TSTP Solution File: ITP168^1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : ITP168^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n025.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 : Mon May 20 22:23:34 EDT 2024
% Result : Theorem 67.01s 22.14s
% Output : Refutation 67.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 157
% Syntax : Number of formulae : 274 ( 112 unt; 42 typ; 0 def)
% Number of atoms : 630 ( 174 equ; 6 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 2500 ( 64 ~; 22 |; 166 &;1924 @)
% ( 0 <=>; 324 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Number of types : 13 ( 12 usr)
% Number of type conns : 208 ( 208 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 30 usr; 11 con; 0-4 aty)
% Number of variables : 1017 ( 38 ^ 773 !; 206 ?;1017 :)
% Comments :
%------------------------------------------------------------------------------
thf(view_e665166499t_unit_type,type,
view_e665166499t_unit: $tType ).
thf(view_e774982825t_unit_type,type,
view_e774982825t_unit: $tType ).
thf(view_ext_real_int_type,type,
view_ext_real_int: $tType ).
thf(view_ext_nat_int_type,type,
view_ext_nat_int: $tType ).
thf(view_ext_nat_type,type,
view_ext_nat: $tType ).
thf(product_unit_type,type,
product_unit: $tType ).
thf(real_int_type,type,
real_int: $tType ).
thf(nat_int_type,type,
nat_int: $tType ).
thf(traffic_type,type,
traffic: $tType ).
thf(real_type,type,
real: $tType ).
thf(cars_type,type,
cars: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(minus_minus_real_type,type,
minus_minus_real: real > real > real ).
thf(defaul1399868459t_unit_type,type,
defaul1399868459t_unit: product_unit ).
thf(move_type,type,
move: traffic > traffic > view_e774982825t_unit > view_e774982825t_unit ).
thf(bot_bot_Product_unit_type,type,
bot_bot_Product_unit: product_unit ).
thf(ord_less_eq_nat_int_type,type,
ord_less_eq_nat_int: nat_int > nat_int > $o ).
thf(ord_less_eq_real_type,type,
ord_less_eq_real: real > real > $o ).
thf(product_Unity_type,type,
product_Unity: product_unit ).
thf(real_R_Chop_type,type,
real_R_Chop: real_int > real_int > real_int > $o ).
thf(real_shift_type,type,
real_shift: real_int > real > real_int ).
thf(abstract_type,type,
abstract: traffic > traffic > $o ).
thf(clm_type,type,
clm: traffic > cars > nat_int ).
thf(create_claim_type,type,
create_claim: traffic > cars > nat > traffic > $o ).
thf(create_reservation_type,type,
create_reservation: traffic > cars > traffic > $o ).
thf(evolve_type,type,
evolve: traffic > traffic > $o ).
thf(pos_type,type,
pos: traffic > cars > real ).
thf(res_type,type,
res: traffic > cars > nat_int ).
thf(withdraw_claim_type,type,
withdraw_claim: traffic > cars > traffic > $o ).
thf(withdraw_reservation_type,type,
withdraw_reservation: traffic > cars > nat > traffic > $o ).
thf(ext_Product_unit_type,type,
ext_Product_unit: view_e774982825t_unit > real_int ).
thf(hchop_type,type,
hchop: view_e774982825t_unit > view_e774982825t_unit > view_e774982825t_unit > $o ).
thf(lan_Product_unit_type,type,
lan_Product_unit: view_e774982825t_unit > nat_int ).
thf(more_Product_unit_type,type,
more_Product_unit: view_e774982825t_unit > product_unit ).
thf(own_Product_unit_type,type,
own_Product_unit: view_e774982825t_unit > cars ).
thf(switch_type,type,
switch: view_e774982825t_unit > cars > view_e774982825t_unit > $o ).
thf(view_e912666823t_unit_type,type,
view_e912666823t_unit: real_int > nat_int > cars > product_unit > view_e774982825t_unit ).
thf(ts_type,type,
ts: traffic ).
thf(ts2_type,type,
ts2: traffic ).
thf(ts_a_type,type,
ts_a: traffic ).
thf(ts3_type,type,
ts3: traffic ).
thf(v_type,type,
v: view_e774982825t_unit ).
thf(102,axiom,
! [A: traffic,B: cars,C: nat,D: traffic,E: view_e774982825t_unit] :
( ( withdraw_reservation @ A @ B @ C @ D )
=> ( ( move @ A @ D @ E )
= E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_traffic_Omove__stability__wdr) ).
thf(533,plain,
! [A: traffic,B: cars,C: nat,D: traffic,E: view_e774982825t_unit] :
( ( withdraw_reservation @ A @ B @ C @ D )
=> ( ( move @ A @ D @ E )
= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(64,axiom,
! [A: traffic,B: traffic,C: traffic] :
( ( evolve @ A @ B )
=> ( ( evolve @ B @ C )
=> ( evolve @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_traffic_Oevolve__trans) ).
thf(320,plain,
! [A: traffic,B: traffic,C: traffic] :
( ( evolve @ A @ B )
=> ( ( evolve @ B @ C )
=> ( evolve @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(73,axiom,
! [A: traffic,B: traffic,C: traffic > $o] :
( ( abstract @ A @ B )
=> ( ( C @ A )
=> ( ! [D: traffic,E: traffic] :
( ( abstract @ A @ D )
=> ( ( C @ D )
=> ( ( evolve @ D @ E )
=> ( C @ E ) ) ) )
=> ( ! [D: traffic,E: traffic] :
( ( abstract @ A @ D )
=> ( ( C @ D )
=> ( ? [F: cars,G: nat] : ( create_claim @ D @ F @ G @ E )
=> ( C @ E ) ) ) )
=> ( ! [D: traffic,E: traffic] :
( ( abstract @ A @ D )
=> ( ( C @ D )
=> ( ? [F: cars] : ( withdraw_claim @ D @ F @ E )
=> ( C @ E ) ) ) )
=> ( ! [D: traffic,E: traffic] :
( ( abstract @ A @ D )
=> ( ( C @ D )
=> ( ? [F: cars] : ( create_reservation @ D @ F @ E )
=> ( C @ E ) ) ) )
=> ( ! [D: traffic,E: traffic] :
( ( abstract @ A @ D )
=> ( ( C @ D )
=> ( ? [F: cars,G: nat] : ( withdraw_reservation @ D @ F @ G @ E )
=> ( C @ E ) ) ) )
=> ( C @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_traffic_Oabstract_Oinducts) ).
thf(351,plain,
! [A: traffic,B: traffic,C: traffic > $o] :
( ( abstract @ A @ B )
=> ( ( C @ A )
=> ( ! [D: traffic,E: traffic] :
( ( abstract @ A @ D )
=> ( ( C @ D )
=> ( ( evolve @ D @ E )
=> ( C @ E ) ) ) )
=> ( ! [D: traffic,E: traffic] :
( ( abstract @ A @ D )
=> ( ( C @ D )
=> ( ? [F: cars,G: nat] : ( create_claim @ D @ F @ G @ E )
=> ( C @ E ) ) ) )
=> ( ! [D: traffic,E: traffic] :
( ( abstract @ A @ D )
=> ( ( C @ D )
=> ( ? [F: cars] : ( withdraw_claim @ D @ F @ E )
=> ( C @ E ) ) ) )
=> ( ! [D: traffic,E: traffic] :
( ( abstract @ A @ D )
=> ( ( C @ D )
=> ( ? [F: cars] : ( create_reservation @ D @ F @ E )
=> ( C @ E ) ) ) )
=> ( ! [D: traffic,E: traffic] :
( ( abstract @ A @ D )
=> ( ( C @ D )
=> ( ? [F: cars,G: nat] : ( withdraw_reservation @ D @ F @ G @ E )
=> ( C @ E ) ) ) )
=> ( C @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(72,axiom,
! [A: traffic,B: cars,C: traffic,D: cars] :
( ( withdraw_claim @ A @ B @ C )
=> ( ( res @ A @ D )
= ( res @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_traffic_Owithdraw__clm__eq__res) ).
thf(347,plain,
! [A: traffic,B: cars,C: traffic,D: cars] :
( ( withdraw_claim @ A @ B @ C )
=> ( ( res @ A @ D )
= ( res @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(42,axiom,
! [A: view_e774982825t_unit,B: view_e774982825t_unit,C: view_e774982825t_unit,D: view_e774982825t_unit,E: cars] :
( ( ( hchop @ A @ B @ C )
& ( switch @ D @ E @ A ) )
=> ? [F: view_e774982825t_unit,G: view_e774982825t_unit] :
( ( switch @ F @ E @ B )
& ( switch @ G @ E @ C )
& ( hchop @ D @ F @ G ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_view_Oswitch__hchop2) ).
thf(249,plain,
! [A: view_e774982825t_unit,B: view_e774982825t_unit,C: view_e774982825t_unit,D: view_e774982825t_unit,E: cars] :
( ( ( hchop @ A @ B @ C )
& ( switch @ D @ E @ A ) )
=> ? [F: view_e774982825t_unit,G: view_e774982825t_unit] :
( ( switch @ F @ E @ B )
& ( switch @ G @ E @ C )
& ( hchop @ D @ F @ G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(96,axiom,
! [A: real_int,B: nat_int,C: cars,D: product_unit,E: real_int,F: nat_int,G: cars,H: product_unit] :
( ( ( view_e912666823t_unit @ A @ B @ C @ D )
= ( view_e912666823t_unit @ E @ F @ G @ H ) )
= ( ( A = E )
& ( B = F )
& ( C = G )
& ( D = H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_ext__inject) ).
thf(518,plain,
! [A: real_int,B: nat_int,C: cars,D: product_unit,E: real_int,F: nat_int,G: cars,H: product_unit] :
( ( ( view_e912666823t_unit @ A @ B @ C @ D )
= ( view_e912666823t_unit @ E @ F @ G @ H ) )
= ( ( A = E )
& ( B = F )
& ( C = G )
& ( D = H ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(90,axiom,
! [A: traffic,B: traffic] :
( ( abstract @ A @ B )
=> ( ( B != A )
=> ( ! [C: traffic] :
( ( abstract @ A @ C )
=> ~ ( evolve @ C @ B ) )
=> ( ! [C: traffic] :
( ( abstract @ A @ C )
=> ~ ? [D: cars,E: nat] : ( create_claim @ C @ D @ E @ B ) )
=> ( ! [C: traffic] :
( ( abstract @ A @ C )
=> ~ ? [D: cars] : ( withdraw_claim @ C @ D @ B ) )
=> ( ! [C: traffic] :
( ( abstract @ A @ C )
=> ~ ? [D: cars] : ( create_reservation @ C @ D @ B ) )
=> ~ ! [C: traffic] :
( ( abstract @ A @ C )
=> ~ ? [D: cars,E: nat] : ( withdraw_reservation @ C @ D @ E @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_traffic_Oabstract_Ocases) ).
thf(481,plain,
! [A: traffic,B: traffic] :
( ( abstract @ A @ B )
=> ( ( B != A )
=> ( ! [C: traffic] :
( ( abstract @ A @ C )
=> ~ ( evolve @ C @ B ) )
=> ( ! [C: traffic] :
( ( abstract @ A @ C )
=> ~ ? [D: cars,E: nat] : ( create_claim @ C @ D @ E @ B ) )
=> ( ! [C: traffic] :
( ( abstract @ A @ C )
=> ~ ? [D: cars] : ( withdraw_claim @ C @ D @ B ) )
=> ( ! [C: traffic] :
( ( abstract @ A @ C )
=> ~ ? [D: cars] : ( create_reservation @ C @ D @ B ) )
=> ~ ! [C: traffic] :
( ( abstract @ A @ C )
=> ~ ? [D: cars,E: nat] : ( withdraw_reservation @ C @ D @ E @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(15,axiom,
! [A: nat_int] : ( ord_less_eq_nat_int @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_dual__order_Orefl) ).
thf(170,plain,
! [A: nat_int] : ( ord_less_eq_nat_int @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(81,axiom,
! [A: view_e774982825t_unit > $o,B: view_e774982825t_unit] :
( ! [C: real_int,D: nat_int,E: cars] : ( A @ ( view_e912666823t_unit @ C @ D @ E @ product_Unity ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_induct) ).
thf(449,plain,
! [A: view_e774982825t_unit > $o,B: view_e774982825t_unit] :
( ! [C: real_int,D: nat_int,E: cars] : ( A @ ( view_e912666823t_unit @ C @ D @ E @ product_Unity ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(41,axiom,
! [A: traffic,B: cars,C: traffic] :
( ( create_reservation @ A @ B @ C )
=> ( ord_less_eq_nat_int @ ( clm @ A @ B ) @ ( res @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_traffic_Ocreate__res__subseteq2) ).
thf(247,plain,
! [A: traffic,B: cars,C: traffic] :
( ( create_reservation @ A @ B @ C )
=> ( ord_less_eq_nat_int @ ( clm @ A @ B ) @ ( res @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(48,axiom,
! [A: cars,B: traffic > view_e774982825t_unit > $o,C: traffic,D: view_e774982825t_unit] :
( ! [E: view_e774982825t_unit] :
( ( switch @ D @ A @ E )
=> ( B @ C @ E ) )
=> ~ ! [E: view_e774982825t_unit] :
( ( switch @ D @ A @ E )
=> ~ ( B @ C @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_local_Ohmlsl_Oat__neg__neg1) ).
thf(269,plain,
! [A: cars,B: traffic > view_e774982825t_unit > $o,C: traffic,D: view_e774982825t_unit] :
( ! [E: view_e774982825t_unit] :
( ( switch @ D @ A @ E )
=> ( B @ C @ E ) )
=> ~ ! [E: view_e774982825t_unit] :
( ( switch @ D @ A @ E )
=> ~ ( B @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(115,axiom,
( ( move @ ts3 @ ts_a @ v )
= ( move @ ts_a @ ts @ ( move @ ts3 @ ts_a @ v ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5__092_060open_062move_Ats_Ats_H_Av_A_061_Amove_Ats_H_Ats_H_H_A_Imove_Ats_Ats_H_Av_J_092_060close_062) ).
thf(570,plain,
( ( move @ ts3 @ ts_a @ v )
= ( move @ ts_a @ ts @ ( move @ ts3 @ ts_a @ v ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(21,axiom,
! [A: nat_int,B: nat_int,C: nat_int > nat_int,D: nat_int] :
( ( ord_less_eq_nat_int @ A @ B )
=> ( ( ord_less_eq_nat_int @ ( C @ B ) @ D )
=> ( ! [E: nat_int,F: nat_int] :
( ( ord_less_eq_nat_int @ E @ F )
=> ( ord_less_eq_nat_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat_int @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_order__subst2) ).
thf(184,plain,
! [A: nat_int,B: nat_int,C: nat_int > nat_int,D: nat_int] :
( ( ord_less_eq_nat_int @ A @ B )
=> ( ( ord_less_eq_nat_int @ ( C @ B ) @ D )
=> ( ! [E: nat_int,F: nat_int] :
( ( ord_less_eq_nat_int @ E @ F )
=> ( ord_less_eq_nat_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat_int @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(71,axiom,
! [A: traffic,B: traffic,C: traffic] :
( ( abstract @ A @ B )
=> ( ? [D: cars] : ( create_reservation @ B @ D @ C )
=> ( abstract @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_traffic_Ocr__res) ).
thf(344,plain,
! [A: traffic,B: traffic,C: traffic] :
( ( abstract @ A @ B )
=> ( ? [D: cars] : ( create_reservation @ B @ D @ C )
=> ( abstract @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(105,axiom,
abstract @ ts3 @ ts_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_cr__res_Ohyps_I1_J) ).
thf(542,plain,
abstract @ ts3 @ ts_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(112,axiom,
! [A: traffic,B: traffic,C: traffic,D: view_e774982825t_unit] :
( ( ( abstract @ A @ B )
& ( abstract @ B @ C ) )
=> ( ( move @ B @ C @ ( move @ A @ B @ D ) )
= ( move @ A @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_traffic_Omove__trans) ).
thf(559,plain,
! [A: traffic,B: traffic,C: traffic,D: view_e774982825t_unit] :
( ( ( abstract @ A @ B )
& ( abstract @ B @ C ) )
=> ( ( move @ B @ C @ ( move @ A @ B @ D ) )
= ( move @ A @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(53,axiom,
! [A: view_e774982825t_unit] :
? [B: view_e774982825t_unit] : ( switch @ B @ ( own_Product_unit @ A ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_view_Oswitch__origin) ).
thf(284,plain,
! [A: view_e774982825t_unit] :
? [B: view_e774982825t_unit] : ( switch @ B @ ( own_Product_unit @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(55,axiom,
! [A: traffic] : ( evolve @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_traffic_Oevolve_Orefl) ).
thf(289,plain,
! [A: traffic] : ( evolve @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(33,axiom,
! [A: cars,B: traffic > view_e774982825t_unit > $o,C: traffic > view_e774982825t_unit > $o,D: traffic,E: view_e774982825t_unit] :
( ! [F: view_e774982825t_unit] :
( ( switch @ E @ A @ F )
=> ? [G: view_e774982825t_unit,H: view_e774982825t_unit] :
( ( hchop @ F @ G @ H )
& ( B @ D @ G )
& ( C @ D @ H ) ) )
=> ? [F: view_e774982825t_unit,G: view_e774982825t_unit] :
( ( hchop @ E @ F @ G )
& ! [H: view_e774982825t_unit] :
( ( switch @ F @ A @ H )
=> ( B @ D @ H ) )
& ! [H: view_e774982825t_unit] :
( ( switch @ G @ A @ H )
=> ( C @ D @ H ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_local_Ohmlsl_Oat__hchop__dist1) ).
thf(216,plain,
! [A: cars,B: traffic > view_e774982825t_unit > $o,C: traffic > view_e774982825t_unit > $o,D: traffic,E: view_e774982825t_unit] :
( ! [F: view_e774982825t_unit] :
( ( switch @ E @ A @ F )
=> ? [G: view_e774982825t_unit,H: view_e774982825t_unit] :
( ( hchop @ F @ G @ H )
& ( B @ D @ G )
& ( C @ D @ H ) ) )
=> ? [F: view_e774982825t_unit,G: view_e774982825t_unit] :
( ( hchop @ E @ F @ G )
& ! [H: view_e774982825t_unit] :
( ( switch @ F @ A @ H )
=> ( B @ D @ H ) )
& ! [H: view_e774982825t_unit] :
( ( switch @ G @ A @ H )
=> ( C @ D @ H ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(13,axiom,
! [A: nat_int,B: nat_int,C: nat_int] :
( ( ord_less_eq_nat_int @ A @ B )
=> ( ( ord_less_eq_nat_int @ B @ C )
=> ( ord_less_eq_nat_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_order__trans) ).
thf(164,plain,
! [A: nat_int,B: nat_int,C: nat_int] :
( ( ord_less_eq_nat_int @ A @ B )
=> ( ( ord_less_eq_nat_int @ B @ C )
=> ( ord_less_eq_nat_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(79,axiom,
! [A: real_int,B: nat_int,C: cars,D: product_unit] :
( ( lan_Product_unit @ ( view_e912666823t_unit @ A @ B @ C @ D ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_select__convs_I2_J) ).
thf(443,plain,
! [A: real_int,B: nat_int,C: cars,D: product_unit] :
( ( lan_Product_unit @ ( view_e912666823t_unit @ A @ B @ C @ D ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(57,axiom,
! [A: view_e774982825t_unit] :
? [B: view_e774982825t_unit] : ( hchop @ A @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_view_Ohorizontal__chop__empty__right) ).
thf(293,plain,
! [A: view_e774982825t_unit] :
? [B: view_e774982825t_unit] : ( hchop @ A @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(6,axiom,
! [A: nat_int,B: nat_int > nat_int,C: nat_int,D: nat_int] :
( ( ord_less_eq_nat_int @ A @ ( B @ C ) )
=> ( ( ord_less_eq_nat_int @ C @ D )
=> ( ! [E: nat_int,F: nat_int] :
( ( ord_less_eq_nat_int @ E @ F )
=> ( ord_less_eq_nat_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat_int @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_order__subst1) ).
thf(132,plain,
! [A: nat_int,B: nat_int > nat_int,C: nat_int,D: nat_int] :
( ( ord_less_eq_nat_int @ A @ ( B @ C ) )
=> ( ( ord_less_eq_nat_int @ C @ D )
=> ( ! [E: nat_int,F: nat_int] :
( ( ord_less_eq_nat_int @ E @ F )
=> ( ord_less_eq_nat_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat_int @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,conjecture,
( ( move @ ts3 @ ts_a @ v )
= ( move @ ts3 @ ts @ v ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( move @ ts3 @ ts_a @ v )
!= ( move @ ts3 @ ts @ v ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(117,plain,
( ( move @ ts3 @ ts_a @ v )
!= ( move @ ts3 @ ts @ v ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(94,axiom,
! [A: view_e774982825t_unit,B: view_e774982825t_unit] :
( ( ( ext_Product_unit @ A )
= ( ext_Product_unit @ B ) )
=> ( ( ( lan_Product_unit @ A )
= ( lan_Product_unit @ B ) )
=> ( ( ( own_Product_unit @ A )
= ( own_Product_unit @ B ) )
=> ( ( ( more_Product_unit @ A )
= ( more_Product_unit @ B ) )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_equality) ).
thf(512,plain,
! [A: view_e774982825t_unit,B: view_e774982825t_unit] :
( ( ( ext_Product_unit @ A )
= ( ext_Product_unit @ B ) )
=> ( ( ( lan_Product_unit @ A )
= ( lan_Product_unit @ B ) )
=> ( ( ( own_Product_unit @ A )
= ( own_Product_unit @ B ) )
=> ( ( ( more_Product_unit @ A )
= ( more_Product_unit @ B ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(100,axiom,
! [A: cars,B: traffic] :
? [C: traffic] : ( create_reservation @ B @ A @ C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_traffic_Oalways__create__res) ).
thf(529,plain,
! [A: cars,B: traffic] :
? [C: traffic] : ( create_reservation @ B @ A @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(107,axiom,
? [A: cars] : ( create_reservation @ ts_a @ A @ ts ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_cr__res_Ohyps_I2_J) ).
thf(546,plain,
? [A: cars] : ( create_reservation @ ts_a @ A @ ts ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(26,axiom,
! [A: cars,B: traffic > view_e774982825t_unit > $o,C: traffic,D: view_e774982825t_unit] :
( ~ ! [E: view_e774982825t_unit] :
( ( switch @ D @ A @ E )
=> ( B @ C @ E ) )
=> ! [E: view_e774982825t_unit] :
( ( switch @ D @ A @ E )
=> ~ ( B @ C @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_local_Ohmlsl_Oat__neg2) ).
thf(201,plain,
! [A: cars,B: traffic > view_e774982825t_unit > $o,C: traffic,D: view_e774982825t_unit] :
( ~ ! [E: view_e774982825t_unit] :
( ( switch @ D @ A @ E )
=> ( B @ C @ E ) )
=> ! [E: view_e774982825t_unit] :
( ( switch @ D @ A @ E )
=> ~ ( B @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(37,axiom,
! [A: cars,B: traffic > view_e774982825t_unit > $o,C: traffic > view_e774982825t_unit > $o,D: traffic,E: view_e774982825t_unit] :
( ( ! [F: view_e774982825t_unit] :
( ( switch @ E @ A @ F )
=> ( ( B @ D @ F )
& ( C @ D @ F ) ) ) )
= ( ! [F: view_e774982825t_unit] :
( ( switch @ E @ A @ F )
=> ( B @ D @ F ) )
& ! [F: view_e774982825t_unit] :
( ( switch @ E @ A @ F )
=> ( C @ D @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_local_Ohmlsl_Oat__conj__distr) ).
thf(233,plain,
! [A: cars,B: traffic > view_e774982825t_unit > $o,C: traffic > view_e774982825t_unit > $o,D: traffic,E: view_e774982825t_unit] :
( ( ! [F: view_e774982825t_unit] :
( ( switch @ E @ A @ F )
=> ( ( B @ D @ F )
& ( C @ D @ F ) ) ) )
= ( ! [F: view_e774982825t_unit] :
( ( switch @ E @ A @ F )
=> ( B @ D @ F ) )
& ! [F: view_e774982825t_unit] :
( ( switch @ E @ A @ F )
=> ( C @ D @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(82,axiom,
! [A: traffic,B: traffic,C: traffic] :
( ( abstract @ A @ B )
=> ( ( evolve @ B @ C )
=> ( abstract @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_traffic_Oevolve) ).
thf(452,plain,
! [A: traffic,B: traffic,C: traffic] :
( ( abstract @ A @ B )
=> ( ( evolve @ B @ C )
=> ( abstract @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(59,axiom,
! [A: view_e774982825t_unit] : ( switch @ A @ ( own_Product_unit @ A ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_view_Oswitch__refl) ).
thf(297,plain,
! [A: view_e774982825t_unit] : ( switch @ A @ ( own_Product_unit @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(74,axiom,
( hchop
= ( ^ [A: view_e774982825t_unit,B: view_e774982825t_unit,C: view_e774982825t_unit] :
( ( real_R_Chop @ ( ext_Product_unit @ A ) @ ( ext_Product_unit @ B ) @ ( ext_Product_unit @ C ) )
& ( ( lan_Product_unit @ A )
= ( lan_Product_unit @ B ) )
& ( ( lan_Product_unit @ A )
= ( lan_Product_unit @ C ) )
& ( ( own_Product_unit @ A )
= ( own_Product_unit @ B ) )
& ( ( own_Product_unit @ A )
= ( own_Product_unit @ C ) )
& ( ( more_Product_unit @ A )
= ( more_Product_unit @ C ) )
& ( ( more_Product_unit @ A )
= ( more_Product_unit @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_view_Ohchop__def) ).
thf(429,plain,
( hchop
= ( ^ [A: view_e774982825t_unit,B: view_e774982825t_unit,C: view_e774982825t_unit] :
( ( real_R_Chop @ ( ext_Product_unit @ A ) @ ( ext_Product_unit @ B ) @ ( ext_Product_unit @ C ) )
& ( ( lan_Product_unit @ A )
= ( lan_Product_unit @ B ) )
& ( ( lan_Product_unit @ A )
= ( lan_Product_unit @ C ) )
& ( ( own_Product_unit @ A )
= ( own_Product_unit @ B ) )
& ( ( own_Product_unit @ A )
= ( own_Product_unit @ C ) )
& ( ( more_Product_unit @ A )
= ( more_Product_unit @ C ) )
& ( ( more_Product_unit @ A )
= ( more_Product_unit @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(36,axiom,
! [A: traffic > view_e774982825t_unit > $o,B: traffic,C: view_e774982825t_unit] :
( ( A @ B @ C )
=> ? [D: view_e774982825t_unit,E: view_e774982825t_unit] :
( ( hchop @ C @ D @ E )
& ? [F: view_e774982825t_unit] :
( ? [G: view_e774982825t_unit] : ( hchop @ E @ F @ G )
& ( A @ B @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_local_Ohmlsl_Ohchop__weaken) ).
thf(229,plain,
! [A: traffic > view_e774982825t_unit > $o,B: traffic,C: view_e774982825t_unit] :
( ( A @ B @ C )
=> ? [D: view_e774982825t_unit,E: view_e774982825t_unit] :
( ( hchop @ C @ D @ E )
& ? [F: view_e774982825t_unit] :
( ? [G: view_e774982825t_unit] : ( hchop @ E @ F @ G )
& ( A @ B @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(85,axiom,
defaul1399868459t_unit = product_Unity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_default__unit__def) ).
thf(461,plain,
defaul1399868459t_unit = product_Unity,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(109,axiom,
abstract @ ts3 @ ts2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_abs) ).
thf(551,plain,
abstract @ ts3 @ ts2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(34,axiom,
! [A: traffic > view_e774982825t_unit > $o,B: traffic,C: view_e774982825t_unit] :
( ( A @ B @ C )
=> ? [D: view_e774982825t_unit,E: view_e774982825t_unit] :
( ( hchop @ C @ D @ E )
& ( A @ B @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_local_Ohmlsl_Ohchop__weaken2) ).
thf(224,plain,
! [A: traffic > view_e774982825t_unit > $o,B: traffic,C: view_e774982825t_unit] :
( ( A @ B @ C )
=> ? [D: view_e774982825t_unit,E: view_e774982825t_unit] :
( ( hchop @ C @ D @ E )
& ( A @ B @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(63,axiom,
! [A: cars,B: traffic > view_e774982825t_unit > $o,C: traffic > view_e774982825t_unit > $o,D: traffic,E: view_e774982825t_unit] :
( ( ? [F: view_e774982825t_unit,G: view_e774982825t_unit] :
( ( hchop @ E @ F @ G )
& ! [H: view_e774982825t_unit] :
( ( switch @ F @ A @ H )
=> ( B @ D @ H ) )
& ! [H: view_e774982825t_unit] :
( ( switch @ G @ A @ H )
=> ( C @ D @ H ) ) ) )
= ( ! [F: view_e774982825t_unit] :
( ( switch @ E @ A @ F )
=> ? [G: view_e774982825t_unit,H: view_e774982825t_unit] :
( ( hchop @ F @ G @ H )
& ( B @ D @ G )
& ( C @ D @ H ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_local_Ohmlsl_Oat__hchop__dist) ).
thf(317,plain,
! [A: cars,B: traffic > view_e774982825t_unit > $o,C: traffic > view_e774982825t_unit > $o,D: traffic,E: view_e774982825t_unit] :
( ( ? [F: view_e774982825t_unit,G: view_e774982825t_unit] :
( ( hchop @ E @ F @ G )
& ! [H: view_e774982825t_unit] :
( ( switch @ F @ A @ H )
=> ( B @ D @ H ) )
& ! [H: view_e774982825t_unit] :
( ( switch @ G @ A @ H )
=> ( C @ D @ H ) ) ) )
= ( ! [F: view_e774982825t_unit] :
( ( switch @ E @ A @ F )
=> ? [G: view_e774982825t_unit,H: view_e774982825t_unit] :
( ( hchop @ F @ G @ H )
& ( B @ D @ G )
& ( C @ D @ H ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(11,axiom,
! [A: nat_int,B: nat_int,C: nat_int] :
( ( ord_less_eq_nat_int @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_nat_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_ord__le__eq__trans) ).
thf(156,plain,
! [A: nat_int,B: nat_int,C: nat_int] :
( ( ord_less_eq_nat_int @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_nat_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(22,axiom,
! [A: nat_int,B: nat_int] :
( ( ord_less_eq_nat_int @ A @ B )
=> ( ( ord_less_eq_nat_int @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_antisym__conv) ).
thf(188,plain,
! [A: nat_int,B: nat_int] :
( ( ord_less_eq_nat_int @ A @ B )
=> ( ( ord_less_eq_nat_int @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(99,axiom,
! [A: traffic,B: cars,C: traffic,D: cars] :
( ( ( create_reservation @ A @ B @ C )
& ( B != D ) )
=> ( ( clm @ A @ D )
= ( clm @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_traffic_Ocreate__res__subseteq2__neq) ).
thf(526,plain,
! [A: traffic,B: cars,C: traffic,D: cars] :
( ( ( create_reservation @ A @ B @ C )
& ( B != D ) )
=> ( ( clm @ A @ D )
= ( clm @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(31,axiom,
! [A: view_e774982825t_unit] :
? [B: view_e774982825t_unit] : ( hchop @ A @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_view_Ohorizontal__chop__empty__left) ).
thf(212,plain,
! [A: view_e774982825t_unit] :
? [B: view_e774982825t_unit] : ( hchop @ A @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(66,axiom,
! [A: traffic > view_e774982825t_unit > $o,B: traffic > view_e774982825t_unit > $o,C: traffic > view_e774982825t_unit > $o,D: traffic,E: view_e774982825t_unit] :
( ( ? [F: view_e774982825t_unit,G: view_e774982825t_unit] :
( ( hchop @ E @ F @ G )
& ( ( A @ D @ F )
| ( B @ D @ F ) )
& ( C @ D @ G ) ) )
= ( ? [F: view_e774982825t_unit,G: view_e774982825t_unit] :
( ( hchop @ E @ F @ G )
& ( A @ D @ F )
& ( C @ D @ G ) )
| ? [F: view_e774982825t_unit,G: view_e774982825t_unit] :
( ( hchop @ E @ F @ G )
& ( B @ D @ F )
& ( C @ D @ G ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_local_Ohmlsl_Ohchop__disj__distr2) ).
thf(328,plain,
! [A: traffic > view_e774982825t_unit > $o,B: traffic > view_e774982825t_unit > $o,C: traffic > view_e774982825t_unit > $o,D: traffic,E: view_e774982825t_unit] :
( ( ? [F: view_e774982825t_unit,G: view_e774982825t_unit] :
( ( hchop @ E @ F @ G )
& ( ( A @ D @ F )
| ( B @ D @ F ) )
& ( C @ D @ G ) ) )
= ( ? [F: view_e774982825t_unit,G: view_e774982825t_unit] :
( ( hchop @ E @ F @ G )
& ( A @ D @ F )
& ( C @ D @ G ) )
| ? [F: view_e774982825t_unit,G: view_e774982825t_unit] :
( ( hchop @ E @ F @ G )
& ( B @ D @ F )
& ( C @ D @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(44,axiom,
! [A: traffic > view_e774982825t_unit > $o,B: traffic,C: view_e774982825t_unit] :
( ( A @ B @ C )
=> ? [D: view_e774982825t_unit] :
( ? [E: view_e774982825t_unit] : ( hchop @ C @ D @ E )
& ( A @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_local_Ohmlsl_Ohchop__weaken1) ).
thf(256,plain,
! [A: traffic > view_e774982825t_unit > $o,B: traffic,C: view_e774982825t_unit] :
( ( A @ B @ C )
=> ? [D: view_e774982825t_unit] :
( ? [E: view_e774982825t_unit] : ( hchop @ C @ D @ E )
& ( A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(24,axiom,
! [A: traffic > view_e774982825t_unit > $o,B: traffic,C: view_e774982825t_unit] :
( ~ ? [D: view_e774982825t_unit] :
( ? [E: view_e774982825t_unit] : ( hchop @ C @ D @ E )
& ( A @ B @ D ) )
=> ? [D: view_e774982825t_unit] :
( ? [E: view_e774982825t_unit] : ( hchop @ C @ D @ E )
& ~ ( A @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_local_Ohmlsl_Ohchop__neg1) ).
thf(193,plain,
! [A: traffic > view_e774982825t_unit > $o,B: traffic,C: view_e774982825t_unit] :
( ~ ? [D: view_e774982825t_unit] :
( ? [E: view_e774982825t_unit] : ( hchop @ C @ D @ E )
& ( A @ B @ D ) )
=> ? [D: view_e774982825t_unit] :
( ? [E: view_e774982825t_unit] : ( hchop @ C @ D @ E )
& ~ ( A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(103,axiom,
( move
= ( ^ [A: traffic,B: traffic,C: view_e774982825t_unit] : ( view_e912666823t_unit @ ( real_shift @ ( ext_Product_unit @ C ) @ ( minus_minus_real @ ( pos @ B @ ( own_Product_unit @ C ) ) @ ( pos @ A @ ( own_Product_unit @ C ) ) ) ) @ ( lan_Product_unit @ C ) @ ( own_Product_unit @ C ) @ product_Unity ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_traffic_Omove__def) ).
thf(537,plain,
( move
= ( ^ [A: traffic,B: traffic,C: view_e774982825t_unit] : ( view_e912666823t_unit @ ( real_shift @ ( ext_Product_unit @ C ) @ ( minus_minus_real @ ( pos @ B @ ( own_Product_unit @ C ) ) @ ( pos @ A @ ( own_Product_unit @ C ) ) ) ) @ ( lan_Product_unit @ C ) @ ( own_Product_unit @ C ) @ product_Unity ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(95,axiom,
! [A: view_e774982825t_unit > $o,B: view_e774982825t_unit] :
( ! [C: real_int,D: nat_int,E: cars,F: product_unit] : ( A @ ( view_e912666823t_unit @ C @ D @ E @ F ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_induct__scheme) ).
thf(515,plain,
! [A: view_e774982825t_unit > $o,B: view_e774982825t_unit] :
( ! [C: real_int,D: nat_int,E: cars,F: product_unit] : ( A @ ( view_e912666823t_unit @ C @ D @ E @ F ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(84,axiom,
! [A: view_e774982825t_unit] :
~ ! [B: real_int,C: nat_int,D: cars,E: product_unit] :
( A
!= ( view_e912666823t_unit @ B @ C @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_cases__scheme) ).
thf(457,plain,
! [A: view_e774982825t_unit] :
~ ! [B: real_int,C: nat_int,D: cars,E: product_unit] :
( A
!= ( view_e912666823t_unit @ B @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(28,axiom,
! [A: traffic > view_e774982825t_unit > $o,B: traffic > view_e774982825t_unit > $o,C: traffic > view_e774982825t_unit > $o,D: traffic,E: view_e774982825t_unit] :
( ( ? [F: view_e774982825t_unit,G: view_e774982825t_unit] :
( ( hchop @ E @ F @ G )
& ( A @ D @ F )
& ( ( B @ D @ G )
| ( C @ D @ G ) ) ) )
= ( ? [F: view_e774982825t_unit,G: view_e774982825t_unit] :
( ( hchop @ E @ F @ G )
& ( A @ D @ F )
& ( B @ D @ G ) )
| ? [F: view_e774982825t_unit,G: view_e774982825t_unit] :
( ( hchop @ E @ F @ G )
& ( A @ D @ F )
& ( C @ D @ G ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_local_Ohmlsl_Ohchop__disj__distr1) ).
thf(205,plain,
! [A: traffic > view_e774982825t_unit > $o,B: traffic > view_e774982825t_unit > $o,C: traffic > view_e774982825t_unit > $o,D: traffic,E: view_e774982825t_unit] :
( ( ? [F: view_e774982825t_unit,G: view_e774982825t_unit] :
( ( hchop @ E @ F @ G )
& ( A @ D @ F )
& ( ( B @ D @ G )
| ( C @ D @ G ) ) ) )
= ( ? [F: view_e774982825t_unit,G: view_e774982825t_unit] :
( ( hchop @ E @ F @ G )
& ( A @ D @ F )
& ( B @ D @ G ) )
| ? [F: view_e774982825t_unit,G: view_e774982825t_unit] :
( ( hchop @ E @ F @ G )
& ( A @ D @ F )
& ( C @ D @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(61,axiom,
! [A: traffic > view_e774982825t_unit > $o,B: traffic > view_e774982825t_unit > $o,C: traffic > view_e774982825t_unit > $o,D: traffic,E: view_e774982825t_unit] :
( ( ? [F: view_e774982825t_unit,G: view_e774982825t_unit] :
( ( hchop @ E @ F @ G )
& ( A @ D @ F )
& ? [H: view_e774982825t_unit,I: view_e774982825t_unit] :
( ( hchop @ G @ H @ I )
& ( B @ D @ H )
& ( C @ D @ I ) ) ) )
= ( ? [F: view_e774982825t_unit,G: view_e774982825t_unit] :
( ( hchop @ E @ F @ G )
& ? [H: view_e774982825t_unit,I: view_e774982825t_unit] :
( ( hchop @ F @ H @ I )
& ( A @ D @ H )
& ( B @ D @ I ) )
& ( C @ D @ G ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_local_Ohmlsl_Ohchop__assoc) ).
thf(311,plain,
! [A: traffic > view_e774982825t_unit > $o,B: traffic > view_e774982825t_unit > $o,C: traffic > view_e774982825t_unit > $o,D: traffic,E: view_e774982825t_unit] :
( ( ? [F: view_e774982825t_unit,G: view_e774982825t_unit] :
( ( hchop @ E @ F @ G )
& ( A @ D @ F )
& ? [H: view_e774982825t_unit,I: view_e774982825t_unit] :
( ( hchop @ G @ H @ I )
& ( B @ D @ H )
& ( C @ D @ I ) ) ) )
= ( ? [F: view_e774982825t_unit,G: view_e774982825t_unit] :
( ( hchop @ E @ F @ G )
& ? [H: view_e774982825t_unit,I: view_e774982825t_unit] :
( ( hchop @ F @ H @ I )
& ( A @ D @ H )
& ( B @ D @ I ) )
& ( C @ D @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(9,axiom,
! [A: traffic,B: cars,C: nat,D: traffic,E: cars] :
( ( withdraw_reservation @ A @ B @ C @ D )
=> ( ord_less_eq_nat_int @ ( res @ D @ E ) @ ( res @ A @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_traffic_Owithdraw__res__subseteq) ).
thf(148,plain,
! [A: traffic,B: cars,C: nat,D: traffic,E: cars] :
( ( withdraw_reservation @ A @ B @ C @ D )
=> ( ord_less_eq_nat_int @ ( res @ D @ E ) @ ( res @ A @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(47,axiom,
! [A: cars,B: traffic > view_e774982825t_unit > $o,C: traffic,D: view_e774982825t_unit] :
( ! [E: view_e774982825t_unit] :
( ( switch @ D @ A @ E )
=> ~ ( B @ C @ E ) )
=> ~ ! [E: view_e774982825t_unit] :
( ( switch @ D @ A @ E )
=> ( B @ C @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_local_Ohmlsl_Oat__neg1) ).
thf(264,plain,
! [A: cars,B: traffic > view_e774982825t_unit > $o,C: traffic,D: view_e774982825t_unit] :
( ! [E: view_e774982825t_unit] :
( ( switch @ D @ A @ E )
=> ~ ( B @ C @ E ) )
=> ~ ! [E: view_e774982825t_unit] :
( ( switch @ D @ A @ E )
=> ( B @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(12,axiom,
! [A: nat_int,B: nat_int,C: nat_int] :
( ( ord_less_eq_nat_int @ A @ B )
=> ( ( ord_less_eq_nat_int @ B @ C )
=> ( ord_less_eq_nat_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_order_Otrans) ).
thf(161,plain,
! [A: nat_int,B: nat_int,C: nat_int] :
( ( ord_less_eq_nat_int @ A @ B )
=> ( ( ord_less_eq_nat_int @ B @ C )
=> ( ord_less_eq_nat_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(51,axiom,
! [A: view_e774982825t_unit,B: view_e774982825t_unit,C: view_e774982825t_unit,D: view_e774982825t_unit,E: view_e774982825t_unit] :
( ( ( hchop @ A @ B @ C )
& ( hchop @ B @ D @ E ) )
=> ? [F: view_e774982825t_unit] :
( ( hchop @ A @ D @ F )
& ( hchop @ F @ E @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_view_Ohorizontal__chop__assoc2) ).
thf(279,plain,
! [A: view_e774982825t_unit,B: view_e774982825t_unit,C: view_e774982825t_unit,D: view_e774982825t_unit,E: view_e774982825t_unit] :
( ( ( hchop @ A @ B @ C )
& ( hchop @ B @ D @ E ) )
=> ? [F: view_e774982825t_unit] :
( ( hchop @ A @ D @ F )
& ( hchop @ F @ E @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(19,axiom,
( ( (=) @ nat_int )
= ( ^ [A: nat_int,B: nat_int] :
( ( ord_less_eq_nat_int @ A @ B )
& ( ord_less_eq_nat_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_eq__iff) ).
thf(180,plain,
( ( (=) @ nat_int )
= ( ^ [A: nat_int,B: nat_int] :
( ( ord_less_eq_nat_int @ A @ B )
& ( ord_less_eq_nat_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(23,axiom,
( ( (=) @ nat_int )
= ( ^ [A: nat_int,B: nat_int] :
( ( ord_less_eq_nat_int @ A @ B )
& ( ord_less_eq_nat_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_order__class_Oorder_Oeq__iff) ).
thf(191,plain,
( ( (=) @ nat_int )
= ( ^ [A: nat_int,B: nat_int] :
( ( ord_less_eq_nat_int @ A @ B )
& ( ord_less_eq_nat_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(54,axiom,
! [A: view_e774982825t_unit,B: cars,C: traffic > view_e774982825t_unit > $o,D: traffic] :
( ( ~ ! [E: view_e774982825t_unit] :
( ( switch @ A @ B @ E )
=> ( C @ D @ E ) ) )
= ( ! [E: view_e774982825t_unit] :
( ( switch @ A @ B @ E )
=> ~ ( C @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_local_Ohmlsl_Oat__neg_H) ).
thf(286,plain,
! [A: view_e774982825t_unit,B: cars,C: traffic > view_e774982825t_unit > $o,D: traffic] :
( ( ~ ! [E: view_e774982825t_unit] :
( ( switch @ A @ B @ E )
=> ( C @ D @ E ) ) )
= ( ! [E: view_e774982825t_unit] :
( ( switch @ A @ B @ E )
=> ~ ( C @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(56,axiom,
! [A: real_int] :
? [B: real_int] : ( real_R_Chop @ A @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_chop__singleton__right) ).
thf(291,plain,
! [A: real_int] :
? [B: real_int] : ( real_R_Chop @ A @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(45,axiom,
! [A: view_e774982825t_unit,B: view_e774982825t_unit,C: view_e774982825t_unit] :
( ( hchop @ A @ B @ C )
=> ( ( own_Product_unit @ B )
= ( own_Product_unit @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_view_Ohorizontal__chop__own__trans) ).
thf(259,plain,
! [A: view_e774982825t_unit,B: view_e774982825t_unit,C: view_e774982825t_unit] :
( ( hchop @ A @ B @ C )
=> ( ( own_Product_unit @ B )
= ( own_Product_unit @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(116,axiom,
! [A: traffic,B: cars,C: nat,D: traffic,E: view_e774982825t_unit] :
( ( create_claim @ A @ B @ C @ D )
=> ( ( move @ A @ D @ E )
= E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_traffic_Omove__stability__clm) ).
thf(572,plain,
! [A: traffic,B: cars,C: nat,D: traffic,E: view_e774982825t_unit] :
( ( create_claim @ A @ B @ C @ D )
=> ( ( move @ A @ D @ E )
= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(87,axiom,
! [A: traffic,B: traffic,C: traffic] :
( ( abstract @ A @ B )
=> ( ? [D: cars,E: nat] : ( create_claim @ B @ D @ E @ C )
=> ( abstract @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_traffic_Ocr__clm) ).
thf(466,plain,
! [A: traffic,B: traffic,C: traffic] :
( ( abstract @ A @ B )
=> ( ? [D: cars,E: nat] : ( create_claim @ B @ D @ E @ C )
=> ( abstract @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(38,axiom,
! [A: view_e774982825t_unit,B: view_e774982825t_unit,C: view_e774982825t_unit,D: view_e774982825t_unit,E: view_e774982825t_unit] :
( ( ( hchop @ A @ B @ C )
& ( hchop @ C @ D @ E ) )
=> ? [F: view_e774982825t_unit] :
( ( hchop @ A @ F @ E )
& ( hchop @ F @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_view_Ohorizontal__chop__assoc1) ).
thf(236,plain,
! [A: view_e774982825t_unit,B: view_e774982825t_unit,C: view_e774982825t_unit,D: view_e774982825t_unit,E: view_e774982825t_unit] :
( ( ( hchop @ A @ B @ C )
& ( hchop @ C @ D @ E ) )
=> ? [F: view_e774982825t_unit] :
( ( hchop @ A @ F @ E )
& ( hchop @ F @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(16,axiom,
! [A: nat_int,B: nat_int] :
( ( ord_less_eq_nat_int @ A @ B )
=> ( ( ord_less_eq_nat_int @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_dual__order_Oantisym) ).
thf(172,plain,
! [A: nat_int,B: nat_int] :
( ( ord_less_eq_nat_int @ A @ B )
=> ( ( ord_less_eq_nat_int @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(49,axiom,
! [A: view_e774982825t_unit,B: cars,C: view_e774982825t_unit,D: view_e774982825t_unit] :
( ( ( switch @ A @ B @ C )
& ( switch @ A @ B @ D ) )
=> ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_view_Oswitch__unique) ).
thf(274,plain,
! [A: view_e774982825t_unit,B: cars,C: view_e774982825t_unit,D: view_e774982825t_unit] :
( ( ( switch @ A @ B @ C )
& ( switch @ A @ B @ D ) )
=> ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(114,axiom,
! [A: traffic > view_e774982825t_unit > $o,B: traffic,C: view_e774982825t_unit] :
( ! [D: traffic] :
( ( abstract @ B @ D )
=> ( A @ D @ ( move @ B @ D @ C ) ) )
=> ( A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_local_Ohmlsl_Oglobally__refl) ).
thf(567,plain,
! [A: traffic > view_e774982825t_unit > $o,B: traffic,C: view_e774982825t_unit] :
( ! [D: traffic] :
( ( abstract @ B @ D )
=> ( A @ D @ ( move @ B @ D @ C ) ) )
=> ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(29,axiom,
! [A: view_e774982825t_unit,B: cars,C: view_e774982825t_unit,D: cars,E: view_e774982825t_unit] :
( ( ( switch @ A @ B @ C )
& ( switch @ C @ D @ E ) )
=> ( switch @ A @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_view_Oswitch__trans) ).
thf(208,plain,
! [A: view_e774982825t_unit,B: cars,C: view_e774982825t_unit,D: cars,E: view_e774982825t_unit] :
( ( ( switch @ A @ B @ C )
& ( switch @ C @ D @ E ) )
=> ( switch @ A @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(93,axiom,
! [A: real_int,B: nat_int,C: cars,D: product_unit] :
( ( ext_Product_unit @ ( view_e912666823t_unit @ A @ B @ C @ D ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_select__convs_I1_J) ).
thf(509,plain,
! [A: real_int,B: nat_int,C: cars,D: product_unit] :
( ( ext_Product_unit @ ( view_e912666823t_unit @ A @ B @ C @ D ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(76,axiom,
! [A: traffic,B: cars,C: nat,D: traffic,E: cars] :
( ( create_claim @ A @ B @ C @ D )
=> ( ( res @ A @ E )
= ( res @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_traffic_Ocreate__clm__eq__res) ).
thf(434,plain,
! [A: traffic,B: cars,C: nat,D: traffic,E: cars] :
( ( create_claim @ A @ B @ C @ D )
=> ( ( res @ A @ E )
= ( res @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(110,axiom,
! [A: traffic,B: cars,C: traffic,D: view_e774982825t_unit] :
( ( withdraw_claim @ A @ B @ C )
=> ( ( move @ A @ C @ D )
= D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_traffic_Omove__stability__wdc) ).
thf(552,plain,
! [A: traffic,B: cars,C: traffic,D: view_e774982825t_unit] :
( ( withdraw_claim @ A @ B @ C )
=> ( ( move @ A @ C @ D )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(65,axiom,
! [A: traffic > view_e774982825t_unit > $o,B: traffic,C: view_e774982825t_unit] :
( ~ ? [D: view_e774982825t_unit,E: view_e774982825t_unit] :
( ( hchop @ C @ D @ E )
& ( A @ B @ E ) )
=> ? [D: view_e774982825t_unit,E: view_e774982825t_unit] :
( ( hchop @ C @ D @ E )
& ~ ( A @ B @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_local_Ohmlsl_Ohchop__neg2) ).
thf(323,plain,
! [A: traffic > view_e774982825t_unit > $o,B: traffic,C: view_e774982825t_unit] :
( ~ ? [D: view_e774982825t_unit,E: view_e774982825t_unit] :
( ( hchop @ C @ D @ E )
& ( A @ B @ E ) )
=> ? [D: view_e774982825t_unit,E: view_e774982825t_unit] :
( ( hchop @ C @ D @ E )
& ~ ( A @ B @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(8,axiom,
! [A: nat_int,B: nat_int,C: nat_int > nat_int,D: nat_int] :
( ( ord_less_eq_nat_int @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: nat_int,F: nat_int] :
( ( ord_less_eq_nat_int @ E @ F )
=> ( ord_less_eq_nat_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat_int @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_ord__le__eq__subst) ).
thf(140,plain,
! [A: nat_int,B: nat_int,C: nat_int > nat_int,D: nat_int] :
( ( ord_less_eq_nat_int @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: nat_int,F: nat_int] :
( ( ord_less_eq_nat_int @ E @ F )
=> ( ord_less_eq_nat_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat_int @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(25,axiom,
! [A: cars,B: traffic > view_e774982825t_unit > $o,C: traffic,D: view_e774982825t_unit] :
( ( ! [E: view_e774982825t_unit] :
( ( switch @ D @ A @ E )
=> ( B @ C @ E ) ) )
= ( ~ ! [E: view_e774982825t_unit] :
( ( switch @ D @ A @ E )
=> ~ ( B @ C @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_local_Ohmlsl_Oat__neg__neg) ).
thf(198,plain,
! [A: cars,B: traffic > view_e774982825t_unit > $o,C: traffic,D: view_e774982825t_unit] :
( ( ! [E: view_e774982825t_unit] :
( ( switch @ D @ A @ E )
=> ( B @ C @ E ) ) )
= ( ~ ! [E: view_e774982825t_unit] :
( ( switch @ D @ A @ E )
=> ~ ( B @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(97,axiom,
! [A: traffic,B: traffic,C: traffic] :
( ( abstract @ A @ B )
=> ( ? [D: cars,E: nat] : ( withdraw_reservation @ B @ D @ E @ C )
=> ( abstract @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_traffic_Owd__res) ).
thf(521,plain,
! [A: traffic,B: traffic,C: traffic] :
( ( abstract @ A @ B )
=> ( ? [D: cars,E: nat] : ( withdraw_reservation @ B @ D @ E @ C )
=> ( abstract @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(5,axiom,
! [A: nat_int] : ( ord_less_eq_nat_int @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_order__refl) ).
thf(130,plain,
! [A: nat_int] : ( ord_less_eq_nat_int @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(83,axiom,
! [A: traffic] : ( abstract @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_traffic_Oabstract_Orefl) ).
thf(455,plain,
! [A: traffic] : ( abstract @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(113,axiom,
! [A: traffic,B: cars,C: traffic,D: view_e774982825t_unit] :
( ( create_reservation @ A @ B @ C )
=> ( ( move @ A @ C @ D )
= D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_traffic_Omove__stability__res) ).
thf(563,plain,
! [A: traffic,B: cars,C: traffic,D: view_e774982825t_unit] :
( ( create_reservation @ A @ B @ C )
=> ( ( move @ A @ C @ D )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(60,axiom,
! [A: cars,B: traffic > view_e774982825t_unit > $o,C: traffic > view_e774982825t_unit > $o,D: traffic,E: view_e774982825t_unit] :
( ? [F: view_e774982825t_unit,G: view_e774982825t_unit] :
( ( hchop @ E @ F @ G )
& ! [H: view_e774982825t_unit] :
( ( switch @ F @ A @ H )
=> ( B @ D @ H ) )
& ! [H: view_e774982825t_unit] :
( ( switch @ G @ A @ H )
=> ( C @ D @ H ) ) )
=> ! [F: view_e774982825t_unit] :
( ( switch @ E @ A @ F )
=> ? [G: view_e774982825t_unit,H: view_e774982825t_unit] :
( ( hchop @ F @ G @ H )
& ( B @ D @ G )
& ( C @ D @ H ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_local_Ohmlsl_Oat__hchop__dist2) ).
thf(299,plain,
! [A: cars,B: traffic > view_e774982825t_unit > $o,C: traffic > view_e774982825t_unit > $o,D: traffic,E: view_e774982825t_unit] :
( ? [F: view_e774982825t_unit,G: view_e774982825t_unit] :
( ( hchop @ E @ F @ G )
& ! [H: view_e774982825t_unit] :
( ( switch @ F @ A @ H )
=> ( B @ D @ H ) )
& ! [H: view_e774982825t_unit] :
( ( switch @ G @ A @ H )
=> ( C @ D @ H ) ) )
=> ! [F: view_e774982825t_unit] :
( ( switch @ E @ A @ F )
=> ? [G: view_e774982825t_unit,H: view_e774982825t_unit] :
( ( hchop @ F @ G @ H )
& ( B @ D @ G )
& ( C @ D @ H ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(75,axiom,
! [A: product_unit] : ( A = product_Unity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_old_Ounit_Oexhaust) ).
thf(431,plain,
! [A: product_unit] : ( A = product_Unity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(14,axiom,
! [A: nat_int,B: nat_int] :
( ( ord_less_eq_nat_int @ A @ B )
=> ( ( ord_less_eq_nat_int @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_order__class_Oorder_Oantisym) ).
thf(167,plain,
! [A: nat_int,B: nat_int] :
( ( ord_less_eq_nat_int @ A @ B )
=> ( ( ord_less_eq_nat_int @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(92,axiom,
! [A: view_e774982825t_unit] :
~ ! [B: real_int,C: nat_int,D: cars] :
( A
!= ( view_e912666823t_unit @ B @ C @ D @ product_Unity ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_cases) ).
thf(505,plain,
! [A: view_e774982825t_unit] :
~ ! [B: real_int,C: nat_int,D: cars] :
( A
!= ( view_e912666823t_unit @ B @ C @ D @ product_Unity ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(77,axiom,
! [A: traffic,B: traffic,C: traffic] :
( ( abstract @ A @ B )
=> ( ( abstract @ C @ A )
=> ( abstract @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_traffic_Oabs__trans) ).
thf(438,plain,
! [A: traffic,B: traffic,C: traffic] :
( ( abstract @ A @ B )
=> ( ( abstract @ C @ A )
=> ( abstract @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(101,axiom,
( abstract
= ( ^ [A: traffic,B: traffic] :
( ( B = A )
| ? [C: traffic,D: traffic] :
( ( B = D )
& ( abstract @ A @ C )
& ( evolve @ C @ D ) )
| ? [C: traffic,D: traffic] :
( ( B = D )
& ( abstract @ A @ C )
& ? [E: cars,F: nat] : ( create_claim @ C @ E @ F @ D ) )
| ? [C: traffic,D: traffic] :
( ( B = D )
& ( abstract @ A @ C )
& ? [E: cars] : ( withdraw_claim @ C @ E @ D ) )
| ? [C: traffic,D: traffic] :
( ( B = D )
& ( abstract @ A @ C )
& ? [E: cars] : ( create_reservation @ C @ E @ D ) )
| ? [C: traffic,D: traffic] :
( ( B = D )
& ( abstract @ A @ C )
& ? [E: cars,F: nat] : ( withdraw_reservation @ C @ E @ F @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_traffic_Oabstract_Osimps) ).
thf(531,plain,
( abstract
= ( ^ [A: traffic,B: traffic] :
( ( B = A )
| ? [C: traffic,D: traffic] :
( ( B = D )
& ( abstract @ A @ C )
& ( evolve @ C @ D ) )
| ? [C: traffic,D: traffic] :
( ( B = D )
& ( abstract @ A @ C )
& ? [E: cars,F: nat] : ( create_claim @ C @ E @ F @ D ) )
| ? [C: traffic,D: traffic] :
( ( B = D )
& ( abstract @ A @ C )
& ? [E: cars] : ( withdraw_claim @ C @ E @ D ) )
| ? [C: traffic,D: traffic] :
( ( B = D )
& ( abstract @ A @ C )
& ? [E: cars] : ( create_reservation @ C @ E @ D ) )
| ? [C: traffic,D: traffic] :
( ( B = D )
& ( abstract @ A @ C )
& ? [E: cars,F: nat] : ( withdraw_reservation @ C @ E @ F @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(108,axiom,
! [A: traffic > view_e774982825t_unit > $o,B: traffic,C: view_e774982825t_unit] :
( ! [D: traffic] :
( ( abstract @ B @ D )
=> ( A @ D @ ( move @ B @ D @ C ) ) )
=> ! [D: traffic] :
( ( abstract @ B @ D )
=> ! [E: traffic] :
( ( abstract @ D @ E )
=> ( A @ E @ ( move @ D @ E @ ( move @ B @ D @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_local_Ohmlsl_Oglobally__4) ).
thf(548,plain,
! [A: traffic > view_e774982825t_unit > $o,B: traffic,C: view_e774982825t_unit] :
( ! [D: traffic] :
( ( abstract @ B @ D )
=> ( A @ D @ ( move @ B @ D @ C ) ) )
=> ! [D: traffic] :
( ( abstract @ B @ D )
=> ! [E: traffic] :
( ( abstract @ D @ E )
=> ( A @ E @ ( move @ D @ E @ ( move @ B @ D @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(58,axiom,
! [A: real_int] :
? [B: real_int,C: real_int] : ( real_R_Chop @ A @ B @ C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_real__int__class_Ochop__always__possible) ).
thf(295,plain,
! [A: real_int] :
? [B: real_int,C: real_int] : ( real_R_Chop @ A @ B @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(52,axiom,
! [A: view_e774982825t_unit,B: cars] :
? [C: view_e774982825t_unit] : ( switch @ A @ B @ C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_view_Oswitch__always__exists) ).
thf(282,plain,
! [A: view_e774982825t_unit,B: cars] :
? [C: view_e774982825t_unit] : ( switch @ A @ B @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(20,axiom,
! [A: traffic,B: cars,C: traffic] :
( ( create_reservation @ A @ B @ C )
=> ( ord_less_eq_nat_int @ ( res @ A @ B ) @ ( res @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_traffic_Ocreate__res__subseteq1) ).
thf(182,plain,
! [A: traffic,B: cars,C: traffic] :
( ( create_reservation @ A @ B @ C )
=> ( ord_less_eq_nat_int @ ( res @ A @ B ) @ ( res @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(67,axiom,
! [A: $o] :
( ( A
= ( product_Unity = product_Unity ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_eq__sym__Unity__conv) ).
thf(331,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(78,axiom,
bot_bot_Product_unit = product_Unity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_bot__unit__def) ).
thf(441,plain,
bot_bot_Product_unit = product_Unity,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(91,axiom,
! [A: real_int,B: nat_int,C: cars,D: product_unit] :
( ( own_Product_unit @ ( view_e912666823t_unit @ A @ B @ C @ D ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_select__convs_I3_J) ).
thf(502,plain,
! [A: real_int,B: nat_int,C: cars,D: product_unit] :
( ( own_Product_unit @ ( view_e912666823t_unit @ A @ B @ C @ D ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(86,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ord_less_eq_real @ ( minus_minus_real @ A @ D ) @ ( minus_minus_real @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_diff__mono) ).
thf(463,plain,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ord_less_eq_real @ ( minus_minus_real @ A @ D ) @ ( minus_minus_real @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(4,axiom,
! [A: nat_int,B: nat_int,C: nat_int] :
( ( ord_less_eq_nat_int @ A @ B )
=> ( ( ord_less_eq_nat_int @ C @ A )
=> ( ord_less_eq_nat_int @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_dual__order_Otrans) ).
thf(127,plain,
! [A: nat_int,B: nat_int,C: nat_int] :
( ( ord_less_eq_nat_int @ A @ B )
=> ( ( ord_less_eq_nat_int @ C @ A )
=> ( ord_less_eq_nat_int @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(69,axiom,
! [A: real_int,B: nat_int,C: cars,D: product_unit] :
( ( more_Product_unit @ ( view_e912666823t_unit @ A @ B @ C @ D ) )
= D ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_select__convs_I4_J) ).
thf(338,plain,
! [A: real_int,B: nat_int,C: cars,D: product_unit] :
( ( more_Product_unit @ ( view_e912666823t_unit @ A @ B @ C @ D ) )
= D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(17,axiom,
! [A: nat_int,B: nat_int] :
( ( ord_less_eq_nat_int @ A @ B )
=> ( ( ord_less_eq_nat_int @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_antisym) ).
thf(175,plain,
! [A: nat_int,B: nat_int] :
( ( ord_less_eq_nat_int @ A @ B )
=> ( ( ord_less_eq_nat_int @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(62,axiom,
! [A: cars,B: traffic > view_e774982825t_unit > $o,C: traffic,D: view_e774982825t_unit] :
( ( ! [E: view_e774982825t_unit] :
( ( switch @ D @ A @ E )
=> ~ ( B @ C @ E ) ) )
= ( ~ ! [E: view_e774982825t_unit] :
( ( switch @ D @ A @ E )
=> ( B @ C @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_local_Ohmlsl_Oat__neg) ).
thf(314,plain,
! [A: cars,B: traffic > view_e774982825t_unit > $o,C: traffic,D: view_e774982825t_unit] :
( ( ! [E: view_e774982825t_unit] :
( ( switch @ D @ A @ E )
=> ~ ( B @ C @ E ) ) )
= ( ~ ! [E: view_e774982825t_unit] :
( ( switch @ D @ A @ E )
=> ( B @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(80,axiom,
! [A: traffic,B: traffic,C: traffic] :
( ( abstract @ A @ B )
=> ( ? [D: cars] : ( withdraw_claim @ B @ D @ C )
=> ( abstract @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_traffic_Owd__clm) ).
thf(446,plain,
! [A: traffic,B: traffic,C: traffic] :
( ( abstract @ A @ B )
=> ( ? [D: cars] : ( withdraw_claim @ B @ D @ C )
=> ( abstract @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(111,axiom,
! [A: traffic,B: traffic] :
( own_Product_unit
= ( ^ [C: view_e774982825t_unit] : ( own_Product_unit @ ( move @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_traffic_Omove__keeps__owner) ).
thf(556,plain,
! [A: traffic,B: traffic] :
( own_Product_unit
= ( ^ [C: view_e774982825t_unit] : ( own_Product_unit @ ( move @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(104,axiom,
! [A: traffic,B: traffic] :
( lan_Product_unit
= ( ^ [C: view_e774982825t_unit] : ( lan_Product_unit @ ( move @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_traffic_Omove__keeps__lanes) ).
thf(539,plain,
! [A: traffic,B: traffic] :
( lan_Product_unit
= ( ^ [C: view_e774982825t_unit] : ( lan_Product_unit @ ( move @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(27,axiom,
! [A: view_e774982825t_unit] :
? [B: cars,C: view_e774982825t_unit] : ( switch @ A @ B @ C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_view_Oswitch__exists) ).
thf(203,plain,
! [A: view_e774982825t_unit] :
? [B: cars,C: view_e774982825t_unit] : ( switch @ A @ B @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(98,axiom,
( switch
= ( ^ [A: view_e774982825t_unit,B: cars,C: view_e774982825t_unit] :
( ( ( ext_Product_unit @ A )
= ( ext_Product_unit @ C ) )
& ( ( lan_Product_unit @ A )
= ( lan_Product_unit @ C ) )
& ( ( own_Product_unit @ C )
= B )
& ( ( more_Product_unit @ A )
= ( more_Product_unit @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_view_Oswitch__def) ).
thf(524,plain,
( switch
= ( ^ [A: view_e774982825t_unit,B: cars,C: view_e774982825t_unit] :
( ( ( ext_Product_unit @ A )
= ( ext_Product_unit @ C ) )
& ( ( lan_Product_unit @ A )
= ( lan_Product_unit @ C ) )
& ( ( own_Product_unit @ C )
= B )
& ( ( more_Product_unit @ A )
= ( more_Product_unit @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(3,axiom,
! [A: nat_int,B: nat_int > nat_int,C: nat_int,D: nat_int] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_nat_int @ C @ D )
=> ( ! [E: nat_int,F: nat_int] :
( ( ord_less_eq_nat_int @ E @ F )
=> ( ord_less_eq_nat_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat_int @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_ord__eq__le__subst) ).
thf(119,plain,
! [A: nat_int,B: nat_int > nat_int,C: nat_int,D: nat_int] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_nat_int @ C @ D )
=> ( ! [E: nat_int,F: nat_int] :
( ( ord_less_eq_nat_int @ E @ F )
=> ( ord_less_eq_nat_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat_int @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(89,axiom,
! [A: traffic,B: cars,C: traffic,D: cars] :
( ( ( create_reservation @ A @ B @ C )
& ( B != D ) )
=> ( ( res @ A @ D )
= ( res @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_traffic_Ocreate__res__subseteq1__neq) ).
thf(478,plain,
! [A: traffic,B: cars,C: traffic,D: cars] :
( ( ( create_reservation @ A @ B @ C )
& ( B != D ) )
=> ( ( res @ A @ D )
= ( res @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(32,axiom,
! [A: traffic > view_e774982825t_unit > $o,B: traffic,C: view_e774982825t_unit] :
( ( A @ B @ C )
=> ? [D: cars] :
! [E: view_e774982825t_unit] :
( ( switch @ C @ D @ E )
=> ( A @ B @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_local_Ohmlsl_Oat__exists) ).
thf(214,plain,
! [A: traffic > view_e774982825t_unit > $o,B: traffic,C: view_e774982825t_unit] :
( ( A @ B @ C )
=> ? [D: cars] :
! [E: view_e774982825t_unit] :
( ( switch @ C @ D @ E )
=> ( A @ B @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(10,axiom,
! [A: nat_int,B: nat_int,C: nat_int] :
( ( A = B )
=> ( ( ord_less_eq_nat_int @ B @ C )
=> ( ord_less_eq_nat_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_ord__eq__le__trans) ).
thf(151,plain,
! [A: nat_int,B: nat_int,C: nat_int] :
( ( A = B )
=> ( ( ord_less_eq_nat_int @ B @ C )
=> ( ord_less_eq_nat_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(46,axiom,
! [A: cars,B: traffic > view_e774982825t_unit > $o,C: traffic,D: view_e774982825t_unit] :
( ~ ! [E: view_e774982825t_unit] :
( ( switch @ D @ A @ E )
=> ~ ( B @ C @ E ) )
=> ! [E: view_e774982825t_unit] :
( ( switch @ D @ A @ E )
=> ( B @ C @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_local_Ohmlsl_Oat__neg__neg2) ).
thf(262,plain,
! [A: cars,B: traffic > view_e774982825t_unit > $o,C: traffic,D: view_e774982825t_unit] :
( ~ ! [E: view_e774982825t_unit] :
( ( switch @ D @ A @ E )
=> ~ ( B @ C @ E ) )
=> ! [E: view_e774982825t_unit] :
( ( switch @ D @ A @ E )
=> ( B @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(30,axiom,
! [A: real_int] :
? [B: real_int] : ( real_R_Chop @ A @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_chop__singleton__left) ).
thf(210,plain,
! [A: real_int] :
? [B: real_int] : ( real_R_Chop @ A @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(7,axiom,
! [A: nat_int,B: nat_int] :
( ( A = B )
=> ( ord_less_eq_nat_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_eq__refl) ).
thf(136,plain,
! [A: nat_int,B: nat_int] :
( ( A = B )
=> ( ord_less_eq_nat_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(70,axiom,
! [A: view_e774982825t_unit] :
( A
= ( view_e912666823t_unit @ ( ext_Product_unit @ A ) @ ( lan_Product_unit @ A ) @ ( own_Product_unit @ A ) @ ( more_Product_unit @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_surjective) ).
thf(341,plain,
! [A: view_e774982825t_unit] :
( A
= ( view_e912666823t_unit @ ( ext_Product_unit @ A ) @ ( lan_Product_unit @ A ) @ ( own_Product_unit @ A ) @ ( more_Product_unit @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(39,axiom,
! [A: cars,B: traffic > view_e774982825t_unit > $o,C: traffic > view_e774982825t_unit > $o,D: traffic,E: view_e774982825t_unit] :
( ( ! [F: view_e774982825t_unit] :
( ( switch @ E @ A @ F )
=> ( ( B @ D @ F )
| ( C @ D @ F ) ) ) )
= ( ! [F: view_e774982825t_unit] :
( ( switch @ E @ A @ F )
=> ( B @ D @ F ) )
| ! [F: view_e774982825t_unit] :
( ( switch @ E @ A @ F )
=> ( C @ D @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_local_Ohmlsl_Oat__disj__dist) ).
thf(239,plain,
! [A: cars,B: traffic > view_e774982825t_unit > $o,C: traffic > view_e774982825t_unit > $o,D: traffic,E: view_e774982825t_unit] :
( ( ! [F: view_e774982825t_unit] :
( ( switch @ E @ A @ F )
=> ( ( B @ D @ F )
| ( C @ D @ F ) ) ) )
= ( ! [F: view_e774982825t_unit] :
( ( switch @ E @ A @ F )
=> ( B @ D @ F ) )
| ! [F: view_e774982825t_unit] :
( ( switch @ E @ A @ F )
=> ( C @ D @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(40,axiom,
! [A: view_e774982825t_unit,B: view_e774982825t_unit,C: view_e774982825t_unit,D: cars,E: view_e774982825t_unit] :
( ( ( hchop @ A @ B @ C )
& ( switch @ A @ D @ E ) )
=> ? [F: view_e774982825t_unit,G: view_e774982825t_unit] :
( ( switch @ B @ D @ F )
& ( switch @ C @ D @ G )
& ( hchop @ E @ F @ G ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_view_Oswitch__hchop1) ).
thf(242,plain,
! [A: view_e774982825t_unit,B: view_e774982825t_unit,C: view_e774982825t_unit,D: cars,E: view_e774982825t_unit] :
( ( ( hchop @ A @ B @ C )
& ( switch @ A @ D @ E ) )
=> ? [F: view_e774982825t_unit,G: view_e774982825t_unit] :
( ( switch @ B @ D @ F )
& ( switch @ C @ D @ G )
& ( hchop @ E @ F @ G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(68,axiom,
! [A: product_unit > $o,B: product_unit] :
( ( A @ product_Unity )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_old_Ounit_Oinducts) ).
thf(332,plain,
! [A: product_unit > $o,B: product_unit] :
( ( A @ product_Unity )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(18,axiom,
( ( (=) @ nat_int )
= ( ^ [A: nat_int,B: nat_int] :
( ( ord_less_eq_nat_int @ B @ A )
& ( ord_less_eq_nat_int @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_dual__order_Oeq__iff) ).
thf(178,plain,
( ( (=) @ nat_int )
= ( ^ [A: nat_int,B: nat_int] :
( ( ord_less_eq_nat_int @ B @ A )
& ( ord_less_eq_nat_int @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(50,axiom,
! [A: view_e774982825t_unit,B: cars,C: view_e774982825t_unit] :
( ( switch @ A @ B @ C )
=> ( switch @ C @ ( own_Product_unit @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_view_Oswitch__symm) ).
thf(277,plain,
! [A: view_e774982825t_unit,B: cars,C: view_e774982825t_unit] :
( ( switch @ A @ B @ C )
=> ( switch @ C @ ( own_Product_unit @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(88,axiom,
! [A: product_unit > $o,B: product_unit > $o] :
( ( ( A @ product_Unity )
=> ( B @ product_Unity ) )
=> ! [C: product_unit] :
( ( A @ C )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_unit__all__impI) ).
thf(469,plain,
! [A: product_unit > $o,B: product_unit > $o] :
( ( ( A @ product_Unity )
=> ( B @ product_Unity ) )
=> ! [C: product_unit] :
( ( A @ C )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(106,axiom,
! [A: traffic,B: view_e774982825t_unit] :
( ( move @ A @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_traffic_Omove__nothing) ).
thf(543,plain,
! [A: traffic,B: view_e774982825t_unit] :
( ( move @ A @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(43,axiom,
! [A: view_e774982825t_unit] :
? [B: view_e774982825t_unit,C: view_e774982825t_unit] : ( hchop @ A @ B @ C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_view_Ohorizontal__chop1) ).
thf(254,plain,
! [A: view_e774982825t_unit] :
? [B: view_e774982825t_unit,C: view_e774982825t_unit] : ( hchop @ A @ B @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(35,axiom,
! [A: view_e774982825t_unit,B: cars,C: view_e774982825t_unit,D: cars,E: view_e774982825t_unit] :
( ( ( switch @ A @ B @ C )
& ( switch @ A @ D @ E ) )
=> ( switch @ C @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_view_Oswitch__triangle) ).
thf(227,plain,
! [A: view_e774982825t_unit,B: cars,C: view_e774982825t_unit,D: cars,E: view_e774982825t_unit] :
( ( ( switch @ A @ B @ C )
& ( switch @ A @ D @ E ) )
=> ( switch @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(16785,plain,
$false,
inference(cvc4,[status(thm)],[533,320,351,347,249,518,481,170,449,247,269,570,184,344,542,559,284,289,216,164,443,293,132,117,512,529,546,201,233,452,297,429,229,461,551,224,317,156,188,526,212,328,256,193,537,515,457,205,311,148,264,161,279,180,191,286,291,259,572,466,236,172,274,567,208,509,434,552,323,140,198,521,130,455,563,299,431,167,505,438,531,548,295,282,182,331,441,502,463,127,338,175,314,446,556,539,203,524,119,478,214,151,262,210,136,341,239,242,332,178,277,469,543,254,227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP168^1 : TPTP v8.2.0. Released v7.5.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n025.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sat May 18 18:06:54 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.95/0.91 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.93/1.17 % [INFO] Parsing done (250ms).
% 2.07/1.17 % [INFO] Running in sequential loop mode.
% 2.71/1.38 % [INFO] eprover registered as external prover.
% 2.71/1.39 % [INFO] cvc4 registered as external prover.
% 2.71/1.39 % [INFO] Scanning for conjecture ...
% 2.97/1.47 % [INFO] Found a conjecture (or negated_conjecture) and 357 axioms. Running axiom selection ...
% 3.15/1.55 % [INFO] Axiom selection finished. Selected 114 axioms (removed 243 axioms).
% 3.62/1.67 % [INFO] Problem is higher-order (TPTP THF).
% 3.74/1.69 % [INFO] Type checking passed.
% 3.74/1.69 % [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 ...
% 6.04/2.34 % [INFO] [Domain constraints] Detected constraint on product_unit
% 6.04/2.34 % [INFO] [Domain constraints] dom(product_unit) ⊆ {product_Unity}
% 6.28/2.41 % [INFO] [Domain constraints] Detected constraint on product_unit
% 6.28/2.41 % [INFO] [Domain constraints] dom(product_unit) ⊆ {product_Unity}
% 67.01/22.13 % External prover 'cvc4' found a proof!
% 67.01/22.13 % [INFO] Killing All external provers ...
% 67.01/22.13 % Time passed: 21601ms (effective reasoning time: 20956ms)
% 67.01/22.13 % 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)>
% 67.01/22.13 % Axioms used in derivation (114): fact_98_local_Ohmlsl_Oat__hchop__dist, fact_95_local_Ohmlsl_Oat__neg__neg, fact_57_select__convs_I4_J, fact_115_unit__all__impI, fact_2_local_Ohmlsl_Oglobally__4, fact_84_chop__singleton__right, fact_38_traffic_Oabs__trans, fact_117_bot__unit__def, fact_15_local_Ohmlsl_Ohchop__assoc, fact_17_local_Ohmlsl_Ohchop__disj__distr2, fact_87_view_Oswitch__def, fact_211_dual__order_Otrans, fact_101_view_Oswitch__always__exists, fact_0_cr__res_Ohyps_I1_J, fact_1_cr__res_Ohyps_I2_J, fact_237_traffic_Ocreate__res__subseteq1, fact_22_local_Ohmlsl_Ohchop__neg1, fact_53_traffic_Oevolve__trans, fact_35_view_Ohorizontal__chop__assoc1, fact_106_view_Oswitch__hchop1, fact_93_local_Ohmlsl_Oat__neg1, fact_20_local_Ohmlsl_Ohchop__weaken, fact_18_local_Ohmlsl_Ohchop__weaken2, fact_43_select__convs_I1_J, fact_194_ord__le__eq__trans, fact_105_view_Oswitch__trans, fact_67_view_Ohchop__def, fact_9_traffic_Omove__keeps__owner, fact_40_cases__scheme, fact_49_traffic_Owithdraw__clm__eq__res, fact_26_traffic_Ocr__clm, fact_42_view_Ohorizontal__chop__own__trans, fact_32_view_Ohorizontal__chop__empty__right, fact_56_traffic_Oevolve, fact_58_equality, fact_88_local_Ohmlsl_Oat__conj__distr, fact_52_traffic_Ocreate__res__subseteq2__neq, fact_102_view_Oswitch__triangle, fact_100_local_Ohmlsl_Oat__hchop__dist2, fact_3_local_Ohmlsl_Oglobally__refl, fact_238_traffic_Owithdraw__res__subseteq, fact_177_order_Otrans, fact_103_view_Oswitch__unique, fact_46_traffic_Oabstract_Osimps, fact_39_induct__scheme, fact_13_traffic_Omove__stability__wdc, fact_86_chop__singleton__left, fact_23_ext__inject, fact_215_dual__order_Oeq__iff, fact_239_default__unit__def, fact_143_ord__eq__le__subst, fact_206_dual__order_Orefl, fact_5__092_060open_062move_Ats_Ats_H_Av_A_061_Amove_Ats_H_Ats_H_H_A_Imove_Ats_Ats_H_Av_J_092_060close_062, fact_45_traffic_Oabstract_Oinducts, fact_186_order__class_Oorder_Oeq__iff, fact_116_eq__sym__Unity__conv, fact_113_old_Ounit_Oexhaust, fact_7_traffic_Omove__def, fact_182_antisym__conv, fact_24_cases, fact_30_select__convs_I3_J, fact_219_dual__order_Oantisym, fact_12_traffic_Omove__stability__clm, fact_123_order__subst1, fact_108_view_Oswitch__refl, fact_10_traffic_Omove__trans, fact_91_local_Ohmlsl_Oat__neg, fact_202_order__trans, fact_96_local_Ohmlsl_Oat__neg__neg1, fact_36_view_Ohorizontal__chop1, fact_16_local_Ohmlsl_Ohchop__disj__distr1, fact_50_traffic_Ocreate__clm__eq__res, fact_28_traffic_Owd__res, fact_34_view_Ohorizontal__chop__assoc2, fact_41_traffic_Oalways__create__res, fact_6_traffic_Omove__nothing, fact_85_real__int__class_Ochop__always__possible, fact_110_view_Oswitch__origin, fact_37_traffic_Oabstract_Orefl, fact_89_local_Ohmlsl_Oat__disj__dist, fact_167_antisym, fact_245_diff__mono, fact_29_traffic_Ocr__res, fact_47_traffic_Oabstract_Ocases, fact_54_traffic_Oevolve_Orefl, fact_114_old_Ounit_Oinducts, fact_4_abs, fact_33_view_Ohorizontal__chop__empty__left, fact_107_view_Oswitch__hchop2, fact_90_local_Ohmlsl_Oat__exists, fact_31_select__convs_I2_J, fact_163_eq__iff, fact_92_local_Ohmlsl_Oat__neg_H, fact_48_surjective, fact_99_local_Ohmlsl_Oat__hchop__dist1, fact_97_local_Ohmlsl_Oat__neg__neg2, fact_172_eq__refl, fact_190_ord__eq__le__trans, fact_8_traffic_Omove__stability__res, fact_51_traffic_Ocreate__res__subseteq1__neq, fact_198_order__class_Oorder_Oantisym, fact_119_order__refl, fact_94_local_Ohmlsl_Oat__neg2, fact_153_ord__le__eq__subst, fact_27_traffic_Owd__clm, fact_133_order__subst2, fact_19_local_Ohmlsl_Ohchop__weaken1, fact_14_traffic_Omove__stability__wdr, fact_21_local_Ohmlsl_Ohchop__neg2, fact_118_traffic_Ocreate__res__subseteq2, fact_104_view_Oswitch__exists, fact_11_traffic_Omove__keeps__lanes, fact_109_view_Oswitch__symm, fact_25_induct
% 67.01/22.13 % No. of inferences in proof: 232
% 67.01/22.14 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 21601 ms resp. 20956 ms w/o parsing
% 67.17/22.21 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 67.17/22.21 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------