%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI696_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 : n020.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 09:33:40 AM UTC 2026
% Result : Theorem 0.19s 1.30s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% 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 : 7 ( 5 ~; 0 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 19 ( 3 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number arithmetic : 387 ( 0 atm; 325 fun; 62 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($difference(c,d),1)),$difference(a,2))),b),$product(-1,$product($product(-1,$sum($sum($sum(a,b),c),d)),$sum(2,c)))) = 0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eq) ).
tff(f2,conjecture,
$sum($sum($product($product(d,b),a),$product(c,b)),$product(-1,$sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($product(2,$product(a,a)),b),$product(b,a)),$product(d,b)),$product(2,c)),$product(-1,$product(c,a))),$product(c,c)),$product($product(c,a),a)),d),$product(2,$product(d,a))),$product(d,b)),$product($product(c,b),a)),$product(d,c)),$product(-1,$product($product(d,a),a))),d))) = 0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
tff(f3,negated_conjecture,
( ( ~ $sum($sum($product($product(d,b),a),$product(c,b)),$product(-1,$sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($product(2,$product(a,a)),b),$product(b,a)),$product(d,b)),$product(2,c)),$product(-1,$product(c,a))),$product(c,c)),$product($product(c,a),a)),d),$product(2,$product(d,a))),$product(d,b)),$product($product(c,b),a)),$product(d,c)),$product(-1,$product($product(d,a),a))),d))) ) = 0 ),
inference(negated_conjecture,[status(cth)],[f2]) ).
tff(f4,plain,
0 = $sum($sum($sum($product(a,a),$product($product($sum(a,b),$sum($sum(c,$uminus(d)),1)),$sum(a,$uminus(2)))),b),$product(-1,$product($product(-1,$sum($sum($sum(a,b),c),d)),$sum(2,c)))),
inference(theory_normalization,[],[f1]) ).
tff(f23,plain,
0 != $sum($sum($product($product(d,b),a),$product(c,b)),$product(-1,$sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($product(2,$product(a,a)),b),$product(b,a)),$product(d,b)),$product(2,c)),$product(-1,$product(c,a))),$product(c,c)),$product($product(c,a),a)),d),$product(2,$product(d,a))),$product(d,b)),$product($product(c,b),a)),$product(d,c)),$product(-1,$product($product(d,a),a))),d))),
inference(flattening,[],[f3]) ).
tff(f24,plain,
0 = $sum($sum($sum($product(a,a),$product($product($sum(a,b),$sum($sum(c,$uminus(d)),1)),$sum(a,$uminus(2)))),b),$product(-1,$product($product(-1,$sum($sum($sum(a,b),c),d)),$sum(2,c)))),
inference(cnf_transformation,[],[f4]) ).
tff(f25,plain,
0 != $sum($sum($product($product(d,b),a),$product(c,b)),$product(-1,$sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($product(2,$product(a,a)),b),$product(b,a)),$product(d,b)),$product(2,c)),$product(-1,$product(c,a))),$product(c,c)),$product($product(c,a),a)),d),$product(2,$product(d,a))),$product(d,b)),$product($product(c,b),a)),$product(d,c)),$product(-1,$product($product(d,a),a))),d))),
inference(cnf_transformation,[],[f23]) ).
tff(f27,plain,
0 = $sum($sum($sum($product(a,a),$product($product($sum(a,b),$sum($sum(c,$uminus(d)),1)),$sum(a,-2))),b),$uminus($product($uminus($sum($sum($sum(a,b),c),d)),$sum(2,c)))),
inference(evaluation,[],[f24]) ).
tff(f28,plain,
0 != $sum($sum($product($product(d,b),a),$product(c,b)),$uminus($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($product(2,$product(a,a)),b),$product(b,a)),$product(d,b)),$product(2,c)),$uminus($product(c,a))),$product(c,c)),$product($product(c,a),a)),d),$product(2,$product(d,a))),$product(d,b)),$product($product(c,b),a)),$product(d,c)),$uminus($product($product(d,a),a))),d))),
inference(evaluation,[],[f25]) ).
tff(f30,definition,
( spl0_1
<=> ( 0 = $sum($sum($sum($product(a,a),$product($product($sum(a,b),$sum($sum(c,$uminus(d)),1)),$sum(a,-2))),b),$uminus($product($uminus($sum($sum($sum(a,b),c),d)),$sum(2,c)))) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
tff(f33,plain,
spl0_1,
inference(avatar_split_clause,[],[f27,f30]) ).
tff(f35,definition,
( spl0_2
<=> ( 0 = $sum($sum($product($product(d,b),a),$product(c,b)),$uminus($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($product(2,$product(a,a)),b),$product(b,a)),$product(d,b)),$product(2,c)),$uminus($product(c,a))),$product(c,c)),$product($product(c,a),a)),d),$product(2,$product(d,a))),$product(d,b)),$product($product(c,b),a)),$product(d,c)),$uminus($product($product(d,a),a))),d))) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
tff(f38,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f28,f35]) ).
tff(f39,plain,
$false,
inference(avatar_smt_refutation,[],[f38,f33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ARI696_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n020.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 20:58:49 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running first-order theorem proving
% 0.07/0.21 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
% 0.19/1.30 % (550098)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 0.19/1.30 % (550109)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2872064484:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 0.19/1.30 % (550109)Instruction limit reached!
% 0.19/1.30 % (550109)------------------------------
% 0.19/1.30 % (550109)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.30 % (550109)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.30 % (550109)CaDiCaL version: 2.1.3
% 0.19/1.30 % (550109)Termination reason: Instruction limit
% 0.19/1.30 % (550109)Termination phase: Saturation
% 0.19/1.30 % (550109)Time elapsed: 0.027 s
% 0.19/1.30 % (550109)Peak memory usage: 117 MB
% 0.19/1.30 % (550109)Instructions burned: 36 (million)
% 0.19/1.30 % (550104)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=419973666:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 0.19/1.30 % (550106)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3004474121:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 0.19/1.30 % (550105)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=216229719:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 0.19/1.30 % (550107)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=2156170872:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 0.19/1.30 % (550103)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=2010348113:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 0.19/1.30 % (550106)Instruction limit reached!
% 0.19/1.30 % (550106)------------------------------
% 0.19/1.30 % (550106)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.30 % (550106)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.30 % (550106)CaDiCaL version: 2.1.3
% 0.19/1.30 % (550106)Termination reason: Instruction limit
% 0.19/1.30 % (550106)Termination phase: Saturation
% 0.19/1.30 % (550106)Time elapsed: 0.004 s
% 0.19/1.30 % (550106)Peak memory usage: 88 MB
% 0.19/1.30 % (550106)Instructions burned: 7 (million)
% 0.19/1.30 % (550107)Instruction limit reached!
% 0.19/1.30 % (550107)------------------------------
% 0.19/1.30 % (550107)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.30 % (550107)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.30 % (550107)CaDiCaL version: 2.1.3
% 0.19/1.30 % (550107)Termination reason: Instruction limit
% 0.19/1.30 % (550107)Termination phase: Saturation
% 0.19/1.30 % (550107)Time elapsed: 0.005 s
% 0.19/1.30 % (550107)Peak memory usage: 88 MB
% 0.19/1.30 % (550107)Instructions burned: 6 (million)
% 0.19/1.30 % (550108)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=201510210:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 0.19/1.30 % (550103)First to succeed.
% 0.19/1.30 % (550103)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-550098"
% 0.19/1.30 % (550108)Also succeeded, but the first one will report.
% 0.19/1.30 % (550111)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=836596303:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.19/1.30 % (550111)Refutation not found, incomplete strategy
% 0.19/1.30 % (550111)------------------------------
% 0.19/1.30 % (550111)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.30 % (550111)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.30 % (550111)CaDiCaL version: 2.1.3
% 0.19/1.30 % (550111)Termination reason: Refutation not found, incomplete strategy
% 0.19/1.30 % (550111)Time elapsed: 0.001 s
% 0.19/1.30 % (550111)Peak memory usage: 88 MB
% 0.19/1.30 % (550111)Instructions burned: 1 (million)
% 0.19/1.30 % (550105)Instruction limit reached!
% 0.19/1.30 % (550105)------------------------------
% 0.19/1.30 % (550105)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.30 % (550105)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.30 % (550105)CaDiCaL version: 2.1.3
% 0.19/1.30 % (550105)Termination reason: Instruction limit
% 0.19/1.30 % (550105)Termination phase: Saturation
% 0.19/1.30 % (550105)Time elapsed: 0.133 s
% 0.19/1.30 % (550105)Peak memory usage: 117 MB
% 0.19/1.30 % (550105)Instructions burned: 202 (million)
% 0.19/1.30 % (550118)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=730162818:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/16Mi)
% 0.19/1.30 % (550117)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=375123550:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 0.19/1.30 % (550104)Instruction limit reached!
% 0.19/1.30 % (550104)------------------------------
% 0.19/1.30 % (550104)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.30 % (550104)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.30 % (550104)CaDiCaL version: 2.1.3
% 0.19/1.30 % (550104)Termination reason: Instruction limit
% 0.19/1.30 % (550104)Termination phase: Saturation
% 0.19/1.30 % (550104)Time elapsed: 0.169 s
% 0.19/1.30 % (550104)Peak memory usage: 118 MB
% 0.19/1.30 % (550104)Instructions burned: 309 (million)
% 0.19/1.30 % (550118)Instruction limit reached!
% 0.19/1.30 % (550118)------------------------------
% 0.19/1.30 % (550118)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.30 % (550118)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.30 % (550118)CaDiCaL version: 2.1.3
% 0.19/1.30 % (550118)Termination reason: Instruction limit
% 0.19/1.30 % (550118)Termination phase: Saturation
% 0.19/1.30 % (550118)Time elapsed: 0.010 s
% 0.19/1.30 % (550118)Peak memory usage: 90 MB
% 0.19/1.30 % (550118)Instructions burned: 18 (million)
% 0.19/1.30 % (550117)Instruction limit reached!
% 0.19/1.30 % (550117)------------------------------
% 0.19/1.30 % (550117)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.30 % (550117)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.30 % (550117)CaDiCaL version: 2.1.3
% 0.19/1.30 % (550117)Termination reason: Instruction limit
% 0.19/1.30 % (550117)Termination phase: Saturation
% 0.19/1.30 % (550117)Time elapsed: 0.017 s
% 0.19/1.30 % (550117)Peak memory usage: 88 MB
% 0.19/1.30 % (550117)Instructions burned: 32 (million)
% 0.19/1.30 % (550111)------------------------------
% 0.19/1.30 % (550111)------------------------------
% 0.19/1.30 % (550103)Refutation found. Thanks to Tanya!
% 0.19/1.30 % SZS status Theorem for theBenchmark
% 0.19/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/1.31 % (550103)------------------------------
% 0.19/1.31 % (550103)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.31 % (550103)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.31 % (550103)CaDiCaL version: 2.1.3
% 0.19/1.31 % (550103)Termination reason: Refutation
% 0.19/1.31 % (550103)Time elapsed: 0.034 s
% 0.19/1.31 % (550103)Peak memory usage: 116 MB
% 0.19/1.31 % (550103)Instructions burned: 13 (million)
% 0.19/1.31 % (550103)------------------------------
% 0.19/1.31 % (550103)------------------------------
% 0.19/1.31 % (550098)Success in time 0.461 s
% 0.19/1.31 % Vampire exiting
%------------------------------------------------------------------------------