%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO231+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/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 01:17:38 PM UTC 2026
% Result : Theorem 13.16s 2.26s
% Output : Proof 13.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 7
% Syntax : Number of formulae : 68 ( 16 unt; 0 def)
% Number of atoms : 174 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 158 ( 52 ~; 79 |; 21 &)
% ( 1 <=>; 5 =>; 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 : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 86 ( 2 sgn 45 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,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',oag6) ).
fof(f10_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)],[f10]) ).
fof(f10_sk,plain,
! [L,M,N] :
( unequally_directed_lines(M,N)
| unequally_directed_lines(L,N)
| ~ unequally_directed_lines(L,M) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c30,plain,
( unequally_directed_lines(X1,X2)
| unequally_directed_lines(X0,X2)
| ~ unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
fof(f31,conjecture,
! [L,M,N] :
( ( ~ unequally_directed_lines(L,N)
& ~ unequally_directed_lines(L,reverse_line(M)) )
=> ~ unequally_directed_lines(M,reverse_line(N)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f31_neg,negated_conjecture,
~ ! [L,M,N] :
( ( ~ unequally_directed_lines(L,N)
& ~ unequally_directed_lines(L,reverse_line(M)) )
=> ~ unequally_directed_lines(M,reverse_line(N)) ),
inference(negated_conjecture,[status(cth)],[f31]) ).
fof(f31_nnf,plain,
? [L,M,N] :
( unequally_directed_lines(M,reverse_line(N))
& ~ unequally_directed_lines(L,N)
& ~ unequally_directed_lines(L,reverse_line(M)) ),
inference(nnf_transformation,[status(thm)],[f31_neg]) ).
fof(f31_sk,plain,
( unequally_directed_lines(sk1,reverse_line(sk2))
& ~ unequally_directed_lines(sk0,sk2)
& ~ unequally_directed_lines(sk0,reverse_line(sk1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f31_nnf]) ).
cnf(c60,plain,
unequally_directed_lines(sk1,reverse_line(sk2)),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(p64,plain,
( unequally_directed_lines(reverse_line(sk2),X0)
| unequally_directed_lines(sk1,X0) ),
inference(resolution,[status(thm)],[c30,c60]) ).
cnf(p66,plain,
( unequally_directed_lines(X0,X1)
| unequally_directed_lines(reverse_line(sk2),X1)
| unequally_directed_lines(sk1,X0) ),
inference(resolution,[status(thm)],[p64,c30]) ).
cnf(p77,plain,
( unequally_directed_lines(X1,X2)
| unequally_directed_lines(sk1,X2)
| unequally_directed_lines(X1,X0)
| unequally_directed_lines(reverse_line(sk2),X0) ),
inference(resolution,[status(thm)],[p66,c30]) ).
fof(f9,axiom,
! [L] : ~ unequally_directed_lines(L,L),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oag5) ).
fof(f9_nnf,plain,
! [L] : ~ unequally_directed_lines(L,L),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [L] : ~ unequally_directed_lines(L,L),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c29,plain,
~ unequally_directed_lines(X0,X0),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p313,plain,
( unequally_directed_lines(X0,X1)
| unequally_directed_lines(sk1,X1)
| unequally_directed_lines(X0,reverse_line(sk2)) ),
inference(resolution,[status(thm)],[p77,c29]) ).
cnf(p361,plain,
( unequally_directed_lines(X0,sk1)
| unequally_directed_lines(X0,reverse_line(sk2)) ),
inference(resolution,[status(thm)],[p313,c29]) ).
cnf(p389,plain,
unequally_directed_lines(reverse_line(sk2),sk1),
inference(resolution,[status(thm)],[p361,c29]) ).
fof(f11,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',oag7) ).
fof(f11_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)],[f11]) ).
fof(f11_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)],[f11_nnf]) ).
cnf(c32,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)],[f11_sk]) ).
cnf(p399,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)],[p389,c32]) ).
cnf(c58,plain,
~ unequally_directed_lines(sk0,reverse_line(sk1)),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(p69,plain,
( unequally_directed_lines(reverse_line(sk2),reverse_line(sk1))
| unequally_directed_lines(sk1,sk0) ),
inference(resolution,[status(thm)],[p66,c58]) ).
cnf(p2476,plain,
( unequally_directed_lines(sk1,sk0)
| unequally_directed_lines(sk1,reverse_line(X0))
| unequally_directed_lines(reverse_line(sk2),X0) ),
inference(resolution,[status(thm)],[p399,p69]) ).
cnf(p2497,plain,
( unequally_directed_lines(sk1,sk0)
| unequally_directed_lines(sk1,reverse_line(reverse_line(sk2))) ),
inference(resolution,[status(thm)],[p2476,c29]) ).
cnf(p224,plain,
( unequally_directed_lines(reverse_line(sk2),reverse_line(X0))
| unequally_directed_lines(sk1,X0)
| ~ unequally_directed_lines(sk1,reverse_line(reverse_line(sk2))) ),
inference(resolution,[status(thm)],[c32,c60]) ).
cnf(p2531,plain,
( unequally_directed_lines(reverse_line(sk2),reverse_line(X0))
| unequally_directed_lines(sk1,X0)
| unequally_directed_lines(sk1,sk0) ),
inference(resolution,[status(thm)],[p2497,p224]) ).
cnf(p2811,plain,
( unequally_directed_lines(sk1,sk2)
| unequally_directed_lines(sk1,sk0) ),
inference(resolution,[status(thm)],[p2531,c29]) ).
cnf(p2865,plain,
( unequally_directed_lines(sk2,X0)
| unequally_directed_lines(sk1,X0)
| unequally_directed_lines(sk1,sk0) ),
inference(resolution,[status(thm)],[p2811,c30]) ).
cnf(p2886,plain,
( unequally_directed_lines(sk2,sk0)
| unequally_directed_lines(sk1,sk0) ),
inference(factoring,[status(thm)],[p2865]) ).
cnf(p2895,plain,
( unequally_directed_lines(sk0,X0)
| unequally_directed_lines(sk2,X0)
| unequally_directed_lines(sk1,sk0) ),
inference(resolution,[status(thm)],[p2886,c30]) ).
cnf(p2926,plain,
( unequally_directed_lines(sk0,sk2)
| unequally_directed_lines(sk1,sk0) ),
inference(resolution,[status(thm)],[p2895,c29]) ).
cnf(p2940,plain,
( unequally_directed_lines(sk0,X0)
| unequally_directed_lines(sk1,X0)
| unequally_directed_lines(sk0,sk2) ),
inference(resolution,[status(thm)],[p2926,c30]) ).
cnf(p2947,plain,
( unequally_directed_lines(sk0,sk1)
| unequally_directed_lines(sk0,sk2) ),
inference(resolution,[status(thm)],[p2940,c29]) ).
cnf(c59,plain,
~ unequally_directed_lines(sk0,sk2),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(p2987,plain,
unequally_directed_lines(sk0,sk1),
inference(resolution,[status(thm)],[p2947,c59]) ).
cnf(p2988,plain,
( unequally_directed_lines(sk1,X0)
| unequally_directed_lines(sk0,X0) ),
inference(resolution,[status(thm)],[p2987,c30]) ).
cnf(p2991,plain,
( unequally_directed_lines(X0,X1)
| unequally_directed_lines(sk1,X1)
| unequally_directed_lines(sk0,X0) ),
inference(resolution,[status(thm)],[p2988,c30]) ).
cnf(p3048,plain,
( unequally_directed_lines(sk2,X0)
| unequally_directed_lines(sk1,X0) ),
inference(resolution,[status(thm)],[p2991,c59]) ).
cnf(p3138,plain,
unequally_directed_lines(sk1,sk2),
inference(resolution,[status(thm)],[p3048,c29]) ).
cnf(p3150,plain,
( unequally_directed_lines(sk2,reverse_line(X0))
| unequally_directed_lines(sk1,X0)
| ~ unequally_directed_lines(sk1,reverse_line(sk2)) ),
inference(resolution,[status(thm)],[p3138,c32]) ).
cnf(p6309,plain,
( unequally_directed_lines(sk2,reverse_line(X0))
| unequally_directed_lines(sk1,X0) ),
inference(resolution,[status(thm)],[p3150,c60]) ).
cnf(p3047,plain,
( unequally_directed_lines(X0,sk1)
| unequally_directed_lines(sk0,X0) ),
inference(resolution,[status(thm)],[p2991,c29]) ).
cnf(p3096,plain,
unequally_directed_lines(sk2,sk1),
inference(resolution,[status(thm)],[p3047,c59]) ).
fof(f1,axiom,
! [L,M] :
( convergent_lines(L,M)
<=> ( unequally_directed_lines(L,reverse_line(M))
& unequally_directed_lines(L,M) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con_def) ).
fof(f1_nnf,plain,
! [L,M] :
( ( ~ unequally_directed_lines(L,reverse_line(M))
| ~ unequally_directed_lines(L,M)
| convergent_lines(L,M) )
& ( ( unequally_directed_lines(L,reverse_line(M))
& unequally_directed_lines(L,M) )
| ~ convergent_lines(L,M) ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [L,M] :
( ( ~ unequally_directed_lines(L,reverse_line(M))
| ~ unequally_directed_lines(L,M)
| convergent_lines(L,M) )
& ( ( unequally_directed_lines(L,reverse_line(M))
& unequally_directed_lines(L,M) )
| ~ convergent_lines(L,M) ) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c5,plain,
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p3119,plain,
( ~ unequally_directed_lines(sk2,reverse_line(sk1))
| convergent_lines(sk2,sk1) ),
inference(resolution,[status(thm)],[p3096,c5]) ).
cnf(p6317,plain,
( convergent_lines(sk2,sk1)
| unequally_directed_lines(sk1,sk1) ),
inference(resolution,[status(thm)],[p6309,p3119]) ).
cnf(p6350,plain,
convergent_lines(sk2,sk1),
inference(resolution,[status(thm)],[p6317,c29]) ).
cnf(c4,plain,
( unequally_directed_lines(X0,reverse_line(X1))
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p6351,plain,
unequally_directed_lines(sk2,reverse_line(sk1)),
inference(resolution,[status(thm)],[p6350,c4]) ).
fof(f13,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/sandbox2/benchmark/theBenchmark.p',oag9) ).
fof(f13_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)],[f13]) ).
fof(f13_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)],[f13_nnf]) ).
cnf(c36,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)],[f13_sk]) ).
cnf(p3124,plain,
( left_convergent_lines(sk2,reverse_line(sk1))
| left_convergent_lines(sk2,sk1)
| ~ unequally_directed_lines(sk2,reverse_line(sk1)) ),
inference(resolution,[status(thm)],[p3096,c36]) ).
cnf(p6362,plain,
( left_convergent_lines(sk2,reverse_line(sk1))
| left_convergent_lines(sk2,sk1) ),
inference(resolution,[status(thm)],[p6351,p3124]) ).
fof(f15,axiom,
! [L,M] :
~ ( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oag11) ).
fof(f15_nnf,plain,
! [L,M] :
( ~ left_convergent_lines(L,reverse_line(M))
& ~ left_convergent_lines(L,M) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [L,M] :
( ~ left_convergent_lines(L,reverse_line(M))
& ~ left_convergent_lines(L,M) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c39,plain,
~ left_convergent_lines(X0,X1),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p6544,plain,
left_convergent_lines(sk2,sk1),
inference(resolution,[status(thm)],[p6362,c39]) ).
cnf(p6545,plain,
$false,
inference(resolution,[status(thm)],[p6544,c39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO231+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.38 % Computer : n008.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Wed Sep 23 11:36:26 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 13.16/2.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.16/2.26 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------