%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT037_1 : TPTP v9.3.1. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 09:47:09 AM UTC 2026
% Result : Theorem 0.19s 1.30s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 53 ( 12 unt; 0 typ; 6 def)
% Number of atoms : 138 ( 49 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 145 ( 60 ~; 54 |; 19 &)
% ( 10 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 92 ( 0 atm; 16 fun; 48 num; 28 var)
% Number of types : 3 ( 1 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 14 ( 6 usr; 8 con; 0-2 aty)
% Number of variables : 48 ( 46 !; 2 ?; 48 :)
% 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(func_def_12,type,
sF1: $int ).
tff(pred_def_1,type,
in: ( $int * collection ) > $o ).
tff(f1,axiom,
! [X0: $int] : ~ in(X0,empty),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
tff(f5,axiom,
! [X0: $int,X2: $int,X1: collection] :
( ( in(X0,X1)
& ( X0 != X2 ) )
<=> in(X0,remove(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).
tff(f7,axiom,
! [X0: collection] :
( ( count(X0) = 0 )
<=> ( X0 = empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
tff(f10,axiom,
! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = $difference(count(X1),1) )
<=> in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).
tff(f13,conjecture,
! [X0: collection] :
( ( in(2,X0)
& ( count(X0) = 1 ) )
=> ~ in(5,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
tff(f14,negated_conjecture,
~ ! [X0: collection] :
( ( in(2,X0)
& ( count(X0) = 1 ) )
=> ~ in(5,X0) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
tff(f15,plain,
! [X1: collection,X0: $int] :
( ( count(remove(X0,X1)) = $sum(count(X1),$uminus(1)) )
<=> in(X0,X1) ),
inference(theory_normalization,[],[f10]) ).
tff(f20,plain,
! [X2: collection,X0: $int,X1: $int] :
( in(X0,remove(X1,X2))
<=> ( ( X0 != X1 )
& in(X0,X2) ) ),
inference(rectify,[],[f5]) ).
tff(f23,plain,
? [X0: collection] :
( in(5,X0)
& in(2,X0)
& ( count(X0) = 1 ) ),
inference(ennf_transformation,[],[f14]) ).
tff(f24,plain,
? [X0: collection] :
( in(5,X0)
& ( count(X0) = 1 )
& in(2,X0) ),
inference(flattening,[],[f23]) ).
tff(f28,plain,
! [X0: collection] :
( ( ( count(X0) = 0 )
| ( empty != X0 ) )
& ( ( X0 = empty )
| ( count(X0) != 0 ) ) ),
inference(nnf_transformation,[],[f7]) ).
tff(f33,plain,
! [X2: collection,X0: $int,X1: $int] :
( ( in(X0,remove(X1,X2))
| ( X0 = X1 )
| ~ in(X0,X2) )
& ( ( ( X0 != X1 )
& in(X0,X2) )
| ~ in(X0,remove(X1,X2)) ) ),
inference(nnf_transformation,[],[f20]) ).
tff(f34,plain,
! [X2: collection,X0: $int,X1: $int] :
( ( in(X0,remove(X1,X2))
| ( X0 = X1 )
| ~ in(X0,X2) )
& ( ( ( X0 != X1 )
& in(X0,X2) )
| ~ in(X0,remove(X1,X2)) ) ),
inference(flattening,[],[f33]) ).
tff(f35,plain,
! [X0: collection,X1: $int,X2: $int] :
( ( in(X1,remove(X2,X0))
| ( X1 = X2 )
| ~ in(X1,X0) )
& ( ( ( X1 != X2 )
& in(X1,X0) )
| ~ in(X1,remove(X2,X0)) ) ),
inference(rectify,[],[f34]) ).
tff(f38,plain,
! [X1: collection,X0: $int] :
( ( ( count(remove(X0,X1)) = $sum(count(X1),$uminus(1)) )
| ~ in(X0,X1) )
& ( in(X0,X1)
| ( count(remove(X0,X1)) != $sum(count(X1),$uminus(1)) ) ) ),
inference(nnf_transformation,[],[f15]) ).
tff(f39,plain,
! [X0: collection,X1: $int] :
( ( ( count(remove(X1,X0)) = $sum(count(X0),$uminus(1)) )
| ~ in(X1,X0) )
& ( in(X1,X0)
| ( count(remove(X1,X0)) != $sum(count(X0),$uminus(1)) ) ) ),
inference(rectify,[],[f38]) ).
tff(f41,plain,
( in(5,sK0)
& ( 1 = count(sK0) )
& in(2,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f24]) ).
tff(f47,plain,
! [X0: collection] :
( ( count(X0) != 0 )
| ( empty = X0 ) ),
inference(cnf_transformation,[],[f28]) ).
tff(f49,plain,
! [X0: $int] : ~ in(X0,empty),
inference(cnf_transformation,[],[f1]) ).
tff(f57,plain,
! [X2: $int,X0: collection,X1: $int] :
( in(X1,remove(X2,X0))
| ~ in(X1,X0)
| ( X1 = X2 ) ),
inference(cnf_transformation,[],[f35]) ).
tff(f61,plain,
! [X0: collection,X1: $int] :
( ( count(remove(X1,X0)) = $sum(count(X0),$uminus(1)) )
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f39]) ).
tff(f63,plain,
in(2,sK0),
inference(cnf_transformation,[],[f41]) ).
tff(f64,plain,
1 = count(sK0),
inference(cnf_transformation,[],[f41]) ).
tff(f65,plain,
in(5,sK0),
inference(cnf_transformation,[],[f41]) ).
tff(f69,definition,
sF1 = count(sK0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
tff(f70,plain,
1 = sF1,
inference(definition_folding,[],[f64,f69]) ).
tff(f72,plain,
! [X0: collection,X1: $int] :
( ( count(remove(X1,X0)) = $sum(count(X0),-1) )
| ~ in(X1,X0) ),
inference(evaluation,[],[f61]) ).
tff(f74,definition,
( spl2_1
<=> ( sF1 = count(sK0) ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
tff(f76,plain,
( ( sF1 = count(sK0) )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f74]) ).
tff(f77,plain,
spl2_1,
inference(avatar_split_clause,[],[f69,f74]) ).
tff(f79,definition,
( spl2_2
<=> ( 1 = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
tff(f81,plain,
( ( 1 = sF1 )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f79]) ).
tff(f82,plain,
spl2_2,
inference(avatar_split_clause,[],[f70,f79]) ).
tff(f89,definition,
( spl2_4
<=> in(2,sK0) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
tff(f91,plain,
( in(2,sK0)
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f89]) ).
tff(f92,plain,
spl2_4,
inference(avatar_split_clause,[],[f63,f89]) ).
tff(f94,definition,
( spl2_5
<=> in(5,sK0) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
tff(f96,plain,
( in(5,sK0)
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f94]) ).
tff(f97,plain,
spl2_5,
inference(avatar_split_clause,[],[f65,f94]) ).
tff(f98,plain,
( ( 1 = count(sK0) )
| ~ spl2_1
| ~ spl2_2 ),
inference(forward_demodulation,[],[f76,f81]) ).
tff(f100,definition,
( spl2_6
<=> ( 1 = count(sK0) ) ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
tff(f102,plain,
( ( 1 = count(sK0) )
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f100]) ).
tff(f103,plain,
( spl2_6
| ~ spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f98,f79,f74,f100]) ).
tff(f155,plain,
! [X0: collection,X1: $int] :
( ( 0 != $sum(count(X0),-1) )
| ~ in(X1,X0)
| ( empty = remove(X1,X0) ) ),
inference(superposition,[],[f47,f72]) ).
tff(f261,plain,
( ! [X0: $int] :
( ( empty = remove(X0,sK0) )
| ( 0 != $sum(1,-1) )
| ~ in(X0,sK0) )
| ~ spl2_6 ),
inference(superposition,[],[f155,f102]) ).
tff(f262,plain,
( ! [X0: $int] :
( ( empty = remove(X0,sK0) )
| ~ in(X0,sK0) )
| ~ spl2_6 ),
inference(evaluation,[],[f261]) ).
tff(f265,plain,
( ! [X0: $int,X1: $int] :
( ~ in(X0,sK0)
| in(X0,empty)
| ( X0 = X1 )
| ~ in(X1,sK0) )
| ~ spl2_6 ),
inference(superposition,[],[f57,f262]) ).
tff(f280,plain,
( ! [X0: $int,X1: $int] :
( ~ in(X1,sK0)
| ~ in(X0,sK0)
| ( X0 = X1 ) )
| ~ spl2_6 ),
inference(forward_subsumption_resolution,[],[f265,f49]) ).
tff(f337,plain,
( ! [X0: $int] :
( ~ in(X0,sK0)
| ( 2 = X0 ) )
| ~ spl2_4
| ~ spl2_6 ),
inference(resolution,[],[f280,f91]) ).
tff(f350,plain,
( ( 2 = 5 )
| ~ spl2_4
| ~ spl2_5
| ~ spl2_6 ),
inference(resolution,[],[f337,f96]) ).
tff(f351,plain,
( $false
| ~ spl2_4
| ~ spl2_5
| ~ spl2_6 ),
inference(evaluation,[],[f350]) ).
tff(f352,plain,
( ~ spl2_4
| ~ spl2_5
| ~ spl2_6 ),
inference(avatar_contradiction_clause,[],[f351]) ).
tff(f353,plain,
$false,
inference(avatar_smt_refutation,[],[f352,f103,f97,f92,f82,f77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : DAT037_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n019.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 00:06:19 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running first-order theorem proving
% 0.08/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.13/1.09 % (394411)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.13/1.09 % (394420)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=4276442564:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.13/1.09 % (394420)Instruction limit reached!
% 3.13/1.09 % (394420)------------------------------
% 3.13/1.09 % (394420)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.13/1.09 % (394420)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.13/1.09 % (394420)CaDiCaL version: 2.1.3
% 3.13/1.09 % (394420)Termination reason: Instruction limit
% 3.13/1.09 % (394420)Termination phase: Saturation
% 3.13/1.09 % (394420)Time elapsed: 0.002 s
% 3.13/1.09 % (394420)Peak memory usage: 88 MB
% 3.13/1.09 % (394420)Instructions burned: 4 (million)
% 3.13/1.09 % (394421)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2466970980:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.13/1.09 % (394422)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2742582955:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.13/1.09 % (394419)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2009582195:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.13/1.09 % (394417)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=783205406:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.13/1.09 % (394416)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=183446379:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.13/1.09 % (394418)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=407160715:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.13/1.09 % (394419)Instruction limit reached!
% 3.13/1.09 % (394419)------------------------------
% 3.13/1.09 % (394419)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.13/1.09 % (394419)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.13/1.09 % (394419)CaDiCaL version: 2.1.3
% 3.13/1.09 % (394419)Termination reason: Instruction limit
% 3.13/1.09 % (394419)Termination phase: Saturation
% 3.13/1.09 % (394419)Time elapsed: 0.005 s
% 3.13/1.09 % (394419)Peak memory usage: 88 MB
% 3.13/1.09 % (394419)Instructions burned: 7 (million)
% 3.13/1.09 % (394416)Instruction limit reached!
% 3.13/1.09 % (394416)------------------------------
% 3.13/1.09 % (394416)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.13/1.09 % (394416)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.13/1.09 % (394416)CaDiCaL version: 2.1.3
% 3.13/1.09 % (394416)Termination reason: Instruction limit
% 3.13/1.09 % (394416)Termination phase: Saturation
% 3.13/1.09 % (394416)Time elapsed: 0.030 s
% 3.13/1.09 % (394416)Peak memory usage: 115 MB
% 3.13/1.09 % (394416)Instructions burned: 13 (million)
% 3.13/1.09 % (394417)First to succeed.
% 3.13/1.09 % (394417)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-394411"
% 3.13/1.09 % (394421)Also succeeded, but the first one will report.
% 3.13/1.09 % (394422)Also succeeded, but the first one will report.
% 3.13/1.09 % (394424)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=3373354906:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.13/1.09 % (394424)Also succeeded, but the first one will report.
% 3.13/1.09 % (394418)Also succeeded, but the first one will report.
% 3.13/1.09 % (394431)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=3532205896:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 3.13/1.09 % (394432)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=2955914958:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/16Mi)
% 3.13/1.09 % (394431)Instruction limit reached!
% 3.13/1.09 % (394431)------------------------------
% 3.13/1.09 % (394431)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.13/1.09 % (394431)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.13/1.09 % (394431)CaDiCaL version: 2.1.3
% 3.13/1.09 % (394431)Termination reason: Instruction limit
% 3.13/1.09 % (394431)Termination phase: Saturation
% 0.19/1.30 % (394431)Time elapsed: 0.022 s
% 0.19/1.30 % (394431)Peak memory usage: 89 MB
% 0.19/1.30 % (394431)Instructions burned: 29 (million)
% 0.19/1.30 % (394432)Instruction limit reached!
% 0.19/1.30 % (394432)------------------------------
% 0.19/1.30 % (394432)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.30 % (394432)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.30 % (394432)CaDiCaL version: 2.1.3
% 0.19/1.30 % (394432)Termination reason: Instruction limit
% 0.19/1.30 % (394432)Termination phase: Saturation
% 0.19/1.30 % (394432)Time elapsed: 0.012 s
% 0.19/1.30 % (394432)Peak memory usage: 90 MB
% 0.19/1.30 % (394432)Instructions burned: 17 (million)
% 0.19/1.30 % (394438)dis+1002_24_to=kbo:sil=128000:si=on:random_seed=2513860226:i=85:gtgl=4:rtra=on:gtg=exists_sym_2996 on theBenchmark for (2996ds/85Mi)
% 0.19/1.30 % (394436)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=2687366259:i=24:canc=force:rtra=on_2996 on theBenchmark for (2996ds/24Mi)
% 0.19/1.30 % (394417)Refutation found. Thanks to Tanya!
% 0.19/1.30 % SZS status Theorem for theBenchmark
% 0.19/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/1.30 % (394417)------------------------------
% 0.19/1.30 % (394417)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.30 % (394417)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.30 % (394417)CaDiCaL version: 2.1.3
% 0.19/1.30 % (394417)Termination reason: Refutation
% 0.19/1.30 % (394417)Time elapsed: 0.040 s
% 0.19/1.30 % (394417)Peak memory usage: 116 MB
% 0.19/1.30 % (394417)Instructions burned: 21 (million)
% 0.19/1.30 % (394417)------------------------------
% 0.19/1.30 % (394417)------------------------------
% 0.19/1.30 % (394411)Success in time 0.445 s
% 0.19/1.30 % Vampire exiting
%------------------------------------------------------------------------------