%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM924_1 : TPTP v9.0.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 : Sat Jun 21 05:22:21 AM UTC 2025
% Result : Theorem 0.19s 0.52s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 20
% Syntax : Number of formulae : 50 ( 34 unt; 0 typ; 0 def)
% Number of atoms : 72 ( 53 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 29 ( 10 ~; 3 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 8 ( 3 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 40 ( 36 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
tff(ord_less_int_type,type,
ord_less_int: ( int * int ) > $o ).
tff(times_times_int_type,type,
times_times_int: ( int * int ) > int ).
tff(zero_zero_int_type,type,
zero_zero_int: int ).
tff(plus_plus_int_type,type,
plus_plus_int: ( int * int ) > int ).
tff(one_one_int_type,type,
one_one_int: int ).
tff(m_type,type,
m: int ).
tff(number_number_of_int_type,type,
number_number_of_int: int > int ).
tff(bit0_type,type,
bit0: int > int ).
tff(bit1_type,type,
bit1: int > int ).
tff(pls_type,type,
pls: int ).
tff(t_type,type,
t: int ).
tff(power_power_int_type,type,
power_power_int: ( int * nat ) > int ).
tff(number_number_of_nat_type,type,
number_number_of_nat: int > nat ).
tff(s_type,type,
s: int ).
tff(1,plain,
( ( zero_zero_int = number_number_of_int(pls) )
<=> ( zero_zero_int = number_number_of_int(pls) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
zero_zero_int = number_number_of_int(pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_zero__is__num__zero) ).
tff(3,plain,
zero_zero_int = number_number_of_int(pls),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
number_number_of_int(pls) = zero_zero_int,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
^ [K_1: int] :
refl(( ( number_number_of_int(K_1) = K_1 )
<=> ( number_number_of_int(K_1) = K_1 ) )),
inference(bind,[status(th)],[]) ).
tff(6,plain,
( ! [K_1: int] : ( number_number_of_int(K_1) = K_1 )
<=> ! [K_1: int] : ( number_number_of_int(K_1) = K_1 ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [K_1: int] : ( number_number_of_int(K_1) = K_1 )
<=> ! [K_1: int] : ( number_number_of_int(K_1) = K_1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
! [K_1: int] : ( number_number_of_int(K_1) = K_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_number__of__is__id) ).
tff(9,plain,
! [K_1: int] : ( number_number_of_int(K_1) = K_1 ),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
! [K_1: int] : ( number_number_of_int(K_1) = K_1 ),
inference(skolemize,[status(sab)],[9]) ).
tff(11,plain,
! [K_1: int] : ( number_number_of_int(K_1) = K_1 ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
( ~ ! [K_1: int] : ( number_number_of_int(K_1) = K_1 )
| ( number_number_of_int(pls) = pls ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
number_number_of_int(pls) = pls,
inference(unit_resolution,[status(thm)],[12,11]) ).
tff(14,plain,
pls = number_number_of_int(pls),
inference(symmetry,[status(thm)],[13]) ).
tff(15,plain,
^ [W: int] :
refl(( ( times_times_int(pls,W) = pls )
<=> ( times_times_int(pls,W) = pls ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [W: int] : ( times_times_int(pls,W) = pls )
<=> ! [W: int] : ( times_times_int(pls,W) = pls ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [W: int] : ( times_times_int(pls,W) = pls )
<=> ! [W: int] : ( times_times_int(pls,W) = pls ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
! [W: int] : ( times_times_int(pls,W) = pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_mult__Pls) ).
tff(19,plain,
! [W: int] : ( times_times_int(pls,W) = pls ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [W: int] : ( times_times_int(pls,W) = pls ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [W: int] : ( times_times_int(pls,W) = pls ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
( ~ ! [W: int] : ( times_times_int(pls,W) = pls )
| ( times_times_int(pls,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) = pls ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(23,plain,
times_times_int(pls,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) = pls,
inference(unit_resolution,[status(thm)],[22,21]) ).
tff(24,plain,
times_times_int(number_number_of_int(pls),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) = times_times_int(pls,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
inference(monotonicity,[status(thm)],[13]) ).
tff(25,plain,
times_times_int(zero_zero_int,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) = times_times_int(number_number_of_int(pls),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
inference(monotonicity,[status(thm)],[3]) ).
tff(26,plain,
^ [Z: int,W: int] :
refl(( ( times_times_int(Z,W) = times_times_int(W,Z) )
<=> ( times_times_int(Z,W) = times_times_int(W,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(27,plain,
( ! [Z: int,W: int] : ( times_times_int(Z,W) = times_times_int(W,Z) )
<=> ! [Z: int,W: int] : ( times_times_int(Z,W) = times_times_int(W,Z) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
( ! [Z: int,W: int] : ( times_times_int(Z,W) = times_times_int(W,Z) )
<=> ! [Z: int,W: int] : ( times_times_int(Z,W) = times_times_int(W,Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,axiom,
! [Z: int,W: int] : ( times_times_int(Z,W) = times_times_int(W,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_zmult__commute) ).
tff(30,plain,
! [Z: int,W: int] : ( times_times_int(Z,W) = times_times_int(W,Z) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [Z: int,W: int] : ( times_times_int(Z,W) = times_times_int(W,Z) ),
inference(skolemize,[status(sab)],[30]) ).
tff(32,plain,
! [Z: int,W: int] : ( times_times_int(Z,W) = times_times_int(W,Z) ),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,plain,
( ~ ! [Z: int,W: int] : ( times_times_int(Z,W) = times_times_int(W,Z) )
| ( times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int) = times_times_int(zero_zero_int,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int) = times_times_int(zero_zero_int,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
inference(unit_resolution,[status(thm)],[33,32]) ).
tff(35,plain,
times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int) = zero_zero_int,
inference(transitivity,[status(thm)],[34,25,24,23,14,4]) ).
tff(36,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(37,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(38,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)],[37,36]) ).
tff(39,plain,
times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t) = plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),
inference(symmetry,[status(thm)],[38]) ).
tff(40,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(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int) ),
inference(monotonicity,[status(thm)],[39,35]) ).
tff(41,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(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(symmetry,[status(thm)],[40]) ).
tff(42,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(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(monotonicity,[status(thm)],[41]) ).
tff(43,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(44,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(45,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)],[44,43]) ).
tff(46,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)],[45,42]) ).
tff(47,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(48,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(49,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)],[48,47]) ).
tff(50,plain,
$false,
inference(unit_resolution,[status(thm)],[49,46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM924_1 : TPTP v9.0.0. Released v5.3.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.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 Jun 20 02:03:33 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.52 % SZS status Theorem
% 0.19/0.52 % SZS output start Proof
% See solution above
% 0.19/0.53 % E exiting
%------------------------------------------------------------------------------