%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM924^2 : 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 : n011.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 08:19:37 AM UTC 2026
% Result : Theorem 3.16s 0.79s
% Output : Refutation 3.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 15
% Syntax : Number of formulae : 72 ( 68 unt; 0 typ; 0 def)
% Number of atoms : 132 ( 72 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 766 ( 12 ~; 4 |; 1 &; 748 @)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 63 ( 60 usr; 18 con; 0-3 aty)
% Number of variables : 44 ( 0 ^; 44 !; 0 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
int: $tType ).
thf(type_def_6,type,
nat: $tType ).
thf(type_def_7,type,
real: $tType ).
thf(type_def_8,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
minus_minus_int: int > int > int ).
thf(func_def_1,type,
minus_minus_nat: nat > nat > nat ).
thf(func_def_2,type,
minus_minus_real: real > real > real ).
thf(func_def_3,type,
one_one_int: int ).
thf(func_def_4,type,
one_one_nat: nat ).
thf(func_def_5,type,
one_one_real: real ).
thf(func_def_6,type,
plus_plus_int: int > int > int ).
thf(func_def_7,type,
plus_plus_nat: nat > nat > nat ).
thf(func_def_8,type,
plus_plus_real: real > real > real ).
thf(func_def_9,type,
times_times_int: int > int > int ).
thf(func_def_10,type,
times_times_nat: nat > nat > nat ).
thf(func_def_11,type,
times_times_real: real > real > real ).
thf(func_def_12,type,
zero_zero_int: int ).
thf(func_def_13,type,
zero_zero_nat: nat ).
thf(func_def_14,type,
zero_zero_real: real ).
thf(func_def_15,type,
zcong: int > int > int > $o ).
thf(func_def_16,type,
zprime: int > $o ).
thf(func_def_17,type,
bit0: int > int ).
thf(func_def_18,type,
bit1: int > int ).
thf(func_def_19,type,
min: int ).
thf(func_def_20,type,
pls: int ).
thf(func_def_21,type,
number_number_of_int: int > int ).
thf(func_def_22,type,
number_number_of_nat: int > nat ).
thf(func_def_23,type,
number267125858f_real: int > real ).
thf(func_def_24,type,
ord_less_int: int > int > $o ).
thf(func_def_25,type,
ord_less_nat: nat > nat > $o ).
thf(func_def_26,type,
ord_less_real: real > real > $o ).
thf(func_def_27,type,
ord_less_eq_int: int > int > $o ).
thf(func_def_28,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_29,type,
ord_less_eq_real: real > real > $o ).
thf(func_def_30,type,
power_power_int: int > nat > int ).
thf(func_def_31,type,
power_power_nat: nat > nat > nat ).
thf(func_def_32,type,
power_power_real: real > nat > real ).
thf(func_def_33,type,
legendre: int > int > int ).
thf(func_def_34,type,
quadRes: int > int > $o ).
thf(func_def_35,type,
dvd_dvd_int: int > int > $o ).
thf(func_def_36,type,
dvd_dvd_nat: nat > nat > $o ).
thf(func_def_37,type,
dvd_dvd_real: real > real > $o ).
thf(func_def_38,type,
twoSqu362149276sum2sq: int > $o ).
thf(func_def_39,type,
m: int ).
thf(func_def_40,type,
s1: int ).
thf(func_def_41,type,
s: int ).
thf(func_def_42,type,
t: int ).
thf(func_def_46,type,
sP0: int > int > $o ).
thf(func_def_47,type,
sP1: int > int > $o ).
thf(func_def_48,type,
sP2: int > int > $o ).
thf(func_def_49,type,
sP3: int > $o ).
thf(func_def_50,type,
sP4: int > int > $o ).
thf(func_def_51,type,
sP5: int > int > $o ).
thf(func_def_52,type,
sP6: nat > real > $o ).
thf(func_def_53,type,
sK7: int ).
thf(func_def_54,type,
sK8: int ).
thf(func_def_55,type,
sK9: int ).
thf(func_def_56,type,
sK10: int > int ).
thf(func_def_57,type,
sK11: int ).
thf(func_def_58,type,
sK12: int > int > int > int ).
thf(func_def_59,type,
sK13: int > int > int ).
thf(func_def_60,type,
sK14: nat > real > real ).
thf(func_def_61,type,
vNOT: $o > $o ).
thf(f3,axiom,
ord_less_int @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096) ).
thf(f4,axiom,
( ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int )
= ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_t) ).
thf(f35,axiom,
! [X0: int] :
( ( number_number_of_int @ X0 )
= X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_number__of__is__id) ).
thf(f90,axiom,
! [X0: int,X1: int] :
( ( times_times_int @ ( bit0 @ X0 ) @ X1 )
= ( bit0 @ ( times_times_int @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_mult__Bit0) ).
thf(f170,axiom,
( ( bit0 @ pls )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_Bit0__Pls) ).
thf(f171,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_Pls__def) ).
thf(f320,axiom,
! [X0: int,X1: int,X2: int] :
( ( times_times_int @ X0 @ ( times_times_int @ X1 @ X2 ) )
= ( times_times_int @ ( times_times_int @ X0 @ X1 ) @ X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(f323,axiom,
! [X0: int,X1: int,X2: int] :
( ( times_times_int @ X0 @ ( times_times_int @ X1 @ X2 ) )
= ( times_times_int @ X1 @ ( times_times_int @ X0 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(f326,axiom,
! [X0: int,X1: int] :
( ( times_times_int @ X0 @ X1 )
= ( times_times_int @ X1 @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(f329,axiom,
! [X0: int,X1: int] :
( ( plus_plus_int @ X0 @ X1 )
= ( plus_plus_int @ X1 @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(f363,axiom,
! [X0: int] :
( ( times_times_int @ X0 @ zero_zero_int )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_362_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
thf(f372,axiom,
! [X0: int,X1: int] :
( ( X0
= ( plus_plus_int @ X0 @ X1 ) )
<=> ( X1 = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_371_add__0__iff) ).
thf(f417,axiom,
! [X0: int,X1: int] :
( ( plus_plus_int @ ( times_times_int @ X0 @ X1 ) @ X1 )
= ( times_times_int @ ( plus_plus_int @ X0 @ one_one_int ) @ X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_416_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(f439,axiom,
! [X0: int] :
( ( times_times_int @ X0 @ X0 )
= ( power_power_int @ X0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_438_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
thf(f699,conjecture,
ord_less_int @ ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) @ zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(f700,negated_conjecture,
~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) @ zero_zero_int ),
inference(negated_conjecture,[status(cth)],[f699]) ).
thf(f705,plain,
ord_less_int @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ zero_zero_int ),
inference(rectify,[],[f3]) ).
thf(f706,plain,
( ( ord_less_int @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ zero_zero_int ) )
= $true ),
inference(fool_elimination,[],[f705]) ).
thf(f1367,plain,
~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) @ zero_zero_int ),
inference(rectify,[],[f700]) ).
thf(f1368,plain,
( ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) @ zero_zero_int )
!= $true ),
inference(fool_elimination,[],[f1367]) ).
thf(f1403,plain,
( ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) @ zero_zero_int )
!= $true ),
inference(flattening,[],[f1368]) ).
thf(f1798,plain,
! [X0: int,X1: int] :
( ( ( X0
= ( plus_plus_int @ X0 @ X1 ) )
| ( zero_zero_int != X1 ) )
& ( ( X1 = zero_zero_int )
| ( ( plus_plus_int @ X0 @ X1 )
!= X0 ) ) ),
inference(nnf_transformation,[],[f372]) ).
thf(f1873,plain,
( ( ord_less_int @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ zero_zero_int ) )
= $true ),
inference(cnf_transformation,[],[f706]) ).
thf(f1874,plain,
( ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t )
= ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) ),
inference(cnf_transformation,[],[f4]) ).
thf(f1917,plain,
! [X0: int] :
( ( number_number_of_int @ X0 )
= X0 ),
inference(cnf_transformation,[],[f35]) ).
thf(f1983,plain,
! [X0: int,X1: int] :
( ( times_times_int @ ( bit0 @ X0 ) @ X1 )
= ( bit0 @ ( times_times_int @ X0 @ X1 ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f2098,plain,
( pls
= ( bit0 @ pls ) ),
inference(cnf_transformation,[],[f170]) ).
thf(f2099,plain,
zero_zero_int = pls,
inference(cnf_transformation,[],[f171]) ).
thf(f2261,plain,
! [X2: int,X0: int,X1: int] :
( ( times_times_int @ ( times_times_int @ X0 @ X1 ) @ X2 )
= ( times_times_int @ X0 @ ( times_times_int @ X1 @ X2 ) ) ),
inference(cnf_transformation,[],[f320]) ).
thf(f2264,plain,
! [X2: int,X0: int,X1: int] :
( ( times_times_int @ X0 @ ( times_times_int @ X1 @ X2 ) )
= ( times_times_int @ X1 @ ( times_times_int @ X0 @ X2 ) ) ),
inference(cnf_transformation,[],[f323]) ).
thf(f2267,plain,
! [X0: int,X1: int] :
( ( times_times_int @ X0 @ X1 )
= ( times_times_int @ X1 @ X0 ) ),
inference(cnf_transformation,[],[f326]) ).
thf(f2270,plain,
! [X0: int,X1: int] :
( ( plus_plus_int @ X0 @ X1 )
= ( plus_plus_int @ X1 @ X0 ) ),
inference(cnf_transformation,[],[f329]) ).
thf(f2308,plain,
! [X0: int] :
( zero_zero_int
= ( times_times_int @ X0 @ zero_zero_int ) ),
inference(cnf_transformation,[],[f363]) ).
thf(f2320,plain,
! [X0: int,X1: int] :
( ( ( plus_plus_int @ X0 @ X1 )
= X0 )
| ( zero_zero_int != X1 ) ),
inference(cnf_transformation,[],[f1798]) ).
thf(f2377,plain,
! [X0: int,X1: int] :
( ( plus_plus_int @ ( times_times_int @ X0 @ X1 ) @ X1 )
= ( times_times_int @ ( plus_plus_int @ X0 @ one_one_int ) @ X1 ) ),
inference(cnf_transformation,[],[f417]) ).
thf(f2408,plain,
! [X0: int] :
( ( power_power_int @ X0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_int @ X0 @ X0 ) ),
inference(cnf_transformation,[],[f439]) ).
thf(f2731,plain,
( ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) @ zero_zero_int )
!= $true ),
inference(cnf_transformation,[],[f1403]) ).
thf(f2735,plain,
( $true
= ( ord_less_int @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ pls ) ) ),
inference(definition_unfolding,[],[f1873,f2099]) ).
thf(f2809,plain,
! [X0: int] :
( pls
= ( times_times_int @ X0 @ pls ) ),
inference(definition_unfolding,[],[f2308,f2099,f2099]) ).
thf(f2812,plain,
! [X0: int,X1: int] :
( ( ( plus_plus_int @ X0 @ X1 )
= X0 )
| ( pls != X1 ) ),
inference(definition_unfolding,[],[f2320,f2099]) ).
thf(f2874,plain,
( $true
!= ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) @ pls ) ),
inference(definition_unfolding,[],[f2731,f2099]) ).
thf(f2924,plain,
! [X0: int] :
( ( plus_plus_int @ X0 @ pls )
= X0 ),
inference(equality_resolution,[],[f2812]) ).
thf(f3279,plain,
( ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t )
= ( plus_plus_int @ one_one_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(forward_demodulation,[],[f1874,f2270]) ).
thf(f3280,plain,
( $true
= ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ t ) @ t ) @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ pls ) ) ),
inference(forward_demodulation,[],[f2735,f2377]) ).
thf(f3333,plain,
( ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t )
= ( plus_plus_int @ one_one_int @ ( times_times_int @ s @ s ) ) ),
inference(forward_demodulation,[],[f3279,f2408]) ).
thf(f3334,plain,
( $true
= ( ord_less_int @ ( plus_plus_int @ t @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ t ) ) @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ pls ) ) ),
inference(forward_demodulation,[],[f3280,f2270]) ).
thf(f3378,plain,
( ( plus_plus_int @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ t ) @ t )
= ( plus_plus_int @ one_one_int @ ( times_times_int @ s @ s ) ) ),
inference(forward_demodulation,[],[f3333,f2377]) ).
thf(f3379,plain,
( $true
= ( ord_less_int @ ( plus_plus_int @ t @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ m @ t ) ) ) @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ pls ) ) ),
inference(forward_demodulation,[],[f3334,f2261]) ).
thf(f3398,plain,
( ( plus_plus_int @ t @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ t ) )
= ( plus_plus_int @ one_one_int @ ( times_times_int @ s @ s ) ) ),
inference(forward_demodulation,[],[f3378,f2270]) ).
thf(f3399,plain,
( $true
= ( ord_less_int @ ( plus_plus_int @ t @ ( times_times_int @ ( times_times_int @ m @ t ) @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ pls ) ) ),
inference(forward_demodulation,[],[f3379,f2267]) ).
thf(f3416,plain,
( ( plus_plus_int @ one_one_int @ ( times_times_int @ s @ s ) )
= ( plus_plus_int @ t @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ m @ t ) ) ) ),
inference(forward_demodulation,[],[f3398,f2261]) ).
thf(f3417,plain,
( $true
= ( ord_less_int @ ( plus_plus_int @ t @ ( times_times_int @ m @ ( times_times_int @ t @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ pls ) ) ),
inference(forward_demodulation,[],[f3399,f2261]) ).
thf(f3428,plain,
( ( plus_plus_int @ one_one_int @ ( times_times_int @ s @ s ) )
= ( plus_plus_int @ t @ ( times_times_int @ ( times_times_int @ m @ t ) @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ),
inference(forward_demodulation,[],[f3416,f2267]) ).
thf(f3429,plain,
( $true
= ( ord_less_int @ ( plus_plus_int @ t @ ( times_times_int @ t @ ( times_times_int @ m @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ pls ) ) ),
inference(forward_demodulation,[],[f3417,f2264]) ).
thf(f3437,plain,
( ( plus_plus_int @ one_one_int @ ( times_times_int @ s @ s ) )
= ( plus_plus_int @ t @ ( times_times_int @ m @ ( times_times_int @ t @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ),
inference(forward_demodulation,[],[f3428,f2261]) ).
thf(f3438,plain,
( $true
= ( ord_less_int @ ( plus_plus_int @ t @ ( times_times_int @ t @ ( times_times_int @ m @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) @ m ) @ one_one_int ) @ pls ) ) ),
inference(forward_demodulation,[],[f3429,f1917]) ).
thf(f3442,plain,
( ( plus_plus_int @ one_one_int @ ( times_times_int @ s @ s ) )
= ( plus_plus_int @ t @ ( times_times_int @ t @ ( times_times_int @ m @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ),
inference(forward_demodulation,[],[f3437,f2264]) ).
thf(f3443,plain,
( $true
= ( ord_less_int @ ( plus_plus_int @ t @ ( times_times_int @ t @ ( times_times_int @ m @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( plus_plus_int @ ( times_times_int @ ( times_times_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) @ m ) @ pls ) @ pls ) ) ),
inference(forward_demodulation,[],[f3438,f2377]) ).
thf(f3446,plain,
( ( plus_plus_int @ one_one_int @ ( times_times_int @ s @ s ) )
= ( plus_plus_int @ t @ ( times_times_int @ t @ ( times_times_int @ m @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ),
inference(forward_demodulation,[],[f3442,f1917]) ).
thf(f3447,plain,
( $true
= ( ord_less_int @ ( plus_plus_int @ t @ ( times_times_int @ t @ ( times_times_int @ m @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) @ m ) @ pls ) ) ),
inference(forward_demodulation,[],[f3443,f2924]) ).
thf(f3449,plain,
( $true
= ( ord_less_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ s @ s ) ) @ ( times_times_int @ ( times_times_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) @ m ) @ pls ) ) ),
inference(forward_demodulation,[],[f3447,f3446]) ).
thf(f3450,plain,
( $true
= ( ord_less_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ s @ s ) ) @ ( times_times_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( times_times_int @ m @ pls ) ) ) ),
inference(forward_demodulation,[],[f3449,f2261]) ).
thf(f3451,plain,
( $true
= ( ord_less_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ s @ s ) ) @ ( bit0 @ ( times_times_int @ ( bit0 @ ( bit1 @ pls ) ) @ ( times_times_int @ m @ pls ) ) ) ) ),
inference(forward_demodulation,[],[f3450,f1983]) ).
thf(f3452,plain,
( $true
= ( ord_less_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ s @ s ) ) @ ( bit0 @ ( bit0 @ ( times_times_int @ ( bit1 @ pls ) @ ( times_times_int @ m @ pls ) ) ) ) ) ),
inference(forward_demodulation,[],[f3451,f1983]) ).
thf(f3453,plain,
( $true
= ( ord_less_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ s @ s ) ) @ ( bit0 @ ( bit0 @ ( times_times_int @ m @ ( times_times_int @ ( bit1 @ pls ) @ pls ) ) ) ) ) ),
inference(forward_demodulation,[],[f3452,f2264]) ).
thf(f3454,plain,
( $true
= ( ord_less_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ s @ s ) ) @ ( bit0 @ ( bit0 @ ( times_times_int @ m @ pls ) ) ) ) ),
inference(forward_demodulation,[],[f3453,f2809]) ).
thf(f3455,plain,
( $true
= ( ord_less_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ s @ s ) ) @ ( bit0 @ ( bit0 @ pls ) ) ) ),
inference(forward_demodulation,[],[f3454,f2809]) ).
thf(f3456,plain,
( $true
= ( ord_less_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ s @ s ) ) @ ( bit0 @ pls ) ) ),
inference(forward_demodulation,[],[f3455,f2098]) ).
thf(f3457,plain,
( $true
= ( ord_less_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ s @ s ) ) @ pls ) ),
inference(forward_demodulation,[],[f3456,f2098]) ).
thf(f3819,plain,
( $true
!= ( ord_less_int @ ( plus_plus_int @ one_one_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ pls ) ),
inference(constrained_superposition,[],[f2874,f2270]) ).
thf(f3822,plain,
( $true
!= ( ord_less_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ s @ s ) ) @ pls ) ),
inference(forward_demodulation,[],[f3819,f2408]) ).
thf(f3824,plain,
$false,
inference(forward_subsumption_resolution,[],[f3822,f3457]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM924^2 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n011.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 13:05:31 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 3.16/0.79 % (59234)Will run a generic schedule for satisfiability detection.
% 3.16/0.79 % (59240)% WARNING: option uhcvi not known.
% 3.16/0.79 % (59242)dis+10_1_sil=32000:sp=arity:random_seed=3638524551:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 3.16/0.79 % (59243)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1157615724:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 3.16/0.79 % (59240)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2363911972:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 3.16/0.79 % (59241)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1144443590:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 3.16/0.79 % (59244)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=897130191:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 3.16/0.79 % (59245)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2022146371:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 3.16/0.79 % (59239)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1051186658_2999 on theBenchmark for (2999ds/0Mi)
% 3.16/0.79 % (59243)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.16/0.79 % (59240)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.16/0.79 % (59244)Instruction limit reached!
% 3.16/0.79 % (59244)------------------------------
% 3.16/0.79 % (59244)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.16/0.79 % (59244)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.16/0.79 % (59244)CaDiCaL version: 2.1.3
% 3.16/0.79 % (59244)Termination reason: Instruction limit
% 3.16/0.79 % (59244)Termination phase: Property scanning
% 3.16/0.79 % (59244)Time elapsed: 0.031 s
% 3.16/0.79 % (59244)Peak memory usage: 12 MB
% 3.16/0.79 % (59244)Instructions burned: 132 (million)
% 3.16/0.79 % (59253)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2480593525:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 3.16/0.79 % (59243)Instruction limit reached!
% 3.16/0.79 % (59243)------------------------------
% 3.16/0.79 % (59243)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.16/0.79 % (59243)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.16/0.79 % (59243)CaDiCaL version: 2.1.3
% 3.16/0.79 % (59243)Termination reason: Instruction limit
% 3.16/0.79 % (59243)Termination phase: Property scanning
% 3.16/0.79 % (59243)Time elapsed: 0.048 s
% 3.16/0.79 % (59243)Peak memory usage: 11 MB
% 3.16/0.79 % (59243)Instructions burned: 117 (million)
% 3.16/0.79 % (59242)Instruction limit reached!
% 3.16/0.79 % (59242)------------------------------
% 3.16/0.79 % (59242)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.16/0.79 % (59242)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.16/0.79 % (59242)CaDiCaL version: 2.1.3
% 3.16/0.79 % (59242)Termination reason: Instruction limit
% 3.16/0.79 % (59242)Termination phase: Property scanning
% 3.16/0.79 % (59242)Time elapsed: 0.050 s
% 3.16/0.79 % (59242)Peak memory usage: 11 MB
% 3.16/0.79 % (59242)Instructions burned: 104 (million)
% 3.16/0.79 % (59240)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.16/0.79 % Exception at run slice level
% 3.16/0.79 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.16/0.79 % (59255)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3461406698:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 3.16/0.79 % Exception at run slice level
% 3.16/0.79 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.16/0.79 % (59256)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=800376236:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 3.16/0.79 % (59259)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2106294071:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 3.16/0.79 % (59245)Instruction limit reached!
% 3.16/0.79 % (59245)------------------------------
% 3.16/0.79 % (59245)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.16/0.79 % (59245)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.16/0.79 % (59245)CaDiCaL version: 2.1.3
% 3.16/0.79 % (59245)Termination reason: Instruction limit
% 3.16/0.79 % (59245)Termination phase: Saturation
% 3.16/0.79 % (59245)Time elapsed: 0.078 s
% 3.16/0.79 % (59245)Peak memory usage: 13 MB
% 3.16/0.79 % (59245)Instructions burned: 161 (million)
% 3.16/0.79 % (59257)ott-21_1_sil=16000:fs=off:random_seed=2636127900:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 3.16/0.79 % (59256)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.16/0.79 % (59262)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=250922049:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 3.16/0.79 % (59255)Instruction limit reached!
% 3.16/0.79 % (59255)------------------------------
% 3.16/0.79 % (59255)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.16/0.79 % (59255)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.16/0.79 % (59255)CaDiCaL version: 2.1.3
% 3.16/0.79 % (59255)Termination reason: Instruction limit
% 3.16/0.79 % (59255)Termination phase: Property scanning
% 3.16/0.79 % (59255)Time elapsed: 0.053 s
% 3.16/0.79 % (59255)Peak memory usage: 11 MB
% 3.16/0.79 % (59255)Instructions burned: 131 (million)
% 3.16/0.79 % (59265)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3630175086:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 3.16/0.79 % (59256)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.16/0.79 % (59257)Instruction limit reached!
% 3.16/0.79 % (59257)------------------------------
% 3.16/0.79 % (59257)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.16/0.79 % (59257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.16/0.79 % (59257)CaDiCaL version: 2.1.3
% 3.16/0.79 % (59257)Termination reason: Instruction limit
% 3.16/0.79 % (59257)Termination phase: Saturation
% 3.16/0.79 % (59257)Time elapsed: 0.091 s
% 3.16/0.79 % (59257)Peak memory usage: 13 MB
% 3.16/0.79 % (59257)Instructions burned: 182 (million)
% 3.16/0.79 % (59267)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2694190197:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 3.16/0.79 % Exception at run slice level
% 3.16/0.79 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.16/0.79 % (59259)Instruction limit reached!
% 3.16/0.79 % (59259)------------------------------
% 3.16/0.79 % (59259)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.16/0.79 % (59259)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.16/0.79 % (59259)CaDiCaL version: 2.1.3
% 3.16/0.79 % (59259)Termination reason: Instruction limit
% 3.16/0.79 % (59259)Termination phase: Saturation
% 3.16/0.79 % (59259)Time elapsed: 0.134 s
% 3.16/0.79 % (59259)Peak memory usage: 14 MB
% 3.16/0.79 % (59259)Instructions burned: 480 (million)
% 3.16/0.79 % (59270)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=2597703847:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 3.16/0.79 % (59269)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=2632886766:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 3.16/0.79 % (59270)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.16/0.79 % (59269)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.16/0.79 % Exception at run slice level
% 3.16/0.79 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.16/0.79 % (59273)fmb+10_1_sil=64000:random_seed=3498001224:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 3.16/0.79 % (59273)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.16/0.79 % Exception at run slice level
% 3.16/0.79 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.16/0.79 % (59277)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=3216533455:i=9515:nm=5_2995 on theBenchmark for (2995ds/9515Mi)
% 3.16/0.79 % (59270)Instruction limit reached!
% 3.16/0.79 % (59270)------------------------------
% 3.16/0.79 % (59270)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.16/0.79 % (59270)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.16/0.79 % (59270)CaDiCaL version: 2.1.3
% 3.16/0.79 % (59270)Termination reason: Instruction limit
% 3.16/0.79 % (59270)Termination phase: Saturation
% 3.16/0.79 % (59270)Time elapsed: 0.227 s
% 3.16/0.79 % (59270)Peak memory usage: 16 MB
% 3.16/0.79 % (59270)Instructions burned: 881 (million)
% 3.16/0.79 % (59279)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=2818100686:fmbsr=1.7:i=920_2994 on theBenchmark for (2994ds/920Mi)
% 3.16/0.79 % Exception at run slice level
% 3.16/0.79 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.16/0.79 % Exception at run slice level
% 3.16/0.79 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.16/0.79 % (59281)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=2740152468:i=5131_2994 on theBenchmark for (2994ds/5131Mi)
% 3.16/0.79 % (59269) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-59234-59269"...
% 3.16/0.79 % (59269)...printing done.
% 3.16/0.79 % (59269)Refutation found. Thanks to Tanya!
% 3.16/0.79 % SZS status Theorem for theBenchmark
% 3.16/0.79 % SZS output start Proof for theBenchmark
% See solution above
% 3.16/0.79 % (59269)------------------------------
% 3.16/0.79 % (59269)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.16/0.79 % (59269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.16/0.79 % (59269)CaDiCaL version: 2.1.3
% 3.16/0.79 % (59269)Termination reason: Refutation
% 3.16/0.79 % (59269)Time elapsed: 0.286 s
% 3.16/0.79 % (59269)Peak memory usage: 16 MB
% 3.16/0.79 % (59269)Instructions burned: 336 (million)
% 3.16/0.79 % (59234)Success in time 0.569 s
% 3.16/0.79 % Vampire exiting
%------------------------------------------------------------------------------