%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU221+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 12:52:27 PM UTC 2026
% Result : Theorem 0.16s 0.48s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of formulae : 74 ( 10 unt; 2 def)
% Number of atoms : 260 ( 54 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 320 ( 134 ~; 128 |; 36 &)
% ( 8 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 46 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
<=> ! [X1,X2] :
( ( in(X1,relation_dom(X0))
& in(X2,relation_dom(X0))
& apply(X0,X1) = apply(X0,X2) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_funct_1) ).
fof(f6,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( relation(function_inverse(X0))
& function(function_inverse(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_1) ).
fof(f35,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( X1 = function_inverse(X0)
<=> ( relation_dom(X1) = relation_rng(X0)
& ! [X2,X3] :
( ( ( in(X2,relation_rng(X0))
& X3 = apply(X1,X2) )
=> ( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) )
& ( ( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
=> ( in(X2,relation_rng(X0))
& X3 = apply(X1,X2) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_funct_1) ).
fof(f36,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( ( one_to_one(X1)
& in(X0,relation_rng(X1)) )
=> ( X0 = apply(X1,apply(function_inverse(X1),X0))
& X0 = apply(relation_composition(function_inverse(X1),X1),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_funct_1) ).
fof(f38,conjecture,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> one_to_one(function_inverse(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_funct_1) ).
fof(f39,negated_conjecture,
~ ! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> one_to_one(function_inverse(X0)) ) ),
inference(negated_conjecture,[status(cth)],[f38]) ).
fof(f52,plain,
! [X0] :
( ( one_to_one(X0)
<=> ! [X1,X2] :
( X1 = X2
| ~ in(X1,relation_dom(X0))
| ~ in(X2,relation_dom(X0))
| apply(X0,X1) != apply(X0,X2) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f53,plain,
! [X0] :
( ( one_to_one(X0)
<=> ! [X1,X2] :
( X1 = X2
| ~ in(X1,relation_dom(X0))
| ~ in(X2,relation_dom(X0))
| apply(X0,X1) != apply(X0,X2) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f52]) ).
fof(f54,plain,
! [X0] :
( ( relation(function_inverse(X0))
& function(function_inverse(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f55,plain,
! [X0] :
( ( relation(function_inverse(X0))
& function(function_inverse(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f54]) ).
fof(f77,plain,
! [X0] :
( ! [X1] :
( ( X1 = function_inverse(X0)
<=> ( relation_dom(X1) = relation_rng(X0)
& ! [X2,X3] :
( ( ( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| ~ in(X2,relation_rng(X0))
| apply(X1,X2) != X3 )
& ( ( in(X2,relation_rng(X0))
& X3 = apply(X1,X2) )
| ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 ) ) ) )
| ~ relation(X1)
| ~ function(X1) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f78,plain,
! [X0] :
( ! [X1] :
( ( X1 = function_inverse(X0)
<=> ( relation_dom(X1) = relation_rng(X0)
& ! [X2,X3] :
( ( ( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| ~ in(X2,relation_rng(X0))
| apply(X1,X2) != X3 )
& ( ( in(X2,relation_rng(X0))
& X3 = apply(X1,X2) )
| ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 ) ) ) )
| ~ relation(X1)
| ~ function(X1) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f77]) ).
fof(f79,plain,
! [X0,X1] :
( ( X0 = apply(X1,apply(function_inverse(X1),X0))
& X0 = apply(relation_composition(function_inverse(X1),X1),X0) )
| ~ one_to_one(X1)
| ~ in(X0,relation_rng(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f36]) ).
fof(f80,plain,
! [X0,X1] :
( ( X0 = apply(X1,apply(function_inverse(X1),X0))
& X0 = apply(relation_composition(function_inverse(X1),X1),X0) )
| ~ one_to_one(X1)
| ~ in(X0,relation_rng(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f79]) ).
fof(f82,plain,
? [X0] :
( ~ one_to_one(function_inverse(X0))
& one_to_one(X0)
& relation(X0)
& function(X0) ),
inference(ennf_transformation,[],[f39]) ).
fof(f83,plain,
? [X0] :
( ~ one_to_one(function_inverse(X0))
& one_to_one(X0)
& relation(X0)
& function(X0) ),
inference(flattening,[],[f82]) ).
fof(f92,plain,
! [X0] :
( one_to_one(X0)
| ~ relation(X0)
| apply(X0,sK0(X0)) = apply(X0,sK1(X0))
| ~ function(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f93,plain,
! [X0] :
( one_to_one(X0)
| ~ relation(X0)
| in(sK1(X0),relation_dom(X0))
| ~ function(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f94,plain,
! [X0] :
( one_to_one(X0)
| ~ relation(X0)
| in(sK0(X0),relation_dom(X0))
| ~ function(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f95,plain,
! [X0] :
( one_to_one(X0)
| ~ relation(X0)
| sK0(X0) != sK1(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f96,plain,
! [X0] :
( function(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f97,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| relation(function_inverse(X0)) ),
inference(cnf_transformation,[],[f55]) ).
fof(f151,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ~ function(X1)
| ~ relation(X1)
| relation_rng(X0) = relation_dom(X1)
| function_inverse(X0) != X1 ),
inference(cnf_transformation,[],[f78]) ).
fof(f153,plain,
! [X0,X1] :
( ~ one_to_one(X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1))
| ~ function(X1)
| apply(X1,apply(function_inverse(X1),X0)) = X0 ),
inference(cnf_transformation,[],[f80]) ).
fof(f155,plain,
function(sK15),
inference(cnf_transformation,[],[f83]) ).
fof(f156,plain,
relation(sK15),
inference(cnf_transformation,[],[f83]) ).
fof(f157,plain,
one_to_one(sK15),
inference(cnf_transformation,[],[f83]) ).
fof(f158,plain,
~ one_to_one(function_inverse(sK15)),
inference(cnf_transformation,[],[f83]) ).
fof(f162,plain,
! [X0] :
( ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0)
| ~ function(function_inverse(X0))
| ~ relation(function_inverse(X0))
| relation_rng(X0) = relation_dom(function_inverse(X0)) ),
inference(equality_resolution,[],[f151]) ).
fof(f214,plain,
( ~ relation(sK15)
| relation(function_inverse(sK15)) ),
inference(resolution,[],[f97,f155]) ).
fof(f215,plain,
relation(function_inverse(sK15)),
inference(forward_subsumption_resolution,[],[f214,f156]) ).
fof(f351,plain,
( ~ relation(function_inverse(sK15))
| in(sK1(function_inverse(sK15)),relation_dom(function_inverse(sK15)))
| ~ function(function_inverse(sK15)) ),
inference(resolution,[],[f93,f158]) ).
fof(f352,plain,
( in(sK1(function_inverse(sK15)),relation_dom(function_inverse(sK15)))
| ~ function(function_inverse(sK15)) ),
inference(forward_subsumption_resolution,[],[f351,f215]) ).
fof(f354,definition,
( spl16_3
<=> function(function_inverse(sK15)) ),
introduced(definition,[new_symbols(definition,[spl16_3])],[avatar_definition]) ).
fof(f355,plain,
( function(function_inverse(sK15))
| ~ spl16_3 ),
inference(avatar_component_clause,[],[f354]) ).
fof(f356,plain,
( ~ function(function_inverse(sK15))
| spl16_3 ),
inference(avatar_component_clause,[],[f354]) ).
fof(f358,definition,
( spl16_4
<=> in(sK1(function_inverse(sK15)),relation_dom(function_inverse(sK15))) ),
introduced(definition,[new_symbols(definition,[spl16_4])],[avatar_definition]) ).
fof(f360,plain,
( in(sK1(function_inverse(sK15)),relation_dom(function_inverse(sK15)))
| ~ spl16_4 ),
inference(avatar_component_clause,[],[f358]) ).
fof(f361,plain,
( ~ spl16_3
| spl16_4 ),
inference(avatar_split_clause,[],[f352,f358,f354]) ).
fof(f362,plain,
( ~ relation(sK15)
| ~ function(sK15)
| spl16_3 ),
inference(resolution,[],[f356,f96]) ).
fof(f363,plain,
( ~ function(sK15)
| spl16_3 ),
inference(forward_subsumption_resolution,[],[f362,f156]) ).
fof(f364,plain,
( $false
| spl16_3 ),
inference(forward_subsumption_resolution,[],[f363,f155]) ).
fof(f365,plain,
spl16_3,
inference(avatar_contradiction_clause,[],[f364]) ).
fof(f366,plain,
( ~ relation(function_inverse(sK15))
| in(sK0(function_inverse(sK15)),relation_dom(function_inverse(sK15)))
| ~ function(function_inverse(sK15)) ),
inference(resolution,[],[f94,f158]) ).
fof(f367,plain,
( in(sK0(function_inverse(sK15)),relation_dom(function_inverse(sK15)))
| ~ function(function_inverse(sK15)) ),
inference(forward_subsumption_resolution,[],[f366,f215]) ).
fof(f368,plain,
( in(sK0(function_inverse(sK15)),relation_dom(function_inverse(sK15)))
| ~ spl16_3 ),
inference(forward_subsumption_resolution,[],[f367,f355]) ).
fof(f371,plain,
( ~ relation(function_inverse(sK15))
| sK1(function_inverse(sK15)) != sK0(function_inverse(sK15))
| ~ function(function_inverse(sK15)) ),
inference(resolution,[],[f95,f158]) ).
fof(f372,plain,
( sK1(function_inverse(sK15)) != sK0(function_inverse(sK15))
| ~ function(function_inverse(sK15)) ),
inference(forward_subsumption_resolution,[],[f371,f215]) ).
fof(f373,plain,
( sK1(function_inverse(sK15)) != sK0(function_inverse(sK15))
| ~ spl16_3 ),
inference(forward_subsumption_resolution,[],[f372,f355]) ).
fof(f404,plain,
( ~ relation(function_inverse(sK15))
| apply(function_inverse(sK15),sK0(function_inverse(sK15))) = apply(function_inverse(sK15),sK1(function_inverse(sK15)))
| ~ function(function_inverse(sK15)) ),
inference(resolution,[],[f92,f158]) ).
fof(f405,plain,
( apply(function_inverse(sK15),sK0(function_inverse(sK15))) = apply(function_inverse(sK15),sK1(function_inverse(sK15)))
| ~ function(function_inverse(sK15)) ),
inference(forward_subsumption_resolution,[],[f404,f215]) ).
fof(f406,plain,
( apply(function_inverse(sK15),sK0(function_inverse(sK15))) = apply(function_inverse(sK15),sK1(function_inverse(sK15)))
| ~ spl16_3 ),
inference(forward_subsumption_resolution,[],[f405,f355]) ).
fof(f428,plain,
! [X0] :
( ~ relation(sK15)
| ~ in(X0,relation_rng(sK15))
| ~ function(sK15)
| apply(sK15,apply(function_inverse(sK15),X0)) = X0 ),
inference(resolution,[],[f153,f157]) ).
fof(f442,plain,
! [X0] :
( ~ in(X0,relation_rng(sK15))
| ~ function(sK15)
| apply(sK15,apply(function_inverse(sK15),X0)) = X0 ),
inference(forward_subsumption_resolution,[],[f428,f156]) ).
fof(f445,plain,
! [X0] :
( ~ in(X0,relation_rng(sK15))
| apply(sK15,apply(function_inverse(sK15),X0)) = X0 ),
inference(forward_subsumption_resolution,[],[f442,f155]) ).
fof(f446,plain,
( ~ relation(sK15)
| ~ function(sK15)
| ~ function(function_inverse(sK15))
| ~ relation(function_inverse(sK15))
| relation_dom(function_inverse(sK15)) = relation_rng(sK15) ),
inference(resolution,[],[f162,f157]) ).
fof(f464,plain,
( ~ function(sK15)
| ~ function(function_inverse(sK15))
| ~ relation(function_inverse(sK15))
| relation_dom(function_inverse(sK15)) = relation_rng(sK15) ),
inference(forward_subsumption_resolution,[],[f446,f156]) ).
fof(f471,plain,
( ~ function(function_inverse(sK15))
| ~ relation(function_inverse(sK15))
| relation_dom(function_inverse(sK15)) = relation_rng(sK15) ),
inference(forward_subsumption_resolution,[],[f464,f155]) ).
fof(f473,plain,
( ~ relation(function_inverse(sK15))
| relation_dom(function_inverse(sK15)) = relation_rng(sK15)
| ~ spl16_3 ),
inference(forward_subsumption_resolution,[],[f471,f355]) ).
fof(f483,plain,
( relation_dom(function_inverse(sK15)) = relation_rng(sK15)
| ~ spl16_3 ),
inference(forward_subsumption_resolution,[],[f473,f215]) ).
fof(f485,plain,
( in(sK0(function_inverse(sK15)),relation_rng(sK15))
| ~ spl16_3 ),
inference(superposition,[],[f368,f483]) ).
fof(f487,plain,
( in(sK1(function_inverse(sK15)),relation_rng(sK15))
| ~ spl16_3
| ~ spl16_4 ),
inference(superposition,[],[f360,f483]) ).
fof(f704,plain,
( sK0(function_inverse(sK15)) = apply(sK15,apply(function_inverse(sK15),sK0(function_inverse(sK15))))
| ~ spl16_3 ),
inference(resolution,[],[f445,f485]) ).
fof(f705,plain,
( sK1(function_inverse(sK15)) = apply(sK15,apply(function_inverse(sK15),sK1(function_inverse(sK15))))
| ~ spl16_3
| ~ spl16_4 ),
inference(resolution,[],[f445,f487]) ).
fof(f706,plain,
( sK1(function_inverse(sK15)) = apply(sK15,apply(function_inverse(sK15),sK0(function_inverse(sK15))))
| ~ spl16_3
| ~ spl16_4 ),
inference(forward_demodulation,[],[f705,f406]) ).
fof(f707,plain,
( sK1(function_inverse(sK15)) = sK0(function_inverse(sK15))
| ~ spl16_3
| ~ spl16_4 ),
inference(forward_demodulation,[],[f706,f704]) ).
fof(f708,plain,
( $false
| ~ spl16_3
| ~ spl16_4 ),
inference(forward_subsumption_resolution,[],[f707,f373]) ).
fof(f709,plain,
( ~ spl16_3
| ~ spl16_4 ),
inference(avatar_contradiction_clause,[],[f708]) ).
cnf(s2,plain,
( ~ spl16_3
| spl16_4 ),
inference(sat_conversion,[],[f361]) ).
cnf(s3,plain,
spl16_3,
inference(sat_conversion,[],[f365]) ).
cnf(s6,plain,
( ~ spl16_3
| ~ spl16_4 ),
inference(sat_conversion,[],[f709]) ).
cnf(s7,plain,
~ spl16_4,
inference(rat,[],[s6,s3]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s2,s7,s3]) ).
fof(f710,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU221+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/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 04:10:40 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.48 % (2985634)Will run a generic schedule for satisfiability detection.
% 0.16/0.48 % (2985639)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1585035789_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.48 % TRYING [1]
% 0.16/0.48 % TRYING [2]
% 0.16/0.48 % (2985640)% WARNING: option uhcvi not known.
% 0.16/0.48 % TRYING [3]
% 0.16/0.48 % TRYING [4]
% 0.16/0.48 % (2985640)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=42571446:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.48 % (2985641)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=481844255:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.48 % (2985642)dis+10_1_sil=32000:sp=arity:random_seed=1601007897:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.48 % (2985645)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3264768080:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.48 % (2985643)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=61428333:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.48 % (2985644)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2988310894:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.48 % TRYING [5]
% 0.16/0.48 % (2985643) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2985634-2985643"...
% 0.16/0.48 % (2985643)...printing done.
% 0.16/0.48 % (2985643)Refutation found. Thanks to Tanya!
% 0.16/0.48 % SZS status Theorem for theBenchmark
% 0.16/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.48 % (2985643)------------------------------
% 0.16/0.48 % (2985643)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.48 % (2985643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.48 % (2985643)CaDiCaL version: 2.1.3
% 0.16/0.48 % (2985643)Termination reason: Refutation
% 0.16/0.48 % (2985643)Time elapsed: 0.016 s
% 0.16/0.48 % (2985643)Peak memory usage: 12 MB
% 0.16/0.48 % (2985643)Instructions burned: 25 (million)
% 0.16/0.48 % (2985634)Success in time 0.054 s
% 0.16/0.48 % Vampire exiting
%------------------------------------------------------------------------------