%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : CAT033+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 09:37:03 AM UTC 2026
% Result : Theorem 0.06s 0.26s
% Output : Refutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 45 ( 14 unt; 1 def)
% Number of atoms : 125 ( 6 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 143 ( 63 ~; 55 |; 14 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 2 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 36 ( 1 sgn 32 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( v2_cat_1(X0)
& l1_cat_1(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_cat_1(X0))
=> m2_cat_1(k20_ens_1(X0,X1),X0,k1_yoneda_1(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_yoneda_1) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( v2_cat_1(X0)
& l1_cat_1(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_cat_1(X0))
=> m2_cat_1(k20_ens_1(X0,X1),X0,k1_yoneda_1(X0)) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f32,axiom,
! [X0,X1] : r1_tarski(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f46,axiom,
! [X0] :
( ( v2_cat_1(X0)
& l1_cat_1(X0) )
=> ~ v1_xboole_0(k17_ens_1(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_ens_1) ).
fof(f53,axiom,
! [X0] :
( ( v2_cat_1(X0)
& l1_cat_1(X0) )
=> k1_yoneda_1(X0) = k12_ens_1(k17_ens_1(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_yoneda_1) ).
fof(f54,axiom,
! [X0] :
( ~ v1_xboole_0(X0)
=> ! [X1] :
( ( v2_cat_1(X1)
& l1_cat_1(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_cat_1(X1))
=> ( r1_tarski(k17_ens_1(X1),X0)
=> m2_cat_1(k20_ens_1(X1,X2),X1,k12_ens_1(X0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_ens_1) ).
fof(f55,plain,
! [X0] : r1_tarski(X0,X0),
inference(rectify,[],[f32]) ).
fof(f58,plain,
? [X0] :
( ? [X1] :
( ~ m2_cat_1(k20_ens_1(X0,X1),X0,k1_yoneda_1(X0))
& m1_subset_1(X1,u1_cat_1(X0)) )
& v2_cat_1(X0)
& l1_cat_1(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f59,plain,
? [X0] :
( ? [X1] :
( ~ m2_cat_1(k20_ens_1(X0,X1),X0,k1_yoneda_1(X0))
& m1_subset_1(X1,u1_cat_1(X0)) )
& v2_cat_1(X0)
& l1_cat_1(X0) ),
inference(flattening,[],[f58]) ).
fof(f94,plain,
! [X0] :
( ~ v1_xboole_0(k17_ens_1(X0))
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f95,plain,
! [X0] :
( ~ v1_xboole_0(k17_ens_1(X0))
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0) ),
inference(flattening,[],[f94]) ).
fof(f100,plain,
! [X0] :
( k1_yoneda_1(X0) = k12_ens_1(k17_ens_1(X0))
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0) ),
inference(ennf_transformation,[],[f53]) ).
fof(f101,plain,
! [X0] :
( k1_yoneda_1(X0) = k12_ens_1(k17_ens_1(X0))
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0) ),
inference(flattening,[],[f100]) ).
fof(f102,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( m2_cat_1(k20_ens_1(X1,X2),X1,k12_ens_1(X0))
| ~ r1_tarski(k17_ens_1(X1),X0)
| ~ m1_subset_1(X2,u1_cat_1(X1)) )
| ~ v2_cat_1(X1)
| ~ l1_cat_1(X1) )
| v1_xboole_0(X0) ),
inference(ennf_transformation,[],[f54]) ).
fof(f103,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( m2_cat_1(k20_ens_1(X1,X2),X1,k12_ens_1(X0))
| ~ r1_tarski(k17_ens_1(X1),X0)
| ~ m1_subset_1(X2,u1_cat_1(X1)) )
| ~ v2_cat_1(X1)
| ~ l1_cat_1(X1) )
| v1_xboole_0(X0) ),
inference(flattening,[],[f102]) ).
fof(f104,plain,
( ~ m2_cat_1(k20_ens_1(sK0,sK1),sK0,k1_yoneda_1(sK0))
& m1_subset_1(sK1,u1_cat_1(sK0))
& v2_cat_1(sK0)
& l1_cat_1(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f59]) ).
fof(f117,plain,
l1_cat_1(sK0),
inference(cnf_transformation,[],[f104]) ).
fof(f118,plain,
v2_cat_1(sK0),
inference(cnf_transformation,[],[f104]) ).
fof(f119,plain,
m1_subset_1(sK1,u1_cat_1(sK0)),
inference(cnf_transformation,[],[f104]) ).
fof(f120,plain,
~ m2_cat_1(k20_ens_1(sK0,sK1),sK0,k1_yoneda_1(sK0)),
inference(cnf_transformation,[],[f104]) ).
fof(f164,plain,
! [X0] : r1_tarski(X0,X0),
inference(cnf_transformation,[],[f55]) ).
fof(f181,plain,
! [X0] :
( ~ v1_xboole_0(k17_ens_1(X0))
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f189,plain,
! [X0] :
( ~ l1_cat_1(X0)
| ~ v2_cat_1(X0)
| k1_yoneda_1(X0) = k12_ens_1(k17_ens_1(X0)) ),
inference(cnf_transformation,[],[f101]) ).
fof(f190,plain,
! [X2,X0,X1] :
( m2_cat_1(k20_ens_1(X1,X2),X1,k12_ens_1(X0))
| ~ r1_tarski(k17_ens_1(X1),X0)
| ~ m1_subset_1(X2,u1_cat_1(X1))
| ~ v2_cat_1(X1)
| ~ l1_cat_1(X1)
| v1_xboole_0(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f255,plain,
( ~ v2_cat_1(sK0)
| k1_yoneda_1(sK0) = k12_ens_1(k17_ens_1(sK0)) ),
inference(resolution,[],[f189,f117]) ).
fof(f266,plain,
k1_yoneda_1(sK0) = k12_ens_1(k17_ens_1(sK0)),
inference(forward_subsumption_resolution,[],[f255,f118]) ).
fof(f273,definition,
( spl12_5
<=> v1_xboole_0(k17_ens_1(sK0)) ),
introduced(definition,[new_symbols(definition,[spl12_5])],[avatar_definition]) ).
fof(f274,plain,
( ~ v1_xboole_0(k17_ens_1(sK0))
| spl12_5 ),
inference(avatar_component_clause,[],[f273]) ).
fof(f275,plain,
( v1_xboole_0(k17_ens_1(sK0))
| ~ spl12_5 ),
inference(avatar_component_clause,[],[f273]) ).
fof(f293,plain,
( ~ v2_cat_1(sK0)
| ~ l1_cat_1(sK0)
| ~ spl12_5 ),
inference(resolution,[],[f275,f181]) ).
fof(f297,plain,
( ~ l1_cat_1(sK0)
| ~ spl12_5 ),
inference(forward_subsumption_resolution,[],[f293,f118]) ).
fof(f298,plain,
( $false
| ~ spl12_5 ),
inference(forward_subsumption_resolution,[],[f297,f117]) ).
fof(f299,plain,
~ spl12_5,
inference(avatar_contradiction_clause,[],[f298]) ).
fof(f350,plain,
! [X0,X1] :
( m2_cat_1(k20_ens_1(X0,X1),X0,k1_yoneda_1(sK0))
| ~ r1_tarski(k17_ens_1(X0),k17_ens_1(sK0))
| ~ m1_subset_1(X1,u1_cat_1(X0))
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0)
| v1_xboole_0(k17_ens_1(sK0)) ),
inference(superposition,[],[f190,f266]) ).
fof(f354,plain,
( ! [X0,X1] :
( m2_cat_1(k20_ens_1(X0,X1),X0,k1_yoneda_1(sK0))
| ~ r1_tarski(k17_ens_1(X0),k17_ens_1(sK0))
| ~ m1_subset_1(X1,u1_cat_1(X0))
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0) )
| spl12_5 ),
inference(forward_subsumption_resolution,[],[f350,f274]) ).
fof(f686,plain,
( ~ r1_tarski(k17_ens_1(sK0),k17_ens_1(sK0))
| ~ m1_subset_1(sK1,u1_cat_1(sK0))
| ~ v2_cat_1(sK0)
| ~ l1_cat_1(sK0)
| spl12_5 ),
inference(resolution,[],[f354,f120]) ).
fof(f689,plain,
( ~ m1_subset_1(sK1,u1_cat_1(sK0))
| ~ v2_cat_1(sK0)
| ~ l1_cat_1(sK0)
| spl12_5 ),
inference(forward_subsumption_resolution,[],[f686,f164]) ).
fof(f690,plain,
( ~ v2_cat_1(sK0)
| ~ l1_cat_1(sK0)
| spl12_5 ),
inference(forward_subsumption_resolution,[],[f689,f119]) ).
fof(f691,plain,
( ~ l1_cat_1(sK0)
| spl12_5 ),
inference(forward_subsumption_resolution,[],[f690,f118]) ).
fof(f692,plain,
( $false
| spl12_5 ),
inference(forward_subsumption_resolution,[],[f691,f117]) ).
fof(f693,plain,
spl12_5,
inference(avatar_contradiction_clause,[],[f692]) ).
cnf(s7,plain,
~ spl12_5,
inference(sat_conversion,[],[f299]) ).
cnf(s49,plain,
spl12_5,
inference(sat_conversion,[],[f693]) ).
cnf(s60,plain,
$false,
inference(rat,[],[s7,s49]) ).
fof(f694,plain,
$false,
inference(avatar_sat_refutation,[],[s60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT033+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.06/0.17 % Computer : n004.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Mon Sep 28 21:20:37 UTC 2026
% 0.06/0.17 % CPUTime :
% 0.06/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.06/0.20 Running first-order model finding
% 0.06/0.20 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.26 % (792544)Will run a generic schedule for satisfiability detection.
% 0.06/0.26 % (792552)dis+10_1_sil=32000:sp=arity:random_seed=2140605286:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.06/0.26 % (792550)% WARNING: option uhcvi not known.
% 0.06/0.26 % (792549)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=240852831_2999 on theBenchmark for (2999ds/0Mi)
% 0.06/0.26 % (792550)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1269280862:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.06/0.26 % (792551)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2260085648:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.06/0.26 % (792553)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3985775292:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.06/0.26 % (792555)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3174069759:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.06/0.26 % (792554)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1458612582:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.06/0.26 % (792552) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-792544-792552"...
% 0.06/0.26 % (792552)...printing done.
% 0.06/0.26 % (792552)Refutation found. Thanks to Tanya!
% 0.06/0.26 % SZS status Theorem for theBenchmark
% 0.06/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.06/0.26 % (792552)------------------------------
% 0.06/0.26 % (792552)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.06/0.26 % (792552)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.06/0.26 % (792552)CaDiCaL version: 2.1.3
% 0.06/0.26 % (792552)Termination reason: Refutation
% 0.06/0.26 % (792552)Time elapsed: 0.009 s
% 0.06/0.26 % (792552)Peak memory usage: 13 MB
% 0.06/0.26 % (792552)Instructions burned: 22 (million)
% 0.06/0.26 % (792544)Success in time 0.041 s
% 0.06/0.26 % Vampire exiting
%------------------------------------------------------------------------------