%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO209+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 : n019.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 3.50s 1.42s
% Output : Refutation 3.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 10 unt; 0 def)
% Number of atoms : 76 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 69 ( 24 ~; 14 |; 23 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 51 ( 43 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
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(f32,axiom,
! [X0,X1] :
( equal_lines(X0,X1)
<=> ~ distinct_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
fof(f33,axiom,
! [X0,X1] :
( parallel_lines(X0,X1)
<=> ~ convergent_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a3) ).
fof(f36,conjecture,
! [X0,X1,X2,X3] :
( ( apart_point_and_line(X0,X1)
& incident_point_and_line(X0,X2)
& incident_point_and_line(X0,X3)
& parallel_lines(X2,X1)
& parallel_lines(X3,X1) )
=> equal_lines(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( apart_point_and_line(X0,X1)
& incident_point_and_line(X0,X2)
& incident_point_and_line(X0,X3)
& parallel_lines(X2,X1)
& parallel_lines(X3,X1) )
=> equal_lines(X2,X3) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f39,plain,
! [X0,X1] :
( parallel_lines(X0,X1)
=> ~ convergent_lines(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f33]) ).
fof(f40,plain,
! [X0,X1] :
( ~ distinct_lines(X0,X1)
=> equal_lines(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f32]) ).
fof(f41,plain,
? [X0,X1,X2,X3] :
( ~ equal_lines(X2,X3)
& apart_point_and_line(X0,X1)
& incident_point_and_line(X0,X2)
& incident_point_and_line(X0,X3)
& parallel_lines(X2,X1)
& parallel_lines(X3,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f42,plain,
? [X0,X1,X2,X3] :
( ~ equal_lines(X2,X3)
& apart_point_and_line(X0,X1)
& incident_point_and_line(X0,X2)
& incident_point_and_line(X0,X3)
& parallel_lines(X2,X1)
& parallel_lines(X3,X1) ),
inference(flattening,[],[f41]) ).
fof(f43,plain,
! [X0,X1] :
( equal_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f40]) ).
fof(f44,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ parallel_lines(X0,X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f48,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f49,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f50,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f49]) ).
fof(f57,plain,
( ~ equal_lines(sK2,sK3)
& apart_point_and_line(sK0,sK1)
& incident_point_and_line(sK0,sK2)
& incident_point_and_line(sK0,sK3)
& parallel_lines(sK2,sK1)
& parallel_lines(sK3,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f42]) ).
fof(f58,plain,
parallel_lines(sK3,sK1),
inference(cnf_transformation,[],[f57]) ).
fof(f59,plain,
parallel_lines(sK2,sK1),
inference(cnf_transformation,[],[f57]) ).
fof(f63,plain,
~ equal_lines(sK2,sK3),
inference(cnf_transformation,[],[f57]) ).
fof(f64,plain,
! [X0,X1] :
( equal_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f65,plain,
! [X0,X1] :
( ~ parallel_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f68,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f69,plain,
! [X2,X0,X1] :
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f50]) ).
fof(f75,plain,
distinct_lines(sK2,sK3),
inference(resolution,[],[f64,f63]) ).
fof(f76,plain,
~ convergent_lines(sK3,sK1),
inference(resolution,[],[f65,f58]) ).
fof(f77,plain,
~ convergent_lines(sK2,sK1),
inference(resolution,[],[f65,f59]) ).
fof(f81,plain,
~ distinct_lines(sK3,sK1),
inference(resolution,[],[f68,f76]) ).
fof(f85,plain,
! [X0] :
( distinct_lines(X0,sK1)
| ~ convergent_lines(sK2,X0) ),
inference(resolution,[],[f69,f77]) ).
fof(f102,plain,
~ convergent_lines(sK2,sK3),
inference(resolution,[],[f85,f81]) ).
fof(f110,plain,
~ distinct_lines(sK2,sK3),
inference(resolution,[],[f102,f68]) ).
fof(f111,plain,
$false,
inference(forward_subsumption_resolution,[],[f110,f75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO209+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n019.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
% 0.10/0.36 % DateTime : Sun Sep 27 07:38:19 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.39 Running first-order theorem proving
% 0.10/0.39 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
% 3.50/1.42 % (2769417)Detected formulas, will run a generic FOF schedule.
% 3.50/1.42 % (2769424)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=4017598705:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.50/1.42 % (2769425)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2162301058:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.50/1.42 % (2769425)Refutation not found, incomplete strategy
% 3.50/1.42 % (2769425)------------------------------
% 3.50/1.42 % (2769425)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.42 % (2769425)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.42 % (2769425)CaDiCaL version: 2.1.3
% 3.50/1.42 % (2769425)Termination reason: Refutation not found, incomplete strategy
% 3.50/1.42 % (2769425)Time elapsed: 0.001 s
% 3.50/1.42 % (2769425)Peak memory usage: 88 MB
% 3.50/1.42 % (2769423)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=4284589482:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.50/1.42 % (2769422)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=2828143983:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.50/1.42 % (2769426)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3392475008:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.50/1.42 % (2769427)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3776147487:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.50/1.42 % (2769428)dis-21_1_sil=8000:lcm=predicate:random_seed=2340920757: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)
% 3.50/1.42 % (2769426)First to succeed.
% 3.50/1.42 % (2769428)Also succeeded, but the first one will report.
% 3.50/1.42 % (2769426)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2769417"
% 3.50/1.42 % (2769427)Also succeeded, but the first one will report.
% 3.50/1.42 % (2769425)------------------------------
% 3.50/1.42 % (2769425)------------------------------
% 3.50/1.42 % (2769426)Refutation found. Thanks to Tanya!
% 3.50/1.42 % SZS status Theorem for theBenchmark
% 3.50/1.42 % SZS output start Proof for theBenchmark
% See solution above
% 3.50/1.42 % (2769426)------------------------------
% 3.50/1.42 % (2769426)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.42 % (2769426)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.42 % (2769426)CaDiCaL version: 2.1.3
% 3.50/1.42 % (2769426)Termination reason: Refutation
% 3.50/1.42 % (2769426)Time elapsed: 0.002 s
% 3.50/1.42 % (2769426)Peak memory usage: 88 MB
% 3.50/1.42 % (2769426)Instructions burned: 2 (million)
% 3.50/1.42 % (2769426)------------------------------
% 3.50/1.42 % (2769426)------------------------------
% 3.50/1.42 % (2769417)Success in time 0.41 s
% 3.50/1.42 % Vampire exiting
%------------------------------------------------------------------------------