%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP140^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:06:55 AM UTC 2026
% Result : Theorem 17.20s 5.13s
% Output : Refutation 17.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 106
% Syntax : Number of formulae : 214 ( 161 unt; 0 typ; 0 def)
% Number of atoms : 631 ( 359 equ; 0 cnn)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 3101 ( 180 ~; 3 |; 42 &;2680 @)
% ( 0 <=>; 196 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 7 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 422 ( 422 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 32 usr; 8 con; 0-8 aty)
% Number of variables : 1019 ( 24 ^; 991 !; 4 ?;1019 :)
% Comments :
%------------------------------------------------------------------------------
thf(paraco415392788lle_tv_type,type,
paraco415392788lle_tv: $tType ).
thf(paraco414474393lle_fm_type,type,
paraco414474393lle_fm: $tType ).
thf(char_type,type,
char: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(if_decl,type,
if:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(paraco753463838ge_int_decl,type,
paraco753463838ge_int: ( nat > nat ) > ( ( list @ char ) > paraco415392788lle_tv ) > ( list @ char ) > paraco415392788lle_tv ).
thf(paraco1920534163nge_tv_decl,type,
paraco1920534163nge_tv: ( nat > nat ) > paraco415392788lle_tv > paraco415392788lle_tv ).
thf(paraco2077297190tv_rel_decl,type,
paraco2077297190tv_rel: ( product_prod @ ( nat > nat ) @ paraco415392788lle_tv ) > ( product_prod @ ( nat > nat ) @ paraco415392788lle_tv ) > $o ).
thf(paraco876059933e_eval_decl,type,
paraco876059933e_eval: ( ( list @ char ) > paraco415392788lle_tv ) > paraco414474393lle_fm > paraco415392788lle_tv ).
thf(paraco2100061555le_Con_decl,type,
paraco2100061555le_Con: paraco414474393lle_fm > paraco414474393lle_fm > paraco414474393lle_fm ).
thf(paraco2084319816le_Eql_decl,type,
paraco2084319816le_Eql: paraco414474393lle_fm > paraco414474393lle_fm > paraco414474393lle_fm ).
thf(paraco1628874225le_Eql_decl,type,
paraco1628874225le_Eql: paraco414474393lle_fm > paraco414474393lle_fm > paraco414474393lle_fm ).
thf(paraco329115265le_Neg_decl,type,
paraco329115265le_Neg: paraco414474393lle_fm > paraco414474393lle_fm ).
thf(paraco27778325le_Pro_decl,type,
paraco27778325le_Pro: ( list @ char ) > paraco414474393lle_fm ).
thf(paraco251304083_Truth_decl,type,
paraco251304083_Truth: paraco414474393lle_fm ).
thf(paraco1246693743ase_fm_decl,type,
paraco1246693743ase_fm:
!>[TA: $tType] : ( ( ( list @ char ) > TA ) > TA > ( paraco414474393lle_fm > TA ) > ( paraco414474393lle_fm > paraco414474393lle_fm > TA ) > ( paraco414474393lle_fm > paraco414474393lle_fm > TA ) > ( paraco414474393lle_fm > paraco414474393lle_fm > TA ) > paraco414474393lle_fm > TA ) ).
thf(paraco815940159rec_fm_decl,type,
paraco815940159rec_fm:
!>[TA: $tType] : ( ( ( list @ char ) > TA ) > TA > ( paraco414474393lle_fm > TA > TA ) > ( paraco414474393lle_fm > paraco414474393lle_fm > TA > TA > TA ) > ( paraco414474393lle_fm > paraco414474393lle_fm > TA > TA > TA ) > ( paraco414474393lle_fm > paraco414474393lle_fm > TA > TA > TA ) > paraco414474393lle_fm > TA ) ).
thf(paraco2040174112le_Det_decl,type,
paraco2040174112le_Det: $o > paraco415392788lle_tv ).
thf(paraco676387099_Indet_decl,type,
paraco676387099_Indet: nat > paraco415392788lle_tv ).
thf(paraco490622181ase_tv_decl,type,
paraco490622181ase_tv:
!>[TA: $tType] : ( ( $o > TA ) > ( nat > TA ) > paraco415392788lle_tv > TA ) ).
thf(paraco152590079rec_tv_decl,type,
paraco152590079rec_tv:
!>[TA: $tType] : ( ( $o > TA ) > ( nat > TA ) > paraco415392788lle_tv > TA ) ).
thf(paraco769098683_valid_decl,type,
paraco769098683_valid: paraco414474393lle_fm > $o ).
thf(paraco2086025920lid_in_decl,type,
paraco2086025920lid_in: ( set @ nat ) > paraco414474393lle_fm > $o ).
thf(product_Pair_decl,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( TB > TA > ( product_prod @ TB @ TA ) ) ).
thf(product_case_bool_decl,type,
product_case_bool:
!>[TA: $tType] : ( TA > TA > $o > TA ) ).
thf(product_curry_decl,type,
product_curry:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( ( product_prod @ TC @ TB ) > TA ) > TC > TB > TA ) ).
thf(produc2004651681e_prod_decl,type,
produc2004651681e_prod:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > TA ) > ( product_prod @ TC @ TB ) > TA ) ).
thf(product_rec_prod_decl,type,
product_rec_prod:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > TA ) > ( product_prod @ TC @ TB ) > TA ) ).
thf(accp_decl,type,
accp:
!>[TA: $tType] : ( ( TA > TA > $o ) > TA > $o ) ).
thf(f_decl,type,
f: nat > nat ).
thf(i_decl,type,
i: ( list @ char ) > paraco415392788lle_tv ).
thf(p1_decl,type,
p1: paraco414474393lle_fm ).
thf(p2_decl,type,
p2: paraco414474393lle_fm ).
thf(83,axiom,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm,C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( ( paraco2100061555le_Con @ A @ B )
!= ( paraco2084319816le_Eql @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_fm_Odistinct_I25_J) ).
thf(457,plain,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm,C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( ( paraco2100061555le_Con @ A @ B )
!= ( paraco2084319816le_Eql @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(32,axiom,
! [TA: $tType] :
( ( product_case_bool @ TA )
= ( ^ [A: TA,B: TA,C: $o] : ( if @ TA @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_bool_Ocase__eq__if) ).
thf(218,plain,
! [TA: $tType] :
( ( product_case_bool @ TA )
= ( ^ [A: TA,B: TA,C: $o] : ( if @ TA @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(66,axiom,
! [A: paraco415392788lle_tv > $o,B: paraco415392788lle_tv] :
( ! [C: $o] : ( A @ ( paraco2040174112le_Det @ C ) )
=> ( ! [C: nat] : ( A @ ( paraco676387099_Indet @ C ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_tv_Oinduct) ).
thf(347,plain,
! [A: paraco415392788lle_tv > $o,B: paraco415392788lle_tv] :
( ! [C: $o] : ( A @ ( paraco2040174112le_Det @ C ) )
=> ( ! [C: nat] : ( A @ ( paraco676387099_Indet @ C ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(94,axiom,
( ( paraco876059933e_eval @ ( paraco753463838ge_int @ f @ i ) @ p1 )
= ( paraco1920534163nge_tv @ f @ ( paraco876059933e_eval @ i @ p1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_ih1) ).
thf(555,plain,
( ( paraco876059933e_eval @ ( paraco753463838ge_int @ f @ i ) @ p1 )
= ( paraco1920534163nge_tv @ f @ ( paraco876059933e_eval @ i @ p1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(67,axiom,
! [TA: $tType,A: ( list @ char ) > TA,B: TA,C: paraco414474393lle_fm > TA > TA,D: paraco414474393lle_fm > paraco414474393lle_fm > TA > TA > TA,E: paraco414474393lle_fm > paraco414474393lle_fm > TA > TA > TA,F: paraco414474393lle_fm > paraco414474393lle_fm > TA > TA > TA] :
( ( paraco815940159rec_fm @ TA @ A @ B @ C @ D @ E @ F @ paraco251304083_Truth )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_fm_Osimps_I43_J) ).
thf(352,plain,
! [TA: $tType,A: ( list @ char ) > TA,B: TA,C: paraco414474393lle_fm > TA > TA,D: paraco414474393lle_fm > paraco414474393lle_fm > TA > TA > TA,E: paraco414474393lle_fm > paraco414474393lle_fm > TA > TA > TA,F: paraco414474393lle_fm > paraco414474393lle_fm > TA > TA > TA] :
( ( paraco815940159rec_fm @ TA @ A @ B @ C @ D @ E @ F @ paraco251304083_Truth )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(19,axiom,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_prod__cases) ).
thf(170,plain,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(102,axiom,
( paraco769098683_valid
= ( ^ [A: paraco414474393lle_fm] :
! [B: ( list @ char ) > paraco415392788lle_tv] :
( ( paraco876059933e_eval @ B @ A )
= ( paraco2040174112le_Det @ $true ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_valid__def) ).
thf(582,plain,
( paraco769098683_valid
= ( ^ [A: paraco414474393lle_fm] :
! [B: ( list @ char ) > paraco415392788lle_tv] :
( ( paraco876059933e_eval @ B @ A )
= ( paraco2040174112le_Det @ $true ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(44,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_old_Oprod_Oinject) ).
thf(276,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(82,axiom,
! [A: ( list @ char ) > paraco415392788lle_tv,B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( ( ( ( paraco876059933e_eval @ A @ B )
= ( paraco876059933e_eval @ A @ C ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco2084319816le_Eql @ B @ C ) )
= ( paraco2040174112le_Det @ $true ) ) )
& ( ( ( paraco876059933e_eval @ A @ B )
!= ( paraco876059933e_eval @ A @ C ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco2084319816le_Eql @ B @ C ) )
= ( paraco2040174112le_Det @ $false ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_eval_Osimps_I5_J) ).
thf(449,plain,
! [A: ( list @ char ) > paraco415392788lle_tv,B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( ( ( ( paraco876059933e_eval @ A @ B )
= ( paraco876059933e_eval @ A @ C ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco2084319816le_Eql @ B @ C ) )
= ( paraco2040174112le_Det @ $true ) ) )
& ( ( ( paraco876059933e_eval @ A @ B )
!= ( paraco876059933e_eval @ A @ C ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco2084319816le_Eql @ B @ C ) )
= ( paraco2040174112le_Det @ $false ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(28,axiom,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm] :
( paraco251304083_Truth
!= ( paraco1628874225le_Eql @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_fm_Odistinct_I17_J) ).
thf(202,plain,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm] :
( paraco251304083_Truth
!= ( paraco1628874225le_Eql @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(89,axiom,
! [A: paraco414474393lle_fm] :
( ! [B: list @ char] :
( A
!= ( paraco27778325le_Pro @ B ) )
=> ( ( A != paraco251304083_Truth )
=> ( ! [B: paraco414474393lle_fm] :
( A
!= ( paraco329115265le_Neg @ B ) )
=> ( ! [B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( A
!= ( paraco2100061555le_Con @ B @ C ) )
=> ( ! [B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( A
!= ( paraco2084319816le_Eql @ B @ C ) )
=> ~ ! [B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( A
!= ( paraco1628874225le_Eql @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_fm_Oexhaust) ).
thf(533,plain,
! [A: paraco414474393lle_fm] :
( ! [B: list @ char] :
( A
!= ( paraco27778325le_Pro @ B ) )
=> ( ( A != paraco251304083_Truth )
=> ( ! [B: paraco414474393lle_fm] :
( A
!= ( paraco329115265le_Neg @ B ) )
=> ( ! [B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( A
!= ( paraco2100061555le_Con @ B @ C ) )
=> ( ! [B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( A
!= ( paraco2084319816le_Eql @ B @ C ) )
=> ~ ! [B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( A
!= ( paraco1628874225le_Eql @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(92,axiom,
( ( paraco876059933e_eval @ ( paraco753463838ge_int @ f @ i ) @ p2 )
= ( paraco1920534163nge_tv @ f @ ( paraco876059933e_eval @ i @ p2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_ih2) ).
thf(550,plain,
( ( paraco876059933e_eval @ ( paraco753463838ge_int @ f @ i ) @ p2 )
= ( paraco1920534163nge_tv @ f @ ( paraco876059933e_eval @ i @ p2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(12,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ E @ ( product_Pair @ TB @ TA @ F @ G ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_prod__cases6) ).
thf(142,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ E @ ( product_Pair @ TB @ TA @ F @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(52,axiom,
! [TA: $tType,A: $o > TA,B: nat > TA,C: nat] :
( ( paraco490622181ase_tv @ TA @ A @ B @ ( paraco676387099_Indet @ C ) )
= ( B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_tv_Osimps_I6_J) ).
thf(301,plain,
! [TA: $tType,A: $o > TA,B: nat > TA,C: nat] :
( ( paraco490622181ase_tv @ TA @ A @ B @ ( paraco676387099_Indet @ C ) )
= ( B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(97,axiom,
! [A: set @ nat,B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( ( paraco2086025920lid_in @ A @ ( paraco2100061555le_Con @ B @ C ) )
= ( ( paraco2086025920lid_in @ A @ B )
& ( paraco2086025920lid_in @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_conjunction__in) ).
thf(565,plain,
! [A: set @ nat,B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( ( paraco2086025920lid_in @ A @ ( paraco2100061555le_Con @ B @ C ) )
= ( ( paraco2086025920lid_in @ A @ B )
& ( paraco2086025920lid_in @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(20,axiom,
! [A: paraco415392788lle_tv > $o,B: paraco415392788lle_tv] :
( ( A @ ( paraco2040174112le_Det @ $true ) )
=> ( ( A @ ( paraco2040174112le_Det @ $false ) )
=> ( ! [C: nat] : ( A @ ( paraco676387099_Indet @ C ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_string__tv_Oinduct) ).
thf(174,plain,
! [A: paraco415392788lle_tv > $o,B: paraco415392788lle_tv] :
( ( A @ ( paraco2040174112le_Det @ $true ) )
=> ( ( A @ ( paraco2040174112le_Det @ $false ) )
=> ( ! [C: nat] : ( A @ ( paraco676387099_Indet @ C ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(76,axiom,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm,C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( ( ( paraco2100061555le_Con @ A @ B )
= ( paraco2100061555le_Con @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_fm_Oinject_I3_J) ).
thf(404,plain,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm,C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( ( ( paraco2100061555le_Con @ A @ B )
= ( paraco2100061555le_Con @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(3,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ B @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ C @ ( product_Pair @ TB @ TA @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_prod__cases4) ).
thf(110,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ B @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ C @ ( product_Pair @ TB @ TA @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(104,axiom,
! [A: ( list @ char ) > paraco415392788lle_tv,B: paraco414474393lle_fm] :
( ( paraco876059933e_eval @ A @ ( paraco329115265le_Neg @ B ) )
= ( paraco490622181ase_tv @ paraco415392788lle_tv @ ( product_case_bool @ paraco415392788lle_tv @ ( paraco2040174112le_Det @ $false ) @ ( paraco2040174112le_Det @ $true ) ) @ paraco676387099_Indet @ ( paraco876059933e_eval @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_eval_Osimps_I3_J) ).
thf(587,plain,
! [A: ( list @ char ) > paraco415392788lle_tv,B: paraco414474393lle_fm] :
( ( paraco876059933e_eval @ A @ ( paraco329115265le_Neg @ B ) )
= ( paraco490622181ase_tv @ paraco415392788lle_tv @ ( product_case_bool @ paraco415392788lle_tv @ ( paraco2040174112le_Det @ $false ) @ ( paraco2040174112le_Det @ $true ) ) @ paraco676387099_Indet @ ( paraco876059933e_eval @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(15,axiom,
! [A: set @ nat,B: paraco414474393lle_fm] :
( ~ ( paraco2086025920lid_in @ A @ B )
=> ~ ( paraco769098683_valid @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_transfer) ).
thf(157,plain,
! [A: set @ nat,B: paraco414474393lle_fm] :
( ~ ( paraco2086025920lid_in @ A @ B )
=> ~ ( paraco769098683_valid @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(24,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( product_rec_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_old_Oprod_Orec) ).
thf(189,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( product_rec_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(78,axiom,
! [A: ( list @ char ) > paraco415392788lle_tv,B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( ( paraco876059933e_eval @ A @ ( paraco2084319816le_Eql @ B @ C ) )
= ( paraco2040174112le_Det
@ ( ( paraco876059933e_eval @ A @ B )
= ( paraco876059933e_eval @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_eval__equality__simplify) ).
thf(421,plain,
! [A: ( list @ char ) > paraco415392788lle_tv,B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( ( paraco876059933e_eval @ A @ ( paraco2084319816le_Eql @ B @ C ) )
= ( paraco2040174112le_Det
@ ( ( paraco876059933e_eval @ A @ B )
= ( paraco876059933e_eval @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(48,axiom,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm] :
( ( ( paraco329115265le_Neg @ A )
= ( paraco329115265le_Neg @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_fm_Oinject_I2_J) ).
thf(289,plain,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm] :
( ( ( paraco329115265le_Neg @ A )
= ( paraco329115265le_Neg @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(57,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( produc2004651681e_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_internal__case__prod__conv) ).
thf(316,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( produc2004651681e_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(36,axiom,
! [A: list @ char,B: paraco414474393lle_fm] :
( ( paraco27778325le_Pro @ A )
!= ( paraco329115265le_Neg @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_fm_Odistinct_I3_J) ).
thf(238,plain,
! [A: list @ char,B: paraco414474393lle_fm] :
( ( paraco27778325le_Pro @ A )
!= ( paraco329115265le_Neg @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(6,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: product_prod @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) )] :
~ ! [B: TG,C: TF,D: TE,E: TD,F: TC,G: TB,H: TA] :
( A
!= ( product_Pair @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ B @ ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ C @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ D @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ E @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ F @ ( product_Pair @ TB @ TA @ G @ H ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_prod__cases7) ).
thf(121,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: product_prod @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) )] :
~ ! [B: TG,C: TF,D: TE,E: TD,F: TC,G: TB,H: TA] :
( A
!= ( product_Pair @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ B @ ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ C @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ D @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ E @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ F @ ( product_Pair @ TB @ TA @ G @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(85,axiom,
( ( paraco876059933e_eval @ ( paraco753463838ge_int @ f @ i ) @ p1 )
!= ( paraco876059933e_eval @ ( paraco753463838ge_int @ f @ i ) @ p2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_b_H) ).
thf(514,plain,
( ( paraco876059933e_eval @ ( paraco753463838ge_int @ f @ i ) @ p1 )
!= ( paraco876059933e_eval @ ( paraco753463838ge_int @ f @ i ) @ p2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(73,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(397,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(33,axiom,
! [A: paraco414474393lle_fm,B: set @ nat] :
( ( paraco769098683_valid @ A )
=> ( paraco2086025920lid_in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_valid__valid__in) ).
thf(221,plain,
! [A: paraco414474393lle_fm,B: set @ nat] :
( ( paraco769098683_valid @ A )
=> ( paraco2086025920lid_in @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(41,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(265,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(56,axiom,
! [A: list @ char] :
( ( paraco27778325le_Pro @ A )
!= paraco251304083_Truth ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_fm_Odistinct_I1_J) ).
thf(312,plain,
! [A: list @ char] :
( ( paraco27778325le_Pro @ A )
!= paraco251304083_Truth ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(29,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_Pair__inject) ).
thf(206,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(54,axiom,
( paraco753463838ge_int
= ( ^ [A: nat > nat,B: ( list @ char ) > paraco415392788lle_tv,C: list @ char] : ( paraco1920534163nge_tv @ A @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_change__int__def) ).
thf(307,plain,
( paraco753463838ge_int
= ( ^ [A: nat > nat,B: ( list @ char ) > paraco415392788lle_tv,C: list @ char] : ( paraco1920534163nge_tv @ A @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(49,axiom,
! [TA: $tType,A: ( list @ char ) > TA,B: TA,C: paraco414474393lle_fm > TA,D: paraco414474393lle_fm > paraco414474393lle_fm > TA,E: paraco414474393lle_fm > paraco414474393lle_fm > TA,F: paraco414474393lle_fm > paraco414474393lle_fm > TA,G: list @ char] :
( ( paraco1246693743ase_fm @ TA @ A @ B @ C @ D @ E @ F @ ( paraco27778325le_Pro @ G ) )
= ( A @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_fm_Osimps_I36_J) ).
thf(292,plain,
! [TA: $tType,A: ( list @ char ) > TA,B: TA,C: paraco414474393lle_fm > TA,D: paraco414474393lle_fm > paraco414474393lle_fm > TA,E: paraco414474393lle_fm > paraco414474393lle_fm > TA,F: paraco414474393lle_fm > paraco414474393lle_fm > TA,G: list @ char] :
( ( paraco1246693743ase_fm @ TA @ A @ B @ C @ D @ E @ F @ ( paraco27778325le_Pro @ G ) )
= ( A @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(39,axiom,
! [A: nat > nat,B: paraco415392788lle_tv,C: paraco415392788lle_tv] :
( ( ( paraco1920534163nge_tv @ A @ B )
= C )
=> ( ! [D: $o] :
( ( B
= ( paraco2040174112le_Det @ D ) )
=> ( C
!= ( paraco2040174112le_Det @ D ) ) )
=> ~ ! [D: nat] :
( ( B
= ( paraco676387099_Indet @ D ) )
=> ( C
!= ( paraco676387099_Indet @ ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_change__tv_Oelims) ).
thf(248,plain,
! [A: nat > nat,B: paraco415392788lle_tv,C: paraco415392788lle_tv] :
( ( ( paraco1920534163nge_tv @ A @ B )
= C )
=> ( ! [D: $o] :
( ( B
= ( paraco2040174112le_Det @ D ) )
=> ( C
!= ( paraco2040174112le_Det @ D ) ) )
=> ~ ! [D: nat] :
( ( B
= ( paraco676387099_Indet @ D ) )
=> ( C
!= ( paraco676387099_Indet @ ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(5,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) @ E @ ( product_Pair @ TD @ TE @ F @ G ) ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_prod__induct5) ).
thf(117,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) @ E @ ( product_Pair @ TD @ TE @ F @ G ) ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(88,axiom,
! [A: product_prod @ ( ( list @ char ) > paraco415392788lle_tv ) @ paraco414474393lle_fm] :
( ! [B: ( list @ char ) > paraco415392788lle_tv,C: list @ char] :
( A
!= ( product_Pair @ ( ( list @ char ) > paraco415392788lle_tv ) @ paraco414474393lle_fm @ B @ ( paraco27778325le_Pro @ C ) ) )
=> ( ! [B: ( list @ char ) > paraco415392788lle_tv] :
( A
!= ( product_Pair @ ( ( list @ char ) > paraco415392788lle_tv ) @ paraco414474393lle_fm @ B @ paraco251304083_Truth ) )
=> ( ! [B: ( list @ char ) > paraco415392788lle_tv,C: paraco414474393lle_fm] :
( A
!= ( product_Pair @ ( ( list @ char ) > paraco415392788lle_tv ) @ paraco414474393lle_fm @ B @ ( paraco329115265le_Neg @ C ) ) )
=> ( ! [B: ( list @ char ) > paraco415392788lle_tv,C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( A
!= ( product_Pair @ ( ( list @ char ) > paraco415392788lle_tv ) @ paraco414474393lle_fm @ B @ ( paraco2100061555le_Con @ C @ D ) ) )
=> ( ! [B: ( list @ char ) > paraco415392788lle_tv,C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( A
!= ( product_Pair @ ( ( list @ char ) > paraco415392788lle_tv ) @ paraco414474393lle_fm @ B @ ( paraco2084319816le_Eql @ C @ D ) ) )
=> ~ ! [B: ( list @ char ) > paraco415392788lle_tv,C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( A
!= ( product_Pair @ ( ( list @ char ) > paraco415392788lle_tv ) @ paraco414474393lle_fm @ B @ ( paraco1628874225le_Eql @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_eval_Ocases) ).
thf(529,plain,
! [A: product_prod @ ( ( list @ char ) > paraco415392788lle_tv ) @ paraco414474393lle_fm] :
( ! [B: ( list @ char ) > paraco415392788lle_tv,C: list @ char] :
( A
!= ( product_Pair @ ( ( list @ char ) > paraco415392788lle_tv ) @ paraco414474393lle_fm @ B @ ( paraco27778325le_Pro @ C ) ) )
=> ( ! [B: ( list @ char ) > paraco415392788lle_tv] :
( A
!= ( product_Pair @ ( ( list @ char ) > paraco415392788lle_tv ) @ paraco414474393lle_fm @ B @ paraco251304083_Truth ) )
=> ( ! [B: ( list @ char ) > paraco415392788lle_tv,C: paraco414474393lle_fm] :
( A
!= ( product_Pair @ ( ( list @ char ) > paraco415392788lle_tv ) @ paraco414474393lle_fm @ B @ ( paraco329115265le_Neg @ C ) ) )
=> ( ! [B: ( list @ char ) > paraco415392788lle_tv,C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( A
!= ( product_Pair @ ( ( list @ char ) > paraco415392788lle_tv ) @ paraco414474393lle_fm @ B @ ( paraco2100061555le_Con @ C @ D ) ) )
=> ( ! [B: ( list @ char ) > paraco415392788lle_tv,C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( A
!= ( product_Pair @ ( ( list @ char ) > paraco415392788lle_tv ) @ paraco414474393lle_fm @ B @ ( paraco2084319816le_Eql @ C @ D ) ) )
=> ~ ! [B: ( list @ char ) > paraco415392788lle_tv,C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( A
!= ( product_Pair @ ( ( list @ char ) > paraco415392788lle_tv ) @ paraco414474393lle_fm @ B @ ( paraco1628874225le_Eql @ C @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(96,axiom,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm,C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( ( paraco2100061555le_Con @ A @ B )
!= ( paraco1628874225le_Eql @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_fm_Odistinct_I27_J) ).
thf(561,plain,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm,C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( ( paraco2100061555le_Con @ A @ B )
!= ( paraco1628874225le_Eql @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(79,axiom,
( ( paraco876059933e_eval @ i @ p2 )
= ( paraco2040174112le_Det @ $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_a) ).
thf(424,plain,
( ( paraco876059933e_eval @ i @ p2 )
= ( paraco2040174112le_Det @ $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(81,axiom,
! [A: ( list @ char ) > paraco415392788lle_tv,B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( ( ( ( paraco876059933e_eval @ A @ B )
= ( paraco876059933e_eval @ A @ C ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco1628874225le_Eql @ B @ C ) )
= ( paraco2040174112le_Det @ $true ) ) )
& ( ( ( paraco876059933e_eval @ A @ B )
!= ( paraco876059933e_eval @ A @ C ) )
=> ( ( ( ( paraco876059933e_eval @ A @ B )
= ( paraco2040174112le_Det @ $true ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco1628874225le_Eql @ B @ C ) )
= ( paraco876059933e_eval @ A @ C ) ) )
& ( ( ( paraco876059933e_eval @ A @ B )
!= ( paraco2040174112le_Det @ $true ) )
=> ( ( ( ( paraco876059933e_eval @ A @ C )
= ( paraco2040174112le_Det @ $true ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco1628874225le_Eql @ B @ C ) )
= ( paraco876059933e_eval @ A @ B ) ) )
& ( ( ( paraco876059933e_eval @ A @ C )
!= ( paraco2040174112le_Det @ $true ) )
=> ( ( ( ( paraco876059933e_eval @ A @ B )
= ( paraco2040174112le_Det @ $false ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco1628874225le_Eql @ B @ C ) )
= ( paraco876059933e_eval @ A @ ( paraco329115265le_Neg @ C ) ) ) )
& ( ( ( paraco876059933e_eval @ A @ B )
!= ( paraco2040174112le_Det @ $false ) )
=> ( ( ( ( paraco876059933e_eval @ A @ C )
= ( paraco2040174112le_Det @ $false ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco1628874225le_Eql @ B @ C ) )
= ( paraco876059933e_eval @ A @ ( paraco329115265le_Neg @ B ) ) ) )
& ( ( ( paraco876059933e_eval @ A @ C )
!= ( paraco2040174112le_Det @ $false ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco1628874225le_Eql @ B @ C ) )
= ( paraco2040174112le_Det @ $false ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_eval__equality) ).
thf(429,plain,
! [A: ( list @ char ) > paraco415392788lle_tv,B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( ( ( ( paraco876059933e_eval @ A @ B )
= ( paraco876059933e_eval @ A @ C ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco1628874225le_Eql @ B @ C ) )
= ( paraco2040174112le_Det @ $true ) ) )
& ( ( ( paraco876059933e_eval @ A @ B )
!= ( paraco876059933e_eval @ A @ C ) )
=> ( ( ( ( paraco876059933e_eval @ A @ B )
= ( paraco2040174112le_Det @ $true ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco1628874225le_Eql @ B @ C ) )
= ( paraco876059933e_eval @ A @ C ) ) )
& ( ( ( paraco876059933e_eval @ A @ B )
!= ( paraco2040174112le_Det @ $true ) )
=> ( ( ( ( paraco876059933e_eval @ A @ C )
= ( paraco2040174112le_Det @ $true ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco1628874225le_Eql @ B @ C ) )
= ( paraco876059933e_eval @ A @ B ) ) )
& ( ( ( paraco876059933e_eval @ A @ C )
!= ( paraco2040174112le_Det @ $true ) )
=> ( ( ( ( paraco876059933e_eval @ A @ B )
= ( paraco2040174112le_Det @ $false ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco1628874225le_Eql @ B @ C ) )
= ( paraco876059933e_eval @ A @ ( paraco329115265le_Neg @ C ) ) ) )
& ( ( ( paraco876059933e_eval @ A @ B )
!= ( paraco2040174112le_Det @ $false ) )
=> ( ( ( ( paraco876059933e_eval @ A @ C )
= ( paraco2040174112le_Det @ $false ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco1628874225le_Eql @ B @ C ) )
= ( paraco876059933e_eval @ A @ ( paraco329115265le_Neg @ B ) ) ) )
& ( ( ( paraco876059933e_eval @ A @ C )
!= ( paraco2040174112le_Det @ $false ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco1628874225le_Eql @ B @ C ) )
= ( paraco2040174112le_Det @ $false ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(25,axiom,
! [A: nat,B: nat] :
( ( ( paraco676387099_Indet @ A )
= ( paraco676387099_Indet @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_tv_Oinject_I2_J) ).
thf(192,plain,
! [A: nat,B: nat] :
( ( ( paraco676387099_Indet @ A )
= ( paraco676387099_Indet @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(77,axiom,
! [A: ( list @ char ) > paraco415392788lle_tv,B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( ( ( ( paraco876059933e_eval @ A @ B )
= ( paraco876059933e_eval @ A @ C ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco2100061555le_Con @ B @ C ) )
= ( paraco876059933e_eval @ A @ B ) ) )
& ( ( ( paraco876059933e_eval @ A @ B )
!= ( paraco876059933e_eval @ A @ C ) )
=> ( ( ( ( paraco876059933e_eval @ A @ B )
= ( paraco2040174112le_Det @ $true ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco2100061555le_Con @ B @ C ) )
= ( paraco876059933e_eval @ A @ C ) ) )
& ( ( ( paraco876059933e_eval @ A @ B )
!= ( paraco2040174112le_Det @ $true ) )
=> ( ( ( ( paraco876059933e_eval @ A @ C )
= ( paraco2040174112le_Det @ $true ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco2100061555le_Con @ B @ C ) )
= ( paraco876059933e_eval @ A @ B ) ) )
& ( ( ( paraco876059933e_eval @ A @ C )
!= ( paraco2040174112le_Det @ $true ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco2100061555le_Con @ B @ C ) )
= ( paraco2040174112le_Det @ $false ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_eval_Osimps_I4_J) ).
thf(407,plain,
! [A: ( list @ char ) > paraco415392788lle_tv,B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( ( ( ( paraco876059933e_eval @ A @ B )
= ( paraco876059933e_eval @ A @ C ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco2100061555le_Con @ B @ C ) )
= ( paraco876059933e_eval @ A @ B ) ) )
& ( ( ( paraco876059933e_eval @ A @ B )
!= ( paraco876059933e_eval @ A @ C ) )
=> ( ( ( ( paraco876059933e_eval @ A @ B )
= ( paraco2040174112le_Det @ $true ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco2100061555le_Con @ B @ C ) )
= ( paraco876059933e_eval @ A @ C ) ) )
& ( ( ( paraco876059933e_eval @ A @ B )
!= ( paraco2040174112le_Det @ $true ) )
=> ( ( ( ( paraco876059933e_eval @ A @ C )
= ( paraco2040174112le_Det @ $true ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco2100061555le_Con @ B @ C ) )
= ( paraco876059933e_eval @ A @ B ) ) )
& ( ( ( paraco876059933e_eval @ A @ C )
!= ( paraco2040174112le_Det @ $true ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco2100061555le_Con @ B @ C ) )
= ( paraco2040174112le_Det @ $false ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(61,axiom,
! [TA: $tType,A: ( list @ char ) > TA,B: TA,C: paraco414474393lle_fm > TA > TA,D: paraco414474393lle_fm > paraco414474393lle_fm > TA > TA > TA,E: paraco414474393lle_fm > paraco414474393lle_fm > TA > TA > TA,F: paraco414474393lle_fm > paraco414474393lle_fm > TA > TA > TA,G: paraco414474393lle_fm,H: paraco414474393lle_fm] :
( ( paraco815940159rec_fm @ TA @ A @ B @ C @ D @ E @ F @ ( paraco2084319816le_Eql @ G @ H ) )
= ( E @ G @ H @ ( paraco815940159rec_fm @ TA @ A @ B @ C @ D @ E @ F @ G ) @ ( paraco815940159rec_fm @ TA @ A @ B @ C @ D @ E @ F @ H ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_fm_Osimps_I46_J) ).
thf(329,plain,
! [TA: $tType,A: ( list @ char ) > TA,B: TA,C: paraco414474393lle_fm > TA > TA,D: paraco414474393lle_fm > paraco414474393lle_fm > TA > TA > TA,E: paraco414474393lle_fm > paraco414474393lle_fm > TA > TA > TA,F: paraco414474393lle_fm > paraco414474393lle_fm > TA > TA > TA,G: paraco414474393lle_fm,H: paraco414474393lle_fm] :
( ( paraco815940159rec_fm @ TA @ A @ B @ C @ D @ E @ F @ ( paraco2084319816le_Eql @ G @ H ) )
= ( E @ G @ H @ ( paraco815940159rec_fm @ TA @ A @ B @ C @ D @ E @ F @ G ) @ ( paraco815940159rec_fm @ TA @ A @ B @ C @ D @ E @ F @ H ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(84,axiom,
! [A: paraco414474393lle_fm > $o,B: paraco414474393lle_fm] :
( ( A @ paraco251304083_Truth )
=> ( ! [C: list @ char] : ( A @ ( paraco27778325le_Pro @ C ) )
=> ( ! [C: paraco414474393lle_fm] :
( ( A @ C )
=> ( A @ ( paraco329115265le_Neg @ C ) ) )
=> ( ! [C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( ( A @ C )
=> ( ( A @ D )
=> ( A @ ( paraco2100061555le_Con @ C @ D ) ) ) )
=> ( ! [C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( ( A @ C )
=> ( ( A @ D )
=> ( A @ ( paraco2084319816le_Eql @ C @ D ) ) ) )
=> ( ! [C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( ( A @ C )
=> ( ( A @ D )
=> ( A @ ( paraco1628874225le_Eql @ C @ D ) ) ) )
=> ( A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_props_Oinduct) ).
thf(461,plain,
! [A: paraco414474393lle_fm > $o,B: paraco414474393lle_fm] :
( ( A @ paraco251304083_Truth )
=> ( ! [C: list @ char] : ( A @ ( paraco27778325le_Pro @ C ) )
=> ( ! [C: paraco414474393lle_fm] :
( ( A @ C )
=> ( A @ ( paraco329115265le_Neg @ C ) ) )
=> ( ! [C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( ( A @ C )
=> ( ( A @ D )
=> ( A @ ( paraco2100061555le_Con @ C @ D ) ) ) )
=> ( ! [C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( ( A @ C )
=> ( ( A @ D )
=> ( A @ ( paraco2084319816le_Eql @ C @ D ) ) ) )
=> ( ! [C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( ( A @ C )
=> ( ( A @ D )
=> ( A @ ( paraco1628874225le_Eql @ C @ D ) ) ) )
=> ( A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(34,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( product_case_bool @ TA @ A @ B @ $false )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_old_Obool_Osimps_I4_J) ).
thf(224,plain,
! [TA: $tType,A: TA,B: TA] :
( ( product_case_bool @ TA @ A @ B @ $false )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(70,axiom,
! [TA: $tType,A: $o > TA,B: nat > TA,C: $o] :
( ( paraco152590079rec_tv @ TA @ A @ B @ ( paraco2040174112le_Det @ C ) )
= ( A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_tv_Osimps_I7_J) ).
thf(388,plain,
! [TA: $tType,A: $o > TA,B: nat > TA,C: $o] :
( ( paraco152590079rec_tv @ TA @ A @ B @ ( paraco2040174112le_Det @ C ) )
= ( A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(106,axiom,
( ( paraco876059933e_eval @ i @ p1 )
!= ( paraco2040174112le_Det @ $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_a_H_H) ).
thf(593,plain,
( ( paraco876059933e_eval @ i @ p1 )
!= ( paraco2040174112le_Det @ $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(7,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ B @ ( product_Pair @ TB @ TA @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_prod__cases3) ).
thf(124,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ B @ ( product_Pair @ TB @ TA @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(64,axiom,
! [A: paraco415392788lle_tv] :
( ! [B: $o] :
( A
!= ( paraco2040174112le_Det @ B ) )
=> ~ ! [B: nat] :
( A
!= ( paraco676387099_Indet @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_tv_Oexhaust) ).
thf(339,plain,
! [A: paraco415392788lle_tv] :
( ! [B: $o] :
( A
!= ( paraco2040174112le_Det @ B ) )
=> ~ ! [B: nat] :
( A
!= ( paraco676387099_Indet @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(90,axiom,
! [A: ( list @ char ) > paraco415392788lle_tv,B: paraco414474393lle_fm] :
( ( ( ( paraco876059933e_eval @ A @ B )
= ( paraco2040174112le_Det @ $false ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco329115265le_Neg @ B ) )
= ( paraco2040174112le_Det @ $true ) ) )
& ( ( ( paraco876059933e_eval @ A @ B )
!= ( paraco2040174112le_Det @ $false ) )
=> ( ( ( ( paraco876059933e_eval @ A @ B )
= ( paraco2040174112le_Det @ $true ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco329115265le_Neg @ B ) )
= ( paraco2040174112le_Det @ $false ) ) )
& ( ( ( paraco876059933e_eval @ A @ B )
!= ( paraco2040174112le_Det @ $true ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco329115265le_Neg @ B ) )
= ( paraco876059933e_eval @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_eval__negation) ).
thf(537,plain,
! [A: ( list @ char ) > paraco415392788lle_tv,B: paraco414474393lle_fm] :
( ( ( ( paraco876059933e_eval @ A @ B )
= ( paraco2040174112le_Det @ $false ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco329115265le_Neg @ B ) )
= ( paraco2040174112le_Det @ $true ) ) )
& ( ( ( paraco876059933e_eval @ A @ B )
!= ( paraco2040174112le_Det @ $false ) )
=> ( ( ( ( paraco876059933e_eval @ A @ B )
= ( paraco2040174112le_Det @ $true ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco329115265le_Neg @ B ) )
= ( paraco2040174112le_Det @ $false ) ) )
& ( ( ( paraco876059933e_eval @ A @ B )
!= ( paraco2040174112le_Det @ $true ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco329115265le_Neg @ B ) )
= ( paraco876059933e_eval @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(105,axiom,
( ( paraco876059933e_eval @ i @ p1 )
!= ( paraco876059933e_eval @ i @ p2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_a_H) ).
thf(590,plain,
( ( paraco876059933e_eval @ i @ p1 )
!= ( paraco876059933e_eval @ i @ p2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(30,axiom,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm,C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( ( ( paraco2084319816le_Eql @ A @ B )
= ( paraco2084319816le_Eql @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_fm_Oinject_I4_J) ).
thf(212,plain,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm,C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( ( ( paraco2084319816le_Eql @ A @ B )
= ( paraco2084319816le_Eql @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(65,axiom,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm,C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( ( paraco2084319816le_Eql @ A @ B )
!= ( paraco1628874225le_Eql @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_fm_Odistinct_I29_J) ).
thf(343,plain,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm,C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( ( paraco2084319816le_Eql @ A @ B )
!= ( paraco1628874225le_Eql @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(74,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA,D: $o] :
( ( A @ ( product_case_bool @ TA @ B @ C @ D ) )
= ( ~ ( ( D
& ~ ( A @ B ) )
| ( ~ D
& ~ ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_bool_Osplit__sel__asm) ).
thf(398,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA,D: $o] :
( ( A @ ( product_case_bool @ TA @ B @ C @ D ) )
= ( ~ ( ( D
& ~ ( A @ B ) )
| ( ~ D
& ~ ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(51,axiom,
! [TA: $tType,A: ( list @ char ) > TA,B: TA,C: paraco414474393lle_fm > TA > TA,D: paraco414474393lle_fm > paraco414474393lle_fm > TA > TA > TA,E: paraco414474393lle_fm > paraco414474393lle_fm > TA > TA > TA,F: paraco414474393lle_fm > paraco414474393lle_fm > TA > TA > TA,G: paraco414474393lle_fm,H: paraco414474393lle_fm] :
( ( paraco815940159rec_fm @ TA @ A @ B @ C @ D @ E @ F @ ( paraco1628874225le_Eql @ G @ H ) )
= ( F @ G @ H @ ( paraco815940159rec_fm @ TA @ A @ B @ C @ D @ E @ F @ G ) @ ( paraco815940159rec_fm @ TA @ A @ B @ C @ D @ E @ F @ H ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_fm_Osimps_I47_J) ).
thf(298,plain,
! [TA: $tType,A: ( list @ char ) > TA,B: TA,C: paraco414474393lle_fm > TA > TA,D: paraco414474393lle_fm > paraco414474393lle_fm > TA > TA > TA,E: paraco414474393lle_fm > paraco414474393lle_fm > TA > TA > TA,F: paraco414474393lle_fm > paraco414474393lle_fm > TA > TA > TA,G: paraco414474393lle_fm,H: paraco414474393lle_fm] :
( ( paraco815940159rec_fm @ TA @ A @ B @ C @ D @ E @ F @ ( paraco1628874225le_Eql @ G @ H ) )
= ( F @ G @ H @ ( paraco815940159rec_fm @ TA @ A @ B @ C @ D @ E @ F @ G ) @ ( paraco815940159rec_fm @ TA @ A @ B @ C @ D @ E @ F @ H ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(18,axiom,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( ( paraco329115265le_Neg @ A )
!= ( paraco1628874225le_Eql @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_fm_Odistinct_I23_J) ).
thf(166,plain,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( ( paraco329115265le_Neg @ A )
!= ( paraco1628874225le_Eql @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(45,axiom,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_old_Oprod_Oinducts) ).
thf(279,plain,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(21,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(180,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(103,axiom,
( ( paraco876059933e_eval @ ( paraco753463838ge_int @ f @ i ) @ p1 )
!= ( paraco2040174112le_Det @ $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_b_H_H) ).
thf(584,plain,
( ( paraco876059933e_eval @ ( paraco753463838ge_int @ f @ i ) @ p1 )
!= ( paraco2040174112le_Det @ $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(47,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA,D: $o] :
( ( A @ ( product_case_bool @ TA @ B @ C @ D ) )
= ( ( D
=> ( A @ B ) )
& ( ~ D
=> ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_bool_Osplit__sel) ).
thf(286,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA,D: $o] :
( ( A @ ( product_case_bool @ TA @ B @ C @ D ) )
= ( ( D
=> ( A @ B ) )
& ( ~ D
=> ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(101,axiom,
! [TA: $tType,A: ( list @ char ) > TA,B: TA,C: paraco414474393lle_fm > TA > TA,D: paraco414474393lle_fm > paraco414474393lle_fm > TA > TA > TA,E: paraco414474393lle_fm > paraco414474393lle_fm > TA > TA > TA,F: paraco414474393lle_fm > paraco414474393lle_fm > TA > TA > TA,G: paraco414474393lle_fm,H: paraco414474393lle_fm] :
( ( paraco815940159rec_fm @ TA @ A @ B @ C @ D @ E @ F @ ( paraco2100061555le_Con @ G @ H ) )
= ( D @ G @ H @ ( paraco815940159rec_fm @ TA @ A @ B @ C @ D @ E @ F @ G ) @ ( paraco815940159rec_fm @ TA @ A @ B @ C @ D @ E @ F @ H ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_fm_Osimps_I45_J) ).
thf(579,plain,
! [TA: $tType,A: ( list @ char ) > TA,B: TA,C: paraco414474393lle_fm > TA > TA,D: paraco414474393lle_fm > paraco414474393lle_fm > TA > TA > TA,E: paraco414474393lle_fm > paraco414474393lle_fm > TA > TA > TA,F: paraco414474393lle_fm > paraco414474393lle_fm > TA > TA > TA,G: paraco414474393lle_fm,H: paraco414474393lle_fm] :
( ( paraco815940159rec_fm @ TA @ A @ B @ C @ D @ E @ F @ ( paraco2100061555le_Con @ G @ H ) )
= ( D @ G @ H @ ( paraco815940159rec_fm @ TA @ A @ B @ C @ D @ E @ F @ G ) @ ( paraco815940159rec_fm @ TA @ A @ B @ C @ D @ E @ F @ H ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(71,axiom,
! [A: ( nat > nat ) > paraco415392788lle_tv > $o,B: nat > nat,C: paraco415392788lle_tv] :
( ! [D: nat > nat,E: $o] : ( A @ D @ ( paraco2040174112le_Det @ E ) )
=> ( ! [D: nat > nat,E: nat] : ( A @ D @ ( paraco676387099_Indet @ E ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_change__tv_Oinduct) ).
thf(391,plain,
! [A: ( nat > nat ) > paraco415392788lle_tv > $o,B: nat > nat,C: paraco415392788lle_tv] :
( ! [D: nat > nat,E: $o] : ( A @ D @ ( paraco2040174112le_Det @ E ) )
=> ( ! [D: nat > nat,E: nat] : ( A @ D @ ( paraco676387099_Indet @ E ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(99,axiom,
! [A: paraco414474393lle_fm] :
( ( A != paraco251304083_Truth )
=> ( ! [B: list @ char] :
( A
!= ( paraco27778325le_Pro @ B ) )
=> ( ! [B: paraco414474393lle_fm] :
( A
!= ( paraco329115265le_Neg @ B ) )
=> ( ! [B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( A
!= ( paraco2100061555le_Con @ B @ C ) )
=> ( ! [B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( A
!= ( paraco2084319816le_Eql @ B @ C ) )
=> ~ ! [B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( A
!= ( paraco1628874225le_Eql @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_props_Ocases) ).
thf(572,plain,
! [A: paraco414474393lle_fm] :
( ( A != paraco251304083_Truth )
=> ( ! [B: list @ char] :
( A
!= ( paraco27778325le_Pro @ B ) )
=> ( ! [B: paraco414474393lle_fm] :
( A
!= ( paraco329115265le_Neg @ B ) )
=> ( ! [B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( A
!= ( paraco2100061555le_Con @ B @ C ) )
=> ( ! [B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( A
!= ( paraco2084319816le_Eql @ B @ C ) )
=> ~ ! [B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( A
!= ( paraco1628874225le_Eql @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(16,axiom,
! [TA: $tType,A: ( list @ char ) > TA,B: TA,C: paraco414474393lle_fm > TA > TA,D: paraco414474393lle_fm > paraco414474393lle_fm > TA > TA > TA,E: paraco414474393lle_fm > paraco414474393lle_fm > TA > TA > TA,F: paraco414474393lle_fm > paraco414474393lle_fm > TA > TA > TA,G: paraco414474393lle_fm] :
( ( paraco815940159rec_fm @ TA @ A @ B @ C @ D @ E @ F @ ( paraco329115265le_Neg @ G ) )
= ( C @ G @ ( paraco815940159rec_fm @ TA @ A @ B @ C @ D @ E @ F @ G ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_fm_Osimps_I44_J) ).
thf(159,plain,
! [TA: $tType,A: ( list @ char ) > TA,B: TA,C: paraco414474393lle_fm > TA > TA,D: paraco414474393lle_fm > paraco414474393lle_fm > TA > TA > TA,E: paraco414474393lle_fm > paraco414474393lle_fm > TA > TA > TA,F: paraco414474393lle_fm > paraco414474393lle_fm > TA > TA > TA,G: paraco414474393lle_fm] :
( ( paraco815940159rec_fm @ TA @ A @ B @ C @ D @ E @ F @ ( paraco329115265le_Neg @ G ) )
= ( C @ G @ ( paraco815940159rec_fm @ TA @ A @ B @ C @ D @ E @ F @ G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(4,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) @ F @ ( product_Pair @ TE @ TF @ G @ H ) ) ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_prod__induct6) ).
thf(113,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) @ F @ ( product_Pair @ TE @ TF @ G @ H ) ) ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(38,axiom,
! [TA: $tType,A: ( list @ char ) > TA,B: TA,C: paraco414474393lle_fm > TA > TA,D: paraco414474393lle_fm > paraco414474393lle_fm > TA > TA > TA,E: paraco414474393lle_fm > paraco414474393lle_fm > TA > TA > TA,F: paraco414474393lle_fm > paraco414474393lle_fm > TA > TA > TA,G: list @ char] :
( ( paraco815940159rec_fm @ TA @ A @ B @ C @ D @ E @ F @ ( paraco27778325le_Pro @ G ) )
= ( A @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_fm_Osimps_I42_J) ).
thf(245,plain,
! [TA: $tType,A: ( list @ char ) > TA,B: TA,C: paraco414474393lle_fm > TA > TA,D: paraco414474393lle_fm > paraco414474393lle_fm > TA > TA > TA,E: paraco414474393lle_fm > paraco414474393lle_fm > TA > TA > TA,F: paraco414474393lle_fm > paraco414474393lle_fm > TA > TA > TA,G: list @ char] :
( ( paraco815940159rec_fm @ TA @ A @ B @ C @ D @ E @ F @ ( paraco27778325le_Pro @ G ) )
= ( A @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(93,axiom,
! [A: ( list @ char ) > paraco415392788lle_tv] :
( ( paraco876059933e_eval @ A @ paraco251304083_Truth )
= ( paraco2040174112le_Det @ $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_eval_Osimps_I2_J) ).
thf(552,plain,
! [A: ( list @ char ) > paraco415392788lle_tv] :
( ( paraco876059933e_eval @ A @ paraco251304083_Truth )
= ( paraco2040174112le_Det @ $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(59,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_old_Oprod_Oexhaust) ).
thf(323,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(1,conjecture,
( ( paraco876059933e_eval @ i @ ( paraco2100061555le_Con @ p1 @ p2 ) )
= ( paraco876059933e_eval @ i @ p1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( paraco876059933e_eval @ i @ ( paraco2100061555le_Con @ p1 @ p2 ) )
!= ( paraco876059933e_eval @ i @ p1 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(108,plain,
( ( paraco876059933e_eval @ i @ ( paraco2100061555le_Con @ p1 @ p2 ) )
!= ( paraco876059933e_eval @ i @ p1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(72,axiom,
! [TA: $tType,A: ( list @ char ) > TA,B: TA,C: paraco414474393lle_fm > TA,D: paraco414474393lle_fm > paraco414474393lle_fm > TA,E: paraco414474393lle_fm > paraco414474393lle_fm > TA,F: paraco414474393lle_fm > paraco414474393lle_fm > TA] :
( ( paraco1246693743ase_fm @ TA @ A @ B @ C @ D @ E @ F @ paraco251304083_Truth )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_fm_Osimps_I37_J) ).
thf(394,plain,
! [TA: $tType,A: ( list @ char ) > TA,B: TA,C: paraco414474393lle_fm > TA,D: paraco414474393lle_fm > paraco414474393lle_fm > TA,E: paraco414474393lle_fm > paraco414474393lle_fm > TA,F: paraco414474393lle_fm > paraco414474393lle_fm > TA] :
( ( paraco1246693743ase_fm @ TA @ A @ B @ C @ D @ E @ F @ paraco251304083_Truth )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(10,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) )] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) @ D @ ( product_Pair @ TC @ TD @ E @ F ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_prod__induct4) ).
thf(135,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) )] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) @ D @ ( product_Pair @ TC @ TD @ E @ F ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(80,axiom,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm] :
( ( paraco769098683_valid @ ( paraco2100061555le_Con @ A @ B ) )
= ( ( paraco769098683_valid @ A )
& ( paraco769098683_valid @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_conjunction) ).
thf(426,plain,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm] :
( ( paraco769098683_valid @ ( paraco2100061555le_Con @ A @ B ) )
= ( ( paraco769098683_valid @ A )
& ( paraco769098683_valid @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(17,axiom,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm] :
( paraco251304083_Truth
!= ( paraco2084319816le_Eql @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_fm_Odistinct_I15_J) ).
thf(162,plain,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm] :
( paraco251304083_Truth
!= ( paraco2084319816le_Eql @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(91,axiom,
( paraco876059933e_eval
= ( ^ [A: ( list @ char ) > paraco415392788lle_tv,B: paraco414474393lle_fm] : ( paraco876059933e_eval @ A @ ( paraco329115265le_Neg @ ( paraco329115265le_Neg @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_double__negation) ).
thf(548,plain,
( paraco876059933e_eval
= ( ^ [A: ( list @ char ) > paraco415392788lle_tv,B: paraco414474393lle_fm] : ( paraco876059933e_eval @ A @ ( paraco329115265le_Neg @ ( paraco329115265le_Neg @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(68,axiom,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( ( paraco329115265le_Neg @ A )
!= ( paraco2084319816le_Eql @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_fm_Odistinct_I21_J) ).
thf(355,plain,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( ( paraco329115265le_Neg @ A )
!= ( paraco2084319816le_Eql @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(13,axiom,
! [A: $o,B: nat] :
( ( paraco2040174112le_Det @ A )
!= ( paraco676387099_Indet @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_tv_Odistinct_I1_J) ).
thf(145,plain,
! [A: $o,B: nat] :
( ( paraco2040174112le_Det @ A )
!= ( paraco676387099_Indet @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(87,axiom,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( ( paraco329115265le_Neg @ A )
!= ( paraco2100061555le_Con @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_fm_Odistinct_I19_J) ).
thf(525,plain,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( ( paraco329115265le_Neg @ A )
!= ( paraco2100061555le_Con @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(95,axiom,
! [A: list @ char,B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( ( paraco27778325le_Pro @ A )
!= ( paraco2100061555le_Con @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_fm_Odistinct_I5_J) ).
thf(557,plain,
! [A: list @ char,B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( ( paraco27778325le_Pro @ A )
!= ( paraco2100061555le_Con @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(50,axiom,
! [TA: $tType,A: $o > TA,B: nat > TA,C: $o] :
( ( paraco490622181ase_tv @ TA @ A @ B @ ( paraco2040174112le_Det @ C ) )
= ( A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_tv_Osimps_I5_J) ).
thf(295,plain,
! [TA: $tType,A: $o > TA,B: nat > TA,C: $o] :
( ( paraco490622181ase_tv @ TA @ A @ B @ ( paraco2040174112le_Det @ C ) )
= ( A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(27,axiom,
! [A: nat > nat,B: $o] :
( ( paraco1920534163nge_tv @ A @ ( paraco2040174112le_Det @ B ) )
= ( paraco2040174112le_Det @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_change__tv_Osimps_I1_J) ).
thf(199,plain,
! [A: nat > nat,B: $o] :
( ( paraco1920534163nge_tv @ A @ ( paraco2040174112le_Det @ B ) )
= ( paraco2040174112le_Det @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(8,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ TC )] :
( ! [C: TA,D: TB,E: TC] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) @ C @ ( product_Pair @ TB @ TC @ D @ E ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_prod__induct3) ).
thf(127,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ TC )] :
( ! [C: TA,D: TB,E: TC] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) @ C @ ( product_Pair @ TB @ TC @ D @ E ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(100,axiom,
! [TA: $tType,A: ( list @ char ) > TA,B: TA,C: paraco414474393lle_fm > TA,D: paraco414474393lle_fm > paraco414474393lle_fm > TA,E: paraco414474393lle_fm > paraco414474393lle_fm > TA,F: paraco414474393lle_fm > paraco414474393lle_fm > TA,G: paraco414474393lle_fm,H: paraco414474393lle_fm] :
( ( paraco1246693743ase_fm @ TA @ A @ B @ C @ D @ E @ F @ ( paraco2100061555le_Con @ G @ H ) )
= ( D @ G @ H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_fm_Osimps_I39_J) ).
thf(576,plain,
! [TA: $tType,A: ( list @ char ) > TA,B: TA,C: paraco414474393lle_fm > TA,D: paraco414474393lle_fm > paraco414474393lle_fm > TA,E: paraco414474393lle_fm > paraco414474393lle_fm > TA,F: paraco414474393lle_fm > paraco414474393lle_fm > TA,G: paraco414474393lle_fm,H: paraco414474393lle_fm] :
( ( paraco1246693743ase_fm @ TA @ A @ B @ C @ D @ E @ F @ ( paraco2100061555le_Con @ G @ H ) )
= ( D @ G @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(69,axiom,
! [A: nat > nat,B: paraco415392788lle_tv,C: paraco415392788lle_tv] :
( ( ( paraco1920534163nge_tv @ A @ B )
= C )
=> ( ( accp @ ( product_prod @ ( nat > nat ) @ paraco415392788lle_tv ) @ paraco2077297190tv_rel @ ( product_Pair @ ( nat > nat ) @ paraco415392788lle_tv @ A @ B ) )
=> ( ! [D: $o] :
( ( B
= ( paraco2040174112le_Det @ D ) )
=> ( ( C
= ( paraco2040174112le_Det @ D ) )
=> ~ ( accp @ ( product_prod @ ( nat > nat ) @ paraco415392788lle_tv ) @ paraco2077297190tv_rel @ ( product_Pair @ ( nat > nat ) @ paraco415392788lle_tv @ A @ ( paraco2040174112le_Det @ D ) ) ) ) )
=> ~ ! [D: nat] :
( ( B
= ( paraco676387099_Indet @ D ) )
=> ( ( C
= ( paraco676387099_Indet @ ( A @ D ) ) )
=> ~ ( accp @ ( product_prod @ ( nat > nat ) @ paraco415392788lle_tv ) @ paraco2077297190tv_rel @ ( product_Pair @ ( nat > nat ) @ paraco415392788lle_tv @ A @ ( paraco676387099_Indet @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_change__tv_Opelims) ).
thf(359,plain,
! [A: nat > nat,B: paraco415392788lle_tv,C: paraco415392788lle_tv] :
( ( ( paraco1920534163nge_tv @ A @ B )
= C )
=> ( ( accp @ ( product_prod @ ( nat > nat ) @ paraco415392788lle_tv ) @ paraco2077297190tv_rel @ ( product_Pair @ ( nat > nat ) @ paraco415392788lle_tv @ A @ B ) )
=> ( ! [D: $o] :
( ( B
= ( paraco2040174112le_Det @ D ) )
=> ( ( C
= ( paraco2040174112le_Det @ D ) )
=> ~ ( accp @ ( product_prod @ ( nat > nat ) @ paraco415392788lle_tv ) @ paraco2077297190tv_rel @ ( product_Pair @ ( nat > nat ) @ paraco415392788lle_tv @ A @ ( paraco2040174112le_Det @ D ) ) ) ) )
=> ~ ! [D: nat] :
( ( B
= ( paraco676387099_Indet @ D ) )
=> ( ( C
= ( paraco676387099_Indet @ ( A @ D ) ) )
=> ~ ( accp @ ( product_prod @ ( nat > nat ) @ paraco415392788lle_tv ) @ paraco2077297190tv_rel @ ( product_Pair @ ( nat > nat ) @ paraco415392788lle_tv @ A @ ( paraco676387099_Indet @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(63,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_prod_Oinject) ).
thf(336,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(14,axiom,
! [TA: $tType,A: ( list @ char ) > TA,B: TA,C: paraco414474393lle_fm > TA,D: paraco414474393lle_fm > paraco414474393lle_fm > TA,E: paraco414474393lle_fm > paraco414474393lle_fm > TA,F: paraco414474393lle_fm > paraco414474393lle_fm > TA,G: paraco414474393lle_fm,H: paraco414474393lle_fm] :
( ( paraco1246693743ase_fm @ TA @ A @ B @ C @ D @ E @ F @ ( paraco1628874225le_Eql @ G @ H ) )
= ( F @ G @ H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_fm_Osimps_I41_J) ).
thf(154,plain,
! [TA: $tType,A: ( list @ char ) > TA,B: TA,C: paraco414474393lle_fm > TA,D: paraco414474393lle_fm > paraco414474393lle_fm > TA,E: paraco414474393lle_fm > paraco414474393lle_fm > TA,F: paraco414474393lle_fm > paraco414474393lle_fm > TA,G: paraco414474393lle_fm,H: paraco414474393lle_fm] :
( ( paraco1246693743ase_fm @ TA @ A @ B @ C @ D @ E @ F @ ( paraco1628874225le_Eql @ G @ H ) )
= ( F @ G @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(86,axiom,
! [A: paraco414474393lle_fm > $o,B: paraco414474393lle_fm] :
( ! [C: list @ char] : ( A @ ( paraco27778325le_Pro @ C ) )
=> ( ( A @ paraco251304083_Truth )
=> ( ! [C: paraco414474393lle_fm] :
( ( A @ C )
=> ( A @ ( paraco329115265le_Neg @ C ) ) )
=> ( ! [C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( ( A @ C )
=> ( ( A @ D )
=> ( A @ ( paraco2100061555le_Con @ C @ D ) ) ) )
=> ( ! [C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( ( A @ C )
=> ( ( A @ D )
=> ( A @ ( paraco2084319816le_Eql @ C @ D ) ) ) )
=> ( ! [C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( ( A @ C )
=> ( ( A @ D )
=> ( A @ ( paraco1628874225le_Eql @ C @ D ) ) ) )
=> ( A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_fm_Oinduct) ).
thf(517,plain,
! [A: paraco414474393lle_fm > $o,B: paraco414474393lle_fm] :
( ! [C: list @ char] : ( A @ ( paraco27778325le_Pro @ C ) )
=> ( ( A @ paraco251304083_Truth )
=> ( ! [C: paraco414474393lle_fm] :
( ( A @ C )
=> ( A @ ( paraco329115265le_Neg @ C ) ) )
=> ( ! [C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( ( A @ C )
=> ( ( A @ D )
=> ( A @ ( paraco2100061555le_Con @ C @ D ) ) ) )
=> ( ! [C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( ( A @ C )
=> ( ( A @ D )
=> ( A @ ( paraco2084319816le_Eql @ C @ D ) ) ) )
=> ( ! [C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( ( A @ C )
=> ( ( A @ D )
=> ( A @ ( paraco1628874225le_Eql @ C @ D ) ) ) )
=> ( A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(58,axiom,
! [A: list @ char,B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( ( paraco27778325le_Pro @ A )
!= ( paraco2084319816le_Eql @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_fm_Odistinct_I7_J) ).
thf(319,plain,
! [A: list @ char,B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( ( paraco27778325le_Pro @ A )
!= ( paraco2084319816le_Eql @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(53,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( product_curry @ TA @ TB @ TC )
= ( ^ [A: ( product_prod @ TA @ TB ) > TC,B: TA,C: TB] : ( A @ ( product_Pair @ TA @ TB @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_curry__conv) ).
thf(304,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( product_curry @ TA @ TB @ TC )
= ( ^ [A: ( product_prod @ TA @ TB ) > TC,B: TA,C: TB] : ( A @ ( product_Pair @ TA @ TB @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(23,axiom,
! [A: list @ char,B: list @ char] :
( ( ( paraco27778325le_Pro @ A )
= ( paraco27778325le_Pro @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_fm_Oinject_I1_J) ).
thf(186,plain,
! [A: list @ char,B: list @ char] :
( ( ( paraco27778325le_Pro @ A )
= ( paraco27778325le_Pro @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(75,axiom,
! [A: nat > nat,B: nat] :
( ( paraco1920534163nge_tv @ A @ ( paraco676387099_Indet @ B ) )
= ( paraco676387099_Indet @ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_change__tv_Osimps_I2_J) ).
thf(401,plain,
! [A: nat > nat,B: nat] :
( ( paraco1920534163nge_tv @ A @ ( paraco676387099_Indet @ B ) )
= ( paraco676387099_Indet @ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(11,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ C @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ D @ ( product_Pair @ TB @ TA @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_prod__cases5) ).
thf(139,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ C @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ D @ ( product_Pair @ TB @ TA @ E @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(98,axiom,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm] :
( paraco251304083_Truth
!= ( paraco2100061555le_Con @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_fm_Odistinct_I13_J) ).
thf(568,plain,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm] :
( paraco251304083_Truth
!= ( paraco2100061555le_Con @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(43,axiom,
! [A: paraco414474393lle_fm] :
( paraco251304083_Truth
!= ( paraco329115265le_Neg @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_fm_Odistinct_I11_J) ).
thf(272,plain,
! [A: paraco414474393lle_fm] :
( paraco251304083_Truth
!= ( paraco329115265le_Neg @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(40,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
? [B: TB,C: TA] :
( A
= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_surj__pair) ).
thf(262,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
? [B: TB,C: TA] :
( A
= ( product_Pair @ TB @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(22,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB,C: TB,D: $o] :
( ( A @ ( product_case_bool @ TB @ B @ C @ D ) )
= ( product_case_bool @ TA @ ( A @ B ) @ ( A @ C ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_bool_Ocase__distrib) ).
thf(183,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB,C: TB,D: $o] :
( ( A @ ( product_case_bool @ TB @ B @ C @ D ) )
= ( product_case_bool @ TA @ ( A @ B ) @ ( A @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(60,axiom,
! [TA: $tType,A: $o > TA,B: nat > TA,C: nat] :
( ( paraco152590079rec_tv @ TA @ A @ B @ ( paraco676387099_Indet @ C ) )
= ( B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_tv_Osimps_I8_J) ).
thf(326,plain,
! [TA: $tType,A: $o > TA,B: nat > TA,C: nat] :
( ( paraco152590079rec_tv @ TA @ A @ B @ ( paraco676387099_Indet @ C ) )
= ( B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(37,axiom,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm,C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( ( ( paraco1628874225le_Eql @ A @ B )
= ( paraco1628874225le_Eql @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_fm_Oinject_I5_J) ).
thf(242,plain,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm,C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( ( ( paraco1628874225le_Eql @ A @ B )
= ( paraco1628874225le_Eql @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(42,axiom,
! [A: product_prod @ ( nat > nat ) @ paraco415392788lle_tv] :
( ! [B: nat > nat,C: $o] :
( A
!= ( product_Pair @ ( nat > nat ) @ paraco415392788lle_tv @ B @ ( paraco2040174112le_Det @ C ) ) )
=> ~ ! [B: nat > nat,C: nat] :
( A
!= ( product_Pair @ ( nat > nat ) @ paraco415392788lle_tv @ B @ ( paraco676387099_Indet @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_change__tv_Ocases) ).
thf(268,plain,
! [A: product_prod @ ( nat > nat ) @ paraco415392788lle_tv] :
( ! [B: nat > nat,C: $o] :
( A
!= ( product_Pair @ ( nat > nat ) @ paraco415392788lle_tv @ B @ ( paraco2040174112le_Det @ C ) ) )
=> ~ ! [B: nat > nat,C: nat] :
( A
!= ( product_Pair @ ( nat > nat ) @ paraco415392788lle_tv @ B @ ( paraco676387099_Indet @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(26,axiom,
! [A: paraco415392788lle_tv] :
( ( A
!= ( paraco2040174112le_Det @ $true ) )
=> ( ( A
!= ( paraco2040174112le_Det @ $false ) )
=> ~ ! [B: nat] :
( A
!= ( paraco676387099_Indet @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_string__tv_Ocases) ).
thf(195,plain,
! [A: paraco415392788lle_tv] :
( ( A
!= ( paraco2040174112le_Det @ $true ) )
=> ( ( A
!= ( paraco2040174112le_Det @ $false ) )
=> ~ ! [B: nat] :
( A
!= ( paraco676387099_Indet @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(46,axiom,
! [TA: $tType,A: ( list @ char ) > TA,B: TA,C: paraco414474393lle_fm > TA,D: paraco414474393lle_fm > paraco414474393lle_fm > TA,E: paraco414474393lle_fm > paraco414474393lle_fm > TA,F: paraco414474393lle_fm > paraco414474393lle_fm > TA,G: paraco414474393lle_fm,H: paraco414474393lle_fm] :
( ( paraco1246693743ase_fm @ TA @ A @ B @ C @ D @ E @ F @ ( paraco2084319816le_Eql @ G @ H ) )
= ( E @ G @ H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_fm_Osimps_I40_J) ).
thf(283,plain,
! [TA: $tType,A: ( list @ char ) > TA,B: TA,C: paraco414474393lle_fm > TA,D: paraco414474393lle_fm > paraco414474393lle_fm > TA,E: paraco414474393lle_fm > paraco414474393lle_fm > TA,F: paraco414474393lle_fm > paraco414474393lle_fm > TA,G: paraco414474393lle_fm,H: paraco414474393lle_fm] :
( ( paraco1246693743ase_fm @ TA @ A @ B @ C @ D @ E @ F @ ( paraco2084319816le_Eql @ G @ H ) )
= ( E @ G @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(62,axiom,
! [A: list @ char,B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( ( paraco27778325le_Pro @ A )
!= ( paraco1628874225le_Eql @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_fm_Odistinct_I9_J) ).
thf(332,plain,
! [A: list @ char,B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( ( paraco27778325le_Pro @ A )
!= ( paraco1628874225le_Eql @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(107,axiom,
! [A: ( list @ char ) > paraco415392788lle_tv,B: list @ char] :
( ( paraco876059933e_eval @ A @ ( paraco27778325le_Pro @ B ) )
= ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_eval_Osimps_I1_J) ).
thf(596,plain,
! [A: ( list @ char ) > paraco415392788lle_tv,B: list @ char] :
( ( paraco876059933e_eval @ A @ ( paraco27778325le_Pro @ B ) )
= ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(9,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF,I: TG] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) @ F @ ( product_Pair @ TE @ ( product_prod @ TF @ TG ) @ G @ ( product_Pair @ TF @ TG @ H @ I ) ) ) ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_prod__induct7) ).
thf(131,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF,I: TG] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) @ F @ ( product_Pair @ TE @ ( product_prod @ TF @ TG ) @ G @ ( product_Pair @ TF @ TG @ H @ I ) ) ) ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(35,axiom,
! [A: $o,B: $o] :
( ( ( paraco2040174112le_Det @ A )
= ( paraco2040174112le_Det @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_tv_Oinject_I1_J) ).
thf(227,plain,
! [A: $o,B: $o] :
( ( ( paraco2040174112le_Det @ A )
= ( paraco2040174112le_Det @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(55,axiom,
! [TA: $tType,A: ( list @ char ) > TA,B: TA,C: paraco414474393lle_fm > TA,D: paraco414474393lle_fm > paraco414474393lle_fm > TA,E: paraco414474393lle_fm > paraco414474393lle_fm > TA,F: paraco414474393lle_fm > paraco414474393lle_fm > TA,G: paraco414474393lle_fm] :
( ( paraco1246693743ase_fm @ TA @ A @ B @ C @ D @ E @ F @ ( paraco329115265le_Neg @ G ) )
= ( C @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_fm_Osimps_I38_J) ).
thf(309,plain,
! [TA: $tType,A: ( list @ char ) > TA,B: TA,C: paraco414474393lle_fm > TA,D: paraco414474393lle_fm > paraco414474393lle_fm > TA,E: paraco414474393lle_fm > paraco414474393lle_fm > TA,F: paraco414474393lle_fm > paraco414474393lle_fm > TA,G: paraco414474393lle_fm] :
( ( paraco1246693743ase_fm @ TA @ A @ B @ C @ D @ E @ F @ ( paraco329115265le_Neg @ G ) )
= ( C @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(31,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( product_case_bool @ TA @ A @ B @ $true )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_old_Obool_Osimps_I3_J) ).
thf(215,plain,
! [TA: $tType,A: TA,B: TA] :
( ( product_case_bool @ TA @ A @ B @ $true )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(609,plain,
$false,
inference(e,[status(thm)],[457,218,347,555,352,170,582,276,449,202,533,550,142,301,565,174,404,110,587,157,189,421,289,316,238,121,514,397,221,265,312,206,307,292,248,117,529,561,424,429,192,407,329,461,224,388,593,124,339,537,590,212,343,398,298,166,279,180,584,286,579,391,572,159,113,245,552,323,108,394,135,426,162,548,355,145,525,557,295,199,127,576,359,336,154,517,319,304,186,401,139,568,272,262,183,326,242,268,195,283,332,596,131,227,309,215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP140^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.12/0.22 % Computer : n016.cluster.edu
% 0.12/0.22 % Model : x86_64 x86_64
% 0.12/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.22 % Memory : 8046.5625MB
% 0.12/0.22 % OS : Linux 6.8.0-71-generic
% 0.12/0.22 % CPULimit : 300
% 0.12/0.22 % WCLimit : 300
% 0.12/0.22 % DateTime : Tue Sep 29 20:04:19 UTC 2026
% 0.12/0.23 % CPUTime :
% 0.12/0.23 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.06/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.80/1.35 % [INFO] Parsing done (543ms).
% 2.80/1.37 % [INFO] Running in sequential loop mode.
% 4.08/1.78 % [INFO] eprover registered as external prover.
% 4.08/1.78 % [INFO] Scanning for conjecture ...
% 4.58/1.96 % [INFO] Found a conjecture (or negated_conjecture) and 276 axioms. Running axiom selection ...
% 4.84/2.09 % [INFO] Axiom selection finished. Selected 105 axioms (removed 171 axioms).
% 5.89/2.34 % [INFO] Problem is higher-order (TPTP THF).
% 5.89/2.36 % [INFO] Type checking passed.
% 5.89/2.36 % [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 ...
% 17.20/5.13 % External prover 'e' found a proof!
% 17.20/5.13 % [INFO] Killing All external provers ...
% 17.20/5.13 % Time passed: 4759ms (effective reasoning time: 3752ms)
% 17.20/5.13 % 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)>
% 17.20/5.13 % Axioms used in derivation (105): fact_96_fm_Odistinct_I7_J, fact_49_tv_Osimps_I8_J, fact_9_tv_Oinject_I1_J, fact_122_prod__cases6, fact_117_prod__induct6, fact_89_bool_Osplit__sel, fact_43_fm_Odistinct_I23_J, fact_100_bool_Osplit__sel__asm, fact_125_prod__cases3, fact_16_fm_Oinject_I4_J, fact_41_fm_Oinject_I5_J, fact_13_fm_Odistinct_I13_J, fact_99_fm_Osimps_I36_J, fact_50_eval__equality, fact_36_fm_Osimps_I41_J, fact_6_ih2, fact_53_string__tv_Oinduct, fact_37_fm_Osimps_I47_J, fact_26_eval__equality__simplify, fact_54_change__tv_Oinduct, fact_5_eval_Osimps_I4_J, fact_109_old_Oprod_Oinject, fact_12_fm_Osimps_I39_J, fact_129_old_Oprod_Orec, fact_24_change__int__def, fact_63_fm_Odistinct_I29_J, fact_94_fm_Odistinct_I5_J, fact_28_eval_Osimps_I2_J, fact_42_tv_Oinject_I2_J, fact_51_double__negation, fact_2_a_H, fact_101_bool_Ocase__distrib, fact_84_fm_Oexhaust, fact_126_Pair__inject, fact_87_old_Obool_Osimps_I4_J, fact_32_tv_Osimps_I5_J, fact_8_b_H_H, fact_67_eval_Osimps_I3_J, fact_60_fm_Odistinct_I11_J, help_If_1_1_T, fact_4_b_H, fact_23_transfer, fact_59_fm_Odistinct_I21_J, fact_124_prod__cases4, fact_14_fm_Osimps_I45_J, fact_52_fm_Odistinct_I19_J, fact_10_conjunction, fact_133_curry__conv, fact_61_fm_Odistinct_I27_J, fact_29_valid__def, fact_19_fm_Osimps_I40_J, fact_123_prod__cases5, fact_92_eval_Osimps_I1_J, fact_127_prod__cases, fact_93_fm_Odistinct_I3_J, fact_128_surj__pair, fact_17_fm_Osimps_I46_J, fact_30_tv_Osimps_I7_J, fact_116_prod__induct7, fact_57_tv_Oinduct, fact_98_fm_Osimps_I42_J, fact_85_props_Ocases, fact_1_a, fact_31_change__tv_Oelims, fact_18_fm_Osimps_I43_J, fact_25_valid__valid__in, fact_95_fm_Odistinct_I9_J, fact_138_change__tv_Ocases, fact_38_fm_Osimps_I38_J, help_If_3_1_T, help_If_2_1_T, fact_120_prod__induct3, fact_33_eval__negation, fact_15_fm_Odistinct_I25_J, fact_7_ih1, fact_44_tv_Osimps_I6_J, fact_88_old_Obool_Osimps_I3_J, fact_104_eval_Ocases, fact_20_fm_Osimps_I37_J, fact_39_fm_Odistinct_I17_J, fact_130_internal__case__prod__conv, fact_0_a_H_H, fact_121_prod__cases7, fact_21_fm_Odistinct_I15_J, fact_35_change__tv_Osimps_I2_J, fact_114_old_Oprod_Oinducts, fact_27_eval_Osimps_I5_J, fact_90_fm_Oinject_I1_J, fact_62_fm_Osimps_I44_J, fact_110_prod_Oinject, fact_3_fm_Oinject_I3_J, fact_119_prod__induct4, fact_40_fm_Oinject_I2_J, fact_102_bool_Ocase__eq__if, fact_97_fm_Odistinct_I1_J, fact_86_props_Oinduct, fact_118_prod__induct5, fact_22_change__tv_Osimps_I1_J, fact_11_conjunction__in, fact_58_tv_Odistinct_I1_J, fact_55_string__tv_Ocases, fact_141_change__tv_Opelims, fact_56_tv_Oexhaust, fact_83_fm_Oinduct, fact_115_old_Oprod_Oexhaust
% 17.20/5.13 % No. of inferences in proof: 214
% 17.20/5.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4759 ms resp. 3752 ms w/o parsing
% 17.98/5.32 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 17.98/5.32 % [INFO] Killing All external provers ...
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