%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV421_1 : TPTP v9.3.1. Released v5.0.0.
% 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 12:59:15 PM UTC 2026
% Result : Theorem 0.17s 0.48s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 40 ( 6 unt; 0 typ; 2 def)
% Number of atoms : 99 ( 55 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 99 ( 40 ~; 34 |; 16 &)
% ( 5 <=>; 2 =>; 0 <=; 2 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 31 ( 0 atm; 0 fun; 25 num; 6 var)
% Number of types : 4 ( 2 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 12 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 10 !; 12 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
set: $tType ).
tff(type_def_6,type,
element: $tType ).
tff(func_def_0,type,
empty_set: set ).
tff(func_def_1,type,
singleton: element > set ).
tff(func_def_2,type,
intersection: ( set * set ) > set ).
tff(func_def_3,type,
union: ( set * set ) > set ).
tff(func_def_4,type,
difference: ( set * set ) > set ).
tff(func_def_5,type,
complement: set > set ).
tff(func_def_6,type,
cardinality: set > $int ).
tff(func_def_11,type,
sK0: set > element ).
tff(func_def_12,type,
sK1: element ).
tff(func_def_13,type,
sK2: set ).
tff(func_def_14,type,
sK3: $int ).
tff(pred_def_1,type,
member: ( element * set ) > $o ).
tff(pred_def_2,type,
subset: ( set * set ) > $o ).
tff(f8,axiom,
! [X0: set] :
( ( cardinality(X0) = 0 )
<=> ( X0 = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cardinality_empty_set) ).
tff(f13,conjecture,
! [X0: element,X1: set,X2: $int] :
( ( ~ member(X0,X1)
& ( X2 = cardinality(X1) ) )
=> ( ( X2 = 0 )
<=> ( X1 = empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',vc1) ).
tff(f14,negated_conjecture,
~ ! [X0: element,X1: set,X2: $int] :
( ( ~ member(X0,X1)
& ( X2 = cardinality(X1) ) )
=> ( ( X2 = 0 )
<=> ( X1 = empty_set ) ) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
tff(f27,plain,
? [X0: element,X1: set,X2: $int] :
( ( ( X2 = 0 )
<~> ( X1 = empty_set ) )
& ~ member(X0,X1)
& ( X2 = cardinality(X1) ) ),
inference(ennf_transformation,[],[f14]) ).
tff(f28,plain,
? [X0: element,X1: set,X2: $int] :
( ( ( X2 = 0 )
<~> ( X1 = empty_set ) )
& ~ member(X0,X1)
& ( X2 = cardinality(X1) ) ),
inference(flattening,[],[f27]) ).
tff(f40,plain,
! [X0: set] :
( ( ( cardinality(X0) = 0 )
| ( empty_set != X0 ) )
& ( ( X0 = empty_set )
| ( cardinality(X0) != 0 ) ) ),
inference(nnf_transformation,[],[f8]) ).
tff(f45,plain,
? [X0: element,X1: set,X2: $int] :
( ( ( empty_set != X1 )
| ( 0 != X2 ) )
& ( ( X1 = empty_set )
| ( X2 = 0 ) )
& ~ member(X0,X1)
& ( X2 = cardinality(X1) ) ),
inference(nnf_transformation,[],[f28]) ).
tff(f46,plain,
? [X0: element,X1: set,X2: $int] :
( ( ( empty_set != X1 )
| ( 0 != X2 ) )
& ( ( X1 = empty_set )
| ( X2 = 0 ) )
& ~ member(X0,X1)
& ( X2 = cardinality(X1) ) ),
inference(flattening,[],[f45]) ).
tff(f47,plain,
( ( ( empty_set != sK2 )
| ( 0 != sK3 ) )
& ( ( empty_set = sK2 )
| ( 0 = sK3 ) )
& ~ member(sK1,sK2)
& ( sK3 = cardinality(sK2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f46]) ).
tff(f63,plain,
! [X0: set] :
( ( cardinality(X0) != 0 )
| ( empty_set = X0 ) ),
inference(cnf_transformation,[],[f40]) ).
tff(f64,plain,
! [X0: set] :
( ( cardinality(X0) = 0 )
| ( empty_set != X0 ) ),
inference(cnf_transformation,[],[f40]) ).
tff(f73,plain,
sK3 = cardinality(sK2),
inference(cnf_transformation,[],[f47]) ).
tff(f75,plain,
( ( empty_set = sK2 )
| ( 0 = sK3 ) ),
inference(cnf_transformation,[],[f47]) ).
tff(f76,plain,
( ( empty_set != sK2 )
| ( 0 != sK3 ) ),
inference(cnf_transformation,[],[f47]) ).
tff(f79,plain,
0 = cardinality(empty_set),
inference(equality_resolution,[],[f64]) ).
tff(f81,definition,
( spl4_1
<=> ( 0 = sK3 ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
tff(f82,plain,
( ( 0 != sK3 )
| spl4_1 ),
inference(avatar_component_clause,[],[f81]) ).
tff(f83,plain,
( ( 0 = sK3 )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f81]) ).
tff(f85,definition,
( spl4_2
<=> ( empty_set = sK2 ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
tff(f86,plain,
( ( empty_set != sK2 )
| spl4_2 ),
inference(avatar_component_clause,[],[f85]) ).
tff(f87,plain,
( ( empty_set = sK2 )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f85]) ).
tff(f88,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f75,f85,f81]) ).
tff(f89,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f76,f85,f81]) ).
tff(f91,plain,
( ( sK3 = cardinality(empty_set) )
| ~ spl4_2 ),
inference(forward_demodulation,[],[f73,f87]) ).
tff(f92,plain,
( ( 0 = sK3 )
| ~ spl4_2 ),
inference(superposition,[],[f79,f91]) ).
tff(f96,plain,
( $false
| spl4_1
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f92,f82]) ).
tff(f97,plain,
( spl4_1
| ~ spl4_2 ),
inference(avatar_contradiction_clause,[],[f96]) ).
tff(f98,plain,
( ( 0 = cardinality(sK2) )
| ~ spl4_1 ),
inference(forward_demodulation,[],[f73,f83]) ).
tff(f110,plain,
( ( 0 != 0 )
| ( empty_set = sK2 )
| ~ spl4_1 ),
inference(superposition,[],[f63,f98]) ).
tff(f111,plain,
( ( empty_set = sK2 )
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f110]) ).
tff(f112,plain,
( $false
| ~ spl4_1
| spl4_2 ),
inference(forward_subsumption_resolution,[],[f111,f86]) ).
tff(f113,plain,
( ~ spl4_1
| spl4_2 ),
inference(avatar_contradiction_clause,[],[f112]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f88]) ).
cnf(s2,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f89]) ).
cnf(s4,plain,
( spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f97]) ).
cnf(s5,plain,
( ~ spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f113]) ).
cnf(s6,plain,
spl4_1,
inference(rat,[],[s1,s4]) ).
cnf(s7,plain,
spl4_2,
inference(rat,[],[s5,s6]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s2,s7,s6]) ).
tff(f114,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV421_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n005.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 06:26:47 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.17/0.44 Running first-order model finding
% 0.17/0.44 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
% 0.17/0.48 % (589350)Will run a generic schedule for satisfiability detection.
% 0.17/0.48 % (589358)dis+10_1_sil=32000:sp=arity:random_seed=1647716254:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.48 % (589358) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-589350-589358"...
% 0.17/0.48 % (589358)...printing done.
% 0.17/0.48 % (589358)Refutation found. Thanks to Tanya!
% 0.17/0.48 % SZS status Theorem for theBenchmark
% 0.17/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.48 % (589358)------------------------------
% 0.17/0.48 % (589358)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.48 % (589358)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.48 % (589358)CaDiCaL version: 2.1.3
% 0.17/0.48 % (589358)Termination reason: Refutation
% 0.17/0.48 % (589358)Time elapsed: 0.003 s
% 0.17/0.48 % (589358)Peak memory usage: 12 MB
% 0.17/0.48 % (589358)Instructions burned: 4 (million)
% 0.17/0.48 % (589350)Success in time 0.025 s
% 0.17/0.48 % Vampire exiting
%------------------------------------------------------------------------------