%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO127+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 : 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 12:24:09 PM UTC 2026
% Result : Theorem 0.09s 0.61s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 22
% Syntax : Number of formulae : 113 ( 12 unt; 12 def)
% Number of atoms : 367 ( 20 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 412 ( 158 ~; 160 |; 67 &)
% ( 23 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 13 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-2 aty)
% Number of variables : 171 ( 142 !; 29 ?)
% Comments :
%------------------------------------------------------------------------------
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(f6,axiom,
! [C] :
( closed(C)
<=> ~ ? [P] : end_point(P,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [C] :
( open(C)
<=> ? [P] : end_point(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(f19,axiom,
! [P,O] :
( start_point(P,O)
<=> ( ! [Q] :
( ( incident_o(Q,O)
& P != Q )
=> ordered_by(O,P,Q) )
& incident_o(P,O) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [O,P,Q] :
( ordered_by(O,P,Q)
=> ( incident_o(Q,O)
& incident_o(P,O) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [O] :
? [C] :
( ! [P] :
( incident_o(P,O)
<=> incident_c(P,C) )
& open(C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [O] :
? [P] : start_point(P,O),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,conjecture,
! [O,P] :
( incident_o(P,O)
<=> ? [Q] :
( ordered_by(O,Q,P)
| ordered_by(O,P,Q) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
~ ! [O,P] :
( incident_o(P,O)
<=> ? [Q] :
( ordered_by(O,Q,P)
| ordered_by(O,P,Q) ) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f46,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(f47,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)],[f46]) ).
fof(f48,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)],[f47]) ).
fof(f49,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))],[f48]) ).
fof(f50,plain,
! [X0,X1] :
( incident_c(X0,X1)
| ~ end_point(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f58,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(f59,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)],[f58]) ).
fof(f60,plain,
! [X0,X1] :
( incident_c(X0,X1)
| ~ inner_point(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f61,plain,
! [X0,X1] :
( ~ end_point(X0,X1)
| ~ inner_point(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f74,plain,
! [C] :
( closed(C)
<=> ! [P] : ~ end_point(P,C) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f75,plain,
! [C] :
( ( ? [P] : end_point(P,C)
| closed(C) )
& ( ! [P] : ~ end_point(P,C)
| ~ closed(C) ) ),
inference(NNF_transformation,[status(thm)],[f74]) ).
fof(f76,plain,
( ! [C] :
( ? [P] : end_point(P,C)
| closed(C) )
& ! [C] :
( ! [P] : ~ end_point(P,C)
| ~ closed(C) ) ),
inference(miniscoping,[status(thm)],[f75]) ).
fof(f77,plain,
( ! [C] :
( end_point(sK5_skl(C),C)
| closed(C) )
& ! [C] :
( ! [P] : ~ end_point(P,C)
| ~ closed(C) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(P,sK5_skl(C))],[f76]) ).
fof(f78,plain,
! [X0,X1] :
( ~ end_point(X1,X0)
| ~ closed(X0) ),
inference(cnf_transformation,[status(thm)],[f77]) ).
fof(f79,plain,
! [X0] :
( end_point(sK5_skl(X0),X0)
| closed(X0) ),
inference(cnf_transformation,[status(thm)],[f77]) ).
fof(f80,plain,
! [C] :
( ( ! [P] : ~ end_point(P,C)
| open(C) )
& ( ? [P] : end_point(P,C)
| ~ open(C) ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f81,plain,
( ! [C] :
( ! [P] : ~ end_point(P,C)
| open(C) )
& ! [C] :
( ? [P] : end_point(P,C)
| ~ open(C) ) ),
inference(miniscoping,[status(thm)],[f80]) ).
fof(f82,plain,
( ! [C] :
( ! [P] : ~ end_point(P,C)
| open(C) )
& ! [C] :
( end_point(sK6_skl(C),C)
| ~ open(C) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(P,sK6_skl(C))],[f81]) ).
fof(f83,plain,
! [X0] :
( end_point(sK6_skl(X0),X0)
| ~ open(X0) ),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f91,plain,
! [C] : inner_point(sK7_skl(C),C),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(P,sK7_skl(C))],[f10]) ).
fof(f92,plain,
! [X0] : inner_point(sK7_skl(X0),X0),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f132,plain,
! [P,O] :
( start_point(P,O)
<=> ( ! [Q] :
( ordered_by(O,P,Q)
| ~ incident_o(Q,O)
| P = Q )
& incident_o(P,O) ) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f133,plain,
! [P,O] :
( ( ? [Q] :
( ~ ordered_by(O,P,Q)
& incident_o(Q,O)
& P != Q )
| ~ incident_o(P,O)
| start_point(P,O) )
& ( ( ! [Q] :
( ordered_by(O,P,Q)
| ~ incident_o(Q,O)
| P = Q )
& incident_o(P,O) )
| ~ start_point(P,O) ) ),
inference(NNF_transformation,[status(thm)],[f132]) ).
fof(f134,plain,
( ! [P,O] :
( ? [Q] :
( ~ ordered_by(O,P,Q)
& incident_o(Q,O)
& P != Q )
| ~ incident_o(P,O)
| start_point(P,O) )
& ! [P,O] :
( ( ! [Q] :
( ordered_by(O,P,Q)
| ~ incident_o(Q,O)
| P = Q )
& incident_o(P,O) )
| ~ start_point(P,O) ) ),
inference(miniscoping,[status(thm)],[f133]) ).
fof(f135,plain,
( ! [P,O] :
( ( ~ ordered_by(O,P,sK14_skl(O,P))
& incident_o(sK14_skl(O,P),O)
& P != sK14_skl(O,P) )
| ~ incident_o(P,O)
| start_point(P,O) )
& ! [P,O] :
( ( ! [Q] :
( ordered_by(O,P,Q)
| ~ incident_o(Q,O)
| P = Q )
& incident_o(P,O) )
| ~ start_point(P,O) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl]),skolemize(Q,sK14_skl(O,P))],[f134]) ).
fof(f137,plain,
! [X0,X1,X2] :
( ordered_by(X1,X0,X2)
| ~ incident_o(X2,X1)
| X0 = X2
| ~ start_point(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f150,plain,
! [O,P,Q] :
( ( incident_o(Q,O)
& incident_o(P,O) )
| ~ ordered_by(O,P,Q) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f151,plain,
! [X0,X1,X2] :
( incident_o(X1,X0)
| ~ ordered_by(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f150]) ).
fof(f152,plain,
! [X0,X1,X2] :
( incident_o(X2,X0)
| ~ ordered_by(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f150]) ).
fof(f153,plain,
! [O] :
? [C] :
( ! [P] :
( ( ~ incident_c(P,C)
| incident_o(P,O) )
& ( incident_c(P,C)
| ~ incident_o(P,O) ) )
& open(C) ),
inference(NNF_transformation,[status(thm)],[f22]) ).
fof(f154,plain,
! [O] :
? [C] :
( ! [P] :
( ~ incident_c(P,C)
| incident_o(P,O) )
& ! [P] :
( incident_c(P,C)
| ~ incident_o(P,O) )
& open(C) ),
inference(miniscoping,[status(thm)],[f153]) ).
fof(f155,plain,
! [O] :
( ! [P] :
( ~ incident_c(P,sK16_skl(O))
| incident_o(P,O) )
& ! [P] :
( incident_c(P,sK16_skl(O))
| ~ incident_o(P,O) )
& open(sK16_skl(O)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16_skl]),skolemize(C,sK16_skl(O))],[f154]) ).
fof(f156,plain,
! [X0] : open(sK16_skl(X0)),
inference(cnf_transformation,[status(thm)],[f155]) ).
fof(f158,plain,
! [X0,X1] :
( ~ incident_c(X0,sK16_skl(X1))
| incident_o(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f155]) ).
fof(f167,plain,
! [O] : start_point(sK19_skl(O),O),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19_skl]),skolemize(P,sK19_skl(O))],[f24]) ).
fof(f168,plain,
! [X0] : start_point(sK19_skl(X0),X0),
inference(cnf_transformation,[status(thm)],[f167]) ).
fof(f188,plain,
? [O,P] :
( incident_o(P,O)
<~> ? [Q] :
( ordered_by(O,Q,P)
| ordered_by(O,P,Q) ) ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f189,plain,
? [O,P] :
( ( ! [Q] :
( ~ ordered_by(O,Q,P)
& ~ ordered_by(O,P,Q) )
| ~ incident_o(P,O) )
& ( ? [Q] :
( ordered_by(O,Q,P)
| ordered_by(O,P,Q) )
| incident_o(P,O) ) ),
inference(NNF_transformation,[status(thm)],[f188]) ).
fof(f190,plain,
? [O,P] :
( ( ( ! [Q] : ~ ordered_by(O,Q,P)
& ! [Q] : ~ ordered_by(O,P,Q) )
| ~ incident_o(P,O) )
& ( ? [Q] : ordered_by(O,Q,P)
| ? [Q] : ordered_by(O,P,Q)
| incident_o(P,O) ) ),
inference(miniscoping,[status(thm)],[f189]) ).
fof(f191,plain,
( ( ( ! [Q] : ~ ordered_by(sK24_skl,Q,sK25_skl)
& ! [Q] : ~ ordered_by(sK24_skl,sK25_skl,Q) )
| ~ incident_o(sK25_skl,sK24_skl) )
& ( ordered_by(sK24_skl,sK27_skl,sK25_skl)
| ordered_by(sK24_skl,sK25_skl,sK26_skl)
| incident_o(sK25_skl,sK24_skl) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24_skl,sK25_skl,sK26_skl,sK27_skl]),skolemize(O,sK24_skl),skolemize(P,sK25_skl),skolemize(Q,sK26_skl),skolemize(Q,sK27_skl)],[f190]) ).
fof(f192,plain,
( ordered_by(sK24_skl,sK27_skl,sK25_skl)
| ordered_by(sK24_skl,sK25_skl,sK26_skl)
| incident_o(sK25_skl,sK24_skl) ),
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f193,plain,
! [X0] :
( ~ ordered_by(sK24_skl,sK25_skl,X0)
| ~ incident_o(sK25_skl,sK24_skl) ),
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f194,plain,
! [X0] :
( ~ ordered_by(sK24_skl,X0,sK25_skl)
| ~ incident_o(sK25_skl,sK24_skl) ),
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f195,definition,
( sQ0_spl
<=> incident_o(sK25_skl,sK24_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f197,plain,
( sQ0_spl
| ~ incident_o(sK25_skl,sK24_skl) ),
inference(component_clause,[status(thm)],[f195]) ).
fof(f198,definition,
( sQ1_spl
<=> ordered_by(sK24_skl,sK25_skl,sK26_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f199,plain,
( ~ sQ1_spl
| ordered_by(sK24_skl,sK25_skl,sK26_skl) ),
inference(component_clause,[status(thm)],[f198]) ).
fof(f201,definition,
( sQ2_spl
<=> ordered_by(sK24_skl,sK27_skl,sK25_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f202,plain,
( ~ sQ2_spl
| ordered_by(sK24_skl,sK27_skl,sK25_skl) ),
inference(component_clause,[status(thm)],[f201]) ).
fof(f204,plain,
( sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f192,f195,f198,f201]) ).
fof(f205,definition,
! [X0] :
( sQ3_spl
<=> ~ ordered_by(sK24_skl,sK25_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f206,plain,
! [X0] :
( ~ sQ3_spl
| ~ ordered_by(sK24_skl,sK25_skl,X0) ),
inference(component_clause,[status(thm)],[f205]) ).
fof(f208,plain,
( sQ3_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f193,f195,f205]) ).
fof(f209,definition,
! [X0] :
( sQ4_spl
<=> ~ ordered_by(sK24_skl,X0,sK25_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f210,plain,
! [X0] :
( ~ sQ4_spl
| ~ ordered_by(sK24_skl,X0,sK25_skl) ),
inference(component_clause,[status(thm)],[f209]) ).
fof(f212,plain,
( sQ4_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f194,f195,f209]) ).
fof(f220,plain,
( ~ sQ1_spl
| incident_o(sK25_skl,sK24_skl) ),
inference(resolution,[status(thm)],[f151,f199]) ).
fof(f221,plain,
( ~ sQ1_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f220,f197]) ).
fof(f222,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f221]) ).
fof(f223,plain,
! [X0] : incident_c(sK7_skl(X0),X0),
inference(resolution,[status(thm)],[f60,f92]) ).
fof(f224,plain,
! [X0] : ~ end_point(sK7_skl(X0),X0),
inference(resolution,[status(thm)],[f61,f92]) ).
fof(f226,plain,
! [X0] :
( incident_c(sK5_skl(X0),X0)
| closed(X0) ),
inference(resolution,[status(thm)],[f79,f50]) ).
fof(f231,plain,
! [X0] :
( ~ closed(X0)
| ~ open(X0) ),
inference(resolution,[status(thm)],[f83,f78]) ).
fof(f234,plain,
! [X0] :
( closed(sK16_skl(X0))
| incident_o(sK5_skl(sK16_skl(X0)),X0) ),
inference(resolution,[status(thm)],[f158,f226]) ).
fof(f236,plain,
! [X0] : incident_o(sK7_skl(sK16_skl(X0)),X0),
inference(resolution,[status(thm)],[f158,f223]) ).
fof(f321,plain,
! [X0] :
( ~ sQ3_spl
| ~ incident_o(X0,sK24_skl)
| sK25_skl = X0
| ~ start_point(sK25_skl,sK24_skl) ),
inference(resolution,[status(thm)],[f137,f206]) ).
fof(f322,plain,
! [X0] :
( ~ sQ4_spl
| ~ incident_o(sK25_skl,sK24_skl)
| X0 = sK25_skl
| ~ start_point(X0,sK24_skl) ),
inference(resolution,[status(thm)],[f137,f210]) ).
fof(f325,definition,
( sQ5_spl
<=> start_point(sK25_skl,sK24_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f327,plain,
( sQ5_spl
| ~ start_point(sK25_skl,sK24_skl) ),
inference(component_clause,[status(thm)],[f325]) ).
fof(f328,definition,
! [X0] :
( sQ6_spl
<=> ( ~ incident_o(X0,sK24_skl)
| sK25_skl = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f329,plain,
! [X0] :
( ~ sQ6_spl
| ~ incident_o(X0,sK24_skl)
| sK25_skl = X0 ),
inference(component_clause,[status(thm)],[f328]) ).
fof(f331,plain,
( ~ sQ3_spl
| sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f321,f325,f328,f205]) ).
fof(f332,definition,
! [X0] :
( sQ7_spl
<=> ( X0 = sK25_skl
| ~ start_point(X0,sK24_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f333,plain,
! [X0] :
( ~ sQ7_spl
| X0 = sK25_skl
| ~ start_point(X0,sK24_skl) ),
inference(component_clause,[status(thm)],[f332]) ).
fof(f335,plain,
( ~ sQ4_spl
| ~ sQ0_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f322,f332,f195,f209]) ).
fof(f336,plain,
( ~ sQ2_spl
| incident_o(sK25_skl,sK24_skl) ),
inference(resolution,[status(thm)],[f202,f152]) ).
fof(f338,plain,
( ~ sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f336,f195,f201]) ).
fof(f343,plain,
( ~ sQ7_spl
| sK19_skl(sK24_skl) = sK25_skl ),
inference(resolution,[status(thm)],[f333,f168]) ).
fof(f345,plain,
( ~ sQ7_spl
| start_point(sK25_skl,sK24_skl) ),
inference(paramodulation,[status(thm)],[f343,f168]) ).
fof(f346,plain,
( ~ sQ7_spl
| sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f345,f327]) ).
fof(f347,plain,
( ~ sQ7_spl
| sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f346]) ).
fof(f370,plain,
( ~ sQ6_spl
| closed(sK16_skl(sK24_skl))
| sK25_skl = sK5_skl(sK16_skl(sK24_skl)) ),
inference(resolution,[status(thm)],[f329,f234]) ).
fof(f372,plain,
( ~ sQ6_spl
| sK25_skl = sK7_skl(sK16_skl(sK24_skl)) ),
inference(resolution,[status(thm)],[f329,f236]) ).
fof(f383,definition,
( sQ10_spl
<=> sK25_skl = sK5_skl(sK16_skl(sK24_skl)) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f384,plain,
( ~ sQ10_spl
| sK25_skl = sK5_skl(sK16_skl(sK24_skl)) ),
inference(component_clause,[status(thm)],[f383]) ).
fof(f386,definition,
( sQ11_spl
<=> closed(sK16_skl(sK24_skl)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f387,plain,
( ~ sQ11_spl
| closed(sK16_skl(sK24_skl)) ),
inference(component_clause,[status(thm)],[f386]) ).
fof(f389,plain,
( ~ sQ6_spl
| sQ11_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f370,f383,f386,f328]) ).
fof(f402,plain,
( ~ sQ6_spl
| ~ end_point(sK25_skl,sK16_skl(sK24_skl)) ),
inference(paramodulation,[status(thm)],[f372,f224]) ).
fof(f408,definition,
( sQ14_spl
<=> open(sK16_skl(sK24_skl)) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f410,plain,
( sQ14_spl
| ~ open(sK16_skl(sK24_skl)) ),
inference(component_clause,[status(thm)],[f408]) ).
fof(f415,definition,
( sQ16_spl
<=> end_point(sK25_skl,sK16_skl(sK24_skl)) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f416,plain,
( ~ sQ16_spl
| end_point(sK25_skl,sK16_skl(sK24_skl)) ),
inference(component_clause,[status(thm)],[f415]) ).
fof(f419,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f410,f156]) ).
fof(f420,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f419]) ).
fof(f435,plain,
( ~ sQ10_spl
| end_point(sK25_skl,sK16_skl(sK24_skl))
| closed(sK16_skl(sK24_skl)) ),
inference(paramodulation,[status(thm)],[f384,f79]) ).
fof(f438,plain,
( ~ sQ10_spl
| sQ16_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f435,f386,f415,f383]) ).
fof(f440,plain,
( ~ sQ11_spl
| ~ open(sK16_skl(sK24_skl)) ),
inference(resolution,[status(thm)],[f387,f231]) ).
fof(f441,plain,
( ~ sQ11_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f440,f408,f386]) ).
fof(f473,plain,
( ~ sQ16_spl
| ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f416,f402]) ).
fof(f474,plain,
( ~ sQ16_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f473]) ).
fof(f475,plain,
$false,
inference(sat_refutation,[status(thm)],[f204,f208,f212,f222,f331,f335,f338,f347,f389,f420,f438,f441,f474]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO127+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.56 % Computer : n016.cluster.edu
% 0.09/0.56 % Model : x86_64 x86_64
% 0.09/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.56 % Memory : 8046.5625MB
% 0.09/0.56 % OS : Linux 6.8.0-71-generic
% 0.09/0.56 % CPULimit : 300
% 0.09/0.56 % WCLimit : 300
% 0.09/0.56 % DateTime : Sun Sep 20 12:05:53 UTC 2026
% 0.09/0.56 % CPUTime :
% 0.09/0.58 % Drodi V4.1.1
% 0.09/0.61 % Refutation found
% 0.09/0.61 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.64 % Elapsed time: 0.063280 seconds
% 0.12/0.64 % CPU time: 0.192409 seconds
% 0.12/0.64 % Total memory used: 84.731 MB
% 0.12/0.64 % Net memory used: 84.520 MB
%------------------------------------------------------------------------------