%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC340+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 : n016.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 02:40:51 PM UTC 2026
% Result : Theorem 10.29s 1.80s
% Output : CNFRefutation 10.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 32
% Syntax : Number of formulae : 154 ( 26 unt; 21 def)
% Number of atoms : 498 ( 56 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 558 ( 214 ~; 224 |; 60 &)
% ( 29 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 31 ( 29 usr; 22 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 7 con; 0-2 aty)
% Number of variables : 132 ( 113 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
? [U] :
( ? [V] :
( U != V
& ssItem(V) )
& ssItem(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( rearsegP(U,V)
<=> ? [W] :
( app(W,V) = U
& ssList(W) ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> cons(V,U) != U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [U] :
( ssList(U)
=> app(nil,U) = U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,axiom,
! [U] :
( ssList(U)
=> rearsegP(U,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f55,axiom,
! [U] :
( ssList(U)
=> segmentP(U,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f93,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ( lt(U,V)
<=> ( leq(U,V)
& U != V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( totalorderedP(U)
& segmentP(V,U) )
| ~ strictorderedP(W)
| ~ segmentP(X,W)
| 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)
=> ( ( totalorderedP(U)
& segmentP(V,U) )
| ~ strictorderedP(W)
| ~ segmentP(X,W)
| U != W
| V != 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(f125,plain,
! [U] :
( ! [V] :
( ( rearsegP(U,V)
<=> ? [W] :
( app(W,V) = U
& ssList(W) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f126,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(W,V) != U
| ~ ssList(W) )
| rearsegP(U,V) )
& ( ? [W] :
( app(W,V) = U
& ssList(W) )
| ~ rearsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f125]) ).
fof(f127,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(W,V) != U
| ~ ssList(W) )
| rearsegP(U,V) )
& ( ( app(sK6_skl(V,U),V) = U
& ssList(sK6_skl(V,U)) )
| ~ rearsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(W,sK6_skl(V,U))],[f126]) ).
fof(f128,plain,
! [X0,X1] :
( ssList(sK6_skl(X1,X0))
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
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(f248,plain,
! [U] :
( app(nil,U) = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f249,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f248]) ).
fof(f304,plain,
! [U] :
( rearsegP(U,U)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f49]) ).
fof(f305,plain,
! [X0] :
( rearsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f304]) ).
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] :
( ( ~ totalorderedP(U)
| ~ segmentP(V,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,
( ( ~ totalorderedP(sK47_skl)
| ~ segmentP(sK48_skl,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)],[f415]) ).
fof(f419,plain,
ssList(sK49_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f420,plain,
ssList(sK50_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f421,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f422,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f423,plain,
segmentP(sK50_skl,sK49_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f424,plain,
strictorderedP(sK49_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f425,plain,
( ~ totalorderedP(sK47_skl)
| ~ segmentP(sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f426,definition,
( sQ0_spl
<=> segmentP(sK48_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f428,plain,
( sQ0_spl
| ~ segmentP(sK48_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f426]) ).
fof(f429,definition,
( sQ1_spl
<=> totalorderedP(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f431,plain,
( sQ1_spl
| ~ totalorderedP(sK47_skl) ),
inference(component_clause,[status(thm)],[f429]) ).
fof(f432,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f425,f426,f429]) ).
fof(f444,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(f465,plain,
( sQ0_spl
| ~ segmentP(sK50_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f421,f428]) ).
fof(f466,plain,
( sQ0_spl
| ~ segmentP(sK50_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f422,f465]) ).
fof(f467,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f466,f423]) ).
fof(f468,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f467]) ).
fof(f469,plain,
( sQ1_spl
| ~ totalorderedP(sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f422,f431]) ).
fof(f489,definition,
( sQ4_spl
<=> ssList(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f491,plain,
( sQ4_spl
| ~ ssList(sK49_skl) ),
inference(component_clause,[status(thm)],[f489]) ).
fof(f557,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f491,f419]) ).
fof(f558,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f557]) ).
fof(f815,plain,
! [X0] :
( ~ ssList(X0)
| ssList(sK6_skl(X0,X0))
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f128,f305]) ).
fof(f820,plain,
! [X0] :
( ssList(sK6_skl(X0,X0))
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f815]) ).
fof(f1047,plain,
ssList(sK6_skl(nil,nil)),
inference(resolution,[status(thm)],[f820,f223]) ).
fof(f1048,plain,
ssList(sK6_skl(sK50_skl,sK50_skl)),
inference(resolution,[status(thm)],[f820,f420]) ).
fof(f1065,definition,
( sQ77_spl
<=> segmentP(sK6_skl(nil,nil),sK6_skl(nil,nil)) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f1067,plain,
( sQ77_spl
| ~ segmentP(sK6_skl(nil,nil),sK6_skl(nil,nil)) ),
inference(component_clause,[status(thm)],[f1065]) ).
fof(f1092,definition,
( sQ80_spl
<=> segmentP(sK6_skl(sK50_skl,sK50_skl),sK6_skl(sK50_skl,sK50_skl)) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f1094,plain,
( sQ80_spl
| ~ segmentP(sK6_skl(sK50_skl,sK50_skl),sK6_skl(sK50_skl,sK50_skl)) ),
inference(component_clause,[status(thm)],[f1092]) ).
fof(f1589,plain,
( sQ80_spl
| ~ ssList(sK6_skl(sK50_skl,sK50_skl)) ),
inference(resolution,[status(thm)],[f1094,f319]) ).
fof(f1594,plain,
( sQ80_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1589,f1048]) ).
fof(f1595,plain,
sQ80_spl,
inference(contradiction_clause,[status(thm)],[f1594]) ).
fof(f1668,plain,
( sQ77_spl
| ~ ssList(sK6_skl(nil,nil)) ),
inference(resolution,[status(thm)],[f1067,f319]) ).
fof(f1673,plain,
( sQ77_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1668,f1047]) ).
fof(f1674,plain,
sQ77_spl,
inference(contradiction_clause,[status(thm)],[f1673]) ).
fof(f1779,plain,
( sQ1_spl
| ssList(sK26_skl(sK49_skl))
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f469,f180]) ).
fof(f1780,definition,
( sQ169_spl
<=> ssList(sK26_skl(sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ169_spl])],[split_symbol_definition]) ).
fof(f1783,plain,
( sQ1_spl
| sQ169_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1779,f489,f1780,f429]) ).
fof(f1786,plain,
app(nil,sK49_skl) = sK49_skl,
inference(resolution,[status(thm)],[f419,f249]) ).
fof(f2375,plain,
( sQ1_spl
| ssList(sK27_skl(sK49_skl))
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f181,f469]) ).
fof(f2377,definition,
( sQ255_spl
<=> ssList(sK27_skl(sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ255_spl])],[split_symbol_definition]) ).
fof(f2380,plain,
( sQ1_spl
| sQ255_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f2375,f489,f2377,f429]) ).
fof(f2453,plain,
( sQ1_spl
| ssList(sK28_skl(sK49_skl))
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f182,f469]) ).
fof(f2455,definition,
( sQ267_spl
<=> ssList(sK28_skl(sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ267_spl])],[split_symbol_definition]) ).
fof(f2458,plain,
( sQ1_spl
| sQ267_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f2453,f489,f2455,f429]) ).
fof(f3407,plain,
! [X0] :
( cons(sK1_skl,X0) != X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f225,f104]) ).
fof(f3408,plain,
! [X0] :
( cons(sK0_skl,X0) != X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f225,f103]) ).
fof(f3443,plain,
cons(sK1_skl,nil) != nil,
inference(resolution,[status(thm)],[f3407,f223]) ).
fof(f3479,plain,
cons(sK0_skl,nil) != nil,
inference(resolution,[status(thm)],[f3408,f223]) ).
fof(f3481,plain,
( sQ1_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
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f183,f469]) ).
fof(f3483,definition,
( sQ400_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,[sQ400_spl])],[split_symbol_definition]) ).
fof(f3484,plain,
( ~ sQ400_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)],[f3483]) ).
fof(f3486,plain,
( sQ1_spl
| sQ400_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f3481,f489,f3483,f429]) ).
fof(f3561,plain,
( ~ sQ400_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)],[f3484,f444]) ).
fof(f3588,definition,
( sQ414_spl
<=> ssItem(sK24_skl(sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ414_spl])],[split_symbol_definition]) ).
fof(f3590,plain,
( sQ414_spl
| ~ ssItem(sK24_skl(sK49_skl)) ),
inference(component_clause,[status(thm)],[f3588]) ).
fof(f3591,definition,
( sQ415_spl
<=> ssItem(sK25_skl(sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ415_spl])],[split_symbol_definition]) ).
fof(f3593,plain,
( sQ415_spl
| ~ ssItem(sK25_skl(sK49_skl)) ),
inference(component_clause,[status(thm)],[f3591]) ).
fof(f3594,definition,
( sQ416_spl
<=> lt(sK24_skl(sK49_skl),sK25_skl(sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ416_spl])],[split_symbol_definition]) ).
fof(f3595,plain,
( ~ sQ416_spl
| lt(sK24_skl(sK49_skl),sK25_skl(sK49_skl)) ),
inference(component_clause,[status(thm)],[f3594]) ).
fof(f3604,definition,
( sQ419_spl
<=> leq(sK24_skl(sK49_skl),sK25_skl(sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ419_spl])],[split_symbol_definition]) ).
fof(f3605,plain,
( ~ sQ419_spl
| leq(sK24_skl(sK49_skl),sK25_skl(sK49_skl)) ),
inference(component_clause,[status(thm)],[f3604]) ).
fof(f3615,definition,
( sQ422_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,[sQ422_spl])],[split_symbol_definition]) ).
fof(f3617,plain,
( sQ422_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)],[f3615]) ).
fof(f3618,plain,
( ~ sQ400_spl
| sQ416_spl
| ~ sQ267_spl
| ~ sQ255_spl
| ~ sQ169_spl
| ~ sQ415_spl
| ~ sQ414_spl
| ~ sQ422_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f3561,f489,f3615,f3588,f3591,f1780,f2377,f2455,f3594,f3483]) ).
fof(f3720,plain,
( sQ415_spl
| totalorderedP(sK49_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f3593,f179]) ).
fof(f3721,definition,
( sQ449_spl
<=> totalorderedP(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ449_spl])],[split_symbol_definition]) ).
fof(f3722,plain,
( ~ sQ449_spl
| totalorderedP(sK49_skl) ),
inference(component_clause,[status(thm)],[f3721]) ).
fof(f3724,plain,
( sQ415_spl
| sQ449_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f3720,f489,f3721,f3591]) ).
fof(f3725,plain,
( sQ414_spl
| totalorderedP(sK49_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f3590,f178]) ).
fof(f3726,plain,
( sQ414_spl
| sQ449_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f3725,f489,f3721,f3588]) ).
fof(f3727,plain,
( ~ sQ449_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3722,f469]) ).
fof(f3728,plain,
( ~ sQ449_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f3727]) ).
fof(f3756,plain,
( sQ422_spl
| ~ sQ400_spl
| ~ strictorderedP(sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f3484,f3617]) ).
fof(f3757,plain,
( sQ422_spl
| ~ sQ400_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3756,f424]) ).
fof(f3758,plain,
( sQ422_spl
| ~ sQ400_spl ),
inference(contradiction_clause,[status(thm)],[f3757]) ).
fof(f4618,definition,
( sQ503_spl
<=> ssItem(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ503_spl])],[split_symbol_definition]) ).
fof(f4620,plain,
( sQ503_spl
| ~ ssItem(sK1_skl) ),
inference(component_clause,[status(thm)],[f4618]) ).
fof(f4629,plain,
( sQ503_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4620,f104]) ).
fof(f4630,plain,
sQ503_spl,
inference(contradiction_clause,[status(thm)],[f4629]) ).
fof(f4633,definition,
( sQ506_spl
<=> ssItem(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ506_spl])],[split_symbol_definition]) ).
fof(f4635,plain,
( sQ506_spl
| ~ ssItem(sK0_skl) ),
inference(component_clause,[status(thm)],[f4633]) ).
fof(f4644,plain,
( sQ506_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4635,f103]) ).
fof(f4645,plain,
sQ506_spl,
inference(contradiction_clause,[status(thm)],[f4644]) ).
fof(f5141,definition,
( sQ528_spl
<=> nil = cons(sK0_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ528_spl])],[split_symbol_definition]) ).
fof(f5142,plain,
( ~ sQ528_spl
| nil = cons(sK0_skl,nil) ),
inference(component_clause,[status(thm)],[f5141]) ).
fof(f5148,definition,
( sQ530_spl
<=> nil = cons(sK1_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ530_spl])],[split_symbol_definition]) ).
fof(f5149,plain,
( ~ sQ530_spl
| nil = cons(sK1_skl,nil) ),
inference(component_clause,[status(thm)],[f5148]) ).
fof(f5359,plain,
( ~ sQ528_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5142,f3479]) ).
fof(f5360,plain,
~ sQ528_spl,
inference(contradiction_clause,[status(thm)],[f5359]) ).
fof(f5361,plain,
( ~ sQ530_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5149,f3443]) ).
fof(f5362,plain,
~ sQ530_spl,
inference(contradiction_clause,[status(thm)],[f5361]) ).
fof(f6438,definition,
( sQ665_spl
<=> ssList(app(nil,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ665_spl])],[split_symbol_definition]) ).
fof(f6440,plain,
( sQ665_spl
| ~ ssList(app(nil,sK49_skl)) ),
inference(component_clause,[status(thm)],[f6438]) ).
fof(f7871,plain,
( ~ sQ419_spl
| totalorderedP(sK49_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f3605,f184]) ).
fof(f7874,plain,
( ~ sQ419_spl
| sQ449_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f7871,f489,f3721,f3604]) ).
fof(f7883,plain,
( sQ665_spl
| ~ ssList(sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f1786,f6440]) ).
fof(f7884,plain,
( sQ665_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7883,f419]) ).
fof(f7885,plain,
sQ665_spl,
inference(contradiction_clause,[status(thm)],[f7884]) ).
fof(f10920,definition,
( sQ1115_spl
<=> app(sK50_skl,sK50_skl) = app(sK50_skl,sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ1115_spl])],[split_symbol_definition]) ).
fof(f10922,plain,
( sQ1115_spl
| app(sK50_skl,sK50_skl) != app(sK50_skl,sK50_skl) ),
inference(component_clause,[status(thm)],[f10920]) ).
fof(f10961,plain,
( sQ1115_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f10922]) ).
fof(f10962,plain,
sQ1115_spl,
inference(contradiction_clause,[status(thm)],[f10961]) ).
fof(f11647,plain,
( ~ sQ416_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,f3595]) ).
fof(f11649,plain,
( ~ sQ416_spl
| sQ419_spl
| ~ sQ415_spl
| ~ sQ414_spl ),
inference(split_clause,[status(thm)],[f11647,f3588,f3591,f3604,f3594]) ).
fof(f11651,plain,
$false,
inference(sat_refutation,[status(thm)],[f432,f468,f558,f1595,f1674,f1783,f2380,f2458,f3486,f3618,f3724,f3726,f3728,f3758,f4630,f4645,f5360,f5362,f7874,f7885,f10962,f11649]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC340+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n016.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 21 08:21:54 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 10.29/1.80 % Refutation found
% 10.29/1.80 % SZS status Theorem for theBenchmark: Theorem is valid
% 10.29/1.80 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 10.06/1.87 % Elapsed time: 1.507123 seconds
% 10.06/1.87 % CPU time: 11.366788 seconds
% 10.06/1.87 % Total memory used: 189.399 MB
% 10.06/1.87 % Net memory used: 182.977 MB
%------------------------------------------------------------------------------