%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI689_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 : n003.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 09:33:39 AM UTC 2026
% Result : Theorem 3.85s 1.32s
% Output : Refutation 3.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 16 ( 13 unt; 0 typ; 3 def)
% Number of atoms : 19 ( 12 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 5 ~; 0 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number arithmetic : 138 ( 0 atm; 100 fun; 38 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 : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 15 ( 4 usr; 12 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
y: $int ).
tff(func_def_1,type,
a: $int ).
tff(func_def_2,type,
x: $int ).
tff(func_def_3,type,
b: $int ).
tff(f1,axiom,
$product(98164184,y) = a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eq1) ).
tff(f2,axiom,
$product(6472,x) = b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eq2) ).
tff(f3,conjecture,
$sum($product(1,$product($product(y,x),b)),$product(-1,$sum($sum($product(166,$product($product(x,b),a)),$product(2427,$product($product(x,x),a))),$product(-2523496,$product($product(y,b),b))))) = 0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
tff(f4,negated_conjecture,
( ( ~ $sum($product(1,$product($product(y,x),b)),$product(-1,$sum($sum($product(166,$product($product(x,b),a)),$product(2427,$product($product(x,x),a))),$product(-2523496,$product($product(y,b),b))))) ) = 0 ),
inference(negated_conjecture,[status(cth)],[f3]) ).
tff(f5,plain,
$sum($product(1,$product($product(y,x),b)),$product(-1,$sum($sum($product(166,$product($product(x,b),a)),$product(2427,$product($product(x,x),a))),$product(-2523496,$product($product(y,b),b))))) != 0,
inference(flattening,[],[f4]) ).
tff(f6,plain,
$sum($product(1,$product($product(y,x),b)),$product(-1,$sum($sum($product(166,$product($product(x,b),a)),$product(2427,$product($product(x,x),a))),$product(-2523496,$product($product(y,b),b))))) != 0,
inference(cnf_transformation,[],[f5]) ).
tff(f7,plain,
$product(6472,x) = b,
inference(cnf_transformation,[],[f2]) ).
tff(f8,plain,
$product(98164184,y) = a,
inference(cnf_transformation,[],[f1]) ).
tff(f9,plain,
0 != $sum($product($product(y,x),b),$uminus($sum($sum($product(166,$product($product(x,b),a)),$product(2427,$product($product(x,x),a))),$product(-2523496,$product($product(y,b),b))))),
inference(evaluation,[],[f6]) ).
tff(f11,definition,
( spl0_1
<=> ( $product(6472,x) = b ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
tff(f14,plain,
spl0_1,
inference(avatar_split_clause,[],[f7,f11]) ).
tff(f16,definition,
( spl0_2
<=> ( 0 = $sum($product($product(y,x),b),$uminus($sum($sum($product(166,$product($product(x,b),a)),$product(2427,$product($product(x,x),a))),$product(-2523496,$product($product(y,b),b))))) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
tff(f19,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f9,f16]) ).
tff(f21,definition,
( spl0_3
<=> ( $product(98164184,y) = a ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
tff(f24,plain,
spl0_3,
inference(avatar_split_clause,[],[f8,f21]) ).
tff(f25,plain,
$false,
inference(avatar_smt_refutation,[],[f24,f19,f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI689_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n003.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 20:59:23 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 2.92/1.13 % (2008636)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.92/1.13 % (2008647)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=955826400:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.92/1.13 % (2008647)Instruction limit reached!
% 2.92/1.13 % (2008647)------------------------------
% 2.92/1.13 % (2008647)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.92/1.13 % (2008647)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.92/1.13 % (2008647)CaDiCaL version: 2.1.3
% 2.92/1.13 % (2008647)Termination reason: Instruction limit
% 2.92/1.13 % (2008647)Termination phase: Saturation
% 2.92/1.13 % (2008647)Time elapsed: 0.026 s
% 2.92/1.13 % (2008647)Peak memory usage: 117 MB
% 2.92/1.13 % (2008647)Instructions burned: 34 (million)
% 2.92/1.13 % (2008645)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3090923764:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.92/1.13 % (2008645)Instruction limit reached!
% 2.92/1.13 % (2008645)------------------------------
% 2.92/1.13 % (2008645)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.92/1.13 % (2008645)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.92/1.13 % (2008645)CaDiCaL version: 2.1.3
% 2.92/1.13 % (2008645)Termination reason: Instruction limit
% 2.92/1.13 % (2008645)Termination phase: Saturation
% 2.92/1.13 % (2008645)Time elapsed: 0.003 s
% 2.92/1.13 % (2008645)Peak memory usage: 88 MB
% 2.92/1.13 % (2008645)Instructions burned: 4 (million)
% 2.92/1.13 % (2008644)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2602604556:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.92/1.13 % (2008641)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1364343525:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.92/1.13 % (2008643)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=633917493:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.92/1.13 % (2008642)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3824273851:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.92/1.13 % (2008644)Instruction limit reached!
% 2.92/1.13 % (2008644)------------------------------
% 2.92/1.13 % (2008644)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.92/1.13 % (2008644)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.92/1.13 % (2008644)CaDiCaL version: 2.1.3
% 2.92/1.13 % (2008644)Termination reason: Instruction limit
% 2.92/1.13 % (2008644)Termination phase: Saturation
% 2.92/1.13 % (2008644)Time elapsed: 0.005 s
% 2.92/1.13 % (2008644)Peak memory usage: 88 MB
% 2.92/1.13 % (2008644)Instructions burned: 9 (million)
% 2.92/1.13 % (2008646)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=4234328056:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.92/1.13 % (2008641)Instruction limit reached!
% 2.92/1.13 % (2008641)------------------------------
% 2.92/1.13 % (2008641)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.92/1.13 % (2008641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.92/1.13 % (2008641)CaDiCaL version: 2.1.3
% 2.92/1.13 % (2008641)Termination reason: Instruction limit
% 2.92/1.13 % (2008641)Termination phase: Saturation
% 2.92/1.13 % (2008641)Time elapsed: 0.030 s
% 2.92/1.13 % (2008641)Peak memory usage: 116 MB
% 2.92/1.13 % (2008641)Instructions burned: 12 (million)
% 2.92/1.13 % (2008646)First to succeed.
% 2.92/1.13 % (2008646)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2008636"
% 2.92/1.13 % (2008649)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=1664004923:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.92/1.13 % (2008649)Refutation not found, incomplete strategy
% 2.92/1.13 % (2008649)------------------------------
% 2.92/1.13 % (2008649)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.92/1.13 % (2008649)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.92/1.13 % (2008649)CaDiCaL version: 2.1.3
% 2.92/1.13 % (2008649)Termination reason: Refutation not found, incomplete strategy
% 2.92/1.13 % (2008649)Time elapsed: 0.001 s
% 2.92/1.13 % (2008649)Peak memory usage: 88 MB
% 2.92/1.13 % (2008655)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=1981835132:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 3.85/1.32 % (2008655)Instruction limit reached!
% 3.85/1.32 % (2008655)------------------------------
% 3.85/1.32 % (2008655)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.85/1.32 % (2008655)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.85/1.32 % (2008655)CaDiCaL version: 2.1.3
% 3.85/1.32 % (2008655)Termination reason: Instruction limit
% 3.85/1.32 % (2008655)Termination phase: Saturation
% 3.85/1.32 % (2008655)Time elapsed: 0.016 s
% 3.85/1.32 % (2008655)Peak memory usage: 88 MB
% 3.85/1.32 % (2008655)Instructions burned: 31 (million)
% 3.85/1.32 % (2008657)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=2031100108:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/16Mi)
% 3.85/1.32 % (2008643)Instruction limit reached!
% 3.85/1.32 % (2008643)------------------------------
% 3.85/1.32 % (2008643)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.85/1.32 % (2008643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.85/1.32 % (2008643)CaDiCaL version: 2.1.3
% 3.85/1.32 % (2008643)Termination reason: Instruction limit
% 3.85/1.32 % (2008643)Termination phase: Saturation
% 3.85/1.32 % (2008643)Time elapsed: 0.156 s
% 3.85/1.32 % (2008643)Peak memory usage: 117 MB
% 3.85/1.32 % (2008643)Instructions burned: 201 (million)
% 3.85/1.32 % (2008657)Instruction limit reached!
% 3.85/1.32 % (2008657)------------------------------
% 3.85/1.32 % (2008657)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.85/1.32 % (2008657)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.85/1.32 % (2008657)CaDiCaL version: 2.1.3
% 3.85/1.32 % (2008657)Termination reason: Instruction limit
% 3.85/1.32 % (2008657)Termination phase: Saturation
% 3.85/1.32 % (2008657)Time elapsed: 0.010 s
% 3.85/1.32 % (2008657)Peak memory usage: 90 MB
% 3.85/1.32 % (2008657)Instructions burned: 18 (million)
% 3.85/1.32 % (2008658)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=371272677:i=24:canc=force:rtra=on_2998 on theBenchmark for (2998ds/24Mi)
% 3.85/1.32 % (2008642)Instruction limit reached!
% 3.85/1.32 % (2008642)------------------------------
% 3.85/1.32 % (2008642)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.85/1.32 % (2008642)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.85/1.32 % (2008642)CaDiCaL version: 2.1.3
% 3.85/1.32 % (2008642)Termination reason: Instruction limit
% 3.85/1.32 % (2008642)Termination phase: Saturation
% 3.85/1.32 % (2008642)Time elapsed: 0.185 s
% 3.85/1.32 % (2008642)Peak memory usage: 117 MB
% 3.85/1.32 % (2008642)Instructions burned: 309 (million)
% 3.85/1.32 % (2008658)Instruction limit reached!
% 3.85/1.32 % (2008658)------------------------------
% 3.85/1.32 % (2008658)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.85/1.32 % (2008658)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.85/1.32 % (2008658)CaDiCaL version: 2.1.3
% 3.85/1.32 % (2008658)Termination reason: Instruction limit
% 3.85/1.32 % (2008658)Termination phase: Saturation
% 3.85/1.32 % (2008658)Time elapsed: 0.013 s
% 3.85/1.32 % (2008658)Peak memory usage: 89 MB
% 3.85/1.32 % (2008658)Instructions burned: 25 (million)
% 3.85/1.32 % (2008649)------------------------------
% 3.85/1.32 % (2008649)------------------------------
% 3.85/1.32 % (2008661)ott+1010_8_to=lpo:sil=128000:si=on:norm_ineq=on:sp=unary_frequency:sos=on:gve=cautious:spb=goal_then_units:uwa=alasca_main_floor:tha=some:random_seed=1707702964:i=27:canc=cautious:fsr=off:rtra=on_2997 on theBenchmark for (2997ds/27Mi)
% 3.85/1.32 % (2008661)Refutation not found, incomplete strategy
% 3.85/1.32 % (2008661)------------------------------
% 3.85/1.32 % (2008661)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.85/1.32 % (2008661)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.85/1.32 % (2008661)CaDiCaL version: 2.1.3
% 3.85/1.32 % (2008661)Termination reason: Refutation not found, incomplete strategy
% 3.85/1.32 % (2008661)Time elapsed: 0.016 s
% 3.85/1.32 % (2008661)Peak memory usage: 89 MB
% 3.85/1.32 % (2008661)Instructions burned: 27 (million)
% 3.85/1.32 % (2008664)ott+1002_1_si=on:sp=occurrence:spb=goal:lcm=predicate:random_seed=2847795918:i=2:bd=preordered:nm=2:ins=3:rtra=on:inst=on:tar=off_2996 on theBenchmark for (2996ds/2Mi)
% 3.85/1.32 % (2008663)dis+1002_24_to=kbo:sil=128000:si=on:random_seed=2520153584:i=85:gtgl=4:rtra=on:gtg=exists_sym_2996 on theBenchmark for (2996ds/85Mi)
% 3.85/1.32 % (2008664)Instruction limit reached!
% 3.85/1.32 % (2008664)------------------------------
% 3.85/1.32 % (2008664)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.85/1.32 % (2008664)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.85/1.32 % (2008664)CaDiCaL version: 2.1.3
% 3.85/1.32 % (2008664)Termination reason: Instruction limit
% 3.85/1.32 % (2008664)Termination phase: Saturation
% 3.85/1.32 % (2008664)Time elapsed: 0.002 s
% 3.85/1.32 % (2008664)Peak memory usage: 88 MB
% 3.85/1.32 % (2008664)Instructions burned: 2 (million)
% 3.85/1.32 % (2008646)Refutation found. Thanks to Tanya!
% 3.85/1.32 % SZS status Theorem for theBenchmark
% 3.85/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 3.85/1.32 % (2008646)------------------------------
% 3.85/1.32 % (2008646)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.85/1.32 % (2008646)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.85/1.32 % (2008646)CaDiCaL version: 2.1.3
% 3.85/1.32 % (2008646)Termination reason: Refutation
% 3.85/1.32 % (2008646)Time elapsed: 0.038 s
% 3.85/1.32 % (2008646)Peak memory usage: 117 MB
% 3.85/1.32 % (2008646)Instructions burned: 16 (million)
% 3.85/1.32 % (2008646)------------------------------
% 3.85/1.32 % (2008646)------------------------------
% 3.85/1.32 % (2008636)Success in time 0.451 s
% 3.85/1.32 % Vampire exiting
%------------------------------------------------------------------------------