%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU223+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 12:47:50 PM UTC 2026
% Result : Theorem 1.63s 1.14s
% Output : Refutation 2.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 62 ( 16 unt; 6 def)
% Number of atoms : 208 ( 43 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 249 ( 103 ~; 96 |; 32 &)
% ( 9 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 6 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 71 ( 0 sgn 62 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f30,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_dom_restriction(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(f32,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(f36,conjecture,
! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
=> apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_funct_1) ).
fof(f37,negated_conjecture,
~ ! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
=> apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,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(f56,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f57,plain,
! [X0,X1] :
( ( relation(relation_dom_restriction(X0,X1))
& function(relation_dom_restriction(X0,X1)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f58,plain,
! [X0,X1] :
( ( relation(relation_dom_restriction(X0,X1))
& function(relation_dom_restriction(X0,X1)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f57]) ).
fof(f63,plain,
? [X0,X1,X2] :
( apply(relation_dom_restriction(X2,X0),X1) != apply(X2,X1)
& in(X1,relation_dom(relation_dom_restriction(X2,X0)))
& relation(X2)
& function(X2) ),
inference(ennf_transformation,[],[f37]) ).
fof(f64,plain,
? [X0,X1,X2] :
( apply(relation_dom_restriction(X2,X0),X1) != apply(X2,X1)
& in(X1,relation_dom(relation_dom_restriction(X2,X0)))
& relation(X2)
& function(X2) ),
inference(flattening,[],[f63]) ).
fof(f65,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,[],[f38]) ).
fof(f66,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,[],[f65]) ).
fof(f76,plain,
( apply(relation_dom_restriction(sK11,sK9),sK10) != apply(sK11,sK10)
& in(sK10,relation_dom(relation_dom_restriction(sK11,sK9)))
& relation(sK11)
& function(sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11]),skolemize(X0,sK9),skolemize(X1,sK10),skolemize(X2,sK11)],[f64]) ).
fof(f77,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_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) ) )
| relation_dom_restriction(X2,X0) != X1 ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(nnf_transformation,[],[f66]) ).
fof(f78,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_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) ) )
| relation_dom_restriction(X2,X0) != X1 ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f77]) ).
fof(f79,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_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X4] :
( apply(X1,X4) = apply(X2,X4)
| ~ in(X4,relation_dom(X1)) ) )
| relation_dom_restriction(X2,X0) != X1 ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(rectify,[],[f78]) ).
fof(f80,plain,
! [X0,X1] :
( ! [X2] :
( ( ( X1 = relation_dom_restriction(X2,X0)
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| ( apply(X1,sK12(X1,X2)) != apply(X2,sK12(X1,X2))
& in(sK12(X1,X2),relation_dom(X1)) ) )
& ( ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X4] :
( apply(X1,X4) = apply(X2,X4)
| ~ in(X4,relation_dom(X1)) ) )
| relation_dom_restriction(X2,X0) != X1 ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X3,sK12(X1,X2))],[f79]) ).
fof(f117,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f120,plain,
! [X0,X1] :
( function(relation_dom_restriction(X0,X1))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f125,plain,
function(sK11),
inference(cnf_transformation,[],[f76]) ).
fof(f126,plain,
relation(sK11),
inference(cnf_transformation,[],[f76]) ).
fof(f127,plain,
in(sK10,relation_dom(relation_dom_restriction(sK11,sK9))),
inference(cnf_transformation,[],[f76]) ).
fof(f128,plain,
apply(relation_dom_restriction(sK11,sK9),sK10) != apply(sK11,sK10),
inference(cnf_transformation,[],[f76]) ).
fof(f129,plain,
! [X2,X0,X1,X4] :
( apply(X1,X4) = apply(X2,X4)
| ~ in(X4,relation_dom(X1))
| relation_dom_restriction(X2,X0) != X1
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f134,plain,
! [X2,X0,X4] :
( apply(X2,X4) = apply(relation_dom_restriction(X2,X0),X4)
| ~ in(X4,relation_dom(relation_dom_restriction(X2,X0)))
| ~ relation(X2)
| ~ function(X2)
| ~ relation(relation_dom_restriction(X2,X0))
| ~ function(relation_dom_restriction(X2,X0)) ),
inference(equality_resolution,[],[f129]) ).
fof(f135,definition,
! [X0,X1] :
( sQ13_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ13_eqProxy])],[equality_proxy_definition]) ).
fof(f141,plain,
~ sQ13_eqProxy(apply(relation_dom_restriction(sK11,sK9),sK10),apply(sK11,sK10)),
inference(equality_proxy_replacement,[],[f128,f135]) ).
fof(f145,plain,
! [X2,X0,X4] :
( sQ13_eqProxy(apply(X2,X4),apply(relation_dom_restriction(X2,X0),X4))
| ~ in(X4,relation_dom(relation_dom_restriction(X2,X0)))
| ~ relation(X2)
| ~ function(X2)
| ~ relation(relation_dom_restriction(X2,X0))
| ~ function(relation_dom_restriction(X2,X0)) ),
inference(equality_proxy_replacement,[],[f134,f135]) ).
fof(f147,plain,
! [X0,X1] :
( sQ13_eqProxy(X1,X0)
| ~ sQ13_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f135]) ).
fof(f161,plain,
~ sQ13_eqProxy(apply(sK11,sK10),apply(relation_dom_restriction(sK11,sK9),sK10)),
inference(resolution,[],[f147,f141]) ).
fof(f193,plain,
( ~ in(sK10,relation_dom(relation_dom_restriction(sK11,sK9)))
| ~ relation(sK11)
| ~ function(sK11)
| ~ relation(relation_dom_restriction(sK11,sK9))
| ~ function(relation_dom_restriction(sK11,sK9)) ),
inference(resolution,[],[f145,f161]) ).
fof(f195,definition,
( spl14_3
<=> function(relation_dom_restriction(sK11,sK9)) ),
introduced(definition,[new_symbols(definition,[spl14_3])],[avatar_definition]) ).
fof(f196,plain,
( ~ function(relation_dom_restriction(sK11,sK9))
| spl14_3 ),
inference(avatar_component_clause,[],[f195]) ).
fof(f198,definition,
( spl14_4
<=> relation(relation_dom_restriction(sK11,sK9)) ),
introduced(definition,[new_symbols(definition,[spl14_4])],[avatar_definition]) ).
fof(f199,plain,
( ~ relation(relation_dom_restriction(sK11,sK9))
| spl14_4 ),
inference(avatar_component_clause,[],[f198]) ).
fof(f201,definition,
( spl14_5
<=> function(sK11) ),
introduced(definition,[new_symbols(definition,[spl14_5])],[avatar_definition]) ).
fof(f202,plain,
( ~ function(sK11)
| spl14_5 ),
inference(avatar_component_clause,[],[f201]) ).
fof(f204,definition,
( spl14_6
<=> relation(sK11) ),
introduced(definition,[new_symbols(definition,[spl14_6])],[avatar_definition]) ).
fof(f205,plain,
( ~ relation(sK11)
| spl14_6 ),
inference(avatar_component_clause,[],[f204]) ).
fof(f207,definition,
( spl14_7
<=> in(sK10,relation_dom(relation_dom_restriction(sK11,sK9))) ),
introduced(definition,[new_symbols(definition,[spl14_7])],[avatar_definition]) ).
fof(f208,plain,
( ~ in(sK10,relation_dom(relation_dom_restriction(sK11,sK9)))
| spl14_7 ),
inference(avatar_component_clause,[],[f207]) ).
fof(f209,plain,
( ~ spl14_3
| ~ spl14_4
| ~ spl14_5
| ~ spl14_6
| ~ spl14_7 ),
inference(avatar_split_clause,[],[f193,f207,f204,f201,f198,f195]) ).
fof(f210,plain,
( ~ relation(sK11)
| ~ function(sK11)
| spl14_3 ),
inference(resolution,[],[f196,f120]) ).
fof(f212,plain,
( ~ spl14_5
| ~ spl14_6
| spl14_3 ),
inference(avatar_split_clause,[],[f210,f195,f204,f201]) ).
fof(f213,plain,
( $false
| spl14_5 ),
inference(resolution,[],[f202,f125]) ).
fof(f215,plain,
spl14_5,
inference(avatar_contradiction_clause,[],[f213]) ).
fof(f216,plain,
( $false
| spl14_6 ),
inference(resolution,[],[f205,f126]) ).
fof(f217,plain,
spl14_6,
inference(avatar_contradiction_clause,[],[f216]) ).
fof(f218,plain,
( ~ relation(sK11)
| spl14_4 ),
inference(resolution,[],[f199,f117]) ).
fof(f219,plain,
( ~ spl14_6
| spl14_4 ),
inference(avatar_split_clause,[],[f218,f198,f204]) ).
fof(f220,plain,
( $false
| spl14_7 ),
inference(resolution,[],[f208,f127]) ).
fof(f221,plain,
spl14_7,
inference(avatar_contradiction_clause,[],[f220]) ).
cnf(s3,plain,
( ~ spl14_3
| ~ spl14_4
| ~ spl14_5
| ~ spl14_6
| ~ spl14_7 ),
inference(sat_conversion,[],[f209]) ).
cnf(s4,plain,
( spl14_3
| ~ spl14_5
| ~ spl14_6 ),
inference(sat_conversion,[],[f212]) ).
cnf(s5,plain,
spl14_5,
inference(sat_conversion,[],[f215]) ).
cnf(s6,plain,
spl14_6,
inference(sat_conversion,[],[f217]) ).
cnf(s7,plain,
( spl14_4
| ~ spl14_6 ),
inference(sat_conversion,[],[f219]) ).
cnf(s8,plain,
spl14_7,
inference(sat_conversion,[],[f221]) ).
cnf(s9,plain,
spl14_4,
inference(rat,[],[s7,s6]) ).
cnf(s10,plain,
spl14_3,
inference(rat,[],[s4,s6,s5]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s3,s8,s6,s5,s9,s10]) ).
fof(f222,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU223+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n009.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 04:09:31 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 1.63/1.14 % (2651040)Detected formulas, will run a generic FOF schedule.
% 1.63/1.14 % (2651051)dis-21_1_sil=8000:lcm=predicate:random_seed=3201944328: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)
% 1.63/1.14 % (2651051)First to succeed.
% 1.63/1.14 % (2651051)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2651040"
% 1.63/1.14 % (2651049)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3652776993:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.63/1.14 % (2651045)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=519110545:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.63/1.14 % (2651050)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2382941652:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.63/1.14 % (2651047)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=2150802917:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.63/1.14 % (2651046)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=3301483891:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.63/1.14 % (2651048)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1790371597:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.63/1.14 % (2651048)Also succeeded, but the first one will report.
% 1.63/1.14 % (2651049)Also succeeded, but the first one will report.
% 1.63/1.14 % (2651050)Also succeeded, but the first one will report.
% 1.63/1.14 % (2651051)Refutation found. Thanks to Tanya!
% 1.63/1.14 % SZS status Theorem for theBenchmark
% 1.63/1.14 % SZS output start Proof for theBenchmark
% See solution above
% 2.56/1.33 % (2651051)------------------------------
% 2.56/1.33 % (2651051)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.56/1.33 % (2651051)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/1.33 % (2651051)CaDiCaL version: 2.1.3
% 2.56/1.33 % (2651051)Termination reason: Refutation
% 2.56/1.33 % (2651051)Time elapsed: 0.003 s
% 2.56/1.33 % (2651051)Peak memory usage: 89 MB
% 2.56/1.33 % (2651051)Instructions burned: 5 (million)
% 2.56/1.33 % (2651051)------------------------------
% 2.56/1.33 % (2651051)------------------------------
% 2.56/1.33 % (2651040)Success in time 0.278 s
% 2.56/1.33 % Vampire exiting
%------------------------------------------------------------------------------