%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU177+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 : n018.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 12:52:15 PM UTC 2026
% Result : Theorem 0.15s 0.46s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 14 unt; 2 def)
% Number of atoms : 158 ( 22 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 186 ( 72 ~; 72 |; 26 &)
% ( 10 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 3 con; 0-2 aty)
% Number of variables : 106 ( 0 sgn 84 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f23,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f24,conjecture,
! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X0,relation_dom(X2))
& in(X1,relation_rng(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_relat_1) ).
fof(f25,negated_conjecture,
~ ! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X0,relation_dom(X2))
& in(X1,relation_rng(X2)) ) ) ),
inference(negated_conjecture,[status(cth)],[f24]) ).
fof(f26,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f27,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f35,plain,
? [X0,X1,X2] :
( ( ~ in(X0,relation_dom(X2))
| ~ in(X1,relation_rng(X2)) )
& in(ordered_pair(X0,X1),X2)
& relation(X2) ),
inference(ennf_transformation,[],[f25]) ).
fof(f36,plain,
? [X0,X1,X2] :
( ( ~ in(X0,relation_dom(X2))
| ~ in(X1,relation_rng(X2)) )
& in(ordered_pair(X0,X1),X2)
& relation(X2) ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
! [X0] :
( ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f38,plain,
! [X0] :
( ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f43,plain,
( ( ~ in(sK4,relation_dom(sK6))
| ~ in(sK5,relation_rng(sK6)) )
& in(ordered_pair(sK4,sK5),sK6)
& relation(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6)],[f36]) ).
fof(f44,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f37]) ).
fof(f45,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( ? [X7] : in(ordered_pair(X5,X7),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f44]) ).
fof(f46,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ( ( ! [X3] : ~ in(ordered_pair(sK7(X0,X1),X3),X0)
| ~ in(sK7(X0,X1),X1) )
& ( in(ordered_pair(sK7(X0,X1),sK8(X0,X1)),X0)
| in(sK7(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK9(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X2,sK7(X0,X1)),skolemize(X4,sK8(X0,X1)),skolemize(X7,sK9(X0,X5))],[f45]) ).
fof(f47,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f38]) ).
fof(f48,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X4,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( ? [X7] : in(ordered_pair(X7,X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f47]) ).
fof(f49,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ( ( ! [X3] : ~ in(ordered_pair(X3,sK10(X0,X1)),X0)
| ~ in(sK10(X0,X1),X1) )
& ( in(ordered_pair(sK11(X0,X1),sK10(X0,X1)),X0)
| in(sK10(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( in(ordered_pair(sK12(X0,X5),X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12]),skolemize(X2,sK10(X0,X1)),skolemize(X4,sK11(X0,X1)),skolemize(X7,sK12(X0,X5))],[f48]) ).
fof(f66,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f23]) ).
fof(f67,plain,
relation(sK6),
inference(cnf_transformation,[],[f43]) ).
fof(f68,plain,
in(ordered_pair(sK4,sK5),sK6),
inference(cnf_transformation,[],[f43]) ).
fof(f69,plain,
( ~ in(sK4,relation_dom(sK6))
| ~ in(sK5,relation_rng(sK6)) ),
inference(cnf_transformation,[],[f43]) ).
fof(f71,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X5,X6),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f75,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X6,X5),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f79,plain,
in(unordered_pair(unordered_pair(sK4,sK5),singleton(sK4)),sK6),
inference(definition_unfolding,[],[f68,f66]) ).
fof(f82,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f71,f66]) ).
fof(f86,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f75,f66]) ).
fof(f88,plain,
! [X0,X6,X5] :
( in(X5,relation_dom(X0))
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f82]) ).
fof(f90,plain,
! [X0,X6,X5] :
( in(X5,relation_rng(X0))
| ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f86]) ).
fof(f96,plain,
~ relation(sK6),
inference(consistent_polarity_flipping,[],[f67]) ).
fof(f99,plain,
! [X0,X6,X5] :
( relation(X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| in(X5,relation_dom(X0)) ),
inference(consistent_polarity_flipping,[],[f88]) ).
fof(f103,plain,
! [X0,X6,X5] :
( relation(X0)
| ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
| in(X5,relation_rng(X0)) ),
inference(consistent_polarity_flipping,[],[f90]) ).
fof(f106,definition,
( spl13_1
<=> in(sK5,relation_rng(sK6)) ),
introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition]) ).
fof(f110,definition,
( spl13_2
<=> in(sK4,relation_dom(sK6)) ),
introduced(definition,[new_symbols(definition,[spl13_2])],[avatar_definition]) ).
fof(f113,plain,
( ~ spl13_1
| ~ spl13_2 ),
inference(avatar_split_clause,[],[f69,f110,f106]) ).
fof(f169,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK6)
| in(X0,relation_dom(sK6)) ),
inference(resolution,[],[f99,f96]) ).
fof(f172,plain,
in(sK4,relation_dom(sK6)),
inference(resolution,[],[f169,f79]) ).
fof(f178,plain,
spl13_2,
inference(avatar_split_clause,[],[f172,f110]) ).
fof(f226,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK6)
| in(X1,relation_rng(sK6)) ),
inference(resolution,[],[f103,f96]) ).
fof(f229,plain,
in(sK5,relation_rng(sK6)),
inference(resolution,[],[f226,f79]) ).
fof(f235,plain,
spl13_1,
inference(avatar_split_clause,[],[f229,f106]) ).
cnf(s1,plain,
( ~ spl13_1
| ~ spl13_2 ),
inference(sat_conversion,[],[f113]) ).
cnf(s2,plain,
spl13_2,
inference(sat_conversion,[],[f178]) ).
cnf(s4,plain,
spl13_1,
inference(sat_conversion,[],[f235]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s2,s4]) ).
fof(f236,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU177+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 % Computer : n018.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 03:56:10 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.43 Running first-order model finding
% 0.11/0.43 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
% 0.15/0.46 % (2979232)Will run a generic schedule for satisfiability detection.
% 0.15/0.46 % (2979243)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2518636422:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.46 % (2979243) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2979232-2979243"...
% 0.15/0.46 % (2979238)% WARNING: option uhcvi not known.
% 0.15/0.46 % (2979243)...printing done.
% 0.15/0.46 % (2979243)Refutation found. Thanks to Tanya!
% 0.15/0.46 % SZS status Theorem for theBenchmark
% 0.15/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.47 % (2979243)------------------------------
% 0.15/0.47 % (2979243)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.47 % (2979243)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.47 % (2979243)CaDiCaL version: 2.1.3
% 0.15/0.47 % (2979243)Termination reason: Refutation
% 0.15/0.47 % (2979243)Time elapsed: 0.003 s
% 0.15/0.47 % (2979243)Peak memory usage: 12 MB
% 0.15/0.47 % (2979243)Instructions burned: 7 (million)
% 0.15/0.47 % (2979232)Success in time 0.03 s
% 0.15/0.47 % Vampire exiting
%------------------------------------------------------------------------------