%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO210+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 : n015.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 09:52:01 AM UTC 2026
% Result : Theorem 2.75s 1.37s
% Output : Refutation 2.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 50 ( 14 unt; 0 def)
% Number of atoms : 114 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 114 ( 50 ~; 37 |; 17 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 94 ( 88 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart3) ).
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(f15,axiom,
! [X0,X1] :
( distinct_lines(X0,X1)
=> convergent_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(f20,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(f21,axiom,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ooc1) ).
fof(f24,axiom,
! [X0,X1] :
~ ( ~ convergent_lines(X0,X1)
& ~ unorthogonal_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',coipo1) ).
fof(f26,axiom,
! [X0,X1,X2] :
( ( ~ unorthogonal_lines(X0,X1)
& ~ unorthogonal_lines(X0,X2) )
=> ~ convergent_lines(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',couo1) ).
fof(f32,axiom,
! [X0,X1] :
( equal_lines(X0,X1)
<=> ~ distinct_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
fof(f35,axiom,
! [X0,X1] :
( orthogonal_lines(X0,X1)
<=> ~ unorthogonal_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a5) ).
fof(f36,conjecture,
! [X0,X1,X2] :
( ( incident_point_and_line(X0,X1)
& orthogonal_lines(X1,X2) )
=> equal_lines(X1,orthogonal_through_point(X2,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1,X2] :
( ( incident_point_and_line(X0,X1)
& orthogonal_lines(X1,X2) )
=> equal_lines(X1,orthogonal_through_point(X2,X0)) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( orthogonal_lines(X0,X1)
=> ~ unorthogonal_lines(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f35]) ).
fof(f40,plain,
! [X0,X1] :
( ~ distinct_lines(X0,X1)
=> equal_lines(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f32]) ).
fof(f42,plain,
? [X0,X1,X2] :
( ~ equal_lines(X1,orthogonal_through_point(X2,X0))
& incident_point_and_line(X0,X1)
& orthogonal_lines(X1,X2) ),
inference(ennf_transformation,[],[f37]) ).
fof(f43,plain,
? [X0,X1,X2] :
( ~ equal_lines(X1,orthogonal_through_point(X2,X0))
& incident_point_and_line(X0,X1)
& orthogonal_lines(X1,X2) ),
inference(flattening,[],[f42]) ).
fof(f44,plain,
! [X0,X1] :
( equal_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f40]) ).
fof(f46,plain,
! [X0,X1] :
( ~ unorthogonal_lines(X0,X1)
| ~ orthogonal_lines(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X1,X2)
| unorthogonal_lines(X0,X1)
| unorthogonal_lines(X0,X2) ),
inference(ennf_transformation,[],[f26]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X1,X2)
| unorthogonal_lines(X0,X1)
| unorthogonal_lines(X0,X2) ),
inference(flattening,[],[f47]) ).
fof(f51,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| unorthogonal_lines(X0,X1) ),
inference(ennf_transformation,[],[f24]) ).
fof(f54,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,[],[f20]) ).
fof(f55,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,[],[f54]) ).
fof(f58,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f59,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f60,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f59]) ).
fof(f67,plain,
( ~ equal_lines(sK1,orthogonal_through_point(sK2,sK0))
& incident_point_and_line(sK0,sK1)
& orthogonal_lines(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f43]) ).
fof(f68,plain,
orthogonal_lines(sK1,sK2),
inference(cnf_transformation,[],[f67]) ).
fof(f70,plain,
~ equal_lines(sK1,orthogonal_through_point(sK2,sK0)),
inference(cnf_transformation,[],[f67]) ).
fof(f72,plain,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f21]) ).
fof(f73,plain,
! [X0,X1] :
( equal_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f75,plain,
! [X0,X1] :
( ~ orthogonal_lines(X0,X1)
| ~ unorthogonal_lines(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f76,plain,
! [X2,X0,X1] :
( unorthogonal_lines(X0,X2)
| unorthogonal_lines(X0,X1)
| ~ convergent_lines(X1,X2) ),
inference(cnf_transformation,[],[f48]) ).
fof(f81,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f83,plain,
! [X2,X0,X1] :
( unorthogonal_lines(X1,X2)
| unorthogonal_lines(X0,X2)
| ~ convergent_lines(X0,X1)
| ~ unorthogonal_lines(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f89,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f58]) ).
fof(f90,plain,
! [X2,X0,X1] :
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f95,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f96,plain,
distinct_lines(sK1,orthogonal_through_point(sK2,sK0)),
inference(resolution,[],[f73,f70]) ).
fof(f98,plain,
~ unorthogonal_lines(sK1,sK2),
inference(resolution,[],[f75,f68]) ).
fof(f100,plain,
convergent_lines(sK1,sK2),
inference(resolution,[],[f81,f98]) ).
fof(f102,plain,
! [X2,X0,X1] :
( unorthogonal_lines(orthogonal_through_point(X0,X1),X2)
| ~ convergent_lines(X2,X0) ),
inference(resolution,[],[f76,f72]) ).
fof(f106,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X1,X0) ),
inference(resolution,[],[f90,f95]) ).
fof(f129,plain,
! [X0] :
( unorthogonal_lines(X0,sK2)
| ~ convergent_lines(X0,sK1)
| ~ unorthogonal_lines(X0,sK1) ),
inference(resolution,[],[f83,f98]) ).
fof(f132,plain,
! [X0] :
( ~ unorthogonal_lines(orthogonal_through_point(sK2,X0),sK1)
| ~ convergent_lines(orthogonal_through_point(sK2,X0),sK1) ),
inference(resolution,[],[f129,f72]) ).
fof(f243,plain,
! [X0] :
( ~ convergent_lines(orthogonal_through_point(sK2,X0),sK1)
| ~ convergent_lines(sK1,sK2) ),
inference(resolution,[],[f132,f102]) ).
fof(f259,plain,
! [X0] : ~ convergent_lines(orthogonal_through_point(sK2,X0),sK1),
inference(forward_subsumption_resolution,[],[f243,f100]) ).
fof(f268,plain,
! [X0] : ~ distinct_lines(orthogonal_through_point(sK2,X0),sK1),
inference(resolution,[],[f259,f89]) ).
fof(f273,plain,
! [X0] : ~ convergent_lines(sK1,orthogonal_through_point(sK2,X0)),
inference(resolution,[],[f268,f106]) ).
fof(f286,plain,
! [X0] : ~ distinct_lines(sK1,orthogonal_through_point(sK2,X0)),
inference(resolution,[],[f273,f89]) ).
fof(f303,plain,
$false,
inference(resolution,[],[f286,f96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO210+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.39 % Computer : n015.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sun Sep 27 07:41:45 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.43 Running first-order theorem proving
% 0.14/0.43 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
% 2.75/1.37 % (1322290)Detected formulas, will run a generic FOF schedule.
% 2.75/1.37 % (1322299)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2832423929:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.75/1.37 % (1322299)First to succeed.
% 2.75/1.37 % (1322299)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1322290"
% 2.75/1.37 % (1322296)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=2635141206:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.75/1.37 % (1322301)dis-21_1_sil=8000:lcm=predicate:random_seed=2544367527: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)
% 2.75/1.37 % (1322298)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=362069676:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.75/1.37 % (1322295)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=963597848:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.75/1.37 % (1322297)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=489670702:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.75/1.37 % (1322298)Refutation not found, incomplete strategy
% 2.75/1.37 % (1322298)------------------------------
% 2.75/1.37 % (1322298)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.75/1.37 % (1322298)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/1.37 % (1322298)CaDiCaL version: 2.1.3
% 2.75/1.37 % (1322298)Termination reason: Refutation not found, incomplete strategy
% 2.75/1.37 % (1322298)Time elapsed: 0.001 s
% 2.75/1.37 % (1322298)Peak memory usage: 87 MB
% 2.75/1.37 % (1322301)Also succeeded, but the first one will report.
% 2.75/1.37 % (1322300)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3170569244:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.75/1.37 % (1322300)Also succeeded, but the first one will report.
% 2.75/1.37 % (1322299)Refutation found. Thanks to Tanya!
% 2.75/1.37 % SZS status Theorem for theBenchmark
% 2.75/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 2.75/1.37 % (1322299)------------------------------
% 2.75/1.37 % (1322299)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.75/1.37 % (1322299)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/1.37 % (1322299)CaDiCaL version: 2.1.3
% 2.75/1.37 % (1322299)Termination reason: Refutation
% 2.75/1.37 % (1322299)Time elapsed: 0.004 s
% 2.75/1.37 % (1322299)Peak memory usage: 88 MB
% 2.75/1.37 % (1322299)Instructions burned: 8 (million)
% 2.75/1.37 % (1322299)------------------------------
% 2.75/1.37 % (1322299)------------------------------
% 2.75/1.37 % (1322290)Success in time 0.311 s
% 2.75/1.37 % Vampire exiting
%------------------------------------------------------------------------------