176]) ).
fof(f182,plain,
! [X0] :
( ssList(sK28_skl(X0))
| totalorderedP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f176]) ).
fof(f183,plain,
! [X0] :
( app(app(sK26_skl(X0),cons(sK24_skl(X0),sK27_skl(X0))),cons(sK25_skl(X0),sK28_skl(X0))) = X0
| totalorderedP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f176]) ).
fof(f184,plain,
! [X0] :
( ~ leq(sK24_skl(X0),sK25_skl(X0))
| totalorderedP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f176]) ).
fof(f185,plain,
! [U] :
( ( strictorderedP(U)
<=> ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( lt(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) ) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f186,plain,
! [U] :
( ( ( ? [V] :
( ? [W] :
( ? [X] :
( ? [Y] :
( ? [Z] :
( ~ lt(V,W)
& app(app(X,cons(V,Y)),cons(W,Z)) = U
& ssList(Z) )
& ssList(Y) )
& ssList(X) )
& ssItem(W) )
& ssItem(V) )
| strictorderedP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( lt(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ strictorderedP(U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f185]) ).
fof(f187,plain,
! [U] :
( ( ( ( ~ lt(sK29_skl(U),sK30_skl(U))
& app(app(sK31_skl(U),cons(sK29_skl(U),sK32_skl(U))),cons(sK30_skl(U),sK33_skl(U))) = U
& ssList(sK33_skl(U))
& ssList(sK32_skl(U))
& ssList(sK31_skl(U))
& ssItem(sK30_skl(U))
& ssItem(sK29_skl(U)) )
| strictorderedP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( lt(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ strictorderedP(U) ) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29_skl,sK30_skl,sK31_skl,sK32_skl,sK33_skl]),skolemize(V,sK29_skl(U)),skolemize(W,sK30_skl(U)),skolemize(X,sK31_skl(U)),skolemize(Y,sK32_skl(U)),skolemize(Z,sK33_skl(U))],[f186]) ).
fof(f188,plain,
! [X0,X1,X2,X3,X4,X5] :
( lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ strictorderedP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f187]) ).
fof(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f224,plain,
! [U] :
( ! [V] :
( cons(V,U) != U
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f225,plain,
! [X0,X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f224]) ).
fof(f234,plain,
! [U] :
( ! [V] :
( nil != cons(V,U)
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f235,plain,
! [X0,X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f234]) ).
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(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] :
( ~ totalorderedP(U)
& strictorderedP(W)
& segmentP(X,W)
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,plain,
? [U] :
( ? [V] :
( ? [W] :
( ~ totalorderedP(U)
& strictorderedP(W)
& ? [X] :
( segmentP(X,W)
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(miniscoping,[status(thm)],[f415]) ).
fof(f417,plain,
( ~ totalorderedP(sK47_skl)
& strictorderedP(sK49_skl)
& segmentP(sK50_skl,sK49_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]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl)],[f416]) ).
fof(f420,plain,
ssList(sK49_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f421,plain,
ssList(sK50_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f423,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f425,plain,
strictorderedP(sK49_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f426,plain,
~ totalorderedP(sK47_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f438,plain,
! [X0,X1,X2,X3,X4] :
( lt(X1,X3)
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ strictorderedP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4))) ),
inference(destructive_equality_resolution,[status(thm)],[f188]) ).
fof(f459,plain,
~ totalorderedP(sK49_skl),
inference(forward_demodulation,[status(thm)],[f423,f426]) ).
fof(f477,definition,
( sQ2_spl
<=> ssList(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f479,plain,
( sQ2_spl
| ~ ssList(sK49_skl) ),
inference(component_clause,[status(thm)],[f477]) ).
fof(f540,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f479,f420]) ).
fof(f541,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f540]) ).
fof(f910,definition,
( sQ68_spl
<=> ssList(app(sK50_skl,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f912,plain,
( sQ68_spl
| ~ ssList(app(sK50_skl,sK49_skl)) ),
inference(component_clause,[status(thm)],[f910]) ).
fof(f2500,plain,
( ssList(sK26_skl(sK49_skl))
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f180,f459]) ).
fof(f2501,definition,
( sQ284_spl
<=> ssList(sK26_skl(sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ284_spl])],[split_symbol_definition]) ).
fof(f2504,plain,
( sQ284_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f2500,f477,f2501]) ).
fof(f3045,plain,
( ssList(sK27_skl(sK49_skl))
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f181,f459]) ).
fof(f3046,definition,
( sQ347_spl
<=> ssList(sK27_skl(sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ347_spl])],[split_symbol_definition]) ).
fof(f3049,plain,
( sQ347_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f3045,f477,f3046]) ).
fof(f3200,plain,
( ssList(sK28_skl(sK49_skl))
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f182,f459]) ).
fof(f3201,definition,
( sQ366_spl
<=> ssList(sK28_skl(sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ366_spl])],[split_symbol_definition]) ).
fof(f3204,plain,
( sQ366_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f3200,f477,f3201]) ).
fof(f3766,plain,
( app(app(sK26_skl(sK49_skl),cons(sK24_skl(sK49_skl),sK27_skl(sK49_skl))),cons(sK25_skl(sK49_skl),sK28_skl(sK49_skl))) = sK49_skl
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f183,f459]) ).
fof(f3767,definition,
( sQ434_spl
<=> app(app(sK26_skl(sK49_skl),cons(sK24_skl(sK49_skl),sK27_skl(sK49_skl))),cons(sK25_skl(sK49_skl),sK28_skl(sK49_skl))) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ434_spl])],[split_symbol_definition]) ).
fof(f3768,plain,
( ~ sQ434_spl
| app(app(sK26_skl(sK49_skl),cons(sK24_skl(sK49_skl),sK27_skl(sK49_skl))),cons(sK25_skl(sK49_skl),sK28_skl(sK49_skl))) = sK49_skl ),
inference(component_clause,[status(thm)],[f3767]) ).
fof(f3770,plain,
( sQ434_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f3766,f477,f3767]) ).
fof(f3905,plain,
( ~ sQ434_spl
| lt(sK24_skl(sK49_skl),sK25_skl(sK49_skl))
| ~ ssList(sK28_skl(sK49_skl))
| ~ ssList(sK27_skl(sK49_skl))
| ~ ssList(sK26_skl(sK49_skl))
| ~ ssItem(sK25_skl(sK49_skl))
| ~ ssItem(sK24_skl(sK49_skl))
| ~ strictorderedP(app(app(sK26_skl(sK49_skl),cons(sK24_skl(sK49_skl),sK27_skl(sK49_skl))),cons(sK25_skl(sK49_skl),sK28_skl(sK49_skl))))
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f3768,f438]) ).
fof(f3923,definition,
( sQ451_spl
<=> ssItem(sK24_skl(sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ451_spl])],[split_symbol_definition]) ).
fof(f3925,plain,
( sQ451_spl
| ~ ssItem(sK24_skl(sK49_skl)) ),
inference(component_clause,[status(thm)],[f3923]) ).
fof(f3926,definition,
( sQ452_spl
<=> ssItem(sK25_skl(sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ452_spl])],[split_symbol_definition]) ).
fof(f3928,plain,
( sQ452_spl
| ~ ssItem(sK25_skl(sK49_skl)) ),
inference(component_clause,[status(thm)],[f3926]) ).
fof(f3929,definition,
( sQ453_spl
<=> lt(sK24_skl(sK49_skl),sK25_skl(sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ453_spl])],[split_symbol_definition]) ).
fof(f3930,plain,
( ~ sQ453_spl
| lt(sK24_skl(sK49_skl),sK25_skl(sK49_skl)) ),
inference(component_clause,[status(thm)],[f3929]) ).
fof(f3939,definition,
( sQ456_spl
<=> leq(sK24_skl(sK49_skl),sK25_skl(sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ456_spl])],[split_symbol_definition]) ).
fof(f3940,plain,
( ~ sQ456_spl
| leq(sK24_skl(sK49_skl),sK25_skl(sK49_skl)) ),
inference(component_clause,[status(thm)],[f3939]) ).
fof(f3954,definition,
( sQ460_spl
<=> strictorderedP(app(app(sK26_skl(sK49_skl),cons(sK24_skl(sK49_skl),sK27_skl(sK49_skl))),cons(sK25_skl(sK49_skl),sK28_skl(sK49_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ460_spl])],[split_symbol_definition]) ).
fof(f3956,plain,
( sQ460_spl
| ~ strictorderedP(app(app(sK26_skl(sK49_skl),cons(sK24_skl(sK49_skl),sK27_skl(sK49_skl))),cons(sK25_skl(sK49_skl),sK28_skl(sK49_skl)))) ),
inference(component_clause,[status(thm)],[f3954]) ).
fof(f3957,plain,
( ~ sQ434_spl
| sQ453_spl
| ~ sQ366_spl
| ~ sQ347_spl
| ~ sQ284_spl
| ~ sQ452_spl
| ~ sQ451_spl
| ~ sQ460_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f3905,f477,f3954,f3923,f3926,f2501,f3046,f3201,f3929,f3767]) ).
fof(f4023,plain,
( sQ452_spl
| totalorderedP(sK49_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f3928,f179]) ).
fof(f4024,definition,
( sQ478_spl
<=> totalorderedP(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ478_spl])],[split_symbol_definition]) ).
fof(f4025,plain,
( ~ sQ478_spl
| totalorderedP(sK49_skl) ),
inference(component_clause,[status(thm)],[f4024]) ).
fof(f4027,plain,
( sQ452_spl
| sQ478_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f4023,f477,f4024,f3926]) ).
fof(f4028,plain,
( sQ451_spl
| totalorderedP(sK49_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f3925,f178]) ).
fof(f4029,plain,
( sQ451_spl
| sQ478_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f4028,f477,f4024,f3923]) ).
fof(f4030,plain,
( ~ sQ478_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4025,f459]) ).
fof(f4031,plain,
~ sQ478_spl,
inference(contradiction_clause,[status(thm)],[f4030]) ).
fof(f4047,plain,
( sQ460_spl
| ~ sQ434_spl
| ~ strictorderedP(sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f3768,f3956]) ).
fof(f4048,plain,
( sQ460_spl
| ~ sQ434_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4047,f425]) ).
fof(f4049,plain,
( sQ460_spl
| ~ sQ434_spl ),
inference(contradiction_clause,[status(thm)],[f4048]) ).
fof(f4805,plain,
! [X0] :
( cons(sK0_skl,X0) != X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f225,f103]) ).
fof(f4806,plain,
! [X0] :
( cons(sK1_skl,X0) != X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f225,f104]) ).
fof(f4870,plain,
cons(sK0_skl,nil) != nil,
inference(resolution,[status(thm)],[f4805,f223]) ).
fof(f4935,plain,
cons(sK1_skl,nil) != nil,
inference(resolution,[status(thm)],[f4806,f223]) ).
fof(f5278,definition,
( sQ592_spl
<=> ssItem(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ592_spl])],[split_symbol_definition]) ).
fof(f5280,plain,
( sQ592_spl
| ~ ssItem(sK1_skl) ),
inference(component_clause,[status(thm)],[f5278]) ).
fof(f5289,plain,
( sQ592_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5280,f104]) ).
fof(f5290,plain,
sQ592_spl,
inference(contradiction_clause,[status(thm)],[f5289]) ).
fof(f5293,definition,
( sQ595_spl
<=> ssItem(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ595_spl])],[split_symbol_definition]) ).
fof(f5295,plain,
( sQ595_spl
| ~ ssItem(sK0_skl) ),
inference(component_clause,[status(thm)],[f5293]) ).
fof(f5304,plain,
( sQ595_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5295,f103]) ).
fof(f5305,plain,
sQ595_spl,
inference(contradiction_clause,[status(thm)],[f5304]) ).
fof(f6096,definition,
( sQ663_spl
<=> nil = cons(sK1_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ663_spl])],[split_symbol_definition]) ).
fof(f6097,plain,
( ~ sQ663_spl
| nil = cons(sK1_skl,nil) ),
inference(component_clause,[status(thm)],[f6096]) ).
fof(f6103,definition,
( sQ665_spl
<=> nil = cons(sK0_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ665_spl])],[split_symbol_definition]) ).
fof(f6104,plain,
( ~ sQ665_spl
| nil = cons(sK0_skl,nil) ),
inference(component_clause,[status(thm)],[f6103]) ).
fof(f6556,plain,
( ~ sQ663_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6097,f4935]) ).
fof(f6557,plain,
~ sQ663_spl,
inference(contradiction_clause,[status(thm)],[f6556]) ).
fof(f6558,plain,
( ~ sQ665_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6104,f4870]) ).
fof(f6559,plain,
~ sQ665_spl,
inference(contradiction_clause,[status(thm)],[f6558]) ).
fof(f6819,plain,
! [X0] :
( nil != cons(sK0_skl,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f235,f103]) ).
fof(f6820,plain,
! [X0] :
( nil != cons(sK1_skl,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f235,f104]) ).
fof(f7086,plain,
! [X0] :
( ssList(app(X0,sK49_skl))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f245,f420]) ).
fof(f7416,plain,
nil != cons(sK0_skl,sK49_skl),
inference(resolution,[status(thm)],[f6819,f420]) ).
fof(f7429,plain,
nil != cons(sK1_skl,sK49_skl),
inference(resolution,[status(thm)],[f6820,f420]) ).
fof(f7723,plain,
ssList(app(sK50_skl,sK49_skl)),
inference(resolution,[status(thm)],[f7086,f421]) ).
fof(f7736,plain,
( sQ68_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7723,f912]) ).
fof(f7737,plain,
sQ68_spl,
inference(contradiction_clause,[status(thm)],[f7736]) ).
fof(f9493,plain,
( ~ sQ456_spl
| totalorderedP(sK49_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f3940,f184]) ).
fof(f9496,plain,
( ~ sQ456_spl
| sQ478_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f9493,f477,f4024,f3939]) ).
fof(f12477,definition,
( sQ1284_spl
<=> nil = cons(sK1_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ1284_spl])],[split_symbol_definition]) ).
fof(f12478,plain,
( ~ sQ1284_spl
| nil = cons(sK1_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f12477]) ).
fof(f12523,definition,
( sQ1294_spl
<=> nil = cons(sK0_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ1294_spl])],[split_symbol_definition]) ).
fof(f12524,plain,
( ~ sQ1294_spl
| nil = cons(sK0_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f12523]) ).
fof(f12553,plain,
( ~ sQ1284_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f12478,f7429]) ).
fof(f12554,plain,
~ sQ1284_spl,
inference(contradiction_clause,[status(thm)],[f12553]) ).
fof(f12557,plain,
( ~ sQ1294_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f12524,f7416]) ).
fof(f12558,plain,
~ sQ1294_spl,
inference(contradiction_clause,[status(thm)],[f12557]) ).
fof(f14206,plain,
( ~ sQ453_spl
| leq(sK24_skl(sK49_skl),sK25_skl(sK49_skl))
| ~ ssItem(sK25_skl(sK49_skl))
| ~ ssItem(sK24_skl(sK49_skl)) ),
inference(resolution,[status(thm)],[f409,f3930]) ).
fof(f14208,plain,
( ~ sQ453_spl
| sQ456_spl
| ~ sQ452_spl
| ~ sQ451_spl ),
inference(split_clause,[status(thm)],[f14206,f3923,f3926,f3939,f3929]) ).
fof(f14210,plain,
$false,
inference(sat_refutation,[status(thm)],[f541,f2504,f3049,f3204,f3770,f3957,f4027,f4029,f4031,f4049,f5290,f5305,f6557,f6559,f7737,f9496,f12554,f12558,f14208]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC270+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.40 % Computer : n011.cluster.edu
% 0.16/0.40 % Model : x86_64 x86_64
% 0.16/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.40 % Memory : 8046.5625MB
% 0.16/0.40 % OS : Linux 6.8.0-71-generic
% 0.16/0.40 % CPULimit : 300
% 0.16/0.40 % WCLimit : 300
% 0.16/0.40 % DateTime : Mon Sep 21 08:09:40 UTC 2026
% 0.16/0.40 % CPUTime :
% 0.20/0.43 % Drodi V4.1.1
% 13.71/2.29 % Refutation found
% 13.71/2.29 % SZS status Theorem for theBenchmark: Theorem is valid
% 13.71/2.29 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.35/2.36 % Elapsed time: 1.934594 seconds
% 1.35/2.36 % CPU time: 14.686566 seconds
% 1.35/2.36 % Total memory used: 190.560 MB
% 1.35/2.36 % Net memory used: 184.383 MB
%------------------------------------------------------------------------------