%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n011.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 12:48:49 PM UTC 2026
% Result : Theorem 0.38s 0.95s
% Output : Refutation 2.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 51 ( 15 unt; 2 def)
% Number of atoms : 182 ( 0 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 212 ( 81 ~; 72 |; 38 &)
% ( 4 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 3 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn 44 !; 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] :
( ~ 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(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] :
( ~ r2_hidden(k4_tarski(X2,X3),u1_orders_2(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)))
| r2_hidden(X2,u1_struct_0(X0))
| ~ r2_hidden(X3,u1_struct_0(X0))
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f159,plain,
( r2_hidden(k4_tarski(sK2,sK3),u1_orders_2(k1_latsum_1(sK0,sK1)))
| ~ 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(k1_latsum_1(sK0,sK1)) ),
inference(resolution,[],[f95,f88]) ).
fof(f160,plain,
( r2_hidden(k4_tarski(sK2,sK3),u1_orders_2(k1_latsum_1(sK0,sK1)))
| ~ m1_subset_1(sK2,u1_struct_0(k1_latsum_1(sK0,sK1)))
| ~ l1_orders_2(k1_latsum_1(sK0,sK1)) ),
inference(forward_subsumption_resolution,[],[f159,f86]) ).
fof(f161,plain,
( r2_hidden(k4_tarski(sK2,sK3),u1_orders_2(k1_latsum_1(sK0,sK1)))
| ~ l1_orders_2(k1_latsum_1(sK0,sK1)) ),
inference(forward_subsumption_resolution,[],[f160,f85]) ).
fof(f163,definition,
( spl10_1
<=> l1_orders_2(k1_latsum_1(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl10_1])],[avatar_definition]) ).
fof(f165,plain,
( ~ l1_orders_2(k1_latsum_1(sK0,sK1))
| spl10_1 ),
inference(avatar_component_clause,[],[f163]) ).
fof(f167,definition,
( spl10_2
<=> r2_hidden(k4_tarski(sK2,sK3),u1_orders_2(k1_latsum_1(sK0,sK1))) ),
introduced(definition,[new_symbols(definition,[spl10_2])],[avatar_definition]) ).
fof(f169,plain,
( r2_hidden(k4_tarski(sK2,sK3),u1_orders_2(k1_latsum_1(sK0,sK1)))
| ~ spl10_2 ),
inference(avatar_component_clause,[],[f167]) ).
fof(f170,plain,
( ~ spl10_1
| spl10_2 ),
inference(avatar_split_clause,[],[f161,f167,f163]) ).
fof(f171,plain,
( ~ l1_orders_2(sK0)
| ~ l1_orders_2(sK1)
| spl10_1 ),
inference(resolution,[],[f165,f99]) ).
fof(f172,plain,
( ~ l1_orders_2(sK1)
| spl10_1 ),
inference(forward_subsumption_resolution,[],[f171,f83]) ).
fof(f173,plain,
( $false
| spl10_1 ),
inference(forward_subsumption_resolution,[],[f172,f84]) ).
fof(f174,plain,
spl10_1,
inference(avatar_contradiction_clause,[],[f173]) ).
fof(f176,plain,
( ~ 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)))
| r2_hidden(sK2,u1_struct_0(sK0))
| ~ r2_hidden(sK3,u1_struct_0(sK0))
| ~ l1_orders_2(sK1)
| ~ l1_orders_2(sK0)
| ~ spl10_2 ),
inference(resolution,[],[f169,f117]) ).
fof(f182,plain,
( ~ m1_subset_1(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),k1_zfmisc_1(u1_struct_0(sK1)))
| r2_hidden(sK2,u1_struct_0(sK0))
| ~ r2_hidden(sK3,u1_struct_0(sK0))
| ~ l1_orders_2(sK1)
| ~ l1_orders_2(sK0)
| ~ spl10_2 ),
inference(forward_subsumption_resolution,[],[f176,f90]) ).
fof(f183,plain,
( r2_hidden(sK2,u1_struct_0(sK0))
| ~ r2_hidden(sK3,u1_struct_0(sK0))
| ~ l1_orders_2(sK1)
| ~ l1_orders_2(sK0)
| ~ spl10_2 ),
inference(forward_subsumption_resolution,[],[f182,f89]) ).
fof(f184,plain,
( ~ r2_hidden(sK3,u1_struct_0(sK0))
| ~ l1_orders_2(sK1)
| ~ l1_orders_2(sK0)
| ~ spl10_2 ),
inference(forward_subsumption_resolution,[],[f183,f91]) ).
fof(f185,plain,
( ~ l1_orders_2(sK1)
| ~ l1_orders_2(sK0)
| ~ spl10_2 ),
inference(forward_subsumption_resolution,[],[f184,f87]) ).
fof(f186,plain,
( ~ l1_orders_2(sK0)
| ~ spl10_2 ),
inference(forward_subsumption_resolution,[],[f185,f84]) ).
fof(f187,plain,
( $false
| ~ spl10_2 ),
inference(forward_subsumption_resolution,[],[f186,f83]) ).
fof(f188,plain,
~ spl10_2,
inference(avatar_contradiction_clause,[],[f187]) ).
cnf(s1,plain,
( ~ spl10_1
| spl10_2 ),
inference(sat_conversion,[],[f170]) ).
cnf(s2,plain,
spl10_1,
inference(sat_conversion,[],[f174]) ).
cnf(s3,plain,
~ spl10_2,
inference(sat_conversion,[],[f188]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f189,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU413+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n011.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 05:14:16 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 0.38/0.95 % (3038153)Detected formulas, will run a generic FOF schedule.
% 0.38/0.95 % (3038163)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3419063016:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.38/0.95 % (3038160)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=31885162:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.38/0.95 % (3038162)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1248751369:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.38/0.95 % (3038161)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3819303450:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.38/0.95 % (3038159)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=3801555946:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.38/0.95 % (3038158)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=1990978168:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.38/0.95 % (3038164)dis-21_1_sil=8000:lcm=predicate:random_seed=4286332733: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)
% 0.38/0.95 % (3038163)First to succeed.
% 0.38/0.95 % (3038163)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3038153"
% 0.38/0.95 % (3038161)Also succeeded, but the first one will report.
% 0.38/0.95 % (3038164)Also succeeded, but the first one will report.
% 0.38/0.95 % (3038162)Also succeeded, but the first one will report.
% 0.38/0.95 % (3038163)Refutation found. Thanks to Tanya!
% 0.38/0.95 % SZS status Theorem for theBenchmark
% 0.38/0.95 % SZS output start Proof for theBenchmark
% See solution above
% 2.65/1.05 % (3038163)------------------------------
% 2.65/1.05 % (3038163)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.05 % (3038163)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.05 % (3038163)CaDiCaL version: 2.1.3
% 2.65/1.05 % (3038163)Termination reason: Refutation
% 2.65/1.05 % (3038163)Time elapsed: 0.004 s
% 2.65/1.05 % (3038163)Peak memory usage: 90 MB
% 2.65/1.05 % (3038163)Instructions burned: 6 (million)
% 2.65/1.05 % (3038163)------------------------------
% 2.65/1.05 % (3038163)------------------------------
% 2.65/1.05 % (3038153)Success in time 0.328 s
% 2.65/1.05 % Vampire exiting
%------------------------------------------------------------------------------