%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM925+1 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 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 : Sun Sep 27 08:10:22 AM UTC 2026
% Result : Theorem 6.71s 4.06s
% Output : Refutation 7.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 107
% Syntax : Number of formulae : 216 ( 134 unt; 0 typ; 0 def)
% Number of atoms : 405 ( 246 equ; 0 cnn)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 1413 ( 48 ~; 10 |; 53 &;1176 @)
% ( 36 <=>; 90 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 19 usr; 8 con; 0-2 aty)
% Number of variables : 236 ( 0 ^; 236 !; 0 ?; 236 :)
% Comments :
%------------------------------------------------------------------------------
thf(power_power_int_decl,type,
power_power_int: $i > $i > $i ).
thf(plus_plus_int_decl,type,
plus_plus_int: $i > $i > $i ).
thf(one_one_int_decl,type,
one_one_int: $i ).
thf(semiri1621563631at_int_decl,type,
semiri1621563631at_int: $i > $i ).
thf(n_decl,type,
n: $i ).
thf(number_number_of_nat_decl,type,
number_number_of_nat: $i > $i ).
thf(bit0_decl,type,
bit0: $i > $i ).
thf(bit1_decl,type,
bit1: $i > $i ).
thf(pls_decl,type,
pls: $i ).
thf(zero_zero_int_decl,type,
zero_zero_int: $i ).
thf(number_number_of_int_decl,type,
number_number_of_int: $i > $i ).
thf(ord_less_int_decl,type,
ord_less_int: $i > $i > $o ).
thf(power_power_nat_decl,type,
power_power_nat: $i > $i > $i ).
thf(zero_zero_nat_decl,type,
zero_zero_nat: $i ).
thf(semiri984289939at_nat_decl,type,
semiri984289939at_nat: $i > $i ).
thf(one_one_nat_decl,type,
one_one_nat: $i ).
thf(ord_less_nat_decl,type,
ord_less_nat: $i > $i > $o ).
thf(t_decl,type,
t: $i ).
thf(plus_plus_nat_decl,type,
plus_plus_nat: $i > $i > $i ).
thf(58,axiom,
! [A: $i] :
( ( A @ number_number_of_int @ ( zero_zero_int @ ord_less_int ) )
<=> ( A @ ( pls @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_less__special_I1_J) ).
thf(352,plain,
! [A: $i] :
( ( ( A @ ( pls @ ord_less_int ) )
=> ( A @ number_number_of_int @ ( zero_zero_int @ ord_less_int ) ) )
& ( ( A @ number_number_of_int @ ( zero_zero_int @ ord_less_int ) )
=> ( A @ ( pls @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B @ number_number_of_int @ ( A @ number_number_of_int @ ord_less_int ) )
<=> ( B @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_less__number__of) ).
thf(125,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ord_less_int ) )
=> ( B @ number_number_of_int @ ( A @ number_number_of_int @ ord_less_int ) ) )
& ( ( B @ number_number_of_int @ ( A @ number_number_of_int @ ord_less_int ) )
=> ( B @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(74,axiom,
! [A: $i] :
( ( zero_zero_int @ ( A @ plus_plus_int ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_zadd__0__right) ).
thf(429,plain,
! [A: $i] :
( ( zero_zero_int @ ( A @ plus_plus_int ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(105,axiom,
! [A: $i,B: $i] :
( ( ~ ( pls @ ( B @ ord_less_int ) )
=> ( ( ~ ( pls @ ( A @ ord_less_int ) )
=> ( ( A @ number_number_of_nat @ ( B @ number_number_of_nat @ plus_plus_nat ) )
= ( A @ ( B @ plus_plus_int ) @ number_number_of_nat ) ) )
& ( ( pls @ ( A @ ord_less_int ) )
=> ( ( A @ number_number_of_nat @ ( B @ number_number_of_nat @ plus_plus_nat ) )
= ( B @ number_number_of_nat ) ) ) ) )
& ( ( pls @ ( B @ ord_less_int ) )
=> ( ( A @ number_number_of_nat @ ( B @ number_number_of_nat @ plus_plus_nat ) )
= ( A @ number_number_of_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_add__nat__number__of) ).
thf(557,plain,
! [A: $i,B: $i] :
( ( ~ ( pls @ ( B @ ord_less_int ) )
=> ( ( ~ ( pls @ ( A @ ord_less_int ) )
=> ( ( A @ number_number_of_nat @ ( B @ number_number_of_nat @ plus_plus_nat ) )
= ( A @ ( B @ plus_plus_int ) @ number_number_of_nat ) ) )
& ( ( pls @ ( A @ ord_less_int ) )
=> ( ( A @ number_number_of_nat @ ( B @ number_number_of_nat @ plus_plus_nat ) )
= ( B @ number_number_of_nat ) ) ) ) )
& ( ( pls @ ( B @ ord_less_int ) )
=> ( ( A @ number_number_of_nat @ ( B @ number_number_of_nat @ plus_plus_nat ) )
= ( A @ number_number_of_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(35,axiom,
! [A: $i] :
( ( zero_zero_int @ ( A @ ( A @ ( one_one_int @ plus_plus_int ) @ plus_plus_int ) @ ord_less_int ) )
<=> ( zero_zero_int @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_odd__less__0) ).
thf(258,plain,
! [A: $i] :
( ( ( zero_zero_int @ ( A @ ord_less_int ) )
=> ( zero_zero_int @ ( A @ ( A @ ( one_one_int @ plus_plus_int ) @ plus_plus_int ) @ ord_less_int ) ) )
& ( ( zero_zero_int @ ( A @ ( A @ ( one_one_int @ plus_plus_int ) @ plus_plus_int ) @ ord_less_int ) )
=> ( zero_zero_int @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(69,axiom,
! [A: $i,B: $i] :
( ( B @ bit0 @ ( A @ bit0 @ plus_plus_int ) )
= ( B @ ( A @ plus_plus_int ) @ bit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_add__Bit0__Bit0) ).
thf(408,plain,
! [A: $i,B: $i] :
( ( B @ bit0 @ ( A @ bit0 @ plus_plus_int ) )
= ( B @ ( A @ plus_plus_int ) @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(21,axiom,
( ( pls @ number_number_of_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_nat__number__of__Pls) ).
thf(202,plain,
( ( pls @ number_number_of_nat )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(103,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ plus_plus_int ) @ number_number_of_int )
= ( B @ number_number_of_int @ ( A @ number_number_of_int @ plus_plus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_number__of__add) ).
thf(550,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ plus_plus_int ) @ number_number_of_int )
= ( B @ number_number_of_int @ ( A @ number_number_of_int @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(98,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ semiri1621563631at_int @ plus_plus_int ) @ ( A @ semiri1621563631at_int @ plus_plus_int ) )
= ( C @ ( B @ ( A @ plus_plus_nat ) @ semiri1621563631at_int @ plus_plus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_zadd__int__left) ).
thf(538,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ semiri1621563631at_int @ plus_plus_int ) @ ( A @ semiri1621563631at_int @ plus_plus_int ) )
= ( C @ ( B @ ( A @ plus_plus_nat ) @ semiri1621563631at_int @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(17,axiom,
( ( pls @ number_number_of_int )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_semiring__numeral__0__eq__0) ).
thf(185,plain,
( ( pls @ number_number_of_int )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ plus_plus_int ) @ plus_plus_int ) )
= ( C @ ( B @ plus_plus_int ) @ ( A @ plus_plus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_zadd__assoc) ).
thf(288,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ plus_plus_int ) @ plus_plus_int ) )
= ( C @ ( B @ plus_plus_int ) @ ( A @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(72,axiom,
! [A: $i,B: $i] :
( ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) )
= zero_zero_int )
<=> ( ( B = zero_zero_int )
& ( A = zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_sum__power2__eq__zero__iff) ).
thf(416,plain,
! [A: $i,B: $i] :
( ( ( ( B = zero_zero_int )
& ( A = zero_zero_int ) )
=> ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) )
= zero_zero_int ) )
& ( ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) )
= zero_zero_int )
=> ( ( B = zero_zero_int )
& ( A = zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(52,axiom,
! [A: $i] :
( ( pls @ number_number_of_int @ ( A @ plus_plus_int ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_add__numeral__0__right) ).
thf(325,plain,
! [A: $i] :
( ( pls @ number_number_of_int @ ( A @ plus_plus_int ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(50,axiom,
! [A: $i] :
( ( zero_zero_int @ ( A @ bit0 @ ord_less_int ) )
<=> ( zero_zero_int @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_bin__less__0__simps_I3_J) ).
thf(316,plain,
! [A: $i] :
( ( ( zero_zero_int @ ( A @ ord_less_int ) )
=> ( zero_zero_int @ ( A @ bit0 @ ord_less_int ) ) )
& ( ( zero_zero_int @ ( A @ bit0 @ ord_less_int ) )
=> ( zero_zero_int @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(86,axiom,
! [A: $i,B: $i] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) @ ( zero_zero_int @ ord_less_int ) )
<=> ( ( B != zero_zero_int )
| ( A != zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_sum__power2__gt__zero__iff) ).
thf(475,plain,
! [A: $i,B: $i] :
( ( ( ( B != zero_zero_int )
| ( A != zero_zero_int ) )
=> ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) @ ( zero_zero_int @ ord_less_int ) ) )
& ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) @ ( zero_zero_int @ ord_less_int ) )
=> ( ( B != zero_zero_int )
| ( A != zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ bit1 )
= ( A @ ( A @ ( one_one_int @ plus_plus_int ) @ plus_plus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_Bit1__def) ).
thf(179,plain,
! [A: $i] :
( ( A @ bit1 )
= ( A @ ( A @ ( one_one_int @ plus_plus_int ) @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(80,axiom,
! [A: $i] :
( ( one_one_int @ ( A @ number_number_of_int @ plus_plus_int ) )
= ( pls @ bit1 @ ( A @ plus_plus_int ) @ number_number_of_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_add__special_I3_J) ).
thf(443,plain,
! [A: $i] :
( ( one_one_int @ ( A @ number_number_of_int @ plus_plus_int ) )
= ( pls @ bit1 @ ( A @ plus_plus_int ) @ number_number_of_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(30,axiom,
! [A: $i] :
( ( pls
= ( A @ bit0 ) )
<=> ( pls = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_rel__simps_I38_J) ).
thf(238,plain,
! [A: $i] :
( ( ( pls = A )
=> ( pls
= ( A @ bit0 ) ) )
& ( ( pls
= ( A @ bit0 ) )
=> ( pls = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(70,axiom,
( ( pls @ number_number_of_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_semiring__numeral__0__eq__0) ).
thf(411,plain,
( ( pls @ number_number_of_nat )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(95,axiom,
! [A: $i] :
~ ( zero_zero_int @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ ord_less_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_power2__less__0) ).
thf(527,plain,
! [A: $i] :
~ ( zero_zero_int @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ ord_less_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(45,axiom,
! [A: $i] :
( ( ( A @ bit0 )
= pls )
<=> ( A = pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_rel__simps_I44_J) ).
thf(292,plain,
! [A: $i] :
( ( ( A = pls )
=> ( ( A @ bit0 )
= pls ) )
& ( ( ( A @ bit0 )
= pls )
=> ( A = pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(82,axiom,
! [A: $i] :
( ( zero_zero_int @ ( A @ ( A @ plus_plus_int ) @ ord_less_int ) )
<=> ( zero_zero_int @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_even__less__0__iff) ).
thf(452,plain,
! [A: $i] :
( ( ( zero_zero_int @ ( A @ ord_less_int ) )
=> ( zero_zero_int @ ( A @ ( A @ plus_plus_int ) @ ord_less_int ) ) )
& ( ( zero_zero_int @ ( A @ ( A @ plus_plus_int ) @ ord_less_int ) )
=> ( zero_zero_int @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( B @ number_number_of_int @ ( A @ number_number_of_int @ plus_plus_int ) )
= ( B @ ( A @ plus_plus_int ) @ number_number_of_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_add__number__of__eq) ).
thf(248,plain,
! [A: $i,B: $i] :
( ( B @ number_number_of_int @ ( A @ number_number_of_int @ plus_plus_int ) )
= ( B @ ( A @ plus_plus_int ) @ number_number_of_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(78,axiom,
( zero_zero_int
= ( pls @ number_number_of_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_semiring__norm_I112_J) ).
thf(439,plain,
( zero_zero_int
= ( pls @ number_number_of_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(101,axiom,
n @ semiri1621563631at_int @ ( one_one_int @ plus_plus_int ) @ ( zero_zero_int @ ord_less_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_n1pos) ).
thf(546,plain,
n @ semiri1621563631at_int @ ( one_one_int @ plus_plus_int ) @ ( zero_zero_int @ ord_less_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(65,axiom,
! [A: $i,B: $i] :
( ( ( A @ bit1 )
= ( B @ bit1 ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_rel__simps_I51_J) ).
thf(381,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( ( A @ bit1 )
= ( B @ bit1 ) ) )
& ( ( ( A @ bit1 )
= ( B @ bit1 ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( B @ bit0 @ ( A @ bit0 @ ord_less_int ) )
<=> ( B @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_less__int__code_I13_J) ).
thf(252,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ord_less_int ) )
=> ( B @ bit0 @ ( A @ bit0 @ ord_less_int ) ) )
& ( ( B @ bit0 @ ( A @ bit0 @ ord_less_int ) )
=> ( B @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(88,axiom,
( ( zero_zero_nat @ semiri1621563631at_int )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_int__0) ).
thf(493,plain,
( ( zero_zero_nat @ semiri1621563631at_int )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(25,axiom,
( one_one_int
= ( pls @ bit1 @ number_number_of_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_one__is__num__one) ).
thf(224,plain,
( one_one_int
= ( pls @ bit1 @ number_number_of_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(107,axiom,
! [A: $i] :
( ( A @ semiri1621563631at_int @ number_number_of_int )
= ( A @ semiri1621563631at_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_number__of__int) ).
thf(578,plain,
! [A: $i] :
( ( A @ semiri1621563631at_int @ number_number_of_int )
= ( A @ semiri1621563631at_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(9,axiom,
! [A: $i] :
( ( pls @ ( A @ plus_plus_int ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_add__Pls__right) ).
thf(156,plain,
! [A: $i] :
( ( pls @ ( A @ plus_plus_int ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(19,axiom,
! [A: $i] :
( ( zero_zero_int @ ( A @ number_number_of_int @ ord_less_int ) )
<=> ( pls @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_less__special_I3_J) ).
thf(193,plain,
! [A: $i] :
( ( ( pls @ ( A @ ord_less_int ) )
=> ( zero_zero_int @ ( A @ number_number_of_int @ ord_less_int ) ) )
& ( ( zero_zero_int @ ( A @ number_number_of_int @ ord_less_int ) )
=> ( pls @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(102,axiom,
! [A: $i] :
( ( A @ number_number_of_int @ ( one_one_int @ plus_plus_int ) )
= ( A @ ( pls @ bit1 @ plus_plus_int ) @ number_number_of_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_add__special_I2_J) ).
thf(547,plain,
! [A: $i] :
( ( A @ number_number_of_int @ ( one_one_int @ plus_plus_int ) )
= ( A @ ( pls @ bit1 @ plus_plus_int ) @ number_number_of_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(1,conjecture,
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( n @ semiri1621563631at_int @ ( one_one_int @ plus_plus_int ) @ power_power_int ) )
!= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( n @ semiri1621563631at_int @ ( one_one_int @ plus_plus_int ) @ power_power_int ) )
!= zero_zero_int ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(109,plain,
~ ( ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( n @ semiri1621563631at_int @ ( one_one_int @ plus_plus_int ) @ power_power_int ) )
!= zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(53,axiom,
! [A: $i] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ power_power_int ) )
= ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_quartic__square__square) ).
thf(328,plain,
! [A: $i] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ power_power_int ) )
= ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(12,axiom,
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( zero_zero_nat @ power_power_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_zero__power2) ).
thf(173,plain,
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( zero_zero_nat @ power_power_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(63,axiom,
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( one_one_int @ power_power_int ) )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_one__power2) ).
thf(371,plain,
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( one_one_int @ power_power_int ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(91,axiom,
! [A: $i,B: $i] :
( ( ( B @ number_number_of_nat @ ( A @ power_power_int ) )
= zero_zero_int )
<=> ( ( ( B @ number_number_of_nat )
!= zero_zero_nat )
& ( A = zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_power__eq__0__iff__number__of) ).
thf(503,plain,
! [A: $i,B: $i] :
( ( ( ( ( B @ number_number_of_nat )
!= zero_zero_nat )
& ( A = zero_zero_int ) )
=> ( ( B @ number_number_of_nat @ ( A @ power_power_int ) )
= zero_zero_int ) )
& ( ( ( B @ number_number_of_nat @ ( A @ power_power_int ) )
= zero_zero_int )
=> ( ( ( B @ number_number_of_nat )
!= zero_zero_nat )
& ( A = zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(56,axiom,
! [A: $i,B: $i] :
( ( B @ bit1 @ ( A @ bit0 @ plus_plus_int ) )
= ( B @ ( A @ plus_plus_int ) @ bit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_add__Bit0__Bit1) ).
thf(343,plain,
! [A: $i,B: $i] :
( ( B @ bit1 @ ( A @ bit0 @ plus_plus_int ) )
= ( B @ ( A @ plus_plus_int ) @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(37,axiom,
( ( pls @ bit0 )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_Bit0__Pls) ).
thf(266,plain,
( ( pls @ bit0 )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(99,axiom,
( ( one_one_nat @ ( one_one_nat @ plus_plus_nat ) )
= ( pls @ bit1 @ bit0 @ number_number_of_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_nat__1__add__1) ).
thf(541,plain,
( ( one_one_nat @ ( one_one_nat @ plus_plus_nat ) )
= ( pls @ bit1 @ bit0 @ number_number_of_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(96,axiom,
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( zero_zero_int @ power_power_int ) )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_zero__power2) ).
thf(530,plain,
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( zero_zero_int @ power_power_int ) )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(92,axiom,
! [A: $i] :
( ( A @ ( zero_zero_int @ plus_plus_int ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_zadd__0) ).
thf(513,plain,
! [A: $i] :
( ( A @ ( zero_zero_int @ plus_plus_int ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(36,axiom,
( ( one_one_int @ ( one_one_int @ plus_plus_int ) )
= ( pls @ bit1 @ bit0 @ number_number_of_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_one__add__one__is__two) ).
thf(264,plain,
( ( one_one_int @ ( one_one_int @ plus_plus_int ) )
= ( pls @ bit1 @ bit0 @ number_number_of_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(42,axiom,
( one_one_int
= ( pls @ bit1 @ number_number_of_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_semiring__norm_I110_J) ).
thf(286,plain,
( one_one_int
= ( pls @ bit1 @ number_number_of_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(44,axiom,
one_one_int @ ( zero_zero_int @ ord_less_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_int__0__less__1) ).
thf(291,plain,
one_one_int @ ( zero_zero_int @ ord_less_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(22,axiom,
! [A: $i] :
( ( A @ ( A @ ( one_one_int @ plus_plus_int ) @ plus_plus_int ) )
!= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_odd__nonzero) ).
thf(204,plain,
! [A: $i] :
( ( A @ ( A @ ( one_one_int @ plus_plus_int ) @ plus_plus_int ) )
!= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(71,axiom,
! [A: $i,B: $i] :
( ( B @ semiri1621563631at_int @ ( A @ semiri1621563631at_int @ plus_plus_int ) )
= ( B @ ( A @ plus_plus_nat ) @ semiri1621563631at_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_zadd__int) ).
thf(413,plain,
! [A: $i,B: $i] :
( ( B @ semiri1621563631at_int @ ( A @ semiri1621563631at_int @ plus_plus_int ) )
= ( B @ ( A @ plus_plus_nat ) @ semiri1621563631at_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(66,axiom,
zero_zero_int != one_one_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_int__0__neq__1) ).
thf(391,plain,
zero_zero_int != one_one_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( B @ number_number_of_int @ ( A @ number_number_of_int @ plus_plus_int ) )
= ( B @ ( A @ plus_plus_int ) @ number_number_of_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_plus__numeral__code_I9_J) ).
thf(313,plain,
! [A: $i,B: $i] :
( ( B @ number_number_of_int @ ( A @ number_number_of_int @ plus_plus_int ) )
= ( B @ ( A @ plus_plus_int ) @ number_number_of_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(10,axiom,
! [A: $i] :
( ( ( ( A @ number_number_of_nat )
!= zero_zero_nat )
=> ( ( A @ number_number_of_nat @ ( zero_zero_int @ power_power_int ) )
= zero_zero_int ) )
& ( ( ( A @ number_number_of_nat )
= zero_zero_nat )
=> ( ( A @ number_number_of_nat @ ( zero_zero_int @ power_power_int ) )
= one_one_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_power__0__left__number__of) ).
thf(159,plain,
! [A: $i] :
( ( ( ( A @ number_number_of_nat )
!= zero_zero_nat )
=> ( ( A @ number_number_of_nat @ ( zero_zero_int @ power_power_int ) )
= zero_zero_int ) )
& ( ( ( A @ number_number_of_nat )
= zero_zero_nat )
=> ( ( A @ number_number_of_nat @ ( zero_zero_int @ power_power_int ) )
= one_one_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( B @ bit0 @ ( A @ bit1 @ ord_less_int ) )
<=> ( B @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_less__int__code_I15_J) ).
thf(187,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ord_less_int ) )
=> ( B @ bit0 @ ( A @ bit1 @ ord_less_int ) ) )
& ( ( B @ bit0 @ ( A @ bit1 @ ord_less_int ) )
=> ( B @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(27,axiom,
( ( pls @ number_number_of_int )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_number__of__Pls) ).
thf(230,plain,
( ( pls @ number_number_of_int )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( B @ bit0 @ ( A @ bit0 @ ord_less_int ) )
<=> ( B @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_rel__simps_I14_J) ).
thf(362,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ord_less_int ) )
=> ( B @ bit0 @ ( A @ bit0 @ ord_less_int ) ) )
& ( ( B @ bit0 @ ( A @ bit0 @ ord_less_int ) )
=> ( B @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(76,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ semiri1621563631at_int @ power_power_int ) )
= ( B @ ( A @ power_power_nat ) @ semiri1621563631at_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_zpower__int) ).
thf(434,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ semiri1621563631at_int @ power_power_int ) )
= ( B @ ( A @ power_power_nat ) @ semiri1621563631at_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(47,axiom,
( ( one_one_int @ ( one_one_int @ plus_plus_int ) )
= ( pls @ bit1 @ bit0 @ number_number_of_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_semiring__one__add__one__is__two) ).
thf(303,plain,
( ( one_one_int @ ( one_one_int @ plus_plus_int ) )
= ( pls @ bit1 @ bit0 @ number_number_of_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(39,axiom,
( ( pls @ bit1 @ number_number_of_int )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_numeral__1__eq__1) ).
thf(271,plain,
( ( pls @ bit1 @ number_number_of_int )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( B @ bit1 @ ( A @ bit1 @ ord_less_int ) )
<=> ( B @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_rel__simps_I17_J) ).
thf(208,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ord_less_int ) )
=> ( B @ bit1 @ ( A @ bit1 @ ord_less_int ) ) )
& ( ( B @ bit1 @ ( A @ bit1 @ ord_less_int ) )
=> ( B @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( B @ number_number_of_int @ ( A @ number_number_of_int @ ord_less_int ) )
<=> ( B @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_less__number__of__int__code) ).
thf(140,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ord_less_int ) )
=> ( B @ number_number_of_int @ ( A @ number_number_of_int @ ord_less_int ) ) )
& ( ( B @ number_number_of_int @ ( A @ number_number_of_int @ ord_less_int ) )
=> ( B @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(33,axiom,
n @ ( zero_zero_nat @ ord_less_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_n0) ).
thf(251,plain,
n @ ( zero_zero_nat @ ord_less_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(67,axiom,
! [A: $i] :
( ( one_one_int @ ( A @ number_number_of_int @ ord_less_int ) )
<=> ( pls @ bit1 @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_less__special_I4_J) ).
thf(394,plain,
! [A: $i] :
( ( ( pls @ bit1 @ ( A @ ord_less_int ) )
=> ( one_one_int @ ( A @ number_number_of_int @ ord_less_int ) ) )
& ( ( one_one_int @ ( A @ number_number_of_int @ ord_less_int ) )
=> ( pls @ bit1 @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( A @ bit1 )
!= ( B @ bit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_rel__simps_I50_J) ).
thf(226,plain,
! [A: $i,B: $i] :
( ( A @ bit1 )
!= ( B @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ number_number_of_int @ ( one_one_int @ ord_less_int ) )
<=> ( A @ ( pls @ bit1 @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_less__special_I2_J) ).
thf(167,plain,
! [A: $i] :
( ( ( A @ ( pls @ bit1 @ ord_less_int ) )
=> ( A @ number_number_of_int @ ( one_one_int @ ord_less_int ) ) )
& ( ( A @ number_number_of_int @ ( one_one_int @ ord_less_int ) )
=> ( A @ ( pls @ bit1 @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(85,axiom,
( ( one_one_nat @ semiri1621563631at_int )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_int__1) ).
thf(473,plain,
( ( one_one_nat @ semiri1621563631at_int )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(73,axiom,
! [A: $i] :
( ( A @ ( pls @ number_number_of_int @ plus_plus_int ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_add__numeral__0) ).
thf(426,plain,
! [A: $i] :
( ( A @ ( pls @ number_number_of_int @ plus_plus_int ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(87,axiom,
! [A: $i] :
( ( pls @ ( A @ bit0 @ ord_less_int ) )
<=> ( pls @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_rel__simps_I10_J) ).
thf(487,plain,
! [A: $i] :
( ( ( pls @ ( A @ ord_less_int ) )
=> ( pls @ ( A @ bit0 @ ord_less_int ) ) )
& ( ( pls @ ( A @ bit0 @ ord_less_int ) )
=> ( pls @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ( A @ number_number_of_int )
= ( B @ number_number_of_int ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_eq__number__of) ).
thf(112,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( ( A @ number_number_of_int )
= ( B @ number_number_of_int ) ) )
& ( ( ( A @ number_number_of_int )
= ( B @ number_number_of_int ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(93,axiom,
! [A: $i] :
( ( ( A @ semiri1621563631at_int )
= zero_zero_int )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_int__eq__0__conv) ).
thf(516,plain,
! [A: $i] :
( ( ( A = zero_zero_nat )
=> ( ( A @ semiri1621563631at_int )
= zero_zero_int ) )
& ( ( ( A @ semiri1621563631at_int )
= zero_zero_int )
=> ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(104,axiom,
! [A: $i] :
( ( A @ bit1 )
!= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_rel__simps_I46_J) ).
thf(553,plain,
! [A: $i] :
( ( A @ bit1 )
!= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(83,axiom,
! [A: $i] :
( ( zero_zero_int @ ( A @ bit1 @ ord_less_int ) )
<=> ( zero_zero_int @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_bin__less__0__simps_I4_J) ).
thf(458,plain,
! [A: $i] :
( ( ( zero_zero_int @ ( A @ ord_less_int ) )
=> ( zero_zero_int @ ( A @ bit1 @ ord_less_int ) ) )
& ( ( zero_zero_int @ ( A @ bit1 @ ord_less_int ) )
=> ( zero_zero_int @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ semiri1621563631at_int @ number_number_of_nat )
= ( A @ semiri984289939at_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_number__of__int) ).
thf(199,plain,
! [A: $i] :
( ( A @ semiri1621563631at_int @ number_number_of_nat )
= ( A @ semiri984289939at_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( one_one_int @ ( B @ plus_plus_int ) @ ( A @ ord_less_int ) )
<=> ( ( A = B )
| ( B @ ( A @ ord_less_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_zless__add1__eq) ).
thf(331,plain,
! [A: $i,B: $i] :
( ( ( ( A = B )
| ( B @ ( A @ ord_less_int ) ) )
=> ( one_one_int @ ( B @ plus_plus_int ) @ ( A @ ord_less_int ) ) )
& ( ( one_one_int @ ( B @ plus_plus_int ) @ ( A @ ord_less_int ) )
=> ( ( A = B )
| ( B @ ( A @ ord_less_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(79,axiom,
( ( one_one_nat @ ( one_one_nat @ plus_plus_nat ) )
= ( pls @ bit1 @ bit0 @ number_number_of_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_semiring__one__add__one__is__two) ).
thf(441,plain,
( ( one_one_nat @ ( one_one_nat @ plus_plus_nat ) )
= ( pls @ bit1 @ bit0 @ number_number_of_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(62,axiom,
t @ ( one_one_int @ ord_less_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_t1) ).
thf(370,plain,
t @ ( one_one_int @ ord_less_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(14,axiom,
~ ( pls @ ( pls @ ord_less_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_rel__simps_I2_J) ).
thf(177,plain,
~ ( pls @ ( pls @ ord_less_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( B @ bit0 @ ( A @ bit1 @ plus_plus_int ) )
= ( B @ ( A @ plus_plus_int ) @ bit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_add__Bit1__Bit0) ).
thf(182,plain,
! [A: $i,B: $i] :
( ( B @ bit0 @ ( A @ bit1 @ plus_plus_int ) )
= ( B @ ( A @ plus_plus_int ) @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(13,axiom,
( zero_zero_int
= ( pls @ number_number_of_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_zero__is__num__zero) ).
thf(175,plain,
( zero_zero_int
= ( pls @ number_number_of_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(81,axiom,
! [A: $i,B: $i] :
( ( B @ bit1 @ ( A @ bit1 @ ord_less_int ) )
<=> ( B @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_less__int__code_I16_J) ).
thf(446,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ord_less_int ) )
=> ( B @ bit1 @ ( A @ bit1 @ ord_less_int ) ) )
& ( ( B @ bit1 @ ( A @ bit1 @ ord_less_int ) )
=> ( B @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(89,axiom,
! [A: $i] :
( ( A @ bit0 @ ( pls @ ord_less_int ) )
<=> ( A @ ( pls @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_rel__simps_I4_J) ).
thf(495,plain,
! [A: $i] :
( ( ( A @ ( pls @ ord_less_int ) )
=> ( A @ bit0 @ ( pls @ ord_less_int ) ) )
& ( ( A @ bit0 @ ( pls @ ord_less_int ) )
=> ( A @ ( pls @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(61,axiom,
( ( pls @ bit1 @ number_number_of_nat )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_nat__numeral__1__eq__1) ).
thf(368,plain,
( ( pls @ bit1 @ number_number_of_nat )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(94,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ plus_plus_int ) )
= ( A @ ( B @ plus_plus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_zadd__commute) ).
thf(524,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ plus_plus_int ) )
= ( A @ ( B @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(108,axiom,
~ ( zero_zero_int @ ( pls @ ord_less_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_bin__less__0__simps_I1_J) ).
thf(581,plain,
~ ( zero_zero_int @ ( pls @ ord_less_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(106,axiom,
! [A: $i,B: $i] :
( ( ( A @ semiri1621563631at_int )
= ( B @ semiri1621563631at_int ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_int__int__eq) ).
thf(568,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( ( A @ semiri1621563631at_int )
= ( B @ semiri1621563631at_int ) ) )
& ( ( ( A @ semiri1621563631at_int )
= ( B @ semiri1621563631at_int ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(57,axiom,
! [A: $i,B: $i] :
( ( B @ bit0 @ ( A @ bit1 @ ord_less_int ) )
<=> ( B @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_rel__simps_I16_J) ).
thf(346,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ord_less_int ) )
=> ( B @ bit0 @ ( A @ bit1 @ ord_less_int ) ) )
& ( ( B @ bit0 @ ( A @ bit1 @ ord_less_int ) )
=> ( B @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( ( A @ bit0 )
= ( B @ bit0 ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_rel__simps_I48_J) ).
thf(214,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( ( A @ bit0 )
= ( B @ bit0 ) ) )
& ( ( ( A @ bit0 )
= ( B @ bit0 ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(29,axiom,
! [A: $i] :
~ ( zero_zero_int @ ( A @ semiri1621563631at_int @ ord_less_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_int__less__0__conv) ).
thf(235,plain,
! [A: $i] :
~ ( zero_zero_int @ ( A @ semiri1621563631at_int @ ord_less_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(31,axiom,
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( one_one_nat @ power_power_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_one__power2) ).
thf(246,plain,
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( one_one_nat @ power_power_nat ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ plus_plus_int ) @ ( A @ plus_plus_int ) )
= ( C @ ( A @ plus_plus_int ) @ ( B @ plus_plus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_zadd__left__commute) ).
thf(300,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ plus_plus_int ) @ ( A @ plus_plus_int ) )
= ( C @ ( A @ plus_plus_int ) @ ( B @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(75,axiom,
( one_one_nat
= ( pls @ bit1 @ number_number_of_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_Numeral1__eq1__nat) ).
thf(432,plain,
( one_one_nat
= ( pls @ bit1 @ number_number_of_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( ( B @ number_number_of_nat @ ( A @ power_power_nat ) )
= zero_zero_nat )
<=> ( ( ( B @ number_number_of_nat )
!= zero_zero_nat )
& ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_power__eq__0__iff__number__of) ).
thf(146,plain,
! [A: $i,B: $i] :
( ( ( ( ( B @ number_number_of_nat )
!= zero_zero_nat )
& ( A = zero_zero_nat ) )
=> ( ( B @ number_number_of_nat @ ( A @ power_power_nat ) )
= zero_zero_nat ) )
& ( ( ( B @ number_number_of_nat @ ( A @ power_power_nat ) )
= zero_zero_nat )
=> ( ( ( B @ number_number_of_nat )
!= zero_zero_nat )
& ( A = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( A @ bit0 )
!= ( B @ bit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_rel__simps_I49_J) ).
thf(273,plain,
! [A: $i,B: $i] :
( ( A @ bit0 )
!= ( B @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(64,axiom,
! [A: $i] :
( ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) )
= zero_zero_int )
<=> ( A = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_zero__eq__power2) ).
thf(373,plain,
! [A: $i] :
( ( ( A = zero_zero_int )
=> ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) )
= zero_zero_int ) )
& ( ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) )
= zero_zero_int )
=> ( A = zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(48,axiom,
! [A: $i] :
( ( ( ( A @ number_number_of_nat )
!= zero_zero_nat )
=> ( ( A @ number_number_of_nat @ ( zero_zero_nat @ power_power_nat ) )
= zero_zero_nat ) )
& ( ( ( A @ number_number_of_nat )
= zero_zero_nat )
=> ( ( A @ number_number_of_nat @ ( zero_zero_nat @ power_power_nat ) )
= one_one_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_power__0__left__number__of) ).
thf(305,plain,
! [A: $i] :
( ( ( ( A @ number_number_of_nat )
!= zero_zero_nat )
=> ( ( A @ number_number_of_nat @ ( zero_zero_nat @ power_power_nat ) )
= zero_zero_nat ) )
& ( ( ( A @ number_number_of_nat )
= zero_zero_nat )
=> ( ( A @ number_number_of_nat @ ( zero_zero_nat @ power_power_nat ) )
= one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ord_less_int ) )
=> ( A @ ( C @ plus_plus_int ) @ ( A @ ( B @ plus_plus_int ) @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_zadd__strict__right__mono) ).
thf(341,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ord_less_int ) )
=> ( A @ ( C @ plus_plus_int ) @ ( A @ ( B @ plus_plus_int ) @ ord_less_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(38,axiom,
! [A: $i] :
( ( A @ ( pls @ plus_plus_int ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_add__Pls) ).
thf(268,plain,
! [A: $i] :
( ( A @ ( pls @ plus_plus_int ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(59,axiom,
! [A: $i] :
( pls
!= ( A @ bit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_rel__simps_I39_J) ).
thf(358,plain,
! [A: $i] :
( pls
!= ( A @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(77,axiom,
( zero_zero_nat
= ( pls @ number_number_of_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_semiring__norm_I113_J) ).
thf(437,plain,
( zero_zero_nat
= ( pls @ number_number_of_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(68,axiom,
! [A: $i] :
( ( ( A @ ( A @ plus_plus_int ) )
= zero_zero_int )
<=> ( A = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_double__eq__0__iff) ).
thf(400,plain,
! [A: $i] :
( ( ( A = zero_zero_int )
=> ( ( A @ ( A @ plus_plus_int ) )
= zero_zero_int ) )
& ( ( ( A @ ( A @ plus_plus_int ) )
= zero_zero_int )
=> ( A = zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(97,axiom,
! [A: $i] :
( ( pls @ ( A @ bit1 @ ord_less_int ) )
<=> ( pls @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_rel__simps_I12_J) ).
thf(532,plain,
! [A: $i] :
( ( ( pls @ ( A @ ord_less_int ) )
=> ( pls @ ( A @ bit1 @ ord_less_int ) ) )
& ( ( pls @ ( A @ bit1 @ ord_less_int ) )
=> ( pls @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(84,axiom,
! [A: $i] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ ( zero_zero_int @ ord_less_int ) )
<=> ( A != zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_zero__less__power2) ).
thf(464,plain,
! [A: $i] :
( ( ( A != zero_zero_int )
=> ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ ( zero_zero_int @ ord_less_int ) ) )
& ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ ( zero_zero_int @ ord_less_int ) )
=> ( A != zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( ( A @ number_number_of_int )
= B )
<=> ( B
= ( A @ number_number_of_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_number__of__reorient) ).
thf(131,plain,
! [A: $i,B: $i] :
( ( ( B
= ( A @ number_number_of_int ) )
=> ( ( A @ number_number_of_int )
= B ) )
& ( ( ( A @ number_number_of_int )
= B )
=> ( B
= ( A @ number_number_of_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( ( A @ number_number_of_nat )
= B )
<=> ( B
= ( A @ number_number_of_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_number__of__reorient) ).
thf(277,plain,
! [A: $i,B: $i] :
( ( ( B
= ( A @ number_number_of_nat ) )
=> ( ( A @ number_number_of_nat )
= B ) )
& ( ( ( A @ number_number_of_nat )
= B )
=> ( B
= ( A @ number_number_of_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(90,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_Pls__def) ).
thf(501,plain,
pls = zero_zero_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(51,axiom,
! [A: $i] :
( ( A @ bit0 )
= ( A @ ( A @ plus_plus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_Bit0__def) ).
thf(322,plain,
! [A: $i] :
( ( A @ bit0 )
= ( A @ ( A @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ord_less_int ) )
| ( A = B )
| ( B @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_zless__linear) ).
thf(122,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ord_less_int ) )
| ( A = B )
| ( B @ ( A @ ord_less_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(100,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ power_power_nat ) @ semiri1621563631at_int )
= ( B @ ( A @ semiri1621563631at_int @ power_power_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_int__power) ).
thf(543,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ power_power_nat ) @ semiri1621563631at_int )
= ( B @ ( A @ semiri1621563631at_int @ power_power_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ number_number_of_int @ plus_plus_int ) @ ( A @ number_number_of_int @ plus_plus_int ) )
= ( C @ ( B @ ( A @ plus_plus_int ) @ number_number_of_int @ plus_plus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_add__number__of__left) ).
thf(232,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ number_number_of_int @ plus_plus_int ) @ ( A @ number_number_of_int @ plus_plus_int ) )
= ( C @ ( B @ ( A @ plus_plus_int ) @ number_number_of_int @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(588,plain,
$false,
inference(e,[status(thm)],[352,125,429,557,258,408,202,550,538,185,288,416,325,316,475,179,443,238,411,527,292,452,248,439,546,381,252,493,224,578,156,193,547,109,328,173,371,503,343,266,541,530,513,264,286,291,204,413,391,313,159,187,230,362,434,303,271,208,140,251,394,226,167,473,426,487,112,516,553,458,199,331,441,370,177,182,175,446,495,368,524,581,568,346,214,235,246,300,432,146,273,373,305,341,268,358,437,400,532,464,131,277,501,322,122,543,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM925+1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.16/0.58 % Computer : n011.cluster.edu
% 0.16/0.58 % Model : x86_64 x86_64
% 0.16/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.58 % Memory : 8046.5625MB
% 0.16/0.58 % OS : Linux 6.8.0-71-generic
% 0.16/0.58 % CPULimit : 300
% 0.16/0.58 % WCLimit : 300
% 0.16/0.58 % DateTime : Sat Sep 26 04:18:30 UTC 2026
% 0.16/0.59 % CPUTime :
% 0.16/0.59 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.97/1.21 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.48/1.53 % [INFO] Parsing done (317ms).
% 1.48/1.54 % [INFO] Running in sequential loop mode.
% 2.16/2.00 % [INFO] eprover registered as external prover.
% 2.16/2.01 % [INFO] Scanning for conjecture ...
% 2.55/2.15 % [INFO] Found a conjecture (or negated_conjecture) and 106 axioms. Running axiom selection ...
% 2.74/2.32 % [INFO] Axiom selection finished. Selected 106 axioms (removed 0 axioms).
% 3.07/2.51 % [INFO] Problem is first-order (TPTP FOF).
% 3.07/2.54 % [INFO] Type checking passed.
% 3.07/2.54 % [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 ...
% 6.71/4.06 % External prover 'e' found a proof!
% 6.71/4.06 % [INFO] Killing All external provers ...
% 6.71/4.06 % Time passed: 3325ms (effective reasoning time: 2510ms)
% 6.71/4.06 % 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)>
% 6.71/4.06 % Axioms used in derivation (106): fact_59_rel__simps_I10_J, fact_81_add__Pls, fact_82_add__Bit0__Bit0, fact_2_sum__power2__eq__zero__iff, fact_33_nat__1__add__1, fact_57_less__int__code_I15_J, fact_28_int__1, fact_36_rel__simps_I2_J, fact_70_double__eq__0__iff, fact_92_power__eq__0__iff__number__of, fact_49_even__less__0__iff, fact_91_add__numeral__0__right, fact_25_int__power, fact_37_less__int__code_I13_J, fact_4_one__power2, fact_58_rel__simps_I16_J, fact_95_add__number__of__eq, fact_31_int__eq__0__conv, fact_46_number__of__reorient, fact_19_zless__linear, fact_53_int__int__eq, fact_80_add__Pls__right, fact_54_less__special_I3_J, fact_7_zero__eq__power2, fact_11_semiring__one__add__one__is__two, fact_6_zero__power2, fact_68_less__special_I2_J, fact_61_bin__less__0__simps_I4_J, fact_29_nat__number__of__Pls, fact_50_zadd__assoc, fact_8_add__special_I2_J, fact_101_number__of__int, fact_17_numeral__1__eq__1, fact_88_number__of__Pls, fact_71_rel__simps_I46_J, fact_73_rel__simps_I50_J, fact_42_nat__numeral__1__eq__1, fact_39_zadd__strict__right__mono, fact_62_bin__less__0__simps_I1_J, fact_99_Bit1__def, fact_16_semiring__norm_I110_J, fact_56_rel__simps_I12_J, fact_26_zadd__int__left, fact_63_bin__less__0__simps_I3_J, fact_102_number__of__int, fact_77_Bit0__Pls, fact_103_zero__less__power2, fact_27_zadd__int, fact_1_t1, fact_23_zero__is__num__zero, fact_86_semiring__numeral__0__eq__0, fact_87_semiring__numeral__0__eq__0, fact_47_rel__simps_I51_J, fact_75_rel__simps_I44_J, fact_20_less__number__of__int__code, fact_69_odd__less__0, fact_83_Bit0__def, fact_48_rel__simps_I48_J, fact_44_eq__number__of, fact_10_one__add__one__is__two, fact_105_sum__power2__gt__zero__iff, fact_9_add__special_I3_J, fact_65_zless__add1__eq, fact_104_power2__less__0, fact_89_semiring__norm_I112_J, fact_74_rel__simps_I49_J, fact_78_Pls__def, fact_38_rel__simps_I14_J, fact_84_zadd__0__right, fact_85_zadd__0, fact_93_power__eq__0__iff__number__of, fact_96_number__of__add, fact_14_power__0__left__number__of, fact_98_add__Bit0__Bit1, fact_52_zadd__commute, fact_72_rel__simps_I39_J, fact_41_one__is__num__one, fact_76_rel__simps_I38_J, fact_79_int__0__neq__1, fact_100_odd__nonzero, fact_66_int__less__0__conv, fact_97_add__Bit1__Bit0, fact_40_add__nat__number__of, fact_22_less__number__of, fact_5_zero__power2, fact_30_semiring__norm_I113_J, fact_51_zadd__left__commute, fact_60_rel__simps_I4_J, fact_12_semiring__one__add__one__is__two, fact_34_less__int__code_I16_J, fact_18_n0, fact_55_less__special_I1_J, fact_24_zpower__int, fact_0_n1pos, fact_90_add__numeral__0, fact_35_rel__simps_I17_J, fact_32_int__0, fact_67_less__special_I4_J, fact_13_quartic__square__square, fact_43_Numeral1__eq1__nat, fact_45_number__of__reorient, fact_3_one__power2, fact_21_plus__numeral__code_I9_J, fact_15_power__0__left__number__of, fact_94_add__number__of__left, fact_64_int__0__less__1
% 6.71/4.06 % No. of inferences in proof: 216
% 6.71/4.06 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3325 ms resp. 2510 ms w/o parsing
% 7.33/4.21 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.33/4.21 % [INFO] Killing All external provers ...
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