%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO263+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 : Tue Sep 29 09:52:17 AM UTC 2026
% Result : Theorem 3.34s 1.36s
% Output : Refutation 3.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 4 unt; 0 def)
% Number of atoms : 79 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 79 ( 28 ~; 21 |; 23 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 66 ( 54 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( unequally_directed_opposite_lines(X0,X1)
<=> unequally_directed_lines(X0,reverse_line(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1_defns) ).
fof(f7,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
<=> ( unequally_directed_lines(X0,X1)
& unequally_directed_opposite_lines(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a7_defns) ).
fof(f19,axiom,
! [X0,X1] :
( ( unequally_directed_lines(X0,X1)
& unequally_directed_lines(X0,reverse_line(X1)) )
=> ( left_convergent_lines(X0,X1)
| left_convergent_lines(X0,reverse_line(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax9_basics) ).
fof(f21,axiom,
! [X0,X1] :
~ ( left_convergent_lines(X0,X1)
| left_convergent_lines(X0,reverse_line(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax11_basics) ).
fof(f37,conjecture,
! [X0,X1,X2,X3,X4,X5] :
( ( between_on_line(X0,X3,X4,X5)
& convergent_lines(X0,X1)
& convergent_lines(X0,X2)
& convergent_lines(X1,X2) )
=> between_on_line(X1,intersection_point(X1,parallel_through_point(X2,X3)),intersection_point(X1,parallel_through_point(X2,X4)),intersection_point(X1,parallel_through_point(X2,X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f38,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5] :
( ( between_on_line(X0,X3,X4,X5)
& convergent_lines(X0,X1)
& convergent_lines(X0,X2)
& convergent_lines(X1,X2) )
=> between_on_line(X1,intersection_point(X1,parallel_through_point(X2,X3)),intersection_point(X1,parallel_through_point(X2,X4)),intersection_point(X1,parallel_through_point(X2,X5))) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f39,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ( unequally_directed_lines(X0,X1)
& unequally_directed_opposite_lines(X0,X1) ) ),
inference(unused_predicate_definition_removal,[],[f7]) ).
fof(f42,plain,
! [X0,X1] :
( unequally_directed_opposite_lines(X0,X1)
=> unequally_directed_lines(X0,reverse_line(X1)) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f43,plain,
! [X0,X1] :
( unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_opposite_lines(X0,X1) ),
inference(ennf_transformation,[],[f42]) ).
fof(f46,plain,
! [X0,X1] :
( ( unequally_directed_lines(X0,X1)
& unequally_directed_opposite_lines(X0,X1) )
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f55,plain,
! [X0,X1] :
( left_convergent_lines(X0,X1)
| left_convergent_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(ennf_transformation,[],[f19]) ).
fof(f56,plain,
! [X0,X1] :
( left_convergent_lines(X0,X1)
| left_convergent_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(flattening,[],[f55]) ).
fof(f58,plain,
! [X0,X1] :
( ~ left_convergent_lines(X0,X1)
& ~ left_convergent_lines(X0,reverse_line(X1)) ),
inference(ennf_transformation,[],[f21]) ).
fof(f80,plain,
? [X0,X1,X2,X3,X4,X5] :
( ~ between_on_line(X1,intersection_point(X1,parallel_through_point(X2,X3)),intersection_point(X1,parallel_through_point(X2,X4)),intersection_point(X1,parallel_through_point(X2,X5)))
& between_on_line(X0,X3,X4,X5)
& convergent_lines(X0,X1)
& convergent_lines(X0,X2)
& convergent_lines(X1,X2) ),
inference(ennf_transformation,[],[f38]) ).
fof(f81,plain,
? [X0,X1,X2,X3,X4,X5] :
( ~ between_on_line(X1,intersection_point(X1,parallel_through_point(X2,X3)),intersection_point(X1,parallel_through_point(X2,X4)),intersection_point(X1,parallel_through_point(X2,X5)))
& between_on_line(X0,X3,X4,X5)
& convergent_lines(X0,X1)
& convergent_lines(X0,X2)
& convergent_lines(X1,X2) ),
inference(flattening,[],[f80]) ).
fof(f87,plain,
( ~ between_on_line(sK1,intersection_point(sK1,parallel_through_point(sK2,sK3)),intersection_point(sK1,parallel_through_point(sK2,sK4)),intersection_point(sK1,parallel_through_point(sK2,sK5)))
& between_on_line(sK0,sK3,sK4,sK5)
& convergent_lines(sK0,sK1)
& convergent_lines(sK0,sK2)
& convergent_lines(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5)],[f81]) ).
fof(f88,plain,
! [X0,X1] :
( unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f94,plain,
! [X0,X1] :
( unequally_directed_opposite_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f95,plain,
! [X0,X1] :
( unequally_directed_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f118,plain,
! [X0,X1] :
( left_convergent_lines(X0,X1)
| left_convergent_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(cnf_transformation,[],[f56]) ).
fof(f122,plain,
! [X0,X1] : ~ left_convergent_lines(X0,X1),
inference(cnf_transformation,[],[f58]) ).
fof(f142,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f87]) ).
fof(f236,plain,
! [X0,X1] :
( left_convergent_lines(X0,X1)
| ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(forward_subsumption_resolution,[],[f118,f122]) ).
fof(f237,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1) ),
inference(forward_subsumption_resolution,[],[f236,f122]) ).
fof(f241,plain,
! [X0,X1] :
( ~ unequally_directed_opposite_lines(X0,X1)
| ~ unequally_directed_lines(X0,X1) ),
inference(resolution,[],[f237,f88]) ).
fof(f246,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[],[f241,f94]) ).
fof(f247,plain,
! [X0,X1] : ~ convergent_lines(X0,X1),
inference(forward_subsumption_resolution,[],[f246,f95]) ).
fof(f251,plain,
$false,
inference(resolution,[],[f247,f142]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO263+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n002.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 07:58:07 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.34/1.36 % (3217835)Detected formulas, will run a generic FOF schedule.
% 3.34/1.36 % (3217840)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3117550285:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.34/1.36 % (3217845)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1790510803:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.34/1.36 % (3217846)dis-21_1_sil=8000:lcm=predicate:random_seed=3214672837:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.34/1.36 % (3217842)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=4060555273:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.34/1.36 % (3217841)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3667836122:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.34/1.36 % (3217845)First to succeed.
% 3.34/1.36 % (3217845)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3217835"
% 3.34/1.36 % (3217844)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=172726594:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.34/1.36 % (3217843)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1749642487:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.34/1.36 % (3217843)Refutation not found, incomplete strategy
% 3.34/1.36 % (3217843)------------------------------
% 3.34/1.36 % (3217843)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.34/1.36 % (3217843)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.34/1.36 % (3217843)CaDiCaL version: 2.1.3
% 3.34/1.36 % (3217843)Termination reason: Refutation not found, incomplete strategy
% 3.34/1.36 % (3217843)Time elapsed: 0.002 s
% 3.34/1.36 % (3217843)Peak memory usage: 88 MB
% 3.34/1.36 % (3217843)Instructions burned: 1 (million)
% 3.34/1.36 % (3217844)Also succeeded, but the first one will report.
% 3.34/1.36 % (3217846)Also succeeded, but the first one will report.
% 3.34/1.36 % (3217843)------------------------------
% 3.34/1.36 % (3217843)------------------------------
% 3.34/1.36 % (3217845)Refutation found. Thanks to Tanya!
% 3.34/1.36 % SZS status Theorem for theBenchmark
% 3.34/1.36 % SZS output start Proof for theBenchmark
% See solution above
% 3.34/1.36 % (3217845)------------------------------
% 3.34/1.36 % (3217845)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.34/1.36 % (3217845)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.34/1.36 % (3217845)CaDiCaL version: 2.1.3
% 3.34/1.36 % (3217845)Termination reason: Refutation
% 3.34/1.36 % (3217845)Time elapsed: 0.005 s
% 3.34/1.36 % (3217845)Peak memory usage: 89 MB
% 3.34/1.36 % (3217845)Instructions burned: 6 (million)
% 3.34/1.36 % (3217845)------------------------------
% 3.34/1.36 % (3217845)------------------------------
% 3.34/1.36 % (3217835)Success in time 0.404 s
% 3.34/1.36 % Vampire exiting
%------------------------------------------------------------------------------