TSTP Solution File: DAT048_1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : DAT048_1 : TPTP v8.2.0. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n002.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 : Mon May 20 19:51:09 EDT 2024
% Result : Theorem 61.03s 9.06s
% Output : Refutation 61.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 85
% Syntax : Number of formulae : 401 ( 31 unt; 6 typ; 0 def)
% Number of atoms : 984 ( 242 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 1042 ( 453 ~; 502 |; 15 &)
% ( 70 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number arithmetic : 1499 ( 131 atm; 157 fun;1084 num; 127 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 7 ( 4 >; 3 *; 0 +; 0 <<)
% Number of predicates : 59 ( 56 usr; 56 prp; 0-2 aty)
% Number of functors : 14 ( 4 usr; 8 con; 0-2 aty)
% Number of variables : 172 ( 172 !; 0 ?; 172 :)
% 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(pred_def_1,type,
in: ( $int * collection ) > $o ).
tff(f89888,plain,
$false,
inference(avatar_sat_refutation,[],[f82,f87,f56812,f70070,f70085,f70091,f70134,f70142,f70148,f70153,f70184,f70186,f70633,f76982,f76987,f76992,f76997,f77002,f77007,f77010,f77013,f77481,f77483,f77522,f86414,f86430,f86435,f86443,f86458,f86463,f86469,f86476,f86489,f86494,f86500,f86507,f86508,f86509,f86510,f86515,f86520,f86525,f86530,f86531,f86536,f86537,f86538,f86539,f86541,f86575,f86580,f86585,f86590,f86595,f86608,f86613,f86621,f86625,f86637,f86639,f86644,f86677,f86683,f89373,f89375,f89828,f89843,f89848,f89856,f89869,f89874,f89880,f89887]) ).
tff(f89887,plain,
( spl0_55
| ~ spl0_2
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f89882,f89840,f84,f89884]) ).
tff(f89884,plain,
( spl0_55
<=> ( 0 = count(remove(5,add(2,empty))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
tff(f84,plain,
( spl0_2
<=> ( 0 = count(empty) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
tff(f89840,plain,
( spl0_50
<=> in(5,add(2,empty)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
tff(f89882,plain,
( ( 0 = count(remove(5,add(2,empty))) )
| ~ spl0_2
| ~ spl0_50 ),
inference(evaluation,[],[f89881]) ).
tff(f89881,plain,
( ( $sum(-1,1) = count(remove(5,add(2,empty))) )
| ~ spl0_2
| ~ spl0_50 ),
inference(forward_demodulation,[],[f89860,f9723]) ).
tff(f9723,plain,
( ! [X0: $int] : ( 1 = count(add(X0,empty)) )
| ~ spl0_2 ),
inference(evaluation,[],[f9722]) ).
tff(f9722,plain,
( ! [X0: $int] : ( $sum(1,0) = count(add(X0,empty)) )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f9718,f86]) ).
tff(f86,plain,
( ( 0 = count(empty) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f84]) ).
tff(f9718,plain,
! [X0: $int] : ( count(add(X0,empty)) = $sum(1,count(empty)) ),
inference(resolution,[],[f89,f52]) ).
tff(f52,plain,
! [X0: $int] : ~ in(X0,empty),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
! [X0: $int] : ~ in(X0,empty),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
tff(f89,plain,
! [X0: $int,X1: collection] :
( in(X0,X1)
| ( count(add(X0,X1)) = $sum(1,count(X1)) ) ),
inference(forward_demodulation,[],[f61,f17]) ).
tff(f17,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(theory_axiom_135,[]) ).
tff(f61,plain,
! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) = $sum(count(X1),1) )
| in(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
tff(f44,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,[],[f36]) ).
tff(f36,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(f89860,plain,
( ( $sum(-1,count(add(2,empty))) = count(remove(5,add(2,empty))) )
| ~ spl0_50 ),
inference(resolution,[],[f89842,f91]) ).
tff(f91,plain,
! [X0: $int,X1: collection] :
( ~ in(X0,X1)
| ( count(remove(X0,X1)) = $sum(-1,count(X1)) ) ),
inference(forward_demodulation,[],[f76,f17]) ).
tff(f76,plain,
! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = $sum(count(X1),-1) )
| ~ in(X0,X1) ),
inference(evaluation,[],[f65]) ).
tff(f65,plain,
! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = $sum(count(X1),$uminus(1)) )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
tff(f46,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,[],[f38]) ).
tff(f38,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(f89842,plain,
( in(5,add(2,empty))
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f89840]) ).
tff(f89880,plain,
( spl0_54
| ~ spl0_2
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f89875,f89840,f84,f89877]) ).
tff(f89877,plain,
( spl0_54
<=> ( 1 = count(add(5,add(2,empty))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
tff(f89875,plain,
( ( 1 = count(add(5,add(2,empty))) )
| ~ spl0_2
| ~ spl0_50 ),
inference(forward_demodulation,[],[f89859,f9723]) ).
tff(f89859,plain,
( ( count(add(2,empty)) = count(add(5,add(2,empty))) )
| ~ spl0_50 ),
inference(resolution,[],[f89842,f63]) ).
tff(f63,plain,
! [X0: $int,X1: collection] :
( ~ in(X0,X1)
| ( count(X1) = count(add(X0,X1)) ) ),
inference(cnf_transformation,[],[f45]) ).
tff(f45,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,[],[f37]) ).
tff(f37,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(f89874,plain,
( spl0_53
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f89858,f89840,f89871]) ).
tff(f89871,plain,
( spl0_53
<=> ( add(2,empty) = add(5,remove(5,add(2,empty))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
tff(f89858,plain,
( ( add(2,empty) = add(5,remove(5,add(2,empty))) )
| ~ spl0_50 ),
inference(resolution,[],[f89842,f58]) ).
tff(f58,plain,
! [X0: $int,X1: collection] :
( ~ in(X0,X1)
| ( add(X0,remove(X0,X1)) = X1 ) ),
inference(cnf_transformation,[],[f41]) ).
tff(f41,plain,
! [X0: $int,X1: collection] :
( ( add(X0,remove(X0,X1)) = X1 )
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f34]) ).
tff(f34,plain,
! [X0: $int,X1: collection] :
( in(X0,X1)
=> ( add(X0,remove(X0,X1)) = X1 ) ),
inference(rectify,[],[f12]) ).
tff(f12,axiom,
! [X21: $int,X22: collection] :
( in(X21,X22)
=> ( add(X21,remove(X21,X22)) = X22 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax7) ).
tff(f89869,plain,
~ spl0_50,
inference(avatar_contradiction_clause,[],[f89868]) ).
tff(f89868,plain,
( $false
| ~ spl0_50 ),
inference(subsumption_resolution,[],[f89867,f52]) ).
tff(f89867,plain,
( in(5,empty)
| ~ spl0_50 ),
inference(evaluation,[],[f89857]) ).
tff(f89857,plain,
( in(5,empty)
| ( 5 = 2 )
| ~ spl0_50 ),
inference(resolution,[],[f89842,f72]) ).
tff(f72,plain,
! [X2: $int,X0: $int,X1: collection] :
( ~ in(X0,add(X2,X1))
| in(X0,X1)
| ( X0 = X2 ) ),
inference(cnf_transformation,[],[f50]) ).
tff(f50,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( ( X0 = X2 )
| in(X0,X1)
| ~ in(X0,add(X2,X1)) )
& ( in(X0,add(X2,X1))
| ( ( X0 != X2 )
& ~ in(X0,X1) ) ) ),
inference(flattening,[],[f49]) ).
tff(f49,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( ( X0 = X2 )
| in(X0,X1)
| ~ in(X0,add(X2,X1)) )
& ( in(X0,add(X2,X1))
| ( ( X0 != X2 )
& ~ in(X0,X1) ) ) ),
inference(nnf_transformation,[],[f40]) ).
tff(f40,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( ( X0 = X2 )
| in(X0,X1) )
<=> in(X0,add(X2,X1)) ),
inference(rectify,[],[f4]) ).
tff(f4,axiom,
! [X5: $int,X6: collection,X7: $int] :
( ( ( X5 = X7 )
| in(X5,X6) )
<=> in(X5,add(X7,X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
tff(f89856,plain,
( spl0_52
| ~ spl0_10
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f89851,f89825,f70139,f89853]) ).
tff(f89853,plain,
( spl0_52
<=> ( 0 = count(remove(5,remove(3,add(2,empty)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
tff(f70139,plain,
( spl0_10
<=> ( 1 = count(remove(3,add(2,empty))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
tff(f89825,plain,
( spl0_49
<=> in(5,remove(3,add(2,empty))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
tff(f89851,plain,
( ( 0 = count(remove(5,remove(3,add(2,empty)))) )
| ~ spl0_10
| ~ spl0_49 ),
inference(evaluation,[],[f89850]) ).
tff(f89850,plain,
( ( $sum(-1,1) = count(remove(5,remove(3,add(2,empty)))) )
| ~ spl0_10
| ~ spl0_49 ),
inference(forward_demodulation,[],[f89832,f70141]) ).
tff(f70141,plain,
( ( 1 = count(remove(3,add(2,empty))) )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f70139]) ).
tff(f89832,plain,
( ( $sum(-1,count(remove(3,add(2,empty)))) = count(remove(5,remove(3,add(2,empty)))) )
| ~ spl0_49 ),
inference(resolution,[],[f89827,f91]) ).
tff(f89827,plain,
( in(5,remove(3,add(2,empty)))
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f89825]) ).
tff(f89848,plain,
( spl0_51
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f89830,f89825,f89845]) ).
tff(f89845,plain,
( spl0_51
<=> ( remove(3,add(2,empty)) = add(5,remove(5,remove(3,add(2,empty)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
tff(f89830,plain,
( ( remove(3,add(2,empty)) = add(5,remove(5,remove(3,add(2,empty)))) )
| ~ spl0_49 ),
inference(resolution,[],[f89827,f58]) ).
tff(f89843,plain,
( spl0_50
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f89829,f89825,f89840]) ).
tff(f89829,plain,
( in(5,add(2,empty))
| ~ spl0_49 ),
inference(resolution,[],[f89827,f68]) ).
tff(f68,plain,
! [X2: $int,X0: $int,X1: collection] :
( ~ in(X0,remove(X2,X1))
| in(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
tff(f48,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( ( ( X0 != X2 )
& in(X0,X1) )
| ~ in(X0,remove(X2,X1)) )
& ( in(X0,remove(X2,X1))
| ( X0 = X2 )
| ~ in(X0,X1) ) ),
inference(flattening,[],[f47]) ).
tff(f47,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( ( ( X0 != X2 )
& in(X0,X1) )
| ~ in(X0,remove(X2,X1)) )
& ( in(X0,remove(X2,X1))
| ( X0 = X2 )
| ~ in(X0,X1) ) ),
inference(nnf_transformation,[],[f39]) ).
tff(f39,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( ( X0 != X2 )
& in(X0,X1) )
<=> in(X0,remove(X2,X1)) ),
inference(rectify,[],[f5]) ).
tff(f5,axiom,
! [X8: $int,X9: collection,X10: $int] :
( ( ( X8 != X10 )
& in(X8,X9) )
<=> in(X8,remove(X10,X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).
tff(f89828,plain,
( spl0_49
| ~ spl0_10
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f89823,f70181,f70139,f89825]) ).
tff(f70181,plain,
( spl0_13
<=> ( 1 = count(add(5,remove(3,add(2,empty)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
tff(f89823,plain,
( in(5,remove(3,add(2,empty)))
| ~ spl0_10
| ~ spl0_13 ),
inference(subsumption_resolution,[],[f89381,f70141]) ).
tff(f89381,plain,
( ( 1 != count(remove(3,add(2,empty))) )
| in(5,remove(3,add(2,empty)))
| ~ spl0_13 ),
inference(superposition,[],[f64,f70183]) ).
tff(f70183,plain,
( ( 1 = count(add(5,remove(3,add(2,empty)))) )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f70181]) ).
tff(f64,plain,
! [X0: $int,X1: collection] :
( ( count(X1) != count(add(X0,X1)) )
| in(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
tff(f89375,plain,
( spl0_22
| ~ spl0_13
| spl0_23 ),
inference(avatar_split_clause,[],[f89370,f86411,f70181,f77519]) ).
tff(f77519,plain,
( spl0_22
<=> ( 2 = count(add(1,add(5,remove(3,add(2,empty))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
tff(f86411,plain,
( spl0_23
<=> in(1,add(5,remove(3,add(2,empty)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
tff(f89370,plain,
( ( 2 = count(add(1,add(5,remove(3,add(2,empty))))) )
| ~ spl0_13
| spl0_23 ),
inference(evaluation,[],[f89369]) ).
tff(f89369,plain,
( ( count(add(1,add(5,remove(3,add(2,empty))))) = $sum(1,1) )
| ~ spl0_13
| spl0_23 ),
inference(forward_demodulation,[],[f89367,f70183]) ).
tff(f89367,plain,
( ( count(add(1,add(5,remove(3,add(2,empty))))) = $sum(1,count(add(5,remove(3,add(2,empty))))) )
| spl0_23 ),
inference(resolution,[],[f86412,f89]) ).
tff(f86412,plain,
( ~ in(1,add(5,remove(3,add(2,empty))))
| spl0_23 ),
inference(avatar_component_clause,[],[f86411]) ).
tff(f89373,plain,
( ~ spl0_13
| spl0_23
| ~ spl0_46 ),
inference(avatar_contradiction_clause,[],[f89372]) ).
tff(f89372,plain,
( $false
| ~ spl0_13
| spl0_23
| ~ spl0_46 ),
inference(evaluation,[],[f89371]) ).
tff(f89371,plain,
( ( 1 = 2 )
| ~ spl0_13
| spl0_23
| ~ spl0_46 ),
inference(forward_demodulation,[],[f89370,f86643]) ).
tff(f86643,plain,
( ( 1 = count(add(1,add(5,remove(3,add(2,empty))))) )
| ~ spl0_46 ),
inference(avatar_component_clause,[],[f86641]) ).
tff(f86641,plain,
( spl0_46
<=> ( 1 = count(add(1,add(5,remove(3,add(2,empty))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
tff(f86683,plain,
( spl0_48
| ~ spl0_2
| spl0_27 ),
inference(avatar_split_clause,[],[f86678,f86455,f84,f86680]) ).
tff(f86680,plain,
( spl0_48
<=> ( 1 = count(remove(1,add(2,empty))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
tff(f86455,plain,
( spl0_27
<=> in(1,add(2,empty)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
tff(f86678,plain,
( ( 1 = count(remove(1,add(2,empty))) )
| ~ spl0_2
| spl0_27 ),
inference(forward_demodulation,[],[f86670,f9723]) ).
tff(f86670,plain,
( ( count(add(2,empty)) = count(remove(1,add(2,empty))) )
| spl0_27 ),
inference(resolution,[],[f86456,f59]) ).
tff(f59,plain,
! [X0: $int,X1: collection] :
( in(X0,X1)
| ( count(remove(X0,X1)) = count(X1) ) ),
inference(cnf_transformation,[],[f43]) ).
tff(f43,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,[],[f35]) ).
tff(f35,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(f86456,plain,
( ~ in(1,add(2,empty))
| spl0_27 ),
inference(avatar_component_clause,[],[f86455]) ).
tff(f86677,plain,
( spl0_47
| ~ spl0_2
| spl0_27 ),
inference(avatar_split_clause,[],[f86672,f86455,f84,f86674]) ).
tff(f86674,plain,
( spl0_47
<=> ( 2 = count(add(1,add(2,empty))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
tff(f86672,plain,
( ( 2 = count(add(1,add(2,empty))) )
| ~ spl0_2
| spl0_27 ),
inference(evaluation,[],[f86671]) ).
tff(f86671,plain,
( ( $sum(1,1) = count(add(1,add(2,empty))) )
| ~ spl0_2
| spl0_27 ),
inference(forward_demodulation,[],[f86669,f9723]) ).
tff(f86669,plain,
( ( $sum(1,count(add(2,empty))) = count(add(1,add(2,empty))) )
| spl0_27 ),
inference(resolution,[],[f86456,f89]) ).
tff(f86644,plain,
( spl0_46
| ~ spl0_10
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f86630,f86572,f70139,f86641]) ).
tff(f86572,plain,
( spl0_39
<=> ( count(add(1,add(5,remove(3,add(2,empty))))) = count(remove(3,add(2,empty))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
tff(f86630,plain,
( ( 1 = count(add(1,add(5,remove(3,add(2,empty))))) )
| ~ spl0_10
| ~ spl0_39 ),
inference(backward_demodulation,[],[f86574,f70141]) ).
tff(f86574,plain,
( ( count(add(1,add(5,remove(3,add(2,empty))))) = count(remove(3,add(2,empty))) )
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f86572]) ).
tff(f86639,plain,
( ~ spl0_10
| spl0_41 ),
inference(avatar_contradiction_clause,[],[f86638]) ).
tff(f86638,plain,
( $false
| ~ spl0_10
| spl0_41 ),
inference(evaluation,[],[f86632]) ).
tff(f86632,plain,
( ~ $less(1,2)
| ~ spl0_10
| spl0_41 ),
inference(backward_demodulation,[],[f86584,f70141]) ).
tff(f86584,plain,
( ~ $less(count(remove(3,add(2,empty))),2)
| spl0_41 ),
inference(avatar_component_clause,[],[f86582]) ).
tff(f86582,plain,
( spl0_41
<=> $less(count(remove(3,add(2,empty))),2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
tff(f86637,plain,
( ~ spl0_10
| ~ spl0_42 ),
inference(avatar_contradiction_clause,[],[f86636]) ).
tff(f86636,plain,
( $false
| ~ spl0_10
| ~ spl0_42 ),
inference(evaluation,[],[f86633]) ).
tff(f86633,plain,
( $less(2,1)
| ~ spl0_10
| ~ spl0_42 ),
inference(backward_demodulation,[],[f86589,f70141]) ).
tff(f86589,plain,
( $less(2,count(remove(3,add(2,empty))))
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f86587]) ).
tff(f86587,plain,
( spl0_42
<=> $less(2,count(remove(3,add(2,empty)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
tff(f86625,plain,
( spl0_10
| ~ spl0_5
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f86623,f70181,f70063,f70139]) ).
tff(f70063,plain,
( spl0_5
<=> ( count(add(5,remove(3,add(2,empty)))) = count(remove(3,add(2,empty))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
tff(f86623,plain,
( ( 1 = count(remove(3,add(2,empty))) )
| ~ spl0_5
| ~ spl0_13 ),
inference(backward_demodulation,[],[f70065,f70183]) ).
tff(f70065,plain,
( ( count(add(5,remove(3,add(2,empty)))) = count(remove(3,add(2,empty))) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f70063]) ).
tff(f86621,plain,
( spl0_45
| ~ spl0_2
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f86616,f70630,f84,f86618]) ).
tff(f86618,plain,
( spl0_45
<=> ( 0 = count(remove(3,add(2,empty))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
tff(f70630,plain,
( spl0_14
<=> in(3,add(2,empty)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
tff(f86616,plain,
( ( 0 = count(remove(3,add(2,empty))) )
| ~ spl0_2
| ~ spl0_14 ),
inference(evaluation,[],[f86615]) ).
tff(f86615,plain,
( ( $sum(-1,1) = count(remove(3,add(2,empty))) )
| ~ spl0_2
| ~ spl0_14 ),
inference(forward_demodulation,[],[f86599,f9723]) ).
tff(f86599,plain,
( ( count(remove(3,add(2,empty))) = $sum(-1,count(add(2,empty))) )
| ~ spl0_14 ),
inference(resolution,[],[f70631,f91]) ).
tff(f70631,plain,
( in(3,add(2,empty))
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f70630]) ).
tff(f86613,plain,
( spl0_44
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f86597,f70630,f86610]) ).
tff(f86610,plain,
( spl0_44
<=> ( add(2,empty) = add(3,remove(3,add(2,empty))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
tff(f86597,plain,
( ( add(2,empty) = add(3,remove(3,add(2,empty))) )
| ~ spl0_14 ),
inference(resolution,[],[f70631,f58]) ).
tff(f86608,plain,
~ spl0_14,
inference(avatar_contradiction_clause,[],[f86607]) ).
tff(f86607,plain,
( $false
| ~ spl0_14 ),
inference(subsumption_resolution,[],[f86606,f52]) ).
tff(f86606,plain,
( in(3,empty)
| ~ spl0_14 ),
inference(evaluation,[],[f86596]) ).
tff(f86596,plain,
( in(3,empty)
| ( 3 = 2 )
| ~ spl0_14 ),
inference(resolution,[],[f70631,f72]) ).
tff(f86595,plain,
( spl0_43
| ~ spl0_5
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f86568,f77004,f70063,f86592]) ).
tff(f86592,plain,
( spl0_43
<=> $less(0,count(remove(3,add(2,empty)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
tff(f77004,plain,
( spl0_20
<=> $less(0,count(add(5,remove(3,add(2,empty))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
tff(f86568,plain,
( $less(0,count(remove(3,add(2,empty))))
| ~ spl0_5
| ~ spl0_20 ),
inference(backward_demodulation,[],[f77006,f70065]) ).
tff(f77006,plain,
( $less(0,count(add(5,remove(3,add(2,empty)))))
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f77004]) ).
tff(f86590,plain,
( spl0_42
| ~ spl0_5
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f86567,f76999,f70063,f86587]) ).
tff(f76999,plain,
( spl0_19
<=> $less(2,count(add(5,remove(3,add(2,empty))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
tff(f86567,plain,
( $less(2,count(remove(3,add(2,empty))))
| ~ spl0_5
| ~ spl0_19 ),
inference(backward_demodulation,[],[f77000,f70065]) ).
tff(f77000,plain,
( $less(2,count(add(5,remove(3,add(2,empty)))))
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f76999]) ).
tff(f86585,plain,
( ~ spl0_41
| ~ spl0_5
| spl0_18 ),
inference(avatar_split_clause,[],[f86566,f76994,f70063,f86582]) ).
tff(f76994,plain,
( spl0_18
<=> $less(count(add(5,remove(3,add(2,empty)))),2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
tff(f86566,plain,
( ~ $less(count(remove(3,add(2,empty))),2)
| ~ spl0_5
| spl0_18 ),
inference(backward_demodulation,[],[f76996,f70065]) ).
tff(f76996,plain,
( ~ $less(count(add(5,remove(3,add(2,empty)))),2)
| spl0_18 ),
inference(avatar_component_clause,[],[f76994]) ).
tff(f86580,plain,
( ~ spl0_40
| ~ spl0_5
| spl0_16 ),
inference(avatar_split_clause,[],[f86564,f76984,f70063,f86577]) ).
tff(f86577,plain,
( spl0_40
<=> $less(count(remove(3,add(2,empty))),-1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
tff(f76984,plain,
( spl0_16
<=> $less(count(add(5,remove(3,add(2,empty)))),-1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
tff(f86564,plain,
( ~ $less(count(remove(3,add(2,empty))),-1)
| ~ spl0_5
| spl0_16 ),
inference(backward_demodulation,[],[f76986,f70065]) ).
tff(f76986,plain,
( ~ $less(count(add(5,remove(3,add(2,empty)))),-1)
| spl0_16 ),
inference(avatar_component_clause,[],[f76984]) ).
tff(f86575,plain,
( spl0_39
| ~ spl0_3
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f86542,f70063,f56805,f86572]) ).
tff(f56805,plain,
( spl0_3
<=> ( count(add(1,add(5,remove(3,add(2,empty))))) = count(add(5,remove(3,add(2,empty)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
tff(f86542,plain,
( ( count(add(1,add(5,remove(3,add(2,empty))))) = count(remove(3,add(2,empty))) )
| ~ spl0_3
| ~ spl0_5 ),
inference(backward_demodulation,[],[f56807,f70065]) ).
tff(f56807,plain,
( ( count(add(1,add(5,remove(3,add(2,empty))))) = count(add(5,remove(3,add(2,empty)))) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f56805]) ).
tff(f86541,plain,
( ( count(add(5,remove(3,add(2,empty)))) != count(remove(3,add(2,empty))) )
| ( 3 != $sum(1,count(add(5,remove(3,add(2,empty))))) )
| ( 3 = $sum(1,count(remove(3,add(2,empty)))) ) ),
introduced(theory_tautology_sat_conflict,[]) ).
tff(f86539,plain,
( spl0_21
| spl0_19
| spl0_18 ),
inference(avatar_split_clause,[],[f77473,f76994,f76999,f77478]) ).
tff(f77478,plain,
( spl0_21
<=> ( 2 = count(add(5,remove(3,add(2,empty)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
tff(f77473,plain,
( $less(2,count(add(5,remove(3,add(2,empty)))))
| ( 2 = count(add(5,remove(3,add(2,empty)))) )
| spl0_18 ),
inference(resolution,[],[f76996,f24]) ).
tff(f24,plain,
! [X0: $int,X1: $int] :
( $less(X1,X0)
| $less(X0,X1)
| ( X0 = X1 ) ),
introduced(theory_axiom_144,[]) ).
tff(f86538,plain,
( spl0_21
| spl0_19
| spl0_18 ),
inference(avatar_split_clause,[],[f77474,f76994,f76999,f77478]) ).
tff(f77474,plain,
( $less(2,count(add(5,remove(3,add(2,empty)))))
| ( 2 = count(add(5,remove(3,add(2,empty)))) )
| spl0_18 ),
inference(resolution,[],[f76996,f24]) ).
tff(f86537,plain,
( spl0_10
| ~ spl0_2
| spl0_14 ),
inference(avatar_split_clause,[],[f70644,f70630,f84,f70139]) ).
tff(f70644,plain,
( ( 1 = count(remove(3,add(2,empty))) )
| ~ spl0_2
| spl0_14 ),
inference(forward_demodulation,[],[f70641,f9723]) ).
tff(f70641,plain,
( ( count(remove(3,add(2,empty))) = count(add(2,empty)) )
| spl0_14 ),
inference(resolution,[],[f70632,f59]) ).
tff(f70632,plain,
( ~ in(3,add(2,empty))
| spl0_14 ),
inference(avatar_component_clause,[],[f70630]) ).
tff(f86536,plain,
( spl0_5
| ~ spl0_38
| spl0_13 ),
inference(avatar_split_clause,[],[f72433,f70181,f86533,f70063]) ).
tff(f86533,plain,
( spl0_38
<=> ( 1 = $sum(1,count(remove(3,add(2,empty)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
tff(f72433,plain,
( ( 1 != $sum(1,count(remove(3,add(2,empty)))) )
| ( count(add(5,remove(3,add(2,empty)))) = count(remove(3,add(2,empty))) )
| spl0_13 ),
inference(superposition,[],[f70182,f9716]) ).
tff(f9716,plain,
! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) = $sum(1,count(X1)) )
| ( count(X1) = count(add(X0,X1)) ) ),
inference(resolution,[],[f89,f63]) ).
tff(f70182,plain,
( ( 1 != count(add(5,remove(3,add(2,empty)))) )
| spl0_13 ),
inference(avatar_component_clause,[],[f70181]) ).
tff(f86531,plain,
( spl0_5
| spl0_6
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f76976,f56809,f70067,f70063]) ).
tff(f70067,plain,
( spl0_6
<=> ( 3 = $sum(2,count(remove(3,add(2,empty)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
tff(f56809,plain,
( spl0_4
<=> ( 3 = $sum(1,count(add(5,remove(3,add(2,empty))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
tff(f76976,plain,
( ( 3 = $sum(2,count(remove(3,add(2,empty)))) )
| ( count(add(5,remove(3,add(2,empty)))) = count(remove(3,add(2,empty))) )
| ~ spl0_4 ),
inference(evaluation,[],[f76935]) ).
tff(f76935,plain,
( ( 3 = $sum(1,$sum(1,count(remove(3,add(2,empty))))) )
| ( count(add(5,remove(3,add(2,empty)))) = count(remove(3,add(2,empty))) )
| ~ spl0_4 ),
inference(superposition,[],[f56810,f9716]) ).
tff(f56810,plain,
( ( 3 = $sum(1,count(add(5,remove(3,add(2,empty))))) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f56809]) ).
tff(f86530,plain,
( spl0_5
| spl0_37
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f77463,f76979,f86527,f70063]) ).
tff(f86527,plain,
( spl0_37
<=> $less($sum(1,count(remove(3,add(2,empty)))),3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
tff(f76979,plain,
( spl0_15
<=> $less(count(add(5,remove(3,add(2,empty)))),3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
tff(f77463,plain,
( $less($sum(1,count(remove(3,add(2,empty)))),3)
| ( count(add(5,remove(3,add(2,empty)))) = count(remove(3,add(2,empty))) )
| ~ spl0_15 ),
inference(superposition,[],[f76981,f9716]) ).
tff(f76981,plain,
( $less(count(add(5,remove(3,add(2,empty)))),3)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f76979]) ).
tff(f86525,plain,
( spl0_5
| ~ spl0_36
| spl0_16 ),
inference(avatar_split_clause,[],[f77467,f76984,f86522,f70063]) ).
tff(f86522,plain,
( spl0_36
<=> $less($sum(1,count(remove(3,add(2,empty)))),-1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
tff(f77467,plain,
( ~ $less($sum(1,count(remove(3,add(2,empty)))),-1)
| ( count(add(5,remove(3,add(2,empty)))) = count(remove(3,add(2,empty))) )
| spl0_16 ),
inference(superposition,[],[f76986,f9716]) ).
tff(f86520,plain,
( spl0_5
| ~ spl0_35
| spl0_17 ),
inference(avatar_split_clause,[],[f77471,f76989,f86517,f70063]) ).
tff(f86517,plain,
( spl0_35
<=> $less(3,$sum(1,count(remove(3,add(2,empty))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
tff(f76989,plain,
( spl0_17
<=> $less(3,count(add(5,remove(3,add(2,empty))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
tff(f77471,plain,
( ~ $less(3,$sum(1,count(remove(3,add(2,empty)))))
| ( count(add(5,remove(3,add(2,empty)))) = count(remove(3,add(2,empty))) )
| spl0_17 ),
inference(superposition,[],[f76991,f9716]) ).
tff(f76991,plain,
( ~ $less(3,count(add(5,remove(3,add(2,empty)))))
| spl0_17 ),
inference(avatar_component_clause,[],[f76989]) ).
tff(f86515,plain,
( spl0_5
| ~ spl0_34
| spl0_18 ),
inference(avatar_split_clause,[],[f77475,f76994,f86512,f70063]) ).
tff(f86512,plain,
( spl0_34
<=> $less($sum(1,count(remove(3,add(2,empty)))),2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
tff(f77475,plain,
( ~ $less($sum(1,count(remove(3,add(2,empty)))),2)
| ( count(add(5,remove(3,add(2,empty)))) = count(remove(3,add(2,empty))) )
| spl0_18 ),
inference(superposition,[],[f76996,f9716]) ).
tff(f86510,plain,
( spl0_9
| ~ spl0_2
| spl0_14 ),
inference(avatar_split_clause,[],[f70643,f70630,f84,f70131]) ).
tff(f70131,plain,
( spl0_9
<=> ( 2 = count(add(3,add(2,empty))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
tff(f70643,plain,
( ( 2 = count(add(3,add(2,empty))) )
| ~ spl0_2
| spl0_14 ),
inference(evaluation,[],[f70642]) ).
tff(f70642,plain,
( ( $sum(1,1) = count(add(3,add(2,empty))) )
| ~ spl0_2
| spl0_14 ),
inference(forward_demodulation,[],[f70640,f9723]) ).
tff(f70640,plain,
( ( count(add(3,add(2,empty))) = $sum(1,count(add(2,empty))) )
| spl0_14 ),
inference(resolution,[],[f70632,f89]) ).
tff(f86509,plain,
( ( 2 != count(add(1,add(5,remove(3,add(2,empty))))) )
| ( count(add(1,add(5,remove(3,add(2,empty))))) != count(add(5,remove(3,add(2,empty)))) )
| ( 2 = count(add(5,remove(3,add(2,empty)))) ) ),
introduced(theory_tautology_sat_conflict,[]) ).
tff(f86508,plain,
( ( 2 != count(add(1,add(5,remove(3,add(2,empty))))) )
| ( count(add(1,add(5,remove(3,add(2,empty))))) != count(add(5,remove(3,add(2,empty)))) )
| ~ $less(2,count(add(5,remove(3,add(2,empty)))))
| $less(count(add(5,remove(3,add(2,empty)))),2) ),
introduced(theory_tautology_sat_conflict,[]) ).
tff(f86507,plain,
( spl0_33
| ~ spl0_2
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f86502,f86455,f84,f86504]) ).
tff(f86504,plain,
( spl0_33
<=> ( 0 = count(remove(1,add(2,empty))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
tff(f86502,plain,
( ( 0 = count(remove(1,add(2,empty))) )
| ~ spl0_2
| ~ spl0_27 ),
inference(evaluation,[],[f86501]) ).
tff(f86501,plain,
( ( $sum(-1,1) = count(remove(1,add(2,empty))) )
| ~ spl0_2
| ~ spl0_27 ),
inference(forward_demodulation,[],[f86480,f9723]) ).
tff(f86480,plain,
( ( $sum(-1,count(add(2,empty))) = count(remove(1,add(2,empty))) )
| ~ spl0_27 ),
inference(resolution,[],[f86457,f91]) ).
tff(f86457,plain,
( in(1,add(2,empty))
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f86455]) ).
tff(f86500,plain,
( spl0_32
| ~ spl0_2
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f86495,f86455,f84,f86497]) ).
tff(f86497,plain,
( spl0_32
<=> ( 1 = count(add(1,add(2,empty))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
tff(f86495,plain,
( ( 1 = count(add(1,add(2,empty))) )
| ~ spl0_2
| ~ spl0_27 ),
inference(forward_demodulation,[],[f86479,f9723]) ).
tff(f86479,plain,
( ( count(add(2,empty)) = count(add(1,add(2,empty))) )
| ~ spl0_27 ),
inference(resolution,[],[f86457,f63]) ).
tff(f86494,plain,
( spl0_31
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f86478,f86455,f86491]) ).
tff(f86491,plain,
( spl0_31
<=> ( add(2,empty) = add(1,remove(1,add(2,empty))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
tff(f86478,plain,
( ( add(2,empty) = add(1,remove(1,add(2,empty))) )
| ~ spl0_27 ),
inference(resolution,[],[f86457,f58]) ).
tff(f86489,plain,
~ spl0_27,
inference(avatar_contradiction_clause,[],[f86488]) ).
tff(f86488,plain,
( $false
| ~ spl0_27 ),
inference(subsumption_resolution,[],[f86487,f52]) ).
tff(f86487,plain,
( in(1,empty)
| ~ spl0_27 ),
inference(evaluation,[],[f86477]) ).
tff(f86477,plain,
( in(1,empty)
| ( 1 = 2 )
| ~ spl0_27 ),
inference(resolution,[],[f86457,f72]) ).
tff(f86476,plain,
( spl0_30
| ~ spl0_10
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f86471,f86427,f70139,f86473]) ).
tff(f86473,plain,
( spl0_30
<=> ( 0 = count(remove(1,remove(3,add(2,empty)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
tff(f86427,plain,
( spl0_24
<=> in(1,remove(3,add(2,empty))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
tff(f86471,plain,
( ( 0 = count(remove(1,remove(3,add(2,empty)))) )
| ~ spl0_10
| ~ spl0_24 ),
inference(evaluation,[],[f86470]) ).
tff(f86470,plain,
( ( $sum(-1,1) = count(remove(1,remove(3,add(2,empty)))) )
| ~ spl0_10
| ~ spl0_24 ),
inference(forward_demodulation,[],[f86447,f70141]) ).
tff(f86447,plain,
( ( count(remove(1,remove(3,add(2,empty)))) = $sum(-1,count(remove(3,add(2,empty)))) )
| ~ spl0_24 ),
inference(resolution,[],[f86429,f91]) ).
tff(f86429,plain,
( in(1,remove(3,add(2,empty)))
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f86427]) ).
tff(f86469,plain,
( spl0_29
| ~ spl0_10
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f86464,f86427,f70139,f86466]) ).
tff(f86466,plain,
( spl0_29
<=> ( 1 = count(add(1,remove(3,add(2,empty)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
tff(f86464,plain,
( ( 1 = count(add(1,remove(3,add(2,empty)))) )
| ~ spl0_10
| ~ spl0_24 ),
inference(forward_demodulation,[],[f86446,f70141]) ).
tff(f86446,plain,
( ( count(remove(3,add(2,empty))) = count(add(1,remove(3,add(2,empty)))) )
| ~ spl0_24 ),
inference(resolution,[],[f86429,f63]) ).
tff(f86463,plain,
( spl0_28
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f86445,f86427,f86460]) ).
tff(f86460,plain,
( spl0_28
<=> ( remove(3,add(2,empty)) = add(1,remove(1,remove(3,add(2,empty)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
tff(f86445,plain,
( ( remove(3,add(2,empty)) = add(1,remove(1,remove(3,add(2,empty)))) )
| ~ spl0_24 ),
inference(resolution,[],[f86429,f58]) ).
tff(f86458,plain,
( spl0_27
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f86444,f86427,f86455]) ).
tff(f86444,plain,
( in(1,add(2,empty))
| ~ spl0_24 ),
inference(resolution,[],[f86429,f68]) ).
tff(f86443,plain,
( spl0_26
| ~ spl0_21
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f86438,f86411,f77478,f86440]) ).
tff(f86440,plain,
( spl0_26
<=> ( 1 = count(remove(1,add(5,remove(3,add(2,empty))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
tff(f86438,plain,
( ( 1 = count(remove(1,add(5,remove(3,add(2,empty))))) )
| ~ spl0_21
| ~ spl0_23 ),
inference(evaluation,[],[f86437]) ).
tff(f86437,plain,
( ( $sum(-1,2) = count(remove(1,add(5,remove(3,add(2,empty))))) )
| ~ spl0_21
| ~ spl0_23 ),
inference(forward_demodulation,[],[f86418,f77480]) ).
tff(f77480,plain,
( ( 2 = count(add(5,remove(3,add(2,empty)))) )
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f77478]) ).
tff(f86418,plain,
( ( count(remove(1,add(5,remove(3,add(2,empty))))) = $sum(-1,count(add(5,remove(3,add(2,empty))))) )
| ~ spl0_23 ),
inference(resolution,[],[f86413,f91]) ).
tff(f86413,plain,
( in(1,add(5,remove(3,add(2,empty))))
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f86411]) ).
tff(f86435,plain,
( spl0_25
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f86416,f86411,f86432]) ).
tff(f86432,plain,
( spl0_25
<=> ( add(5,remove(3,add(2,empty))) = add(1,remove(1,add(5,remove(3,add(2,empty))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
tff(f86416,plain,
( ( add(5,remove(3,add(2,empty))) = add(1,remove(1,add(5,remove(3,add(2,empty))))) )
| ~ spl0_23 ),
inference(resolution,[],[f86413,f58]) ).
tff(f86430,plain,
( spl0_24
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f86425,f86411,f86427]) ).
tff(f86425,plain,
( in(1,remove(3,add(2,empty)))
| ~ spl0_23 ),
inference(evaluation,[],[f86415]) ).
tff(f86415,plain,
( in(1,remove(3,add(2,empty)))
| ( 1 = 5 )
| ~ spl0_23 ),
inference(resolution,[],[f86413,f72]) ).
tff(f86414,plain,
( spl0_23
| ~ spl0_21
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f86409,f77519,f77478,f86411]) ).
tff(f86409,plain,
( in(1,add(5,remove(3,add(2,empty))))
| ~ spl0_21
| ~ spl0_22 ),
inference(subsumption_resolution,[],[f85966,f77480]) ).
tff(f85966,plain,
( ( 2 != count(add(5,remove(3,add(2,empty)))) )
| in(1,add(5,remove(3,add(2,empty))))
| ~ spl0_22 ),
inference(superposition,[],[f64,f77521]) ).
tff(f77521,plain,
( ( 2 = count(add(1,add(5,remove(3,add(2,empty))))) )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f77519]) ).
tff(f77522,plain,
( spl0_22
| ~ spl0_3
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f77485,f77478,f56805,f77519]) ).
tff(f77485,plain,
( ( 2 = count(add(1,add(5,remove(3,add(2,empty))))) )
| ~ spl0_3
| ~ spl0_21 ),
inference(backward_demodulation,[],[f56807,f77480]) ).
tff(f77483,plain,
( spl0_21
| spl0_18
| spl0_19 ),
inference(avatar_split_clause,[],[f77482,f76999,f76994,f77478]) ).
tff(f77482,plain,
( ( 2 = count(add(5,remove(3,add(2,empty)))) )
| spl0_18
| spl0_19 ),
inference(subsumption_resolution,[],[f77474,f77001]) ).
tff(f77001,plain,
( ~ $less(2,count(add(5,remove(3,add(2,empty)))))
| spl0_19 ),
inference(avatar_component_clause,[],[f76999]) ).
tff(f77481,plain,
( spl0_21
| spl0_18
| spl0_19 ),
inference(avatar_split_clause,[],[f77476,f76999,f76994,f77478]) ).
tff(f77476,plain,
( ( 2 = count(add(5,remove(3,add(2,empty)))) )
| spl0_18
| spl0_19 ),
inference(subsumption_resolution,[],[f77473,f77001]) ).
tff(f77013,plain,
( spl0_6
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f77012]) ).
tff(f77012,plain,
( $false
| spl0_6
| ~ spl0_10 ),
inference(evaluation,[],[f77011]) ).
tff(f77011,plain,
( ( 3 != $sum(2,1) )
| spl0_6
| ~ spl0_10 ),
inference(forward_demodulation,[],[f70069,f70141]) ).
tff(f70069,plain,
( ( 3 != $sum(2,count(remove(3,add(2,empty)))) )
| spl0_6 ),
inference(avatar_component_clause,[],[f70067]) ).
tff(f77010,plain,
( ~ spl0_7
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f77009]) ).
tff(f77009,plain,
( $false
| ~ spl0_7
| ~ spl0_9 ),
inference(evaluation,[],[f77008]) ).
tff(f77008,plain,
( ( 1 = 2 )
| ~ spl0_7
| ~ spl0_9 ),
inference(backward_demodulation,[],[f70133,f70084]) ).
tff(f70084,plain,
( ( 1 = count(add(3,add(2,empty))) )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f70082]) ).
tff(f70082,plain,
( spl0_7
<=> ( 1 = count(add(3,add(2,empty))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
tff(f70133,plain,
( ( 2 = count(add(3,add(2,empty))) )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f70131]) ).
tff(f77007,plain,
( spl0_20
| ~ spl0_4
| ~ spl0_6
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f76971,f70139,f70067,f56809,f77004]) ).
tff(f76971,plain,
( $less(0,count(add(5,remove(3,add(2,empty)))))
| ~ spl0_4
| ~ spl0_6
| ~ spl0_10 ),
inference(evaluation,[],[f76950]) ).
tff(f76950,plain,
( ~ $less(1,3)
| $less(0,count(add(5,remove(3,add(2,empty)))))
| ~ spl0_4
| ~ spl0_6
| ~ spl0_10 ),
inference(superposition,[],[f74678,f56810]) ).
tff(f74678,plain,
( ! [X0: $int] :
( ~ $less(1,$sum(1,X0))
| $less(0,X0) )
| ~ spl0_6
| ~ spl0_10 ),
inference(superposition,[],[f73317,f17]) ).
tff(f73317,plain,
( ! [X0: $int] :
( ~ $less(1,$sum(X0,1))
| $less(0,X0) )
| ~ spl0_6
| ~ spl0_10 ),
inference(resolution,[],[f72058,f72288]) ).
tff(f72288,plain,
( ! [X0: $int] :
( $less($sum(2,X0),3)
| $less(0,X0) )
| ~ spl0_6
| ~ spl0_10 ),
inference(evaluation,[],[f72284]) ).
tff(f72284,plain,
( ! [X0: $int] :
( $less(0,X0)
| $less($sum($uminus(-2),X0),3) )
| ~ spl0_6
| ~ spl0_10 ),
inference(superposition,[],[f72193,f6698]) ).
tff(f6698,plain,
! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 ),
inference(evaluation,[],[f6403]) ).
tff(f6403,plain,
! [X0: $int,X1: $int] : ( $sum(0,X1) = $sum(X0,$sum($uminus(X0),X1)) ),
inference(superposition,[],[f18,f21]) ).
tff(f21,plain,
! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
introduced(theory_axiom_140,[]) ).
tff(f18,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(theory_axiom_136,[]) ).
tff(f72193,plain,
( ! [X0: $int] :
( $less(0,$sum(-2,X0))
| $less(X0,3) )
| ~ spl0_6
| ~ spl0_10 ),
inference(resolution,[],[f72094,f139]) ).
tff(f139,plain,
! [X0: $int] :
( $less(X0,1)
| $less(0,X0) ),
inference(superposition,[],[f107,f19]) ).
tff(f19,plain,
! [X0: $int] : ( $sum(X0,0) = X0 ),
introduced(theory_axiom_137,[]) ).
tff(f107,plain,
! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,X1) ),
inference(superposition,[],[f26,f17]) ).
tff(f26,plain,
! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,X1) ),
introduced(theory_axiom_147,[]) ).
tff(f72094,plain,
( ! [X0: $int] :
( ~ $less($sum(-2,X0),1)
| $less(X0,3) )
| ~ spl0_6
| ~ spl0_10 ),
inference(evaluation,[],[f72090]) ).
tff(f72090,plain,
( ! [X0: $int] :
( $less(X0,3)
| ~ $less($sum($uminus(2),X0),1) )
| ~ spl0_6
| ~ spl0_10 ),
inference(superposition,[],[f72018,f6698]) ).
tff(f72018,plain,
( ! [X0: $int] :
( $less($sum(2,X0),3)
| ~ $less(X0,1) )
| ~ spl0_6
| ~ spl0_10 ),
inference(superposition,[],[f70163,f17]) ).
tff(f70163,plain,
( ! [X0: $int] :
( $less($sum(X0,2),3)
| ~ $less(X0,1) )
| ~ spl0_6
| ~ spl0_10 ),
inference(backward_demodulation,[],[f70112,f70141]) ).
tff(f70112,plain,
( ! [X0: $int] :
( $less($sum(X0,2),3)
| ~ $less(X0,count(remove(3,add(2,empty)))) )
| ~ spl0_6 ),
inference(superposition,[],[f2066,f70068]) ).
tff(f70068,plain,
( ( 3 = $sum(2,count(remove(3,add(2,empty)))) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f70067]) ).
tff(f2066,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,X1),$sum(X1,X0))
| ~ $less(X2,X0) ),
inference(superposition,[],[f25,f17]) ).
tff(f25,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X0,X2),$sum(X1,X2))
| ~ $less(X0,X1) ),
introduced(theory_axiom_145,[]) ).
tff(f72058,plain,
( ! [X0: $int] :
( ~ $less($sum(2,X0),3)
| ~ $less(1,$sum(X0,1)) )
| ~ spl0_6
| ~ spl0_10 ),
inference(resolution,[],[f71997,f6419]) ).
tff(f6419,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X2,$sum(X0,$sum(X1,1)))
| ~ $less($sum(X0,X1),X2) ),
inference(superposition,[],[f28,f18]) ).
tff(f28,plain,
! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(X0,1))
| ~ $less(X0,X1) ),
introduced(theory_axiom_161,[]) ).
tff(f71997,plain,
( ! [X0: $int] :
( $less(3,$sum(2,X0))
| ~ $less(1,X0) )
| ~ spl0_6
| ~ spl0_10 ),
inference(superposition,[],[f70161,f17]) ).
tff(f70161,plain,
( ! [X0: $int] :
( $less(3,$sum(X0,2))
| ~ $less(1,X0) )
| ~ spl0_6
| ~ spl0_10 ),
inference(backward_demodulation,[],[f70109,f70141]) ).
tff(f70109,plain,
( ! [X0: $int] :
( $less(3,$sum(X0,2))
| ~ $less(count(remove(3,add(2,empty))),X0) )
| ~ spl0_6 ),
inference(superposition,[],[f2060,f70068]) ).
tff(f2060,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X1,X0),$sum(X2,X1))
| ~ $less(X0,X2) ),
inference(superposition,[],[f25,f17]) ).
tff(f77002,plain,
( ~ spl0_19
| ~ spl0_4
| ~ spl0_6
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f76972,f70139,f70067,f56809,f76999]) ).
tff(f76972,plain,
( ~ $less(2,count(add(5,remove(3,add(2,empty)))))
| ~ spl0_4
| ~ spl0_6
| ~ spl0_10 ),
inference(evaluation,[],[f76945]) ).
tff(f76945,plain,
( $less(3,3)
| ~ $less(2,count(add(5,remove(3,add(2,empty)))))
| ~ spl0_4
| ~ spl0_6
| ~ spl0_10 ),
inference(superposition,[],[f70164,f56810]) ).
tff(f70164,plain,
( ! [X0: $int] :
( $less(3,$sum(1,X0))
| ~ $less(2,X0) )
| ~ spl0_6
| ~ spl0_10 ),
inference(backward_demodulation,[],[f70113,f70141]) ).
tff(f70113,plain,
( ! [X0: $int] :
( $less(3,$sum(count(remove(3,add(2,empty))),X0))
| ~ $less(2,X0) )
| ~ spl0_6 ),
inference(superposition,[],[f2066,f70068]) ).
tff(f76997,plain,
( ~ spl0_18
| ~ spl0_4
| ~ spl0_6
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f76973,f70139,f70067,f56809,f76994]) ).
tff(f76973,plain,
( ~ $less(count(add(5,remove(3,add(2,empty)))),2)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_10 ),
inference(evaluation,[],[f76944]) ).
tff(f76944,plain,
( $less(3,3)
| ~ $less(count(add(5,remove(3,add(2,empty)))),2)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_10 ),
inference(superposition,[],[f70162,f56810]) ).
tff(f70162,plain,
( ! [X0: $int] :
( $less($sum(1,X0),3)
| ~ $less(X0,2) )
| ~ spl0_6
| ~ spl0_10 ),
inference(backward_demodulation,[],[f70110,f70141]) ).
tff(f70110,plain,
( ! [X0: $int] :
( $less($sum(count(remove(3,add(2,empty))),X0),3)
| ~ $less(X0,2) )
| ~ spl0_6 ),
inference(superposition,[],[f2060,f70068]) ).
tff(f76992,plain,
( ~ spl0_17
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f76943,f56809,f76989]) ).
tff(f76943,plain,
( ~ $less(3,count(add(5,remove(3,add(2,empty)))))
| ~ spl0_4 ),
inference(superposition,[],[f239,f56810]) ).
tff(f239,plain,
! [X0: $int] : ~ $less($sum(1,X0),X0),
inference(superposition,[],[f223,f17]) ).
tff(f223,plain,
! [X0: $int] : ~ $less($sum(X0,1),X0),
inference(resolution,[],[f207,f22]) ).
tff(f22,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(theory_axiom_142,[]) ).
tff(f207,plain,
! [X0: $int,X1: $int] :
( $less(X0,$sum(X1,1))
| ~ $less(X0,X1) ),
inference(resolution,[],[f23,f106]) ).
tff(f106,plain,
! [X0: $int] : $less(X0,$sum(X0,1)),
inference(resolution,[],[f26,f22]) ).
tff(f23,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X1,X2)
| ~ $less(X0,X1)
| $less(X0,X2) ),
introduced(theory_axiom_143,[]) ).
tff(f76987,plain,
( ~ spl0_16
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f76975,f56809,f76984]) ).
tff(f76975,plain,
( ~ $less(count(add(5,remove(3,add(2,empty)))),-1)
| ~ spl0_4 ),
inference(evaluation,[],[f76940]) ).
tff(f76940,plain,
( $less(3,0)
| ~ $less(count(add(5,remove(3,add(2,empty)))),-1)
| ~ spl0_4 ),
inference(superposition,[],[f152,f56810]) ).
tff(f152,plain,
! [X0: $int] :
( $less($sum(1,X0),0)
| ~ $less(X0,-1) ),
inference(resolution,[],[f126,f110]) ).
tff(f110,plain,
! [X0: $int] :
( $less(X0,0)
| $less(-1,X0) ),
inference(evaluation,[],[f109]) ).
tff(f109,plain,
! [X0: $int] :
( $less(X0,0)
| $less($uminus(1),X0) ),
inference(superposition,[],[f26,f93]) ).
tff(f93,plain,
! [X0: $int] : ( 0 = $sum($uminus(X0),X0) ),
inference(superposition,[],[f21,f27]) ).
tff(f27,plain,
! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
introduced(theory_axiom_148,[]) ).
tff(f126,plain,
! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(1,X0))
| ~ $less(X0,X1) ),
inference(superposition,[],[f28,f17]) ).
tff(f76982,plain,
( spl0_15
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f76937,f56809,f76979]) ).
tff(f76937,plain,
( $less(count(add(5,remove(3,add(2,empty)))),3)
| ~ spl0_4 ),
inference(superposition,[],[f111,f56810]) ).
tff(f111,plain,
! [X0: $int] : $less(X0,$sum(1,X0)),
inference(superposition,[],[f106,f17]) ).
tff(f70633,plain,
( ~ spl0_14
| ~ spl0_2
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f70628,f70131,f84,f70630]) ).
tff(f70628,plain,
( ~ in(3,add(2,empty))
| ~ spl0_2
| ~ spl0_9 ),
inference(evaluation,[],[f70627]) ).
tff(f70627,plain,
( ( 2 != $sum(1,1) )
| ~ in(3,add(2,empty))
| ~ spl0_2
| ~ spl0_9 ),
inference(forward_demodulation,[],[f70189,f9723]) ).
tff(f70189,plain,
( ( 2 != $sum(1,count(add(2,empty))) )
| ~ in(3,add(2,empty))
| ~ spl0_9 ),
inference(superposition,[],[f88,f70133]) ).
tff(f88,plain,
! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) != $sum(1,count(X1)) )
| ~ in(X0,X1) ),
inference(forward_demodulation,[],[f62,f17]) ).
tff(f62,plain,
! [X0: $int,X1: collection] :
( ~ in(X0,X1)
| ( count(add(X0,X1)) != $sum(count(X1),1) ) ),
inference(cnf_transformation,[],[f44]) ).
tff(f70186,plain,
( ~ spl0_13
| spl0_5
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f70185,f70139,f70063,f70181]) ).
tff(f70185,plain,
( ( 1 != count(add(5,remove(3,add(2,empty)))) )
| spl0_5
| ~ spl0_10 ),
inference(forward_demodulation,[],[f70064,f70141]) ).
tff(f70064,plain,
( ( count(add(5,remove(3,add(2,empty)))) != count(remove(3,add(2,empty))) )
| spl0_5 ),
inference(avatar_component_clause,[],[f70063]) ).
tff(f70184,plain,
( spl0_13
| ~ spl0_5
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f70154,f70139,f70063,f70181]) ).
tff(f70154,plain,
( ( 1 = count(add(5,remove(3,add(2,empty)))) )
| ~ spl0_5
| ~ spl0_10 ),
inference(backward_demodulation,[],[f70065,f70141]) ).
tff(f70153,plain,
( spl0_12
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f70104,f70067,f70150]) ).
tff(f70150,plain,
( spl0_12
<=> $less(count(remove(3,add(2,empty))),3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
tff(f70104,plain,
( $less(count(remove(3,add(2,empty))),3)
| ~ spl0_6 ),
inference(superposition,[],[f243,f70068]) ).
tff(f243,plain,
! [X0: $int] : $less(X0,$sum(2,X0)),
inference(evaluation,[],[f235]) ).
tff(f235,plain,
! [X0: $int] : $less(X0,$sum($sum(X0,1),1)),
inference(resolution,[],[f223,f26]) ).
tff(f70148,plain,
( ~ spl0_11
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f70103,f70067,f70145]) ).
tff(f70145,plain,
( spl0_11
<=> $less(3,count(remove(3,add(2,empty)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
tff(f70103,plain,
( ~ $less(3,count(remove(3,add(2,empty))))
| ~ spl0_6 ),
inference(superposition,[],[f244,f70068]) ).
tff(f244,plain,
! [X0: $int] : ~ $less($sum(2,X0),X0),
inference(evaluation,[],[f234]) ).
tff(f234,plain,
! [X0: $int] : ~ $less($sum($sum(X0,1),1),X0),
inference(resolution,[],[f223,f207]) ).
tff(f70142,plain,
( spl0_10
| ~ spl0_2
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f70137,f70067,f84,f70139]) ).
tff(f70137,plain,
( ( 1 = count(remove(3,add(2,empty))) )
| ~ spl0_2
| ~ spl0_6 ),
inference(forward_demodulation,[],[f70136,f9723]) ).
tff(f70136,plain,
( ( count(remove(3,add(2,empty))) = count(add(2,empty)) )
| ~ spl0_2
| ~ spl0_6 ),
inference(evaluation,[],[f70135]) ).
tff(f70135,plain,
( ( 3 = $sum(1,1) )
| ( count(remove(3,add(2,empty))) = count(add(2,empty)) )
| ~ spl0_2
| ~ spl0_6 ),
inference(forward_demodulation,[],[f70124,f9723]) ).
tff(f70124,plain,
( ( 3 = $sum(1,count(add(2,empty))) )
| ( count(remove(3,add(2,empty))) = count(add(2,empty)) )
| ~ spl0_6 ),
inference(evaluation,[],[f70101]) ).
tff(f70101,plain,
( ( 3 = $sum(2,$sum(-1,count(add(2,empty)))) )
| ( count(remove(3,add(2,empty))) = count(add(2,empty)) )
| ~ spl0_6 ),
inference(superposition,[],[f70068,f11231]) ).
tff(f11231,plain,
! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = $sum(-1,count(X1)) )
| ( count(remove(X0,X1)) = count(X1) ) ),
inference(resolution,[],[f91,f59]) ).
tff(f70134,plain,
( spl0_9
| ~ spl0_2
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f70129,f70067,f84,f70131]) ).
tff(f70129,plain,
( ( 2 = count(add(3,add(2,empty))) )
| ~ spl0_2
| ~ spl0_6 ),
inference(evaluation,[],[f70128]) ).
tff(f70128,plain,
( ( $sum(1,1) = count(add(3,add(2,empty))) )
| ~ spl0_2
| ~ spl0_6 ),
inference(forward_demodulation,[],[f70127,f9723]) ).
tff(f70127,plain,
( ( count(add(3,add(2,empty))) = $sum(1,count(add(2,empty))) )
| ~ spl0_2
| ~ spl0_6 ),
inference(evaluation,[],[f70126]) ).
tff(f70126,plain,
( ( 3 = $sum(1,1) )
| ( count(add(3,add(2,empty))) = $sum(1,count(add(2,empty))) )
| ~ spl0_2
| ~ spl0_6 ),
inference(forward_demodulation,[],[f70125,f9723]) ).
tff(f70125,plain,
( ( 3 = $sum(1,count(add(2,empty))) )
| ( count(add(3,add(2,empty))) = $sum(1,count(add(2,empty))) )
| ~ spl0_6 ),
inference(evaluation,[],[f70100]) ).
tff(f70100,plain,
( ( 3 = $sum(2,$sum(-1,count(add(2,empty)))) )
| ( count(add(3,add(2,empty))) = $sum(1,count(add(2,empty))) )
| ~ spl0_6 ),
inference(superposition,[],[f70068,f11230]) ).
tff(f11230,plain,
! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = $sum(-1,count(X1)) )
| ( count(add(X0,X1)) = $sum(1,count(X1)) ) ),
inference(resolution,[],[f91,f89]) ).
tff(f70091,plain,
( ~ spl0_8
| spl0_4
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f70086,f70063,f56809,f70088]) ).
tff(f70088,plain,
( spl0_8
<=> ( 3 = $sum(1,count(remove(3,add(2,empty)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
tff(f70086,plain,
( ( 3 != $sum(1,count(remove(3,add(2,empty)))) )
| spl0_4
| ~ spl0_5 ),
inference(backward_demodulation,[],[f56811,f70065]) ).
tff(f56811,plain,
( ( 3 != $sum(1,count(add(5,remove(3,add(2,empty))))) )
| spl0_4 ),
inference(avatar_component_clause,[],[f56809]) ).
tff(f70085,plain,
( spl0_7
| ~ spl0_2
| spl0_6 ),
inference(avatar_split_clause,[],[f70080,f70067,f84,f70082]) ).
tff(f70080,plain,
( ( 1 = count(add(3,add(2,empty))) )
| ~ spl0_2
| spl0_6 ),
inference(forward_demodulation,[],[f70079,f9723]) ).
tff(f70079,plain,
( ( count(add(2,empty)) = count(add(3,add(2,empty))) )
| ~ spl0_2
| spl0_6 ),
inference(evaluation,[],[f70078]) ).
tff(f70078,plain,
( ( 3 != $sum(2,1) )
| ( count(add(2,empty)) = count(add(3,add(2,empty))) )
| ~ spl0_2
| spl0_6 ),
inference(forward_demodulation,[],[f70073,f9723]) ).
tff(f70073,plain,
( ( 3 != $sum(2,count(add(2,empty))) )
| ( count(add(2,empty)) = count(add(3,add(2,empty))) )
| spl0_6 ),
inference(superposition,[],[f70069,f4961]) ).
tff(f4961,plain,
! [X0: collection,X1: $int] :
( ( count(X0) = count(remove(X1,X0)) )
| ( count(X0) = count(add(X1,X0)) ) ),
inference(resolution,[],[f63,f59]) ).
tff(f70070,plain,
( spl0_5
| ~ spl0_6
| spl0_4 ),
inference(avatar_split_clause,[],[f70061,f56809,f70067,f70063]) ).
tff(f70061,plain,
( ( 3 != $sum(2,count(remove(3,add(2,empty)))) )
| ( count(add(5,remove(3,add(2,empty)))) = count(remove(3,add(2,empty))) )
| spl0_4 ),
inference(evaluation,[],[f70060]) ).
tff(f70060,plain,
( ( 3 != $sum(1,$sum(1,count(remove(3,add(2,empty))))) )
| ( count(add(5,remove(3,add(2,empty)))) = count(remove(3,add(2,empty))) )
| spl0_4 ),
inference(superposition,[],[f56811,f9716]) ).
tff(f56812,plain,
( spl0_3
| ~ spl0_4
| spl0_1 ),
inference(avatar_split_clause,[],[f56439,f79,f56809,f56805]) ).
tff(f79,plain,
( spl0_1
<=> ( 3 = count(add(1,add(5,remove(3,add(2,empty))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
tff(f56439,plain,
( ( 3 != $sum(1,count(add(5,remove(3,add(2,empty))))) )
| ( count(add(1,add(5,remove(3,add(2,empty))))) = count(add(5,remove(3,add(2,empty)))) )
| spl0_1 ),
inference(superposition,[],[f81,f9716]) ).
tff(f81,plain,
( ( 3 != count(add(1,add(5,remove(3,add(2,empty))))) )
| spl0_1 ),
inference(avatar_component_clause,[],[f79]) ).
tff(f87,plain,
spl0_2,
inference(avatar_split_clause,[],[f73,f84]) ).
tff(f73,plain,
0 = count(empty),
inference(equality_resolution,[],[f54]) ).
tff(f54,plain,
! [X0: collection] :
( ( 0 = count(X0) )
| ( empty != X0 ) ),
inference(cnf_transformation,[],[f42]) ).
tff(f42,plain,
! [X0: collection] :
( ( ( empty = X0 )
| ( 0 != count(X0) ) )
& ( ( 0 = count(X0) )
| ( empty != X0 ) ) ),
inference(nnf_transformation,[],[f31]) ).
tff(f31,plain,
! [X0: collection] :
( ( empty = X0 )
<=> ( 0 = count(X0) ) ),
inference(rectify,[],[f7]) ).
tff(f7,axiom,
! [X12: collection] :
( ( empty = X12 )
<=> ( 0 = count(X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
tff(f82,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f51,f79]) ).
tff(f51,plain,
3 != count(add(1,add(5,remove(3,add(2,empty))))),
inference(cnf_transformation,[],[f29]) ).
tff(f29,plain,
3 != count(add(1,add(5,remove(3,add(2,empty))))),
inference(flattening,[],[f14]) ).
tff(f14,negated_conjecture,
( ~ 3 = count(add(1,add(5,remove(3,add(2,empty))))) ),
inference(negated_conjecture,[],[f13]) ).
tff(f13,conjecture,
3 = count(add(1,add(5,remove(3,add(2,empty))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : DAT048_1 : TPTP v8.2.0. Released v5.0.0.
% 0.15/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.36 % Computer : n002.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Sun May 19 23:16:53 EDT 2024
% 0.22/0.36 % CPUTime :
% 0.22/0.36 % (24173)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.38 % (24176)WARNING: value z3 for option sas not known
% 0.22/0.38 % (24175)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.38 % (24174)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.38 % (24177)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.38 % (24178)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)
% 0.22/0.38 % (24176)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)
% 0.22/0.38 % (24179)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)
% 0.22/0.38 % (24180)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)
% 0.22/0.38 % (24177)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.22/0.38 % (24175)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.22/0.38 % (24174)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.22/0.38 % (24175)Terminated due to inappropriate strategy.
% 0.22/0.38 % (24175)------------------------------
% 0.22/0.38 % (24175)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.38 % (24174)Terminated due to inappropriate strategy.
% 0.22/0.38 % (24174)------------------------------
% 0.22/0.38 % (24174)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.38 % (24174)Termination reason: Inappropriate
% 0.22/0.38
% 0.22/0.38 % (24174)Memory used [KB]: 765
% 0.22/0.38 % (24174)Time elapsed: 0.003 s
% 0.22/0.38 % (24174)Instructions burned: 3 (million)
% 0.22/0.38 % (24177)Terminated due to inappropriate strategy.
% 0.22/0.38 % (24177)------------------------------
% 0.22/0.38 % (24177)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.38 % (24177)Termination reason: Inappropriate
% 0.22/0.38
% 0.22/0.38 % (24177)Memory used [KB]: 765
% 0.22/0.38 % (24177)Time elapsed: 0.003 s
% 0.22/0.38 % (24177)Instructions burned: 3 (million)
% 0.22/0.38 % (24175)Termination reason: Inappropriate
% 0.22/0.38
% 0.22/0.38 % (24175)Memory used [KB]: 765
% 0.22/0.38 % (24175)Time elapsed: 0.003 s
% 0.22/0.38 % (24175)Instructions burned: 3 (million)
% 0.22/0.38 % (24177)------------------------------
% 0.22/0.38 % (24177)------------------------------
% 0.22/0.38 % (24174)------------------------------
% 0.22/0.38 % (24174)------------------------------
% 0.22/0.38 % (24175)------------------------------
% 0.22/0.38 % (24175)------------------------------
% 0.22/0.40 % (24181)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.22/0.40 % (24182)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)
% 0.22/0.40 % (24183)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)
% 0.22/0.40 % (24181)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.22/0.40 % (24181)Terminated due to inappropriate strategy.
% 0.22/0.40 % (24181)------------------------------
% 0.22/0.40 % (24181)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.40 % (24181)Termination reason: Inappropriate
% 0.22/0.40
% 0.22/0.40 % (24181)Memory used [KB]: 764
% 0.22/0.40 % (24181)Time elapsed: 0.002 s
% 0.22/0.40 % (24181)Instructions burned: 3 (million)
% 0.22/0.40 % (24181)------------------------------
% 0.22/0.40 % (24181)------------------------------
% 0.22/0.42 % (24184)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)
% 61.03/9.06 % (24184)First to succeed.
% 61.03/9.06 % (24184)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-24173"
% 61.03/9.06 % (24184)Refutation found. Thanks to Tanya!
% 61.03/9.06 % SZS status Theorem for theBenchmark
% 61.03/9.06 % SZS output start Proof for theBenchmark
% See solution above
% 61.03/9.07 % (24184)------------------------------
% 61.03/9.07 % (24184)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 61.03/9.07 % (24184)Termination reason: Refutation
% 61.03/9.07
% 61.03/9.07 % (24184)Memory used [KB]: 27401
% 61.03/9.07 % (24184)Time elapsed: 8.645 s
% 61.03/9.07 % (24184)Instructions burned: 29043 (million)
% 61.03/9.07 % (24173)Success in time 8.63 s
%------------------------------------------------------------------------------