%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO183+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 12:24:20 PM UTC 2026
% Result : Theorem 0.13s 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 66 ( 9 unt; 4 def)
% Number of atoms : 168 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 161 ( 59 ~; 70 |; 19 &)
% ( 6 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 98 ( 90 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : ~ distinct_points(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( distinct_points(Y,Z)
| distinct_points(X,Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(X,line_connecting(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( apart_point_and_line(Z,Y)
| distinct_points(X,Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [X,Y] :
( equal_lines(X,Y)
<=> ~ distinct_lines(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [X,Y] :
( incident_point_and_line(X,Y)
<=> ~ apart_point_and_line(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,conjecture,
! [X,Y,U,V] :
( ( equal_lines(U,line_connecting(X,Y))
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> ( incident_point_and_line(Y,U)
& incident_point_and_line(X,U) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
~ ! [X,Y,U,V] :
( ( equal_lines(U,line_connecting(X,Y))
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> ( incident_point_and_line(Y,U)
& incident_point_and_line(X,U) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f41,plain,
! [X,Y,Z] :
( distinct_points(Y,Z)
| distinct_points(X,Z)
| ~ distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f42,plain,
! [X,Y] :
( ! [Z] :
( distinct_points(Y,Z)
| distinct_points(X,Z) )
| ~ distinct_points(X,Y) ),
inference(miniscoping,[status(thm)],[f41]) ).
fof(f43,plain,
! [X0,X1,X2] :
( distinct_points(X1,X2)
| distinct_points(X0,X2)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f50,plain,
! [X,Y] :
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f51,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f52,plain,
! [X,Y] :
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f53,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f60,plain,
! [X,Y,Z] :
( apart_point_and_line(Z,Y)
| distinct_points(X,Z)
| ~ apart_point_and_line(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f61,plain,
! [X,Y] :
( ! [Z] :
( apart_point_and_line(Z,Y)
| distinct_points(X,Z) )
| ~ apart_point_and_line(X,Y) ),
inference(miniscoping,[status(thm)],[f60]) ).
fof(f62,plain,
! [X0,X1,X2] :
( apart_point_and_line(X2,X1)
| distinct_points(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f63,plain,
! [X,Y,Z] :
( apart_point_and_line(X,Z)
| distinct_lines(Y,Z)
| ~ apart_point_and_line(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f64,plain,
! [X,Y] :
( ! [Z] :
( apart_point_and_line(X,Z)
| distinct_lines(Y,Z) )
| ~ apart_point_and_line(X,Y) ),
inference(miniscoping,[status(thm)],[f63]) ).
fof(f65,plain,
! [X0,X1,X2] :
( apart_point_and_line(X0,X2)
| distinct_lines(X1,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f111,plain,
! [X,Y] :
( ( distinct_lines(X,Y)
| equal_lines(X,Y) )
& ( ~ distinct_lines(X,Y)
| ~ equal_lines(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f32]) ).
fof(f112,plain,
( ! [X,Y] :
( distinct_lines(X,Y)
| equal_lines(X,Y) )
& ! [X,Y] :
( ~ distinct_lines(X,Y)
| ~ equal_lines(X,Y) ) ),
inference(miniscoping,[status(thm)],[f111]) ).
fof(f113,plain,
! [X0,X1] :
( ~ distinct_lines(X0,X1)
| ~ equal_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f119,plain,
! [X,Y] :
( ( apart_point_and_line(X,Y)
| incident_point_and_line(X,Y) )
& ( ~ apart_point_and_line(X,Y)
| ~ incident_point_and_line(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f34]) ).
fof(f120,plain,
( ! [X,Y] :
( apart_point_and_line(X,Y)
| incident_point_and_line(X,Y) )
& ! [X,Y] :
( ~ apart_point_and_line(X,Y)
| ~ incident_point_and_line(X,Y) ) ),
inference(miniscoping,[status(thm)],[f119]) ).
fof(f122,plain,
! [X0,X1] :
( apart_point_and_line(X0,X1)
| incident_point_and_line(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f127,plain,
? [X,Y,U,V] :
( ( ~ incident_point_and_line(Y,U)
| ~ incident_point_and_line(X,U) )
& equal_lines(U,line_connecting(X,Y))
& convergent_lines(U,V)
& distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f128,plain,
? [X,Y,U] :
( ( ~ incident_point_and_line(Y,U)
| ~ incident_point_and_line(X,U) )
& equal_lines(U,line_connecting(X,Y))
& ? [V] : convergent_lines(U,V)
& distinct_points(X,Y) ),
inference(miniscoping,[status(thm)],[f127]) ).
fof(f129,plain,
( ( ~ incident_point_and_line(sK1_skl,sK2_skl)
| ~ incident_point_and_line(sK0_skl,sK2_skl) )
& equal_lines(sK2_skl,line_connecting(sK0_skl,sK1_skl))
& convergent_lines(sK2_skl,sK3_skl)
& distinct_points(sK0_skl,sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl),skolemize(U,sK2_skl),skolemize(V,sK3_skl)],[f128]) ).
fof(f130,plain,
distinct_points(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f132,plain,
equal_lines(sK2_skl,line_connecting(sK0_skl,sK1_skl)),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f133,plain,
( ~ incident_point_and_line(sK1_skl,sK2_skl)
| ~ incident_point_and_line(sK0_skl,sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f144,definition,
( sQ0_spl
<=> incident_point_and_line(sK0_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( sQ0_spl
| ~ incident_point_and_line(sK0_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f144]) ).
fof(f147,definition,
( sQ1_spl
<=> incident_point_and_line(sK1_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f149,plain,
( sQ1_spl
| ~ incident_point_and_line(sK1_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f147]) ).
fof(f150,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f133,f144,f147]) ).
fof(f152,plain,
~ distinct_lines(sK2_skl,line_connecting(sK0_skl,sK1_skl)),
inference(resolution,[status(thm)],[f113,f132]) ).
fof(f154,plain,
( sQ0_spl
| apart_point_and_line(sK0_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f122,f146]) ).
fof(f161,plain,
! [X0] :
( sQ0_spl
| apart_point_and_line(X0,sK2_skl)
| distinct_points(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f62,f154]) ).
fof(f167,plain,
! [X0,X1] :
( sQ0_spl
| distinct_points(X0,X1)
| distinct_points(sK0_skl,X1)
| apart_point_and_line(X0,sK2_skl) ),
inference(resolution,[status(thm)],[f161,f43]) ).
fof(f177,plain,
! [X0,X1] :
( sQ0_spl
| distinct_points(X1,X0)
| distinct_points(sK0_skl,X0)
| apart_point_and_line(sK0_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f167,f43]) ).
fof(f183,definition,
( sQ2_spl
<=> apart_point_and_line(sK0_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f184,plain,
( ~ sQ2_spl
| apart_point_and_line(sK0_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f183]) ).
fof(f186,definition,
! [X0,X1] :
( sQ3_spl
<=> ( distinct_points(X1,X0)
| distinct_points(sK0_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f187,plain,
! [X0,X1] :
( ~ sQ3_spl
| distinct_points(X1,X0)
| distinct_points(sK0_skl,X0) ),
inference(component_clause,[status(thm)],[f186]) ).
fof(f189,plain,
( sQ0_spl
| sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f177,f183,f186,f144]) ).
fof(f190,plain,
( sQ1_spl
| apart_point_and_line(sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f149,f122]) ).
fof(f193,plain,
! [X0] :
( ~ sQ3_spl
| distinct_points(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f187,f38]) ).
fof(f195,plain,
( ~ sQ3_spl
| $false ),
inference(resolution,[status(thm)],[f193,f38]) ).
fof(f196,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f195]) ).
fof(f216,plain,
! [X0] :
( ~ sQ2_spl
| apart_point_and_line(sK0_skl,X0)
| distinct_lines(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f65,f184]) ).
fof(f217,plain,
! [X0] :
( sQ1_spl
| apart_point_and_line(sK1_skl,X0)
| distinct_lines(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f65,f190]) ).
fof(f218,plain,
( ~ sQ2_spl
| apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(resolution,[status(thm)],[f216,f152]) ).
fof(f223,plain,
( sQ1_spl
| apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(resolution,[status(thm)],[f217,f152]) ).
fof(f228,plain,
( ~ sQ2_spl
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f218,f51]) ).
fof(f231,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f228,f130]) ).
fof(f232,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f231]) ).
fof(f234,plain,
( sQ1_spl
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f223,f53]) ).
fof(f237,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f234,f130]) ).
fof(f238,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f237]) ).
fof(f239,plain,
$false,
inference(sat_refutation,[status(thm)],[f150,f189,f196,f232,f238]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO183+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n001.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 13:13:58 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.13/0.40 % Refutation found
% 0.13/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.43 % Elapsed time: 0.055204 seconds
% 0.13/0.43 % CPU time: 0.232217 seconds
% 0.13/0.43 % Total memory used: 17.487 MB
% 0.13/0.43 % Net memory used: 17.227 MB
%------------------------------------------------------------------------------