TSTP Solution File: DAT049_1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : DAT049_1 : TPTP v8.1.2. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n020.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 : Fri Sep 1 14:16:33 EDT 2023
% Result : Theorem 0.18s 0.49s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 17
% Syntax : Number of formulae : 56 ( 17 unt; 8 typ; 0 def)
% Number of atoms : 87 ( 47 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 71 ( 32 ~; 24 |; 4 &)
% ( 10 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number arithmetic : 82 ( 0 atm; 28 fun; 21 num; 33 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 7 ( 4 >; 3 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 11 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 64 (; 60 !; 4 ?; 64 :)
% 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_9,type,
sK0: collection ).
tff(func_def_10,type,
sK1: $int ).
tff(pred_def_1,type,
in: ( $int * collection ) > $o ).
tff(f3157,plain,
$false,
inference(avatar_sat_refutation,[],[f3139,f3156]) ).
tff(f3156,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[],[f3155]) ).
tff(f3155,plain,
( $false
| ~ spl2_1 ),
inference(subsumption_resolution,[],[f3152,f3119]) ).
tff(f3119,plain,
count(remove(sK1,sK0)) != $sum(-1,count(sK0)),
inference(backward_demodulation,[],[f2321,f3118]) ).
tff(f3118,plain,
count(add(sK1,sK0)) = count(sK0),
inference(subsumption_resolution,[],[f3112,f332]) ).
tff(f332,plain,
! [X8: collection,X9: $int] :
( ( count(X8) = count(remove(X9,X8)) )
| ( count(X8) = count(add(X9,X8)) ) ),
inference(resolution,[],[f65,f61]) ).
tff(f61,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/sandbox/tmp/tmp.v45SUXeueX/Vampire---4.8_12734',ax6) ).
tff(f65,plain,
! [X0: $int,X1: collection] :
( ~ in(X0,X1)
| ( count(X1) = count(add(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/sandbox/tmp/tmp.v45SUXeueX/Vampire---4.8_12734',ax4) ).
tff(f3112,plain,
( ( count(remove(sK1,sK0)) != count(sK0) )
| ( count(add(sK1,sK0)) = count(sK0) ) ),
inference(evaluation,[],[f3104]) ).
tff(f3104,plain,
( ( count(remove(sK1,sK0)) != $sum(-1,$sum(1,count(sK0))) )
| ( count(add(sK1,sK0)) = count(sK0) ) ),
inference(superposition,[],[f2321,f497]) ).
tff(f497,plain,
! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) = $sum(1,count(X1)) )
| ( count(X1) = count(add(X0,X1)) ) ),
inference(resolution,[],[f78,f65]) ).
tff(f78,plain,
! [X0: $int,X1: collection] :
( in(X0,X1)
| ( count(add(X0,X1)) = $sum(1,count(X1)) ) ),
inference(forward_demodulation,[],[f63,f17]) ).
tff(f17,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(theory_axiom_138,[]) ).
tff(f63,plain,
! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) = $sum(count(X1),1) )
| in(X0,X1) ),
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/sandbox/tmp/tmp.v45SUXeueX/Vampire---4.8_12734',ax3) ).
tff(f2321,plain,
count(remove(sK1,sK0)) != $sum(-1,count(add(sK1,sK0))),
inference(superposition,[],[f53,f547]) ).
tff(f547,plain,
! [X0: $int,X1: collection] : ( count(remove(X0,add(X0,X1))) = $sum(-1,count(add(X0,X1))) ),
inference(resolution,[],[f80,f59]) ).
tff(f59,plain,
! [X0: $int,X1: collection] : in(X0,add(X0,X1)),
inference(cnf_transformation,[],[f32]) ).
tff(f32,plain,
! [X0: $int,X1: collection] : in(X0,add(X0,X1)),
inference(rectify,[],[f2]) ).
tff(f2,axiom,
! [X1: $int,X2: collection] : in(X1,add(X1,X2)),
file('/export/starexec/sandbox/tmp/tmp.v45SUXeueX/Vampire---4.8_12734',ax2) ).
tff(f80,plain,
! [X0: $int,X1: collection] :
( ~ in(X0,X1)
| ( count(remove(X0,X1)) = $sum(-1,count(X1)) ) ),
inference(forward_demodulation,[],[f75,f17]) ).
tff(f75,plain,
! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = $sum(count(X1),-1) )
| ~ in(X0,X1) ),
inference(evaluation,[],[f67]) ).
tff(f67,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/sandbox/tmp/tmp.v45SUXeueX/Vampire---4.8_12734',ax5) ).
tff(f53,plain,
count(remove(sK1,add(sK1,sK0))) != count(remove(sK1,sK0)),
inference(cnf_transformation,[],[f43]) ).
tff(f43,plain,
count(remove(sK1,add(sK1,sK0))) != count(remove(sK1,sK0)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f40,f42]) ).
tff(f42,plain,
( ? [X0: collection,X1: $int] : ( count(remove(X1,add(X1,X0))) != count(remove(X1,X0)) )
=> ( count(remove(sK1,add(sK1,sK0))) != count(remove(sK1,sK0)) ) ),
introduced(choice_axiom,[]) ).
tff(f40,plain,
? [X0: collection,X1: $int] : ( count(remove(X1,add(X1,X0))) != count(remove(X1,X0)) ),
inference(ennf_transformation,[],[f14]) ).
tff(f14,negated_conjecture,
~ ! [X0: collection,X1: $int] : ( count(remove(X1,add(X1,X0))) = count(remove(X1,X0)) ),
inference(negated_conjecture,[],[f13]) ).
tff(f13,conjecture,
! [X0: collection,X1: $int] : ( count(remove(X1,add(X1,X0))) = count(remove(X1,X0)) ),
file('/export/starexec/sandbox/tmp/tmp.v45SUXeueX/Vampire---4.8_12734',co1) ).
tff(f3152,plain,
( ( count(remove(sK1,sK0)) = $sum(-1,count(sK0)) )
| ~ spl2_1 ),
inference(resolution,[],[f3132,f80]) ).
tff(f3132,plain,
( in(sK1,sK0)
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f3131]) ).
tff(f3131,plain,
( spl2_1
<=> in(sK1,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).
tff(f3139,plain,
spl2_1,
inference(avatar_split_clause,[],[f3129,f3131]) ).
tff(f3129,plain,
in(sK1,sK0),
inference(trivial_inequality_removal,[],[f3123]) ).
tff(f3123,plain,
( ( count(sK0) != count(sK0) )
| in(sK1,sK0) ),
inference(superposition,[],[f66,f3118]) ).
tff(f66,plain,
! [X0: $int,X1: collection] :
( ( count(X1) != count(add(X0,X1)) )
| in(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13 % Problem : DAT049_1 : TPTP v8.1.2. Released v5.0.0.
% 0.12/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.13/0.35 % Computer : n020.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 30 14:39:58 EDT 2023
% 0.18/0.35 % CPUTime :
% 0.18/0.41 % (12843)Running in auto input_syntax mode. Trying TPTP
% 0.18/0.42 % (12847)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.18/0.42 % (12845)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.18/0.42 % (12848)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 Vampire---4 for (531ds/0Mi)
% 0.18/0.42 % (12846)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 Vampire---4 for (569ds/0Mi)
% 0.18/0.42 % (12850)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 Vampire---4 for (497ds/0Mi)
% 0.18/0.42 % (12849)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 Vampire---4 for (522ds/0Mi)
% 0.18/0.42 % (12845)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.18/0.42 % (12847)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.18/0.42 % (12847)Terminated due to inappropriate strategy.
% 0.18/0.42 % (12847)------------------------------
% 0.18/0.42 % (12847)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.18/0.42 % (12847)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.18/0.42 % (12847)Termination reason: Inappropriate
% 0.18/0.42
% 0.18/0.42 % (12847)Memory used [KB]: 895
% 0.18/0.42 % (12847)Time elapsed: 0.002 s
% 0.18/0.42 % (12847)------------------------------
% 0.18/0.42 % (12847)------------------------------
% 0.18/0.42 % (12845)Terminated due to inappropriate strategy.
% 0.18/0.42 % (12845)------------------------------
% 0.18/0.42 % (12845)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.18/0.42 % (12845)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.18/0.42 % (12845)Termination reason: Inappropriate
% 0.18/0.42
% 0.18/0.42 % (12845)Memory used [KB]: 895
% 0.18/0.42 % (12845)Time elapsed: 0.002 s
% 0.18/0.42 % (12845)------------------------------
% 0.18/0.42 % (12845)------------------------------
% 0.18/0.42 % (12844)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.18/0.42 % (12844)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.18/0.42 % (12844)Terminated due to inappropriate strategy.
% 0.18/0.42 % (12844)------------------------------
% 0.18/0.42 % (12844)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.18/0.42 % (12844)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.18/0.42 % (12844)Termination reason: Inappropriate
% 0.18/0.42
% 0.18/0.42 % (12844)Memory used [KB]: 895
% 0.18/0.42 % (12844)Time elapsed: 0.003 s
% 0.18/0.42 % (12844)------------------------------
% 0.18/0.42 % (12844)------------------------------
% 0.18/0.42 % (12851)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on Vampire---4 for (411ds/0Mi)
% 0.18/0.42 % (12852)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on Vampire---4 for (382ds/0Mi)
% 0.18/0.42 % (12851)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.18/0.42 % (12851)Terminated due to inappropriate strategy.
% 0.18/0.42 % (12851)------------------------------
% 0.18/0.42 % (12851)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.18/0.42 % (12851)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.18/0.42 % (12851)Termination reason: Inappropriate
% 0.18/0.42
% 0.18/0.42 % (12851)Memory used [KB]: 895
% 0.18/0.42 % (12851)Time elapsed: 0.002 s
% 0.18/0.42 % (12851)------------------------------
% 0.18/0.42 % (12851)------------------------------
% 0.18/0.42 % (12853)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on Vampire---4 for (367ds/0Mi)
% 0.18/0.43 % (12854)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 Vampire---4 for (354ds/0Mi)
% 0.18/0.49 % (12853)First to succeed.
% 0.18/0.49 % (12853)Refutation found. Thanks to Tanya!
% 0.18/0.49 % SZS status Theorem for Vampire---4
% 0.18/0.49 % SZS output start Proof for Vampire---4
% See solution above
% 0.18/0.49 % (12853)------------------------------
% 0.18/0.49 % (12853)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.18/0.49 % (12853)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.18/0.49 % (12853)Termination reason: Refutation
% 0.18/0.49
% 0.18/0.49 % (12853)Memory used [KB]: 7547
% 0.18/0.49 % (12853)Time elapsed: 0.066 s
% 0.18/0.49 % (12853)------------------------------
% 0.18/0.49 % (12853)------------------------------
% 0.18/0.49 % (12843)Success in time 0.133 s
% 0.18/0.49 % Vampire---4.8 exiting
%------------------------------------------------------------------------------