%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO002-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 09:51:08 AM UTC 2026
% Result : Unsatisfiable 4.77s 1.81s
% Output : Refutation 4.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 40 ( 9 unt; 2 def)
% Number of atoms : 88 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 101 ( 53 ~; 46 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-5 aty)
% Number of variables : 61 ( 0 sgn 61 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1] :
( between(X0,X1,X3)
| ~ between(X1,X3,X2)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_for_betweeness) ).
fof(f2,axiom,
! [X2,X0,X1] :
( equalish(X0,X1)
| ~ equidistant(X0,X1,X2,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_equidistance) ).
fof(f3,axiom,
! [X2,X3,X0,X1,X4] :
( between(X0,outer_pasch(X1,X0,X3,X4,X2),X3)
| ~ between(X3,X2,X4)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',outer_pasch1) ).
fof(f4,axiom,
! [X2,X3,X0,X1,X4] :
( between(X4,X1,outer_pasch(X1,X0,X3,X4,X2))
| ~ between(X3,X2,X4)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',outer_pasch2) ).
fof(f5,axiom,
! [X2,X3,X0,X1] : between(X0,X1,extension(X0,X1,X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',segment_construction1) ).
fof(f6,axiom,
! [X2,X3,X0,X1] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',segment_construction2) ).
fof(f7,axiom,
! [X2,X3,X0,X1] :
( ~ equalish(X0,X1)
| ~ between(X2,X3,X0)
| between(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',between_substitution3) ).
fof(f8,negated_conjecture,
~ between(a,a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_between_a_and_b) ).
fof(f9,plain,
! [X2,X3,X0,X1,X4] :
( ~ equidistant(X2,X3,X4,X4)
| between(X0,X1,X3)
| ~ between(X0,X1,X2) ),
inference(resolution,[],[f7,f2]) ).
fof(f10,plain,
! [X0] :
( ~ between(a,b,X0)
| ~ between(a,a,X0) ),
inference(resolution,[],[f1,f8]) ).
fof(f12,plain,
! [X0,X1] :
( ~ between(b,X0,X1)
| ~ between(a,a,X0)
| ~ between(a,b,X1) ),
inference(resolution,[],[f10,f1]) ).
fof(f18,plain,
! [X2,X3,X0,X1] :
( ~ between(a,a,outer_pasch(X0,b,X1,X2,X3))
| ~ between(a,b,X1)
| ~ between(X1,X3,X2)
| ~ between(b,X0,X3) ),
inference(resolution,[],[f12,f3]) ).
fof(f19,plain,
! [X2,X3,X0,X1,X4] :
( between(X0,X1,extension(X2,X3,X4,X4))
| ~ between(X0,X1,X3) ),
inference(resolution,[],[f9,f6]) ).
fof(f63,plain,
! [X0,X1] :
( ~ between(a,b,X0)
| ~ between(X0,X1,a)
| ~ between(b,a,X1)
| ~ between(X0,X1,a)
| ~ between(b,a,X1) ),
inference(resolution,[],[f18,f4]) ).
fof(f65,plain,
! [X0,X1] :
( ~ between(a,b,X0)
| ~ between(X0,X1,a)
| ~ between(b,a,X1) ),
inference(duplicate_literal_removal,[],[f63]) ).
fof(f83,plain,
( ~ between(a,b,b)
| ~ between(b,a,a) ),
inference(factoring,[],[f65]) ).
fof(f85,definition,
( spl0_1
<=> between(b,a,a) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f86,plain,
( ~ between(b,a,a)
| spl0_1 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f88,definition,
( spl0_2
<=> between(a,b,b) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f89,plain,
( ~ between(a,b,b)
| spl0_2 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f90,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f83,f88,f85]) ).
fof(f91,plain,
( ! [X0] :
( ~ between(b,a,X0)
| ~ between(a,a,X0) )
| spl0_1 ),
inference(resolution,[],[f86,f1]) ).
fof(f92,plain,
( ! [X0,X1] : ~ between(a,a,extension(b,a,X0,X1))
| spl0_1 ),
inference(resolution,[],[f91,f5]) ).
fof(f96,plain,
( ~ between(a,a,a)
| spl0_1 ),
inference(resolution,[],[f92,f19]) ).
fof(f101,plain,
( ! [X0] :
( ~ between(a,a,X0)
| ~ between(a,a,X0) )
| spl0_1 ),
inference(resolution,[],[f96,f1]) ).
fof(f102,plain,
( ! [X0] : ~ between(a,a,X0)
| spl0_1 ),
inference(duplicate_literal_removal,[],[f101]) ).
fof(f120,plain,
( $false
| spl0_1 ),
inference(resolution,[],[f102,f5]) ).
fof(f124,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f120]) ).
fof(f125,plain,
( ! [X0] :
( ~ between(b,b,X0)
| ~ between(a,b,X0) )
| spl0_2 ),
inference(resolution,[],[f89,f1]) ).
fof(f127,plain,
( ! [X2,X0,X1] :
( ~ between(a,b,extension(X0,X1,X2,X2))
| ~ between(b,b,X1) )
| spl0_2 ),
inference(resolution,[],[f125,f19]) ).
fof(f132,plain,
( ~ between(b,b,b)
| spl0_2 ),
inference(resolution,[],[f127,f5]) ).
fof(f145,plain,
( ! [X0] :
( ~ between(b,b,X0)
| ~ between(b,b,X0) )
| spl0_2 ),
inference(resolution,[],[f132,f1]) ).
fof(f146,plain,
( ! [X0] : ~ between(b,b,X0)
| spl0_2 ),
inference(duplicate_literal_removal,[],[f145]) ).
fof(f148,plain,
( $false
| spl0_2 ),
inference(resolution,[],[f146,f5]) ).
fof(f152,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f148]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f90]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f124]) ).
cnf(s3,plain,
spl0_2,
inference(sat_conversion,[],[f152]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f153,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO002-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n004.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 06:29:22 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.45 Running first-order theorem proving
% 0.11/0.45 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
% 4.77/1.81 % (3144207)Input is clausal, will run a generic CNF schedule.
% 4.77/1.81 % (3144222)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=3830883236:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.77/1.81 % (3144228)dis-21_1_sil=8000:lcm=predicate:random_seed=3006260552: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)
% 4.77/1.81 % (3144228)First to succeed.
% 4.77/1.81 % (3144228)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3144207"
% 4.77/1.81 % (3144227)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1908108478:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.77/1.81 % (3144227)Also succeeded, but the first one will report.
% 4.77/1.81 % (3144225)lrs+10_1_sil=8000:sp=occurrence:random_seed=2771864496:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.77/1.81 % (3144223)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1822029311:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.77/1.81 % (3144226)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=173941250:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.77/1.81 % (3144224)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4142441151:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.77/1.81 % (3144226)Instruction limit reached!
% 4.77/1.81 % (3144226)------------------------------
% 4.77/1.81 % (3144226)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.77/1.81 % (3144226)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.77/1.81 % (3144226)CaDiCaL version: 2.1.3
% 4.77/1.81 % (3144226)Termination reason: Instruction limit
% 4.77/1.81 % (3144226)Termination phase: Saturation
% 4.77/1.81 % (3144226)Time elapsed: 0.070 s
% 4.77/1.81 % (3144226)Peak memory usage: 87 MB
% 4.77/1.81 % (3144226)Instructions burned: 114 (million)
% 4.77/1.81 % (3144225)Also succeeded, but the first one will report.
% 4.77/1.81 % (3144241)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=3851960694:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 4.77/1.81 % (3144241)Refutation not found, incomplete strategy
% 4.77/1.81 % (3144241)------------------------------
% 4.77/1.81 % (3144241)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.77/1.81 % (3144241)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.77/1.81 % (3144241)CaDiCaL version: 2.1.3
% 4.77/1.81 % (3144241)Termination reason: Refutation not found, incomplete strategy
% 4.77/1.81 % (3144241)Time elapsed: 0.001 s
% 4.77/1.81 % (3144241)Peak memory usage: 87 MB
% 4.77/1.81 % (3144228)Refutation found. Thanks to Tanya!
% 4.77/1.81 % SZS status Unsatisfiable for theBenchmark
% 4.77/1.81 % SZS output start Proof for theBenchmark
% See solution above
% 4.77/1.81 % (3144228)------------------------------
% 4.77/1.81 % (3144228)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.77/1.81 % (3144228)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.77/1.81 % (3144228)CaDiCaL version: 2.1.3
% 4.77/1.81 % (3144228)Termination reason: Refutation
% 4.77/1.81 % (3144228)Time elapsed: 0.006 s
% 4.77/1.81 % (3144228)Peak memory usage: 89 MB
% 4.77/1.81 % (3144228)Instructions burned: 6 (million)
% 4.77/1.81 % (3144228)------------------------------
% 4.77/1.81 % (3144228)------------------------------
% 4.77/1.81 % (3144207)Success in time 0.553 s
% 4.77/1.81 % Vampire exiting
%------------------------------------------------------------------------------