%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO219+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 09:52:05 AM UTC 2026
% Result : Theorem 2.69s 1.33s
% Output : Refutation 2.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 7 unt; 0 def)
% Number of atoms : 69 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 83 ( 40 ~; 25 |; 14 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 44 ( 38 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( convergent_lines(X0,X2)
| convergent_lines(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart6) ).
fof(f13,axiom,
! [X0,X1] :
~ ( ~ convergent_lines(X0,X1)
& ~ unorthogonal_lines(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',coipo1) ).
fof(f14,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(f16,conjecture,
! [X0,X1,X2] :
( ( ~ unorthogonal_lines(X0,X1)
& ~ convergent_lines(X0,X2) )
=> ~ unorthogonal_lines(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f17,negated_conjecture,
~ ! [X0,X1,X2] :
( ( ~ unorthogonal_lines(X0,X1)
& ~ convergent_lines(X0,X2) )
=> ~ unorthogonal_lines(X1,X2) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f18,plain,
? [X0,X1,X2] :
( unorthogonal_lines(X1,X2)
& ~ unorthogonal_lines(X0,X1)
& ~ convergent_lines(X0,X2) ),
inference(ennf_transformation,[],[f17]) ).
fof(f19,plain,
? [X0,X1,X2] :
( unorthogonal_lines(X1,X2)
& ~ unorthogonal_lines(X0,X1)
& ~ convergent_lines(X0,X2) ),
inference(flattening,[],[f18]) ).
fof(f20,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f21,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f20]) ).
fof(f24,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,[],[f14]) ).
fof(f25,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,[],[f24]) ).
fof(f26,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| unorthogonal_lines(X0,X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f27,plain,
( unorthogonal_lines(sK1,sK2)
& ~ unorthogonal_lines(sK0,sK1)
& ~ convergent_lines(sK0,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f19]) ).
fof(f28,plain,
~ convergent_lines(sK0,sK2),
inference(cnf_transformation,[],[f27]) ).
fof(f29,plain,
~ unorthogonal_lines(sK0,sK1),
inference(cnf_transformation,[],[f27]) ).
fof(f30,plain,
unorthogonal_lines(sK1,sK2),
inference(cnf_transformation,[],[f27]) ).
fof(f31,plain,
! [X2,X0,X1] :
( convergent_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f35,plain,
! [X2,X0,X1] :
( unorthogonal_lines(X0,X1)
| ~ unorthogonal_lines(X1,X2)
| ~ convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f25]) ).
fof(f38,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f39,plain,
convergent_lines(sK0,sK1),
inference(resolution,[],[f38,f29]) ).
fof(f49,plain,
! [X0] :
( convergent_lines(sK0,X0)
| ~ convergent_lines(sK1,X0)
| ~ unorthogonal_lines(sK1,X0) ),
inference(resolution,[],[f35,f29]) ).
fof(f50,plain,
( ~ convergent_lines(sK1,sK2)
| ~ unorthogonal_lines(sK1,sK2) ),
inference(resolution,[],[f49,f28]) ).
fof(f52,plain,
~ convergent_lines(sK1,sK2),
inference(forward_subsumption_resolution,[],[f50,f30]) ).
fof(f54,plain,
! [X0] :
( convergent_lines(X0,sK2)
| ~ convergent_lines(X0,sK1) ),
inference(resolution,[],[f52,f31]) ).
fof(f64,plain,
~ convergent_lines(sK0,sK1),
inference(resolution,[],[f54,f28]) ).
fof(f66,plain,
$false,
inference(forward_subsumption_resolution,[],[f64,f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO219+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n003.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 07:43:25 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
% 2.69/1.33 % (172112)Detected formulas, will run a generic FOF schedule.
% 2.69/1.33 % (172121)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3664925646:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.69/1.33 % (172121)First to succeed.
% 2.69/1.33 % (172121)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-172112"
% 2.69/1.33 % (172117)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=1958621452:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.69/1.33 % (172120)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2014580471:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.69/1.33 % (172118)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=4037791534:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.69/1.33 % (172123)dis-21_1_sil=8000:lcm=predicate:random_seed=1377225087: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)
% 2.69/1.33 % (172119)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=2433976764:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.69/1.33 % (172122)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1578526099:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.69/1.33 % (172122)Also succeeded, but the first one will report.
% 2.69/1.33 % (172123)Also succeeded, but the first one will report.
% 2.69/1.33 % (172120)Also succeeded, but the first one will report.
% 2.69/1.33 % (172121)Refutation found. Thanks to Tanya!
% 2.69/1.33 % SZS status Theorem for theBenchmark
% 2.69/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 2.69/1.33 % (172121)------------------------------
% 2.69/1.33 % (172121)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.33 % (172121)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.33 % (172121)CaDiCaL version: 2.1.3
% 2.69/1.33 % (172121)Termination reason: Refutation
% 2.69/1.33 % (172121)Time elapsed: 0.001 s
% 2.69/1.33 % (172121)Peak memory usage: 88 MB
% 2.69/1.33 % (172121)Instructions burned: 1 (million)
% 2.69/1.33 % (172121)------------------------------
% 2.69/1.33 % (172121)------------------------------
% 2.69/1.33 % (172112)Success in time 0.294 s
% 2.69/1.33 % Vampire exiting
%------------------------------------------------------------------------------