%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU217+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 12:52:26 PM UTC 2026
% Result : Theorem 0.11s 0.44s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 6 unt; 0 def)
% Number of atoms : 88 ( 47 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 110 ( 44 ~; 40 |; 19 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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; 2 con; 0-2 aty)
% Number of variables : 43 ( 38 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f19,axiom,
! [X0] :
( relation(identity_relation(X0))
& function(identity_relation(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(f30,conjecture,
! [X0,X1] :
( in(X1,X0)
=> apply(identity_relation(X0),X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_funct_1) ).
fof(f31,negated_conjecture,
~ ! [X0,X1] :
( in(X1,X0)
=> apply(identity_relation(X0),X1) = X1 ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f32,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/sandbox2/benchmark/theBenchmark.p',t34_funct_1) ).
fof(f54,plain,
? [X0,X1] :
( apply(identity_relation(X0),X1) != X1
& in(X1,X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f55,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,[],[f32]) ).
fof(f56,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,[],[f55]) ).
fof(f66,plain,
( sK10 != apply(identity_relation(sK9),sK10)
& in(sK10,sK9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10]),skolemize(X0,sK9),skolemize(X1,sK10)],[f54]) ).
fof(f67,plain,
! [X0,X1] :
( ( ( X1 = identity_relation(X0)
| relation_dom(X1) != X0
| ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) ) )
& ( ( relation_dom(X1) = X0
& ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) ) )
| identity_relation(X0) != X1 ) )
| ~ relation(X1)
| ~ function(X1) ),
inference(nnf_transformation,[],[f56]) ).
fof(f68,plain,
! [X0,X1] :
( ( ( X1 = identity_relation(X0)
| relation_dom(X1) != X0
| ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) ) )
& ( ( relation_dom(X1) = X0
& ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) ) )
| identity_relation(X0) != X1 ) )
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f67]) ).
fof(f69,plain,
! [X0,X1] :
( ( ( X1 = identity_relation(X0)
| relation_dom(X1) != X0
| ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) ) )
& ( ( relation_dom(X1) = X0
& ! [X3] :
( apply(X1,X3) = X3
| ~ in(X3,X0) ) )
| identity_relation(X0) != X1 ) )
| ~ relation(X1)
| ~ function(X1) ),
inference(rectify,[],[f68]) ).
fof(f70,plain,
! [X0,X1] :
( ( ( X1 = identity_relation(X0)
| relation_dom(X1) != X0
| ( sK11(X0,X1) != apply(X1,sK11(X0,X1))
& in(sK11(X0,X1),X0) ) )
& ( ( relation_dom(X1) = X0
& ! [X3] :
( apply(X1,X3) = X3
| ~ in(X3,X0) ) )
| identity_relation(X0) != X1 ) )
| ~ relation(X1)
| ~ function(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X2,sK11(X0,X1))],[f69]) ).
fof(f92,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f19]) ).
fof(f93,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f19]) ).
fof(f109,plain,
in(sK10,sK9),
inference(cnf_transformation,[],[f66]) ).
fof(f110,plain,
sK10 != apply(identity_relation(sK9),sK10),
inference(cnf_transformation,[],[f66]) ).
fof(f111,plain,
! [X3,X0,X1] :
( ~ function(X1)
| ~ in(X3,X0)
| identity_relation(X0) != X1
| ~ relation(X1)
| apply(X1,X3) = X3 ),
inference(cnf_transformation,[],[f70]) ).
fof(f280,plain,
! [X2,X0,X1] :
( ~ in(X0,X1)
| identity_relation(X1) != identity_relation(X2)
| ~ relation(identity_relation(X2))
| apply(identity_relation(X2),X0) = X0 ),
inference(resolution,[],[f111,f92]) ).
fof(f289,plain,
! [X2,X0,X1] :
( ~ in(X0,X1)
| identity_relation(X1) != identity_relation(X2)
| apply(identity_relation(X2),X0) = X0 ),
inference(forward_subsumption_resolution,[],[f280,f93]) ).
fof(f719,plain,
! [X0] :
( identity_relation(X0) != identity_relation(sK9)
| sK10 = apply(identity_relation(X0),sK10) ),
inference(resolution,[],[f289,f109]) ).
fof(f720,plain,
sK10 = apply(identity_relation(sK9),sK10),
inference(equality_resolution,[],[f719]) ).
fof(f721,plain,
$false,
inference(forward_subsumption_resolution,[],[f720,f110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU217+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 04:07:15 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.44 % (3010522)Will run a generic schedule for satisfiability detection.
% 0.11/0.44 % (3010532)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3889290419:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.44 % (3010528)% WARNING: option uhcvi not known.
% 0.11/0.44 % (3010532) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3010522-3010532"...
% 0.11/0.44 % (3010527)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2216441100_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.44 % (3010533)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3906206433:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.44 % (3010529)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=730514129:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.44 % (3010530)dis+10_1_sil=32000:sp=arity:random_seed=1413260508:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.44 % (3010532)...printing done.
% 0.11/0.44 % (3010531)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1765750848:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.44 % (3010532)Refutation found. Thanks to Tanya!
% 0.11/0.44 % SZS status Theorem for theBenchmark
% 0.11/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.44 % (3010532)------------------------------
% 0.11/0.44 % (3010532)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.44 % (3010532)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.44 % (3010532)CaDiCaL version: 2.1.3
% 0.11/0.44 % (3010532)Termination reason: Refutation
% 0.11/0.44 % (3010532)Time elapsed: 0.007 s
% 0.11/0.44 % (3010532)Peak memory usage: 11 MB
% 0.11/0.44 % (3010532)Instructions burned: 17 (million)
% 0.11/0.44 % (3010522)Success in time 0.032 s
% 0.11/0.44 % Vampire exiting
%------------------------------------------------------------------------------