%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO198+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n004.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 09:53:57 AM UTC 2026
% Result : Theorem 0.17s 0.48s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 64 ( 19 unt; 4 def)
% Number of atoms : 160 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 155 ( 59 ~; 66 |; 19 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 71 ( 0 sgn 65 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart3) ).
fof(f9,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/GEO006+0.ax',ci4) ).
fof(f11,axiom,
! [X0,X1,X2,X3] :
( ( distinct_points(X0,X1)
& distinct_lines(X2,X3) )
=> ( apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',cu1) ).
fof(f12,axiom,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
=> ( distinct_points(X0,X2)
| apart_point_and_line(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ceq1) ).
fof(f14,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( distinct_lines(X1,X2)
| convergent_lines(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ceq3) ).
fof(f15,conjecture,
! [X0,X1,X2] :
( ( convergent_lines(X0,X1)
& convergent_lines(X2,X1)
& convergent_lines(X0,X2)
& ~ apart_point_and_line(intersection_point(X0,X1),X2) )
=> ~ apart_point_and_line(intersection_point(X0,X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f16,negated_conjecture,
~ ! [X0,X1,X2] :
( ( convergent_lines(X0,X1)
& convergent_lines(X2,X1)
& convergent_lines(X0,X2)
& ~ apart_point_and_line(intersection_point(X0,X1),X2) )
=> ~ apart_point_and_line(intersection_point(X0,X2),X1) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f25,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f26,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f27,plain,
! [X0,X1,X2,X3] :
( apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X3)
| ~ distinct_points(X0,X1)
| ~ distinct_lines(X2,X3) ),
inference(ennf_transformation,[],[f11]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X3)
| ~ distinct_points(X0,X1)
| ~ distinct_lines(X2,X3) ),
inference(flattening,[],[f27]) ).
fof(f29,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| apart_point_and_line(X2,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f30,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| apart_point_and_line(X2,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f29]) ).
fof(f33,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f34,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f33]) ).
fof(f35,plain,
? [X0,X1,X2] :
( apart_point_and_line(intersection_point(X0,X2),X1)
& convergent_lines(X0,X1)
& convergent_lines(X2,X1)
& convergent_lines(X0,X2)
& ~ apart_point_and_line(intersection_point(X0,X1),X2) ),
inference(ennf_transformation,[],[f16]) ).
fof(f36,plain,
? [X0,X1,X2] :
( apart_point_and_line(intersection_point(X0,X2),X1)
& convergent_lines(X0,X1)
& convergent_lines(X2,X1)
& convergent_lines(X0,X2)
& ~ apart_point_and_line(intersection_point(X0,X1),X2) ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
( apart_point_and_line(intersection_point(sK0,sK2),sK1)
& convergent_lines(sK0,sK1)
& convergent_lines(sK2,sK1)
& convergent_lines(sK0,sK2)
& ~ apart_point_and_line(intersection_point(sK0,sK1),sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f36]) ).
fof(f40,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f46,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f47,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f48,plain,
! [X2,X3,X0,X1] :
( ~ distinct_lines(X2,X3)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X3)
| ~ distinct_points(X0,X1)
| apart_point_and_line(X0,X2) ),
inference(cnf_transformation,[],[f28]) ).
fof(f49,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f51,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f34]) ).
fof(f52,plain,
~ apart_point_and_line(intersection_point(sK0,sK1),sK2),
inference(cnf_transformation,[],[f37]) ).
fof(f53,plain,
convergent_lines(sK0,sK2),
inference(cnf_transformation,[],[f37]) ).
fof(f55,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f37]) ).
fof(f56,plain,
apart_point_and_line(intersection_point(sK0,sK2),sK1),
inference(cnf_transformation,[],[f37]) ).
fof(f60,plain,
! [X0] :
( apart_point_and_line(X0,sK1)
| distinct_points(intersection_point(sK0,sK2),X0) ),
inference(resolution,[],[f49,f56]) ).
fof(f66,plain,
! [X0] :
( convergent_lines(sK0,X0)
| distinct_lines(sK2,X0) ),
inference(resolution,[],[f51,f53]) ).
fof(f76,plain,
distinct_lines(sK2,sK0),
inference(resolution,[],[f66,f40]) ).
fof(f79,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| apart_point_and_line(X1,sK2)
| apart_point_and_line(X1,sK0)
| apart_point_and_line(X0,sK0)
| apart_point_and_line(X0,sK2) ),
inference(resolution,[],[f76,f48]) ).
fof(f92,plain,
! [X0] :
( ~ convergent_lines(X0,sK1)
| distinct_points(intersection_point(sK0,sK2),intersection_point(X0,sK1)) ),
inference(resolution,[],[f60,f47]) ).
fof(f233,plain,
distinct_points(intersection_point(sK0,sK2),intersection_point(sK0,sK1)),
inference(resolution,[],[f92,f55]) ).
fof(f282,definition,
( spl3_6
<=> distinct_points(intersection_point(sK0,sK2),intersection_point(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
fof(f284,plain,
( distinct_points(intersection_point(sK0,sK2),intersection_point(sK0,sK1))
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f282]) ).
fof(f296,plain,
spl3_6,
inference(avatar_split_clause,[],[f233,f282]) ).
fof(f1996,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK2)
| apart_point_and_line(intersection_point(sK0,sK1),sK0)
| apart_point_and_line(intersection_point(sK0,sK2),sK0)
| apart_point_and_line(intersection_point(sK0,sK2),sK2)
| ~ spl3_6 ),
inference(resolution,[],[f79,f284]) ).
fof(f1997,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK0)
| apart_point_and_line(intersection_point(sK0,sK2),sK0)
| apart_point_and_line(intersection_point(sK0,sK2),sK2)
| ~ spl3_6 ),
inference(forward_subsumption_resolution,[],[f1996,f52]) ).
fof(f1999,definition,
( spl3_54
<=> apart_point_and_line(intersection_point(sK0,sK2),sK2) ),
introduced(definition,[new_symbols(definition,[spl3_54])],[avatar_definition]) ).
fof(f2001,plain,
( apart_point_and_line(intersection_point(sK0,sK2),sK2)
| ~ spl3_54 ),
inference(avatar_component_clause,[],[f1999]) ).
fof(f2003,definition,
( spl3_55
<=> apart_point_and_line(intersection_point(sK0,sK2),sK0) ),
introduced(definition,[new_symbols(definition,[spl3_55])],[avatar_definition]) ).
fof(f2005,plain,
( apart_point_and_line(intersection_point(sK0,sK2),sK0)
| ~ spl3_55 ),
inference(avatar_component_clause,[],[f2003]) ).
fof(f2034,definition,
( spl3_62
<=> apart_point_and_line(intersection_point(sK0,sK1),sK0) ),
introduced(definition,[new_symbols(definition,[spl3_62])],[avatar_definition]) ).
fof(f2036,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK0)
| ~ spl3_62 ),
inference(avatar_component_clause,[],[f2034]) ).
fof(f2037,plain,
( spl3_54
| spl3_55
| spl3_62
| ~ spl3_6 ),
inference(avatar_split_clause,[],[f1997,f282,f2034,f2003,f1999]) ).
fof(f2038,plain,
( ~ convergent_lines(sK0,sK2)
| ~ spl3_54 ),
inference(resolution,[],[f2001,f47]) ).
fof(f2041,plain,
( $false
| ~ spl3_54 ),
inference(forward_subsumption_resolution,[],[f2038,f53]) ).
fof(f2042,plain,
~ spl3_54,
inference(avatar_contradiction_clause,[],[f2041]) ).
fof(f2057,plain,
( ~ convergent_lines(sK0,sK2)
| ~ spl3_55 ),
inference(resolution,[],[f2005,f46]) ).
fof(f2060,plain,
( $false
| ~ spl3_55 ),
inference(forward_subsumption_resolution,[],[f2057,f53]) ).
fof(f2061,plain,
~ spl3_55,
inference(avatar_contradiction_clause,[],[f2060]) ).
fof(f2076,plain,
( ~ convergent_lines(sK0,sK1)
| ~ spl3_62 ),
inference(resolution,[],[f2036,f46]) ).
fof(f2079,plain,
( $false
| ~ spl3_62 ),
inference(forward_subsumption_resolution,[],[f2076,f55]) ).
fof(f2080,plain,
~ spl3_62,
inference(avatar_contradiction_clause,[],[f2079]) ).
cnf(s10,plain,
spl3_6,
inference(sat_conversion,[],[f296]) ).
cnf(s111,plain,
( ~ spl3_6
| spl3_54
| spl3_55
| spl3_62 ),
inference(sat_conversion,[],[f2037]) ).
cnf(s112,plain,
~ spl3_54,
inference(sat_conversion,[],[f2042]) ).
cnf(s113,plain,
~ spl3_55,
inference(sat_conversion,[],[f2061]) ).
cnf(s114,plain,
~ spl3_62,
inference(sat_conversion,[],[f2080]) ).
cnf(s115,plain,
~ spl3_6,
inference(rat,[],[s111,s114,s113,s112]) ).
cnf(s119,plain,
$false,
inference(rat,[],[s10,s115]) ).
fof(f2081,plain,
$false,
inference(avatar_sat_refutation,[],[s119]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO198+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.37 % Computer : n004.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 07:33:21 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.41 Running first-order model finding
% 0.09/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.48 % (3175484)Will run a generic schedule for satisfiability detection.
% 0.17/0.48 % (3175494)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2221176330:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.48 % (3175490)% WARNING: option uhcvi not known.
% 0.17/0.48 % (3175489)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2828601402_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.48 % (3175490)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2506271193:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.48 % (3175491)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3798989803:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.48 % (3175492)dis+10_1_sil=32000:sp=arity:random_seed=2169467469:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.48 % (3175493)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3646311180:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.48 % (3175495)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3791788911:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.48 % TRYING [1]
% 0.17/0.48 % TRYING [2]
% 0.17/0.48 % TRYING [3]
% 0.17/0.48 % TRYING [4]
% 0.17/0.48 % TRYING [5]
% 0.17/0.48 % TRYING [6]
% 0.17/0.48 % TRYING [7]
% 0.17/0.48 % (3175494) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3175484-3175494"...
% 0.17/0.48 % (3175494)...printing done.
% 0.17/0.48 % (3175494)Refutation found. Thanks to Tanya!
% 0.17/0.48 % SZS status Theorem for theBenchmark
% 0.17/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.48 % (3175494)------------------------------
% 0.17/0.48 % (3175494)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.48 % (3175494)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.48 % (3175494)CaDiCaL version: 2.1.3
% 0.17/0.48 % (3175494)Termination reason: Refutation
% 0.17/0.48 % (3175494)Time elapsed: 0.027 s
% 0.17/0.48 % (3175494)Peak memory usage: 13 MB
% 0.17/0.48 % (3175494)Instructions burned: 83 (million)
% 0.17/0.48 % (3175484)Success in time 0.062 s
% 0.17/0.48 % Vampire exiting
%------------------------------------------------------------------------------