%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWB029+2 : TPTP v9.3.1. Released v5.2.0.
% 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 02:37:12 PM UTC 2026
% Result : Theorem 0.08s 0.38s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 60 ( 12 unt; 5 def)
% Number of atoms : 279 ( 0 equ)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 363 ( 144 ~; 134 |; 71 &)
% ( 12 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 6 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 14 con; 0-4 aty)
% Number of variables : 126 ( 116 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,C] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [Z,C] :
( iext(uri_owl_complementOf,Z,C)
=> ( ! [X] :
( icext(Z,X)
<=> ~ icext(C,X) )
& ic(C)
& ic(Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [Z,S1,C1,S2,C2] :
( ( iext(uri_rdf_rest,S2,uri_rdf_nil)
& iext(uri_rdf_first,S2,C2)
& iext(uri_rdf_rest,S1,S2)
& iext(uri_rdf_first,S1,C1) )
=> ( iext(uri_owl_intersectionOf,Z,S1)
<=> ( ! [X] :
( icext(Z,X)
<=> ( icext(C2,X)
& icext(C1,X) ) )
& ic(C2)
& ic(C1)
& ic(Z) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
? [BNODE_x,BNODE_y,BNODE_l1,BNODE_l2] :
( iext(uri_owl_complementOf,BNODE_y,uri_ex_A)
& iext(uri_rdf_rest,BNODE_l2,uri_rdf_nil)
& iext(uri_rdf_first,BNODE_l2,BNODE_y)
& iext(uri_rdf_rest,BNODE_l1,BNODE_l2)
& iext(uri_rdf_first,BNODE_l1,uri_ex_A)
& iext(uri_owl_intersectionOf,BNODE_x,BNODE_l1)
& iext(uri_rdf_type,uri_ex_w,BNODE_x)
& iext(uri_rdf_type,uri_ex_B,uri_owl_Class)
& iext(uri_rdf_type,uri_ex_A,uri_owl_Class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,plain,
! [X,C] :
( ( ~ icext(C,X)
| iext(uri_rdf_type,X,C) )
& ( icext(C,X)
| ~ iext(uri_rdf_type,X,C) ) ),
inference(NNF_transformation,[status(thm)],[f1]) ).
fof(f8,plain,
( ! [X,C] :
( ~ icext(C,X)
| iext(uri_rdf_type,X,C) )
& ! [X,C] :
( icext(C,X)
| ~ iext(uri_rdf_type,X,C) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f9,plain,
! [X0,X1] :
( icext(X1,X0)
| ~ iext(uri_rdf_type,X0,X1) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f11,plain,
! [Z,C] :
( ( ! [X] :
( icext(Z,X)
<=> ~ icext(C,X) )
& ic(C)
& ic(Z) )
| ~ iext(uri_owl_complementOf,Z,C) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f12,plain,
! [Z,C] :
( ( ! [X] :
( ( icext(C,X)
| icext(Z,X) )
& ( ~ icext(C,X)
| ~ icext(Z,X) ) )
& ic(C)
& ic(Z) )
| ~ iext(uri_owl_complementOf,Z,C) ),
inference(NNF_transformation,[status(thm)],[f11]) ).
fof(f13,plain,
! [Z,C] :
( ( ! [X] :
( icext(C,X)
| icext(Z,X) )
& ! [X] :
( ~ icext(C,X)
| ~ icext(Z,X) )
& ic(C)
& ic(Z) )
| ~ iext(uri_owl_complementOf,Z,C) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ~ icext(X1,X2)
| ~ icext(X0,X2)
| ~ iext(uri_owl_complementOf,X0,X1) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f18,plain,
! [Z,S1,C1,S2,C2] :
( ( iext(uri_owl_intersectionOf,Z,S1)
<=> ( ! [X] :
( icext(Z,X)
<=> ( icext(C2,X)
& icext(C1,X) ) )
& ic(C2)
& ic(C1)
& ic(Z) ) )
| ~ iext(uri_rdf_rest,S2,uri_rdf_nil)
| ~ iext(uri_rdf_first,S2,C2)
| ~ iext(uri_rdf_rest,S1,S2)
| ~ iext(uri_rdf_first,S1,C1) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f19,plain,
! [Z,S1,C1,S2,C2] :
( ( ( ? [X] :
( ( ( icext(C2,X)
& icext(C1,X) )
| icext(Z,X) )
& ( ~ icext(C2,X)
| ~ icext(C1,X)
| ~ icext(Z,X) ) )
| ~ ic(C2)
| ~ ic(C1)
| ~ ic(Z)
| iext(uri_owl_intersectionOf,Z,S1) )
& ( ( ! [X] :
( ( ~ icext(C2,X)
| ~ icext(C1,X)
| icext(Z,X) )
& ( ( icext(C2,X)
& icext(C1,X) )
| ~ icext(Z,X) ) )
& ic(C2)
& ic(C1)
& ic(Z) )
| ~ iext(uri_owl_intersectionOf,Z,S1) ) )
| ~ iext(uri_rdf_rest,S2,uri_rdf_nil)
| ~ iext(uri_rdf_first,S2,C2)
| ~ iext(uri_rdf_rest,S1,S2)
| ~ iext(uri_rdf_first,S1,C1) ),
inference(NNF_transformation,[status(thm)],[f18]) ).
fof(f20,plain,
! [S1,C1,C2] :
( ( ! [Z] :
( ? [X] :
( ( ( icext(C2,X)
& icext(C1,X) )
| icext(Z,X) )
& ( ~ icext(C2,X)
| ~ icext(C1,X)
| ~ icext(Z,X) ) )
| ~ ic(C2)
| ~ ic(C1)
| ~ ic(Z)
| iext(uri_owl_intersectionOf,Z,S1) )
& ! [Z] :
( ( ! [X] :
( ~ icext(C2,X)
| ~ icext(C1,X)
| icext(Z,X) )
& ! [X] :
( ( icext(C2,X)
& icext(C1,X) )
| ~ icext(Z,X) )
& ic(C2)
& ic(C1)
& ic(Z) )
| ~ iext(uri_owl_intersectionOf,Z,S1) ) )
| ! [S2] :
( ~ iext(uri_rdf_rest,S2,uri_rdf_nil)
| ~ iext(uri_rdf_first,S2,C2)
| ~ iext(uri_rdf_rest,S1,S2)
| ~ iext(uri_rdf_first,S1,C1) ) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f21,plain,
! [S1,C1,C2] :
( ( ! [Z] :
( ( ( ( icext(C2,sK0_skl(Z,C2,C1,S1))
& icext(C1,sK0_skl(Z,C2,C1,S1)) )
| icext(Z,sK0_skl(Z,C2,C1,S1)) )
& ( ~ icext(C2,sK0_skl(Z,C2,C1,S1))
| ~ icext(C1,sK0_skl(Z,C2,C1,S1))
| ~ icext(Z,sK0_skl(Z,C2,C1,S1)) ) )
| ~ ic(C2)
| ~ ic(C1)
| ~ ic(Z)
| iext(uri_owl_intersectionOf,Z,S1) )
& ! [Z] :
( ( ! [X] :
( ~ icext(C2,X)
| ~ icext(C1,X)
| icext(Z,X) )
& ! [X] :
( ( icext(C2,X)
& icext(C1,X) )
| ~ icext(Z,X) )
& ic(C2)
& ic(C1)
& ic(Z) )
| ~ iext(uri_owl_intersectionOf,Z,S1) ) )
| ! [S2] :
( ~ iext(uri_rdf_rest,S2,uri_rdf_nil)
| ~ iext(uri_rdf_first,S2,C2)
| ~ iext(uri_rdf_rest,S1,S2)
| ~ iext(uri_rdf_first,S1,C1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X,sK0_skl(Z,C2,C1,S1))],[f20]) ).
fof(f25,plain,
! [X0,X1,X2,X3,X4,X5] :
( icext(X1,X5)
| ~ icext(X4,X5)
| ~ iext(uri_owl_intersectionOf,X4,X0)
| ~ iext(uri_rdf_rest,X2,uri_rdf_nil)
| ~ iext(uri_rdf_first,X2,X3)
| ~ iext(uri_rdf_rest,X0,X2)
| ~ iext(uri_rdf_first,X0,X1) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f26,plain,
! [X0,X1,X2,X3,X4,X5] :
( icext(X3,X5)
| ~ icext(X4,X5)
| ~ iext(uri_owl_intersectionOf,X4,X0)
| ~ iext(uri_rdf_rest,X2,uri_rdf_nil)
| ~ iext(uri_rdf_first,X2,X3)
| ~ iext(uri_rdf_rest,X0,X2)
| ~ iext(uri_rdf_first,X0,X1) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f32,plain,
? [BNODE_y] :
( iext(uri_owl_complementOf,BNODE_y,uri_ex_A)
& ? [BNODE_l2] :
( iext(uri_rdf_rest,BNODE_l2,uri_rdf_nil)
& iext(uri_rdf_first,BNODE_l2,BNODE_y)
& ? [BNODE_l1] :
( iext(uri_rdf_rest,BNODE_l1,BNODE_l2)
& iext(uri_rdf_first,BNODE_l1,uri_ex_A)
& ? [BNODE_x] :
( iext(uri_owl_intersectionOf,BNODE_x,BNODE_l1)
& iext(uri_rdf_type,uri_ex_w,BNODE_x)
& iext(uri_rdf_type,uri_ex_B,uri_owl_Class)
& iext(uri_rdf_type,uri_ex_A,uri_owl_Class) ) ) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f33,plain,
( iext(uri_owl_complementOf,sK1_skl,uri_ex_A)
& iext(uri_rdf_rest,sK2_skl,uri_rdf_nil)
& iext(uri_rdf_first,sK2_skl,sK1_skl)
& iext(uri_rdf_rest,sK3_skl,sK2_skl)
& iext(uri_rdf_first,sK3_skl,uri_ex_A)
& iext(uri_owl_intersectionOf,sK4_skl,sK3_skl)
& iext(uri_rdf_type,uri_ex_w,sK4_skl)
& iext(uri_rdf_type,uri_ex_B,uri_owl_Class)
& iext(uri_rdf_type,uri_ex_A,uri_owl_Class) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl,sK3_skl,sK4_skl]),skolemize(BNODE_y,sK1_skl),skolemize(BNODE_l2,sK2_skl),skolemize(BNODE_l1,sK3_skl),skolemize(BNODE_x,sK4_skl)],[f32]) ).
fof(f36,plain,
iext(uri_rdf_type,uri_ex_w,sK4_skl),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f37,plain,
iext(uri_owl_intersectionOf,sK4_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f38,plain,
iext(uri_rdf_first,sK3_skl,uri_ex_A),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f39,plain,
iext(uri_rdf_rest,sK3_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f40,plain,
iext(uri_rdf_first,sK2_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f41,plain,
iext(uri_rdf_rest,sK2_skl,uri_rdf_nil),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f42,plain,
iext(uri_owl_complementOf,sK1_skl,uri_ex_A),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f43,plain,
icext(sK4_skl,uri_ex_w),
inference(resolution,[status(thm)],[f9,f36]) ).
fof(f51,plain,
! [X0] :
( ~ icext(uri_ex_A,X0)
| ~ icext(sK1_skl,X0) ),
inference(resolution,[status(thm)],[f16,f42]) ).
fof(f57,definition,
! [X2] :
( sQ1_spl
<=> ~ iext(uri_rdf_first,sK2_skl,X2) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f58,plain,
! [X0] :
( ~ sQ1_spl
| ~ iext(uri_rdf_first,sK2_skl,X0) ),
inference(component_clause,[status(thm)],[f57]) ).
fof(f66,plain,
( ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f40,f58]) ).
fof(f67,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f66]) ).
fof(f72,definition,
! [X0] :
( sQ3_spl
<=> ~ iext(uri_rdf_first,sK3_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f73,plain,
! [X0] :
( ~ sQ3_spl
| ~ iext(uri_rdf_first,sK3_skl,X0) ),
inference(component_clause,[status(thm)],[f72]) ).
fof(f79,plain,
( ~ sQ3_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f38,f73]) ).
fof(f80,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f79]) ).
fof(f86,definition,
! [X1] :
( sQ6_spl
<=> ~ iext(uri_owl_intersectionOf,X1,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f87,plain,
! [X0] :
( ~ sQ6_spl
| ~ iext(uri_owl_intersectionOf,X0,sK3_skl) ),
inference(component_clause,[status(thm)],[f86]) ).
fof(f98,plain,
! [X0,X1,X2,X3,X4] :
( icext(X1,X4)
| ~ icext(X3,X4)
| ~ iext(uri_owl_intersectionOf,X3,X0)
| ~ iext(uri_rdf_first,sK2_skl,X2)
| ~ iext(uri_rdf_rest,X0,sK2_skl)
| ~ iext(uri_rdf_first,X0,X1) ),
inference(resolution,[status(thm)],[f25,f41]) ).
fof(f99,definition,
! [X0,X1,X3,X4] :
( sQ9_spl
<=> ( icext(X1,X4)
| ~ icext(X3,X4)
| ~ iext(uri_owl_intersectionOf,X3,X0)
| ~ iext(uri_rdf_rest,X0,sK2_skl)
| ~ iext(uri_rdf_first,X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f100,plain,
! [X0,X1,X2,X3] :
( ~ sQ9_spl
| icext(X1,X3)
| ~ icext(X2,X3)
| ~ iext(uri_owl_intersectionOf,X2,X0)
| ~ iext(uri_rdf_rest,X0,sK2_skl)
| ~ iext(uri_rdf_first,X0,X1) ),
inference(component_clause,[status(thm)],[f99]) ).
fof(f102,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f98,f99,f57]) ).
fof(f106,plain,
( ~ sQ6_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f37,f87]) ).
fof(f107,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f106]) ).
fof(f115,plain,
! [X0,X1,X2,X3,X4] :
( icext(X2,X4)
| ~ icext(X3,X4)
| ~ iext(uri_owl_intersectionOf,X3,X0)
| ~ iext(uri_rdf_first,sK2_skl,X2)
| ~ iext(uri_rdf_rest,X0,sK2_skl)
| ~ iext(uri_rdf_first,X0,X1) ),
inference(resolution,[status(thm)],[f26,f41]) ).
fof(f119,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| icext(X0,X2)
| ~ icext(X1,X2)
| ~ iext(uri_owl_intersectionOf,X1,sK3_skl)
| ~ iext(uri_rdf_first,sK3_skl,X0) ),
inference(resolution,[status(thm)],[f100,f39]) ).
fof(f120,plain,
! [X0,X1] :
( ~ sQ9_spl
| icext(X0,X1)
| ~ icext(sK4_skl,X1)
| ~ iext(uri_rdf_first,sK3_skl,X0) ),
inference(resolution,[status(thm)],[f119,f37]) ).
fof(f121,plain,
! [X0] :
( ~ sQ9_spl
| icext(X0,uri_ex_w)
| ~ iext(uri_rdf_first,sK3_skl,X0) ),
inference(resolution,[status(thm)],[f120,f43]) ).
fof(f122,plain,
( ~ sQ9_spl
| icext(uri_ex_A,uri_ex_w) ),
inference(resolution,[status(thm)],[f121,f38]) ).
fof(f123,plain,
( ~ sQ9_spl
| ~ icext(sK1_skl,uri_ex_w) ),
inference(resolution,[status(thm)],[f122,f51]) ).
fof(f126,plain,
! [X0,X1,X2,X3] :
( icext(X1,X3)
| ~ icext(X2,X3)
| ~ iext(uri_owl_intersectionOf,X2,sK3_skl)
| ~ iext(uri_rdf_first,sK2_skl,X1)
| ~ iext(uri_rdf_first,sK3_skl,X0) ),
inference(resolution,[status(thm)],[f115,f39]) ).
fof(f127,definition,
! [X1,X2,X3] :
( sQ10_spl
<=> ( icext(X1,X3)
| ~ icext(X2,X3)
| ~ iext(uri_owl_intersectionOf,X2,sK3_skl)
| ~ iext(uri_rdf_first,sK2_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f128,plain,
! [X0,X1,X2] :
( ~ sQ10_spl
| icext(X0,X2)
| ~ icext(X1,X2)
| ~ iext(uri_owl_intersectionOf,X1,sK3_skl)
| ~ iext(uri_rdf_first,sK2_skl,X0) ),
inference(component_clause,[status(thm)],[f127]) ).
fof(f130,plain,
( sQ10_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f126,f72,f127]) ).
fof(f131,plain,
! [X0,X1] :
( ~ sQ10_spl
| icext(X0,X1)
| ~ icext(sK4_skl,X1)
| ~ iext(uri_rdf_first,sK2_skl,X0) ),
inference(resolution,[status(thm)],[f128,f37]) ).
fof(f132,plain,
! [X0] :
( ~ sQ10_spl
| icext(X0,uri_ex_w)
| ~ iext(uri_rdf_first,sK2_skl,X0) ),
inference(resolution,[status(thm)],[f131,f43]) ).
fof(f133,plain,
( ~ sQ10_spl
| icext(sK1_skl,uri_ex_w) ),
inference(resolution,[status(thm)],[f132,f40]) ).
fof(f134,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f133,f123]) ).
fof(f135,plain,
( ~ sQ10_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f134]) ).
fof(f136,plain,
$false,
inference(sat_refutation,[status(thm)],[f67,f80,f102,f107,f130,f135]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWB029+2 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n016.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 07:47:07 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.08/0.38 % Refutation found
% 0.08/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.41 % Elapsed time: 0.044449 seconds
% 0.14/0.41 % CPU time: 0.125193 seconds
% 0.14/0.41 % Total memory used: 17.676 MB
% 0.14/0.41 % Net memory used: 17.315 MB
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