%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO179+1 : TPTP v9.3.1. Released v3.3.0.
% 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 12:24:18 PM UTC 2026
% Result : Theorem 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 49 ( 4 unt; 5 def)
% Number of atoms : 112 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 103 ( 40 ~; 44 |; 8 &)
% ( 5 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 47 ( 44 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(X,line_connecting(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,conjecture,
! [X,Y,Z] :
( ( apart_point_and_line(Z,line_connecting(X,Y))
& distinct_points(X,Y) )
=> ( distinct_lines(line_connecting(X,Y),line_connecting(Z,Y))
& distinct_lines(line_connecting(X,Y),line_connecting(Z,X)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
~ ! [X,Y,Z] :
( ( apart_point_and_line(Z,line_connecting(X,Y))
& distinct_points(X,Y) )
=> ( distinct_lines(line_connecting(X,Y),line_connecting(Z,Y))
& distinct_lines(line_connecting(X,Y),line_connecting(Z,X)) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f29,plain,
! [X,Y] :
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f30,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f31,plain,
! [X,Y] :
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f32,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f39,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(f40,plain,
! [X,Y] :
( ! [Z] :
( apart_point_and_line(Z,Y)
| distinct_points(X,Z) )
| ~ apart_point_and_line(X,Y) ),
inference(miniscoping,[status(thm)],[f39]) ).
fof(f41,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)],[f40]) ).
fof(f42,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(f43,plain,
! [X,Y] :
( ! [Z] :
( apart_point_and_line(X,Z)
| distinct_lines(Y,Z) )
| ~ apart_point_and_line(X,Y) ),
inference(miniscoping,[status(thm)],[f42]) ).
fof(f44,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)],[f43]) ).
fof(f48,plain,
? [X,Y,Z] :
( ( ~ distinct_lines(line_connecting(X,Y),line_connecting(Z,Y))
| ~ distinct_lines(line_connecting(X,Y),line_connecting(Z,X)) )
& apart_point_and_line(Z,line_connecting(X,Y))
& distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f49,plain,
( ( ~ distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK2_skl,sK1_skl))
| ~ distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK2_skl,sK0_skl)) )
& apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl))
& distinct_points(sK0_skl,sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl),skolemize(Z,sK2_skl)],[f48]) ).
fof(f50,plain,
distinct_points(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f51,plain,
apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl)),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f52,plain,
( ~ distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK2_skl,sK1_skl))
| ~ distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK2_skl,sK0_skl)) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f53,definition,
( sQ0_spl
<=> distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK2_skl,sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f55,plain,
( sQ0_spl
| ~ distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK2_skl,sK0_skl)) ),
inference(component_clause,[status(thm)],[f53]) ).
fof(f56,definition,
( sQ1_spl
<=> distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK2_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f58,plain,
( sQ1_spl
| ~ distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK2_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f56]) ).
fof(f59,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f52,f53,f56]) ).
fof(f63,plain,
! [X0] :
( apart_point_and_line(X0,line_connecting(sK0_skl,sK1_skl))
| distinct_points(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f41,f51]) ).
fof(f64,plain,
! [X0] :
( apart_point_and_line(sK2_skl,X0)
| distinct_lines(line_connecting(sK0_skl,sK1_skl),X0) ),
inference(resolution,[status(thm)],[f44,f51]) ).
fof(f82,definition,
( sQ4_spl
<=> distinct_points(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f84,plain,
( sQ4_spl
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f82]) ).
fof(f92,plain,
( ~ distinct_points(sK0_skl,sK1_skl)
| distinct_points(sK2_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f63,f32]) ).
fof(f93,plain,
( ~ distinct_points(sK0_skl,sK1_skl)
| distinct_points(sK2_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f63,f30]) ).
fof(f96,definition,
( sQ6_spl
<=> distinct_points(sK2_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f97,plain,
( ~ sQ6_spl
| distinct_points(sK2_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f96]) ).
fof(f99,plain,
( ~ sQ4_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f92,f96,f82]) ).
fof(f100,definition,
( sQ7_spl
<=> distinct_points(sK2_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f101,plain,
( ~ sQ7_spl
| distinct_points(sK2_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f100]) ).
fof(f103,plain,
( ~ sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f93,f100,f82]) ).
fof(f104,plain,
( sQ0_spl
| apart_point_and_line(sK2_skl,line_connecting(sK2_skl,sK0_skl)) ),
inference(resolution,[status(thm)],[f64,f55]) ).
fof(f114,plain,
( sQ0_spl
| ~ distinct_points(sK2_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f104,f30]) ).
fof(f117,plain,
( sQ0_spl
| ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f114,f101]) ).
fof(f118,plain,
( sQ0_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f117]) ).
fof(f119,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f84,f50]) ).
fof(f120,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f119]) ).
fof(f128,plain,
( sQ1_spl
| apart_point_and_line(sK2_skl,line_connecting(sK2_skl,sK1_skl)) ),
inference(resolution,[status(thm)],[f58,f64]) ).
fof(f132,plain,
( sQ1_spl
| ~ distinct_points(sK2_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f128,f30]) ).
fof(f135,plain,
( sQ1_spl
| ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f132,f97]) ).
fof(f136,plain,
( sQ1_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f135]) ).
fof(f137,plain,
$false,
inference(sat_refutation,[status(thm)],[f59,f99,f103,f118,f120,f136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO179+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n011.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sun Sep 20 13:01:10 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.12/0.35 % Drodi V4.1.1
% 0.12/0.37 % Refutation found
% 0.12/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.39 % Elapsed time: 0.038215 seconds
% 0.12/0.39 % CPU time: 0.097351 seconds
% 0.12/0.39 % Total memory used: 12.868 MB
% 0.12/0.39 % Net memory used: 12.559 MB
%------------------------------------------------------------------------------