%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO181+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 : 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 : Tue Sep 29 09:53:50 AM UTC 2026
% Result : Theorem 0.10s 0.48s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of formulae : 83 ( 16 unt; 6 def)
% Number of atoms : 208 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 223 ( 98 ~; 102 |; 7 &)
% ( 6 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 7 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 101 ( 0 sgn 95 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart1) ).
fof(f4,axiom,
! [X0,X1,X2] :
( distinct_points(X0,X1)
=> ( distinct_points(X0,X2)
| distinct_points(X1,X2) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/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(f13,axiom,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
=> ( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ceq2) ).
fof(f15,conjecture,
! [X0,X1,X2] :
( distinct_points(X0,X1)
=> ( apart_point_and_line(X2,line_connecting(X0,X1))
=> apart_point_and_line(X1,line_connecting(X0,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f16,negated_conjecture,
~ ! [X0,X1,X2] :
( distinct_points(X0,X1)
=> ( apart_point_and_line(X2,line_connecting(X0,X1))
=> apart_point_and_line(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(f31,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f32,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f31]) ).
fof(f35,plain,
? [X0,X1,X2] :
( ~ apart_point_and_line(X1,line_connecting(X0,X2))
& apart_point_and_line(X2,line_connecting(X0,X1))
& distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f36,plain,
? [X0,X1,X2] :
( ~ apart_point_and_line(X1,line_connecting(X0,X2))
& apart_point_and_line(X2,line_connecting(X0,X1))
& distinct_points(X0,X1) ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
( ~ apart_point_and_line(sK1,line_connecting(sK0,sK2))
& apart_point_and_line(sK2,line_connecting(sK0,sK1))
& distinct_points(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f36]) ).
fof(f38,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f41,plain,
! [X2,X0,X1] :
( distinct_points(X1,X2)
| distinct_points(X0,X2)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f44,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f45,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f48,plain,
! [X2,X3,X0,X1] :
( 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(cnf_transformation,[],[f28]) ).
fof(f49,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(f50,plain,
! [X2,X0,X1] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f52,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f37]) ).
fof(f53,plain,
apart_point_and_line(sK2,line_connecting(sK0,sK1)),
inference(cnf_transformation,[],[f37]) ).
fof(f54,plain,
~ apart_point_and_line(sK1,line_connecting(sK0,sK2)),
inference(cnf_transformation,[],[f37]) ).
fof(f57,plain,
! [X0,X1] :
( apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(consistent_polarity_flipping,[],[f44]) ).
fof(f58,plain,
! [X0,X1] :
( apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(consistent_polarity_flipping,[],[f45]) ).
fof(f61,plain,
! [X2,X3,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)
| ~ distinct_points(X0,X1)
| distinct_lines(X2,X3) ),
inference(consistent_polarity_flipping,[],[f48]) ).
fof(f62,plain,
! [X2,X0,X1] :
( apart_point_and_line(X0,X1)
| ~ apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ),
inference(consistent_polarity_flipping,[],[f49]) ).
fof(f63,plain,
! [X2,X0,X1] :
( apart_point_and_line(X0,X1)
| ~ apart_point_and_line(X0,X2)
| ~ distinct_lines(X1,X2) ),
inference(consistent_polarity_flipping,[],[f50]) ).
fof(f65,plain,
apart_point_and_line(sK1,line_connecting(sK0,sK2)),
inference(consistent_polarity_flipping,[],[f54]) ).
fof(f66,plain,
~ apart_point_and_line(sK2,line_connecting(sK0,sK1)),
inference(consistent_polarity_flipping,[],[f53]) ).
fof(f69,plain,
! [X0] :
( ~ apart_point_and_line(X0,line_connecting(sK0,sK1))
| distinct_points(sK2,X0) ),
inference(resolution,[],[f62,f66]) ).
fof(f70,plain,
( distinct_points(sK2,sK0)
| ~ distinct_points(sK0,sK1) ),
inference(resolution,[],[f69,f57]) ).
fof(f76,definition,
( spl3_1
<=> distinct_points(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f78,plain,
( ~ distinct_points(sK0,sK1)
| spl3_1 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f85,definition,
( spl3_3
<=> distinct_points(sK2,sK0) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f88,plain,
( ~ spl3_1
| spl3_3 ),
inference(avatar_split_clause,[],[f70,f85,f76]) ).
fof(f89,plain,
( $false
| spl3_1 ),
inference(resolution,[],[f78,f52]) ).
fof(f91,plain,
spl3_1,
inference(avatar_contradiction_clause,[],[f89]) ).
fof(f92,plain,
! [X0] :
( ~ apart_point_and_line(sK2,X0)
| ~ distinct_lines(line_connecting(sK0,sK1),X0) ),
inference(resolution,[],[f63,f66]) ).
fof(f95,plain,
! [X0] :
( ~ distinct_lines(line_connecting(sK0,sK1),line_connecting(X0,sK2))
| ~ distinct_points(X0,sK2) ),
inference(resolution,[],[f92,f58]) ).
fof(f214,plain,
! [X0,X1] :
( distinct_lines(X0,line_connecting(sK0,sK2))
| ~ apart_point_and_line(X1,line_connecting(sK0,sK2))
| ~ apart_point_and_line(X1,X0)
| ~ distinct_points(X1,sK1)
| ~ apart_point_and_line(sK1,X0) ),
inference(resolution,[],[f61,f65]) ).
fof(f326,plain,
! [X0] :
( ~ apart_point_and_line(X0,line_connecting(sK0,sK2))
| ~ apart_point_and_line(X0,line_connecting(sK0,sK1))
| ~ distinct_points(X0,sK1)
| ~ apart_point_and_line(sK1,line_connecting(sK0,sK1))
| ~ distinct_points(sK0,sK2) ),
inference(resolution,[],[f214,f95]) ).
fof(f395,definition,
( spl3_20
<=> distinct_points(sK0,sK2) ),
introduced(definition,[new_symbols(definition,[spl3_20])],[avatar_definition]) ).
fof(f397,plain,
( ~ distinct_points(sK0,sK2)
| spl3_20 ),
inference(avatar_component_clause,[],[f395]) ).
fof(f412,definition,
( spl3_24
<=> apart_point_and_line(sK1,line_connecting(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_24])],[avatar_definition]) ).
fof(f414,plain,
( ~ apart_point_and_line(sK1,line_connecting(sK0,sK1))
| spl3_24 ),
inference(avatar_component_clause,[],[f412]) ).
fof(f416,definition,
( spl3_25
<=> ! [X0] :
( ~ apart_point_and_line(X0,line_connecting(sK0,sK2))
| ~ distinct_points(X0,sK1)
| ~ apart_point_and_line(X0,line_connecting(sK0,sK1)) ) ),
introduced(definition,[new_symbols(definition,[spl3_25])],[avatar_definition]) ).
fof(f417,plain,
( ! [X0] :
( ~ apart_point_and_line(X0,line_connecting(sK0,sK2))
| ~ distinct_points(X0,sK1)
| ~ apart_point_and_line(X0,line_connecting(sK0,sK1)) )
| ~ spl3_25 ),
inference(avatar_component_clause,[],[f416]) ).
fof(f457,plain,
( ~ spl3_20
| ~ spl3_24
| spl3_25 ),
inference(avatar_split_clause,[],[f326,f416,f412,f395]) ).
fof(f458,plain,
( ! [X0] :
( distinct_points(X0,sK2)
| ~ distinct_points(X0,sK0) )
| spl3_20 ),
inference(resolution,[],[f397,f41]) ).
fof(f459,plain,
( ~ distinct_points(sK0,sK1)
| spl3_24 ),
inference(resolution,[],[f414,f58]) ).
fof(f462,plain,
( ~ spl3_1
| spl3_24 ),
inference(avatar_split_clause,[],[f459,f412,f76]) ).
fof(f471,plain,
( ~ distinct_points(sK2,sK0)
| spl3_20 ),
inference(resolution,[],[f458,f38]) ).
fof(f473,plain,
( ~ spl3_3
| spl3_20 ),
inference(avatar_split_clause,[],[f471,f395,f85]) ).
fof(f489,plain,
( ~ distinct_points(sK0,sK1)
| ~ apart_point_and_line(sK0,line_connecting(sK0,sK1))
| ~ distinct_points(sK0,sK2)
| ~ spl3_25 ),
inference(resolution,[],[f417,f57]) ).
fof(f496,definition,
( spl3_34
<=> apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_34])],[avatar_definition]) ).
fof(f498,plain,
( ~ apart_point_and_line(sK0,line_connecting(sK0,sK1))
| spl3_34 ),
inference(avatar_component_clause,[],[f496]) ).
fof(f499,plain,
( ~ spl3_20
| ~ spl3_34
| ~ spl3_1
| ~ spl3_25 ),
inference(avatar_split_clause,[],[f489,f416,f76,f496,f395]) ).
fof(f500,plain,
( ~ distinct_points(sK0,sK1)
| spl3_34 ),
inference(resolution,[],[f498,f57]) ).
fof(f503,plain,
( ~ spl3_1
| spl3_34 ),
inference(avatar_split_clause,[],[f500,f496,f76]) ).
cnf(s2,plain,
( ~ spl3_1
| spl3_3 ),
inference(sat_conversion,[],[f88]) ).
cnf(s3,plain,
spl3_1,
inference(sat_conversion,[],[f91]) ).
cnf(s37,plain,
( ~ spl3_20
| ~ spl3_24
| spl3_25 ),
inference(sat_conversion,[],[f457]) ).
cnf(s38,plain,
( ~ spl3_1
| spl3_24 ),
inference(sat_conversion,[],[f462]) ).
cnf(s39,plain,
( ~ spl3_3
| spl3_20 ),
inference(sat_conversion,[],[f473]) ).
cnf(s40,plain,
( ~ spl3_1
| ~ spl3_20
| ~ spl3_25
| ~ spl3_34 ),
inference(sat_conversion,[],[f499]) ).
cnf(s41,plain,
( ~ spl3_1
| spl3_34 ),
inference(sat_conversion,[],[f503]) ).
cnf(s42,plain,
spl3_34,
inference(rat,[],[s41,s3]) ).
cnf(s43,plain,
spl3_24,
inference(rat,[],[s38,s3]) ).
cnf(s50,plain,
spl3_3,
inference(rat,[],[s2,s3]) ).
cnf(s51,plain,
spl3_20,
inference(rat,[],[s39,s50]) ).
cnf(s52,plain,
~ spl3_25,
inference(rat,[],[s40,s42,s3,s51]) ).
cnf(s53,plain,
$false,
inference(rat,[],[s37,s43,s52,s51]) ).
fof(f504,plain,
$false,
inference(avatar_sat_refutation,[],[s53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO181+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n007.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 07:23:55 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.42 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
% 0.10/0.48 % (1069630)Will run a generic schedule for satisfiability detection.
% 0.10/0.48 % (1069637)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=456405745:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.48 % (1069636)% WARNING: option uhcvi not known.
% 0.10/0.48 % (1069635)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1688155675_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.48 % (1069638)dis+10_1_sil=32000:sp=arity:random_seed=595371045:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.48 % (1069639)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2023582444:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.48 % (1069636)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1479920213:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.48 % (1069640)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1773859045:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.48 % (1069641)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=838117844:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.48 % TRYING [1]
% 0.10/0.48 % TRYING [2]
% 0.10/0.48 % TRYING [3]
% 0.10/0.48 % TRYING [4]
% 0.10/0.48 % TRYING [5]
% 0.10/0.48 % TRYING [6]
% 0.10/0.48 % (1069641) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1069630-1069641"...
% 0.10/0.48 % TRYING [7]
% 0.10/0.48 % (1069641)...printing done.
% 0.10/0.48 % (1069641)Refutation found. Thanks to Tanya!
% 0.10/0.48 % SZS status Theorem for theBenchmark
% 0.10/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.48 % (1069641)------------------------------
% 0.10/0.48 % (1069641)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.48 % (1069641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.48 % (1069641)CaDiCaL version: 2.1.3
% 0.10/0.48 % (1069641)Termination reason: Refutation
% 0.10/0.48 % (1069641)Time elapsed: 0.012 s
% 0.10/0.48 % (1069641)Peak memory usage: 12 MB
% 0.10/0.48 % (1069641)Instructions burned: 17 (million)
% 0.10/0.48 % (1069630)Success in time 0.051 s
% 0.10/0.48 % Vampire exiting
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