TSTP Solution File: COL088-2 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : COL088-2 : TPTP v8.1.2. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n008.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 : Tue May 7 07:29:31 EDT 2024
% Result : Unsatisfiable 7.05s 2.51s
% Output : Refutation 7.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 272
% Syntax : Number of formulae : 459 ( 53 unt; 86 typ; 0 def)
% Number of atoms : 801 ( 142 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 3662 ( 406 ~; 428 |; 0 &;2828 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 165 ( 165 >; 0 *; 0 +; 0 <<)
% Number of symbols : 88 ( 86 usr; 11 con; 0-8 aty)
% Number of variables : 1088 ( 0 ^1088 !; 0 ?;1088 :)
% Comments :
%------------------------------------------------------------------------------
thf(member_type,type,
member: $i > $i > $o ).
thf(pair_type,type,
pair: $i > $i > $i ).
thf(comb_app_type,type,
comb_app: $i > $i > $i ).
thf(p_type,type,
p: $i ).
thf(r_type,type,
r: $i ).
thf(z_type,type,
z: $i ).
thf(rtrancl_type,type,
rtrancl: $i > $i ).
thf(contract_type,type,
contract: $i ).
thf(inl_type,type,
inl: $i > $i ).
thf(inr_type,type,
inr: $i > $i ).
thf(cons_type,type,
cons: $i > $i > $i ).
thf(eptset_type,type,
eptset: $i ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(qPair_type,type,
qPair: $i > $i > $i ).
thf(le_type,type,
le: $i > $i > $o ).
thf(ord_type,type,
ord: $i > $o ).
thf(qInl_type,type,
qInl: $i > $i ).
thf(qInr_type,type,
qInr: $i > $i ).
thf(card_type,type,
card: $i > $o ).
thf(card_Union_sk1_type,type,
card_Union_sk1: $i > $i ).
thf(union_type,type,
union: $i > $i ).
thf(succ_type,type,
succ: $i > $i ).
thf(combK_type,type,
combK: $i ).
thf(combS_type,type,
combS: $i ).
thf(order_Union_sk1_type,type,
order_Union_sk1: $i > $i ).
thf(rmultE_c2_type,type,
rmultE_c2: $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(lt_type,type,
lt: $i > $i > $o ).
thf(order_Inter_sk1_type,type,
order_Inter_sk1: $i > $i ).
thf(inter_type,type,
inter: $i > $i ).
thf(un_type,type,
un: $i > $i > $i ).
thf(comp_type,type,
comp: $i > $i > $i ).
thf(compE_sk2_type,type,
compE_sk2: $i > $i > $i > $i ).
thf(compE_sk3_type,type,
compE_sk3: $i > $i > $i > $i ).
thf(ap_contractE_c4_type,type,
ap_contractE_c4: $i > $i > $i > $o ).
thf(comb_type,type,
comb: $i ).
thf(subsetD_sk1_type,type,
subsetD_sk1: $i > $i > $i > $i ).
thf(rmultE_c1_type,type,
rmultE_c1: $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(int_type,type,
int: $i > $i > $i ).
thf(qsum_type,type,
qsum: $i > $i > $i ).
thf(qsumE_sk1_type,type,
qsumE_sk1: $i > $i > $i > $i ).
thf(qsumE_sk2_type,type,
qsumE_sk2: $i > $i > $i > $i ).
thf(id_type,type,
id: $i > $i ).
thf(idE_sk1_type,type,
idE_sk1: $i > $i > $i ).
thf(converse_type,type,
converse: $i > $i ).
thf(converseE_sk2_type,type,
converseE_sk2: $i > $i > $i ).
thf(converseE_sk1_type,type,
converseE_sk1: $i > $i > $i ).
thf(disjsum_type,type,
disjsum: $i > $i > $i ).
thf(vimage_type,type,
vimage: $i > $i > $i ).
thf(vimageE_sk1_type,type,
vimageE_sk1: $i > $i > $i > $i ).
thf(pow_type,type,
pow: $i > $i ).
thf(radd_type,type,
radd: $i > $i > $i > $i > $i ).
thf(field_type,type,
field: $i > $i ).
thf(fieldE_sk1_type,type,
fieldE_sk1: $i > $i > $i ).
thf(fieldE_sk2_type,type,
fieldE_sk2: $i > $i > $i ).
thf(cons_subsetE_sk1_type,type,
cons_subsetE_sk1: $i > $i > $i > $i ).
thf(image_type,type,
image: $i > $i > $i ).
thf(imageE_sk1_type,type,
imageE_sk1: $i > $i > $i > $i ).
thf(sumE_sk1_type,type,
sumE_sk1: $i > $i > $i > $i ).
thf(sumE_sk2_type,type,
sumE_sk2: $i > $i > $i > $i ).
thf(qconverse_type,type,
qconverse: $i > $i ).
thf(ap_contractE_c3_type,type,
ap_contractE_c3: $i > $i > $i > $o ).
thf(ap_contractE_sk2q_type,type,
ap_contractE_sk2q: $i > $i > $i > $i ).
thf(ap_contractE_sk3q_type,type,
ap_contractE_sk3q: $i > $i > $i > $i ).
thf(subsetI_sk1_type,type,
subsetI_sk1: $i > $i > $i ).
thf(memrel_type,type,
memrel: $i > $i ).
thf(diff_type,type,
diff: $i > $i > $i ).
thf(ap_contractE_c2_type,type,
ap_contractE_c2: $i > $i > $i > $o ).
thf(ap_contractE_sk1p_type,type,
ap_contractE_sk1p: $i > $i > $i > $i ).
thf(ap_contractE_sk1q_type,type,
ap_contractE_sk1q: $i > $i > $i > $i ).
thf(interI_sk1_type,type,
interI_sk1: $i > $i > $i ).
thf(trans_type,type,
trans: $i > $o ).
thf(rmult_type,type,
rmult: $i > $i > $i > $i > $i ).
thf(cons_subsetI_sk1_type,type,
cons_subsetI_sk1: $i > $i > $i > $i ).
thf(compE_sk1_type,type,
compE_sk1: $i > $i > $i > $i ).
thf(ap_contractE_c1_type,type,
ap_contractE_c1: $i > $i > $i > $o ).
thf(y_type,type,
y: $i ).
thf(powI_sk1_type,type,
powI_sk1: $i > $i > $i ).
thf(domain_type,type,
domain: $i > $i ).
thf(domainE_sk1_type,type,
domainE_sk1: $i > $i > $i ).
thf(fin_type,type,
fin: $i > $i ).
thf(qconverseE_sk1_type,type,
qconverseE_sk1: $i > $i > $i ).
thf(qconverseE_sk2_type,type,
qconverseE_sk2: $i > $i > $i ).
thf(nat_type,type,
nat: $i ).
thf(unionE_sk1_type,type,
unionE_sk1: $i > $i > $i ).
thf(range_type,type,
range: $i > $i ).
thf(rangeE_sk1_type,type,
rangeE_sk1: $i > $i > $i ).
thf(123,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( comp @ B @ C ) )
| ( A
= ( pair @ ( compE_sk1 @ A @ B @ C ) @ ( compE_sk3 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause79) ).
thf(479,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( comp @ B @ C ) )
| ( A
= ( pair @ ( compE_sk1 @ A @ B @ C ) @ ( compE_sk3 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(63,axiom,
! [B: $i,A: $i] :
( ( pair @ A @ B )
!= eptset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause127) ).
thf(347,plain,
! [B: $i,A: $i] :
( ( pair @ A @ B )
!= eptset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(56,axiom,
! [A: $i] : ( member @ A @ ( cons @ A @ eptset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause14) ).
thf(333,plain,
! [A: $i] : ( member @ A @ ( cons @ A @ eptset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(141,axiom,
! [B: $i,A: $i] :
( ( A != B )
| ( member @ A @ ( succ @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause13) ).
thf(518,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( member @ A @ ( succ @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(157,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( succ @ B ) )
| ( A = B )
| ( member @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause110) ).
thf(555,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( succ @ B ) )
| ( A = B )
| ( member @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(108,axiom,
member @ ( pair @ y @ z ) @ contract,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_reduce1_2h4) ).
thf(449,plain,
member @ ( pair @ y @ z ) @ contract,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(77,axiom,
! [C: $i,B: $i,A: $i] :
( ( member @ ( cons_subsetE_sk1 @ A @ B @ C ) @ ( cons @ A @ B ) )
| ( member @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause99) ).
thf(379,plain,
! [C: $i,B: $i,A: $i] :
( ( member @ ( cons_subsetE_sk1 @ A @ B @ C ) @ ( cons @ A @ B ) )
| ( member @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(184,axiom,
! [B: $i,A: $i] :
( ~ ( member @ ( comb_app @ A @ B ) @ comb )
| ( member @ A @ comb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_E1) ).
thf(614,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( comb_app @ A @ B ) @ comb )
| ( member @ A @ comb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( qInl @ A )
!= ( qInr @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause38) ).
thf(217,plain,
! [B: $i,A: $i] :
( ( qInl @ A )
!= ( qInr @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(31,axiom,
! [A: $i] :
( ~ ( le @ eptset @ ( succ @ A ) )
| ( ord @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause72) ).
thf(276,plain,
! [A: $i] :
( ~ ( le @ eptset @ ( succ @ A ) )
| ( ord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( qPair @ A @ B )
!= ( qPair @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause48) ).
thf(202,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( qPair @ A @ B )
!= ( qPair @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(175,axiom,
member @ p @ comb,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_reduce1_2h2) ).
thf(597,plain,
member @ p @ comb,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(80,axiom,
! [A: $i] :
( ( member @ ( order_Union_sk1 @ A ) @ A )
| ( ord @ ( union @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause31) ).
thf(385,plain,
! [A: $i] :
( ( member @ ( order_Union_sk1 @ A ) @ A )
| ( ord @ ( union @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(132,axiom,
! [B: $i,A: $i] : ( member @ A @ ( cons @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause1) ).
thf(500,plain,
! [B: $i,A: $i] : ( member @ A @ ( cons @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(150,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ A @ C )
| ( member @ A @ ( diff @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause17) ).
thf(538,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ A @ C )
| ( member @ A @ ( diff @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(36,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c4 @ A @ B @ C )
| ( member @ A @ comb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_contractE14) ).
thf(288,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c4 @ A @ B @ C )
| ( member @ A @ comb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(42,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( id @ B ) )
| ( member @ ( idE_sk1 @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause82) ).
thf(301,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( id @ B ) )
| ( member @ ( idE_sk1 @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(50,axiom,
! [B: $i,A: $i] :
( ( pair @ A @ B )
!= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause129) ).
thf(320,plain,
! [B: $i,A: $i] :
( ( pair @ A @ B )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(82,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ A @ B ) @ ( memrel @ C ) )
| ( member @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause74) ).
thf(389,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ A @ B ) @ ( memrel @ C ) )
| ( member @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(171,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( range @ B ) )
| ( member @ ( pair @ ( rangeE_sk1 @ A @ B ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause97) ).
thf(587,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( range @ B ) )
| ( member @ ( pair @ ( rangeE_sk1 @ A @ B ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( ( cons @ A @ eptset )
!= ( cons @ B @ eptset ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause108) ).
thf(196,plain,
! [B: $i,A: $i] :
( ( ( cons @ A @ eptset )
!= ( cons @ B @ eptset ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(152,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( qsum @ B @ C ) )
| ( A
= ( qInl @ ( qsumE_sk1 @ A @ B @ C ) ) )
| ( member @ ( qsumE_sk2 @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause43) ).
thf(542,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( qsum @ B @ C ) )
| ( A
= ( qInl @ ( qsumE_sk1 @ A @ B @ C ) ) )
| ( member @ ( qsumE_sk2 @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(114,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ ( cons @ A @ B ) @ C )
| ( member @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause102_1) ).
thf(460,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ ( cons @ A @ B ) @ C )
| ( member @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( inl @ A )
!= ( inr @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause85) ).
thf(189,plain,
! [B: $i,A: $i] :
( ( inl @ A )
!= ( inr @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(180,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ~ ( member @ C @ ( cons @ A @ D ) )
| ( member @ ( cons_subsetI_sk1 @ A @ D @ B ) @ D )
| ( member @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause8) ).
thf(606,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ~ ( member @ C @ ( cons @ A @ D ) )
| ( member @ ( cons_subsetI_sk1 @ A @ D @ B ) @ D )
| ( member @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(93,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( un @ B @ C ) )
| ( member @ A @ B )
| ( member @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause117) ).
thf(416,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( un @ B @ C ) )
| ( member @ A @ B )
| ( member @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(52,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ ( cons_subsetE_sk1 @ C @ B @ D ) @ ( cons @ C @ B ) )
| ( member @ A @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause101) ).
thf(325,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ ( cons_subsetE_sk1 @ C @ B @ D ) @ ( cons @ C @ B ) )
| ( member @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(48,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
~ ( member @ ( pair @ ( inr @ A ) @ ( inl @ B ) ) @ ( radd @ C @ D @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause62) ).
thf(316,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
~ ( member @ ( pair @ ( inr @ A ) @ ( inl @ B ) ) @ ( radd @ C @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(121,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ A @ B ) @ C )
| ( member @ ( pair @ B @ A ) @ ( converse @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause10) ).
thf(475,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ A @ B ) @ C )
| ( member @ ( pair @ B @ A ) @ ( converse @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(173,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ A @ B ) @ ( memrel @ C ) )
| ( member @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause73) ).
thf(591,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ A @ B ) @ ( memrel @ C ) )
| ( member @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(105,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rmultE_c2 @ A @ B @ C @ D @ E @ F @ G @ H )
| ( member @ B @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause60) ).
thf(443,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rmultE_c2 @ A @ B @ C @ D @ E @ F @ G @ H )
| ( member @ B @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause134) ).
thf(211,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(139,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ A @ ( un @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause20) ).
thf(514,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ A @ ( un @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(165,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c3 @ A @ B @ C )
| ( member @ B @ comb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_contractE11) ).
thf(574,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c3 @ A @ B @ C )
| ( member @ B @ comb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(65,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( diff @ B @ C ) )
| ~ ( member @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause114) ).
thf(353,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( diff @ B @ C ) )
| ~ ( member @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(33,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ ( cons @ A @ B ) @ C )
| ( subset @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause102_2) ).
thf(280,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ ( cons @ A @ B ) @ C )
| ( subset @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(111,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ A @ B ) @ C )
| ( member @ A @ ( field @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause126) ).
thf(453,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ A @ B ) @ C )
| ( member @ A @ ( field @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(85,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( pair @ A @ B )
!= ( pair @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause107) ).
thf(396,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( pair @ A @ B )
!= ( pair @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(136,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rmultE_c1 @ A @ B @ C @ D @ E @ F @ G @ H )
| ( member @ C @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause54) ).
thf(507,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rmultE_c1 @ A @ B @ C @ D @ E @ F @ G @ H )
| ( member @ C @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(46,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( vimage @ B @ C ) )
| ( member @ ( pair @ A @ ( vimageE_sk1 @ A @ B @ C ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause92) ).
thf(312,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( vimage @ B @ C ) )
| ( member @ ( pair @ A @ ( vimageE_sk1 @ A @ B @ C ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( inr @ A )
!= ( inl @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause84) ).
thf(206,plain,
! [B: $i,A: $i] :
( ( inr @ A )
!= ( inl @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(44,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( converse @ B ) )
| ( A
= ( pair @ ( converseE_sk2 @ A @ B ) @ ( converseE_sk1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause103) ).
thf(307,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( converse @ B ) )
| ( A
= ( pair @ ( converseE_sk2 @ A @ B ) @ ( converseE_sk1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(38,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rmultE_c1 @ A @ B @ C @ D @ E @ F @ G @ H )
| ( member @ B @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause55) ).
thf(292,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rmultE_c1 @ A @ B @ C @ D @ E @ F @ G @ H )
| ( member @ B @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ( ( inl @ A )
!= ( inl @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause87) ).
thf(233,plain,
! [B: $i,A: $i] :
( ( ( inl @ A )
!= ( inl @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(21,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rmultE_c2 @ A @ B @ C @ D @ E @ F @ G @ H )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause59) ).
thf(248,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rmultE_c2 @ A @ B @ C @ D @ E @ F @ G @ H )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(27,axiom,
! [B: $i,A: $i] :
( ~ ( le @ ( succ @ A ) @ B )
| ( lt @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause71) ).
thf(270,plain,
! [B: $i,A: $i] :
( ~ ( le @ ( succ @ A ) @ B )
| ( lt @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(78,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( qsum @ B @ C ) )
| ( member @ ( qsumE_sk1 @ A @ B @ C ) @ B )
| ( member @ ( qsumE_sk2 @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause41) ).
thf(381,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( qsum @ B @ C ) )
| ( member @ ( qsumE_sk1 @ A @ B @ C ) @ B )
| ( member @ ( qsumE_sk2 @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(148,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( inter @ B ) )
| ~ ( member @ C @ B )
| ( member @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause122) ).
thf(534,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( inter @ B ) )
| ~ ( member @ C @ B )
| ( member @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(138,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ ( comb_app @ A @ B ) @ C ) @ contract )
| ( ap_contractE_c1 @ A @ B @ C )
| ( ap_contractE_c2 @ A @ B @ C )
| ( ap_contractE_c3 @ A @ B @ C )
| ( ap_contractE_c4 @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_contractE1) ).
thf(512,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ ( comb_app @ A @ B ) @ C ) @ contract )
| ( ap_contractE_c1 @ A @ B @ C )
| ( ap_contractE_c2 @ A @ B @ C )
| ( ap_contractE_c3 @ A @ B @ C )
| ( ap_contractE_c4 @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(104,axiom,
! [B: $i,A: $i] :
( ( A != eptset )
| ~ ( member @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause121) ).
thf(439,plain,
! [B: $i,A: $i] :
( ( A != eptset )
| ~ ( member @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( A != B )
| ( ( inl @ A )
= ( inl @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause5) ).
thf(220,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( ( inl @ A )
= ( inl @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(71,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ~ ( subset @ C @ B )
| ( subset @ ( cons @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause9_1) ).
thf(366,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ~ ( subset @ C @ B )
| ( subset @ ( cons @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(57,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c3 @ A @ B @ C )
| ( C
= ( comb_app @ ( ap_contractE_sk2q @ A @ B @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_contractE12) ).
thf(334,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c3 @ A @ B @ C )
| ( C
= ( comb_app @ ( ap_contractE_sk2q @ A @ B @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(176,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ ( inr @ A ) @ ( inr @ B ) ) @ ( radd @ C @ D @ E @ F ) )
| ( member @ A @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause63) ).
thf(598,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ ( inr @ A ) @ ( inr @ B ) ) @ ( radd @ C @ D @ E @ F ) )
| ( member @ A @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(99,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c3 @ A @ B @ C )
| ( member @ ( pair @ A @ ( ap_contractE_sk2q @ A @ B @ C ) ) @ contract ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_contractE10) ).
thf(429,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c3 @ A @ B @ C )
| ( member @ ( pair @ A @ ( ap_contractE_sk2q @ A @ B @ C ) ) @ contract ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(30,axiom,
! [A: $i] : ( subset @ eptset @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause136) ).
thf(275,plain,
! [A: $i] : ( subset @ eptset @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( ( inr @ A )
!= ( inr @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause86) ).
thf(192,plain,
! [B: $i,A: $i] :
( ( ( inr @ A )
!= ( inr @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(89,axiom,
! [B: $i,A: $i] :
( ( pair @ A @ B )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause128) ).
thf(407,plain,
! [B: $i,A: $i] :
( ( pair @ A @ B )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(117,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( cons_subsetE_sk1 @ A @ B @ C ) @ C )
| ( member @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause100) ).
thf(467,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( cons_subsetE_sk1 @ A @ B @ C ) @ C )
| ( member @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(102,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ A @ ( cons @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause2) ).
thf(435,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ A @ ( cons @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(54,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( disjsum @ B @ C ) )
| ( member @ ( sumE_sk1 @ A @ B @ C ) @ B )
| ( member @ ( sumE_sk2 @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause88) ).
thf(329,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( disjsum @ B @ C ) )
| ( member @ ( sumE_sk1 @ A @ B @ C ) @ B )
| ( member @ ( sumE_sk2 @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(129,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( diff @ B @ C ) )
| ( member @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause113) ).
thf(493,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( diff @ B @ C ) )
| ( member @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(155,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( id @ B ) )
| ( A
= ( pair @ ( idE_sk1 @ A @ B ) @ ( idE_sk1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause83) ).
thf(551,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( id @ B ) )
| ( A
= ( pair @ ( idE_sk1 @ A @ B ) @ ( idE_sk1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(13,axiom,
! [A: $i] :
( ~ ( card @ ( card_Union_sk1 @ A ) )
| ( card @ ( union @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause26) ).
thf(224,plain,
! [A: $i] :
( ~ ( card @ ( card_Union_sk1 @ A ) )
| ( card @ ( union @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( ( succ @ A )
!= ( succ @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause109) ).
thf(229,plain,
! [B: $i,A: $i] :
( ( ( succ @ A )
!= ( succ @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(162,axiom,
! [B: $i,A: $i] :
( ~ ( member @ ( pair @ A @ B ) @ contract )
| ( member @ B @ comb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contract_combD2) ).
thf(566,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( pair @ A @ B ) @ contract )
| ( member @ B @ comb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(169,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ A @ ( cons @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause15) ).
thf(583,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ A @ ( cons @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(142,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( fin @ B ) )
| ( member @ ( int @ A @ C ) @ ( fin @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause27) ).
thf(522,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( fin @ B ) )
| ( member @ ( int @ A @ C ) @ ( fin @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(167,axiom,
! [B: $i,A: $i] :
( combK
!= ( comb_app @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_app) ).
thf(578,plain,
! [B: $i,A: $i] :
( combK
!= ( comb_app @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(87,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ ( pair @ A @ B ) @ ( pair @ C @ D ) ) @ ( rmult @ E @ F @ G @ H ) )
| ( rmultE_c1 @ A @ B @ C @ D @ E @ F @ G @ H )
| ( rmultE_c2 @ A @ B @ C @ D @ E @ F @ G @ H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause51) ).
thf(403,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ ( pair @ A @ B ) @ ( pair @ C @ D ) ) @ ( rmult @ E @ F @ G @ H ) )
| ( rmultE_c1 @ A @ B @ C @ D @ E @ F @ G @ H )
| ( rmultE_c2 @ A @ B @ C @ D @ E @ F @ G @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(174,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( pair @ A @ B )
!= ( pair @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause106) ).
thf(593,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( pair @ A @ B )
!= ( pair @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(182,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rmultE_c2 @ A @ B @ C @ D @ E @ F @ G @ H )
| ( member @ ( pair @ B @ D ) @ H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause57) ).
thf(610,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rmultE_c2 @ A @ B @ C @ D @ E @ F @ G @ H )
| ( member @ ( pair @ B @ D ) @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(95,axiom,
! [B: $i,A: $i] :
( ~ ( member @ ( comb_app @ A @ B ) @ comb )
| ( member @ B @ comb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_E2) ).
thf(420,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( comb_app @ A @ B ) @ comb )
| ( member @ B @ comb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(119,axiom,
! [B: $i,A: $i] :
( ( member @ ( powI_sk1 @ A @ B ) @ A )
| ( member @ A @ ( pow @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause21) ).
thf(471,plain,
! [B: $i,A: $i] :
( ( member @ ( powI_sk1 @ A @ B ) @ A )
| ( member @ A @ ( pow @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(59,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rmultE_c1 @ A @ B @ C @ D @ E @ F @ G @ H )
| ( member @ ( pair @ A @ C ) @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause52) ).
thf(339,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rmultE_c1 @ A @ B @ C @ D @ E @ F @ G @ H )
| ( member @ ( pair @ A @ C ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(156,axiom,
member @ ( pair @ ( comb_app @ p @ r ) @ ( comb_app @ y @ r ) ) @ ( rtrancl @ contract ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_reduce1_2h5) ).
thf(554,plain,
member @ ( pair @ ( comb_app @ p @ r ) @ ( comb_app @ y @ r ) ) @ ( rtrancl @ contract ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(144,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c1 @ A @ B @ C )
| ( member @ C @ comb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_contractE2) ).
thf(526,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c1 @ A @ B @ C )
| ( member @ C @ comb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(127,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ comb )
| ~ ( member @ B @ comb )
| ~ ( member @ ( pair @ A @ C ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ A ) @ B ) @ C ) @ ( rtrancl @ contract ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reduction_rls_1) ).
thf(489,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ comb )
| ~ ( member @ B @ comb )
| ~ ( member @ ( pair @ A @ C ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ A ) @ B ) @ C ) @ ( rtrancl @ contract ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(84,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( qsum @ B @ C ) )
| ( member @ ( qsumE_sk1 @ A @ B @ C ) @ B )
| ( A
= ( qInr @ ( qsumE_sk2 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause42) ).
thf(393,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( qsum @ B @ C ) )
| ( member @ ( qsumE_sk1 @ A @ B @ C ) @ B )
| ( A
= ( qInr @ ( qsumE_sk2 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(113,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c1 @ A @ B @ C )
| ( A
= ( comb_app @ combK @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_contractE4) ).
thf(457,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c1 @ A @ B @ C )
| ( A
= ( comb_app @ combK @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(74,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ A @ B ) @ contract )
| ~ ( member @ C @ comb )
| ~ ( member @ ( pair @ ( comb_app @ B @ C ) @ D ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ A @ C ) @ D ) @ ( rtrancl @ contract ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reduction_rls_3) ).
thf(371,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ A @ B ) @ contract )
| ~ ( member @ C @ comb )
| ~ ( member @ ( pair @ ( comb_app @ B @ C ) @ D ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ A @ C ) @ D ) @ ( rtrancl @ contract ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(134,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( domain @ B ) )
| ( member @ ( pair @ A @ ( domainE_sk1 @ A @ B ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause98) ).
thf(503,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( domain @ B ) )
| ( member @ ( pair @ A @ ( domainE_sk1 @ A @ B ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(19,axiom,
! [A: $i] :
( ~ ( ord @ ( succ @ A ) )
| ( ord @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause78) ).
thf(244,plain,
! [A: $i] :
( ~ ( ord @ ( succ @ A ) )
| ( ord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(26,axiom,
! [B: $i,A: $i] :
( ( A != B )
| ( ( cons @ A @ eptset )
= ( cons @ B @ eptset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause11) ).
thf(266,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( ( cons @ A @ eptset )
= ( cons @ B @ eptset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(68,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ~ ( member @ A @ C )
| ( member @ A @ ( int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause18) ).
thf(360,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ~ ( member @ A @ C )
| ( member @ A @ ( int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(158,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ A @ B ) @ C )
| ( member @ B @ ( field @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause125) ).
thf(558,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ A @ B ) @ C )
| ( member @ B @ ( field @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(146,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( fin @ B ) )
| ( member @ ( int @ C @ A ) @ ( fin @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause28) ).
thf(530,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( fin @ B ) )
| ( member @ ( int @ C @ A ) @ ( fin @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(61,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ A @ B ) @ ( memrel @ C ) )
| ( member @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause75) ).
thf(343,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ A @ B ) @ ( memrel @ C ) )
| ( member @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(17,axiom,
combK != combS,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_s) ).
thf(237,plain,
combK != combS,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(41,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( qsum @ B @ C ) )
| ( A
= ( qInl @ ( qsumE_sk1 @ A @ B @ C ) ) )
| ( A
= ( qInr @ ( qsumE_sk2 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause44) ).
thf(298,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( qsum @ B @ C ) )
| ( A
= ( qInl @ ( qsumE_sk1 @ A @ B @ C ) ) )
| ( A
= ( qInr @ ( qsumE_sk2 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(91,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ ( inl @ A ) @ ( inl @ B ) ) @ ( radd @ C @ D @ E @ F ) )
| ( member @ ( pair @ A @ B ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause68) ).
thf(412,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ ( inl @ A ) @ ( inl @ B ) ) @ ( radd @ C @ D @ E @ F ) )
| ( member @ ( pair @ A @ B ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(186,axiom,
member @ combK @ comb,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',comb_intros1) ).
thf(618,plain,
member @ combK @ comb,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(97,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ ( inr @ A ) @ ( inr @ B ) ) @ ( radd @ C @ D @ E @ F ) )
| ( member @ B @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause64) ).
thf(425,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ ( inr @ A ) @ ( inr @ B ) ) @ ( radd @ C @ D @ E @ F ) )
| ( member @ B @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(40,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ comb )
| ~ ( member @ B @ comb )
| ( member @ ( comb_app @ A @ B ) @ comb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',comb_intros3) ).
thf(296,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ comb )
| ~ ( member @ B @ comb )
| ( member @ ( comb_app @ A @ B ) @ comb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(76,axiom,
! [C: $i,B: $i,A: $i] :
( ( A != B )
| ( member @ A @ ( cons @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause16) ).
thf(375,plain,
! [C: $i,B: $i,A: $i] :
( ( A != B )
| ( member @ A @ ( cons @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(178,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( cons @ B @ eptset ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause111) ).
thf(601,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( cons @ B @ eptset ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(160,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rmultE_c1 @ A @ B @ C @ D @ E @ F @ G @ H )
| ( member @ D @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause56) ).
thf(562,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rmultE_c1 @ A @ B @ C @ D @ E @ F @ G @ H )
| ( member @ D @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(35,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( comp @ B @ C ) )
| ( member @ ( pair @ ( compE_sk2 @ A @ B @ C ) @ ( compE_sk3 @ A @ B @ C ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause81) ).
thf(286,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( comp @ B @ C ) )
| ( member @ ( pair @ ( compE_sk2 @ A @ B @ C ) @ ( compE_sk3 @ A @ B @ C ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(153,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( comb_app @ A @ B )
!= ( comb_app @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',app_app1) ).
thf(545,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( comb_app @ A @ B )
!= ( comb_app @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(83,axiom,
! [A: $i] :
( ( member @ ( order_Inter_sk1 @ A ) @ A )
| ( ord @ ( inter @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause29) ).
thf(391,plain,
! [A: $i] :
( ( member @ ( order_Inter_sk1 @ A ) @ A )
| ( ord @ ( inter @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(106,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ ( inl @ A ) @ ( inr @ B ) ) @ ( radd @ C @ D @ E @ F ) )
| ( member @ B @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause70) ).
thf(445,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ ( inl @ A ) @ ( inr @ B ) ) @ ( radd @ C @ D @ E @ F ) )
| ( member @ B @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(131,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ ( interI_sk1 @ C @ B ) @ B )
| ( member @ C @ ( inter @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause23) ).
thf(498,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ ( interI_sk1 @ C @ B ) @ B )
| ( member @ C @ ( inter @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(64,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( cons @ B @ C ) )
| ( A = B )
| ( member @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause112) ).
thf(350,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( cons @ B @ C ) )
| ( A = B )
| ( member @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(151,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ A @ B ) @ C )
| ~ ( member @ A @ D )
| ( member @ B @ ( image @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause36) ).
thf(540,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ A @ B ) @ C )
| ~ ( member @ A @ D )
| ( member @ B @ ( image @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(179,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( union @ B ) )
| ( member @ ( unionE_sk1 @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause120) ).
thf(604,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( union @ B ) )
| ( member @ ( unionE_sk1 @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(1,negated_conjecture,
~ ( member @ ( pair @ ( comb_app @ p @ r ) @ ( comb_app @ z @ r ) ) @ ( rtrancl @ contract ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_reduce1_2c1) ).
thf(187,plain,
~ ( member @ ( pair @ ( comb_app @ p @ r ) @ ( comb_app @ z @ r ) ) @ ( rtrancl @ contract ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(49,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( field @ B ) )
| ( member @ ( pair @ A @ ( fieldE_sk1 @ A @ B ) ) @ B )
| ( member @ ( pair @ ( fieldE_sk2 @ A @ B ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause96) ).
thf(318,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( field @ B ) )
| ( member @ ( pair @ A @ ( fieldE_sk1 @ A @ B ) ) @ B )
| ( member @ ( pair @ ( fieldE_sk2 @ A @ B ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(137,axiom,
! [B: $i,A: $i] :
( combS
!= ( comb_app @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_app) ).
thf(509,plain,
! [B: $i,A: $i] :
( combS
!= ( comb_app @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(69,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( interI_sk1 @ A @ B ) )
| ~ ( member @ C @ B )
| ( member @ A @ ( inter @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause24) ).
thf(362,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( interI_sk1 @ A @ B ) )
| ~ ( member @ C @ B )
| ( member @ A @ ( inter @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(110,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ A @ ( succ @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause12) ).
thf(451,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ A @ ( succ @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(185,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( int @ B @ C ) )
| ( member @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause115) ).
thf(616,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( int @ B @ C ) )
| ( member @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(43,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A != B )
| ( C != D )
| ( ( comb_app @ A @ C )
= ( comb_app @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',app_app3) ).
thf(303,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A != B )
| ( C != D )
| ( ( comb_app @ A @ C )
= ( comb_app @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(122,axiom,
! [B: $i,A: $i] :
( ~ ( member @ ( powI_sk1 @ A @ B ) @ B )
| ( member @ A @ ( pow @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause22) ).
thf(477,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( powI_sk1 @ A @ B ) @ B )
| ( member @ A @ ( pow @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(81,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ A @ ( un @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause19) ).
thf(387,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ A @ ( un @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(62,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rmultE_c2 @ A @ B @ C @ D @ E @ F @ G @ H )
| ( member @ D @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause61) ).
thf(345,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rmultE_c2 @ A @ B @ C @ D @ E @ F @ G @ H )
| ( member @ D @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(51,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( member @ C @ A )
| ( member @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetD) ).
thf(323,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( member @ C @ A )
| ( member @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( A != B )
| ( subset @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause150) ).
thf(213,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( subset @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(115,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( disjsum @ B @ C ) )
| ( member @ ( sumE_sk1 @ A @ B @ C ) @ B )
| ( A
= ( inr @ ( sumE_sk2 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause89) ).
thf(462,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( disjsum @ B @ C ) )
| ( member @ ( sumE_sk1 @ A @ B @ C ) @ B )
| ( A
= ( inr @ ( sumE_sk2 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ( ( qInr @ A )
!= ( qInr @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause39) ).
thf(240,plain,
! [B: $i,A: $i] :
( ( ( qInr @ A )
!= ( qInr @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(22,axiom,
! [B: $i,A: $i] :
( ( A != B )
| ( ( inr @ A )
= ( inr @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause4) ).
thf(251,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( ( inr @ A )
= ( inr @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(32,axiom,
! [B: $i,A: $i] :
( ~ ( ord @ A )
| ~ ( ord @ B )
| ( ord @ ( un @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause33) ).
thf(278,plain,
! [B: $i,A: $i] :
( ~ ( ord @ A )
| ~ ( ord @ B )
| ( ord @ ( un @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(112,axiom,
! [A: $i] :
( ( member @ ( card_Union_sk1 @ A ) @ A )
| ( card @ ( union @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause25) ).
thf(455,plain,
! [A: $i] :
( ( member @ ( card_Union_sk1 @ A ) @ A )
| ( card @ ( union @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(181,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( converse @ B ) )
| ( member @ ( pair @ ( converseE_sk1 @ A @ B ) @ ( converseE_sk2 @ A @ B ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause104) ).
thf(608,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( converse @ B ) )
| ( member @ ( pair @ ( converseE_sk1 @ A @ B ) @ ( converseE_sk2 @ A @ B ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(14,axiom,
! [A: $i] :
( ~ ( le @ A @ eptset )
| ( A = eptset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause76) ).
thf(226,plain,
! [A: $i] :
( ~ ( le @ A @ eptset )
| ( A = eptset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(135,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ ( inr @ A ) @ ( inr @ B ) ) @ ( radd @ C @ D @ E @ F ) )
| ( member @ ( pair @ A @ B ) @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause65) ).
thf(505,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ ( inr @ A ) @ ( inr @ B ) ) @ ( radd @ C @ D @ E @ F ) )
| ( member @ ( pair @ A @ B ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(100,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( comp @ B @ C ) )
| ( member @ ( pair @ ( compE_sk1 @ A @ B @ C ) @ ( compE_sk2 @ A @ B @ C ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause80) ).
thf(431,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( comp @ B @ C ) )
| ( member @ ( pair @ ( compE_sk1 @ A @ B @ C ) @ ( compE_sk2 @ A @ B @ C ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(120,axiom,
! [B: $i,A: $i] :
( ( member @ ( subsetI_sk1 @ A @ B ) @ A )
| ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause131) ).
thf(473,plain,
! [B: $i,A: $i] :
( ( member @ ( subsetI_sk1 @ A @ B ) @ A )
| ( subset @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(172,axiom,
! [A: $i] :
( ~ ( member @ ( succ @ A ) @ nat )
| ( member @ A @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause50) ).
thf(589,plain,
! [A: $i] :
( ~ ( member @ ( succ @ A ) @ nat )
| ( member @ A @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(23,axiom,
! [B: $i,A: $i] :
( ( qInr @ A )
!= ( qInl @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause37) ).
thf(255,plain,
! [B: $i,A: $i] :
( ( qInr @ A )
!= ( qInl @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(140,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ eptset )
| ( member @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause135) ).
thf(516,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ eptset )
| ( member @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(66,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c2 @ A @ B @ C )
| ( A
= ( comb_app @ ( comb_app @ combS @ ( ap_contractE_sk1p @ A @ B @ C ) ) @ ( ap_contractE_sk1q @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_contractE9) ).
thf(355,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c2 @ A @ B @ C )
| ( A
= ( comb_app @ ( comb_app @ combS @ ( ap_contractE_sk1p @ A @ B @ C ) ) @ ( ap_contractE_sk1q @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(8,axiom,
! [A: $i] :
( ~ ( le @ A @ A )
| ( ord @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause77) ).
thf(209,plain,
! [A: $i] :
( ~ ( le @ A @ A )
| ( ord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(126,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rmultE_c1 @ A @ B @ C @ D @ E @ F @ G @ H )
| ( member @ A @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause53) ).
thf(487,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rmultE_c1 @ A @ B @ C @ D @ E @ F @ G @ H )
| ( member @ A @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(34,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( qPair @ A @ B )
!= ( qPair @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause49) ).
thf(282,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( qPair @ A @ B )
!= ( qPair @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(92,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ comb )
| ~ ( member @ B @ comb )
| ~ ( member @ C @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ A ) @ B ) @ C ) @ ( comb_app @ ( comb_app @ A @ C ) @ ( comb_app @ B @ C ) ) ) @ contract ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contract_S) ).
thf(414,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ comb )
| ~ ( member @ B @ comb )
| ~ ( member @ C @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ A ) @ B ) @ C ) @ ( comb_app @ ( comb_app @ A @ C ) @ ( comb_app @ B @ C ) ) ) @ contract ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(53,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( image @ B @ C ) )
| ( member @ ( pair @ ( imageE_sk1 @ A @ B @ C ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause94) ).
thf(327,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( image @ B @ C ) )
| ( member @ ( pair @ ( imageE_sk1 @ A @ B @ C ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(45,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ ( inr @ A ) @ ( disjsum @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause7) ).
thf(310,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ ( inr @ A ) @ ( disjsum @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause148) ).
thf(199,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(55,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( qPair @ A @ B ) @ ( qconverse @ C ) )
| ( member @ ( qPair @ B @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause47) ).
thf(331,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( qPair @ A @ B ) @ ( qconverse @ C ) )
| ( member @ ( qPair @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(170,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( union @ B ) )
| ( member @ A @ ( unionE_sk1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause119) ).
thf(585,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( union @ B ) )
| ( member @ A @ ( unionE_sk1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(166,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ ( inl @ A ) @ ( inl @ B ) ) @ ( radd @ C @ D @ E @ F ) )
| ( member @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause66) ).
thf(576,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ ( inl @ A ) @ ( inl @ B ) ) @ ( radd @ C @ D @ E @ F ) )
| ( member @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(177,axiom,
member @ ( pair @ p @ y ) @ ( rtrancl @ contract ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_reduce1_2h3) ).
thf(600,plain,
member @ ( pair @ p @ y ) @ ( rtrancl @ contract ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(47,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( pow @ B ) )
| ~ ( member @ C @ A )
| ( member @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause118) ).
thf(314,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( pow @ B ) )
| ~ ( member @ C @ A )
| ( member @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(164,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c4 @ A @ B @ C )
| ( C
= ( comb_app @ A @ ( ap_contractE_sk3q @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_contractE15) ).
thf(571,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c4 @ A @ B @ C )
| ( C
= ( comb_app @ A @ ( ap_contractE_sk3q @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(183,axiom,
! [A: $i] :
~ ( member @ ( pair @ combS @ A ) @ contract ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_contractE) ).
thf(612,plain,
! [A: $i] :
~ ( member @ ( pair @ combS @ A ) @ contract ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(116,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ A @ B ) @ C )
| ~ ( member @ B @ D )
| ( member @ A @ ( vimage @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause35) ).
thf(465,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ A @ B ) @ C )
| ~ ( member @ B @ D )
| ( member @ A @ ( vimage @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(109,axiom,
member @ combS @ comb,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',comb_intros2) ).
thf(450,plain,
member @ combS @ comb,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(124,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( comb_app @ A @ B )
!= ( comb_app @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',app_app2) ).
thf(482,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( comb_app @ A @ B )
!= ( comb_app @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(130,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c2 @ A @ B @ C )
| ( C
= ( comb_app @ ( comb_app @ ( ap_contractE_sk1p @ A @ B @ C ) @ B ) @ ( comb_app @ ( ap_contractE_sk1q @ A @ B @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_contractE8) ).
thf(495,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c2 @ A @ B @ C )
| ( C
= ( comb_app @ ( comb_app @ ( ap_contractE_sk1p @ A @ B @ C ) @ B ) @ ( comb_app @ ( ap_contractE_sk1q @ A @ B @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(72,axiom,
! [A: $i] : ( trans @ ( rtrancl @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',trans_rtrancl) ).
thf(368,plain,
! [A: $i] : ( trans @ ( rtrancl @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(143,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( trans @ A )
| ~ ( member @ ( pair @ B @ C ) @ A )
| ~ ( member @ ( pair @ C @ D ) @ A )
| ( member @ ( pair @ B @ D ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transD) ).
thf(524,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( trans @ A )
| ~ ( member @ ( pair @ B @ C ) @ A )
| ~ ( member @ ( pair @ C @ D ) @ A )
| ( member @ ( pair @ B @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(168,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c2 @ A @ B @ C )
| ( member @ ( ap_contractE_sk1p @ A @ B @ C ) @ comb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_contractE5) ).
thf(581,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c2 @ A @ B @ C )
| ( member @ ( ap_contractE_sk1p @ A @ B @ C ) @ comb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(24,axiom,
! [B: $i,A: $i] :
( ( ( qInl @ A )
!= ( qInl @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause40) ).
thf(258,plain,
! [B: $i,A: $i] :
( ( ( qInl @ A )
!= ( qInl @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(94,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( cons_subsetE_sk1 @ A @ B @ C ) @ C )
| ~ ( member @ D @ B )
| ( member @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause102) ).
thf(418,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( cons_subsetE_sk1 @ A @ B @ C ) @ C )
| ~ ( member @ D @ B )
| ( member @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(163,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( qconverse @ B ) )
| ( A
= ( qPair @ ( qconverseE_sk2 @ A @ B ) @ ( qconverseE_sk1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause45) ).
thf(568,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( qconverse @ B ) )
| ( A
= ( qPair @ ( qconverseE_sk2 @ A @ B ) @ ( qconverseE_sk1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(37,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( subsetD_sk1 @ A @ B @ C ) @ B )
| ~ ( member @ C @ A )
| ( member @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause124) ).
thf(290,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( subsetD_sk1 @ A @ B @ C ) @ B )
| ~ ( member @ C @ A )
| ( member @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(20,axiom,
! [A: $i] :
( ~ ( ord @ ( order_Union_sk1 @ A ) )
| ( ord @ ( union @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause32) ).
thf(246,plain,
! [A: $i] :
( ~ ( ord @ ( order_Union_sk1 @ A ) )
| ( ord @ ( union @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(101,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ A @ B ) @ C )
| ~ ( member @ ( pair @ B @ D ) @ E )
| ( member @ ( pair @ A @ D ) @ ( comp @ E @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause34) ).
thf(433,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ A @ B ) @ C )
| ~ ( member @ ( pair @ B @ D ) @ E )
| ( member @ ( pair @ A @ D ) @ ( comp @ E @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(28,axiom,
! [A: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause133) ).
thf(272,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(79,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( vimage @ B @ C ) )
| ( member @ ( vimageE_sk1 @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause93) ).
thf(383,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( vimage @ B @ C ) )
| ( member @ ( vimageE_sk1 @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(154,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ A @ comb )
| ~ ( member @ B @ comb )
| ~ ( member @ C @ comb )
| ~ ( member @ ( pair @ ( comb_app @ ( comb_app @ A @ C ) @ ( comb_app @ B @ C ) ) @ D ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ A ) @ B ) @ C ) @ D ) @ ( rtrancl @ contract ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reduction_rls_2) ).
thf(549,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ A @ comb )
| ~ ( member @ B @ comb )
| ~ ( member @ C @ comb )
| ~ ( member @ ( pair @ ( comb_app @ ( comb_app @ A @ C ) @ ( comb_app @ B @ C ) ) @ D ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ A ) @ B ) @ C ) @ D ) @ ( rtrancl @ contract ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(149,axiom,
! [A: $i] :
( ~ ( member @ A @ nat )
| ( member @ ( succ @ A ) @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause3) ).
thf(536,plain,
! [A: $i] :
( ~ ( member @ A @ nat )
| ( member @ ( succ @ A ) @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(107,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c2 @ A @ B @ C )
| ( member @ ( ap_contractE_sk1q @ A @ B @ C ) @ comb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_contractE6) ).
thf(447,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c2 @ A @ B @ C )
| ( member @ ( ap_contractE_sk1q @ A @ B @ C ) @ comb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(90,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ~ ( member @ ( cons_subsetI_sk1 @ A @ C @ B ) @ B )
| ~ ( member @ D @ ( cons @ A @ C ) )
| ( member @ D @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause9) ).
thf(410,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ~ ( member @ ( cons_subsetI_sk1 @ A @ C @ B ) @ B )
| ~ ( member @ D @ ( cons @ A @ C ) )
| ( member @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( ( A != B )
| ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause149) ).
thf(262,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( subset @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(88,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ ( inl @ A ) @ ( inr @ B ) ) @ ( radd @ C @ D @ E @ F ) )
| ( member @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause69) ).
thf(405,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ ( inl @ A ) @ ( inr @ B ) ) @ ( radd @ C @ D @ E @ F ) )
| ( member @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(96,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( disjsum @ B @ C ) )
| ( A
= ( inl @ ( sumE_sk1 @ A @ B @ C ) ) )
| ( member @ ( sumE_sk2 @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause90) ).
thf(422,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( disjsum @ B @ C ) )
| ( A
= ( inl @ ( sumE_sk1 @ A @ B @ C ) ) )
| ( member @ ( sumE_sk2 @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(29,axiom,
! [A: $i] :
( ~ ( ord @ ( order_Inter_sk1 @ A ) )
| ( ord @ ( inter @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause30) ).
thf(273,plain,
! [A: $i] :
( ~ ( ord @ ( order_Inter_sk1 @ A ) )
| ( ord @ ( inter @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(75,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ ( subsetD_sk1 @ B @ C @ A ) @ B )
| ( member @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause123) ).
thf(373,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ ( subsetD_sk1 @ B @ C @ A ) @ B )
| ( member @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(161,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ A @ B ) @ contract )
| ~ ( member @ C @ comb )
| ~ ( member @ ( pair @ ( comb_app @ C @ B ) @ D ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ C @ A ) @ D ) @ ( rtrancl @ contract ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reduction_rls_4) ).
thf(564,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ A @ B ) @ contract )
| ~ ( member @ C @ comb )
| ~ ( member @ ( pair @ ( comb_app @ C @ B ) @ D ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ C @ A ) @ D ) @ ( rtrancl @ contract ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(39,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( int @ B @ C ) )
| ( member @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause116) ).
thf(294,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( int @ B @ C ) )
| ( member @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(60,axiom,
! [B: $i,A: $i] :
( ~ ( member @ ( subsetI_sk1 @ A @ B ) @ B )
| ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause132) ).
thf(341,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( subsetI_sk1 @ A @ B ) @ B )
| ( subset @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(67,axiom,
! [A: $i] :
~ ( member @ ( pair @ combK @ A ) @ contract ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_contractE) ).
thf(358,plain,
! [A: $i] :
~ ( member @ ( pair @ combK @ A ) @ contract ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(103,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c1 @ A @ B @ C )
| ( member @ B @ comb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_contractE3) ).
thf(437,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c1 @ A @ B @ C )
| ( member @ B @ comb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(86,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( disjsum @ B @ C ) )
| ( A
= ( inl @ ( sumE_sk1 @ A @ B @ C ) ) )
| ( A
= ( inr @ ( sumE_sk2 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause91) ).
thf(400,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( disjsum @ B @ C ) )
| ( A
= ( inl @ ( sumE_sk1 @ A @ B @ C ) ) )
| ( A
= ( inr @ ( sumE_sk2 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(147,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( qconverse @ B ) )
| ( member @ ( qPair @ ( qconverseE_sk1 @ A @ B ) @ ( qconverseE_sk2 @ A @ B ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause46) ).
thf(532,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( qconverse @ B ) )
| ( member @ ( qPair @ ( qconverseE_sk1 @ A @ B ) @ ( qconverseE_sk2 @ A @ B ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(98,axiom,
! [A: $i] :
( ~ ( member @ A @ comb )
| ( member @ ( pair @ A @ A ) @ ( rtrancl @ contract ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reduction_refl) ).
thf(427,plain,
! [A: $i] :
( ~ ( member @ A @ comb )
| ( member @ ( pair @ A @ A ) @ ( rtrancl @ contract ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(145,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( image @ B @ C ) )
| ( member @ ( imageE_sk1 @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause95) ).
thf(528,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( image @ B @ C ) )
| ( member @ ( imageE_sk1 @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(133,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rmultE_c2 @ A @ B @ C @ D @ E @ F @ G @ H )
| ( member @ C @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause58) ).
thf(501,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rmultE_c2 @ A @ B @ C @ D @ E @ F @ G @ H )
| ( member @ C @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(73,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ ( inl @ A ) @ ( inl @ B ) ) @ ( radd @ C @ D @ E @ F ) )
| ( member @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause67) ).
thf(369,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ ( inl @ A ) @ ( inl @ B ) ) @ ( radd @ C @ D @ E @ F ) )
| ( member @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(125,axiom,
member @ r @ comb,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_reduce1_2h1) ).
thf(486,plain,
member @ r @ comb,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(58,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c4 @ A @ B @ C )
| ( member @ ( pair @ B @ ( ap_contractE_sk3q @ A @ B @ C ) ) @ contract ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_contractE13) ).
thf(337,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c4 @ A @ B @ C )
| ( member @ ( pair @ B @ ( ap_contractE_sk3q @ A @ B @ C ) ) @ contract ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(118,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c2 @ A @ B @ C )
| ( member @ B @ comb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_contractE7) ).
thf(469,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c2 @ A @ B @ C )
| ( member @ B @ comb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(159,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ A @ B ) @ ( converse @ C ) )
| ( member @ ( pair @ B @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause105) ).
thf(560,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ A @ B ) @ ( converse @ C ) )
| ( member @ ( pair @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(128,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ ( inl @ A ) @ ( disjsum @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause6) ).
thf(491,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ ( inl @ A ) @ ( disjsum @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(70,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ comb )
| ~ ( member @ B @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ A ) @ B ) @ A ) @ contract ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contract_K) ).
thf(364,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ comb )
| ~ ( member @ B @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ A ) @ B ) @ A ) @ contract ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(691,plain,
$false,
inference(cvc4,[status(thm)],[479,347,333,518,555,449,379,614,217,276,202,597,385,500,538,288,301,320,389,587,196,542,460,189,606,416,325,316,475,591,443,211,514,574,353,280,453,396,507,312,206,307,292,233,248,270,381,534,512,439,220,366,334,598,429,275,192,407,467,435,329,493,551,224,229,566,583,522,578,403,593,610,420,471,339,554,526,489,393,457,371,503,244,266,360,558,530,343,237,298,412,618,425,296,375,601,562,286,545,391,445,498,350,540,604,187,318,509,362,451,616,303,477,387,345,323,213,462,240,251,278,455,608,226,505,431,473,589,255,516,355,209,487,282,414,327,310,199,331,585,576,600,314,571,612,465,450,482,495,368,524,581,258,418,568,290,246,433,272,383,549,536,447,410,262,405,422,273,373,564,294,341,358,437,400,532,427,528,501,369,486,337,469,560,491,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : COL088-2 : TPTP v8.1.2. Released v2.7.0.
% 0.11/0.14 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n008.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon May 6 14:02:24 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.90/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.20/1.01 % [INFO] Parsing done (174ms).
% 1.20/1.01 % [INFO] Running in sequential loop mode.
% 1.85/1.22 % [INFO] eprover registered as external prover.
% 1.95/1.22 % [INFO] cvc4 registered as external prover.
% 1.95/1.22 % [INFO] Scanning for conjecture ...
% 1.98/1.30 % [INFO] Found a conjecture and 185 axioms. Running axiom selection ...
% 2.17/1.37 % [INFO] Axiom selection finished. Selected 185 axioms (removed 0 axioms).
% 2.79/1.46 % [INFO] Problem is propositional (TPTP CNF).
% 2.79/1.47 % [INFO] Type checking passed.
% 2.79/1.48 % [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 ...
% 7.05/2.51 % External prover 'cvc4' found a proof!
% 7.05/2.51 % [INFO] Killing All external provers ...
% 7.05/2.51 % Time passed: 2006ms (effective reasoning time: 1494ms)
% 7.05/2.51 % 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)>
% 7.05/2.51 % Axioms used in derivation (185): ap_contractE7, clause82, clause60, clause65, app_app3, ap_reduce1_2h1, clause71, clause113, clause128, ap_contractE10, clause43, clause3, comb_intros3, clause29, clause32, clause18, clause54, clause117, clause88, clause59, clause99, clause48, clause37, clause105, clause108, clause93, clause77, clause135, clause95, clause101, clause129, clause81, clause55, clause66, clause118, clause17, clause70, ap_contractE2, clause22, clause124, clause92, ap_contractE14, clause87, clause84, clause7, clause25, clause11, clause14, clause112, clause76, clause49, ap_contractE4, clause13, clause31, clause24, clause132, app_app2, s_app, clause121, clause42, clause109, clause104, clause2, clause64, k_s, k_contractE, transD, clause38, ap_E1, clause16, clause28, ap_contractE11, clause98, clause53, reduction_rls_1, clause12, clause111, clause79, clause102_2, clause136, clause97, ap_contractE15, ap_contractE1, clause9_1, clause75, ap_reduce1_2h5, contract_K, clause100, clause23, ap_contractE8, clause125, clause114, clause86, clause6, clause133, app_app1, clause122, clause103, clause1, clause34, s_contractE, clause69, trans_rtrancl, reduction_refl, clause5, ap_contractE5, ap_contractE12, clause102_1, clause68, clause148, clause134, clause27, comb_intros1, clause110, clause41, ap_E2, clause39, clause57, reduction_rls_4, clause35, clause8, k_app, clause30, clause20, clause52, clause46, clause90, clause126, clause115, clause63, clause89, ap_reduce1_2h2, clause44, clause50, clause102, clause150, ap_reduce1_2h4, clause33, clause94, clause73, reduction_rls_2, clause83, clause72, ap_contractE9, contract_combD2, clause107, clause19, contract_S, clause78, subsetD, clause123, comb_intros2, ap_contractE6, clause116, clause4, clause26, clause149, ap_contractE13, clause58, clause96, clause9, clause131, clause120, clause56, clause10, clause15, clause67, clause21, clause127, clause119, clause80, reduction_rls_3, clause45, clause85, clause91, clause51, ap_contractE3, clause40, clause106, clause61, clause62, clause74, clause47, clause36, ap_reduce1_2h3
% 7.05/2.51 % No. of inferences in proof: 373
% 7.05/2.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2006 ms resp. 1494 ms w/o parsing
% 7.20/2.59 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.20/2.59 % [INFO] Killing All external provers ...
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