%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT055_1 : TPTP v9.3.1. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 09:47:12 AM UTC 2026
% Result : Theorem 3.94s 1.42s
% Output : Refutation 3.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 35 ( 18 unt; 0 typ; 10 def)
% Number of atoms : 64 ( 10 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 56 ( 27 ~; 7 |; 12 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 47 ( 32 atm; 8 fun; 7 num; 0 var)
% Number of types : 2 ( 1 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 7 usr; 8 prp; 0-2 aty)
% Number of functors : 10 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 6 ( 6 !; 0 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
list: $tType ).
tff(func_def_0,type,
a: list ).
tff(func_def_1,type,
l: $int ).
tff(func_def_2,type,
k: $int ).
tff(func_def_3,type,
min: list > $int ).
tff(func_def_4,type,
max: list > $int ).
tff(func_def_9,type,
sF0: $int ).
tff(func_def_10,type,
sF1: $int ).
tff(func_def_11,type,
sF2: $int ).
tff(f1,conjecture,
( ( ! [X0: list] : $lesseq(min(X0),max(X0))
& $lesseq(l,min(a))
& $less(0,k) )
=> $less(l,$sum(max(a),k)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',boyer_moore_max_min) ).
tff(f2,negated_conjecture,
~ ( ( ! [X0: list] : $lesseq(min(X0),max(X0))
& $lesseq(l,min(a))
& $less(0,k) )
=> $less(l,$sum(max(a),k)) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ( ( ! [X0: list] : ~ $less(max(X0),min(X0))
& $less(0,k)
& ~ $less(min(a),l) )
=> $less(l,$sum(max(a),k)) ),
inference(theory_normalization,[],[f2]) ).
tff(f16,plain,
( ~ $less(l,$sum(max(a),k))
& ! [X0: list] : ~ $less(max(X0),min(X0))
& $less(0,k)
& ~ $less(min(a),l) ),
inference(ennf_transformation,[],[f3]) ).
tff(f17,plain,
( ! [X0: list] : ~ $less(max(X0),min(X0))
& ~ $less(l,$sum(max(a),k))
& $less(0,k)
& ~ $less(min(a),l) ),
inference(flattening,[],[f16]) ).
tff(f18,plain,
~ $less(min(a),l),
inference(cnf_transformation,[],[f17]) ).
tff(f19,plain,
$less(0,k),
inference(cnf_transformation,[],[f17]) ).
tff(f20,plain,
~ $less(l,$sum(max(a),k)),
inference(cnf_transformation,[],[f17]) ).
tff(f21,plain,
! [X0: list] : ~ $less(max(X0),min(X0)),
inference(cnf_transformation,[],[f17]) ).
tff(f22,definition,
sF0 = max(a),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
tff(f23,plain,
max(a) = sF0,
inference(reorient_equations,[],[f22]) ).
tff(f24,definition,
sF1 = $sum(sF0,k),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
tff(f25,plain,
~ $less(l,sF1),
inference(definition_folding,[],[f20,f24,f23]) ).
tff(f26,definition,
sF2 = min(a),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
tff(f27,plain,
min(a) = sF2,
inference(reorient_equations,[],[f26]) ).
tff(f28,plain,
~ $less(sF2,l),
inference(definition_folding,[],[f18,f27]) ).
tff(f30,definition,
( spl3_1
<=> ( sF1 = $sum(sF0,k) ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
tff(f33,plain,
spl3_1,
inference(avatar_split_clause,[],[f24,f30]) ).
tff(f35,definition,
( spl3_2
<=> $less(l,sF1) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
tff(f38,plain,
~ spl3_2,
inference(avatar_split_clause,[],[f25,f35]) ).
tff(f40,definition,
( spl3_3
<=> $less(sF2,l) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
tff(f43,plain,
~ spl3_3,
inference(avatar_split_clause,[],[f28,f40]) ).
tff(f45,definition,
( spl3_4
<=> ( max(a) = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
tff(f47,plain,
( ( max(a) = sF0 )
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f45]) ).
tff(f48,plain,
spl3_4,
inference(avatar_split_clause,[],[f23,f45]) ).
tff(f50,definition,
( spl3_5
<=> $less(0,k) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
tff(f53,plain,
spl3_5,
inference(avatar_split_clause,[],[f19,f50]) ).
tff(f55,definition,
( spl3_6
<=> ( min(a) = sF2 ) ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
tff(f57,plain,
( ( min(a) = sF2 )
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f55]) ).
tff(f58,plain,
spl3_6,
inference(avatar_split_clause,[],[f27,f55]) ).
tff(f59,plain,
( ~ $less(sF0,min(a))
| ~ spl3_4 ),
inference(superposition,[],[f21,f47]) ).
tff(f60,plain,
( ~ $less(sF0,sF2)
| ~ spl3_4
| ~ spl3_6 ),
inference(forward_demodulation,[],[f59,f57]) ).
tff(f62,definition,
( spl3_7
<=> $less(sF0,sF2) ),
introduced(definition,[new_symbols(definition,[spl3_7])],[avatar_definition]) ).
tff(f65,plain,
( ~ spl3_7
| ~ spl3_4
| ~ spl3_6 ),
inference(avatar_split_clause,[],[f60,f55,f45,f62]) ).
tff(f66,plain,
$false,
inference(avatar_smt_refutation,[],[f65,f58,f53,f48,f43,f38,f33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT055_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n013.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 00:06:51 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 Running first-order theorem proving
% 0.08/0.20 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.94/1.42 % (1711567)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.94/1.42 % (1711661)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=1695329770:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.94/1.42 % (1711661)Instruction limit reached!
% 3.94/1.42 % (1711661)------------------------------
% 3.94/1.42 % (1711661)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.42 % (1711661)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.42 % (1711661)CaDiCaL version: 2.1.3
% 3.94/1.42 % (1711661)Termination reason: Instruction limit
% 3.94/1.42 % (1711661)Termination phase: Saturation
% 3.94/1.42 % (1711661)Time elapsed: 0.003 s
% 3.94/1.42 % (1711661)Peak memory usage: 89 MB
% 3.94/1.42 % (1711661)Instructions burned: 7 (million)
% 3.94/1.42 % (1711659)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1214580840:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.94/1.42 % (1711655)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=763177634:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.94/1.42 % (1711665)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=38845753:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.94/1.42 % (1711664)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=1279338735:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.94/1.42 % (1711657)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=371072398:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.94/1.42 % (1711660)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2400633926:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.94/1.42 % (1711664)Refutation not found, incomplete strategy
% 3.94/1.42 % (1711664)------------------------------
% 3.94/1.42 % (1711664)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.42 % (1711664)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.42 % (1711664)CaDiCaL version: 2.1.3
% 3.94/1.42 % (1711664)Termination reason: Refutation not found, incomplete strategy
% 3.94/1.42 % (1711664)Time elapsed: 0.030 s
% 3.94/1.42 % (1711664)Peak memory usage: 115 MB
% 3.94/1.42 % (1711664)Instructions burned: 6 (million)
% 3.94/1.42 % (1711655)Instruction limit reached!
% 3.94/1.42 % (1711655)------------------------------
% 3.94/1.42 % (1711655)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.42 % (1711655)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.42 % (1711655)CaDiCaL version: 2.1.3
% 3.94/1.42 % (1711655)Termination reason: Instruction limit
% 3.94/1.42 % (1711655)Termination phase: Saturation
% 3.94/1.42 % (1711655)Time elapsed: 0.031 s
% 3.94/1.42 % (1711655)Peak memory usage: 115 MB
% 3.94/1.42 % (1711655)Instructions burned: 12 (million)
% 3.94/1.42 % (1711665)First to succeed.
% 3.94/1.42 % (1711665)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1711567"
% 3.94/1.42 % (1711660)Instruction limit reached!
% 3.94/1.42 % (1711660)------------------------------
% 3.94/1.42 % (1711660)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.42 % (1711660)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.42 % (1711660)CaDiCaL version: 2.1.3
% 3.94/1.42 % (1711660)Termination reason: Instruction limit
% 3.94/1.42 % (1711660)Termination phase: Saturation
% 3.94/1.42 % (1711660)Time elapsed: 0.009 s
% 3.94/1.42 % (1711660)Peak memory usage: 88 MB
% 3.94/1.42 % (1711660)Instructions burned: 7 (million)
% 3.94/1.42 % (1711657)Also succeeded, but the first one will report.
% 3.94/1.42 % (1711695)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=1543496147:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.94/1.42 % (1711695)Refutation not found, incomplete strategy
% 3.94/1.42 % (1711695)------------------------------
% 3.94/1.42 % (1711695)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.42 % (1711695)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.42 % (1711695)CaDiCaL version: 2.1.3
% 3.94/1.42 % (1711695)Termination reason: Refutation not found, incomplete strategy
% 3.94/1.42 % (1711695)Time elapsed: 0.001 s
% 3.94/1.42 % (1711695)Peak memory usage: 88 MB
% 3.94/1.42 % (1711659)Instruction limit reached!
% 3.94/1.42 % (1711659)------------------------------
% 3.94/1.42 % (1711659)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.42 % (1711659)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.42 % (1711659)CaDiCaL version: 2.1.3
% 3.94/1.42 % (1711659)Termination reason: Instruction limit
% 3.94/1.42 % (1711659)Termination phase: Saturation
% 3.94/1.42 % (1711659)Time elapsed: 0.168 s
% 3.94/1.42 % (1711659)Peak memory usage: 117 MB
% 3.94/1.42 % (1711659)Instructions burned: 201 (million)
% 3.94/1.42 % (1711717)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=1474149591:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2997 on theBenchmark for (2997ds/29Mi)
% 3.94/1.42 % (1711717)Instruction limit reached!
% 3.94/1.42 % (1711717)------------------------------
% 3.94/1.42 % (1711717)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.42 % (1711717)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.42 % (1711717)CaDiCaL version: 2.1.3
% 3.94/1.42 % (1711717)Termination reason: Instruction limit
% 3.94/1.42 % (1711717)Termination phase: Saturation
% 3.94/1.42 % (1711717)Time elapsed: 0.021 s
% 3.94/1.42 % (1711717)Peak memory usage: 88 MB
% 3.94/1.42 % (1711717)Instructions burned: 29 (million)
% 3.94/1.42 % (1711664)------------------------------
% 3.94/1.42 % (1711664)------------------------------
% 3.94/1.42 % (1711718)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=203838788:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/16Mi)
% 3.94/1.42 % (1711718)Also succeeded, but the first one will report.
% 3.94/1.42 % (1711665)Refutation found. Thanks to Tanya!
% 3.94/1.42 % SZS status Theorem for theBenchmark
% 3.94/1.42 % SZS output start Proof for theBenchmark
% See solution above
% 3.94/1.42 % (1711665)------------------------------
% 3.94/1.42 % (1711665)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.42 % (1711665)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.42 % (1711665)CaDiCaL version: 2.1.3
% 3.94/1.42 % (1711665)Termination reason: Refutation
% 3.94/1.42 % (1711665)Time elapsed: 0.035 s
% 3.94/1.42 % (1711665)Peak memory usage: 116 MB
% 3.94/1.42 % (1711665)Instructions burned: 11 (million)
% 3.94/1.42 % (1711665)------------------------------
% 3.94/1.42 % (1711665)------------------------------
% 3.94/1.42 % (1711567)Success in time 0.461 s
% 3.94/1.42 % Vampire exiting
%------------------------------------------------------------------------------