TSTP Solution File: DAT255^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : DAT255^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:39:52 EDT 2024
% Result : Theorem 10.12s 5.09s
% Output : Refutation 10.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 55
% Syntax : Number of formulae : 95 ( 56 unt; 17 typ; 0 def)
% Number of atoms : 278 ( 86 equ; 6 cnn)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 1833 ( 42 ~; 0 |; 10 &;1747 @)
% ( 0 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 11 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 153 ( 153 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 8 con; 0-9 aty)
% Number of variables : 611 ( 0 ^ 574 !; 4 ?; 611 :)
% ( 33 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(nat_type,type,
nat: $tType ).
thf(d_type,type,
d: $tType ).
thf(c_type,type,
c: $tType ).
thf(b_type,type,
b: $tType ).
thf(a_type,type,
a: $tType ).
thf(product_Pair_type,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( TB > TA > ( product_prod @ TB @ TA ) ) ).
thf(produc2004651681e_prod_type,type,
produc2004651681e_prod:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > TA ) > ( product_prod @ TC @ TB ) > TA ) ).
thf(product_rec_prod_type,type,
product_rec_prod:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > TA ) > ( product_prod @ TC @ TB ) > TA ) ).
thf(stream5064451run_mu_type,type,
stream5064451run_mu:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( stream901396144_sp_mu @ TC @ TB @ TA ) > ( stream @ TC ) > ( product_prod @ ( product_prod @ TB @ TA ) @ ( stream @ TC ) ) ) ).
thf(stream1294929701mu_Get_type,type,
stream1294929701mu_Get:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > ( stream901396144_sp_mu @ TC @ TB @ TA ) ) > ( stream901396144_sp_mu @ TC @ TB @ TA ) ) ).
thf(stream1370332830mu_Put_type,type,
stream1370332830mu_Put:
!>[TA: $tType,TB: $tType,TC: $tType] : ( TC > TB > ( stream901396144_sp_mu @ TA @ TC @ TB ) ) ).
thf(stream160000856_sp_mu_type,type,
stream160000856_sp_mu:
!>[TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( ( ( TD > ( stream901396144_sp_mu @ TD @ TC @ TB ) ) > TA ) > ( TC > TB > TA ) > ( stream901396144_sp_mu @ TD @ TC @ TB ) > TA ) ).
thf(stream123009735_sp_mu_type,type,
stream123009735_sp_mu:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > $o ) > ( TB > $o ) > ( stream901396144_sp_mu @ TA @ TC @ TB ) > $o ) ).
thf(stream674629690_sp_mu_type,type,
stream674629690_sp_mu:
!>[TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( ( ( TD > ( product_prod @ ( stream901396144_sp_mu @ TD @ TC @ TB ) @ TA ) ) > TA ) > ( TC > TB > TA ) > ( stream901396144_sp_mu @ TD @ TC @ TB ) > TA ) ).
thf(stream1924447089_sp_mu_type,type,
stream1924447089_sp_mu:
!>[TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] : ( ( TE > TD > $o ) > ( TC > TB > $o ) > ( stream901396144_sp_mu @ TA @ TE @ TC ) > ( stream901396144_sp_mu @ TA @ TD @ TB ) > $o ) ).
thf(p_type,type,
p: $o ).
thf(x_type,type,
x: product_prod @ ( stream901396144_sp_mu @ a @ b @ c ) @ ( stream901396144_sp_mu @ d @ a @ ( stream1273403375_sp_nu @ d @ a ) ) ).
thf(13,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ B @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ C @ ( product_Pair @ TB @ TA @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_prod__cases4) ).
thf(69,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ B @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ C @ ( product_Pair @ TB @ TA @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(31,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: ( TD > ( stream901396144_sp_mu @ TD @ TC @ TA ) ) > TB,B: TC > TA > TB,C: TC,D: TA] :
( ( stream160000856_sp_mu @ TD @ TC @ TA @ TB @ A @ B @ ( stream1370332830mu_Put @ TC @ TA @ TD @ C @ D ) )
= ( B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_sp_092_060_094sub_062_092_060mu_062_Osimps_I6_J) ).
thf(120,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: ( TD > ( stream901396144_sp_mu @ TD @ TC @ TA ) ) > TB,B: TC > TA > TB,C: TC,D: TA] :
( ( stream160000856_sp_mu @ TD @ TC @ TA @ TB @ A @ B @ ( stream1370332830mu_Put @ TC @ TA @ TD @ C @ D ) )
= ( B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(33,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TE > TC > $o,B: TD > TA > $o,C: TB > ( stream901396144_sp_mu @ TB @ TE @ TD ),D: TC,E: TA] :
~ ( stream1924447089_sp_mu @ TE @ TC @ TD @ TA @ TB @ A @ B @ ( stream1294929701mu_Get @ TB @ TE @ TD @ C ) @ ( stream1370332830mu_Put @ TC @ TA @ TB @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_sp_092_060_094sub_062_092_060mu_062_Orel__distinct_I1_J) ).
thf(125,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TE > TC > $o,B: TD > TA > $o,C: TB > ( stream901396144_sp_mu @ TB @ TE @ TD ),D: TC,E: TA] :
~ ( stream1924447089_sp_mu @ TE @ TC @ TD @ TA @ TB @ A @ B @ ( stream1294929701mu_Get @ TB @ TE @ TD @ C ) @ ( stream1370332830mu_Put @ TC @ TA @ TB @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(19,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: stream901396144_sp_mu @ TB @ TC @ TA] :
( ! [B: TB > ( stream901396144_sp_mu @ TB @ TC @ TA )] :
( A
!= ( stream1294929701mu_Get @ TB @ TC @ TA @ B ) )
=> ~ ! [B: TC,C: TA] :
( A
!= ( stream1370332830mu_Put @ TC @ TA @ TB @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_sp_092_060_094sub_062_092_060mu_062_Oexhaust) ).
thf(84,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: stream901396144_sp_mu @ TB @ TC @ TA] :
( ! [B: TB > ( stream901396144_sp_mu @ TB @ TC @ TA )] :
( A
!= ( stream1294929701mu_Get @ TB @ TC @ TA @ B ) )
=> ~ ! [B: TC,C: TA] :
( A
!= ( stream1370332830mu_Put @ TC @ TA @ TB @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(37,axiom,
! [A: b,B: c,C: stream901396144_sp_mu @ d @ a @ ( stream1273403375_sp_nu @ d @ a )] :
( ( x
= ( product_Pair @ ( stream901396144_sp_mu @ a @ b @ c ) @ ( stream901396144_sp_mu @ d @ a @ ( stream1273403375_sp_nu @ d @ a ) ) @ ( stream1370332830mu_Put @ b @ c @ a @ A @ B ) @ C ) )
=> p ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(137,plain,
! [A: b,B: c,C: stream901396144_sp_mu @ d @ a @ ( stream1273403375_sp_nu @ d @ a )] :
( ( x
= ( product_Pair @ ( stream901396144_sp_mu @ a @ b @ c ) @ ( stream901396144_sp_mu @ d @ a @ ( stream1273403375_sp_nu @ d @ a ) ) @ ( stream1370332830mu_Put @ b @ c @ a @ A @ B ) @ C ) )
=> p ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(38,axiom,
! [A: a > ( stream901396144_sp_mu @ a @ b @ c ),B: a,C: stream1273403375_sp_nu @ d @ a] :
( ( x
= ( product_Pair @ ( stream901396144_sp_mu @ a @ b @ c ) @ ( stream901396144_sp_mu @ d @ a @ ( stream1273403375_sp_nu @ d @ a ) ) @ ( stream1294929701mu_Get @ a @ b @ c @ A ) @ ( stream1370332830mu_Put @ a @ ( stream1273403375_sp_nu @ d @ a ) @ d @ B @ C ) ) )
=> p ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(141,plain,
! [A: a > ( stream901396144_sp_mu @ a @ b @ c ),B: a,C: stream1273403375_sp_nu @ d @ a] :
( ( x
= ( product_Pair @ ( stream901396144_sp_mu @ a @ b @ c ) @ ( stream901396144_sp_mu @ d @ a @ ( stream1273403375_sp_nu @ d @ a ) ) @ ( stream1294929701mu_Get @ a @ b @ c @ A ) @ ( stream1370332830mu_Put @ a @ ( stream1273403375_sp_nu @ d @ a ) @ d @ B @ C ) ) )
=> p ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(3,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ E @ ( product_Pair @ TB @ TA @ F @ G ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_prod__cases6) ).
thf(41,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ E @ ( product_Pair @ TB @ TA @ F @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(26,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > ( stream901396144_sp_mu @ TB @ TC @ TA ),B: TC,C: TA] :
( ( stream1294929701mu_Get @ TB @ TC @ TA @ A )
!= ( stream1370332830mu_Put @ TC @ TA @ TB @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_sp_092_060_094sub_062_092_060mu_062_Odistinct_I1_J) ).
thf(105,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > ( stream901396144_sp_mu @ TB @ TC @ TA ),B: TC,C: TA] :
( ( stream1294929701mu_Get @ TB @ TC @ TA @ A )
!= ( stream1370332830mu_Put @ TC @ TA @ TB @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(11,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ C @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ D @ ( product_Pair @ TB @ TA @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_prod__cases5) ).
thf(64,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ C @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ D @ ( product_Pair @ TB @ TA @ E @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(4,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TB > $o,B: TC > TC > $o,C: stream901396144_sp_mu @ TA @ TB @ TC] :
( ! [D: TB] : ( A @ D @ D )
=> ( ! [D: TC] : ( B @ D @ D )
=> ( stream1924447089_sp_mu @ TB @ TB @ TC @ TC @ TA @ A @ B @ C @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_sp_092_060_094sub_062_092_060mu_062_Orel__refl) ).
thf(44,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TB > $o,B: TC > TC > $o,C: stream901396144_sp_mu @ TA @ TB @ TC] :
( ! [D: TB] : ( A @ D @ D )
=> ( ! [D: TC] : ( B @ D @ D )
=> ( stream1924447089_sp_mu @ TB @ TB @ TC @ TC @ TA @ A @ B @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(27,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( produc2004651681e_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_internal__case__prod__conv) ).
thf(108,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( produc2004651681e_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(35,axiom,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_prod__cases) ).
thf(130,plain,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(14,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) @ E @ ( product_Pair @ TD @ TE @ F @ G ) ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_prod__induct5) ).
thf(72,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) @ E @ ( product_Pair @ TD @ TE @ F @ G ) ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(18,axiom,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_old_Oprod_Oinducts) ).
thf(82,plain,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(6,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: product_prod @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) )] :
~ ! [B: TG,C: TF,D: TE,E: TD,F: TC,G: TB,H: TA] :
( A
!= ( product_Pair @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ B @ ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ C @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ D @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ E @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ F @ ( product_Pair @ TB @ TA @ G @ H ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_prod__cases7) ).
thf(51,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: product_prod @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) )] :
~ ! [B: TG,C: TF,D: TE,E: TD,F: TC,G: TB,H: TA] :
( A
!= ( product_Pair @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ B @ ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ C @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ D @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ E @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ F @ ( product_Pair @ TB @ TA @ G @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(17,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_old_Oprod_Oexhaust) ).
thf(79,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(10,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ TC )] :
( ! [C: TA,D: TB,E: TC] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) @ C @ ( product_Pair @ TB @ TC @ D @ E ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_prod__induct3) ).
thf(62,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ TC )] :
( ! [C: TA,D: TB,E: TC] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) @ C @ ( product_Pair @ TB @ TC @ D @ E ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(22,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_old_Oprod_Oinject) ).
thf(93,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(8,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( stream1924447089_sp_mu @ TB @ TB @ TC @ TC @ TA @ ( (=) @ TB ) @ ( (=) @ TC ) )
= ( (=) @ ( stream901396144_sp_mu @ TA @ TB @ TC ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_sp_092_060_094sub_062_092_060mu_062_Orel__eq) ).
thf(57,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( stream1924447089_sp_mu @ TB @ TB @ TC @ TC @ TA @ ( (=) @ TB ) @ ( (=) @ TC ) )
= ( (=) @ ( stream901396144_sp_mu @ TA @ TB @ TC ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(36,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_Pair__inject) ).
thf(132,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(15,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ B @ ( product_Pair @ TB @ TA @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_prod__cases3) ).
thf(74,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ B @ ( product_Pair @ TB @ TA @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(25,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( product_rec_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_old_Oprod_Orec) ).
thf(102,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( product_rec_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(9,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TD > TC > $o,B: TD,C: TC,D: TE > TA > $o,E: TE,F: TA] :
( ( A @ B @ C )
=> ( ( D @ E @ F )
=> ( stream1924447089_sp_mu @ TD @ TC @ TE @ TA @ TB @ A @ D @ ( stream1370332830mu_Put @ TD @ TE @ TB @ B @ E ) @ ( stream1370332830mu_Put @ TC @ TA @ TB @ C @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_sp_092_060_094sub_062_092_060mu_062_Orel__intros_I2_J) ).
thf(60,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TD > TC > $o,B: TD,C: TC,D: TE > TA > $o,E: TE,F: TA] :
( ( A @ B @ C )
=> ( ( D @ E @ F )
=> ( stream1924447089_sp_mu @ TD @ TC @ TE @ TA @ TB @ A @ D @ ( stream1370332830mu_Put @ TD @ TE @ TB @ B @ E ) @ ( stream1370332830mu_Put @ TC @ TA @ TB @ C @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(30,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB,B: TC,C: stream @ TA] :
( ( stream5064451run_mu @ TA @ TB @ TC @ ( stream1370332830mu_Put @ TB @ TC @ TA @ A @ B ) @ C )
= ( product_Pair @ ( product_prod @ TB @ TC ) @ ( stream @ TA ) @ ( product_Pair @ TB @ TC @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_run_092_060_094sub_062_092_060mu_062_Osimps_I2_J) ).
thf(117,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB,B: TC,C: stream @ TA] :
( ( stream5064451run_mu @ TA @ TB @ TC @ ( stream1370332830mu_Put @ TB @ TC @ TA @ A @ B ) @ C )
= ( product_Pair @ ( product_prod @ TB @ TC ) @ ( stream @ TA ) @ ( product_Pair @ TB @ TC @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(16,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) )] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) @ D @ ( product_Pair @ TC @ TD @ E @ F ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_prod__induct4) ).
thf(77,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) )] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) @ D @ ( product_Pair @ TC @ TD @ E @ F ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(23,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: ( TD > ( product_prod @ ( stream901396144_sp_mu @ TD @ TC @ TA ) @ TB ) ) > TB,B: TC > TA > TB,C: TC,D: TA] :
( ( stream674629690_sp_mu @ TD @ TC @ TA @ TB @ A @ B @ ( stream1370332830mu_Put @ TC @ TA @ TD @ C @ D ) )
= ( B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_sp_092_060_094sub_062_092_060mu_062_Osimps_I8_J) ).
thf(96,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: ( TD > ( product_prod @ ( stream901396144_sp_mu @ TD @ TC @ TA ) @ TB ) ) > TB,B: TC > TA > TB,C: TC,D: TA] :
( ( stream674629690_sp_mu @ TD @ TC @ TA @ TB @ A @ B @ ( stream1370332830mu_Put @ TC @ TA @ TD @ C @ D ) )
= ( B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(7,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TC > TD > $o,B: TB > TA > $o,C: TC,D: TB,E: TD,F: TA] :
( ( stream1924447089_sp_mu @ TC @ TD @ TB @ TA @ TE @ A @ B @ ( stream1370332830mu_Put @ TC @ TB @ TE @ C @ D ) @ ( stream1370332830mu_Put @ TD @ TA @ TE @ E @ F ) )
= ( ( A @ C @ E )
& ( B @ D @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_sp_092_060_094sub_062_092_060mu_062_Orel__inject_I2_J) ).
thf(54,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TC > TD > $o,B: TB > TA > $o,C: TC,D: TB,E: TD,F: TA] :
( ( stream1924447089_sp_mu @ TC @ TD @ TB @ TA @ TE @ A @ B @ ( stream1370332830mu_Put @ TC @ TB @ TE @ C @ D ) @ ( stream1370332830mu_Put @ TD @ TA @ TE @ E @ F ) )
= ( ( A @ C @ E )
& ( B @ D @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF,I: TG] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) @ F @ ( product_Pair @ TE @ ( product_prod @ TF @ TG ) @ G @ ( product_Pair @ TF @ TG @ H @ I ) ) ) ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_prod__induct7) ).
thf(49,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF,I: TG] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) @ F @ ( product_Pair @ TE @ ( product_prod @ TF @ TG ) @ G @ ( product_Pair @ TF @ TG @ H @ I ) ) ) ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(32,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TD > TB > $o,B: TE > TC > $o,C: TD,D: TE,E: TA > ( stream901396144_sp_mu @ TA @ TB @ TC )] :
~ ( stream1924447089_sp_mu @ TD @ TB @ TE @ TC @ TA @ A @ B @ ( stream1370332830mu_Put @ TD @ TE @ TA @ C @ D ) @ ( stream1294929701mu_Get @ TA @ TB @ TC @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_sp_092_060_094sub_062_092_060mu_062_Orel__distinct_I2_J) ).
thf(123,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TD > TB > $o,B: TE > TC > $o,C: TD,D: TE,E: TA > ( stream901396144_sp_mu @ TA @ TB @ TC )] :
~ ( stream1924447089_sp_mu @ TD @ TB @ TE @ TC @ TA @ A @ B @ ( stream1370332830mu_Put @ TD @ TE @ TA @ C @ D ) @ ( stream1294929701mu_Get @ TA @ TB @ TC @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(39,axiom,
! [A: a > ( stream901396144_sp_mu @ a @ b @ c ),B: d > ( stream901396144_sp_mu @ d @ a @ ( stream1273403375_sp_nu @ d @ a ) )] :
( ( x
= ( product_Pair @ ( stream901396144_sp_mu @ a @ b @ c ) @ ( stream901396144_sp_mu @ d @ a @ ( stream1273403375_sp_nu @ d @ a ) ) @ ( stream1294929701mu_Get @ a @ b @ c @ A ) @ ( stream1294929701mu_Get @ d @ a @ ( stream1273403375_sp_nu @ d @ a ) @ B ) ) )
=> p ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
thf(145,plain,
! [A: a > ( stream901396144_sp_mu @ a @ b @ c ),B: d > ( stream901396144_sp_mu @ d @ a @ ( stream1273403375_sp_nu @ d @ a ) )] :
( ( x
= ( product_Pair @ ( stream901396144_sp_mu @ a @ b @ c ) @ ( stream901396144_sp_mu @ d @ a @ ( stream1273403375_sp_nu @ d @ a ) ) @ ( stream1294929701mu_Get @ a @ b @ c @ A ) @ ( stream1294929701mu_Get @ d @ a @ ( stream1273403375_sp_nu @ d @ a ) @ B ) ) )
=> p ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(12,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) @ F @ ( product_Pair @ TE @ TF @ G @ H ) ) ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_prod__induct6) ).
thf(67,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) @ F @ ( product_Pair @ TE @ TF @ G @ H ) ) ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(34,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_prod_Oinject) ).
thf(127,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(24,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( stream1370332830mu_Put @ TB @ TA @ TC @ A @ B )
= ( stream1370332830mu_Put @ TB @ TA @ TC @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_sp_092_060_094sub_062_092_060mu_062_Oinject_I2_J) ).
thf(99,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( stream1370332830mu_Put @ TB @ TA @ TC @ A @ B )
= ( stream1370332830mu_Put @ TB @ TA @ TC @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(20,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > $o,B: TA > $o,C: TB,D: TA] :
( ( stream123009735_sp_mu @ TB @ TA @ TC @ A @ B @ ( stream1370332830mu_Put @ TB @ TA @ TC @ C @ D ) )
= ( ( A @ C )
& ( B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_sp_092_060_094sub_062_092_060mu_062_Opred__inject_I2_J) ).
thf(87,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > $o,B: TA > $o,C: TB,D: TA] :
( ( stream123009735_sp_mu @ TB @ TA @ TC @ A @ B @ ( stream1370332830mu_Put @ TB @ TA @ TC @ C @ D ) )
= ( ( A @ C )
& ( B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(1,conjecture,
p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3) ).
thf(2,negated_conjecture,
~ p,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(40,plain,
~ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(29,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > ( stream901396144_sp_mu @ TA @ TB @ TC ),B: TA > ( stream901396144_sp_mu @ TA @ TB @ TC )] :
( ( ( stream1294929701mu_Get @ TA @ TB @ TC @ A )
= ( stream1294929701mu_Get @ TA @ TB @ TC @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_sp_092_060_094sub_062_092_060mu_062_Oinject_I1_J) ).
thf(114,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > ( stream901396144_sp_mu @ TA @ TB @ TC ),B: TA > ( stream901396144_sp_mu @ TA @ TB @ TC )] :
( ( ( stream1294929701mu_Get @ TA @ TB @ TC @ A )
= ( stream1294929701mu_Get @ TA @ TB @ TC @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(21,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: ( TA > ( stream901396144_sp_mu @ TA @ TB @ TC ) ) > TD,B: TB > TC > TD,C: TA > ( stream901396144_sp_mu @ TA @ TB @ TC )] :
( ( stream160000856_sp_mu @ TA @ TB @ TC @ TD @ A @ B @ ( stream1294929701mu_Get @ TA @ TB @ TC @ C ) )
= ( A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_sp_092_060_094sub_062_092_060mu_062_Osimps_I5_J) ).
thf(90,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: ( TA > ( stream901396144_sp_mu @ TA @ TB @ TC ) ) > TD,B: TB > TC > TD,C: TA > ( stream901396144_sp_mu @ TA @ TB @ TC )] :
( ( stream160000856_sp_mu @ TA @ TB @ TC @ TD @ A @ B @ ( stream1294929701mu_Get @ TA @ TB @ TC @ C ) )
= ( A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(28,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
? [B: TB,C: TA] :
( A
= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_surj__pair) ).
thf(111,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
? [B: TB,C: TA] :
( A
= ( product_Pair @ TB @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(149,plain,
$false,
inference(e,[status(thm)],[69,120,125,84,137,141,41,105,64,44,108,130,72,82,51,79,62,93,57,132,74,102,60,117,77,96,54,49,123,145,67,127,99,87,40,114,90,111]) ).
%------------------------------------------------------------------------------
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% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Mon May 6 11:33:54 EDT 2024
% 0.17/0.37 % CPUTime :
% 0.93/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.69/1.13 % [INFO] Parsing done (262ms).
% 1.69/1.14 % [INFO] Running in sequential loop mode.
% 2.71/1.37 % [INFO] eprover registered as external prover.
% 2.71/1.37 % [INFO] cvc4 registered as external prover.
% 2.71/1.37 % [INFO] Scanning for conjecture ...
% 2.97/1.47 % [INFO] Found a conjecture and 274 axioms. Running axiom selection ...
% 3.25/1.55 % [INFO] Axiom selection finished. Selected 37 axioms (removed 237 axioms).
% 3.55/1.68 % [INFO] Problem is higher-order (TPTP THF).
% 3.55/1.69 % [INFO] Type checking passed.
% 3.55/1.69 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 10.12/5.08 % External prover 'e' found a proof!
% 10.12/5.08 % [INFO] Killing All external provers ...
% 10.12/5.09 % Time passed: 4547ms (effective reasoning time: 3943ms)
% 10.12/5.09 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 10.12/5.09 % Axioms used in derivation (37): fact_19_prod__induct6, fact_5_prod_Oinject, fact_1_sp_092_060_094sub_062_092_060mu_062_Oinject_I2_J, fact_23_old_Oprod_Orec, fact_28_sp_092_060_094sub_062_092_060mu_062_Osimps_I5_J, fact_38_sp_092_060_094sub_062_092_060mu_062_Orel__distinct_I1_J, conj_1, fact_2_sp_092_060_094sub_062_092_060mu_062_Odistinct_I1_J, fact_10_Pair__inject, fact_30_sp_092_060_094sub_062_092_060mu_062_Osimps_I8_J, fact_9_prod__cases, fact_13_prod__cases5, fact_16_old_Oprod_Oinducts, fact_6_old_Oprod_Oinject, fact_51_sp_092_060_094sub_062_092_060mu_062_Orel__eq, fact_11_prod__cases3, fact_3_sp_092_060_094sub_062_092_060mu_062_Oexhaust, fact_12_prod__cases4, fact_22_prod__induct3, fact_52_sp_092_060_094sub_062_092_060mu_062_Orel__refl, conj_2, fact_37_sp_092_060_094sub_062_092_060mu_062_Orel__distinct_I2_J, fact_21_prod__induct4, fact_31_sp_092_060_094sub_062_092_060mu_062_Opred__inject_I2_J, fact_27_sp_092_060_094sub_062_092_060mu_062_Osimps_I6_J, fact_14_prod__cases6, fact_56_sp_092_060_094sub_062_092_060mu_062_Orel__intros_I2_J, fact_0_sp_092_060_094sub_062_092_060mu_062_Oinject_I1_J, fact_57_sp_092_060_094sub_062_092_060mu_062_Orel__inject_I2_J, fact_24_internal__case__prod__conv, fact_20_prod__induct5, fact_18_prod__induct7, fact_7_run_092_060_094sub_062_092_060mu_062_Osimps_I2_J, conj_0, fact_17_old_Oprod_Oexhaust, fact_15_prod__cases7, fact_8_surj__pair
% 10.12/5.09 % No. of inferences in proof: 78
% 10.12/5.09 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4547 ms resp. 3943 ms w/o parsing
% 10.40/5.14 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.40/5.14 % [INFO] Killing All external provers ...
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