%------------------------------------------------------------------------------
% 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/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 : Unsatisfiable 0.09s 0.55s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 40 ( 8 unt; 3 def)
% Number of atoms : 105 ( 9 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 138 ( 73 ~; 62 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 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 : 74 ( 74 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f49,axiom,
! [A,B,C,D] :
( B != D
| ~ between_c(A,B,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,axiom,
! [A,B,C,D] :
( part_of(ax1_sk1(D,C,B,A),A)
| ~ between_c(A,B,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,axiom,
! [A,B,C,D] :
( end_point(B,ax1_sk1(D,C,B,A))
| ~ between_c(A,B,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f52,axiom,
! [A,B,C,D] :
( end_point(D,ax1_sk1(D,C,B,A))
| ~ between_c(A,B,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,axiom,
! [A,B,C,D] :
( inner_point(C,ax1_sk1(D,C,B,A))
| ~ between_c(A,B,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,axiom,
! [A,B,C,D,E] :
( between_c(D,A,E,B)
| ~ inner_point(E,C)
| ~ end_point(B,C)
| ~ end_point(A,C)
| ~ part_of(C,D)
| A = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f55,negated_conjecture,
between_c(sk15,sk16,sk17,sk18),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f56,negated_conjecture,
~ between_c(sk15,sk18,sk17,sk16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f121,plain,
! [B,D] :
( B != D
| ! [A,C] : ~ between_c(A,B,C,D) ),
inference(miniscoping,[status(thm)],[f49]) ).
fof(f122,plain,
! [X0,X1,X2,X3] :
( X1 != X3
| ~ between_c(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f123,plain,
! [X0,X1,X2,X3] :
( part_of(ax1_sk1(X3,X2,X1,X0),X0)
| ~ between_c(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f124,plain,
! [X0,X1,X2,X3] :
( end_point(X1,ax1_sk1(X3,X2,X1,X0))
| ~ between_c(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f125,plain,
! [X0,X1,X2,X3] :
( end_point(X3,ax1_sk1(X3,X2,X1,X0))
| ~ between_c(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f126,plain,
! [X0,X1,X2,X3] :
( inner_point(X2,ax1_sk1(X3,X2,X1,X0))
| ~ between_c(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f127,plain,
! [A,B,D,E] :
( between_c(D,A,E,B)
| ! [C] :
( ~ inner_point(E,C)
| ~ end_point(B,C)
| ~ end_point(A,C)
| ~ part_of(C,D)
| A = B ) ),
inference(miniscoping,[status(thm)],[f54]) ).
fof(f128,plain,
! [X0,X1,X2,X3,X4] :
( between_c(X3,X0,X4,X1)
| ~ inner_point(X4,X2)
| ~ end_point(X1,X2)
| ~ end_point(X0,X2)
| ~ part_of(X2,X3)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f129,plain,
between_c(sk15,sk16,sk17,sk18),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f130,plain,
~ between_c(sk15,sk18,sk17,sk16),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f135,plain,
! [X0,X1,X2] : ~ between_c(X0,X1,X2,X1),
inference(destructive_equality_resolution,[status(thm)],[f122]) ).
fof(f136,plain,
! [X0] :
( ~ inner_point(sk17,X0)
| ~ end_point(sk16,X0)
| ~ end_point(sk18,X0)
| ~ part_of(X0,sk15)
| sk18 = sk16 ),
inference(resolution,[status(thm)],[f128,f130]) ).
fof(f138,definition,
( sQ0_spl
<=> sk18 = sk16 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f139,plain,
( ~ sQ0_spl
| sk18 = sk16 ),
inference(component_clause,[status(thm)],[f138]) ).
fof(f141,definition,
! [X0] :
( sQ1_spl
<=> ( ~ inner_point(sk17,X0)
| ~ end_point(sk16,X0)
| ~ end_point(sk18,X0)
| ~ part_of(X0,sk15) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f142,plain,
! [X0] :
( ~ sQ1_spl
| ~ inner_point(sk17,X0)
| ~ end_point(sk16,X0)
| ~ end_point(sk18,X0)
| ~ part_of(X0,sk15) ),
inference(component_clause,[status(thm)],[f141]) ).
fof(f144,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f136,f138,f141]) ).
fof(f146,plain,
( ~ sQ0_spl
| between_c(sk15,sk16,sk17,sk16) ),
inference(backward_demodulation,[status(thm)],[f139,f129]) ).
fof(f147,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f146,f135]) ).
fof(f148,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f147]) ).
fof(f230,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ end_point(sk16,ax1_sk1(X2,sk17,X1,X0))
| ~ end_point(sk18,ax1_sk1(X2,sk17,X1,X0))
| ~ part_of(ax1_sk1(X2,sk17,X1,X0),sk15)
| ~ between_c(X0,X1,sk17,X2) ),
inference(resolution,[status(thm)],[f126,f142]) ).
fof(f233,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ between_c(sk15,X0,sk17,X1)
| ~ end_point(sk16,ax1_sk1(X1,sk17,X0,sk15))
| ~ end_point(sk18,ax1_sk1(X1,sk17,X0,sk15))
| ~ between_c(sk15,X0,sk17,X1) ),
inference(resolution,[status(thm)],[f230,f123]) ).
fof(f234,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ end_point(sk16,ax1_sk1(X1,sk17,X0,sk15))
| ~ end_point(sk18,ax1_sk1(X1,sk17,X0,sk15))
| ~ between_c(sk15,X0,sk17,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f233]) ).
fof(f235,plain,
! [X0] :
( ~ sQ1_spl
| ~ between_c(sk15,X0,sk17,sk18)
| ~ end_point(sk16,ax1_sk1(sk18,sk17,X0,sk15))
| ~ between_c(sk15,X0,sk17,sk18) ),
inference(resolution,[status(thm)],[f234,f125]) ).
fof(f237,plain,
! [X0] :
( ~ sQ1_spl
| ~ end_point(sk16,ax1_sk1(sk18,sk17,X0,sk15))
| ~ between_c(sk15,X0,sk17,sk18) ),
inference(duplicate_literals_removal,[status(thm)],[f235]) ).
fof(f239,plain,
( ~ sQ1_spl
| ~ between_c(sk15,sk16,sk17,sk18)
| ~ between_c(sk15,sk16,sk17,sk18) ),
inference(resolution,[status(thm)],[f237,f124]) ).
fof(f240,definition,
( sQ2_spl
<=> between_c(sk15,sk16,sk17,sk18) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f242,plain,
( sQ2_spl
| ~ between_c(sk15,sk16,sk17,sk18) ),
inference(component_clause,[status(thm)],[f240]) ).
fof(f243,plain,
( ~ sQ1_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f239,f240,f141]) ).
fof(f244,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f242,f129]) ).
fof(f245,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f244]) ).
fof(f246,plain,
$false,
inference(sat_refutation,[status(thm)],[f144,f148,f243,f245]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO112-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.51 % Computer : n020.cluster.edu
% 0.09/0.51 % Model : x86_64 x86_64
% 0.09/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.51 % Memory : 8046.5625MB
% 0.09/0.51 % OS : Linux 6.8.0-71-generic
% 0.09/0.51 % CPULimit : 300
% 0.09/0.51 % WCLimit : 300
% 0.09/0.51 % DateTime : Sun Sep 20 11:28:47 UTC 2026
% 0.09/0.51 % CPUTime :
% 0.09/0.52 % Drodi V4.1.1
% 0.09/0.55 % Refutation found
% 0.09/0.55 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.58 % Elapsed time: 0.057765 seconds
% 0.09/0.58 % CPU time: 0.192451 seconds
% 0.09/0.58 % Total memory used: 72.848 MB
% 0.09/0.58 % Net memory used: 72.658 MB
%------------------------------------------------------------------------------