%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU219+2 : 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 : n008.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 3.39s 1.25s
% Output : Refutation 3.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 11 unt; 2 def)
% Number of atoms : 87 ( 31 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 83 ( 32 ~; 26 |; 16 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 7 ( 5 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(f42,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(f174,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(f202,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(f203,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)],[f202]) ).
fof(f274,plain,
! [X0] :
( function_inverse(X0) = relation_inverse(X0)
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f275,plain,
! [X0] :
( function_inverse(X0) = relation_inverse(X0)
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f274]) ).
fof(f381,plain,
! [X0] :
( ( relation_rng(X0) = relation_dom(relation_inverse(X0))
& relation_dom(X0) = relation_rng(relation_inverse(X0)) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f174]) ).
fof(f408,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,[],[f203]) ).
fof(f409,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,[],[f408]) ).
fof(f579,plain,
( ( relation_rng(sK73) != relation_dom(function_inverse(sK73))
| relation_dom(sK73) != relation_rng(function_inverse(sK73)) )
& one_to_one(sK73)
& relation(sK73)
& function(sK73) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(X0,sK73)],[f409]) ).
fof(f741,plain,
! [X0] :
( ~ one_to_one(X0)
| relation_inverse(X0) = function_inverse(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f275]) ).
fof(f905,plain,
! [X0] :
( relation_dom(X0) = relation_rng(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f381]) ).
fof(f906,plain,
! [X0] :
( relation_rng(X0) = relation_dom(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f381]) ).
fof(f956,plain,
function(sK73),
inference(cnf_transformation,[],[f579]) ).
fof(f957,plain,
relation(sK73),
inference(cnf_transformation,[],[f579]) ).
fof(f958,plain,
one_to_one(sK73),
inference(cnf_transformation,[],[f579]) ).
fof(f959,plain,
( relation_rng(sK73) != relation_dom(function_inverse(sK73))
| relation_dom(sK73) != relation_rng(function_inverse(sK73)) ),
inference(cnf_transformation,[],[f579]) ).
fof(f1094,definition,
( spl78_1
<=> relation_dom(sK73) = relation_rng(function_inverse(sK73)) ),
introduced(definition,[new_symbols(definition,[spl78_1])],[avatar_definition]) ).
fof(f1096,plain,
( relation_dom(sK73) != relation_rng(function_inverse(sK73))
| spl78_1 ),
inference(avatar_component_clause,[],[f1094]) ).
fof(f1098,definition,
( spl78_2
<=> relation_rng(sK73) = relation_dom(function_inverse(sK73)) ),
introduced(definition,[new_symbols(definition,[spl78_2])],[avatar_definition]) ).
fof(f1101,plain,
( ~ spl78_1
| ~ spl78_2 ),
inference(avatar_split_clause,[],[f959,f1098,f1094]) ).
fof(f1279,plain,
( function_inverse(sK73) = relation_inverse(sK73)
| ~ relation(sK73)
| ~ function(sK73) ),
inference(resolution,[],[f741,f958]) ).
fof(f1285,plain,
( function_inverse(sK73) = relation_inverse(sK73)
| ~ function(sK73) ),
inference(forward_subsumption_resolution,[],[f1279,f957]) ).
fof(f1288,plain,
function_inverse(sK73) = relation_inverse(sK73),
inference(forward_subsumption_resolution,[],[f1285,f956]) ).
fof(f1291,plain,
( relation_rng(sK73) = relation_dom(function_inverse(sK73))
| ~ relation(sK73) ),
inference(superposition,[],[f906,f1288]) ).
fof(f1292,plain,
( relation_dom(sK73) = relation_rng(function_inverse(sK73))
| ~ relation(sK73) ),
inference(superposition,[],[f905,f1288]) ).
fof(f1293,plain,
( ~ relation(sK73)
| spl78_1 ),
inference(forward_subsumption_resolution,[],[f1292,f1096]) ).
fof(f1294,plain,
relation_rng(sK73) = relation_dom(function_inverse(sK73)),
inference(forward_subsumption_resolution,[],[f1291,f957]) ).
fof(f1295,plain,
( $false
| spl78_1 ),
inference(forward_subsumption_resolution,[],[f1293,f957]) ).
fof(f1296,plain,
spl78_1,
inference(avatar_contradiction_clause,[],[f1295]) ).
fof(f1297,plain,
spl78_2,
inference(avatar_split_clause,[],[f1294,f1098]) ).
cnf(s1,plain,
( ~ spl78_1
| ~ spl78_2 ),
inference(sat_conversion,[],[f1101]) ).
cnf(s7,plain,
spl78_1,
inference(sat_conversion,[],[f1296]) ).
cnf(s8,plain,
spl78_2,
inference(sat_conversion,[],[f1297]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s1,s8,s7]) ).
fof(f1298,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU219+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n008.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 04:08:09 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 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
% 3.39/1.25 % (1859290)Detected formulas, will run a generic FOF schedule.
% 3.39/1.25 % (1859295)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=4113670350:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.39/1.25 % (1859296)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=2928752881:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.39/1.25 % (1859298)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3315564647:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.39/1.25 % (1859297)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=4253412397:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.39/1.25 % (1859299)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1885744982:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.39/1.25 % (1859300)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1693417007:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.39/1.25 % (1859301)dis-21_1_sil=8000:lcm=predicate:random_seed=215049098: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)
% 3.39/1.25 % (1859300)First to succeed.
% 3.39/1.25 % (1859300)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1859290"
% 3.39/1.25 % (1859298)Also succeeded, but the first one will report.
% 3.39/1.25 % (1859299)Also succeeded, but the first one will report.
% 3.39/1.25 % (1859301)Instruction limit reached!
% 3.39/1.25 % (1859301)------------------------------
% 3.39/1.25 % (1859301)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.39/1.25 % (1859301)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/1.25 % (1859301)CaDiCaL version: 2.1.3
% 3.39/1.25 % (1859301)Termination reason: Instruction limit
% 3.39/1.25 % (1859301)Termination phase: Saturation
% 3.39/1.25 % (1859301)Time elapsed: 0.075 s
% 3.39/1.25 % (1859301)Peak memory usage: 90 MB
% 3.39/1.25 % (1859301)Instructions burned: 129 (million)
% 3.39/1.25 % (1859309)lrs+10_1_sil=8000:sp=occurrence:random_seed=1236947259:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.39/1.25 % (1859300)Refutation found. Thanks to Tanya!
% 3.39/1.25 % SZS status Theorem for theBenchmark
% 3.39/1.25 % SZS output start Proof for theBenchmark
% See solution above
% 3.39/1.25 % (1859300)------------------------------
% 3.39/1.25 % (1859300)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.39/1.25 % (1859300)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/1.25 % (1859300)CaDiCaL version: 2.1.3
% 3.39/1.25 % (1859300)Termination reason: Refutation
% 3.39/1.25 % (1859300)Time elapsed: 0.018 s
% 3.39/1.25 % (1859300)Peak memory usage: 90 MB
% 3.39/1.25 % (1859300)Instructions burned: 25 (million)
% 3.39/1.25 % (1859300)------------------------------
% 3.39/1.25 % (1859300)------------------------------
% 3.39/1.25 % (1859290)Success in time 0.428 s
% 3.39/1.25 % Vampire exiting
%------------------------------------------------------------------------------