%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT044_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 : n018.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 09:47:10 AM UTC 2026
% Result : Theorem 4.04s 1.33s
% Output : Refutation 4.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 40 ( 7 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 36 ( 15 ~; 8 |; 3 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 58 ( 20 atm; 9 fun; 9 num; 20 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 : 5 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 29 ( 27 !; 2 ?; 29 :)
% 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: $int ).
tff(func_def_10,type,
sK1: collection ).
tff(pred_def_1,type,
in: ( $int * collection ) > $o ).
tff(f8,negated_conjecture,
! [X1: collection,X0: $int] :
( ~ in(X0,X1)
<=> ( count(add(X0,X1)) = $sum(count(X1),1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
tff(f13,conjecture,
! [X1: $int,X0: collection] :
( ! [X2: $int] :
( in(X2,X0)
=> $greater(X1,X2) )
=> $greater(count(add(X1,X0)),count(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
tff(f14,negated_conjecture,
~ ! [X1: $int,X0: collection] :
( ! [X2: $int] :
( in(X2,X0)
=> $greater(X1,X2) )
=> $greater(count(add(X1,X0)),count(X0)) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
tff(f16,plain,
~ ! [X1: $int,X0: collection] :
( ! [X2: $int] :
( in(X2,X0)
=> $less(X2,X1) )
=> $less(count(X0),count(add(X1,X0))) ),
inference(theory_normalization,[],[f14]) ).
tff(f23,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(definition,[],[tha_non-reflexivity]) ).
tff(f27,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ),
introduced(definition,[],[tha_order_plus_one_dichotomy]) ).
tff(f30,plain,
! [X0: collection,X1: $int] :
( ( count(add(X1,X0)) = $sum(count(X0),1) )
<=> ~ in(X1,X0) ),
inference(rectify,[],[f8]) ).
tff(f31,plain,
~ ! [X1: collection,X0: $int] :
( ! [X2: $int] :
( in(X2,X1)
=> $less(X2,X0) )
=> $less(count(X1),count(add(X0,X1))) ),
inference(rectify,[],[f16]) ).
tff(f40,plain,
? [X0: $int,X1: collection] :
( ~ $less(count(X1),count(add(X0,X1)))
& ! [X2: $int] :
( ~ in(X2,X1)
| $less(X2,X0) ) ),
inference(ennf_transformation,[],[f31]) ).
tff(f48,plain,
! [X0: collection,X1: $int] :
( ( ( count(add(X1,X0)) = $sum(count(X0),1) )
| in(X1,X0) )
& ( ~ in(X1,X0)
| ( count(add(X1,X0)) != $sum(count(X0),1) ) ) ),
inference(nnf_transformation,[],[f30]) ).
tff(f56,plain,
( ~ $less(count(sK1),count(add(sK0,sK1)))
& ! [X2: $int] :
( ~ in(X2,sK1)
| $less(X2,sK0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f40]) ).
tff(f66,plain,
! [X0: collection,X1: $int] :
( in(X1,X0)
| ( count(add(X1,X0)) = $sum(count(X0),1) ) ),
inference(cnf_transformation,[],[f48]) ).
tff(f78,plain,
! [X2: $int] :
( ~ in(X2,sK1)
| $less(X2,sK0) ),
inference(cnf_transformation,[],[f56]) ).
tff(f79,plain,
~ $less(count(sK1),count(add(sK0,sK1))),
inference(cnf_transformation,[],[f56]) ).
tff(f85,plain,
! [X0: $int] :
( $less(X0,sK0)
| ( count(add(X0,sK1)) = $sum(count(sK1),1) ) ),
inference(resolution,[],[f66,f78]) ).
tff(f89,plain,
$sum(count(sK1),1) = count(add(sK0,sK1)),
inference(resolution,[],[f23,f85]) ).
tff(f93,plain,
~ $less(count(sK1),$sum(count(sK1),1)),
inference(superposition,[],[f79,f89]) ).
tff(f619,plain,
$less(count(sK1),count(sK1)),
inference(resolution,[],[f27,f93]) ).
tff(f641,plain,
$false,
inference(forward_subsumption_resolution,[],[f619,f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT044_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n018.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 00:09:27 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running first-order theorem proving
% 0.07/0.21 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
% 4.04/1.33 % (3911899)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 4.04/1.33 % (3911904)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3773070479:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 4.04/1.33 % (3911904)Refutation not found, incomplete strategy
% 4.04/1.33 % (3911904)------------------------------
% 4.04/1.33 % (3911904)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.04/1.33 % (3911904)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.04/1.33 % (3911904)CaDiCaL version: 2.1.3
% 4.04/1.33 % (3911904)Termination reason: Refutation not found, incomplete strategy
% 4.04/1.33 % (3911904)Time elapsed: 0.021 s
% 4.04/1.33 % (3911904)Peak memory usage: 116 MB
% 4.04/1.33 % (3911904)Instructions burned: 11 (million)
% 4.04/1.33 % (3911905)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1812107246:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 4.04/1.33 % (3911908)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=2422250912:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 4.04/1.33 % (3911906)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1816435010:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 4.04/1.33 % (3911907)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=456379350:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 4.04/1.33 % (3911909)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2387505240:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 4.04/1.33 % (3911910)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=61256467:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 4.04/1.33 % (3911908)Instruction limit reached!
% 4.04/1.33 % (3911908)------------------------------
% 4.04/1.33 % (3911908)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.04/1.33 % (3911908)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.04/1.33 % (3911908)CaDiCaL version: 2.1.3
% 4.04/1.33 % (3911908)Termination reason: Instruction limit
% 4.04/1.33 % (3911908)Termination phase: Saturation
% 4.04/1.33 % (3911908)Time elapsed: 0.004 s
% 4.04/1.33 % (3911908)Peak memory usage: 88 MB
% 4.04/1.33 % (3911908)Instructions burned: 5 (million)
% 4.04/1.33 % (3911907)Instruction limit reached!
% 4.04/1.33 % (3911907)------------------------------
% 4.04/1.33 % (3911907)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.04/1.33 % (3911907)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.04/1.33 % (3911907)CaDiCaL version: 2.1.3
% 4.04/1.33 % (3911907)Termination reason: Instruction limit
% 4.04/1.33 % (3911907)Termination phase: Saturation
% 4.04/1.33 % (3911907)Time elapsed: 0.005 s
% 4.04/1.33 % (3911907)Peak memory usage: 88 MB
% 4.04/1.33 % (3911907)Instructions burned: 7 (million)
% 4.04/1.33 % (3911906)First to succeed.
% 4.04/1.33 % (3911906)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3911899"
% 4.04/1.33 % (3911909)Also succeeded, but the first one will report.
% 4.04/1.33 % (3911910)Instruction limit reached!
% 4.04/1.33 % (3911910)------------------------------
% 4.04/1.33 % (3911910)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.04/1.33 % (3911910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.04/1.33 % (3911910)CaDiCaL version: 2.1.3
% 4.04/1.33 % (3911910)Termination reason: Instruction limit
% 4.04/1.33 % (3911910)Termination phase: Saturation
% 4.04/1.33 % (3911910)Time elapsed: 0.048 s
% 4.04/1.33 % (3911910)Peak memory usage: 116 MB
% 4.04/1.33 % (3911910)Instructions burned: 33 (million)
% 4.04/1.33 % (3911904)------------------------------
% 4.04/1.33 % (3911904)------------------------------
% 4.04/1.33 % (3911918)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=3102162186:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 4.04/1.33 % (3911919)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=2726872116:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 4.04/1.33 % (3911918)Instruction limit reached!
% 4.04/1.33 % (3911918)------------------------------
% 4.04/1.33 % (3911918)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.04/1.33 % (3911918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.04/1.33 % (3911918)CaDiCaL version: 2.1.3
% 4.04/1.33 % (3911918)Termination reason: Instruction limit
% 4.04/1.33 % (3911918)Termination phase: Saturation
% 4.04/1.33 % (3911918)Time elapsed: 0.011 s
% 4.04/1.33 % (3911918)Peak memory usage: 88 MB
% 4.04/1.33 % (3911918)Instructions burned: 14 (million)
% 4.04/1.33 % (3911919)Instruction limit reached!
% 4.04/1.33 % (3911919)------------------------------
% 4.04/1.33 % (3911919)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.04/1.33 % (3911919)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.04/1.33 % (3911919)CaDiCaL version: 2.1.3
% 4.04/1.33 % (3911919)Termination reason: Instruction limit
% 4.04/1.33 % (3911919)Termination phase: Saturation
% 4.04/1.33 % (3911919)Time elapsed: 0.022 s
% 4.04/1.33 % (3911919)Peak memory usage: 88 MB
% 4.04/1.33 % (3911919)Instructions burned: 29 (million)
% 4.04/1.33 % (3911920)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=480954374:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/16Mi)
% 4.04/1.33 % (3911905)Instruction limit reached!
% 4.04/1.33 % (3911905)------------------------------
% 4.04/1.33 % (3911905)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.04/1.33 % (3911905)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.04/1.33 % (3911905)CaDiCaL version: 2.1.3
% 4.04/1.33 % (3911905)Termination reason: Instruction limit
% 4.04/1.33 % (3911905)Termination phase: Saturation
% 4.04/1.33 % (3911905)Time elapsed: 0.223 s
% 4.04/1.33 % (3911905)Peak memory usage: 116 MB
% 4.04/1.33 % (3911905)Instructions burned: 307 (million)
% 4.04/1.33 % (3911920)Instruction limit reached!
% 4.04/1.33 % (3911920)------------------------------
% 4.04/1.33 % (3911920)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.04/1.33 % (3911920)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.04/1.33 % (3911920)CaDiCaL version: 2.1.3
% 4.04/1.33 % (3911920)Termination reason: Instruction limit
% 4.04/1.33 % (3911920)Termination phase: Saturation
% 4.04/1.33 % (3911920)Time elapsed: 0.012 s
% 4.04/1.33 % (3911920)Peak memory usage: 90 MB
% 4.04/1.33 % (3911920)Instructions burned: 16 (million)
% 4.04/1.33 % (3911921)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=4157992047:i=24:canc=force:rtra=on_2997 on theBenchmark for (2997ds/24Mi)
% 4.04/1.33 % (3911921)Also succeeded, but the first one will report.
% 4.04/1.33 % (3911906)Refutation found. Thanks to Tanya!
% 4.04/1.33 % SZS status Theorem for theBenchmark
% 4.04/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 4.04/1.33 % (3911906)------------------------------
% 4.04/1.33 % (3911906)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.04/1.33 % (3911906)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.04/1.33 % (3911906)CaDiCaL version: 2.1.3
% 4.04/1.33 % (3911906)Termination reason: Refutation
% 4.04/1.33 % (3911906)Time elapsed: 0.046 s
% 4.04/1.33 % (3911906)Peak memory usage: 113 MB
% 4.04/1.33 % (3911906)Instructions burned: 36 (million)
% 4.04/1.33 % (3911906)------------------------------
% 4.04/1.33 % (3911906)------------------------------
% 4.04/1.33 % (3911899)Success in time 0.48 s
% 4.04/1.33 % Vampire exiting
%------------------------------------------------------------------------------