%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO094+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 12:24:03 PM UTC 2026
% Result : Theorem 0.23s 0.55s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 79 ( 16 unt; 7 def)
% Number of atoms : 304 ( 0 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 359 ( 134 ~; 131 |; 75 &)
% ( 14 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 8 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 142 ( 125 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [C,C1] :
( part_of(C1,C)
<=> ! [P] :
( incident_c(P,C1)
=> incident_c(P,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [P,C] :
( end_point(P,C)
<=> ( ! [C1,C2] :
( ( incident_c(P,C2)
& incident_c(P,C1)
& part_of(C2,C)
& part_of(C1,C) )
=> ( part_of(C2,C1)
| part_of(C1,C2) ) )
& incident_c(P,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [P,C] :
( inner_point(P,C)
<=> ( ~ end_point(P,C)
& incident_c(P,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [P,C,C1] :
( meet(P,C,C1)
<=> ( ! [Q] :
( ( incident_c(Q,C1)
& incident_c(Q,C) )
=> ( end_point(Q,C1)
& end_point(Q,C) ) )
& incident_c(P,C1)
& incident_c(P,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [C] :
? [P] : inner_point(P,C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,conjecture,
! [C,C1,C2,P] :
( ( part_of(C2,C)
& part_of(C1,C)
& meet(P,C1,C2) )
=> ~ end_point(P,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [C,C1,C2,P] :
( ( part_of(C2,C)
& part_of(C1,C)
& meet(P,C1,C2) )
=> ~ end_point(P,C) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [C,C1] :
( part_of(C1,C)
<=> ! [P] :
( incident_c(P,C)
| ~ incident_c(P,C1) ) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f20,plain,
! [C,C1] :
( ( ? [P] :
( ~ incident_c(P,C)
& incident_c(P,C1) )
| part_of(C1,C) )
& ( ! [P] :
( incident_c(P,C)
| ~ incident_c(P,C1) )
| ~ part_of(C1,C) ) ),
inference(NNF_transformation,[status(thm)],[f19]) ).
fof(f21,plain,
( ! [C,C1] :
( ? [P] :
( ~ incident_c(P,C)
& incident_c(P,C1) )
| part_of(C1,C) )
& ! [C,C1] :
( ! [P] :
( incident_c(P,C)
| ~ incident_c(P,C1) )
| ~ part_of(C1,C) ) ),
inference(miniscoping,[status(thm)],[f20]) ).
fof(f22,plain,
( ! [C,C1] :
( ( ~ incident_c(sK0_skl(C1,C),C)
& incident_c(sK0_skl(C1,C),C1) )
| part_of(C1,C) )
& ! [C,C1] :
( ! [P] :
( incident_c(P,C)
| ~ incident_c(P,C1) )
| ~ part_of(C1,C) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(P,sK0_skl(C1,C))],[f21]) ).
fof(f23,plain,
! [X0,X1,X2] :
( incident_c(X2,X1)
| ~ incident_c(X2,X0)
| ~ part_of(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f35,plain,
! [P,C] :
( end_point(P,C)
<=> ( ! [C1,C2] :
( part_of(C2,C1)
| part_of(C1,C2)
| ~ incident_c(P,C2)
| ~ incident_c(P,C1)
| ~ part_of(C2,C)
| ~ part_of(C1,C) )
& incident_c(P,C) ) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f36,plain,
! [P,C] :
( ( ? [C1,C2] :
( ~ part_of(C2,C1)
& ~ part_of(C1,C2)
& incident_c(P,C2)
& incident_c(P,C1)
& part_of(C2,C)
& part_of(C1,C) )
| ~ incident_c(P,C)
| end_point(P,C) )
& ( ( ! [C1,C2] :
( part_of(C2,C1)
| part_of(C1,C2)
| ~ incident_c(P,C2)
| ~ incident_c(P,C1)
| ~ part_of(C2,C)
| ~ part_of(C1,C) )
& incident_c(P,C) )
| ~ end_point(P,C) ) ),
inference(NNF_transformation,[status(thm)],[f35]) ).
fof(f37,plain,
( ! [P,C] :
( ? [C1,C2] :
( ~ part_of(C2,C1)
& ~ part_of(C1,C2)
& incident_c(P,C2)
& incident_c(P,C1)
& part_of(C2,C)
& part_of(C1,C) )
| ~ incident_c(P,C)
| end_point(P,C) )
& ! [P,C] :
( ( ! [C1,C2] :
( part_of(C2,C1)
| part_of(C1,C2)
| ~ incident_c(P,C2)
| ~ incident_c(P,C1)
| ~ part_of(C2,C)
| ~ part_of(C1,C) )
& incident_c(P,C) )
| ~ end_point(P,C) ) ),
inference(miniscoping,[status(thm)],[f36]) ).
fof(f38,plain,
( ! [P,C] :
( ( ~ part_of(sK3_skl(C,P),sK2_skl(C,P))
& ~ part_of(sK2_skl(C,P),sK3_skl(C,P))
& incident_c(P,sK3_skl(C,P))
& incident_c(P,sK2_skl(C,P))
& part_of(sK3_skl(C,P),C)
& part_of(sK2_skl(C,P),C) )
| ~ incident_c(P,C)
| end_point(P,C) )
& ! [P,C] :
( ( ! [C1,C2] :
( part_of(C2,C1)
| part_of(C1,C2)
| ~ incident_c(P,C2)
| ~ incident_c(P,C1)
| ~ part_of(C2,C)
| ~ part_of(C1,C) )
& incident_c(P,C) )
| ~ end_point(P,C) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(C1,sK2_skl(C,P)),skolemize(C2,sK3_skl(C,P))],[f37]) ).
fof(f40,plain,
! [X0,X1,X2,X3] :
( part_of(X3,X2)
| part_of(X2,X3)
| ~ incident_c(X0,X3)
| ~ incident_c(X0,X2)
| ~ part_of(X3,X1)
| ~ part_of(X2,X1)
| ~ end_point(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f47,plain,
! [P,C] :
( ( end_point(P,C)
| ~ incident_c(P,C)
| inner_point(P,C) )
& ( ( ~ end_point(P,C)
& incident_c(P,C) )
| ~ inner_point(P,C) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f48,plain,
( ! [P,C] :
( end_point(P,C)
| ~ incident_c(P,C)
| inner_point(P,C) )
& ! [P,C] :
( ( ~ end_point(P,C)
& incident_c(P,C) )
| ~ inner_point(P,C) ) ),
inference(miniscoping,[status(thm)],[f47]) ).
fof(f49,plain,
! [X0,X1] :
( incident_c(X0,X1)
| ~ inner_point(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f50,plain,
! [X0,X1] :
( ~ end_point(X0,X1)
| ~ inner_point(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f52,plain,
! [P,C,C1] :
( meet(P,C,C1)
<=> ( ! [Q] :
( ( end_point(Q,C1)
& end_point(Q,C) )
| ~ incident_c(Q,C1)
| ~ incident_c(Q,C) )
& incident_c(P,C1)
& incident_c(P,C) ) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f53,plain,
! [P,C,C1] :
( ( ? [Q] :
( ( ~ end_point(Q,C1)
| ~ end_point(Q,C) )
& incident_c(Q,C1)
& incident_c(Q,C) )
| ~ incident_c(P,C1)
| ~ incident_c(P,C)
| meet(P,C,C1) )
& ( ( ! [Q] :
( ( end_point(Q,C1)
& end_point(Q,C) )
| ~ incident_c(Q,C1)
| ~ incident_c(Q,C) )
& incident_c(P,C1)
& incident_c(P,C) )
| ~ meet(P,C,C1) ) ),
inference(NNF_transformation,[status(thm)],[f52]) ).
fof(f54,plain,
( ! [P,C,C1] :
( ? [Q] :
( ( ~ end_point(Q,C1)
| ~ end_point(Q,C) )
& incident_c(Q,C1)
& incident_c(Q,C) )
| ~ incident_c(P,C1)
| ~ incident_c(P,C)
| meet(P,C,C1) )
& ! [P,C,C1] :
( ( ! [Q] :
( ( end_point(Q,C1)
& end_point(Q,C) )
| ~ incident_c(Q,C1)
| ~ incident_c(Q,C) )
& incident_c(P,C1)
& incident_c(P,C) )
| ~ meet(P,C,C1) ) ),
inference(miniscoping,[status(thm)],[f53]) ).
fof(f55,plain,
( ! [P,C,C1] :
( ( ( ~ end_point(sK4_skl(C1,C,P),C1)
| ~ end_point(sK4_skl(C1,C,P),C) )
& incident_c(sK4_skl(C1,C,P),C1)
& incident_c(sK4_skl(C1,C,P),C) )
| ~ incident_c(P,C1)
| ~ incident_c(P,C)
| meet(P,C,C1) )
& ! [P,C,C1] :
( ( ! [Q] :
( ( end_point(Q,C1)
& end_point(Q,C) )
| ~ incident_c(Q,C1)
| ~ incident_c(Q,C) )
& incident_c(P,C1)
& incident_c(P,C) )
| ~ meet(P,C,C1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(Q,sK4_skl(C1,C,P))],[f54]) ).
fof(f56,plain,
! [X0,X1,X2] :
( incident_c(X0,X1)
| ~ meet(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f57,plain,
! [X0,X1,X2] :
( incident_c(X0,X2)
| ~ meet(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f58,plain,
! [X0,X1,X2,X3] :
( end_point(X3,X1)
| ~ incident_c(X3,X2)
| ~ incident_c(X3,X1)
| ~ meet(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f59,plain,
! [X0,X1,X2,X3] :
( end_point(X3,X2)
| ~ incident_c(X3,X2)
| ~ incident_c(X3,X1)
| ~ meet(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f80,plain,
! [C] : inner_point(sK7_skl(C),C),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(P,sK7_skl(C))],[f10]) ).
fof(f81,plain,
! [X0] : inner_point(sK7_skl(X0),X0),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f104,plain,
? [C,C1,C2,P] :
( end_point(P,C)
& part_of(C2,C)
& part_of(C1,C)
& meet(P,C1,C2) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f105,plain,
? [C,P] :
( end_point(P,C)
& ? [C2] :
( part_of(C2,C)
& ? [C1] :
( part_of(C1,C)
& meet(P,C1,C2) ) ) ),
inference(miniscoping,[status(thm)],[f104]) ).
fof(f106,plain,
( end_point(sK14_skl,sK13_skl)
& part_of(sK15_skl,sK13_skl)
& part_of(sK16_skl,sK13_skl)
& meet(sK14_skl,sK16_skl,sK15_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl,sK15_skl,sK16_skl]),skolemize(C,sK13_skl),skolemize(P,sK14_skl),skolemize(C2,sK15_skl),skolemize(C1,sK16_skl)],[f105]) ).
fof(f107,plain,
meet(sK14_skl,sK16_skl,sK15_skl),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f108,plain,
part_of(sK16_skl,sK13_skl),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f109,plain,
part_of(sK15_skl,sK13_skl),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f110,plain,
end_point(sK14_skl,sK13_skl),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f118,plain,
incident_c(sK14_skl,sK16_skl),
inference(resolution,[status(thm)],[f56,f107]) ).
fof(f119,plain,
incident_c(sK14_skl,sK15_skl),
inference(resolution,[status(thm)],[f57,f107]) ).
fof(f122,plain,
! [X0] :
( end_point(X0,sK16_skl)
| ~ incident_c(X0,sK15_skl)
| ~ incident_c(X0,sK16_skl) ),
inference(resolution,[status(thm)],[f58,f107]) ).
fof(f124,definition,
( sQ0_spl
<=> incident_c(sK14_skl,sK15_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( sQ0_spl
| ~ incident_c(sK14_skl,sK15_skl) ),
inference(component_clause,[status(thm)],[f124]) ).
fof(f131,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f126,f119]) ).
fof(f132,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f131]) ).
fof(f134,plain,
! [X0] :
( end_point(X0,sK15_skl)
| ~ incident_c(X0,sK15_skl)
| ~ incident_c(X0,sK16_skl) ),
inference(resolution,[status(thm)],[f59,f107]) ).
fof(f142,plain,
! [X0,X1] :
( part_of(X1,sK15_skl)
| part_of(sK15_skl,X1)
| ~ incident_c(X0,X1)
| ~ incident_c(X0,sK15_skl)
| ~ part_of(X1,sK13_skl)
| ~ end_point(X0,sK13_skl) ),
inference(resolution,[status(thm)],[f40,f109]) ).
fof(f225,plain,
! [X0] : incident_c(sK7_skl(X0),X0),
inference(resolution,[status(thm)],[f49,f81]) ).
fof(f227,plain,
( end_point(sK7_skl(sK16_skl),sK16_skl)
| ~ incident_c(sK7_skl(sK16_skl),sK15_skl) ),
inference(resolution,[status(thm)],[f225,f122]) ).
fof(f230,definition,
( sQ13_spl
<=> incident_c(sK7_skl(sK16_skl),sK15_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f237,definition,
( sQ15_spl
<=> end_point(sK7_skl(sK16_skl),sK16_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f238,plain,
( ~ sQ15_spl
| end_point(sK7_skl(sK16_skl),sK16_skl) ),
inference(component_clause,[status(thm)],[f237]) ).
fof(f240,plain,
( sQ15_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f227,f230,f237]) ).
fof(f241,plain,
! [X0] : ~ end_point(sK7_skl(X0),X0),
inference(resolution,[status(thm)],[f50,f81]) ).
fof(f261,plain,
! [X0] :
( part_of(sK16_skl,sK15_skl)
| part_of(sK15_skl,sK16_skl)
| ~ incident_c(X0,sK16_skl)
| ~ incident_c(X0,sK15_skl)
| ~ end_point(X0,sK13_skl) ),
inference(resolution,[status(thm)],[f142,f108]) ).
fof(f263,definition,
! [X0] :
( sQ18_spl
<=> ( ~ incident_c(X0,sK16_skl)
| ~ incident_c(X0,sK15_skl)
| ~ end_point(X0,sK13_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f264,plain,
! [X0] :
( ~ sQ18_spl
| ~ incident_c(X0,sK16_skl)
| ~ incident_c(X0,sK15_skl)
| ~ end_point(X0,sK13_skl) ),
inference(component_clause,[status(thm)],[f263]) ).
fof(f266,definition,
( sQ19_spl
<=> part_of(sK15_skl,sK16_skl) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f267,plain,
( ~ sQ19_spl
| part_of(sK15_skl,sK16_skl) ),
inference(component_clause,[status(thm)],[f266]) ).
fof(f269,definition,
( sQ20_spl
<=> part_of(sK16_skl,sK15_skl) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f270,plain,
( ~ sQ20_spl
| part_of(sK16_skl,sK15_skl) ),
inference(component_clause,[status(thm)],[f269]) ).
fof(f272,plain,
( sQ20_spl
| sQ19_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f261,f263,f266,f269]) ).
fof(f281,plain,
! [X0] :
( ~ sQ20_spl
| incident_c(X0,sK15_skl)
| ~ incident_c(X0,sK16_skl) ),
inference(resolution,[status(thm)],[f270,f23]) ).
fof(f306,plain,
! [X0] :
( ~ sQ19_spl
| incident_c(X0,sK16_skl)
| ~ incident_c(X0,sK15_skl) ),
inference(resolution,[status(thm)],[f267,f23]) ).
fof(f327,plain,
( ~ sQ18_spl
| ~ incident_c(sK14_skl,sK16_skl)
| ~ incident_c(sK14_skl,sK15_skl) ),
inference(resolution,[status(thm)],[f264,f110]) ).
fof(f328,definition,
( sQ25_spl
<=> incident_c(sK14_skl,sK16_skl) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f330,plain,
( sQ25_spl
| ~ incident_c(sK14_skl,sK16_skl) ),
inference(component_clause,[status(thm)],[f328]) ).
fof(f331,plain,
( ~ sQ18_spl
| ~ sQ25_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f327,f124,f328,f263]) ).
fof(f332,plain,
( sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f330,f118]) ).
fof(f333,plain,
sQ25_spl,
inference(contradiction_clause,[status(thm)],[f332]) ).
fof(f354,plain,
! [X0] :
( ~ sQ19_spl
| end_point(X0,sK15_skl)
| ~ incident_c(X0,sK15_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f134,f306]) ).
fof(f356,plain,
( ~ sQ19_spl
| end_point(sK7_skl(sK15_skl),sK15_skl) ),
inference(resolution,[status(thm)],[f354,f225]) ).
fof(f358,plain,
( ~ sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f356,f241]) ).
fof(f359,plain,
~ sQ19_spl,
inference(contradiction_clause,[status(thm)],[f358]) ).
fof(f485,plain,
( ~ sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f238,f241]) ).
fof(f486,plain,
~ sQ15_spl,
inference(contradiction_clause,[status(thm)],[f485]) ).
fof(f540,plain,
( ~ sQ20_spl
| incident_c(sK7_skl(sK16_skl),sK15_skl) ),
inference(resolution,[status(thm)],[f281,f225]) ).
fof(f542,plain,
( ~ sQ20_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f540,f230,f269]) ).
fof(f543,plain,
$false,
inference(sat_refutation,[status(thm)],[f132,f240,f272,f331,f333,f359,f486,f542]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO094+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.48 % Computer : n011.cluster.edu
% 0.20/0.48 % Model : x86_64 x86_64
% 0.20/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.48 % Memory : 8046.5625MB
% 0.20/0.48 % OS : Linux 6.8.0-71-generic
% 0.20/0.48 % CPULimit : 300
% 0.20/0.48 % WCLimit : 300
% 0.20/0.48 % DateTime : Sun Sep 20 10:40:56 UTC 2026
% 0.20/0.48 % CPUTime :
% 0.20/0.50 % Drodi V4.1.1
% 0.23/0.55 % Refutation found
% 0.23/0.55 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.23/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/0.58 % Elapsed time: 0.085656 seconds
% 0.23/0.58 % CPU time: 0.388624 seconds
% 0.23/0.58 % Total memory used: 69.170 MB
% 0.23/0.58 % Net memory used: 68.847 MB
%------------------------------------------------------------------------------