TSTP Solution File: SET787-2 by Leo-III---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SET787-2 : TPTP v8.2.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n021.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 21 03:03:52 EDT 2024
% Result : Unsatisfiable 5.31s 2.45s
% Output : Refutation 6.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 218
% Syntax : Number of formulae : 368 ( 45 unt; 69 typ; 0 def)
% Number of atoms : 617 ( 128 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 2694 ( 300 ~; 318 |; 0 &;2076 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 129 ( 129 >; 0 *; 0 +; 0 <<)
% Number of symbols : 71 ( 69 usr; 6 con; 0-8 aty)
% Number of variables : 900 ( 0 ^ 900 !; 0 ?; 900 :)
% Comments :
%------------------------------------------------------------------------------
thf(member_type,type,
member: $i > $i > $o ).
thf(sk2_type,type,
sk2: $i ).
thf(union_type,type,
union: $i > $i ).
thf(cons_type,type,
cons: $i > $i > $i ).
thf(a_type,type,
a: $i ).
thf(b_type,type,
b: $i ).
thf(eptset_type,type,
eptset: $i ).
thf(un_type,type,
un: $i > $i > $i ).
thf(snd_type,type,
snd: $i > $i ).
thf(pair_type,type,
pair: $i > $i > $i ).
thf(inr_type,type,
inr: $i > $i ).
thf(inl_type,type,
inl: $i > $i ).
thf(qInl_type,type,
qInl: $i > $i ).
thf(qPair_type,type,
qPair: $i > $i > $i ).
thf(le_type,type,
le: $i > $i > $o ).
thf(ord_type,type,
ord: $i > $o ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(qInr_type,type,
qInr: $i > $i ).
thf(order_Inter_sk1_type,type,
order_Inter_sk1: $i > $i ).
thf(inter_type,type,
inter: $i > $i ).
thf(fst_type,type,
fst: $i > $i ).
thf(succ_type,type,
succ: $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(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(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(disjsum_type,type,
disjsum: $i > $i > $i ).
thf(pow_type,type,
pow: $i > $i ).
thf(radd_type,type,
radd: $i > $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(subsetI_sk1_type,type,
subsetI_sk1: $i > $i > $i ).
thf(upair_type,type,
upair: $i > $i > $i ).
thf(memrel_type,type,
memrel: $i > $i ).
thf(diff_type,type,
diff: $i > $i > $i ).
thf(interI_sk1_type,type,
interI_sk1: $i > $i > $i ).
thf(order_Union_sk1_type,type,
order_Union_sk1: $i > $i ).
thf(converse_type,type,
converse: $i > $i ).
thf(converseE_sk2_type,type,
converseE_sk2: $i > $i ).
thf(converseE_sk1_type,type,
converseE_sk1: $i > $i ).
thf(rmult_type,type,
rmult: $i > $i > $i > $i > $i ).
thf(sigma_type,type,
sigma: $i > $i > $i ).
thf(apply_type,type,
apply: $i > $i > $i ).
thf(compE_sk1_type,type,
compE_sk1: $i > $i > $i > $i ).
thf(field_type,type,
field: $i > $i ).
thf(card_Union_sk1_type,type,
card_Union_sk1: $i > $i ).
thf(card_type,type,
card: $i > $o ).
thf(converse_sk1_type,type,
converse_sk1: $i > $i ).
thf(converse_sk2_type,type,
converse_sk2: $i > $i ).
thf(vimage_type,type,
vimage: $i > $i > $i ).
thf(powI_sk1_type,type,
powI_sk1: $i > $i > $i ).
thf(sigmaE_sk1x_type,type,
sigmaE_sk1x: $i > $i > $i > $i ).
thf(sigmaE_sk1y_type,type,
sigmaE_sk1y: $i > $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(image_type,type,
image: $i > $i > $i ).
thf(unionE_sk1_type,type,
unionE_sk1: $i > $i > $i ).
thf(82,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(352,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)],[82]) ).
thf(108,axiom,
! [A: $i] :
( ~ ( le @ A @ eptset )
| ( A = eptset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause76) ).
thf(408,plain,
! [A: $i] :
( ~ ( le @ A @ eptset )
| ( A = eptset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(62,axiom,
! [C: $i,B: $i,A: $i] :
( ( A != B )
| ( member @ A @ ( cons @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause16) ).
thf(308,plain,
! [C: $i,B: $i,A: $i] :
( ( A != B )
| ( member @ A @ ( cons @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(95,axiom,
! [A: $i] :
( ( member @ ( card_Union_sk1 @ A ) @ A )
| ( card @ ( union @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause25) ).
thf(379,plain,
! [A: $i] :
( ( member @ ( card_Union_sk1 @ A ) @ A )
| ( card @ ( union @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(123,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(440,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)],[123]) ).
thf(43,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(269,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)],[43]) ).
thf(98,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(385,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)],[98]) ).
thf(76,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ~ ( member @ C @ A )
| ( member @ C @ ( union @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause143) ).
thf(340,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ~ ( member @ C @ A )
| ( member @ C @ ( union @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( snd @ ( pair @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause157) ).
thf(153,plain,
! [B: $i,A: $i] :
( ( snd @ ( pair @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(14,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(185,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)],[14]) ).
thf(112,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( sigma @ B @ C ) )
| ( member @ ( sigmaE_sk1y @ B @ C @ A ) @ ( apply @ C @ ( sigmaE_sk1x @ B @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause145) ).
thf(417,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( sigma @ B @ C ) )
| ( member @ ( sigmaE_sk1y @ B @ C @ A ) @ ( apply @ C @ ( sigmaE_sk1x @ B @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(122,axiom,
! [B: $i,A: $i] :
( ( A != B )
| ( member @ A @ ( succ @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause13) ).
thf(436,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( member @ A @ ( succ @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(13,axiom,
! [A: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause133) ).
thf(184,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(78,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(344,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)],[78]) ).
thf(85,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( member @ C @ A )
| ( member @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause137) ).
thf(357,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( member @ C @ A )
| ( member @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ( pair @ A @ B )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause128) ).
thf(196,plain,
! [B: $i,A: $i] :
( ( pair @ A @ B )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( A != B )
| ( subset @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause150) ).
thf(189,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( subset @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(114,axiom,
! [B: $i,A: $i] : ( member @ A @ ( cons @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause1) ).
thf(421,plain,
! [B: $i,A: $i] : ( member @ A @ ( cons @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(51,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(284,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)],[51]) ).
thf(69,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ A @ ( un @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unI1) ).
thf(325,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ A @ ( un @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(53,axiom,
! [B: $i,A: $i] : ( member @ A @ ( upair @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause139) ).
thf(289,plain,
! [B: $i,A: $i] : ( member @ A @ ( upair @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(127,axiom,
! [B: $i,A: $i] :
( ~ ( ord @ A )
| ~ ( ord @ B )
| ( ord @ ( un @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause33) ).
thf(448,plain,
! [B: $i,A: $i] :
( ~ ( ord @ A )
| ~ ( ord @ B )
| ( ord @ ( un @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(65,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ A @ ( un @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause19) ).
thf(316,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ A @ ( un @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(39,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(261,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ ( inr @ A ) @ ( disjsum @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(24,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(216,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)],[24]) ).
thf(67,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(321,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ A @ B ) @ ( memrel @ C ) )
| ( member @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(80,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(348,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)],[80]) ).
thf(141,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( union @ B ) )
| ( member @ A @ ( unionE_sk1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause119) ).
thf(480,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( union @ B ) )
| ( member @ A @ ( unionE_sk1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(55,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( diff @ B @ C ) )
| ~ ( member @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause114) ).
thf(293,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( diff @ B @ C ) )
| ~ ( member @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(103,axiom,
! [B: $i,A: $i] :
( ( member @ ( subsetI_sk1 @ A @ B ) @ A )
| ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause131) ).
thf(396,plain,
! [B: $i,A: $i] :
( ( member @ ( subsetI_sk1 @ A @ B ) @ A )
| ( subset @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(109,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(411,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ ( inl @ A ) @ ( disjsum @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(118,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(428,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)],[118]) ).
thf(41,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(265,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)],[41]) ).
thf(63,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(312,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)],[63]) ).
thf(129,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(452,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)],[129]) ).
thf(33,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(248,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)],[33]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ( fst @ ( pair @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause156) ).
thf(201,plain,
! [B: $i,A: $i] :
( ( fst @ ( pair @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(96,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( converse @ B ) )
| ( member @ ( pair @ ( converse_sk1 @ A ) @ ( converse_sk2 @ A ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converseE_2) ).
thf(381,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( converse @ B ) )
| ( member @ ( pair @ ( converse_sk1 @ A ) @ ( converse_sk2 @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( ( qInr @ A )
!= ( qInl @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause37) ).
thf(220,plain,
! [B: $i,A: $i] :
( ( qInr @ A )
!= ( qInl @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(73,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(334,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)],[73]) ).
thf(59,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(302,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)],[59]) ).
thf(101,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ A @ ( un @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unI2) ).
thf(392,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ A @ ( un @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(116,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(424,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)],[116]) ).
thf(135,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(467,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ A @ B ) @ C )
| ( member @ B @ ( field @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(143,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(484,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ A @ B ) @ ( memrel @ C ) )
| ( member @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(35,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(252,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)],[35]) ).
thf(87,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ A @ ( cons @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause2) ).
thf(361,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ A @ ( cons @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(131,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(456,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)],[131]) ).
thf(106,axiom,
! [B: $i,A: $i] :
( ~ ( member @ ( powI_sk1 @ A @ B ) @ B )
| ( member @ A @ ( pow @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause22) ).
thf(403,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( powI_sk1 @ A @ B ) @ B )
| ( member @ A @ ( pow @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(99,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(388,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)],[99]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( ( qInl @ A )
!= ( qInl @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause40) ).
thf(169,plain,
! [B: $i,A: $i] :
( ( ( qInl @ A )
!= ( qInl @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(145,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( upair @ B @ C ) )
| ( A = B )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause140) ).
thf(488,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( upair @ B @ C ) )
| ( A = B )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ( qInl @ A )
!= ( qInr @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause38) ).
thf(193,plain,
! [B: $i,A: $i] :
( ( qInl @ A )
!= ( qInr @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(139,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(476,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)],[139]) ).
thf(23,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A != B )
| ( C != D )
| ( ( pair @ A @ C )
= ( pair @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause130) ).
thf(212,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A != B )
| ( C != D )
| ( ( pair @ A @ C )
= ( pair @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(71,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(328,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)],[71]) ).
thf(137,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(471,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)],[137]) ).
thf(37,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(256,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)],[37]) ).
thf(9,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(173,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)],[9]) ).
thf(91,axiom,
! [A: $i] :
( ~ ( le @ eptset @ ( succ @ A ) )
| ( ord @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause72) ).
thf(371,plain,
! [A: $i] :
( ~ ( le @ eptset @ ( succ @ A ) )
| ( ord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(32,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(244,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)],[32]) ).
thf(104,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(398,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)],[104]) ).
thf(119,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( sigma @ B @ C ) )
| ( member @ ( sigmaE_sk1x @ B @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause144) ).
thf(430,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( sigma @ B @ C ) )
| ( member @ ( sigmaE_sk1x @ B @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( pair @ A @ B )
!= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause129) ).
thf(166,plain,
! [B: $i,A: $i] :
( ( pair @ A @ B )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(48,axiom,
! [B: $i,A: $i] :
( ~ ( member @ ( subsetI_sk1 @ A @ B ) @ B )
| ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause132) ).
thf(279,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( subsetI_sk1 @ A @ B ) @ B )
| ( subset @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(125,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(444,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)],[125]) ).
thf(93,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ A @ ( succ @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause12) ).
thf(375,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ A @ ( succ @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(11,axiom,
! [A: $i] :
( ~ ( le @ A @ A )
| ( ord @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause77) ).
thf(180,plain,
! [A: $i] :
( ~ ( le @ A @ A )
| ( ord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(57,axiom,
! [B: $i,A: $i] :
( ( A != B )
| ( ( cons @ A @ eptset )
= ( cons @ B @ eptset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause11) ).
thf(296,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( ( cons @ A @ eptset )
= ( cons @ B @ eptset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(52,axiom,
! [B: $i,A: $i] :
( ( pair @ A @ B )
!= eptset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause127) ).
thf(286,plain,
! [B: $i,A: $i] :
( ( pair @ A @ B )
!= eptset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(49,axiom,
! [B: $i,A: $i] : ( member @ A @ ( upair @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause138) ).
thf(281,plain,
! [B: $i,A: $i] : ( member @ A @ ( upair @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(38,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( id @ B ) )
| ( member @ ( idE_sk1 @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause82) ).
thf(259,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( id @ B ) )
| ( member @ ( idE_sk1 @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(110,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(413,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)],[110]) ).
thf(149,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( int @ B @ C ) )
| ( member @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause115) ).
thf(498,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( int @ B @ C ) )
| ( member @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(30,axiom,
! [B: $i,A: $i] :
( ( ( succ @ A )
!= ( succ @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause109) ).
thf(236,plain,
! [B: $i,A: $i] :
( ( ( succ @ A )
!= ( succ @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( inl @ A )
!= ( inr @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause85) ).
thf(159,plain,
! [B: $i,A: $i] :
( ( inl @ A )
!= ( inr @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(46,axiom,
! [B: $i,A: $i] :
( ( ( cons @ A @ eptset )
!= ( cons @ B @ eptset ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause108) ).
thf(274,plain,
! [B: $i,A: $i] :
( ( ( cons @ A @ eptset )
!= ( cons @ B @ eptset ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(113,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(419,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)],[113]) ).
thf(94,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(377,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ A @ B ) @ C )
| ( member @ A @ ( field @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(28,axiom,
! [B: $i,A: $i] :
( ~ ( le @ ( succ @ A ) @ B )
| ( lt @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause71) ).
thf(230,plain,
! [B: $i,A: $i] :
( ~ ( le @ ( succ @ A ) @ B )
| ( lt @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(66,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( converse @ B ) )
| ( A
= ( pair @ ( converseE_sk2 @ A ) @ ( converseE_sk1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converseE_1) ).
thf(318,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( converse @ B ) )
| ( A
= ( pair @ ( converseE_sk2 @ A ) @ ( converseE_sk1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(121,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ eptset )
| ( member @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause135) ).
thf(434,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ eptset )
| ( member @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(44,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(271,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)],[44]) ).
thf(147,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( union @ B ) )
| ( member @ ( unionE_sk1 @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause120) ).
thf(494,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( union @ B ) )
| ( member @ ( unionE_sk1 @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(89,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(367,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)],[89]) ).
thf(68,axiom,
! [A: $i] :
( ( member @ ( order_Inter_sk1 @ A ) @ A )
| ( ord @ ( inter @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause29) ).
thf(323,plain,
! [A: $i] :
( ( member @ ( order_Inter_sk1 @ A ) @ A )
| ( ord @ ( inter @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(31,axiom,
! [B: $i,A: $i] :
( ( ( inl @ A )
!= ( inl @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause87) ).
thf(240,plain,
! [B: $i,A: $i] :
( ( ( inl @ A )
!= ( inl @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( A != B )
| ( ( inr @ A )
= ( inr @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause4) ).
thf(155,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( ( inr @ A )
= ( inr @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(133,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( succ @ B ) )
| ( A = B )
| ( member @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause110) ).
thf(462,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( succ @ B ) )
| ( A = B )
| ( member @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(26,axiom,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause148) ).
thf(223,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(27,axiom,
! [B: $i,A: $i] :
( ( A != B )
| ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause149) ).
thf(226,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( subset @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(42,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(267,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( member @ C @ A )
| ( member @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(102,axiom,
! [B: $i,A: $i] :
( ( member @ ( powI_sk1 @ A @ B ) @ A )
| ( member @ A @ ( pow @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause21) ).
thf(394,plain,
! [B: $i,A: $i] :
( ( member @ ( powI_sk1 @ A @ B ) @ A )
| ( member @ A @ ( pow @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(61,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(306,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)],[61]) ).
thf(117,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(426,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)],[117]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( ( inr @ A )
!= ( inr @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause86) ).
thf(162,plain,
! [B: $i,A: $i] :
( ( ( inr @ A )
!= ( inr @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(22,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(209,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)],[22]) ).
thf(77,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( sigma @ B @ C ) )
| ( member @ ( fst @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause154) ).
thf(342,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( sigma @ B @ C ) )
| ( member @ ( fst @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(84,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(355,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)],[84]) ).
thf(56,axiom,
! [A: $i] : ( member @ eptset @ ( pow @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause151) ).
thf(295,plain,
! [A: $i] : ( member @ eptset @ ( pow @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(50,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(282,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ A @ B ) @ ( memrel @ C ) )
| ( member @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(1,negated_conjecture,
member @ sk2 @ ( union @ ( cons @ a @ ( cons @ b @ eptset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',un_eq_Union_2_c1) ).
thf(150,plain,
member @ sk2 @ ( union @ ( cons @ a @ ( cons @ b @ eptset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(70,axiom,
! [A: $i] : ( member @ A @ ( succ @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause141) ).
thf(327,plain,
! [A: $i] : ( member @ A @ ( succ @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(40,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(263,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)],[40]) ).
thf(18,axiom,
! [A: $i] :
( ~ ( ord @ ( order_Inter_sk1 @ A ) )
| ( ord @ ( inter @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause30) ).
thf(199,plain,
! [A: $i] :
( ~ ( ord @ ( order_Inter_sk1 @ A ) )
| ( ord @ ( inter @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(72,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(331,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)],[72]) ).
thf(75,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(338,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)],[75]) ).
thf(86,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(359,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)],[86]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( inr @ A )
!= ( inl @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause84) ).
thf(177,plain,
! [B: $i,A: $i] :
( ( inr @ A )
!= ( inl @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(12,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(182,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(74,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(336,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)],[74]) ).
thf(64,axiom,
! [A: $i] :
( ( member @ ( order_Union_sk1 @ A ) @ A )
| ( ord @ ( union @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause31) ).
thf(314,plain,
! [A: $i] :
( ( member @ ( order_Union_sk1 @ A ) @ A )
| ( ord @ ( union @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(126,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(446,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)],[126]) ).
thf(128,axiom,
! [A: $i] :
( ~ ( member @ A @ nat )
| ( member @ ( succ @ A ) @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause3) ).
thf(450,plain,
! [A: $i] :
( ~ ( member @ A @ nat )
| ( member @ ( succ @ A ) @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(88,axiom,
! [B: $i,A: $i] :
( ( A != eptset )
| ~ ( member @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause121) ).
thf(363,plain,
! [B: $i,A: $i] :
( ( A != eptset )
| ~ ( member @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(34,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(250,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)],[34]) ).
thf(134,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ A @ ( succ @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause142) ).
thf(465,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ A @ ( succ @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(142,axiom,
! [A: $i] :
( ~ ( member @ ( succ @ A ) @ nat )
| ( member @ A @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause50) ).
thf(482,plain,
! [A: $i] :
( ~ ( member @ ( succ @ A ) @ nat )
| ( member @ A @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( ( ( qInr @ A )
!= ( qInr @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause39) ).
thf(203,plain,
! [B: $i,A: $i] :
( ( ( qInr @ A )
!= ( qInr @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(60,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(304,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)],[60]) ).
thf(81,axiom,
! [A: $i] : ( member @ A @ ( pow @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause152) ).
thf(351,plain,
! [A: $i] : ( member @ A @ ( pow @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(100,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( sigma @ B @ C ) )
| ( member @ ( snd @ A ) @ ( apply @ C @ ( fst @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause155) ).
thf(390,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( sigma @ B @ C ) )
| ( member @ ( snd @ A ) @ ( apply @ C @ ( fst @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(54,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(290,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)],[54]) ).
thf(21,axiom,
! [A: $i] :
( ~ ( ord @ ( succ @ A ) )
| ( ord @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause78) ).
thf(207,plain,
! [A: $i] :
( ~ ( ord @ ( succ @ A ) )
| ( ord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(140,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ A @ ( cons @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause15) ).
thf(478,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ A @ ( cons @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(97,axiom,
! [A: $i] :
( ~ ( card @ ( card_Union_sk1 @ A ) )
| ( card @ ( union @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause26) ).
thf(383,plain,
! [A: $i] :
( ~ ( card @ ( card_Union_sk1 @ A ) )
| ( card @ ( union @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(79,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ~ ( member @ C @ ( apply @ D @ A ) )
| ( member @ ( pair @ A @ C ) @ ( sigma @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause153) ).
thf(346,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ~ ( member @ C @ ( apply @ D @ A ) )
| ( member @ ( pair @ A @ C ) @ ( sigma @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(2,negated_conjecture,
~ ( member @ sk2 @ ( un @ a @ b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',un_eq_Union_2_c2) ).
thf(151,plain,
~ ( member @ sk2 @ ( un @ a @ b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(58,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(300,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)],[58]) ).
thf(120,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ A @ ( un @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause20) ).
thf(432,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ A @ ( un @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(107,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(405,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)],[107]) ).
thf(115,axiom,
! [A: $i] :
~ ( member @ A @ eptset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause158) ).
thf(422,plain,
! [A: $i] :
~ ( member @ A @ eptset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(45,axiom,
! [A: $i] : ( member @ A @ ( cons @ A @ eptset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause14) ).
thf(273,plain,
! [A: $i] : ( member @ A @ ( cons @ A @ eptset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(92,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',converseD) ).
thf(373,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)],[92]) ).
thf(138,axiom,
! [A: $i] :
( ~ ( ord @ ( order_Union_sk1 @ A ) )
| ( ord @ ( union @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause32) ).
thf(474,plain,
! [A: $i] :
( ~ ( ord @ ( order_Union_sk1 @ A ) )
| ( ord @ ( union @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(105,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( sigma @ B @ C ) )
| ( A
= ( pair @ ( sigmaE_sk1x @ B @ C @ A ) @ ( sigmaE_sk1y @ B @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause147) ).
thf(400,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( sigma @ B @ C ) )
| ( A
= ( pair @ ( sigmaE_sk1x @ B @ C @ A ) @ ( sigmaE_sk1y @ B @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(111,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( diff @ B @ C ) )
| ( member @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause113) ).
thf(415,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( diff @ B @ C ) )
| ( member @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(132,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(459,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)],[132]) ).
thf(47,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(277,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)],[47]) ).
thf(124,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(442,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)],[124]) ).
thf(90,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(369,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)],[90]) ).
thf(36,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( int @ B @ C ) )
| ( member @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause116) ).
thf(254,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( int @ B @ C ) )
| ( member @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(144,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(486,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)],[144]) ).
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 @ D @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause56) ).
thf(469,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)],[136]) ).
thf(83,axiom,
! [A: $i] : ( subset @ eptset @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause136) ).
thf(354,plain,
! [A: $i] : ( subset @ eptset @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(146,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( cons @ B @ eptset ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause111) ).
thf(491,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( cons @ B @ eptset ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(29,axiom,
! [B: $i,A: $i] :
( ( A != B )
| ( ( inl @ A )
= ( inl @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause5) ).
thf(232,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( ( inl @ A )
= ( inl @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(148,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(496,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)],[148]) ).
thf(130,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(454,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)],[130]) ).
thf(507,plain,
$false,
inference(cvc4,[status(thm)],[352,408,308,379,440,269,385,340,153,185,417,436,184,344,357,196,189,421,284,325,289,448,316,261,216,321,348,480,293,396,411,428,265,312,452,248,201,381,220,334,302,392,424,467,484,252,361,456,403,388,169,488,193,476,212,328,471,256,173,371,244,398,430,166,279,444,375,180,296,286,281,259,413,498,236,159,274,419,377,230,318,434,271,494,367,323,240,155,462,223,226,267,394,306,426,162,209,342,355,295,282,150,327,263,199,331,338,359,177,182,336,314,446,450,363,250,465,482,203,304,351,390,290,207,478,383,346,151,300,432,405,422,273,373,474,400,415,459,277,442,369,254,486,469,354,491,232,496,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET787-2 : TPTP v8.2.0. Released v2.7.0.
% 0.13/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n021.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon May 20 12:39:09 EDT 2024
% 0.16/0.38 % CPUTime :
% 1.01/0.89 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.36/1.05 % [INFO] Parsing done (158ms).
% 1.36/1.06 % [INFO] Running in sequential loop mode.
% 1.81/1.29 % [INFO] eprover registered as external prover.
% 1.81/1.30 % [INFO] cvc4 registered as external prover.
% 1.81/1.30 % [INFO] Scanning for conjecture ...
% 2.07/1.38 % [INFO] Found a conjecture (or negated_conjecture) and 147 axioms. Running axiom selection ...
% 2.07/1.45 % [INFO] Axiom selection finished. Selected 147 axioms (removed 0 axioms).
% 2.58/1.52 % [INFO] Problem is propositional (TPTP CNF).
% 2.58/1.53 % [INFO] Type checking passed.
% 2.58/1.53 % [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 ...
% 5.31/2.45 % External prover 'cvc4' found a proof!
% 5.31/2.45 % [INFO] Killing All external provers ...
% 5.31/2.45 % Time passed: 1905ms (effective reasoning time: 1386ms)
% 5.31/2.45 % Axioms used in derivation (147): clause147, clause140, clause144, clause57, clause82, clause60, clause65, clause128, clause71, clause113, clause43, clause139, clause3, clause29, clause32, clause18, clause54, clause117, clause88, clause59, clause48, clause37, converseD, clause108, clause77, clause135, clause129, clause81, clause55, clause154, clause66, unI2, clause118, clause17, clause70, clause22, clause124, clause157, clause84, clause7, clause25, clause11, clause14, converseE_1, clause87, clause112, clause76, clause130, clause49, converseE_2, clause13, clause31, clause24, clause132, clause121, clause42, clause109, clause2, clause158, clause141, clause143, clause64, clause38, clause16, clause28, unI1, clause53, clause152, clause155, clause136, clause12, clause111, clause79, clause75, clause23, clause125, clause114, clause86, clause6, clause133, clause122, clause1, clause151, clause34, clause5, clause69, clause68, clause148, clause134, clause27, clause110, clause41, clause39, clause137, clause35, clause30, clause145, clause20, clause52, clause46, clause156, clause90, clause126, clause115, clause63, clause89, clause44, clause50, clause150, clause72, clause33, clause73, clause83, clause107, clause19, clause78, subsetD, clause123, clause116, clause4, clause26, clause149, clause58, clause142, clause131, clause120, clause80, clause56, clause10, clause67, clause138, clause21, clause127, clause119, clause15, clause153, clause45, clause40, clause85, clause91, clause51, clause106, clause61, clause62, clause74, clause47, clause36
% 5.31/2.45 % No. of inferences in proof: 299
% 5.31/2.45 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1905 ms resp. 1386 ms w/o parsing
% 6.01/2.52 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.01/2.52 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------