%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU219+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 12:47:48 PM UTC 2026
% Result : Theorem 2.64s 1.34s
% Output : Refutation 2.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 46 ( 12 unt; 4 def)
% Number of atoms : 118 ( 22 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 133 ( 61 ~; 47 |; 16 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-1 aty)
% Number of variables : 12 ( 0 sgn 10 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> function_inverse(X0) = relation_inverse(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_funct_1) ).
fof(f10,axiom,
! [X0] :
( relation(X0)
=> ( relation_rng(X0) = relation_dom(relation_inverse(X0))
& relation_dom(X0) = relation_rng(relation_inverse(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_relat_1) ).
fof(f11,conjecture,
! [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(f12,negated_conjecture,
~ ! [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)) ) ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,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,[],[f12]) ).
fof(f14,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,[],[f13]) ).
fof(f18,plain,
! [X0] :
( function_inverse(X0) = relation_inverse(X0)
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f19,plain,
! [X0] :
( function_inverse(X0) = relation_inverse(X0)
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f18]) ).
fof(f20,plain,
! [X0] :
( ( relation_rng(X0) = relation_dom(relation_inverse(X0))
& relation_dom(X0) = relation_rng(relation_inverse(X0)) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f23,plain,
( ( relation_rng(sK0) != relation_dom(function_inverse(sK0))
| relation_dom(sK0) != relation_rng(function_inverse(sK0)) )
& one_to_one(sK0)
& relation(sK0)
& function(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f14]) ).
fof(f26,plain,
function(sK0),
inference(cnf_transformation,[],[f23]) ).
fof(f27,plain,
relation(sK0),
inference(cnf_transformation,[],[f23]) ).
fof(f28,plain,
one_to_one(sK0),
inference(cnf_transformation,[],[f23]) ).
fof(f29,plain,
( relation_rng(sK0) != relation_dom(function_inverse(sK0))
| relation_dom(sK0) != relation_rng(function_inverse(sK0)) ),
inference(cnf_transformation,[],[f23]) ).
fof(f33,plain,
! [X0] :
( function_inverse(X0) = relation_inverse(X0)
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f36,plain,
! [X0] :
( relation_dom(X0) = relation_rng(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f37,plain,
! [X0] :
( relation_rng(X0) = relation_dom(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f43,definition,
~ sP3(relation_rng(sK0)),
introduced(definition,[new_symbols(definition,[sP3])],[inequality_splitting_name_introduction]) ).
fof(f44,definition,
~ sP4(relation_dom(sK0)),
introduced(definition,[new_symbols(definition,[sP4])],[inequality_splitting_name_introduction]) ).
fof(f45,plain,
( sP3(relation_dom(function_inverse(sK0)))
| sP4(relation_rng(function_inverse(sK0))) ),
inference(inequality_splitting,[],[f29,f44,f43]) ).
fof(f47,definition,
( spl5_1
<=> sP4(relation_rng(function_inverse(sK0))) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f49,plain,
( sP4(relation_rng(function_inverse(sK0)))
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f51,definition,
( spl5_2
<=> sP3(relation_dom(function_inverse(sK0))) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f53,plain,
( sP3(relation_dom(function_inverse(sK0)))
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f54,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f45,f51,f47]) ).
fof(f55,plain,
( ~ sP4(relation_rng(relation_inverse(sK0)))
| ~ relation(sK0) ),
inference(superposition,[],[f44,f36]) ).
fof(f56,plain,
~ sP4(relation_rng(relation_inverse(sK0))),
inference(forward_subsumption_resolution,[],[f55,f27]) ).
fof(f57,plain,
( sP3(relation_dom(relation_inverse(sK0)))
| ~ one_to_one(sK0)
| ~ relation(sK0)
| ~ function(sK0)
| ~ spl5_2 ),
inference(superposition,[],[f53,f33]) ).
fof(f68,plain,
( sP3(relation_dom(relation_inverse(sK0)))
| ~ relation(sK0)
| ~ function(sK0)
| ~ spl5_2 ),
inference(forward_subsumption_resolution,[],[f57,f28]) ).
fof(f69,plain,
( sP3(relation_dom(relation_inverse(sK0)))
| ~ function(sK0)
| ~ spl5_2 ),
inference(forward_subsumption_resolution,[],[f68,f27]) ).
fof(f70,plain,
( sP3(relation_dom(relation_inverse(sK0)))
| ~ spl5_2 ),
inference(forward_subsumption_resolution,[],[f69,f26]) ).
fof(f82,plain,
( sP3(relation_rng(sK0))
| ~ relation(sK0)
| ~ spl5_2 ),
inference(superposition,[],[f70,f37]) ).
fof(f93,plain,
( ~ relation(sK0)
| ~ spl5_2 ),
inference(forward_subsumption_resolution,[],[f82,f43]) ).
fof(f94,plain,
( $false
| ~ spl5_2 ),
inference(forward_subsumption_resolution,[],[f93,f27]) ).
fof(f95,plain,
~ spl5_2,
inference(avatar_contradiction_clause,[],[f94]) ).
fof(f96,plain,
( sP4(relation_rng(relation_inverse(sK0)))
| ~ one_to_one(sK0)
| ~ relation(sK0)
| ~ function(sK0)
| ~ spl5_1 ),
inference(superposition,[],[f49,f33]) ).
fof(f97,plain,
( ~ one_to_one(sK0)
| ~ relation(sK0)
| ~ function(sK0)
| ~ spl5_1 ),
inference(forward_subsumption_resolution,[],[f96,f56]) ).
fof(f98,plain,
( ~ relation(sK0)
| ~ function(sK0)
| ~ spl5_1 ),
inference(forward_subsumption_resolution,[],[f97,f28]) ).
fof(f99,plain,
( ~ function(sK0)
| ~ spl5_1 ),
inference(forward_subsumption_resolution,[],[f98,f27]) ).
fof(f100,plain,
( $false
| ~ spl5_1 ),
inference(forward_subsumption_resolution,[],[f99,f26]) ).
fof(f101,plain,
~ spl5_1,
inference(avatar_contradiction_clause,[],[f100]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f54]) ).
cnf(s6,plain,
~ spl5_2,
inference(sat_conversion,[],[f95]) ).
cnf(s7,plain,
~ spl5_1,
inference(sat_conversion,[],[f101]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s6,s7]) ).
fof(f102,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU219+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n006.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 04:07:11 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 2.64/1.34 % (3569110)Detected formulas, will run a generic FOF schedule.
% 2.64/1.34 % (3569118)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1098857866:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.64/1.34 % (3569118)First to succeed.
% 2.64/1.34 % (3569118)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3569110"
% 2.64/1.34 % (3569116)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=4193686036:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.64/1.34 % (3569117)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=3386486581:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.64/1.34 % (3569115)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=3423319985:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.64/1.34 % (3569119)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=62914617:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.64/1.34 % (3569121)dis-21_1_sil=8000:lcm=predicate:random_seed=3646056057: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)
% 2.64/1.34 % (3569120)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=175114844:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.64/1.34 % (3569119)Also succeeded, but the first one will report.
% 2.64/1.34 % (3569120)Also succeeded, but the first one will report.
% 2.64/1.34 % (3569121)Instruction limit reached!
% 2.64/1.34 % (3569121)------------------------------
% 2.64/1.34 % (3569121)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.64/1.34 % (3569121)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.64/1.34 % (3569121)CaDiCaL version: 2.1.3
% 2.64/1.34 % (3569121)Termination reason: Instruction limit
% 2.64/1.34 % (3569121)Termination phase: Saturation
% 2.64/1.34 % (3569121)Time elapsed: 0.054 s
% 2.64/1.34 % (3569121)Peak memory usage: 88 MB
% 2.64/1.34 % (3569121)Instructions burned: 131 (million)
% 2.64/1.34 % (3569118)Refutation found. Thanks to Tanya!
% 2.64/1.34 % SZS status Theorem for theBenchmark
% 2.64/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 2.64/1.34 % (3569118)------------------------------
% 2.64/1.34 % (3569118)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.64/1.34 % (3569118)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.64/1.34 % (3569118)CaDiCaL version: 2.1.3
% 2.64/1.34 % (3569118)Termination reason: Refutation
% 2.64/1.34 % (3569118)Time elapsed: 0.002 s
% 2.64/1.34 % (3569118)Peak memory usage: 89 MB
% 2.64/1.34 % (3569118)Instructions burned: 2 (million)
% 2.64/1.34 % (3569118)------------------------------
% 2.64/1.34 % (3569118)------------------------------
% 2.64/1.34 % (3569110)Success in time 0.285 s
% 2.64/1.34 % Vampire exiting
%------------------------------------------------------------------------------