%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU225+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n016.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 12:52:29 PM UTC 2026
% Result : Theorem 0.18s 0.48s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 8
% Syntax : Number of formulae : 71 ( 15 unt; 2 def)
% Number of atoms : 241 ( 53 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 262 ( 92 ~; 118 |; 25 &)
% ( 14 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 100 ( 0 sgn 94 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1,X2] :
( ( in(X1,relation_dom(X0))
=> ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) ) )
& ( ~ in(X1,relation_dom(X0))
=> ( X2 = apply(X0,X1)
<=> X2 = empty_set ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).
fof(f9,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_dom_restriction(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(f19,axiom,
! [X0,X1] :
( ( relation(X0)
& function(X0) )
=> ( relation(relation_dom_restriction(X0,X1))
& function(relation_dom_restriction(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_funct_1) ).
fof(f24,axiom,
! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
<=> ( in(X1,relation_dom(X2))
& in(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l82_funct_1) ).
fof(f42,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( X1 = relation_dom_restriction(X2,X0)
<=> ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X3] :
( in(X3,relation_dom(X1))
=> apply(X1,X3) = apply(X2,X3) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_funct_1) ).
fof(f44,conjecture,
! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X1,X0)
=> apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_funct_1) ).
fof(f45,negated_conjecture,
~ ! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X1,X0)
=> apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f58,plain,
! [X0] :
( ! [X1,X2] :
( ( ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) )
| ~ in(X1,relation_dom(X0)) )
& ( ( X2 = apply(X0,X1)
<=> X2 = empty_set )
| in(X1,relation_dom(X0)) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f59,plain,
! [X0] :
( ! [X1,X2] :
( ( ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) )
| ~ in(X1,relation_dom(X0)) )
& ( ( X2 = apply(X0,X1)
<=> X2 = empty_set )
| in(X1,relation_dom(X0)) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f58]) ).
fof(f60,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f65,plain,
! [X0,X1] :
( ( relation(relation_dom_restriction(X0,X1))
& function(relation_dom_restriction(X0,X1)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f66,plain,
! [X0,X1] :
( ( relation(relation_dom_restriction(X0,X1))
& function(relation_dom_restriction(X0,X1)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f65]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
<=> ( in(X1,relation_dom(X2))
& in(X1,X0) ) )
| ~ relation(X2)
| ~ function(X2) ),
inference(ennf_transformation,[],[f24]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
<=> ( in(X1,relation_dom(X2))
& in(X1,X0) ) )
| ~ relation(X2)
| ~ function(X2) ),
inference(flattening,[],[f70]) ).
fof(f80,plain,
! [X0,X1] :
( ! [X2] :
( ( X1 = relation_dom_restriction(X2,X0)
<=> ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) ) ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f42]) ).
fof(f81,plain,
! [X0,X1] :
( ! [X2] :
( ( X1 = relation_dom_restriction(X2,X0)
<=> ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) ) ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f80]) ).
fof(f83,plain,
? [X0,X1,X2] :
( apply(relation_dom_restriction(X2,X0),X1) != apply(X2,X1)
& in(X1,X0)
& relation(X2)
& function(X2) ),
inference(ennf_transformation,[],[f45]) ).
fof(f84,plain,
? [X0,X1,X2] :
( apply(relation_dom_restriction(X2,X0),X1) != apply(X2,X1)
& in(X1,X0)
& relation(X2)
& function(X2) ),
inference(flattening,[],[f83]) ).
fof(f95,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(X1,relation_dom(X0))
| empty_set = X2
| apply(X0,X1) != X2 ),
inference(cnf_transformation,[],[f59]) ).
fof(f97,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f110,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| function(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f66]) ).
fof(f120,plain,
! [X2,X0,X1] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(X1,X0)
| ~ in(X1,relation_dom(X2))
| in(X1,relation_dom(relation_dom_restriction(X2,X0))) ),
inference(cnf_transformation,[],[f71]) ).
fof(f149,plain,
! [X2,X3,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X3,relation_dom(X1))
| apply(X1,X3) = apply(X2,X3)
| relation_dom_restriction(X2,X0) != X1 ),
inference(cnf_transformation,[],[f81]) ).
fof(f152,plain,
function(sK14),
inference(cnf_transformation,[],[f84]) ).
fof(f153,plain,
relation(sK14),
inference(cnf_transformation,[],[f84]) ).
fof(f154,plain,
in(sK13,sK12),
inference(cnf_transformation,[],[f84]) ).
fof(f155,plain,
apply(relation_dom_restriction(sK14,sK12),sK13) != apply(sK14,sK13),
inference(cnf_transformation,[],[f84]) ).
fof(f161,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(X1,relation_dom(X0))
| apply(X0,X1) = empty_set ),
inference(equality_resolution,[],[f95]) ).
fof(f165,plain,
! [X2,X3,X0] :
( ~ function(relation_dom_restriction(X2,X0))
| ~ relation(relation_dom_restriction(X2,X0))
| ~ function(X2)
| ~ relation(X2)
| ~ in(X3,relation_dom(relation_dom_restriction(X2,X0)))
| apply(X2,X3) = apply(relation_dom_restriction(X2,X0),X3) ),
inference(equality_resolution,[],[f149]) ).
fof(f168,plain,
! [X0,X1] :
( ~ in(X1,relation_dom(X0))
| ~ relation(X0)
| function(X0)
| apply(X0,X1) = empty_set ),
inference(consistent_polarity_flipping,[],[f161]) ).
fof(f177,plain,
! [X0,X1] :
( ~ function(relation_dom_restriction(X0,X1))
| ~ relation(X0)
| function(X0) ),
inference(consistent_polarity_flipping,[],[f110]) ).
fof(f178,plain,
! [X2,X0,X1] :
( ~ in(X1,relation_dom(relation_dom_restriction(X2,X0)))
| ~ relation(X2)
| in(X1,X0)
| in(X1,relation_dom(X2))
| function(X2) ),
inference(consistent_polarity_flipping,[],[f120]) ).
fof(f194,plain,
! [X2,X3,X0] :
( function(relation_dom_restriction(X2,X0))
| ~ relation(relation_dom_restriction(X2,X0))
| function(X2)
| ~ relation(X2)
| in(X3,relation_dom(relation_dom_restriction(X2,X0)))
| apply(X2,X3) = apply(relation_dom_restriction(X2,X0),X3) ),
inference(consistent_polarity_flipping,[],[f165]) ).
fof(f197,plain,
~ in(sK13,sK12),
inference(consistent_polarity_flipping,[],[f154]) ).
fof(f198,plain,
~ function(sK14),
inference(consistent_polarity_flipping,[],[f152]) ).
fof(f349,plain,
! [X2,X3,X0] :
( ~ relation(relation_dom_restriction(X2,X0))
| function(X2)
| ~ relation(X2)
| in(X3,relation_dom(relation_dom_restriction(X2,X0)))
| apply(X2,X3) = apply(relation_dom_restriction(X2,X0),X3) ),
inference(forward_subsumption_resolution,[],[f194,f177]) ).
fof(f350,plain,
! [X2,X3,X0] :
( in(X3,relation_dom(relation_dom_restriction(X2,X0)))
| ~ relation(X2)
| function(X2)
| apply(X2,X3) = apply(relation_dom_restriction(X2,X0),X3) ),
inference(forward_subsumption_resolution,[],[f349,f97]) ).
fof(f352,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| function(X0)
| apply(X0,X1) = apply(relation_dom_restriction(X0,X2),X1)
| ~ relation(relation_dom_restriction(X0,X2))
| function(relation_dom_restriction(X0,X2))
| empty_set = apply(relation_dom_restriction(X0,X2),X1) ),
inference(resolution,[],[f350,f168]) ).
fof(f358,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| function(X0)
| apply(X0,X1) = apply(relation_dom_restriction(X0,X2),X1)
| function(relation_dom_restriction(X0,X2))
| empty_set = apply(relation_dom_restriction(X0,X2),X1) ),
inference(forward_subsumption_resolution,[],[f352,f97]) ).
fof(f360,plain,
! [X2,X0,X1] :
( function(X0)
| ~ relation(X0)
| apply(X0,X1) = apply(relation_dom_restriction(X0,X2),X1)
| empty_set = apply(relation_dom_restriction(X0,X2),X1) ),
inference(forward_subsumption_resolution,[],[f358,f177]) ).
fof(f866,plain,
! [X0,X1] :
( ~ relation(sK14)
| apply(sK14,X0) = apply(relation_dom_restriction(sK14,X1),X0)
| empty_set = apply(relation_dom_restriction(sK14,X1),X0) ),
inference(resolution,[],[f360,f198]) ).
fof(f867,plain,
! [X0,X1] :
( apply(sK14,X0) = apply(relation_dom_restriction(sK14,X1),X0)
| empty_set = apply(relation_dom_restriction(sK14,X1),X0) ),
inference(forward_subsumption_resolution,[],[f866,f153]) ).
fof(f1391,plain,
( apply(sK14,sK13) != apply(sK14,sK13)
| empty_set = apply(relation_dom_restriction(sK14,sK12),sK13) ),
inference(superposition,[],[f155,f867]) ).
fof(f1397,plain,
empty_set = apply(relation_dom_restriction(sK14,sK12),sK13),
inference(trivial_inequality_removal,[],[f1391]) ).
fof(f1432,plain,
empty_set != apply(sK14,sK13),
inference(superposition,[],[f155,f1397]) ).
fof(f1438,definition,
( spl15_35
<=> in(sK13,relation_dom(relation_dom_restriction(sK14,sK12))) ),
introduced(definition,[new_symbols(definition,[spl15_35])],[avatar_definition]) ).
fof(f1439,plain,
( ~ in(sK13,relation_dom(relation_dom_restriction(sK14,sK12)))
| spl15_35 ),
inference(avatar_component_clause,[],[f1438]) ).
fof(f1440,plain,
( in(sK13,relation_dom(relation_dom_restriction(sK14,sK12)))
| ~ spl15_35 ),
inference(avatar_component_clause,[],[f1438]) ).
fof(f1488,plain,
( ~ relation(sK14)
| in(sK13,sK12)
| in(sK13,relation_dom(sK14))
| function(sK14)
| ~ spl15_35 ),
inference(resolution,[],[f1440,f178]) ).
fof(f1503,plain,
( in(sK13,sK12)
| in(sK13,relation_dom(sK14))
| function(sK14)
| ~ spl15_35 ),
inference(forward_subsumption_resolution,[],[f1488,f153]) ).
fof(f1505,plain,
( in(sK13,relation_dom(sK14))
| function(sK14)
| ~ spl15_35 ),
inference(forward_subsumption_resolution,[],[f1503,f197]) ).
fof(f1506,plain,
( in(sK13,relation_dom(sK14))
| ~ spl15_35 ),
inference(forward_subsumption_resolution,[],[f1505,f198]) ).
fof(f1507,plain,
( ~ relation(sK14)
| function(sK14)
| apply(relation_dom_restriction(sK14,sK12),sK13) = apply(sK14,sK13)
| spl15_35 ),
inference(resolution,[],[f1439,f350]) ).
fof(f1518,definition,
( spl15_45
<=> in(sK13,relation_dom(sK14)) ),
introduced(definition,[new_symbols(definition,[spl15_45])],[avatar_definition]) ).
fof(f1520,plain,
( in(sK13,relation_dom(sK14))
| ~ spl15_45 ),
inference(avatar_component_clause,[],[f1518]) ).
fof(f1523,plain,
( function(sK14)
| apply(relation_dom_restriction(sK14,sK12),sK13) = apply(sK14,sK13)
| spl15_35 ),
inference(forward_subsumption_resolution,[],[f1507,f153]) ).
fof(f1525,plain,
( apply(relation_dom_restriction(sK14,sK12),sK13) = apply(sK14,sK13)
| spl15_35 ),
inference(forward_subsumption_resolution,[],[f1523,f198]) ).
fof(f1527,plain,
( $false
| spl15_35 ),
inference(forward_subsumption_resolution,[],[f1525,f155]) ).
fof(f1528,plain,
spl15_35,
inference(avatar_contradiction_clause,[],[f1527]) ).
fof(f1529,plain,
( spl15_45
| ~ spl15_35 ),
inference(avatar_split_clause,[],[f1506,f1438,f1518]) ).
fof(f1536,plain,
( ~ relation(sK14)
| function(sK14)
| empty_set = apply(sK14,sK13)
| ~ spl15_45 ),
inference(resolution,[],[f1520,f168]) ).
fof(f1540,plain,
( function(sK14)
| empty_set = apply(sK14,sK13)
| ~ spl15_45 ),
inference(forward_subsumption_resolution,[],[f1536,f153]) ).
fof(f1542,plain,
( empty_set = apply(sK14,sK13)
| ~ spl15_45 ),
inference(forward_subsumption_resolution,[],[f1540,f198]) ).
fof(f1544,plain,
( $false
| ~ spl15_45 ),
inference(forward_subsumption_resolution,[],[f1542,f1432]) ).
fof(f1545,plain,
~ spl15_45,
inference(avatar_contradiction_clause,[],[f1544]) ).
cnf(s44,plain,
spl15_35,
inference(sat_conversion,[],[f1528]) ).
cnf(s45,plain,
( ~ spl15_35
| spl15_45 ),
inference(sat_conversion,[],[f1529]) ).
cnf(s47,plain,
~ spl15_45,
inference(sat_conversion,[],[f1545]) ).
cnf(s48,plain,
~ spl15_35,
inference(rat,[],[s45,s47]) ).
cnf(s49,plain,
$false,
inference(rat,[],[s44,s48]) ).
fof(f1546,plain,
$false,
inference(avatar_sat_refutation,[],[s49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU225+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n016.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 04:14:47 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 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
% 0.18/0.48 % (3251114)Will run a generic schedule for satisfiability detection.
% 0.18/0.48 % (3251120)% WARNING: option uhcvi not known.
% 0.18/0.48 % (3251120)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4111704344:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.48 % (3251119)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1549091267_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.48 % (3251121)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1832063764:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.48 % (3251122)dis+10_1_sil=32000:sp=arity:random_seed=4025646296:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.48 % (3251123)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=274974903:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.48 % TRYING [1]
% 0.18/0.48 % TRYING [2]
% 0.18/0.48 % TRYING [3]
% 0.18/0.48 % (3251124)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2944022125:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.48 % (3251125)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2837616311:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.48 % TRYING [4]
% 0.18/0.48 % (3251120) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3251114-3251120"...
% 0.18/0.48 % (3251120)...printing done.
% 0.18/0.48 % (3251120)Refutation found. Thanks to Tanya!
% 0.18/0.48 % SZS status Theorem for theBenchmark
% 0.18/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.49 % (3251120)------------------------------
% 0.18/0.49 % (3251120)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.49 % (3251120)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.49 % (3251120)CaDiCaL version: 2.1.3
% 0.18/0.49 % (3251120)Termination reason: Refutation
% 0.18/0.49 % (3251120)Time elapsed: 0.021 s
% 0.18/0.49 % (3251120)Peak memory usage: 13 MB
% 0.18/0.49 % (3251120)Instructions burned: 55 (million)
% 0.18/0.49 % (3251114)Success in time 0.055 s
% 0.18/0.49 % Vampire exiting
%------------------------------------------------------------------------------