%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU217+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 3.04s 1.41s
% Output : Refutation 3.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 8 unt; 1 def)
% Number of atoms : 92 ( 43 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 114 ( 47 ~; 41 |; 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 : 42 ( 37 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f78,axiom,
! [X0] :
( relation(identity_relation(X0))
& function(identity_relation(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(f164,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(f165,conjecture,
! [X0,X1] :
( in(X1,X0)
=> apply(identity_relation(X0),X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_funct_1) ).
fof(f166,negated_conjecture,
~ ! [X0,X1] :
( in(X1,X0)
=> apply(identity_relation(X0),X1) = X1 ),
inference(negated_conjecture,[status(cth)],[f165]) ).
fof(f288,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,[],[f164]) ).
fof(f289,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,[],[f288]) ).
fof(f290,plain,
? [X0,X1] :
( apply(identity_relation(X0),X1) != X1
& in(X1,X0) ),
inference(ennf_transformation,[],[f166]) ).
fof(f429,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,[],[f289]) ).
fof(f430,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,[],[f429]) ).
fof(f431,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,[],[f430]) ).
fof(f432,plain,
! [X0,X1] :
( ( ( X1 = identity_relation(X0)
| relation_dom(X1) != X0
| ( sK4(X0,X1) != apply(X1,sK4(X0,X1))
& in(sK4(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,[sK4]),skolemize(X2,sK4(X0,X1))],[f431]) ).
fof(f433,plain,
( sK6 != apply(identity_relation(sK5),sK6)
& in(sK6,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X0,sK5),skolemize(X1,sK6)],[f290]) ).
fof(f618,plain,
! [X3,X0,X1] :
( apply(X1,X3) = X3
| ~ in(X3,X0)
| identity_relation(X0) != X1
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f432]) ).
fof(f622,plain,
in(sK6,sK5),
inference(cnf_transformation,[],[f433]) ).
fof(f623,plain,
sK6 != apply(identity_relation(sK5),sK6),
inference(cnf_transformation,[],[f433]) ).
fof(f868,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f78]) ).
fof(f869,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f78]) ).
fof(f1043,definition,
~ sP70(sK6),
introduced(definition,[new_symbols(definition,[sP70])],[inequality_splitting_name_introduction]) ).
fof(f1044,plain,
sP70(apply(identity_relation(sK5),sK6)),
inference(inequality_splitting,[],[f623,f1043]) ).
fof(f1069,plain,
! [X3,X0] :
( apply(identity_relation(X0),X3) = X3
| ~ in(X3,X0)
| ~ relation(identity_relation(X0))
| ~ function(identity_relation(X0)) ),
inference(equality_resolution,[],[f618]) ).
fof(f1183,plain,
! [X3,X0] :
( apply(identity_relation(X0),X3) = X3
| ~ in(X3,X0)
| ~ function(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[],[f1069,f869]) ).
fof(f1198,plain,
! [X3,X0] :
( apply(identity_relation(X0),X3) = X3
| ~ in(X3,X0) ),
inference(forward_subsumption_resolution,[],[f1183,f868]) ).
fof(f2272,plain,
( sP70(sK6)
| ~ in(sK6,sK5) ),
inference(superposition,[],[f1044,f1198]) ).
fof(f2277,plain,
~ in(sK6,sK5),
inference(forward_subsumption_resolution,[],[f2272,f1043]) ).
fof(f2282,plain,
$false,
inference(forward_subsumption_resolution,[],[f2277,f622]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU217+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n008.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Mon Sep 28 04:06:54 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.04/1.41 % (1857816)Detected formulas, will run a generic FOF schedule.
% 3.04/1.41 % (1857925)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2975507434:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.04/1.41 % (1857925)First to succeed.
% 3.04/1.41 % (1857925)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1857816"
% 3.04/1.41 % (1857922)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=2079021932:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.04/1.41 % (1857923)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=921492264:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.04/1.41 % (1857924)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=3475849725:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.04/1.41 % (1857928)dis-21_1_sil=8000:lcm=predicate:random_seed=1269792536: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)
% 3.04/1.41 % (1857927)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2144864148:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.04/1.41 % (1857926)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=270362788:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.04/1.41 % (1857927)Also succeeded, but the first one will report.
% 3.04/1.41 % (1857928)Instruction limit reached!
% 3.04/1.41 % (1857928)------------------------------
% 3.04/1.41 % (1857928)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.04/1.41 % (1857928)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.04/1.41 % (1857928)CaDiCaL version: 2.1.3
% 3.04/1.41 % (1857928)Termination reason: Instruction limit
% 3.04/1.41 % (1857928)Termination phase: Saturation
% 3.04/1.41 % (1857928)Time elapsed: 0.076 s
% 3.04/1.41 % (1857928)Peak memory usage: 89 MB
% 3.04/1.41 % (1857928)Instructions burned: 129 (million)
% 3.04/1.41 % (1857926)Instruction limit reached!
% 3.04/1.41 % (1857926)------------------------------
% 3.04/1.41 % (1857926)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.04/1.41 % (1857926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.04/1.41 % (1857926)CaDiCaL version: 2.1.3
% 3.04/1.41 % (1857926)Termination reason: Instruction limit
% 3.04/1.41 % (1857926)Termination phase: Saturation
% 3.04/1.41 % (1857926)Time elapsed: 0.088 s
% 3.04/1.41 % (1857926)Peak memory usage: 89 MB
% 3.04/1.41 % (1857926)Instructions burned: 121 (million)
% 3.04/1.41 % (1857925)Refutation found. Thanks to Tanya!
% 3.04/1.41 % SZS status Theorem for theBenchmark
% 3.04/1.41 % SZS output start Proof for theBenchmark
% See solution above
% 3.04/1.41 % (1857925)------------------------------
% 3.04/1.41 % (1857925)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.04/1.41 % (1857925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.04/1.41 % (1857925)CaDiCaL version: 2.1.3
% 3.04/1.41 % (1857925)Termination reason: Refutation
% 3.04/1.41 % (1857925)Time elapsed: 0.025 s
% 3.04/1.41 % (1857925)Peak memory usage: 90 MB
% 3.04/1.41 % (1857925)Instructions burned: 70 (million)
% 3.04/1.41 % (1857925)------------------------------
% 3.04/1.41 % (1857925)------------------------------
% 3.04/1.41 % (1857816)Success in time 0.344 s
% 3.04/1.41 % Vampire exiting
%------------------------------------------------------------------------------