%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO032-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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 09:51:16 AM UTC 2026
% Result : Unsatisfiable 3.64s 1.44s
% Output : Refutation 3.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 36 ( 17 unt; 4 def)
% Number of atoms : 81 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 94 ( 49 ~; 41 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 5 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 22 ( 0 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f41,axiom,
! [X0,X1] : equidistant(X0,X0,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7) ).
fof(f74,axiom,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( equidistant(X1,X6,X3,X7)
| ~ equidistant(X0,X4,X2,X5)
| ~ equidistant(X0,X6,X2,X7)
| ~ equidistant(X4,X6,X5,X7)
| ~ between(X0,X1,X4)
| ~ between(X2,X3,X5)
| ~ equidistant(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12) ).
fof(f75,axiom,
between(u,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_between_u_and_w) ).
fof(f76,axiom,
between(u1,v1,w1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v1_between_u1_and_w1) ).
fof(f77,axiom,
equidistant(u,v,u1,v1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_to_v_equals_u1_to_v1) ).
fof(f78,axiom,
equidistant(u,w,u1,w1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_to_w_equals_u1_to_w1) ).
fof(f79,negated_conjecture,
~ equidistant(v,w,v1,w1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_to_w_equals_v1_to_w1) ).
fof(f441,plain,
! [X2,X3,X0,X1] :
( ~ equidistant(X0,X1,X2,X3)
| ~ equidistant(X0,w,X2,w1)
| ~ equidistant(X1,w,X3,w1)
| ~ between(X0,v,X1)
| ~ between(X2,v1,X3)
| ~ equidistant(X0,v,X2,v1) ),
inference(resolution,[],[f74,f79]) ).
fof(f729,plain,
! [X0,X1] :
( ~ equidistant(X0,w,X1,w1)
| ~ equidistant(X0,w,X1,w1)
| ~ between(X0,v,w)
| ~ between(X1,v1,w1)
| ~ equidistant(X0,v,X1,v1) ),
inference(resolution,[],[f441,f41]) ).
fof(f734,plain,
! [X0,X1] :
( ~ equidistant(X0,w,X1,w1)
| ~ between(X0,v,w)
| ~ between(X1,v1,w1)
| ~ equidistant(X0,v,X1,v1) ),
inference(duplicate_literal_removal,[],[f729]) ).
fof(f740,definition,
( spl1_5
<=> ! [X0,X1] :
( ~ equidistant(X0,w,X1,w1)
| ~ equidistant(X0,v,X1,v1)
| ~ between(X1,v1,w1)
| ~ between(X0,v,w) ) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
fof(f741,plain,
( ! [X0,X1] :
( ~ equidistant(X0,w,X1,w1)
| ~ equidistant(X0,v,X1,v1)
| ~ between(X1,v1,w1)
| ~ between(X0,v,w) )
| ~ spl1_5 ),
inference(avatar_component_clause,[],[f740]) ).
fof(f743,plain,
spl1_5,
inference(avatar_split_clause,[],[f734,f740]) ).
fof(f752,definition,
( spl1_8
<=> equidistant(u,v,u1,v1) ),
introduced(definition,[new_symbols(definition,[spl1_8])],[avatar_definition]) ).
fof(f753,plain,
( ~ equidistant(u,v,u1,v1)
| spl1_8 ),
inference(avatar_component_clause,[],[f752]) ).
fof(f781,plain,
( $false
| spl1_8 ),
inference(resolution,[],[f753,f77]) ).
fof(f793,plain,
spl1_8,
inference(avatar_contradiction_clause,[],[f781]) ).
fof(f805,plain,
( ~ equidistant(u,v,u1,v1)
| ~ between(u1,v1,w1)
| ~ between(u,v,w)
| ~ spl1_5 ),
inference(resolution,[],[f741,f78]) ).
fof(f820,definition,
( spl1_10
<=> between(u,v,w) ),
introduced(definition,[new_symbols(definition,[spl1_10])],[avatar_definition]) ).
fof(f821,plain,
( ~ between(u,v,w)
| spl1_10 ),
inference(avatar_component_clause,[],[f820]) ).
fof(f823,definition,
( spl1_11
<=> between(u1,v1,w1) ),
introduced(definition,[new_symbols(definition,[spl1_11])],[avatar_definition]) ).
fof(f824,plain,
( ~ between(u1,v1,w1)
| spl1_11 ),
inference(avatar_component_clause,[],[f823]) ).
fof(f825,plain,
( ~ spl1_10
| ~ spl1_11
| ~ spl1_8
| ~ spl1_5 ),
inference(avatar_split_clause,[],[f805,f740,f752,f823,f820]) ).
fof(f826,plain,
( $false
| spl1_10 ),
inference(resolution,[],[f821,f75]) ).
fof(f832,plain,
spl1_10,
inference(avatar_contradiction_clause,[],[f826]) ).
fof(f882,plain,
( $false
| spl1_11 ),
inference(resolution,[],[f824,f76]) ).
fof(f888,plain,
spl1_11,
inference(avatar_contradiction_clause,[],[f882]) ).
cnf(s3,plain,
spl1_5,
inference(sat_conversion,[],[f743]) ).
cnf(s7,plain,
spl1_8,
inference(sat_conversion,[],[f793]) ).
cnf(s8,plain,
( ~ spl1_5
| ~ spl1_8
| ~ spl1_10
| ~ spl1_11 ),
inference(sat_conversion,[],[f825]) ).
cnf(s9,plain,
spl1_10,
inference(sat_conversion,[],[f832]) ).
cnf(s13,plain,
spl1_11,
inference(sat_conversion,[],[f888]) ).
cnf(s15,plain,
( ~ spl1_5
| ~ spl1_8 ),
inference(rat,[],[s8,s13,s9]) ).
cnf(s16,plain,
~ spl1_5,
inference(rat,[],[s15,s7]) ).
cnf(s19,plain,
$false,
inference(rat,[],[s3,s16]) ).
fof(f889,plain,
$false,
inference(avatar_sat_refutation,[],[s19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO032-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n002.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % 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 06:40:51 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 3.64/1.44 % (3182576)Input is clausal, will run a generic CNF schedule.
% 3.64/1.44 % (3182631)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1324630150:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.64/1.44 % (3182629)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=2828612006:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.64/1.44 % (3182630)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1703678981:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.64/1.44 % (3182635)dis-21_1_sil=8000:lcm=predicate:random_seed=48400645: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)
% 3.64/1.44 % (3182632)lrs+10_1_sil=8000:sp=occurrence:random_seed=2529510753:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.64/1.44 % (3182634)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3122391384:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.64/1.44 % (3182635)First to succeed.
% 3.64/1.44 % (3182635)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3182576"
% 3.64/1.44 % (3182633)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3744317615:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.64/1.44 % (3182632)Also succeeded, but the first one will report.
% 3.64/1.44 % (3182634)Also succeeded, but the first one will report.
% 3.64/1.44 % (3182633)Instruction limit reached!
% 3.64/1.44 % (3182633)------------------------------
% 3.64/1.44 % (3182633)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.44 % (3182633)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.44 % (3182633)CaDiCaL version: 2.1.3
% 3.64/1.44 % (3182633)Termination reason: Instruction limit
% 3.64/1.44 % (3182633)Termination phase: Saturation
% 3.64/1.44 % (3182633)Time elapsed: 0.110 s
% 3.64/1.44 % (3182633)Peak memory usage: 88 MB
% 3.64/1.44 % (3182633)Instructions burned: 114 (million)
% 3.64/1.44 % (3182635)Refutation found. Thanks to Tanya!
% 3.64/1.44 % SZS status Unsatisfiable for theBenchmark
% 3.64/1.44 % SZS output start Proof for theBenchmark
% See solution above
% 3.64/1.44 % (3182635)------------------------------
% 3.64/1.44 % (3182635)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.44 % (3182635)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.44 % (3182635)CaDiCaL version: 2.1.3
% 3.64/1.44 % (3182635)Termination reason: Refutation
% 3.64/1.44 % (3182635)Time elapsed: 0.013 s
% 3.64/1.44 % (3182635)Peak memory usage: 89 MB
% 3.64/1.44 % (3182635)Instructions burned: 21 (million)
% 3.64/1.44 % (3182635)------------------------------
% 3.64/1.44 % (3182635)------------------------------
% 3.64/1.44 % (3182576)Success in time 0.449 s
% 3.64/1.44 % Vampire exiting
%------------------------------------------------------------------------------