%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO268+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 : n020.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 01:17:47 PM UTC 2026
% Result : Theorem 21.96s 3.51s
% Output : Proof 21.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 7
% Syntax : Number of formulae : 61 ( 14 unt; 0 def)
% Number of atoms : 146 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 119 ( 34 ~; 64 |; 15 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 86 ( 0 sgn 43 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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(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]) ).
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(c1,plain,
( ~ unequally_directed_lines(X0,reverse_line(X1))
| unequally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p73,plain,
( unequally_directed_opposite_lines(X0,X1)
| unequally_directed_lines(X0,X1) ),
inference(resolution,[status(thm)],[c43,c1]) ).
cnf(p82,plain,
( unequally_directed_opposite_lines(X0,X1)
| unequally_directed_opposite_lines(X0,reverse_line(X1)) ),
inference(resolution,[status(thm)],[p73,c1]) ).
fof(f36,conjecture,
! [L,M] :
( unequally_directed_lines(L,M)
<=> unequally_directed_opposite_lines(L,reverse_line(M)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f36_neg,negated_conjecture,
~ ! [L,M] :
( unequally_directed_lines(L,M)
<=> unequally_directed_opposite_lines(L,reverse_line(M)) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f36_nnf,plain,
? [L,M] :
( ( unequally_directed_opposite_lines(L,reverse_line(M))
& ~ unequally_directed_lines(L,M) )
| ( ~ unequally_directed_opposite_lines(L,reverse_line(M))
& unequally_directed_lines(L,M) ) ),
inference(nnf_transformation,[status(thm)],[f36_neg]) ).
fof(f36_sk,plain,
( ( unequally_directed_opposite_lines(sk0,reverse_line(sk1))
& ~ unequally_directed_lines(sk0,sk1) )
| ( ~ unequally_directed_opposite_lines(sk0,reverse_line(sk1))
& unequally_directed_lines(sk0,sk1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f36_nnf]) ).
cnf(c68,plain,
( ~ unequally_directed_lines(sk0,sk1)
| ~ unequally_directed_opposite_lines(sk0,reverse_line(sk1)) ),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(p90,plain,
( ~ unequally_directed_lines(sk0,sk1)
| unequally_directed_opposite_lines(sk0,sk1) ),
inference(resolution,[status(thm)],[p82,c68]) ).
cnf(p92,plain,
( unequally_directed_opposite_lines(sk0,sk1)
| unequally_directed_opposite_lines(sk0,sk1) ),
inference(resolution,[status(thm)],[p90,p73]) ).
cnf(p93,plain,
unequally_directed_opposite_lines(sk0,sk1),
inference(factoring,[status(thm)],[p92]) ).
cnf(c0,plain,
( unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p94,plain,
unequally_directed_lines(sk0,reverse_line(sk1)),
inference(resolution,[status(thm)],[p93,c0]) ).
cnf(p195,plain,
( unequally_directed_lines(reverse_line(sk1),reverse_line(X0))
| unequally_directed_lines(sk0,X0)
| ~ unequally_directed_lines(sk0,reverse_line(reverse_line(sk1))) ),
inference(resolution,[status(thm)],[c40,p94]) ).
cnf(c67,plain,
( unequally_directed_opposite_lines(sk0,reverse_line(sk1))
| unequally_directed_lines(sk0,sk1) ),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(p70,plain,
( unequally_directed_lines(sk0,sk1)
| unequally_directed_lines(sk0,reverse_line(reverse_line(sk1))) ),
inference(resolution,[status(thm)],[c0,c67]) ).
cnf(p2613,plain,
( unequally_directed_lines(sk0,sk1)
| unequally_directed_lines(reverse_line(sk1),reverse_line(X0))
| unequally_directed_lines(sk0,X0) ),
inference(resolution,[status(thm)],[p195,p70]) ).
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(p71,plain,
~ unequally_directed_lines(X0,X0),
inference(resolution,[status(thm)],[c6,c37]) ).
cnf(p2634,plain,
( unequally_directed_lines(sk0,sk1)
| unequally_directed_lines(sk0,sk1) ),
inference(resolution,[status(thm)],[p2613,p71]) ).
cnf(p2662,plain,
unequally_directed_lines(sk0,sk1),
inference(factoring,[status(thm)],[p2634]) ).
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(p2664,plain,
( unequally_directed_lines(sk1,X0)
| unequally_directed_lines(sk0,X0) ),
inference(resolution,[status(thm)],[p2662,c38]) ).
cnf(p2816,plain,
( unequally_directed_lines(X0,X1)
| unequally_directed_lines(sk1,X1)
| unequally_directed_lines(sk0,X0) ),
inference(resolution,[status(thm)],[p2664,c38]) ).
cnf(p3232,plain,
( unequally_directed_lines(X0,sk1)
| unequally_directed_lines(sk0,X0) ),
inference(resolution,[status(thm)],[p2816,p71]) ).
cnf(p3279,plain,
( unequally_directed_lines(X0,X1)
| unequally_directed_lines(sk0,X1)
| unequally_directed_lines(X0,sk1) ),
inference(resolution,[status(thm)],[p3232,c38]) ).
cnf(p3490,plain,
( unequally_directed_opposite_lines(sk0,X1)
| unequally_directed_lines(X0,reverse_line(X1))
| unequally_directed_lines(X0,sk1) ),
inference(resolution,[status(thm)],[p3279,c1]) ).
cnf(p4298,plain,
( unequally_directed_opposite_lines(X0,X1)
| unequally_directed_opposite_lines(sk0,X1)
| unequally_directed_lines(X0,sk1) ),
inference(resolution,[status(thm)],[p3490,c1]) ).
cnf(p4340,plain,
( ~ unequally_directed_lines(sk0,sk1)
| unequally_directed_opposite_lines(X0,reverse_line(sk1))
| unequally_directed_lines(X0,sk1) ),
inference(resolution,[status(thm)],[p4298,c68]) ).
cnf(p4768,plain,
( unequally_directed_opposite_lines(X0,reverse_line(sk1))
| unequally_directed_lines(X0,sk1) ),
inference(resolution,[status(thm)],[p4340,p2662]) ).
cnf(p4769,plain,
( unequally_directed_lines(X0,reverse_line(reverse_line(sk1)))
| unequally_directed_lines(X0,sk1) ),
inference(resolution,[status(thm)],[p4768,c0]) ).
cnf(p4809,plain,
unequally_directed_lines(reverse_line(reverse_line(sk1)),sk1),
inference(resolution,[status(thm)],[p4769,p71]) ).
cnf(p4823,plain,
( unequally_directed_lines(sk1,X0)
| unequally_directed_lines(reverse_line(reverse_line(sk1)),X0) ),
inference(resolution,[status(thm)],[p4809,c38]) ).
cnf(p4837,plain,
unequally_directed_lines(sk1,reverse_line(reverse_line(sk1))),
inference(resolution,[status(thm)],[p4823,p71]) ).
cnf(p83,plain,
unequally_directed_opposite_lines(X0,X0),
inference(resolution,[status(thm)],[p73,p71]) ).
cnf(p85,plain,
unequally_directed_lines(X0,reverse_line(X0)),
inference(resolution,[status(thm)],[p83,c0]) ).
cnf(p193,plain,
( unequally_directed_lines(reverse_line(X0),reverse_line(X1))
| unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(reverse_line(X0))) ),
inference(resolution,[status(thm)],[c40,p85]) ).
cnf(p4883,plain,
( unequally_directed_lines(reverse_line(sk1),reverse_line(X0))
| unequally_directed_lines(sk1,X0) ),
inference(resolution,[status(thm)],[p4837,p193]) ).
cnf(p4886,plain,
unequally_directed_lines(sk1,sk1),
inference(resolution,[status(thm)],[p4883,p71]) ).
cnf(p4922,plain,
$false,
inference(resolution,[status(thm)],[p4886,p71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO268+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.36 % Computer : n020.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Sep 23 11:46:47 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 21.96/3.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.96/3.51 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------