%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO222+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 09:52:06 AM UTC 2026
% Result : Theorem 5.47s 1.73s
% Output : Refutation 5.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of formulae : 37 ( 18 unt; 0 def)
% Number of atoms : 92 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 82 ( 27 ~; 44 |; 7 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 85 ( 83 !; 2 ?)
% 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(f14,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( distinct_lines(X1,X2)
| convergent_lines(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq3) ).
fof(f18,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
| unorthogonal_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',occu1) ).
fof(f19,axiom,
! [X0,X1,X2] :
( ( convergent_lines(X0,X1)
& unorthogonal_lines(X0,X1) )
=> ( ( convergent_lines(X0,X2)
& unorthogonal_lines(X0,X2) )
| ( convergent_lines(X1,X2)
& unorthogonal_lines(X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',oac1) ).
fof(f20,axiom,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ooc1) ).
fof(f21,axiom,
! [X0,X1] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ooc2) ).
fof(f22,axiom,
! [X0,X1,X2,X3] :
( distinct_lines(X1,X2)
=> ( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| unorthogonal_lines(X1,X3)
| unorthogonal_lines(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ouo1) ).
fof(f23,conjecture,
! [X0,X1] : ~ convergent_lines(X1,orthogonal_through_point(orthogonal_through_point(X1,X0),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f24,negated_conjecture,
~ ! [X0,X1] : ~ convergent_lines(X1,orthogonal_through_point(orthogonal_through_point(X1,X0),X0)),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f29,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f30,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f29]) ).
fof(f41,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f42,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f41]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ( convergent_lines(X0,X2)
& unorthogonal_lines(X0,X2) )
| ( convergent_lines(X1,X2)
& unorthogonal_lines(X1,X2) )
| ~ convergent_lines(X0,X1)
| ~ unorthogonal_lines(X0,X1) ),
inference(ennf_transformation,[],[f19]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ( convergent_lines(X0,X2)
& unorthogonal_lines(X0,X2) )
| ( convergent_lines(X1,X2)
& unorthogonal_lines(X1,X2) )
| ~ convergent_lines(X0,X1)
| ~ unorthogonal_lines(X0,X1) ),
inference(flattening,[],[f45]) ).
fof(f47,plain,
! [X0,X1,X2,X3] :
( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| unorthogonal_lines(X1,X3)
| unorthogonal_lines(X2,X3)
| ~ distinct_lines(X1,X2) ),
inference(ennf_transformation,[],[f22]) ).
fof(f48,plain,
! [X0,X1,X2,X3] :
( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| unorthogonal_lines(X1,X3)
| unorthogonal_lines(X2,X3)
| ~ distinct_lines(X1,X2) ),
inference(flattening,[],[f47]) ).
fof(f49,plain,
? [X0,X1] : convergent_lines(X1,orthogonal_through_point(orthogonal_through_point(X1,X0),X0)),
inference(ennf_transformation,[],[f24]) ).
fof(f50,plain,
convergent_lines(sK1,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f49]) ).
fof(f53,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f56,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f64,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f42]) ).
fof(f68,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f69,plain,
! [X2,X0,X1] :
( ~ unorthogonal_lines(X0,X1)
| unorthogonal_lines(X1,X2)
| ~ convergent_lines(X0,X1)
| unorthogonal_lines(X0,X2) ),
inference(cnf_transformation,[],[f46]) ).
fof(f71,plain,
! [X2,X0,X1] :
( ~ unorthogonal_lines(X0,X1)
| unorthogonal_lines(X1,X2)
| ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f46]) ).
fof(f73,plain,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f20]) ).
fof(f74,plain,
! [X0,X1] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
inference(cnf_transformation,[],[f21]) ).
fof(f75,plain,
! [X2,X3,X0,X1] :
( ~ distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| unorthogonal_lines(X1,X3)
| unorthogonal_lines(X2,X3)
| apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f76,plain,
convergent_lines(sK1,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),
inference(cnf_transformation,[],[f50]) ).
fof(f78,plain,
convergent_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),sK1),
inference(unit_resulting_resolution,[],[f56,f53,f76]) ).
fof(f83,plain,
! [X0,X1] : convergent_lines(orthogonal_through_point(X0,X1),X0),
inference(unit_resulting_resolution,[],[f68,f73]) ).
fof(f88,plain,
! [X0,X1] : convergent_lines(X0,orthogonal_through_point(X0,X1)),
inference(unit_resulting_resolution,[],[f56,f53,f83]) ).
fof(f97,plain,
! [X0,X1] : distinct_lines(X0,orthogonal_through_point(X0,X1)),
inference(unit_resulting_resolution,[],[f64,f53,f83]) ).
fof(f105,plain,
! [X0,X1] : ~ unorthogonal_lines(X0,orthogonal_through_point(X0,X1)),
inference(unit_resulting_resolution,[],[f71,f53,f73,f88]) ).
fof(f112,plain,
! [X0,X1] : unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(X0,X1),X1),X0),
inference(unit_resulting_resolution,[],[f75,f74,f73,f74,f97]) ).
fof(f147,plain,
$false,
inference(unit_resulting_resolution,[],[f69,f105,f73,f78,f112]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO222+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n002.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 07:45:51 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 4.11/1.53 % (3211776)Detected formulas, will run a generic FOF schedule.
% 4.11/1.53 % (3211785)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1186388484:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.11/1.53 % (3211782)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=1270976826:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.11/1.53 % (3211787)dis-21_1_sil=8000:lcm=predicate:random_seed=2338276217: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)
% 4.11/1.53 % (3211781)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=1499035517:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.11/1.53 % (3211784)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4059698562:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.11/1.53 % (3211783)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=4205699517:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.11/1.53 % (3211784)Refutation not found, incomplete strategy
% 4.11/1.53 % (3211784)------------------------------
% 4.11/1.53 % (3211784)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.11/1.53 % (3211784)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.11/1.53 % (3211784)CaDiCaL version: 2.1.3
% 4.11/1.53 % (3211784)Termination reason: Refutation not found, incomplete strategy
% 4.11/1.53 % (3211784)Time elapsed: 0.001 s
% 4.11/1.53 % (3211784)Peak memory usage: 87 MB
% 4.11/1.53 % (3211786)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2445810191:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.11/1.53 % (3211785)Instruction limit reached!
% 4.11/1.53 % (3211785)------------------------------
% 4.11/1.53 % (3211785)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.11/1.53 % (3211785)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.11/1.53 % (3211785)CaDiCaL version: 2.1.3
% 4.11/1.53 % (3211785)Termination reason: Instruction limit
% 4.11/1.53 % (3211785)Termination phase: Saturation
% 4.11/1.53 % (3211785)Time elapsed: 0.037 s
% 4.11/1.53 % (3211785)Peak memory usage: 87 MB
% 4.11/1.53 % (3211785)Instructions burned: 120 (million)
% 4.11/1.53 % (3211787)Instruction limit reached!
% 4.11/1.53 % (3211787)------------------------------
% 4.11/1.53 % (3211787)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.11/1.53 % (3211787)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.11/1.53 % (3211787)CaDiCaL version: 2.1.3
% 4.11/1.53 % (3211787)Termination reason: Instruction limit
% 4.11/1.53 % (3211787)Termination phase: Saturation
% 4.11/1.53 % (3211787)Time elapsed: 0.069 s
% 4.11/1.53 % (3211787)Peak memory usage: 88 MB
% 4.11/1.53 % (3211787)Instructions burned: 130 (million)
% 4.11/1.53 % (3211786)Instruction limit reached!
% 4.11/1.53 % (3211786)------------------------------
% 4.11/1.53 % (3211786)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.11/1.53 % (3211786)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.11/1.53 % (3211786)CaDiCaL version: 2.1.3
% 4.11/1.53 % (3211786)Termination reason: Instruction limit
% 4.11/1.53 % (3211786)Termination phase: Saturation
% 4.11/1.53 % (3211786)Time elapsed: 0.086 s
% 4.11/1.53 % (3211786)Peak memory usage: 88 MB
% 4.11/1.53 % (3211786)Instructions burned: 140 (million)
% 4.11/1.53 % (3211795)lrs+10_1_sil=8000:sp=occurrence:random_seed=2787697690:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 4.11/1.53 % (3211795)Instruction limit reached!
% 4.11/1.53 % (3211795)------------------------------
% 4.11/1.53 % (3211795)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.11/1.53 % (3211795)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.11/1.53 % (3211795)CaDiCaL version: 2.1.3
% 4.11/1.53 % (3211795)Termination reason: Instruction limit
% 4.11/1.53 % (3211795)Termination phase: Saturation
% 4.11/1.53 % (3211795)Time elapsed: 0.081 s
% 4.11/1.53 % (3211795)Peak memory usage: 89 MB
% 4.11/1.53 % (3211795)Instructions burned: 286 (million)
% 4.11/1.53 % (3211796)lrs+10_1_sil=32000:urr=on:br=off:random_seed=116772906:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.47/1.73 % (3211796)Refutation not found, incomplete strategy
% 5.47/1.73 % (3211796)------------------------------
% 5.47/1.73 % (3211796)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.47/1.73 % (3211796)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.47/1.73 % (3211796)CaDiCaL version: 2.1.3
% 5.47/1.73 % (3211796)Termination reason: Refutation not found, incomplete strategy
% 5.47/1.73 % (3211796)Time elapsed: 0.001 s
% 5.47/1.73 % (3211796)Peak memory usage: 88 MB
% 5.47/1.73 % (3211797)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2233433169:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 5.47/1.73 % (3211784)------------------------------
% 5.47/1.73 % (3211784)------------------------------
% 5.47/1.73 % (3211799)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=3194157797:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 5.47/1.73 % (3211799)First to succeed.
% 5.47/1.73 % (3211799)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3211776"
% 5.47/1.73 % (3211802)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=161479811:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 5.47/1.73 % (3211802)Refutation not found, incomplete strategy
% 5.47/1.73 % (3211802)------------------------------
% 5.47/1.73 % (3211802)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.47/1.73 % (3211802)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.47/1.73 % (3211802)CaDiCaL version: 2.1.3
% 5.47/1.73 % (3211802)Termination reason: Refutation not found, incomplete strategy
% 5.47/1.73 % (3211802)Time elapsed: 0.001 s
% 5.47/1.73 % (3211802)Peak memory usage: 87 MB
% 5.47/1.73 % (3211797)Instruction limit reached!
% 5.47/1.73 % (3211797)------------------------------
% 5.47/1.73 % (3211797)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.47/1.73 % (3211797)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.47/1.73 % (3211797)CaDiCaL version: 2.1.3
% 5.47/1.73 % (3211797)Termination reason: Instruction limit
% 5.47/1.73 % (3211797)Termination phase: Saturation
% 5.47/1.73 % (3211797)Time elapsed: 0.209 s
% 5.47/1.73 % (3211797)Peak memory usage: 89 MB
% 5.47/1.73 % (3211797)Instructions burned: 326 (million)
% 5.47/1.73 % (3211796)------------------------------
% 5.47/1.73 % (3211796)------------------------------
% 5.47/1.73 % (3211799)Refutation found. Thanks to Tanya!
% 5.47/1.73 % SZS status Theorem for theBenchmark
% 5.47/1.73 % SZS output start Proof for theBenchmark
% See solution above
% 5.47/1.73 % (3211799)------------------------------
% 5.47/1.73 % (3211799)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.47/1.73 % (3211799)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.47/1.73 % (3211799)CaDiCaL version: 2.1.3
% 5.47/1.73 % (3211799)Termination reason: Refutation
% 5.47/1.73 % (3211799)Time elapsed: 0.003 s
% 5.47/1.73 % (3211799)Peak memory usage: 88 MB
% 5.47/1.73 % (3211799)Instructions burned: 5 (million)
% 5.47/1.73 % (3211799)------------------------------
% 5.47/1.73 % (3211799)------------------------------
% 5.47/1.73 % (3211776)Success in time 0.685 s
% 5.47/1.73 % Vampire exiting
%------------------------------------------------------------------------------