%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT041_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 : n002.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 3.90s 1.55s
% Output : Refutation 3.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 41 ( 16 unt; 0 typ; 1 def)
% Number of atoms : 87 ( 34 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 88 ( 42 ~; 30 |; 10 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 94 ( 11 atm; 16 fun; 30 num; 37 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 : 6 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 8 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 62 ( 54 !; 8 ?; 62 :)
% 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(f1,axiom,
! [X0: $int] : ~ in(X0,empty),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
tff(f4,axiom,
! [X1: collection,X0: $int,X2: $int] :
( ( in(X0,X1)
| ( X0 = X2 ) )
<=> in(X0,add(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
tff(f7,axiom,
! [X0: collection] :
( ( count(X0) = 0 )
<=> ( X0 = empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
tff(f8,axiom,
! [X1: collection,X0: $int] :
( ~ in(X0,X1)
<=> ( count(add(X0,X1)) = $sum(count(X1),1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
tff(f9,axiom,
! [X1: collection,X0: $int] :
( in(X0,X1)
<=> ( count(add(X0,X1)) = count(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
tff(f13,conjecture,
? [X1: $int,X0: collection] : $greater($sum(count(X0),1),count(add(X1,X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
tff(f14,negated_conjecture,
~ ? [X1: $int,X0: collection] : $greater($sum(count(X0),1),count(add(X1,X0))),
inference(negated_conjecture,[status(cth)],[f13]) ).
tff(f16,plain,
~ ? [X1: $int,X0: collection] : $less(count(add(X1,X0)),$sum(count(X0),1)),
inference(theory_normalization,[],[f14]) ).
tff(f18,plain,
~ ? [X1: collection,X0: $int] : $less(count(add(X0,X1)),$sum(count(X1),1)),
inference(rectify,[],[f16]) ).
tff(f22,plain,
! [X0: collection,X1: $int] :
( in(X1,X0)
<=> ( count(X0) = count(add(X1,X0)) ) ),
inference(rectify,[],[f9]) ).
tff(f23,plain,
! [X1: collection,X0: $int] : ~ $less(count(add(X0,X1)),$sum(count(X1),1)),
inference(ennf_transformation,[],[f18]) ).
tff(f25,plain,
! [X1: collection,X0: $int,X2: $int] :
( ( in(X0,X1)
| ( X0 = X2 )
| ~ in(X0,add(X2,X1)) )
& ( in(X0,add(X2,X1))
| ( ~ in(X0,X1)
& ( X0 != X2 ) ) ) ),
inference(nnf_transformation,[],[f4]) ).
tff(f26,plain,
! [X1: collection,X0: $int,X2: $int] :
( ( in(X0,X1)
| ( X0 = X2 )
| ~ in(X0,add(X2,X1)) )
& ( in(X0,add(X2,X1))
| ( ~ in(X0,X1)
& ( X0 != X2 ) ) ) ),
inference(flattening,[],[f25]) ).
tff(f27,plain,
! [X0: collection,X1: $int,X2: $int] :
( ( in(X1,X0)
| ( X1 = X2 )
| ~ in(X1,add(X2,X0)) )
& ( in(X1,add(X2,X0))
| ( ~ in(X1,X0)
& ( X1 != X2 ) ) ) ),
inference(rectify,[],[f26]) ).
tff(f32,plain,
! [X1: collection,X0: $int] :
( ( ~ 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,[],[f8]) ).
tff(f33,plain,
! [X0: collection,X1: $int] :
( ( ~ in(X1,X0)
| ( $sum(count(X0),1) != count(add(X1,X0)) ) )
& ( ( $sum(count(X0),1) = count(add(X1,X0)) )
| in(X1,X0) ) ),
inference(rectify,[],[f32]) ).
tff(f37,plain,
! [X0: collection,X1: $int] :
( ( in(X1,X0)
| ( count(X0) != count(add(X1,X0)) ) )
& ( ( count(X0) = count(add(X1,X0)) )
| ~ in(X1,X0) ) ),
inference(nnf_transformation,[],[f22]) ).
tff(f39,plain,
! [X0: collection] :
( ( ( count(X0) = 0 )
| ( empty != X0 ) )
& ( ( X0 = empty )
| ( count(X0) != 0 ) ) ),
inference(nnf_transformation,[],[f7]) ).
tff(f40,plain,
! [X0: collection,X1: $int] : ~ $less(count(add(X1,X0)),$sum(count(X0),1)),
inference(rectify,[],[f23]) ).
tff(f42,plain,
! [X2: $int,X0: collection,X1: $int] :
( in(X1,add(X2,X0))
| ( X1 != X2 ) ),
inference(cnf_transformation,[],[f27]) ).
tff(f48,plain,
! [X0: $int] : ~ in(X0,empty),
inference(cnf_transformation,[],[f1]) ).
tff(f51,plain,
! [X0: collection,X1: $int] :
( in(X1,X0)
| ( $sum(count(X0),1) = count(add(X1,X0)) ) ),
inference(cnf_transformation,[],[f33]) ).
tff(f56,plain,
! [X0: collection,X1: $int] :
( ~ in(X1,X0)
| ( count(X0) = count(add(X1,X0)) ) ),
inference(cnf_transformation,[],[f37]) ).
tff(f61,plain,
! [X0: collection] :
( ( count(X0) = 0 )
| ( empty != X0 ) ),
inference(cnf_transformation,[],[f39]) ).
tff(f62,plain,
! [X0: collection,X1: $int] : ~ $less(count(add(X1,X0)),$sum(count(X0),1)),
inference(cnf_transformation,[],[f40]) ).
tff(f64,plain,
! [X2: $int,X0: collection] : in(X2,add(X2,X0)),
inference(equality_resolution,[],[f42]) ).
tff(f66,plain,
0 = count(empty),
inference(equality_resolution,[],[f61]) ).
tff(f70,definition,
( spl0_1
<=> ( 0 = count(empty) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
tff(f72,plain,
( ( 0 = count(empty) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f70]) ).
tff(f73,plain,
spl0_1,
inference(avatar_split_clause,[],[f66,f70]) ).
tff(f84,plain,
! [X0: $int,X1: collection] : ( count(add(X0,X1)) = count(add(X0,add(X0,X1))) ),
inference(resolution,[],[f56,f64]) ).
tff(f109,plain,
! [X0: $int] : ( $sum(count(empty),1) = count(add(X0,empty)) ),
inference(resolution,[],[f51,f48]) ).
tff(f113,plain,
( ! [X0: $int] : ( $sum(0,1) = count(add(X0,empty)) )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f109,f72]) ).
tff(f114,plain,
( ! [X0: $int] : ( 1 = count(add(X0,empty)) )
| ~ spl0_1 ),
inference(evaluation,[],[f113]) ).
tff(f120,plain,
( ! [X0: $int,X1: $int] : ~ $less(count(add(X0,add(X1,empty))),$sum(1,1))
| ~ spl0_1 ),
inference(superposition,[],[f62,f114]) ).
tff(f121,plain,
( ! [X0: $int,X1: $int] : ~ $less(count(add(X0,add(X1,empty))),2)
| ~ spl0_1 ),
inference(evaluation,[],[f120]) ).
tff(f168,plain,
( ! [X0: $int] : ~ $less(count(add(X0,empty)),2)
| ~ spl0_1 ),
inference(superposition,[],[f121,f84]) ).
tff(f177,plain,
( ~ $less(1,2)
| ~ spl0_1 ),
inference(forward_demodulation,[],[f168,f114]) ).
tff(f178,plain,
( $false
| ~ spl0_1 ),
inference(evaluation,[],[f177]) ).
tff(f179,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f178]) ).
tff(f181,plain,
$false,
inference(avatar_smt_refutation,[],[f179,f73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT041_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.23 % Computer : n002.cluster.edu
% 0.11/0.23 % Model : x86_64 x86_64
% 0.11/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.23 % Memory : 8046.5625MB
% 0.11/0.23 % OS : Linux 6.8.0-71-generic
% 0.11/0.23 % CPULimit : 300
% 0.11/0.23 % WCLimit : 300
% 0.11/0.23 % DateTime : Tue Sep 29 00:08:52 UTC 2026
% 0.11/0.24 % CPUTime :
% 0.11/0.24 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.29 Running first-order theorem proving
% 0.24/0.29 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
% 3.90/1.55 % (909610)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.90/1.55 % (909620)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3639640484:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.90/1.55 % (909620)First to succeed.
% 3.90/1.55 % (909620)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-909610"
% 3.90/1.55 % (909618)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2252364349:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.90/1.55 % (909617)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2261364615:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.90/1.55 % (909615)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=612540250:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.90/1.55 % (909616)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3011010450:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.90/1.55 % (909619)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=4188559783:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.90/1.55 % (909621)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=114156242:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.90/1.55 % (909619)Instruction limit reached!
% 3.90/1.55 % (909619)------------------------------
% 3.90/1.55 % (909619)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.90/1.55 % (909619)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.90/1.55 % (909619)CaDiCaL version: 2.1.3
% 3.90/1.55 % (909619)Termination reason: Instruction limit
% 3.90/1.55 % (909619)Termination phase: Saturation
% 3.90/1.55 % (909619)Time elapsed: 0.006 s
% 3.90/1.55 % (909619)Peak memory usage: 88 MB
% 3.90/1.55 % (909619)Instructions burned: 4 (million)
% 3.90/1.55 % (909618)Instruction limit reached!
% 3.90/1.55 % (909618)------------------------------
% 3.90/1.55 % (909618)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.90/1.55 % (909618)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.90/1.55 % (909618)CaDiCaL version: 2.1.3
% 3.90/1.55 % (909618)Termination reason: Instruction limit
% 3.90/1.55 % (909618)Termination phase: Saturation
% 3.90/1.55 % (909618)Time elapsed: 0.008 s
% 3.90/1.55 % (909618)Peak memory usage: 88 MB
% 3.90/1.55 % (909618)Instructions burned: 7 (million)
% 3.90/1.55 % (909615)Refutation not found, incomplete strategy
% 3.90/1.55 % (909615)------------------------------
% 3.90/1.55 % (909615)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.90/1.55 % (909615)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.90/1.55 % (909615)CaDiCaL version: 2.1.3
% 3.90/1.55 % (909615)Termination reason: Refutation not found, incomplete strategy
% 3.90/1.55 % (909615)Time elapsed: 0.045 s
% 3.90/1.55 % (909615)Peak memory usage: 112 MB
% 3.90/1.55 % (909615)Instructions burned: 11 (million)
% 3.90/1.55 % (909616)Also succeeded, but the first one will report.
% 3.90/1.55 % (909621)Instruction limit reached!
% 3.90/1.55 % (909621)------------------------------
% 3.90/1.55 % (909621)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.90/1.55 % (909621)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.90/1.55 % (909621)CaDiCaL version: 2.1.3
% 3.90/1.55 % (909621)Termination reason: Instruction limit
% 3.90/1.55 % (909621)Termination phase: Saturation
% 3.90/1.55 % (909621)Time elapsed: 0.067 s
% 3.90/1.55 % (909621)Peak memory usage: 115 MB
% 3.90/1.55 % (909621)Instructions burned: 33 (million)
% 3.90/1.55 % (909620)Refutation found. Thanks to Tanya!
% 3.90/1.55 % SZS status Theorem for theBenchmark
% 3.90/1.55 % SZS output start Proof for theBenchmark
% See solution above
% 3.90/1.55 % (909620)------------------------------
% 3.90/1.55 % (909620)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.90/1.55 % (909620)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.90/1.55 % (909620)CaDiCaL version: 2.1.3
% 3.90/1.55 % (909620)Termination reason: Refutation
% 3.90/1.55 % (909620)Time elapsed: 0.022 s
% 3.90/1.55 % (909620)Peak memory usage: 116 MB
% 3.90/1.55 % (909620)Instructions burned: 14 (million)
% 3.90/1.55 % (909620)------------------------------
% 3.90/1.55 % (909620)------------------------------
% 3.90/1.55 % (909610)Success in time 0.423 s
% 3.90/1.55 % Vampire exiting
%------------------------------------------------------------------------------