%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO524+1 : TPTP v9.3.1. Released v7.0.0.
% 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 09:52:51 AM UTC 2026
% Result : Theorem 3.39s 1.34s
% Output : Refutation 3.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 12 unt; 4 def)
% Number of atoms : 69 ( 39 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 60 ( 27 ~; 27 |; 4 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-3 aty)
% Number of variables : 34 ( 0 sgn 30 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f186,axiom,
! [X0,X1,X2,X3] :
( X0 = X1
| reflect(X0,X1,X2) != X3
| reflect(X0,X1,X3) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_4) ).
fof(f188,axiom,
! [X0,X1,X2,X3] :
( X0 = X1
| reflect(X0,X1,X2) != X3
| X2 = reflect(X0,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_6) ).
fof(f189,conjecture,
! [X0,X1,X2,X3] :
( X0 = X1
| reflect(X0,X1,X2) != reflect(X0,X1,X3)
| X2 = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_7) ).
fof(f190,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( X0 = X1
| reflect(X0,X1,X2) != reflect(X0,X1,X3)
| X2 = X3 ),
inference(negated_conjecture,[status(cth)],[f189]) ).
fof(f206,plain,
? [X0,X1,X2,X3] :
( X0 != X1
& reflect(X0,X1,X2) = reflect(X0,X1,X3)
& X2 != X3 ),
inference(ennf_transformation,[],[f190]) ).
fof(f207,plain,
( sK0 != sK1
& reflect(sK0,sK1,sK2) = reflect(sK0,sK1,sK3)
& sK2 != sK3 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f206]) ).
fof(f208,plain,
sK2 != sK3,
inference(cnf_transformation,[],[f207]) ).
fof(f209,plain,
reflect(sK0,sK1,sK2) = reflect(sK0,sK1,sK3),
inference(cnf_transformation,[],[f207]) ).
fof(f210,plain,
sK0 != sK1,
inference(cnf_transformation,[],[f207]) ).
fof(f211,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| reflect(X0,X1,X2) != X3
| reflect(X0,X1,X3) = X2 ),
inference(cnf_transformation,[],[f188]) ).
fof(f213,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| reflect(X0,X1,X2) != X3
| reflect(X0,X1,X3) = X2 ),
inference(cnf_transformation,[],[f186]) ).
fof(f214,definition,
~ sP4(sK0),
introduced(definition,[new_symbols(definition,[sP4])],[inequality_splitting_name_introduction]) ).
fof(f215,plain,
sP4(sK1),
inference(inequality_splitting,[],[f210,f214]) ).
fof(f216,definition,
~ sP5(sK2),
introduced(definition,[new_symbols(definition,[sP5])],[inequality_splitting_name_introduction]) ).
fof(f217,plain,
sP5(sK3),
inference(inequality_splitting,[],[f208,f216]) ).
fof(f218,plain,
! [X2,X0,X1] :
( reflect(X0,X1,reflect(X0,X1,X2)) = X2
| X0 = X1 ),
inference(equality_resolution,[],[f211]) ).
fof(f219,plain,
! [X2,X0,X1] :
( reflect(X0,X1,reflect(X0,X1,X2)) = X2
| X0 = X1 ),
inference(equality_resolution,[],[f213]) ).
fof(f220,plain,
( sK3 = reflect(sK0,sK1,reflect(sK0,sK1,sK2))
| sK0 = sK1 ),
inference(superposition,[],[f219,f209]) ).
fof(f224,definition,
( spl6_1
<=> sK0 = sK1 ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
fof(f226,plain,
( sK0 = sK1
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f224]) ).
fof(f228,definition,
( spl6_2
<=> sK3 = reflect(sK0,sK1,reflect(sK0,sK1,sK2)) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
fof(f230,plain,
( sK3 = reflect(sK0,sK1,reflect(sK0,sK1,sK2))
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f228]) ).
fof(f233,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f220,f228,f224]) ).
fof(f235,plain,
( sP5(reflect(sK0,sK1,reflect(sK0,sK1,sK2)))
| ~ spl6_2 ),
inference(superposition,[],[f217,f230]) ).
fof(f238,plain,
( sP5(sK2)
| sK0 = sK1
| ~ spl6_2 ),
inference(superposition,[],[f235,f218]) ).
fof(f239,plain,
( sK0 = sK1
| ~ spl6_2 ),
inference(forward_subsumption_resolution,[],[f238,f216]) ).
fof(f242,plain,
( spl6_1
| ~ spl6_2 ),
inference(avatar_split_clause,[],[f239,f228,f224]) ).
fof(f245,plain,
( sP4(sK0)
| ~ spl6_1 ),
inference(superposition,[],[f215,f226]) ).
fof(f246,plain,
( $false
| ~ spl6_1 ),
inference(forward_subsumption_resolution,[],[f245,f214]) ).
fof(f247,plain,
~ spl6_1,
inference(avatar_contradiction_clause,[],[f246]) ).
cnf(s3,plain,
( spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f233]) ).
cnf(s4,plain,
( spl6_1
| ~ spl6_2 ),
inference(sat_conversion,[],[f242]) ).
cnf(s7,plain,
~ spl6_1,
inference(sat_conversion,[],[f247]) ).
cnf(s8,plain,
~ spl6_2,
inference(rat,[],[s4,s7]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s3,s8,s7]) ).
fof(f250,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO524+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n018.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 08:28:08 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 3.39/1.34 % (2026122)Detected formulas, will run a generic FOF schedule.
% 3.39/1.34 % (2026137)dis-21_1_sil=8000:lcm=predicate:random_seed=1640150281:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.39/1.34 % (2026131)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=2562156603:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.39/1.34 % (2026133)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3520485218:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.39/1.34 % (2026132)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2271398127:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.39/1.34 % (2026134)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3377562561:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.39/1.34 % (2026137)Instruction limit reached!
% 3.39/1.34 % (2026137)------------------------------
% 3.39/1.34 % (2026137)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.39/1.34 % (2026137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/1.34 % (2026137)CaDiCaL version: 2.1.3
% 3.39/1.34 % (2026137)Termination reason: Instruction limit
% 3.39/1.34 % (2026137)Termination phase: Saturation
% 3.39/1.34 % (2026137)Time elapsed: 0.040 s
% 3.39/1.34 % (2026137)Peak memory usage: 89 MB
% 3.39/1.34 % (2026137)Instructions burned: 131 (million)
% 3.39/1.34 % (2026134)First to succeed.
% 3.39/1.34 % (2026134)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2026122"
% 3.39/1.34 % (2026136)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1123422654:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.39/1.34 % (2026135)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=134121804:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.39/1.34 % (2026135)Also succeeded, but the first one will report.
% 3.39/1.34 % (2026136)Also succeeded, but the first one will report.
% 3.39/1.34 % (2026143)lrs+10_1_sil=8000:sp=occurrence:random_seed=110126939:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.39/1.34 % (2026143)Also succeeded, but the first one will report.
% 3.39/1.34 % (2026134)Refutation found. Thanks to Tanya!
% 3.39/1.34 % SZS status Theorem for theBenchmark
% 3.39/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 3.39/1.34 % (2026134)------------------------------
% 3.39/1.34 % (2026134)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.39/1.34 % (2026134)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/1.34 % (2026134)CaDiCaL version: 2.1.3
% 3.39/1.34 % (2026134)Termination reason: Refutation
% 3.39/1.34 % (2026134)Time elapsed: 0.003 s
% 3.39/1.34 % (2026134)Peak memory usage: 90 MB
% 3.39/1.34 % (2026134)Instructions burned: 2 (million)
% 3.39/1.34 % (2026134)------------------------------
% 3.39/1.34 % (2026134)------------------------------
% 3.39/1.34 % (2026122)Success in time 0.41 s
% 3.39/1.34 % Vampire exiting
%------------------------------------------------------------------------------