%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COL091-2 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n015.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 : Sun Sep 27 06:56:27 AM UTC 2026
% Result : Unsatisfiable 9.83s 3.97s
% Output : Refutation 10.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 175
% Syntax : Number of formulae : 351 ( 41 unt; 0 typ; 0 def)
% Number of atoms : 747 ( 144 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 3346 ( 374 ~; 396 |; 0 &;2576 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 85 ( 83 usr; 9 con; 0-8 aty)
% Number of variables : 1046 ( 0 ^;1046 !; 0 ?;1046 :)
% Comments :
%------------------------------------------------------------------------------
thf(r_decl,type,
r: $i ).
thf(comb_app_decl,type,
comb_app: $i > $i > $i ).
thf(combK_decl,type,
combK: $i ).
thf(member_decl,type,
member: $i > $i > $o ).
thf(pair_decl,type,
pair: $i > $i > $i ).
thf(p_decl,type,
p: $i ).
thf(contract_decl,type,
contract: $i ).
thf(inl_decl,type,
inl: $i > $i ).
thf(inr_decl,type,
inr: $i > $i ).
thf(cons_decl,type,
cons: $i > $i > $i ).
thf(eptset_decl,type,
eptset: $i ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(qPair_decl,type,
qPair: $i > $i > $i ).
thf(le_decl,type,
le: $i > $i > $o ).
thf(ord_decl,type,
ord: $i > $o ).
thf(qInl_decl,type,
qInl: $i > $i ).
thf(qInr_decl,type,
qInr: $i > $i ).
thf(card_decl,type,
card: $i > $o ).
thf(card_Union_sk1_decl,type,
card_Union_sk1: $i > $i ).
thf(union_decl,type,
union: $i > $i ).
thf(succ_decl,type,
succ: $i > $i ).
thf(order_Union_sk1_decl,type,
order_Union_sk1: $i > $i ).
thf(rmultE_c2_decl,type,
rmultE_c2: $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(lt_decl,type,
lt: $i > $i > $o ).
thf(order_Inter_sk1_decl,type,
order_Inter_sk1: $i > $i ).
thf(inter_decl,type,
inter: $i > $i ).
thf(un_decl,type,
un: $i > $i > $i ).
thf(comp_decl,type,
comp: $i > $i > $i ).
thf(compE_sk2_decl,type,
compE_sk2: $i > $i > $i > $i ).
thf(compE_sk3_decl,type,
compE_sk3: $i > $i > $i > $i ).
thf(ap_contractE_c4_decl,type,
ap_contractE_c4: $i > $i > $i > $o ).
thf(comb_decl,type,
comb: $i ).
thf(subsetD_sk1_decl,type,
subsetD_sk1: $i > $i > $i > $i ).
thf(rmultE_c1_decl,type,
rmultE_c1: $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(int_decl,type,
int: $i > $i > $i ).
thf(qsum_decl,type,
qsum: $i > $i > $i ).
thf(qsumE_sk1_decl,type,
qsumE_sk1: $i > $i > $i > $i ).
thf(qsumE_sk2_decl,type,
qsumE_sk2: $i > $i > $i > $i ).
thf(id_decl,type,
id: $i > $i ).
thf(idE_sk1_decl,type,
idE_sk1: $i > $i > $i ).
thf(converse_decl,type,
converse: $i > $i ).
thf(converseE_sk2_decl,type,
converseE_sk2: $i > $i > $i ).
thf(converseE_sk1_decl,type,
converseE_sk1: $i > $i > $i ).
thf(disjsum_decl,type,
disjsum: $i > $i > $i ).
thf(vimage_decl,type,
vimage: $i > $i > $i ).
thf(vimageE_sk1_decl,type,
vimageE_sk1: $i > $i > $i > $i ).
thf(pow_decl,type,
pow: $i > $i ).
thf(radd_decl,type,
radd: $i > $i > $i > $i > $i ).
thf(field_decl,type,
field: $i > $i ).
thf(fieldE_sk1_decl,type,
fieldE_sk1: $i > $i > $i ).
thf(fieldE_sk2_decl,type,
fieldE_sk2: $i > $i > $i ).
thf(cons_subsetE_sk1_decl,type,
cons_subsetE_sk1: $i > $i > $i > $i ).
thf(image_decl,type,
image: $i > $i > $i ).
thf(imageE_sk1_decl,type,
imageE_sk1: $i > $i > $i > $i ).
thf(sumE_sk1_decl,type,
sumE_sk1: $i > $i > $i > $i ).
thf(sumE_sk2_decl,type,
sumE_sk2: $i > $i > $i > $i ).
thf(qconverse_decl,type,
qconverse: $i > $i ).
thf(ap_contractE_c3_decl,type,
ap_contractE_c3: $i > $i > $i > $o ).
thf(ap_contractE_sk2q_decl,type,
ap_contractE_sk2q: $i > $i > $i > $i ).
thf(ap_contractE_sk3q_decl,type,
ap_contractE_sk3q: $i > $i > $i > $i ).
thf(subsetI_sk1_decl,type,
subsetI_sk1: $i > $i > $i ).
thf(memrel_decl,type,
memrel: $i > $i ).
thf(diff_decl,type,
diff: $i > $i > $i ).
thf(ap_contractE_c2_decl,type,
ap_contractE_c2: $i > $i > $i > $o ).
thf(combS_decl,type,
combS: $i ).
thf(ap_contractE_sk1p_decl,type,
ap_contractE_sk1p: $i > $i > $i > $i ).
thf(ap_contractE_sk1q_decl,type,
ap_contractE_sk1q: $i > $i > $i > $i ).
thf(interI_sk1_decl,type,
interI_sk1: $i > $i > $i ).
thf(rmult_decl,type,
rmult: $i > $i > $i > $i > $i ).
thf(cons_subsetI_sk1_decl,type,
cons_subsetI_sk1: $i > $i > $i > $i ).
thf(rtrancl_decl,type,
rtrancl: $i > $i ).
thf(compE_sk1_decl,type,
compE_sk1: $i > $i > $i > $i ).
thf(ap_contractE_c1_decl,type,
ap_contractE_c1: $i > $i > $i > $o ).
thf(powI_sk1_decl,type,
powI_sk1: $i > $i > $i ).
thf(domain_decl,type,
domain: $i > $i ).
thf(domainE_sk1_decl,type,
domainE_sk1: $i > $i > $i ).
thf(fin_decl,type,
fin: $i > $i ).
thf(qconverseE_sk1_decl,type,
qconverseE_sk1: $i > $i > $i ).
thf(qconverseE_sk2_decl,type,
qconverseE_sk2: $i > $i > $i ).
thf(nat_decl,type,
nat: $i ).
thf(unionE_sk1_decl,type,
unionE_sk1: $i > $i > $i ).
thf(range_decl,type,
range: $i > $i ).
thf(rangeE_sk1_decl,type,
rangeE_sk1: $i > $i > $i ).
thf(113,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ vimage ) @ ( A @ member ) )
| ~ ( D @ ( B @ member ) )
| ~ ( C @ ( B @ ( A @ pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause35) ).
thf(457,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ vimage ) @ ( A @ member ) )
| ~ ( D @ ( B @ member ) )
| ~ ( C @ ( B @ ( A @ pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(122,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( A @ member ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ rmultE_c1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause53) ).
thf(479,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( A @ member ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ rmultE_c1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(64,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ member ) )
| ~ ( C @ ( B @ diff ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause114) ).
thf(347,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ member ) )
| ~ ( C @ ( B @ diff ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(58,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( C @ ( A @ pair ) @ member ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ rmultE_c1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause52) ).
thf(333,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( C @ ( A @ pair ) @ member ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ rmultE_c1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(140,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ fin @ ( A @ ( C @ int ) @ member ) )
| ~ ( B @ fin @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause28) ).
thf(518,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ fin @ ( A @ ( C @ int ) @ member ) )
| ~ ( B @ fin @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(123,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ disjsum ) @ ( A @ inl @ member ) )
| ~ ( B @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause6) ).
thf(481,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ disjsum ) @ ( A @ inl @ member ) )
| ~ ( B @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(66,axiom,
! [A: $i] :
~ ( contract @ ( A @ ( combK @ pair ) @ member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_contractE) ).
thf(352,plain,
! [A: $i] :
~ ( contract @ ( A @ ( combK @ pair ) @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(90,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ( B @ ( A @ member ) )
| ~ ( C @ ( B @ un ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause117) ).
thf(408,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ( B @ ( A @ member ) )
| ~ ( C @ ( B @ un ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(46,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ pow @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause118) ).
thf(308,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ pow @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(110,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( combK @ comb_app ) ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE4) ).
thf(449,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( combK @ comb_app ) ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(105,axiom,
! [C: $i,B: $i,A: $i] :
( ( comb @ ( C @ ( B @ ( A @ ap_contractE_sk1q ) ) @ member ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE6) ).
thf(440,plain,
! [C: $i,B: $i,A: $i] :
( ( comb @ ( C @ ( B @ ( A @ ap_contractE_sk1q ) ) @ member ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(81,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( B @ ( A @ qsumE_sk2 ) ) @ qInr ) )
| ( B @ ( C @ ( B @ ( A @ qsumE_sk1 ) ) @ member ) )
| ~ ( C @ ( B @ qsum ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause42) ).
thf(384,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( B @ ( A @ qsumE_sk2 ) ) @ qInr ) )
| ( B @ ( C @ ( B @ ( A @ qsumE_sk1 ) ) @ member ) )
| ~ ( C @ ( B @ qsum ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(147,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ comb_app ) )
!= ( D @ ( C @ comb_app ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',app_app1) ).
thf(533,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ comb_app ) )
!= ( D @ ( C @ comb_app ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(148,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ ( A @ idE_sk1 ) @ ( B @ ( A @ idE_sk1 ) @ pair ) ) )
| ~ ( B @ id @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause83) ).
thf(538,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ ( A @ idE_sk1 ) @ ( B @ ( A @ idE_sk1 ) @ pair ) ) )
| ~ ( B @ id @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(88,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ pair ) @ member ) )
| ~ ( F @ ( E @ ( D @ ( C @ radd ) ) ) @ ( B @ inl @ ( A @ inl @ pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause68) ).
thf(404,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ pair ) @ member ) )
| ~ ( F @ ( E @ ( D @ ( C @ radd ) ) ) @ ( B @ inl @ ( A @ inl @ pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(94,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( B @ member ) )
| ~ ( F @ ( E @ ( D @ ( C @ radd ) ) ) @ ( B @ inr @ ( A @ inr @ pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause64) ).
thf(417,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( B @ member ) )
| ~ ( F @ ( E @ ( D @ ( C @ radd ) ) ) @ ( B @ inr @ ( A @ inr @ pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(38,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ~ ( C @ ( B @ int ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause116) ).
thf(288,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ~ ( C @ ( B @ int ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(43,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ ( A @ converseE_sk1 ) @ ( B @ ( A @ converseE_sk2 ) @ pair ) ) )
| ~ ( B @ converse @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause103) ).
thf(301,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ ( A @ converseE_sk1 ) @ ( B @ ( A @ converseE_sk2 ) @ pair ) ) )
| ~ ( B @ converse @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(103,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( B @ member ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ rmultE_c2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause60) ).
thf(436,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( B @ member ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ rmultE_c2 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(161,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ unionE_sk1 ) @ ( A @ member ) )
| ~ ( B @ union @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause119) ).
thf(570,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unionE_sk1 ) @ ( A @ member ) )
| ~ ( B @ union @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(75,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ qsumE_sk2 ) ) @ member ) )
| ( B @ ( C @ ( B @ ( A @ qsumE_sk1 ) ) @ member ) )
| ~ ( C @ ( B @ qsum ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause41) ).
thf(372,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ qsumE_sk2 ) ) @ member ) )
| ( B @ ( C @ ( B @ ( A @ qsumE_sk1 ) ) @ member ) )
| ~ ( C @ ( B @ qsum ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(134,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ un ) @ ( A @ member ) )
| ~ ( B @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause20) ).
thf(504,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ un ) @ ( A @ member ) )
| ~ ( B @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(63,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ( A = B )
| ~ ( C @ ( B @ cons ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause112) ).
thf(344,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ( A = B )
| ~ ( C @ ( B @ cons ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(156,axiom,
! [C: $i,B: $i,A: $i] :
( ( comb @ ( B @ member ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE11) ).
thf(559,plain,
! [C: $i,B: $i,A: $i] :
( ( comb @ ( B @ member ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(96,axiom,
! [C: $i,B: $i,A: $i] :
( ( contract @ ( C @ ( B @ ( A @ ap_contractE_sk2q ) ) @ ( A @ pair ) @ member ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE10) ).
thf(421,plain,
! [C: $i,B: $i,A: $i] :
( ( contract @ ( C @ ( B @ ( A @ ap_contractE_sk2q ) ) @ ( A @ pair ) @ member ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(36,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( C @ ( B @ ( A @ subsetD_sk1 ) ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause124) ).
thf(284,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( C @ ( B @ ( A @ subsetD_sk1 ) ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(54,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ qPair ) @ member ) )
| ~ ( C @ qconverse @ ( B @ ( A @ qPair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause47) ).
thf(325,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ qPair ) @ member ) )
| ~ ( C @ qconverse @ ( B @ ( A @ qPair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(27,axiom,
! [A: $i] :
( ( A @ inter @ ord )
| ~ ( A @ order_Inter_sk1 @ ord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause30) ).
thf(261,plain,
! [A: $i] :
( ( A @ inter @ ord )
| ~ ( A @ order_Inter_sk1 @ ord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ union @ card )
| ~ ( A @ card_Union_sk1 @ card ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause26) ).
thf(216,plain,
! [A: $i] :
( ( A @ union @ card )
| ~ ( A @ card_Union_sk1 @ card ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( A @ inl )
!= ( B @ inr ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause85) ).
thf(179,plain,
! [B: $i,A: $i] :
( ( A @ inl )
!= ( B @ inr ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(107,axiom,
! [B: $i,A: $i] :
( ( B @ succ @ ( A @ member ) )
| ~ ( B @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause12) ).
thf(443,plain,
! [B: $i,A: $i] :
( ( B @ succ @ ( A @ member ) )
| ~ ( B @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(52,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ ( B @ ( A @ imageE_sk1 ) ) @ pair ) @ member ) )
| ~ ( C @ ( B @ image ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause94) ).
thf(321,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ ( B @ ( A @ imageE_sk1 ) ) @ pair ) @ member ) )
| ~ ( C @ ( B @ image ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(77,axiom,
! [A: $i] :
( ( A @ union @ ord )
| ( A @ ( A @ order_Union_sk1 @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause31) ).
thf(376,plain,
! [A: $i] :
( ( A @ union @ ord )
| ( A @ ( A @ order_Union_sk1 @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(125,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( C @ ( B @ ( A @ ap_contractE_sk1q ) ) @ comb_app ) @ ( B @ ( C @ ( B @ ( A @ ap_contractE_sk1p ) ) @ comb_app ) @ comb_app ) ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE8) ).
thf(485,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( C @ ( B @ ( A @ ap_contractE_sk1q ) ) @ comb_app ) @ ( B @ ( C @ ( B @ ( A @ ap_contractE_sk1p ) ) @ comb_app ) @ comb_app ) ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( ( ( A @ inr )
= ( B @ inr ) )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause4) ).
thf(238,plain,
! [B: $i,A: $i] :
( ( ( A @ inr )
= ( B @ inr ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(138,axiom,
! [C: $i,B: $i,A: $i] :
( ( comb @ ( C @ member ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE2) ).
thf(514,plain,
! [C: $i,B: $i,A: $i] :
( ( comb @ ( C @ member ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(163,axiom,
! [A: $i] :
( ( nat @ ( A @ member ) )
| ~ ( nat @ ( A @ succ @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause50) ).
thf(574,plain,
! [A: $i] :
( ( nat @ ( A @ member ) )
| ~ ( nat @ ( A @ succ @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(175,axiom,
comb @ ( combK @ member ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',comb_intros1) ).
thf(602,plain,
comb @ ( combK @ member ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(85,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ~ ( F @ ( E @ ( D @ ( C @ radd ) ) ) @ ( B @ inr @ ( A @ inl @ pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause69) ).
thf(397,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ~ ( F @ ( E @ ( D @ ( C @ radd ) ) ) @ ( B @ inr @ ( A @ inl @ pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(34,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( A @ compE_sk3 ) ) @ ( C @ ( B @ ( A @ compE_sk2 ) ) @ pair ) @ member ) )
| ~ ( C @ ( B @ comp ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause81) ).
thf(280,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( A @ compE_sk3 ) ) @ ( C @ ( B @ ( A @ compE_sk2 ) ) @ pair ) @ member ) )
| ~ ( C @ ( B @ comp ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ succ )
!= ( B @ succ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause109) ).
thf(221,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ succ )
!= ( B @ succ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(48,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ ( A @ fieldE_sk2 ) @ pair ) @ member ) )
| ( B @ ( B @ ( A @ fieldE_sk1 ) @ ( A @ pair ) @ member ) )
| ~ ( B @ field @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause96) ).
thf(312,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ ( A @ fieldE_sk2 ) @ pair ) @ member ) )
| ( B @ ( B @ ( A @ fieldE_sk1 ) @ ( A @ pair ) @ member ) )
| ~ ( B @ field @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(40,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( B @ ( A @ qsumE_sk2 ) ) @ qInr ) )
| ( A
= ( C @ ( B @ ( A @ qsumE_sk1 ) ) @ qInl ) )
| ~ ( C @ ( B @ qsum ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause44) ).
thf(292,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( B @ ( A @ qsumE_sk2 ) ) @ qInr ) )
| ( A
= ( C @ ( B @ ( A @ qsumE_sk1 ) ) @ qInl ) )
| ~ ( C @ ( B @ qsum ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(79,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ member ) )
| ~ ( C @ memrel @ ( B @ ( A @ pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause74) ).
thf(380,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ member ) )
| ~ ( C @ memrel @ ( B @ ( A @ pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(137,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ fin @ ( C @ ( A @ int ) @ member ) )
| ~ ( B @ fin @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause27) ).
thf(512,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ fin @ ( C @ ( A @ int ) @ member ) )
| ~ ( B @ fin @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(151,axiom,
combK != combS,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_s) ).
thf(546,plain,
combK != combS,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ ord )
| ~ ( A @ ( A @ le ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause77) ).
thf(201,plain,
! [A: $i] :
( ( A @ ord )
| ~ ( A @ ( A @ le ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(73,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cons ) @ ( A @ member ) )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause16) ).
thf(366,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cons ) @ ( A @ member ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ union @ ord )
| ~ ( A @ order_Union_sk1 @ ord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause32) ).
thf(233,plain,
! [A: $i] :
( ( A @ union @ ord )
| ~ ( A @ order_Union_sk1 @ ord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(111,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ~ ( C @ ( B @ ( A @ cons ) @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause102_1) ).
thf(452,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ~ ( C @ ( B @ ( A @ cons ) @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(173,axiom,
! [B: $i,A: $i] :
( ( comb @ ( A @ member ) )
| ~ ( comb @ ( B @ ( A @ comb_app ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_E1) ).
thf(598,plain,
! [B: $i,A: $i] :
( ( comb @ ( A @ member ) )
| ~ ( comb @ ( B @ ( A @ comb_app ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(157,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ~ ( F @ ( E @ ( D @ ( C @ radd ) ) ) @ ( B @ inl @ ( A @ inl @ pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause66) ).
thf(561,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ~ ( F @ ( E @ ( D @ ( C @ radd ) ) ) @ ( B @ inl @ ( A @ inl @ pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(83,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( B @ ( A @ sumE_sk2 ) ) @ inr ) )
| ( A
= ( C @ ( B @ ( A @ sumE_sk1 ) ) @ inl ) )
| ~ ( C @ ( B @ disjsum ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause91) ).
thf(392,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( B @ ( A @ sumE_sk2 ) ) @ inr ) )
| ( A
= ( C @ ( B @ ( A @ sumE_sk1 ) ) @ inl ) )
| ~ ( C @ ( B @ disjsum ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(42,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ comb_app ) )
= ( D @ ( B @ comb_app ) ) )
| ( C != D )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',app_app3) ).
thf(297,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ comb_app ) )
= ( D @ ( B @ comb_app ) ) )
| ( C != D )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(100,axiom,
! [C: $i,B: $i,A: $i] :
( ( comb @ ( B @ member ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE3) ).
thf(429,plain,
! [C: $i,B: $i,A: $i] :
( ( comb @ ( B @ member ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(33,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ qPair ) )
!= ( D @ ( C @ qPair ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause49) ).
thf(275,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ qPair ) )
!= ( D @ ( C @ qPair ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(26,axiom,
! [A: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause133) ).
thf(260,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(65,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( B @ ( A @ ap_contractE_sk1q ) ) @ ( C @ ( B @ ( A @ ap_contractE_sk1p ) ) @ ( combS @ comb_app ) @ comb_app ) ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE9) ).
thf(349,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( B @ ( A @ ap_contractE_sk1q ) ) @ ( C @ ( B @ ( A @ ap_contractE_sk1p ) ) @ ( combS @ comb_app ) @ comb_app ) ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(118,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ converse @ ( A @ ( B @ pair ) @ member ) )
| ~ ( C @ ( B @ ( A @ pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause10) ).
thf(467,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ converse @ ( A @ ( B @ pair ) @ member ) )
| ~ ( C @ ( B @ ( A @ pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(159,axiom,
! [C: $i,B: $i,A: $i] :
( ( comb @ ( C @ ( B @ ( A @ ap_contractE_sk1p ) ) @ member ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE5) ).
thf(566,plain,
! [C: $i,B: $i,A: $i] :
( ( comb @ ( C @ ( B @ ( A @ ap_contractE_sk1p ) ) @ member ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(102,axiom,
contract @ ( r @ ( p @ ( combK @ comb_app ) @ pair ) @ member ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k1_contractD_h1) ).
thf(435,plain,
contract @ ( r @ ( p @ ( combK @ comb_app ) @ pair ) @ member ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(115,axiom,
! [C: $i,B: $i,A: $i] :
( ( comb @ ( B @ member ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE7) ).
thf(461,plain,
! [C: $i,B: $i,A: $i] :
( ( comb @ ( B @ member ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(129,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ domainE_sk1 ) @ ( A @ pair ) @ member ) )
| ~ ( B @ domain @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause98) ).
thf(493,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ domainE_sk1 ) @ ( A @ pair ) @ member ) )
| ~ ( B @ domain @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(153,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( D @ member ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ rmultE_c1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause56) ).
thf(551,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( D @ member ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ rmultE_c1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(166,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( A @ member ) )
| ~ ( F @ ( E @ ( D @ ( C @ radd ) ) ) @ ( B @ inr @ ( A @ inr @ pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause63) ).
thf(583,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( A @ member ) )
| ~ ( F @ ( E @ ( D @ ( C @ radd ) ) ) @ ( B @ inr @ ( A @ inr @ pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(142,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ~ ( B @ ( C @ member ) )
| ~ ( B @ inter @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause122) ).
thf(522,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ~ ( B @ ( C @ member ) )
| ~ ( B @ inter @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(165,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ pair ) )
!= ( D @ ( C @ pair ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause106) ).
thf(578,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ pair ) )
!= ( D @ ( C @ pair ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(50,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetD) ).
thf(317,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(68,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ inter @ ( A @ member ) )
| ~ ( B @ ( C @ member ) )
| ~ ( B @ ( A @ interI_sk1 ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause24) ).
thf(356,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ inter @ ( A @ member ) )
| ~ ( B @ ( C @ member ) )
| ~ ( B @ ( A @ interI_sk1 ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(132,axiom,
! [B: $i,A: $i] :
( combS
!= ( B @ ( A @ comb_app ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_app) ).
thf(499,plain,
! [B: $i,A: $i] :
( combS
!= ( B @ ( A @ comb_app ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(126,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ inter @ ( C @ member ) )
| ( B @ ( B @ ( C @ interI_sk1 ) @ member ) )
| ~ ( B @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause23) ).
thf(488,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ inter @ ( C @ member ) )
| ( B @ ( B @ ( C @ interI_sk1 ) @ member ) )
| ~ ( B @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(61,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( D @ member ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ rmultE_c2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause61) ).
thf(339,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( D @ member ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ rmultE_c2 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ qPair ) )
!= ( D @ ( C @ qPair ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause48) ).
thf(193,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ qPair ) )
!= ( D @ ( C @ qPair ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(144,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ diff ) @ ( A @ member ) )
| ( C @ ( A @ member ) )
| ~ ( B @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause17) ).
thf(526,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ diff ) @ ( A @ member ) )
| ( C @ ( A @ member ) )
| ~ ( B @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(169,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ member ) )
| ( D @ ( B @ ( D @ ( A @ cons_subsetI_sk1 ) ) @ member ) )
| ~ ( D @ ( A @ cons ) @ ( C @ member ) )
| ~ ( B @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause8) ).
thf(590,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ member ) )
| ( D @ ( B @ ( D @ ( A @ cons_subsetI_sk1 ) ) @ member ) )
| ~ ( D @ ( A @ cons ) @ ( C @ member ) )
| ~ ( B @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( ( A @ inl )
= ( B @ inl ) )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause5) ).
thf(212,plain,
! [B: $i,A: $i] :
( ( ( A @ inl )
= ( B @ inl ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(56,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( C @ ( B @ ( A @ ap_contractE_sk2q ) ) @ comb_app ) ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE12) ).
thf(328,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( C @ ( B @ ( A @ ap_contractE_sk2q ) ) @ comb_app ) ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(120,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( B @ ( A @ compE_sk3 ) ) @ ( C @ ( B @ ( A @ compE_sk1 ) ) @ pair ) ) )
| ~ ( C @ ( B @ comp ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause79) ).
thf(471,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( B @ ( A @ compE_sk3 ) ) @ ( C @ ( B @ ( A @ compE_sk1 ) ) @ pair ) ) )
| ~ ( C @ ( B @ comp ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(30,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ un ) @ ord )
| ~ ( B @ ord )
| ~ ( A @ ord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause33) ).
thf(266,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ un ) @ ord )
| ~ ( B @ ord )
| ~ ( A @ ord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(70,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ cons ) @ subset ) )
| ~ ( B @ ( C @ subset ) )
| ~ ( B @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause9_1) ).
thf(360,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ cons ) @ subset ) )
| ~ ( B @ ( C @ subset ) )
| ~ ( B @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ subset ) )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause150) ).
thf(205,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ subset ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(136,axiom,
! [B: $i,A: $i] :
( ( B @ succ @ ( A @ member ) )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause13) ).
thf(508,plain,
! [B: $i,A: $i] :
( ( B @ succ @ ( A @ member ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(149,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ( A = B )
| ~ ( B @ succ @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause110) ).
thf(541,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ( A = B )
| ~ ( B @ succ @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(146,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ qsumE_sk2 ) ) @ member ) )
| ( A
= ( C @ ( B @ ( A @ qsumE_sk1 ) ) @ qInl ) )
| ~ ( C @ ( B @ qsum ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause43) ).
thf(530,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ qsumE_sk2 ) ) @ member ) )
| ( A
= ( C @ ( B @ ( A @ qsumE_sk1 ) ) @ qInl ) )
| ~ ( C @ ( B @ qsum ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(92,axiom,
! [B: $i,A: $i] :
( ( comb @ ( B @ member ) )
| ~ ( comb @ ( B @ ( A @ comb_app ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_E2) ).
thf(412,plain,
! [B: $i,A: $i] :
( ( comb @ ( B @ member ) )
| ~ ( comb @ ( B @ ( A @ comb_app ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(98,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( E @ comp ) @ ( D @ ( A @ pair ) @ member ) )
| ~ ( E @ ( D @ ( B @ pair ) @ member ) )
| ~ ( C @ ( B @ ( A @ pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause34) ).
thf(425,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( E @ comp ) @ ( D @ ( A @ pair ) @ member ) )
| ~ ( E @ ( D @ ( B @ pair ) @ member ) )
| ~ ( C @ ( B @ ( A @ pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(29,axiom,
! [A: $i] :
( ( A @ ord )
| ~ ( A @ succ @ ( eptset @ le ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause72) ).
thf(264,plain,
! [A: $i] :
( ( A @ ord )
| ~ ( A @ succ @ ( eptset @ le ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(1,negated_conjecture,
! [A: $i] :
( ~ ( contract @ ( A @ ( p @ pair ) @ member ) )
| ( r
!= ( A @ ( combK @ comb_app ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k1_contractD_c1) ).
thf(176,plain,
! [A: $i] :
( ~ ( contract @ ( A @ ( p @ pair ) @ member ) )
| ( r
!= ( A @ ( combK @ comb_app ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(97,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ compE_sk2 ) ) @ ( C @ ( B @ ( A @ compE_sk1 ) ) @ pair ) @ member ) )
| ~ ( C @ ( B @ comp ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause80) ).
thf(423,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ compE_sk2 ) ) @ ( C @ ( B @ ( A @ compE_sk1 ) ) @ pair ) @ member ) )
| ~ ( C @ ( B @ comp ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(87,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ member ) )
| ~ ( C @ ( A @ cons ) @ ( D @ member ) )
| ~ ( B @ ( B @ ( C @ ( A @ cons_subsetI_sk1 ) ) @ member ) )
| ~ ( B @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause9) ).
thf(402,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ member ) )
| ~ ( C @ ( A @ cons ) @ ( D @ member ) )
| ~ ( B @ ( B @ ( C @ ( A @ cons_subsetI_sk1 ) ) @ member ) )
| ~ ( B @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(37,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( B @ member ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ rmultE_c1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause55) ).
thf(286,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( B @ member ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ rmultE_c1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(108,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ field @ ( A @ member ) )
| ~ ( C @ ( B @ ( A @ pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause126) ).
thf(445,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ field @ ( A @ member ) )
| ~ ( C @ ( B @ ( A @ pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(80,axiom,
! [A: $i] :
( ( A @ inter @ ord )
| ( A @ ( A @ order_Inter_sk1 @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause29) ).
thf(382,plain,
! [A: $i] :
( ( A @ inter @ ord )
| ( A @ ( A @ order_Inter_sk1 @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(162,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ ( A @ rangeE_sk1 ) @ pair ) @ member ) )
| ~ ( B @ range @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause97) ).
thf(572,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ ( A @ rangeE_sk1 ) @ pair ) @ member ) )
| ~ ( B @ range @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(59,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( B @ ( A @ subsetI_sk1 ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause132) ).
thf(335,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( B @ ( A @ subsetI_sk1 ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( eptset @ ( A @ cons ) )
!= ( eptset @ ( B @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause108) ).
thf(187,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( eptset @ ( A @ cons ) )
!= ( eptset @ ( B @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(89,axiom,
! [C: $i,B: $i,A: $i] :
( ( contract @ ( C @ ( B @ comb_app ) @ ( C @ ( A @ comb_app ) @ comb_app ) @ ( C @ ( B @ ( A @ ( combS @ comb_app ) @ comb_app ) @ comb_app ) @ pair ) @ member ) )
| ~ ( comb @ ( C @ member ) )
| ~ ( comb @ ( B @ member ) )
| ~ ( comb @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contract_S) ).
thf(406,plain,
! [C: $i,B: $i,A: $i] :
( ( contract @ ( C @ ( B @ comb_app ) @ ( C @ ( A @ comb_app ) @ comb_app ) @ ( C @ ( B @ ( A @ ( combS @ comb_app ) @ comb_app ) @ comb_app ) @ pair ) @ member ) )
| ~ ( comb @ ( C @ member ) )
| ~ ( comb @ ( B @ member ) )
| ~ ( comb @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(95,axiom,
! [A: $i] :
( ( contract @ rtrancl @ ( A @ ( A @ pair ) @ member ) )
| ~ ( comb @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reduction_refl) ).
thf(419,plain,
! [A: $i] :
( ( contract @ rtrancl @ ( A @ ( A @ pair ) @ member ) )
| ~ ( comb @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(71,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ member ) )
| ~ ( F @ ( E @ ( D @ ( C @ radd ) ) ) @ ( B @ inl @ ( A @ inl @ pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause67) ).
thf(362,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ member ) )
| ~ ( F @ ( E @ ( D @ ( C @ radd ) ) ) @ ( B @ inl @ ( A @ inl @ pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(22,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ qInl )
!= ( B @ qInl ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause40) ).
thf(245,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ qInl )
!= ( B @ qInl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(82,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ pair ) )
!= ( D @ ( C @ pair ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause107) ).
thf(387,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ pair ) )
!= ( D @ ( C @ pair ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(53,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ sumE_sk2 ) ) @ member ) )
| ( B @ ( C @ ( B @ ( A @ sumE_sk1 ) ) @ member ) )
| ~ ( C @ ( B @ disjsum ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause88) ).
thf(323,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ sumE_sk2 ) ) @ member ) )
| ( B @ ( C @ ( B @ ( A @ sumE_sk1 ) ) @ member ) )
| ~ ( C @ ( B @ disjsum ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(171,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ ( D @ ( B @ pair ) @ member ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ rmultE_c2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause57) ).
thf(594,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ ( D @ ( B @ pair ) @ member ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ rmultE_c2 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(124,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( C @ ( B @ diff ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause113) ).
thf(483,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( C @ ( B @ diff ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(141,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ qconverseE_sk2 ) @ ( B @ ( A @ qconverseE_sk1 ) @ qPair ) @ member ) )
| ~ ( B @ qconverse @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause46) ).
thf(520,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ qconverseE_sk2 ) @ ( B @ ( A @ qconverseE_sk1 ) @ qPair ) @ member ) )
| ~ ( B @ qconverse @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( A @ inr )
!= ( B @ inl ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause84) ).
thf(198,plain,
! [B: $i,A: $i] :
( ( A @ inr )
!= ( B @ inl ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(86,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ pair ) )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause128) ).
thf(399,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ pair ) )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(45,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( A @ vimageE_sk1 ) ) @ ( A @ pair ) @ member ) )
| ~ ( C @ ( B @ vimage ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause92) ).
thf(306,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( A @ vimageE_sk1 ) ) @ ( A @ pair ) @ member ) )
| ~ ( C @ ( B @ vimage ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(158,axiom,
! [B: $i,A: $i] :
( combK
!= ( B @ ( A @ comb_app ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_app) ).
thf(563,plain,
! [B: $i,A: $i] :
( combK
!= ( B @ ( A @ comb_app ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ qInr )
!= ( B @ qInr ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause39) ).
thf(226,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ qInr )
!= ( B @ qInr ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(104,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( B @ member ) )
| ~ ( F @ ( E @ ( D @ ( C @ radd ) ) ) @ ( B @ inr @ ( A @ inl @ pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause70) ).
thf(438,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( B @ member ) )
| ~ ( F @ ( E @ ( D @ ( C @ radd ) ) ) @ ( B @ inr @ ( A @ inl @ pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(101,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ member ) )
| ( A != eptset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause121) ).
thf(431,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ member ) )
| ( A != eptset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(127,axiom,
! [B: $i,A: $i] : ( B @ ( A @ cons ) @ ( A @ member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause1) ).
thf(490,plain,
! [B: $i,A: $i] : ( B @ ( A @ cons ) @ ( A @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(76,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ vimageE_sk1 ) ) @ member ) )
| ~ ( C @ ( B @ vimage ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause93) ).
thf(374,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ vimageE_sk1 ) ) @ member ) )
| ~ ( C @ ( B @ vimage ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( A @ qInl )
!= ( B @ qInr ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause38) ).
thf(209,plain,
! [B: $i,A: $i] :
( ( A @ qInl )
!= ( B @ qInr ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(139,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ imageE_sk1 ) ) @ member ) )
| ~ ( C @ ( B @ image ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause95) ).
thf(516,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ imageE_sk1 ) ) @ member ) )
| ~ ( C @ ( B @ image ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(154,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ ( A @ qconverseE_sk1 ) @ ( B @ ( A @ qconverseE_sk2 ) @ qPair ) ) )
| ~ ( B @ qconverse @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause45) ).
thf(553,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ ( A @ qconverseE_sk1 ) @ ( B @ ( A @ qconverseE_sk2 ) @ qPair ) ) )
| ~ ( B @ qconverse @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(41,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ idE_sk1 ) @ member ) )
| ~ ( B @ id @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause82) ).
thf(295,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ idE_sk1 ) @ member ) )
| ~ ( B @ id @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(35,axiom,
! [C: $i,B: $i,A: $i] :
( ( comb @ ( A @ member ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE14) ).
thf(282,plain,
! [C: $i,B: $i,A: $i] :
( ( comb @ ( A @ member ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(93,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ sumE_sk2 ) ) @ member ) )
| ( A
= ( C @ ( B @ ( A @ sumE_sk1 ) ) @ inl ) )
| ~ ( C @ ( B @ disjsum ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause90) ).
thf(414,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ sumE_sk2 ) ) @ member ) )
| ( A
= ( C @ ( B @ ( A @ sumE_sk1 ) ) @ inl ) )
| ~ ( C @ ( B @ disjsum ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(55,axiom,
! [A: $i] : ( eptset @ ( A @ cons ) @ ( A @ member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause14) ).
thf(327,plain,
! [A: $i] : ( eptset @ ( A @ cons ) @ ( A @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(28,axiom,
! [A: $i] : ( A @ ( eptset @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause136) ).
thf(263,plain,
! [A: $i] : ( A @ ( eptset @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(47,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
~ ( F @ ( E @ ( D @ ( C @ radd ) ) ) @ ( B @ inl @ ( A @ inr @ pair ) @ member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause62) ).
thf(310,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
~ ( F @ ( E @ ( D @ ( C @ radd ) ) ) @ ( B @ inl @ ( A @ inr @ pair ) @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ inr )
!= ( B @ inr ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause86) ).
thf(182,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ inr )
!= ( B @ inr ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(57,axiom,
! [C: $i,B: $i,A: $i] :
( ( contract @ ( C @ ( B @ ( A @ ap_contractE_sk3q ) ) @ ( B @ pair ) @ member ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE13) ).
thf(331,plain,
! [C: $i,B: $i,A: $i] :
( ( contract @ ( C @ ( B @ ( A @ ap_contractE_sk3q ) ) @ ( B @ pair ) @ member ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(133,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ap_contractE_c4 ) ) )
| ( C @ ( B @ ( A @ ap_contractE_c3 ) ) )
| ( C @ ( B @ ( A @ ap_contractE_c2 ) ) )
| ( C @ ( B @ ( A @ ap_contractE_c1 ) ) )
| ~ ( contract @ ( C @ ( B @ ( A @ comb_app ) @ pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE1) ).
thf(502,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ap_contractE_c4 ) ) )
| ( C @ ( B @ ( A @ ap_contractE_c3 ) ) )
| ( C @ ( B @ ( A @ ap_contractE_c2 ) ) )
| ( C @ ( B @ ( A @ ap_contractE_c1 ) ) )
| ~ ( contract @ ( C @ ( B @ ( A @ comb_app ) @ pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(116,axiom,
! [B: $i,A: $i] :
( ( B @ pow @ ( A @ member ) )
| ( A @ ( B @ ( A @ powI_sk1 ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause21) ).
thf(463,plain,
! [B: $i,A: $i] :
( ( B @ pow @ ( A @ member ) )
| ( A @ ( B @ ( A @ powI_sk1 ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(164,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ~ ( C @ memrel @ ( B @ ( A @ pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause73) ).
thf(576,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ~ ( C @ memrel @ ( B @ ( A @ pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(150,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ field @ ( B @ member ) )
| ~ ( C @ ( B @ ( A @ pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause125) ).
thf(544,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ field @ ( B @ member ) )
| ~ ( C @ ( B @ ( A @ pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(167,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( eptset @ ( B @ cons ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause111) ).
thf(585,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( eptset @ ( B @ cons ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(74,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ( B @ ( A @ cons ) @ ( C @ ( B @ ( A @ cons_subsetE_sk1 ) ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause99) ).
thf(370,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ( B @ ( A @ cons ) @ ( C @ ( B @ ( A @ cons_subsetE_sk1 ) ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(174,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( C @ ( B @ int ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause115) ).
thf(600,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( C @ ( B @ int ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(49,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ pair ) )
!= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause129) ).
thf(314,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ pair ) )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(131,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ member ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ rmultE_c1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause54) ).
thf(497,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ member ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ rmultE_c1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(155,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( C @ ( B @ ( A @ ap_contractE_sk3q ) ) @ ( A @ comb_app ) ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE15) ).
thf(556,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( C @ ( B @ ( A @ ap_contractE_sk3q ) ) @ ( A @ comb_app ) ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ subset ) )
| ~ ( C @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause134) ).
thf(203,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ subset ) )
| ~ ( C @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(143,axiom,
! [A: $i] :
( ( nat @ ( A @ succ @ member ) )
| ~ ( nat @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause3) ).
thf(524,plain,
! [A: $i] :
( ( nat @ ( A @ succ @ member ) )
| ~ ( nat @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(130,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( B @ ( A @ pair ) @ member ) )
| ~ ( F @ ( E @ ( D @ ( C @ radd ) ) ) @ ( B @ inr @ ( A @ inr @ pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause65) ).
thf(495,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( B @ ( A @ pair ) @ member ) )
| ~ ( F @ ( E @ ( D @ ( C @ radd ) ) ) @ ( B @ inr @ ( A @ inr @ pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(14,axiom,
! [A: $i] :
( ( A = eptset )
| ~ ( eptset @ ( A @ le ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause76) ).
thf(218,plain,
! [A: $i] :
( ( A = eptset )
| ~ ( eptset @ ( A @ le ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(23,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause149) ).
thf(250,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(117,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A @ ( B @ ( A @ subsetI_sk1 ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause131) ).
thf(465,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A @ ( B @ ( A @ subsetI_sk1 ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ ord )
| ~ ( A @ succ @ ord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause78) ).
thf(231,plain,
! [A: $i] :
( ( A @ ord )
| ~ ( A @ succ @ ord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(168,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ unionE_sk1 ) @ member ) )
| ~ ( B @ union @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause120) ).
thf(588,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ unionE_sk1 ) @ member ) )
| ~ ( B @ union @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(51,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ member ) )
| ( B @ ( C @ cons ) @ ( D @ ( B @ ( C @ cons_subsetE_sk1 ) ) @ member ) )
| ~ ( B @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause101) ).
thf(319,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ member ) )
| ( B @ ( C @ cons ) @ ( D @ ( B @ ( C @ cons_subsetE_sk1 ) ) @ member ) )
| ~ ( B @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(44,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ disjsum ) @ ( A @ inr @ member ) )
| ~ ( B @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause7) ).
thf(304,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ disjsum ) @ ( A @ inr @ member ) )
| ~ ( B @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ lt ) )
| ~ ( B @ ( A @ succ @ le ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause71) ).
thf(258,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ lt ) )
| ~ ( B @ ( A @ succ @ le ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(160,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ cons ) @ ( A @ member ) )
| ~ ( B @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause15) ).
thf(568,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ cons ) @ ( A @ member ) )
| ~ ( B @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(19,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ rmultE_c2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause59) ).
thf(235,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ rmultE_c2 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(152,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ pair ) @ member ) )
| ~ ( C @ converse @ ( B @ ( A @ pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause105) ).
thf(549,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ pair ) @ member ) )
| ~ ( C @ converse @ ( B @ ( A @ pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(39,axiom,
! [B: $i,A: $i] :
( ( comb @ ( B @ ( A @ comb_app ) @ member ) )
| ~ ( comb @ ( B @ member ) )
| ~ ( comb @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',comb_intros3) ).
thf(290,plain,
! [B: $i,A: $i] :
( ( comb @ ( B @ ( A @ comb_app ) @ member ) )
| ~ ( comb @ ( B @ member ) )
| ~ ( comb @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(78,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ un ) @ ( A @ member ) )
| ~ ( B @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause19) ).
thf(378,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ un ) @ ( A @ member ) )
| ~ ( B @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(109,axiom,
! [A: $i] :
( ( A @ union @ card )
| ( A @ ( A @ card_Union_sk1 @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause25) ).
thf(447,plain,
! [A: $i] :
( ( A @ union @ card )
| ( A @ ( A @ card_Union_sk1 @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(91,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ member ) )
| ~ ( B @ ( D @ member ) )
| ~ ( C @ ( C @ ( B @ ( A @ cons_subsetE_sk1 ) ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause102) ).
thf(410,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ member ) )
| ~ ( B @ ( D @ member ) )
| ~ ( C @ ( C @ ( B @ ( A @ cons_subsetE_sk1 ) ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause148) ).
thf(190,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(32,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ subset ) )
| ~ ( C @ ( B @ ( A @ cons ) @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause102_2) ).
thf(273,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ subset ) )
| ~ ( C @ ( B @ ( A @ cons ) @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( ( A @ qInr )
!= ( B @ qInl ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause37) ).
thf(242,plain,
! [B: $i,A: $i] :
( ( A @ qInr )
!= ( B @ qInl ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(62,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ pair ) )
!= eptset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause127) ).
thf(341,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ pair ) )
!= eptset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(69,axiom,
! [B: $i,A: $i] :
( ( contract @ ( A @ ( B @ ( A @ ( combK @ comb_app ) @ comb_app ) @ pair ) @ member ) )
| ~ ( comb @ ( B @ member ) )
| ~ ( comb @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contract_K) ).
thf(358,plain,
! [B: $i,A: $i] :
( ( contract @ ( A @ ( B @ ( A @ ( combK @ comb_app ) @ comb_app ) @ pair ) @ member ) )
| ~ ( comb @ ( B @ member ) )
| ~ ( comb @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(121,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ comb_app ) )
!= ( D @ ( C @ comb_app ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',app_app2) ).
thf(474,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ comb_app ) )
!= ( D @ ( C @ comb_app ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(135,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( eptset @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause135) ).
thf(506,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( eptset @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(31,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ inl )
!= ( B @ inl ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause87) ).
thf(268,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ inl )
!= ( B @ inl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(84,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ rmultE_c2 ) ) ) ) ) ) ) )
| ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ rmultE_c1 ) ) ) ) ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ rmult ) ) ) @ ( D @ ( C @ pair ) @ ( B @ ( A @ pair ) @ pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause51) ).
thf(395,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ rmultE_c2 ) ) ) ) ) ) ) )
| ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ rmultE_c1 ) ) ) ) ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ rmult ) ) ) @ ( D @ ( C @ pair ) @ ( B @ ( A @ pair ) @ pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(99,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ cons ) @ ( A @ member ) )
| ~ ( B @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause2) ).
thf(427,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ cons ) @ ( A @ member ) )
| ~ ( B @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(172,axiom,
! [A: $i] :
~ ( contract @ ( A @ ( combS @ pair ) @ member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_contractE) ).
thf(596,plain,
! [A: $i] :
~ ( contract @ ( A @ ( combS @ pair ) @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(145,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ image ) @ ( B @ member ) )
| ~ ( D @ ( A @ member ) )
| ~ ( C @ ( B @ ( A @ pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause36) ).
thf(528,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ image ) @ ( B @ member ) )
| ~ ( D @ ( A @ member ) )
| ~ ( C @ ( B @ ( A @ pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(114,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ~ ( C @ ( C @ ( B @ ( A @ cons_subsetE_sk1 ) ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause100) ).
thf(459,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ~ ( C @ ( C @ ( B @ ( A @ cons_subsetE_sk1 ) ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(106,axiom,
comb @ ( combS @ member ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',comb_intros2) ).
thf(442,plain,
comb @ ( combS @ member ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(24,axiom,
! [B: $i,A: $i] :
( ( ( eptset @ ( A @ cons ) )
= ( eptset @ ( B @ cons ) ) )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause11) ).
thf(254,plain,
! [B: $i,A: $i] :
( ( ( eptset @ ( A @ cons ) )
= ( eptset @ ( B @ cons ) ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(60,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( C @ memrel @ ( B @ ( A @ pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause75) ).
thf(337,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( C @ memrel @ ( B @ ( A @ pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(119,axiom,
! [B: $i,A: $i] :
( ( B @ pow @ ( A @ member ) )
| ~ ( B @ ( B @ ( A @ powI_sk1 ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause22) ).
thf(469,plain,
! [B: $i,A: $i] :
( ( B @ pow @ ( A @ member ) )
| ~ ( B @ ( B @ ( A @ powI_sk1 ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(67,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ int ) @ ( A @ member ) )
| ~ ( C @ ( A @ member ) )
| ~ ( B @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause18) ).
thf(354,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ int ) @ ( A @ member ) )
| ~ ( C @ ( A @ member ) )
| ~ ( B @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(128,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ member ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ rmultE_c2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause58) ).
thf(491,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ member ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ rmultE_c2 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(170,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ converseE_sk2 ) @ ( B @ ( A @ converseE_sk1 ) @ pair ) @ member ) )
| ~ ( B @ converse @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause104) ).
thf(592,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ converseE_sk2 ) @ ( B @ ( A @ converseE_sk1 ) @ pair ) @ member ) )
| ~ ( B @ converse @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(112,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( B @ ( A @ sumE_sk2 ) ) @ inr ) )
| ( B @ ( C @ ( B @ ( A @ sumE_sk1 ) ) @ member ) )
| ~ ( C @ ( B @ disjsum ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause89) ).
thf(454,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( B @ ( A @ sumE_sk2 ) ) @ inr ) )
| ( B @ ( C @ ( B @ ( A @ sumE_sk1 ) ) @ member ) )
| ~ ( C @ ( B @ disjsum ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(72,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ( B @ ( A @ ( C @ ( B @ subsetD_sk1 ) ) @ member ) )
| ~ ( B @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause123) ).
thf(364,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ( B @ ( A @ ( C @ ( B @ subsetD_sk1 ) ) @ member ) )
| ~ ( B @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(893,plain,
$false,
inference(e,[status(thm)],[457,479,347,333,518,481,352,408,308,449,440,384,533,538,404,417,288,301,436,570,372,504,344,559,421,284,325,261,216,179,443,321,376,485,238,514,574,602,397,280,221,312,292,380,512,546,201,366,233,452,598,561,392,297,429,275,260,349,467,566,435,461,493,551,583,522,578,317,356,499,488,339,193,526,590,212,328,471,266,360,205,508,541,530,412,425,264,176,423,402,286,445,382,572,335,187,406,419,362,245,387,323,594,483,520,198,399,306,563,226,438,431,490,374,209,516,553,295,282,414,327,263,310,182,331,502,463,576,544,585,370,600,314,497,556,203,524,495,218,250,465,231,588,319,304,258,568,235,549,290,378,447,410,190,273,242,341,358,474,506,268,395,427,596,528,459,442,254,337,469,354,491,592,454,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL091-2 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.12/0.40 % Computer : n015.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sat Sep 26 23:16:59 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.84/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.45/1.23 % [INFO] Parsing done (249ms).
% 1.45/1.24 % [INFO] Running in sequential loop mode.
% 2.31/1.63 % [INFO] eprover registered as external prover.
% 2.31/1.64 % [INFO] Scanning for conjecture ...
% 2.48/1.76 % [INFO] Found a conjecture (or negated_conjecture) and 174 axioms. Running axiom selection ...
% 2.65/1.88 % [INFO] Axiom selection finished. Selected 174 axioms (removed 0 axioms).
% 2.95/2.00 % [INFO] Problem is propositional (TPTP CNF).
% 2.95/2.02 % [INFO] Type checking passed.
% 2.95/2.02 % [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 ...
% 9.83/3.96 % External prover 'e' found a proof!
% 9.83/3.96 % [INFO] Killing All external provers ...
% 9.83/3.97 % Time passed: 3420ms (effective reasoning time: 2715ms)
% 9.83/3.97 % Axioms used in derivation (174): clause57, ap_contractE7, clause82, clause60, clause65, app_app3, 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, clause38, ap_E1, clause16, clause28, ap_contractE11, clause98, clause53, clause12, clause111, clause79, clause102_2, clause136, clause97, ap_contractE15, ap_contractE1, clause9_1, clause75, contract_K, clause100, clause23, ap_contractE8, clause125, clause114, clause86, clause6, clause133, app_app1, clause122, clause103, clause1, clause34, s_contractE, clause69, reduction_refl, clause5, ap_contractE5, ap_contractE12, clause102_1, clause68, clause148, clause134, clause27, comb_intros1, clause110, clause41, ap_E2, clause39, clause35, clause8, k_app, clause30, clause20, clause52, clause46, clause90, clause126, clause115, clause63, clause89, clause44, clause102, clause150, clause50, k1_contractD_h1, clause33, clause94, clause73, clause83, clause72, ap_contractE9, clause107, clause19, contract_S, clause78, subsetD, clause123, comb_intros2, ap_contractE6, clause116, clause4, clause26, clause149, ap_contractE13, clause58, clause96, clause9, clause131, clause120, clause80, clause56, clause10, clause15, clause67, clause21, clause127, clause119, clause45, clause85, clause91, clause51, ap_contractE3, clause40, clause106, clause61, clause62, clause74, clause47, clause36
% 9.83/3.97 % No. of inferences in proof: 351
% 9.83/3.97 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 3420 ms resp. 2715 ms w/o parsing
% 10.66/4.11 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.66/4.11 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------