%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI682_1 : TPTP v9.3.1. Released v6.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 09:33:38 AM UTC 2026
% Result : Theorem 3.75s 1.55s
% Output : Refutation 3.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 29 ( 23 unt; 0 typ; 9 def)
% Number of atoms : 35 ( 8 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 12 ( 6 ~; 0 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 49 ( 14 atm; 23 fun; 12 num; 0 var)
% Number of types : 1 ( 0 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 6 usr; 7 prp; 0-2 aty)
% Number of functors : 9 ( 5 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
b: $int ).
tff(func_def_1,type,
a: $int ).
tff(func_def_6,type,
sF0: $int ).
tff(func_def_7,type,
sF1: $int ).
tff(func_def_8,type,
sF2: $int ).
tff(f1,axiom,
$less(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
tff(f2,axiom,
$lesseq(0,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_001) ).
tff(f3,conjecture,
$lesseq($sum(a,1),$sum($product(a,b),b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_002) ).
tff(f4,negated_conjecture,
~ $lesseq($sum(a,1),$sum($product(a,b),b)),
inference(negated_conjecture,[status(cth)],[f3]) ).
tff(f5,plain,
~ ~ $less($sum($product(a,b),b),$sum(a,1)),
inference(theory_normalization,[],[f4]) ).
tff(f6,plain,
~ $less(a,0),
inference(theory_normalization,[],[f2]) ).
tff(f7,plain,
$less($sum($product(a,b),b),$sum(a,1)),
inference(flattening,[],[f5]) ).
tff(f8,plain,
~ $less(a,0),
inference(cnf_transformation,[],[f6]) ).
tff(f9,plain,
$less(a,b),
inference(cnf_transformation,[],[f1]) ).
tff(f10,plain,
$less($sum($product(a,b),b),$sum(a,1)),
inference(cnf_transformation,[],[f7]) ).
tff(f11,definition,
sF0 = $product(a,b),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
tff(f12,plain,
$product(a,b) = sF0,
inference(reorient_equations,[],[f11]) ).
tff(f13,definition,
sF1 = $sum(sF0,b),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
tff(f14,definition,
sF2 = $sum(a,1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
tff(f15,plain,
$sum(a,1) = sF2,
inference(reorient_equations,[],[f14]) ).
tff(f16,plain,
$less(sF1,sF2),
inference(definition_folding,[],[f10,f15,f13,f12]) ).
tff(f18,definition,
( spl3_1
<=> $less(sF1,sF2) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
tff(f21,plain,
spl3_1,
inference(avatar_split_clause,[],[f16,f18]) ).
tff(f23,definition,
( spl3_2
<=> $less(a,b) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
tff(f26,plain,
spl3_2,
inference(avatar_split_clause,[],[f9,f23]) ).
tff(f28,definition,
( spl3_3
<=> ( $sum(a,1) = sF2 ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
tff(f31,plain,
spl3_3,
inference(avatar_split_clause,[],[f15,f28]) ).
tff(f33,definition,
( spl3_4
<=> $less(a,0) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
tff(f36,plain,
~ spl3_4,
inference(avatar_split_clause,[],[f8,f33]) ).
tff(f38,definition,
( spl3_5
<=> ( $product(a,b) = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
tff(f41,plain,
spl3_5,
inference(avatar_split_clause,[],[f12,f38]) ).
tff(f43,definition,
( spl3_6
<=> ( sF1 = $sum(sF0,b) ) ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
tff(f46,plain,
spl3_6,
inference(avatar_split_clause,[],[f13,f43]) ).
tff(f47,plain,
$false,
inference(avatar_smt_refutation,[],[f46,f41,f36,f31,f26,f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ARI682_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n017.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Mon Sep 28 20:51:21 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 Running first-order theorem proving
% 0.09/0.20 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
% 3.75/1.55 % (4017415)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.75/1.55 % (4017474)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=697130323:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.75/1.55 % (4017478)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=4088554050:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.75/1.55 % (4017474)First to succeed.
% 3.75/1.55 % (4017474)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4017415"
% 3.75/1.55 % (4017478)Also succeeded, but the first one will report.
% 3.75/1.55 % (4017473)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3394641496:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.75/1.55 % (4017475)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=4001691208:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.75/1.55 % (4017477)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3395315180:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.75/1.55 % (4017477)Instruction limit reached!
% 3.75/1.55 % (4017477)------------------------------
% 3.75/1.55 % (4017477)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.75/1.55 % (4017477)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.75/1.55 % (4017477)CaDiCaL version: 2.1.3
% 3.75/1.55 % (4017477)Termination reason: Instruction limit
% 3.75/1.55 % (4017477)Termination phase: Saturation
% 3.75/1.55 % (4017477)Time elapsed: 0.007 s
% 3.75/1.55 % (4017477)Peak memory usage: 88 MB
% 3.75/1.55 % (4017477)Instructions burned: 4 (million)
% 3.75/1.55 % (4017479)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=642191280:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.75/1.55 % (4017476)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3638849267:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.75/1.55 % (4017476)Instruction limit reached!
% 3.75/1.55 % (4017476)------------------------------
% 3.75/1.55 % (4017476)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.75/1.55 % (4017476)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.75/1.55 % (4017476)CaDiCaL version: 2.1.3
% 3.75/1.55 % (4017476)Termination reason: Instruction limit
% 3.75/1.55 % (4017476)Termination phase: Saturation
% 3.75/1.55 % (4017476)Time elapsed: 0.010 s
% 3.75/1.55 % (4017476)Peak memory usage: 88 MB
% 3.75/1.55 % (4017476)Instructions burned: 7 (million)
% 3.75/1.55 % (4017473)Also succeeded, but the first one will report.
% 3.75/1.55 % (4017479)Also succeeded, but the first one will report.
% 3.75/1.55 % (4017474)Refutation found. Thanks to Tanya!
% 3.75/1.55 % SZS status Theorem for theBenchmark
% 3.75/1.55 % SZS output start Proof for theBenchmark
% See solution above
% 3.75/1.55 % (4017474)------------------------------
% 3.75/1.55 % (4017474)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.75/1.55 % (4017474)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.75/1.55 % (4017474)CaDiCaL version: 2.1.3
% 3.75/1.55 % (4017474)Termination reason: Refutation
% 3.75/1.55 % (4017474)Time elapsed: 0.028 s
% 3.75/1.55 % (4017474)Peak memory usage: 116 MB
% 3.75/1.55 % (4017474)Instructions burned: 10 (million)
% 3.75/1.55 % (4017474)------------------------------
% 3.75/1.55 % (4017474)------------------------------
% 3.75/1.55 % (4017415)Success in time 0.407 s
% 3.75/1.55 % Vampire exiting
%------------------------------------------------------------------------------