%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV421_1 : TPTP v9.3.1. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 12:57:39 PM UTC 2026
% Result : Theorem 3.60s 1.48s
% Output : Refutation 3.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 2
% Syntax : Number of formulae : 23 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 68 ( 58 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 74 ( 29 ~; 16 |; 20 &)
% ( 4 <=>; 3 =>; 0 <=; 2 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 33 ( 0 atm; 0 fun; 25 num; 8 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 28 ( 13 !; 15 ?; 28 :)
% 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: $int ).
tff(func_def_12,type,
sK1: set ).
tff(func_def_13,type,
sK2: element ).
tff(func_def_14,type,
sK3: set > element ).
tff(pred_def_1,type,
member: ( element * set ) > $o ).
tff(pred_def_2,type,
subset: ( set * set ) > $o ).
tff(f8,axiom,
! [X0: set] :
( ( X0 = empty_set )
<=> ( cardinality(X0) = 0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cardinality_empty_set) ).
tff(f13,conjecture,
! [X0: element,X2: $int,X1: set] :
( ( ~ member(X0,X1)
& ( X2 = cardinality(X1) ) )
=> ( ( X1 = empty_set )
<=> ( X2 = 0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',vc1) ).
tff(f14,negated_conjecture,
~ ! [X0: element,X2: $int,X1: set] :
( ( ~ member(X0,X1)
& ( X2 = cardinality(X1) ) )
=> ( ( X1 = empty_set )
<=> ( X2 = 0 ) ) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
tff(f29,plain,
~ ! [X2: set,X0: element,X1: $int] :
( ( ( cardinality(X2) = X1 )
& ~ member(X0,X2) )
=> ( ( empty_set = X2 )
<=> ( 0 = X1 ) ) ),
inference(rectify,[],[f14]) ).
tff(f33,plain,
? [X2: set,X0: element,X1: $int] :
( ( ( empty_set = X2 )
<~> ( 0 = X1 ) )
& ( cardinality(X2) = X1 )
& ~ member(X0,X2) ),
inference(ennf_transformation,[],[f29]) ).
tff(f34,plain,
? [X1: $int,X2: set,X0: element] :
( ~ member(X0,X2)
& ( ( empty_set = X2 )
<~> ( 0 = X1 ) )
& ( cardinality(X2) = X1 ) ),
inference(flattening,[],[f33]) ).
tff(f40,plain,
? [X1: $int,X2: set,X0: element] :
( ~ member(X0,X2)
& ( ( 0 != X1 )
| ( empty_set != X2 ) )
& ( ( 0 = X1 )
| ( empty_set = X2 ) )
& ( cardinality(X2) = X1 ) ),
inference(nnf_transformation,[],[f34]) ).
tff(f41,plain,
? [X1: $int,X2: set,X0: element] :
( ~ member(X0,X2)
& ( ( 0 != X1 )
| ( empty_set != X2 ) )
& ( ( 0 = X1 )
| ( empty_set = X2 ) )
& ( cardinality(X2) = X1 ) ),
inference(flattening,[],[f40]) ).
tff(f42,plain,
? [X0: $int,X1: set,X2: element] :
( ~ member(X2,X1)
& ( ( 0 != X0 )
| ( empty_set != X1 ) )
& ( ( 0 = X0 )
| ( empty_set = X1 ) )
& ( cardinality(X1) = X0 ) ),
inference(rectify,[],[f41]) ).
tff(f43,plain,
( ~ member(sK2,sK1)
& ( ( 0 != sK0 )
| ( empty_set != sK1 ) )
& ( ( 0 = sK0 )
| ( empty_set = sK1 ) )
& ( sK0 = cardinality(sK1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f42]) ).
tff(f51,plain,
! [X0: set] :
( ( ( X0 = empty_set )
| ( cardinality(X0) != 0 ) )
& ( ( cardinality(X0) = 0 )
| ( empty_set != X0 ) ) ),
inference(nnf_transformation,[],[f8]) ).
tff(f67,plain,
sK0 = cardinality(sK1),
inference(cnf_transformation,[],[f43]) ).
tff(f68,plain,
( ( 0 = sK0 )
| ( empty_set = sK1 ) ),
inference(cnf_transformation,[],[f43]) ).
tff(f69,plain,
( ( empty_set != sK1 )
| ( 0 != sK0 ) ),
inference(cnf_transformation,[],[f43]) ).
tff(f79,plain,
! [X0: set] :
( ( cardinality(X0) = 0 )
| ( empty_set != X0 ) ),
inference(cnf_transformation,[],[f51]) ).
tff(f80,plain,
! [X0: set] :
( ( empty_set = X0 )
| ( cardinality(X0) != 0 ) ),
inference(cnf_transformation,[],[f51]) ).
tff(f89,plain,
0 = cardinality(empty_set),
inference(equality_resolution,[],[f79]) ).
tff(f92,plain,
( ( 0 = cardinality(sK1) )
| ( empty_set = sK1 ) ),
inference(forward_demodulation,[],[f68,f67]) ).
tff(f94,plain,
( ( empty_set != sK1 )
| ( 0 != cardinality(sK1) ) ),
inference(forward_demodulation,[],[f69,f67]) ).
tff(f95,plain,
empty_set = sK1,
inference(forward_subsumption_resolution,[],[f92,f80]) ).
tff(f96,plain,
0 != cardinality(sK1),
inference(forward_subsumption_resolution,[],[f94,f80]) ).
tff(f97,plain,
0 != cardinality(empty_set),
inference(forward_demodulation,[],[f96,f95]) ).
tff(f98,plain,
$false,
inference(forward_subsumption_resolution,[],[f97,f89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV421_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n011.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 06:27:16 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 3.60/1.48 % (3196457)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.60/1.48 % (3196462)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=2980339104:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.60/1.48 % (3196462)Instruction limit reached!
% 3.60/1.48 % (3196462)------------------------------
% 3.60/1.48 % (3196462)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.60/1.48 % (3196462)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/1.48 % (3196462)CaDiCaL version: 2.1.3
% 3.60/1.48 % (3196462)Termination reason: Instruction limit
% 3.60/1.48 % (3196462)Termination phase: Saturation
% 3.60/1.48 % (3196462)Time elapsed: 0.019 s
% 3.60/1.48 % (3196462)Peak memory usage: 115 MB
% 3.60/1.48 % (3196462)Instructions burned: 14 (million)
% 3.60/1.48 % (3196465)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2839945232:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.60/1.48 % (3196464)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=708154416:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.60/1.48 % (3196466)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=2633778040:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.60/1.48 % (3196468)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=3527127079:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.60/1.48 % (3196463)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1432763754:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.60/1.48 % (3196465)First to succeed.
% 3.60/1.48 % (3196465)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3196457"
% 3.60/1.48 % (3196467)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2149478950:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.60/1.48 % (3196466)Instruction limit reached!
% 3.60/1.48 % (3196466)------------------------------
% 3.60/1.48 % (3196466)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.60/1.48 % (3196466)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/1.48 % (3196466)CaDiCaL version: 2.1.3
% 3.60/1.48 % (3196466)Termination reason: Instruction limit
% 3.60/1.48 % (3196466)Termination phase: Saturation
% 3.60/1.48 % (3196466)Time elapsed: 0.006 s
% 3.60/1.48 % (3196466)Peak memory usage: 89 MB
% 3.60/1.48 % (3196466)Instructions burned: 9 (million)
% 3.60/1.48 % (3196464)Also succeeded, but the first one will report.
% 3.60/1.48 % (3196468)Also succeeded, but the first one will report.
% 3.60/1.48 % (3196463)Also succeeded, but the first one will report.
% 3.60/1.48 % (3196467)Also succeeded, but the first one will report.
% 3.60/1.48 % (3196470)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=3047467333:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.60/1.48 % (3196470)Also succeeded, but the first one will report.
% 3.60/1.48 % (3196477)dis+1011_2:1_to=kbo:sil=128000:tgt=full:fde=none:si=on:norm_ineq=on:spb=goal_then_units:tha=some:nwc=2:sac=on:random_seed=2169314415:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 3.60/1.48 % (3196477)Also succeeded, but the first one will report.
% 3.60/1.48 % (3196465)Refutation found. Thanks to Tanya!
% 3.60/1.48 % SZS status Theorem for theBenchmark
% 3.60/1.48 % SZS output start Proof for theBenchmark
% See solution above
% 3.60/1.48 % (3196465)------------------------------
% 3.60/1.48 % (3196465)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.60/1.48 % (3196465)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/1.48 % (3196465)CaDiCaL version: 2.1.3
% 3.60/1.48 % (3196465)Termination reason: Refutation
% 3.60/1.48 % (3196465)Time elapsed: 0.003 s
% 3.60/1.48 % (3196465)Peak memory usage: 88 MB
% 3.60/1.48 % (3196465)Instructions burned: 3 (million)
% 3.60/1.48 % (3196465)------------------------------
% 3.60/1.48 % (3196465)------------------------------
% 3.60/1.48 % (3196457)Success in time 0.431 s
% 3.60/1.48 % Vampire exiting
%------------------------------------------------------------------------------