%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU008+1 : 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 : n019.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 12:51:46 PM UTC 2026
% Result : Theorem 0.15s 0.51s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 47 ( 16 unt; 0 def)
% Number of atoms : 144 ( 40 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 148 ( 51 ~; 67 |; 16 &)
% ( 5 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 81 ( 75 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& in(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f7,axiom,
! [X0] : relation(identity_relation(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(f15,axiom,
! [X0] :
( relation(identity_relation(X0))
& function(identity_relation(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(f31,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X0,relation_dom(X1))
=> apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_1) ).
fof(f34,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( X1 = identity_relation(X0)
<=> ( relation_dom(X1) = X0
& ! [X2] :
( in(X2,X0)
=> apply(X1,X2) = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_1) ).
fof(f35,conjecture,
! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X1,set_intersection2(relation_dom(X2),X0))
=> apply(X2,X1) = apply(relation_composition(identity_relation(X0),X2),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_funct_1) ).
fof(f36,negated_conjecture,
~ ! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X1,set_intersection2(relation_dom(X2),X0))
=> apply(X2,X1) = apply(relation_composition(identity_relation(X0),X2),X1) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f66,plain,
! [X0,X1] :
( ! [X2] :
( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f67,plain,
! [X0,X1] :
( ! [X2] :
( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f66]) ).
fof(f70,plain,
! [X0,X1] :
( ( X1 = identity_relation(X0)
<=> ( relation_dom(X1) = X0
& ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) ) ) )
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f71,plain,
! [X0,X1] :
( ( X1 = identity_relation(X0)
<=> ( relation_dom(X1) = X0
& ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) ) ) )
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f70]) ).
fof(f72,plain,
? [X0,X1,X2] :
( apply(X2,X1) != apply(relation_composition(identity_relation(X0),X2),X1)
& in(X1,set_intersection2(relation_dom(X2),X0))
& relation(X2)
& function(X2) ),
inference(ennf_transformation,[],[f36]) ).
fof(f73,plain,
? [X0,X1,X2] :
( apply(X2,X1) != apply(relation_composition(identity_relation(X0),X2),X1)
& in(X1,set_intersection2(relation_dom(X2),X0))
& relation(X2)
& function(X2) ),
inference(flattening,[],[f72]) ).
fof(f88,plain,
! [X2,X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f5]) ).
fof(f92,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f103,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f128,plain,
! [X2,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X0,relation_dom(X1))
| apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ),
inference(cnf_transformation,[],[f67]) ).
fof(f133,plain,
! [X2,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ in(X2,X0)
| apply(X1,X2) = X2
| identity_relation(X0) != X1 ),
inference(cnf_transformation,[],[f71]) ).
fof(f134,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| relation_dom(X1) = X0
| identity_relation(X0) != X1 ),
inference(cnf_transformation,[],[f71]) ).
fof(f135,plain,
function(sK13),
inference(cnf_transformation,[],[f73]) ).
fof(f136,plain,
relation(sK13),
inference(cnf_transformation,[],[f73]) ).
fof(f137,plain,
in(sK12,set_intersection2(relation_dom(sK13),sK11)),
inference(cnf_transformation,[],[f73]) ).
fof(f138,plain,
apply(sK13,sK12) != apply(relation_composition(identity_relation(sK11),sK13),sK12),
inference(cnf_transformation,[],[f73]) ).
fof(f147,plain,
! [X3,X0,X1] :
( ~ in(X3,set_intersection2(X0,X1))
| in(X3,X1) ),
inference(equality_resolution,[],[f88]) ).
fof(f148,plain,
! [X0] :
( ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| relation_dom(identity_relation(X0)) = X0 ),
inference(equality_resolution,[],[f134]) ).
fof(f149,plain,
! [X2,X0] :
( ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(X2,X0)
| apply(identity_relation(X0),X2) = X2 ),
inference(equality_resolution,[],[f133]) ).
fof(f155,plain,
! [X0] : ~ relation(identity_relation(X0)),
inference(consistent_polarity_flipping,[],[f92]) ).
fof(f167,plain,
! [X0] : ~ function(identity_relation(X0)),
inference(consistent_polarity_flipping,[],[f103]) ).
fof(f189,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_dom(X1))
| relation(X1)
| function(X2)
| relation(X2)
| function(X1)
| apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ),
inference(consistent_polarity_flipping,[],[f128]) ).
fof(f191,plain,
! [X0] :
( function(identity_relation(X0))
| relation(identity_relation(X0))
| relation_dom(identity_relation(X0)) = X0 ),
inference(consistent_polarity_flipping,[],[f148]) ).
fof(f192,plain,
! [X2,X0] :
( function(identity_relation(X0))
| relation(identity_relation(X0))
| ~ in(X2,X0)
| apply(identity_relation(X0),X2) = X2 ),
inference(consistent_polarity_flipping,[],[f149]) ).
fof(f195,plain,
~ relation(sK13),
inference(consistent_polarity_flipping,[],[f136]) ).
fof(f196,plain,
~ function(sK13),
inference(consistent_polarity_flipping,[],[f135]) ).
fof(f237,plain,
in(sK12,sK11),
inference(resolution,[],[f147,f137]) ).
fof(f274,plain,
! [X0] :
( relation(identity_relation(X0))
| relation_dom(identity_relation(X0)) = X0 ),
inference(forward_subsumption_resolution,[],[f191,f167]) ).
fof(f275,plain,
! [X0] : relation_dom(identity_relation(X0)) = X0,
inference(forward_subsumption_resolution,[],[f274,f155]) ).
fof(f280,plain,
! [X2,X0] :
( relation(identity_relation(X0))
| ~ in(X2,X0)
| apply(identity_relation(X0),X2) = X2 ),
inference(forward_subsumption_resolution,[],[f192,f167]) ).
fof(f281,plain,
! [X2,X0] :
( ~ in(X2,X0)
| apply(identity_relation(X0),X2) = X2 ),
inference(forward_subsumption_resolution,[],[f280,f155]) ).
fof(f284,plain,
sK12 = apply(identity_relation(sK11),sK12),
inference(resolution,[],[f281,f237]) ).
fof(f338,plain,
! [X2,X0,X1] :
( ~ in(X1,X0)
| relation(identity_relation(X0))
| function(X2)
| relation(X2)
| function(identity_relation(X0))
| apply(relation_composition(identity_relation(X0),X2),X1) = apply(X2,apply(identity_relation(X0),X1)) ),
inference(superposition,[],[f189,f275]) ).
fof(f340,plain,
! [X2,X0,X1] :
( ~ in(X1,X0)
| function(X2)
| relation(X2)
| function(identity_relation(X0))
| apply(relation_composition(identity_relation(X0),X2),X1) = apply(X2,apply(identity_relation(X0),X1)) ),
inference(forward_subsumption_resolution,[],[f338,f155]) ).
fof(f342,plain,
! [X2,X0,X1] :
( ~ in(X1,X0)
| function(X2)
| relation(X2)
| apply(relation_composition(identity_relation(X0),X2),X1) = apply(X2,apply(identity_relation(X0),X1)) ),
inference(forward_subsumption_resolution,[],[f340,f167]) ).
fof(f804,plain,
! [X0] :
( function(X0)
| relation(X0)
| apply(relation_composition(identity_relation(sK11),X0),sK12) = apply(X0,apply(identity_relation(sK11),sK12)) ),
inference(resolution,[],[f342,f237]) ).
fof(f805,plain,
! [X0] :
( function(X0)
| apply(relation_composition(identity_relation(sK11),X0),sK12) = apply(X0,sK12)
| relation(X0) ),
inference(forward_demodulation,[],[f804,f284]) ).
fof(f1810,plain,
( apply(sK13,sK12) = apply(relation_composition(identity_relation(sK11),sK13),sK12)
| relation(sK13) ),
inference(resolution,[],[f805,f196]) ).
fof(f1811,plain,
relation(sK13),
inference(forward_subsumption_resolution,[],[f1810,f138]) ).
fof(f1816,plain,
$false,
inference(forward_subsumption_resolution,[],[f1811,f195]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU008+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n019.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
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 03:21:48 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 0.15/0.51 % (3630934)Will run a generic schedule for satisfiability detection.
% 0.15/0.51 % (3630941)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1283357847:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.51 % (3630940)% WARNING: option uhcvi not known.
% 0.15/0.51 % (3630942)dis+10_1_sil=32000:sp=arity:random_seed=3600400806:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.51 % (3630939)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=952488651_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.51 % (3630940)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1320747284:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.51 % (3630944)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3889965923:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.51 % (3630943)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=584659470:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.51 % (3630945)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3605947957:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.51 % TRYING [1]
% 0.15/0.51 % TRYING [2]
% 0.15/0.51 % TRYING [3]
% 0.15/0.51 % TRYING [4]
% 0.15/0.51 % TRYING [5]
% 0.15/0.51 % (3630940) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3630934-3630940"...
% 0.15/0.51 % TRYING [6]
% 0.15/0.51 % (3630940)...printing done.
% 0.15/0.51 % (3630940)Refutation found. Thanks to Tanya!
% 0.15/0.51 % SZS status Theorem for theBenchmark
% 0.15/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.51 % (3630940)------------------------------
% 0.15/0.51 % (3630940)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.51 % (3630940)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.51 % (3630940)CaDiCaL version: 2.1.3
% 0.15/0.51 % (3630940)Termination reason: Refutation
% 0.15/0.51 % (3630940)Time elapsed: 0.048 s
% 0.15/0.51 % (3630940)Peak memory usage: 12 MB
% 0.15/0.51 % (3630940)Instructions burned: 77 (million)
% 0.15/0.51 % (3630934)Success in time 0.087 s
% 0.15/0.51 % Vampire exiting
%------------------------------------------------------------------------------