%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO036-2 : 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 : 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 09:51:17 AM UTC 2026
% Result : Unsatisfiable 3.40s 1.46s
% Output : Refutation 3.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 31 ( 15 unt; 3 def)
% Number of atoms : 50 ( 11 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 41 ( 22 ~; 16 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-4 aty)
% Number of variables : 16 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X2,X0,X1] :
( ~ equidistant(X0,X1,X2,X2)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_equidistance) ).
fof(f4,axiom,
! [X2,X3,X0,X1] : between(X0,X1,extension(X0,X1,X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',segment_construction1) ).
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(f10,axiom,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension1) ).
fof(f11,axiom,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension2) ).
fof(f12,axiom,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension3) ).
fof(f19,negated_conjecture,
( lower_dimension_point_1 = lower_dimension_point_2
| lower_dimension_point_2 = lower_dimension_point_3
| lower_dimension_point_1 = lower_dimension_point_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_axioms_points_are_distinct) ).
fof(f21,definition,
( spl0_1
<=> lower_dimension_point_1 = lower_dimension_point_3 ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f23,plain,
( lower_dimension_point_1 = lower_dimension_point_3
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f21]) ).
fof(f25,definition,
( spl0_2
<=> lower_dimension_point_2 = lower_dimension_point_3 ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f27,plain,
( lower_dimension_point_2 = lower_dimension_point_3
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f25]) ).
fof(f29,definition,
( spl0_3
<=> lower_dimension_point_1 = lower_dimension_point_2 ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f31,plain,
( lower_dimension_point_1 = lower_dimension_point_2
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f29]) ).
fof(f32,plain,
( spl0_1
| spl0_2
| spl0_3 ),
inference(avatar_split_clause,[],[f19,f29,f25,f21]) ).
fof(f33,plain,
( ~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_2)
| ~ spl0_2 ),
inference(superposition,[],[f10,f27]) ).
fof(f37,plain,
! [X2,X0,X1] : extension(X1,X0,X2,X2) = X0,
inference(resolution,[],[f5,f3]) ).
fof(f39,plain,
! [X0,X1] : between(X1,X0,X0),
inference(superposition,[],[f4,f37]) ).
fof(f43,plain,
( $false
| ~ spl0_2 ),
inference(resolution,[],[f39,f33]) ).
fof(f44,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f43]) ).
fof(f45,plain,
( ~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_1)
| ~ spl0_3 ),
inference(superposition,[],[f12,f31]) ).
fof(f48,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f45,f39]) ).
fof(f49,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f48]) ).
fof(f52,plain,
( ~ between(lower_dimension_point_2,lower_dimension_point_1,lower_dimension_point_1)
| ~ spl0_1 ),
inference(superposition,[],[f11,f23]) ).
fof(f54,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f52,f39]) ).
fof(f55,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f54]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f32]) ).
cnf(s2,plain,
~ spl0_2,
inference(sat_conversion,[],[f44]) ).
cnf(s3,plain,
~ spl0_3,
inference(sat_conversion,[],[f49]) ).
cnf(s4,plain,
~ spl0_1,
inference(sat_conversion,[],[f55]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s3,s2,s4]) ).
fof(f56,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO036-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 % Computer : n018.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sun Sep 27 06:42:09 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.44 Running first-order theorem proving
% 0.13/0.44 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
% 3.40/1.46 % (1971517)Input is clausal, will run a generic CNF schedule.
% 3.40/1.46 % (1971526)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2352443475:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.40/1.46 % (1971525)lrs+10_1_sil=8000:sp=occurrence:random_seed=1512785651:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.40/1.46 % (1971526)Instruction limit reached!
% 3.40/1.46 % (1971526)------------------------------
% 3.40/1.46 % (1971526)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.46 % (1971526)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.46 % (1971526)CaDiCaL version: 2.1.3
% 3.40/1.46 % (1971526)Termination reason: Instruction limit
% 3.40/1.46 % (1971526)Termination phase: Saturation
% 3.40/1.46 % (1971526)Time elapsed: 0.034 s
% 3.40/1.46 % (1971526)Peak memory usage: 88 MB
% 3.40/1.46 % (1971526)Instructions burned: 115 (million)
% 3.40/1.46 % (1971525)First to succeed.
% 3.40/1.46 % (1971525)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1971517"
% 3.40/1.46 % (1971523)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2286791933:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.40/1.46 % (1971522)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=789433605:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.40/1.46 % (1971524)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2409065823:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.40/1.46 % (1971528)dis-21_1_sil=8000:lcm=predicate:random_seed=3112097638: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)
% 3.40/1.46 % (1971528)Refutation not found, incomplete strategy
% 3.40/1.46 % (1971528)------------------------------
% 3.40/1.46 % (1971528)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.46 % (1971528)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.46 % (1971528)CaDiCaL version: 2.1.3
% 3.40/1.46 % (1971528)Termination reason: Refutation not found, incomplete strategy
% 3.40/1.46 % (1971528)Time elapsed: 0.002 s
% 3.40/1.46 % (1971528)Peak memory usage: 88 MB
% 3.40/1.46 % (1971528)Instructions burned: 1 (million)
% 3.40/1.46 % (1971527)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3892537794:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.40/1.46 % (1971527)Also succeeded, but the first one will report.
% 3.40/1.46 % (1971534)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=1674359585:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.40/1.46 % (1971534)Refutation not found, incomplete strategy
% 3.40/1.46 % (1971534)------------------------------
% 3.40/1.46 % (1971534)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.46 % (1971534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.46 % (1971534)CaDiCaL version: 2.1.3
% 3.40/1.46 % (1971534)Termination reason: Refutation not found, incomplete strategy
% 3.40/1.46 % (1971534)Time elapsed: 0.002 s
% 3.40/1.46 % (1971534)Peak memory usage: 88 MB
% 3.40/1.46 % (1971534)Instructions burned: 1 (million)
% 3.40/1.46 % (1971525)Refutation found. Thanks to Tanya!
% 3.40/1.46 % SZS status Unsatisfiable for theBenchmark
% 3.40/1.46 % SZS output start Proof for theBenchmark
% See solution above
% 3.40/1.46 % (1971525)------------------------------
% 3.40/1.46 % (1971525)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.46 % (1971525)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.46 % (1971525)CaDiCaL version: 2.1.3
% 3.40/1.46 % (1971525)Termination reason: Refutation
% 3.40/1.46 % (1971525)Time elapsed: 0.003 s
% 3.40/1.46 % (1971525)Peak memory usage: 89 MB
% 3.40/1.46 % (1971525)Instructions burned: 2 (million)
% 3.40/1.46 % (1971525)------------------------------
% 3.40/1.46 % (1971525)------------------------------
% 3.40/1.46 % (1971517)Success in time 0.397 s
% 3.40/1.46 % Vampire exiting
%------------------------------------------------------------------------------