TSTP Solution File: ITP009_3 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP009_3 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n025.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 07:46:41 EDT 2024
% Result : Theorem 174.00s 50.01s
% Output : Refutation 174.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 90
% Syntax : Number of formulae : 201 ( 81 unt; 47 typ; 0 def)
% Number of atoms : 767 ( 131 equ; 0 cnn)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 3295 ( 91 ~; 37 |; 82 &;2960 @)
% ( 26 <=>; 99 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 7 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 45 ( 43 usr; 17 con; 0-7 aty)
% Number of variables : 391 ( 0 ^ 344 !; 3 ?; 391 :)
% ( 44 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(tyop_2Emin_2Ebool_type,type,
tyop_2Emin_2Ebool: $tType ).
thf(app_2E2_type,type,
app_2E2:
!>[TA: $tType,TB: $tType] : ( ( tyop_2Emin_2Efun @ TB @ TA ) > TB > TA ) ).
thf(p_type,type,
p: tyop_2Emin_2Ebool > $o ).
thf(combin_i_2E0_type,type,
combin_i_2E0:
!>[TA: $tType] : ( tyop_2Emin_2Efun @ TA @ TA ) ).
thf(combin_k_2E0_type,type,
combin_k_2E0:
!>[TA: $tType,TB: $tType] : ( tyop_2Emin_2Efun @ TB @ ( tyop_2Emin_2Efun @ TA @ TB ) ) ).
thf(combin_s_2E0_type,type,
combin_s_2E0:
!>[TA: $tType,TB: $tType,TC: $tType] : ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TC @ ( tyop_2Emin_2Efun @ TB @ TA ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TC @ TB ) @ ( tyop_2Emin_2Efun @ TC @ TA ) ) ) ).
thf(c_2Ebool_2E_21_2E0_type,type,
c_2Ebool_2E_21_2E0:
!>[TA: $tType] : ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ).
thf(c_2Ebool_2E_21_2E1_type,type,
c_2Ebool_2E_21_2E1:
!>[TA: $tType] : ( ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ) ).
thf(c_2Equotient_2E_2D_2D_3E_2E0_type,type,
c_2Equotient_2E_2D_2D_3E_2E0:
!>[TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TD @ TB ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TC @ TA ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TC ) @ ( tyop_2Emin_2Efun @ TD @ TA ) ) ) ) ).
thf(c_2Equotient_2E_2D_2D_3E_2E2_type,type,
c_2Equotient_2E_2D_2D_3E_2E2:
!>[TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( ( tyop_2Emin_2Efun @ TD @ TB ) > ( tyop_2Emin_2Efun @ TC @ TA ) > ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TC ) @ ( tyop_2Emin_2Efun @ TD @ TA ) ) ) ).
thf(c_2Equotient_2E_2D_2D_3E_2E3_type,type,
c_2Equotient_2E_2D_2D_3E_2E3:
!>[TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( ( tyop_2Emin_2Efun @ TD @ TB ) > ( tyop_2Emin_2Efun @ TC @ TA ) > ( tyop_2Emin_2Efun @ TB @ TC ) > ( tyop_2Emin_2Efun @ TD @ TA ) ) ).
thf(c_2Ebool_2E_2F_5C_2E0_type,type,
c_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ).
thf(c_2Ebool_2E_2F_5C_2E2_type,type,
c_2Ebool_2E_2F_5C_2E2: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
thf(c_2Emin_2E_3D_2E0_type,type,
c_2Emin_2E_3D_2E0:
!>[TA: $tType] : ( tyop_2Emin_2Efun @ TA @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) ) ).
thf(c_2Emin_2E_3D_2E2_type,type,
c_2Emin_2E_3D_2E2:
!>[TA: $tType] : ( TA > TA > tyop_2Emin_2Ebool ) ).
thf(c_2Equotient_2E_3D_3D_3D_3E_2E0_type,type,
c_2Equotient_2E_3D_3D_3D_3E_2E0:
!>[TA: $tType,TB: $tType] : ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ ( tyop_2Emin_2Efun @ TB @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TA @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ tyop_2Emin_2Ebool ) ) ) ) ).
thf(c_2Equotient_2E_3D_3D_3D_3E_2E2_type,type,
c_2Equotient_2E_3D_3D_3D_3E_2E2:
!>[TA: $tType,TB: $tType] : ( ( tyop_2Emin_2Efun @ TB @ ( tyop_2Emin_2Efun @ TB @ tyop_2Emin_2Ebool ) ) > ( tyop_2Emin_2Efun @ TA @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) ) > ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ tyop_2Emin_2Ebool ) ) ) ).
thf(c_2Equotient_2E_3D_3D_3D_3E_2E4_type,type,
c_2Equotient_2E_3D_3D_3D_3E_2E4:
!>[TA: $tType,TB: $tType] : ( ( tyop_2Emin_2Efun @ TB @ ( tyop_2Emin_2Efun @ TB @ tyop_2Emin_2Ebool ) ) > ( tyop_2Emin_2Efun @ TA @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) ) > ( tyop_2Emin_2Efun @ TB @ TA ) > ( tyop_2Emin_2Efun @ TB @ TA ) > tyop_2Emin_2Ebool ) ).
thf(c_2Emin_2E_3D_3D_3E_2E0_type,type,
c_2Emin_2E_3D_3D_3E_2E0: tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ).
thf(c_2Emin_2E_3D_3D_3E_2E2_type,type,
c_2Emin_2E_3D_3D_3E_2E2: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
thf(c_2Ebool_2E_3F_2E0_type,type,
c_2Ebool_2E_3F_2E0:
!>[TA: $tType] : ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ).
thf(c_2Ebool_2E_3F_2E1_type,type,
c_2Ebool_2E_3F_2E1:
!>[TA: $tType] : ( ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ) ).
thf(c_2Ebool_2EF_2E0_type,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
thf(c_2Equotient_2EQUOTIENT_2E0_type,type,
c_2Equotient_2EQUOTIENT_2E0:
!>[TA: $tType,TB: $tType] : ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ ( tyop_2Emin_2Efun @ TB @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TA @ TB ) @ tyop_2Emin_2Ebool ) ) ) ).
thf(c_2Equotient_2EQUOTIENT_2E3_type,type,
c_2Equotient_2EQUOTIENT_2E3:
!>[TA: $tType,TB: $tType] : ( ( tyop_2Emin_2Efun @ TB @ ( tyop_2Emin_2Efun @ TB @ tyop_2Emin_2Ebool ) ) > ( tyop_2Emin_2Efun @ TB @ TA ) > ( tyop_2Emin_2Efun @ TA @ TB ) > tyop_2Emin_2Ebool ) ).
thf(c_2Ebool_2ET_2E0_type,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
thf(c_2Ecombin_2EW_2E0_type,type,
c_2Ecombin_2EW_2E0:
!>[TA: $tType,TB: $tType] : ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ ( tyop_2Emin_2Efun @ TB @ TA ) ) @ ( tyop_2Emin_2Efun @ TB @ TA ) ) ).
thf(c_2Ecombin_2EW_2E2_type,type,
c_2Ecombin_2EW_2E2:
!>[TA: $tType,TB: $tType] : ( ( tyop_2Emin_2Efun @ TB @ ( tyop_2Emin_2Efun @ TB @ TA ) ) > TB > TA ) ).
thf(c_2Ebool_2E_5C_2F_2E0_type,type,
c_2Ebool_2E_5C_2F_2E0: tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ).
thf(c_2Ebool_2E_5C_2F_2E2_type,type,
c_2Ebool_2E_5C_2F_2E2: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
thf(c_2Equotient_2Erespects_2E0_type,type,
c_2Equotient_2Erespects_2E0:
!>[TA: $tType,TB: $tType] : ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ ( tyop_2Emin_2Efun @ TB @ TA ) ) @ ( tyop_2Emin_2Efun @ TB @ TA ) ) ).
thf(c_2Equotient_2Erespects_2E2_type,type,
c_2Equotient_2Erespects_2E2:
!>[TA: $tType,TB: $tType] : ( ( tyop_2Emin_2Efun @ TB @ ( tyop_2Emin_2Efun @ TB @ TA ) ) > TB > TA ) ).
thf(c_2Ebool_2E_7E_2E0_type,type,
c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ).
thf(c_2Ebool_2E_7E_2E1_type,type,
c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
thf(skt1_type,type,
skt1: $tType ).
thf(skt2_type,type,
skt2: $tType ).
thf(skt3_type,type,
skt3: $tType ).
thf(skt4_type,type,
skt4: $tType ).
thf(sk1_type,type,
sk1: tyop_2Emin_2Efun @ skt1 @ ( tyop_2Emin_2Efun @ skt1 @ tyop_2Emin_2Ebool ) ).
thf(sk2_type,type,
sk2: tyop_2Emin_2Efun @ skt1 @ skt3 ).
thf(sk3_type,type,
sk3: tyop_2Emin_2Efun @ skt3 @ skt1 ).
thf(sk4_type,type,
sk4: tyop_2Emin_2Efun @ skt2 @ ( tyop_2Emin_2Efun @ skt2 @ tyop_2Emin_2Ebool ) ).
thf(sk5_type,type,
sk5: tyop_2Emin_2Efun @ skt2 @ skt4 ).
thf(sk6_type,type,
sk6: tyop_2Emin_2Efun @ skt4 @ skt2 ).
thf(sk7_type,type,
sk7: tyop_2Emin_2Efun @ skt1 @ skt2 ).
thf(sk8_type,type,
sk8: tyop_2Emin_2Efun @ skt1 @ skt2 ).
thf(sk9_type,type,
sk9: $o ).
thf(3,axiom,
! [A: tyop_2Emin_2Ebool] :
( ( A = c_2Ebool_2ET_2E0 )
| ( A = c_2Ebool_2EF_2E0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Ebool__cases__ax) ).
thf(56,plain,
! [A: tyop_2Emin_2Ebool] :
( ( A = c_2Ebool_2ET_2E0 )
| ( A = c_2Ebool_2EF_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(23,axiom,
! [A: tyop_2Emin_2Ebool] :
( ( ( c_2Ebool_2ET_2E0 = A )
<=> ( p @ A ) )
& ( ( A = c_2Ebool_2ET_2E0 )
<=> ( p @ A ) )
& ( ( c_2Ebool_2EF_2E0 = A )
<=> ~ ( p @ A ) )
& ( ( A = c_2Ebool_2EF_2E0 )
<=> ~ ( p @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__CLAUSES) ).
thf(165,plain,
! [A: tyop_2Emin_2Ebool] :
( ( ( c_2Ebool_2ET_2E0 = A )
=> ( p @ A ) )
& ( ( p @ A )
=> ( c_2Ebool_2ET_2E0 = A ) )
& ( ( A = c_2Ebool_2ET_2E0 )
=> ( p @ A ) )
& ( ( p @ A )
=> ( A = c_2Ebool_2ET_2E0 ) )
& ( ( c_2Ebool_2EF_2E0 = A )
=> ~ ( p @ A ) )
& ( ~ ( p @ A )
=> ( c_2Ebool_2EF_2E0 = A ) )
& ( ( A = c_2Ebool_2EF_2E0 )
=> ~ ( p @ A ) )
& ( ~ ( p @ A )
=> ( A = c_2Ebool_2EF_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(166,plain,
( ! [A: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2ET_2E0 = A )
=> ( p @ A ) )
& ! [A: tyop_2Emin_2Ebool] :
( ( p @ A )
=> ( c_2Ebool_2ET_2E0 = A ) )
& ! [A: tyop_2Emin_2Ebool] :
( ( A = c_2Ebool_2ET_2E0 )
=> ( p @ A ) )
& ! [A: tyop_2Emin_2Ebool] :
( ( p @ A )
=> ( A = c_2Ebool_2ET_2E0 ) )
& ! [A: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2EF_2E0 = A )
=> ~ ( p @ A ) )
& ! [A: tyop_2Emin_2Ebool] :
( ~ ( p @ A )
=> ( c_2Ebool_2EF_2E0 = A ) )
& ! [A: tyop_2Emin_2Ebool] :
( ( A = c_2Ebool_2EF_2E0 )
=> ~ ( p @ A ) )
& ! [A: tyop_2Emin_2Ebool] :
( ~ ( p @ A )
=> ( A = c_2Ebool_2EF_2E0 ) ) ),
inference(miniscope,[status(thm)],[165]) ).
thf(167,plain,
! [A: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2ET_2E0 != A )
| ( p @ A ) ),
inference(cnf,[status(esa)],[166]) ).
thf(185,plain,
! [A: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2ET_2E0 != A )
| ( p @ A ) ),
inference(lifteq,[status(thm)],[167]) ).
thf(186,plain,
p @ c_2Ebool_2ET_2E0,
inference(simp,[status(thm)],[185]) ).
thf(11,axiom,
~ ( p @ c_2Ebool_2EF_2E0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Enotfalse) ).
thf(106,plain,
~ ( p @ c_2Ebool_2EF_2E0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(107,plain,
~ ( p @ c_2Ebool_2EF_2E0 ),
inference(polarity_switch,[status(thm)],[106]) ).
thf(284,plain,
( ( p @ c_2Ebool_2ET_2E0 )
!= ( p @ c_2Ebool_2EF_2E0 ) ),
inference(paramod_ordered,[status(thm)],[186,107]) ).
thf(288,plain,
c_2Ebool_2ET_2E0 != c_2Ebool_2EF_2E0,
inference(simp,[status(thm)],[284]) ).
thf(1,conjecture,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: tyop_2Emin_2Efun @ TD @ ( tyop_2Emin_2Efun @ TD @ tyop_2Emin_2Ebool ),B: tyop_2Emin_2Efun @ TD @ TB,C: tyop_2Emin_2Efun @ TB @ TD] :
( ( p @ ( c_2Equotient_2EQUOTIENT_2E3 @ TD @ TB @ A @ B @ C ) )
=> ! [D: tyop_2Emin_2Efun @ TC @ ( tyop_2Emin_2Efun @ TC @ tyop_2Emin_2Ebool ),E: tyop_2Emin_2Efun @ TC @ TA,F: tyop_2Emin_2Efun @ TA @ TC] :
( ( p @ ( c_2Equotient_2EQUOTIENT_2E3 @ TC @ TA @ D @ E @ F ) )
=> ! [G: tyop_2Emin_2Efun @ TD @ TC,H: tyop_2Emin_2Efun @ TD @ TC] :
( ( p @ ( c_2Equotient_2E_3D_3D_3D_3E_2E4 @ TD @ TC @ A @ D @ G @ H ) )
<=> ( ( p @ ( c_2Equotient_2Erespects_2E2 @ ( tyop_2Emin_2Efun @ TD @ TC ) @ tyop_2Emin_2Ebool @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ TD @ TC @ A @ D ) @ G ) )
& ( p @ ( c_2Equotient_2Erespects_2E2 @ ( tyop_2Emin_2Efun @ TD @ TC ) @ tyop_2Emin_2Ebool @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ TD @ TC @ A @ D ) @ H ) )
& ( ( c_2Equotient_2E_2D_2D_3E_2E3 @ TB @ TC @ TD @ TA @ C @ E @ G )
= ( c_2Equotient_2E_2D_2D_3E_2E3 @ TB @ TC @ TD @ TA @ C @ E @ H ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Equotient_2EFUN__REL__EQ__REL) ).
thf(2,negated_conjecture,
~ ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: tyop_2Emin_2Efun @ TD @ ( tyop_2Emin_2Efun @ TD @ tyop_2Emin_2Ebool ),B: tyop_2Emin_2Efun @ TD @ TB,C: tyop_2Emin_2Efun @ TB @ TD] :
( ( p @ ( c_2Equotient_2EQUOTIENT_2E3 @ TD @ TB @ A @ B @ C ) )
=> ! [D: tyop_2Emin_2Efun @ TC @ ( tyop_2Emin_2Efun @ TC @ tyop_2Emin_2Ebool ),E: tyop_2Emin_2Efun @ TC @ TA,F: tyop_2Emin_2Efun @ TA @ TC] :
( ( p @ ( c_2Equotient_2EQUOTIENT_2E3 @ TC @ TA @ D @ E @ F ) )
=> ! [G: tyop_2Emin_2Efun @ TD @ TC,H: tyop_2Emin_2Efun @ TD @ TC] :
( ( p @ ( c_2Equotient_2E_3D_3D_3D_3E_2E4 @ TD @ TC @ A @ D @ G @ H ) )
<=> ( ( p @ ( c_2Equotient_2Erespects_2E2 @ ( tyop_2Emin_2Efun @ TD @ TC ) @ tyop_2Emin_2Ebool @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ TD @ TC @ A @ D ) @ G ) )
& ( p @ ( c_2Equotient_2Erespects_2E2 @ ( tyop_2Emin_2Efun @ TD @ TC ) @ tyop_2Emin_2Ebool @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ TD @ TC @ A @ D ) @ H ) )
& ( ( c_2Equotient_2E_2D_2D_3E_2E3 @ TB @ TC @ TD @ TA @ C @ E @ G )
= ( c_2Equotient_2E_2D_2D_3E_2E3 @ TB @ TC @ TD @ TA @ C @ E @ H ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(45,plain,
~ ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: tyop_2Emin_2Efun @ TD @ ( tyop_2Emin_2Efun @ TD @ tyop_2Emin_2Ebool ),B: tyop_2Emin_2Efun @ TD @ TB,C: tyop_2Emin_2Efun @ TB @ TD] :
( ( p @ ( c_2Equotient_2EQUOTIENT_2E3 @ TD @ TB @ A @ B @ C ) )
=> ! [D: tyop_2Emin_2Efun @ TC @ ( tyop_2Emin_2Efun @ TC @ tyop_2Emin_2Ebool ),E: tyop_2Emin_2Efun @ TC @ TA,F: tyop_2Emin_2Efun @ TA @ TC] :
( ( p @ ( c_2Equotient_2EQUOTIENT_2E3 @ TC @ TA @ D @ E @ F ) )
=> ! [G: tyop_2Emin_2Efun @ TD @ TC,H: tyop_2Emin_2Efun @ TD @ TC] :
( ( ( p @ ( c_2Equotient_2E_3D_3D_3D_3E_2E4 @ TD @ TC @ A @ D @ G @ H ) )
=> ( ( p @ ( c_2Equotient_2Erespects_2E2 @ ( tyop_2Emin_2Efun @ TD @ TC ) @ tyop_2Emin_2Ebool @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ TD @ TC @ A @ D ) @ G ) )
& ( p @ ( c_2Equotient_2Erespects_2E2 @ ( tyop_2Emin_2Efun @ TD @ TC ) @ tyop_2Emin_2Ebool @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ TD @ TC @ A @ D ) @ H ) )
& ( ( c_2Equotient_2E_2D_2D_3E_2E3 @ TB @ TC @ TD @ TA @ C @ E @ G )
= ( c_2Equotient_2E_2D_2D_3E_2E3 @ TB @ TC @ TD @ TA @ C @ E @ H ) ) ) )
& ( ( ( p @ ( c_2Equotient_2Erespects_2E2 @ ( tyop_2Emin_2Efun @ TD @ TC ) @ tyop_2Emin_2Ebool @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ TD @ TC @ A @ D ) @ G ) )
& ( p @ ( c_2Equotient_2Erespects_2E2 @ ( tyop_2Emin_2Efun @ TD @ TC ) @ tyop_2Emin_2Ebool @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ TD @ TC @ A @ D ) @ H ) )
& ( ( c_2Equotient_2E_2D_2D_3E_2E3 @ TB @ TC @ TD @ TA @ C @ E @ G )
= ( c_2Equotient_2E_2D_2D_3E_2E3 @ TB @ TC @ TD @ TA @ C @ E @ H ) ) )
=> ( p @ ( c_2Equotient_2E_3D_3D_3D_3E_2E4 @ TD @ TC @ A @ D @ G @ H ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(52,plain,
( sk9
| ~ ( p @ ( c_2Equotient_2E_3D_3D_3D_3E_2E4 @ skt1 @ skt2 @ sk1 @ sk4 @ sk7 @ sk8 ) ) ),
inference(cnf,[status(esa)],[45]) ).
thf(18,axiom,
! [A: tyop_2Emin_2Ebool] :
( ~ ( p @ A )
<=> ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ c_2Ebool_2E_7E_2E0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_7E_2E1) ).
thf(132,plain,
! [A: tyop_2Emin_2Ebool] :
( ( ~ ( p @ A )
=> ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ c_2Ebool_2E_7E_2E0 @ A ) ) )
& ( ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ c_2Ebool_2E_7E_2E0 @ A ) )
=> ~ ( p @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(53,plain,
p @ ( c_2Equotient_2EQUOTIENT_2E3 @ skt1 @ skt3 @ sk1 @ sk2 @ sk3 ),
inference(cnf,[status(esa)],[45]) ).
thf(133,plain,
( ! [A: tyop_2Emin_2Ebool] :
( ~ ( p @ A )
=> ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ c_2Ebool_2E_7E_2E0 @ A ) ) )
& ! [A: tyop_2Emin_2Ebool] :
( ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ c_2Ebool_2E_7E_2E0 @ A ) )
=> ~ ( p @ A ) ) ),
inference(miniscope,[status(thm)],[132]) ).
thf(134,plain,
! [A: tyop_2Emin_2Ebool] :
( ~ ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ c_2Ebool_2E_7E_2E0 @ A ) )
| ~ ( p @ A ) ),
inference(cnf,[status(esa)],[133]) ).
thf(136,plain,
! [A: tyop_2Emin_2Ebool] :
( ~ ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ c_2Ebool_2E_7E_2E0 @ A ) )
| ~ ( p @ A ) ),
inference(simp,[status(thm)],[134]) ).
thf(286,plain,
! [A: tyop_2Emin_2Ebool] :
( ~ ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ c_2Ebool_2E_7E_2E0 @ A ) )
| ( ( p @ c_2Ebool_2ET_2E0 )
!= ( p @ A ) ) ),
inference(paramod_ordered,[status(thm)],[186,136]) ).
thf(287,plain,
~ ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ c_2Ebool_2E_7E_2E0 @ c_2Ebool_2ET_2E0 ) ),
inference(pattern_uni,[status(thm)],[286:[bind(A,$thf( c_2Ebool_2ET_2E0 ))]]) ).
thf(357,plain,
( ( p @ ( c_2Equotient_2EQUOTIENT_2E3 @ skt1 @ skt3 @ sk1 @ sk2 @ sk3 ) )
!= ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ c_2Ebool_2E_7E_2E0 @ c_2Ebool_2ET_2E0 ) ) ),
inference(paramod_ordered,[status(thm)],[53,287]) ).
thf(362,plain,
( ( c_2Equotient_2EQUOTIENT_2E3 @ skt1 @ skt3 @ sk1 @ sk2 @ sk3 )
!= ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ c_2Ebool_2E_7E_2E0 @ c_2Ebool_2ET_2E0 ) ),
inference(simp,[status(thm)],[357]) ).
thf(48,plain,
( sk9
| ( p @ ( c_2Equotient_2Erespects_2E2 @ ( tyop_2Emin_2Efun @ skt1 @ skt2 ) @ tyop_2Emin_2Ebool @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ skt1 @ skt2 @ sk1 @ sk4 ) @ sk8 ) ) ),
inference(cnf,[status(esa)],[45]) ).
thf(51,plain,
p @ ( c_2Equotient_2EQUOTIENT_2E3 @ skt2 @ skt4 @ sk4 @ sk5 @ sk6 ),
inference(cnf,[status(esa)],[45]) ).
thf(27,axiom,
! [A: tyop_2Emin_2Ebool] :
( ( p @ ( c_2Ebool_2E_7E_2E1 @ A ) )
<=> ~ ( p @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',logicdef_2E_7E) ).
thf(200,plain,
! [A: tyop_2Emin_2Ebool] :
( ( ( p @ ( c_2Ebool_2E_7E_2E1 @ A ) )
=> ~ ( p @ A ) )
& ( ~ ( p @ A )
=> ( p @ ( c_2Ebool_2E_7E_2E1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(201,plain,
( ! [A: tyop_2Emin_2Ebool] :
( ( p @ ( c_2Ebool_2E_7E_2E1 @ A ) )
=> ~ ( p @ A ) )
& ! [A: tyop_2Emin_2Ebool] :
( ~ ( p @ A )
=> ( p @ ( c_2Ebool_2E_7E_2E1 @ A ) ) ) ),
inference(miniscope,[status(thm)],[200]) ).
thf(203,plain,
! [A: tyop_2Emin_2Ebool] :
( ~ ( p @ ( c_2Ebool_2E_7E_2E1 @ A ) )
| ~ ( p @ A ) ),
inference(cnf,[status(esa)],[201]) ).
thf(282,plain,
! [A: tyop_2Emin_2Ebool] :
( ~ ( p @ ( c_2Ebool_2E_7E_2E1 @ A ) )
| ( ( p @ c_2Ebool_2ET_2E0 )
!= ( p @ A ) ) ),
inference(paramod_ordered,[status(thm)],[186,203]) ).
thf(283,plain,
~ ( p @ ( c_2Ebool_2E_7E_2E1 @ c_2Ebool_2ET_2E0 ) ),
inference(pattern_uni,[status(thm)],[282:[bind(A,$thf( c_2Ebool_2ET_2E0 ))]]) ).
thf(327,plain,
( ( p @ ( c_2Ebool_2E_7E_2E1 @ c_2Ebool_2ET_2E0 ) )
!= ( p @ ( c_2Equotient_2EQUOTIENT_2E3 @ skt2 @ skt4 @ sk4 @ sk5 @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[51,283]) ).
thf(331,plain,
( ( c_2Ebool_2E_7E_2E1 @ c_2Ebool_2ET_2E0 )
!= ( c_2Equotient_2EQUOTIENT_2E3 @ skt2 @ skt4 @ sk4 @ sk5 @ sk6 ) ),
inference(simp,[status(thm)],[327]) ).
thf(360,plain,
( ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ c_2Ebool_2E_7E_2E0 @ c_2Ebool_2ET_2E0 ) )
!= ( p @ c_2Ebool_2ET_2E0 ) ),
inference(paramod_ordered,[status(thm)],[186,287]) ).
thf(365,plain,
( ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ c_2Ebool_2E_7E_2E0 @ c_2Ebool_2ET_2E0 )
!= c_2Ebool_2ET_2E0 ),
inference(simp,[status(thm)],[360]) ).
thf(37,axiom,
! [TA: $tType,TB: $tType,A: tyop_2Emin_2Efun @ TB @ ( tyop_2Emin_2Efun @ TB @ tyop_2Emin_2Ebool ),B: tyop_2Emin_2Efun @ TB @ TA,C: tyop_2Emin_2Efun @ TA @ TB] :
( ( p @ ( c_2Equotient_2EQUOTIENT_2E3 @ TB @ TA @ A @ B @ C ) )
=> ! [D: TB,E: TB] :
( ( p @ ( app_2E2 @ TB @ tyop_2Emin_2Ebool @ ( app_2E2 @ TB @ ( tyop_2Emin_2Efun @ TB @ tyop_2Emin_2Ebool ) @ A @ D ) @ E ) )
<=> ( ( p @ ( app_2E2 @ TB @ tyop_2Emin_2Ebool @ ( app_2E2 @ TB @ ( tyop_2Emin_2Efun @ TB @ tyop_2Emin_2Ebool ) @ A @ D ) @ D ) )
& ( p @ ( app_2E2 @ TB @ tyop_2Emin_2Ebool @ ( app_2E2 @ TB @ ( tyop_2Emin_2Efun @ TB @ tyop_2Emin_2Ebool ) @ A @ E ) @ E ) )
& ( ( app_2E2 @ TB @ TA @ B @ D )
= ( app_2E2 @ TB @ TA @ B @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Equotient_2EQUOTIENT__REL) ).
thf(234,plain,
! [TA: $tType,TB: $tType,A: tyop_2Emin_2Efun @ TB @ ( tyop_2Emin_2Efun @ TB @ tyop_2Emin_2Ebool ),B: tyop_2Emin_2Efun @ TB @ TA,C: tyop_2Emin_2Efun @ TA @ TB] :
( ( p @ ( c_2Equotient_2EQUOTIENT_2E3 @ TB @ TA @ A @ B @ C ) )
=> ! [D: TB,E: TB] :
( ( ( p @ ( app_2E2 @ TB @ tyop_2Emin_2Ebool @ ( app_2E2 @ TB @ ( tyop_2Emin_2Efun @ TB @ tyop_2Emin_2Ebool ) @ A @ D ) @ E ) )
=> ( ( p @ ( app_2E2 @ TB @ tyop_2Emin_2Ebool @ ( app_2E2 @ TB @ ( tyop_2Emin_2Efun @ TB @ tyop_2Emin_2Ebool ) @ A @ D ) @ D ) )
& ( p @ ( app_2E2 @ TB @ tyop_2Emin_2Ebool @ ( app_2E2 @ TB @ ( tyop_2Emin_2Efun @ TB @ tyop_2Emin_2Ebool ) @ A @ E ) @ E ) )
& ( ( app_2E2 @ TB @ TA @ B @ D )
= ( app_2E2 @ TB @ TA @ B @ E ) ) ) )
& ( ( ( p @ ( app_2E2 @ TB @ tyop_2Emin_2Ebool @ ( app_2E2 @ TB @ ( tyop_2Emin_2Efun @ TB @ tyop_2Emin_2Ebool ) @ A @ D ) @ D ) )
& ( p @ ( app_2E2 @ TB @ tyop_2Emin_2Ebool @ ( app_2E2 @ TB @ ( tyop_2Emin_2Efun @ TB @ tyop_2Emin_2Ebool ) @ A @ E ) @ E ) )
& ( ( app_2E2 @ TB @ TA @ B @ D )
= ( app_2E2 @ TB @ TA @ B @ E ) ) )
=> ( p @ ( app_2E2 @ TB @ tyop_2Emin_2Ebool @ ( app_2E2 @ TB @ ( tyop_2Emin_2Efun @ TB @ tyop_2Emin_2Ebool ) @ A @ D ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(15,axiom,
! [TA: $tType,TB: $tType,A: tyop_2Emin_2Efun @ TB @ ( tyop_2Emin_2Efun @ TB @ tyop_2Emin_2Ebool ),B: tyop_2Emin_2Efun @ TB @ TA,C: tyop_2Emin_2Efun @ TA @ TB] :
( ( c_2Equotient_2EQUOTIENT_2E3 @ TB @ TA @ A @ B @ C )
= ( app_2E2 @ ( tyop_2Emin_2Efun @ TA @ TB ) @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TA @ TB ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( tyop_2Emin_2Efun @ TB @ ( tyop_2Emin_2Efun @ TB @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TA @ TB ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient_2EQUOTIENT_2E0 @ TB @ TA ) @ A ) @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2EA_27a_20mono_2EA_27c) ).
thf(120,plain,
! [TA: $tType,TB: $tType,A: tyop_2Emin_2Efun @ TB @ ( tyop_2Emin_2Efun @ TB @ tyop_2Emin_2Ebool ),B: tyop_2Emin_2Efun @ TB @ TA,C: tyop_2Emin_2Efun @ TA @ TB] :
( ( c_2Equotient_2EQUOTIENT_2E3 @ TB @ TA @ A @ B @ C )
= ( app_2E2 @ ( tyop_2Emin_2Efun @ TA @ TB ) @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TA @ TB ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( tyop_2Emin_2Efun @ TB @ ( tyop_2Emin_2Efun @ TB @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TA @ TB ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient_2EQUOTIENT_2E0 @ TB @ TA ) @ A ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(40,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( p @ A )
=> ( ( p @ B )
=> ( p @ C ) ) )
<=> ( ( ( p @ A )
& ( p @ B ) )
=> ( p @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EAND__IMP__INTRO) ).
thf(247,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( ( p @ A )
=> ( ( p @ B )
=> ( p @ C ) ) )
=> ( ( ( p @ A )
& ( p @ B ) )
=> ( p @ C ) ) )
& ( ( ( ( p @ A )
& ( p @ B ) )
=> ( p @ C ) )
=> ( ( p @ A )
=> ( ( p @ B )
=> ( p @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(46,plain,
( ( p @ ( c_2Equotient_2E_3D_3D_3D_3E_2E4 @ skt1 @ skt2 @ sk1 @ sk4 @ sk7 @ sk8 ) )
| ~ sk9 ),
inference(cnf,[status(esa)],[45]) ).
thf(296,plain,
! [A: tyop_2Emin_2Ebool] :
( ~ ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ c_2Ebool_2E_7E_2E0 @ A ) )
| ( ( p @ ( c_2Equotient_2EQUOTIENT_2E3 @ skt2 @ skt4 @ sk4 @ sk5 @ sk6 ) )
!= ( p @ A ) ) ),
inference(paramod_ordered,[status(thm)],[51,136]) ).
thf(297,plain,
~ ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ c_2Ebool_2E_7E_2E0 @ ( c_2Equotient_2EQUOTIENT_2E3 @ skt2 @ skt4 @ sk4 @ sk5 @ sk6 ) ) ),
inference(pattern_uni,[status(thm)],[296:[bind(A,$thf( c_2Equotient_2EQUOTIENT_2E3 @ skt2 @ skt4 @ sk4 @ sk5 @ sk6 ))]]) ).
thf(409,plain,
( ( p @ c_2Ebool_2ET_2E0 )
!= ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ c_2Ebool_2E_7E_2E0 @ ( c_2Equotient_2EQUOTIENT_2E3 @ skt2 @ skt4 @ sk4 @ sk5 @ sk6 ) ) ) ),
inference(paramod_ordered,[status(thm)],[186,297]) ).
thf(416,plain,
( c_2Ebool_2ET_2E0
!= ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ c_2Ebool_2E_7E_2E0 @ ( c_2Equotient_2EQUOTIENT_2E3 @ skt2 @ skt4 @ sk4 @ sk5 @ sk6 ) ) ),
inference(simp,[status(thm)],[409]) ).
thf(34,axiom,
p @ c_2Ebool_2ET_2E0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Etruth) ).
thf(228,plain,
p @ c_2Ebool_2ET_2E0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(9,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( p @ ( c_2Ebool_2E_2F_5C_2E2 @ A @ B ) )
<=> ( ( p @ A )
& ( p @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',logicdef_2E_2F_5C) ).
thf(78,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ ( c_2Ebool_2E_2F_5C_2E2 @ A @ B ) )
=> ( ( p @ A )
& ( p @ B ) ) )
& ( ( ( p @ A )
& ( p @ B ) )
=> ( p @ ( c_2Ebool_2E_2F_5C_2E2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(42,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( A = B )
<=> ( p @ ( app_2E2 @ TA @ tyop_2Emin_2Ebool @ ( app_2E2 @ TA @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) @ ( c_2Emin_2E_3D_2E0 @ TA ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) ).
thf(261,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( A = B )
=> ( p @ ( app_2E2 @ TA @ tyop_2Emin_2Ebool @ ( app_2E2 @ TA @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) @ ( c_2Emin_2E_3D_2E0 @ TA ) @ A ) @ B ) ) )
& ( ( p @ ( app_2E2 @ TA @ tyop_2Emin_2Ebool @ ( app_2E2 @ TA @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) @ ( c_2Emin_2E_3D_2E0 @ TA ) @ A ) @ B ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(29,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: tyop_2Emin_2Efun @ TB @ TD,B: tyop_2Emin_2Efun @ TC @ TA] :
( ( c_2Equotient_2E_2D_2D_3E_2E2 @ TB @ TC @ TD @ TA @ A @ B )
= ( app_2E2 @ ( tyop_2Emin_2Efun @ TC @ TA ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TD @ TC ) @ ( tyop_2Emin_2Efun @ TB @ TA ) ) @ ( app_2E2 @ ( tyop_2Emin_2Efun @ TB @ TD ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TC @ TA ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TD @ TC ) @ ( tyop_2Emin_2Efun @ TB @ TA ) ) ) @ ( c_2Equotient_2E_2D_2D_3E_2E0 @ TB @ TC @ TD @ TA ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Equotient_2E_2D_2D_3E_2E2_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a_20mono_2EA_27d) ).
thf(211,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: tyop_2Emin_2Efun @ TB @ TD,B: tyop_2Emin_2Efun @ TC @ TA] :
( ( c_2Equotient_2E_2D_2D_3E_2E2 @ TB @ TC @ TD @ TA @ A @ B )
= ( app_2E2 @ ( tyop_2Emin_2Efun @ TC @ TA ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TD @ TC ) @ ( tyop_2Emin_2Efun @ TB @ TA ) ) @ ( app_2E2 @ ( tyop_2Emin_2Efun @ TB @ TD ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TC @ TA ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TD @ TC ) @ ( tyop_2Emin_2Efun @ TB @ TA ) ) ) @ ( c_2Equotient_2E_2D_2D_3E_2E0 @ TB @ TC @ TD @ TA ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(10,axiom,
! [A: tyop_2Emin_2Ebool] :
( ( ( ( p @ c_2Ebool_2ET_2E0 )
& ( p @ A ) )
<=> ( p @ A ) )
& ( ( ( p @ A )
& ( p @ c_2Ebool_2ET_2E0 ) )
<=> ( p @ A ) )
& ( ( ( p @ c_2Ebool_2EF_2E0 )
& ( p @ A ) )
<=> ( p @ c_2Ebool_2EF_2E0 ) )
& ( ( ( p @ A )
& ( p @ c_2Ebool_2EF_2E0 ) )
<=> ( p @ c_2Ebool_2EF_2E0 ) )
& ( ( ( p @ A )
& ( p @ A ) )
<=> ( p @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EAND__CLAUSES) ).
thf(84,plain,
! [A: tyop_2Emin_2Ebool] :
( ( ( ( p @ c_2Ebool_2ET_2E0 )
& ( p @ A ) )
=> ( p @ A ) )
& ( ( p @ A )
=> ( ( p @ c_2Ebool_2ET_2E0 )
& ( p @ A ) ) )
& ( ( ( p @ A )
& ( p @ c_2Ebool_2ET_2E0 ) )
=> ( p @ A ) )
& ( ( p @ A )
=> ( ( p @ A )
& ( p @ c_2Ebool_2ET_2E0 ) ) )
& ( ( ( p @ c_2Ebool_2EF_2E0 )
& ( p @ A ) )
=> ( p @ c_2Ebool_2EF_2E0 ) )
& ( ( p @ c_2Ebool_2EF_2E0 )
=> ( ( p @ c_2Ebool_2EF_2E0 )
& ( p @ A ) ) )
& ( ( ( p @ A )
& ( p @ c_2Ebool_2EF_2E0 ) )
=> ( p @ c_2Ebool_2EF_2E0 ) )
& ( ( p @ c_2Ebool_2EF_2E0 )
=> ( ( p @ A )
& ( p @ c_2Ebool_2EF_2E0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(306,plain,
! [A: tyop_2Emin_2Ebool] :
( ~ ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ c_2Ebool_2E_7E_2E0 @ A ) )
| ( ( p @ ( c_2Equotient_2EQUOTIENT_2E3 @ skt1 @ skt3 @ sk1 @ sk2 @ sk3 ) )
!= ( p @ A ) ) ),
inference(paramod_ordered,[status(thm)],[53,136]) ).
thf(307,plain,
~ ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ c_2Ebool_2E_7E_2E0 @ ( c_2Equotient_2EQUOTIENT_2E3 @ skt1 @ skt3 @ sk1 @ sk2 @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[306:[bind(A,$thf( c_2Equotient_2EQUOTIENT_2E3 @ skt1 @ skt3 @ sk1 @ sk2 @ sk3 ))]]) ).
thf(14,axiom,
! [TA: $tType,TB: $tType,A: tyop_2Emin_2Efun @ TB @ ( tyop_2Emin_2Efun @ TB @ tyop_2Emin_2Ebool ),B: tyop_2Emin_2Efun @ TB @ TA,C: tyop_2Emin_2Efun @ TA @ TB] :
( ( c_2Equotient_2EQUOTIENT_2E3 @ TB @ TA @ A @ B @ C )
= ( app_2E2 @ ( tyop_2Emin_2Efun @ TA @ TB ) @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TA @ TB ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( tyop_2Emin_2Efun @ TB @ ( tyop_2Emin_2Efun @ TB @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TA @ TB ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient_2EQUOTIENT_2E0 @ TB @ TA ) @ A ) @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2EA_27b_20mono_2EA_27d) ).
thf(117,plain,
! [TA: $tType,TB: $tType,A: tyop_2Emin_2Efun @ TB @ ( tyop_2Emin_2Efun @ TB @ tyop_2Emin_2Ebool ),B: tyop_2Emin_2Efun @ TB @ TA,C: tyop_2Emin_2Efun @ TA @ TB] :
( ( c_2Equotient_2EQUOTIENT_2E3 @ TB @ TA @ A @ B @ C )
= ( app_2E2 @ ( tyop_2Emin_2Efun @ TA @ TB ) @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TA @ TB ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( tyop_2Emin_2Efun @ TB @ ( tyop_2Emin_2Efun @ TB @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TA @ TB ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient_2EQUOTIENT_2E0 @ TB @ TA ) @ A ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(44,axiom,
! [TA: $tType,TB: $tType,A: tyop_2Emin_2Efun @ TB @ ( tyop_2Emin_2Efun @ TB @ TA ),B: TB] :
( ( c_2Ecombin_2EW_2E2 @ TB @ TA @ A @ B )
= ( app_2E2 @ TB @ TA @ ( app_2E2 @ TB @ ( tyop_2Emin_2Efun @ TB @ TA ) @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecombin_2EW__THM) ).
thf(270,plain,
! [TA: $tType,TB: $tType,A: tyop_2Emin_2Efun @ TB @ ( tyop_2Emin_2Efun @ TB @ TA ),B: TB] :
( ( c_2Ecombin_2EW_2E2 @ TB @ TA @ A @ B )
= ( app_2E2 @ TB @ TA @ ( app_2E2 @ TB @ ( tyop_2Emin_2Efun @ TB @ TA ) @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(19,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
=> ( p @ B ) )
=> ( ( ( p @ B )
=> ( p @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__ANTISYM__AX) ).
thf(137,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
=> ( p @ B ) )
=> ( ( ( p @ B )
=> ( p @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(35,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: tyop_2Emin_2Efun @ TD @ ( tyop_2Emin_2Efun @ TD @ tyop_2Emin_2Ebool ),B: tyop_2Emin_2Efun @ TD @ TB,C: tyop_2Emin_2Efun @ TB @ TD] :
( ( p @ ( c_2Equotient_2EQUOTIENT_2E3 @ TD @ TB @ A @ B @ C ) )
=> ! [D: tyop_2Emin_2Efun @ TC @ ( tyop_2Emin_2Efun @ TC @ tyop_2Emin_2Ebool ),E: tyop_2Emin_2Efun @ TC @ TA,F: tyop_2Emin_2Efun @ TA @ TC] :
( ( p @ ( c_2Equotient_2EQUOTIENT_2E3 @ TC @ TA @ D @ E @ F ) )
=> ( p @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( tyop_2Emin_2Efun @ TD @ TC ) @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ TD @ TC @ A @ D ) @ ( c_2Equotient_2E_2D_2D_3E_2E2 @ TB @ TC @ TD @ TA @ C @ E ) @ ( c_2Equotient_2E_2D_2D_3E_2E2 @ TD @ TA @ TB @ TC @ B @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Equotient_2EFUN__QUOTIENT) ).
thf(229,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: tyop_2Emin_2Efun @ TD @ ( tyop_2Emin_2Efun @ TD @ tyop_2Emin_2Ebool ),B: tyop_2Emin_2Efun @ TD @ TB,C: tyop_2Emin_2Efun @ TB @ TD] :
( ( p @ ( c_2Equotient_2EQUOTIENT_2E3 @ TD @ TB @ A @ B @ C ) )
=> ! [D: tyop_2Emin_2Efun @ TC @ ( tyop_2Emin_2Efun @ TC @ tyop_2Emin_2Ebool ),E: tyop_2Emin_2Efun @ TC @ TA,F: tyop_2Emin_2Efun @ TA @ TC] :
( ( p @ ( c_2Equotient_2EQUOTIENT_2E3 @ TC @ TA @ D @ E @ F ) )
=> ( p @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( tyop_2Emin_2Efun @ TD @ TC ) @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ TD @ TC @ A @ D ) @ ( c_2Equotient_2E_2D_2D_3E_2E2 @ TB @ TC @ TD @ TA @ C @ E ) @ ( c_2Equotient_2E_2D_2D_3E_2E2 @ TD @ TA @ TB @ TC @ B @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(26,axiom,
! [TA: $tType,TB: $tType,A: tyop_2Emin_2Efun @ TB @ ( tyop_2Emin_2Efun @ TB @ TA ),B: TB] :
( ( c_2Ecombin_2EW_2E2 @ TB @ TA @ A @ B )
= ( app_2E2 @ TB @ TA @ ( app_2E2 @ ( tyop_2Emin_2Efun @ TB @ ( tyop_2Emin_2Efun @ TB @ TA ) ) @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( c_2Ecombin_2EW_2E0 @ TB @ TA ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Ecombin_2EW_2E2_2Emono_2EA_27a_20mono_2EA_27b) ).
thf(197,plain,
! [TA: $tType,TB: $tType,A: tyop_2Emin_2Efun @ TB @ ( tyop_2Emin_2Efun @ TB @ TA ),B: TB] :
( ( c_2Ecombin_2EW_2E2 @ TB @ TA @ A @ B )
= ( app_2E2 @ TB @ TA @ ( app_2E2 @ ( tyop_2Emin_2Efun @ TB @ ( tyop_2Emin_2Efun @ TB @ TA ) ) @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( c_2Ecombin_2EW_2E0 @ TB @ TA ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(6,axiom,
! [TA: $tType,TB: $tType,A: tyop_2Emin_2Efun @ TB @ TA,B: tyop_2Emin_2Efun @ TB @ TA] :
( ! [C: TB] :
( ( app_2E2 @ TB @ TA @ A @ C )
= ( app_2E2 @ TB @ TA @ B @ C ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Eeq__ext) ).
thf(65,plain,
! [TA: $tType,TB: $tType,A: tyop_2Emin_2Efun @ TB @ TA,B: tyop_2Emin_2Efun @ TB @ TA] :
( ! [C: TB] :
( ( app_2E2 @ TB @ TA @ A @ C )
= ( app_2E2 @ TB @ TA @ B @ C ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(325,plain,
( ( p @ ( c_2Ebool_2E_7E_2E1 @ c_2Ebool_2ET_2E0 ) )
!= ( p @ ( c_2Equotient_2EQUOTIENT_2E3 @ skt1 @ skt3 @ sk1 @ sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[53,283]) ).
thf(329,plain,
( ( c_2Ebool_2E_7E_2E1 @ c_2Ebool_2ET_2E0 )
!= ( c_2Equotient_2EQUOTIENT_2E3 @ skt1 @ skt3 @ sk1 @ sk2 @ sk3 ) ),
inference(simp,[status(thm)],[325]) ).
thf(22,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
<=> ( p @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Eboolext) ).
thf(156,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ( p @ A )
=> ( p @ B ) )
& ( ( p @ B )
=> ( p @ A ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(57,plain,
! [A: tyop_2Emin_2Ebool] :
( ( A = c_2Ebool_2ET_2E0 )
| ( A = c_2Ebool_2EF_2E0 ) ),
inference(cnf,[status(esa)],[56]) ).
thf(58,plain,
! [A: tyop_2Emin_2Ebool] :
( ( A = c_2Ebool_2ET_2E0 )
| ( A = c_2Ebool_2EF_2E0 ) ),
inference(lifteq,[status(thm)],[57]) ).
thf(292,plain,
! [A: tyop_2Emin_2Ebool] :
( ~ ( p @ ( c_2Ebool_2E_7E_2E1 @ A ) )
| ( ( p @ ( c_2Equotient_2EQUOTIENT_2E3 @ skt2 @ skt4 @ sk4 @ sk5 @ sk6 ) )
!= ( p @ A ) ) ),
inference(paramod_ordered,[status(thm)],[51,203]) ).
thf(293,plain,
~ ( p @ ( c_2Ebool_2E_7E_2E1 @ ( c_2Equotient_2EQUOTIENT_2E3 @ skt2 @ skt4 @ sk4 @ sk5 @ sk6 ) ) ),
inference(pattern_uni,[status(thm)],[292:[bind(A,$thf( c_2Equotient_2EQUOTIENT_2E3 @ skt2 @ skt4 @ sk4 @ sk5 @ sk6 ))]]) ).
thf(372,plain,
( ( p @ ( c_2Ebool_2E_7E_2E1 @ ( c_2Equotient_2EQUOTIENT_2E3 @ skt2 @ skt4 @ sk4 @ sk5 @ sk6 ) ) )
!= ( p @ c_2Ebool_2ET_2E0 ) ),
inference(paramod_ordered,[status(thm)],[186,293]) ).
thf(374,plain,
( ( c_2Ebool_2E_7E_2E1 @ ( c_2Equotient_2EQUOTIENT_2E3 @ skt2 @ skt4 @ sk4 @ sk5 @ sk6 ) )
!= c_2Ebool_2ET_2E0 ),
inference(simp,[status(thm)],[372]) ).
thf(470,plain,
! [A: tyop_2Emin_2Ebool] :
( ( A = c_2Ebool_2EF_2E0 )
| ( A
!= ( c_2Ebool_2E_7E_2E1 @ ( c_2Equotient_2EQUOTIENT_2E3 @ skt2 @ skt4 @ sk4 @ sk5 @ sk6 ) ) ) ),
inference(paramod_ordered,[status(thm)],[58,374]) ).
thf(471,plain,
( ( c_2Ebool_2E_7E_2E1 @ ( c_2Equotient_2EQUOTIENT_2E3 @ skt2 @ skt4 @ sk4 @ sk5 @ sk6 ) )
= c_2Ebool_2EF_2E0 ),
inference(pattern_uni,[status(thm)],[470:[bind(A,$thf( c_2Ebool_2E_7E_2E1 @ ( c_2Equotient_2EQUOTIENT_2E3 @ skt2 @ skt4 @ sk4 @ sk5 @ sk6 ) ))]]) ).
thf(33,axiom,
! [TA: $tType,TB: $tType,A: tyop_2Emin_2Efun @ TB @ ( tyop_2Emin_2Efun @ TB @ tyop_2Emin_2Ebool ),B: tyop_2Emin_2Efun @ TA @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool )] :
( ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ TB @ TA @ A @ B )
= ( app_2E2 @ ( tyop_2Emin_2Efun @ TA @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( tyop_2Emin_2Efun @ TB @ ( tyop_2Emin_2Efun @ TB @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TA @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Equotient_2E_3D_3D_3D_3E_2E0 @ TB @ TA ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Equotient_2E_3D_3D_3D_3E_2E2_2Emono_2EA_27a_20mono_2EA_27b) ).
thf(225,plain,
! [TA: $tType,TB: $tType,A: tyop_2Emin_2Efun @ TB @ ( tyop_2Emin_2Efun @ TB @ tyop_2Emin_2Ebool ),B: tyop_2Emin_2Efun @ TA @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool )] :
( ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ TB @ TA @ A @ B )
= ( app_2E2 @ ( tyop_2Emin_2Efun @ TA @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( tyop_2Emin_2Efun @ TB @ ( tyop_2Emin_2Efun @ TB @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TA @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Equotient_2E_3D_3D_3D_3E_2E0 @ TB @ TA ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(39,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( app_2E2 @ TA @ TB @ ( app_2E2 @ TB @ ( tyop_2Emin_2Efun @ TA @ TB ) @ ( combin_k_2E0 @ TB @ TA ) @ A ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Ek__thm) ).
thf(244,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( app_2E2 @ TA @ TB @ ( app_2E2 @ TB @ ( tyop_2Emin_2Efun @ TA @ TB ) @ ( combin_k_2E0 @ TB @ TA ) @ A ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(28,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
=> ( p @ B ) )
<=> ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ ( app_2E2 @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Emin_2E_3D_3D_3E_2E0 @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) ).
thf(205,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ( p @ A )
=> ( p @ B ) )
=> ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ ( app_2E2 @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Emin_2E_3D_3D_3E_2E0 @ A ) @ B ) ) )
& ( ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ ( app_2E2 @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Emin_2E_3D_3D_3E_2E0 @ A ) @ B ) )
=> ( ( p @ A )
=> ( p @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(5,axiom,
! [TA: $tType,TB: $tType] :
( ( c_2Equotient_2Erespects_2E0 @ TB @ TA )
= ( c_2Ecombin_2EW_2E0 @ TB @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Equotient_2Erespects__def) ).
thf(62,plain,
! [TA: $tType,TB: $tType] :
( ( c_2Equotient_2Erespects_2E0 @ TB @ TA )
= ( c_2Ecombin_2EW_2E0 @ TB @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(63,plain,
! [TA: $tType,TB: $tType] :
( ( c_2Equotient_2Erespects_2E0 @ TA @ TB )
= ( c_2Ecombin_2EW_2E0 @ TA @ TB ) ),
inference(cnf,[status(esa)],[62]) ).
thf(64,plain,
! [TA: $tType,TB: $tType] :
( ( c_2Equotient_2Erespects_2E0 @ TA @ TB )
= ( c_2Ecombin_2EW_2E0 @ TA @ TB ) ),
inference(lifteq,[status(thm)],[63]) ).
thf(21,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( p @ ( c_2Emin_2E_3D_3D_3E_2E2 @ A @ B ) )
<=> ( ( p @ A )
=> ( p @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',logicdef_2E_3D_3D_3E) ).
thf(149,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ ( c_2Emin_2E_3D_3D_3E_2E2 @ A @ B ) )
=> ( ( p @ A )
=> ( p @ B ) ) )
& ( ( ( p @ A )
=> ( p @ B ) )
=> ( p @ ( c_2Emin_2E_3D_3D_3E_2E2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(24,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: tyop_2Emin_2Efun @ TC @ ( tyop_2Emin_2Efun @ TB @ TA ),B: tyop_2Emin_2Efun @ TC @ TB,C: TC] :
( ( app_2E2 @ TC @ TA @ ( app_2E2 @ ( tyop_2Emin_2Efun @ TC @ TB ) @ ( tyop_2Emin_2Efun @ TC @ TA ) @ ( app_2E2 @ ( tyop_2Emin_2Efun @ TC @ ( tyop_2Emin_2Efun @ TB @ TA ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TC @ TB ) @ ( tyop_2Emin_2Efun @ TC @ TA ) ) @ ( combin_s_2E0 @ TC @ TB @ TA ) @ A ) @ B ) @ C )
= ( app_2E2 @ TB @ TA @ ( app_2E2 @ TC @ ( tyop_2Emin_2Efun @ TB @ TA ) @ A @ C ) @ ( app_2E2 @ TC @ TB @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Es__thm) ).
thf(191,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: tyop_2Emin_2Efun @ TC @ ( tyop_2Emin_2Efun @ TB @ TA ),B: tyop_2Emin_2Efun @ TC @ TB,C: TC] :
( ( app_2E2 @ TC @ TA @ ( app_2E2 @ ( tyop_2Emin_2Efun @ TC @ TB ) @ ( tyop_2Emin_2Efun @ TC @ TA ) @ ( app_2E2 @ ( tyop_2Emin_2Efun @ TC @ ( tyop_2Emin_2Efun @ TB @ TA ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TC @ TB ) @ ( tyop_2Emin_2Efun @ TC @ TA ) ) @ ( combin_s_2E0 @ TC @ TB @ TA ) @ A ) @ B ) @ C )
= ( app_2E2 @ TB @ TA @ ( app_2E2 @ TC @ ( tyop_2Emin_2Efun @ TB @ TA ) @ A @ C ) @ ( app_2E2 @ TC @ TB @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(4,axiom,
! [TA: $tType,A: TA] :
( ( app_2E2 @ TA @ TA @ ( combin_i_2E0 @ TA ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Ei__thm) ).
thf(59,plain,
! [TA: $tType,A: TA] :
( ( app_2E2 @ TA @ TA @ ( combin_i_2E0 @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(50,plain,
( sk9
| ( ( c_2Equotient_2E_2D_2D_3E_2E3 @ skt3 @ skt2 @ skt1 @ skt4 @ sk3 @ sk5 @ sk7 )
= ( c_2Equotient_2E_2D_2D_3E_2E3 @ skt3 @ skt2 @ skt1 @ skt4 @ sk3 @ sk5 @ sk8 ) ) ),
inference(cnf,[status(esa)],[45]) ).
thf(54,plain,
( ( ( c_2Equotient_2E_2D_2D_3E_2E3 @ skt3 @ skt2 @ skt1 @ skt4 @ sk3 @ sk5 @ sk8 )
= ( c_2Equotient_2E_2D_2D_3E_2E3 @ skt3 @ skt2 @ skt1 @ skt4 @ sk3 @ sk5 @ sk7 ) )
| sk9 ),
inference(lifteq,[status(thm)],[50]) ).
thf(49,plain,
( sk9
| ( p @ ( c_2Equotient_2Erespects_2E2 @ ( tyop_2Emin_2Efun @ skt1 @ skt2 ) @ tyop_2Emin_2Ebool @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ skt1 @ skt2 @ sk1 @ sk4 ) @ sk7 ) ) ),
inference(cnf,[status(esa)],[45]) ).
thf(302,plain,
! [A: tyop_2Emin_2Ebool] :
( ~ ( p @ ( c_2Ebool_2E_7E_2E1 @ A ) )
| ( ( p @ ( c_2Equotient_2EQUOTIENT_2E3 @ skt1 @ skt3 @ sk1 @ sk2 @ sk3 ) )
!= ( p @ A ) ) ),
inference(paramod_ordered,[status(thm)],[53,203]) ).
thf(303,plain,
~ ( p @ ( c_2Ebool_2E_7E_2E1 @ ( c_2Equotient_2EQUOTIENT_2E3 @ skt1 @ skt3 @ sk1 @ sk2 @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[302:[bind(A,$thf( c_2Equotient_2EQUOTIENT_2E3 @ skt1 @ skt3 @ sk1 @ sk2 @ sk3 ))]]) ).
thf(384,plain,
( ( p @ ( c_2Ebool_2E_7E_2E1 @ ( c_2Equotient_2EQUOTIENT_2E3 @ skt1 @ skt3 @ sk1 @ sk2 @ sk3 ) ) )
!= ( p @ c_2Ebool_2ET_2E0 ) ),
inference(paramod_ordered,[status(thm)],[186,303]) ).
thf(389,plain,
( ( c_2Ebool_2E_7E_2E1 @ ( c_2Equotient_2EQUOTIENT_2E3 @ skt1 @ skt3 @ sk1 @ sk2 @ sk3 ) )
!= c_2Ebool_2ET_2E0 ),
inference(simp,[status(thm)],[384]) ).
thf(482,plain,
! [A: tyop_2Emin_2Ebool] :
( ( A = c_2Ebool_2EF_2E0 )
| ( A
!= ( c_2Ebool_2E_7E_2E1 @ ( c_2Equotient_2EQUOTIENT_2E3 @ skt1 @ skt3 @ sk1 @ sk2 @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[58,389]) ).
thf(483,plain,
( ( c_2Ebool_2E_7E_2E1 @ ( c_2Equotient_2EQUOTIENT_2E3 @ skt1 @ skt3 @ sk1 @ sk2 @ sk3 ) )
= c_2Ebool_2EF_2E0 ),
inference(pattern_uni,[status(thm)],[482:[bind(A,$thf( c_2Ebool_2E_7E_2E1 @ ( c_2Equotient_2EQUOTIENT_2E3 @ skt1 @ skt3 @ sk1 @ sk2 @ sk3 ) ))]]) ).
thf(12,axiom,
! [TA: $tType,TB: $tType,A: tyop_2Emin_2Efun @ TB @ ( tyop_2Emin_2Efun @ TB @ tyop_2Emin_2Ebool ),B: tyop_2Emin_2Efun @ TB @ TA,C: tyop_2Emin_2Efun @ TA @ TB] :
( ( c_2Equotient_2EQUOTIENT_2E3 @ TB @ TA @ A @ B @ C )
= ( app_2E2 @ ( tyop_2Emin_2Efun @ TA @ TB ) @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TA @ TB ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( tyop_2Emin_2Efun @ TB @ ( tyop_2Emin_2Efun @ TB @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TA @ TB ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient_2EQUOTIENT_2E0 @ TB @ TA ) @ A ) @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2EA_27a_20mono_2EA_27b) ).
thf(108,plain,
! [TA: $tType,TB: $tType,A: tyop_2Emin_2Efun @ TB @ ( tyop_2Emin_2Efun @ TB @ tyop_2Emin_2Ebool ),B: tyop_2Emin_2Efun @ TB @ TA,C: tyop_2Emin_2Efun @ TA @ TB] :
( ( c_2Equotient_2EQUOTIENT_2E3 @ TB @ TA @ A @ B @ C )
= ( app_2E2 @ ( tyop_2Emin_2Efun @ TA @ TB ) @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TA @ TB ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( tyop_2Emin_2Efun @ TB @ ( tyop_2Emin_2Efun @ TB @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TA @ TB ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient_2EQUOTIENT_2E0 @ TB @ TA ) @ A ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(326,plain,
( ( p @ ( c_2Ebool_2E_7E_2E1 @ c_2Ebool_2ET_2E0 ) )
!= ( p @ c_2Ebool_2ET_2E0 ) ),
inference(paramod_ordered,[status(thm)],[186,283]) ).
thf(330,plain,
( ( c_2Ebool_2E_7E_2E1 @ c_2Ebool_2ET_2E0 )
!= c_2Ebool_2ET_2E0 ),
inference(simp,[status(thm)],[326]) ).
thf(43,axiom,
! [TA: $tType,A: tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool] :
( ( c_2Ebool_2E_3F_2E1 @ TA @ A )
= ( app_2E2 @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E0 @ TA ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) ).
thf(267,plain,
! [TA: $tType,A: tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool] :
( ( c_2Ebool_2E_3F_2E1 @ TA @ A )
= ( app_2E2 @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E0 @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TD @ TC ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TD @ TC ) @ tyop_2Emin_2Ebool ),B: tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TD @ TC ) @ ( tyop_2Emin_2Efun @ TB @ TA ),C: tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( tyop_2Emin_2Efun @ TD @ TC )] :
( ( c_2Equotient_2EQUOTIENT_2E3 @ ( tyop_2Emin_2Efun @ TD @ TC ) @ ( tyop_2Emin_2Efun @ TB @ TA ) @ A @ B @ C )
= ( app_2E2 @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( tyop_2Emin_2Efun @ TD @ TC ) ) @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TD @ TC ) @ ( tyop_2Emin_2Efun @ TB @ TA ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( tyop_2Emin_2Efun @ TD @ TC ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TD @ TC ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TD @ TC ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TD @ TC ) @ ( tyop_2Emin_2Efun @ TB @ TA ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( tyop_2Emin_2Efun @ TD @ TC ) ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient_2EQUOTIENT_2E0 @ ( tyop_2Emin_2Efun @ TD @ TC ) @ ( tyop_2Emin_2Efun @ TB @ TA ) ) @ A ) @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Efun_28A_27c_2CA_27d_29) ).
thf(241,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TD @ TC ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TD @ TC ) @ tyop_2Emin_2Ebool ),B: tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TD @ TC ) @ ( tyop_2Emin_2Efun @ TB @ TA ),C: tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( tyop_2Emin_2Efun @ TD @ TC )] :
( ( c_2Equotient_2EQUOTIENT_2E3 @ ( tyop_2Emin_2Efun @ TD @ TC ) @ ( tyop_2Emin_2Efun @ TB @ TA ) @ A @ B @ C )
= ( app_2E2 @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( tyop_2Emin_2Efun @ TD @ TC ) ) @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TD @ TC ) @ ( tyop_2Emin_2Efun @ TB @ TA ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( tyop_2Emin_2Efun @ TD @ TC ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TD @ TC ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TD @ TC ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TD @ TC ) @ ( tyop_2Emin_2Efun @ TB @ TA ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( tyop_2Emin_2Efun @ TD @ TC ) ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient_2EQUOTIENT_2E0 @ ( tyop_2Emin_2Efun @ TD @ TC ) @ ( tyop_2Emin_2Efun @ TB @ TA ) ) @ A ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(16,axiom,
! [TA: $tType,TB: $tType,A: tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ tyop_2Emin_2Ebool ),B: tyop_2Emin_2Efun @ TB @ TA] :
( ( c_2Equotient_2Erespects_2E2 @ ( tyop_2Emin_2Efun @ TB @ TA ) @ tyop_2Emin_2Ebool @ A @ B )
= ( app_2E2 @ ( tyop_2Emin_2Efun @ TB @ TA ) @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ tyop_2Emin_2Ebool ) @ ( c_2Equotient_2Erespects_2E0 @ ( tyop_2Emin_2Efun @ TB @ TA ) @ tyop_2Emin_2Ebool ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Equotient_2Erespects_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Ebool) ).
thf(123,plain,
! [TA: $tType,TB: $tType,A: tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ tyop_2Emin_2Ebool ),B: tyop_2Emin_2Efun @ TB @ TA] :
( ( c_2Equotient_2Erespects_2E2 @ ( tyop_2Emin_2Efun @ TB @ TA ) @ tyop_2Emin_2Ebool @ A @ B )
= ( app_2E2 @ ( tyop_2Emin_2Efun @ TB @ TA ) @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ tyop_2Emin_2Ebool ) @ ( c_2Equotient_2Erespects_2E0 @ ( tyop_2Emin_2Efun @ TB @ TA ) @ tyop_2Emin_2Ebool ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(25,axiom,
! [TA: $tType,A: tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool] :
( ( p @ ( c_2Ebool_2E_3F_2E1 @ TA @ A ) )
<=> ? [B: TA] : ( p @ ( app_2E2 @ TA @ tyop_2Emin_2Ebool @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantdef_2E_3F) ).
thf(194,plain,
! [TA: $tType,A: tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool] :
( ( ( p @ ( c_2Ebool_2E_3F_2E1 @ TA @ A ) )
=> ? [B: TA] : ( p @ ( app_2E2 @ TA @ tyop_2Emin_2Ebool @ A @ B ) ) )
& ( ? [B: TA] : ( p @ ( app_2E2 @ TA @ tyop_2Emin_2Ebool @ A @ B ) )
=> ( p @ ( c_2Ebool_2E_3F_2E1 @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(36,axiom,
! [TA: $tType,A: tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool] :
( ( p @ ( c_2Ebool_2E_21_2E1 @ TA @ A ) )
<=> ! [B: TA] : ( p @ ( app_2E2 @ TA @ tyop_2Emin_2Ebool @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantdef_2E_21) ).
thf(231,plain,
! [TA: $tType,A: tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool] :
( ( ( p @ ( c_2Ebool_2E_21_2E1 @ TA @ A ) )
=> ! [B: TA] : ( p @ ( app_2E2 @ TA @ tyop_2Emin_2Ebool @ A @ B ) ) )
& ( ! [B: TA] : ( p @ ( app_2E2 @ TA @ tyop_2Emin_2Ebool @ A @ B ) )
=> ( p @ ( c_2Ebool_2E_21_2E1 @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(361,plain,
( ( p @ ( c_2Equotient_2EQUOTIENT_2E3 @ skt2 @ skt4 @ sk4 @ sk5 @ sk6 ) )
!= ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ c_2Ebool_2E_7E_2E0 @ c_2Ebool_2ET_2E0 ) ) ),
inference(paramod_ordered,[status(thm)],[51,287]) ).
thf(363,plain,
( ( c_2Equotient_2EQUOTIENT_2E3 @ skt2 @ skt4 @ sk4 @ sk5 @ sk6 )
!= ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ c_2Ebool_2E_7E_2E0 @ c_2Ebool_2ET_2E0 ) ),
inference(simp,[status(thm)],[361]) ).
thf(32,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( p @ ( c_2Ebool_2E_5C_2F_2E2 @ A @ B ) )
<=> ( ( p @ A )
| ( p @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',logicdef_2E_5C_2F) ).
thf(218,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ ( c_2Ebool_2E_5C_2F_2E2 @ A @ B ) )
=> ( ( p @ A )
| ( p @ B ) ) )
& ( ( ( p @ A )
| ( p @ B ) )
=> ( p @ ( c_2Ebool_2E_5C_2F_2E2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(314,plain,
( ~ sk9
| ( ( p @ ( c_2Equotient_2E_3D_3D_3D_3E_2E4 @ skt1 @ skt2 @ sk1 @ sk4 @ sk7 @ sk8 ) )
!= ( p @ c_2Ebool_2EF_2E0 ) ) ),
inference(paramod_ordered,[status(thm)],[46,107]) ).
thf(319,plain,
( ~ sk9
| ( ( c_2Equotient_2E_3D_3D_3D_3E_2E4 @ skt1 @ skt2 @ sk1 @ sk4 @ sk7 @ sk8 )
!= c_2Ebool_2EF_2E0 ) ),
inference(simp,[status(thm)],[314]) ).
thf(41,axiom,
! [TA: $tType,TB: $tType,A: tyop_2Emin_2Efun @ TB @ ( tyop_2Emin_2Efun @ TB @ tyop_2Emin_2Ebool ),B: tyop_2Emin_2Efun @ TA @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ),C: tyop_2Emin_2Efun @ TB @ TA,D: tyop_2Emin_2Efun @ TB @ TA] :
( ( c_2Equotient_2E_3D_3D_3D_3E_2E4 @ TB @ TA @ A @ B @ C @ D )
= ( app_2E2 @ ( tyop_2Emin_2Efun @ TB @ TA ) @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( tyop_2Emin_2Efun @ TA @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( tyop_2Emin_2Efun @ TB @ ( tyop_2Emin_2Efun @ TB @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TA @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Equotient_2E_3D_3D_3D_3E_2E0 @ TB @ TA ) @ A ) @ B ) @ C ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq4_2Ec_2Equotient_2E_3D_3D_3D_3E_2E4_2Emono_2EA_27a_20mono_2EA_27b) ).
thf(258,plain,
! [TA: $tType,TB: $tType,A: tyop_2Emin_2Efun @ TB @ ( tyop_2Emin_2Efun @ TB @ tyop_2Emin_2Ebool ),B: tyop_2Emin_2Efun @ TA @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ),C: tyop_2Emin_2Efun @ TB @ TA,D: tyop_2Emin_2Efun @ TB @ TA] :
( ( c_2Equotient_2E_3D_3D_3D_3E_2E4 @ TB @ TA @ A @ B @ C @ D )
= ( app_2E2 @ ( tyop_2Emin_2Efun @ TB @ TA ) @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( tyop_2Emin_2Efun @ TA @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( tyop_2Emin_2Efun @ TB @ ( tyop_2Emin_2Efun @ TB @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TA @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Equotient_2E_3D_3D_3D_3E_2E0 @ TB @ TA ) @ A ) @ B ) @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(47,plain,
( ~ ( p @ ( c_2Equotient_2Erespects_2E2 @ ( tyop_2Emin_2Efun @ skt1 @ skt2 ) @ tyop_2Emin_2Ebool @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ skt1 @ skt2 @ sk1 @ sk4 ) @ sk7 ) )
| ~ ( p @ ( c_2Equotient_2Erespects_2E2 @ ( tyop_2Emin_2Efun @ skt1 @ skt2 ) @ tyop_2Emin_2Ebool @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ skt1 @ skt2 @ sk1 @ sk4 ) @ sk8 ) )
| ( ( c_2Equotient_2E_2D_2D_3E_2E3 @ skt3 @ skt2 @ skt1 @ skt4 @ sk3 @ sk5 @ sk7 )
!= ( c_2Equotient_2E_2D_2D_3E_2E3 @ skt3 @ skt2 @ skt1 @ skt4 @ sk3 @ sk5 @ sk8 ) )
| ~ sk9 ),
inference(cnf,[status(esa)],[45]) ).
thf(55,plain,
( ( ( c_2Equotient_2E_2D_2D_3E_2E3 @ skt3 @ skt2 @ skt1 @ skt4 @ sk3 @ sk5 @ sk8 )
!= ( c_2Equotient_2E_2D_2D_3E_2E3 @ skt3 @ skt2 @ skt1 @ skt4 @ sk3 @ sk5 @ sk7 ) )
| ~ ( p @ ( c_2Equotient_2Erespects_2E2 @ ( tyop_2Emin_2Efun @ skt1 @ skt2 ) @ tyop_2Emin_2Ebool @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ skt1 @ skt2 @ sk1 @ sk4 ) @ sk7 ) )
| ~ ( p @ ( c_2Equotient_2Erespects_2E2 @ ( tyop_2Emin_2Efun @ skt1 @ skt2 ) @ tyop_2Emin_2Ebool @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ skt1 @ skt2 @ sk1 @ sk4 ) @ sk8 ) )
| ~ sk9 ),
inference(lifteq,[status(thm)],[47]) ).
thf(8,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: tyop_2Emin_2Efun @ TB @ TD,B: tyop_2Emin_2Efun @ TC @ TA,C: tyop_2Emin_2Efun @ TD @ TC] :
( ( c_2Equotient_2E_2D_2D_3E_2E3 @ TB @ TC @ TD @ TA @ A @ B @ C )
= ( app_2E2 @ ( tyop_2Emin_2Efun @ TD @ TC ) @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( app_2E2 @ ( tyop_2Emin_2Efun @ TC @ TA ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TD @ TC ) @ ( tyop_2Emin_2Efun @ TB @ TA ) ) @ ( app_2E2 @ ( tyop_2Emin_2Efun @ TB @ TD ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TC @ TA ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TD @ TC ) @ ( tyop_2Emin_2Efun @ TB @ TA ) ) ) @ ( c_2Equotient_2E_2D_2D_3E_2E0 @ TB @ TC @ TD @ TA ) @ A ) @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq3_2Ec_2Equotient_2E_2D_2D_3E_2E3_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a_20mono_2EA_27d) ).
thf(75,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: tyop_2Emin_2Efun @ TB @ TD,B: tyop_2Emin_2Efun @ TC @ TA,C: tyop_2Emin_2Efun @ TD @ TC] :
( ( c_2Equotient_2E_2D_2D_3E_2E3 @ TB @ TC @ TD @ TA @ A @ B @ C )
= ( app_2E2 @ ( tyop_2Emin_2Efun @ TD @ TC ) @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( app_2E2 @ ( tyop_2Emin_2Efun @ TC @ TA ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TD @ TC ) @ ( tyop_2Emin_2Efun @ TB @ TA ) ) @ ( app_2E2 @ ( tyop_2Emin_2Efun @ TB @ TD ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TC @ TA ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TD @ TC ) @ ( tyop_2Emin_2Efun @ TB @ TA ) ) ) @ ( c_2Equotient_2E_2D_2D_3E_2E0 @ TB @ TC @ TD @ TA ) @ A ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(30,axiom,
p @ c_2Ebool_2ET_2E0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ETRUTH) ).
thf(214,plain,
p @ c_2Ebool_2ET_2E0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(294,plain,
( ( p @ ( c_2Equotient_2EQUOTIENT_2E3 @ skt2 @ skt4 @ sk4 @ sk5 @ sk6 ) )
!= ( p @ c_2Ebool_2EF_2E0 ) ),
inference(paramod_ordered,[status(thm)],[51,107]) ).
thf(300,plain,
( ( c_2Equotient_2EQUOTIENT_2E3 @ skt2 @ skt4 @ sk4 @ sk5 @ sk6 )
!= c_2Ebool_2EF_2E0 ),
inference(simp,[status(thm)],[294]) ).
thf(20,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: tyop_2Emin_2Efun @ TD @ TB,B: tyop_2Emin_2Efun @ TA @ TC] :
( ( c_2Equotient_2E_2D_2D_3E_2E2 @ TD @ TA @ TB @ TC @ A @ B )
= ( app_2E2 @ ( tyop_2Emin_2Efun @ TA @ TC ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( tyop_2Emin_2Efun @ TD @ TC ) ) @ ( app_2E2 @ ( tyop_2Emin_2Efun @ TD @ TB ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TA @ TC ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( tyop_2Emin_2Efun @ TD @ TC ) ) ) @ ( c_2Equotient_2E_2D_2D_3E_2E0 @ TD @ TA @ TB @ TC ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Equotient_2E_2D_2D_3E_2E2_2Emono_2EA_27a_20mono_2EA_27d_20mono_2EA_27c_20mono_2EA_27b) ).
thf(146,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: tyop_2Emin_2Efun @ TD @ TB,B: tyop_2Emin_2Efun @ TA @ TC] :
( ( c_2Equotient_2E_2D_2D_3E_2E2 @ TD @ TA @ TB @ TC @ A @ B )
= ( app_2E2 @ ( tyop_2Emin_2Efun @ TA @ TC ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( tyop_2Emin_2Efun @ TD @ TC ) ) @ ( app_2E2 @ ( tyop_2Emin_2Efun @ TD @ TB ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TA @ TC ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TB @ TA ) @ ( tyop_2Emin_2Efun @ TD @ TC ) ) ) @ ( c_2Equotient_2E_2D_2D_3E_2E0 @ TD @ TA @ TB @ TC ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(17,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( p @ ( c_2Emin_2E_3D_2E2 @ TA @ A @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',logicdef_2E_3D) ).
thf(126,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( p @ ( c_2Emin_2E_3D_2E2 @ TA @ A @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( p @ ( c_2Emin_2E_3D_2E2 @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(7,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
& ( p @ B ) )
<=> ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ ( app_2E2 @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_2F_5C_2E0 @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) ).
thf(68,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ( p @ A )
& ( p @ B ) )
=> ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ ( app_2E2 @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_2F_5C_2E0 @ A ) @ B ) ) )
& ( ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ ( app_2E2 @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_2F_5C_2E0 @ A ) @ B ) )
=> ( ( p @ A )
& ( p @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(13,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
| ( p @ B ) )
<=> ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ ( app_2E2 @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_5C_2F_2E0 @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) ).
thf(111,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ( p @ A )
| ( p @ B ) )
=> ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ ( app_2E2 @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_5C_2F_2E0 @ A ) @ B ) ) )
& ( ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ ( app_2E2 @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_5C_2F_2E0 @ A ) @ B ) )
=> ( ( p @ A )
| ( p @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(304,plain,
( ( p @ ( c_2Equotient_2EQUOTIENT_2E3 @ skt1 @ skt3 @ sk1 @ sk2 @ sk3 ) )
!= ( p @ c_2Ebool_2EF_2E0 ) ),
inference(paramod_ordered,[status(thm)],[53,107]) ).
thf(309,plain,
( ( c_2Equotient_2EQUOTIENT_2E3 @ skt1 @ skt3 @ sk1 @ sk2 @ sk3 )
!= c_2Ebool_2EF_2E0 ),
inference(simp,[status(thm)],[304]) ).
thf(31,axiom,
! [TA: $tType,A: tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool] :
( ( c_2Ebool_2E_21_2E1 @ TA @ A )
= ( app_2E2 @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E0 @ TA ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) ).
thf(215,plain,
! [TA: $tType,A: tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool] :
( ( c_2Ebool_2E_21_2E1 @ TA @ A )
= ( app_2E2 @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E0 @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(22675,plain,
$false,
inference(cvc4,[status(thm)],[56,288,52,132,362,48,331,365,234,120,247,46,416,228,78,261,211,106,84,307,117,270,297,137,165,229,197,65,329,156,53,471,225,244,205,45,64,149,191,59,54,49,483,108,330,267,241,123,194,231,363,203,218,319,258,186,55,75,58,214,287,300,146,51,107,283,126,136,200,68,62,111,309,215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : ITP009_3 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.10/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n025.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon May 6 14:19:09 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.84/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.46/1.01 % [INFO] Parsing done (180ms).
% 1.46/1.02 % [INFO] Running in sequential loop mode.
% 1.97/1.25 % [INFO] eprover registered as external prover.
% 1.97/1.25 % [INFO] cvc4 registered as external prover.
% 1.97/1.26 % [INFO] Scanning for conjecture ...
% 2.18/1.37 % [INFO] Found a conjecture and 42 axioms. Running axiom selection ...
% 2.35/1.44 % [INFO] Axiom selection finished. Selected 42 axioms (removed 0 axioms).
% 2.80/1.52 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.87/1.54 % [INFO] Type checking passed.
% 2.87/1.55 % [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 ...
% 3.44/1.78 % [INFO] [Domain constraints] Detected constraint on tyop_2Emin_2Ebool
% 3.44/1.78 % [INFO] [Domain constraints] dom(tyop_2Emin_2Ebool) ⊆ {c_2Ebool_2ET_2E0,c_2Ebool_2EF_2E0}
% 174.00/50.00 % External prover 'cvc4' found a proof!
% 174.00/50.00 % [INFO] Killing All external provers ...
% 174.00/50.00 % Time passed: 49480ms (effective reasoning time: 48975ms)
% 174.00/50.00 % 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)>
% 174.00/50.01 % Axioms used in derivation (42): thm_2Eextra_2Dho_2Eboolext, thm_2Equotient_2Erespects__def, logicdef_2E_3D, arityeq2_2Ec_2Equotient_2E_3D_3D_3D_3E_2E2_2Emono_2EA_27a_20mono_2EA_27b, thm_2Eextra_2Dho_2Enotfalse, thm_2Ebool_2EAND__IMP__INTRO, logicdef_2E_3D_3D_3E, arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a, arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a, logicdef_2E_2F_5C, logicdef_2E_7E, thm_2Eextra_2Dho_2Es__thm, arityeq2_2Ec_2Ecombin_2EW_2E2_2Emono_2EA_27a_20mono_2EA_27b, arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Efun_28A_27c_2CA_27d_29, arityeq4_2Ec_2Equotient_2E_3D_3D_3D_3E_2E4_2Emono_2EA_27a_20mono_2EA_27b, thm_2Eextra_2Dho_2Eeq__ext, thm_2Ebool_2EEQ__CLAUSES, thm_2Ebool_2EIMP__ANTISYM__AX, arityeq3_2Ec_2Equotient_2E_2D_2D_3E_2E3_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a_20mono_2EA_27d, thm_2Eextra_2Dho_2Ei__thm, arityeq2_2Ec_2Ebool_2E_2F_5C_2E2, arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2, thm_2Eextra_2Dho_2Ebool__cases__ax, logicdef_2E_5C_2F, arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2EA_27b_20mono_2EA_27d, arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2EA_27a_20mono_2EA_27b, thm_2Eextra_2Dho_2Ek__thm, quantdef_2E_21, arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a, thm_2Ecombin_2EW__THM, thm_2Ebool_2ETRUTH, thm_2Equotient_2EFUN__QUOTIENT, arityeq2_2Ec_2Equotient_2E_2D_2D_3E_2E2_2Emono_2EA_27a_20mono_2EA_27d_20mono_2EA_27c_20mono_2EA_27b, thm_2Eextra_2Dho_2Etruth, arityeq1_2Ec_2Ebool_2E_7E_2E1, arityeq2_2Ec_2Ebool_2E_5C_2F_2E2, arityeq2_2Ec_2Equotient_2Erespects_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Ebool, arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2EA_27a_20mono_2EA_27c, thm_2Ebool_2EAND__CLAUSES, thm_2Equotient_2EQUOTIENT__REL, arityeq2_2Ec_2Equotient_2E_2D_2D_3E_2E2_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a_20mono_2EA_27d, quantdef_2E_3F
% 174.00/50.01 % No. of inferences in proof: 154
% 174.00/50.01 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 49480 ms resp. 48975 ms w/o parsing
% 174.13/50.10 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 174.13/50.10 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------