TSTP Solution File: NUM924+6 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM924+6 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 13:12:40 EDT 2022
% Result : Theorem 0.94s 0.92s
% Output : Proof 1.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 87
% Syntax : Number of formulae : 176 ( 57 unt; 21 typ; 0 def)
% Number of atoms : 518 ( 144 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 537 ( 198 ~; 214 |; 7 &)
% ( 101 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of FOOLs : 24 ( 24 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 14 >; 14 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 7 con; 0-3 aty)
% Number of variables : 218 ( 196 !; 0 ?; 218 :)
% Comments :
%------------------------------------------------------------------------------
tff(ti_type,type,
ti: ( $i * $i ) > $i ).
tff(times_times_type,type,
times_times: ( $i * $i * $i ) > $i ).
tff(zero_zero_type,type,
zero_zero: $i > $i ).
tff(int_type,type,
int: $i ).
tff(plus_plus_type,type,
plus_plus: ( $i * $i * $i ) > $i ).
tff(one_one_type,type,
one_one: $i > $i ).
tff(m_type,type,
m: $i ).
tff(number_number_of_type,type,
number_number_of: ( $i * $i ) > $i ).
tff(bit0_type,type,
bit0: $i > $i ).
tff(bit1_type,type,
bit1: $i > $i ).
tff(t_type,type,
t: $i ).
tff(power_type,type,
power: $i > $o ).
tff(pls_type,type,
pls: $i ).
tff(mult_zero_type,type,
mult_zero: $i > $o ).
tff(ord_less_type,type,
ord_less: ( $i * $i * $i ) > $o ).
tff(ord_less_eq_type,type,
ord_less_eq: ( $i * $i * $i ) > $o ).
tff(minus_minus_type,type,
minus_minus: ( $i * $i * $i ) > $i ).
tff(min_type,type,
min: $i ).
tff(power_power_type,type,
power_power: ( $i * $i * $i ) > $i ).
tff(nat_type,type,
nat: $i ).
tff(s_type,type,
s: $i ).
tff(1,plain,
( power(int)
<=> power(int) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
power(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Power_Opower) ).
tff(3,plain,
power(int),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [B_1_1: $i,B_2_1: $i,X_a: $i] :
refl(
( ( ~ power(X_a)
| ( ti(X_a,times_times(X_a,B_1_1,B_2_1)) = times_times(X_a,B_1_1,B_2_1) ) )
<=> ( ~ power(X_a)
| ( ti(X_a,times_times(X_a,B_1_1,B_2_1)) = times_times(X_a,B_1_1,B_2_1) ) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ~ power(X_a)
| ( ti(X_a,times_times(X_a,B_1_1,B_2_1)) = times_times(X_a,B_1_1,B_2_1) ) )
<=> ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ~ power(X_a)
| ( ti(X_a,times_times(X_a,B_1_1,B_2_1)) = times_times(X_a,B_1_1,B_2_1) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ~ power(X_a)
| ( ti(X_a,times_times(X_a,B_1_1,B_2_1)) = times_times(X_a,B_1_1,B_2_1) ) )
<=> ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ~ power(X_a)
| ( ti(X_a,times_times(X_a,B_1_1,B_2_1)) = times_times(X_a,B_1_1,B_2_1) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
^ [B_1_1: $i,B_2_1: $i,X_a: $i] :
rewrite(
( ( power(X_a)
=> ( ti(X_a,times_times(X_a,B_1_1,B_2_1)) = times_times(X_a,B_1_1,B_2_1) ) )
<=> ( ~ power(X_a)
| ( ti(X_a,times_times(X_a,B_1_1,B_2_1)) = times_times(X_a,B_1_1,B_2_1) ) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( power(X_a)
=> ( ti(X_a,times_times(X_a,B_1_1,B_2_1)) = times_times(X_a,B_1_1,B_2_1) ) )
<=> ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ~ power(X_a)
| ( ti(X_a,times_times(X_a,B_1_1,B_2_1)) = times_times(X_a,B_1_1,B_2_1) ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( power(X_a)
=> ( ti(X_a,times_times(X_a,B_1_1,B_2_1)) = times_times(X_a,B_1_1,B_2_1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_4_res) ).
tff(10,plain,
! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ~ power(X_a)
| ( ti(X_a,times_times(X_a,B_1_1,B_2_1)) = times_times(X_a,B_1_1,B_2_1) ) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ~ power(X_a)
| ( ti(X_a,times_times(X_a,B_1_1,B_2_1)) = times_times(X_a,B_1_1,B_2_1) ) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ~ power(X_a)
| ( ti(X_a,times_times(X_a,B_1_1,B_2_1)) = times_times(X_a,B_1_1,B_2_1) ) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ~ power(X_a)
| ( ti(X_a,times_times(X_a,B_1_1,B_2_1)) = times_times(X_a,B_1_1,B_2_1) ) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ~ power(X_a)
| ( ti(X_a,times_times(X_a,B_1_1,B_2_1)) = times_times(X_a,B_1_1,B_2_1) ) )
| ~ power(int)
| ( ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),zero_zero(int))) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),zero_zero(int)) ) )
<=> ( ~ ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ~ power(X_a)
| ( ti(X_a,times_times(X_a,B_1_1,B_2_1)) = times_times(X_a,B_1_1,B_2_1) ) )
| ~ power(int)
| ( ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),zero_zero(int))) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),zero_zero(int)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ~ ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ~ power(X_a)
| ( ti(X_a,times_times(X_a,B_1_1,B_2_1)) = times_times(X_a,B_1_1,B_2_1) ) )
| ~ power(int)
| ( ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),zero_zero(int))) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),zero_zero(int)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
( ~ ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ~ power(X_a)
| ( ti(X_a,times_times(X_a,B_1_1,B_2_1)) = times_times(X_a,B_1_1,B_2_1) ) )
| ~ power(int)
| ( ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),zero_zero(int))) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),zero_zero(int)) ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),zero_zero(int))) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),zero_zero(int)),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),zero_zero(int)) = ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),zero_zero(int))),
inference(symmetry,[status(thm)],[17]) ).
tff(19,plain,
( ( one_one(int) = number_number_of(int,bit1(pls)) )
<=> ( one_one(int) = number_number_of(int,bit1(zero_zero(int))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(20,plain,
( ( one_one(int) = number_number_of(int,bit1(pls)) )
<=> ( one_one(int) = number_number_of(int,bit1(pls)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
one_one(int) = number_number_of(int,bit1(pls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_one__is__num__one) ).
tff(22,plain,
one_one(int) = number_number_of(int,bit1(pls)),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
one_one(int) = number_number_of(int,bit1(zero_zero(int))),
inference(modus_ponens,[status(thm)],[22,19]) ).
tff(24,plain,
plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),number_number_of(int,bit1(zero_zero(int)))),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),zero_zero(int)) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),number_number_of(int,bit1(zero_zero(int)))),zero_zero(int)),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),number_number_of(int,bit1(zero_zero(int)))),zero_zero(int)) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),zero_zero(int)),
inference(symmetry,[status(thm)],[25]) ).
tff(27,plain,
( mult_zero(int)
<=> mult_zero(int) ),
inference(rewrite,[status(thm)],]) ).
tff(28,axiom,
mult_zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Omult__zero) ).
tff(29,plain,
mult_zero(int),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
^ [X_a: $i] :
refl(
( ( ~ mult_zero(X_a)
| ! [A_1: $i] : ( times_times(X_a,A_1,zero_zero(X_a)) = zero_zero(X_a) ) )
<=> ( ~ mult_zero(X_a)
| ! [A_1: $i] : ( times_times(X_a,A_1,zero_zero(X_a)) = zero_zero(X_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [X_a: $i] :
( ~ mult_zero(X_a)
| ! [A_1: $i] : ( times_times(X_a,A_1,zero_zero(X_a)) = zero_zero(X_a) ) )
<=> ! [X_a: $i] :
( ~ mult_zero(X_a)
| ! [A_1: $i] : ( times_times(X_a,A_1,zero_zero(X_a)) = zero_zero(X_a) ) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
^ [X_a: $i] :
rewrite(
( ( ~ mult_zero(X_a)
| ! [A_1: $i] : ( times_times(X_a,A_1,zero_zero(X_a)) = zero_zero(X_a) ) )
<=> ( ~ mult_zero(X_a)
| ! [A_1: $i] : ( times_times(X_a,A_1,zero_zero(X_a)) = zero_zero(X_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [X_a: $i] :
( ~ mult_zero(X_a)
| ! [A_1: $i] : ( times_times(X_a,A_1,zero_zero(X_a)) = zero_zero(X_a) ) )
<=> ! [X_a: $i] :
( ~ mult_zero(X_a)
| ! [A_1: $i] : ( times_times(X_a,A_1,zero_zero(X_a)) = zero_zero(X_a) ) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [X_a: $i] :
( ~ mult_zero(X_a)
| ! [A_1: $i] : ( times_times(X_a,A_1,zero_zero(X_a)) = zero_zero(X_a) ) )
<=> ! [X_a: $i] :
( ~ mult_zero(X_a)
| ! [A_1: $i] : ( times_times(X_a,A_1,zero_zero(X_a)) = zero_zero(X_a) ) ) ),
inference(transitivity,[status(thm)],[33,31]) ).
tff(35,plain,
( ! [X_a: $i] :
( ~ mult_zero(X_a)
| ! [A_1: $i] : ( times_times(X_a,A_1,zero_zero(X_a)) = zero_zero(X_a) ) )
<=> ! [X_a: $i] :
( ~ mult_zero(X_a)
| ! [A_1: $i] : ( times_times(X_a,A_1,zero_zero(X_a)) = zero_zero(X_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
^ [X_a: $i] :
rewrite(
( ( mult_zero(X_a)
=> ! [A_1: $i] : ( times_times(X_a,A_1,zero_zero(X_a)) = zero_zero(X_a) ) )
<=> ( ~ mult_zero(X_a)
| ! [A_1: $i] : ( times_times(X_a,A_1,zero_zero(X_a)) = zero_zero(X_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(37,plain,
( ! [X_a: $i] :
( mult_zero(X_a)
=> ! [A_1: $i] : ( times_times(X_a,A_1,zero_zero(X_a)) = zero_zero(X_a) ) )
<=> ! [X_a: $i] :
( ~ mult_zero(X_a)
| ! [A_1: $i] : ( times_times(X_a,A_1,zero_zero(X_a)) = zero_zero(X_a) ) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,axiom,
! [X_a: $i] :
( mult_zero(X_a)
=> ! [A_1: $i] : ( times_times(X_a,A_1,zero_zero(X_a)) = zero_zero(X_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_468_mult__zero__right) ).
tff(39,plain,
! [X_a: $i] :
( ~ mult_zero(X_a)
| ! [A_1: $i] : ( times_times(X_a,A_1,zero_zero(X_a)) = zero_zero(X_a) ) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [X_a: $i] :
( ~ mult_zero(X_a)
| ! [A_1: $i] : ( times_times(X_a,A_1,zero_zero(X_a)) = zero_zero(X_a) ) ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
! [X_a: $i] :
( ~ mult_zero(X_a)
| ! [A_1: $i] : ( times_times(X_a,A_1,zero_zero(X_a)) = zero_zero(X_a) ) ),
inference(skolemize,[status(sab)],[40]) ).
tff(42,plain,
! [X_a: $i] :
( ~ mult_zero(X_a)
| ! [A_1: $i] : ( times_times(X_a,A_1,zero_zero(X_a)) = zero_zero(X_a) ) ),
inference(modus_ponens,[status(thm)],[41,34]) ).
tff(43,plain,
( ( ~ ! [X_a: $i] :
( ~ mult_zero(X_a)
| ! [A_1: $i] : ( times_times(X_a,A_1,zero_zero(X_a)) = zero_zero(X_a) ) )
| ~ mult_zero(int)
| ! [A_1: $i] : ( times_times(int,A_1,zero_zero(int)) = zero_zero(int) ) )
<=> ( ~ ! [X_a: $i] :
( ~ mult_zero(X_a)
| ! [A_1: $i] : ( times_times(X_a,A_1,zero_zero(X_a)) = zero_zero(X_a) ) )
| ~ mult_zero(int)
| ! [A_1: $i] : ( times_times(int,A_1,zero_zero(int)) = zero_zero(int) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
( ~ ! [X_a: $i] :
( ~ mult_zero(X_a)
| ! [A_1: $i] : ( times_times(X_a,A_1,zero_zero(X_a)) = zero_zero(X_a) ) )
| ~ mult_zero(int)
| ! [A_1: $i] : ( times_times(int,A_1,zero_zero(int)) = zero_zero(int) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(45,plain,
( ~ ! [X_a: $i] :
( ~ mult_zero(X_a)
| ! [A_1: $i] : ( times_times(X_a,A_1,zero_zero(X_a)) = zero_zero(X_a) ) )
| ~ mult_zero(int)
| ! [A_1: $i] : ( times_times(int,A_1,zero_zero(int)) = zero_zero(int) ) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [A_1: $i] : ( times_times(int,A_1,zero_zero(int)) = zero_zero(int) ),
inference(unit_resolution,[status(thm)],[45,42,29]) ).
tff(47,plain,
( ~ ! [A_1: $i] : ( times_times(int,A_1,zero_zero(int)) = zero_zero(int) )
| ( times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),number_number_of(int,bit1(zero_zero(int)))),zero_zero(int)) = zero_zero(int) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(48,plain,
times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),number_number_of(int,bit1(zero_zero(int)))),zero_zero(int)) = zero_zero(int),
inference(unit_resolution,[status(thm)],[47,46]) ).
tff(49,plain,
zero_zero(int) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),number_number_of(int,bit1(zero_zero(int)))),zero_zero(int)),
inference(symmetry,[status(thm)],[48]) ).
tff(50,plain,
( ( ti(int,pls) = pls )
<=> ( ti(int,zero_zero(int)) = zero_zero(int) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
( ( ti(int,pls) = pls )
<=> ( ti(int,pls) = pls ) ),
inference(rewrite,[status(thm)],]) ).
tff(52,axiom,
ti(int,pls) = pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Int_OPls_res) ).
tff(53,plain,
ti(int,pls) = pls,
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
ti(int,zero_zero(int)) = zero_zero(int),
inference(modus_ponens,[status(thm)],[53,50]) ).
tff(55,plain,
^ [Z_1: $i] :
refl(
( ( ord_less_eq(int,one_one(int),Z_1)
<=> ord_less(int,zero_zero(int),Z_1) )
<=> ( ord_less_eq(int,one_one(int),Z_1)
<=> ord_less(int,zero_zero(int),Z_1) ) )),
inference(bind,[status(th)],]) ).
tff(56,plain,
( ! [Z_1: $i] :
( ord_less_eq(int,one_one(int),Z_1)
<=> ord_less(int,zero_zero(int),Z_1) )
<=> ! [Z_1: $i] :
( ord_less_eq(int,one_one(int),Z_1)
<=> ord_less(int,zero_zero(int),Z_1) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,plain,
( ! [Z_1: $i] :
( ord_less_eq(int,one_one(int),Z_1)
<=> ord_less(int,zero_zero(int),Z_1) )
<=> ! [Z_1: $i] :
( ord_less_eq(int,one_one(int),Z_1)
<=> ord_less(int,zero_zero(int),Z_1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(58,axiom,
! [Z_1: $i] :
( ord_less_eq(int,one_one(int),Z_1)
<=> ord_less(int,zero_zero(int),Z_1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_int__one__le__iff__zero__less) ).
tff(59,plain,
! [Z_1: $i] :
( ord_less_eq(int,one_one(int),Z_1)
<=> ord_less(int,zero_zero(int),Z_1) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
! [Z_1: $i] :
( ord_less_eq(int,one_one(int),Z_1)
<=> ord_less(int,zero_zero(int),Z_1) ),
inference(skolemize,[status(sab)],[59]) ).
tff(61,plain,
! [Z_1: $i] :
( ord_less_eq(int,one_one(int),Z_1)
<=> ord_less(int,zero_zero(int),Z_1) ),
inference(modus_ponens,[status(thm)],[60,56]) ).
tff(62,plain,
( ~ ! [Z_1: $i] :
( ord_less_eq(int,one_one(int),Z_1)
<=> ord_less(int,zero_zero(int),Z_1) )
| ( ord_less_eq(int,one_one(int),t)
<=> ord_less(int,zero_zero(int),t) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(63,plain,
( ord_less_eq(int,one_one(int),t)
<=> ord_less(int,zero_zero(int),t) ),
inference(unit_resolution,[status(thm)],[62,61]) ).
tff(64,plain,
( ~ ord_less_eq(int,one_one(int),t)
<=> ~ ord_less_eq(int,one_one(int),t) ),
inference(rewrite,[status(thm)],]) ).
tff(65,axiom,
~ ord_less_eq(int,one_one(int),t),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5__096_126_A1_A_060_061_At_096) ).
tff(66,plain,
~ ord_less_eq(int,one_one(int),t),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
( ~ ( ord_less_eq(int,one_one(int),t)
<=> ord_less(int,zero_zero(int),t) )
| ord_less_eq(int,one_one(int),t)
| ~ ord_less(int,zero_zero(int),t) ),
inference(tautology,[status(thm)],]) ).
tff(68,plain,
( ~ ( ord_less_eq(int,one_one(int),t)
<=> ord_less(int,zero_zero(int),t) )
| ~ ord_less(int,zero_zero(int),t) ),
inference(unit_resolution,[status(thm)],[67,66]) ).
tff(69,plain,
~ ord_less(int,zero_zero(int),t),
inference(unit_resolution,[status(thm)],[68,63]) ).
tff(70,plain,
^ [B: $i,A_1: $i] :
refl(
( ( ord_less(int,zero_zero(int),B)
| ~ ord_less(int,zero_zero(int),A_1)
| ~ ord_less(int,zero_zero(int),times_times(int,A_1,B)) )
<=> ( ord_less(int,zero_zero(int),B)
| ~ ord_less(int,zero_zero(int),A_1)
| ~ ord_less(int,zero_zero(int),times_times(int,A_1,B)) ) )),
inference(bind,[status(th)],]) ).
tff(71,plain,
( ! [B: $i,A_1: $i] :
( ord_less(int,zero_zero(int),B)
| ~ ord_less(int,zero_zero(int),A_1)
| ~ ord_less(int,zero_zero(int),times_times(int,A_1,B)) )
<=> ! [B: $i,A_1: $i] :
( ord_less(int,zero_zero(int),B)
| ~ ord_less(int,zero_zero(int),A_1)
| ~ ord_less(int,zero_zero(int),times_times(int,A_1,B)) ) ),
inference(quant_intro,[status(thm)],[70]) ).
tff(72,plain,
( ! [B: $i,A_1: $i] :
( ord_less(int,zero_zero(int),B)
| ~ ord_less(int,zero_zero(int),A_1)
| ~ ord_less(int,zero_zero(int),times_times(int,A_1,B)) )
<=> ! [B: $i,A_1: $i] :
( ord_less(int,zero_zero(int),B)
| ~ ord_less(int,zero_zero(int),A_1)
| ~ ord_less(int,zero_zero(int),times_times(int,A_1,B)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(73,plain,
^ [B: $i,A_1: $i] :
trans(
monotonicity(
rewrite(
( ( ord_less(int,zero_zero(int),times_times(int,A_1,B))
=> ord_less(int,zero_zero(int),B) )
<=> ( ~ ord_less(int,zero_zero(int),times_times(int,A_1,B))
| ord_less(int,zero_zero(int),B) ) )),
( ( ord_less(int,zero_zero(int),A_1)
=> ( ord_less(int,zero_zero(int),times_times(int,A_1,B))
=> ord_less(int,zero_zero(int),B) ) )
<=> ( ord_less(int,zero_zero(int),A_1)
=> ( ~ ord_less(int,zero_zero(int),times_times(int,A_1,B))
| ord_less(int,zero_zero(int),B) ) ) )),
rewrite(
( ( ord_less(int,zero_zero(int),A_1)
=> ( ~ ord_less(int,zero_zero(int),times_times(int,A_1,B))
| ord_less(int,zero_zero(int),B) ) )
<=> ( ord_less(int,zero_zero(int),B)
| ~ ord_less(int,zero_zero(int),A_1)
| ~ ord_less(int,zero_zero(int),times_times(int,A_1,B)) ) )),
( ( ord_less(int,zero_zero(int),A_1)
=> ( ord_less(int,zero_zero(int),times_times(int,A_1,B))
=> ord_less(int,zero_zero(int),B) ) )
<=> ( ord_less(int,zero_zero(int),B)
| ~ ord_less(int,zero_zero(int),A_1)
| ~ ord_less(int,zero_zero(int),times_times(int,A_1,B)) ) )),
inference(bind,[status(th)],]) ).
tff(74,plain,
( ! [B: $i,A_1: $i] :
( ord_less(int,zero_zero(int),A_1)
=> ( ord_less(int,zero_zero(int),times_times(int,A_1,B))
=> ord_less(int,zero_zero(int),B) ) )
<=> ! [B: $i,A_1: $i] :
( ord_less(int,zero_zero(int),B)
| ~ ord_less(int,zero_zero(int),A_1)
| ~ ord_less(int,zero_zero(int),times_times(int,A_1,B)) ) ),
inference(quant_intro,[status(thm)],[73]) ).
tff(75,axiom,
! [B: $i,A_1: $i] :
( ord_less(int,zero_zero(int),A_1)
=> ( ord_less(int,zero_zero(int),times_times(int,A_1,B))
=> ord_less(int,zero_zero(int),B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_pos__zmult__pos) ).
tff(76,plain,
! [B: $i,A_1: $i] :
( ord_less(int,zero_zero(int),B)
| ~ ord_less(int,zero_zero(int),A_1)
| ~ ord_less(int,zero_zero(int),times_times(int,A_1,B)) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
! [B: $i,A_1: $i] :
( ord_less(int,zero_zero(int),B)
| ~ ord_less(int,zero_zero(int),A_1)
| ~ ord_less(int,zero_zero(int),times_times(int,A_1,B)) ),
inference(modus_ponens,[status(thm)],[76,72]) ).
tff(78,plain,
! [B: $i,A_1: $i] :
( ord_less(int,zero_zero(int),B)
| ~ ord_less(int,zero_zero(int),A_1)
| ~ ord_less(int,zero_zero(int),times_times(int,A_1,B)) ),
inference(skolemize,[status(sab)],[77]) ).
tff(79,plain,
! [B: $i,A_1: $i] :
( ord_less(int,zero_zero(int),B)
| ~ ord_less(int,zero_zero(int),A_1)
| ~ ord_less(int,zero_zero(int),times_times(int,A_1,B)) ),
inference(modus_ponens,[status(thm)],[78,71]) ).
tff(80,plain,
( ord_less(int,zero_zero(int),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
<=> ord_less(int,zero_zero(int),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int))) ),
inference(rewrite,[status(thm)],]) ).
tff(81,plain,
( ord_less(int,zero_zero(int),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
<=> ord_less(int,zero_zero(int),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) ),
inference(rewrite,[status(thm)],]) ).
tff(82,axiom,
ord_less(int,zero_zero(int),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_p0) ).
tff(83,plain,
ord_less(int,zero_zero(int),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
ord_less(int,zero_zero(int),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int))),
inference(modus_ponens,[status(thm)],[83,80]) ).
tff(85,plain,
( ( ~ ! [B: $i,A_1: $i] :
( ord_less(int,zero_zero(int),B)
| ~ ord_less(int,zero_zero(int),A_1)
| ~ ord_less(int,zero_zero(int),times_times(int,A_1,B)) )
| ~ ord_less(int,zero_zero(int),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)))
| ord_less(int,zero_zero(int),t)
| ~ ord_less(int,zero_zero(int),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t)) )
<=> ( ~ ! [B: $i,A_1: $i] :
( ord_less(int,zero_zero(int),B)
| ~ ord_less(int,zero_zero(int),A_1)
| ~ ord_less(int,zero_zero(int),times_times(int,A_1,B)) )
| ~ ord_less(int,zero_zero(int),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)))
| ord_less(int,zero_zero(int),t)
| ~ ord_less(int,zero_zero(int),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(86,plain,
( ( ord_less(int,zero_zero(int),t)
| ~ ord_less(int,zero_zero(int),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)))
| ~ ord_less(int,zero_zero(int),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t)) )
<=> ( ~ ord_less(int,zero_zero(int),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)))
| ord_less(int,zero_zero(int),t)
| ~ ord_less(int,zero_zero(int),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(87,plain,
( ( ~ ! [B: $i,A_1: $i] :
( ord_less(int,zero_zero(int),B)
| ~ ord_less(int,zero_zero(int),A_1)
| ~ ord_less(int,zero_zero(int),times_times(int,A_1,B)) )
| ord_less(int,zero_zero(int),t)
| ~ ord_less(int,zero_zero(int),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)))
| ~ ord_less(int,zero_zero(int),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t)) )
<=> ( ~ ! [B: $i,A_1: $i] :
( ord_less(int,zero_zero(int),B)
| ~ ord_less(int,zero_zero(int),A_1)
| ~ ord_less(int,zero_zero(int),times_times(int,A_1,B)) )
| ~ ord_less(int,zero_zero(int),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)))
| ord_less(int,zero_zero(int),t)
| ~ ord_less(int,zero_zero(int),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t)) ) ),
inference(monotonicity,[status(thm)],[86]) ).
tff(88,plain,
( ( ~ ! [B: $i,A_1: $i] :
( ord_less(int,zero_zero(int),B)
| ~ ord_less(int,zero_zero(int),A_1)
| ~ ord_less(int,zero_zero(int),times_times(int,A_1,B)) )
| ord_less(int,zero_zero(int),t)
| ~ ord_less(int,zero_zero(int),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)))
| ~ ord_less(int,zero_zero(int),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t)) )
<=> ( ~ ! [B: $i,A_1: $i] :
( ord_less(int,zero_zero(int),B)
| ~ ord_less(int,zero_zero(int),A_1)
| ~ ord_less(int,zero_zero(int),times_times(int,A_1,B)) )
| ~ ord_less(int,zero_zero(int),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)))
| ord_less(int,zero_zero(int),t)
| ~ ord_less(int,zero_zero(int),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t)) ) ),
inference(transitivity,[status(thm)],[87,85]) ).
tff(89,plain,
( ~ ! [B: $i,A_1: $i] :
( ord_less(int,zero_zero(int),B)
| ~ ord_less(int,zero_zero(int),A_1)
| ~ ord_less(int,zero_zero(int),times_times(int,A_1,B)) )
| ord_less(int,zero_zero(int),t)
| ~ ord_less(int,zero_zero(int),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)))
| ~ ord_less(int,zero_zero(int),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t)) ),
inference(quant_inst,[status(thm)],]) ).
tff(90,plain,
( ~ ! [B: $i,A_1: $i] :
( ord_less(int,zero_zero(int),B)
| ~ ord_less(int,zero_zero(int),A_1)
| ~ ord_less(int,zero_zero(int),times_times(int,A_1,B)) )
| ~ ord_less(int,zero_zero(int),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)))
| ord_less(int,zero_zero(int),t)
| ~ ord_less(int,zero_zero(int),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t)) ),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
( ord_less(int,zero_zero(int),t)
| ~ ord_less(int,zero_zero(int),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t)) ),
inference(unit_resolution,[status(thm)],[90,84,79]) ).
tff(92,plain,
~ ord_less(int,zero_zero(int),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t)),
inference(unit_resolution,[status(thm)],[91,69]) ).
tff(93,plain,
( ( plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(zero_zero(int))))),one_one(int)) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t) )
<=> ( minus_minus(int,power_power(int,s,number_number_of(nat,bit0(bit1(zero_zero(int))))),number_number_of(int,min)) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t) ) ),
inference(rewrite,[status(thm)],]) ).
tff(94,plain,
( ( plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t) )
<=> ( plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(zero_zero(int))))),one_one(int)) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t) ) ),
inference(rewrite,[status(thm)],]) ).
tff(95,plain,
( ( plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t) )
<=> ( plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t) ) ),
inference(rewrite,[status(thm)],]) ).
tff(96,axiom,
plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_t) ).
tff(97,plain,
plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(zero_zero(int))))),one_one(int)) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t),
inference(modus_ponens,[status(thm)],[97,94]) ).
tff(99,plain,
minus_minus(int,power_power(int,s,number_number_of(nat,bit0(bit1(zero_zero(int))))),number_number_of(int,min)) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t),
inference(modus_ponens,[status(thm)],[98,93]) ).
tff(100,plain,
times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t) = minus_minus(int,power_power(int,s,number_number_of(nat,bit0(bit1(zero_zero(int))))),number_number_of(int,min)),
inference(symmetry,[status(thm)],[99]) ).
tff(101,plain,
( ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t),zero_zero(int))
<=> ord_less(int,minus_minus(int,power_power(int,s,number_number_of(nat,bit0(bit1(zero_zero(int))))),number_number_of(int,min)),zero_zero(int)) ),
inference(monotonicity,[status(thm)],[100]) ).
tff(102,plain,
( ord_less(int,minus_minus(int,power_power(int,s,number_number_of(nat,bit0(bit1(zero_zero(int))))),number_number_of(int,min)),zero_zero(int))
<=> ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t),zero_zero(int)) ),
inference(symmetry,[status(thm)],[101]) ).
tff(103,plain,
( ~ ord_less(int,minus_minus(int,power_power(int,s,number_number_of(nat,bit0(bit1(zero_zero(int))))),number_number_of(int,min)),zero_zero(int))
<=> ~ ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t),zero_zero(int)) ),
inference(monotonicity,[status(thm)],[102]) ).
tff(104,plain,
( ~ ord_less(int,plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(zero_zero(int))))),one_one(int)),zero_zero(int))
<=> ~ ord_less(int,minus_minus(int,power_power(int,s,number_number_of(nat,bit0(bit1(zero_zero(int))))),number_number_of(int,min)),zero_zero(int)) ),
inference(rewrite,[status(thm)],]) ).
tff(105,plain,
( ~ ord_less(int,plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),zero_zero(int))
<=> ~ ord_less(int,plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(zero_zero(int))))),one_one(int)),zero_zero(int)) ),
inference(rewrite,[status(thm)],]) ).
tff(106,plain,
( ~ ord_less(int,plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),zero_zero(int))
<=> ~ ord_less(int,plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),zero_zero(int)) ),
inference(rewrite,[status(thm)],]) ).
tff(107,axiom,
~ ord_less(int,plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),zero_zero(int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(108,plain,
~ ord_less(int,plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),zero_zero(int)),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
~ ord_less(int,plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(zero_zero(int))))),one_one(int)),zero_zero(int)),
inference(modus_ponens,[status(thm)],[108,105]) ).
tff(110,plain,
~ ord_less(int,minus_minus(int,power_power(int,s,number_number_of(nat,bit0(bit1(zero_zero(int))))),number_number_of(int,min)),zero_zero(int)),
inference(modus_ponens,[status(thm)],[109,104]) ).
tff(111,plain,
~ ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t),zero_zero(int)),
inference(modus_ponens,[status(thm)],[110,103]) ).
tff(112,plain,
^ [X: $i,Y: $i] :
refl(
( ( ( ti(int,X) = ti(int,Y) )
| ord_less(int,X,Y)
| ord_less(int,Y,X) )
<=> ( ( ti(int,X) = ti(int,Y) )
| ord_less(int,X,Y)
| ord_less(int,Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(113,plain,
( ! [X: $i,Y: $i] :
( ( ti(int,X) = ti(int,Y) )
| ord_less(int,X,Y)
| ord_less(int,Y,X) )
<=> ! [X: $i,Y: $i] :
( ( ti(int,X) = ti(int,Y) )
| ord_less(int,X,Y)
| ord_less(int,Y,X) ) ),
inference(quant_intro,[status(thm)],[112]) ).
tff(114,plain,
( ! [X: $i,Y: $i] :
( ( ti(int,X) = ti(int,Y) )
| ord_less(int,X,Y)
| ord_less(int,Y,X) )
<=> ! [X: $i,Y: $i] :
( ( ti(int,X) = ti(int,Y) )
| ord_less(int,X,Y)
| ord_less(int,Y,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(115,plain,
^ [X: $i,Y: $i] :
trans(
monotonicity(
rewrite(
( ( ord_less(int,X,Y)
| ( ti(int,X) = ti(int,Y) ) )
<=> ( ( ti(int,X) = ti(int,Y) )
| ord_less(int,X,Y) ) )),
( ( ord_less(int,X,Y)
| ( ti(int,X) = ti(int,Y) )
| ord_less(int,Y,X) )
<=> ( ( ti(int,X) = ti(int,Y) )
| ord_less(int,X,Y)
| ord_less(int,Y,X) ) )),
rewrite(
( ( ( ti(int,X) = ti(int,Y) )
| ord_less(int,X,Y)
| ord_less(int,Y,X) )
<=> ( ( ti(int,X) = ti(int,Y) )
| ord_less(int,X,Y)
| ord_less(int,Y,X) ) )),
( ( ord_less(int,X,Y)
| ( ti(int,X) = ti(int,Y) )
| ord_less(int,Y,X) )
<=> ( ( ti(int,X) = ti(int,Y) )
| ord_less(int,X,Y)
| ord_less(int,Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(116,plain,
( ! [X: $i,Y: $i] :
( ord_less(int,X,Y)
| ( ti(int,X) = ti(int,Y) )
| ord_less(int,Y,X) )
<=> ! [X: $i,Y: $i] :
( ( ti(int,X) = ti(int,Y) )
| ord_less(int,X,Y)
| ord_less(int,Y,X) ) ),
inference(quant_intro,[status(thm)],[115]) ).
tff(117,axiom,
! [X: $i,Y: $i] :
( ord_less(int,X,Y)
| ( ti(int,X) = ti(int,Y) )
| ord_less(int,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_zless__linear) ).
tff(118,plain,
! [X: $i,Y: $i] :
( ( ti(int,X) = ti(int,Y) )
| ord_less(int,X,Y)
| ord_less(int,Y,X) ),
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
! [X: $i,Y: $i] :
( ( ti(int,X) = ti(int,Y) )
| ord_less(int,X,Y)
| ord_less(int,Y,X) ),
inference(modus_ponens,[status(thm)],[118,114]) ).
tff(120,plain,
! [X: $i,Y: $i] :
( ( ti(int,X) = ti(int,Y) )
| ord_less(int,X,Y)
| ord_less(int,Y,X) ),
inference(skolemize,[status(sab)],[119]) ).
tff(121,plain,
! [X: $i,Y: $i] :
( ( ti(int,X) = ti(int,Y) )
| ord_less(int,X,Y)
| ord_less(int,Y,X) ),
inference(modus_ponens,[status(thm)],[120,113]) ).
tff(122,plain,
( ( ~ ! [X: $i,Y: $i] :
( ( ti(int,X) = ti(int,Y) )
| ord_less(int,X,Y)
| ord_less(int,Y,X) )
| ( ti(int,zero_zero(int)) = ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t)) )
| ord_less(int,zero_zero(int),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t))
| ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t),zero_zero(int)) )
<=> ( ~ ! [X: $i,Y: $i] :
( ( ti(int,X) = ti(int,Y) )
| ord_less(int,X,Y)
| ord_less(int,Y,X) )
| ( ti(int,zero_zero(int)) = ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t)) )
| ord_less(int,zero_zero(int),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t))
| ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t),zero_zero(int)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(123,plain,
( ~ ! [X: $i,Y: $i] :
( ( ti(int,X) = ti(int,Y) )
| ord_less(int,X,Y)
| ord_less(int,Y,X) )
| ( ti(int,zero_zero(int)) = ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t)) )
| ord_less(int,zero_zero(int),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t))
| ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t),zero_zero(int)) ),
inference(quant_inst,[status(thm)],]) ).
tff(124,plain,
( ~ ! [X: $i,Y: $i] :
( ( ti(int,X) = ti(int,Y) )
| ord_less(int,X,Y)
| ord_less(int,Y,X) )
| ( ti(int,zero_zero(int)) = ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t)) )
| ord_less(int,zero_zero(int),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t))
| ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t),zero_zero(int)) ),
inference(modus_ponens,[status(thm)],[123,122]) ).
tff(125,plain,
( ( ti(int,zero_zero(int)) = ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t)) )
| ord_less(int,zero_zero(int),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t))
| ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t),zero_zero(int)) ),
inference(unit_resolution,[status(thm)],[124,121]) ).
tff(126,plain,
ti(int,zero_zero(int)) = ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t)),
inference(unit_resolution,[status(thm)],[125,111,92]) ).
tff(127,plain,
ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t)) = ti(int,zero_zero(int)),
inference(symmetry,[status(thm)],[126]) ).
tff(128,plain,
ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t)) = ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),zero_zero(int))),
inference(transitivity,[status(thm)],[127,54,49,26,18]) ).
tff(129,plain,
^ [Z_1: $i,W_1: $i] :
refl(
( ( ord_less(int,Z_1,W_1)
<=> ~ ( ~ ord_less_eq(int,Z_1,W_1)
| ( ti(int,Z_1) = ti(int,W_1) ) ) )
<=> ( ord_less(int,Z_1,W_1)
<=> ~ ( ~ ord_less_eq(int,Z_1,W_1)
| ( ti(int,Z_1) = ti(int,W_1) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(130,plain,
( ! [Z_1: $i,W_1: $i] :
( ord_less(int,Z_1,W_1)
<=> ~ ( ~ ord_less_eq(int,Z_1,W_1)
| ( ti(int,Z_1) = ti(int,W_1) ) ) )
<=> ! [Z_1: $i,W_1: $i] :
( ord_less(int,Z_1,W_1)
<=> ~ ( ~ ord_less_eq(int,Z_1,W_1)
| ( ti(int,Z_1) = ti(int,W_1) ) ) ) ),
inference(quant_intro,[status(thm)],[129]) ).
tff(131,plain,
^ [Z_1: $i,W_1: $i] :
rewrite(
( ( ord_less(int,Z_1,W_1)
<=> ( ord_less_eq(int,Z_1,W_1)
& ( ti(int,Z_1) != ti(int,W_1) ) ) )
<=> ( ord_less(int,Z_1,W_1)
<=> ~ ( ~ ord_less_eq(int,Z_1,W_1)
| ( ti(int,Z_1) = ti(int,W_1) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(132,plain,
( ! [Z_1: $i,W_1: $i] :
( ord_less(int,Z_1,W_1)
<=> ( ord_less_eq(int,Z_1,W_1)
& ( ti(int,Z_1) != ti(int,W_1) ) ) )
<=> ! [Z_1: $i,W_1: $i] :
( ord_less(int,Z_1,W_1)
<=> ~ ( ~ ord_less_eq(int,Z_1,W_1)
| ( ti(int,Z_1) = ti(int,W_1) ) ) ) ),
inference(quant_intro,[status(thm)],[131]) ).
tff(133,plain,
( ! [Z_1: $i,W_1: $i] :
( ord_less(int,Z_1,W_1)
<=> ( ord_less_eq(int,Z_1,W_1)
& ( ti(int,Z_1) != ti(int,W_1) ) ) )
<=> ! [Z_1: $i,W_1: $i] :
( ord_less(int,Z_1,W_1)
<=> ( ord_less_eq(int,Z_1,W_1)
& ( ti(int,Z_1) != ti(int,W_1) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(134,axiom,
! [Z_1: $i,W_1: $i] :
( ord_less(int,Z_1,W_1)
<=> ( ord_less_eq(int,Z_1,W_1)
& ( ti(int,Z_1) != ti(int,W_1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_zless__le) ).
tff(135,plain,
! [Z_1: $i,W_1: $i] :
( ord_less(int,Z_1,W_1)
<=> ( ord_less_eq(int,Z_1,W_1)
& ( ti(int,Z_1) != ti(int,W_1) ) ) ),
inference(modus_ponens,[status(thm)],[134,133]) ).
tff(136,plain,
! [Z_1: $i,W_1: $i] :
( ord_less(int,Z_1,W_1)
<=> ( ord_less_eq(int,Z_1,W_1)
& ( ti(int,Z_1) != ti(int,W_1) ) ) ),
inference(skolemize,[status(sab)],[135]) ).
tff(137,plain,
! [Z_1: $i,W_1: $i] :
( ord_less(int,Z_1,W_1)
<=> ~ ( ~ ord_less_eq(int,Z_1,W_1)
| ( ti(int,Z_1) = ti(int,W_1) ) ) ),
inference(modus_ponens,[status(thm)],[136,132]) ).
tff(138,plain,
! [Z_1: $i,W_1: $i] :
( ord_less(int,Z_1,W_1)
<=> ~ ( ~ ord_less_eq(int,Z_1,W_1)
| ( ti(int,Z_1) = ti(int,W_1) ) ) ),
inference(modus_ponens,[status(thm)],[137,130]) ).
tff(139,plain,
( ~ ! [Z_1: $i,W_1: $i] :
( ord_less(int,Z_1,W_1)
<=> ~ ( ~ ord_less_eq(int,Z_1,W_1)
| ( ti(int,Z_1) = ti(int,W_1) ) ) )
| ( ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),zero_zero(int)))
<=> ~ ( ~ ord_less_eq(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),zero_zero(int)))
| ( ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t)) = ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),zero_zero(int))) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(140,plain,
( ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),zero_zero(int)))
<=> ~ ( ~ ord_less_eq(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),zero_zero(int)))
| ( ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t)) = ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),zero_zero(int))) ) ) ),
inference(unit_resolution,[status(thm)],[139,138]) ).
tff(141,plain,
( ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),zero_zero(int)))
<=> ord_less(int,minus_minus(int,power_power(int,s,number_number_of(nat,bit0(bit1(zero_zero(int))))),number_number_of(int,min)),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),zero_zero(int))) ),
inference(monotonicity,[status(thm)],[100]) ).
tff(142,plain,
( ord_less(int,minus_minus(int,power_power(int,s,number_number_of(nat,bit0(bit1(zero_zero(int))))),number_number_of(int,min)),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),zero_zero(int)))
<=> ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),zero_zero(int))) ),
inference(symmetry,[status(thm)],[141]) ).
tff(143,plain,
( ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),zero_zero(int)))
<=> ord_less(int,minus_minus(int,power_power(int,s,number_number_of(nat,bit0(bit1(zero_zero(int))))),number_number_of(int,min)),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),zero_zero(int))) ),
inference(rewrite,[status(thm)],]) ).
tff(144,plain,
( ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int)))
<=> ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),zero_zero(int))) ),
inference(rewrite,[status(thm)],]) ).
tff(145,plain,
( ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int)))
<=> ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int))) ),
inference(rewrite,[status(thm)],]) ).
tff(146,axiom,
ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096) ).
tff(147,plain,
ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int))),
inference(modus_ponens,[status(thm)],[146,145]) ).
tff(148,plain,
ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),zero_zero(int))),
inference(modus_ponens,[status(thm)],[147,144]) ).
tff(149,plain,
ord_less(int,minus_minus(int,power_power(int,s,number_number_of(nat,bit0(bit1(zero_zero(int))))),number_number_of(int,min)),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),zero_zero(int))),
inference(modus_ponens,[status(thm)],[148,143]) ).
tff(150,plain,
ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),zero_zero(int))),
inference(modus_ponens,[status(thm)],[149,142]) ).
tff(151,plain,
( ~ ( ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),zero_zero(int)))
<=> ~ ( ~ ord_less_eq(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),zero_zero(int)))
| ( ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t)) = ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),zero_zero(int))) ) ) )
| ~ ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),zero_zero(int)))
| ~ ( ~ ord_less_eq(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),zero_zero(int)))
| ( ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t)) = ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),zero_zero(int))) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(152,plain,
~ ( ~ ord_less_eq(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),zero_zero(int)))
| ( ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t)) = ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),zero_zero(int))) ) ),
inference(unit_resolution,[status(thm)],[151,150,140]) ).
tff(153,plain,
( ~ ord_less_eq(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),zero_zero(int)))
| ( ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t)) = ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),zero_zero(int))) )
| ( ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t)) != ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),zero_zero(int))) ) ),
inference(tautology,[status(thm)],]) ).
tff(154,plain,
ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),t)) != ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int))))),m),one_one(int)),zero_zero(int))),
inference(unit_resolution,[status(thm)],[153,152]) ).
tff(155,plain,
$false,
inference(unit_resolution,[status(thm)],[154,128]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUM924+6 : TPTP v8.1.0. Released v5.3.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Sep 2 15:49:43 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.94/0.92 % SZS status Theorem
% 0.94/0.92 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------