%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM925^1 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 : Wed Sep 30 08:19:38 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 100 ( 57 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 213 ( 26 ~; 19 |; 9 &; 155 @)
% ( 4 <=>; 0 =>; 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 : 24 ( 21 usr; 9 con; 0-2 aty)
% Number of variables : 34 ( 0 ^; 34 !; 0 ?; 34 :)
% 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,
zero_zero_int: int ).
thf(func_def_5,type,
zero_zero_nat: nat ).
thf(func_def_6,type,
bit0: int > int ).
thf(func_def_7,type,
bit1: int > int ).
thf(func_def_8,type,
pls: int ).
thf(func_def_9,type,
number_number_of_int: int > int ).
thf(func_def_10,type,
number_number_of_nat: int > nat ).
thf(func_def_11,type,
semiri1621563631at_int: nat > int ).
thf(func_def_12,type,
semiri984289939at_nat: nat > nat ).
thf(func_def_13,type,
ord_less_int: int > int > $o ).
thf(func_def_14,type,
ord_less_nat: nat > nat > $o ).
thf(func_def_15,type,
power_power_int: int > nat > int ).
thf(func_def_16,type,
power_power_nat: nat > nat > nat ).
thf(func_def_17,type,
n: nat ).
thf(func_def_18,type,
t: int ).
thf(func_def_22,type,
vNOT: $o > $o ).
thf(f53,axiom,
! [X0: int,X1: int] :
( ( plus_plus_int @ X0 @ X1 )
= ( plus_plus_int @ X1 @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_zadd__commute) ).
thf(f66,axiom,
! [X0: int,X1: int] :
( ( ord_less_int @ X0 @ ( plus_plus_int @ X1 @ one_one_int ) )
<=> ( ( X0 = X1 )
| ( ord_less_int @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_zless__add1__eq) ).
thf(f67,axiom,
! [X0: nat] :
~ ( ord_less_int @ ( semiri1621563631at_int @ X0 ) @ zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_int__less__0__conv) ).
thf(f79,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_Pls__def) ).
thf(f93,axiom,
! [X0: int,X1: int] :
( ( ( power_power_int @ X0 @ ( number_number_of_nat @ X1 ) )
= zero_zero_int )
<=> ( ( ( number_number_of_nat @ X1 )
!= zero_zero_nat )
& ( X0 = zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_power__eq__0__iff__number__of) ).
thf(f107,conjecture,
( ( power_power_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(f108,negated_conjecture,
~ ( ( ( power_power_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int ) ),
inference(negated_conjecture,[status(cth)],[f107]) ).
thf(f159,plain,
! [X0: int,X1: int] :
( ( ord_less_int @ X0 @ ( plus_plus_int @ X1 @ one_one_int ) )
<=> ( ( X0 = X1 )
| ( ord_less_int @ X0 @ X1 ) ) ),
inference(rectify,[],[f66]) ).
thf(f160,plain,
! [X0: int,X1: int] :
( ( ( ord_less_int @ X0 @ ( plus_plus_int @ X1 @ one_one_int ) )
= $true )
<=> ( ( X0 = X1 )
| ( ( ord_less_int @ X0 @ X1 )
= $true ) ) ),
inference(fool_elimination,[],[f159]) ).
thf(f161,plain,
! [X0: nat] :
~ ( ord_less_int @ ( semiri1621563631at_int @ X0 ) @ zero_zero_int ),
inference(rectify,[],[f67]) ).
thf(f162,plain,
! [X0: nat] :
( ( ord_less_int @ ( semiri1621563631at_int @ X0 ) @ zero_zero_int )
!= $true ),
inference(fool_elimination,[],[f161]) ).
thf(f178,plain,
! [X0: nat] :
( ( ord_less_int @ ( semiri1621563631at_int @ X0 ) @ zero_zero_int )
!= $true ),
inference(flattening,[],[f162]) ).
thf(f180,plain,
( zero_zero_int
= ( power_power_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(flattening,[],[f108]) ).
thf(f195,plain,
! [X0: int,X1: int] :
( ( ( ( ord_less_int @ X0 @ ( plus_plus_int @ X1 @ one_one_int ) )
= $true )
| ( ( X0 != X1 )
& ( ( ord_less_int @ X0 @ X1 )
!= $true ) ) )
& ( ( X0 = X1 )
| ( ( ord_less_int @ X0 @ X1 )
= $true )
| ( ( ord_less_int @ X0 @ ( plus_plus_int @ X1 @ one_one_int ) )
!= $true ) ) ),
inference(nnf_transformation,[],[f160]) ).
thf(f196,plain,
! [X0: int,X1: int] :
( ( ( ( ord_less_int @ X0 @ ( plus_plus_int @ X1 @ one_one_int ) )
= $true )
| ( ( X0 != X1 )
& ( ( ord_less_int @ X0 @ X1 )
!= $true ) ) )
& ( ( X0 = X1 )
| ( ( ord_less_int @ X0 @ X1 )
= $true )
| ( ( ord_less_int @ X0 @ ( plus_plus_int @ X1 @ one_one_int ) )
!= $true ) ) ),
inference(flattening,[],[f195]) ).
thf(f200,plain,
! [X0: int,X1: int] :
( ( ( ( power_power_int @ X0 @ ( number_number_of_nat @ X1 ) )
= zero_zero_int )
| ( zero_zero_nat
= ( number_number_of_nat @ X1 ) )
| ( zero_zero_int != X0 ) )
& ( ( ( ( number_number_of_nat @ X1 )
!= zero_zero_nat )
& ( X0 = zero_zero_int ) )
| ( zero_zero_int
!= ( power_power_int @ X0 @ ( number_number_of_nat @ X1 ) ) ) ) ),
inference(nnf_transformation,[],[f93]) ).
thf(f201,plain,
! [X0: int,X1: int] :
( ( ( ( power_power_int @ X0 @ ( number_number_of_nat @ X1 ) )
= zero_zero_int )
| ( zero_zero_nat
= ( number_number_of_nat @ X1 ) )
| ( zero_zero_int != X0 ) )
& ( ( ( ( number_number_of_nat @ X1 )
!= zero_zero_nat )
& ( X0 = zero_zero_int ) )
| ( zero_zero_int
!= ( power_power_int @ X0 @ ( number_number_of_nat @ X1 ) ) ) ) ),
inference(flattening,[],[f200]) ).
thf(f272,plain,
! [X0: int,X1: int] :
( ( plus_plus_int @ X0 @ X1 )
= ( plus_plus_int @ X1 @ X0 ) ),
inference(cnf_transformation,[],[f53]) ).
thf(f288,plain,
! [X0: int,X1: int] :
( ( ( ord_less_int @ X0 @ ( plus_plus_int @ X1 @ one_one_int ) )
= $true )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f196]) ).
thf(f289,plain,
! [X0: nat] :
( ( ord_less_int @ ( semiri1621563631at_int @ X0 ) @ zero_zero_int )
!= $true ),
inference(cnf_transformation,[],[f178]) ).
thf(f304,plain,
zero_zero_int = pls,
inference(cnf_transformation,[],[f79]) ).
thf(f318,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = X0 )
| ( zero_zero_int
!= ( power_power_int @ X0 @ ( number_number_of_nat @ X1 ) ) ) ),
inference(cnf_transformation,[],[f201]) ).
thf(f339,plain,
( zero_zero_int
= ( power_power_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(cnf_transformation,[],[f180]) ).
thf(f362,plain,
! [X0: nat] :
( $true
!= ( ord_less_int @ ( semiri1621563631at_int @ X0 ) @ pls ) ),
inference(definition_unfolding,[],[f289,f304]) ).
thf(f374,plain,
! [X0: int,X1: int] :
( ( pls
!= ( power_power_int @ X0 @ ( number_number_of_nat @ X1 ) ) )
| ( pls = X0 ) ),
inference(definition_unfolding,[],[f318,f304,f304]) ).
thf(f382,plain,
( pls
= ( power_power_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(definition_unfolding,[],[f339,f304]) ).
thf(f395,plain,
! [X1: int] :
( $true
= ( ord_less_int @ X1 @ ( plus_plus_int @ X1 @ one_one_int ) ) ),
inference(equality_resolution,[],[f288]) ).
thf(f1648,plain,
( ( pls != pls )
| ( ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) )
= pls ) ),
inference(constrained_superposition,[],[f374,f382]) ).
thf(f1651,plain,
( ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) )
= pls ),
inference(trivial_inequality_removal,[],[f1648]) ).
thf(f1699,plain,
! [X0: int] :
( $true
= ( ord_less_int @ X0 @ ( plus_plus_int @ one_one_int @ X0 ) ) ),
inference(constrained_superposition,[],[f395,f272]) ).
thf(f1705,plain,
( $true
= ( ord_less_int @ ( semiri1621563631at_int @ n ) @ pls ) ),
inference(constrained_superposition,[],[f1699,f1651]) ).
thf(f1706,plain,
$false,
inference(forward_subsumption_resolution,[],[f1705,f362]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM925^1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.19 % Computer : n019.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 13:05:48 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.22 Running first-order model finding
% 0.10/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.28 % (728601)Will run a generic schedule for satisfiability detection.
% 0.20/0.28 % (728610)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1390268888:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.28 % (728608)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=794008090_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.28 % (728611)dis+10_1_sil=32000:sp=arity:random_seed=264204985:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.28 % (728612)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=381212151:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.28 % (728609)% WARNING: option uhcvi not known.
% 0.20/0.28 % (728612)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.28 % Exception at run slice level
% 0.20/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.28 % (728609)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=987469308:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.28 % (728609)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.28 % (728614)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3937627951:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.28 % (728613)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2218932866:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.28 % (728610) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-728601-728610"...
% 0.20/0.28 % (728609)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.28 % (728610)...printing done.
% 0.20/0.28 % (728610)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (728610)------------------------------
% 0.20/0.28 % (728610)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (728610)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (728610)CaDiCaL version: 2.1.3
% 0.20/0.28 % (728610)Termination reason: Refutation
% 0.20/0.28 % (728610)Time elapsed: 0.025 s
% 0.20/0.28 % (728610)Peak memory usage: 13 MB
% 0.20/0.28 % (728610)Instructions burned: 83 (million)
% 0.20/0.28 % (728601)Success in time 0.058 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------