%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU212+3 : TPTP v9.3.1. Released v3.2.0.
% 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 12:47:46 PM UTC 2026
% Result : Theorem 1.13s 1.14s
% Output : Refutation 2.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 72 ( 9 unt; 5 def)
% Number of atoms : 270 ( 42 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 326 ( 128 ~; 136 |; 38 &)
% ( 16 <=>; 6 =>; 0 <=; 2 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 74 ( 0 sgn 54 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,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(f6,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f35,conjecture,
! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( in(ordered_pair(X0,X1),X2)
<=> ( in(X0,relation_dom(X2))
& X1 = apply(X2,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_funct_1) ).
fof(f36,negated_conjecture,
~ ! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( in(ordered_pair(X0,X1),X2)
<=> ( in(X0,relation_dom(X2))
& X1 = apply(X2,X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f37,plain,
? [X0,X1,X2] :
( ( in(ordered_pair(X0,X1),X2)
<~> ( in(X0,relation_dom(X2))
& X1 = apply(X2,X0) ) )
& relation(X2)
& function(X2) ),
inference(ennf_transformation,[],[f36]) ).
fof(f38,plain,
? [X0,X1,X2] :
( ( in(ordered_pair(X0,X1),X2)
<~> ( in(X0,relation_dom(X2))
& X1 = apply(X2,X0) ) )
& relation(X2)
& function(X2) ),
inference(flattening,[],[f37]) ).
fof(f45,plain,
! [X0] :
( ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f46,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,[],[f5]) ).
fof(f47,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,[],[f46]) ).
fof(f50,plain,
? [X0,X1,X2] :
( ( ~ in(X0,relation_dom(X2))
| apply(X2,X0) != X1
| ~ in(ordered_pair(X0,X1),X2) )
& ( ( in(X0,relation_dom(X2))
& X1 = apply(X2,X0) )
| in(ordered_pair(X0,X1),X2) )
& relation(X2)
& function(X2) ),
inference(nnf_transformation,[],[f38]) ).
fof(f51,plain,
? [X0,X1,X2] :
( ( ~ in(X0,relation_dom(X2))
| apply(X2,X0) != X1
| ~ in(ordered_pair(X0,X1),X2) )
& ( ( in(X0,relation_dom(X2))
& X1 = apply(X2,X0) )
| in(ordered_pair(X0,X1),X2) )
& relation(X2)
& function(X2) ),
inference(flattening,[],[f50]) ).
fof(f52,plain,
( ( ~ in(sK0,relation_dom(sK2))
| sK1 != apply(sK2,sK0)
| ~ in(ordered_pair(sK0,sK1),sK2) )
& ( ( in(sK0,relation_dom(sK2))
& sK1 = apply(sK2,sK0) )
| in(ordered_pair(sK0,sK1),sK2) )
& relation(sK2)
& function(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f51]) ).
fof(f53,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f45]) ).
fof(f54,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( ? [X7] : in(ordered_pair(X5,X7),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f53]) ).
fof(f55,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ( ( ! [X3] : ~ in(ordered_pair(sK3(X0,X1),X3),X0)
| ~ in(sK3(X0,X1),X1) )
& ( in(ordered_pair(sK3(X0,X1),sK4(X0,X1)),X0)
| in(sK3(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK5(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X2,sK3(X0,X1)),skolemize(X4,sK4(X0,X1)),skolemize(X7,sK5(X0,X5))],[f54]) ).
fof(f56,plain,
! [X0] :
( ! [X1,X2] :
( ( ( ( X2 = apply(X0,X1)
| ~ in(ordered_pair(X1,X2),X0) )
& ( in(ordered_pair(X1,X2),X0)
| apply(X0,X1) != X2 ) )
| ~ in(X1,relation_dom(X0)) )
& ( ( ( X2 = apply(X0,X1)
| empty_set != X2 )
& ( X2 = empty_set
| apply(X0,X1) != X2 ) )
| in(X1,relation_dom(X0)) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f47]) ).
fof(f60,plain,
function(sK2),
inference(cnf_transformation,[],[f52]) ).
fof(f61,plain,
relation(sK2),
inference(cnf_transformation,[],[f52]) ).
fof(f62,plain,
( sK1 = apply(sK2,sK0)
| in(ordered_pair(sK0,sK1),sK2) ),
inference(cnf_transformation,[],[f52]) ).
fof(f63,plain,
( in(sK0,relation_dom(sK2))
| in(ordered_pair(sK0,sK1),sK2) ),
inference(cnf_transformation,[],[f52]) ).
fof(f64,plain,
( ~ in(sK0,relation_dom(sK2))
| sK1 != apply(sK2,sK0)
| ~ in(ordered_pair(sK0,sK1),sK2) ),
inference(cnf_transformation,[],[f52]) ).
fof(f72,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X5,X6),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f77,plain,
! [X2,X0,X1] :
( in(ordered_pair(X1,X2),X0)
| apply(X0,X1) != X2
| ~ in(X1,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f78,plain,
! [X2,X0,X1] :
( ~ in(ordered_pair(X1,X2),X0)
| apply(X0,X1) = X2
| ~ in(X1,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f88,definition,
~ sP9(sK1),
introduced(definition,[new_symbols(definition,[sP9])],[inequality_splitting_name_introduction]) ).
fof(f89,plain,
( ~ in(sK0,relation_dom(sK2))
| sP9(apply(sK2,sK0))
| ~ in(ordered_pair(sK0,sK1),sK2) ),
inference(inequality_splitting,[],[f64,f88]) ).
fof(f92,plain,
! [X0,X6,X5] :
( ~ in(ordered_pair(X5,X6),X0)
| in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f72]) ).
fof(f94,plain,
! [X0,X1] :
( in(ordered_pair(X1,apply(X0,X1)),X0)
| ~ in(X1,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f77]) ).
fof(f97,definition,
( spl11_1
<=> in(ordered_pair(sK0,sK1),sK2) ),
introduced(definition,[new_symbols(definition,[spl11_1])],[avatar_definition]) ).
fof(f98,plain,
( ~ in(ordered_pair(sK0,sK1),sK2)
| spl11_1 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f99,plain,
( in(ordered_pair(sK0,sK1),sK2)
| ~ spl11_1 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f101,definition,
( spl11_2
<=> sK1 = apply(sK2,sK0) ),
introduced(definition,[new_symbols(definition,[spl11_2])],[avatar_definition]) ).
fof(f102,plain,
( sK1 != apply(sK2,sK0)
| spl11_2 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f103,plain,
( sK1 = apply(sK2,sK0)
| ~ spl11_2 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f104,plain,
( spl11_1
| spl11_2 ),
inference(avatar_split_clause,[],[f62,f101,f97]) ).
fof(f106,definition,
( spl11_3
<=> in(sK0,relation_dom(sK2)) ),
introduced(definition,[new_symbols(definition,[spl11_3])],[avatar_definition]) ).
fof(f107,plain,
( ~ in(sK0,relation_dom(sK2))
| spl11_3 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f108,plain,
( in(sK0,relation_dom(sK2))
| ~ spl11_3 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f109,plain,
( spl11_1
| spl11_3 ),
inference(avatar_split_clause,[],[f63,f106,f97]) ).
fof(f111,definition,
( spl11_4
<=> sP9(apply(sK2,sK0)) ),
introduced(definition,[new_symbols(definition,[spl11_4])],[avatar_definition]) ).
fof(f114,plain,
( ~ spl11_1
| spl11_4
| ~ spl11_3 ),
inference(avatar_split_clause,[],[f89,f106,f111,f97]) ).
fof(f118,plain,
( ~ in(ordered_pair(sK0,apply(sK2,sK0)),sK2)
| spl11_1
| ~ spl11_2 ),
inference(superposition,[],[f98,f103]) ).
fof(f119,plain,
( ~ sP9(apply(sK2,sK0))
| ~ spl11_2 ),
inference(superposition,[],[f88,f103]) ).
fof(f120,plain,
( ~ spl11_4
| ~ spl11_2 ),
inference(avatar_split_clause,[],[f119,f101,f111]) ).
fof(f123,plain,
( ~ in(sK0,relation_dom(sK2))
| ~ relation(sK2)
| ~ function(sK2)
| spl11_1
| ~ spl11_2 ),
inference(resolution,[],[f118,f94]) ).
fof(f126,plain,
( ~ relation(sK2)
| ~ function(sK2)
| spl11_1
| ~ spl11_2
| ~ spl11_3 ),
inference(forward_subsumption_resolution,[],[f123,f108]) ).
fof(f127,plain,
( ~ function(sK2)
| spl11_1
| ~ spl11_2
| ~ spl11_3 ),
inference(forward_subsumption_resolution,[],[f126,f61]) ).
fof(f128,plain,
( $false
| spl11_1
| ~ spl11_2
| ~ spl11_3 ),
inference(forward_subsumption_resolution,[],[f127,f60]) ).
fof(f129,plain,
( spl11_1
| ~ spl11_2
| ~ spl11_3 ),
inference(avatar_contradiction_clause,[],[f128]) ).
fof(f132,plain,
( sK1 = apply(sK2,sK0)
| ~ in(sK0,relation_dom(sK2))
| ~ relation(sK2)
| ~ function(sK2)
| ~ spl11_1 ),
inference(resolution,[],[f99,f78]) ).
fof(f133,plain,
( in(sK0,relation_dom(sK2))
| ~ relation(sK2)
| ~ spl11_1 ),
inference(resolution,[],[f99,f92]) ).
fof(f136,plain,
( ~ in(sK0,relation_dom(sK2))
| ~ relation(sK2)
| ~ function(sK2)
| ~ spl11_1
| spl11_2 ),
inference(forward_subsumption_resolution,[],[f132,f102]) ).
fof(f137,plain,
( ~ relation(sK2)
| ~ function(sK2)
| ~ spl11_1
| spl11_2
| ~ spl11_3 ),
inference(forward_subsumption_resolution,[],[f136,f108]) ).
fof(f138,plain,
( ~ function(sK2)
| ~ spl11_1
| spl11_2
| ~ spl11_3 ),
inference(forward_subsumption_resolution,[],[f137,f61]) ).
fof(f139,plain,
( $false
| ~ spl11_1
| spl11_2
| ~ spl11_3 ),
inference(forward_subsumption_resolution,[],[f138,f60]) ).
fof(f140,plain,
( ~ spl11_1
| spl11_2
| ~ spl11_3 ),
inference(avatar_contradiction_clause,[],[f139]) ).
fof(f143,plain,
( ~ relation(sK2)
| ~ spl11_1
| spl11_3 ),
inference(forward_subsumption_resolution,[],[f133,f107]) ).
fof(f146,plain,
( $false
| ~ spl11_1
| spl11_3 ),
inference(forward_subsumption_resolution,[],[f143,f61]) ).
fof(f147,plain,
( ~ spl11_1
| spl11_3 ),
inference(avatar_contradiction_clause,[],[f146]) ).
cnf(s1,plain,
( spl11_1
| spl11_2 ),
inference(sat_conversion,[],[f104]) ).
cnf(s2,plain,
( spl11_1
| spl11_3 ),
inference(sat_conversion,[],[f109]) ).
cnf(s3,plain,
( ~ spl11_1
| ~ spl11_3
| spl11_4 ),
inference(sat_conversion,[],[f114]) ).
cnf(s4,plain,
( ~ spl11_2
| ~ spl11_4 ),
inference(sat_conversion,[],[f120]) ).
cnf(s5,plain,
( spl11_1
| ~ spl11_2
| ~ spl11_3 ),
inference(sat_conversion,[],[f129]) ).
cnf(s6,plain,
( ~ spl11_1
| spl11_2
| ~ spl11_3 ),
inference(sat_conversion,[],[f140]) ).
cnf(s7,plain,
( ~ spl11_1
| spl11_3 ),
inference(sat_conversion,[],[f147]) ).
cnf(s8,plain,
spl11_1,
inference(rat,[],[s5,s1,s2]) ).
cnf(s9,plain,
spl11_3,
inference(rat,[],[s7,s8]) ).
cnf(s10,plain,
spl11_2,
inference(rat,[],[s6,s9,s8]) ).
cnf(s11,plain,
spl11_4,
inference(rat,[],[s3,s9,s8]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s4,s11,s10]) ).
fof(f150,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU212+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n011.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 04:04:31 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.40 Running first-order theorem proving
% 0.15/0.40 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
% 1.13/1.14 % (3009286)Detected formulas, will run a generic FOF schedule.
% 1.13/1.14 % (3009294)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3351361203:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.13/1.14 % (3009294)First to succeed.
% 1.13/1.14 % (3009294)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3009286"
% 1.13/1.14 % (3009296)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2017731496:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.13/1.14 % (3009291)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=3928391353:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.13/1.14 % (3009293)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=1797098193:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.13/1.14 % (3009292)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=4002145129:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.13/1.14 % (3009296)Also succeeded, but the first one will report.
% 1.13/1.14 % (3009297)dis-21_1_sil=8000:lcm=predicate:random_seed=3716602092: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)
% 1.13/1.14 % (3009295)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3257543121:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.13/1.14 % (3009295)Also succeeded, but the first one will report.
% 1.13/1.14 % (3009297)Instruction limit reached!
% 1.13/1.14 % (3009297)------------------------------
% 1.13/1.14 % (3009297)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.13/1.14 % (3009297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.13/1.14 % (3009297)CaDiCaL version: 2.1.3
% 1.13/1.14 % (3009297)Termination reason: Instruction limit
% 1.13/1.14 % (3009297)Termination phase: Saturation
% 1.13/1.14 % (3009297)Time elapsed: 0.087 s
% 1.13/1.14 % (3009297)Peak memory usage: 90 MB
% 1.13/1.14 % (3009297)Instructions burned: 130 (million)
% 1.13/1.14 % (3009294)Refutation found. Thanks to Tanya!
% 1.13/1.14 % SZS status Theorem for theBenchmark
% 1.13/1.14 % SZS output start Proof for theBenchmark
% See solution above
% 2.66/1.33 % (3009294)------------------------------
% 2.66/1.33 % (3009294)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.33 % (3009294)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.33 % (3009294)CaDiCaL version: 2.1.3
% 2.66/1.33 % (3009294)Termination reason: Refutation
% 2.66/1.33 % (3009294)Time elapsed: 0.003 s
% 2.66/1.33 % (3009294)Peak memory usage: 89 MB
% 2.66/1.33 % (3009294)Instructions burned: 4 (million)
% 2.66/1.33 % (3009294)------------------------------
% 2.66/1.33 % (3009294)------------------------------
% 2.66/1.33 % (3009286)Success in time 0.288 s
% 2.66/1.33 % Vampire exiting
%------------------------------------------------------------------------------