%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO266+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n002.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 6.79s 11.48s
% Output : Proof 6.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 7
% Syntax : Number of formulae : 57 ( 12 unt; 0 def)
% Number of atoms : 143 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 120 ( 34 ~; 65 |; 15 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 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 : 83 ( 0 sgn 43 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [L,M,N] :
( unequally_directed_lines(L,M)
=> ( unequally_directed_lines(M,N)
| unequally_directed_lines(L,N) ) ),
file('/export/starexec/sandbox2/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]) ).
fof(f17,axiom,
! [L,M] :
( unequally_directed_lines(L,reverse_line(M))
| unequally_directed_lines(L,M) ),
file('/export/starexec/sandbox2/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/sandbox2/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(p97,plain,
( unequally_directed_opposite_lines(X0,X2)
| unequally_directed_lines(X2,X1)
| unequally_directed_lines(X0,X1) ),
inference(resolution,[status(thm)],[c38,p73]) ).
fof(f36,conjecture,
! [L,M] :
( unequally_directed_opposite_lines(L,M)
<=> unequally_directed_opposite_lines(M,L) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f36_neg,negated_conjecture,
~ ! [L,M] :
( unequally_directed_opposite_lines(L,M)
<=> unequally_directed_opposite_lines(M,L) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f36_nnf,plain,
? [L,M] :
( ( unequally_directed_opposite_lines(M,L)
& ~ unequally_directed_opposite_lines(L,M) )
| ( ~ unequally_directed_opposite_lines(M,L)
& unequally_directed_opposite_lines(L,M) ) ),
inference(nnf_transformation,[status(thm)],[f36_neg]) ).
fof(f36_sk,plain,
( ( unequally_directed_opposite_lines(sk1,sk0)
& ~ unequally_directed_opposite_lines(sk0,sk1) )
| ( ~ unequally_directed_opposite_lines(sk1,sk0)
& unequally_directed_opposite_lines(sk0,sk1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f36_nnf]) ).
cnf(c68,plain,
( ~ unequally_directed_opposite_lines(sk0,sk1)
| ~ unequally_directed_opposite_lines(sk1,sk0) ),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(p1043,plain,
( ~ unequally_directed_opposite_lines(sk0,sk1)
| unequally_directed_lines(sk0,X0)
| unequally_directed_lines(sk1,X0) ),
inference(resolution,[status(thm)],[p97,c68]) ).
cnf(p1072,plain,
( unequally_directed_lines(sk1,X1)
| unequally_directed_lines(sk0,X1)
| unequally_directed_lines(sk0,X0)
| unequally_directed_lines(sk1,X0) ),
inference(resolution,[status(thm)],[p1043,p97]) ).
cnf(p1073,plain,
( unequally_directed_lines(sk0,X0)
| unequally_directed_lines(sk0,X0)
| unequally_directed_lines(sk1,X0) ),
inference(factoring,[status(thm)],[p1072]) ).
cnf(p1084,plain,
( unequally_directed_lines(sk0,X0)
| unequally_directed_lines(sk1,X0) ),
inference(factoring,[status(thm)],[p1073]) ).
cnf(p1088,plain,
( unequally_directed_lines(X0,X1)
| unequally_directed_lines(sk1,X1)
| unequally_directed_lines(sk0,X0) ),
inference(resolution,[status(thm)],[p1084,c38]) ).
fof(f3,axiom,
! [X,Y] :
( equally_directed_lines(X,Y)
<=> ~ unequally_directed_lines(X,Y) ),
file('/export/starexec/sandbox2/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/sandbox2/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(p1202,plain,
( unequally_directed_lines(X0,sk1)
| unequally_directed_lines(sk0,X0) ),
inference(resolution,[status(thm)],[p1088,p71]) ).
cnf(p1234,plain,
( unequally_directed_lines(X0,X1)
| unequally_directed_lines(sk0,X1)
| unequally_directed_lines(X0,sk1) ),
inference(resolution,[status(thm)],[p1202,c38]) ).
cnf(p1306,plain,
( unequally_directed_lines(X0,sk0)
| unequally_directed_lines(X0,sk1) ),
inference(resolution,[status(thm)],[p1234,p71]) ).
cnf(p1328,plain,
unequally_directed_lines(sk1,sk0),
inference(resolution,[status(thm)],[p1306,p71]) ).
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/sandbox2/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]) ).
cnf(p1338,plain,
( unequally_directed_lines(sk0,reverse_line(X0))
| unequally_directed_lines(sk1,X0)
| ~ unequally_directed_lines(sk1,reverse_line(sk0)) ),
inference(resolution,[status(thm)],[p1328,c40]) ).
cnf(c0,plain,
( unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(c67,plain,
( unequally_directed_opposite_lines(sk1,sk0)
| unequally_directed_opposite_lines(sk0,sk1) ),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(p70,plain,
( unequally_directed_opposite_lines(sk0,sk1)
| unequally_directed_lines(sk1,reverse_line(sk0)) ),
inference(resolution,[status(thm)],[c0,c67]) ).
cnf(p2163,plain,
( unequally_directed_opposite_lines(sk0,sk1)
| unequally_directed_lines(sk0,reverse_line(X0))
| unequally_directed_lines(sk1,X0) ),
inference(resolution,[status(thm)],[p1338,p70]) ).
cnf(p2196,plain,
( unequally_directed_opposite_lines(sk0,X0)
| unequally_directed_opposite_lines(sk0,sk1)
| unequally_directed_lines(sk1,X0) ),
inference(resolution,[status(thm)],[p2163,c1]) ).
cnf(p2208,plain,
( unequally_directed_opposite_lines(sk0,sk1)
| unequally_directed_lines(sk1,sk1) ),
inference(factoring,[status(thm)],[p2196]) ).
cnf(p2218,plain,
unequally_directed_opposite_lines(sk0,sk1),
inference(resolution,[status(thm)],[p2208,p71]) ).
cnf(p2219,plain,
unequally_directed_lines(sk0,reverse_line(sk1)),
inference(resolution,[status(thm)],[p2218,c0]) ).
cnf(p1086,plain,
unequally_directed_lines(sk0,sk1),
inference(resolution,[status(thm)],[p1084,p71]) ).
cnf(p1106,plain,
( unequally_directed_lines(sk1,reverse_line(X0))
| unequally_directed_lines(sk0,X0)
| ~ unequally_directed_lines(sk0,reverse_line(sk1)) ),
inference(resolution,[status(thm)],[p1086,c40]) ).
cnf(p2231,plain,
( unequally_directed_lines(sk1,reverse_line(X0))
| unequally_directed_lines(sk0,X0) ),
inference(resolution,[status(thm)],[p2219,p1106]) ).
cnf(p2296,plain,
( unequally_directed_opposite_lines(sk1,X0)
| unequally_directed_lines(sk0,X0) ),
inference(resolution,[status(thm)],[p2231,c1]) ).
cnf(p2307,plain,
unequally_directed_opposite_lines(sk1,sk0),
inference(resolution,[status(thm)],[p2296,p71]) ).
cnf(p2316,plain,
~ unequally_directed_opposite_lines(sk0,sk1),
inference(resolution,[status(thm)],[p2307,c68]) ).
cnf(p2371,plain,
$false,
inference(resolution,[status(thm)],[p2316,p2218]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO266+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/10.37 % Computer : n002.cluster.edu
% 0.09/10.37 % Model : x86_64 x86_64
% 0.09/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.37 % Memory : 8046.5625MB
% 0.09/10.37 % OS : Linux 6.8.0-71-generic
% 0.09/10.37 % CPULimit : 300
% 0.09/10.37 % WCLimit : 300
% 0.09/10.37 % DateTime : Wed Sep 23 11:48:30 UTC 2026
% 0.09/10.38 % CPUTime :
% 0.09/10.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.79/11.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.79/11.48 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------