%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU413+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n003.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 12:53:11 PM UTC 2026
% Result : Theorem 0.21s 0.55s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 49 ( 15 unt; 1 def)
% Number of atoms : 184 ( 0 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 220 ( 85 ~; 77 |; 38 &)
% ( 3 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 2 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn 56 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( l1_orders_2(X0)
=> ! [X1] :
( l1_orders_2(X1)
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(k1_latsum_1(X0,X1)))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(k1_latsum_1(X0,X1)))
=> ( ( v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1)
& m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
& r1_orders_2(k1_latsum_1(X0,X1),X2,X3)
& r2_hidden(X3,u1_struct_0(X0)) )
=> r2_hidden(X2,u1_struct_0(X0)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_latsum_1) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( l1_orders_2(X0)
=> ! [X1] :
( l1_orders_2(X1)
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(k1_latsum_1(X0,X1)))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(k1_latsum_1(X0,X1)))
=> ( ( v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1)
& m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
& r1_orders_2(k1_latsum_1(X0,X1),X2,X3)
& r2_hidden(X3,u1_struct_0(X0)) )
=> r2_hidden(X2,u1_struct_0(X0)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f7,axiom,
! [X0] :
( l1_orders_2(X0)
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
=> ( r1_orders_2(X0,X1,X2)
<=> r2_hidden(k4_tarski(X1,X2),u1_orders_2(X0)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_orders_2) ).
fof(f9,axiom,
! [X0,X1] :
( ( l1_orders_2(X0)
& l1_orders_2(X1) )
=> ( v1_orders_2(k1_latsum_1(X0,X1))
& l1_orders_2(k1_latsum_1(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_latsum_1) ).
fof(f35,axiom,
! [X0] :
( l1_orders_2(X0)
=> ! [X1] :
( l1_orders_2(X1)
=> ! [X2,X3] :
( ( v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1)
& m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
& r2_hidden(k4_tarski(X2,X3),u1_orders_2(k1_latsum_1(X0,X1)))
& r2_hidden(X3,u1_struct_0(X0)) )
=> r2_hidden(X2,u1_struct_0(X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_latsum_1) ).
fof(f50,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ r2_hidden(X2,u1_struct_0(X0))
& v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1)
& m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
& r1_orders_2(k1_latsum_1(X0,X1),X2,X3)
& r2_hidden(X3,u1_struct_0(X0))
& m1_subset_1(X3,u1_struct_0(k1_latsum_1(X0,X1))) )
& m1_subset_1(X2,u1_struct_0(k1_latsum_1(X0,X1))) )
& l1_orders_2(X1) )
& l1_orders_2(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f51,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ r2_hidden(X2,u1_struct_0(X0))
& v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1)
& m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
& r1_orders_2(k1_latsum_1(X0,X1),X2,X3)
& r2_hidden(X3,u1_struct_0(X0))
& m1_subset_1(X3,u1_struct_0(k1_latsum_1(X0,X1))) )
& m1_subset_1(X2,u1_struct_0(k1_latsum_1(X0,X1))) )
& l1_orders_2(X1) )
& l1_orders_2(X0) ),
inference(flattening,[],[f50]) ).
fof(f55,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( r1_orders_2(X0,X1,X2)
<=> r2_hidden(k4_tarski(X1,X2),u1_orders_2(X0)) )
| ~ m1_subset_1(X2,u1_struct_0(X0)) )
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| ~ l1_orders_2(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f57,plain,
! [X0,X1] :
( ( v1_orders_2(k1_latsum_1(X0,X1))
& l1_orders_2(k1_latsum_1(X0,X1)) )
| ~ l1_orders_2(X0)
| ~ l1_orders_2(X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f58,plain,
! [X0,X1] :
( ( v1_orders_2(k1_latsum_1(X0,X1))
& l1_orders_2(k1_latsum_1(X0,X1)) )
| ~ l1_orders_2(X0)
| ~ l1_orders_2(X1) ),
inference(flattening,[],[f57]) ).
fof(f63,plain,
! [X0] :
( ! [X1] :
( ! [X2,X3] :
( r2_hidden(X2,u1_struct_0(X0))
| ~ v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1)
| ~ m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
| ~ r2_hidden(k4_tarski(X2,X3),u1_orders_2(k1_latsum_1(X0,X1)))
| ~ r2_hidden(X3,u1_struct_0(X0)) )
| ~ l1_orders_2(X1) )
| ~ l1_orders_2(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f64,plain,
! [X0] :
( ! [X1] :
( ! [X2,X3] :
( r2_hidden(X2,u1_struct_0(X0))
| ~ v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1)
| ~ m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
| ~ r2_hidden(k4_tarski(X2,X3),u1_orders_2(k1_latsum_1(X0,X1)))
| ~ r2_hidden(X3,u1_struct_0(X0)) )
| ~ l1_orders_2(X1) )
| ~ l1_orders_2(X0) ),
inference(flattening,[],[f63]) ).
fof(f74,plain,
( ~ r2_hidden(sK2,u1_struct_0(sK0))
& v12_waybel_0(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),sK1)
& m1_subset_1(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),k1_zfmisc_1(u1_struct_0(sK1)))
& r1_orders_2(k1_latsum_1(sK0,sK1),sK2,sK3)
& r2_hidden(sK3,u1_struct_0(sK0))
& m1_subset_1(sK3,u1_struct_0(k1_latsum_1(sK0,sK1)))
& m1_subset_1(sK2,u1_struct_0(k1_latsum_1(sK0,sK1)))
& l1_orders_2(sK1)
& l1_orders_2(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f51]) ).
fof(f75,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( r1_orders_2(X0,X1,X2)
| ~ r2_hidden(k4_tarski(X1,X2),u1_orders_2(X0)) )
& ( r2_hidden(k4_tarski(X1,X2),u1_orders_2(X0))
| ~ r1_orders_2(X0,X1,X2) ) )
| ~ m1_subset_1(X2,u1_struct_0(X0)) )
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| ~ l1_orders_2(X0) ),
inference(nnf_transformation,[],[f55]) ).
fof(f83,plain,
l1_orders_2(sK0),
inference(cnf_transformation,[],[f74]) ).
fof(f84,plain,
l1_orders_2(sK1),
inference(cnf_transformation,[],[f74]) ).
fof(f85,plain,
m1_subset_1(sK2,u1_struct_0(k1_latsum_1(sK0,sK1))),
inference(cnf_transformation,[],[f74]) ).
fof(f86,plain,
m1_subset_1(sK3,u1_struct_0(k1_latsum_1(sK0,sK1))),
inference(cnf_transformation,[],[f74]) ).
fof(f87,plain,
r2_hidden(sK3,u1_struct_0(sK0)),
inference(cnf_transformation,[],[f74]) ).
fof(f88,plain,
r1_orders_2(k1_latsum_1(sK0,sK1),sK2,sK3),
inference(cnf_transformation,[],[f74]) ).
fof(f89,plain,
m1_subset_1(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),k1_zfmisc_1(u1_struct_0(sK1))),
inference(cnf_transformation,[],[f74]) ).
fof(f90,plain,
v12_waybel_0(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),sK1),
inference(cnf_transformation,[],[f74]) ).
fof(f91,plain,
~ r2_hidden(sK2,u1_struct_0(sK0)),
inference(cnf_transformation,[],[f74]) ).
fof(f95,plain,
! [X2,X0,X1] :
( r2_hidden(k4_tarski(X1,X2),u1_orders_2(X0))
| ~ r1_orders_2(X0,X1,X2)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_orders_2(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f99,plain,
! [X0,X1] :
( l1_orders_2(k1_latsum_1(X0,X1))
| ~ l1_orders_2(X0)
| ~ l1_orders_2(X1) ),
inference(cnf_transformation,[],[f58]) ).
fof(f117,plain,
! [X2,X3,X0,X1] :
( ~ m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
| ~ v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1)
| r2_hidden(X2,u1_struct_0(X0))
| ~ r2_hidden(k4_tarski(X2,X3),u1_orders_2(k1_latsum_1(X0,X1)))
| ~ r2_hidden(X3,u1_struct_0(X0))
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f187,definition,
( spl10_6
<=> l1_orders_2(k1_latsum_1(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl10_6])],[avatar_definition]) ).
fof(f188,plain,
( l1_orders_2(k1_latsum_1(sK0,sK1))
| ~ spl10_6 ),
inference(avatar_component_clause,[],[f187]) ).
fof(f189,plain,
( ~ l1_orders_2(k1_latsum_1(sK0,sK1))
| spl10_6 ),
inference(avatar_component_clause,[],[f187]) ).
fof(f218,plain,
( ~ l1_orders_2(sK0)
| ~ l1_orders_2(sK1)
| spl10_6 ),
inference(resolution,[],[f189,f99]) ).
fof(f219,plain,
( ~ l1_orders_2(sK1)
| spl10_6 ),
inference(forward_subsumption_resolution,[],[f218,f83]) ).
fof(f220,plain,
( $false
| spl10_6 ),
inference(forward_subsumption_resolution,[],[f219,f84]) ).
fof(f221,plain,
spl10_6,
inference(avatar_contradiction_clause,[],[f220]) ).
fof(f235,plain,
! [X0,X1] :
( ~ v12_waybel_0(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),sK1)
| r2_hidden(X0,u1_struct_0(sK0))
| ~ r2_hidden(k4_tarski(X0,X1),u1_orders_2(k1_latsum_1(sK0,sK1)))
| ~ r2_hidden(X1,u1_struct_0(sK0))
| ~ l1_orders_2(sK1)
| ~ l1_orders_2(sK0) ),
inference(resolution,[],[f117,f89]) ).
fof(f241,plain,
! [X0,X1] :
( r2_hidden(X0,u1_struct_0(sK0))
| ~ r2_hidden(k4_tarski(X0,X1),u1_orders_2(k1_latsum_1(sK0,sK1)))
| ~ r2_hidden(X1,u1_struct_0(sK0))
| ~ l1_orders_2(sK1)
| ~ l1_orders_2(sK0) ),
inference(forward_subsumption_resolution,[],[f235,f90]) ).
fof(f242,plain,
! [X0,X1] :
( r2_hidden(X0,u1_struct_0(sK0))
| ~ r2_hidden(k4_tarski(X0,X1),u1_orders_2(k1_latsum_1(sK0,sK1)))
| ~ r2_hidden(X1,u1_struct_0(sK0))
| ~ l1_orders_2(sK0) ),
inference(forward_subsumption_resolution,[],[f241,f84]) ).
fof(f243,plain,
! [X0,X1] :
( ~ r2_hidden(k4_tarski(X0,X1),u1_orders_2(k1_latsum_1(sK0,sK1)))
| r2_hidden(X0,u1_struct_0(sK0))
| ~ r2_hidden(X1,u1_struct_0(sK0)) ),
inference(forward_subsumption_resolution,[],[f242,f83]) ).
fof(f248,plain,
! [X0,X1] :
( r2_hidden(X0,u1_struct_0(sK0))
| ~ r2_hidden(X1,u1_struct_0(sK0))
| ~ r1_orders_2(k1_latsum_1(sK0,sK1),X0,X1)
| ~ m1_subset_1(X1,u1_struct_0(k1_latsum_1(sK0,sK1)))
| ~ m1_subset_1(X0,u1_struct_0(k1_latsum_1(sK0,sK1)))
| ~ l1_orders_2(k1_latsum_1(sK0,sK1)) ),
inference(resolution,[],[f243,f95]) ).
fof(f249,plain,
( ! [X0,X1] :
( ~ r1_orders_2(k1_latsum_1(sK0,sK1),X0,X1)
| ~ r2_hidden(X1,u1_struct_0(sK0))
| r2_hidden(X0,u1_struct_0(sK0))
| ~ m1_subset_1(X1,u1_struct_0(k1_latsum_1(sK0,sK1)))
| ~ m1_subset_1(X0,u1_struct_0(k1_latsum_1(sK0,sK1))) )
| ~ spl10_6 ),
inference(forward_subsumption_resolution,[],[f248,f188]) ).
fof(f251,plain,
( ~ r2_hidden(sK3,u1_struct_0(sK0))
| r2_hidden(sK2,u1_struct_0(sK0))
| ~ m1_subset_1(sK3,u1_struct_0(k1_latsum_1(sK0,sK1)))
| ~ m1_subset_1(sK2,u1_struct_0(k1_latsum_1(sK0,sK1)))
| ~ spl10_6 ),
inference(resolution,[],[f249,f88]) ).
fof(f252,plain,
( r2_hidden(sK2,u1_struct_0(sK0))
| ~ m1_subset_1(sK3,u1_struct_0(k1_latsum_1(sK0,sK1)))
| ~ m1_subset_1(sK2,u1_struct_0(k1_latsum_1(sK0,sK1)))
| ~ spl10_6 ),
inference(forward_subsumption_resolution,[],[f251,f87]) ).
fof(f253,plain,
( ~ m1_subset_1(sK3,u1_struct_0(k1_latsum_1(sK0,sK1)))
| ~ m1_subset_1(sK2,u1_struct_0(k1_latsum_1(sK0,sK1)))
| ~ spl10_6 ),
inference(forward_subsumption_resolution,[],[f252,f91]) ).
fof(f254,plain,
( ~ m1_subset_1(sK2,u1_struct_0(k1_latsum_1(sK0,sK1)))
| ~ spl10_6 ),
inference(forward_subsumption_resolution,[],[f253,f86]) ).
fof(f255,plain,
( $false
| ~ spl10_6 ),
inference(forward_subsumption_resolution,[],[f254,f85]) ).
fof(f256,plain,
~ spl10_6,
inference(avatar_contradiction_clause,[],[f255]) ).
cnf(s6,plain,
spl10_6,
inference(sat_conversion,[],[f221]) ).
cnf(s8,plain,
~ spl10_6,
inference(sat_conversion,[],[f256]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s6,s8]) ).
fof(f257,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU413+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.17/0.43 % Computer : n003.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 28 05:15:41 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.21/0.49 Running first-order model finding
% 0.21/0.49 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.55 % (1228928)Will run a generic schedule for satisfiability detection.
% 0.21/0.55 % (1228938)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3919502038:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.55 % (1228934)% WARNING: option uhcvi not known.
% 0.21/0.55 % (1228934)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=901759597:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.55 % (1228933)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=287472951_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.55 % (1228936)dis+10_1_sil=32000:sp=arity:random_seed=993669710:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.55 % (1228935)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1669076739:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.55 % (1228937)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=628880399:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.55 % (1228939)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2522229405:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.21/0.55 % TRYING [1]
% 0.21/0.55 % TRYING [2]
% 0.21/0.55 % TRYING [3]
% 0.21/0.55 % (1228937) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1228928-1228937"...
% 0.21/0.55 % (1228936) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1228928-1228936"...
% 0.21/0.55 % (1228937)...printing done.
% 0.21/0.55 % (1228936)...printing done.
% 0.21/0.55 % (1228936)Refutation found. Thanks to Tanya!
% 0.21/0.55 % SZS status Theorem for theBenchmark
% 0.21/0.55 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.55 % (1228936)------------------------------
% 0.21/0.55 % (1228936)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.55 % (1228936)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.55 % (1228936)CaDiCaL version: 2.1.3
% 0.21/0.55 % (1228936)Termination reason: Refutation
% 0.21/0.55 % (1228936)Time elapsed: 0.010 s
% 0.21/0.55 % (1228936)Peak memory usage: 12 MB
% 0.21/0.55 % (1228936)Instructions burned: 8 (million)
% 0.21/0.55 % (1228928)Success in time 0.049 s
% 0.21/0.55 % Vampire exiting
%------------------------------------------------------------------------------