%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI685_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 : n010.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 3.84s 1.36s
% Output : Refutation 3.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 12 unt; 0 typ; 2 def)
% Number of atoms : 16 ( 11 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 6 ~; 0 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 18 ( 3 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number arithmetic : 482 ( 0 atm; 377 fun; 105 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 : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 13 ( 4 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
a: $int ).
tff(func_def_1,type,
b: $int ).
tff(func_def_2,type,
c: $int ).
tff(func_def_3,type,
d: $int ).
tff(f1,axiom,
$sum($sum($sum($product(a,a),$product($product($sum(a,b),$sum($sum(c,d),1)),$sum(a,2))),b),$product(-1,$product($sum($sum($sum(a,b),c),d),$sum(2,c)))) = 0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eq) ).
tff(f2,conjecture,
$sum($product($product(d,b),a),$product(-1,$sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($difference($sum($product(-2,$product(a,a)),$product(-1,$product(c,a))),b),$product(-1,$product(b,a))),$product(2,c)),$product(-1,$product(c,b))),$product(c,c)),$product(-1,$product($product(c,a),a))),$product(-1,$product(2,$product(d,a)))),$product(-1,$product(2,$product(d,b)))),$product(-1,$product($product(c,b),a))),$product(d,c)),$product(-1,$product($product(d,a),a))),$product(2,d)))) = 0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
tff(f3,negated_conjecture,
( ( ~ $sum($product($product(d,b),a),$product(-1,$sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($difference($sum($product(-2,$product(a,a)),$product(-1,$product(c,a))),b),$product(-1,$product(b,a))),$product(2,c)),$product(-1,$product(c,b))),$product(c,c)),$product(-1,$product($product(c,a),a))),$product(-1,$product(2,$product(d,a)))),$product(-1,$product(2,$product(d,b)))),$product(-1,$product($product(c,b),a))),$product(d,c)),$product(-1,$product($product(d,a),a))),$product(2,d)))) ) = 0 ),
inference(negated_conjecture,[status(cth)],[f2]) ).
tff(f4,plain,
( ( ~ 0 ) = $sum($product($product(d,b),a),$product(-1,$sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($product(-2,$product(a,a)),$product(-1,$product(c,a))),$uminus(b)),$product(-1,$product(b,a))),$product(2,c)),$product(-1,$product(c,b))),$product(c,c)),$product(-1,$product($product(c,a),a))),$product(-1,$product(2,$product(d,a)))),$product(-1,$product(2,$product(d,b)))),$product(-1,$product($product(c,b),a))),$product(d,c)),$product(-1,$product($product(d,a),a))),$product(2,d)))) ),
inference(theory_normalization,[],[f3]) ).
tff(f5,plain,
0 != $sum($product($product(d,b),a),$product(-1,$sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($product(-2,$product(a,a)),$product(-1,$product(c,a))),$uminus(b)),$product(-1,$product(b,a))),$product(2,c)),$product(-1,$product(c,b))),$product(c,c)),$product(-1,$product($product(c,a),a))),$product(-1,$product(2,$product(d,a)))),$product(-1,$product(2,$product(d,b)))),$product(-1,$product($product(c,b),a))),$product(d,c)),$product(-1,$product($product(d,a),a))),$product(2,d)))),
inference(flattening,[],[f4]) ).
tff(f6,plain,
0 != $sum($product($product(d,b),a),$product(-1,$sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($product(-2,$product(a,a)),$product(-1,$product(c,a))),$uminus(b)),$product(-1,$product(b,a))),$product(2,c)),$product(-1,$product(c,b))),$product(c,c)),$product(-1,$product($product(c,a),a))),$product(-1,$product(2,$product(d,a)))),$product(-1,$product(2,$product(d,b)))),$product(-1,$product($product(c,b),a))),$product(d,c)),$product(-1,$product($product(d,a),a))),$product(2,d)))),
inference(cnf_transformation,[],[f5]) ).
tff(f7,plain,
$sum($sum($sum($product(a,a),$product($product($sum(a,b),$sum($sum(c,d),1)),$sum(a,2))),b),$product(-1,$product($sum($sum($sum(a,b),c),d),$sum(2,c)))) = 0,
inference(cnf_transformation,[],[f1]) ).
tff(f8,plain,
0 = $sum($sum($sum($product(a,a),$product($product($sum(a,b),$sum($sum(c,d),1)),$sum(a,2))),b),$uminus($product($sum($sum($sum(a,b),c),d),$sum(2,c)))),
inference(evaluation,[],[f7]) ).
tff(f9,plain,
0 != $sum($product($product(d,b),a),$uminus($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($product(-2,$product(a,a)),$uminus($product(c,a))),$uminus(b)),$uminus($product(b,a))),$product(2,c)),$uminus($product(c,b))),$product(c,c)),$uminus($product($product(c,a),a))),$uminus($product(2,$product(d,a)))),$uminus($product(2,$product(d,b)))),$uminus($product($product(c,b),a))),$product(d,c)),$uminus($product($product(d,a),a))),$product(2,d)))),
inference(evaluation,[],[f6]) ).
tff(f11,definition,
( spl0_1
<=> ( 0 = $sum($sum($sum($product(a,a),$product($product($sum(a,b),$sum($sum(c,d),1)),$sum(a,2))),b),$uminus($product($sum($sum($sum(a,b),c),d),$sum(2,c)))) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
tff(f14,plain,
spl0_1,
inference(avatar_split_clause,[],[f8,f11]) ).
tff(f16,definition,
( spl0_2
<=> ( 0 = $sum($product($product(d,b),a),$uminus($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($product(-2,$product(a,a)),$uminus($product(c,a))),$uminus(b)),$uminus($product(b,a))),$product(2,c)),$uminus($product(c,b))),$product(c,c)),$uminus($product($product(c,a),a))),$uminus($product(2,$product(d,a)))),$uminus($product(2,$product(d,b)))),$uminus($product($product(c,b),a))),$product(d,c)),$uminus($product($product(d,a),a))),$product(2,d)))) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
tff(f19,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f9,f16]) ).
tff(f20,plain,
$false,
inference(avatar_smt_refutation,[],[f19,f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI685_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.20 % Computer : n010.cluster.edu
% 0.11/0.20 % Model : x86_64 x86_64
% 0.11/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.20 % Memory : 8046.5625MB
% 0.11/0.20 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Mon Sep 28 20:57:58 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.24 Running first-order theorem proving
% 0.11/0.24 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
% 3.04/1.15 % (2326019)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.04/1.15 % (2326147)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2628276947:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.04/1.15 % (2326151)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=4006199760:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.04/1.15 % (2326150)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3592600071:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.04/1.15 % (2326148)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2756402195:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.04/1.15 % (2326149)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=807423096:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.04/1.15 % (2326146)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=95356514:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.04/1.15 % (2326145)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=2324899890:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.04/1.15 % (2326149)Instruction limit reached!
% 3.04/1.15 % (2326149)------------------------------
% 3.04/1.15 % (2326149)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.04/1.15 % (2326149)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.04/1.15 % (2326149)CaDiCaL version: 2.1.3
% 3.04/1.15 % (2326149)Termination reason: Instruction limit
% 3.04/1.15 % (2326149)Termination phase: Saturation
% 3.04/1.15 % (2326149)Time elapsed: 0.003 s
% 3.04/1.15 % (2326149)Peak memory usage: 88 MB
% 3.04/1.15 % (2326149)Instructions burned: 4 (million)
% 3.04/1.15 % (2326148)Instruction limit reached!
% 3.04/1.15 % (2326148)------------------------------
% 3.04/1.15 % (2326148)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.04/1.15 % (2326148)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.04/1.15 % (2326148)CaDiCaL version: 2.1.3
% 3.04/1.15 % (2326148)Termination reason: Instruction limit
% 3.04/1.15 % (2326148)Termination phase: Saturation
% 3.04/1.15 % (2326148)Time elapsed: 0.004 s
% 3.04/1.15 % (2326148)Peak memory usage: 88 MB
% 3.04/1.15 % (2326148)Instructions burned: 7 (million)
% 3.04/1.15 % (2326147)Instruction limit reached!
% 3.04/1.15 % (2326147)------------------------------
% 3.04/1.15 % (2326147)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.04/1.15 % (2326147)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.04/1.15 % (2326147)CaDiCaL version: 2.1.3
% 3.04/1.15 % (2326147)Termination reason: Instruction limit
% 3.04/1.15 % (2326147)Termination phase: Saturation
% 3.04/1.15 % (2326147)Time elapsed: 0.075 s
% 3.04/1.15 % (2326147)Peak memory usage: 117 MB
% 3.04/1.15 % (2326147)Instructions burned: 203 (million)
% 3.04/1.15 % (2326150)First to succeed.
% 3.04/1.15 % (2326145)Also succeeded, but the first one will report.
% 3.04/1.15 % (2326150)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2326019"
% 3.04/1.15 % (2326151)Instruction limit reached!
% 3.04/1.15 % (2326151)------------------------------
% 3.04/1.15 % (2326151)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.04/1.15 % (2326151)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.04/1.15 % (2326151)CaDiCaL version: 2.1.3
% 3.04/1.15 % (2326151)Termination reason: Instruction limit
% 3.04/1.15 % (2326151)Termination phase: Saturation
% 3.04/1.15 % (2326151)Time elapsed: 0.071 s
% 3.04/1.15 % (2326151)Peak memory usage: 117 MB
% 3.04/1.15 % (2326151)Instructions burned: 33 (million)
% 3.04/1.15 % (2326161)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=147826251:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/16Mi)
% 3.04/1.15 % (2326159)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=1805378282:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.04/1.15 % (2326159)Refutation not found, incomplete strategy
% 3.04/1.15 % (2326159)------------------------------
% 3.04/1.15 % (2326159)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.04/1.15 % (2326159)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.84/1.36 % (2326159)CaDiCaL version: 2.1.3
% 3.84/1.36 % (2326159)Termination reason: Refutation not found, incomplete strategy
% 3.84/1.36 % (2326159)Time elapsed: 0.002 s
% 3.84/1.36 % (2326159)Peak memory usage: 88 MB
% 3.84/1.36 % (2326159)Instructions burned: 1 (million)
% 3.84/1.36 % (2326161)Instruction limit reached!
% 3.84/1.36 % (2326161)------------------------------
% 3.84/1.36 % (2326161)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.84/1.36 % (2326161)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.84/1.36 % (2326161)CaDiCaL version: 2.1.3
% 3.84/1.36 % (2326161)Termination reason: Instruction limit
% 3.84/1.36 % (2326161)Termination phase: Saturation
% 3.84/1.36 % (2326161)Time elapsed: 0.005 s
% 3.84/1.36 % (2326161)Peak memory usage: 90 MB
% 3.84/1.36 % (2326161)Instructions burned: 17 (million)
% 3.84/1.36 % (2326146)Instruction limit reached!
% 3.84/1.36 % (2326146)------------------------------
% 3.84/1.36 % (2326146)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.84/1.36 % (2326146)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.84/1.36 % (2326146)CaDiCaL version: 2.1.3
% 3.84/1.36 % (2326146)Termination reason: Instruction limit
% 3.84/1.36 % (2326146)Termination phase: Saturation
% 3.84/1.36 % (2326146)Time elapsed: 0.179 s
% 3.84/1.36 % (2326146)Peak memory usage: 118 MB
% 3.84/1.36 % (2326146)Instructions burned: 308 (million)
% 3.84/1.36 % (2326162)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=230217085:i=24:canc=force:rtra=on_2997 on theBenchmark for (2997ds/24Mi)
% 3.84/1.36 % (2326162)Instruction limit reached!
% 3.84/1.36 % (2326162)------------------------------
% 3.84/1.36 % (2326162)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.84/1.36 % (2326162)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.84/1.36 % (2326162)CaDiCaL version: 2.1.3
% 3.84/1.36 % (2326162)Termination reason: Instruction limit
% 3.84/1.36 % (2326162)Termination phase: Saturation
% 3.84/1.36 % (2326162)Time elapsed: 0.016 s
% 3.84/1.36 % (2326162)Peak memory usage: 89 MB
% 3.84/1.36 % (2326162)Instructions burned: 25 (million)
% 3.84/1.36 % (2326160)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=3832423355:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 3.84/1.36 % (2326165)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=1409341425:i=27:canc=cautious:fsr=off:rtra=on_2996 on theBenchmark for (2996ds/27Mi)
% 3.84/1.36 % (2326165)Instruction limit reached!
% 3.84/1.36 % (2326165)------------------------------
% 3.84/1.36 % (2326165)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.84/1.36 % (2326165)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.84/1.36 % (2326165)CaDiCaL version: 2.1.3
% 3.84/1.36 % (2326165)Termination reason: Instruction limit
% 3.84/1.36 % (2326165)Termination phase: Saturation
% 3.84/1.36 % (2326165)Time elapsed: 0.008 s
% 3.84/1.36 % (2326165)Peak memory usage: 89 MB
% 3.84/1.36 % (2326165)Instructions burned: 30 (million)
% 3.84/1.36 % (2326150)Refutation found. Thanks to Tanya!
% 3.84/1.36 % SZS status Theorem for theBenchmark
% 3.84/1.36 % SZS output start Proof for theBenchmark
% See solution above
% 3.84/1.36 % (2326150)------------------------------
% 3.84/1.36 % (2326150)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.84/1.36 % (2326150)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.84/1.36 % (2326150)CaDiCaL version: 2.1.3
% 3.84/1.36 % (2326150)Termination reason: Refutation
% 3.84/1.36 % (2326150)Time elapsed: 0.033 s
% 3.84/1.36 % (2326150)Peak memory usage: 116 MB
% 3.84/1.36 % (2326150)Instructions burned: 12 (million)
% 3.84/1.36 % (2326150)------------------------------
% 3.84/1.36 % (2326150)------------------------------
% 3.84/1.36 % (2326019)Success in time 0.463 s
% 3.84/1.36 % Vampire exiting
%------------------------------------------------------------------------------