%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI705_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 : n002.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 09:33:41 AM UTC 2026
% Result : Theorem 4.15s 1.52s
% Output : Refutation 4.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 9 unt; 0 typ; 2 def)
% Number of atoms : 13 ( 8 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 4 ~; 0 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number arithmetic : 39 ( 0 atm; 29 fun; 10 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 : 8 ( 4 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
d: $int ).
tff(func_def_1,type,
a: $int ).
tff(func_def_2,type,
c: $int ).
tff(func_def_3,type,
b: $int ).
tff(f1,axiom,
$product(d,d) = $sum($product(d,d),a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eq) ).
tff(f2,conjecture,
$product($product($product($product(d,c),a),b),2) = 0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
tff(f3,negated_conjecture,
( ( ~ $product($product($product($product(d,c),a),b),2) ) = 0 ),
inference(negated_conjecture,[status(cth)],[f2]) ).
tff(f4,plain,
$product($product($product($product(d,c),a),b),2) != 0,
inference(flattening,[],[f3]) ).
tff(f5,plain,
$product(d,d) = $sum($product(d,d),a),
inference(cnf_transformation,[],[f1]) ).
tff(f6,plain,
$product($product($product($product(d,c),a),b),2) != 0,
inference(cnf_transformation,[],[f4]) ).
tff(f8,definition,
( spl0_1
<=> ( $product(d,d) = $sum($product(d,d),a) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
tff(f11,plain,
spl0_1,
inference(avatar_split_clause,[],[f5,f8]) ).
tff(f13,definition,
( spl0_2
<=> ( $product($product($product($product(d,c),a),b),2) = 0 ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
tff(f16,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f6,f13]) ).
tff(f17,plain,
$false,
inference(avatar_smt_refutation,[],[f16,f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI705_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.24 % Computer : n002.cluster.edu
% 0.11/0.24 % Model : x86_64 x86_64
% 0.11/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.24 % Memory : 8046.5625MB
% 0.11/0.24 % OS : Linux 6.8.0-71-generic
% 0.11/0.24 % CPULimit : 300
% 0.11/0.24 % WCLimit : 300
% 0.11/0.24 % DateTime : Mon Sep 28 21:00:37 UTC 2026
% 0.11/0.24 % CPUTime :
% 0.11/0.24 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.30 Running first-order theorem proving
% 0.23/0.30 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
% 4.15/1.52 % (754133)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 4.15/1.52 % (754143)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3413125136:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 4.15/1.52 % (754140)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2639855716:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 4.15/1.52 % (754143)First to succeed.
% 4.15/1.52 % (754143)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-754133"
% 4.15/1.52 % (754139)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=4270543393:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 4.15/1.52 % (754138)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3979830715:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 4.15/1.52 % (754140)Also succeeded, but the first one will report.
% 4.15/1.52 % (754139)Also succeeded, but the first one will report.
% 4.15/1.52 % (754142)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3976859860:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 4.15/1.52 % (754141)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=4163006805:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 4.15/1.52 % (754142)Instruction limit reached!
% 4.15/1.52 % (754142)------------------------------
% 4.15/1.52 % (754142)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.15/1.52 % (754142)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.15/1.52 % (754142)CaDiCaL version: 2.1.3
% 4.15/1.52 % (754142)Termination reason: Instruction limit
% 4.15/1.52 % (754142)Termination phase: Saturation
% 4.15/1.52 % (754142)Time elapsed: 0.005 s
% 4.15/1.52 % (754142)Peak memory usage: 89 MB
% 4.15/1.52 % (754142)Instructions burned: 4 (million)
% 4.15/1.52 % (754141)Instruction limit reached!
% 4.15/1.52 % (754141)------------------------------
% 4.15/1.52 % (754141)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.15/1.52 % (754141)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.15/1.52 % (754141)CaDiCaL version: 2.1.3
% 4.15/1.52 % (754141)Termination reason: Instruction limit
% 4.15/1.52 % (754141)Termination phase: Saturation
% 4.15/1.52 % (754141)Time elapsed: 0.009 s
% 4.15/1.52 % (754141)Peak memory usage: 88 MB
% 4.15/1.52 % (754141)Instructions burned: 7 (million)
% 4.15/1.52 % (754138)Also succeeded, but the first one will report.
% 4.15/1.52 % (754144)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1923253125:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 4.15/1.52 % (754144)Also succeeded, but the first one will report.
% 4.15/1.52 % (754143)Refutation found. Thanks to Tanya!
% 4.15/1.52 % SZS status Theorem for theBenchmark
% 4.15/1.52 % SZS output start Proof for theBenchmark
% See solution above
% 4.15/1.52 % (754143)------------------------------
% 4.15/1.52 % (754143)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.15/1.52 % (754143)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.15/1.52 % (754143)CaDiCaL version: 2.1.3
% 4.15/1.52 % (754143)Termination reason: Refutation
% 4.15/1.52 % (754143)Time elapsed: 0.025 s
% 4.15/1.52 % (754143)Peak memory usage: 115 MB
% 4.15/1.52 % (754143)Instructions burned: 8 (million)
% 4.15/1.52 % (754143)------------------------------
% 4.15/1.52 % (754143)------------------------------
% 4.15/1.52 % (754133)Success in time 0.472 s
% 4.15/1.52 % Vampire exiting
%------------------------------------------------------------------------------