%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU180+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n007.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 12:52:16 PM UTC 2026
% Result : Theorem 0.12s 0.45s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 56 ( 17 unt; 2 def)
% Number of atoms : 125 ( 19 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 116 ( 47 ~; 44 |; 6 &)
% ( 12 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 89 ( 0 sgn 79 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f4,axiom,
! [X0,X1,X2] :
( X2 = set_union2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
| in(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f5,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f7,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f8,axiom,
! [X0] :
( relation(X0)
=> relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_relat_1) ).
fof(f33,conjecture,
! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X0,relation_field(X2))
& in(X1,relation_field(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_relat_1) ).
fof(f34,negated_conjecture,
~ ! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X0,relation_field(X2))
& in(X1,relation_field(X2)) ) ) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f40,plain,
! [X0] :
( ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f41,plain,
! [X0] :
( ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f42,plain,
! [X0] :
( relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f50,plain,
? [X0,X1,X2] :
( ( ~ in(X0,relation_field(X2))
| ~ in(X1,relation_field(X2)) )
& in(ordered_pair(X0,X1),X2)
& relation(X2) ),
inference(ennf_transformation,[],[f34]) ).
fof(f51,plain,
? [X0,X1,X2] :
( ( ~ in(X0,relation_field(X2))
| ~ in(X1,relation_field(X2)) )
& in(ordered_pair(X0,X1),X2)
& relation(X2) ),
inference(flattening,[],[f50]) ).
fof(f56,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f62,plain,
! [X2,X3,X0,X1] :
( ~ in(X3,X1)
| in(X3,X2)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f4]) ).
fof(f63,plain,
! [X2,X3,X0,X1] :
( ~ in(X3,X0)
| in(X3,X2)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f4]) ).
fof(f64,plain,
! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ in(ordered_pair(X2,X3),X0)
| in(X2,X1)
| relation_dom(X0) != X1 ),
inference(cnf_transformation,[],[f40]) ).
fof(f68,plain,
! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ in(ordered_pair(X3,X2),X0)
| in(X2,X1)
| relation_rng(X0) != X1 ),
inference(cnf_transformation,[],[f41]) ).
fof(f72,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f73,plain,
! [X0] :
( ~ relation(X0)
| relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0)) ),
inference(cnf_transformation,[],[f42]) ).
fof(f90,plain,
( ~ in(sK12,relation_field(sK13))
| ~ in(sK11,relation_field(sK13)) ),
inference(cnf_transformation,[],[f51]) ).
fof(f91,plain,
relation(sK13),
inference(cnf_transformation,[],[f51]) ).
fof(f92,plain,
in(ordered_pair(sK11,sK12),sK13),
inference(cnf_transformation,[],[f51]) ).
fof(f99,plain,
! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),X0)
| in(X2,X1)
| relation_dom(X0) != X1 ),
inference(definition_unfolding,[],[f64,f72]) ).
fof(f103,plain,
! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X3,X2),singleton(X3)),X0)
| in(X2,X1)
| relation_rng(X0) != X1 ),
inference(definition_unfolding,[],[f68,f72]) ).
fof(f105,plain,
in(unordered_pair(unordered_pair(sK11,sK12),singleton(sK11)),sK13),
inference(definition_unfolding,[],[f92,f72]) ).
fof(f106,plain,
! [X3,X0,X1] :
( in(X3,set_union2(X0,X1))
| ~ in(X3,X0) ),
inference(equality_resolution,[],[f63]) ).
fof(f107,plain,
! [X3,X0,X1] :
( in(X3,set_union2(X0,X1))
| ~ in(X3,X1) ),
inference(equality_resolution,[],[f62]) ).
fof(f110,plain,
! [X2,X3,X0] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),X0)
| in(X2,relation_dom(X0)) ),
inference(equality_resolution,[],[f99]) ).
fof(f112,plain,
! [X2,X3,X0] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X3,X2),singleton(X3)),X0)
| in(X2,relation_rng(X0)) ),
inference(equality_resolution,[],[f103]) ).
fof(f114,definition,
( spl14_1
<=> in(sK11,relation_field(sK13)) ),
introduced(definition,[new_symbols(definition,[spl14_1])],[avatar_definition]) ).
fof(f116,plain,
( ~ in(sK11,relation_field(sK13))
| spl14_1 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f118,definition,
( spl14_2
<=> in(sK12,relation_field(sK13)) ),
introduced(definition,[new_symbols(definition,[spl14_2])],[avatar_definition]) ).
fof(f120,plain,
( ~ in(sK12,relation_field(sK13))
| spl14_2 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f121,plain,
( ~ spl14_1
| ~ spl14_2 ),
inference(avatar_split_clause,[],[f90,f118,f114]) ).
fof(f144,plain,
in(unordered_pair(singleton(sK11),unordered_pair(sK11,sK12)),sK13),
inference(superposition,[],[f105,f56]) ).
fof(f206,plain,
relation_field(sK13) = set_union2(relation_dom(sK13),relation_rng(sK13)),
inference(resolution,[],[f73,f91]) ).
fof(f211,plain,
! [X0] :
( in(X0,relation_field(sK13))
| ~ in(X0,relation_dom(sK13)) ),
inference(superposition,[],[f106,f206]) ).
fof(f212,plain,
! [X0] :
( in(X0,relation_field(sK13))
| ~ in(X0,relation_rng(sK13)) ),
inference(superposition,[],[f107,f206]) ).
fof(f253,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK13)
| in(X0,relation_dom(sK13)) ),
inference(resolution,[],[f110,f91]) ).
fof(f254,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK13)
| in(X0,relation_dom(sK13)) ),
inference(forward_demodulation,[],[f253,f56]) ).
fof(f260,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK13)
| in(X1,relation_rng(sK13)) ),
inference(resolution,[],[f112,f91]) ).
fof(f261,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK13)
| in(X1,relation_rng(sK13)) ),
inference(forward_demodulation,[],[f260,f56]) ).
fof(f284,plain,
( ~ in(sK11,relation_dom(sK13))
| spl14_1 ),
inference(resolution,[],[f211,f116]) ).
fof(f386,plain,
in(sK11,relation_dom(sK13)),
inference(resolution,[],[f254,f144]) ).
fof(f389,plain,
( $false
| spl14_1 ),
inference(forward_subsumption_resolution,[],[f386,f284]) ).
fof(f390,plain,
spl14_1,
inference(avatar_contradiction_clause,[],[f389]) ).
fof(f391,plain,
( ~ in(sK12,relation_rng(sK13))
| spl14_2 ),
inference(resolution,[],[f120,f212]) ).
fof(f393,plain,
in(sK12,relation_rng(sK13)),
inference(resolution,[],[f261,f144]) ).
fof(f396,plain,
( $false
| spl14_2 ),
inference(forward_subsumption_resolution,[],[f393,f391]) ).
fof(f397,plain,
spl14_2,
inference(avatar_contradiction_clause,[],[f396]) ).
cnf(s1,plain,
( ~ spl14_1
| ~ spl14_2 ),
inference(sat_conversion,[],[f121]) ).
cnf(s5,plain,
spl14_1,
inference(sat_conversion,[],[f390]) ).
cnf(s6,plain,
spl14_2,
inference(sat_conversion,[],[f397]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s1,s6,s5]) ).
fof(f398,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU180+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.37 % Computer : n007.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 28 03:53:11 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.40 Running first-order model finding
% 0.12/0.40 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.45 % (2009156)Will run a generic schedule for satisfiability detection.
% 0.12/0.45 % (2009165)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2578922998:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.12/0.45 % (2009162)% WARNING: option uhcvi not known.
% 0.12/0.45 % (2009165) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2009156-2009165"...
% 0.12/0.45 % (2009161)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2278260669_2999 on theBenchmark for (2999ds/0Mi)
% 0.12/0.45 % (2009162)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=692462097:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.12/0.45 % (2009163)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2019582179:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.12/0.45 % (2009164)dis+10_1_sil=32000:sp=arity:random_seed=64089339:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.12/0.45 % (2009165)...printing done.
% 0.12/0.45 % (2009167)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=295919573:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.12/0.45 % (2009165)Refutation found. Thanks to Tanya!
% 0.12/0.45 % SZS status Theorem for theBenchmark
% 0.12/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.46 % (2009165)------------------------------
% 0.12/0.46 % (2009165)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.46 % (2009165)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.46 % (2009165)CaDiCaL version: 2.1.3
% 0.12/0.46 % (2009165)Termination reason: Refutation
% 0.12/0.46 % (2009165)Time elapsed: 0.006 s
% 0.12/0.46 % (2009165)Peak memory usage: 12 MB
% 0.12/0.46 % (2009165)Instructions burned: 14 (million)
% 0.12/0.46 % (2009156)Success in time 0.043 s
% 0.12/0.46 % Vampire exiting
%------------------------------------------------------------------------------