%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO231+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n007.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 01:17:38 PM UTC 2026
% Result : Theorem 81.88s 12.25s
% Output : Proof 81.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 11
% Syntax : Number of formulae : 86 ( 28 unt; 0 def)
% Number of atoms : 194 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 159 ( 51 ~; 78 |; 22 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 129 ( 7 sgn 69 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f18,axiom,
! [L,M] :
( ( unequally_directed_lines(L,reverse_line(M))
& unequally_directed_lines(L,M) )
=> ( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax9_basics) ).
fof(f18_nnf,plain,
! [L,M] :
( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M))
| ~ unequally_directed_lines(L,M) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [L,M] :
( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M))
| ~ unequally_directed_lines(L,M) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c44,plain,
( left_convergent_lines(X0,reverse_line(X1))
| left_convergent_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
fof(f4,axiom,
! [X,Y] :
( equally_directed_opposite_lines(X,Y)
<=> ~ unequally_directed_opposite_lines(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a5_defns) ).
fof(f4_nnf,plain,
! [X,Y] :
( ( unequally_directed_opposite_lines(X,Y)
| equally_directed_opposite_lines(X,Y) )
& ( ~ unequally_directed_opposite_lines(X,Y)
| ~ equally_directed_opposite_lines(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y] :
( ( unequally_directed_opposite_lines(X,Y)
| equally_directed_opposite_lines(X,Y) )
& ( ~ unequally_directed_opposite_lines(X,Y)
| ~ equally_directed_opposite_lines(X,Y) ) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c9,plain,
( unequally_directed_opposite_lines(X0,X1)
| equally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
fof(f36,conjecture,
! [L,M,N] :
( ( equally_directed_lines(L,N)
& equally_directed_opposite_lines(L,M) )
=> equally_directed_opposite_lines(M,N) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f36_neg,negated_conjecture,
~ ! [L,M,N] :
( ( equally_directed_lines(L,N)
& equally_directed_opposite_lines(L,M) )
=> equally_directed_opposite_lines(M,N) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f36_nnf,plain,
? [L,M,N] :
( ~ equally_directed_opposite_lines(M,N)
& equally_directed_lines(L,N)
& equally_directed_opposite_lines(L,M) ),
inference(nnf_transformation,[status(thm)],[f36_neg]) ).
fof(f36_sk,plain,
( ~ equally_directed_opposite_lines(sk1,sk2)
& equally_directed_lines(sk0,sk2)
& equally_directed_opposite_lines(sk0,sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f36_nnf]) ).
cnf(c68,plain,
~ equally_directed_opposite_lines(sk1,sk2),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(p73,plain,
unequally_directed_opposite_lines(sk1,sk2),
inference(resolution,[status(thm)],[c9,c68]) ).
fof(f0,axiom,
! [X,Y] :
( unequally_directed_opposite_lines(X,Y)
<=> unequally_directed_lines(X,reverse_line(Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1_defns) ).
fof(f0_nnf,plain,
! [X,Y] :
( ( ~ unequally_directed_lines(X,reverse_line(Y))
| unequally_directed_opposite_lines(X,Y) )
& ( unequally_directed_lines(X,reverse_line(Y))
| ~ unequally_directed_opposite_lines(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] :
( ( ~ unequally_directed_lines(X,reverse_line(Y))
| unequally_directed_opposite_lines(X,Y) )
& ( unequally_directed_lines(X,reverse_line(Y))
| ~ unequally_directed_opposite_lines(X,Y) ) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p74,plain,
unequally_directed_lines(sk1,reverse_line(sk2)),
inference(resolution,[status(thm)],[p73,c0]) ).
cnf(p313,plain,
( left_convergent_lines(sk1,reverse_line(reverse_line(sk2)))
| left_convergent_lines(sk1,reverse_line(sk2))
| ~ unequally_directed_lines(sk1,reverse_line(reverse_line(sk2))) ),
inference(resolution,[status(thm)],[c44,p74]) ).
fof(f16,axiom,
! [L,M,N] :
( ( unequally_directed_lines(L,reverse_line(M))
& unequally_directed_lines(L,M) )
=> ( ( unequally_directed_lines(M,reverse_line(N))
& unequally_directed_lines(M,N) )
| ( unequally_directed_lines(L,reverse_line(N))
& unequally_directed_lines(L,N) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax7_basics) ).
fof(f16_nnf,plain,
! [L,M,N] :
( ( unequally_directed_lines(M,reverse_line(N))
& unequally_directed_lines(M,N) )
| ( unequally_directed_lines(L,reverse_line(N))
& unequally_directed_lines(L,N) )
| ~ unequally_directed_lines(L,reverse_line(M))
| ~ unequally_directed_lines(L,M) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [L,M,N] :
( ( unequally_directed_lines(M,reverse_line(N))
& unequally_directed_lines(M,N) )
| ( unequally_directed_lines(L,reverse_line(N))
& unequally_directed_lines(L,N) )
| ~ unequally_directed_lines(L,reverse_line(M))
| ~ unequally_directed_lines(L,M) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c40,plain,
( unequally_directed_lines(X1,reverse_line(X2))
| unequally_directed_lines(X0,X2)
| ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
fof(f15,axiom,
! [L,M,N] :
( unequally_directed_lines(L,M)
=> ( unequally_directed_lines(M,N)
| unequally_directed_lines(L,N) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax6_basics) ).
fof(f15_nnf,plain,
! [L,M,N] :
( unequally_directed_lines(M,N)
| unequally_directed_lines(L,N)
| ~ unequally_directed_lines(L,M) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [L,M,N] :
( unequally_directed_lines(M,N)
| unequally_directed_lines(L,N)
| ~ unequally_directed_lines(L,M) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c38,plain,
( unequally_directed_lines(X1,X2)
| unequally_directed_lines(X0,X2)
| ~ unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p98,plain,
( unequally_directed_lines(reverse_line(sk2),X0)
| unequally_directed_lines(sk1,X0) ),
inference(resolution,[status(thm)],[c38,p74]) ).
cnf(p108,plain,
( unequally_directed_lines(X0,X1)
| unequally_directed_lines(reverse_line(sk2),X1)
| unequally_directed_lines(sk1,X0) ),
inference(resolution,[status(thm)],[p98,c38]) ).
fof(f3,axiom,
! [X,Y] :
( equally_directed_lines(X,Y)
<=> ~ unequally_directed_lines(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a4_defns) ).
fof(f3_nnf,plain,
! [X,Y] :
( ( unequally_directed_lines(X,Y)
| equally_directed_lines(X,Y) )
& ( ~ unequally_directed_lines(X,Y)
| ~ equally_directed_lines(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y] :
( ( unequally_directed_lines(X,Y)
| equally_directed_lines(X,Y) )
& ( ~ unequally_directed_lines(X,Y)
| ~ equally_directed_lines(X,Y) ) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c6,plain,
( ~ unequally_directed_lines(X0,X1)
| ~ equally_directed_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
fof(f14,axiom,
! [L] : equally_directed_lines(L,L),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5_basics) ).
fof(f14_nnf,plain,
! [L] : equally_directed_lines(L,L),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [L] : equally_directed_lines(L,L),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c37,plain,
equally_directed_lines(X0,X0),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p70,plain,
~ unequally_directed_lines(X0,X0),
inference(resolution,[status(thm)],[c6,c37]) ).
cnf(p129,plain,
( unequally_directed_lines(X0,reverse_line(sk2))
| unequally_directed_lines(sk1,X0) ),
inference(resolution,[status(thm)],[p108,p70]) ).
cnf(c1,plain,
( ~ unequally_directed_lines(X0,reverse_line(X1))
| unequally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p137,plain,
( unequally_directed_opposite_lines(X0,sk2)
| unequally_directed_lines(sk1,X0) ),
inference(resolution,[status(thm)],[p129,c1]) ).
cnf(p145,plain,
( unequally_directed_lines(X0,X1)
| unequally_directed_lines(sk1,X1)
| unequally_directed_opposite_lines(X0,sk2) ),
inference(resolution,[status(thm)],[p137,c38]) ).
cnf(p156,plain,
( unequally_directed_lines(X0,sk1)
| unequally_directed_opposite_lines(X0,sk2) ),
inference(resolution,[status(thm)],[p145,p70]) ).
fof(f30,axiom,
! [A,L] : equally_directed_lines(parallel_through_point(L,A),L),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax10_cons_objs) ).
fof(f30_nnf,plain,
! [A,L] : equally_directed_lines(parallel_through_point(L,A),L),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [L,A] : equally_directed_lines(parallel_through_point(L,A),L),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c60,plain,
equally_directed_lines(parallel_through_point(X1,X0),X1),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(p71,plain,
~ unequally_directed_lines(parallel_through_point(X0,X1),X0),
inference(resolution,[status(thm)],[c6,c60]) ).
cnf(p163,plain,
unequally_directed_opposite_lines(parallel_through_point(sk1,X0),sk2),
inference(resolution,[status(thm)],[p156,p71]) ).
cnf(p165,plain,
unequally_directed_lines(parallel_through_point(sk1,X0),reverse_line(sk2)),
inference(resolution,[status(thm)],[p163,c0]) ).
cnf(p167,plain,
( unequally_directed_lines(reverse_line(sk2),X1)
| unequally_directed_lines(parallel_through_point(sk1,X0),X1) ),
inference(resolution,[status(thm)],[p165,c38]) ).
cnf(p172,plain,
unequally_directed_lines(reverse_line(sk2),sk1),
inference(resolution,[status(thm)],[p167,p71]) ).
cnf(p217,plain,
( unequally_directed_lines(sk1,reverse_line(X0))
| unequally_directed_lines(reverse_line(sk2),X0)
| ~ unequally_directed_lines(reverse_line(sk2),reverse_line(sk1)) ),
inference(resolution,[status(thm)],[c40,p172]) ).
fof(f17,axiom,
! [L,M] :
( unequally_directed_lines(L,reverse_line(M))
| unequally_directed_lines(L,M) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax8_basics) ).
fof(f17_nnf,plain,
! [L,M] :
( unequally_directed_lines(L,reverse_line(M))
| unequally_directed_lines(L,M) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [L,M] :
( unequally_directed_lines(L,reverse_line(M))
| unequally_directed_lines(L,M) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c43,plain,
( unequally_directed_lines(X0,reverse_line(X1))
| unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(p75,plain,
( unequally_directed_opposite_lines(X0,X1)
| unequally_directed_lines(X0,X1) ),
inference(resolution,[status(thm)],[c43,c1]) ).
cnf(c67,plain,
equally_directed_lines(sk0,sk2),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(p69,plain,
~ unequally_directed_lines(sk0,sk2),
inference(resolution,[status(thm)],[c6,c67]) ).
cnf(p85,plain,
unequally_directed_opposite_lines(sk0,sk2),
inference(resolution,[status(thm)],[p75,p69]) ).
cnf(p88,plain,
unequally_directed_lines(sk0,reverse_line(sk2)),
inference(resolution,[status(thm)],[p85,c0]) ).
cnf(p103,plain,
( unequally_directed_lines(reverse_line(sk2),X0)
| unequally_directed_lines(sk0,X0) ),
inference(resolution,[status(thm)],[c38,p88]) ).
cnf(p111,plain,
( unequally_directed_lines(X0,X1)
| unequally_directed_lines(reverse_line(sk2),X1)
| unequally_directed_lines(sk0,X0) ),
inference(resolution,[status(thm)],[p103,c38]) ).
cnf(p224,plain,
( unequally_directed_lines(X0,reverse_line(sk2))
| unequally_directed_lines(sk0,X0) ),
inference(resolution,[status(thm)],[p111,p70]) ).
cnf(p235,plain,
( unequally_directed_opposite_lines(X0,sk2)
| unequally_directed_lines(sk0,X0) ),
inference(resolution,[status(thm)],[p224,c1]) ).
cnf(p244,plain,
( unequally_directed_lines(X0,X1)
| unequally_directed_lines(sk0,X1)
| unequally_directed_opposite_lines(X0,sk2) ),
inference(resolution,[status(thm)],[p235,c38]) ).
cnf(p296,plain,
( unequally_directed_opposite_lines(sk0,X1)
| unequally_directed_lines(X0,reverse_line(X1))
| unequally_directed_opposite_lines(X0,sk2) ),
inference(resolution,[status(thm)],[p244,c1]) ).
cnf(p536,plain,
( unequally_directed_opposite_lines(X0,X1)
| unequally_directed_opposite_lines(sk0,X1)
| unequally_directed_opposite_lines(X0,sk2) ),
inference(resolution,[status(thm)],[p296,c1]) ).
cnf(c8,plain,
( ~ unequally_directed_opposite_lines(X0,X1)
| ~ equally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(c66,plain,
equally_directed_opposite_lines(sk0,sk1),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(p72,plain,
~ unequally_directed_opposite_lines(sk0,sk1),
inference(resolution,[status(thm)],[c8,c66]) ).
cnf(p547,plain,
( unequally_directed_opposite_lines(X0,sk1)
| unequally_directed_opposite_lines(X0,sk2) ),
inference(resolution,[status(thm)],[p536,p72]) ).
cnf(p554,plain,
( unequally_directed_lines(X0,reverse_line(sk2))
| unequally_directed_opposite_lines(X0,sk1) ),
inference(resolution,[status(thm)],[p547,c0]) ).
cnf(p556,plain,
unequally_directed_opposite_lines(reverse_line(sk2),sk1),
inference(resolution,[status(thm)],[p554,p70]) ).
cnf(p565,plain,
unequally_directed_lines(reverse_line(sk2),reverse_line(sk1)),
inference(resolution,[status(thm)],[p556,c0]) ).
cnf(p5037,plain,
( unequally_directed_lines(sk1,reverse_line(X0))
| unequally_directed_lines(reverse_line(sk2),X0) ),
inference(resolution,[status(thm)],[p217,p565]) ).
cnf(p5039,plain,
unequally_directed_lines(sk1,reverse_line(reverse_line(sk2))),
inference(resolution,[status(thm)],[p5037,p70]) ).
cnf(p12007,plain,
( left_convergent_lines(sk1,reverse_line(reverse_line(sk2)))
| left_convergent_lines(sk1,reverse_line(sk2)) ),
inference(resolution,[status(thm)],[p313,p5039]) ).
fof(f20,axiom,
! [L,M] :
~ ( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax11_basics) ).
fof(f20_nnf,plain,
! [L,M] :
( ~ left_convergent_lines(L,reverse_line(M))
& ~ left_convergent_lines(L,M) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [L,M] :
( ~ left_convergent_lines(L,reverse_line(M))
& ~ left_convergent_lines(L,M) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c47,plain,
~ left_convergent_lines(X0,X1),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(p12008,plain,
left_convergent_lines(sk1,reverse_line(sk2)),
inference(resolution,[status(thm)],[p12007,c47]) ).
cnf(p12009,plain,
$false,
inference(resolution,[status(thm)],[p12008,c47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO231+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.38 % Computer : n007.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 11:33:07 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 81.88/12.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 81.88/12.25 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------