%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO178+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n008.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 01:17:17 PM UTC 2026
% Result : Theorem 4.41s 1.09s
% Output : Proof 4.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 8 unt; 0 def)
% Number of atoms : 56 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 57 ( 27 ~; 17 |; 8 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 27 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,conjecture,
! [X,Y,Z] :
( ( apart_point_and_line(Z,line_connecting(X,Y))
& distinct_points(X,Y) )
=> ( distinct_points(Z,Y)
& distinct_points(Z,X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f14_neg,negated_conjecture,
~ ! [X,Y,Z] :
( ( apart_point_and_line(Z,line_connecting(X,Y))
& distinct_points(X,Y) )
=> ( distinct_points(Z,Y)
& distinct_points(Z,X) ) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f14_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)],[f14_neg]) ).
fof(f14_sk,plain,
( ( ~ distinct_points(sk2,sk1)
| ~ distinct_points(sk2,sk0) )
& apart_point_and_line(sk2,line_connecting(sk0,sk1))
& distinct_points(sk0,sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f14_nnf]) ).
cnf(c15,plain,
apart_point_and_line(sk2,line_connecting(sk0,sk1)),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
fof(f11,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',ceq1) ).
fof(f11_nnf,plain,
! [X,Y,Z] :
( apart_point_and_line(Z,Y)
| distinct_points(X,Z)
| ~ apart_point_and_line(X,Y) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X,Y,Z] :
( apart_point_and_line(Z,Y)
| distinct_points(X,Z)
| ~ apart_point_and_line(X,Y) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( apart_point_and_line(X2,X1)
| distinct_points(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p21,plain,
( apart_point_and_line(X0,line_connecting(sk0,sk1))
| distinct_points(sk2,X0) ),
inference(resolution,[status(thm)],[c15,c11]) ).
cnf(c14,plain,
distinct_points(sk0,sk1),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
fof(f6,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(X,line_connecting(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ci1) ).
fof(f6_nnf,plain,
! [X,Y] :
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Y] :
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p18,plain,
~ apart_point_and_line(sk0,line_connecting(sk0,sk1)),
inference(resolution,[status(thm)],[c14,c6]) ).
cnf(p29,plain,
distinct_points(sk2,sk0),
inference(resolution,[status(thm)],[p21,p18]) ).
cnf(c16,plain,
( ~ distinct_points(sk2,sk1)
| ~ distinct_points(sk2,sk0) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p71,plain,
~ distinct_points(sk2,sk1),
inference(resolution,[status(thm)],[p29,c16]) ).
fof(f7,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ci2) ).
fof(f7_nnf,plain,
! [X,Y] :
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,Y] :
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p19,plain,
~ apart_point_and_line(sk1,line_connecting(sk0,sk1)),
inference(resolution,[status(thm)],[c14,c7]) ).
cnf(p30,plain,
distinct_points(sk2,sk1),
inference(resolution,[status(thm)],[p21,p19]) ).
cnf(p293,plain,
$false,
inference(resolution,[status(thm)],[p71,p30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO178+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.38 % Computer : n008.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Wed Sep 23 11:18:26 UTC 2026
% 0.03/0.38 % CPUTime :
% 0.03/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.41/1.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.41/1.09 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------