%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU031+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 12:47:06 PM UTC 2026
% Result : Theorem 0.43s 0.82s
% Output : Refutation 2.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 8
% Syntax : Number of formulae : 65 ( 16 unt; 3 def)
% Number of atoms : 270 ( 89 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 355 ( 150 ~; 142 |; 46 &)
% ( 2 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn 45 !; 4 ?)
% 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(f21,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( ( relation_rng(X1) = X0
& relation_composition(X1,X2) = identity_relation(relation_dom(X3))
& relation_composition(X2,X3) = identity_relation(X0) )
=> X3 = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l72_funct_1) ).
fof(f37,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(f39,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(f40,conjecture,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ( one_to_one(X0)
& relation_rng(X1) = relation_dom(X0)
& relation_composition(X1,X0) = identity_relation(relation_rng(X0)) )
=> X1 = function_inverse(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_funct_1) ).
fof(f41,negated_conjecture,
~ ! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ( one_to_one(X0)
& relation_rng(X1) = relation_dom(X0)
& relation_composition(X1,X0) = identity_relation(relation_rng(X0)) )
=> X1 = function_inverse(X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f40]) ).
fof(f45,plain,
? [X0] :
( ? [X1] :
( function_inverse(X0) != X1
& one_to_one(X0)
& relation_rng(X1) = relation_dom(X0)
& relation_composition(X1,X0) = identity_relation(relation_rng(X0))
& relation(X1)
& function(X1) )
& relation(X0)
& function(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f46,plain,
? [X0] :
( ? [X1] :
( function_inverse(X0) != X1
& one_to_one(X0)
& relation_rng(X1) = relation_dom(X0)
& relation_composition(X1,X0) = identity_relation(relation_rng(X0))
& relation(X1)
& function(X1) )
& relation(X0)
& function(X0) ),
inference(flattening,[],[f45]) ).
fof(f48,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,[],[f39]) ).
fof(f49,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,[],[f48]) ).
fof(f50,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,[],[f37]) ).
fof(f51,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,[],[f50]) ).
fof(f52,plain,
! [X0] :
( ( relation(function_inverse(X0))
& function(function_inverse(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f53,plain,
! [X0] :
( ( relation(function_inverse(X0))
& function(function_inverse(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f52]) ).
fof(f62,plain,
! [X0,X1] :
( ! [X2] :
( ! [X3] :
( X3 = X1
| relation_rng(X1) != X0
| relation_composition(X1,X2) != identity_relation(relation_dom(X3))
| identity_relation(X0) != relation_composition(X2,X3)
| ~ relation(X3)
| ~ function(X3) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f63,plain,
! [X0,X1] :
( ! [X2] :
( ! [X3] :
( X3 = X1
| relation_rng(X1) != X0
| relation_composition(X1,X2) != identity_relation(relation_dom(X3))
| identity_relation(X0) != relation_composition(X2,X3)
| ~ relation(X3)
| ~ function(X3) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f62]) ).
fof(f74,plain,
( sK1 != function_inverse(sK0)
& one_to_one(sK0)
& relation_dom(sK0) = relation_rng(sK1)
& relation_composition(sK1,sK0) = identity_relation(relation_rng(sK0))
& relation(sK1)
& function(sK1)
& relation(sK0)
& function(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f46]) ).
fof(f80,plain,
function(sK0),
inference(cnf_transformation,[],[f74]) ).
fof(f81,plain,
relation(sK0),
inference(cnf_transformation,[],[f74]) ).
fof(f82,plain,
function(sK1),
inference(cnf_transformation,[],[f74]) ).
fof(f83,plain,
relation(sK1),
inference(cnf_transformation,[],[f74]) ).
fof(f84,plain,
relation_composition(sK1,sK0) = identity_relation(relation_rng(sK0)),
inference(cnf_transformation,[],[f74]) ).
fof(f85,plain,
relation_dom(sK0) = relation_rng(sK1),
inference(cnf_transformation,[],[f74]) ).
fof(f86,plain,
one_to_one(sK0),
inference(cnf_transformation,[],[f74]) ).
fof(f87,plain,
sK1 != function_inverse(sK0),
inference(cnf_transformation,[],[f74]) ).
fof(f90,plain,
! [X0] :
( relation_composition(X0,function_inverse(X0)) = identity_relation(relation_dom(X0))
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f92,plain,
! [X0] :
( relation_rng(X0) = relation_dom(function_inverse(X0))
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f93,plain,
! [X0] :
( function(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f94,plain,
! [X0] :
( relation(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f102,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| relation_rng(X1) != X0
| relation_composition(X1,X2) != identity_relation(relation_dom(X3))
| identity_relation(X0) != relation_composition(X2,X3)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f129,definition,
~ sP7(sK1),
introduced(definition,[new_symbols(definition,[sP7])],[inequality_splitting_name_introduction]) ).
fof(f130,plain,
sP7(function_inverse(sK0)),
inference(inequality_splitting,[],[f87,f129]) ).
fof(f131,plain,
! [X2,X3,X1] :
( relation_composition(X2,X3) != identity_relation(relation_rng(X1))
| relation_composition(X1,X2) != identity_relation(relation_dom(X3))
| X1 = X3
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(equality_resolution,[],[f102]) ).
fof(f147,plain,
! [X0,X1] :
( relation_composition(X0,X1) != identity_relation(relation_dom(sK0))
| relation_composition(sK1,X0) != identity_relation(relation_dom(X1))
| sK1 = X1
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X0)
| ~ function(X0)
| ~ relation(sK1)
| ~ function(sK1) ),
inference(superposition,[],[f131,f85]) ).
fof(f148,plain,
! [X0,X1] :
( relation_composition(X0,X1) != identity_relation(relation_dom(sK0))
| relation_composition(sK1,X0) != identity_relation(relation_dom(X1))
| sK1 = X1
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X0)
| ~ function(X0)
| ~ function(sK1) ),
inference(forward_subsumption_resolution,[],[f147,f83]) ).
fof(f150,plain,
! [X0,X1] :
( relation_composition(sK1,X0) != identity_relation(relation_dom(X1))
| relation_composition(X0,X1) != identity_relation(relation_dom(sK0))
| sK1 = X1
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[],[f148,f82]) ).
fof(f195,plain,
! [X0] :
( identity_relation(relation_dom(X0)) != identity_relation(relation_rng(sK0))
| identity_relation(relation_dom(sK0)) != relation_composition(sK0,X0)
| sK1 = X0
| ~ relation(X0)
| ~ function(X0)
| ~ relation(sK0)
| ~ function(sK0) ),
inference(superposition,[],[f150,f84]) ).
fof(f200,plain,
! [X0] :
( identity_relation(relation_dom(X0)) != identity_relation(relation_rng(sK0))
| identity_relation(relation_dom(sK0)) != relation_composition(sK0,X0)
| sK1 = X0
| ~ relation(X0)
| ~ function(X0)
| ~ function(sK0) ),
inference(forward_subsumption_resolution,[],[f195,f81]) ).
fof(f203,plain,
! [X0] :
( identity_relation(relation_dom(sK0)) != relation_composition(sK0,X0)
| identity_relation(relation_dom(X0)) != identity_relation(relation_rng(sK0))
| sK1 = X0
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[],[f200,f80]) ).
fof(f210,plain,
( identity_relation(relation_dom(sK0)) != identity_relation(relation_dom(sK0))
| identity_relation(relation_rng(sK0)) != identity_relation(relation_dom(function_inverse(sK0)))
| sK1 = function_inverse(sK0)
| ~ relation(function_inverse(sK0))
| ~ function(function_inverse(sK0))
| ~ one_to_one(sK0)
| ~ relation(sK0)
| ~ function(sK0) ),
inference(superposition,[],[f203,f90]) ).
fof(f211,plain,
( identity_relation(relation_rng(sK0)) != identity_relation(relation_dom(function_inverse(sK0)))
| sK1 = function_inverse(sK0)
| ~ relation(function_inverse(sK0))
| ~ function(function_inverse(sK0))
| ~ one_to_one(sK0)
| ~ relation(sK0)
| ~ function(sK0) ),
inference(trivial_inequality_removal,[],[f210]) ).
fof(f212,plain,
( identity_relation(relation_rng(sK0)) != identity_relation(relation_dom(function_inverse(sK0)))
| sK1 = function_inverse(sK0)
| ~ function(function_inverse(sK0))
| ~ one_to_one(sK0)
| ~ relation(sK0)
| ~ function(sK0) ),
inference(forward_subsumption_resolution,[],[f211,f94]) ).
fof(f213,plain,
( identity_relation(relation_rng(sK0)) != identity_relation(relation_dom(function_inverse(sK0)))
| sK1 = function_inverse(sK0)
| ~ one_to_one(sK0)
| ~ relation(sK0)
| ~ function(sK0) ),
inference(forward_subsumption_resolution,[],[f212,f93]) ).
fof(f214,plain,
( identity_relation(relation_rng(sK0)) != identity_relation(relation_dom(function_inverse(sK0)))
| sK1 = function_inverse(sK0)
| ~ relation(sK0)
| ~ function(sK0) ),
inference(forward_subsumption_resolution,[],[f213,f86]) ).
fof(f215,plain,
( identity_relation(relation_rng(sK0)) != identity_relation(relation_dom(function_inverse(sK0)))
| sK1 = function_inverse(sK0)
| ~ function(sK0) ),
inference(forward_subsumption_resolution,[],[f214,f81]) ).
fof(f216,plain,
( identity_relation(relation_rng(sK0)) != identity_relation(relation_dom(function_inverse(sK0)))
| sK1 = function_inverse(sK0) ),
inference(forward_subsumption_resolution,[],[f215,f80]) ).
fof(f218,definition,
( spl8_9
<=> sK1 = function_inverse(sK0) ),
introduced(definition,[new_symbols(definition,[spl8_9])],[avatar_definition]) ).
fof(f220,plain,
( sK1 = function_inverse(sK0)
| ~ spl8_9 ),
inference(avatar_component_clause,[],[f218]) ).
fof(f222,definition,
( spl8_10
<=> identity_relation(relation_rng(sK0)) = identity_relation(relation_dom(function_inverse(sK0))) ),
introduced(definition,[new_symbols(definition,[spl8_10])],[avatar_definition]) ).
fof(f224,plain,
( identity_relation(relation_rng(sK0)) != identity_relation(relation_dom(function_inverse(sK0)))
| spl8_10 ),
inference(avatar_component_clause,[],[f222]) ).
fof(f225,plain,
( spl8_9
| ~ spl8_10 ),
inference(avatar_split_clause,[],[f216,f222,f218]) ).
fof(f228,plain,
( identity_relation(relation_rng(sK0)) != identity_relation(relation_rng(sK0))
| ~ one_to_one(sK0)
| ~ relation(sK0)
| ~ function(sK0)
| spl8_10 ),
inference(superposition,[],[f224,f92]) ).
fof(f229,plain,
( ~ one_to_one(sK0)
| ~ relation(sK0)
| ~ function(sK0)
| spl8_10 ),
inference(trivial_inequality_removal,[],[f228]) ).
fof(f230,plain,
( ~ relation(sK0)
| ~ function(sK0)
| spl8_10 ),
inference(forward_subsumption_resolution,[],[f229,f86]) ).
fof(f231,plain,
( ~ function(sK0)
| spl8_10 ),
inference(forward_subsumption_resolution,[],[f230,f81]) ).
fof(f232,plain,
( $false
| spl8_10 ),
inference(forward_subsumption_resolution,[],[f231,f80]) ).
fof(f233,plain,
spl8_10,
inference(avatar_contradiction_clause,[],[f232]) ).
fof(f249,plain,
( ~ sP7(function_inverse(sK0))
| ~ spl8_9 ),
inference(superposition,[],[f129,f220]) ).
fof(f255,plain,
( $false
| ~ spl8_9 ),
inference(forward_subsumption_resolution,[],[f249,f130]) ).
fof(f256,plain,
~ spl8_9,
inference(avatar_contradiction_clause,[],[f255]) ).
cnf(s5,plain,
( spl8_9
| ~ spl8_10 ),
inference(sat_conversion,[],[f225]) ).
cnf(s6,plain,
spl8_10,
inference(sat_conversion,[],[f233]) ).
cnf(s7,plain,
~ spl8_9,
inference(sat_conversion,[],[f256]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s5,s6,s7]) ).
fof(f257,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU031+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Mon Sep 28 03:25:27 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.32 Running first-order theorem proving
% 0.04/0.32 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.43/0.82 % (2989018)Detected formulas, will run a generic FOF schedule.
% 0.43/0.82 % (2989024)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=286454287:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.43/0.82 % (2989026)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1378271177:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.43/0.82 % (2989028)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2384127780:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.43/0.82 % (2989023)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=3686956821:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.43/0.82 % (2989027)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1237053934:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.43/0.82 % (2989029)dis-21_1_sil=8000:lcm=predicate:random_seed=856835031: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)
% 0.43/0.82 % (2989025)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=2345383336:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.43/0.82 % (2989026)First to succeed.
% 0.43/0.82 % (2989026)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2989018"
% 0.43/0.82 % (2989027)Also succeeded, but the first one will report.
% 0.43/0.82 % (2989028)Also succeeded, but the first one will report.
% 0.43/0.82 % (2989029)Instruction limit reached!
% 0.43/0.82 % (2989029)------------------------------
% 0.43/0.82 % (2989029)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.43/0.82 % (2989029)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.43/0.82 % (2989029)CaDiCaL version: 2.1.3
% 0.43/0.82 % (2989029)Termination reason: Instruction limit
% 0.43/0.82 % (2989029)Termination phase: Saturation
% 0.43/0.82 % (2989029)Time elapsed: 0.042 s
% 0.43/0.82 % (2989029)Peak memory usage: 90 MB
% 0.43/0.82 % (2989029)Instructions burned: 129 (million)
% 0.43/0.82 % (2989026)Refutation found. Thanks to Tanya!
% 0.43/0.82 % SZS status Theorem for theBenchmark
% 0.43/0.82 % SZS output start Proof for theBenchmark
% See solution above
% 2.34/0.92 % (2989026)------------------------------
% 2.34/0.92 % (2989026)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.34/0.92 % (2989026)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.34/0.92 % (2989026)CaDiCaL version: 2.1.3
% 2.34/0.92 % (2989026)Termination reason: Refutation
% 2.34/0.92 % (2989026)Time elapsed: 0.004 s
% 2.34/0.92 % (2989026)Peak memory usage: 90 MB
% 2.34/0.92 % (2989026)Instructions burned: 8 (million)
% 2.34/0.92 % (2989026)------------------------------
% 2.34/0.92 % (2989026)------------------------------
% 2.34/0.92 % (2989018)Success in time 0.297 s
% 2.34/0.92 % Vampire exiting
%------------------------------------------------------------------------------