%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO221+2 : 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 : n013.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 3.69s 1.44s
% Output : Refutation 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 8 unt; 0 def)
% Number of atoms : 45 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 43 ( 17 ~; 21 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 40 ( 37 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f18,axiom,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ooc1) ).
fof(f19,axiom,
! [X0,X1] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ooc2) ).
fof(f20,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(f21,conjecture,
! [X0,X1,X2] :
( ~ apart_point_and_line(X1,orthogonal_through_point(X2,X0))
=> ~ distinct_lines(orthogonal_through_point(X2,X0),orthogonal_through_point(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f22,negated_conjecture,
~ ! [X0,X1,X2] :
( ~ apart_point_and_line(X1,orthogonal_through_point(X2,X0))
=> ~ distinct_lines(orthogonal_through_point(X2,X0),orthogonal_through_point(X2,X1)) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f23,plain,
? [X0,X1,X2] :
( distinct_lines(orthogonal_through_point(X2,X0),orthogonal_through_point(X2,X1))
& ~ apart_point_and_line(X1,orthogonal_through_point(X2,X0)) ),
inference(ennf_transformation,[],[f22]) ).
fof(f33,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,[],[f20]) ).
fof(f34,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,[],[f33]) ).
fof(f37,plain,
( distinct_lines(orthogonal_through_point(sK2,sK0),orthogonal_through_point(sK2,sK1))
& ~ apart_point_and_line(sK1,orthogonal_through_point(sK2,sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f23]) ).
fof(f38,plain,
~ apart_point_and_line(sK1,orthogonal_through_point(sK2,sK0)),
inference(cnf_transformation,[],[f37]) ).
fof(f39,plain,
distinct_lines(orthogonal_through_point(sK2,sK0),orthogonal_through_point(sK2,sK1)),
inference(cnf_transformation,[],[f37]) ).
fof(f45,plain,
! [X0,X1] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
inference(cnf_transformation,[],[f19]) ).
fof(f46,plain,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f18]) ).
fof(f49,plain,
! [X2,X3,X0,X1] :
( unorthogonal_lines(X2,X3)
| apart_point_and_line(X0,X2)
| unorthogonal_lines(X1,X3)
| apart_point_and_line(X0,X1)
| ~ distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f34]) ).
fof(f70,plain,
! [X2,X3,X0,X1] :
( apart_point_and_line(X0,orthogonal_through_point(X1,X2))
| unorthogonal_lines(X3,X1)
| apart_point_and_line(X0,X3)
| ~ distinct_lines(X3,orthogonal_through_point(X1,X2)) ),
inference(resolution,[],[f49,f46]) ).
fof(f100,plain,
! [X2,X0,X1] :
( ~ distinct_lines(X0,orthogonal_through_point(X1,X2))
| apart_point_and_line(X2,X0)
| unorthogonal_lines(X0,X1) ),
inference(resolution,[],[f70,f45]) ).
fof(f105,plain,
( apart_point_and_line(sK1,orthogonal_through_point(sK2,sK0))
| unorthogonal_lines(orthogonal_through_point(sK2,sK0),sK2) ),
inference(resolution,[],[f100,f39]) ).
fof(f110,plain,
unorthogonal_lines(orthogonal_through_point(sK2,sK0),sK2),
inference(forward_subsumption_resolution,[],[f105,f38]) ).
fof(f111,plain,
$false,
inference(forward_subsumption_resolution,[],[f110,f46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO221+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n013.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 07:41:51 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 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
% 3.69/1.44 % (4089398)Detected formulas, will run a generic FOF schedule.
% 3.69/1.44 % (4089406)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3150636121:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.69/1.44 % (4089406)Refutation not found, incomplete strategy
% 3.69/1.44 % (4089406)------------------------------
% 3.69/1.44 % (4089406)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.44 % (4089406)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.44 % (4089406)CaDiCaL version: 2.1.3
% 3.69/1.44 % (4089406)Termination reason: Refutation not found, incomplete strategy
% 3.69/1.44 % (4089406)Time elapsed: 0.001 s
% 3.69/1.44 % (4089406)Peak memory usage: 87 MB
% 3.69/1.44 % (4089404)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=730428370:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.69/1.44 % (4089405)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=3785693428:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.69/1.44 % (4089403)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=256265333:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.69/1.44 % (4089409)dis-21_1_sil=8000:lcm=predicate:random_seed=1837636014: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)
% 3.69/1.44 % (4089407)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3319246949:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.69/1.44 % (4089408)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=733147131:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.69/1.44 % (4089407)First to succeed.
% 3.69/1.44 % (4089409)Also succeeded, but the first one will report.
% 3.69/1.44 % (4089407)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4089398"
% 3.69/1.44 % (4089408)Also succeeded, but the first one will report.
% 3.69/1.44 % (4089406)------------------------------
% 3.69/1.44 % (4089406)------------------------------
% 3.69/1.44 % (4089417)lrs+10_1_sil=8000:sp=occurrence:random_seed=3201306251:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.69/1.44 % (4089417)Also succeeded, but the first one will report.
% 3.69/1.44 % (4089407)Refutation found. Thanks to Tanya!
% 3.69/1.44 % SZS status Theorem for theBenchmark
% 3.69/1.44 % SZS output start Proof for theBenchmark
% See solution above
% 3.69/1.44 % (4089407)------------------------------
% 3.69/1.44 % (4089407)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.44 % (4089407)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.44 % (4089407)CaDiCaL version: 2.1.3
% 3.69/1.44 % (4089407)Termination reason: Refutation
% 3.69/1.44 % (4089407)Time elapsed: 0.003 s
% 3.69/1.44 % (4089407)Peak memory usage: 88 MB
% 3.69/1.44 % (4089407)Instructions burned: 3 (million)
% 3.69/1.44 % (4089407)------------------------------
% 3.69/1.44 % (4089407)------------------------------
% 3.69/1.44 % (4089398)Success in time 0.448 s
% 3.69/1.44 % Vampire exiting
%------------------------------------------------------------------------------