%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO222+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 : n026.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 4.63s 1.63s
% Output : Refutation 4.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 40 ( 18 unt; 0 def)
% Number of atoms : 100 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 96 ( 36 ~; 45 |; 9 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 85 ( 83 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart1) ).
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart3) ).
fof(f6,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( convergent_lines(X0,X2)
| convergent_lines(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart6) ).
fof(f8,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( ( apart_point_and_line(X2,X0)
| apart_point_and_line(X2,X1) )
=> distinct_points(X2,intersection_point(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con2) ).
fof(f12,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> distinct_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq3) ).
fof(f16,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
| unorthogonal_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',occu1) ).
fof(f17,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(f18,axiom,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ooc1) ).
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] : ~ convergent_lines(X1,orthogonal_through_point(orthogonal_through_point(X1,X0),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f22,negated_conjecture,
~ ! [X0,X1] : ~ convergent_lines(X1,orthogonal_through_point(orthogonal_through_point(X1,X0),X0)),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f27,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f28,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f27]) ).
fof(f31,plain,
! [X0,X1,X2] :
( distinct_points(X2,intersection_point(X0,X1))
| ( ~ apart_point_and_line(X2,X0)
& ~ apart_point_and_line(X2,X1) )
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f32,plain,
! [X0,X1,X2] :
( distinct_points(X2,intersection_point(X0,X1))
| ( ~ apart_point_and_line(X2,X0)
& ~ apart_point_and_line(X2,X1) )
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f31]) ).
fof(f39,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f42,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,[],[f17]) ).
fof(f43,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,[],[f42]) ).
fof(f44,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(f45,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,[],[f44]) ).
fof(f46,plain,
? [X0,X1] : convergent_lines(X1,orthogonal_through_point(orthogonal_through_point(X1,X0),X0)),
inference(ennf_transformation,[],[f22]) ).
fof(f47,plain,
convergent_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)],[f46]) ).
fof(f48,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f50,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f53,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f28]) ).
fof(f56,plain,
! [X2,X0,X1] :
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f57,plain,
! [X2,X0,X1] :
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f61,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f65,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f68,plain,
! [X2,X0,X1] :
( ~ unorthogonal_lines(X0,X1)
| unorthogonal_lines(X1,X2)
| ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f43]) ).
fof(f70,plain,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f18]) ).
fof(f72,plain,
! [X2,X3,X0,X1] :
( ~ distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| unorthogonal_lines(X1,X3)
| unorthogonal_lines(X2,X3)
| apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f73,plain,
convergent_lines(sK1,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),
inference(cnf_transformation,[],[f47]) ).
fof(f80,plain,
! [X0,X1] : convergent_lines(orthogonal_through_point(X0,X1),X0),
inference(unit_resulting_resolution,[],[f65,f70]) ).
fof(f85,plain,
! [X0,X1] : convergent_lines(X0,orthogonal_through_point(X0,X1)),
inference(unit_resulting_resolution,[],[f53,f50,f80]) ).
fof(f87,plain,
distinct_lines(sK1,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),
inference(unit_resulting_resolution,[],[f61,f73]) ).
fof(f98,plain,
! [X0,X1] : ~ unorthogonal_lines(X0,orthogonal_through_point(X0,X1)),
inference(unit_resulting_resolution,[],[f68,f50,f70,f85]) ).
fof(f115,plain,
~ apart_point_and_line(intersection_point(sK1,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),
inference(unit_resulting_resolution,[],[f56,f73,f48]) ).
fof(f119,plain,
~ apart_point_and_line(intersection_point(sK1,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),sK1),
inference(unit_resulting_resolution,[],[f57,f73,f48]) ).
fof(f235,plain,
$false,
inference(unit_resulting_resolution,[],[f72,f119,f115,f87,f70,f98]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO222+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n026.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 07:45:42 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 3.26/1.44 % (2505494)Detected formulas, will run a generic FOF schedule.
% 3.26/1.44 % (2505503)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2160778302:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.26/1.44 % (2505499)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=1692195886:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.26/1.44 % (2505503)Instruction limit reached!
% 3.26/1.44 % (2505503)------------------------------
% 3.26/1.44 % (2505503)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.26/1.44 % (2505503)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.26/1.44 % (2505503)CaDiCaL version: 2.1.3
% 3.26/1.44 % (2505503)Termination reason: Instruction limit
% 3.26/1.44 % (2505503)Termination phase: Saturation
% 3.26/1.44 % (2505503)Time elapsed: 0.037 s
% 3.26/1.44 % (2505503)Peak memory usage: 87 MB
% 3.26/1.44 % (2505503)Instructions burned: 122 (million)
% 3.26/1.44 % (2505500)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=2802525903:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.26/1.44 % (2505502)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3260424389:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.26/1.44 % (2505501)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=369319920:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.26/1.44 % (2505504)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4264946067:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.26/1.44 % (2505502)Refutation not found, incomplete strategy
% 3.26/1.44 % (2505502)------------------------------
% 3.26/1.44 % (2505502)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.26/1.44 % (2505502)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.26/1.44 % (2505502)CaDiCaL version: 2.1.3
% 3.26/1.44 % (2505502)Termination reason: Refutation not found, incomplete strategy
% 3.26/1.44 % (2505502)Time elapsed: 0.001 s
% 3.26/1.44 % (2505502)Peak memory usage: 87 MB
% 3.26/1.44 % (2505505)dis-21_1_sil=8000:lcm=predicate:random_seed=196271218: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)
% 3.26/1.44 % (2505505)Instruction limit reached!
% 3.26/1.44 % (2505505)------------------------------
% 3.26/1.44 % (2505505)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.26/1.44 % (2505505)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.26/1.44 % (2505505)CaDiCaL version: 2.1.3
% 3.26/1.44 % (2505505)Termination reason: Instruction limit
% 3.26/1.44 % (2505505)Termination phase: Saturation
% 3.26/1.44 % (2505505)Time elapsed: 0.066 s
% 3.26/1.44 % (2505505)Peak memory usage: 88 MB
% 3.26/1.44 % (2505505)Instructions burned: 130 (million)
% 3.26/1.44 % (2505512)lrs+10_1_sil=8000:sp=occurrence:random_seed=768741177:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.26/1.44 % (2505504)Instruction limit reached!
% 3.26/1.44 % (2505504)------------------------------
% 3.26/1.44 % (2505504)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.26/1.44 % (2505504)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.26/1.44 % (2505504)CaDiCaL version: 2.1.3
% 3.26/1.44 % (2505504)Termination reason: Instruction limit
% 3.26/1.44 % (2505504)Termination phase: Saturation
% 3.26/1.44 % (2505504)Time elapsed: 0.097 s
% 3.26/1.44 % (2505504)Peak memory usage: 89 MB
% 3.26/1.44 % (2505504)Instructions burned: 140 (million)
% 3.26/1.44 % (2505512)Instruction limit reached!
% 3.26/1.44 % (2505512)------------------------------
% 3.26/1.44 % (2505512)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.26/1.44 % (2505512)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.26/1.44 % (2505512)CaDiCaL version: 2.1.3
% 3.26/1.44 % (2505512)Termination reason: Instruction limit
% 3.26/1.44 % (2505512)Termination phase: Saturation
% 3.26/1.44 % (2505512)Time elapsed: 0.079 s
% 3.26/1.44 % (2505512)Peak memory usage: 89 MB
% 3.26/1.44 % (2505512)Instructions burned: 288 (million)
% 3.26/1.44 % (2505514)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2061514334:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.63/1.63 % (2505514)Refutation not found, incomplete strategy
% 4.63/1.63 % (2505514)------------------------------
% 4.63/1.63 % (2505514)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.63/1.63 % (2505514)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.63/1.63 % (2505514)CaDiCaL version: 2.1.3
% 4.63/1.63 % (2505514)Termination reason: Refutation not found, incomplete strategy
% 4.63/1.63 % (2505514)Time elapsed: 0.001 s
% 4.63/1.63 % (2505514)Peak memory usage: 88 MB
% 4.63/1.63 % (2505516)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1450272735:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.63/1.63 % (2505502)------------------------------
% 4.63/1.63 % (2505502)------------------------------
% 4.63/1.63 % (2505517)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=2382789763:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 4.63/1.63 % (2505517)First to succeed.
% 4.63/1.63 % (2505517)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2505494"
% 4.63/1.63 % (2505521)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=892460186:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 4.63/1.63 % (2505521)Refutation not found, incomplete strategy
% 4.63/1.63 % (2505521)------------------------------
% 4.63/1.63 % (2505521)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.63/1.63 % (2505521)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.63/1.63 % (2505521)CaDiCaL version: 2.1.3
% 4.63/1.63 % (2505521)Termination reason: Refutation not found, incomplete strategy
% 4.63/1.63 % (2505521)Time elapsed: 0.001 s
% 4.63/1.63 % (2505521)Peak memory usage: 88 MB
% 4.63/1.63 % (2505517)Refutation found. Thanks to Tanya!
% 4.63/1.63 % SZS status Theorem for theBenchmark
% 4.63/1.63 % SZS output start Proof for theBenchmark
% See solution above
% 4.63/1.63 % (2505517)------------------------------
% 4.63/1.63 % (2505517)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.63/1.63 % (2505517)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.63/1.63 % (2505517)CaDiCaL version: 2.1.3
% 4.63/1.63 % (2505517)Termination reason: Refutation
% 4.63/1.63 % (2505517)Time elapsed: 0.004 s
% 4.63/1.63 % (2505517)Peak memory usage: 88 MB
% 4.63/1.63 % (2505517)Instructions burned: 11 (million)
% 4.63/1.63 % (2505517)------------------------------
% 4.63/1.63 % (2505517)------------------------------
% 4.63/1.63 % (2505494)Success in time 0.566 s
% 4.63/1.63 % Vampire exiting
%------------------------------------------------------------------------------