TSTP Solution File: DAT033_1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : DAT033_1 : TPTP v8.1.2. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 11:03:43 EDT 2024
% Result : Theorem 0.22s 0.45s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 17
% Syntax : Number of formulae : 66 ( 4 unt; 7 typ; 0 def)
% Number of atoms : 128 ( 58 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 123 ( 54 ~; 46 |; 8 &)
% ( 12 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number arithmetic : 131 ( 0 atm; 32 fun; 74 num; 25 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 7 ( 4 >; 3 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 12 ( 5 usr; 6 con; 0-2 aty)
% Number of variables : 52 ( 50 !; 2 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
collection: $tType ).
tff(func_def_0,type,
empty: collection ).
tff(func_def_1,type,
add: ( $int * collection ) > collection ).
tff(func_def_2,type,
remove: ( $int * collection ) > collection ).
tff(func_def_3,type,
count: collection > $int ).
tff(func_def_11,type,
sK0: collection ).
tff(pred_def_1,type,
in: ( $int * collection ) > $o ).
tff(f636,plain,
$false,
inference(avatar_sat_refutation,[],[f539,f545,f577,f635]) ).
tff(f635,plain,
( spl1_3
| ~ spl1_5 ),
inference(avatar_contradiction_clause,[],[f634]) ).
tff(f634,plain,
( $false
| spl1_3
| ~ spl1_5 ),
inference(subsumption_resolution,[],[f633,f581]) ).
tff(f581,plain,
( ( count(remove(5,sK0)) != count(sK0) )
| spl1_3 ),
inference(backward_demodulation,[],[f54,f580]) ).
tff(f580,plain,
( ( count(remove(3,sK0)) = count(sK0) )
| spl1_3 ),
inference(resolution,[],[f383,f62]) ).
tff(f62,plain,
! [X0: $int,X1: collection] :
( in(X0,X1)
| ( count(remove(X0,X1)) = count(X1) ) ),
inference(cnf_transformation,[],[f45]) ).
tff(f45,plain,
! [X0: $int,X1: collection] :
( ( ~ in(X0,X1)
| ( count(remove(X0,X1)) != count(X1) ) )
& ( ( count(remove(X0,X1)) = count(X1) )
| in(X0,X1) ) ),
inference(nnf_transformation,[],[f34]) ).
tff(f34,plain,
! [X0: $int,X1: collection] :
( ~ in(X0,X1)
<=> ( count(remove(X0,X1)) = count(X1) ) ),
inference(rectify,[],[f11]) ).
tff(f11,axiom,
! [X19: $int,X20: collection] :
( ~ in(X19,X20)
<=> ( count(remove(X19,X20)) = count(X20) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6) ).
tff(f383,plain,
( ~ in(3,sK0)
| spl1_3 ),
inference(avatar_component_clause,[],[f382]) ).
tff(f382,plain,
( spl1_3
<=> in(3,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_3])]) ).
tff(f54,plain,
count(remove(5,sK0)) != count(remove(3,sK0)),
inference(cnf_transformation,[],[f43]) ).
tff(f43,plain,
( ( count(remove(5,sK0)) != count(remove(3,sK0)) )
& ( count(add(5,sK0)) = count(add(3,sK0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f40,f42]) ).
tff(f42,plain,
( ? [X0: collection] :
( ( count(remove(5,X0)) != count(remove(3,X0)) )
& ( count(add(5,X0)) = count(add(3,X0)) ) )
=> ( ( count(remove(5,sK0)) != count(remove(3,sK0)) )
& ( count(add(5,sK0)) = count(add(3,sK0)) ) ) ),
introduced(choice_axiom,[]) ).
tff(f40,plain,
? [X0: collection] :
( ( count(remove(5,X0)) != count(remove(3,X0)) )
& ( count(add(5,X0)) = count(add(3,X0)) ) ),
inference(ennf_transformation,[],[f14]) ).
tff(f14,negated_conjecture,
~ ! [X0: collection] :
( ( count(add(5,X0)) = count(add(3,X0)) )
=> ( count(remove(5,X0)) = count(remove(3,X0)) ) ),
inference(negated_conjecture,[],[f13]) ).
tff(f13,conjecture,
! [X0: collection] :
( ( count(add(5,X0)) = count(add(3,X0)) )
=> ( count(remove(5,X0)) = count(remove(3,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
tff(f633,plain,
( ( count(remove(5,sK0)) = count(sK0) )
| ~ spl1_5 ),
inference(resolution,[],[f630,f62]) ).
tff(f630,plain,
( ~ in(5,sK0)
| ~ spl1_5 ),
inference(trivial_inequality_removal,[],[f624]) ).
tff(f624,plain,
( ( $sum(1,count(sK0)) != $sum(1,count(sK0)) )
| ~ in(5,sK0)
| ~ spl1_5 ),
inference(superposition,[],[f81,f510]) ).
tff(f510,plain,
( ( count(add(5,sK0)) = $sum(1,count(sK0)) )
| ~ spl1_5 ),
inference(avatar_component_clause,[],[f509]) ).
tff(f509,plain,
( spl1_5
<=> ( count(add(5,sK0)) = $sum(1,count(sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_5])]) ).
tff(f81,plain,
! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) != $sum(1,count(X1)) )
| ~ in(X0,X1) ),
inference(forward_demodulation,[],[f65,f17]) ).
tff(f17,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(theory_axiom_135,[]) ).
tff(f65,plain,
! [X0: $int,X1: collection] :
( ~ in(X0,X1)
| ( count(add(X0,X1)) != $sum(count(X1),1) ) ),
inference(cnf_transformation,[],[f46]) ).
tff(f46,plain,
! [X0: $int,X1: collection] :
( ( ~ in(X0,X1)
| ( count(add(X0,X1)) != $sum(count(X1),1) ) )
& ( ( count(add(X0,X1)) = $sum(count(X1),1) )
| in(X0,X1) ) ),
inference(nnf_transformation,[],[f35]) ).
tff(f35,plain,
! [X0: $int,X1: collection] :
( ~ in(X0,X1)
<=> ( count(add(X0,X1)) = $sum(count(X1),1) ) ),
inference(rectify,[],[f8]) ).
tff(f8,axiom,
! [X13: $int,X14: collection] :
( ~ in(X13,X14)
<=> ( count(add(X13,X14)) = $sum(count(X14),1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
tff(f577,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f576]) ).
tff(f576,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(subsumption_resolution,[],[f574,f575]) ).
tff(f575,plain,
( ( count(remove(5,sK0)) != $sum(-1,count(sK0)) )
| ~ spl1_3 ),
inference(backward_demodulation,[],[f54,f573]) ).
tff(f573,plain,
( ( count(remove(3,sK0)) = $sum(-1,count(sK0)) )
| ~ spl1_3 ),
inference(resolution,[],[f84,f384]) ).
tff(f384,plain,
( in(3,sK0)
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f382]) ).
tff(f84,plain,
! [X0: $int,X1: collection] :
( ~ in(X0,X1)
| ( count(remove(X0,X1)) = $sum(-1,count(X1)) ) ),
inference(forward_demodulation,[],[f79,f17]) ).
tff(f79,plain,
! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = $sum(count(X1),-1) )
| ~ in(X0,X1) ),
inference(evaluation,[],[f68]) ).
tff(f68,plain,
! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = $sum(count(X1),$uminus(1)) )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
tff(f48,plain,
! [X0: $int,X1: collection] :
( ( in(X0,X1)
| ( count(remove(X0,X1)) != $sum(count(X1),$uminus(1)) ) )
& ( ( count(remove(X0,X1)) = $sum(count(X1),$uminus(1)) )
| ~ in(X0,X1) ) ),
inference(nnf_transformation,[],[f37]) ).
tff(f37,plain,
! [X0: $int,X1: collection] :
( in(X0,X1)
<=> ( count(remove(X0,X1)) = $sum(count(X1),$uminus(1)) ) ),
inference(rectify,[],[f16]) ).
tff(f16,plain,
! [X17: $int,X18: collection] :
( in(X17,X18)
<=> ( count(remove(X17,X18)) = $sum(count(X18),$uminus(1)) ) ),
inference(theory_normalization,[],[f10]) ).
tff(f10,axiom,
! [X17: $int,X18: collection] :
( in(X17,X18)
<=> ( count(remove(X17,X18)) = $difference(count(X18),1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).
tff(f574,plain,
( ( count(remove(5,sK0)) = $sum(-1,count(sK0)) )
| ~ spl1_4 ),
inference(resolution,[],[f84,f553]) ).
tff(f553,plain,
( in(5,sK0)
| ~ spl1_4 ),
inference(trivial_inequality_removal,[],[f549]) ).
tff(f549,plain,
( ( count(sK0) != count(sK0) )
| in(5,sK0)
| ~ spl1_4 ),
inference(superposition,[],[f67,f387]) ).
tff(f387,plain,
( ( count(add(5,sK0)) = count(sK0) )
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f386]) ).
tff(f386,plain,
( spl1_4
<=> ( count(add(5,sK0)) = count(sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_4])]) ).
tff(f67,plain,
! [X0: $int,X1: collection] :
( ( count(X1) != count(add(X0,X1)) )
| in(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
tff(f47,plain,
! [X0: $int,X1: collection] :
( ( in(X0,X1)
| ( count(X1) != count(add(X0,X1)) ) )
& ( ( count(X1) = count(add(X0,X1)) )
| ~ in(X0,X1) ) ),
inference(nnf_transformation,[],[f36]) ).
tff(f36,plain,
! [X0: $int,X1: collection] :
( in(X0,X1)
<=> ( count(X1) = count(add(X0,X1)) ) ),
inference(rectify,[],[f9]) ).
tff(f9,axiom,
! [X15: $int,X16: collection] :
( in(X15,X16)
<=> ( count(add(X15,X16)) = count(X16) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
tff(f545,plain,
( spl1_4
| ~ spl1_3 ),
inference(avatar_split_clause,[],[f542,f382,f386]) ).
tff(f542,plain,
( ( count(add(5,sK0)) = count(sK0) )
| ~ spl1_3 ),
inference(backward_demodulation,[],[f53,f540]) ).
tff(f540,plain,
( ( count(add(3,sK0)) = count(sK0) )
| ~ spl1_3 ),
inference(resolution,[],[f384,f66]) ).
tff(f66,plain,
! [X0: $int,X1: collection] :
( ~ in(X0,X1)
| ( count(X1) = count(add(X0,X1)) ) ),
inference(cnf_transformation,[],[f47]) ).
tff(f53,plain,
count(add(5,sK0)) = count(add(3,sK0)),
inference(cnf_transformation,[],[f43]) ).
tff(f539,plain,
( spl1_5
| spl1_3 ),
inference(avatar_split_clause,[],[f538,f382,f509]) ).
tff(f538,plain,
( ( count(add(5,sK0)) = $sum(1,count(sK0)) )
| spl1_3 ),
inference(backward_demodulation,[],[f53,f535]) ).
tff(f535,plain,
( ( count(add(3,sK0)) = $sum(1,count(sK0)) )
| spl1_3 ),
inference(resolution,[],[f82,f383]) ).
tff(f82,plain,
! [X0: $int,X1: collection] :
( in(X0,X1)
| ( count(add(X0,X1)) = $sum(1,count(X1)) ) ),
inference(forward_demodulation,[],[f64,f17]) ).
tff(f64,plain,
! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) = $sum(count(X1),1) )
| in(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.12 % Problem : DAT033_1 : TPTP v8.1.2. Released v5.0.0.
% 0.13/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n010.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon Apr 29 22:02:35 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (28461)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.39 % (28466)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.39 % (28468)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.39 % (28467)WARNING: value z3 for option sas not known
% 0.15/0.39 % (28466)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.15/0.39 % (28466)Terminated due to inappropriate strategy.
% 0.15/0.39 % (28466)------------------------------
% 0.15/0.39 % (28466)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.39 % (28466)Termination reason: Inappropriate
% 0.15/0.39
% 0.15/0.39 % (28466)Memory used [KB]: 766
% 0.15/0.39 % (28466)Time elapsed: 0.004 s
% 0.15/0.39 % (28466)Instructions burned: 3 (million)
% 0.15/0.39 % (28466)------------------------------
% 0.15/0.39 % (28466)------------------------------
% 0.15/0.39 % (28468)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.15/0.39 % (28468)Terminated due to inappropriate strategy.
% 0.15/0.39 % (28468)------------------------------
% 0.15/0.39 % (28468)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.39 % (28468)Termination reason: Inappropriate
% 0.15/0.39
% 0.15/0.39 % (28468)Memory used [KB]: 766
% 0.15/0.39 % (28468)Time elapsed: 0.004 s
% 0.15/0.39 % (28468)Instructions burned: 3 (million)
% 0.15/0.39 % (28468)------------------------------
% 0.15/0.39 % (28468)------------------------------
% 0.15/0.39 % (28467)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.39 % (28470)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.39 % (28465)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.39 % (28469)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.39 % (28471)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.39 % (28465)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.15/0.39 % (28465)Terminated due to inappropriate strategy.
% 0.15/0.39 % (28465)------------------------------
% 0.15/0.39 % (28465)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.39 % (28465)Termination reason: Inappropriate
% 0.15/0.39
% 0.15/0.39 % (28465)Memory used [KB]: 766
% 0.15/0.39 % (28465)Time elapsed: 0.004 s
% 0.15/0.39 % (28465)Instructions burned: 3 (million)
% 0.15/0.39 % (28465)------------------------------
% 0.15/0.39 % (28465)------------------------------
% 0.15/0.41 % (28475)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.15/0.41 % (28476)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.15/0.41 % (28475)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.15/0.41 % (28475)Terminated due to inappropriate strategy.
% 0.15/0.41 % (28475)------------------------------
% 0.15/0.41 % (28475)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.41 % (28475)Termination reason: Inappropriate
% 0.15/0.41
% 0.15/0.41 % (28475)Memory used [KB]: 765
% 0.15/0.41 % (28475)Time elapsed: 0.004 s
% 0.15/0.41 % (28475)Instructions burned: 3 (million)
% 0.15/0.41 % (28475)------------------------------
% 0.15/0.41 % (28475)------------------------------
% 0.15/0.42 % (28477)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.22/0.44 % (28482)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 0.22/0.44 % (28477)First to succeed.
% 0.22/0.45 % (28477)Refutation found. Thanks to Tanya!
% 0.22/0.45 % SZS status Theorem for theBenchmark
% 0.22/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.45 % (28477)------------------------------
% 0.22/0.45 % (28477)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.45 % (28477)Termination reason: Refutation
% 0.22/0.45
% 0.22/0.45 % (28477)Memory used [KB]: 1064
% 0.22/0.45 % (28477)Time elapsed: 0.034 s
% 0.22/0.45 % (28477)Instructions burned: 30 (million)
% 0.22/0.45 % (28477)------------------------------
% 0.22/0.45 % (28477)------------------------------
% 0.22/0.45 % (28461)Success in time 0.085 s
%------------------------------------------------------------------------------