%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU030+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 : n004.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 2.72s 1.28s
% Output : Refutation 3.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 6
% Syntax : Number of formulae : 50 ( 13 unt; 1 def)
% Number of atoms : 243 ( 88 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 332 ( 139 ~; 132 |; 46 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 49 ( 45 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,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(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/sandbox2/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/sandbox2/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/sandbox2/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(X0) = relation_dom(X1)
& relation_composition(X0,X1) = identity_relation(relation_dom(X0)) )
=> X1 = function_inverse(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_funct_1) ).
fof(f41,negated_conjecture,
~ ! [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) ) ) ),
inference(negated_conjecture,[status(cth)],[f40]) ).
fof(f45,plain,
? [X0] :
( ? [X1] :
( function_inverse(X0) != X1
& 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,[],[f41]) ).
fof(f46,plain,
? [X0] :
( ? [X1] :
( function_inverse(X0) != X1
& 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,[],[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_rng(sK0) = relation_dom(sK1)
& relation_composition(sK0,sK1) = identity_relation(relation_dom(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(sK0,sK1) = identity_relation(relation_dom(sK0)),
inference(cnf_transformation,[],[f74]) ).
fof(f85,plain,
relation_rng(sK0) = relation_dom(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(f89,plain,
! [X0] :
( relation_composition(function_inverse(X0),X0) = identity_relation(relation_rng(X0))
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f91,plain,
! [X0] :
( relation_dom(X0) = relation_rng(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(f156,plain,
! [X0] :
( identity_relation(relation_rng(X0)) != identity_relation(relation_dom(sK0))
| identity_relation(relation_dom(sK1)) != relation_composition(X0,sK0)
| sK1 = X0
| ~ relation(sK1)
| ~ function(sK1)
| ~ relation(sK0)
| ~ function(sK0)
| ~ relation(X0)
| ~ function(X0) ),
inference(superposition,[],[f131,f84]) ).
fof(f157,plain,
! [X0] :
( identity_relation(relation_rng(X0)) != identity_relation(relation_dom(sK0))
| identity_relation(relation_dom(sK1)) != relation_composition(X0,sK0)
| sK1 = X0
| ~ function(sK1)
| ~ relation(sK0)
| ~ function(sK0)
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[],[f156,f83]) ).
fof(f159,plain,
! [X0] :
( identity_relation(relation_rng(X0)) != identity_relation(relation_dom(sK0))
| identity_relation(relation_dom(sK1)) != relation_composition(X0,sK0)
| sK1 = X0
| ~ relation(sK0)
| ~ function(sK0)
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[],[f157,f82]) ).
fof(f169,plain,
! [X0] :
( identity_relation(relation_rng(X0)) != identity_relation(relation_dom(sK0))
| identity_relation(relation_dom(sK1)) != relation_composition(X0,sK0)
| sK1 = X0
| ~ function(sK0)
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[],[f159,f81]) ).
fof(f170,plain,
! [X0] :
( identity_relation(relation_rng(X0)) != identity_relation(relation_dom(sK0))
| identity_relation(relation_dom(sK1)) != relation_composition(X0,sK0)
| sK1 = X0
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[],[f169,f80]) ).
fof(f171,plain,
! [X0] :
( identity_relation(relation_rng(X0)) != identity_relation(relation_dom(sK0))
| relation_composition(X0,sK0) != identity_relation(relation_rng(sK0))
| sK1 = X0
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_demodulation,[],[f170,f85]) ).
fof(f173,plain,
! [X0] :
( identity_relation(relation_dom(X0)) != identity_relation(relation_dom(sK0))
| identity_relation(relation_rng(sK0)) != relation_composition(function_inverse(X0),sK0)
| function_inverse(X0) = sK1
| ~ relation(function_inverse(X0))
| ~ function(function_inverse(X0))
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(superposition,[],[f171,f91]) ).
fof(f174,plain,
! [X0] :
( identity_relation(relation_dom(X0)) != identity_relation(relation_dom(sK0))
| identity_relation(relation_rng(sK0)) != relation_composition(function_inverse(X0),sK0)
| function_inverse(X0) = sK1
| ~ function(function_inverse(X0))
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[],[f173,f94]) ).
fof(f175,plain,
! [X0] :
( identity_relation(relation_rng(sK0)) != relation_composition(function_inverse(X0),sK0)
| identity_relation(relation_dom(X0)) != identity_relation(relation_dom(sK0))
| function_inverse(X0) = sK1
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[],[f174,f93]) ).
fof(f176,plain,
( identity_relation(relation_rng(sK0)) != identity_relation(relation_rng(sK0))
| identity_relation(relation_dom(sK0)) != identity_relation(relation_dom(sK0))
| sK1 = function_inverse(sK0)
| ~ one_to_one(sK0)
| ~ relation(sK0)
| ~ function(sK0)
| ~ one_to_one(sK0)
| ~ relation(sK0)
| ~ function(sK0) ),
inference(superposition,[],[f175,f89]) ).
fof(f177,plain,
( identity_relation(relation_rng(sK0)) != identity_relation(relation_rng(sK0))
| identity_relation(relation_dom(sK0)) != identity_relation(relation_dom(sK0))
| sK1 = function_inverse(sK0)
| ~ one_to_one(sK0)
| ~ relation(sK0)
| ~ function(sK0) ),
inference(duplicate_literal_removal,[],[f176]) ).
fof(f178,plain,
( sK1 = function_inverse(sK0)
| ~ one_to_one(sK0)
| ~ relation(sK0)
| ~ function(sK0) ),
inference(trivial_inequality_removal,[],[f177]) ).
fof(f179,plain,
( sK1 = function_inverse(sK0)
| ~ relation(sK0)
| ~ function(sK0) ),
inference(forward_subsumption_resolution,[],[f178,f86]) ).
fof(f180,plain,
( sK1 = function_inverse(sK0)
| ~ function(sK0) ),
inference(forward_subsumption_resolution,[],[f179,f81]) ).
fof(f181,plain,
sK1 = function_inverse(sK0),
inference(forward_subsumption_resolution,[],[f180,f80]) ).
fof(f186,plain,
~ sP7(function_inverse(sK0)),
inference(superposition,[],[f129,f181]) ).
fof(f188,plain,
$false,
inference(forward_subsumption_resolution,[],[f186,f130]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU030+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.36 % Computer : n004.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Mon Sep 28 03:25:45 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 2.72/1.28 % (4120984)Detected formulas, will run a generic FOF schedule.
% 2.72/1.28 % (4120995)dis-21_1_sil=8000:lcm=predicate:random_seed=2127623478: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)
% 2.72/1.28 % (4120990)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=2293467315:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.72/1.28 % (4120992)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3173319648:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.72/1.28 % (4120991)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=834537806:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.72/1.28 % (4120993)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4156861624:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.72/1.28 % (4120989)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=242571438:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.72/1.28 % (4120994)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=644612395:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.72/1.28 % (4120995)Instruction limit reached!
% 2.72/1.28 % (4120995)------------------------------
% 2.72/1.28 % (4120995)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.72/1.28 % (4120995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/1.28 % (4120995)CaDiCaL version: 2.1.3
% 2.72/1.28 % (4120995)Termination reason: Instruction limit
% 2.72/1.28 % (4120995)Termination phase: Saturation
% 2.72/1.28 % (4120995)Time elapsed: 0.042 s
% 2.72/1.28 % (4120995)Peak memory usage: 90 MB
% 2.72/1.28 % (4120995)Instructions burned: 129 (million)
% 2.72/1.28 % (4120992)First to succeed.
% 2.72/1.28 % (4120993)Also succeeded, but the first one will report.
% 2.72/1.28 % (4120992)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4120984"
% 2.72/1.28 % (4120994)Also succeeded, but the first one will report.
% 2.72/1.28 % (4121003)lrs+10_1_sil=8000:sp=occurrence:random_seed=1343216921:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.72/1.28 % (4121003)Instruction limit reached!
% 2.72/1.28 % (4121003)------------------------------
% 2.72/1.28 % (4121003)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.72/1.28 % (4121003)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/1.28 % (4121003)CaDiCaL version: 2.1.3
% 2.72/1.28 % (4121003)Termination reason: Instruction limit
% 2.72/1.28 % (4121003)Termination phase: Saturation
% 2.72/1.28 % (4121003)Time elapsed: 0.082 s
% 2.72/1.28 % (4121003)Peak memory usage: 92 MB
% 2.72/1.28 % (4121003)Instructions burned: 287 (million)
% 2.72/1.28 % (4120992)Refutation found. Thanks to Tanya!
% 2.72/1.28 % SZS status Theorem for theBenchmark
% 2.72/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.63/1.48 % (4120992)------------------------------
% 3.63/1.48 % (4120992)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.48 % (4120992)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.48 % (4120992)CaDiCaL version: 2.1.3
% 3.63/1.48 % (4120992)Termination reason: Refutation
% 3.63/1.48 % (4120992)Time elapsed: 0.005 s
% 3.63/1.48 % (4120992)Peak memory usage: 88 MB
% 3.63/1.48 % (4120992)Instructions burned: 6 (million)
% 3.63/1.48 % (4120992)------------------------------
% 3.63/1.48 % (4120992)------------------------------
% 3.63/1.48 % (4120984)Success in time 0.432 s
% 3.63/1.48 % Vampire exiting
%------------------------------------------------------------------------------