%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO223+1 : 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 : n018.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 1.72s 1.13s
% Output : Refutation 2.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 55 ( 22 unt; 0 def)
% Number of atoms : 136 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 126 ( 45 ~; 69 |; 7 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 117 ( 115 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ax6) ).
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] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp1) ).
fof(f16,axiom,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp2) ).
fof(f17,axiom,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
=> ( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| convergent_lines(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cup1) ).
fof(f18,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
| unorthogonal_lines(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',occu1) ).
fof(f19,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(f20,axiom,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ooc1) ).
fof(f21,axiom,
! [X0,X1] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ooc2) ).
fof(f22,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/sandbox2/benchmark/theBenchmark.p',ouo1) ).
fof(f23,conjecture,
! [X0,X1] : ~ distinct_lines(parallel_through_point(X1,X0),orthogonal_through_point(orthogonal_through_point(X1,X0),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f24,negated_conjecture,
~ ! [X0,X1] : ~ distinct_lines(parallel_through_point(X1,X0),orthogonal_through_point(orthogonal_through_point(X1,X0),X0)),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f25,plain,
? [X0,X1] : distinct_lines(parallel_through_point(X1,X0),orthogonal_through_point(orthogonal_through_point(X1,X0),X0)),
inference(ennf_transformation,[],[f24]) ).
fof(f26,plain,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| convergent_lines(X1,X2)
| ~ distinct_lines(X1,X2) ),
inference(ennf_transformation,[],[f17]) ).
fof(f27,plain,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| convergent_lines(X1,X2)
| ~ distinct_lines(X1,X2) ),
inference(flattening,[],[f26]) ).
fof(f28,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f29,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f28]) ).
fof(f34,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f35,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f34]) ).
fof(f36,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,[],[f22]) ).
fof(f37,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,[],[f36]) ).
fof(f38,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,[],[f19]) ).
fof(f39,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,[],[f38]) ).
fof(f40,plain,
distinct_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f25]) ).
fof(f41,plain,
distinct_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),
inference(cnf_transformation,[],[f40]) ).
fof(f42,plain,
! [X2,X0,X1] :
( apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1)
| convergent_lines(X1,X2)
| ~ distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f27]) ).
fof(f43,plain,
! [X2,X0,X1] :
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f47,plain,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[],[f16]) ).
fof(f48,plain,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f15]) ).
fof(f49,plain,
! [X0,X1] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
inference(cnf_transformation,[],[f21]) ).
fof(f50,plain,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f20]) ).
fof(f51,plain,
! [X2,X0,X1] :
( convergent_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
fof(f52,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f53,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,[],[f37]) ).
fof(f56,plain,
! [X2,X0,X1] :
( unorthogonal_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1)
| ~ unorthogonal_lines(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f58,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f59,plain,
! [X0,X1] : convergent_lines(orthogonal_through_point(X0,X1),X0),
inference(resolution,[],[f58,f50]) ).
fof(f60,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X1,X0) ),
inference(resolution,[],[f43,f52]) ).
fof(f70,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,parallel_through_point(X1,X2))
| convergent_lines(X0,X1) ),
inference(resolution,[],[f51,f48]) ).
fof(f72,plain,
! [X2,X3,X0,X1] :
( convergent_lines(X2,parallel_through_point(X1,X3))
| convergent_lines(X0,X1)
| ~ convergent_lines(X2,X0) ),
inference(resolution,[],[f70,f51]) ).
fof(f76,plain,
! [X2,X0,X1] :
( convergent_lines(X1,orthogonal_through_point(X2,X0))
| apart_point_and_line(X0,X1)
| ~ distinct_lines(X1,orthogonal_through_point(X2,X0)) ),
inference(resolution,[],[f42,f49]) ).
fof(f91,plain,
! [X2,X0,X1] :
( ~ unorthogonal_lines(X0,orthogonal_through_point(X1,X2))
| ~ convergent_lines(X0,orthogonal_through_point(X1,X2))
| convergent_lines(X0,X1) ),
inference(resolution,[],[f56,f50]) ).
fof(f101,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,[],[f53,f50]) ).
fof(f174,plain,
! [X2,X0,X1] :
( ~ distinct_lines(X0,orthogonal_through_point(X1,X2))
| apart_point_and_line(X2,X0)
| unorthogonal_lines(X0,X1) ),
inference(resolution,[],[f101,f49]) ).
fof(f175,plain,
( apart_point_and_line(sK0,parallel_through_point(sK1,sK0))
| unorthogonal_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(sK1,sK0)) ),
inference(resolution,[],[f174,f41]) ).
fof(f181,plain,
unorthogonal_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(sK1,sK0)),
inference(forward_subsumption_resolution,[],[f175,f47]) ).
fof(f186,plain,
( ~ convergent_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(sK1,sK0))
| convergent_lines(parallel_through_point(sK1,sK0),sK1) ),
inference(resolution,[],[f181,f91]) ).
fof(f188,plain,
~ convergent_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(sK1,sK0)),
inference(forward_subsumption_resolution,[],[f186,f48]) ).
fof(f189,plain,
( apart_point_and_line(sK0,parallel_through_point(sK1,sK0))
| ~ distinct_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(sK1,sK0)) ),
inference(resolution,[],[f188,f76]) ).
fof(f192,plain,
~ distinct_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(sK1,sK0)),
inference(forward_subsumption_resolution,[],[f189,f47]) ).
fof(f203,plain,
~ convergent_lines(orthogonal_through_point(sK1,sK0),parallel_through_point(sK1,sK0)),
inference(resolution,[],[f192,f60]) ).
fof(f213,plain,
! [X0] :
( ~ convergent_lines(orthogonal_through_point(sK1,sK0),X0)
| convergent_lines(X0,sK1) ),
inference(resolution,[],[f203,f72]) ).
fof(f225,plain,
convergent_lines(sK1,sK1),
inference(resolution,[],[f213,f59]) ).
fof(f233,plain,
$false,
inference(forward_subsumption_resolution,[],[f225,f52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO223+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n018.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 07:45:53 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
% 1.72/1.13 % (1997473)Detected formulas, will run a generic FOF schedule.
% 1.72/1.13 % (1997482)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1985867828:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.72/1.13 % (1997482)First to succeed.
% 1.72/1.13 % (1997482)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1997473"
% 1.72/1.13 % (1997478)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=2385848902:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.72/1.13 % (1997480)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=3030855809:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.72/1.13 % (1997481)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3720227038:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.72/1.13 % (1997479)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=4139803642:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.72/1.13 % (1997483)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2028051123:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.72/1.13 % (1997484)dis-21_1_sil=8000:lcm=predicate:random_seed=3398944857: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)
% 1.72/1.13 % (1997484)Also succeeded, but the first one will report.
% 1.72/1.13 % (1997481)Instruction limit reached!
% 1.72/1.13 % (1997481)------------------------------
% 1.72/1.13 % (1997481)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.72/1.13 % (1997481)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.72/1.13 % (1997481)CaDiCaL version: 2.1.3
% 1.72/1.13 % (1997481)Termination reason: Instruction limit
% 1.72/1.13 % (1997481)Termination phase: Saturation
% 1.72/1.13 % (1997481)Time elapsed: 0.063 s
% 1.72/1.13 % (1997481)Peak memory usage: 88 MB
% 1.72/1.13 % (1997481)Instructions burned: 109 (million)
% 1.72/1.13 % (1997483)Instruction limit reached!
% 1.72/1.13 % (1997483)------------------------------
% 1.72/1.13 % (1997483)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.72/1.13 % (1997483)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.72/1.13 % (1997483)CaDiCaL version: 2.1.3
% 1.72/1.13 % (1997483)Termination reason: Instruction limit
% 1.72/1.13 % (1997483)Termination phase: Saturation
% 1.72/1.13 % (1997483)Time elapsed: 0.092 s
% 1.72/1.13 % (1997483)Peak memory usage: 88 MB
% 1.72/1.13 % (1997483)Instructions burned: 140 (million)
% 1.72/1.13 % (1997482)Refutation found. Thanks to Tanya!
% 1.72/1.13 % SZS status Theorem for theBenchmark
% 1.72/1.13 % SZS output start Proof for theBenchmark
% See solution above
% 2.63/1.33 % (1997482)------------------------------
% 2.63/1.33 % (1997482)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.63/1.33 % (1997482)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/1.33 % (1997482)CaDiCaL version: 2.1.3
% 2.63/1.33 % (1997482)Termination reason: Refutation
% 2.63/1.33 % (1997482)Time elapsed: 0.003 s
% 2.63/1.33 % (1997482)Peak memory usage: 88 MB
% 2.63/1.33 % (1997482)Instructions burned: 7 (million)
% 2.63/1.33 % (1997482)------------------------------
% 2.63/1.33 % (1997482)------------------------------
% 2.63/1.33 % (1997473)Success in time 0.284 s
% 2.63/1.33 % Vampire exiting
%------------------------------------------------------------------------------