%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU045+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 : 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 12:51:50 PM UTC 2026
% Result : Theorem 0.15s 0.47s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 31 ( 8 unt; 0 def)
% Number of atoms : 121 ( 22 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 133 ( 43 ~; 46 |; 24 &)
% ( 8 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 64 ( 58 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f19,axiom,
! [X0,X1] :
( relation(X1)
=> relation(relation_rng_restriction(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relat_1) ).
fof(f20,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( relation(relation_rng_restriction(X0,X1))
& function(relation_rng_restriction(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_funct_1) ).
fof(f33,conjecture,
! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X1,relation_dom(relation_rng_restriction(X0,X2)))
=> apply(relation_rng_restriction(X0,X2),X1) = apply(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t87_funct_1) ).
fof(f34,negated_conjecture,
~ ! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X1,relation_dom(relation_rng_restriction(X0,X2)))
=> apply(relation_rng_restriction(X0,X2),X1) = apply(X2,X1) ) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f35,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( X1 = relation_rng_restriction(X0,X2)
<=> ( ! [X3] :
( in(X3,relation_dom(X1))
<=> ( in(X3,relation_dom(X2))
& in(apply(X2,X3),X0) ) )
& ! [X3] :
( in(X3,relation_dom(X1))
=> apply(X1,X3) = apply(X2,X3) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_funct_1) ).
fof(f37,plain,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( X1 = relation_rng_restriction(X0,X2)
<=> ( ! [X3] :
( in(X3,relation_dom(X1))
<=> ( in(X3,relation_dom(X2))
& in(apply(X2,X3),X0) ) )
& ! [X4] :
( in(X4,relation_dom(X1))
=> apply(X2,X4) = apply(X1,X4) ) ) ) ) ),
inference(rectify,[],[f35]) ).
fof(f59,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f19]) ).
fof(f60,plain,
! [X0,X1] :
( ( relation(relation_rng_restriction(X0,X1))
& function(relation_rng_restriction(X0,X1)) )
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f20]) ).
fof(f61,plain,
! [X0,X1] :
( ( relation(relation_rng_restriction(X0,X1))
& function(relation_rng_restriction(X0,X1)) )
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f60]) ).
fof(f65,plain,
? [X0,X1,X2] :
( apply(relation_rng_restriction(X0,X2),X1) != apply(X2,X1)
& in(X1,relation_dom(relation_rng_restriction(X0,X2)))
& relation(X2)
& function(X2) ),
inference(ennf_transformation,[],[f34]) ).
fof(f66,plain,
? [X0,X1,X2] :
( apply(relation_rng_restriction(X0,X2),X1) != apply(X2,X1)
& in(X1,relation_dom(relation_rng_restriction(X0,X2)))
& relation(X2)
& function(X2) ),
inference(flattening,[],[f65]) ).
fof(f67,plain,
! [X0,X1] :
( ! [X2] :
( ( X1 = relation_rng_restriction(X0,X2)
<=> ( ! [X3] :
( in(X3,relation_dom(X1))
<=> ( in(X3,relation_dom(X2))
& in(apply(X2,X3),X0) ) )
& ! [X4] :
( apply(X2,X4) = apply(X1,X4)
| ~ in(X4,relation_dom(X1)) ) ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f68,plain,
! [X0,X1] :
( ! [X2] :
( ( X1 = relation_rng_restriction(X0,X2)
<=> ( ! [X3] :
( in(X3,relation_dom(X1))
<=> ( in(X3,relation_dom(X2))
& in(apply(X2,X3),X0) ) )
& ! [X4] :
( apply(X2,X4) = apply(X1,X4)
| ~ in(X4,relation_dom(X1)) ) ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f67]) ).
fof(f89,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f90,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| function(relation_rng_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f61]) ).
fof(f112,plain,
function(sK13),
inference(cnf_transformation,[],[f66]) ).
fof(f113,plain,
relation(sK13),
inference(cnf_transformation,[],[f66]) ).
fof(f114,plain,
in(sK12,relation_dom(relation_rng_restriction(sK11,sK13))),
inference(cnf_transformation,[],[f66]) ).
fof(f115,plain,
apply(relation_rng_restriction(sK11,sK13),sK12) != apply(sK13,sK12),
inference(cnf_transformation,[],[f66]) ).
fof(f125,plain,
! [X2,X0,X1,X4] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X4,relation_dom(X1))
| apply(X2,X4) = apply(X1,X4)
| relation_rng_restriction(X0,X2) != X1 ),
inference(cnf_transformation,[],[f68]) ).
fof(f126,plain,
! [X2,X0,X4] :
( ~ function(relation_rng_restriction(X0,X2))
| ~ relation(relation_rng_restriction(X0,X2))
| ~ function(X2)
| ~ relation(X2)
| ~ in(X4,relation_dom(relation_rng_restriction(X0,X2)))
| apply(X2,X4) = apply(relation_rng_restriction(X0,X2),X4) ),
inference(equality_resolution,[],[f125]) ).
fof(f146,plain,
! [X0,X1] :
( ~ function(relation_rng_restriction(X0,X1))
| ~ relation(X1)
| function(X1) ),
inference(consistent_polarity_flipping,[],[f90]) ).
fof(f160,plain,
~ in(sK12,relation_dom(relation_rng_restriction(sK11,sK13))),
inference(consistent_polarity_flipping,[],[f114]) ).
fof(f161,plain,
~ function(sK13),
inference(consistent_polarity_flipping,[],[f112]) ).
fof(f162,plain,
! [X2,X0,X4] :
( function(relation_rng_restriction(X0,X2))
| ~ relation(relation_rng_restriction(X0,X2))
| function(X2)
| ~ relation(X2)
| in(X4,relation_dom(relation_rng_restriction(X0,X2)))
| apply(X2,X4) = apply(relation_rng_restriction(X0,X2),X4) ),
inference(consistent_polarity_flipping,[],[f126]) ).
fof(f232,plain,
! [X2,X0,X4] :
( ~ relation(relation_rng_restriction(X0,X2))
| function(X2)
| ~ relation(X2)
| in(X4,relation_dom(relation_rng_restriction(X0,X2)))
| apply(X2,X4) = apply(relation_rng_restriction(X0,X2),X4) ),
inference(forward_subsumption_resolution,[],[f162,f146]) ).
fof(f233,plain,
! [X2,X0,X4] :
( in(X4,relation_dom(relation_rng_restriction(X0,X2)))
| ~ relation(X2)
| function(X2)
| apply(X2,X4) = apply(relation_rng_restriction(X0,X2),X4) ),
inference(forward_subsumption_resolution,[],[f232,f89]) ).
fof(f234,plain,
( ~ relation(sK13)
| function(sK13)
| apply(relation_rng_restriction(sK11,sK13),sK12) = apply(sK13,sK12) ),
inference(resolution,[],[f233,f160]) ).
fof(f236,plain,
( function(sK13)
| apply(relation_rng_restriction(sK11,sK13),sK12) = apply(sK13,sK12) ),
inference(forward_subsumption_resolution,[],[f234,f113]) ).
fof(f237,plain,
apply(relation_rng_restriction(sK11,sK13),sK12) = apply(sK13,sK12),
inference(forward_subsumption_resolution,[],[f236,f161]) ).
fof(f238,plain,
$false,
inference(forward_subsumption_resolution,[],[f237,f115]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU045+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n009.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 03:27:38 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 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
% 0.15/0.47 % (2636442)Will run a generic schedule for satisfiability detection.
% 0.15/0.47 % (2636450)dis+10_1_sil=32000:sp=arity:random_seed=3464905151:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.47 % (2636448)% WARNING: option uhcvi not known.
% 0.15/0.47 % (2636451)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1938811683:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.47 % (2636447)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3270237647_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.47 % (2636448)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=197151609:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.47 % (2636449)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3889330904:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.47 % (2636453)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3613838683:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.47 % (2636452)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1433162253:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.47 % (2636448) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2636442-2636448"...
% 0.15/0.47 % TRYING [1]
% 0.15/0.47 % TRYING [2]
% 0.15/0.47 % (2636448)...printing done.
% 0.15/0.47 % TRYING [3]
% 0.15/0.47 % (2636450) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2636442-2636450"...
% 0.15/0.47 % (2636448)Refutation found. Thanks to Tanya!
% 0.15/0.47 % SZS status Theorem for theBenchmark
% 0.15/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.47 % (2636448)------------------------------
% 0.15/0.47 % (2636448)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.47 % (2636448)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.47 % (2636448)CaDiCaL version: 2.1.3
% 0.15/0.47 % (2636448)Termination reason: Refutation
% 0.15/0.47 % (2636448)Time elapsed: 0.005 s
% 0.15/0.47 % (2636448)Peak memory usage: 12 MB
% 0.15/0.47 % (2636448)Instructions burned: 6 (million)
% 0.15/0.47 % (2636442)Success in time 0.044 s
% 0.15/0.47 % Vampire exiting
%------------------------------------------------------------------------------