%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU041+1 : 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 : 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 12:47:07 PM UTC 2026
% Result : Theorem 3.35s 1.37s
% Output : Refutation 3.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 39 ( 10 unt; 4 def)
% Number of atoms : 97 ( 20 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 105 ( 47 ~; 35 |; 13 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 30 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f32,conjecture,
! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( subset(X0,X1)
=> ( relation_dom_restriction(relation_dom_restriction(X2,X0),X1) = relation_dom_restriction(X2,X0)
& relation_dom_restriction(relation_dom_restriction(X2,X1),X0) = relation_dom_restriction(X2,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_funct_1) ).
fof(f33,negated_conjecture,
~ ! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( subset(X0,X1)
=> ( relation_dom_restriction(relation_dom_restriction(X2,X0),X1) = relation_dom_restriction(X2,X0)
& relation_dom_restriction(relation_dom_restriction(X2,X1),X0) = relation_dom_restriction(X2,X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f34,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( subset(X0,X1)
=> relation_dom_restriction(relation_dom_restriction(X2,X0),X1) = relation_dom_restriction(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t102_relat_1) ).
fof(f35,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( subset(X0,X1)
=> relation_dom_restriction(relation_dom_restriction(X2,X1),X0) = relation_dom_restriction(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t103_relat_1) ).
fof(f37,plain,
? [X0,X1,X2] :
( ( relation_dom_restriction(X2,X0) != relation_dom_restriction(relation_dom_restriction(X2,X0),X1)
| relation_dom_restriction(X2,X0) != relation_dom_restriction(relation_dom_restriction(X2,X1),X0) )
& subset(X0,X1)
& relation(X2)
& function(X2) ),
inference(ennf_transformation,[],[f33]) ).
fof(f38,plain,
? [X0,X1,X2] :
( ( relation_dom_restriction(X2,X0) != relation_dom_restriction(relation_dom_restriction(X2,X0),X1)
| relation_dom_restriction(X2,X0) != relation_dom_restriction(relation_dom_restriction(X2,X1),X0) )
& subset(X0,X1)
& relation(X2)
& function(X2) ),
inference(flattening,[],[f37]) ).
fof(f39,plain,
! [X0,X1,X2] :
( relation_dom_restriction(relation_dom_restriction(X2,X1),X0) = relation_dom_restriction(X2,X0)
| ~ subset(X0,X1)
| ~ relation(X2) ),
inference(ennf_transformation,[],[f35]) ).
fof(f40,plain,
! [X0,X1,X2] :
( relation_dom_restriction(relation_dom_restriction(X2,X1),X0) = relation_dom_restriction(X2,X0)
| ~ subset(X0,X1)
| ~ relation(X2) ),
inference(flattening,[],[f39]) ).
fof(f41,plain,
! [X0,X1,X2] :
( relation_dom_restriction(relation_dom_restriction(X2,X0),X1) = relation_dom_restriction(X2,X0)
| ~ subset(X0,X1)
| ~ relation(X2) ),
inference(ennf_transformation,[],[f34]) ).
fof(f42,plain,
! [X0,X1,X2] :
( relation_dom_restriction(relation_dom_restriction(X2,X0),X1) = relation_dom_restriction(X2,X0)
| ~ subset(X0,X1)
| ~ relation(X2) ),
inference(flattening,[],[f41]) ).
fof(f49,plain,
( ( relation_dom_restriction(sK2,sK0) != relation_dom_restriction(relation_dom_restriction(sK2,sK0),sK1)
| relation_dom_restriction(sK2,sK0) != relation_dom_restriction(relation_dom_restriction(sK2,sK1),sK0) )
& subset(sK0,sK1)
& relation(sK2)
& function(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f38]) ).
fof(f56,plain,
relation(sK2),
inference(cnf_transformation,[],[f49]) ).
fof(f57,plain,
subset(sK0,sK1),
inference(cnf_transformation,[],[f49]) ).
fof(f58,plain,
( relation_dom_restriction(sK2,sK0) != relation_dom_restriction(relation_dom_restriction(sK2,sK0),sK1)
| relation_dom_restriction(sK2,sK0) != relation_dom_restriction(relation_dom_restriction(sK2,sK1),sK0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f59,plain,
! [X2,X0,X1] :
( relation_dom_restriction(X2,X0) = relation_dom_restriction(relation_dom_restriction(X2,X1),X0)
| ~ subset(X0,X1)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f40]) ).
fof(f60,plain,
! [X2,X0,X1] :
( relation_dom_restriction(X2,X0) = relation_dom_restriction(relation_dom_restriction(X2,X0),X1)
| ~ subset(X0,X1)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f42]) ).
fof(f79,definition,
~ sP7(relation_dom_restriction(sK2,sK0)),
introduced(definition,[new_symbols(definition,[sP7])],[inequality_splitting_name_introduction]) ).
fof(f80,definition,
~ sP8(relation_dom_restriction(sK2,sK0)),
introduced(definition,[new_symbols(definition,[sP8])],[inequality_splitting_name_introduction]) ).
fof(f81,plain,
( sP7(relation_dom_restriction(relation_dom_restriction(sK2,sK0),sK1))
| sP8(relation_dom_restriction(relation_dom_restriction(sK2,sK1),sK0)) ),
inference(inequality_splitting,[],[f58,f80,f79]) ).
fof(f83,definition,
( spl9_1
<=> sP8(relation_dom_restriction(relation_dom_restriction(sK2,sK1),sK0)) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
fof(f85,plain,
( sP8(relation_dom_restriction(relation_dom_restriction(sK2,sK1),sK0))
| ~ spl9_1 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f87,definition,
( spl9_2
<=> sP7(relation_dom_restriction(relation_dom_restriction(sK2,sK0),sK1)) ),
introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition]) ).
fof(f89,plain,
( sP7(relation_dom_restriction(relation_dom_restriction(sK2,sK0),sK1))
| ~ spl9_2 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f90,plain,
( spl9_1
| spl9_2 ),
inference(avatar_split_clause,[],[f81,f87,f83]) ).
fof(f91,plain,
( sP7(relation_dom_restriction(sK2,sK0))
| ~ subset(sK0,sK1)
| ~ relation(sK2)
| ~ spl9_2 ),
inference(superposition,[],[f89,f60]) ).
fof(f94,plain,
( ~ subset(sK0,sK1)
| ~ relation(sK2)
| ~ spl9_2 ),
inference(forward_subsumption_resolution,[],[f91,f79]) ).
fof(f104,plain,
( ~ relation(sK2)
| ~ spl9_2 ),
inference(forward_subsumption_resolution,[],[f94,f57]) ).
fof(f105,plain,
( $false
| ~ spl9_2 ),
inference(forward_subsumption_resolution,[],[f104,f56]) ).
fof(f106,plain,
~ spl9_2,
inference(avatar_contradiction_clause,[],[f105]) ).
fof(f108,plain,
( sP8(relation_dom_restriction(sK2,sK0))
| ~ subset(sK0,sK1)
| ~ relation(sK2)
| ~ spl9_1 ),
inference(superposition,[],[f85,f59]) ).
fof(f109,plain,
( ~ subset(sK0,sK1)
| ~ relation(sK2)
| ~ spl9_1 ),
inference(forward_subsumption_resolution,[],[f108,f80]) ).
fof(f111,plain,
( ~ relation(sK2)
| ~ spl9_1 ),
inference(forward_subsumption_resolution,[],[f109,f57]) ).
fof(f117,plain,
( $false
| ~ spl9_1 ),
inference(forward_subsumption_resolution,[],[f111,f56]) ).
fof(f118,plain,
~ spl9_1,
inference(avatar_contradiction_clause,[],[f117]) ).
cnf(s1,plain,
( spl9_1
| spl9_2 ),
inference(sat_conversion,[],[f90]) ).
cnf(s3,plain,
~ spl9_2,
inference(sat_conversion,[],[f106]) ).
cnf(s5,plain,
~ spl9_1,
inference(sat_conversion,[],[f118]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s3,s5]) ).
fof(f119,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU041+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n013.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Mon Sep 28 03:27:00 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 3.35/1.37 % (776323)Detected formulas, will run a generic FOF schedule.
% 3.35/1.37 % (776328)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=3929907789:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.35/1.37 % (776330)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=1411777307:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.35/1.37 % (776329)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=2543195:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.35/1.37 % (776331)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=142934788:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.35/1.37 % (776332)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=595973787:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.35/1.37 % (776334)dis-21_1_sil=8000:lcm=predicate:random_seed=902480717: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)
% 3.35/1.37 % (776333)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=642830536:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.35/1.37 % (776331)First to succeed.
% 3.35/1.37 % (776332)Also succeeded, but the first one will report.
% 3.35/1.37 % (776331)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-776323"
% 3.35/1.37 % (776334)Also succeeded, but the first one will report.
% 3.35/1.37 % (776333)Also succeeded, but the first one will report.
% 3.35/1.37 % (776331)Refutation found. Thanks to Tanya!
% 3.35/1.37 % SZS status Theorem for theBenchmark
% 3.35/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 3.35/1.37 % (776331)------------------------------
% 3.35/1.37 % (776331)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.35/1.37 % (776331)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/1.37 % (776331)CaDiCaL version: 2.1.3
% 3.35/1.37 % (776331)Termination reason: Refutation
% 3.35/1.37 % (776331)Time elapsed: 0.003 s
% 3.35/1.37 % (776331)Peak memory usage: 89 MB
% 3.35/1.37 % (776331)Instructions burned: 2 (million)
% 3.35/1.37 % (776331)------------------------------
% 3.35/1.37 % (776331)------------------------------
% 3.35/1.37 % (776323)Success in time 0.406 s
% 3.35/1.37 % Vampire exiting
%------------------------------------------------------------------------------