%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO059-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 09:51:23 AM UTC 2026
% Result : Unsatisfiable 3.65s 1.61s
% Output : Refutation 3.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 12 ( 8 unt; 0 def)
% Number of atoms : 17 ( 1 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 16 ( 11 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-4 aty)
% Number of variables : 22 ( 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X2,X3,X0,X1] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',segment_construction2) ).
fof(f19,axiom,
! [X0,X1] : reflection(X0,X1) = extension(X0,X1,X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflection) ).
fof(f21,axiom,
! [X2,X3,X0,X1] :
( equidistant(X2,X3,X0,X1)
| ~ equidistant(X0,X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2) ).
fof(f24,axiom,
! [X2,X3,X0,X1] :
( equidistant(X1,X0,X3,X2)
| ~ equidistant(X0,X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_2) ).
fof(f28,axiom,
! [X2,X3,X0,X1,X4,X5] :
( equidistant(X0,X1,X4,X5)
| ~ equidistant(X2,X3,X4,X5)
| ~ equidistant(X0,X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5) ).
fof(f48,negated_conjecture,
~ equidistant(v,u,v,reflection(reflection(u,v),v)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_congruence) ).
fof(f54,plain,
~ equidistant(v,u,v,extension(extension(u,v,u,v),v,extension(u,v,u,v),v)),
inference(definition_unfolding,[],[f48,f19,f19]) ).
fof(f72,plain,
~ equidistant(v,extension(extension(u,v,u,v),v,extension(u,v,u,v),v),v,u),
inference(resolution,[],[f21,f54]) ).
fof(f143,plain,
! [X0,X1] :
( ~ equidistant(v,extension(extension(u,v,u,v),v,extension(u,v,u,v),v),X0,X1)
| ~ equidistant(X0,X1,v,u) ),
inference(resolution,[],[f28,f72]) ).
fof(f322,plain,
~ equidistant(extension(u,v,u,v),v,v,u),
inference(resolution,[],[f143,f5]) ).
fof(f339,plain,
~ equidistant(v,extension(u,v,u,v),u,v),
inference(resolution,[],[f322,f24]) ).
fof(f426,plain,
$false,
inference(resolution,[],[f339,f5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO059-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.60 % Computer : n020.cluster.edu
% 0.13/0.60 % Model : x86_64 x86_64
% 0.13/0.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.60 % Memory : 8046.5625MB
% 0.13/0.60 % OS : Linux 6.8.0-71-generic
% 0.13/0.60 % CPULimit : 300
% 0.13/0.60 % WCLimit : 300
% 0.13/0.60 % DateTime : Sun Sep 27 06:47:20 UTC 2026
% 0.13/0.60 % CPUTime :
% 0.13/0.60 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.64 Running first-order theorem proving
% 0.16/0.64 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
% 3.65/1.61 % (3052631)Input is clausal, will run a generic CNF schedule.
% 3.65/1.61 % (3052636)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=2708223493:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.65/1.61 % (3052637)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1170402482:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.65/1.61 % (3052640)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1404149169:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.65/1.61 % (3052641)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=43608544:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.65/1.61 % (3052639)lrs+10_1_sil=8000:sp=occurrence:random_seed=195994713:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.65/1.61 % (3052642)dis-21_1_sil=8000:lcm=predicate:random_seed=1857605551:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 3.65/1.61 % (3052638)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3971283553:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.65/1.61 % (3052642)First to succeed.
% 3.65/1.61 % (3052642)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3052631"
% 3.65/1.61 % (3052639)Also succeeded, but the first one will report.
% 3.65/1.61 % (3052641)Also succeeded, but the first one will report.
% 3.65/1.61 % (3052640)Also succeeded, but the first one will report.
% 3.65/1.61 % (3052642)Refutation found. Thanks to Tanya!
% 3.65/1.61 % SZS status Unsatisfiable for theBenchmark
% 3.65/1.61 % SZS output start Proof for theBenchmark
% See solution above
% 3.65/1.61 % (3052642)------------------------------
% 3.65/1.61 % (3052642)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.61 % (3052642)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.61 % (3052642)CaDiCaL version: 2.1.3
% 3.65/1.61 % (3052642)Termination reason: Refutation
% 3.65/1.61 % (3052642)Time elapsed: 0.007 s
% 3.65/1.61 % (3052642)Peak memory usage: 88 MB
% 3.65/1.61 % (3052642)Instructions burned: 10 (million)
% 3.65/1.61 % (3052642)------------------------------
% 3.65/1.61 % (3052642)------------------------------
% 3.65/1.61 % (3052631)Success in time 0.44 s
% 3.65/1.61 % Vampire exiting
%------------------------------------------------------------------------------