%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n018.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 : Wed Sep 30 08:19:38 AM UTC 2026
% Result : Theorem 0.22s 0.34s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 107 ( 52 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 393 ( 22 ~; 17 |; 7 &; 340 @)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 29 usr; 13 con; 0-2 aty)
% Number of variables : 32 ( 0 ^; 16 !; 16 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
int: $tType ).
thf(type_def_6,type,
nat: $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
one_one_int: int ).
thf(func_def_1,type,
one_one_nat: nat ).
thf(func_def_2,type,
plus_plus_int: int > int > int ).
thf(func_def_3,type,
plus_plus_nat: nat > nat > nat ).
thf(func_def_4,type,
times_times_int: int > int > int ).
thf(func_def_5,type,
times_times_nat: nat > nat > nat ).
thf(func_def_6,type,
zprime: int > $o ).
thf(func_def_7,type,
bit0: int > int ).
thf(func_def_8,type,
bit1: int > int ).
thf(func_def_9,type,
pls: int ).
thf(func_def_10,type,
number_number_of_int: int > int ).
thf(func_def_11,type,
number_number_of_nat: int > nat ).
thf(func_def_12,type,
ord_less_int: int > int > $o ).
thf(func_def_13,type,
ord_less_nat: nat > nat > $o ).
thf(func_def_14,type,
ord_less_eq_int: int > int > $o ).
thf(func_def_15,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_16,type,
power_power_int: int > nat > int ).
thf(func_def_17,type,
power_power_nat: nat > nat > nat ).
thf(func_def_18,type,
twoSqu1013291560sum2sq: int > $o ).
thf(func_def_19,type,
m: int ).
thf(func_def_20,type,
s: int ).
thf(func_def_21,type,
t: int ).
thf(func_def_25,type,
sK0: int ).
thf(func_def_26,type,
sK1: int ).
thf(func_def_27,type,
sK2: int ).
thf(func_def_28,type,
sK3: int ).
thf(func_def_29,type,
sK4: int ).
thf(func_def_30,type,
vNOT: $o > $o ).
thf(f1,axiom,
ord_less_eq_int @ one_one_int @ t,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_tpos) ).
thf(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) ).
thf(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) ).
thf(f29,axiom,
! [X0: int,X1: int] :
( ( ord_less_int @ X0 @ X1 )
<=> ( ( X0 != X1 )
& ( ord_less_eq_int @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_zless__le) ).
thf(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) ).
thf(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]) ).
thf(f126,plain,
ord_less_eq_int @ one_one_int @ t,
inference(rectify,[],[f1]) ).
thf(f127,plain,
( ( ord_less_eq_int @ one_one_int @ t )
= $true ),
inference(fool_elimination,[],[f126]) ).
thf(f128,plain,
( ( 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 ) ) ),
inference(rectify,[],[f3]) ).
thf(f129,plain,
( ( ( ord_less_int @ one_one_int @ t )
= $true )
=> ? [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(fool_elimination,[],[f128]) ).
thf(f140,plain,
! [X0: int,X1: int] :
( ( ord_less_int @ X0 @ X1 )
<=> ( ( X0 != X1 )
& ( ord_less_eq_int @ X0 @ X1 ) ) ),
inference(rectify,[],[f29]) ).
thf(f141,plain,
! [X0: int,X1: int] :
( ( ( ord_less_int @ X0 @ X1 )
= $true )
<=> ( ( X0 != X1 )
& ( ( ord_less_eq_int @ X0 @ X1 )
= $true ) ) ),
inference(fool_elimination,[],[f140]) ).
thf(f230,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]) ).
thf(f231,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 )
!= $true ) ),
inference(ennf_transformation,[],[f129]) ).
thf(f245,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]) ).
thf(f246,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)],[f230]) ).
thf(f247,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 )
!= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f231]) ).
thf(f249,plain,
! [X0: int,X1: int] :
( ( ( ( ord_less_int @ X0 @ X1 )
= $true )
| ( X0 = X1 )
| ( ( ord_less_eq_int @ X0 @ X1 )
!= $true ) )
& ( ( ( X0 != X1 )
& ( ( ord_less_eq_int @ X0 @ X1 )
= $true ) )
| ( ( ord_less_int @ X0 @ X1 )
!= $true ) ) ),
inference(nnf_transformation,[],[f141]) ).
thf(f250,plain,
! [X0: int,X1: int] :
( ( ( ( ord_less_int @ X0 @ X1 )
= $true )
| ( X0 = X1 )
| ( ( ord_less_eq_int @ X0 @ X1 )
!= $true ) )
& ( ( ( X0 != X1 )
& ( ( ord_less_eq_int @ X0 @ X1 )
= $true ) )
| ( ( ord_less_int @ X0 @ X1 )
!= $true ) ) ),
inference(flattening,[],[f249]) ).
thf(f258,plain,
( ( ord_less_eq_int @ one_one_int @ t )
= $true ),
inference(cnf_transformation,[],[f127]) ).
thf(f259,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,[],[f246]) ).
thf(f260,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 )
!= $true ) ),
inference(cnf_transformation,[],[f247]) ).
thf(f288,plain,
! [X0: int,X1: int] :
( ( ( ord_less_eq_int @ X0 @ X1 )
!= $true )
| ( X0 = X1 )
| ( ( ord_less_int @ X0 @ X1 )
= $true ) ),
inference(cnf_transformation,[],[f250]) ).
thf(f392,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,[],[f245]) ).
thf(f504,plain,
( ( ord_less_int @ one_one_int @ t )
!= $true ),
inference(forward_subsumption_resolution,[],[f260,f392]) ).
thf(f505,plain,
one_one_int != t,
inference(forward_subsumption_resolution,[],[f259,f392]) ).
thf(f686,plain,
( ( $true != $true )
| ( one_one_int = t )
| ( ( ord_less_int @ one_one_int @ t )
= $true ) ),
inference(constrained_superposition,[],[f288,f258]) ).
thf(f687,plain,
( ( one_one_int = t )
| ( ( ord_less_int @ one_one_int @ t )
= $true ) ),
inference(trivial_inequality_removal,[],[f686]) ).
thf(f692,plain,
( ( ord_less_int @ one_one_int @ t )
= $true ),
inference(forward_subsumption_resolution,[],[f687,f505]) ).
thf(f693,plain,
$false,
inference(forward_subsumption_resolution,[],[f692,f504]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM926^1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 % Computer : n018.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.23 % CPULimit : 300
% 0.09/0.23 % WCLimit : 300
% 0.09/0.23 % DateTime : Tue Sep 29 13:07:56 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.22/0.26 Running first-order model finding
% 0.22/0.26 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.34 % (41163)Will run a generic schedule for satisfiability detection.
% 0.22/0.34 % (41169)% WARNING: option uhcvi not known.
% 0.22/0.34 % (41170)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2470515836:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.22/0.34 % (41168)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=998644673_2999 on theBenchmark for (2999ds/0Mi)
% 0.22/0.34 % (41172)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2737135801:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.22/0.34 % (41169)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4249642538:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.22/0.34 % (41172)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.34 % (41169)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.34 % Exception at run slice level
% 0.22/0.34 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.34 % (41169)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.22/0.34 % (41171)dis+10_1_sil=32000:sp=arity:random_seed=4293054285:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.22/0.34 % (41173)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3605976426:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.22/0.34 % (41174)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1191038708:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.22/0.34 % (41172) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-41163-41172"...
% 0.22/0.34 % (41172)...printing done.
% 0.22/0.34 % (41179)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2093387289:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.22/0.34 % (41172)Refutation found. Thanks to Tanya!
% 0.22/0.34 % SZS status Theorem for theBenchmark
% 0.22/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.34 % (41172)------------------------------
% 0.22/0.34 % (41172)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (41172)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (41172)CaDiCaL version: 2.1.3
% 0.22/0.34 % (41172)Termination reason: Refutation
% 0.22/0.34 % (41172)Time elapsed: 0.025 s
% 0.22/0.34 % (41172)Peak memory usage: 13 MB
% 0.22/0.34 % (41172)Instructions burned: 54 (million)
% 0.22/0.34 % (41163)Success in time 0.069 s
% 0.22/0.34 % Vampire exiting
%------------------------------------------------------------------------------