%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU292+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 12:52:45 PM UTC 2026
% Result : Theorem 0.19s 0.48s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 69 ( 20 unt; 3 def)
% Number of atoms : 200 ( 51 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 202 ( 71 ~; 78 |; 27 &)
% ( 10 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 4 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 95 ( 0 sgn 85 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
=> relation(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f6,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> ( ( ( X1 = empty_set
=> X0 = empty_set )
=> ( quasi_total(X2,X0,X1)
<=> X0 = relation_dom_as_subset(X0,X1,X2) ) )
& ( X1 = empty_set
=> ( X0 = empty_set
| ( quasi_total(X2,X0,X1)
<=> X2 = empty_set ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_funct_2) ).
fof(f16,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> element(X2,powerset(cartesian_product2(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f44,axiom,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
=> relation_dom_as_subset(X0,X1,X2) = relation_dom(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).
fof(f45,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f48,conjecture,
! [X0,X1,X2,X3] :
( ( function(X3)
& quasi_total(X3,X0,X1)
& relation_of2_as_subset(X3,X0,X1) )
=> ! [X4] :
( ( relation(X4)
& function(X4) )
=> ( in(X2,X0)
=> ( X1 = empty_set
| apply(relation_composition(X3,X4),X2) = apply(X4,apply(X3,X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funct_2) ).
fof(f49,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( function(X3)
& quasi_total(X3,X0,X1)
& relation_of2_as_subset(X3,X0,X1) )
=> ! [X4] :
( ( relation(X4)
& function(X4) )
=> ( in(X2,X0)
=> ( X1 = empty_set
| apply(relation_composition(X3,X4),X2) = apply(X4,apply(X3,X2)) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f50,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X0,relation_dom(X1))
=> apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_1) ).
fof(f69,plain,
! [X0,X1,X2] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(ennf_transformation,[],[f4]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ( ( ( quasi_total(X2,X0,X1)
<=> X0 = relation_dom_as_subset(X0,X1,X2) )
| ( empty_set != X0
& X1 = empty_set ) )
& ( X0 = empty_set
| ( quasi_total(X2,X0,X1)
<=> X2 = empty_set )
| empty_set != X1 ) )
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ( ( ( quasi_total(X2,X0,X1)
<=> X0 = relation_dom_as_subset(X0,X1,X2) )
| ( empty_set != X0
& X1 = empty_set ) )
& ( X0 = empty_set
| ( quasi_total(X2,X0,X1)
<=> X2 = empty_set )
| empty_set != X1 ) )
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(flattening,[],[f72]) ).
fof(f77,plain,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f90,plain,
! [X0,X1,X2] :
( relation_dom_as_subset(X0,X1,X2) = relation_dom(X2)
| ~ relation_of2(X2,X0,X1) ),
inference(ennf_transformation,[],[f44]) ).
fof(f92,plain,
? [X0,X1,X2,X3] :
( ? [X4] :
( empty_set != X1
& apply(relation_composition(X3,X4),X2) != apply(X4,apply(X3,X2))
& in(X2,X0)
& relation(X4)
& function(X4) )
& function(X3)
& quasi_total(X3,X0,X1)
& relation_of2_as_subset(X3,X0,X1) ),
inference(ennf_transformation,[],[f49]) ).
fof(f93,plain,
? [X0,X1,X2,X3] :
( ? [X4] :
( empty_set != X1
& apply(relation_composition(X3,X4),X2) != apply(X4,apply(X3,X2))
& in(X2,X0)
& relation(X4)
& function(X4) )
& function(X3)
& quasi_total(X3,X0,X1)
& relation_of2_as_subset(X3,X0,X1) ),
inference(flattening,[],[f92]) ).
fof(f94,plain,
! [X0,X1] :
( ! [X2] :
( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f50]) ).
fof(f95,plain,
! [X0,X1] :
( ! [X2] :
( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f94]) ).
fof(f108,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(cartesian_product2(X0,X1)))
| relation(X2) ),
inference(cnf_transformation,[],[f69]) ).
fof(f112,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| empty_set = X1
| relation_dom_as_subset(X0,X1,X2) = X0
| ~ quasi_total(X2,X0,X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f117,plain,
! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f167,plain,
! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| relation_dom_as_subset(X0,X1,X2) = relation_dom(X2) ),
inference(cnf_transformation,[],[f90]) ).
fof(f169,plain,
! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f172,plain,
function(sK21),
inference(cnf_transformation,[],[f93]) ).
fof(f173,plain,
relation(sK21),
inference(cnf_transformation,[],[f93]) ).
fof(f174,plain,
in(sK19,sK17),
inference(cnf_transformation,[],[f93]) ).
fof(f175,plain,
apply(relation_composition(sK20,sK21),sK19) != apply(sK21,apply(sK20,sK19)),
inference(cnf_transformation,[],[f93]) ).
fof(f176,plain,
empty_set != sK18,
inference(cnf_transformation,[],[f93]) ).
fof(f177,plain,
relation_of2_as_subset(sK20,sK17,sK18),
inference(cnf_transformation,[],[f93]) ).
fof(f178,plain,
quasi_total(sK20,sK17,sK18),
inference(cnf_transformation,[],[f93]) ).
fof(f179,plain,
function(sK20),
inference(cnf_transformation,[],[f93]) ).
fof(f180,plain,
! [X2,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X0,relation_dom(X1))
| apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ),
inference(cnf_transformation,[],[f95]) ).
fof(f195,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(consistent_polarity_flipping,[],[f108]) ).
fof(f218,plain,
~ in(sK19,sK17),
inference(consistent_polarity_flipping,[],[f174]) ).
fof(f219,plain,
~ relation(sK21),
inference(consistent_polarity_flipping,[],[f173]) ).
fof(f220,plain,
! [X2,X0,X1] :
( ~ function(X2)
| relation(X1)
| ~ function(X1)
| relation(X2)
| in(X0,relation_dom(X1))
| apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ),
inference(consistent_polarity_flipping,[],[f180]) ).
fof(f308,plain,
( empty_set = sK18
| sK17 = relation_dom_as_subset(sK17,sK18,sK20)
| ~ quasi_total(sK20,sK17,sK18) ),
inference(resolution,[],[f112,f177]) ).
fof(f310,plain,
( sK17 = relation_dom_as_subset(sK17,sK18,sK20)
| ~ quasi_total(sK20,sK17,sK18) ),
inference(forward_subsumption_resolution,[],[f308,f176]) ).
fof(f311,plain,
sK17 = relation_dom_as_subset(sK17,sK18,sK20),
inference(forward_subsumption_resolution,[],[f310,f178]) ).
fof(f325,plain,
! [X0,X1] :
( relation(X0)
| ~ function(X0)
| relation(sK21)
| in(X1,relation_dom(X0))
| apply(relation_composition(X0,sK21),X1) = apply(sK21,apply(X0,X1)) ),
inference(resolution,[],[f220,f172]) ).
fof(f326,plain,
! [X0,X1] :
( in(X1,relation_dom(X0))
| ~ function(X0)
| relation(X0)
| apply(relation_composition(X0,sK21),X1) = apply(sK21,apply(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f325,f219]) ).
fof(f328,definition,
( spl22_1
<=> relation(sK20) ),
introduced(definition,[new_symbols(definition,[spl22_1])],[avatar_definition]) ).
fof(f330,plain,
( relation(sK20)
| ~ spl22_1 ),
inference(avatar_component_clause,[],[f328]) ).
fof(f358,definition,
( spl22_3
<=> relation_of2(sK20,sK17,sK18) ),
introduced(definition,[new_symbols(definition,[spl22_3])],[avatar_definition]) ).
fof(f359,plain,
( relation_of2(sK20,sK17,sK18)
| ~ spl22_3 ),
inference(avatar_component_clause,[],[f358]) ).
fof(f360,plain,
( ~ relation_of2(sK20,sK17,sK18)
| spl22_3 ),
inference(avatar_component_clause,[],[f358]) ).
fof(f366,plain,
( ~ relation_of2_as_subset(sK20,sK17,sK18)
| spl22_3 ),
inference(resolution,[],[f360,f169]) ).
fof(f367,plain,
( $false
| spl22_3 ),
inference(forward_subsumption_resolution,[],[f366,f177]) ).
fof(f368,plain,
spl22_3,
inference(avatar_contradiction_clause,[],[f367]) ).
fof(f373,plain,
( relation_dom_as_subset(sK17,sK18,sK20) = relation_dom(sK20)
| ~ spl22_3 ),
inference(resolution,[],[f359,f167]) ).
fof(f375,plain,
( sK17 = relation_dom(sK20)
| ~ spl22_3 ),
inference(forward_demodulation,[],[f373,f311]) ).
fof(f418,plain,
( ! [X0] :
( in(X0,sK17)
| ~ function(sK20)
| relation(sK20)
| apply(relation_composition(sK20,sK21),X0) = apply(sK21,apply(sK20,X0)) )
| ~ spl22_3 ),
inference(superposition,[],[f326,f375]) ).
fof(f432,plain,
( ! [X0] :
( in(X0,sK17)
| relation(sK20)
| apply(relation_composition(sK20,sK21),X0) = apply(sK21,apply(sK20,X0)) )
| ~ spl22_3 ),
inference(forward_subsumption_resolution,[],[f418,f179]) ).
fof(f441,definition,
( spl22_8
<=> ! [X0] :
( in(X0,sK17)
| apply(relation_composition(sK20,sK21),X0) = apply(sK21,apply(sK20,X0)) ) ),
introduced(definition,[new_symbols(definition,[spl22_8])],[avatar_definition]) ).
fof(f442,plain,
( ! [X0] :
( in(X0,sK17)
| apply(relation_composition(sK20,sK21),X0) = apply(sK21,apply(sK20,X0)) )
| ~ spl22_8 ),
inference(avatar_component_clause,[],[f441]) ).
fof(f443,plain,
( spl22_1
| spl22_8
| ~ spl22_3 ),
inference(avatar_split_clause,[],[f432,f358,f441,f328]) ).
fof(f488,plain,
( apply(relation_composition(sK20,sK21),sK19) = apply(sK21,apply(sK20,sK19))
| ~ spl22_8 ),
inference(resolution,[],[f442,f218]) ).
fof(f489,plain,
( $false
| ~ spl22_8 ),
inference(forward_subsumption_resolution,[],[f488,f175]) ).
fof(f490,plain,
~ spl22_8,
inference(avatar_contradiction_clause,[],[f489]) ).
fof(f491,plain,
( ! [X0,X1] : ~ element(sK20,powerset(cartesian_product2(X0,X1)))
| ~ spl22_1 ),
inference(resolution,[],[f330,f195]) ).
fof(f493,plain,
( ! [X0,X1] : ~ relation_of2_as_subset(sK20,X0,X1)
| ~ spl22_1 ),
inference(resolution,[],[f491,f117]) ).
fof(f500,plain,
( $false
| ~ spl22_1 ),
inference(backward_subsumption_resolution,[],[f177,f493]) ).
fof(f501,plain,
~ spl22_1,
inference(avatar_contradiction_clause,[],[f500]) ).
cnf(s3,plain,
spl22_3,
inference(sat_conversion,[],[f368]) ).
cnf(s7,plain,
( spl22_1
| ~ spl22_3
| spl22_8 ),
inference(sat_conversion,[],[f443]) ).
cnf(s16,plain,
~ spl22_8,
inference(sat_conversion,[],[f490]) ).
cnf(s17,plain,
~ spl22_1,
inference(sat_conversion,[],[f501]) ).
cnf(s20,plain,
~ spl22_3,
inference(rat,[],[s7,s16,s17]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s3,s20]) ).
fof(f502,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU292+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n018.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 04:34:24 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.43 Running first-order model finding
% 0.11/0.43 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.48 % (2991218)Will run a generic schedule for satisfiability detection.
% 0.19/0.48 % (2991225)% WARNING: option uhcvi not known.
% 0.19/0.48 % (2991229)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2033338483:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.48 % (2991225)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1438051240:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.48 % (2991227)dis+10_1_sil=32000:sp=arity:random_seed=2059447704:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.48 % (2991224)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1502511701_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.48 % (2991228)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3643886205:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.48 % (2991226)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3032100748:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.48 % (2991230)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2955190818:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.48 % (2991225) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2991218-2991225"...
% 0.19/0.48 % (2991225)...printing done.
% 0.19/0.48 % (2991225)Refutation found. Thanks to Tanya!
% 0.19/0.48 % SZS status Theorem for theBenchmark
% 0.19/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.48 % (2991225)------------------------------
% 0.19/0.48 % (2991225)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.48 % (2991225)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.48 % (2991225)CaDiCaL version: 2.1.3
% 0.19/0.48 % (2991225)Termination reason: Refutation
% 0.19/0.48 % (2991225)Time elapsed: 0.013 s
% 0.19/0.48 % (2991225)Peak memory usage: 13 MB
% 0.19/0.48 % (2991225)Instructions burned: 14 (million)
% 0.19/0.48 % (2991218)Success in time 0.04 s
% 0.19/0.48 % Vampire exiting
%------------------------------------------------------------------------------