%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO187+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 : Sun Sep 27 07:17:21 AM UTC 2026
% Result : Theorem 0.17s 0.48s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 12 unt; 0 def)
% Number of atoms : 64 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 60 ( 24 ~; 14 |; 16 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 55 ( 9 sgn 23 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart2,axiom,
! [X] : ~ distinct_lines(X,X),
file('theBenchmark.p',apart2) ).
fof(apart5,axiom,
! [X,Y,Z] :
( distinct_lines(X,Y)
=> ( distinct_lines(Y,Z)
| distinct_lines(X,Z) ) ),
file('theBenchmark.p',apart5) ).
fof(ceq2,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ) ),
file('theBenchmark.p',ceq2) ).
fof(p1,axiom,
! [X,Y] :
( distinct_lines(X,Y)
=> convergent_lines(X,Y) ),
file('theBenchmark.p',p1) ).
fof(cp1,axiom,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
file('theBenchmark.p',cp1) ).
fof(cp2,axiom,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
file('theBenchmark.p',cp2) ).
fof(a4,axiom,
! [X,Y] :
( incident_point_and_line(X,Y)
<=> ~ apart_point_and_line(X,Y) ),
file('theBenchmark.p',a4) ).
fof(con,conjecture,
! [X,Y,U,V] :
( ( incident_point_and_line(Y,line_connecting(U,V))
& incident_point_and_line(X,line_connecting(U,V))
& distinct_points(U,V)
& distinct_points(X,Y) )
=> ( incident_point_and_line(V,line_connecting(X,Y))
& incident_point_and_line(U,line_connecting(X,Y)) ) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [X,Y,U,V] :
( ( incident_point_and_line(Y,line_connecting(U,V))
& incident_point_and_line(X,line_connecting(U,V))
& distinct_points(U,V)
& distinct_points(X,Y) )
=> ( incident_point_and_line(V,line_connecting(X,Y))
& incident_point_and_line(U,line_connecting(X,Y)) ) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_46,plain,
~ distinct_lines(A,A),
inference(clausify,[status(thm)],[apart2]) ).
cnf(c_49,plain,
( distinct_lines(B,C)
| distinct_lines(A,C)
| ~ distinct_lines(A,B) ),
inference(clausify,[status(thm)],[apart5]) ).
cnf(c_57,plain,
( apart_point_and_line(A,C)
| distinct_lines(B,C)
| ~ apart_point_and_line(A,B) ),
inference(clausify,[status(thm)],[ceq2]) ).
cnf(c_59,plain,
( convergent_lines(A,B)
| ~ distinct_lines(A,B) ),
inference(clausify,[status(thm)],[p1]) ).
cnf(c_60,plain,
~ convergent_lines(parallel_through_point(A,B),A),
inference(clausify,[status(thm)],[cp1]) ).
cnf(c_61,plain,
~ apart_point_and_line(A,parallel_through_point(B,A)),
inference(clausify,[status(thm)],[cp2]) ).
cnf(c_79,plain,
( apart_point_and_line(A,B)
| incident_point_and_line(A,B) ),
inference(clausify,[status(thm)],[a4]) ).
fof(nnf_36,plain,
? [X,Y,U,V] :
( ( ~ incident_point_and_line(V,line_connecting(X,Y))
| ~ incident_point_and_line(U,line_connecting(X,Y)) )
& incident_point_and_line(Y,line_connecting(U,V))
& incident_point_and_line(X,line_connecting(U,V))
& distinct_points(U,V)
& distinct_points(X,Y) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( ( ~ incident_point_and_line(sK3,line_connecting(sK1,sK2))
| ~ incident_point_and_line(sK0,line_connecting(sK1,sK2)) )
& incident_point_and_line(sK2,line_connecting(sK0,sK3))
& incident_point_and_line(sK1,line_connecting(sK0,sK3))
& distinct_points(sK0,sK3)
& distinct_points(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK0,sK3]),skolemize(X,sK1),skolemize(Y,sK2),skolemize(U,sK0),skolemize(V,sK3)],[nnf_36]) ).
cnf(c_84,negated_conjecture,
( ~ incident_point_and_line(sK3,line_connecting(sK1,sK2))
| ~ incident_point_and_line(sK0,line_connecting(sK1,sK2)) ),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_85,plain,
~ distinct_lines(parallel_through_point(A,B),A),
inference(resolve,[status(thm)],[c_59,c_60]) ).
cnf(c_101,plain,
( apart_point_and_line(sK3,line_connecting(sK1,sK2))
| ~ incident_point_and_line(sK0,line_connecting(sK1,sK2)) ),
inference(resolve,[status(thm)],[c_84,c_79]) ).
cnf(c_148,plain,
( distinct_lines(B,A)
| ~ distinct_lines(A,B) ),
inference(resolve,[status(thm)],[c_49,c_46]) ).
cnf(c_105,plain,
~ distinct_lines(A,parallel_through_point(A,B)),
inference(resolve,[status(thm)],[c_148,c_85]) ).
cnf(c_149,plain,
( apart_point_and_line(A,parallel_through_point(B,C))
| ~ apart_point_and_line(A,B) ),
inference(resolve,[status(thm)],[c_57,c_105]) ).
cnf(c_139,plain,
~ apart_point_and_line(A,B),
inference(resolve,[status(thm)],[c_149,c_61]) ).
cnf(c_144,plain,
~ incident_point_and_line(sK0,line_connecting(sK1,sK2)),
inference(resolve,[status(thm)],[c_139,c_101]) ).
cnf(c_146,plain,
incident_point_and_line(A,B),
inference(resolve,[status(thm)],[c_139,c_79]) ).
cnf(c_147,plain,
$false,
inference(resolve,[status(thm)],[c_146,c_144]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO187+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n016.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Fri Sep 25 13:08:14 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 2440132 was started by sandbox on n016,
% 0.17/0.43 % Fri Sep 25 13:08:14 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.45
% 0.17/0.45 % From the command line: assign(max_seconds, 300).
% 0.17/0.48
% 0.17/0.48 % SZS status Theorem for theBenchmark
% 0.17/0.48
% 0.17/0.48 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.17/0.48 % Length of proof is 23.
% 0.17/0.48 % Level of proof is 6.
% 0.17/0.48 % Maximum clause weight is 10.000.
% 0.17/0.48 % Given clauses 53.
% 0.17/0.48
% 0.17/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------