%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO026-2 : 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 : n026.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 09:51:14 AM UTC 2026
% Result : Unsatisfiable 3.32s 1.22s
% Output : Refutation 3.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 45 ( 17 unt; 3 def)
% Number of atoms : 104 ( 13 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 116 ( 57 ~; 56 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 43 ( 0 sgn 43 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : equidistant(X0,X1,X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_for_equidistance) ).
fof(f2,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ equidistant(X0,X1,X4,X5)
| ~ equidistant(X0,X1,X2,X3)
| equidistant(X2,X3,X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_for_equidistance) ).
fof(f3,axiom,
! [X2,X0,X1] :
( ~ equidistant(X0,X1,X2,X2)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_equidistance) ).
fof(f6,axiom,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ equidistant(X1,X6,X3,X7)
| ~ equidistant(X1,X4,X3,X5)
| ~ equidistant(X0,X6,X2,X7)
| ~ equidistant(X0,X1,X2,X3)
| ~ between(X0,X1,X4)
| ~ between(X2,X3,X5)
| X0 = X1
| equidistant(X4,X6,X5,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',outer_five_segment) ).
fof(f19,axiom,
between(u,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_between_u_and_w) ).
fof(f20,axiom,
between(u,v,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_between_u_and_x) ).
fof(f21,axiom,
equidistant(v,w,v,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_to_w_equals_v_to_x) ).
fof(f22,axiom,
u != v,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_not_v) ).
fof(f23,negated_conjecture,
w != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_w_is_x) ).
fof(f25,plain,
! [X0,X1] :
( ~ equidistant(v,w,X0,X1)
| equidistant(X0,X1,v,x) ),
inference(resolution,[],[f2,f21]) ).
fof(f26,plain,
! [X2,X3,X0,X1] :
( ~ equidistant(X0,X1,X2,X3)
| equidistant(X2,X3,X1,X0) ),
inference(resolution,[],[f2,f1]) ).
fof(f35,plain,
equidistant(v,x,v,x),
inference(resolution,[],[f25,f21]) ).
fof(f36,plain,
equidistant(w,v,v,x),
inference(resolution,[],[f25,f1]) ).
fof(f39,plain,
! [X0,X1] : equidistant(X0,X1,X0,X1),
inference(resolution,[],[f26,f1]) ).
fof(f41,plain,
! [X2,X3,X0,X1] :
( ~ equidistant(v,X0,v,X1)
| ~ equidistant(X2,x,X3,x)
| ~ equidistant(X2,v,X3,v)
| ~ between(X2,v,X0)
| ~ between(X3,v,X1)
| v = X2
| equidistant(X0,x,X1,x) ),
inference(resolution,[],[f35,f6]) ).
fof(f63,plain,
equidistant(v,x,v,w),
inference(resolution,[],[f36,f26]) ).
fof(f123,plain,
! [X2,X3,X0,X1] :
( ~ equidistant(X0,X1,X2,X3)
| equidistant(X2,X3,X0,X1) ),
inference(resolution,[],[f39,f2]) ).
fof(f351,plain,
! [X0,X1] :
( ~ equidistant(X0,x,X1,x)
| ~ equidistant(X0,v,X1,v)
| ~ between(X0,v,x)
| ~ between(X1,v,w)
| v = X0
| equidistant(x,x,w,x) ),
inference(resolution,[],[f41,f63]) ).
fof(f355,definition,
( spl0_13
<=> equidistant(x,x,w,x) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f357,plain,
( equidistant(x,x,w,x)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f355]) ).
fof(f359,definition,
( spl0_14
<=> ! [X0,X1] :
( ~ equidistant(X0,x,X1,x)
| v = X0
| ~ between(X1,v,w)
| ~ between(X0,v,x)
| ~ equidistant(X0,v,X1,v) ) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f360,plain,
( ! [X0,X1] :
( ~ equidistant(X0,x,X1,x)
| v = X0
| ~ between(X1,v,w)
| ~ between(X0,v,x)
| ~ equidistant(X0,v,X1,v) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f359]) ).
fof(f361,plain,
( spl0_13
| spl0_14 ),
inference(avatar_split_clause,[],[f351,f359,f355]) ).
fof(f363,definition,
( spl0_15
<=> equidistant(w,x,x,x) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f364,plain,
( ~ equidistant(w,x,x,x)
| spl0_15 ),
inference(avatar_component_clause,[],[f363]) ).
fof(f365,plain,
( equidistant(w,x,x,x)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f363]) ).
fof(f372,plain,
( equidistant(w,x,x,x)
| ~ spl0_13 ),
inference(resolution,[],[f357,f123]) ).
fof(f438,plain,
( w = x
| ~ spl0_15 ),
inference(resolution,[],[f365,f3]) ).
fof(f445,plain,
( $false
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f438,f23]) ).
fof(f446,plain,
~ spl0_15,
inference(avatar_contradiction_clause,[],[f445]) ).
fof(f453,plain,
( $false
| ~ spl0_13
| spl0_15 ),
inference(forward_subsumption_resolution,[],[f372,f364]) ).
fof(f454,plain,
( ~ spl0_13
| spl0_15 ),
inference(avatar_contradiction_clause,[],[f453]) ).
fof(f609,plain,
( ! [X0] :
( v = X0
| ~ between(X0,v,w)
| ~ between(X0,v,x)
| ~ equidistant(X0,v,X0,v) )
| ~ spl0_14 ),
inference(resolution,[],[f360,f39]) ).
fof(f611,plain,
( ! [X0] :
( ~ between(X0,v,x)
| ~ between(X0,v,w)
| v = X0 )
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f609,f39]) ).
fof(f776,plain,
( ~ between(u,v,w)
| u = v
| ~ spl0_14 ),
inference(resolution,[],[f611,f20]) ).
fof(f777,plain,
( u = v
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f776,f19]) ).
fof(f778,plain,
( $false
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f777,f22]) ).
fof(f779,plain,
~ spl0_14,
inference(avatar_contradiction_clause,[],[f778]) ).
cnf(s9,plain,
( spl0_13
| spl0_14 ),
inference(sat_conversion,[],[f361]) ).
cnf(s17,plain,
~ spl0_15,
inference(sat_conversion,[],[f446]) ).
cnf(s20,plain,
( ~ spl0_13
| spl0_15 ),
inference(sat_conversion,[],[f454]) ).
cnf(s40,plain,
~ spl0_14,
inference(sat_conversion,[],[f779]) ).
cnf(s44,plain,
~ spl0_13,
inference(rat,[],[s20,s17]) ).
cnf(s48,plain,
$false,
inference(rat,[],[s9,s40,s44]) ).
fof(f780,plain,
$false,
inference(avatar_sat_refutation,[],[s48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO026-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n026.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 06:38:56 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 3.32/1.22 % (2470352)Input is clausal, will run a generic CNF schedule.
% 3.32/1.22 % (2470362)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1858167552:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.32/1.22 % (2470360)lrs+10_1_sil=8000:sp=occurrence:random_seed=2428483727:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.32/1.22 % (2470358)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1391873016:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.32/1.22 % (2470359)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3841171549:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.32/1.22 % (2470357)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=3016976324:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.32/1.22 % (2470361)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1863265273:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.32/1.22 % (2470363)dis-21_1_sil=8000:lcm=predicate:random_seed=113124497: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)
% 3.32/1.22 % (2470360)First to succeed.
% 3.32/1.22 % (2470360)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2470352"
% 3.32/1.22 % (2470362)Instruction limit reached!
% 3.32/1.22 % (2470362)------------------------------
% 3.32/1.22 % (2470362)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.32/1.22 % (2470362)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.32/1.22 % (2470362)CaDiCaL version: 2.1.3
% 3.32/1.22 % (2470362)Termination reason: Instruction limit
% 3.32/1.22 % (2470362)Termination phase: Saturation
% 3.32/1.22 % (2470362)Time elapsed: 0.056 s
% 3.32/1.22 % (2470362)Peak memory usage: 89 MB
% 3.32/1.22 % (2470362)Instructions burned: 183 (million)
% 3.32/1.22 % (2470361)Instruction limit reached!
% 3.32/1.22 % (2470361)------------------------------
% 3.32/1.22 % (2470361)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.32/1.22 % (2470361)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.32/1.22 % (2470361)CaDiCaL version: 2.1.3
% 3.32/1.22 % (2470361)Termination reason: Instruction limit
% 3.32/1.22 % (2470361)Termination phase: Saturation
% 3.32/1.22 % (2470361)Time elapsed: 0.067 s
% 3.32/1.22 % (2470361)Peak memory usage: 88 MB
% 3.32/1.22 % (2470361)Instructions burned: 114 (million)
% 3.32/1.22 % (2470363)Instruction limit reached!
% 3.32/1.22 % (2470363)------------------------------
% 3.32/1.22 % (2470363)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.32/1.22 % (2470363)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.32/1.22 % (2470363)CaDiCaL version: 2.1.3
% 3.32/1.22 % (2470363)Termination reason: Instruction limit
% 3.32/1.22 % (2470363)Termination phase: Saturation
% 3.32/1.22 % (2470363)Time elapsed: 0.068 s
% 3.32/1.22 % (2470363)Peak memory usage: 88 MB
% 3.32/1.22 % (2470363)Instructions burned: 118 (million)
% 3.32/1.22 % (2470373)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2022591144:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 3.32/1.22 % (2470371)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=623328996:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.32/1.22 % (2470372)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1790779477:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 3.32/1.22 % (2470373)Instruction limit reached!
% 3.32/1.22 % (2470373)------------------------------
% 3.32/1.22 % (2470373)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.32/1.22 % (2470373)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.32/1.22 % (2470373)CaDiCaL version: 2.1.3
% 3.32/1.22 % (2470373)Termination reason: Instruction limit
% 3.32/1.22 % (2470373)Termination phase: Saturation
% 3.32/1.22 % (2470373)Time elapsed: 0.063 s
% 3.32/1.22 % (2470373)Peak memory usage: 89 MB
% 3.32/1.22 % (2470373)Instructions burned: 219 (million)
% 3.32/1.22 % (2470371)Instruction limit reached!
% 3.32/1.22 % (2470371)------------------------------
% 3.32/1.22 % (2470371)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.32/1.22 % (2470371)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.32/1.22 % (2470371)CaDiCaL version: 2.1.3
% 3.32/1.22 % (2470371)Termination reason: Instruction limit
% 3.32/1.22 % (2470371)Termination phase: Saturation
% 3.32/1.22 % (2470371)Time elapsed: 0.091 s
% 3.32/1.22 % (2470371)Peak memory usage: 89 MB
% 3.32/1.22 % (2470371)Instructions burned: 144 (million)
% 3.32/1.22 % (2470360)Refutation found. Thanks to Tanya!
% 3.32/1.22 % SZS status Unsatisfiable for theBenchmark
% 3.32/1.22 % SZS output start Proof for theBenchmark
% See solution above
% 3.32/1.22 % (2470360)------------------------------
% 3.32/1.22 % (2470360)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.32/1.22 % (2470360)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.32/1.22 % (2470360)CaDiCaL version: 2.1.3
% 3.32/1.22 % (2470360)Termination reason: Refutation
% 3.32/1.22 % (2470360)Time elapsed: 0.020 s
% 3.32/1.22 % (2470360)Peak memory usage: 89 MB
% 3.32/1.22 % (2470360)Instructions burned: 26 (million)
% 3.32/1.22 % (2470360)------------------------------
% 3.32/1.22 % (2470360)------------------------------
% 3.32/1.22 % (2470352)Success in time 0.41 s
% 3.32/1.22 % Vampire exiting
%------------------------------------------------------------------------------