%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU212+1 : 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 : 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 12:47:45 PM UTC 2026
% Result : Theorem 2.71s 1.26s
% Output : Refutation 3.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 61 ( 7 unt; 3 def)
% Number of atoms : 228 ( 44 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 265 ( 98 ~; 106 |; 38 &)
% ( 15 <=>; 6 =>; 0 <=; 2 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 83 ( 0 sgn 63 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1,X2] :
( ( in(X1,relation_dom(X0))
=> ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) ) )
& ( ~ in(X1,relation_dom(X0))
=> ( X2 = apply(X0,X1)
<=> X2 = empty_set ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f35,conjecture,
! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( in(ordered_pair(X0,X1),X2)
<=> ( in(X0,relation_dom(X2))
& X1 = apply(X2,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_funct_1) ).
fof(f36,negated_conjecture,
~ ! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( in(ordered_pair(X0,X1),X2)
<=> ( in(X0,relation_dom(X2))
& X1 = apply(X2,X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f42,plain,
! [X0] :
( ! [X1,X2] :
( ( ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) )
| ~ in(X1,relation_dom(X0)) )
& ( ( X2 = apply(X0,X1)
<=> X2 = empty_set )
| in(X1,relation_dom(X0)) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f43,plain,
! [X0] :
( ! [X1,X2] :
( ( ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) )
| ~ in(X1,relation_dom(X0)) )
& ( ( X2 = apply(X0,X1)
<=> X2 = empty_set )
| in(X1,relation_dom(X0)) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f42]) ).
fof(f44,plain,
! [X0] :
( ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f54,plain,
? [X0,X1,X2] :
( ( in(ordered_pair(X0,X1),X2)
<~> ( in(X0,relation_dom(X2))
& X1 = apply(X2,X0) ) )
& relation(X2)
& function(X2) ),
inference(ennf_transformation,[],[f36]) ).
fof(f55,plain,
? [X0,X1,X2] :
( ( in(ordered_pair(X0,X1),X2)
<~> ( in(X0,relation_dom(X2))
& X1 = apply(X2,X0) ) )
& relation(X2)
& function(X2) ),
inference(flattening,[],[f54]) ).
fof(f56,plain,
! [X0] :
( ! [X1,X2] :
( ( ( ( X2 = apply(X0,X1)
| ~ in(ordered_pair(X1,X2),X0) )
& ( in(ordered_pair(X1,X2),X0)
| apply(X0,X1) != X2 ) )
| ~ in(X1,relation_dom(X0)) )
& ( ( ( X2 = apply(X0,X1)
| empty_set != X2 )
& ( X2 = empty_set
| apply(X0,X1) != X2 ) )
| in(X1,relation_dom(X0)) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f43]) ).
fof(f57,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f44]) ).
fof(f58,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( ? [X7] : in(ordered_pair(X5,X7),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f57]) ).
fof(f59,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ( ( ! [X3] : ~ in(ordered_pair(sK0(X0,X1),X3),X0)
| ~ in(sK0(X0,X1),X1) )
& ( in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0)
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK2(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X2,sK0(X0,X1)),skolemize(X4,sK1(X0,X1)),skolemize(X7,sK2(X0,X5))],[f58]) ).
fof(f67,plain,
? [X0,X1,X2] :
( ( ~ in(X0,relation_dom(X2))
| apply(X2,X0) != X1
| ~ in(ordered_pair(X0,X1),X2) )
& ( ( in(X0,relation_dom(X2))
& X1 = apply(X2,X0) )
| in(ordered_pair(X0,X1),X2) )
& relation(X2)
& function(X2) ),
inference(nnf_transformation,[],[f55]) ).
fof(f68,plain,
? [X0,X1,X2] :
( ( ~ in(X0,relation_dom(X2))
| apply(X2,X0) != X1
| ~ in(ordered_pair(X0,X1),X2) )
& ( ( in(X0,relation_dom(X2))
& X1 = apply(X2,X0) )
| in(ordered_pair(X0,X1),X2) )
& relation(X2)
& function(X2) ),
inference(flattening,[],[f67]) ).
fof(f69,plain,
( ( ~ in(sK10,relation_dom(sK12))
| sK11 != apply(sK12,sK10)
| ~ in(ordered_pair(sK10,sK11),sK12) )
& ( ( in(sK10,relation_dom(sK12))
& sK11 = apply(sK12,sK10) )
| in(ordered_pair(sK10,sK11),sK12) )
& relation(sK12)
& function(sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12]),skolemize(X0,sK10),skolemize(X1,sK11),skolemize(X2,sK12)],[f68]) ).
fof(f76,plain,
! [X2,X0,X1] :
( in(ordered_pair(X1,X2),X0)
| apply(X0,X1) != X2
| ~ in(X1,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f77,plain,
! [X2,X0,X1] :
( apply(X0,X1) = X2
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(X1,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f79,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X5,X6),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f109,plain,
function(sK12),
inference(cnf_transformation,[],[f69]) ).
fof(f110,plain,
relation(sK12),
inference(cnf_transformation,[],[f69]) ).
fof(f111,plain,
( sK11 = apply(sK12,sK10)
| in(ordered_pair(sK10,sK11),sK12) ),
inference(cnf_transformation,[],[f69]) ).
fof(f112,plain,
( in(sK10,relation_dom(sK12))
| in(ordered_pair(sK10,sK11),sK12) ),
inference(cnf_transformation,[],[f69]) ).
fof(f113,plain,
( ~ in(sK10,relation_dom(sK12))
| sK11 != apply(sK12,sK10)
| ~ in(ordered_pair(sK10,sK11),sK12) ),
inference(cnf_transformation,[],[f69]) ).
fof(f114,plain,
! [X0,X1] :
( ~ function(X0)
| ~ in(X1,relation_dom(X0))
| ~ relation(X0)
| in(ordered_pair(X1,apply(X0,X1)),X0) ),
inference(equality_resolution,[],[f76]) ).
fof(f117,plain,
! [X0,X6,X5] :
( ~ in(ordered_pair(X5,X6),X0)
| in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f79]) ).
fof(f120,definition,
( spl13_1
<=> in(ordered_pair(sK10,sK11),sK12) ),
introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition]) ).
fof(f121,plain,
( ~ in(ordered_pair(sK10,sK11),sK12)
| spl13_1 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f122,plain,
( in(ordered_pair(sK10,sK11),sK12)
| ~ spl13_1 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f124,definition,
( spl13_2
<=> sK11 = apply(sK12,sK10) ),
introduced(definition,[new_symbols(definition,[spl13_2])],[avatar_definition]) ).
fof(f126,plain,
( sK11 = apply(sK12,sK10)
| ~ spl13_2 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f127,plain,
( spl13_1
| spl13_2 ),
inference(avatar_split_clause,[],[f111,f124,f120]) ).
fof(f129,definition,
( spl13_3
<=> in(sK10,relation_dom(sK12)) ),
introduced(definition,[new_symbols(definition,[spl13_3])],[avatar_definition]) ).
fof(f131,plain,
( in(sK10,relation_dom(sK12))
| ~ spl13_3 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f132,plain,
( spl13_1
| spl13_3 ),
inference(avatar_split_clause,[],[f112,f129,f120]) ).
fof(f133,plain,
( ~ spl13_1
| ~ spl13_2
| ~ spl13_3 ),
inference(avatar_split_clause,[],[f113,f129,f124,f120]) ).
fof(f198,plain,
! [X0] :
( ~ in(X0,relation_dom(sK12))
| ~ relation(sK12)
| in(ordered_pair(X0,apply(sK12,X0)),sK12) ),
inference(resolution,[],[f114,f109]) ).
fof(f203,plain,
! [X0] :
( ~ in(X0,relation_dom(sK12))
| in(ordered_pair(X0,apply(sK12,X0)),sK12) ),
inference(forward_subsumption_resolution,[],[f198,f110]) ).
fof(f204,plain,
( in(ordered_pair(sK10,apply(sK12,sK10)),sK12)
| ~ spl13_3 ),
inference(resolution,[],[f203,f131]) ).
fof(f216,plain,
( in(ordered_pair(sK10,sK11),sK12)
| ~ spl13_2
| ~ spl13_3 ),
inference(forward_demodulation,[],[f204,f126]) ).
fof(f217,plain,
( $false
| spl13_1
| ~ spl13_2
| ~ spl13_3 ),
inference(forward_subsumption_resolution,[],[f216,f121]) ).
fof(f218,plain,
( spl13_1
| ~ spl13_2
| ~ spl13_3 ),
inference(avatar_contradiction_clause,[],[f217]) ).
fof(f219,plain,
( in(sK10,relation_dom(sK12))
| ~ relation(sK12)
| ~ spl13_1 ),
inference(resolution,[],[f122,f117]) ).
fof(f225,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ in(ordered_pair(X1,X2),X0)
| ~ relation(X0)
| apply(X0,X1) = X2 ),
inference(forward_subsumption_resolution,[],[f77,f117]) ).
fof(f230,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,X1),sK12)
| ~ relation(sK12)
| apply(sK12,X0) = X1 ),
inference(resolution,[],[f225,f109]) ).
fof(f234,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,X1),sK12)
| apply(sK12,X0) = X1 ),
inference(forward_subsumption_resolution,[],[f230,f110]) ).
fof(f236,plain,
( sK11 = apply(sK12,sK10)
| ~ spl13_1 ),
inference(resolution,[],[f234,f122]) ).
fof(f251,plain,
( in(sK10,relation_dom(sK12))
| ~ spl13_1 ),
inference(forward_subsumption_resolution,[],[f219,f110]) ).
fof(f253,plain,
( spl13_2
| ~ spl13_1 ),
inference(avatar_split_clause,[],[f236,f120,f124]) ).
fof(f254,plain,
( spl13_3
| ~ spl13_1 ),
inference(avatar_split_clause,[],[f251,f120,f129]) ).
cnf(s1,plain,
( spl13_1
| spl13_2 ),
inference(sat_conversion,[],[f127]) ).
cnf(s2,plain,
( spl13_1
| spl13_3 ),
inference(sat_conversion,[],[f132]) ).
cnf(s3,plain,
( ~ spl13_1
| ~ spl13_2
| ~ spl13_3 ),
inference(sat_conversion,[],[f133]) ).
cnf(s5,plain,
( spl13_1
| ~ spl13_2
| ~ spl13_3 ),
inference(sat_conversion,[],[f218]) ).
cnf(s9,plain,
( ~ spl13_1
| spl13_2 ),
inference(sat_conversion,[],[f253]) ).
cnf(s10,plain,
( ~ spl13_1
| spl13_3 ),
inference(sat_conversion,[],[f254]) ).
cnf(s11,plain,
spl13_1,
inference(rat,[],[s5,s1,s2]) ).
cnf(s12,plain,
spl13_3,
inference(rat,[],[s10,s11]) ).
cnf(s13,plain,
spl13_2,
inference(rat,[],[s9,s11]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s3,s12,s13,s11]) ).
fof(f255,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU212+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n011.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 04:04:16 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 2.71/1.26 % (3008886)Detected formulas, will run a generic FOF schedule.
% 2.71/1.26 % (3008893)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=775376672:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.71/1.26 % (3008896)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=792673405:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.71/1.26 % (3008891)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=765143615:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.71/1.26 % (3008895)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=580008662:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.71/1.26 % (3008892)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=1398391511:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.71/1.26 % (3008894)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3888552237:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.71/1.26 % (3008896)First to succeed.
% 2.71/1.26 % (3008896)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3008886"
% 2.71/1.26 % (3008894)Also succeeded, but the first one will report.
% 2.71/1.26 % (3008895)Also succeeded, but the first one will report.
% 2.71/1.26 % (3008897)dis-21_1_sil=8000:lcm=predicate:random_seed=383476585: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)
% 2.71/1.26 % (3008897)Instruction limit reached!
% 2.71/1.26 % (3008897)------------------------------
% 2.71/1.26 % (3008897)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.71/1.26 % (3008897)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/1.26 % (3008897)CaDiCaL version: 2.1.3
% 2.71/1.26 % (3008897)Termination reason: Instruction limit
% 2.71/1.26 % (3008897)Termination phase: Saturation
% 2.71/1.26 % (3008897)Time elapsed: 0.062 s
% 2.71/1.26 % (3008897)Peak memory usage: 88 MB
% 2.71/1.26 % (3008897)Instructions burned: 130 (million)
% 2.71/1.26 % (3008905)lrs+10_1_sil=8000:sp=occurrence:random_seed=2380883477:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.71/1.26 % (3008905)Also succeeded, but the first one will report.
% 2.71/1.26 % (3008896)Refutation found. Thanks to Tanya!
% 2.71/1.26 % SZS status Theorem for theBenchmark
% 2.71/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 3.49/1.46 % (3008896)------------------------------
% 3.49/1.46 % (3008896)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.46 % (3008896)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.46 % (3008896)CaDiCaL version: 2.1.3
% 3.49/1.46 % (3008896)Termination reason: Refutation
% 3.49/1.46 % (3008896)Time elapsed: 0.009 s
% 3.49/1.46 % (3008896)Peak memory usage: 90 MB
% 3.49/1.46 % (3008896)Instructions burned: 8 (million)
% 3.49/1.46 % (3008896)------------------------------
% 3.49/1.46 % (3008896)------------------------------
% 3.49/1.46 % (3008886)Success in time 0.408 s
% 3.49/1.46 % Vampire exiting
%------------------------------------------------------------------------------