%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU217+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 12:47:48 PM UTC 2026
% Result : Theorem 5.45s 1.98s
% Output : Refutation 5.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 8 unt; 1 def)
% Number of atoms : 94 ( 41 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 120 ( 51 ~; 43 |; 19 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 38 ( 33 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f24,axiom,
! [X0] :
( relation(identity_relation(X0))
& function(identity_relation(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(f27,conjecture,
! [X0,X1] :
( in(X1,X0)
=> apply(identity_relation(X0),X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_funct_1) ).
fof(f28,negated_conjecture,
~ ! [X0,X1] :
( in(X1,X0)
=> apply(identity_relation(X0),X1) = X1 ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,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(f33,plain,
? [X0,X1] :
( apply(identity_relation(X0),X1) != X1
& in(X1,X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f34,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,[],[f29]) ).
fof(f35,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,[],[f34]) ).
fof(f37,plain,
( sK1 != apply(identity_relation(sK0),sK1)
& in(sK1,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f33]) ).
fof(f38,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,[],[f35]) ).
fof(f39,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,[],[f38]) ).
fof(f40,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,[],[f39]) ).
fof(f41,plain,
! [X0,X1] :
( ( ( X1 = identity_relation(X0)
| relation_dom(X1) != X0
| ( sK2(X0,X1) != apply(X1,sK2(X0,X1))
& in(sK2(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,[sK2]),skolemize(X2,sK2(X0,X1))],[f40]) ).
fof(f42,plain,
in(sK1,sK0),
inference(cnf_transformation,[],[f37]) ).
fof(f43,plain,
sK1 != apply(identity_relation(sK0),sK1),
inference(cnf_transformation,[],[f37]) ).
fof(f44,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f24]) ).
fof(f45,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f24]) ).
fof(f47,plain,
! [X3,X0,X1] :
( apply(X1,X3) = X3
| ~ in(X3,X0)
| identity_relation(X0) != X1
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f52,definition,
~ sP3(sK1),
introduced(definition,[new_symbols(definition,[sP3])],[inequality_splitting_name_introduction]) ).
fof(f53,plain,
sP3(apply(identity_relation(sK0),sK1)),
inference(inequality_splitting,[],[f43,f52]) ).
fof(f57,plain,
! [X3,X0] :
( apply(identity_relation(X0),X3) = X3
| ~ in(X3,X0)
| ~ relation(identity_relation(X0))
| ~ function(identity_relation(X0)) ),
inference(equality_resolution,[],[f47]) ).
fof(f59,plain,
( sP3(sK1)
| ~ in(sK1,sK0)
| ~ relation(identity_relation(sK0))
| ~ function(identity_relation(sK0)) ),
inference(superposition,[],[f53,f57]) ).
fof(f60,plain,
( ~ in(sK1,sK0)
| ~ relation(identity_relation(sK0))
| ~ function(identity_relation(sK0)) ),
inference(forward_subsumption_resolution,[],[f59,f52]) ).
fof(f61,plain,
( ~ relation(identity_relation(sK0))
| ~ function(identity_relation(sK0)) ),
inference(forward_subsumption_resolution,[],[f60,f42]) ).
fof(f62,plain,
~ function(identity_relation(sK0)),
inference(forward_subsumption_resolution,[],[f61,f45]) ).
fof(f63,plain,
$false,
inference(forward_subsumption_resolution,[],[f62,f44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU217+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 % Computer : n013.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Mon Sep 28 04:05:21 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.45 Running first-order theorem proving
% 0.15/0.45 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.45/1.98 % (791308)Detected formulas, will run a generic FOF schedule.
% 5.45/1.98 % (791316)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=747689630:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.45/1.98 % (791318)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4135413736:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.45/1.98 % (791318)First to succeed.
% 5.45/1.98 % (791318)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-791308"
% 5.45/1.98 % (791315)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=32897791:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.45/1.98 % (791317)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=3181533065:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.45/1.98 % (791320)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2832751653:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.45/1.98 % (791321)dis-21_1_sil=8000:lcm=predicate:random_seed=1761401996: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)
% 5.45/1.98 % (791319)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=810604011:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.45/1.98 % (791319)Also succeeded, but the first one will report.
% 5.45/1.98 % (791320)Also succeeded, but the first one will report.
% 5.45/1.98 % (791321)Also succeeded, but the first one will report.
% 5.45/1.98 % (791318)Refutation found. Thanks to Tanya!
% 5.45/1.98 % SZS status Theorem for theBenchmark
% 5.45/1.98 % SZS output start Proof for theBenchmark
% See solution above
% 5.45/1.98 % (791318)------------------------------
% 5.45/1.98 % (791318)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.45/1.98 % (791318)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.45/1.98 % (791318)CaDiCaL version: 2.1.3
% 5.45/1.98 % (791318)Termination reason: Refutation
% 5.45/1.98 % (791318)Time elapsed: 0.004 s
% 5.45/1.98 % (791318)Peak memory usage: 89 MB
% 5.45/1.98 % (791318)Instructions burned: 1 (million)
% 5.45/1.98 % (791318)------------------------------
% 5.45/1.98 % (791318)------------------------------
% 5.45/1.98 % (791308)Success in time 0.648 s
% 5.45/1.98 % Vampire exiting
%------------------------------------------------------------------------------