%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO254+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 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 : Sun Sep 27 07:17:43 AM UTC 2026
% Result : Theorem 1.63s 0.59s
% Output : CNFRefutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 10
% Syntax : Number of formulae : 82 ( 25 unt; 0 def)
% Number of atoms : 186 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 169 ( 65 ~; 82 |; 16 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 119 ( 4 sgn 25 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(bf_def,axiom,
! [L,A,B] :
( before_on_line(L,A,B)
<=> ( ~ unequally_directed_lines(L,line_connecting(A,B))
& ~ ( left_apart_point(B,reverse_line(L))
| left_apart_point(B,L) )
& ~ ( left_apart_point(A,reverse_line(L))
| left_apart_point(A,L) )
& distinct_points(A,B) ) ),
file('theBenchmark.p',bf_def) ).
fof(oag1,axiom,
! [A] : ~ distinct_points(A,A),
file('theBenchmark.p',oag1) ).
fof(oag2,axiom,
! [A,B,C] :
( distinct_points(A,B)
=> ( distinct_points(B,C)
| distinct_points(A,C) ) ),
file('theBenchmark.p',oag2) ).
fof(oag5,axiom,
! [L] : ~ unequally_directed_lines(L,L),
file('theBenchmark.p',oag5) ).
fof(oag6,axiom,
! [L,M,N] :
( unequally_directed_lines(L,M)
=> ( unequally_directed_lines(M,N)
| unequally_directed_lines(L,N) ) ),
file('theBenchmark.p',oag6) ).
fof(oag9,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('theBenchmark.p',oag9) ).
fof(oag10,axiom,
! [A,L] :
~ ( left_apart_point(A,reverse_line(L))
| left_apart_point(A,L) ),
file('theBenchmark.p',oag10) ).
fof(oag11,axiom,
! [L,M] :
~ ( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M) ),
file('theBenchmark.p',oag11) ).
fof(oagco9,axiom,
! [A,B] : ~ unequally_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A))),
file('theBenchmark.p',oagco9) ).
fof(con,conjecture,
! [A,B,L] :
( ( ~ apart_point_and_line(B,L)
& ~ apart_point_and_line(A,L)
& distinct_points(A,B) )
=> ( before_on_line(L,B,A)
& before_on_line(L,A,B) ) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [A,B,L] :
( ( ~ apart_point_and_line(B,L)
& ~ apart_point_and_line(A,L)
& distinct_points(A,B) )
=> ( before_on_line(L,B,A)
& before_on_line(L,A,B) ) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_63,plain,
( ~ unequally_directed_lines(A,line_connecting(B,C))
| ~ before_on_line(A,B,C) ),
inference(clausify,[status(thm)],[bf_def]) ).
cnf(c_64,plain,
( unequally_directed_lines(A,line_connecting(B,C))
| left_apart_point(C,reverse_line(A))
| left_apart_point(C,A)
| left_apart_point(B,reverse_line(A))
| left_apart_point(B,A)
| ~ distinct_points(B,C)
| before_on_line(A,B,C) ),
inference(clausify,[status(thm)],[bf_def]) ).
cnf(c_65,plain,
~ distinct_points(A,A),
inference(clausify,[status(thm)],[oag1]) ).
cnf(c_66,plain,
( distinct_points(B,C)
| distinct_points(A,C)
| ~ distinct_points(A,B) ),
inference(clausify,[status(thm)],[oag2]) ).
cnf(c_69,plain,
~ unequally_directed_lines(A,A),
inference(clausify,[status(thm)],[oag5]) ).
cnf(c_70,plain,
( unequally_directed_lines(B,C)
| unequally_directed_lines(A,C)
| ~ unequally_directed_lines(A,B) ),
inference(clausify,[status(thm)],[oag6]) ).
cnf(c_74,plain,
( left_convergent_lines(A,reverse_line(B))
| left_convergent_lines(A,B)
| ~ unequally_directed_lines(A,reverse_line(B))
| ~ unequally_directed_lines(A,B) ),
inference(clausify,[status(thm)],[oag9]) ).
cnf(c_75,plain,
~ left_apart_point(A,B),
inference(clausify,[status(thm)],[oag10]) ).
cnf(c_76,plain,
~ left_convergent_lines(A,B),
inference(clausify,[status(thm)],[oag11]) ).
cnf(c_82,plain,
~ unequally_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A))),
inference(clausify,[status(thm)],[oagco9]) ).
fof(nnf_32,plain,
? [A,B,L] :
( ( ~ before_on_line(L,B,A)
| ~ before_on_line(L,A,B) )
& ~ apart_point_and_line(B,L)
& ~ apart_point_and_line(A,L)
& distinct_points(A,B) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( ( ~ before_on_line(sK2,sK1,sK0)
| ~ before_on_line(sK2,sK0,sK1) )
& ~ apart_point_and_line(sK1,sK2)
& ~ apart_point_and_line(sK0,sK2)
& distinct_points(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK0),skolemize(B,sK1),skolemize(L,sK2)],[nnf_32]) ).
cnf(c_90,negated_conjecture,
distinct_points(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_91,negated_conjecture,
( ~ before_on_line(sK2,sK1,sK0)
| ~ before_on_line(sK2,sK0,sK1) ),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_1394,plain,
( unequally_directed_lines(A,line_connecting(B,C))
| left_apart_point(C,reverse_line(A))
| left_apart_point(C,A)
| left_apart_point(B,reverse_line(A))
| ~ distinct_points(B,C)
| before_on_line(A,B,C) ),
inference(resolve,[status(thm)],[c_75,c_64]) ).
cnf(c_1395,plain,
( unequally_directed_lines(A,line_connecting(B,C))
| left_apart_point(C,reverse_line(A))
| left_apart_point(C,A)
| ~ distinct_points(B,C)
| before_on_line(A,B,C) ),
inference(resolve,[status(thm)],[c_75,c_1394]) ).
cnf(c_1396,plain,
( unequally_directed_lines(A,line_connecting(B,C))
| left_apart_point(C,reverse_line(A))
| ~ distinct_points(B,C)
| before_on_line(A,B,C) ),
inference(resolve,[status(thm)],[c_75,c_1395]) ).
cnf(c_93,plain,
( unequally_directed_lines(A,line_connecting(B,C))
| ~ distinct_points(B,C)
| before_on_line(A,B,C) ),
inference(resolve,[status(thm)],[c_75,c_1396]) ).
cnf(c_1397,plain,
( left_convergent_lines(A,reverse_line(B))
| ~ unequally_directed_lines(A,reverse_line(B))
| ~ unequally_directed_lines(A,B) ),
inference(resolve,[status(thm)],[c_76,c_74]) ).
cnf(c_94,plain,
( ~ unequally_directed_lines(A,reverse_line(B))
| ~ unequally_directed_lines(A,B) ),
inference(resolve,[status(thm)],[c_76,c_1397]) ).
cnf(c_1398,plain,
( unequally_directed_lines(B,A)
| ~ unequally_directed_lines(A,B) ),
inference(resolve,[status(thm)],[c_70,c_69]) ).
cnf(c_97,plain,
~ unequally_directed_lines(reverse_line(line_connecting(A,B)),line_connecting(B,A)),
inference(resolve,[status(thm)],[c_1398,c_82]) ).
cnf(c_104,plain,
( distinct_points(sK1,A)
| distinct_points(sK0,A) ),
inference(resolve,[status(thm)],[c_90,c_66]) ).
cnf(c_106,plain,
( unequally_directed_lines(A,line_connecting(sK0,sK1))
| before_on_line(A,sK0,sK1) ),
inference(resolve,[status(thm)],[c_93,c_90]) ).
cnf(c_116,plain,
distinct_points(sK1,sK0),
inference(resolve,[status(thm)],[c_104,c_65]) ).
cnf(c_120,plain,
( unequally_directed_lines(A,line_connecting(sK1,sK0))
| before_on_line(A,sK1,sK0) ),
inference(resolve,[status(thm)],[c_116,c_93]) ).
cnf(c_198,plain,
( unequally_directed_lines(line_connecting(sK0,sK1),B)
| unequally_directed_lines(A,B)
| before_on_line(A,sK0,sK1) ),
inference(resolve,[status(thm)],[c_106,c_70]) ).
cnf(c_206,plain,
( ~ before_on_line(sK2,sK0,sK1)
| unequally_directed_lines(sK2,line_connecting(sK1,sK0)) ),
inference(resolve,[status(thm)],[c_120,c_91]) ).
cnf(c_212,plain,
( unequally_directed_lines(line_connecting(sK1,sK0),B)
| unequally_directed_lines(A,B)
| before_on_line(A,sK1,sK0) ),
inference(resolve,[status(thm)],[c_120,c_70]) ).
cnf(c_548,plain,
( unequally_directed_lines(line_connecting(sK0,sK1),A)
| before_on_line(A,sK0,sK1) ),
inference(resolve,[status(thm)],[c_198,c_69]) ).
cnf(c_563,plain,
( ~ unequally_directed_lines(line_connecting(sK0,sK1),A)
| before_on_line(reverse_line(A),sK0,sK1) ),
inference(resolve,[status(thm)],[c_548,c_94]) ).
cnf(c_564,plain,
( ~ unequally_directed_lines(line_connecting(sK0,sK1),reverse_line(A))
| before_on_line(A,sK0,sK1) ),
inference(resolve,[status(thm)],[c_548,c_94]) ).
cnf(c_582,plain,
( unequally_directed_lines(B,A)
| before_on_line(B,sK0,sK1)
| before_on_line(reverse_line(A),sK0,sK1) ),
inference(resolve,[status(thm)],[c_563,c_198]) ).
cnf(c_596,plain,
( unequally_directed_lines(reverse_line(A),A)
| before_on_line(reverse_line(A),sK0,sK1) ),
inference(factor,[status(thm)],[c_582]) ).
cnf(c_613,plain,
before_on_line(reverse_line(line_connecting(A,A)),sK0,sK1),
inference(resolve,[status(thm)],[c_596,c_97]) ).
cnf(c_617,plain,
~ unequally_directed_lines(reverse_line(line_connecting(A,A)),line_connecting(sK0,sK1)),
inference(resolve,[status(thm)],[c_613,c_63]) ).
cnf(c_618,plain,
( unequally_directed_lines(B,reverse_line(A))
| before_on_line(B,sK0,sK1)
| before_on_line(A,sK0,sK1) ),
inference(resolve,[status(thm)],[c_564,c_198]) ).
cnf(c_619,plain,
( unequally_directed_lines(A,reverse_line(A))
| before_on_line(A,sK0,sK1) ),
inference(factor,[status(thm)],[c_618]) ).
cnf(c_620,plain,
( unequally_directed_lines(sK2,line_connecting(sK1,sK0))
| unequally_directed_lines(sK2,reverse_line(sK2)) ),
inference(resolve,[status(thm)],[c_619,c_206]) ).
cnf(c_621,plain,
( ~ before_on_line(sK2,sK1,sK0)
| unequally_directed_lines(sK2,reverse_line(sK2)) ),
inference(resolve,[status(thm)],[c_619,c_91]) ).
cnf(c_1399,plain,
( unequally_directed_lines(B,A)
| ~ unequally_directed_lines(A,B) ),
inference(resolve,[status(thm)],[c_70,c_69]) ).
cnf(c_645,plain,
~ unequally_directed_lines(line_connecting(sK0,sK1),reverse_line(line_connecting(A,A))),
inference(resolve,[status(thm)],[c_1399,c_617]) ).
cnf(c_1400,plain,
( unequally_directed_lines(C,reverse_line(line_connecting(B,A)))
| ~ unequally_directed_lines(line_connecting(A,B),C) ),
inference(resolve,[status(thm)],[c_70,c_82]) ).
cnf(c_659,plain,
~ unequally_directed_lines(line_connecting(A,A),line_connecting(sK0,sK1)),
inference(resolve,[status(thm)],[c_1400,c_645]) ).
cnf(c_1401,plain,
( unequally_directed_lines(A,reverse_line(line_connecting(B,B)))
| ~ unequally_directed_lines(line_connecting(sK0,sK1),A) ),
inference(resolve,[status(thm)],[c_70,c_645]) ).
cnf(c_666,plain,
~ unequally_directed_lines(line_connecting(sK0,sK1),line_connecting(A,A)),
inference(resolve,[status(thm)],[c_1401,c_82]) ).
cnf(c_1402,plain,
( unequally_directed_lines(B,line_connecting(sK0,sK1))
| ~ unequally_directed_lines(reverse_line(line_connecting(A,A)),B) ),
inference(resolve,[status(thm)],[c_70,c_617]) ).
cnf(c_668,plain,
~ unequally_directed_lines(reverse_line(line_connecting(A,A)),line_connecting(B,B)),
inference(resolve,[status(thm)],[c_1402,c_659]) ).
cnf(c_684,plain,
( unequally_directed_lines(A,line_connecting(B,B))
| before_on_line(A,sK0,sK1) ),
inference(resolve,[status(thm)],[c_666,c_198]) ).
cnf(c_688,plain,
( unequally_directed_lines(line_connecting(sK1,sK0),A)
| unequally_directed_lines(sK2,A)
| unequally_directed_lines(sK2,reverse_line(sK2)) ),
inference(resolve,[status(thm)],[c_620,c_70]) ).
cnf(c_690,plain,
( unequally_directed_lines(line_connecting(sK1,sK0),reverse_line(sK2))
| unequally_directed_lines(sK2,reverse_line(sK2)) ),
inference(factor,[status(thm)],[c_688]) ).
cnf(c_773,plain,
( ~ unequally_directed_lines(line_connecting(sK1,sK0),sK2)
| unequally_directed_lines(sK2,reverse_line(sK2)) ),
inference(resolve,[status(thm)],[c_690,c_94]) ).
cnf(c_1009,plain,
( unequally_directed_lines(line_connecting(sK1,sK0),A)
| before_on_line(A,sK1,sK0) ),
inference(resolve,[status(thm)],[c_212,c_69]) ).
cnf(c_1066,plain,
( unequally_directed_lines(sK2,reverse_line(sK2))
| before_on_line(sK2,sK1,sK0) ),
inference(resolve,[status(thm)],[c_1009,c_773]) ).
cnf(c_1403,plain,
( unequally_directed_lines(sK2,reverse_line(sK2))
| unequally_directed_lines(sK2,reverse_line(sK2)) ),
inference(resolve,[status(thm)],[c_1066,c_621]) ).
cnf(c_1076,plain,
unequally_directed_lines(sK2,reverse_line(sK2)),
inference(copy,[status(thm)],[c_1403]) ).
cnf(c_1080,plain,
( unequally_directed_lines(reverse_line(sK2),A)
| unequally_directed_lines(sK2,A) ),
inference(resolve,[status(thm)],[c_1076,c_70]) ).
cnf(c_1091,plain,
( ~ unequally_directed_lines(sK2,A)
| unequally_directed_lines(reverse_line(sK2),reverse_line(A)) ),
inference(resolve,[status(thm)],[c_1080,c_94]) ).
cnf(c_1109,plain,
( ~ unequally_directed_lines(reverse_line(sK2),A)
| unequally_directed_lines(sK2,reverse_line(A)) ),
inference(resolve,[status(thm)],[c_1080,c_94]) ).
cnf(c_1223,plain,
( unequally_directed_lines(sK2,A)
| unequally_directed_lines(sK2,reverse_line(A)) ),
inference(resolve,[status(thm)],[c_1109,c_1080]) ).
cnf(c_1224,plain,
( before_on_line(reverse_line(sK2),sK0,sK1)
| unequally_directed_lines(sK2,reverse_line(line_connecting(A,A))) ),
inference(resolve,[status(thm)],[c_1109,c_684]) ).
cnf(c_1253,plain,
( unequally_directed_lines(reverse_line(A),B)
| unequally_directed_lines(sK2,B)
| unequally_directed_lines(sK2,A) ),
inference(resolve,[status(thm)],[c_1223,c_70]) ).
cnf(c_1267,plain,
( unequally_directed_lines(reverse_line(A),A)
| unequally_directed_lines(sK2,A) ),
inference(factor,[status(thm)],[c_1253]) ).
cnf(c_1289,plain,
unequally_directed_lines(sK2,line_connecting(A,A)),
inference(resolve,[status(thm)],[c_1267,c_668]) ).
cnf(c_1296,plain,
unequally_directed_lines(reverse_line(sK2),reverse_line(line_connecting(A,A))),
inference(resolve,[status(thm)],[c_1289,c_1091]) ).
cnf(c_1297,plain,
~ unequally_directed_lines(sK2,reverse_line(line_connecting(A,A))),
inference(resolve,[status(thm)],[c_1289,c_94]) ).
cnf(c_1299,plain,
before_on_line(reverse_line(sK2),sK0,sK1),
inference(resolve,[status(thm)],[c_1297,c_1224]) ).
cnf(c_1300,plain,
~ unequally_directed_lines(reverse_line(sK2),line_connecting(sK0,sK1)),
inference(resolve,[status(thm)],[c_1299,c_63]) ).
cnf(c_1404,plain,
( unequally_directed_lines(A,line_connecting(sK0,sK1))
| ~ unequally_directed_lines(reverse_line(sK2),A) ),
inference(resolve,[status(thm)],[c_70,c_1300]) ).
cnf(c_1405,plain,
~ unequally_directed_lines(reverse_line(sK2),reverse_line(line_connecting(A,A))),
inference(resolve,[status(thm)],[c_1404,c_617]) ).
cnf(c_1393,plain,
$false,
inference(resolve,[status(thm)],[c_1296,c_1405]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO254+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 13:08:53 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 1078151 was started by sandbox2 on n007,
% 0.13/0.36 % Fri Sep 25 13:08:53 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 1.63/0.59
% 1.63/0.59 % SZS status Theorem for theBenchmark
% 1.63/0.59
% 1.63/0.59 % Proof 1 at 0.13 (+ 0.06) seconds.
% 1.63/0.59 % Length of proof is 67.
% 1.63/0.59 % Level of proof is 24.
% 1.63/0.59 % Maximum clause weight is 30.000.
% 1.63/0.59 % Given clauses 284.
% 1.63/0.59
% 1.63/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------