%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW498_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n020.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 : Sun Sep 27 09:10:41 AM UTC 2026
% Result : Theorem 38.97s 13.95s
% Output : Refutation 39.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 126
% Syntax : Number of formulae : 254 ( 126 unt; 0 typ; 0 def)
% Number of atoms : 476 ( 183 equ; 0 cnn)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 2295 ( 25 ~; 5 |; 46 &;2048 @)
% ( 26 <=>; 145 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 22 usr; 5 con; 0-3 aty)
% Number of variables : 322 ( 0 ^; 322 !; 0 ?; 322 :)
% Comments :
%------------------------------------------------------------------------------
thf(complex_type,type,
complex: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(int_type,type,
int: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(real_type,type,
real: $tType ).
thf(number_decl,type,
number:
!>[TA: $tType] : $o ).
thf(number_ring_decl,type,
number_ring:
!>[TA: $tType] : $o ).
thf(ring_char_0_decl,type,
ring_char_0:
!>[TA: $tType] : $o ).
thf(semiring_1_decl,type,
semiring_1:
!>[TA: $tType] : $o ).
thf(monoid_mult_decl,type,
monoid_mult:
!>[TA: $tType] : $o ).
thf(number_semiring_decl,type,
number_semiring:
!>[TA: $tType] : $o ).
thf(comm_semiring_1_decl,type,
comm_semiring_1:
!>[TA: $tType] : $o ).
thf(linordered_idom_decl,type,
linordered_idom:
!>[TA: $tType] : $o ).
thf(fundam1563812824_csqrt_decl,type,
fundam1563812824_csqrt: complex > complex ).
thf(abs_abs_decl,type,
abs_abs:
!>[TA: $tType] : ( TA > TA ) ).
thf(one_one_decl,type,
one_one:
!>[TA: $tType] : TA ).
thf(plus_plus_decl,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(times_times_decl,type,
times_times:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(bit0_decl,type,
bit0: int > int ).
thf(bit1_decl,type,
bit1: int > int ).
thf(min_decl,type,
min: int ).
thf(pls_decl,type,
pls: int ).
thf(number_number_of_decl,type,
number_number_of:
!>[TA: $tType] : ( int > TA ) ).
thf(ord_less_eq_decl,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(power_power_decl,type,
power_power:
!>[TA: $tType] : ( TA > nat > TA ) ).
thf(x_decl,type,
x: real ).
thf(y_decl,type,
y: real ).
thf(16,axiom,
int @ monoid_mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__mult) ).
thf(142,plain,
int @ monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(34,axiom,
! [A: int,B: int] :
( ( A @ ( B @ bit0 @ ( int @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ bit0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_mult__Bit0) ).
thf(196,plain,
! [A: int,B: int] :
( ( A @ ( B @ bit0 @ ( int @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(12,axiom,
int @ comm_semiring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring__1) ).
thf(138,plain,
int @ comm_semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(113,axiom,
real @ number_semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber__semiring) ).
thf(479,plain,
real @ number_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(52,axiom,
! [A: int] :
( ( A @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_rel__simps_I22_J) ).
thf(234,plain,
! [A: int] :
( ( ( A @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( A @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(125,axiom,
pls @ ( pls @ ( int @ ord_less_eq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_rel__simps_I19_J) ).
thf(523,plain,
pls @ ( pls @ ( int @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(70,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( A @ ( TA @ abs_abs ) @ ( A @ ( TA @ abs_abs ) @ ( TA @ times_times ) ) )
= ( A @ ( A @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_abs__mult__self) ).
thf(308,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( A @ ( TA @ abs_abs ) @ ( A @ ( TA @ abs_abs ) @ ( TA @ times_times ) ) )
= ( A @ ( A @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(42,axiom,
real @ one_one @ ( x @ ( pls @ bit1 @ bit0 @ ( real @ number_number_of ) @ ( real @ times_times ) ) @ ( real @ abs_abs ) @ ( real @ ord_less_eq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4__096abs_A_I2_A_K_Ax_J_A_060_061_A1_096) ).
thf(217,plain,
real @ one_one @ ( x @ ( pls @ bit1 @ bit0 @ ( real @ number_number_of ) @ ( real @ times_times ) ) @ ( real @ abs_abs ) @ ( real @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(61,axiom,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ( ( min @ ( TA @ number_number_of ) @ ( TA @ abs_abs ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_abs__minus__one) ).
thf(276,plain,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ( ( min @ ( TA @ number_number_of ) @ ( TA @ abs_abs ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(31,axiom,
real @ one_one @ ( y @ ( pls @ bit1 @ bit0 @ ( real @ number_number_of ) @ ( real @ times_times ) ) @ ( real @ abs_abs ) @ ( real @ ord_less_eq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5__096abs_A_I2_A_K_Ay_J_A_060_061_A1_096) ).
thf(185,plain,
real @ one_one @ ( y @ ( pls @ bit1 @ bit0 @ ( real @ number_number_of ) @ ( real @ times_times ) ) @ ( real @ abs_abs ) @ ( real @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(73,axiom,
( ( nat @ one_one )
= ( pls @ bit1 @ ( nat @ number_number_of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_Numeral1__eq1__nat) ).
thf(320,plain,
( ( nat @ one_one )
= ( pls @ bit1 @ ( nat @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(58,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_arith__simps_I32_J) ).
thf(257,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ ( TA @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(101,axiom,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int,B: int] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_le__number__of) ).
thf(416,plain,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) ) )
& ( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(49,axiom,
real @ one_one @ ( y @ ( pls @ bit1 @ bit0 @ ( real @ number_number_of ) @ ( real @ times_times ) ) @ ( real @ ord_less_eq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__0962_A_K_Ay_A_060_061_A1_096) ).
thf(228,plain,
real @ one_one @ ( y @ ( pls @ bit1 @ bit0 @ ( real @ number_number_of ) @ ( real @ times_times ) ) @ ( real @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(64,axiom,
nat @ monoid_mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__mult) ).
thf(289,plain,
nat @ monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(41,axiom,
real @ ring_char_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Oring__char__0) ).
thf(216,plain,
real @ ring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(29,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( TA @ abs_abs ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_abs__power2) ).
thf(179,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( TA @ abs_abs ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(123,axiom,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: nat,B: TA] :
( ( A @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) @ ( B @ ( TA @ power_power ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ power_power ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_power__even__eq) ).
thf(514,plain,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: nat,B: TA] :
( ( A @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) @ ( B @ ( TA @ power_power ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ power_power ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(83,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA] :
( ( pls @ bit1 @ ( TA @ number_number_of ) @ ( A @ ( TA @ times_times ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_mult__numeral__1__right) ).
thf(348,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA] :
( ( pls @ bit1 @ ( TA @ number_number_of ) @ ( A @ ( TA @ times_times ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(114,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA,B: int,C: int] :
( ( A @ ( B @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( C @ ( int @ times_times ) ) @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_mult__number__of__left) ).
thf(480,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA,B: int,C: int] :
( ( A @ ( B @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( C @ ( int @ times_times ) ) @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(44,axiom,
y @ ( pls @ bit1 @ bit0 @ ( real @ number_number_of ) @ ( real @ times_times ) ) @ ( min @ ( real @ number_number_of ) @ ( real @ ord_less_eq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42__096_N1_A_060_061_A2_A_K_Ay_096) ).
thf(221,plain,
y @ ( pls @ bit1 @ bit0 @ ( real @ number_number_of ) @ ( real @ times_times ) ) @ ( min @ ( real @ number_number_of ) @ ( real @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(66,axiom,
! [A: int] :
( ( A @ bit1 @ ( min @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( min @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_rel__simps_I26_J) ).
thf(293,plain,
! [A: int] :
( ( ( A @ ( min @ ( int @ ord_less_eq ) ) )
=> ( A @ bit1 @ ( min @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ bit1 @ ( min @ ( int @ ord_less_eq ) ) )
=> ( A @ ( min @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(6,axiom,
complex @ number,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Int_Onumber) ).
thf(132,plain,
complex @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(7,axiom,
int @ number_ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
thf(133,plain,
int @ number_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(54,axiom,
nat @ comm_semiring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring__1) ).
thf(243,plain,
nat @ comm_semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(127,axiom,
real @ linordered_idom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__idom) ).
thf(527,plain,
real @ linordered_idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(107,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( TA @ one_one @ ( A @ ( TA @ times_times ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(452,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( TA @ one_one @ ( A @ ( TA @ times_times ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(56,axiom,
! [TA: $tType] :
( ( TA @ number )
=> ! [A: TA,B: int] :
( ( ( B @ ( TA @ number_number_of ) )
= A )
<=> ( A
= ( B @ ( TA @ number_number_of ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_number__of__reorient) ).
thf(248,plain,
! [TA: $tType] :
( ( TA @ number )
=> ! [A: TA,B: int] :
( ( ( A
= ( B @ ( TA @ number_number_of ) ) )
=> ( ( B @ ( TA @ number_number_of ) )
= A ) )
& ( ( ( B @ ( TA @ number_number_of ) )
= A )
=> ( A
= ( B @ ( TA @ number_number_of ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(91,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( B @ ( int @ times_times ) ) @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_number__of__mult) ).
thf(380,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( B @ ( int @ times_times ) ) @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(122,axiom,
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( y @ ( real @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( x @ ( real @ power_power ) ) @ ( real @ plus_plus ) ) )
= ( real @ one_one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_xy) ).
thf(512,plain,
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( y @ ( real @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( x @ ( real @ power_power ) ) @ ( real @ plus_plus ) ) )
= ( real @ one_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(37,axiom,
( ( pls @ ( int @ number_number_of ) )
!= ( min @ ( int @ number_number_of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_eq__number__of__Pls__Min) ).
thf(201,plain,
( ( pls @ ( int @ number_number_of ) )
!= ( min @ ( int @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(88,axiom,
real @ one_one @ ( x @ ( pls @ bit1 @ bit0 @ ( real @ number_number_of ) @ ( real @ times_times ) ) @ ( real @ ord_less_eq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__0962_A_K_Ax_A_060_061_A1_096) ).
thf(366,plain,
real @ one_one @ ( x @ ( pls @ bit1 @ bit0 @ ( real @ number_number_of ) @ ( real @ times_times ) ) @ ( real @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(68,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: nat] :
( ( A @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) @ ( min @ ( TA @ number_number_of ) @ ( TA @ power_power ) ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_power__m1__even) ).
thf(302,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: nat] :
( ( A @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) @ ( min @ ( TA @ number_number_of ) @ ( TA @ power_power ) ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(59,axiom,
! [A: int] :
( ( ( A @ bit1 )
= min )
<=> ( A = min ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_rel__simps_I47_J) ).
thf(260,plain,
! [A: int] :
( ( ( A = min )
=> ( ( A @ bit1 )
= min ) )
& ( ( ( A @ bit1 )
= min )
=> ( A = min ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(99,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( TA @ times_times ) ) @ ( B @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(407,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( TA @ times_times ) ) @ ( B @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(104,axiom,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ times_times ) ) )
= ( int @ one_one ) )
=> ( ( B
= ( min @ ( int @ number_number_of ) ) )
| ( B
= ( int @ one_one ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_pos__zmult__eq__1__iff__lemma) ).
thf(429,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ times_times ) ) )
= ( int @ one_one ) )
=> ( ( B
= ( min @ ( int @ number_number_of ) ) )
| ( B
= ( int @ one_one ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(11,axiom,
int @ linordered_idom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
thf(137,plain,
int @ linordered_idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(50,axiom,
min != pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_rel__simps_I40_J) ).
thf(229,plain,
min != pls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(106,axiom,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ times_times ) ) )
= ( int @ one_one ) )
<=> ( ( ( A
= ( min @ ( int @ number_number_of ) ) )
& ( B
= ( min @ ( int @ number_number_of ) ) ) )
| ( ( A
= ( int @ one_one ) )
& ( B
= ( int @ one_one ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_zmult__eq__1__iff) ).
thf(435,plain,
! [A: int,B: int] :
( ( ( ( ( A
= ( min @ ( int @ number_number_of ) ) )
& ( B
= ( min @ ( int @ number_number_of ) ) ) )
| ( ( A
= ( int @ one_one ) )
& ( B
= ( int @ one_one ) ) ) )
=> ( ( A @ ( B @ ( int @ times_times ) ) )
= ( int @ one_one ) ) )
& ( ( ( A @ ( B @ ( int @ times_times ) ) )
= ( int @ one_one ) )
=> ( ( ( A
= ( min @ ( int @ number_number_of ) ) )
& ( B
= ( min @ ( int @ number_number_of ) ) ) )
| ( ( A
= ( int @ one_one ) )
& ( B
= ( int @ one_one ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(109,axiom,
! [A: int,B: int] :
( ( A @ ( int @ number_number_of ) @ ( B @ ( int @ number_number_of ) @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_less__eq__number__of__int__code) ).
thf(456,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ ( int @ number_number_of ) @ ( B @ ( int @ number_number_of ) @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ ( int @ number_number_of ) @ ( B @ ( int @ number_number_of ) @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(63,axiom,
! [A: int,B: int] :
( ( B @ bit0 )
!= ( A @ bit1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_rel__simps_I49_J) ).
thf(285,plain,
! [A: int,B: int] :
( ( B @ bit0 )
!= ( A @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(23,axiom,
! [A: nat] : ( A @ ( pls @ bit1 @ bit0 @ ( real @ number_number_of ) @ ( real @ power_power ) ) @ ( real @ one_one @ ( real @ ord_less_eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_two__realpow__ge__one) ).
thf(156,plain,
! [A: nat] : ( A @ ( pls @ bit1 @ bit0 @ ( real @ number_number_of ) @ ( real @ power_power ) ) @ ( real @ one_one @ ( real @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(33,axiom,
! [A: int] :
( ( pls
= ( A @ bit0 ) )
<=> ( pls = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_rel__simps_I38_J) ).
thf(188,plain,
! [A: int] :
( ( ( pls = A )
=> ( pls
= ( A @ bit0 ) ) )
& ( ( pls
= ( A @ bit0 ) )
=> ( pls = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(15,axiom,
int @ number_semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__semiring) ).
thf(141,plain,
int @ number_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(102,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( nat @ one_one @ ( A @ ( TA @ power_power ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(420,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( nat @ one_one @ ( A @ ( TA @ power_power ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(112,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( A @ ( TA @ one_one @ ( TA @ times_times ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(476,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( A @ ( TA @ one_one @ ( TA @ times_times ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(77,axiom,
! [A: int] :
( ( A @ ( pls @ ( int @ times_times ) ) )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_mult__Pls) ).
thf(328,plain,
! [A: int] :
( ( A @ ( pls @ ( int @ times_times ) ) )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(57,axiom,
nat @ number,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber) ).
thf(256,plain,
nat @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(27,axiom,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: nat] :
( ( A @ ( min @ ( TA @ number_number_of ) @ ( TA @ power_power ) ) @ ( TA @ abs_abs ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_abs__power__minus__one) ).
thf(173,plain,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: nat] :
( ( A @ ( min @ ( TA @ number_number_of ) @ ( TA @ power_power ) ) @ ( TA @ abs_abs ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(3,axiom,
int @ number,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
thf(129,plain,
int @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
complex @ number_ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Int_Onumber__ring) ).
thf(134,plain,
complex @ number_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,conjecture,
real @ one_one @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( x @ ( real @ power_power ) ) @ ( pls @ bit1 @ bit0 @ bit0 @ ( real @ number_number_of ) @ ( real @ times_times ) ) @ ( real @ ord_less_eq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( real @ one_one @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( x @ ( real @ power_power ) ) @ ( pls @ bit1 @ bit0 @ bit0 @ ( real @ number_number_of ) @ ( real @ times_times ) ) @ ( real @ ord_less_eq ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(128,plain,
~ ( real @ one_one @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( x @ ( real @ power_power ) ) @ ( pls @ bit1 @ bit0 @ bit0 @ ( real @ number_number_of ) @ ( real @ times_times ) ) @ ( real @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(55,axiom,
! [A: int] :
( ( A @ bit1 )
!= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_rel__simps_I46_J) ).
thf(244,plain,
! [A: int] :
( ( A @ bit1 )
!= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(86,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) )
= ( B @ ( A @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(360,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) )
= ( B @ ( A @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(121,axiom,
! [A: int] :
( ( A @ bit0 )
!= min ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_rel__simps_I45_J) ).
thf(508,plain,
! [A: int] :
( ( A @ bit0 )
!= min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(71,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( TA @ times_times ) ) @ ( D @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(311,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( TA @ times_times ) ) @ ( D @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(97,axiom,
! [A: int] :
( ( min
= ( A @ bit1 ) )
<=> ( min = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_rel__simps_I43_J) ).
thf(398,plain,
! [A: int] :
( ( ( min = A )
=> ( min
= ( A @ bit1 ) ) )
& ( ( min
= ( A @ bit1 ) )
=> ( min = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(20,axiom,
! [A: real] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( real @ power_power ) ) @ ( pls @ bit1 @ bit0 @ bit0 @ ( real @ number_number_of ) @ ( real @ times_times ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( pls @ bit1 @ bit0 @ ( real @ number_number_of ) @ ( real @ times_times ) ) @ ( real @ power_power ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_four__x__squared) ).
thf(148,plain,
! [A: real] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( real @ power_power ) ) @ ( pls @ bit1 @ bit0 @ bit0 @ ( real @ number_number_of ) @ ( real @ times_times ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( pls @ bit1 @ bit0 @ ( real @ number_number_of ) @ ( real @ times_times ) ) @ ( real @ power_power ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(25,axiom,
! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_less__eq__int__code_I14_J) ).
thf(161,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(62,axiom,
! [A: int] :
( ( pls @ ( A @ bit0 @ ( int @ ord_less_eq ) ) )
<=> ( pls @ ( A @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_rel__simps_I27_J) ).
thf(279,plain,
! [A: int] :
( ( ( pls @ ( A @ ( int @ ord_less_eq ) ) )
=> ( pls @ ( A @ bit0 @ ( int @ ord_less_eq ) ) ) )
& ( ( pls @ ( A @ bit0 @ ( int @ ord_less_eq ) ) )
=> ( pls @ ( A @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(28,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: nat,B: TA] :
( ( A @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) @ ( B @ ( TA @ power_power ) ) )
= ( A @ ( B @ ( TA @ power_power ) ) @ ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
thf(176,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: nat,B: TA] :
( ( A @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) @ ( B @ ( TA @ power_power ) ) )
= ( A @ ( B @ ( TA @ power_power ) ) @ ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(103,axiom,
! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_less__eq__int__code_I16_J) ).
thf(423,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(38,axiom,
! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_rel__simps_I32_J) ).
thf(204,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(95,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(391,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(18,axiom,
real @ number_ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber__ring) ).
thf(144,plain,
real @ number_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(119,axiom,
! [A: int,B: int] :
( ( A @ ( nat @ number_number_of ) @ ( B @ ( nat @ number_number_of ) @ ( nat @ ord_less_eq ) ) )
<=> ( ~ ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( pls @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_le__nat__number__of) ).
thf(498,plain,
! [A: int,B: int] :
( ( ( ~ ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( pls @ ( B @ ( int @ ord_less_eq ) ) ) )
=> ( A @ ( nat @ number_number_of ) @ ( B @ ( nat @ number_number_of ) @ ( nat @ ord_less_eq ) ) ) )
& ( ( A @ ( nat @ number_number_of ) @ ( B @ ( nat @ number_number_of ) @ ( nat @ ord_less_eq ) ) )
=> ( ~ ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( pls @ ( B @ ( int @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(111,axiom,
! [A: int,B: int] :
( ( ( B @ bit1 )
= ( A @ bit1 ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_rel__simps_I51_J) ).
thf(466,plain,
! [A: int,B: int] :
( ( ( B = A )
=> ( ( B @ bit1 )
= ( A @ bit1 ) ) )
& ( ( ( B @ bit1 )
= ( A @ bit1 ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(98,axiom,
pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( real @ one_one @ ( real @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( y @ ( pls @ bit1 @ bit0 @ ( real @ number_number_of ) @ ( real @ times_times ) ) @ ( real @ abs_abs ) @ ( real @ power_power ) ) @ ( real @ ord_less_eq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096abs_A_I2_A_K_Ay_J_A_094_A2_A_060_061_A1_A_094_A2_096) ).
thf(406,plain,
pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( real @ one_one @ ( real @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( y @ ( pls @ bit1 @ bit0 @ ( real @ number_number_of ) @ ( real @ times_times ) ) @ ( real @ abs_abs ) @ ( real @ power_power ) ) @ ( real @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(90,axiom,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ! [A: int,B: int] :
( ( B @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( ( A @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ ( TA @ number_number_of ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_semiring__mult__number__of) ).
thf(377,plain,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ! [A: int,B: int] :
( ( B @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( ( A @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ ( TA @ number_number_of ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(75,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( ( TA @ one_one @ ( TA @ abs_abs ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_abs__one) ).
thf(323,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( ( TA @ one_one @ ( TA @ abs_abs ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(14,axiom,
int @ semiring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
thf(140,plain,
int @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(40,axiom,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: TA] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) )
= ( A @ ( A @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_power2__eq__square) ).
thf(213,plain,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: TA] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) )
= ( A @ ( A @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(115,axiom,
! [A: int] :
( pls
!= ( A @ bit1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_rel__simps_I39_J) ).
thf(483,plain,
! [A: int] :
( pls
!= ( A @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(53,axiom,
! [A: complex] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ fundam1563812824_csqrt @ ( complex @ power_power ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_csqrt) ).
thf(240,plain,
! [A: complex] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ fundam1563812824_csqrt @ ( complex @ power_power ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(110,axiom,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
<=> ( pls @ bit1 @ ( A @ ( int @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_le__special_I4_J) ).
thf(462,plain,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( ( pls @ bit1 @ ( A @ ( int @ ord_less_eq ) ) )
=> ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) ) )
& ( ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
=> ( pls @ bit1 @ ( A @ ( int @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(82,axiom,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: TA] :
( ( pls @ bit1 @ bit1 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) )
= ( A @ ( A @ ( A @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_power3__eq__cube) ).
thf(345,plain,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: TA] :
( ( pls @ bit1 @ bit1 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) )
= ( A @ ( A @ ( A @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(89,axiom,
! [A: int,B: int] :
( ( ( B @ bit0 )
= ( A @ bit0 ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_rel__simps_I48_J) ).
thf(367,plain,
! [A: int,B: int] :
( ( ( B = A )
=> ( ( B @ bit0 )
= ( A @ bit0 ) ) )
& ( ( ( B @ bit0 )
= ( A @ bit0 ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(4,axiom,
complex @ monoid_mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Omonoid__mult) ).
thf(130,plain,
complex @ monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(108,axiom,
pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( real @ one_one @ ( real @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( x @ ( pls @ bit1 @ bit0 @ ( real @ number_number_of ) @ ( real @ times_times ) ) @ ( real @ abs_abs ) @ ( real @ power_power ) ) @ ( real @ ord_less_eq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__096abs_A_I2_A_K_Ax_J_A_094_A2_A_060_061_A1_A_094_A2_096) ).
thf(455,plain,
pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( real @ one_one @ ( real @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( x @ ( pls @ bit1 @ bit0 @ ( real @ number_number_of ) @ ( real @ times_times ) ) @ ( real @ abs_abs ) @ ( real @ power_power ) ) @ ( real @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(46,axiom,
pls != min,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_rel__simps_I37_J) ).
thf(223,plain,
pls != min,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(96,axiom,
! [A: int] :
( min
!= ( A @ bit0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_rel__simps_I42_J) ).
thf(394,plain,
! [A: int] :
( min
!= ( A @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(9,axiom,
complex @ ring_char_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Int_Oring__char__0) ).
thf(135,plain,
complex @ ring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(67,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(299,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(47,axiom,
pls @ ( min @ ( int @ ord_less_eq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_rel__simps_I23_J) ).
thf(226,plain,
pls @ ( min @ ( int @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(26,axiom,
! [A: int] :
( ( min @ ( A @ bit0 @ ( int @ ord_less_eq ) ) )
<=> ( min @ ( A @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_rel__simps_I28_J) ).
thf(167,plain,
! [A: int] :
( ( ( min @ ( A @ ( int @ ord_less_eq ) ) )
=> ( min @ ( A @ bit0 @ ( int @ ord_less_eq ) ) ) )
& ( ( min @ ( A @ bit0 @ ( int @ ord_less_eq ) ) )
=> ( min @ ( A @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(117,axiom,
! [TA: $tType] :
( ( ( TA @ ring_char_0 )
& ( TA @ number_ring ) )
=> ! [A: int,B: int] :
( ( ( B @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_eq__number__of) ).
thf(490,plain,
! [TA: $tType] :
( ( ( TA @ ring_char_0 )
& ( TA @ number_ring ) )
=> ! [A: int,B: int] :
( ( ( B = A )
=> ( ( B @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) ) ) )
& ( ( ( B @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(116,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( TA @ one_one )
= ( pls @ bit1 @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_semiring__norm_I110_J) ).
thf(487,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( TA @ one_one )
= ( pls @ bit1 @ ( TA @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(81,axiom,
! [A: nat,B: nat,C: int] :
( ( A @ ( B @ ( C @ ( int @ power_power ) ) @ ( int @ power_power ) ) )
= ( A @ ( B @ ( nat @ times_times ) ) @ ( C @ ( int @ power_power ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_zpower__zpower) ).
thf(342,plain,
! [A: nat,B: nat,C: int] :
( ( A @ ( B @ ( C @ ( int @ power_power ) ) @ ( int @ power_power ) ) )
= ( A @ ( B @ ( nat @ times_times ) ) @ ( C @ ( int @ power_power ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(19,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( TA @ one_one @ ( TA @ power_power ) ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_one__power2) ).
thf(145,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( TA @ one_one @ ( TA @ power_power ) ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(35,axiom,
nat @ semiring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(199,plain,
nat @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(30,axiom,
! [TA: $tType] :
( ( ( TA @ number )
& ( TA @ monoid_mult ) )
=> ! [A: int] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ number_number_of ) @ ( TA @ power_power ) ) )
= ( A @ ( TA @ number_number_of ) @ ( A @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_power2__eq__square__number__of) ).
thf(182,plain,
! [TA: $tType] :
( ( ( TA @ number )
& ( TA @ monoid_mult ) )
=> ! [A: int] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ number_number_of ) @ ( TA @ power_power ) ) )
= ( A @ ( TA @ number_number_of ) @ ( A @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(78,axiom,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_rel__simps_I31_J) ).
thf(331,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(80,axiom,
! [A: int,B: int] :
( ( B @ bit1 )
!= ( A @ bit0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_rel__simps_I50_J) ).
thf(338,plain,
! [A: int,B: int] :
( ( B @ bit1 )
!= ( A @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(22,axiom,
( ( int @ one_one )
= ( pls @ bit1 @ ( int @ number_number_of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_one__is__num__one) ).
thf(154,plain,
( ( int @ one_one )
= ( pls @ bit1 @ ( int @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(93,axiom,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ ord_less_eq ) ) )
<=> ( A @ ( pls @ bit1 @ ( int @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_le__special_I2_J) ).
thf(386,plain,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( ( A @ ( pls @ bit1 @ ( int @ ord_less_eq ) ) )
=> ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ ord_less_eq ) ) ) )
& ( ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( pls @ bit1 @ ( int @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(72,axiom,
! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_rel__simps_I34_J) ).
thf(314,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(17,axiom,
int @ ring_char_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
thf(143,plain,
int @ ring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(118,axiom,
real @ comm_semiring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ocomm__semiring__1) ).
thf(497,plain,
real @ comm_semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(87,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) @ ( B @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(363,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) @ ( B @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(126,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) )
= ( B @ ( A @ ( C @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(524,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) )
= ( B @ ( A @ ( C @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(43,axiom,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: nat] :
( ( A @ ( TA @ one_one @ ( TA @ power_power ) ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_power__one) ).
thf(218,plain,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: nat] :
( ( A @ ( TA @ one_one @ ( TA @ power_power ) ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(124,axiom,
! [A: int] :
( ( min @ ( A @ bit1 @ ( int @ ord_less_eq ) ) )
<=> ( min @ ( A @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_rel__simps_I30_J) ).
thf(517,plain,
! [A: int] :
( ( ( min @ ( A @ ( int @ ord_less_eq ) ) )
=> ( min @ ( A @ bit1 @ ( int @ ord_less_eq ) ) ) )
& ( ( min @ ( A @ bit1 @ ( int @ ord_less_eq ) ) )
=> ( min @ ( A @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(94,axiom,
min @ ( min @ ( int @ ord_less_eq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_rel__simps_I24_J) ).
thf(390,plain,
min @ ( min @ ( int @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(32,axiom,
( ( min @ bit1 )
= min ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_Bit1__Min) ).
thf(186,plain,
( ( min @ bit1 )
= min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(13,axiom,
complex @ number_semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Int_Onumber__semiring) ).
thf(139,plain,
complex @ number_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(24,axiom,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ( ( pls @ bit1 @ ( TA @ number_number_of ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_semiring__numeral__1__eq__1) ).
thf(158,plain,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ( ( pls @ bit1 @ ( TA @ number_number_of ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(84,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( TA @ times_times ) ) @ ( B @ ( D @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(351,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( TA @ times_times ) ) @ ( B @ ( D @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(65,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA] :
( ( A @ ( pls @ bit1 @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_mult__numeral__1) ).
thf(290,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA] :
( ( A @ ( pls @ bit1 @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(92,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: nat,B: nat,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ power_power ) ) @ ( TA @ power_power ) ) )
= ( A @ ( B @ ( nat @ times_times ) ) @ ( C @ ( TA @ power_power ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
thf(383,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: nat,B: nat,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ power_power ) ) @ ( TA @ power_power ) ) )
= ( A @ ( B @ ( nat @ times_times ) ) @ ( C @ ( TA @ power_power ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(21,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ abs_abs ) @ ( TA @ power_power ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_power2__abs) ).
thf(151,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ abs_abs ) @ ( TA @ power_power ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(105,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( pls @ bit1 @ ( TA @ number_number_of ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_numeral__1__eq__1) ).
thf(432,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( pls @ bit1 @ ( TA @ number_number_of ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(100,axiom,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_less__eq__int__code_I13_J) ).
thf(410,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(69,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ times_times ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
thf(305,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ times_times ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(39,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: nat,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ power_power ) ) )
= ( A @ ( B @ ( TA @ power_power ) ) @ ( A @ ( C @ ( TA @ power_power ) ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(210,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: nat,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ power_power ) ) )
= ( A @ ( B @ ( TA @ power_power ) ) @ ( A @ ( C @ ( TA @ power_power ) ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(76,axiom,
~ ( min @ ( pls @ ( int @ ord_less_eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_rel__simps_I20_J) ).
thf(326,plain,
~ ( min @ ( pls @ ( int @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(10,axiom,
complex @ comm_semiring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Ocomm__semiring__1) ).
thf(136,plain,
complex @ comm_semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(120,axiom,
( ( pls @ bit1 @ ( nat @ number_number_of ) )
= ( nat @ one_one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_nat__numeral__1__eq__1) ).
thf(506,plain,
( ( pls @ bit1 @ ( nat @ number_number_of ) )
= ( nat @ one_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(60,axiom,
! [A: int] :
( ( ( A @ bit0 )
= pls )
<=> ( A = pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_rel__simps_I44_J) ).
thf(268,plain,
! [A: int] :
( ( ( A = pls )
=> ( ( A @ bit0 )
= pls ) )
& ( ( ( A @ bit0 )
= pls )
=> ( A = pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(5,axiom,
complex @ semiring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Osemiring__1) ).
thf(131,plain,
complex @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(36,axiom,
x @ ( pls @ bit1 @ bit0 @ ( real @ number_number_of ) @ ( real @ times_times ) ) @ ( min @ ( real @ number_number_of ) @ ( real @ ord_less_eq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16__096_N1_A_060_061_A2_A_K_Ax_096) ).
thf(200,plain,
x @ ( pls @ bit1 @ bit0 @ ( real @ number_number_of ) @ ( real @ times_times ) ) @ ( min @ ( real @ number_number_of ) @ ( real @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(48,axiom,
real @ number,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber) ).
thf(227,plain,
real @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(74,axiom,
real @ monoid_mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Omonoid__mult) ).
thf(322,plain,
real @ monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(79,axiom,
nat @ number_semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber__semiring) ).
thf(337,plain,
nat @ number_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(85,axiom,
! [A: int] :
( ( A @ bit0 @ ( pls @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_rel__simps_I21_J) ).
thf(354,plain,
! [A: int] :
( ( ( A @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( A @ bit0 @ ( pls @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ bit0 @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(45,axiom,
real @ semiring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Osemiring__1) ).
thf(222,plain,
real @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(51,axiom,
( ( pls @ bit0 )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_Bit0__Pls) ).
thf(232,plain,
( ( pls @ bit0 )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(5085,plain,
$false,
inference(e,[status(thm)],[142,196,138,479,234,523,308,217,276,185,320,257,416,228,289,216,179,514,348,480,221,293,132,133,243,527,452,248,380,512,201,366,302,260,407,429,137,229,435,456,285,156,188,141,420,476,328,256,173,129,134,128,244,360,508,311,398,148,161,279,176,423,204,391,144,498,466,406,377,323,140,213,483,240,462,345,367,130,455,223,394,135,299,226,167,490,487,342,145,199,182,331,338,154,386,314,143,497,363,524,218,517,390,186,139,158,351,290,383,151,432,410,305,210,326,136,506,268,131,200,227,322,337,354,222,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW498_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.14/5.42 % Computer : n020.cluster.edu
% 0.14/5.42 % Model : x86_64 x86_64
% 0.14/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.42 % Memory : 8046.5625MB
% 0.14/5.42 % OS : Linux 6.8.0-71-generic
% 0.14/5.42 % CPULimit : 300
% 0.14/5.42 % WCLimit : 300
% 0.14/5.42 % DateTime : Sat Sep 26 16:10:25 UTC 2026
% 0.14/5.43 % CPUTime :
% 0.14/5.43 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.07/6.04 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.68/6.34 % [INFO] Parsing done (291ms).
% 1.68/6.35 % [INFO] Running in sequential loop mode.
% 2.57/6.77 % [INFO] eprover registered as external prover.
% 2.57/6.78 % [INFO] Scanning for conjecture ...
% 2.94/6.93 % [INFO] Found a conjecture (or negated_conjecture) and 127 axioms. Running axiom selection ...
% 3.21/7.04 % [INFO] Axiom selection finished. Selected 125 axioms (removed 2 axioms).
% 3.59/7.20 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.59/7.22 % [INFO] Type checking passed.
% 3.59/7.23 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 38.97/13.95 % External prover 'e' found a proof!
% 38.97/13.95 % [INFO] Killing All external provers ...
% 38.97/13.95 % Time passed: 8365ms (effective reasoning time: 7590ms)
% 38.97/13.95 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 38.97/13.95 % Axioms used in derivation (125): fact_57_power2__abs, arity_Complex_Ocomplex___Int_Onumber__ring, fact_7_one__power2, fact_27_rel__simps_I50_J, fact_14_power2__eq__square, fact_52_rel__simps_I23_J, arity_Nat_Onat___Groups_Omonoid__mult, arity_Int_Oint___Rings_Olinordered__idom, arity_Nat_Onat___Rings_Osemiring__1, fact_60_less__eq__number__of__int__code, arity_Int_Oint___Int_Oring__char__0, fact_37_rel__simps_I37_J, fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, fact_36_Bit1__Min, fact_23_mult__number__of__left, fact_69_less__eq__int__code_I14_J, arity_Complex_Ocomplex___Rings_Ocomm__semiring__1, fact_31_rel__simps_I34_J, arity_Nat_Onat___Int_Onumber__semiring, fact_17_Bit0__Pls, arity_RealDef_Oreal___Int_Onumber__semiring, fact_50_rel__simps_I26_J, fact_48_rel__simps_I21_J, arity_Complex_Ocomplex___Int_Oring__char__0, fact_32_rel__simps_I19_J, fact_68_one__is__num__one, fact_85_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, fact_61_zmult__eq__1__iff, fact_22_rel__simps_I48_J, fact_49_le__nat__number__of, fact_88_mult__numeral__1__right, fact_70_semiring__mult__number__of, fact_9_le__special_I4_J, arity_Int_Oint___Int_Onumber__ring, fact_1__096abs_A_I2_A_K_Ax_J_A_094_A2_A_060_061_A1_A_094_A2_096, fact_13_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J, fact_92_xy, fact_81_number__of__reorient, arity_Int_Oint___Int_Onumber__semiring, fact_67_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, fact_41_rel__simps_I24_J, arity_Int_Oint___Rings_Osemiring__1, fact_91_power3__eq__cube, fact_24_arith__simps_I32_J, fact_45_nat__numeral__1__eq__1, fact_40_rel__simps_I42_J, fact_87_mult__numeral__1, fact_96_csqrt, fact_93_abs__one, fact_64_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J, fact_18_eq__number__of, fact_63_pos__zmult__eq__1__iff__lemma, fact_2__0962_A_K_Ax_A_060_061_A1_096, arity_RealDef_Oreal___Rings_Ocomm__semiring__1, fact_66_less__eq__int__code_I13_J, fact_5__096abs_A_I2_A_K_Ay_J_A_060_061_A1_096, fact_29_rel__simps_I44_J, fact_71_Numeral1__eq1__nat, arity_RealDef_Oreal___Rings_Osemiring__1, fact_55_abs__minus__one, fact_43_le__number__of, fact_39_rel__simps_I45_J, fact_28_rel__simps_I49_J, arity_RealDef_Oreal___Int_Onumber__ring, fact_95_power__one, arity_Int_Oint___Groups_Omonoid__mult, fact_73_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, fact_47_rel__simps_I27_J, fact_33_rel__simps_I31_J, fact_19_rel__simps_I51_J, fact_59_eq__number__of__Pls__Min, arity_RealDef_Oreal___Rings_Olinordered__idom, fact_0__096abs_A_I2_A_K_Ay_J_A_094_A2_A_060_061_A1_A_094_A2_096, fact_12_two__realpow__ge__one, fact_3__0962_A_K_Ay_A_060_061_A1_096, fact_51_rel__simps_I30_J, fact_75_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J, fact_94_abs__mult__self, fact_56_abs__power__minus__one, fact_16__096_N1_A_060_061_A2_A_K_Ax_096, fact_82_power__even__eq, arity_Nat_Onat___Rings_Ocomm__semiring__1, fact_84_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, fact_44_rel__simps_I22_J, arity_RealDef_Oreal___Int_Oring__char__0, fact_76_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J, fact_54_rel__simps_I28_J, fact_26_rel__simps_I39_J, arity_Complex_Ocomplex___Rings_Osemiring__1, arity_Int_Oint___Rings_Ocomm__semiring__1, arity_Nat_Onat___Int_Onumber, fact_11_four__x__squared, fact_89_semiring__numeral__1__eq__1, fact_46_rel__simps_I32_J, fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, fact_86_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J, fact_90_semiring__norm_I110_J, fact_20_mult__Pls, arity_RealDef_Oreal___Groups_Omonoid__mult, fact_42__096_N1_A_060_061_A2_A_K_Ay_096, arity_Complex_Ocomplex___Groups_Omonoid__mult, fact_58_abs__power2, fact_8_le__special_I2_J, fact_72_power__m1__even, fact_62_zpower__zpower, fact_77_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, fact_65_less__eq__int__code_I16_J, fact_34_rel__simps_I47_J, fact_10_numeral__1__eq__1, arity_Complex_Ocomplex___Int_Onumber__semiring, fact_4__096abs_A_I2_A_K_Ax_J_A_060_061_A1_096, arity_Complex_Ocomplex___Int_Onumber, arity_RealDef_Oreal___Int_Onumber, arity_Int_Oint___Int_Onumber, fact_35_rel__simps_I43_J, fact_53_rel__simps_I20_J, fact_15_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J, fact_21_mult__Bit0, fact_83_number__of__mult, fact_6_power2__eq__square__number__of, fact_74_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, fact_38_rel__simps_I40_J, fact_25_rel__simps_I46_J, fact_80_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, fact_30_rel__simps_I38_J
% 38.97/13.95 % No. of inferences in proof: 254
% 38.97/13.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 8365 ms resp. 7590 ms w/o parsing
% 39.73/14.06 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 39.73/14.07 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------