%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO222+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 3.09s 1.09s
% Output : Refutation 3.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 51 ( 16 unt; 0 def)
% Number of atoms : 132 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 142 ( 61 ~; 60 |; 14 &)
% ( 1 <=>; 6 =>; 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 : 109 ( 107 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ceq3) ).
fof(f15,axiom,
! [X0,X1] :
( distinct_lines(X0,X1)
=> convergent_lines(X0,X1) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',oac1) ).
fof(f21,axiom,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ooc1) ).
fof(f24,axiom,
! [X0,X1] :
~ ( ~ convergent_lines(X0,X1)
& ~ unorthogonal_lines(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',coipo1) ).
fof(f25,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/sandbox2/benchmark/theBenchmark.p',cotno1) ).
fof(f26,axiom,
! [X0,X1,X2] :
( ( ~ unorthogonal_lines(X0,X1)
& ~ unorthogonal_lines(X0,X2) )
=> ~ convergent_lines(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',couo1) ).
fof(f33,axiom,
! [X0,X1] :
( parallel_lines(X0,X1)
<=> ~ convergent_lines(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3) ).
fof(f36,conjecture,
! [X0,X1] : parallel_lines(X1,orthogonal_through_point(orthogonal_through_point(X1,X0),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1] : parallel_lines(X1,orthogonal_through_point(orthogonal_through_point(X1,X0),X0)),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
=> parallel_lines(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f33]) ).
fof(f40,plain,
? [X0,X1] : ~ parallel_lines(X1,orthogonal_through_point(orthogonal_through_point(X1,X0),X0)),
inference(ennf_transformation,[],[f37]) ).
fof(f41,plain,
! [X0,X1] :
( parallel_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X1,X2)
| unorthogonal_lines(X0,X1)
| unorthogonal_lines(X0,X2) ),
inference(ennf_transformation,[],[f26]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X1,X2)
| unorthogonal_lines(X0,X1)
| unorthogonal_lines(X0,X2) ),
inference(flattening,[],[f42]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X1,X2)
| ~ unorthogonal_lines(X1,X2)
| ( convergent_lines(X0,X1)
& unorthogonal_lines(X0,X1) )
| ( convergent_lines(X0,X2)
& unorthogonal_lines(X0,X2) ) ),
inference(ennf_transformation,[],[f25]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X1,X2)
| ~ unorthogonal_lines(X1,X2)
| ( convergent_lines(X0,X1)
& unorthogonal_lines(X0,X1) )
| ( convergent_lines(X0,X2)
& unorthogonal_lines(X0,X2) ) ),
inference(flattening,[],[f44]) ).
fof(f46,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| unorthogonal_lines(X0,X1) ),
inference(ennf_transformation,[],[f24]) ).
fof(f49,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(f50,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,[],[f49]) ).
fof(f55,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f56,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f57,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f56]) ).
fof(f62,plain,
~ parallel_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)],[f40]) ).
fof(f63,plain,
~ parallel_lines(sK1,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),
inference(cnf_transformation,[],[f62]) ).
fof(f65,plain,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f21]) ).
fof(f66,plain,
! [X0,X1] :
( parallel_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f67,plain,
! [X2,X0,X1] :
( unorthogonal_lines(X0,X2)
| unorthogonal_lines(X0,X1)
| ~ convergent_lines(X1,X2) ),
inference(cnf_transformation,[],[f43]) ).
fof(f69,plain,
! [X2,X0,X1] :
( unorthogonal_lines(X0,X1)
| ~ unorthogonal_lines(X1,X2)
| ~ convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f45]) ).
fof(f72,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f74,plain,
! [X2,X0,X1] :
( unorthogonal_lines(X1,X2)
| unorthogonal_lines(X0,X2)
| ~ convergent_lines(X0,X1)
| ~ unorthogonal_lines(X0,X1) ),
inference(cnf_transformation,[],[f50]) ).
fof(f75,plain,
! [X2,X0,X1] :
( unorthogonal_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1)
| ~ unorthogonal_lines(X0,X1) ),
inference(cnf_transformation,[],[f50]) ).
fof(f80,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f82,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f83,plain,
! [X2,X0,X1] :
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f87,plain,
convergent_lines(sK1,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),
inference(resolution,[],[f66,f63]) ).
fof(f88,plain,
! [X0,X1] : convergent_lines(orthogonal_through_point(X0,X1),X0),
inference(resolution,[],[f72,f65]) ).
fof(f93,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X1,X0) ),
inference(resolution,[],[f83,f80]) ).
fof(f98,plain,
! [X2,X0,X1] :
( convergent_lines(orthogonal_through_point(X0,X2),X1)
| ~ convergent_lines(X0,X1)
| ~ unorthogonal_lines(X0,X1) ),
inference(resolution,[],[f69,f65]) ).
fof(f100,plain,
! [X0,X1] :
( ~ unorthogonal_lines(X0,orthogonal_through_point(X0,X1))
| ~ convergent_lines(X0,orthogonal_through_point(X0,X1)) ),
inference(resolution,[],[f98,f80]) ).
fof(f114,plain,
! [X2,X0,X1] :
( ~ unorthogonal_lines(orthogonal_through_point(X1,X2),X0)
| ~ convergent_lines(orthogonal_through_point(X1,X2),X0)
| convergent_lines(X0,X1) ),
inference(resolution,[],[f75,f65]) ).
fof(f140,plain,
! [X2,X3,X0,X1] :
( ~ convergent_lines(orthogonal_through_point(X0,X1),X2)
| convergent_lines(X2,X0)
| unorthogonal_lines(X3,X2)
| ~ convergent_lines(X3,orthogonal_through_point(X0,X1))
| ~ unorthogonal_lines(X3,orthogonal_through_point(X0,X1)) ),
inference(resolution,[],[f114,f74]) ).
fof(f145,plain,
! [X2,X3,X0,X1] :
( ~ convergent_lines(orthogonal_through_point(X0,X1),X2)
| convergent_lines(X2,X0)
| unorthogonal_lines(X3,X2)
| ~ convergent_lines(X3,orthogonal_through_point(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f140,f67]) ).
fof(f363,plain,
! [X2,X0,X1] :
( convergent_lines(X0,X0)
| unorthogonal_lines(X1,X0)
| ~ convergent_lines(X1,orthogonal_through_point(X0,X2)) ),
inference(resolution,[],[f145,f88]) ).
fof(f380,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X1,orthogonal_through_point(X0,X2))
| unorthogonal_lines(X1,X0) ),
inference(forward_subsumption_resolution,[],[f363,f80]) ).
fof(f613,plain,
unorthogonal_lines(sK1,orthogonal_through_point(sK1,sK0)),
inference(resolution,[],[f380,f87]) ).
fof(f630,plain,
~ convergent_lines(sK1,orthogonal_through_point(sK1,sK0)),
inference(resolution,[],[f613,f100]) ).
fof(f648,plain,
~ distinct_lines(sK1,orthogonal_through_point(sK1,sK0)),
inference(resolution,[],[f630,f82]) ).
fof(f669,plain,
~ convergent_lines(orthogonal_through_point(sK1,sK0),sK1),
inference(resolution,[],[f648,f93]) ).
fof(f670,plain,
$false,
inference(forward_subsumption_resolution,[],[f669,f88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO222+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 07:43:45 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.09/1.09 % (1699465)Detected formulas, will run a generic FOF schedule.
% 3.09/1.09 % (1699475)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=925853001:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.09/1.09 % (1699473)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1504270699:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.09/1.09 % (1699476)dis-21_1_sil=8000:lcm=predicate:random_seed=3778605469: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)
% 3.09/1.09 % (1699474)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4017004104:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.09/1.09 % (1699472)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=3085417314:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.09/1.09 % (1699471)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=682307881:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.09/1.09 % (1699470)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=1737647210:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.09/1.09 % (1699473)Refutation not found, incomplete strategy
% 3.09/1.09 % (1699473)------------------------------
% 3.09/1.09 % (1699473)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.09/1.09 % (1699473)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.09/1.09 % (1699473)CaDiCaL version: 2.1.3
% 3.09/1.09 % (1699473)Termination reason: Refutation not found, incomplete strategy
% 3.09/1.09 % (1699473)Time elapsed: 0.001 s
% 3.09/1.09 % (1699473)Peak memory usage: 87 MB
% 3.09/1.09 % (1699474)First to succeed.
% 3.09/1.09 % (1699474)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1699465"
% 3.09/1.09 % (1699475)Also succeeded, but the first one will report.
% 3.09/1.09 % (1699476)Instruction limit reached!
% 3.09/1.09 % (1699476)------------------------------
% 3.09/1.09 % (1699476)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.09/1.09 % (1699476)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.09/1.09 % (1699476)CaDiCaL version: 2.1.3
% 3.09/1.09 % (1699476)Termination reason: Instruction limit
% 3.09/1.09 % (1699476)Termination phase: Saturation
% 3.09/1.09 % (1699476)Time elapsed: 0.072 s
% 3.09/1.09 % (1699476)Peak memory usage: 88 MB
% 3.09/1.09 % (1699476)Instructions burned: 130 (million)
% 3.09/1.09 % (1699484)lrs+10_1_sil=8000:sp=occurrence:random_seed=3940324221:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.09/1.09 % (1699484)Also succeeded, but the first one will report.
% 3.09/1.09 % (1699473)------------------------------
% 3.09/1.09 % (1699473)------------------------------
% 3.09/1.09 % (1699474)Refutation found. Thanks to Tanya!
% 3.09/1.09 % SZS status Theorem for theBenchmark
% 3.09/1.09 % SZS output start Proof for theBenchmark
% See solution above
% 3.09/1.09 % (1699474)------------------------------
% 3.09/1.09 % (1699474)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.09/1.09 % (1699474)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.09/1.09 % (1699474)CaDiCaL version: 2.1.3
% 3.09/1.09 % (1699474)Termination reason: Refutation
% 3.09/1.09 % (1699474)Time elapsed: 0.016 s
% 3.09/1.09 % (1699474)Peak memory usage: 88 MB
% 3.09/1.09 % (1699474)Instructions burned: 26 (million)
% 3.09/1.09 % (1699474)------------------------------
% 3.09/1.09 % (1699474)------------------------------
% 3.09/1.09 % (1699465)Success in time 0.402 s
% 3.09/1.09 % Vampire exiting
%------------------------------------------------------------------------------