%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : CAT033+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 09:36:47 AM UTC 2026
% Result : Theorem 3.63s 1.18s
% Output : Refutation 3.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 9 unt; 0 def)
% Number of atoms : 107 ( 4 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 137 ( 62 ~; 51 |; 14 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 38 ( 34 !; 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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',t49_ens_1) ).
fof(f55,plain,
! [X0] : r1_tarski(X0,X0),
inference(rectify,[],[f32]) ).
fof(f64,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(f65,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,[],[f64]) ).
fof(f67,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(f68,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,[],[f67]) ).
fof(f69,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(f70,plain,
! [X0] :
( k1_yoneda_1(X0) = k12_ens_1(k17_ens_1(X0))
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0) ),
inference(flattening,[],[f69]) ).
fof(f78,plain,
! [X0] :
( ~ v1_xboole_0(k17_ens_1(X0))
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f79,plain,
! [X0] :
( ~ v1_xboole_0(k17_ens_1(X0))
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0) ),
inference(flattening,[],[f78]) ).
fof(f91,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)],[f65]) ).
fof(f100,plain,
l1_cat_1(sK0),
inference(cnf_transformation,[],[f91]) ).
fof(f101,plain,
v2_cat_1(sK0),
inference(cnf_transformation,[],[f91]) ).
fof(f102,plain,
m1_subset_1(sK1,u1_cat_1(sK0)),
inference(cnf_transformation,[],[f91]) ).
fof(f103,plain,
~ m2_cat_1(k20_ens_1(sK0,sK1),sK0,k1_yoneda_1(sK0)),
inference(cnf_transformation,[],[f91]) ).
fof(f105,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,[],[f68]) ).
fof(f107,plain,
! [X0] :
( k1_yoneda_1(X0) = k12_ens_1(k17_ens_1(X0))
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f118,plain,
! [X0] : r1_tarski(X0,X0),
inference(cnf_transformation,[],[f55]) ).
fof(f119,plain,
! [X0] :
( ~ v1_xboole_0(k17_ens_1(X0))
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f167,plain,
! [X2,X0,X1] :
( m2_cat_1(k20_ens_1(X1,X2),X1,k1_yoneda_1(X0))
| ~ r1_tarski(k17_ens_1(X1),k17_ens_1(X0))
| ~ m1_subset_1(X2,u1_cat_1(X1))
| ~ v2_cat_1(X1)
| ~ l1_cat_1(X1)
| v1_xboole_0(k17_ens_1(X0))
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0) ),
inference(superposition,[],[f105,f107]) ).
fof(f168,plain,
! [X2,X0,X1] :
( m2_cat_1(k20_ens_1(X1,X2),X1,k1_yoneda_1(X0))
| ~ r1_tarski(k17_ens_1(X1),k17_ens_1(X0))
| ~ m1_subset_1(X2,u1_cat_1(X1))
| ~ v2_cat_1(X1)
| ~ l1_cat_1(X1)
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0) ),
inference(forward_subsumption_resolution,[],[f167,f119]) ).
fof(f186,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)
| ~ v2_cat_1(sK0)
| ~ l1_cat_1(sK0) ),
inference(resolution,[],[f168,f103]) ).
fof(f187,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) ),
inference(duplicate_literal_removal,[],[f186]) ).
fof(f188,plain,
( ~ m1_subset_1(sK1,u1_cat_1(sK0))
| ~ v2_cat_1(sK0)
| ~ l1_cat_1(sK0) ),
inference(forward_subsumption_resolution,[],[f187,f118]) ).
fof(f189,plain,
( ~ v2_cat_1(sK0)
| ~ l1_cat_1(sK0) ),
inference(forward_subsumption_resolution,[],[f188,f102]) ).
fof(f190,plain,
~ l1_cat_1(sK0),
inference(forward_subsumption_resolution,[],[f189,f101]) ).
fof(f191,plain,
$false,
inference(forward_subsumption_resolution,[],[f190,f100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT033+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.17 % Computer : n008.cluster.edu
% 0.11/0.17 % Model : x86_64 x86_64
% 0.11/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.17 % Memory : 8046.5625MB
% 0.11/0.17 % OS : Linux 6.8.0-71-generic
% 0.11/0.17 % CPULimit : 300
% 0.11/0.17 % WCLimit : 300
% 0.11/0.17 % DateTime : Mon Sep 28 21:21:24 UTC 2026
% 0.11/0.17 % CPUTime :
% 0.11/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.20 Running first-order theorem proving
% 0.11/0.20 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
% 3.63/1.18 % (2666762)Detected formulas, will run a generic FOF schedule.
% 3.63/1.18 % (2666767)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=4154458948:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.63/1.18 % (2666768)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=1158112889:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.63/1.18 % (2666769)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=4079389361:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.63/1.18 % (2666773)dis-21_1_sil=8000:lcm=predicate:random_seed=3980412249: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)
% 3.63/1.18 % (2666771)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2852811580:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.63/1.18 % (2666772)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1403144473:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.63/1.18 % (2666770)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1229929391:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.63/1.18 % (2666770)Refutation not found, incomplete strategy
% 3.63/1.18 % (2666770)------------------------------
% 3.63/1.18 % (2666770)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.18 % (2666770)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.18 % (2666770)CaDiCaL version: 2.1.3
% 3.63/1.18 % (2666770)Termination reason: Refutation not found, incomplete strategy
% 3.63/1.18 % (2666770)Time elapsed: 0.002 s
% 3.63/1.18 % (2666770)Peak memory usage: 88 MB
% 3.63/1.18 % (2666771)First to succeed.
% 3.63/1.18 % (2666771)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2666762"
% 3.63/1.18 % (2666772)Also succeeded, but the first one will report.
% 3.63/1.18 % (2666773)Instruction limit reached!
% 3.63/1.18 % (2666773)------------------------------
% 3.63/1.18 % (2666773)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.18 % (2666773)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.18 % (2666773)CaDiCaL version: 2.1.3
% 3.63/1.18 % (2666773)Termination reason: Instruction limit
% 3.63/1.18 % (2666773)Termination phase: Saturation
% 3.63/1.18 % (2666773)Time elapsed: 0.072 s
% 3.63/1.18 % (2666773)Peak memory usage: 90 MB
% 3.63/1.18 % (2666773)Instructions burned: 131 (million)
% 3.63/1.18 % (2666781)lrs+10_1_sil=8000:sp=occurrence:random_seed=3842964113:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.63/1.18 % (2666770)------------------------------
% 3.63/1.18 % (2666770)------------------------------
% 3.63/1.18 % (2666781)Also succeeded, but the first one will report.
% 3.63/1.18 % (2666771)Refutation found. Thanks to Tanya!
% 3.63/1.18 % SZS status Theorem for theBenchmark
% 3.63/1.18 % SZS output start Proof for theBenchmark
% See solution above
% 3.63/1.18 % (2666771)------------------------------
% 3.63/1.18 % (2666771)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.18 % (2666771)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.18 % (2666771)CaDiCaL version: 2.1.3
% 3.63/1.18 % (2666771)Termination reason: Refutation
% 3.63/1.18 % (2666771)Time elapsed: 0.005 s
% 3.63/1.18 % (2666771)Peak memory usage: 88 MB
% 3.63/1.18 % (2666771)Instructions burned: 5 (million)
% 3.63/1.18 % (2666771)------------------------------
% 3.63/1.18 % (2666771)------------------------------
% 3.63/1.18 % (2666762)Success in time 0.44 s
% 3.63/1.18 % Vampire exiting
%------------------------------------------------------------------------------