%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU223+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 : n015.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 2.18s 1.16s
% 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(f23,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_dom_restriction(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(f24,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(f38,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(f39,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)],[f38]) ).
fof(f40,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(f64,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f65,plain,
! [X0,X1] :
( ( relation(relation_dom_restriction(X0,X1))
& function(relation_dom_restriction(X0,X1)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f24]) ).
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(f72,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,[],[f39]) ).
fof(f73,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,[],[f72]) ).
fof(f74,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,[],[f40]) ).
fof(f75,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,[],[f74]) ).
fof(f87,plain,
( apply(relation_dom_restriction(sK13,sK11),sK12) != apply(sK13,sK12)
& in(sK12,relation_dom(relation_dom_restriction(sK13,sK11)))
& relation(sK13)
& function(sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13]),skolemize(X0,sK11),skolemize(X1,sK12),skolemize(X2,sK13)],[f73]) ).
fof(f88,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,[],[f75]) ).
fof(f89,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,[],[f88]) ).
fof(f90,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,[],[f89]) ).
fof(f91,plain,
! [X0,X1] :
( ! [X2] :
( ( ( X1 = relation_dom_restriction(X2,X0)
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| ( apply(X1,sK14(X1,X2)) != apply(X2,sK14(X1,X2))
& in(sK14(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,[sK14]),skolemize(X3,sK14(X1,X2))],[f90]) ).
fof(f120,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f121,plain,
! [X0,X1] :
( function(relation_dom_restriction(X0,X1))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f145,plain,
function(sK13),
inference(cnf_transformation,[],[f87]) ).
fof(f146,plain,
relation(sK13),
inference(cnf_transformation,[],[f87]) ).
fof(f147,plain,
in(sK12,relation_dom(relation_dom_restriction(sK13,sK11))),
inference(cnf_transformation,[],[f87]) ).
fof(f148,plain,
apply(relation_dom_restriction(sK13,sK11),sK12) != apply(sK13,sK12),
inference(cnf_transformation,[],[f87]) ).
fof(f149,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,[],[f91]) ).
fof(f154,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,[],[f149]) ).
fof(f155,definition,
! [X0,X1] :
( sQ15_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ15_eqProxy])],[equality_proxy_definition]) ).
fof(f161,plain,
~ sQ15_eqProxy(apply(relation_dom_restriction(sK13,sK11),sK12),apply(sK13,sK12)),
inference(equality_proxy_replacement,[],[f148,f155]) ).
fof(f165,plain,
! [X2,X0,X4] :
( sQ15_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,[],[f154,f155]) ).
fof(f167,plain,
! [X0,X1] :
( sQ15_eqProxy(X1,X0)
| ~ sQ15_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f155]) ).
fof(f183,plain,
~ sQ15_eqProxy(apply(sK13,sK12),apply(relation_dom_restriction(sK13,sK11),sK12)),
inference(resolution,[],[f167,f161]) ).
fof(f228,plain,
( ~ in(sK12,relation_dom(relation_dom_restriction(sK13,sK11)))
| ~ relation(sK13)
| ~ function(sK13)
| ~ relation(relation_dom_restriction(sK13,sK11))
| ~ function(relation_dom_restriction(sK13,sK11)) ),
inference(resolution,[],[f165,f183]) ).
fof(f230,definition,
( spl16_3
<=> function(relation_dom_restriction(sK13,sK11)) ),
introduced(definition,[new_symbols(definition,[spl16_3])],[avatar_definition]) ).
fof(f231,plain,
( ~ function(relation_dom_restriction(sK13,sK11))
| spl16_3 ),
inference(avatar_component_clause,[],[f230]) ).
fof(f233,definition,
( spl16_4
<=> relation(relation_dom_restriction(sK13,sK11)) ),
introduced(definition,[new_symbols(definition,[spl16_4])],[avatar_definition]) ).
fof(f234,plain,
( ~ relation(relation_dom_restriction(sK13,sK11))
| spl16_4 ),
inference(avatar_component_clause,[],[f233]) ).
fof(f236,definition,
( spl16_5
<=> function(sK13) ),
introduced(definition,[new_symbols(definition,[spl16_5])],[avatar_definition]) ).
fof(f237,plain,
( ~ function(sK13)
| spl16_5 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f239,definition,
( spl16_6
<=> relation(sK13) ),
introduced(definition,[new_symbols(definition,[spl16_6])],[avatar_definition]) ).
fof(f240,plain,
( ~ relation(sK13)
| spl16_6 ),
inference(avatar_component_clause,[],[f239]) ).
fof(f242,definition,
( spl16_7
<=> in(sK12,relation_dom(relation_dom_restriction(sK13,sK11))) ),
introduced(definition,[new_symbols(definition,[spl16_7])],[avatar_definition]) ).
fof(f243,plain,
( ~ in(sK12,relation_dom(relation_dom_restriction(sK13,sK11)))
| spl16_7 ),
inference(avatar_component_clause,[],[f242]) ).
fof(f244,plain,
( ~ spl16_3
| ~ spl16_4
| ~ spl16_5
| ~ spl16_6
| ~ spl16_7 ),
inference(avatar_split_clause,[],[f228,f242,f239,f236,f233,f230]) ).
fof(f245,plain,
( ~ relation(sK13)
| ~ function(sK13)
| spl16_3 ),
inference(resolution,[],[f231,f121]) ).
fof(f247,plain,
( ~ spl16_5
| ~ spl16_6
| spl16_3 ),
inference(avatar_split_clause,[],[f245,f230,f239,f236]) ).
fof(f248,plain,
( $false
| spl16_5 ),
inference(resolution,[],[f237,f145]) ).
fof(f250,plain,
spl16_5,
inference(avatar_contradiction_clause,[],[f248]) ).
fof(f251,plain,
( $false
| spl16_6 ),
inference(resolution,[],[f240,f146]) ).
fof(f252,plain,
spl16_6,
inference(avatar_contradiction_clause,[],[f251]) ).
fof(f253,plain,
( ~ relation(sK13)
| spl16_4 ),
inference(resolution,[],[f234,f120]) ).
fof(f254,plain,
( ~ spl16_6
| spl16_4 ),
inference(avatar_split_clause,[],[f253,f233,f239]) ).
fof(f255,plain,
( $false
| spl16_7 ),
inference(resolution,[],[f243,f147]) ).
fof(f256,plain,
spl16_7,
inference(avatar_contradiction_clause,[],[f255]) ).
cnf(s3,plain,
( ~ spl16_3
| ~ spl16_4
| ~ spl16_5
| ~ spl16_6
| ~ spl16_7 ),
inference(sat_conversion,[],[f244]) ).
cnf(s4,plain,
( spl16_3
| ~ spl16_5
| ~ spl16_6 ),
inference(sat_conversion,[],[f247]) ).
cnf(s5,plain,
spl16_5,
inference(sat_conversion,[],[f250]) ).
cnf(s6,plain,
spl16_6,
inference(sat_conversion,[],[f252]) ).
cnf(s7,plain,
( spl16_4
| ~ spl16_6 ),
inference(sat_conversion,[],[f254]) ).
cnf(s8,plain,
spl16_7,
inference(sat_conversion,[],[f256]) ).
cnf(s9,plain,
spl16_4,
inference(rat,[],[s7,s6]) ).
cnf(s10,plain,
spl16_3,
inference(rat,[],[s4,s6,s5]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s3,s8,s6,s5,s9,s10]) ).
fof(f257,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU223+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 % Computer : n015.cluster.edu
% 0.13/0.41 % Model : x86_64 x86_64
% 0.13/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.41 % Memory : 8046.5625MB
% 0.13/0.41 % OS : Linux 6.8.0-71-generic
% 0.13/0.41 % CPULimit : 300
% 0.13/0.41 % WCLimit : 300
% 0.13/0.41 % DateTime : Mon Sep 28 04:12:32 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.45 Running first-order theorem proving
% 0.13/0.45 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
% 2.18/1.16 % (2249049)Detected formulas, will run a generic FOF schedule.
% 2.18/1.16 % (2249060)dis-21_1_sil=8000:lcm=predicate:random_seed=2040459201: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)
% 2.18/1.16 % (2249060)First to succeed.
% 2.18/1.16 % (2249060)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2249049"
% 2.18/1.16 % (2249056)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=2108044228:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.18/1.16 % (2249059)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3915517055:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.18/1.16 % (2249058)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3075047838:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.18/1.16 % (2249054)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=2404162340:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.18/1.16 % (2249057)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=103517474:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.18/1.16 % (2249055)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=2379050080:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.18/1.16 % (2249057)Also succeeded, but the first one will report.
% 2.18/1.16 % (2249058)Also succeeded, but the first one will report.
% 2.18/1.16 % (2249059)Also succeeded, but the first one will report.
% 2.18/1.16 % (2249060)Refutation found. Thanks to Tanya!
% 2.18/1.16 % SZS status Theorem for theBenchmark
% 2.18/1.16 % SZS output start Proof for theBenchmark
% See solution above
% 2.56/1.36 % (2249060)------------------------------
% 2.56/1.36 % (2249060)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.56/1.36 % (2249060)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/1.36 % (2249060)CaDiCaL version: 2.1.3
% 2.56/1.36 % (2249060)Termination reason: Refutation
% 2.56/1.36 % (2249060)Time elapsed: 0.003 s
% 2.56/1.36 % (2249060)Peak memory usage: 89 MB
% 2.56/1.36 % (2249060)Instructions burned: 5 (million)
% 2.56/1.36 % (2249060)------------------------------
% 2.56/1.36 % (2249060)------------------------------
% 2.56/1.36 % (2249049)Success in time 0.275 s
% 2.56/1.36 % Vampire exiting
%------------------------------------------------------------------------------