%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n018.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 3.33s 1.34s
% Output : Refutation 3.33s
% 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(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(f33,plain,
? [X0,X1] :
( apply(identity_relation(X0),X1) != X1
& in(X1,X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f36,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(f37,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,[],[f36]) ).
fof(f43,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(f44,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,[],[f37]) ).
fof(f45,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,[],[f44]) ).
fof(f46,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,[],[f45]) ).
fof(f47,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))],[f46]) ).
fof(f48,plain,
in(sK1,sK0),
inference(cnf_transformation,[],[f43]) ).
fof(f49,plain,
sK1 != apply(identity_relation(sK0),sK1),
inference(cnf_transformation,[],[f43]) ).
fof(f52,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f19]) ).
fof(f53,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f19]) ).
fof(f55,plain,
! [X3,X0,X1] :
( apply(X1,X3) = X3
| ~ in(X3,X0)
| identity_relation(X0) != X1
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f63,definition,
~ sP3(sK1),
introduced(definition,[new_symbols(definition,[sP3])],[inequality_splitting_name_introduction]) ).
fof(f64,plain,
sP3(apply(identity_relation(sK0),sK1)),
inference(inequality_splitting,[],[f49,f63]) ).
fof(f68,plain,
! [X3,X0] :
( apply(identity_relation(X0),X3) = X3
| ~ in(X3,X0)
| ~ relation(identity_relation(X0))
| ~ function(identity_relation(X0)) ),
inference(equality_resolution,[],[f55]) ).
fof(f70,plain,
( sP3(sK1)
| ~ in(sK1,sK0)
| ~ relation(identity_relation(sK0))
| ~ function(identity_relation(sK0)) ),
inference(superposition,[],[f64,f68]) ).
fof(f71,plain,
( ~ in(sK1,sK0)
| ~ relation(identity_relation(sK0))
| ~ function(identity_relation(sK0)) ),
inference(forward_subsumption_resolution,[],[f70,f63]) ).
fof(f72,plain,
( ~ relation(identity_relation(sK0))
| ~ function(identity_relation(sK0)) ),
inference(forward_subsumption_resolution,[],[f71,f48]) ).
fof(f73,plain,
~ function(identity_relation(sK0)),
inference(forward_subsumption_resolution,[],[f72,f53]) ).
fof(f74,plain,
$false,
inference(forward_subsumption_resolution,[],[f73,f52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU217+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n018.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 04:09:24 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 3.33/1.34 % (2984723)Detected formulas, will run a generic FOF schedule.
% 3.33/1.34 % (2984729)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=439766984:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.33/1.34 % (2984731)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4181222543:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.33/1.34 % (2984732)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2985899912:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.33/1.34 % (2984734)dis-21_1_sil=8000:lcm=predicate:random_seed=2519693530: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)
% 3.33/1.34 % (2984728)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=3324646972:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.33/1.34 % (2984730)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=4267731239:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.33/1.34 % (2984731)First to succeed.
% 3.33/1.34 % (2984732)Also succeeded, but the first one will report.
% 3.33/1.34 % (2984731)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2984723"
% 3.33/1.34 % (2984734)Also succeeded, but the first one will report.
% 3.33/1.34 % (2984733)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3540750599:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.33/1.34 % (2984733)Also succeeded, but the first one will report.
% 3.33/1.34 % (2984731)Refutation found. Thanks to Tanya!
% 3.33/1.34 % SZS status Theorem for theBenchmark
% 3.33/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 3.33/1.34 % (2984731)------------------------------
% 3.33/1.34 % (2984731)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.33/1.34 % (2984731)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.33/1.34 % (2984731)CaDiCaL version: 2.1.3
% 3.33/1.34 % (2984731)Termination reason: Refutation
% 3.33/1.34 % (2984731)Time elapsed: 0.002 s
% 3.33/1.34 % (2984731)Peak memory usage: 88 MB
% 3.33/1.34 % (2984731)Instructions burned: 2 (million)
% 3.33/1.34 % (2984731)------------------------------
% 3.33/1.34 % (2984731)------------------------------
% 3.33/1.34 % (2984723)Success in time 0.402 s
% 3.33/1.34 % Vampire exiting
%------------------------------------------------------------------------------