%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO059-2 : 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 : n005.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 09:51:23 AM UTC 2026
% Result : Unsatisfiable 3.01s 1.09s
% Output : Refutation 3.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 29 ( 11 unt; 2 def)
% Number of atoms : 58 ( 1 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 73 ( 44 ~; 27 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-4 aty)
% Number of variables : 46 ( 0 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : equidistant(X0,X1,X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_for_equidistance) ).
fof(f2,axiom,
! [X2,X3,X0,X1,X4,X5] :
( equidistant(X2,X3,X4,X5)
| ~ equidistant(X0,X1,X4,X5)
| ~ equidistant(X0,X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_for_equidistance) ).
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(f19,axiom,
! [X0,X1] : reflection(X0,X1) = extension(X0,X1,X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflection) ).
fof(f20,negated_conjecture,
~ equidistant(v,u,v,reflection(reflection(u,v),v)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_congruence) ).
fof(f21,plain,
~ equidistant(v,u,v,extension(extension(u,v,u,v),v,extension(u,v,u,v),v)),
inference(definition_unfolding,[],[f20,f19,f19]) ).
fof(f32,plain,
! [X0,X1] :
( ~ equidistant(X0,X1,v,extension(extension(u,v,u,v),v,extension(u,v,u,v),v))
| ~ equidistant(X0,X1,v,u) ),
inference(resolution,[],[f2,f21]) ).
fof(f34,plain,
! [X2,X3,X0,X1] :
( ~ equidistant(X0,X1,v,u)
| ~ equidistant(X2,X3,v,extension(extension(u,v,u,v),v,extension(u,v,u,v),v))
| ~ equidistant(X2,X3,X0,X1) ),
inference(resolution,[],[f32,f2]) ).
fof(f50,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ equidistant(X2,X3,v,u)
| ~ equidistant(X0,X1,X2,X3)
| ~ equidistant(X4,X5,v,extension(extension(u,v,u,v),v,extension(u,v,u,v),v))
| ~ equidistant(X4,X5,X0,X1) ),
inference(resolution,[],[f34,f2]) ).
fof(f113,plain,
! [X2,X3,X0,X1] :
( ~ equidistant(X2,X3,v,u)
| ~ equidistant(v,extension(extension(u,v,u,v),v,extension(u,v,u,v),v),X2,X3)
| ~ equidistant(X0,X1,v,extension(extension(u,v,u,v),v,extension(u,v,u,v),v)) ),
inference(factoring,[],[f50]) ).
fof(f115,definition,
( spl1_1
<=> ! [X0,X1] : ~ equidistant(X0,X1,v,extension(extension(u,v,u,v),v,extension(u,v,u,v),v)) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f116,plain,
( ! [X0,X1] : ~ equidistant(X0,X1,v,extension(extension(u,v,u,v),v,extension(u,v,u,v),v))
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f118,definition,
( spl1_2
<=> ! [X2,X3] :
( ~ equidistant(X2,X3,v,u)
| ~ equidistant(v,extension(extension(u,v,u,v),v,extension(u,v,u,v),v),X2,X3) ) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f119,plain,
( ! [X2,X3] :
( ~ equidistant(v,extension(extension(u,v,u,v),v,extension(u,v,u,v),v),X2,X3)
| ~ equidistant(X2,X3,v,u) )
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f120,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f113,f118,f115]) ).
fof(f121,plain,
( ~ equidistant(extension(u,v,u,v),v,v,u)
| ~ spl1_2 ),
inference(resolution,[],[f119,f5]) ).
fof(f125,plain,
( ! [X0,X1] :
( ~ equidistant(X0,X1,extension(u,v,u,v),v)
| ~ equidistant(X0,X1,v,u) )
| ~ spl1_2 ),
inference(resolution,[],[f121,f2]) ).
fof(f127,plain,
( ! [X2,X3,X0,X1] :
( ~ equidistant(X0,X1,v,u)
| ~ equidistant(X2,X3,extension(u,v,u,v),v)
| ~ equidistant(X2,X3,X0,X1) )
| ~ spl1_2 ),
inference(resolution,[],[f125,f2]) ).
fof(f139,plain,
( ! [X0,X1] :
( ~ equidistant(v,extension(u,v,u,v),X0,X1)
| ~ equidistant(X0,X1,v,u) )
| ~ spl1_2 ),
inference(resolution,[],[f127,f1]) ).
fof(f156,plain,
( ~ equidistant(u,v,v,u)
| ~ spl1_2 ),
inference(resolution,[],[f139,f5]) ).
fof(f172,plain,
( $false
| ~ spl1_2 ),
inference(resolution,[],[f156,f1]) ).
fof(f174,plain,
~ spl1_2,
inference(avatar_contradiction_clause,[],[f172]) ).
fof(f175,plain,
( $false
| ~ spl1_1 ),
inference(resolution,[],[f116,f1]) ).
fof(f179,plain,
~ spl1_1,
inference(avatar_contradiction_clause,[],[f175]) ).
cnf(s1,plain,
( spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f120]) ).
cnf(s2,plain,
~ spl1_2,
inference(sat_conversion,[],[f174]) ).
cnf(s4,plain,
~ spl1_1,
inference(sat_conversion,[],[f179]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s2,s4]) ).
fof(f180,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO059-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n005.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 06:46:21 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 3.01/1.09 % (3635091)Input is clausal, will run a generic CNF schedule.
% 3.01/1.09 % (3635101)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=735846651:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.01/1.09 % (3635102)dis-21_1_sil=8000:lcm=predicate:random_seed=2973992787: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)
% 3.01/1.09 % (3635099)lrs+10_1_sil=8000:sp=occurrence:random_seed=3219686786:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.01/1.09 % (3635097)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2234868576:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.01/1.09 % (3635098)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=959599528:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.01/1.09 % (3635100)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2716733769:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.01/1.09 % (3635096)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=1891962485:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.01/1.09 % (3635102)First to succeed.
% 3.01/1.09 % (3635102)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3635091"
% 3.01/1.09 % (3635101)Also succeeded, but the first one will report.
% 3.01/1.09 % (3635099)Also succeeded, but the first one will report.
% 3.01/1.09 % (3635100)Instruction limit reached!
% 3.01/1.09 % (3635100)------------------------------
% 3.01/1.09 % (3635100)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.01/1.09 % (3635100)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.01/1.09 % (3635100)CaDiCaL version: 2.1.3
% 3.01/1.09 % (3635100)Termination reason: Instruction limit
% 3.01/1.09 % (3635100)Termination phase: Saturation
% 3.01/1.09 % (3635100)Time elapsed: 0.068 s
% 3.01/1.09 % (3635100)Peak memory usage: 89 MB
% 3.01/1.09 % (3635100)Instructions burned: 114 (million)
% 3.01/1.09 % (3635110)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=3631380072:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.01/1.09 % (3635110)Refutation not found, incomplete strategy
% 3.01/1.09 % (3635110)------------------------------
% 3.01/1.09 % (3635110)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.01/1.09 % (3635110)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.01/1.09 % (3635110)CaDiCaL version: 2.1.3
% 3.01/1.09 % (3635110)Termination reason: Refutation not found, incomplete strategy
% 3.01/1.09 % (3635110)Time elapsed: 0.001 s
% 3.01/1.09 % (3635110)Peak memory usage: 88 MB
% 3.01/1.09 % (3635110)Instructions burned: 1 (million)
% 3.01/1.09 % (3635102)Refutation found. Thanks to Tanya!
% 3.01/1.09 % SZS status Unsatisfiable for theBenchmark
% 3.01/1.09 % SZS output start Proof for theBenchmark
% See solution above
% 3.01/1.09 % (3635102)------------------------------
% 3.01/1.09 % (3635102)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.01/1.09 % (3635102)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.01/1.09 % (3635102)CaDiCaL version: 2.1.3
% 3.01/1.09 % (3635102)Termination reason: Refutation
% 3.01/1.09 % (3635102)Time elapsed: 0.007 s
% 3.01/1.09 % (3635102)Peak memory usage: 89 MB
% 3.01/1.09 % (3635102)Instructions burned: 9 (million)
% 3.01/1.09 % (3635102)------------------------------
% 3.01/1.09 % (3635102)------------------------------
% 3.01/1.09 % (3635091)Success in time 0.391 s
% 3.01/1.09 % Vampire exiting
%------------------------------------------------------------------------------