%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO037-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 09:51:18 AM UTC 2026
% Result : Unsatisfiable 0.15s 1.51s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 32 ( 11 unt; 3 def)
% Number of atoms : 58 ( 7 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 50 ( 24 ~; 23 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-4 aty)
% Number of variables : 26 ( 0 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X2,X0,X1] :
( ~ equidistant(X0,X1,X2,X2)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_equidistance) ).
fof(f4,axiom,
! [X2,X3,X0,X1] : between(X0,X1,extension(X0,X1,X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction1) ).
fof(f5,axiom,
! [X2,X3,X0,X1] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction2) ).
fof(f21,axiom,
! [X2,X3,X0,X1] :
( equidistant(X2,X3,X0,X1)
| ~ equidistant(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2) ).
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/sandbox/benchmark/theBenchmark.p',d5) ).
fof(f65,axiom,
lower_dimension_point_1 != lower_dimension_point_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e2_1) ).
fof(f68,negated_conjecture,
( v = extension(u,v,lower_dimension_point_1,lower_dimension_point_2)
| ~ equidistant(v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2),x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2))
| ~ between(u,v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lengthen) ).
fof(f80,definition,
( spl0_1
<=> between(u,v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f81,plain,
( ~ between(u,v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2))
| spl0_1 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f83,definition,
( spl0_2
<=> equidistant(v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2),x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f84,plain,
( ~ equidistant(v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2),x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2))
| spl0_2 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f86,definition,
( spl0_3
<=> v = extension(u,v,lower_dimension_point_1,lower_dimension_point_2) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f87,plain,
( v = extension(u,v,lower_dimension_point_1,lower_dimension_point_2)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f88,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_3 ),
inference(avatar_split_clause,[],[f68,f86,f83,f80]) ).
fof(f94,plain,
( $false
| spl0_1 ),
inference(resolution,[],[f4,f81]) ).
fof(f96,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f94]) ).
fof(f119,plain,
! [X2,X0,X1] :
( ~ equidistant(X0,X0,X1,X2)
| X1 = X2 ),
inference(resolution,[],[f21,f3]) ).
fof(f256,plain,
( ! [X0,X1] :
( ~ equidistant(v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2),X0,X1)
| ~ equidistant(X0,X1,x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2)) )
| spl0_2 ),
inference(resolution,[],[f28,f84]) ).
fof(f712,plain,
( ~ equidistant(lower_dimension_point_1,lower_dimension_point_2,x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2))
| spl0_2 ),
inference(resolution,[],[f256,f5]) ).
fof(f732,plain,
( ~ equidistant(x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2),lower_dimension_point_1,lower_dimension_point_2)
| spl0_2 ),
inference(resolution,[],[f712,f21]) ).
fof(f744,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f732,f5]) ).
fof(f745,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f744]) ).
fof(f751,plain,
( equidistant(v,v,lower_dimension_point_1,lower_dimension_point_2)
| ~ spl0_3 ),
inference(superposition,[],[f5,f87]) ).
fof(f768,plain,
( lower_dimension_point_1 = lower_dimension_point_2
| ~ spl0_3 ),
inference(resolution,[],[f119,f751]) ).
fof(f769,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f768,f65]) ).
fof(f770,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f769]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f88]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f96]) ).
cnf(s45,plain,
spl0_2,
inference(sat_conversion,[],[f745]) ).
cnf(s46,plain,
~ spl0_3,
inference(sat_conversion,[],[f770]) ).
cnf(s47,plain,
$false,
inference(rat,[],[s1,s46,s45,s2]) ).
fof(f771,plain,
$false,
inference(avatar_sat_refutation,[],[s47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO037-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n002.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 06:42:51 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.15/1.51 % (3184795)Input is clausal, will run a generic CNF schedule.
% 0.15/1.51 % (3184801)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3746604111:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.15/1.51 % (3184806)dis-21_1_sil=8000:lcm=predicate:random_seed=3821888145: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)
% 0.15/1.51 % (3184803)lrs+10_1_sil=8000:sp=occurrence:random_seed=3114538604:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.15/1.51 % (3184804)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=787767522:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.15/1.51 % (3184802)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2856495500:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.15/1.51 % (3184800)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=162771261:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.15/1.51 % (3184805)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1802257690:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.15/1.51 % (3184804)First to succeed.
% 0.15/1.51 % (3184804)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3184795"
% 0.15/1.51 % (3184803)Also succeeded, but the first one will report.
% 0.15/1.51 % (3184806)Instruction limit reached!
% 0.15/1.51 % (3184806)------------------------------
% 0.15/1.51 % (3184806)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.51 % (3184806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.51 % (3184806)CaDiCaL version: 2.1.3
% 0.15/1.51 % (3184806)Termination reason: Instruction limit
% 0.15/1.51 % (3184806)Termination phase: Saturation
% 0.15/1.51 % (3184806)Time elapsed: 0.062 s
% 0.15/1.51 % (3184806)Peak memory usage: 88 MB
% 0.15/1.51 % (3184806)Instructions burned: 118 (million)
% 0.15/1.51 % (3184805)Also succeeded, but the first one will report.
% 0.15/1.51 % (3184814)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=3052614999:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 0.15/1.51 % (3184814)Refutation not found, incomplete strategy
% 0.15/1.51 % (3184814)------------------------------
% 0.15/1.51 % (3184814)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.51 % (3184814)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.51 % (3184814)CaDiCaL version: 2.1.3
% 0.15/1.51 % (3184814)Termination reason: Refutation not found, incomplete strategy
% 0.15/1.51 % (3184814)Time elapsed: 0.003 s
% 0.15/1.51 % (3184814)Peak memory usage: 88 MB
% 0.15/1.51 % (3184814)Instructions burned: 3 (million)
% 0.15/1.51 % (3184804)Refutation found. Thanks to Tanya!
% 0.15/1.51 % SZS status Unsatisfiable for theBenchmark
% 0.15/1.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/1.51 % (3184804)------------------------------
% 0.15/1.51 % (3184804)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.51 % (3184804)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.51 % (3184804)CaDiCaL version: 2.1.3
% 0.15/1.51 % (3184804)Termination reason: Refutation
% 0.15/1.51 % (3184804)Time elapsed: 0.026 s
% 0.15/1.51 % (3184804)Peak memory usage: 89 MB
% 0.15/1.51 % (3184804)Instructions burned: 41 (million)
% 0.15/1.51 % (3184804)------------------------------
% 0.15/1.51 % (3184804)------------------------------
% 0.15/1.51 % (3184795)Success in time 0.459 s
% 0.15/1.51 % Vampire exiting
%------------------------------------------------------------------------------