%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO191+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 : n016.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 09:51:54 AM UTC 2026
% Result : Theorem 3.63s 1.44s
% Output : Refutation 3.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 45 ( 13 unt; 2 def)
% Number of atoms : 109 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 101 ( 37 ~; 41 |; 16 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 66 ( 0 sgn 58 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart3) ).
fof(f6,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( convergent_lines(X0,X2)
| convergent_lines(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax6) ).
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/theBenchmark.p',ceq2) ).
fof(f15,axiom,
! [X0,X1] :
( distinct_lines(X0,X1)
=> convergent_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(f16,axiom,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cp1) ).
fof(f17,axiom,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cp2) ).
fof(f36,conjecture,
! [X0,X1,X2,X3] :
( ( convergent_lines(X0,X1)
& convergent_lines(X2,X3)
& ( apart_point_and_line(intersection_point(X0,X1),X2)
| apart_point_and_line(intersection_point(X0,X1),X3) ) )
=> ( apart_point_and_line(intersection_point(X2,X3),X0)
| apart_point_and_line(intersection_point(X2,X3),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( convergent_lines(X0,X1)
& convergent_lines(X2,X3)
& ( apart_point_and_line(intersection_point(X0,X1),X2)
| apart_point_and_line(intersection_point(X0,X1),X3) ) )
=> ( apart_point_and_line(intersection_point(X2,X3),X0)
| apart_point_and_line(intersection_point(X2,X3),X1) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f42,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f43,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f42]) ).
fof(f52,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(f53,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f52]) ).
fof(f56,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f76,plain,
? [X0,X1,X2,X3] :
( ~ apart_point_and_line(intersection_point(X2,X3),X0)
& ~ apart_point_and_line(intersection_point(X2,X3),X1)
& convergent_lines(X0,X1)
& convergent_lines(X2,X3)
& ( apart_point_and_line(intersection_point(X0,X1),X2)
| apart_point_and_line(intersection_point(X0,X1),X3) ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f77,plain,
? [X0,X1,X2,X3] :
( ~ apart_point_and_line(intersection_point(X2,X3),X0)
& ~ apart_point_and_line(intersection_point(X2,X3),X1)
& convergent_lines(X0,X1)
& convergent_lines(X2,X3)
& ( apart_point_and_line(intersection_point(X0,X1),X2)
| apart_point_and_line(intersection_point(X0,X1),X3) ) ),
inference(flattening,[],[f76]) ).
fof(f78,plain,
( ~ apart_point_and_line(intersection_point(sK2,sK3),sK0)
& ~ apart_point_and_line(intersection_point(sK2,sK3),sK1)
& convergent_lines(sK0,sK1)
& convergent_lines(sK2,sK3)
& ( apart_point_and_line(intersection_point(sK0,sK1),sK2)
| apart_point_and_line(intersection_point(sK0,sK1),sK3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f77]) ).
fof(f81,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f84,plain,
! [X2,X0,X1] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f91,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f53]) ).
fof(f93,plain,
! [X0,X1] :
( ~ distinct_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
fof(f94,plain,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f16]) ).
fof(f95,plain,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f115,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK2)
| apart_point_and_line(intersection_point(sK0,sK1),sK3) ),
inference(cnf_transformation,[],[f78]) ).
fof(f121,definition,
( spl4_1
<=> apart_point_and_line(intersection_point(sK0,sK1),sK3) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f123,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK3)
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f125,definition,
( spl4_2
<=> apart_point_and_line(intersection_point(sK0,sK1),sK2) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f127,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK2)
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f128,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f115,f125,f121]) ).
fof(f130,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| ~ convergent_lines(X1,X0) ),
inference(resolution,[],[f84,f81]) ).
fof(f133,plain,
! [X0,X1] : ~ convergent_lines(X0,parallel_through_point(X0,X1)),
inference(resolution,[],[f130,f94]) ).
fof(f136,plain,
( ! [X0] :
( distinct_lines(sK2,X0)
| apart_point_and_line(intersection_point(sK0,sK1),X0) )
| ~ spl4_2 ),
inference(resolution,[],[f91,f127]) ).
fof(f138,plain,
( ! [X0] :
( convergent_lines(sK2,X0)
| apart_point_and_line(intersection_point(sK0,sK1),X0) )
| ~ spl4_2 ),
inference(resolution,[],[f136,f93]) ).
fof(f146,plain,
( ! [X0] : apart_point_and_line(intersection_point(sK0,sK1),parallel_through_point(sK2,X0))
| ~ spl4_2 ),
inference(resolution,[],[f133,f138]) ).
fof(f147,plain,
( $false
| ~ spl4_2 ),
inference(resolution,[],[f146,f95]) ).
fof(f150,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f147]) ).
fof(f151,plain,
( ! [X0] :
( distinct_lines(sK3,X0)
| apart_point_and_line(intersection_point(sK0,sK1),X0) )
| ~ spl4_1 ),
inference(resolution,[],[f123,f91]) ).
fof(f154,plain,
( ! [X0] :
( convergent_lines(sK3,X0)
| apart_point_and_line(intersection_point(sK0,sK1),X0) )
| ~ spl4_1 ),
inference(resolution,[],[f151,f93]) ).
fof(f159,plain,
( ! [X0] : apart_point_and_line(intersection_point(sK0,sK1),parallel_through_point(sK3,X0))
| ~ spl4_1 ),
inference(resolution,[],[f154,f133]) ).
fof(f161,plain,
( $false
| ~ spl4_1 ),
inference(resolution,[],[f159,f95]) ).
fof(f164,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f161]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f128]) ).
cnf(s2,plain,
~ spl4_2,
inference(sat_conversion,[],[f150]) ).
cnf(s3,plain,
~ spl4_1,
inference(sat_conversion,[],[f164]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f165,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO191+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n016.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 07:35:31 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 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
% 3.63/1.44 % (2293812)Detected formulas, will run a generic FOF schedule.
% 3.63/1.44 % (2293846)dis-21_1_sil=8000:lcm=predicate:random_seed=726817141: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)
% 3.63/1.44 % (2293841)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=1672949368:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.63/1.44 % (2293840)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=482172757:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.63/1.44 % (2293842)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=1592510532:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.63/1.44 % (2293844)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2100261373:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.63/1.44 % (2293843)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2851739031:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.63/1.44 % (2293845)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1087848565:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.63/1.44 % (2293843)Refutation not found, incomplete strategy
% 3.63/1.44 % (2293843)------------------------------
% 3.63/1.44 % (2293843)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.44 % (2293843)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.44 % (2293843)CaDiCaL version: 2.1.3
% 3.63/1.44 % (2293843)Termination reason: Refutation not found, incomplete strategy
% 3.63/1.44 % (2293843)Time elapsed: 0.001 s
% 3.63/1.44 % (2293843)Peak memory usage: 87 MB
% 3.63/1.44 % (2293844)Refutation not found, incomplete strategy
% 3.63/1.44 % (2293844)------------------------------
% 3.63/1.44 % (2293844)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.44 % (2293844)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.44 % (2293844)CaDiCaL version: 2.1.3
% 3.63/1.44 % (2293844)Termination reason: Refutation not found, incomplete strategy
% 3.63/1.44 % (2293844)Time elapsed: 0.001 s
% 3.63/1.44 % (2293844)Peak memory usage: 87 MB
% 3.63/1.44 % (2293846)Instruction limit reached!
% 3.63/1.44 % (2293846)------------------------------
% 3.63/1.44 % (2293846)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.44 % (2293846)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.44 % (2293846)CaDiCaL version: 2.1.3
% 3.63/1.44 % (2293846)Termination reason: Instruction limit
% 3.63/1.44 % (2293846)Termination phase: Saturation
% 3.63/1.44 % (2293846)Time elapsed: 0.041 s
% 3.63/1.44 % (2293846)Peak memory usage: 89 MB
% 3.63/1.44 % (2293846)Instructions burned: 134 (million)
% 3.63/1.44 % (2293845)First to succeed.
% 3.63/1.44 % (2293845)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2293812"
% 3.63/1.44 % (2293854)lrs+10_1_sil=8000:sp=occurrence:random_seed=970382927:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.63/1.44 % (2293854)Instruction limit reached!
% 3.63/1.44 % (2293854)------------------------------
% 3.63/1.44 % (2293854)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.44 % (2293854)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.44 % (2293854)CaDiCaL version: 2.1.3
% 3.63/1.44 % (2293854)Termination reason: Instruction limit
% 3.63/1.44 % (2293854)Termination phase: Saturation
% 3.63/1.44 % (2293854)Time elapsed: 0.081 s
% 3.63/1.44 % (2293854)Peak memory usage: 90 MB
% 3.63/1.44 % (2293854)Instructions burned: 286 (million)
% 3.63/1.44 % (2293844)------------------------------
% 3.63/1.44 % (2293844)------------------------------
% 3.63/1.44 % (2293843)------------------------------
% 3.63/1.44 % (2293843)------------------------------
% 3.63/1.44 % (2293845)Refutation found. Thanks to Tanya!
% 3.63/1.44 % SZS status Theorem for theBenchmark
% 3.63/1.44 % SZS output start Proof for theBenchmark
% See solution above
% 3.63/1.44 % (2293845)------------------------------
% 3.63/1.44 % (2293845)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.44 % (2293845)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.44 % (2293845)CaDiCaL version: 2.1.3
% 3.63/1.44 % (2293845)Termination reason: Refutation
% 3.63/1.44 % (2293845)Time elapsed: 0.004 s
% 3.63/1.44 % (2293845)Peak memory usage: 89 MB
% 3.63/1.44 % (2293845)Instructions burned: 4 (million)
% 3.63/1.44 % (2293845)------------------------------
% 3.63/1.44 % (2293845)------------------------------
% 3.63/1.44 % (2293812)Success in time 0.43 s
% 3.63/1.44 % Vampire exiting
%------------------------------------------------------------------------------