%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO192+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 : n009.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 12:24:24 PM UTC 2026
% Result : Theorem 0.17s 0.45s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 51 ( 6 unt; 5 def)
% Number of atoms : 118 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 113 ( 46 ~; 46 |; 8 &)
% ( 5 <=>; 8 =>; 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 : 53 ( 47 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X] : ~ distinct_lines(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y,Z] :
( distinct_lines(X,Y)
=> ( distinct_lines(Y,Z)
| distinct_lines(X,Z) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),Y) ),
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] :
( convergent_lines(X,Y)
=> ( apart_point_and_line(intersection_point(X,Y),Z)
=> ( distinct_lines(Y,Z)
& distinct_lines(X,Z) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
~ ! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( apart_point_and_line(intersection_point(X,Y),Z)
=> ( distinct_lines(Y,Z)
& distinct_lines(X,Z) ) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f18,plain,
! [X0] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f23,plain,
! [X,Y,Z] :
( distinct_lines(Y,Z)
| distinct_lines(X,Z)
| ~ distinct_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f24,plain,
! [X,Y] :
( ! [Z] :
( distinct_lines(Y,Z)
| distinct_lines(X,Z) )
| ~ distinct_lines(X,Y) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f25,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| distinct_lines(X0,X2)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f33,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),X)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f34,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f35,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),Y)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f36,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
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(Y,Z)
| ~ distinct_lines(X,Z) )
& apart_point_and_line(intersection_point(X,Y),Z)
& convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f49,plain,
? [X,Y] :
( ? [Z] :
( ( ~ distinct_lines(Y,Z)
| ~ distinct_lines(X,Z) )
& apart_point_and_line(intersection_point(X,Y),Z) )
& convergent_lines(X,Y) ),
inference(miniscoping,[status(thm)],[f48]) ).
fof(f50,plain,
( ( ~ distinct_lines(sK1_skl,sK2_skl)
| ~ distinct_lines(sK0_skl,sK2_skl) )
& apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl)
& convergent_lines(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)],[f49]) ).
fof(f51,plain,
convergent_lines(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f52,plain,
apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f53,plain,
( ~ distinct_lines(sK1_skl,sK2_skl)
| ~ distinct_lines(sK0_skl,sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f54,definition,
( sQ0_spl
<=> distinct_lines(sK0_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f56,plain,
( sQ0_spl
| ~ distinct_lines(sK0_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f54]) ).
fof(f57,definition,
( sQ1_spl
<=> distinct_lines(sK1_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f59,plain,
( sQ1_spl
| ~ distinct_lines(sK1_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f57]) ).
fof(f60,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f53,f54,f57]) ).
fof(f64,plain,
! [X0] :
( apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X0)
| distinct_lines(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f44,f52]) ).
fof(f75,plain,
( ~ convergent_lines(sK0_skl,sK1_skl)
| distinct_lines(sK2_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f64,f36]) ).
fof(f76,plain,
( ~ convergent_lines(sK0_skl,sK1_skl)
| distinct_lines(sK2_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f64,f34]) ).
fof(f81,definition,
( sQ2_spl
<=> distinct_lines(sK2_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ2_spl
| distinct_lines(sK2_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f84,definition,
( sQ3_spl
<=> convergent_lines(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( sQ3_spl
| ~ convergent_lines(sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f84]) ).
fof(f87,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f75,f81,f84]) ).
fof(f88,definition,
( sQ4_spl
<=> distinct_lines(sK2_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f89,plain,
( ~ sQ4_spl
| distinct_lines(sK2_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f88]) ).
fof(f91,plain,
( ~ sQ3_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f76,f88,f84]) ).
fof(f92,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f86,f51]) ).
fof(f93,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f92]) ).
fof(f97,plain,
! [X0] :
( ~ sQ2_spl
| distinct_lines(sK1_skl,X0)
| distinct_lines(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f82,f25]) ).
fof(f98,plain,
! [X0] :
( ~ sQ4_spl
| distinct_lines(sK0_skl,X0)
| distinct_lines(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f89,f25]) ).
fof(f100,plain,
( ~ sQ2_spl
| distinct_lines(sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f97,f18]) ).
fof(f139,plain,
( ~ sQ4_spl
| distinct_lines(sK0_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f98,f18]) ).
fof(f140,plain,
( ~ sQ4_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f139,f56]) ).
fof(f141,plain,
( ~ sQ4_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f140]) ).
fof(f142,plain,
( sQ1_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f59,f100]) ).
fof(f143,plain,
( sQ1_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f142]) ).
fof(f144,plain,
$false,
inference(sat_refutation,[status(thm)],[f60,f87,f91,f93,f141,f143]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO192+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n009.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sun Sep 20 13:13:43 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.45 % Drodi V4.1.1
% 0.17/0.45 % Refutation found
% 0.17/0.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/0.47 % Elapsed time: 0.028427 seconds
% 0.22/0.47 % CPU time: 0.047913 seconds
% 0.22/0.47 % Total memory used: 2.728 MB
% 0.22/0.47 % Net memory used: 2.692 MB
%------------------------------------------------------------------------------