%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO174+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n013.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 : Fri Sep 25 01:17:15 PM UTC 2026
% Result : Theorem 5.57s 1.13s
% Output : Proof 5.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 8 unt; 0 def)
% Number of atoms : 102 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 89 ( 25 ~; 45 |; 13 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 66 ( 0 sgn 38 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,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',ceq2) ).
fof(f10_nnf,plain,
! [X,Y,Z] :
( apart_point_and_line(X,Z)
| distinct_lines(Y,Z)
| ~ apart_point_and_line(X,Y) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X,Y,Z] :
( apart_point_and_line(X,Z)
| distinct_lines(Y,Z)
| ~ apart_point_and_line(X,Y) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c12,plain,
( apart_point_and_line(X0,X2)
| distinct_lines(X1,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
fof(f12,conjecture,
! [X,Y,U,V] :
( ( ( apart_point_and_line(Y,U)
| apart_point_and_line(X,U) )
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> distinct_lines(U,line_connecting(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f12_neg,negated_conjecture,
~ ! [X,Y,U,V] :
( ( ( apart_point_and_line(Y,U)
| apart_point_and_line(X,U) )
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> distinct_lines(U,line_connecting(X,Y)) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f12_nnf,plain,
? [X,Y,U,V] :
( ~ distinct_lines(U,line_connecting(X,Y))
& ( apart_point_and_line(Y,U)
| apart_point_and_line(X,U) )
& convergent_lines(U,V)
& distinct_points(X,Y) ),
inference(nnf_transformation,[status(thm)],[f12_neg]) ).
fof(f12_sk,plain,
( ~ distinct_lines(sk2,line_connecting(sk0,sk1))
& ( apart_point_and_line(sk1,sk2)
| apart_point_and_line(sk0,sk2) )
& convergent_lines(sk2,sk3)
& distinct_points(sk0,sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2,sk3])],[f12_nnf]) ).
cnf(c16,plain,
( apart_point_and_line(sk1,sk2)
| apart_point_and_line(sk0,sk2) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p33,plain,
( apart_point_and_line(sk0,sk2)
| apart_point_and_line(sk1,X0)
| distinct_lines(sk2,X0) ),
inference(resolution,[status(thm)],[c12,c16]) ).
fof(f6,axiom,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( apart_point_and_line(Z,line_connecting(X,Y))
=> ( distinct_points(Z,Y)
& distinct_points(Z,X) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con1) ).
fof(f6_nnf,plain,
! [X,Y,Z] :
( ( distinct_points(Z,Y)
& distinct_points(Z,X) )
| ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Y,Z] :
( ( distinct_points(Z,Y)
& distinct_points(Z,X) )
| ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c7,plain,
( distinct_points(X2,X1)
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(c14,plain,
distinct_points(sk0,sk1),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p30,plain,
( distinct_points(X0,sk1)
| ~ apart_point_and_line(X0,line_connecting(sk0,sk1)) ),
inference(resolution,[status(thm)],[c7,c14]) ).
cnf(p130,plain,
( distinct_points(sk1,sk1)
| apart_point_and_line(sk0,sk2)
| distinct_lines(sk2,line_connecting(sk0,sk1)) ),
inference(resolution,[status(thm)],[p33,p30]) ).
cnf(c17,plain,
~ distinct_lines(sk2,line_connecting(sk0,sk1)),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p495,plain,
( distinct_points(sk1,sk1)
| apart_point_and_line(sk0,sk2) ),
inference(resolution,[status(thm)],[p130,c17]) ).
cnf(p498,plain,
( apart_point_and_line(sk0,X0)
| distinct_lines(sk2,X0)
| distinct_points(sk1,sk1) ),
inference(resolution,[status(thm)],[p495,c12]) ).
fof(f3,axiom,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( distinct_points(Y,Z)
| distinct_points(X,Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart4) ).
fof(f3_nnf,plain,
! [X,Y,Z] :
( distinct_points(Y,Z)
| distinct_points(X,Z)
| ~ distinct_points(X,Y) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y,Z] :
( distinct_points(Y,Z)
| distinct_points(X,Z)
| ~ distinct_points(X,Y) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( distinct_points(X1,X2)
| distinct_points(X0,X2)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p18,plain,
( distinct_points(sk1,X0)
| distinct_points(sk0,X0) ),
inference(resolution,[status(thm)],[c3,c14]) ).
cnf(p21,plain,
( distinct_points(X0,X1)
| distinct_points(sk1,X1)
| distinct_points(sk0,X0) ),
inference(resolution,[status(thm)],[p18,c3]) ).
fof(f0,axiom,
! [X] : ~ distinct_points(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart1) ).
fof(f0_nnf,plain,
! [X] : ~ distinct_points(X,X),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X] : ~ distinct_points(X,X),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
~ distinct_points(X0,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p34,plain,
( distinct_points(X0,sk1)
| distinct_points(sk0,X0) ),
inference(resolution,[status(thm)],[p21,c0]) ).
cnf(c6,plain,
( distinct_points(X2,X0)
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p49,plain,
( distinct_points(X1,X0)
| ~ apart_point_and_line(X1,line_connecting(X0,sk1))
| distinct_points(sk0,X0) ),
inference(resolution,[status(thm)],[p34,c6]) ).
cnf(p423,plain,
( ~ apart_point_and_line(sk0,line_connecting(X0,sk1))
| distinct_points(sk0,X0) ),
inference(factoring,[status(thm)],[p49]) ).
cnf(p564,plain,
( distinct_points(sk0,X0)
| distinct_lines(sk2,line_connecting(X0,sk1))
| distinct_points(sk1,sk1) ),
inference(resolution,[status(thm)],[p498,p423]) ).
cnf(p1111,plain,
( distinct_points(sk0,sk0)
| distinct_points(sk1,sk1) ),
inference(resolution,[status(thm)],[p564,c17]) ).
cnf(p1113,plain,
distinct_points(sk0,sk0),
inference(resolution,[status(thm)],[p1111,c0]) ).
cnf(p1114,plain,
$false,
inference(resolution,[status(thm)],[p1113,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO174+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.06/0.33 % Computer : n013.cluster.edu
% 0.06/0.33 % Model : x86_64 x86_64
% 0.06/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.33 % Memory : 8046.5625MB
% 0.06/0.33 % OS : Linux 6.8.0-71-generic
% 0.06/0.33 % CPULimit : 300
% 0.06/0.33 % WCLimit : 300
% 0.06/0.33 % DateTime : Wed Sep 23 11:15:50 UTC 2026
% 0.06/0.34 % CPUTime :
% 0.06/0.34 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.57/1.13 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.57/1.13 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------