%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO112+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 : n026.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 12:24:06 PM UTC 2026
% Result : Theorem 0.22s 0.51s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 6 unt; 3 def)
% Number of atoms : 129 ( 12 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 169 ( 78 ~; 64 |; 21 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 4 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-4 aty)
% Number of variables : 82 ( 75 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
! [C,P,Q,R] :
( between_c(C,P,Q,R)
<=> ( ? [Cpp] :
( inner_point(Q,Cpp)
& end_point(R,Cpp)
& end_point(P,Cpp)
& part_of(Cpp,C) )
& P != R ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,conjecture,
! [C,P,Q,R] :
( between_c(C,P,Q,R)
=> between_c(C,R,Q,P) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
~ ! [C,P,Q,R] :
( between_c(C,P,Q,R)
=> between_c(C,R,Q,P) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f105,plain,
! [C,P,Q,R] :
( ( ! [Cpp] :
( ~ inner_point(Q,Cpp)
| ~ end_point(R,Cpp)
| ~ end_point(P,Cpp)
| ~ part_of(Cpp,C) )
| P = R
| between_c(C,P,Q,R) )
& ( ( ? [Cpp] :
( inner_point(Q,Cpp)
& end_point(R,Cpp)
& end_point(P,Cpp)
& part_of(Cpp,C) )
& P != R )
| ~ between_c(C,P,Q,R) ) ),
inference(NNF_transformation,[status(thm)],[f17]) ).
fof(f106,plain,
( ! [C,P,Q,R] :
( ! [Cpp] :
( ~ inner_point(Q,Cpp)
| ~ end_point(R,Cpp)
| ~ end_point(P,Cpp)
| ~ part_of(Cpp,C) )
| P = R
| between_c(C,P,Q,R) )
& ! [C,P,Q,R] :
( ( ? [Cpp] :
( inner_point(Q,Cpp)
& end_point(R,Cpp)
& end_point(P,Cpp)
& part_of(Cpp,C) )
& P != R )
| ~ between_c(C,P,Q,R) ) ),
inference(miniscoping,[status(thm)],[f105]) ).
fof(f107,plain,
( ! [C,P,Q,R] :
( ! [Cpp] :
( ~ inner_point(Q,Cpp)
| ~ end_point(R,Cpp)
| ~ end_point(P,Cpp)
| ~ part_of(Cpp,C) )
| P = R
| between_c(C,P,Q,R) )
& ! [C,P,Q,R] :
( ( inner_point(Q,sK13_skl(R,Q,P,C))
& end_point(R,sK13_skl(R,Q,P,C))
& end_point(P,sK13_skl(R,Q,P,C))
& part_of(sK13_skl(R,Q,P,C),C)
& P != R )
| ~ between_c(C,P,Q,R) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl]),skolemize(Cpp,sK13_skl(R,Q,P,C))],[f106]) ).
fof(f108,plain,
! [X0,X1,X2,X3] :
( X1 != X3
| ~ between_c(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f109,plain,
! [X0,X1,X2,X3] :
( part_of(sK13_skl(X3,X2,X1,X0),X0)
| ~ between_c(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f110,plain,
! [X0,X1,X2,X3] :
( end_point(X1,sK13_skl(X3,X2,X1,X0))
| ~ between_c(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f111,plain,
! [X0,X1,X2,X3] :
( end_point(X3,sK13_skl(X3,X2,X1,X0))
| ~ between_c(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f112,plain,
! [X0,X1,X2,X3] :
( inner_point(X2,sK13_skl(X3,X2,X1,X0))
| ~ between_c(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f113,plain,
! [X0,X1,X2,X3,X4] :
( ~ inner_point(X2,X4)
| ~ end_point(X3,X4)
| ~ end_point(X1,X4)
| ~ part_of(X4,X0)
| X1 = X3
| between_c(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f114,plain,
? [C,P,Q,R] :
( ~ between_c(C,R,Q,P)
& between_c(C,P,Q,R) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f115,plain,
( ~ between_c(sK14_skl,sK17_skl,sK16_skl,sK15_skl)
& between_c(sK14_skl,sK15_skl,sK16_skl,sK17_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl,sK15_skl,sK16_skl,sK17_skl]),skolemize(C,sK14_skl),skolemize(P,sK15_skl),skolemize(Q,sK16_skl),skolemize(R,sK17_skl)],[f114]) ).
fof(f116,plain,
between_c(sK14_skl,sK15_skl,sK16_skl,sK17_skl),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f117,plain,
~ between_c(sK14_skl,sK17_skl,sK16_skl,sK15_skl),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f122,plain,
! [X0,X1,X2] : ~ between_c(X0,X1,X2,X1),
inference(destructive_equality_resolution,[status(thm)],[f108]) ).
fof(f123,plain,
! [X0] :
( ~ inner_point(sK16_skl,X0)
| ~ end_point(sK15_skl,X0)
| ~ end_point(sK17_skl,X0)
| ~ part_of(X0,sK14_skl)
| sK17_skl = sK15_skl ),
inference(resolution,[status(thm)],[f113,f117]) ).
fof(f125,definition,
( sQ0_spl
<=> sK17_skl = sK15_skl ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ0_spl
| sK17_skl = sK15_skl ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f128,definition,
! [X0] :
( sQ1_spl
<=> ( ~ inner_point(sK16_skl,X0)
| ~ end_point(sK15_skl,X0)
| ~ end_point(sK17_skl,X0)
| ~ part_of(X0,sK14_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f129,plain,
! [X0] :
( ~ sQ1_spl
| ~ inner_point(sK16_skl,X0)
| ~ end_point(sK15_skl,X0)
| ~ end_point(sK17_skl,X0)
| ~ part_of(X0,sK14_skl) ),
inference(component_clause,[status(thm)],[f128]) ).
fof(f131,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f123,f125,f128]) ).
fof(f133,plain,
( ~ sQ0_spl
| between_c(sK14_skl,sK15_skl,sK16_skl,sK15_skl) ),
inference(backward_demodulation,[status(thm)],[f126,f116]) ).
fof(f134,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f133,f122]) ).
fof(f135,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f134]) ).
fof(f226,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ end_point(sK15_skl,sK13_skl(X2,sK16_skl,X1,X0))
| ~ end_point(sK17_skl,sK13_skl(X2,sK16_skl,X1,X0))
| ~ part_of(sK13_skl(X2,sK16_skl,X1,X0),sK14_skl)
| ~ between_c(X0,X1,sK16_skl,X2) ),
inference(resolution,[status(thm)],[f112,f129]) ).
fof(f229,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ between_c(sK14_skl,X0,sK16_skl,X1)
| ~ end_point(sK15_skl,sK13_skl(X1,sK16_skl,X0,sK14_skl))
| ~ end_point(sK17_skl,sK13_skl(X1,sK16_skl,X0,sK14_skl))
| ~ between_c(sK14_skl,X0,sK16_skl,X1) ),
inference(resolution,[status(thm)],[f226,f109]) ).
fof(f230,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ end_point(sK15_skl,sK13_skl(X1,sK16_skl,X0,sK14_skl))
| ~ end_point(sK17_skl,sK13_skl(X1,sK16_skl,X0,sK14_skl))
| ~ between_c(sK14_skl,X0,sK16_skl,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f229]) ).
fof(f231,plain,
! [X0] :
( ~ sQ1_spl
| ~ between_c(sK14_skl,X0,sK16_skl,sK17_skl)
| ~ end_point(sK15_skl,sK13_skl(sK17_skl,sK16_skl,X0,sK14_skl))
| ~ between_c(sK14_skl,X0,sK16_skl,sK17_skl) ),
inference(resolution,[status(thm)],[f230,f111]) ).
fof(f233,plain,
! [X0] :
( ~ sQ1_spl
| ~ end_point(sK15_skl,sK13_skl(sK17_skl,sK16_skl,X0,sK14_skl))
| ~ between_c(sK14_skl,X0,sK16_skl,sK17_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f231]) ).
fof(f235,plain,
( ~ sQ1_spl
| ~ between_c(sK14_skl,sK15_skl,sK16_skl,sK17_skl)
| ~ between_c(sK14_skl,sK15_skl,sK16_skl,sK17_skl) ),
inference(resolution,[status(thm)],[f233,f110]) ).
fof(f236,definition,
( sQ2_spl
<=> between_c(sK14_skl,sK15_skl,sK16_skl,sK17_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f238,plain,
( sQ2_spl
| ~ between_c(sK14_skl,sK15_skl,sK16_skl,sK17_skl) ),
inference(component_clause,[status(thm)],[f236]) ).
fof(f239,plain,
( ~ sQ1_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f235,f236,f128]) ).
fof(f240,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f238,f116]) ).
fof(f241,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f240]) ).
fof(f242,plain,
$false,
inference(sat_refutation,[status(thm)],[f131,f135,f239,f241]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO112+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.47 % Computer : n026.cluster.edu
% 0.22/0.47 % Model : x86_64 x86_64
% 0.22/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.47 % Memory : 8046.5625MB
% 0.22/0.47 % OS : Linux 6.8.0-71-generic
% 0.22/0.47 % CPULimit : 300
% 0.22/0.47 % WCLimit : 300
% 0.22/0.47 % DateTime : Sun Sep 20 11:25:07 UTC 2026
% 0.22/0.47 % CPUTime :
% 0.22/0.49 % Drodi V4.1.1
% 0.22/0.51 % Refutation found
% 0.22/0.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.22/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.25/0.57 % Elapsed time: 0.095014 seconds
% 0.25/0.57 % CPU time: 0.182313 seconds
% 0.25/0.57 % Total memory used: 34.004 MB
% 0.25/0.57 % Net memory used: 33.924 MB
%------------------------------------------------------------------------------