%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM926_1 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 12:17:35 PM UTC 2026
% Result : Theorem 2.70s 1.31s
% Output : Refutation 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 54 ( 18 unt; 0 typ; 6 def)
% Number of atoms : 104 ( 23 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 91 ( 41 ~; 36 |; 5 &)
% ( 7 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 7 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 6 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 11 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 22 !; 12 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
int: $tType ).
tff(type_def_6,type,
nat: $tType ).
tff(func_def_0,type,
one_one_int: int ).
tff(func_def_1,type,
one_one_nat: nat ).
tff(func_def_2,type,
plus_plus_int: ( int * int ) > int ).
tff(func_def_3,type,
plus_plus_nat: ( nat * nat ) > nat ).
tff(func_def_4,type,
times_times_int: ( int * int ) > int ).
tff(func_def_5,type,
times_times_nat: ( nat * nat ) > nat ).
tff(func_def_6,type,
bit0: int > int ).
tff(func_def_7,type,
bit1: int > int ).
tff(func_def_8,type,
pls: int ).
tff(func_def_9,type,
number_number_of_int: int > int ).
tff(func_def_10,type,
number_number_of_nat: int > nat ).
tff(func_def_11,type,
power_power_int: ( int * nat ) > int ).
tff(func_def_12,type,
power_power_nat: ( nat * nat ) > nat ).
tff(func_def_13,type,
m: int ).
tff(func_def_14,type,
s: int ).
tff(func_def_15,type,
t: int ).
tff(func_def_16,type,
sK0: int ).
tff(func_def_17,type,
sK1: int ).
tff(func_def_18,type,
sK2: int ).
tff(func_def_19,type,
sK3: int ).
tff(func_def_20,type,
sK4: int ).
tff(pred_def_1,type,
zprime: int > $o ).
tff(pred_def_2,type,
ord_less_int: ( int * int ) > $o ).
tff(pred_def_3,type,
ord_less_nat: ( nat * nat ) > $o ).
tff(pred_def_4,type,
ord_less_eq_int: ( int * int ) > $o ).
tff(pred_def_5,type,
ord_less_eq_nat: ( nat * nat ) > $o ).
tff(pred_def_6,type,
twoSqu1431725154sum2sq: int > $o ).
tff(pred_def_7,type,
sQ5_eqProxy: ( int * int ) > $o ).
tff(pred_def_8,type,
sQ6_eqProxy: ( nat * nat ) > $o ).
tff(f1,axiom,
ord_less_eq_int(one_one_int,t),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_tpos) ).
tff(f2,axiom,
( ( t = one_one_int )
=> ? [X0: int,X1: int] : ( plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
tff(f3,axiom,
( ord_less_int(one_one_int,t)
=> ? [X0: int,X1: int] : ( plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
tff(f29,axiom,
! [X0: int,X1: int] :
( ord_less_int(X0,X1)
<=> ( ord_less_eq_int(X0,X1)
& ( X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_zless__le) ).
tff(f124,conjecture,
? [X0: int,X1: int] : ( plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f125,negated_conjecture,
~ ? [X0: int,X1: int] : ( plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ),
inference(negated_conjecture,[status(cth)],[f124]) ).
tff(f128,plain,
( ? [X0: int,X1: int] : ( plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) )
| ( one_one_int != t ) ),
inference(ennf_transformation,[],[f2]) ).
tff(f129,plain,
( ? [X0: int,X1: int] : ( plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) )
| ~ ord_less_int(one_one_int,t) ),
inference(ennf_transformation,[],[f3]) ).
tff(f143,plain,
! [X0: int,X1: int] : ( plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) != plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ),
inference(ennf_transformation,[],[f125]) ).
tff(f144,plain,
( ( plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) = plus_plus_int(power_power_int(sK0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(sK1,number_number_of_nat(bit0(bit1(pls))))) )
| ( one_one_int != t ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f128]) ).
tff(f145,plain,
( ( plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) = plus_plus_int(power_power_int(sK2,number_number_of_nat(bit0(bit1(pls)))),power_power_int(sK3,number_number_of_nat(bit0(bit1(pls))))) )
| ~ ord_less_int(one_one_int,t) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f129]) ).
tff(f147,plain,
! [X0: int,X1: int] :
( ( ord_less_int(X0,X1)
| ~ ord_less_eq_int(X0,X1)
| ( X0 = X1 ) )
& ( ( ord_less_eq_int(X0,X1)
& ( X0 != X1 ) )
| ~ ord_less_int(X0,X1) ) ),
inference(nnf_transformation,[],[f29]) ).
tff(f148,plain,
! [X0: int,X1: int] :
( ( ord_less_int(X0,X1)
| ~ ord_less_eq_int(X0,X1)
| ( X0 = X1 ) )
& ( ( ord_less_eq_int(X0,X1)
& ( X0 != X1 ) )
| ~ ord_less_int(X0,X1) ) ),
inference(flattening,[],[f147]) ).
tff(f184,plain,
ord_less_eq_int(one_one_int,t),
inference(cnf_transformation,[],[f1]) ).
tff(f185,plain,
( ( plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) = plus_plus_int(power_power_int(sK0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(sK1,number_number_of_nat(bit0(bit1(pls))))) )
| ( one_one_int != t ) ),
inference(cnf_transformation,[],[f144]) ).
tff(f186,plain,
( ( plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) = plus_plus_int(power_power_int(sK2,number_number_of_nat(bit0(bit1(pls)))),power_power_int(sK3,number_number_of_nat(bit0(bit1(pls))))) )
| ~ ord_less_int(one_one_int,t) ),
inference(cnf_transformation,[],[f145]) ).
tff(f213,plain,
! [X0: int,X1: int] :
( ord_less_int(X0,X1)
| ~ ord_less_eq_int(X0,X1)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f148]) ).
tff(f344,plain,
! [X0: int,X1: int] : ( plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) != plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ),
inference(cnf_transformation,[],[f143]) ).
tff(f353,definition,
! [X0: int,X1: int] :
( sQ5_eqProxy(X0,X1)
<=> ( X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ5_eqProxy])],[equality_proxy_definition]) ).
tff(f354,plain,
( sQ5_eqProxy(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),plus_plus_int(power_power_int(sK0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(sK1,number_number_of_nat(bit0(bit1(pls))))))
| ~ sQ5_eqProxy(one_one_int,t) ),
inference(equality_proxy_replacement,[],[f185,f353,f353]) ).
tff(f355,plain,
( sQ5_eqProxy(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),plus_plus_int(power_power_int(sK2,number_number_of_nat(bit0(bit1(pls)))),power_power_int(sK3,number_number_of_nat(bit0(bit1(pls))))))
| ~ ord_less_int(one_one_int,t) ),
inference(equality_proxy_replacement,[],[f186,f353]) ).
tff(f377,plain,
! [X0: int,X1: int] :
( sQ5_eqProxy(X0,X1)
| ~ ord_less_eq_int(X0,X1)
| ord_less_int(X0,X1) ),
inference(equality_proxy_replacement,[],[f213,f353]) ).
tff(f440,plain,
! [X0: int,X1: int] : ~ sQ5_eqProxy(plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
inference(equality_proxy_replacement,[],[f344,f353]) ).
tff(f442,plain,
! [X0: int,X1: int] :
( sQ5_eqProxy(X1,X0)
| ~ sQ5_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f353]) ).
tff(f446,definition,
( spl7_1
<=> ord_less_int(one_one_int,t) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
tff(f449,definition,
( spl7_2
<=> sQ5_eqProxy(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),plus_plus_int(power_power_int(sK2,number_number_of_nat(bit0(bit1(pls)))),power_power_int(sK3,number_number_of_nat(bit0(bit1(pls)))))) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
tff(f450,plain,
( sQ5_eqProxy(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),plus_plus_int(power_power_int(sK2,number_number_of_nat(bit0(bit1(pls)))),power_power_int(sK3,number_number_of_nat(bit0(bit1(pls))))))
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f449]) ).
tff(f451,plain,
( ~ spl7_1
| spl7_2 ),
inference(avatar_split_clause,[],[f355,f449,f446]) ).
tff(f453,definition,
( spl7_3
<=> sQ5_eqProxy(one_one_int,t) ),
introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition]) ).
tff(f454,plain,
( ~ sQ5_eqProxy(one_one_int,t)
| spl7_3 ),
inference(avatar_component_clause,[],[f453]) ).
tff(f456,definition,
( spl7_4
<=> sQ5_eqProxy(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),plus_plus_int(power_power_int(sK0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(sK1,number_number_of_nat(bit0(bit1(pls)))))) ),
introduced(definition,[new_symbols(definition,[spl7_4])],[avatar_definition]) ).
tff(f457,plain,
( sQ5_eqProxy(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),plus_plus_int(power_power_int(sK0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(sK1,number_number_of_nat(bit0(bit1(pls))))))
| ~ spl7_4 ),
inference(avatar_component_clause,[],[f456]) ).
tff(f458,plain,
( ~ spl7_3
| spl7_4 ),
inference(avatar_split_clause,[],[f354,f456,f453]) ).
tff(f459,plain,
! [X0: int,X1: int] : ~ sQ5_eqProxy(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls)))))),
inference(resolution,[],[f442,f440]) ).
tff(f614,definition,
( spl7_7
<=> ord_less_eq_int(one_one_int,t) ),
introduced(definition,[new_symbols(definition,[spl7_7])],[avatar_definition]) ).
tff(f615,plain,
( ~ ord_less_eq_int(one_one_int,t)
| spl7_7 ),
inference(avatar_component_clause,[],[f614]) ).
tff(f617,plain,
( $false
| spl7_7 ),
inference(resolution,[],[f615,f184]) ).
tff(f623,plain,
spl7_7,
inference(avatar_contradiction_clause,[],[f617]) ).
tff(f629,plain,
( $false
| ~ spl7_4 ),
inference(resolution,[],[f457,f459]) ).
tff(f630,plain,
~ spl7_4,
inference(avatar_contradiction_clause,[],[f629]) ).
tff(f631,plain,
( ~ ord_less_eq_int(one_one_int,t)
| ord_less_int(one_one_int,t)
| spl7_3 ),
inference(resolution,[],[f454,f377]) ).
tff(f633,plain,
( spl7_1
| ~ spl7_7
| spl7_3 ),
inference(avatar_split_clause,[],[f631,f453,f614,f446]) ).
tff(f639,plain,
( $false
| ~ spl7_2 ),
inference(resolution,[],[f450,f459]) ).
tff(f640,plain,
~ spl7_2,
inference(avatar_contradiction_clause,[],[f639]) ).
cnf(s1,plain,
( ~ spl7_1
| spl7_2 ),
inference(sat_conversion,[],[f451]) ).
cnf(s2,plain,
( ~ spl7_3
| spl7_4 ),
inference(sat_conversion,[],[f458]) ).
cnf(s5,plain,
spl7_7,
inference(sat_conversion,[],[f623]) ).
cnf(s6,plain,
~ spl7_4,
inference(sat_conversion,[],[f630]) ).
cnf(s7,plain,
( spl7_1
| spl7_3
| ~ spl7_7 ),
inference(sat_conversion,[],[f633]) ).
cnf(s8,plain,
~ spl7_2,
inference(sat_conversion,[],[f640]) ).
cnf(s10,plain,
~ spl7_3,
inference(rat,[],[s2,s6]) ).
cnf(s11,plain,
spl7_1,
inference(rat,[],[s7,s5,s10]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s1,s8,s11]) ).
tff(f641,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM926_1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n019.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 21:44:03 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 2.70/1.31 % (3438119)Detected formulas, will run a generic FOF schedule.
% 2.70/1.31 % (3438125)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2937874164:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.70/1.31 % (3438124)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2717165562:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.70/1.31 % (3438128)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=216751154:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.70/1.31 % (3438130)dis-21_1_sil=8000:lcm=predicate:random_seed=1209000025:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.70/1.31 % (3438129)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2487375481:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.70/1.31 % (3438127)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1123954776:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.70/1.31 % (3438126)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1748104495:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.70/1.31 % (3438130)First to succeed.
% 2.70/1.31 % (3438130)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3438119"
% 2.70/1.31 % (3438127)Instruction limit reached!
% 2.70/1.31 % (3438127)------------------------------
% 2.70/1.31 % (3438127)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.70/1.31 % (3438127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/1.31 % (3438127)CaDiCaL version: 2.1.3
% 2.70/1.31 % (3438127)Termination reason: Instruction limit
% 2.70/1.31 % (3438127)Termination phase: Saturation
% 2.70/1.31 % (3438127)Time elapsed: 0.058 s
% 2.70/1.31 % (3438127)Peak memory usage: 88 MB
% 2.70/1.31 % (3438127)Instructions burned: 109 (million)
% 2.70/1.31 % (3438128)Instruction limit reached!
% 2.70/1.31 % (3438128)------------------------------
% 2.70/1.31 % (3438128)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.70/1.31 % (3438128)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/1.31 % (3438128)CaDiCaL version: 2.1.3
% 2.70/1.31 % (3438128)Termination reason: Instruction limit
% 2.70/1.31 % (3438128)Termination phase: Saturation
% 2.70/1.31 % (3438128)Time elapsed: 0.063 s
% 2.70/1.31 % (3438128)Peak memory usage: 88 MB
% 2.70/1.31 % (3438128)Instructions burned: 119 (million)
% 2.70/1.31 % (3438129)Also succeeded, but the first one will report.
% 2.70/1.31 % (3438138)lrs+10_1_sil=8000:sp=occurrence:random_seed=1107493749:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.70/1.31 % (3438139)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3287545368:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.70/1.31 % (3438130)Refutation found. Thanks to Tanya!
% 2.70/1.31 % SZS status Theorem for theBenchmark
% 2.70/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 3.69/1.41 % (3438130)------------------------------
% 3.69/1.41 % (3438130)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.41 % (3438130)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.41 % (3438130)CaDiCaL version: 2.1.3
% 3.69/1.41 % (3438130)Termination reason: Refutation
% 3.69/1.41 % (3438130)Time elapsed: 0.009 s
% 3.69/1.41 % (3438130)Peak memory usage: 89 MB
% 3.69/1.41 % (3438130)Instructions burned: 13 (million)
% 3.69/1.41 % (3438130)------------------------------
% 3.69/1.41 % (3438130)------------------------------
% 3.69/1.41 % (3438119)Success in time 0.448 s
% 3.69/1.41 % Vampire exiting
%------------------------------------------------------------------------------