%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET677+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 12:41:37 PM UTC 2026
% Result : Theorem 2.69s 1.34s
% Output : Refutation 2.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 54 ( 10 unt; 3 def)
% Number of atoms : 165 ( 30 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 188 ( 77 ~; 72 |; 18 &)
% ( 5 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 58 ( 0 sgn 54 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X1,X0))
=> ( subset(identity_relation_of(X1),X2)
=> ( X1 = domain(X1,X0,X2)
& subset(X1,range(X1,X0,X2)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f2,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ( subset(identity_relation_of(X1),X2)
=> ( subset(X1,domain(X0,X1,X2))
& X1 = range(X0,X1,X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(f5,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,identity_relation_of_type(X0))
<=> ilf_type(X1,relation_type(X0,X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5) ).
fof(f34,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p34) ).
fof(f35,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,identity_relation_of_type(X0))
=> ( subset(identity_relation_of(X0),X1)
=> ( X0 = domain(X0,X0,X1)
& X0 = range(X0,X0,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_44) ).
fof(f36,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,identity_relation_of_type(X0))
=> ( subset(identity_relation_of(X0),X1)
=> ( X0 = domain(X0,X0,X1)
& X0 = range(X0,X0,X1) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f37,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X1 = domain(X1,X0,X2)
& subset(X1,range(X1,X0,X2)) )
| ~ subset(identity_relation_of(X1),X2)
| ~ ilf_type(X2,relation_type(X1,X0)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f38,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X1 = domain(X1,X0,X2)
& subset(X1,range(X1,X0,X2)) )
| ~ subset(identity_relation_of(X1),X2)
| ~ ilf_type(X2,relation_type(X1,X0)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f37]) ).
fof(f39,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( subset(X1,domain(X0,X1,X2))
& X1 = range(X0,X1,X2) )
| ~ subset(identity_relation_of(X1),X2)
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f2]) ).
fof(f40,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( subset(X1,domain(X0,X1,X2))
& X1 = range(X0,X1,X2) )
| ~ subset(identity_relation_of(X1),X2)
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f39]) ).
fof(f43,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X1,identity_relation_of_type(X0))
<=> ilf_type(X1,relation_type(X0,X0)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f5]) ).
fof(f78,plain,
? [X0] :
( ? [X1] :
( ( domain(X0,X0,X1) != X0
| range(X0,X0,X1) != X0 )
& subset(identity_relation_of(X0),X1)
& ilf_type(X1,identity_relation_of_type(X0)) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f36]) ).
fof(f79,plain,
? [X0] :
( ? [X1] :
( ( domain(X0,X0,X1) != X0
| range(X0,X0,X1) != X0 )
& subset(identity_relation_of(X0),X1)
& ilf_type(X1,identity_relation_of_type(X0)) )
& ilf_type(X0,set_type) ),
inference(flattening,[],[f78]) ).
fof(f82,plain,
! [X0] :
( ! [X1] :
( ( ( ilf_type(X1,identity_relation_of_type(X0))
| ~ ilf_type(X1,relation_type(X0,X0)) )
& ( ilf_type(X1,relation_type(X0,X0))
| ~ ilf_type(X1,identity_relation_of_type(X0)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f43]) ).
fof(f109,plain,
( ( sK13 != domain(sK13,sK13,sK14)
| sK13 != range(sK13,sK13,sK14) )
& subset(identity_relation_of(sK13),sK14)
& ilf_type(sK14,identity_relation_of_type(sK13))
& ilf_type(sK13,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14]),skolemize(X0,sK13),skolemize(X1,sK14)],[f79]) ).
fof(f111,plain,
! [X2,X0,X1] :
( domain(X1,X0,X2) = X1
| ~ subset(identity_relation_of(X1),X2)
| ~ ilf_type(X2,relation_type(X1,X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f38]) ).
fof(f112,plain,
! [X2,X0,X1] :
( range(X0,X1,X2) = X1
| ~ subset(identity_relation_of(X1),X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f40]) ).
fof(f118,plain,
! [X0,X1] :
( ilf_type(X1,relation_type(X0,X0))
| ~ ilf_type(X1,identity_relation_of_type(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f82]) ).
fof(f173,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f34]) ).
fof(f175,plain,
ilf_type(sK14,identity_relation_of_type(sK13)),
inference(cnf_transformation,[],[f109]) ).
fof(f176,plain,
subset(identity_relation_of(sK13),sK14),
inference(cnf_transformation,[],[f109]) ).
fof(f177,plain,
( sK13 != domain(sK13,sK13,sK14)
| sK13 != range(sK13,sK13,sK14) ),
inference(cnf_transformation,[],[f109]) ).
fof(f186,definition,
( spl15_1
<=> sK13 = range(sK13,sK13,sK14) ),
introduced(definition,[new_symbols(definition,[spl15_1])],[avatar_definition]) ).
fof(f190,definition,
( spl15_2
<=> sK13 = domain(sK13,sK13,sK14) ),
introduced(definition,[new_symbols(definition,[spl15_2])],[avatar_definition]) ).
fof(f192,plain,
( sK13 != domain(sK13,sK13,sK14)
| spl15_2 ),
inference(avatar_component_clause,[],[f190]) ).
fof(f193,plain,
( ~ spl15_1
| ~ spl15_2 ),
inference(avatar_split_clause,[],[f177,f190,f186]) ).
fof(f215,plain,
! [X0,X1] :
( ilf_type(X1,relation_type(X0,X0))
| ~ ilf_type(X1,identity_relation_of_type(X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f118,f173]) ).
fof(f216,plain,
! [X0,X1] :
( ilf_type(X1,relation_type(X0,X0))
| ~ ilf_type(X1,identity_relation_of_type(X0)) ),
inference(forward_subsumption_resolution,[],[f215,f173]) ).
fof(f329,definition,
( spl15_7
<=> ilf_type(sK14,relation_type(sK13,sK13)) ),
introduced(definition,[new_symbols(definition,[spl15_7])],[avatar_definition]) ).
fof(f330,plain,
( ilf_type(sK14,relation_type(sK13,sK13))
| ~ spl15_7 ),
inference(avatar_component_clause,[],[f329]) ).
fof(f331,plain,
( ~ ilf_type(sK14,relation_type(sK13,sK13))
| spl15_7 ),
inference(avatar_component_clause,[],[f329]) ).
fof(f337,plain,
( ~ ilf_type(sK14,identity_relation_of_type(sK13))
| spl15_7 ),
inference(resolution,[],[f331,f216]) ).
fof(f339,plain,
( $false
| spl15_7 ),
inference(forward_subsumption_resolution,[],[f337,f175]) ).
fof(f340,plain,
spl15_7,
inference(avatar_contradiction_clause,[],[f339]) ).
fof(f374,plain,
! [X2,X0,X1] :
( domain(X1,X0,X2) = X1
| ~ subset(identity_relation_of(X1),X2)
| ~ ilf_type(X2,relation_type(X1,X0))
| ~ ilf_type(X1,set_type) ),
inference(forward_subsumption_resolution,[],[f111,f173]) ).
fof(f375,plain,
! [X2,X0,X1] :
( domain(X1,X0,X2) = X1
| ~ subset(identity_relation_of(X1),X2)
| ~ ilf_type(X2,relation_type(X1,X0)) ),
inference(forward_subsumption_resolution,[],[f374,f173]) ).
fof(f386,plain,
! [X2,X0,X1] :
( range(X0,X1,X2) = X1
| ~ subset(identity_relation_of(X1),X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type) ),
inference(forward_subsumption_resolution,[],[f112,f173]) ).
fof(f387,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| ~ subset(identity_relation_of(X1),X2)
| range(X0,X1,X2) = X1 ),
inference(forward_subsumption_resolution,[],[f386,f173]) ).
fof(f402,plain,
( ~ subset(identity_relation_of(sK13),sK14)
| sK13 = range(sK13,sK13,sK14)
| ~ spl15_7 ),
inference(resolution,[],[f387,f330]) ).
fof(f403,plain,
( sK13 = range(sK13,sK13,sK14)
| ~ spl15_7 ),
inference(forward_subsumption_resolution,[],[f402,f176]) ).
fof(f406,plain,
( spl15_1
| ~ spl15_7 ),
inference(avatar_split_clause,[],[f403,f329,f186]) ).
fof(f422,plain,
( sK13 != sK13
| ~ subset(identity_relation_of(sK13),sK14)
| ~ ilf_type(sK14,relation_type(sK13,sK13))
| spl15_2 ),
inference(superposition,[],[f192,f375]) ).
fof(f424,plain,
( ~ subset(identity_relation_of(sK13),sK14)
| ~ ilf_type(sK14,relation_type(sK13,sK13))
| spl15_2 ),
inference(trivial_inequality_removal,[],[f422]) ).
fof(f426,plain,
( ~ ilf_type(sK14,relation_type(sK13,sK13))
| spl15_2 ),
inference(forward_subsumption_resolution,[],[f424,f176]) ).
fof(f427,plain,
( $false
| spl15_2
| ~ spl15_7 ),
inference(forward_subsumption_resolution,[],[f426,f330]) ).
fof(f428,plain,
( spl15_2
| ~ spl15_7 ),
inference(avatar_contradiction_clause,[],[f427]) ).
cnf(s1,plain,
( ~ spl15_1
| ~ spl15_2 ),
inference(sat_conversion,[],[f193]) ).
cnf(s6,plain,
spl15_7,
inference(sat_conversion,[],[f340]) ).
cnf(s9,plain,
( spl15_1
| ~ spl15_7 ),
inference(sat_conversion,[],[f406]) ).
cnf(s14,plain,
( spl15_2
| ~ spl15_7 ),
inference(sat_conversion,[],[f428]) ).
cnf(s15,plain,
spl15_2,
inference(rat,[],[s14,s6]) ).
cnf(s16,plain,
spl15_1,
inference(rat,[],[s9,s6]) ).
cnf(s19,plain,
$false,
inference(rat,[],[s1,s15,s16]) ).
fof(f429,plain,
$false,
inference(avatar_sat_refutation,[],[s19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET677+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n015.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 28 02:32:46 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 2.69/1.34 % (2208626)Detected formulas, will run a generic FOF schedule.
% 2.69/1.34 % (2208636)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2094933140:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.69/1.34 % (2208636)First to succeed.
% 2.69/1.34 % (2208636)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2208626"
% 2.69/1.34 % (2208631)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=4043786596:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.69/1.34 % (2208633)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=85144260:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.69/1.34 % (2208632)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=2678092130:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.69/1.34 % (2208634)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2720011056:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.69/1.34 % (2208637)dis-21_1_sil=8000:lcm=predicate:random_seed=4072432133: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)
% 2.69/1.34 % (2208635)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4280590858:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.69/1.34 % (2208635)Also succeeded, but the first one will report.
% 2.69/1.34 % (2208634)Also succeeded, but the first one will report.
% 2.69/1.34 % (2208637)Also succeeded, but the first one will report.
% 2.69/1.34 % (2208636)Refutation found. Thanks to Tanya!
% 2.69/1.34 % SZS status Theorem for theBenchmark
% 2.69/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 2.69/1.34 % (2208636)------------------------------
% 2.69/1.34 % (2208636)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.34 % (2208636)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.34 % (2208636)CaDiCaL version: 2.1.3
% 2.69/1.34 % (2208636)Termination reason: Refutation
% 2.69/1.34 % (2208636)Time elapsed: 0.006 s
% 2.69/1.34 % (2208636)Peak memory usage: 90 MB
% 2.69/1.34 % (2208636)Instructions burned: 13 (million)
% 2.69/1.34 % (2208636)------------------------------
% 2.69/1.34 % (2208636)------------------------------
% 2.69/1.34 % (2208626)Success in time 0.298 s
% 2.69/1.34 % Vampire exiting
%------------------------------------------------------------------------------