%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO204+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n026.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 09:53:59 AM UTC 2026
% Result : Theorem 0.10s 0.45s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 54 ( 9 unt; 2 def)
% Number of atoms : 145 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 156 ( 65 ~; 73 |; 9 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn 62 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2] :
( distinct_points(X0,X1)
=> ( distinct_points(X0,X2)
| distinct_points(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart4) ).
fof(f7,axiom,
! [X0,X1] :
( distinct_points(X0,X1)
=> ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ci1) ).
fof(f8,axiom,
! [X0,X1] :
( distinct_points(X0,X1)
=> ~ apart_point_and_line(X1,line_connecting(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ci2) ).
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/sandbox2/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/sandbox2/benchmark/Axioms/GEO006+0.ax',ceq1) ).
fof(f15,conjecture,
! [X0,X1,X2] :
( ( distinct_points(X0,X1)
& ~ distinct_points(X1,X2) )
=> ( distinct_points(X0,X2)
& ~ distinct_lines(line_connecting(X0,X1),line_connecting(X0,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f16,negated_conjecture,
~ ! [X0,X1,X2] :
( ( distinct_points(X0,X1)
& ~ distinct_points(X1,X2) )
=> ( distinct_points(X0,X2)
& ~ distinct_lines(line_connecting(X0,X1),line_connecting(X0,X2)) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f17,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| distinct_points(X1,X2)
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f18,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| distinct_points(X1,X2)
| ~ distinct_points(X0,X1) ),
inference(flattening,[],[f17]) ).
fof(f23,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f24,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
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(f35,plain,
? [X0,X1,X2] :
( ( ~ distinct_points(X0,X2)
| distinct_lines(line_connecting(X0,X1),line_connecting(X0,X2)) )
& distinct_points(X0,X1)
& ~ distinct_points(X1,X2) ),
inference(ennf_transformation,[],[f16]) ).
fof(f36,plain,
? [X0,X1,X2] :
( ( ~ distinct_points(X0,X2)
| distinct_lines(line_connecting(X0,X1),line_connecting(X0,X2)) )
& distinct_points(X0,X1)
& ~ distinct_points(X1,X2) ),
inference(flattening,[],[f35]) ).
fof(f40,plain,
! [X2,X0,X1] :
( ~ distinct_points(X0,X1)
| distinct_points(X1,X2)
| distinct_points(X0,X2) ),
inference(cnf_transformation,[],[f18]) ).
fof(f43,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
inference(cnf_transformation,[],[f23]) ).
fof(f44,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X1,line_connecting(X0,X1)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f47,plain,
! [X2,X3,X0,X1] :
( ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1)
| apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2) ),
inference(cnf_transformation,[],[f28]) ).
fof(f48,plain,
! [X2,X0,X1] :
( distinct_points(X0,X2)
| apart_point_and_line(X2,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f51,plain,
( distinct_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2))
| ~ distinct_points(sK0,sK2) ),
inference(cnf_transformation,[],[f36]) ).
fof(f52,plain,
~ distinct_points(sK1,sK2),
inference(cnf_transformation,[],[f36]) ).
fof(f53,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f36]) ).
fof(f55,definition,
( spl3_1
<=> distinct_points(sK0,sK2) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f56,plain,
( distinct_points(sK0,sK2)
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f55]) ).
fof(f57,plain,
( ~ distinct_points(sK0,sK2)
| spl3_1 ),
inference(avatar_component_clause,[],[f55]) ).
fof(f59,definition,
( spl3_2
<=> distinct_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2)) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f61,plain,
( distinct_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2))
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f62,plain,
( ~ spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f51,f59,f55]) ).
fof(f63,plain,
~ apart_point_and_line(sK0,line_connecting(sK0,sK1)),
inference(resolution,[],[f43,f53]) ).
fof(f64,plain,
~ apart_point_and_line(sK1,line_connecting(sK0,sK1)),
inference(resolution,[],[f44,f53]) ).
fof(f67,plain,
! [X0] :
( distinct_points(X0,sK2)
| ~ distinct_points(X0,sK1) ),
inference(resolution,[],[f40,f52]) ).
fof(f88,plain,
( ~ distinct_points(sK0,sK1)
| spl3_1 ),
inference(resolution,[],[f67,f57]) ).
fof(f93,plain,
( $false
| spl3_1 ),
inference(forward_subsumption_resolution,[],[f88,f53]) ).
fof(f94,plain,
spl3_1,
inference(avatar_contradiction_clause,[],[f93]) ).
fof(f95,plain,
( ~ apart_point_and_line(sK2,line_connecting(sK0,sK2))
| ~ spl3_1 ),
inference(resolution,[],[f56,f44]) ).
fof(f96,plain,
( ~ apart_point_and_line(sK0,line_connecting(sK0,sK2))
| ~ spl3_1 ),
inference(resolution,[],[f56,f43]) ).
fof(f116,plain,
! [X0] :
( apart_point_and_line(sK2,X0)
| ~ apart_point_and_line(sK1,X0) ),
inference(resolution,[],[f48,f52]) ).
fof(f127,plain,
( ~ apart_point_and_line(sK1,line_connecting(sK0,sK2))
| ~ spl3_1 ),
inference(resolution,[],[f116,f95]) ).
fof(f139,plain,
( ! [X0,X1] :
( ~ distinct_points(X0,X1)
| apart_point_and_line(X1,line_connecting(sK0,sK2))
| apart_point_and_line(X1,line_connecting(sK0,sK1))
| apart_point_and_line(X0,line_connecting(sK0,sK2))
| apart_point_and_line(X0,line_connecting(sK0,sK1)) )
| ~ spl3_2 ),
inference(resolution,[],[f47,f61]) ).
fof(f157,plain,
( apart_point_and_line(sK1,line_connecting(sK0,sK2))
| apart_point_and_line(sK1,line_connecting(sK0,sK1))
| apart_point_and_line(sK0,line_connecting(sK0,sK2))
| apart_point_and_line(sK0,line_connecting(sK0,sK1))
| ~ spl3_2 ),
inference(resolution,[],[f139,f53]) ).
fof(f169,plain,
( apart_point_and_line(sK1,line_connecting(sK0,sK1))
| apart_point_and_line(sK0,line_connecting(sK0,sK2))
| apart_point_and_line(sK0,line_connecting(sK0,sK1))
| ~ spl3_1
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f157,f127]) ).
fof(f184,plain,
( apart_point_and_line(sK0,line_connecting(sK0,sK2))
| apart_point_and_line(sK0,line_connecting(sK0,sK1))
| ~ spl3_1
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f169,f64]) ).
fof(f186,plain,
( apart_point_and_line(sK0,line_connecting(sK0,sK1))
| ~ spl3_1
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f184,f96]) ).
fof(f188,plain,
( $false
| ~ spl3_1
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f186,f63]) ).
fof(f189,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_contradiction_clause,[],[f188]) ).
cnf(s1,plain,
( ~ spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f62]) ).
cnf(s2,plain,
spl3_1,
inference(sat_conversion,[],[f94]) ).
cnf(s6,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f189]) ).
cnf(s7,plain,
~ spl3_2,
inference(rat,[],[s6,s2]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s7,s2]) ).
fof(f190,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO204+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 07:38:26 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
% 0.10/0.45 % (2499749)Will run a generic schedule for satisfiability detection.
% 0.10/0.45 % (2499756)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1738394000:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.45 % (2499755)% WARNING: option uhcvi not known.
% 0.10/0.45 % (2499754)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2806247377_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.45 % (2499760)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2688368080:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.45 % (2499757)dis+10_1_sil=32000:sp=arity:random_seed=2062742249:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.45 % (2499758)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1055090983:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.45 % (2499759)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=347702713:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.45 % (2499755)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3260243288:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.45 % TRYING [1]
% 0.10/0.45 % TRYING [2]
% 0.10/0.45 % TRYING [3]
% 0.10/0.45 % TRYING [4]
% 0.10/0.45 % TRYING [5]
% 0.10/0.45 % (2499758) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2499749-2499758"...
% 0.10/0.45 % (2499757) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2499749-2499757"...
% 0.10/0.45 % (2499755) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2499749-2499755"...
% 0.10/0.45 % (2499758)...printing done.
% 0.10/0.45 % TRYING [6]
% 0.10/0.45 % (2499759) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2499749-2499759"...
% 0.10/0.45 % (2499758)Refutation found. Thanks to Tanya!
% 0.10/0.45 % SZS status Theorem for theBenchmark
% 0.10/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.46 % (2499758)------------------------------
% 0.10/0.46 % (2499758)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.46 % (2499758)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.46 % (2499758)CaDiCaL version: 2.1.3
% 0.10/0.46 % (2499758)Termination reason: Refutation
% 0.10/0.46 % (2499758)Time elapsed: 0.005 s
% 0.10/0.46 % (2499758)Peak memory usage: 12 MB
% 0.10/0.46 % (2499758)Instructions burned: 7 (million)
% 0.10/0.46 % (2499749)Success in time 0.043 s
% 0.10/0.46 % Vampire exiting
%------------------------------------------------------------------------------