%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU219+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 12:52:26 PM UTC 2026
% Result : Theorem 0.15s 0.47s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 57 ( 15 unt; 3 def)
% Number of atoms : 135 ( 39 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 128 ( 50 ~; 46 |; 20 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-1 aty)
% Number of variables : 18 ( 0 sgn 16 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> function_inverse(X0) = relation_inverse(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_funct_1) ).
fof(f3,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(f7,axiom,
! [X0] :
( relation(X0)
=> relation_inverse(relation_inverse(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k4_relat_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/sandbox2/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/sandbox2/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] :
( function_inverse(X0) = relation_inverse(X0)
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f14,plain,
! [X0] :
( function_inverse(X0) = relation_inverse(X0)
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f13]) ).
fof(f15,plain,
! [X0] :
( ( relation(function_inverse(X0))
& function(function_inverse(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f16,plain,
! [X0] :
( ( relation(function_inverse(X0))
& function(function_inverse(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f15]) ).
fof(f20,plain,
! [X0] :
( relation_inverse(relation_inverse(X0)) = X0
| ~ relation(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f21,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(f22,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(f23,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,[],[f22]) ).
fof(f26,plain,
( ( relation_rng(sK2) != relation_dom(function_inverse(sK2))
| relation_dom(sK2) != relation_rng(function_inverse(sK2)) )
& one_to_one(sK2)
& relation(sK2)
& function(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f23]) ).
fof(f27,plain,
! [X0] :
( ~ one_to_one(X0)
| function_inverse(X0) = relation_inverse(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f29,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| relation(function_inverse(X0)) ),
inference(cnf_transformation,[],[f16]) ).
fof(f33,plain,
! [X0] :
( ~ relation(X0)
| relation_inverse(relation_inverse(X0)) = X0 ),
inference(cnf_transformation,[],[f20]) ).
fof(f39,plain,
! [X0] :
( ~ relation(X0)
| relation_dom(X0) = relation_rng(relation_inverse(X0)) ),
inference(cnf_transformation,[],[f21]) ).
fof(f41,plain,
function(sK2),
inference(cnf_transformation,[],[f26]) ).
fof(f42,plain,
relation(sK2),
inference(cnf_transformation,[],[f26]) ).
fof(f43,plain,
one_to_one(sK2),
inference(cnf_transformation,[],[f26]) ).
fof(f44,plain,
( relation_rng(sK2) != relation_dom(function_inverse(sK2))
| relation_dom(sK2) != relation_rng(function_inverse(sK2)) ),
inference(cnf_transformation,[],[f26]) ).
fof(f46,definition,
( spl3_1
<=> relation_dom(sK2) = relation_rng(function_inverse(sK2)) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f48,plain,
( relation_dom(sK2) != relation_rng(function_inverse(sK2))
| spl3_1 ),
inference(avatar_component_clause,[],[f46]) ).
fof(f50,definition,
( spl3_2
<=> relation_rng(sK2) = relation_dom(function_inverse(sK2)) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f52,plain,
( relation_rng(sK2) != relation_dom(function_inverse(sK2))
| spl3_2 ),
inference(avatar_component_clause,[],[f50]) ).
fof(f53,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f44,f50,f46]) ).
fof(f70,definition,
( spl3_4
<=> relation(function_inverse(sK2)) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f71,plain,
( relation(function_inverse(sK2))
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f72,plain,
( ~ relation(function_inverse(sK2))
| spl3_4 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f77,plain,
( ~ relation(sK2)
| relation(function_inverse(sK2)) ),
inference(resolution,[],[f29,f41]) ).
fof(f78,plain,
relation(function_inverse(sK2)),
inference(forward_subsumption_resolution,[],[f77,f42]) ).
fof(f81,plain,
( $false
| spl3_4 ),
inference(forward_subsumption_resolution,[],[f78,f72]) ).
fof(f82,plain,
spl3_4,
inference(avatar_contradiction_clause,[],[f81]) ).
fof(f89,plain,
sK2 = relation_inverse(relation_inverse(sK2)),
inference(resolution,[],[f33,f42]) ).
fof(f94,plain,
( relation_dom(function_inverse(sK2)) = relation_rng(relation_inverse(function_inverse(sK2)))
| ~ spl3_4 ),
inference(resolution,[],[f39,f71]) ).
fof(f99,plain,
relation_dom(sK2) = relation_rng(relation_inverse(sK2)),
inference(resolution,[],[f39,f42]) ).
fof(f134,plain,
( function_inverse(sK2) = relation_inverse(sK2)
| ~ relation(sK2)
| ~ function(sK2) ),
inference(resolution,[],[f27,f43]) ).
fof(f137,plain,
( function_inverse(sK2) = relation_inverse(sK2)
| ~ function(sK2) ),
inference(forward_subsumption_resolution,[],[f134,f42]) ).
fof(f139,plain,
function_inverse(sK2) = relation_inverse(sK2),
inference(forward_subsumption_resolution,[],[f137,f41]) ).
fof(f158,plain,
sK2 = relation_inverse(function_inverse(sK2)),
inference(superposition,[],[f89,f139]) ).
fof(f163,plain,
( relation_rng(function_inverse(sK2)) != relation_rng(relation_inverse(sK2))
| spl3_1 ),
inference(superposition,[],[f48,f99]) ).
fof(f164,plain,
( relation_rng(function_inverse(sK2)) != relation_rng(function_inverse(sK2))
| spl3_1 ),
inference(forward_demodulation,[],[f163,f139]) ).
fof(f165,plain,
( $false
| spl3_1 ),
inference(trivial_inequality_removal,[],[f164]) ).
fof(f166,plain,
spl3_1,
inference(avatar_contradiction_clause,[],[f165]) ).
fof(f167,plain,
( relation_rng(sK2) != relation_rng(relation_inverse(function_inverse(sK2)))
| spl3_2
| ~ spl3_4 ),
inference(forward_demodulation,[],[f52,f94]) ).
fof(f168,plain,
( relation_rng(sK2) != relation_rng(sK2)
| spl3_2
| ~ spl3_4 ),
inference(forward_demodulation,[],[f167,f158]) ).
fof(f169,plain,
( $false
| spl3_2
| ~ spl3_4 ),
inference(trivial_inequality_removal,[],[f168]) ).
fof(f170,plain,
( spl3_2
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[],[f169]) ).
cnf(s1,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f53]) ).
cnf(s3,plain,
spl3_4,
inference(sat_conversion,[],[f82]) ).
cnf(s4,plain,
spl3_1,
inference(sat_conversion,[],[f166]) ).
cnf(s5,plain,
( spl3_2
| ~ spl3_4 ),
inference(sat_conversion,[],[f170]) ).
cnf(s6,plain,
spl3_2,
inference(rat,[],[s5,s3]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s6,s4]) ).
fof(f171,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU219+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39 % Computer : n005.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Mon Sep 28 04:07:17 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.42 Running first-order model finding
% 0.13/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.47 % (424655)Will run a generic schedule for satisfiability detection.
% 0.15/0.47 % (424665)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4037577502:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.47 % (424665) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-424655-424665"...
% 0.15/0.47 % (424661)% WARNING: option uhcvi not known.
% 0.15/0.47 % (424665)...printing done.
% 0.15/0.47 % (424665)Refutation found. Thanks to Tanya!
% 0.15/0.47 % SZS status Theorem for theBenchmark
% 0.15/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.47 % (424665)------------------------------
% 0.15/0.47 % (424665)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.47 % (424665)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.47 % (424665)CaDiCaL version: 2.1.3
% 0.15/0.47 % (424665)Termination reason: Refutation
% 0.15/0.47 % (424665)Time elapsed: 0.002 s
% 0.15/0.47 % (424665)Peak memory usage: 12 MB
% 0.15/0.47 % (424665)Instructions burned: 4 (million)
% 0.15/0.47 % (424655)Success in time 0.038 s
% 0.15/0.47 % Vampire exiting
%------------------------------------------------------------------------------