%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU032+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n026.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 12:51:49 PM UTC 2026
% Result : Theorem 0.16s 0.48s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 9
% Syntax : Number of formulae : 76 ( 16 unt; 3 def)
% Number of atoms : 245 ( 52 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 304 ( 135 ~; 124 |; 28 &)
% ( 3 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn 28 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( relation(function_inverse(X0))
& function(function_inverse(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_1) ).
fof(f36,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> ( relation_rng(X0) = relation_dom(function_inverse(X0))
& relation_dom(X0) = relation_rng(function_inverse(X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_funct_1) ).
fof(f38,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> ( relation_composition(X0,function_inverse(X0)) = identity_relation(relation_dom(X0))
& relation_composition(function_inverse(X0),X0) = identity_relation(relation_rng(X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_funct_1) ).
fof(f39,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> one_to_one(function_inverse(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_funct_1) ).
fof(f40,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ( one_to_one(X0)
& relation_rng(X0) = relation_dom(X1)
& relation_composition(X0,X1) = identity_relation(relation_dom(X0)) )
=> X1 = function_inverse(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_funct_1) ).
fof(f41,conjecture,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> function_inverse(function_inverse(X0)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_funct_1) ).
fof(f42,negated_conjecture,
~ ! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> function_inverse(function_inverse(X0)) = X0 ) ),
inference(negated_conjecture,[status(cth)],[f41]) ).
fof(f55,plain,
! [X0] :
( ( relation(function_inverse(X0))
& function(function_inverse(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f56,plain,
! [X0] :
( ( relation(function_inverse(X0))
& function(function_inverse(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f55]) ).
fof(f78,plain,
! [X0] :
( ( relation_rng(X0) = relation_dom(function_inverse(X0))
& relation_dom(X0) = relation_rng(function_inverse(X0)) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f79,plain,
! [X0] :
( ( relation_rng(X0) = relation_dom(function_inverse(X0))
& relation_dom(X0) = relation_rng(function_inverse(X0)) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f78]) ).
fof(f81,plain,
! [X0] :
( ( relation_composition(X0,function_inverse(X0)) = identity_relation(relation_dom(X0))
& relation_composition(function_inverse(X0),X0) = identity_relation(relation_rng(X0)) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f82,plain,
! [X0] :
( ( relation_composition(X0,function_inverse(X0)) = identity_relation(relation_dom(X0))
& relation_composition(function_inverse(X0),X0) = identity_relation(relation_rng(X0)) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f81]) ).
fof(f83,plain,
! [X0] :
( one_to_one(function_inverse(X0))
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f39]) ).
fof(f84,plain,
! [X0] :
( one_to_one(function_inverse(X0))
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f83]) ).
fof(f85,plain,
! [X0] :
( ! [X1] :
( X1 = function_inverse(X0)
| ~ one_to_one(X0)
| relation_rng(X0) != relation_dom(X1)
| relation_composition(X0,X1) != identity_relation(relation_dom(X0))
| ~ relation(X1)
| ~ function(X1) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f86,plain,
! [X0] :
( ! [X1] :
( X1 = function_inverse(X0)
| ~ one_to_one(X0)
| relation_rng(X0) != relation_dom(X1)
| relation_composition(X0,X1) != identity_relation(relation_dom(X0))
| ~ relation(X1)
| ~ function(X1) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f85]) ).
fof(f87,plain,
? [X0] :
( function_inverse(function_inverse(X0)) != X0
& one_to_one(X0)
& relation(X0)
& function(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f88,plain,
? [X0] :
( function_inverse(function_inverse(X0)) != X0
& one_to_one(X0)
& relation(X0)
& function(X0) ),
inference(flattening,[],[f87]) ).
fof(f103,plain,
( sK11 != function_inverse(function_inverse(sK11))
& one_to_one(sK11)
& relation(sK11)
& function(sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X0,sK11)],[f88]) ).
fof(f110,plain,
! [X0] :
( function(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f111,plain,
! [X0] :
( relation(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f159,plain,
! [X0] :
( ~ one_to_one(X0)
| relation_dom(X0) = relation_rng(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f160,plain,
! [X0] :
( ~ one_to_one(X0)
| relation_rng(X0) = relation_dom(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f162,plain,
! [X0] :
( ~ one_to_one(X0)
| relation_composition(function_inverse(X0),X0) = identity_relation(relation_rng(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f164,plain,
! [X0] :
( one_to_one(function_inverse(X0))
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f165,plain,
! [X0,X1] :
( relation_composition(X0,X1) != identity_relation(relation_dom(X0))
| ~ one_to_one(X0)
| relation_rng(X0) != relation_dom(X1)
| function_inverse(X0) = X1
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f166,plain,
function(sK11),
inference(cnf_transformation,[],[f103]) ).
fof(f167,plain,
relation(sK11),
inference(cnf_transformation,[],[f103]) ).
fof(f168,plain,
one_to_one(sK11),
inference(cnf_transformation,[],[f103]) ).
fof(f169,plain,
sK11 != function_inverse(function_inverse(sK11)),
inference(cnf_transformation,[],[f103]) ).
fof(f296,plain,
( relation_dom(sK11) = relation_rng(function_inverse(sK11))
| ~ relation(sK11)
| ~ function(sK11) ),
inference(resolution,[],[f159,f168]) ).
fof(f297,plain,
( relation_dom(sK11) = relation_rng(function_inverse(sK11))
| ~ function(sK11) ),
inference(forward_subsumption_resolution,[],[f296,f167]) ).
fof(f301,plain,
relation_dom(sK11) = relation_rng(function_inverse(sK11)),
inference(forward_subsumption_resolution,[],[f297,f166]) ).
fof(f330,definition,
( spl12_7
<=> relation(function_inverse(sK11)) ),
introduced(definition,[new_symbols(definition,[spl12_7])],[avatar_definition]) ).
fof(f331,plain,
( relation(function_inverse(sK11))
| ~ spl12_7 ),
inference(avatar_component_clause,[],[f330]) ).
fof(f332,plain,
( ~ relation(function_inverse(sK11))
| spl12_7 ),
inference(avatar_component_clause,[],[f330]) ).
fof(f337,plain,
( relation_rng(sK11) = relation_dom(function_inverse(sK11))
| ~ relation(sK11)
| ~ function(sK11) ),
inference(resolution,[],[f160,f168]) ).
fof(f338,plain,
( relation_rng(sK11) = relation_dom(function_inverse(sK11))
| ~ function(sK11) ),
inference(forward_subsumption_resolution,[],[f337,f167]) ).
fof(f342,plain,
relation_rng(sK11) = relation_dom(function_inverse(sK11)),
inference(forward_subsumption_resolution,[],[f338,f166]) ).
fof(f349,plain,
( relation_composition(function_inverse(sK11),sK11) = identity_relation(relation_rng(sK11))
| ~ relation(sK11)
| ~ function(sK11) ),
inference(resolution,[],[f162,f168]) ).
fof(f350,plain,
( relation_composition(function_inverse(sK11),sK11) = identity_relation(relation_rng(sK11))
| ~ function(sK11) ),
inference(forward_subsumption_resolution,[],[f349,f167]) ).
fof(f354,plain,
relation_composition(function_inverse(sK11),sK11) = identity_relation(relation_rng(sK11)),
inference(forward_subsumption_resolution,[],[f350,f166]) ).
fof(f358,plain,
( ~ relation(sK11)
| ~ function(sK11)
| spl12_7 ),
inference(resolution,[],[f332,f111]) ).
fof(f359,plain,
( ~ function(sK11)
| spl12_7 ),
inference(forward_subsumption_resolution,[],[f358,f167]) ).
fof(f360,plain,
( $false
| spl12_7 ),
inference(forward_subsumption_resolution,[],[f359,f166]) ).
fof(f361,plain,
spl12_7,
inference(avatar_contradiction_clause,[],[f360]) ).
fof(f392,plain,
( identity_relation(relation_rng(sK11)) != identity_relation(relation_dom(function_inverse(sK11)))
| ~ one_to_one(function_inverse(sK11))
| relation_dom(sK11) != relation_rng(function_inverse(sK11))
| sK11 = function_inverse(function_inverse(sK11))
| ~ relation(sK11)
| ~ function(sK11)
| ~ relation(function_inverse(sK11))
| ~ function(function_inverse(sK11)) ),
inference(superposition,[],[f165,f354]) ).
fof(f393,plain,
( identity_relation(relation_rng(sK11)) != identity_relation(relation_dom(function_inverse(sK11)))
| ~ one_to_one(function_inverse(sK11))
| sK11 = function_inverse(function_inverse(sK11))
| ~ relation(sK11)
| ~ function(sK11)
| ~ relation(function_inverse(sK11))
| ~ function(function_inverse(sK11)) ),
inference(forward_subsumption_resolution,[],[f392,f301]) ).
fof(f394,plain,
( identity_relation(relation_rng(sK11)) != identity_relation(relation_dom(function_inverse(sK11)))
| ~ one_to_one(function_inverse(sK11))
| ~ relation(sK11)
| ~ function(sK11)
| ~ relation(function_inverse(sK11))
| ~ function(function_inverse(sK11)) ),
inference(forward_subsumption_resolution,[],[f393,f169]) ).
fof(f395,plain,
( identity_relation(relation_rng(sK11)) != identity_relation(relation_dom(function_inverse(sK11)))
| ~ one_to_one(function_inverse(sK11))
| ~ function(sK11)
| ~ relation(function_inverse(sK11))
| ~ function(function_inverse(sK11)) ),
inference(forward_subsumption_resolution,[],[f394,f167]) ).
fof(f396,plain,
( identity_relation(relation_rng(sK11)) != identity_relation(relation_dom(function_inverse(sK11)))
| ~ one_to_one(function_inverse(sK11))
| ~ relation(function_inverse(sK11))
| ~ function(function_inverse(sK11)) ),
inference(forward_subsumption_resolution,[],[f395,f166]) ).
fof(f397,plain,
( identity_relation(relation_rng(sK11)) != identity_relation(relation_dom(function_inverse(sK11)))
| ~ one_to_one(function_inverse(sK11))
| ~ function(function_inverse(sK11))
| ~ spl12_7 ),
inference(forward_subsumption_resolution,[],[f396,f331]) ).
fof(f398,plain,
( identity_relation(relation_rng(sK11)) != identity_relation(relation_rng(sK11))
| ~ one_to_one(function_inverse(sK11))
| ~ function(function_inverse(sK11))
| ~ spl12_7 ),
inference(forward_demodulation,[],[f397,f342]) ).
fof(f399,plain,
( ~ one_to_one(function_inverse(sK11))
| ~ function(function_inverse(sK11))
| ~ spl12_7 ),
inference(trivial_inequality_removal,[],[f398]) ).
fof(f401,definition,
( spl12_9
<=> function(function_inverse(sK11)) ),
introduced(definition,[new_symbols(definition,[spl12_9])],[avatar_definition]) ).
fof(f403,plain,
( ~ function(function_inverse(sK11))
| spl12_9 ),
inference(avatar_component_clause,[],[f401]) ).
fof(f405,definition,
( spl12_10
<=> one_to_one(function_inverse(sK11)) ),
introduced(definition,[new_symbols(definition,[spl12_10])],[avatar_definition]) ).
fof(f407,plain,
( ~ one_to_one(function_inverse(sK11))
| spl12_10 ),
inference(avatar_component_clause,[],[f405]) ).
fof(f408,plain,
( ~ spl12_9
| ~ spl12_10
| ~ spl12_7 ),
inference(avatar_split_clause,[],[f399,f330,f405,f401]) ).
fof(f416,plain,
( ~ relation(sK11)
| ~ function(sK11)
| spl12_9 ),
inference(resolution,[],[f403,f110]) ).
fof(f417,plain,
( ~ function(sK11)
| spl12_9 ),
inference(forward_subsumption_resolution,[],[f416,f167]) ).
fof(f418,plain,
( $false
| spl12_9 ),
inference(forward_subsumption_resolution,[],[f417,f166]) ).
fof(f419,plain,
spl12_9,
inference(avatar_contradiction_clause,[],[f418]) ).
fof(f447,plain,
( ~ one_to_one(sK11)
| ~ relation(sK11)
| ~ function(sK11)
| spl12_10 ),
inference(resolution,[],[f407,f164]) ).
fof(f448,plain,
( ~ relation(sK11)
| ~ function(sK11)
| spl12_10 ),
inference(forward_subsumption_resolution,[],[f447,f168]) ).
fof(f449,plain,
( ~ function(sK11)
| spl12_10 ),
inference(forward_subsumption_resolution,[],[f448,f167]) ).
fof(f450,plain,
( $false
| spl12_10 ),
inference(forward_subsumption_resolution,[],[f449,f166]) ).
fof(f451,plain,
spl12_10,
inference(avatar_contradiction_clause,[],[f450]) ).
cnf(s7,plain,
spl12_7,
inference(sat_conversion,[],[f361]) ).
cnf(s9,plain,
( ~ spl12_7
| ~ spl12_9
| ~ spl12_10 ),
inference(sat_conversion,[],[f408]) ).
cnf(s10,plain,
spl12_9,
inference(sat_conversion,[],[f419]) ).
cnf(s11,plain,
spl12_10,
inference(sat_conversion,[],[f451]) ).
cnf(s12,plain,
~ spl12_7,
inference(rat,[],[s9,s11,s10]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s7,s12]) ).
fof(f452,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU032+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n026.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 03:28:11 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 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
% 0.16/0.48 % (3436035)Will run a generic schedule for satisfiability detection.
% 0.16/0.48 % (3436044)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4062929762:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.48 % (3436041)% WARNING: option uhcvi not known.
% 0.16/0.48 % (3436040)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3548657169_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.48 % (3436045)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3862547325:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.48 % (3436041)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=205628334:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.48 % (3436042)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=377739561:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.48 % (3436043)dis+10_1_sil=32000:sp=arity:random_seed=2315115124:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.48 % (3436046)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1245107363:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.48 % TRYING [1]
% 0.16/0.48 % TRYING [2]
% 0.16/0.48 % TRYING [3]
% 0.16/0.48 % TRYING [4]
% 0.16/0.48 % (3436043) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3436035-3436043"...
% 0.16/0.48 % TRYING [5]
% 0.16/0.48 % (3436043)...printing done.
% 0.16/0.48 % (3436043)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 % (3436043)------------------------------
% 0.16/0.48 % (3436043)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.48 % (3436043)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.48 % (3436043)CaDiCaL version: 2.1.3
% 0.16/0.48 % (3436043)Termination reason: Refutation
% 0.16/0.48 % (3436043)Time elapsed: 0.008 s
% 0.16/0.48 % (3436043)Peak memory usage: 12 MB
% 0.16/0.48 % (3436043)Instructions burned: 10 (million)
% 0.16/0.48 % (3436035)Success in time 0.054 s
% 0.16/0.48 % Vampire exiting
%------------------------------------------------------------------------------