%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO226+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 09:54:08 AM UTC 2026
% Result : Theorem 0.10s 0.44s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 3 unt; 0 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 66 ( 26 ~; 14 |; 18 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 37 ( 31 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ci3) ).
fof(f10,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ci4) ).
fof(f34,axiom,
! [X0,X1] :
( incident_point_and_line(X0,X1)
<=> ~ apart_point_and_line(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+6.ax',a4) ).
fof(f36,conjecture,
! [X0,X1] :
( ( line(X0)
& line(X1)
& convergent_lines(X0,X1) )
=> ? [X2] :
( point(X2)
=> ( incident_point_and_line(X2,X0)
& incident_point_and_line(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1] :
( ( line(X0)
& line(X1)
& convergent_lines(X0,X1) )
=> ? [X2] :
( point(X2)
=> ( incident_point_and_line(X2,X0)
& incident_point_and_line(X2,X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,X1)
=> incident_point_and_line(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f34]) ).
fof(f47,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f48,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f77,plain,
! [X0,X1] :
( incident_point_and_line(X0,X1)
| apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f78,plain,
? [X0,X1] :
( ! [X2] :
( ( ~ incident_point_and_line(X2,X0)
| ~ incident_point_and_line(X2,X1) )
& point(X2) )
& line(X0)
& line(X1)
& convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f79,plain,
? [X0,X1] :
( ! [X2] :
( ( ~ incident_point_and_line(X2,X0)
| ~ incident_point_and_line(X2,X1) )
& point(X2) )
& line(X0)
& line(X1)
& convergent_lines(X0,X1) ),
inference(flattening,[],[f78]) ).
fof(f80,plain,
( ! [X2] :
( ( ~ incident_point_and_line(X2,sK0)
| ~ incident_point_and_line(X2,sK1) )
& point(X2) )
& line(sK0)
& line(sK1)
& convergent_lines(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f79]) ).
fof(f89,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f90,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f117,plain,
! [X0,X1] :
( incident_point_and_line(X0,X1)
| apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f118,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f80]) ).
fof(f122,plain,
! [X2] :
( ~ incident_point_and_line(X2,sK1)
| ~ incident_point_and_line(X2,sK0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f124,plain,
! [X0] :
( ~ incident_point_and_line(X0,sK0)
| apart_point_and_line(X0,sK1) ),
inference(resolution,[],[f117,f122]) ).
fof(f125,plain,
! [X0] :
( apart_point_and_line(X0,sK1)
| apart_point_and_line(X0,sK0) ),
inference(resolution,[],[f124,f117]) ).
fof(f128,plain,
! [X0] :
( apart_point_and_line(intersection_point(X0,sK1),sK0)
| ~ convergent_lines(X0,sK1) ),
inference(resolution,[],[f90,f125]) ).
fof(f132,plain,
( ~ convergent_lines(sK0,sK1)
| ~ convergent_lines(sK0,sK1) ),
inference(resolution,[],[f128,f89]) ).
fof(f133,plain,
~ convergent_lines(sK0,sK1),
inference(duplicate_literal_removal,[],[f132]) ).
fof(f134,plain,
$false,
inference(forward_subsumption_resolution,[],[f133,f118]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO226+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n002.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 07:48:21 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.44 % (3213108)Will run a generic schedule for satisfiability detection.
% 0.10/0.44 % (3213114)% WARNING: option uhcvi not known.
% 0.10/0.44 % (3213113)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2059782400_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.44 % (3213115)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=299872786:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.44 % (3213116)dis+10_1_sil=32000:sp=arity:random_seed=169132618:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.44 % (3213117)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2630098957:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.44 % (3213118)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3407014833:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.44 % (3213119)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=980709288:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.44 % (3213114)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1994569752:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.44 % (3213116) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3213108-3213116"...
% 0.10/0.44 % TRYING [1]
% 0.10/0.44 % TRYING [2]
% 0.10/0.44 % (3213119) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3213108-3213119"...
% 0.10/0.44 % (3213114) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3213108-3213114"...
% 0.10/0.44 % TRYING [3]
% 0.10/0.44 % (3213117) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3213108-3213117"...
% 0.10/0.44 % (3213116)...printing done.
% 0.10/0.44 % (3213114)...printing done.
% 0.10/0.44 % (3213115) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3213108-3213115"...
% 0.10/0.44 % (3213119)...printing done.
% 0.10/0.44 % TRYING [4]
% 0.10/0.44 % (3213116)Refutation found. Thanks to Tanya!
% 0.10/0.44 % SZS status Theorem for theBenchmark
% 0.10/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.44 % (3213116)------------------------------
% 0.10/0.44 % (3213116)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.44 % (3213116)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.44 % (3213116)CaDiCaL version: 2.1.3
% 0.10/0.44 % (3213116)Termination reason: Refutation
% 0.10/0.44 % (3213116)Time elapsed: 0.002 s
% 0.10/0.44 % (3213116)Peak memory usage: 11 MB
% 0.10/0.44 % (3213116)Instructions burned: 2 (million)
% 0.10/0.44 % (3213108)Success in time 0.035 s
% 0.10/0.44 % Vampire exiting
%------------------------------------------------------------------------------