TSTP Solution File: ITP135^1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : ITP135^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n013.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 22:23:15 EDT 2024
% Result : Theorem 10.13s 3.80s
% Output : Refutation 10.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 173
% Syntax : Number of formulae : 287 ( 145 unt; 61 typ; 0 def)
% Number of atoms : 578 ( 417 equ; 0 cnn)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 1846 ( 168 ~; 3 |; 46 &;1385 @)
% ( 0 <=>; 244 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 23 ( 22 usr)
% Number of type conns : 293 ( 293 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 39 usr; 7 con; 0-3 aty)
% Number of variables : 675 ( 20 ^ 643 !; 12 ?; 675 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_Pr1723822845lle_tv_type,type,
set_Pr1723822845lle_tv: $tType ).
thf(set_Pr2120184979lle_fm_type,type,
set_Pr2120184979lle_fm: $tType ).
thf(produc1443694919lle_tv_type,type,
produc1443694919lle_tv: $tType ).
thf(produc696645085lle_fm_type,type,
produc696645085lle_fm: $tType ).
thf(set_Pr2014382200lle_tv_type,type,
set_Pr2014382200lle_tv: $tType ).
thf(set_Pr840833727at_nat_type,type,
set_Pr840833727at_nat: $tType ).
thf(set_Pr560526279lle_tv_type,type,
set_Pr560526279lle_tv: $tType ).
thf(produc1647334210lle_tv_type,type,
produc1647334210lle_tv: $tType ).
thf(produc596913417at_nat_type,type,
produc596913417at_nat: $tType ).
thf(produc931990033lle_tv_type,type,
produc931990033lle_tv: $tType ).
thf(set_Pr1725653840tv_nat_type,type,
set_Pr1725653840tv_nat: $tType ).
thf(set_Pr13445366lle_tv_type,type,
set_Pr13445366lle_tv: $tType ).
thf(produc194167194tv_nat_type,type,
produc194167194tv_nat: $tType ).
thf(produc270694976lle_tv_type,type,
produc270694976lle_tv: $tType ).
thf(set_Pr1986765409at_nat_type,type,
set_Pr1986765409at_nat: $tType ).
thf(set_Pa1764573435lle_tv_type,type,
set_Pa1764573435lle_tv: $tType ).
thf(product_prod_nat_nat_type,type,
product_prod_nat_nat: $tType ).
thf(paraco1605129243lle_tv_type,type,
paraco1605129243lle_tv: $tType ).
thf(paraco1604210848lle_fm_type,type,
paraco1604210848lle_fm: $tType ).
thf(list_char_type,type,
list_char: $tType ).
thf(set_nat_type,type,
set_nat: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(inj_on_nat_nat_type,type,
inj_on_nat_nat: ( nat > nat ) > set_nat > $o ).
thf(inj_on772319074lle_tv_type,type,
inj_on772319074lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > $o ).
thf(the_inv_into_nat_nat_type,type,
the_inv_into_nat_nat: set_nat > ( nat > nat ) > nat > nat ).
thf(if_Par1134130401lle_tv_type,type,
if_Par1134130401lle_tv: $o > paraco1605129243lle_tv > paraco1605129243lle_tv > paraco1605129243lle_tv ).
thf(top_top_set_nat_type,type,
top_top_set_nat: set_nat ).
thf(top_to1057771083lle_tv_type,type,
top_to1057771083lle_tv: set_Pa1764573435lle_tv ).
thf(paraco761681009ge_int_type,type,
paraco761681009ge_int: ( nat > nat ) > ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv ).
thf(paraco1147068288nge_tv_type,type,
paraco1147068288nge_tv: ( nat > nat ) > paraco1605129243lle_tv > paraco1605129243lle_tv ).
thf(paraco1632582009tv_rel_type,type,
paraco1632582009tv_rel: produc931990033lle_tv > produc931990033lle_tv > $o ).
thf(paraco1325918602e_eval_type,type,
paraco1325918602e_eval: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > paraco1605129243lle_tv ).
thf(paraco69239110le_Con_type,type,
paraco69239110le_Con: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).
thf(paraco1389086619le_Eql_type,type,
paraco1389086619le_Eql: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).
thf(paraco1745535428le_Eql_type,type,
paraco1745535428le_Eql: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).
thf(paraco445776468le_Neg_type,type,
paraco445776468le_Neg: paraco1604210848lle_fm > paraco1604210848lle_fm ).
thf(paraco1480028776le_Pro_type,type,
paraco1480028776le_Pro: list_char > paraco1604210848lle_fm ).
thf(paraco367965286_Truth_type,type,
paraco367965286_Truth: paraco1604210848lle_fm ).
thf(paraco1344940915le_Det_type,type,
paraco1344940915le_Det: $o > paraco1605129243lle_tv ).
thf(paraco793048302_Indet_type,type,
paraco793048302_Indet: nat > paraco1605129243lle_tv ).
thf(paraco2051596139lle_tv_type,type,
paraco2051596139lle_tv: ( $o > paraco1605129243lle_tv ) > ( nat > paraco1605129243lle_tv ) > paraco1605129243lle_tv > paraco1605129243lle_tv ).
thf(paraco327635598_valid_type,type,
paraco327635598_valid: paraco1604210848lle_fm > $o ).
thf(paraco55203475lid_in_type,type,
paraco55203475lid_in: set_nat > paraco1604210848lle_fm > $o ).
thf(produc1710735575lle_fm_type,type,
produc1710735575lle_fm: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > produc696645085lle_fm ).
thf(produc1680557635lle_tv_type,type,
produc1680557635lle_tv: ( nat > nat ) > paraco1605129243lle_tv > produc931990033lle_tv ).
thf(produc939316703lle_tv_type,type,
produc939316703lle_tv: ( ( nat > nat ) > nat > nat ) > produc931990033lle_tv > produc931990033lle_tv ).
thf(produc109093078at_nat_type,type,
produc109093078at_nat: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc931990033lle_tv > produc931990033lle_tv ).
thf(produc234482697lle_tv_type,type,
produc234482697lle_tv: paraco1605129243lle_tv > paraco1605129243lle_tv > $o > paraco1605129243lle_tv ).
thf(produc752649287e_tv_o_type,type,
produc752649287e_tv_o: ( produc931990033lle_tv > $o ) > ( nat > nat ) > paraco1605129243lle_tv > $o ).
thf(produc532909085lle_tv_type,type,
produc532909085lle_tv: ( ( nat > nat ) > nat > nat ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc931990033lle_tv > produc931990033lle_tv ).
thf(produc1589291287at_nat_type,type,
produc1589291287at_nat: produc596913417at_nat > paraco1605129243lle_tv ).
thf(produc500618325at_nat_type,type,
produc500618325at_nat: produc596913417at_nat > nat > nat ).
thf(produc178635363at_nat_type,type,
produc178635363at_nat: produc596913417at_nat > produc931990033lle_tv ).
thf(inv_image_nat_nat_type,type,
inv_image_nat_nat: set_Pr1986765409at_nat > ( nat > nat ) > set_Pr1986765409at_nat ).
thf(total_on_nat_type,type,
total_on_nat: set_nat > set_Pr1986765409at_nat > $o ).
thf(image_nat_nat_type,type,
image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
thf(accp_P2085826120lle_tv_type,type,
accp_P2085826120lle_tv: ( produc931990033lle_tv > produc931990033lle_tv > $o ) > produc931990033lle_tv > $o ).
thf(f_type,type,
f: nat > nat ).
thf(i_type,type,
i: list_char > paraco1605129243lle_tv ).
thf(p1_type,type,
p1: paraco1604210848lle_fm ).
thf(p2_type,type,
p2: paraco1604210848lle_fm ).
thf(14,axiom,
! [A: produc696645085lle_fm] :
~ ! [B: list_char > paraco1605129243lle_tv,C: paraco1604210848lle_fm] :
( A
!= ( produc1710735575lle_fm @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_old_Oprod_Oexhaust) ).
thf(153,plain,
! [A: produc696645085lle_fm] :
~ ! [B: list_char > paraco1605129243lle_tv,C: paraco1604210848lle_fm] :
( A
!= ( produc1710735575lle_fm @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(73,axiom,
! [A: paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
( ( produc234482697lle_tv @ A @ B @ $false )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_old_Obool_Osimps_I4_J) ).
thf(398,plain,
! [A: paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
( ( produc234482697lle_tv @ A @ B @ $false )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(87,axiom,
! [A: produc931990033lle_tv] :
( ! [B: nat > nat,C: $o] :
( A
!= ( produc1680557635lle_tv @ B @ ( paraco1344940915le_Det @ C ) ) )
=> ~ ! [B: nat > nat,C: nat] :
( A
!= ( produc1680557635lle_tv @ B @ ( paraco793048302_Indet @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_change__tv_Ocases) ).
thf(445,plain,
! [A: produc931990033lle_tv] :
( ! [B: nat > nat,C: $o] :
( A
!= ( produc1680557635lle_tv @ B @ ( paraco1344940915le_Det @ C ) ) )
=> ~ ! [B: nat > nat,C: nat] :
( A
!= ( produc1680557635lle_tv @ B @ ( paraco793048302_Indet @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(63,axiom,
! [A: list_char,B: list_char] :
( ( ( paraco1480028776le_Pro @ A )
= ( paraco1480028776le_Pro @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_fm_Oinject_I1_J) ).
thf(365,plain,
! [A: list_char,B: list_char] :
( ( ( paraco1480028776le_Pro @ A )
= ( paraco1480028776le_Pro @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(29,axiom,
! [A: list_char,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( ( paraco1480028776le_Pro @ A )
!= ( paraco1745535428le_Eql @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_fm_Odistinct_I9_J) ).
thf(249,plain,
! [A: list_char,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( ( paraco1480028776le_Pro @ A )
!= ( paraco1745535428le_Eql @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(106,axiom,
! [A: paraco1605129243lle_tv] :
( ( A
!= ( paraco1344940915le_Det @ $true ) )
=> ( ( A
!= ( paraco1344940915le_Det @ $false ) )
=> ~ ! [B: nat] :
( A
!= ( paraco793048302_Indet @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_string__tv_Ocases) ).
thf(555,plain,
! [A: paraco1605129243lle_tv] :
( ( A
!= ( paraco1344940915le_Det @ $true ) )
=> ( ( A
!= ( paraco1344940915le_Det @ $false ) )
=> ~ ! [B: nat] :
( A
!= ( paraco793048302_Indet @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(76,axiom,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm] :
( ( paraco327635598_valid @ ( paraco69239110le_Con @ A @ B ) )
= ( ( paraco327635598_valid @ A )
& ( paraco327635598_valid @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_conjunction) ).
thf(408,plain,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm] :
( ( paraco327635598_valid @ ( paraco69239110le_Con @ A @ B ) )
= ( ( paraco327635598_valid @ A )
& ( paraco327635598_valid @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(36,axiom,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( ( paraco69239110le_Con @ A @ B )
!= ( paraco1745535428le_Eql @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_fm_Odistinct_I27_J) ).
thf(276,plain,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( ( paraco69239110le_Con @ A @ B )
!= ( paraco1745535428le_Eql @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(47,axiom,
! [A: paraco1604210848lle_fm] :
( ! [B: list_char] :
( A
!= ( paraco1480028776le_Pro @ B ) )
=> ( ( A != paraco367965286_Truth )
=> ( ! [B: paraco1604210848lle_fm] :
( A
!= ( paraco445776468le_Neg @ B ) )
=> ( ! [B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( A
!= ( paraco69239110le_Con @ B @ C ) )
=> ( ! [B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( A
!= ( paraco1389086619le_Eql @ B @ C ) )
=> ~ ! [B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( A
!= ( paraco1745535428le_Eql @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_fm_Oexhaust) ).
thf(308,plain,
! [A: paraco1604210848lle_fm] :
( ! [B: list_char] :
( A
!= ( paraco1480028776le_Pro @ B ) )
=> ( ( A != paraco367965286_Truth )
=> ( ! [B: paraco1604210848lle_fm] :
( A
!= ( paraco445776468le_Neg @ B ) )
=> ( ! [B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( A
!= ( paraco69239110le_Con @ B @ C ) )
=> ( ! [B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( A
!= ( paraco1389086619le_Eql @ B @ C ) )
=> ~ ! [B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( A
!= ( paraco1745535428le_Eql @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(88,axiom,
( paraco1325918602e_eval
= ( ^ [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] : ( paraco1325918602e_eval @ A @ ( paraco445776468le_Neg @ ( paraco445776468le_Neg @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_double__negation) ).
thf(449,plain,
( paraco1325918602e_eval
= ( ^ [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] : ( paraco1325918602e_eval @ A @ ( paraco445776468le_Neg @ ( paraco445776468le_Neg @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(112,axiom,
( ( paraco1325918602e_eval @ i @ p1 )
!= ( paraco1325918602e_eval @ i @ p2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_a_H) ).
thf(597,plain,
( ( paraco1325918602e_eval @ i @ p1 )
!= ( paraco1325918602e_eval @ i @ p2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(40,axiom,
! [A: produc931990033lle_tv > $o,B: produc931990033lle_tv] :
( ! [C: nat > nat,D: paraco1605129243lle_tv] : ( A @ ( produc1680557635lle_tv @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_old_Oprod_Oinducts) ).
thf(288,plain,
! [A: produc931990033lle_tv > $o,B: produc931990033lle_tv] :
( ! [C: nat > nat,D: paraco1605129243lle_tv] : ( A @ ( produc1680557635lle_tv @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(108,axiom,
( paraco761681009ge_int
= ( ^ [A: nat > nat,B: list_char > paraco1605129243lle_tv,C: list_char] : ( paraco1147068288nge_tv @ A @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_change__int__def) ).
thf(565,plain,
( paraco761681009ge_int
= ( ^ [A: nat > nat,B: list_char > paraco1605129243lle_tv,C: list_char] : ( paraco1147068288nge_tv @ A @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(31,axiom,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( ( paraco69239110le_Con @ A @ B )
!= ( paraco1389086619le_Eql @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_fm_Odistinct_I25_J) ).
thf(257,plain,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( ( paraco69239110le_Con @ A @ B )
!= ( paraco1389086619le_Eql @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(57,axiom,
! [A: produc696645085lle_fm] :
( ! [B: list_char > paraco1605129243lle_tv,C: list_char] :
( A
!= ( produc1710735575lle_fm @ B @ ( paraco1480028776le_Pro @ C ) ) )
=> ( ! [B: list_char > paraco1605129243lle_tv] :
( A
!= ( produc1710735575lle_fm @ B @ paraco367965286_Truth ) )
=> ( ! [B: list_char > paraco1605129243lle_tv,C: paraco1604210848lle_fm] :
( A
!= ( produc1710735575lle_fm @ B @ ( paraco445776468le_Neg @ C ) ) )
=> ( ! [B: list_char > paraco1605129243lle_tv,C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( A
!= ( produc1710735575lle_fm @ B @ ( paraco69239110le_Con @ C @ D ) ) )
=> ( ! [B: list_char > paraco1605129243lle_tv,C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( A
!= ( produc1710735575lle_fm @ B @ ( paraco1389086619le_Eql @ C @ D ) ) )
=> ~ ! [B: list_char > paraco1605129243lle_tv,C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( A
!= ( produc1710735575lle_fm @ B @ ( paraco1745535428le_Eql @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_eval_Ocases) ).
thf(344,plain,
! [A: produc696645085lle_fm] :
( ! [B: list_char > paraco1605129243lle_tv,C: list_char] :
( A
!= ( produc1710735575lle_fm @ B @ ( paraco1480028776le_Pro @ C ) ) )
=> ( ! [B: list_char > paraco1605129243lle_tv] :
( A
!= ( produc1710735575lle_fm @ B @ paraco367965286_Truth ) )
=> ( ! [B: list_char > paraco1605129243lle_tv,C: paraco1604210848lle_fm] :
( A
!= ( produc1710735575lle_fm @ B @ ( paraco445776468le_Neg @ C ) ) )
=> ( ! [B: list_char > paraco1605129243lle_tv,C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( A
!= ( produc1710735575lle_fm @ B @ ( paraco69239110le_Con @ C @ D ) ) )
=> ( ! [B: list_char > paraco1605129243lle_tv,C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( A
!= ( produc1710735575lle_fm @ B @ ( paraco1389086619le_Eql @ C @ D ) ) )
=> ~ ! [B: list_char > paraco1605129243lle_tv,C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( A
!= ( produc1710735575lle_fm @ B @ ( paraco1745535428le_Eql @ C @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(92,axiom,
! [A: nat > nat,B: paraco1605129243lle_tv,C: paraco1605129243lle_tv] :
( ( ( paraco1147068288nge_tv @ A @ B )
= C )
=> ( ! [D: $o] :
( ( B
= ( paraco1344940915le_Det @ D ) )
=> ( C
!= ( paraco1344940915le_Det @ D ) ) )
=> ~ ! [D: nat] :
( ( B
= ( paraco793048302_Indet @ D ) )
=> ( C
!= ( paraco793048302_Indet @ ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_change__tv_Oelims) ).
thf(460,plain,
! [A: nat > nat,B: paraco1605129243lle_tv,C: paraco1605129243lle_tv] :
( ( ( paraco1147068288nge_tv @ A @ B )
= C )
=> ( ! [D: $o] :
( ( B
= ( paraco1344940915le_Det @ D ) )
=> ( C
!= ( paraco1344940915le_Det @ D ) ) )
=> ~ ! [D: nat] :
( ( B
= ( paraco793048302_Indet @ D ) )
=> ( C
!= ( paraco793048302_Indet @ ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(15,axiom,
! [A: produc696645085lle_fm > $o,B: produc696645085lle_fm] :
( ! [C: list_char > paraco1605129243lle_tv,D: paraco1604210848lle_fm] : ( A @ ( produc1710735575lle_fm @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_prod__cases) ).
thf(157,plain,
! [A: produc696645085lle_fm > $o,B: produc696645085lle_fm] :
( ! [C: list_char > paraco1605129243lle_tv,D: paraco1604210848lle_fm] : ( A @ ( produc1710735575lle_fm @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(107,axiom,
! [A: paraco1605129243lle_tv > $o,B: paraco1605129243lle_tv] :
( ( A @ ( paraco1344940915le_Det @ $true ) )
=> ( ( A @ ( paraco1344940915le_Det @ $false ) )
=> ( ! [C: nat] : ( A @ ( paraco793048302_Indet @ C ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_string__tv_Oinduct) ).
thf(559,plain,
! [A: paraco1605129243lle_tv > $o,B: paraco1605129243lle_tv] :
( ( A @ ( paraco1344940915le_Det @ $true ) )
=> ( ( A @ ( paraco1344940915le_Det @ $false ) )
=> ( ! [C: nat] : ( A @ ( paraco793048302_Indet @ C ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(80,axiom,
( ( paraco1325918602e_eval @ i @ p1 )
!= ( paraco1344940915le_Det @ $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_a_H_H) ).
thf(421,plain,
( ( paraco1325918602e_eval @ i @ p1 )
!= ( paraco1344940915le_Det @ $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(49,axiom,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm] :
( ( ( paraco445776468le_Neg @ A )
= ( paraco445776468le_Neg @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_fm_Oinject_I2_J) ).
thf(316,plain,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm] :
( ( ( paraco445776468le_Neg @ A )
= ( paraco445776468le_Neg @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(32,axiom,
! [A: nat > nat,B: paraco1605129243lle_tv,C: nat > nat,D: paraco1605129243lle_tv] :
( ( ( produc1680557635lle_tv @ A @ B )
= ( produc1680557635lle_tv @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_Pair__inject) ).
thf(261,plain,
! [A: nat > nat,B: paraco1605129243lle_tv,C: nat > nat,D: paraco1605129243lle_tv] :
( ( ( produc1680557635lle_tv @ A @ B )
= ( produc1680557635lle_tv @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(94,axiom,
! [A: paraco1605129243lle_tv > $o,B: paraco1605129243lle_tv] :
( ! [C: $o] : ( A @ ( paraco1344940915le_Det @ C ) )
=> ( ! [C: nat] : ( A @ ( paraco793048302_Indet @ C ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_tv_Oinduct) ).
thf(475,plain,
! [A: paraco1605129243lle_tv > $o,B: paraco1605129243lle_tv] :
( ! [C: $o] : ( A @ ( paraco1344940915le_Det @ C ) )
=> ( ! [C: nat] : ( A @ ( paraco793048302_Indet @ C ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(86,axiom,
( ( paraco1147068288nge_tv @ f @ ( paraco1325918602e_eval @ i @ p2 ) )
= ( paraco1344940915le_Det @ $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__092_060open_062change__tv_Af_A_Ieval_Ai_Ap2_J_A_061_ADet_ATrue_092_060close_062) ).
thf(443,plain,
( ( paraco1147068288nge_tv @ f @ ( paraco1325918602e_eval @ i @ p2 ) )
= ( paraco1344940915le_Det @ $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(30,axiom,
! [A: list_char] :
( ( paraco1480028776le_Pro @ A )
!= paraco367965286_Truth ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_fm_Odistinct_I1_J) ).
thf(253,plain,
! [A: list_char] :
( ( paraco1480028776le_Pro @ A )
!= paraco367965286_Truth ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(58,axiom,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: paraco1605129243lle_tv,C: paraco1605129243lle_tv,D: $o] :
( ( A @ ( produc234482697lle_tv @ B @ C @ D ) )
= ( produc234482697lle_tv @ ( A @ B ) @ ( A @ C ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_bool_Ocase__distrib) ).
thf(348,plain,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: paraco1605129243lle_tv,C: paraco1605129243lle_tv,D: $o] :
( ( A @ ( produc234482697lle_tv @ B @ C @ D ) )
= ( produc234482697lle_tv @ ( A @ B ) @ ( A @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(12,axiom,
! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,C: list_char > paraco1605129243lle_tv,D: paraco1604210848lle_fm] :
( ( ( produc1710735575lle_fm @ A @ B )
= ( produc1710735575lle_fm @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_old_Oprod_Oinject) ).
thf(147,plain,
! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,C: list_char > paraco1605129243lle_tv,D: paraco1604210848lle_fm] :
( ( ( produc1710735575lle_fm @ A @ B )
= ( produc1710735575lle_fm @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(37,axiom,
! [A: set_nat,B: paraco1604210848lle_fm] :
( ~ ( paraco55203475lid_in @ A @ B )
=> ~ ( paraco327635598_valid @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_transfer) ).
thf(280,plain,
! [A: set_nat,B: paraco1604210848lle_fm] :
( ~ ( paraco55203475lid_in @ A @ B )
=> ~ ( paraco327635598_valid @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(8,axiom,
! [A: nat > nat,B: nat] :
( ( ( image_nat_nat @ A @ top_top_set_nat )
= top_top_set_nat )
=> ? [C: nat] :
( B
= ( A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_surjD) ).
thf(133,plain,
! [A: nat > nat,B: nat] :
( ( ( image_nat_nat @ A @ top_top_set_nat )
= top_top_set_nat )
=> ? [C: nat] :
( B
= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(77,axiom,
! [A: paraco1605129243lle_tv > $o,B: paraco1605129243lle_tv,C: paraco1605129243lle_tv,D: $o] :
( ( A @ ( produc234482697lle_tv @ B @ C @ D ) )
= ( ~ ( ( D
& ~ ( A @ B ) )
| ( ~ D
& ~ ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_bool_Osplit__sel__asm) ).
thf(411,plain,
! [A: paraco1605129243lle_tv > $o,B: paraco1605129243lle_tv,C: paraco1605129243lle_tv,D: $o] :
( ( A @ ( produc234482697lle_tv @ B @ C @ D ) )
= ( ~ ( ( D
& ~ ( A @ B ) )
| ( ~ D
& ~ ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(3,axiom,
! [A: nat > nat] :
( ( ( image_nat_nat @ A @ top_top_set_nat )
= top_top_set_nat )
= ( ! [B: nat] :
? [C: nat] :
( B
= ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_surj__def) ).
thf(116,plain,
! [A: nat > nat] :
( ( ( image_nat_nat @ A @ top_top_set_nat )
= top_top_set_nat )
= ( ! [B: nat] :
? [C: nat] :
( B
= ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(28,axiom,
! [A: paraco1604210848lle_fm > $o,B: paraco1604210848lle_fm] :
( ( A @ paraco367965286_Truth )
=> ( ! [C: list_char] : ( A @ ( paraco1480028776le_Pro @ C ) )
=> ( ! [C: paraco1604210848lle_fm] :
( ( A @ C )
=> ( A @ ( paraco445776468le_Neg @ C ) ) )
=> ( ! [C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( ( A @ C )
=> ( ( A @ D )
=> ( A @ ( paraco69239110le_Con @ C @ D ) ) ) )
=> ( ! [C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( ( A @ C )
=> ( ( A @ D )
=> ( A @ ( paraco1389086619le_Eql @ C @ D ) ) ) )
=> ( ! [C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( ( A @ C )
=> ( ( A @ D )
=> ( A @ ( paraco1745535428le_Eql @ C @ D ) ) ) )
=> ( A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_props_Oinduct) ).
thf(206,plain,
! [A: paraco1604210848lle_fm > $o,B: paraco1604210848lle_fm] :
( ( A @ paraco367965286_Truth )
=> ( ! [C: list_char] : ( A @ ( paraco1480028776le_Pro @ C ) )
=> ( ! [C: paraco1604210848lle_fm] :
( ( A @ C )
=> ( A @ ( paraco445776468le_Neg @ C ) ) )
=> ( ! [C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( ( A @ C )
=> ( ( A @ D )
=> ( A @ ( paraco69239110le_Con @ C @ D ) ) ) )
=> ( ! [C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( ( A @ C )
=> ( ( A @ D )
=> ( A @ ( paraco1389086619le_Eql @ C @ D ) ) ) )
=> ( ! [C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( ( A @ C )
=> ( ( A @ D )
=> ( A @ ( paraco1745535428le_Eql @ C @ D ) ) ) )
=> ( A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(101,axiom,
( paraco327635598_valid
= ( ^ [A: paraco1604210848lle_fm] :
! [B: list_char > paraco1605129243lle_tv] :
( ( paraco1325918602e_eval @ B @ A )
= ( paraco1344940915le_Det @ $true ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_valid__def) ).
thf(527,plain,
( paraco327635598_valid
= ( ^ [A: paraco1604210848lle_fm] :
! [B: list_char > paraco1605129243lle_tv] :
( ( paraco1325918602e_eval @ B @ A )
= ( paraco1344940915le_Det @ $true ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(48,axiom,
! [A: list_char,B: paraco1604210848lle_fm] :
( ( paraco1480028776le_Pro @ A )
!= ( paraco445776468le_Neg @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_fm_Odistinct_I3_J) ).
thf(312,plain,
! [A: list_char,B: paraco1604210848lle_fm] :
( ( paraco1480028776le_Pro @ A )
!= ( paraco445776468le_Neg @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(68,axiom,
! [A: paraco1604210848lle_fm,B: set_nat] :
( ( paraco327635598_valid @ A )
=> ( paraco55203475lid_in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_valid__valid__in) ).
thf(380,plain,
! [A: paraco1604210848lle_fm,B: set_nat] :
( ( paraco327635598_valid @ A )
=> ( paraco55203475lid_in @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(98,axiom,
! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( ( paraco1325918602e_eval @ A @ ( paraco1389086619le_Eql @ B @ C ) )
= ( paraco1344940915le_Det
@ ( ( paraco1325918602e_eval @ A @ B )
= ( paraco1325918602e_eval @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_eval__equality__simplify) ).
thf(512,plain,
! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( ( paraco1325918602e_eval @ A @ ( paraco1389086619le_Eql @ B @ C ) )
= ( paraco1344940915le_Det
@ ( ( paraco1325918602e_eval @ A @ B )
= ( paraco1325918602e_eval @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(102,axiom,
! [A: paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
( ( if_Par1134130401lle_tv @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_If_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_T) ).
thf(529,plain,
! [A: paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
( ( if_Par1134130401lle_tv @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(26,axiom,
! [A: produc931990033lle_tv > $o,B: nat > nat,C: paraco1605129243lle_tv] :
( ( A @ ( produc1680557635lle_tv @ B @ C ) )
=> ( produc752649287e_tv_o @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_curryI) ).
thf(201,plain,
! [A: produc931990033lle_tv > $o,B: nat > nat,C: paraco1605129243lle_tv] :
( ( A @ ( produc1680557635lle_tv @ B @ C ) )
=> ( produc752649287e_tv_o @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(54,axiom,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm] :
( paraco367965286_Truth
!= ( paraco1745535428le_Eql @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_fm_Odistinct_I17_J) ).
thf(334,plain,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm] :
( paraco367965286_Truth
!= ( paraco1745535428le_Eql @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(45,axiom,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( ( paraco1389086619le_Eql @ A @ B )
!= ( paraco1745535428le_Eql @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_fm_Odistinct_I29_J) ).
thf(302,plain,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( ( paraco1389086619le_Eql @ A @ B )
!= ( paraco1745535428le_Eql @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(16,axiom,
! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,C: list_char > paraco1605129243lle_tv,D: paraco1604210848lle_fm] :
( ( ( produc1710735575lle_fm @ A @ B )
= ( produc1710735575lle_fm @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_Pair__inject) ).
thf(160,plain,
! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,C: list_char > paraco1605129243lle_tv,D: paraco1604210848lle_fm] :
( ( ( produc1710735575lle_fm @ A @ B )
= ( produc1710735575lle_fm @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(43,axiom,
! [A: produc931990033lle_tv > $o,B: nat > nat,C: paraco1605129243lle_tv] :
( ( produc752649287e_tv_o @ A @ B @ C )
=> ( A @ ( produc1680557635lle_tv @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_curryD) ).
thf(297,plain,
! [A: produc931990033lle_tv > $o,B: nat > nat,C: paraco1605129243lle_tv] :
( ( produc752649287e_tv_o @ A @ B @ C )
=> ( A @ ( produc1680557635lle_tv @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(81,axiom,
! [A: paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
( ( produc234482697lle_tv @ A @ B @ $true )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_old_Obool_Osimps_I3_J) ).
thf(424,plain,
! [A: paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
( ( produc234482697lle_tv @ A @ B @ $true )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(83,axiom,
! [A: nat > nat,B: $o] :
( ( paraco1147068288nge_tv @ A @ ( paraco1344940915le_Det @ B ) )
= ( paraco1344940915le_Det @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_change__tv_Osimps_I1_J) ).
thf(429,plain,
! [A: nat > nat,B: $o] :
( ( paraco1147068288nge_tv @ A @ ( paraco1344940915le_Det @ B ) )
= ( paraco1344940915le_Det @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(9,axiom,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ( inj_on772319074lle_tv @ A @ top_to1057771083lle_tv )
= ( ! [B: paraco1605129243lle_tv,C: paraco1605129243lle_tv] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_inj__def) ).
thf(137,plain,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ( inj_on772319074lle_tv @ A @ top_to1057771083lle_tv )
= ( ! [B: paraco1605129243lle_tv,C: paraco1605129243lle_tv] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(97,axiom,
! [A: nat > nat,B: paraco1605129243lle_tv,C: paraco1605129243lle_tv] :
( ( ( paraco1147068288nge_tv @ A @ B )
= C )
=> ( ( accp_P2085826120lle_tv @ paraco1632582009tv_rel @ ( produc1680557635lle_tv @ A @ B ) )
=> ( ! [D: $o] :
( ( B
= ( paraco1344940915le_Det @ D ) )
=> ( ( C
= ( paraco1344940915le_Det @ D ) )
=> ~ ( accp_P2085826120lle_tv @ paraco1632582009tv_rel @ ( produc1680557635lle_tv @ A @ ( paraco1344940915le_Det @ D ) ) ) ) )
=> ~ ! [D: nat] :
( ( B
= ( paraco793048302_Indet @ D ) )
=> ( ( C
= ( paraco793048302_Indet @ ( A @ D ) ) )
=> ~ ( accp_P2085826120lle_tv @ paraco1632582009tv_rel @ ( produc1680557635lle_tv @ A @ ( paraco793048302_Indet @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_change__tv_Opelims) ).
thf(484,plain,
! [A: nat > nat,B: paraco1605129243lle_tv,C: paraco1605129243lle_tv] :
( ( ( paraco1147068288nge_tv @ A @ B )
= C )
=> ( ( accp_P2085826120lle_tv @ paraco1632582009tv_rel @ ( produc1680557635lle_tv @ A @ B ) )
=> ( ! [D: $o] :
( ( B
= ( paraco1344940915le_Det @ D ) )
=> ( ( C
= ( paraco1344940915le_Det @ D ) )
=> ~ ( accp_P2085826120lle_tv @ paraco1632582009tv_rel @ ( produc1680557635lle_tv @ A @ ( paraco1344940915le_Det @ D ) ) ) ) )
=> ~ ! [D: nat] :
( ( B
= ( paraco793048302_Indet @ D ) )
=> ( ( C
= ( paraco793048302_Indet @ ( A @ D ) ) )
=> ~ ( accp_P2085826120lle_tv @ paraco1632582009tv_rel @ ( produc1680557635lle_tv @ A @ ( paraco793048302_Indet @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(25,axiom,
! [A: paraco1604210848lle_fm] :
( paraco367965286_Truth
!= ( paraco445776468le_Neg @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_fm_Odistinct_I11_J) ).
thf(197,plain,
! [A: paraco1604210848lle_fm] :
( paraco367965286_Truth
!= ( paraco445776468le_Neg @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(39,axiom,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: nat > nat,C: paraco1605129243lle_tv] :
( ( produc109093078at_nat @ A @ ( produc1680557635lle_tv @ B @ C ) )
= ( produc1680557635lle_tv @ B @ ( A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_apsnd__conv) ).
thf(285,plain,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: nat > nat,C: paraco1605129243lle_tv] :
( ( produc109093078at_nat @ A @ ( produc1680557635lle_tv @ B @ C ) )
= ( produc1680557635lle_tv @ B @ ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(99,axiom,
inj_on_nat_nat @ f @ top_top_set_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_assms) ).
thf(515,plain,
inj_on_nat_nat @ f @ top_top_set_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(91,axiom,
! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] :
( ( paraco1325918602e_eval @ A @ ( paraco445776468le_Neg @ B ) )
= ( paraco2051596139lle_tv @ ( produc234482697lle_tv @ ( paraco1344940915le_Det @ $false ) @ ( paraco1344940915le_Det @ $true ) ) @ paraco793048302_Indet @ ( paraco1325918602e_eval @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_eval_Osimps_I3_J) ).
thf(457,plain,
! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] :
( ( paraco1325918602e_eval @ A @ ( paraco445776468le_Neg @ B ) )
= ( paraco2051596139lle_tv @ ( produc234482697lle_tv @ ( paraco1344940915le_Det @ $false ) @ ( paraco1344940915le_Det @ $true ) ) @ paraco793048302_Indet @ ( paraco1325918602e_eval @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(19,axiom,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ! [B: paraco1605129243lle_tv,C: paraco1605129243lle_tv] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) )
=> ( inj_on772319074lle_tv @ A @ top_to1057771083lle_tv ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_injI) ).
thf(173,plain,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ! [B: paraco1605129243lle_tv,C: paraco1605129243lle_tv] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) )
=> ( inj_on772319074lle_tv @ A @ top_to1057771083lle_tv ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(7,axiom,
! [A: nat > nat,B: nat > nat] :
( ! [C: nat] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image_nat_nat @ A @ top_top_set_nat )
= top_top_set_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_surjI) ).
thf(129,plain,
! [A: nat > nat,B: nat > nat] :
( ! [C: nat] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image_nat_nat @ A @ top_top_set_nat )
= top_top_set_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(110,axiom,
! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( ( ( ( paraco1325918602e_eval @ A @ B )
= ( paraco1325918602e_eval @ A @ C ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco1745535428le_Eql @ B @ C ) )
= ( paraco1344940915le_Det @ $true ) ) )
& ( ( ( paraco1325918602e_eval @ A @ B )
!= ( paraco1325918602e_eval @ A @ C ) )
=> ( ( ( ( paraco1325918602e_eval @ A @ B )
= ( paraco1344940915le_Det @ $true ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco1745535428le_Eql @ B @ C ) )
= ( paraco1325918602e_eval @ A @ C ) ) )
& ( ( ( paraco1325918602e_eval @ A @ B )
!= ( paraco1344940915le_Det @ $true ) )
=> ( ( ( ( paraco1325918602e_eval @ A @ C )
= ( paraco1344940915le_Det @ $true ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco1745535428le_Eql @ B @ C ) )
= ( paraco1325918602e_eval @ A @ B ) ) )
& ( ( ( paraco1325918602e_eval @ A @ C )
!= ( paraco1344940915le_Det @ $true ) )
=> ( ( ( ( paraco1325918602e_eval @ A @ B )
= ( paraco1344940915le_Det @ $false ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco1745535428le_Eql @ B @ C ) )
= ( paraco1325918602e_eval @ A @ ( paraco445776468le_Neg @ C ) ) ) )
& ( ( ( paraco1325918602e_eval @ A @ B )
!= ( paraco1344940915le_Det @ $false ) )
=> ( ( ( ( paraco1325918602e_eval @ A @ C )
= ( paraco1344940915le_Det @ $false ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco1745535428le_Eql @ B @ C ) )
= ( paraco1325918602e_eval @ A @ ( paraco445776468le_Neg @ B ) ) ) )
& ( ( ( paraco1325918602e_eval @ A @ C )
!= ( paraco1344940915le_Det @ $false ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco1745535428le_Eql @ B @ C ) )
= ( paraco1344940915le_Det @ $false ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_eval__equality) ).
thf(569,plain,
! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( ( ( ( paraco1325918602e_eval @ A @ B )
= ( paraco1325918602e_eval @ A @ C ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco1745535428le_Eql @ B @ C ) )
= ( paraco1344940915le_Det @ $true ) ) )
& ( ( ( paraco1325918602e_eval @ A @ B )
!= ( paraco1325918602e_eval @ A @ C ) )
=> ( ( ( ( paraco1325918602e_eval @ A @ B )
= ( paraco1344940915le_Det @ $true ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco1745535428le_Eql @ B @ C ) )
= ( paraco1325918602e_eval @ A @ C ) ) )
& ( ( ( paraco1325918602e_eval @ A @ B )
!= ( paraco1344940915le_Det @ $true ) )
=> ( ( ( ( paraco1325918602e_eval @ A @ C )
= ( paraco1344940915le_Det @ $true ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco1745535428le_Eql @ B @ C ) )
= ( paraco1325918602e_eval @ A @ B ) ) )
& ( ( ( paraco1325918602e_eval @ A @ C )
!= ( paraco1344940915le_Det @ $true ) )
=> ( ( ( ( paraco1325918602e_eval @ A @ B )
= ( paraco1344940915le_Det @ $false ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco1745535428le_Eql @ B @ C ) )
= ( paraco1325918602e_eval @ A @ ( paraco445776468le_Neg @ C ) ) ) )
& ( ( ( paraco1325918602e_eval @ A @ B )
!= ( paraco1344940915le_Det @ $false ) )
=> ( ( ( ( paraco1325918602e_eval @ A @ C )
= ( paraco1344940915le_Det @ $false ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco1745535428le_Eql @ B @ C ) )
= ( paraco1325918602e_eval @ A @ ( paraco445776468le_Neg @ B ) ) ) )
& ( ( ( paraco1325918602e_eval @ A @ C )
!= ( paraco1344940915le_Det @ $false ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco1745535428le_Eql @ B @ C ) )
= ( paraco1344940915le_Det @ $false ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(41,axiom,
! [A: paraco1605129243lle_tv > $o,B: paraco1605129243lle_tv,C: paraco1605129243lle_tv,D: $o] :
( ( A @ ( produc234482697lle_tv @ B @ C @ D ) )
= ( ( D
=> ( A @ B ) )
& ( ~ D
=> ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_bool_Osplit__sel) ).
thf(291,plain,
! [A: paraco1605129243lle_tv > $o,B: paraco1605129243lle_tv,C: paraco1605129243lle_tv,D: $o] :
( ( A @ ( produc234482697lle_tv @ B @ C @ D ) )
= ( ( D
=> ( A @ B ) )
& ( ~ D
=> ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(104,axiom,
! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( ( ( ( paraco1325918602e_eval @ A @ B )
= ( paraco1325918602e_eval @ A @ C ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco1389086619le_Eql @ B @ C ) )
= ( paraco1344940915le_Det @ $true ) ) )
& ( ( ( paraco1325918602e_eval @ A @ B )
!= ( paraco1325918602e_eval @ A @ C ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco1389086619le_Eql @ B @ C ) )
= ( paraco1344940915le_Det @ $false ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_eval_Osimps_I5_J) ).
thf(545,plain,
! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( ( ( ( paraco1325918602e_eval @ A @ B )
= ( paraco1325918602e_eval @ A @ C ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco1389086619le_Eql @ B @ C ) )
= ( paraco1344940915le_Det @ $true ) ) )
& ( ( ( paraco1325918602e_eval @ A @ B )
!= ( paraco1325918602e_eval @ A @ C ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco1389086619le_Eql @ B @ C ) )
= ( paraco1344940915le_Det @ $false ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(34,axiom,
! [A: nat > nat] :
( ( inj_on_nat_nat @ A @ top_top_set_nat )
=> ( inj_on772319074lle_tv @ ( paraco1147068288nge_tv @ A ) @ top_to1057771083lle_tv ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_change__tv__injection) ).
thf(271,plain,
! [A: nat > nat] :
( ( inj_on_nat_nat @ A @ top_top_set_nat )
=> ( inj_on772319074lle_tv @ ( paraco1147068288nge_tv @ A ) @ top_to1057771083lle_tv ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(62,axiom,
! [A: nat > nat,B: paraco1605129243lle_tv,C: nat > nat,D: paraco1605129243lle_tv] :
( ( ( produc1680557635lle_tv @ A @ B )
= ( produc1680557635lle_tv @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_old_Oprod_Oinject) ).
thf(362,plain,
! [A: nat > nat,B: paraco1605129243lle_tv,C: nat > nat,D: paraco1605129243lle_tv] :
( ( ( produc1680557635lle_tv @ A @ B )
= ( produc1680557635lle_tv @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(89,axiom,
! [A: ( nat > nat ) > paraco1605129243lle_tv > $o,B: nat > nat,C: paraco1605129243lle_tv] :
( ! [D: nat > nat,E: $o] : ( A @ D @ ( paraco1344940915le_Det @ E ) )
=> ( ! [D: nat > nat,E: nat] : ( A @ D @ ( paraco793048302_Indet @ E ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_change__tv_Oinduct) ).
thf(451,plain,
! [A: ( nat > nat ) > paraco1605129243lle_tv > $o,B: nat > nat,C: paraco1605129243lle_tv] :
( ! [D: nat > nat,E: $o] : ( A @ D @ ( paraco1344940915le_Det @ E ) )
=> ( ! [D: nat > nat,E: nat] : ( A @ D @ ( paraco793048302_Indet @ E ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(109,axiom,
( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p1 )
= ( paraco1147068288nge_tv @ f @ ( paraco1325918602e_eval @ i @ p1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_ih1) ).
thf(567,plain,
( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p1 )
= ( paraco1147068288nge_tv @ f @ ( paraco1325918602e_eval @ i @ p1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(105,axiom,
! [A: $o > paraco1605129243lle_tv,B: nat > paraco1605129243lle_tv,C: $o] :
( ( paraco2051596139lle_tv @ A @ B @ ( paraco1344940915le_Det @ C ) )
= ( A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_tv_Osimps_I5_J) ).
thf(552,plain,
! [A: $o > paraco1605129243lle_tv,B: nat > paraco1605129243lle_tv,C: $o] :
( ( paraco2051596139lle_tv @ A @ B @ ( paraco1344940915le_Det @ C ) )
= ( A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(10,axiom,
! [A: produc696645085lle_fm > $o,B: produc696645085lle_fm] :
( ! [C: list_char > paraco1605129243lle_tv,D: paraco1604210848lle_fm] : ( A @ ( produc1710735575lle_fm @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_old_Oprod_Oinducts) ).
thf(140,plain,
! [A: produc696645085lle_fm > $o,B: produc696645085lle_fm] :
( ! [C: list_char > paraco1605129243lle_tv,D: paraco1604210848lle_fm] : ( A @ ( produc1710735575lle_fm @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(53,axiom,
! [A: nat > nat,B: nat] :
( ( inj_on_nat_nat @ A @ top_top_set_nat )
=> ( ( the_inv_into_nat_nat @ top_top_set_nat @ A @ ( A @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_the__inv__f__f) ).
thf(330,plain,
! [A: nat > nat,B: nat] :
( ( inj_on_nat_nat @ A @ top_top_set_nat )
=> ( ( the_inv_into_nat_nat @ top_top_set_nat @ A @ ( A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(44,axiom,
! [A: ( nat > nat ) > nat > nat,B: paraco1605129243lle_tv > paraco1605129243lle_tv,C: nat > nat,D: paraco1605129243lle_tv] :
( ( produc532909085lle_tv @ A @ B @ ( produc1680557635lle_tv @ C @ D ) )
= ( produc1680557635lle_tv @ ( A @ C ) @ ( B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_map__prod__simp) ).
thf(299,plain,
! [A: ( nat > nat ) > nat > nat,B: paraco1605129243lle_tv > paraco1605129243lle_tv,C: nat > nat,D: paraco1605129243lle_tv] :
( ( produc532909085lle_tv @ A @ B @ ( produc1680557635lle_tv @ C @ D ) )
= ( produc1680557635lle_tv @ ( A @ C ) @ ( B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(17,axiom,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: paraco1605129243lle_tv,C: paraco1605129243lle_tv] :
( ( inj_on772319074lle_tv @ A @ top_to1057771083lle_tv )
=> ( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_inj__eq) ).
thf(167,plain,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: paraco1605129243lle_tv,C: paraco1605129243lle_tv] :
( ( inj_on772319074lle_tv @ A @ top_to1057771083lle_tv )
=> ( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(72,axiom,
! [A: list_char,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( ( paraco1480028776le_Pro @ A )
!= ( paraco69239110le_Con @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_fm_Odistinct_I5_J) ).
thf(394,plain,
! [A: list_char,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( ( paraco1480028776le_Pro @ A )
!= ( paraco69239110le_Con @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(46,axiom,
( produc178635363at_nat
= ( ^ [A: produc596913417at_nat] : ( produc1680557635lle_tv @ ( produc500618325at_nat @ A ) @ ( produc1589291287at_nat @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_prod_Oswap__def) ).
thf(306,plain,
( produc178635363at_nat
= ( ^ [A: produc596913417at_nat] : ( produc1680557635lle_tv @ ( produc500618325at_nat @ A ) @ ( produc1589291287at_nat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(93,axiom,
( ( paraco1325918602e_eval @ i @ ( paraco1745535428le_Eql @ p1 @ p2 ) )
= ( paraco1325918602e_eval @ i @ p1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_yes) ).
thf(473,plain,
( ( paraco1325918602e_eval @ i @ ( paraco1745535428le_Eql @ p1 @ p2 ) )
= ( paraco1325918602e_eval @ i @ p1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(100,axiom,
! [A: $o,B: $o] :
( ( ( paraco1344940915le_Det @ A )
= ( paraco1344940915le_Det @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_tv_Oinject_I1_J) ).
thf(516,plain,
! [A: $o,B: $o] :
( ( ( paraco1344940915le_Det @ A )
= ( paraco1344940915le_Det @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(5,axiom,
! [A: nat > nat,B: set_nat] :
( ( inj_on_nat_nat @ A @ B )
=> ( ( image_nat_nat @ ( the_inv_into_nat_nat @ B @ A ) @ ( image_nat_nat @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_the__inv__into__onto) ).
thf(123,plain,
! [A: nat > nat,B: set_nat] :
( ( inj_on_nat_nat @ A @ B )
=> ( ( image_nat_nat @ ( the_inv_into_nat_nat @ B @ A ) @ ( image_nat_nat @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(24,axiom,
! [A: $o > paraco1605129243lle_tv,B: nat > paraco1605129243lle_tv,C: nat] :
( ( paraco2051596139lle_tv @ A @ B @ ( paraco793048302_Indet @ C ) )
= ( B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_tv_Osimps_I6_J) ).
thf(194,plain,
! [A: $o > paraco1605129243lle_tv,B: nat > paraco1605129243lle_tv,C: nat] :
( ( paraco2051596139lle_tv @ A @ B @ ( paraco793048302_Indet @ C ) )
= ( B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(38,axiom,
! [A: nat > nat,B: set_Pr1986765409at_nat] :
( ( inj_on_nat_nat @ A @ top_top_set_nat )
=> ( ( total_on_nat @ top_top_set_nat @ B )
=> ( total_on_nat @ top_top_set_nat @ ( inv_image_nat_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_total__inv__image) ).
thf(282,plain,
! [A: nat > nat,B: set_Pr1986765409at_nat] :
( ( inj_on_nat_nat @ A @ top_top_set_nat )
=> ( ( total_on_nat @ top_top_set_nat @ B )
=> ( total_on_nat @ top_top_set_nat @ ( inv_image_nat_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(13,axiom,
! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,C: list_char > paraco1605129243lle_tv,D: paraco1604210848lle_fm] :
( ( ( produc1710735575lle_fm @ A @ B )
= ( produc1710735575lle_fm @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_prod_Oinject) ).
thf(150,plain,
! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,C: list_char > paraco1605129243lle_tv,D: paraco1604210848lle_fm] :
( ( ( produc1710735575lle_fm @ A @ B )
= ( produc1710735575lle_fm @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(78,axiom,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( ( paraco445776468le_Neg @ A )
!= ( paraco69239110le_Con @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_fm_Odistinct_I19_J) ).
thf(414,plain,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( ( paraco445776468le_Neg @ A )
!= ( paraco69239110le_Con @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(21,axiom,
! [A: produc931990033lle_tv] :
~ ! [B: nat > nat,C: paraco1605129243lle_tv] :
( A
!= ( produc1680557635lle_tv @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_old_Oprod_Oexhaust) ).
thf(182,plain,
! [A: produc931990033lle_tv] :
~ ! [B: nat > nat,C: paraco1605129243lle_tv] :
( A
!= ( produc1680557635lle_tv @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(65,axiom,
! [A: nat > nat] :
( ( inj_on_nat_nat @ A @ top_top_set_nat )
= ( ! [B: nat,C: nat] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_inj__def) ).
thf(370,plain,
! [A: nat > nat] :
( ( inj_on_nat_nat @ A @ top_top_set_nat )
= ( ! [B: nat,C: nat] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(55,axiom,
! [A: set_nat,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( ( paraco55203475lid_in @ A @ ( paraco69239110le_Con @ B @ C ) )
= ( ( paraco55203475lid_in @ A @ B )
& ( paraco55203475lid_in @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_conjunction__in) ).
thf(338,plain,
! [A: set_nat,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( ( paraco55203475lid_in @ A @ ( paraco69239110le_Con @ B @ C ) )
= ( ( paraco55203475lid_in @ A @ B )
& ( paraco55203475lid_in @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(113,axiom,
! [A: list_char > paraco1605129243lle_tv] :
( ( paraco1325918602e_eval @ A @ paraco367965286_Truth )
= ( paraco1344940915le_Det @ $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_eval_Osimps_I2_J) ).
thf(600,plain,
! [A: list_char > paraco1605129243lle_tv] :
( ( paraco1325918602e_eval @ A @ paraco367965286_Truth )
= ( paraco1344940915le_Det @ $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(70,axiom,
! [A: paraco1604210848lle_fm] :
( ( A != paraco367965286_Truth )
=> ( ! [B: list_char] :
( A
!= ( paraco1480028776le_Pro @ B ) )
=> ( ! [B: paraco1604210848lle_fm] :
( A
!= ( paraco445776468le_Neg @ B ) )
=> ( ! [B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( A
!= ( paraco69239110le_Con @ B @ C ) )
=> ( ! [B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( A
!= ( paraco1389086619le_Eql @ B @ C ) )
=> ~ ! [B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( A
!= ( paraco1745535428le_Eql @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_props_Ocases) ).
thf(386,plain,
! [A: paraco1604210848lle_fm] :
( ( A != paraco367965286_Truth )
=> ( ! [B: list_char] :
( A
!= ( paraco1480028776le_Pro @ B ) )
=> ( ! [B: paraco1604210848lle_fm] :
( A
!= ( paraco445776468le_Neg @ B ) )
=> ( ! [B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( A
!= ( paraco69239110le_Con @ B @ C ) )
=> ( ! [B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( A
!= ( paraco1389086619le_Eql @ B @ C ) )
=> ~ ! [B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( A
!= ( paraco1745535428le_Eql @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(11,axiom,
! [A: nat > nat,B: nat] :
( ( ( image_nat_nat @ A @ top_top_set_nat )
= top_top_set_nat )
=> ~ ! [C: nat] :
( B
!= ( A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_surjE) ).
thf(143,plain,
! [A: nat > nat,B: nat] :
( ( ( image_nat_nat @ A @ top_top_set_nat )
= top_top_set_nat )
=> ~ ! [C: nat] :
( B
!= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(64,axiom,
! [A: produc931990033lle_tv > $o,B: nat > nat,C: paraco1605129243lle_tv] :
( ( produc752649287e_tv_o @ A @ B @ C )
=> ( A @ ( produc1680557635lle_tv @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_curryE) ).
thf(368,plain,
! [A: produc931990033lle_tv > $o,B: nat > nat,C: paraco1605129243lle_tv] :
( ( produc752649287e_tv_o @ A @ B @ C )
=> ( A @ ( produc1680557635lle_tv @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(96,axiom,
( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p2 )
= ( paraco1147068288nge_tv @ f @ ( paraco1325918602e_eval @ i @ p2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_ih2) ).
thf(482,plain,
( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p2 )
= ( paraco1147068288nge_tv @ f @ ( paraco1325918602e_eval @ i @ p2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(27,axiom,
! [A: nat > nat,B: nat] :
( ( paraco1147068288nge_tv @ A @ ( paraco793048302_Indet @ B ) )
= ( paraco793048302_Indet @ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_change__tv_Osimps_I2_J) ).
thf(203,plain,
! [A: nat > nat,B: nat] :
( ( paraco1147068288nge_tv @ A @ ( paraco793048302_Indet @ B ) )
= ( paraco793048302_Indet @ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(111,axiom,
! [A: $o,B: nat] :
( ( paraco1344940915le_Det @ A )
!= ( paraco793048302_Indet @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_tv_Odistinct_I1_J) ).
thf(588,plain,
! [A: $o,B: nat] :
( ( paraco1344940915le_Det @ A )
!= ( paraco793048302_Indet @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(50,axiom,
! [A: produc931990033lle_tv > $o,B: produc931990033lle_tv] :
( ! [C: nat > nat,D: paraco1605129243lle_tv] : ( A @ ( produc1680557635lle_tv @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_prod__cases) ).
thf(319,plain,
! [A: produc931990033lle_tv > $o,B: produc931990033lle_tv] :
( ! [C: nat > nat,D: paraco1605129243lle_tv] : ( A @ ( produc1680557635lle_tv @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(59,axiom,
! [A: ( nat > nat ) > nat > nat,B: nat > nat,C: paraco1605129243lle_tv] :
( ( produc939316703lle_tv @ A @ ( produc1680557635lle_tv @ B @ C ) )
= ( produc1680557635lle_tv @ ( A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_apfst__conv) ).
thf(351,plain,
! [A: ( nat > nat ) > nat > nat,B: nat > nat,C: paraco1605129243lle_tv] :
( ( produc939316703lle_tv @ A @ ( produc1680557635lle_tv @ B @ C ) )
= ( produc1680557635lle_tv @ ( A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(71,axiom,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm] :
( paraco367965286_Truth
!= ( paraco69239110le_Con @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_fm_Odistinct_I13_J) ).
thf(390,plain,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm] :
( paraco367965286_Truth
!= ( paraco69239110le_Con @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(22,axiom,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm] :
( paraco367965286_Truth
!= ( paraco1389086619le_Eql @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_fm_Odistinct_I15_J) ).
thf(186,plain,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm] :
( paraco367965286_Truth
!= ( paraco1389086619le_Eql @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(1,conjecture,
( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p2 )
= ( paraco1344940915le_Det @ $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p2 )
!= ( paraco1344940915le_Det @ $true ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(114,plain,
( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p2 )
!= ( paraco1344940915le_Det @ $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(74,axiom,
! [A: nat > nat,B: nat,C: nat] :
( ( inj_on_nat_nat @ A @ top_top_set_nat )
=> ( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_inj__eq) ).
thf(401,plain,
! [A: nat > nat,B: nat,C: nat] :
( ( inj_on_nat_nat @ A @ top_top_set_nat )
=> ( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(18,axiom,
! [A: nat > nat,B: set_nat] :
( ( inj_on_nat_nat @ A @ B )
=> ( inj_on_nat_nat @ ( the_inv_into_nat_nat @ B @ A ) @ ( image_nat_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_inj__on__the__inv__into) ).
thf(171,plain,
! [A: nat > nat,B: set_nat] :
( ( inj_on_nat_nat @ A @ B )
=> ( inj_on_nat_nat @ ( the_inv_into_nat_nat @ B @ A ) @ ( image_nat_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(79,axiom,
! [A: nat,B: nat] :
( ( ( paraco793048302_Indet @ A )
= ( paraco793048302_Indet @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_tv_Oinject_I2_J) ).
thf(418,plain,
! [A: nat,B: nat] :
( ( ( paraco793048302_Indet @ A )
= ( paraco793048302_Indet @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(85,axiom,
! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] :
( ( ( ( paraco1325918602e_eval @ A @ B )
= ( paraco1344940915le_Det @ $false ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco445776468le_Neg @ B ) )
= ( paraco1344940915le_Det @ $true ) ) )
& ( ( ( paraco1325918602e_eval @ A @ B )
!= ( paraco1344940915le_Det @ $false ) )
=> ( ( ( ( paraco1325918602e_eval @ A @ B )
= ( paraco1344940915le_Det @ $true ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco445776468le_Neg @ B ) )
= ( paraco1344940915le_Det @ $false ) ) )
& ( ( ( paraco1325918602e_eval @ A @ B )
!= ( paraco1344940915le_Det @ $true ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco445776468le_Neg @ B ) )
= ( paraco1325918602e_eval @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_eval__negation) ).
thf(433,plain,
! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] :
( ( ( ( paraco1325918602e_eval @ A @ B )
= ( paraco1344940915le_Det @ $false ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco445776468le_Neg @ B ) )
= ( paraco1344940915le_Det @ $true ) ) )
& ( ( ( paraco1325918602e_eval @ A @ B )
!= ( paraco1344940915le_Det @ $false ) )
=> ( ( ( ( paraco1325918602e_eval @ A @ B )
= ( paraco1344940915le_Det @ $true ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco445776468le_Neg @ B ) )
= ( paraco1344940915le_Det @ $false ) ) )
& ( ( ( paraco1325918602e_eval @ A @ B )
!= ( paraco1344940915le_Det @ $true ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco445776468le_Neg @ B ) )
= ( paraco1325918602e_eval @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(95,axiom,
! [A: paraco1605129243lle_tv] :
( ! [B: $o] :
( A
!= ( paraco1344940915le_Det @ B ) )
=> ~ ! [B: nat] :
( A
!= ( paraco793048302_Indet @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_tv_Oexhaust) ).
thf(478,plain,
! [A: paraco1605129243lle_tv] :
( ! [B: $o] :
( A
!= ( paraco1344940915le_Det @ B ) )
=> ~ ! [B: nat] :
( A
!= ( paraco793048302_Indet @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(69,axiom,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( ( ( paraco1389086619le_Eql @ A @ B )
= ( paraco1389086619le_Eql @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_fm_Oinject_I4_J) ).
thf(383,plain,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( ( ( paraco1389086619le_Eql @ A @ B )
= ( paraco1389086619le_Eql @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(4,axiom,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: paraco1605129243lle_tv,C: paraco1605129243lle_tv] :
( ( inj_on772319074lle_tv @ A @ top_to1057771083lle_tv )
=> ( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_injD) ).
thf(119,plain,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: paraco1605129243lle_tv,C: paraco1605129243lle_tv] :
( ( inj_on772319074lle_tv @ A @ top_to1057771083lle_tv )
=> ( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(67,axiom,
( produc234482697lle_tv
= ( ^ [A: paraco1605129243lle_tv,B: paraco1605129243lle_tv,C: $o] : ( if_Par1134130401lle_tv @ C @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_bool_Ocase__eq__if) ).
thf(378,plain,
( produc234482697lle_tv
= ( ^ [A: paraco1605129243lle_tv,B: paraco1605129243lle_tv,C: $o] : ( if_Par1134130401lle_tv @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(84,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_If_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_T) ).
thf(432,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(75,axiom,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( ( ( paraco69239110le_Con @ A @ B )
= ( paraco69239110le_Con @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_fm_Oinject_I3_J) ).
thf(405,plain,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( ( ( paraco69239110le_Con @ A @ B )
= ( paraco69239110le_Con @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(23,axiom,
! [A: list_char,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( ( paraco1480028776le_Pro @ A )
!= ( paraco1389086619le_Eql @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_fm_Odistinct_I7_J) ).
thf(190,plain,
! [A: list_char,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( ( paraco1480028776le_Pro @ A )
!= ( paraco1389086619le_Eql @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(35,axiom,
! [A: produc931990033lle_tv] :
? [B: nat > nat,C: paraco1605129243lle_tv] :
( A
= ( produc1680557635lle_tv @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_surj__pair) ).
thf(273,plain,
! [A: produc931990033lle_tv] :
? [B: nat > nat,C: paraco1605129243lle_tv] :
( A
= ( produc1680557635lle_tv @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(66,axiom,
! [A: nat > nat] :
( ! [B: nat,C: nat] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) )
=> ( inj_on_nat_nat @ A @ top_top_set_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_injI) ).
thf(373,plain,
! [A: nat > nat] :
( ! [B: nat,C: nat] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) )
=> ( inj_on_nat_nat @ A @ top_top_set_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(52,axiom,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( ( paraco445776468le_Neg @ A )
!= ( paraco1745535428le_Eql @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_fm_Odistinct_I23_J) ).
thf(326,plain,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( ( paraco445776468le_Neg @ A )
!= ( paraco1745535428le_Eql @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(56,axiom,
! [A: paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
( ( if_Par1134130401lle_tv @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_T) ).
thf(341,plain,
! [A: paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
( ( if_Par1134130401lle_tv @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(33,axiom,
! [A: nat > nat,B: paraco1605129243lle_tv,C: nat > nat,D: paraco1605129243lle_tv] :
( ( ( produc1680557635lle_tv @ A @ B )
= ( produc1680557635lle_tv @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_prod_Oinject) ).
thf(268,plain,
! [A: nat > nat,B: paraco1605129243lle_tv,C: nat > nat,D: paraco1605129243lle_tv] :
( ( ( produc1680557635lle_tv @ A @ B )
= ( produc1680557635lle_tv @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(61,axiom,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( ( paraco445776468le_Neg @ A )
!= ( paraco1389086619le_Eql @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_fm_Odistinct_I21_J) ).
thf(358,plain,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( ( paraco445776468le_Neg @ A )
!= ( paraco1389086619le_Eql @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(103,axiom,
! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( ( ( ( paraco1325918602e_eval @ A @ B )
= ( paraco1325918602e_eval @ A @ C ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco69239110le_Con @ B @ C ) )
= ( paraco1325918602e_eval @ A @ B ) ) )
& ( ( ( paraco1325918602e_eval @ A @ B )
!= ( paraco1325918602e_eval @ A @ C ) )
=> ( ( ( ( paraco1325918602e_eval @ A @ B )
= ( paraco1344940915le_Det @ $true ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco69239110le_Con @ B @ C ) )
= ( paraco1325918602e_eval @ A @ C ) ) )
& ( ( ( paraco1325918602e_eval @ A @ B )
!= ( paraco1344940915le_Det @ $true ) )
=> ( ( ( ( paraco1325918602e_eval @ A @ C )
= ( paraco1344940915le_Det @ $true ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco69239110le_Con @ B @ C ) )
= ( paraco1325918602e_eval @ A @ B ) ) )
& ( ( ( paraco1325918602e_eval @ A @ C )
!= ( paraco1344940915le_Det @ $true ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco69239110le_Con @ B @ C ) )
= ( paraco1344940915le_Det @ $false ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_eval_Osimps_I4_J) ).
thf(532,plain,
! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( ( ( ( paraco1325918602e_eval @ A @ B )
= ( paraco1325918602e_eval @ A @ C ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco69239110le_Con @ B @ C ) )
= ( paraco1325918602e_eval @ A @ B ) ) )
& ( ( ( paraco1325918602e_eval @ A @ B )
!= ( paraco1325918602e_eval @ A @ C ) )
=> ( ( ( ( paraco1325918602e_eval @ A @ B )
= ( paraco1344940915le_Det @ $true ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco69239110le_Con @ B @ C ) )
= ( paraco1325918602e_eval @ A @ C ) ) )
& ( ( ( paraco1325918602e_eval @ A @ B )
!= ( paraco1344940915le_Det @ $true ) )
=> ( ( ( ( paraco1325918602e_eval @ A @ C )
= ( paraco1344940915le_Det @ $true ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco69239110le_Con @ B @ C ) )
= ( paraco1325918602e_eval @ A @ B ) ) )
& ( ( ( paraco1325918602e_eval @ A @ C )
!= ( paraco1344940915le_Det @ $true ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco69239110le_Con @ B @ C ) )
= ( paraco1344940915le_Det @ $false ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(42,axiom,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( ( ( paraco1745535428le_Eql @ A @ B )
= ( paraco1745535428le_Eql @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_fm_Oinject_I5_J) ).
thf(294,plain,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( ( ( paraco1745535428le_Eql @ A @ B )
= ( paraco1745535428le_Eql @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(6,axiom,
! [A: produc696645085lle_fm] :
? [B: list_char > paraco1605129243lle_tv,C: paraco1604210848lle_fm] :
( A
= ( produc1710735575lle_fm @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_surj__pair) ).
thf(126,plain,
! [A: produc696645085lle_fm] :
? [B: list_char > paraco1605129243lle_tv,C: paraco1604210848lle_fm] :
( A
= ( produc1710735575lle_fm @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(82,axiom,
( ( paraco1325918602e_eval @ i @ p2 )
= ( paraco1344940915le_Det @ $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_a) ).
thf(427,plain,
( ( paraco1325918602e_eval @ i @ p2 )
= ( paraco1344940915le_Det @ $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(20,axiom,
! [A: nat > nat,B: set_nat,C: set_nat] :
( ( inj_on_nat_nat @ A @ top_top_set_nat )
=> ( ( ( image_nat_nat @ A @ B )
= ( image_nat_nat @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_inj__image__eq__iff) ).
thf(178,plain,
! [A: nat > nat,B: set_nat,C: set_nat] :
( ( inj_on_nat_nat @ A @ top_top_set_nat )
=> ( ( ( image_nat_nat @ A @ B )
= ( image_nat_nat @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(51,axiom,
! [A: paraco1604210848lle_fm > $o,B: paraco1604210848lle_fm] :
( ! [C: list_char] : ( A @ ( paraco1480028776le_Pro @ C ) )
=> ( ( A @ paraco367965286_Truth )
=> ( ! [C: paraco1604210848lle_fm] :
( ( A @ C )
=> ( A @ ( paraco445776468le_Neg @ C ) ) )
=> ( ! [C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( ( A @ C )
=> ( ( A @ D )
=> ( A @ ( paraco69239110le_Con @ C @ D ) ) ) )
=> ( ! [C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( ( A @ C )
=> ( ( A @ D )
=> ( A @ ( paraco1389086619le_Eql @ C @ D ) ) ) )
=> ( ! [C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( ( A @ C )
=> ( ( A @ D )
=> ( A @ ( paraco1745535428le_Eql @ C @ D ) ) ) )
=> ( A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_fm_Oinduct) ).
thf(322,plain,
! [A: paraco1604210848lle_fm > $o,B: paraco1604210848lle_fm] :
( ! [C: list_char] : ( A @ ( paraco1480028776le_Pro @ C ) )
=> ( ( A @ paraco367965286_Truth )
=> ( ! [C: paraco1604210848lle_fm] :
( ( A @ C )
=> ( A @ ( paraco445776468le_Neg @ C ) ) )
=> ( ! [C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( ( A @ C )
=> ( ( A @ D )
=> ( A @ ( paraco69239110le_Con @ C @ D ) ) ) )
=> ( ! [C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( ( A @ C )
=> ( ( A @ D )
=> ( A @ ( paraco1389086619le_Eql @ C @ D ) ) ) )
=> ( ! [C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( ( A @ C )
=> ( ( A @ D )
=> ( A @ ( paraco1745535428le_Eql @ C @ D ) ) ) )
=> ( A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(60,axiom,
! [A: nat > nat,B: nat,C: nat] :
( ( inj_on_nat_nat @ A @ top_top_set_nat )
=> ( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_injD) ).
thf(354,plain,
! [A: nat > nat,B: nat,C: nat] :
( ( inj_on_nat_nat @ A @ top_top_set_nat )
=> ( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(90,axiom,
! [A: list_char > paraco1605129243lle_tv,B: list_char] :
( ( paraco1325918602e_eval @ A @ ( paraco1480028776le_Pro @ B ) )
= ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_eval_Osimps_I1_J) ).
thf(454,plain,
! [A: list_char > paraco1605129243lle_tv,B: list_char] :
( ( paraco1325918602e_eval @ A @ ( paraco1480028776le_Pro @ B ) )
= ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(606,plain,
$false,
inference(e,[status(thm)],[153,398,445,365,249,555,408,276,308,449,597,288,565,257,344,460,157,559,421,316,261,475,443,253,348,147,280,133,411,116,206,527,312,380,512,529,201,334,302,160,297,424,429,137,484,197,285,515,457,173,129,569,291,545,271,362,451,567,552,140,330,299,167,394,306,473,516,123,194,282,150,414,182,370,338,600,386,143,368,482,203,588,319,351,390,186,114,401,171,418,433,478,383,119,378,432,405,190,273,373,326,341,268,358,532,294,126,427,178,322,354,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14 % Problem : ITP135^1 : TPTP v8.2.0. Released v7.5.0.
% 0.15/0.17 % Command : run_Leo-III %s %d
% 0.15/0.38 % Computer : n013.cluster.edu
% 0.15/0.38 % Model : x86_64 x86_64
% 0.15/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.38 % Memory : 8042.1875MB
% 0.15/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.38 % CPULimit : 300
% 0.15/0.38 % WCLimit : 300
% 0.15/0.38 % DateTime : Sat May 18 16:53:24 EDT 2024
% 0.15/0.38 % CPUTime :
% 1.05/1.01 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.23/1.42 % [INFO] Parsing done (404ms).
% 2.23/1.43 % [INFO] Running in sequential loop mode.
% 3.13/1.79 % [INFO] eprover registered as external prover.
% 3.13/1.79 % [INFO] cvc4 registered as external prover.
% 3.13/1.80 % [INFO] Scanning for conjecture ...
% 3.37/1.93 % [INFO] Found a conjecture (or negated_conjecture) and 358 axioms. Running axiom selection ...
% 3.87/2.05 % [INFO] Axiom selection finished. Selected 111 axioms (removed 247 axioms).
% 4.31/2.23 % [INFO] Problem is higher-order (TPTP THF).
% 4.31/2.24 % [INFO] Type checking passed.
% 4.31/2.24 % [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 ...
% 10.13/3.79 % External prover 'e' found a proof!
% 10.13/3.79 % [INFO] Killing All external provers ...
% 10.13/3.79 % Time passed: 3251ms (effective reasoning time: 2353ms)
% 10.13/3.79 % 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)>
% 10.13/3.79 % Axioms used in derivation (111): fact_217_old_Obool_Osimps_I3_J, fact_81_inj__def, fact_188_valid__valid__in, fact_99_props_Ocases, fact_240_curryI, fact_28_fm_Odistinct_I17_J, fact_205_change__tv_Osimps_I2_J, fact_207_prod_Oinject, fact_9_yes, fact_109_fm_Odistinct_I9_J, fact_82_inj__def, fact_197_tv_Oexhaust, fact_220_old_Oprod_Oinducts, fact_187_change__tv_Oelims, fact_196_string__tv_Ocases, fact_32_conjunction, fact_19_fm_Oinject_I3_J, fact_29_fm_Odistinct_I15_J, fact_305_total__inv__image, fact_21_fm_Oinject_I4_J, fact_16_eval__negation, fact_222_old_Oprod_Oexhaust, fact_108_fm_Odistinct_I5_J, fact_314_prod_Oswap__def, fact_60_injD, fact_106_eval_Osimps_I1_J, fact_4_a_H_H, fact_13_eval__equality__simplify, fact_7_change__int__def, fact_224_Pair__inject, fact_204_tv_Osimps_I6_J, fact_180_props_Oinduct, fact_84_fm_Oexhaust, fact_1__092_060open_062change__tv_Af_A_Ieval_Ai_Ap2_J_A_061_ADet_ATrue_092_060close_062, fact_3_tv_Oinject_I1_J, fact_23_fm_Odistinct_I27_J, fact_193_tv_Oinject_I2_J, fact_225_Pair__inject, fact_206_prod_Oinject, help_If_1_1_If_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_T, fact_195_change__tv_Oinduct, fact_234_change__tv_Opelims, fact_10_valid__def, fact_194_string__tv_Oinduct, fact_74_inj__eq, help_If_2_1_If_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_T, fact_218_old_Obool_Osimps_I4_J, fact_27_fm_Odistinct_I19_J, fact_31_fm_Odistinct_I11_J, fact_112_change__tv__injection, fact_233_apsnd__conv, fact_212_surj__pair, fact_216_bool_Osplit__sel, fact_26_fm_Odistinct_I21_J, fact_5_a_H, fact_2_ih2, help_If_3_1_If_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_T, fact_265_surjD, fact_293_inj__image__eq__iff, fact_192_conjunction__in, fact_227_prod__cases, fact_249_the__inv__into__onto, fact_190_the__inv__f__f, fact_17_assms, fact_110_fm_Odistinct_I7_J, fact_67_injI, fact_107_fm_Odistinct_I3_J, fact_269_surjE, fact_213_bool_Osplit__sel__asm, fact_246_curryD, fact_198_tv_Oinduct, fact_248_curryE, fact_189_transfer, fact_209_old_Oprod_Oinject, fact_277_surj__def, fact_68_injI, fact_273_surjI, fact_30_fm_Odistinct_I13_J, fact_221_old_Oprod_Oinducts, fact_215_bool_Ocase__eq__if, fact_210_eval_Osimps_I3_J, fact_244_map__prod__simp, fact_11_eval_Osimps_I2_J, fact_18_fm_Oinject_I2_J, fact_208_old_Oprod_Oinject, fact_14_eval_Osimps_I4_J, fact_33_eval__equality, fact_15_tv_Osimps_I5_J, fact_6_ih1, fact_181_eval_Ocases, fact_214_bool_Ocase__distrib, fact_75_inj__eq, fact_22_fm_Odistinct_I29_J, fact_20_fm_Oinject_I5_J, fact_111_fm_Odistinct_I1_J, fact_34_double__negation, fact_199_tv_Odistinct_I1_J, fact_61_injD, fact_226_prod__cases, fact_231_apfst__conv, fact_223_old_Oprod_Oexhaust, fact_24_fm_Odistinct_I25_J, fact_25_fm_Odistinct_I23_J, fact_12_eval_Osimps_I5_J, fact_211_surj__pair, fact_303_inj__on__the__inv__into, fact_83_fm_Oinduct, fact_100_fm_Oinject_I1_J, fact_0_a, fact_219_change__tv_Ocases, fact_8_change__tv_Osimps_I1_J
% 10.13/3.80 % No. of inferences in proof: 226
% 10.13/3.80 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3251 ms resp. 2353 ms w/o parsing
% 10.93/3.93 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.93/3.94 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------