TSTP Solution File: ITP038^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP038^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n018.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 : Thu Aug 31 03:17:41 EDT 2023
% Result : Theorem 0.52s 1.05s
% Output : Proof 0.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.19 % Problem : ITP038^1 : TPTP v8.1.2. Released v7.5.0.
% 0.13/0.20 % Command : do_cvc5 %s %d
% 0.20/0.41 % Computer : n018.cluster.edu
% 0.20/0.41 % Model : x86_64 x86_64
% 0.20/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.41 % Memory : 8042.1875MB
% 0.20/0.41 % OS : Linux 3.10.0-693.el7.x86_64
% 0.20/0.41 % CPULimit : 300
% 0.20/0.41 % WCLimit : 300
% 0.20/0.41 % DateTime : Sun Aug 27 15:39:46 EDT 2023
% 0.20/0.42 % CPUTime :
% 0.26/0.61 %----Proving TH0
% 0.26/0.62 %------------------------------------------------------------------------------
% 0.26/0.62 % File : ITP038^1 : TPTP v8.1.2. Released v7.5.0.
% 0.26/0.62 % Domain : Interactive Theorem Proving
% 0.26/0.62 % Problem : Sledgehammer Coincidence problem prob_231__7211966_1
% 0.26/0.62 % Version : Especial.
% 0.26/0.62 % English :
% 0.26/0.62
% 0.26/0.62 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.26/0.62 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.26/0.62 % Source : [Des21]
% 0.26/0.62 % Names : Coincidence/prob_231__7211966_1 [Des21]
% 0.26/0.62
% 0.26/0.62 % Status : Theorem
% 0.26/0.62 % Rating : 0.23 v8.1.0, 0.27 v7.5.0
% 0.26/0.62 % Syntax : Number of formulae : 558 ( 170 unt; 200 typ; 0 def)
% 0.26/0.62 % Number of atoms : 896 ( 365 equ; 0 cnn)
% 0.26/0.62 % Maximal formula atoms : 12 ( 2 avg)
% 0.26/0.62 % Number of connectives : 2644 ( 54 ~; 1 |; 87 &;2190 @)
% 0.26/0.62 % ( 0 <=>; 312 =>; 0 <=; 0 <~>)
% 0.26/0.62 % Maximal formula depth : 25 ( 6 avg)
% 0.26/0.62 % Number of types : 45 ( 44 usr)
% 0.26/0.62 % Number of type conns : 550 ( 550 >; 0 *; 0 +; 0 <<)
% 0.26/0.62 % Number of symbols : 159 ( 156 usr; 14 con; 0-10 aty)
% 0.26/0.62 % Number of variables : 1070 ( 122 ^; 925 !; 23 ?;1070 :)
% 0.26/0.62 % SPC : TH0_THM_EQU_NAR
% 0.26/0.62
% 0.26/0.62 % Comments : This file was generated by Sledgehammer 2021-02-23 15:38:01.725
% 0.26/0.62 %------------------------------------------------------------------------------
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% 0.26/0.62 type_d46389773_sf_sz: ( frechet_strm_sf_sz > trm_sf_sz ) > ( trm_sf_sz > frechet_strm_sf_sz ) > set_trm_sf_sz > $o ).
% 0.26/0.62
% 0.26/0.62 thf(sy_c_member_001t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__a_Mtf__b_Mtf__c_Mt__Product____Type__Ounit_J,type,
% 0.26/0.62 member1777622435t_unit: denota231621370t_unit > set_De455519194t_unit > $o ).
% 0.26/0.62
% 0.26/0.62 thf(sy_c_member_001t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J,type,
% 0.26/0.62 member754147591t_unit: denota610675952t_unit > set_De208295462t_unit > $o ).
% 0.26/0.62
% 0.26/0.62 thf(sy_c_member_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J,type,
% 0.26/0.62 member1693951742eal_sz: finite824932053eal_sz > set_Fi291318197eal_sz > $o ).
% 0.26/0.62
% 0.26/0.62 thf(sy_c_member_001t__Product____Type__Oprod_It__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_Mt__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_J,type,
% 0.26/0.62 member1057565379_sc_sz: produc1821101996_sc_sz > set_Pr1169339874_sc_sz > $o ).
% 0.26/0.62
% 0.26/0.62 thf(sy_c_member_001t__Sum____Type__Osum_Itf__a_Mt__Sum____Type__Osum_Itf__b_Mtf__c_J_J,type,
% 0.26/0.62 member1893232190um_b_c: sum_su737395349um_b_c > set_Su1783761653um_b_c > $o ).
% 0.26/0.62
% 0.26/0.62 thf(sy_c_member_001t__Syntax__Otrm_Itf__a_Mtf__c_J,type,
% 0.26/0.62 member_trm_a_c: trm_a_c > set_trm_a_c > $o ).
% 0.26/0.62
% 0.26/0.62 thf(sy_c_member_001t__Syntax__Otrm_Itf__sf_Mtf__sz_J,type,
% 0.26/0.62 member_trm_sf_sz: trm_sf_sz > set_trm_sf_sz > $o ).
% 0.26/0.62
% 0.26/0.62 thf(sy_c_member_001tf__a,type,
% 0.26/0.62 member_a: a > set_a > $o ).
% 0.26/0.62
% 0.26/0.62 thf(sy_v_I,type,
% 0.26/0.62 i: denota231621370t_unit ).
% 0.26/0.62
% 0.26/0.62 thf(sy_v_J,type,
% 0.26/0.62 j: denota231621370t_unit ).
% 0.26/0.62
% 0.26/0.62 thf(sy_v__092_060nu_062,type,
% 0.26/0.62 nu: produc190496183real_c ).
% 0.26/0.62
% 0.26/0.62 thf(sy_v__092_060nu_062_H,type,
% 0.26/0.62 nu2: produc190496183real_c ).
% 0.26/0.62
% 0.26/0.62 thf(sy_v_t1____,type,
% 0.26/0.62 t1: trm_a_c ).
% 0.26/0.62
% 0.26/0.62 thf(sy_v_t2____,type,
% 0.26/0.62 t2: trm_a_c ).
% 0.26/0.62
% 0.26/0.62 % Relevant facts (354)
% 0.26/0.62 thf(fact_0_agree__plus2,axiom,
% 0.26/0.62 ! [Nu: produc1149990247eal_sz,Nu2: produc1149990247eal_sz,T1: trm_sf_sz,T2: trm_sf_sz] :
% 0.26/0.62 ( ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ ( plus_sf_sz @ T1 @ T2 ) ) )
% 0.26/0.62 => ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ T2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % agree_plus2
% 0.26/0.62 thf(fact_1_agree__plus2,axiom,
% 0.26/0.62 ! [Nu: produc190496183real_c,Nu2: produc190496183real_c,T1: trm_a_c,T2: trm_a_c] :
% 0.26/0.62 ( ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ ( plus_a_c @ T1 @ T2 ) ) )
% 0.26/0.62 => ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ T2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % agree_plus2
% 0.26/0.62 thf(fact_2_agree,axiom,
% 0.26/0.62 denota1997846518gree_c @ nu @ nu2 @ ( static_FVDiff_a_c @ ( plus_a_c @ t1 @ t2 ) ) ).
% 0.26/0.62
% 0.26/0.62 % agree
% 0.26/0.62 thf(fact_3_agree1,axiom,
% 0.26/0.62 denota1997846518gree_c @ nu @ nu2 @ ( static_FVDiff_a_c @ t1 ) ).
% 0.26/0.62
% 0.26/0.62 % agree1
% 0.26/0.62 thf(fact_4_dfree2,axiom,
% 0.26/0.62 dfree_a_c @ t2 ).
% 0.26/0.62
% 0.26/0.62 % dfree2
% 0.26/0.62 thf(fact_5_agree__plus1,axiom,
% 0.26/0.62 ! [Nu: produc1149990247eal_sz,Nu2: produc1149990247eal_sz,T1: trm_sf_sz,T2: trm_sf_sz] :
% 0.26/0.62 ( ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ ( plus_sf_sz @ T1 @ T2 ) ) )
% 0.26/0.62 => ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ T1 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % agree_plus1
% 0.26/0.62 thf(fact_6_agree__plus1,axiom,
% 0.26/0.62 ! [Nu: produc190496183real_c,Nu2: produc190496183real_c,T1: trm_a_c,T2: trm_a_c] :
% 0.26/0.62 ( ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ ( plus_a_c @ T1 @ T2 ) ) )
% 0.26/0.62 => ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ T1 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % agree_plus1
% 0.26/0.62 thf(fact_7_agree__comm,axiom,
% 0.26/0.62 ! [A: produc1149990247eal_sz,B: produc1149990247eal_sz,V: set_Sum_sum_sz_sz] :
% 0.26/0.62 ( ( denota102713844ree_sz @ A @ B @ V )
% 0.26/0.62 => ( denota102713844ree_sz @ B @ A @ V ) ) ).
% 0.26/0.62
% 0.26/0.62 % agree_comm
% 0.26/0.62 thf(fact_8_agree__comm,axiom,
% 0.26/0.62 ! [A: produc190496183real_c,B: produc190496183real_c,V: set_Sum_sum_c_c] :
% 0.26/0.62 ( ( denota1997846518gree_c @ A @ B @ V )
% 0.26/0.62 => ( denota1997846518gree_c @ B @ A @ V ) ) ).
% 0.26/0.62
% 0.26/0.62 % agree_comm
% 0.26/0.62 thf(fact_9_agree__refl,axiom,
% 0.26/0.62 ! [Nu: produc1149990247eal_sz,A: set_Sum_sum_sz_sz] : ( denota102713844ree_sz @ Nu @ Nu @ A ) ).
% 0.26/0.62
% 0.26/0.62 % agree_refl
% 0.26/0.62 thf(fact_10_agree__refl,axiom,
% 0.26/0.62 ! [Nu: produc190496183real_c,A: set_Sum_sum_c_c] : ( denota1997846518gree_c @ Nu @ Nu @ A ) ).
% 0.26/0.62
% 0.26/0.62 % agree_refl
% 0.26/0.62 thf(fact_11_dfree1,axiom,
% 0.26/0.62 dfree_a_c @ t1 ).
% 0.26/0.62
% 0.26/0.62 % dfree1
% 0.26/0.62 thf(fact_12_raw__interp__inject,axiom,
% 0.26/0.62 ! [X: freche2095075217_sc_sz,Y: freche2095075217_sc_sz] :
% 0.26/0.62 ( ( ( freche1421597129_sc_sz @ X )
% 0.26/0.62 = ( freche1421597129_sc_sz @ Y ) )
% 0.26/0.62 = ( X = Y ) ) ).
% 0.26/0.62
% 0.26/0.62 % raw_interp_inject
% 0.26/0.62 thf(fact_13_raw__term__inject,axiom,
% 0.26/0.62 ! [X: frechet_strm_sf_sz,Y: frechet_strm_sf_sz] :
% 0.26/0.62 ( ( ( freche782854530_sf_sz @ X )
% 0.26/0.62 = ( freche782854530_sf_sz @ Y ) )
% 0.26/0.62 = ( X = Y ) ) ).
% 0.26/0.62
% 0.26/0.62 % raw_term_inject
% 0.26/0.62 thf(fact_14_raw__term__inject,axiom,
% 0.26/0.62 ! [X: frechet_strm_a_c,Y: frechet_strm_a_c] :
% 0.26/0.62 ( ( ( frechet_raw_term_a_c @ X )
% 0.26/0.62 = ( frechet_raw_term_a_c @ Y ) )
% 0.26/0.62 = ( X = Y ) ) ).
% 0.26/0.62
% 0.26/0.62 % raw_term_inject
% 0.26/0.62 thf(fact_15_agree__times1,axiom,
% 0.26/0.62 ! [Nu: produc1149990247eal_sz,Nu2: produc1149990247eal_sz,T1: trm_sf_sz,T2: trm_sf_sz] :
% 0.26/0.62 ( ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ ( times_sf_sz @ T1 @ T2 ) ) )
% 0.26/0.62 => ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ T1 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % agree_times1
% 0.26/0.62 thf(fact_16_agree__times1,axiom,
% 0.26/0.62 ! [Nu: produc190496183real_c,Nu2: produc190496183real_c,T1: trm_a_c,T2: trm_a_c] :
% 0.26/0.62 ( ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ ( times_a_c @ T1 @ T2 ) ) )
% 0.26/0.62 => ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ T1 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % agree_times1
% 0.26/0.62 thf(fact_17_agree__times2,axiom,
% 0.26/0.62 ! [Nu: produc1149990247eal_sz,Nu2: produc1149990247eal_sz,T1: trm_sf_sz,T2: trm_sf_sz] :
% 0.26/0.62 ( ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ ( times_sf_sz @ T1 @ T2 ) ) )
% 0.26/0.62 => ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ T2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % agree_times2
% 0.26/0.62 thf(fact_18_agree__times2,axiom,
% 0.26/0.62 ! [Nu: produc190496183real_c,Nu2: produc190496183real_c,T1: trm_a_c,T2: trm_a_c] :
% 0.26/0.62 ( ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ ( times_a_c @ T1 @ T2 ) ) )
% 0.26/0.62 => ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ T2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % agree_times2
% 0.26/0.62 thf(fact_19_agree__func,axiom,
% 0.26/0.62 ! [Nu: produc1149990247eal_sz,Nu2: produc1149990247eal_sz,Var: sf,Args: sz > trm_sf_sz,I: sz] :
% 0.26/0.62 ( ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ ( function_sf_sz @ Var @ Args ) ) )
% 0.26/0.62 => ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ ( Args @ I ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % agree_func
% 0.26/0.62 thf(fact_20_agree__func,axiom,
% 0.26/0.62 ! [Nu: produc190496183real_c,Nu2: produc190496183real_c,Var: a,Args: c > trm_a_c,I: c] :
% 0.26/0.62 ( ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ ( function_a_c @ Var @ Args ) ) )
% 0.26/0.62 => ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ ( Args @ I ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % agree_func
% 0.26/0.62 thf(fact_21_P__def,axiom,
% 0.26/0.62 p_sc_sf_sz = predic913887884_sf_sz ).
% 0.26/0.62
% 0.26/0.62 % P_def
% 0.26/0.62 thf(fact_22_IH2,axiom,
% 0.26/0.62 ( ( denota1997846518gree_c @ nu @ nu2 @ ( static_FVDiff_a_c @ t2 ) )
% 0.26/0.62 => ( ( denota69106024_a_b_c @ i @ j
% 0.26/0.62 @ ( collec2086029184um_b_c
% 0.26/0.62 @ ^ [Uu: sum_su737395349um_b_c] :
% 0.26/0.62 ? [X2: a] :
% 0.26/0.62 ( ( Uu
% 0.26/0.62 = ( sum_In2139678582um_b_c @ X2 ) )
% 0.26/0.62 & ( member_a @ X2 @ ( static_SIGT_a_c @ t2 ) ) ) ) )
% 0.26/0.62 => ( ( denota229585092_a_b_c @ i @ t2 @ ( produc2010422875real_c @ nu ) @ ( produc314122909real_c @ nu ) )
% 0.26/0.62 = ( denota229585092_a_b_c @ j @ t2 @ ( produc2010422875real_c @ nu2 ) @ ( produc314122909real_c @ nu2 ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % IH2
% 0.26/0.62 thf(fact_23_seq__sem_Ocases,axiom,
% 0.26/0.62 ! [X: produc1821101996_sc_sz] :
% 0.26/0.62 ~ ! [I2: denota610675952t_unit,S: produc866628903_sc_sz] :
% 0.26/0.62 ( X
% 0.26/0.62 != ( produc789536734_sc_sz @ I2 @ S ) ) ).
% 0.26/0.62
% 0.26/0.62 % seq_sem.cases
% 0.26/0.62 thf(fact_24_raw__term,axiom,
% 0.26/0.62 ! [X: frechet_strm_a_c] : ( member_trm_a_c @ ( frechet_raw_term_a_c @ X ) @ ( collect_trm_a_c @ dfree_a_c ) ) ).
% 0.26/0.62
% 0.26/0.62 % raw_term
% 0.26/0.62 thf(fact_25_raw__term,axiom,
% 0.26/0.62 ! [X: frechet_strm_sf_sz] : ( member_trm_sf_sz @ ( freche782854530_sf_sz @ X ) @ ( collect_trm_sf_sz @ dfree_sf_sz ) ) ).
% 0.26/0.62
% 0.26/0.62 % raw_term
% 0.26/0.62 thf(fact_26_raw__term__cases,axiom,
% 0.26/0.62 ! [Y: trm_a_c] :
% 0.26/0.62 ( ( member_trm_a_c @ Y @ ( collect_trm_a_c @ dfree_a_c ) )
% 0.26/0.62 => ~ ! [X3: frechet_strm_a_c] :
% 0.26/0.62 ( Y
% 0.26/0.62 != ( frechet_raw_term_a_c @ X3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % raw_term_cases
% 0.26/0.62 thf(fact_27_raw__term__cases,axiom,
% 0.26/0.62 ! [Y: trm_sf_sz] :
% 0.26/0.62 ( ( member_trm_sf_sz @ Y @ ( collect_trm_sf_sz @ dfree_sf_sz ) )
% 0.26/0.62 => ~ ! [X3: frechet_strm_sf_sz] :
% 0.26/0.62 ( Y
% 0.26/0.62 != ( freche782854530_sf_sz @ X3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % raw_term_cases
% 0.26/0.62 thf(fact_28_raw__term__induct,axiom,
% 0.26/0.62 ! [Y: trm_a_c,P: trm_a_c > $o] :
% 0.26/0.62 ( ( member_trm_a_c @ Y @ ( collect_trm_a_c @ dfree_a_c ) )
% 0.26/0.62 => ( ! [X3: frechet_strm_a_c] : ( P @ ( frechet_raw_term_a_c @ X3 ) )
% 0.26/0.62 => ( P @ Y ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % raw_term_induct
% 0.26/0.62 thf(fact_29_raw__term__induct,axiom,
% 0.26/0.62 ! [Y: trm_sf_sz,P: trm_sf_sz > $o] :
% 0.26/0.62 ( ( member_trm_sf_sz @ Y @ ( collect_trm_sf_sz @ dfree_sf_sz ) )
% 0.26/0.62 => ( ! [X3: frechet_strm_sf_sz] : ( P @ ( freche782854530_sf_sz @ X3 ) )
% 0.26/0.62 => ( P @ Y ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % raw_term_induct
% 0.26/0.62 thf(fact_30_coincidence__frechet,axiom,
% 0.26/0.62 ! [Theta: trm_a_c,Nu: produc190496183real_c,Nu2: produc190496183real_c,I3: denota231621370t_unit] :
% 0.26/0.62 ( ( dfree_a_c @ Theta )
% 0.26/0.62 => ( ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ Theta ) )
% 0.26/0.62 => ( ( denota229585092_a_b_c @ I3 @ Theta @ ( produc2010422875real_c @ Nu ) @ ( produc314122909real_c @ Nu ) )
% 0.26/0.62 = ( denota229585092_a_b_c @ I3 @ Theta @ ( produc2010422875real_c @ Nu2 ) @ ( produc314122909real_c @ Nu2 ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % coincidence_frechet
% 0.26/0.62 thf(fact_31_coincidence__frechet,axiom,
% 0.26/0.62 ! [Theta: trm_sf_sz,Nu: produc1149990247eal_sz,Nu2: produc1149990247eal_sz,I3: denota610675952t_unit] :
% 0.26/0.62 ( ( dfree_sf_sz @ Theta )
% 0.26/0.62 => ( ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ Theta ) )
% 0.26/0.62 => ( ( denota1979904720_sc_sz @ I3 @ Theta @ ( produc1111759555eal_sz @ Nu ) @ ( produc1269210629eal_sz @ Nu ) )
% 0.26/0.62 = ( denota1979904720_sc_sz @ I3 @ Theta @ ( produc1111759555eal_sz @ Nu2 ) @ ( produc1269210629eal_sz @ Nu2 ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % coincidence_frechet
% 0.26/0.62 thf(fact_32_IA,axiom,
% 0.26/0.62 ( denota69106024_a_b_c @ i @ j
% 0.26/0.62 @ ( collec2086029184um_b_c
% 0.26/0.62 @ ^ [Uu: sum_su737395349um_b_c] :
% 0.26/0.62 ? [X2: a] :
% 0.26/0.62 ( ( Uu
% 0.26/0.62 = ( sum_In2139678582um_b_c @ X2 ) )
% 0.26/0.62 & ( member_a @ X2 @ ( static_SIGT_a_c @ ( plus_a_c @ t1 @ t2 ) ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % IA
% 0.26/0.62 thf(fact_33_IA1,axiom,
% 0.26/0.62 ( denota69106024_a_b_c @ i @ j
% 0.26/0.62 @ ( collec2086029184um_b_c
% 0.26/0.62 @ ^ [Uu: sum_su737395349um_b_c] :
% 0.26/0.62 ? [X2: a] :
% 0.26/0.62 ( ( Uu
% 0.26/0.62 = ( sum_In2139678582um_b_c @ X2 ) )
% 0.26/0.62 & ( member_a @ X2 @ ( static_SIGT_a_c @ t1 ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % IA1
% 0.26/0.62 thf(fact_34_IA2,axiom,
% 0.26/0.62 ( denota69106024_a_b_c @ i @ j
% 0.26/0.62 @ ( collec2086029184um_b_c
% 0.26/0.62 @ ^ [Uu: sum_su737395349um_b_c] :
% 0.26/0.62 ? [X2: a] :
% 0.26/0.62 ( ( Uu
% 0.26/0.62 = ( sum_In2139678582um_b_c @ X2 ) )
% 0.26/0.62 & ( member_a @ X2 @ ( static_SIGT_a_c @ t2 ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % IA2
% 0.26/0.62 thf(fact_35_IH1,axiom,
% 0.26/0.62 ( ( denota1997846518gree_c @ nu @ nu2 @ ( static_FVDiff_a_c @ t1 ) )
% 0.26/0.62 => ( ( denota69106024_a_b_c @ i @ j
% 0.26/0.62 @ ( collec2086029184um_b_c
% 0.26/0.62 @ ^ [Uu: sum_su737395349um_b_c] :
% 0.26/0.62 ? [X2: a] :
% 0.26/0.62 ( ( Uu
% 0.26/0.62 = ( sum_In2139678582um_b_c @ X2 ) )
% 0.26/0.62 & ( member_a @ X2 @ ( static_SIGT_a_c @ t1 ) ) ) ) )
% 0.26/0.62 => ( ( denota229585092_a_b_c @ i @ t1 @ ( produc2010422875real_c @ nu ) @ ( produc314122909real_c @ nu ) )
% 0.26/0.62 = ( denota229585092_a_b_c @ j @ t1 @ ( produc2010422875real_c @ nu2 ) @ ( produc314122909real_c @ nu2 ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % IH1
% 0.26/0.62 thf(fact_36_Iagree__comm,axiom,
% 0.26/0.62 ! [A: denota231621370t_unit,B: denota231621370t_unit,V: set_Su1783761653um_b_c] :
% 0.26/0.62 ( ( denota69106024_a_b_c @ A @ B @ V )
% 0.26/0.62 => ( denota69106024_a_b_c @ B @ A @ V ) ) ).
% 0.26/0.62
% 0.26/0.62 % Iagree_comm
% 0.26/0.62 thf(fact_37_Iagree__refl,axiom,
% 0.26/0.62 ! [I3: denota231621370t_unit,A: set_Su1783761653um_b_c] : ( denota69106024_a_b_c @ I3 @ I3 @ A ) ).
% 0.26/0.62
% 0.26/0.62 % Iagree_refl
% 0.26/0.62 thf(fact_38_subs_I2_J,axiom,
% 0.26/0.62 ( ord_le929608341um_b_c
% 0.26/0.62 @ ( collec2086029184um_b_c
% 0.26/0.62 @ ^ [Uu: sum_su737395349um_b_c] :
% 0.26/0.62 ? [X2: a] :
% 0.26/0.62 ( ( Uu
% 0.26/0.62 = ( sum_In2139678582um_b_c @ X2 ) )
% 0.26/0.62 & ( member_a @ X2 @ ( static_SIGT_a_c @ t2 ) ) ) )
% 0.26/0.62 @ ( collec2086029184um_b_c
% 0.26/0.62 @ ^ [Uu: sum_su737395349um_b_c] :
% 0.26/0.62 ? [X2: a] :
% 0.26/0.62 ( ( Uu
% 0.26/0.62 = ( sum_In2139678582um_b_c @ X2 ) )
% 0.26/0.62 & ( member_a @ X2 @ ( static_SIGT_a_c @ ( plus_a_c @ t1 @ t2 ) ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % subs(2)
% 0.26/0.62 thf(fact_39_subs_I1_J,axiom,
% 0.26/0.62 ( ord_le929608341um_b_c
% 0.26/0.62 @ ( collec2086029184um_b_c
% 0.26/0.62 @ ^ [Uu: sum_su737395349um_b_c] :
% 0.26/0.62 ? [X2: a] :
% 0.26/0.62 ( ( Uu
% 0.26/0.62 = ( sum_In2139678582um_b_c @ X2 ) )
% 0.26/0.62 & ( member_a @ X2 @ ( static_SIGT_a_c @ t1 ) ) ) )
% 0.26/0.62 @ ( collec2086029184um_b_c
% 0.26/0.62 @ ^ [Uu: sum_su737395349um_b_c] :
% 0.26/0.62 ? [X2: a] :
% 0.26/0.62 ( ( Uu
% 0.26/0.62 = ( sum_In2139678582um_b_c @ X2 ) )
% 0.26/0.62 & ( member_a @ X2 @ ( static_SIGT_a_c @ ( plus_a_c @ t1 @ t2 ) ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % subs(1)
% 0.26/0.62 thf(fact_40_simple__term__inverse,axiom,
% 0.26/0.62 ! [Y: trm_a_c] :
% 0.26/0.62 ( ( member_trm_a_c @ Y @ ( collect_trm_a_c @ dfree_a_c ) )
% 0.26/0.62 => ( ( frechet_raw_term_a_c @ ( freche665377492rm_a_c @ Y ) )
% 0.26/0.62 = Y ) ) ).
% 0.26/0.62
% 0.26/0.62 % simple_term_inverse
% 0.26/0.62 thf(fact_41_simple__term__inverse,axiom,
% 0.26/0.62 ! [Y: trm_sf_sz] :
% 0.26/0.62 ( ( member_trm_sf_sz @ Y @ ( collect_trm_sf_sz @ dfree_sf_sz ) )
% 0.26/0.62 => ( ( freche782854530_sf_sz @ ( freche1046279700_sf_sz @ Y ) )
% 0.26/0.62 = Y ) ) ).
% 0.26/0.62
% 0.26/0.62 % simple_term_inverse
% 0.26/0.62 thf(fact_42_prod_Ocollapse,axiom,
% 0.26/0.62 ! [Prod: produc866628903_sc_sz] :
% 0.26/0.62 ( ( produc1822718231_sc_sz @ ( produc548504323_sc_sz @ Prod ) @ ( produc4753477_sc_sz @ Prod ) )
% 0.26/0.62 = Prod ) ).
% 0.26/0.62
% 0.26/0.62 % prod.collapse
% 0.26/0.62 thf(fact_43_prod_Ocollapse,axiom,
% 0.26/0.62 ! [Prod: produc1241881959eal_sz] :
% 0.26/0.62 ( ( produc1235791063eal_sz @ ( produc286845635eal_sz @ Prod ) @ ( produc1746886149eal_sz @ Prod ) )
% 0.26/0.62 = Prod ) ).
% 0.26/0.62
% 0.26/0.62 % prod.collapse
% 0.26/0.62 thf(fact_44_prod_Ocollapse,axiom,
% 0.26/0.62 ! [Prod: produc1892666919z_real] :
% 0.26/0.62 ( ( produc784663575z_real @ ( produc870616579z_real @ Prod ) @ ( produc1422611269z_real @ Prod ) )
% 0.26/0.62 = Prod ) ).
% 0.26/0.62
% 0.26/0.62 % prod.collapse
% 0.26/0.62 thf(fact_45_prod_Ocollapse,axiom,
% 0.26/0.62 ! [Prod: produc1149990247eal_sz] :
% 0.26/0.62 ( ( produc1308130519eal_sz @ ( produc1111759555eal_sz @ Prod ) @ ( produc1269210629eal_sz @ Prod ) )
% 0.26/0.62 = Prod ) ).
% 0.26/0.62
% 0.26/0.62 % prod.collapse
% 0.26/0.62 thf(fact_46_prod_Ocollapse,axiom,
% 0.26/0.62 ! [Prod: produc1821101996_sc_sz] :
% 0.26/0.62 ( ( produc789536734_sc_sz @ ( produc1503602930_sc_sz @ Prod ) @ ( produc974239792_sc_sz @ Prod ) )
% 0.26/0.62 = Prod ) ).
% 0.26/0.62
% 0.26/0.62 % prod.collapse
% 0.26/0.62 thf(fact_47_prod_Ocollapse,axiom,
% 0.26/0.62 ! [Prod: produc190496183real_c] :
% 0.26/0.62 ( ( produc394644079real_c @ ( produc2010422875real_c @ Prod ) @ ( produc314122909real_c @ Prod ) )
% 0.26/0.62 = Prod ) ).
% 0.26/0.62
% 0.26/0.62 % prod.collapse
% 0.26/0.62 thf(fact_48_cr__good__interp__def,axiom,
% 0.26/0.62 ( freche58918398_sc_sz
% 0.26/0.62 = ( ^ [X2: denota610675952t_unit,Y2: freche2095075217_sc_sz] :
% 0.26/0.62 ( X2
% 0.26/0.62 = ( freche1421597129_sc_sz @ Y2 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % cr_good_interp_def
% 0.26/0.62 thf(fact_49_cr__strm__def,axiom,
% 0.26/0.62 ( freche1244000341_sf_sz
% 0.26/0.62 = ( ^ [X2: trm_sf_sz,Y2: frechet_strm_sf_sz] :
% 0.26/0.62 ( X2
% 0.26/0.62 = ( freche782854530_sf_sz @ Y2 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % cr_strm_def
% 0.26/0.62 thf(fact_50_cr__strm__def,axiom,
% 0.26/0.62 ( frechet_cr_strm_a_c
% 0.26/0.62 = ( ^ [X2: trm_a_c,Y2: frechet_strm_a_c] :
% 0.26/0.62 ( X2
% 0.26/0.62 = ( frechet_raw_term_a_c @ Y2 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % cr_strm_def
% 0.26/0.62 thf(fact_51_dfree__Times__simps,axiom,
% 0.26/0.62 ! [A2: trm_a_c,B2: trm_a_c] :
% 0.26/0.62 ( ( dfree_a_c @ ( times_a_c @ A2 @ B2 ) )
% 0.26/0.62 = ( ( dfree_a_c @ A2 )
% 0.26/0.62 & ( dfree_a_c @ B2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % dfree_Times_simps
% 0.26/0.62 thf(fact_52_dfree__Times__simps,axiom,
% 0.26/0.62 ! [A2: trm_sf_sz,B2: trm_sf_sz] :
% 0.26/0.62 ( ( dfree_sf_sz @ ( times_sf_sz @ A2 @ B2 ) )
% 0.26/0.62 = ( ( dfree_sf_sz @ A2 )
% 0.26/0.62 & ( dfree_sf_sz @ B2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % dfree_Times_simps
% 0.26/0.62 thf(fact_53_dfree__Plus__simps,axiom,
% 0.26/0.62 ! [A2: trm_sf_sz,B2: trm_sf_sz] :
% 0.26/0.62 ( ( dfree_sf_sz @ ( plus_sf_sz @ A2 @ B2 ) )
% 0.26/0.62 = ( ( dfree_sf_sz @ A2 )
% 0.26/0.62 & ( dfree_sf_sz @ B2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % dfree_Plus_simps
% 0.26/0.62 thf(fact_54_dfree__Plus__simps,axiom,
% 0.26/0.62 ! [A2: trm_a_c,B2: trm_a_c] :
% 0.26/0.62 ( ( dfree_a_c @ ( plus_a_c @ A2 @ B2 ) )
% 0.26/0.62 = ( ( dfree_a_c @ A2 )
% 0.26/0.62 & ( dfree_a_c @ B2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % dfree_Plus_simps
% 0.26/0.62 thf(fact_55_dfree__Fun__simps,axiom,
% 0.26/0.62 ! [I: a,Args: c > trm_a_c] :
% 0.26/0.62 ( ( dfree_a_c @ ( function_a_c @ I @ Args ) )
% 0.26/0.62 = ( ! [X2: c] : ( dfree_a_c @ ( Args @ X2 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % dfree_Fun_simps
% 0.26/0.62 thf(fact_56_dfree__Fun__simps,axiom,
% 0.26/0.62 ! [I: sf,Args: sz > trm_sf_sz] :
% 0.26/0.62 ( ( dfree_sf_sz @ ( function_sf_sz @ I @ Args ) )
% 0.26/0.62 = ( ! [X2: sz] : ( dfree_sf_sz @ ( Args @ X2 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % dfree_Fun_simps
% 0.26/0.62 thf(fact_57_simple__term__cases,axiom,
% 0.26/0.62 ! [X: frechet_strm_a_c] :
% 0.26/0.62 ~ ! [Y3: trm_a_c] :
% 0.26/0.62 ( ( X
% 0.26/0.62 = ( freche665377492rm_a_c @ Y3 ) )
% 0.26/0.62 => ~ ( member_trm_a_c @ Y3 @ ( collect_trm_a_c @ dfree_a_c ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % simple_term_cases
% 0.26/0.62 thf(fact_58_simple__term__cases,axiom,
% 0.26/0.62 ! [X: frechet_strm_sf_sz] :
% 0.26/0.62 ~ ! [Y3: trm_sf_sz] :
% 0.26/0.62 ( ( X
% 0.26/0.62 = ( freche1046279700_sf_sz @ Y3 ) )
% 0.26/0.62 => ~ ( member_trm_sf_sz @ Y3 @ ( collect_trm_sf_sz @ dfree_sf_sz ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % simple_term_cases
% 0.26/0.62 thf(fact_59_raw__term__inverse,axiom,
% 0.26/0.62 ! [X: frechet_strm_a_c] :
% 0.26/0.62 ( ( freche665377492rm_a_c @ ( frechet_raw_term_a_c @ X ) )
% 0.26/0.62 = X ) ).
% 0.26/0.62
% 0.26/0.62 % raw_term_inverse
% 0.26/0.62 thf(fact_60_raw__term__inverse,axiom,
% 0.26/0.62 ! [X: frechet_strm_sf_sz] :
% 0.26/0.62 ( ( freche1046279700_sf_sz @ ( freche782854530_sf_sz @ X ) )
% 0.26/0.62 = X ) ).
% 0.26/0.62
% 0.26/0.62 % raw_term_inverse
% 0.26/0.62 thf(fact_61_simple__term__inject,axiom,
% 0.26/0.62 ! [X: trm_a_c,Y: trm_a_c] :
% 0.26/0.62 ( ( member_trm_a_c @ X @ ( collect_trm_a_c @ dfree_a_c ) )
% 0.26/0.62 => ( ( member_trm_a_c @ Y @ ( collect_trm_a_c @ dfree_a_c ) )
% 0.26/0.62 => ( ( ( freche665377492rm_a_c @ X )
% 0.26/0.62 = ( freche665377492rm_a_c @ Y ) )
% 0.26/0.62 = ( X = Y ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % simple_term_inject
% 0.26/0.62 thf(fact_62_simple__term__inject,axiom,
% 0.26/0.62 ! [X: trm_sf_sz,Y: trm_sf_sz] :
% 0.26/0.62 ( ( member_trm_sf_sz @ X @ ( collect_trm_sf_sz @ dfree_sf_sz ) )
% 0.26/0.62 => ( ( member_trm_sf_sz @ Y @ ( collect_trm_sf_sz @ dfree_sf_sz ) )
% 0.26/0.62 => ( ( ( freche1046279700_sf_sz @ X )
% 0.26/0.62 = ( freche1046279700_sf_sz @ Y ) )
% 0.26/0.62 = ( X = Y ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % simple_term_inject
% 0.26/0.62 thf(fact_63_simple__term__induct,axiom,
% 0.26/0.62 ! [P: frechet_strm_a_c > $o,X: frechet_strm_a_c] :
% 0.26/0.62 ( ! [Y3: trm_a_c] :
% 0.26/0.62 ( ( member_trm_a_c @ Y3 @ ( collect_trm_a_c @ dfree_a_c ) )
% 0.26/0.62 => ( P @ ( freche665377492rm_a_c @ Y3 ) ) )
% 0.26/0.62 => ( P @ X ) ) ).
% 0.26/0.62
% 0.26/0.62 % simple_term_induct
% 0.26/0.62 thf(fact_64_simple__term__induct,axiom,
% 0.26/0.62 ! [P: frechet_strm_sf_sz > $o,X: frechet_strm_sf_sz] :
% 0.26/0.62 ( ! [Y3: trm_sf_sz] :
% 0.26/0.62 ( ( member_trm_sf_sz @ Y3 @ ( collect_trm_sf_sz @ dfree_sf_sz ) )
% 0.26/0.62 => ( P @ ( freche1046279700_sf_sz @ Y3 ) ) )
% 0.26/0.62 => ( P @ X ) ) ).
% 0.26/0.62
% 0.26/0.62 % simple_term_induct
% 0.26/0.62 thf(fact_65_old_Oprod_Oinject,axiom,
% 0.26/0.62 ! [A2: finite1398487019real_c,B2: finite1398487019real_c,A3: finite1398487019real_c,B3: finite1398487019real_c] :
% 0.26/0.62 ( ( ( produc394644079real_c @ A2 @ B2 )
% 0.26/0.62 = ( produc394644079real_c @ A3 @ B3 ) )
% 0.26/0.62 = ( ( A2 = A3 )
% 0.26/0.62 & ( B2 = B3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % old.prod.inject
% 0.26/0.62 thf(fact_66_old_Oprod_Oinject,axiom,
% 0.26/0.62 ! [A2: list_f1238882004_sc_sz,B2: list_f1238882004_sc_sz,A3: list_f1238882004_sc_sz,B3: list_f1238882004_sc_sz] :
% 0.26/0.62 ( ( ( produc1822718231_sc_sz @ A2 @ B2 )
% 0.26/0.62 = ( produc1822718231_sc_sz @ A3 @ B3 ) )
% 0.26/0.62 = ( ( A2 = A3 )
% 0.26/0.62 & ( B2 = B3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % old.prod.inject
% 0.26/0.62 thf(fact_67_old_Oprod_Oinject,axiom,
% 0.26/0.62 ! [A2: set_Fi291318197eal_sz,B2: set_Fi291318197eal_sz,A3: set_Fi291318197eal_sz,B3: set_Fi291318197eal_sz] :
% 0.26/0.62 ( ( ( produc1235791063eal_sz @ A2 @ B2 )
% 0.26/0.62 = ( produc1235791063eal_sz @ A3 @ B3 ) )
% 0.26/0.62 = ( ( A2 = A3 )
% 0.26/0.62 & ( B2 = B3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % old.prod.inject
% 0.26/0.62 thf(fact_68_old_Oprod_Oinject,axiom,
% 0.26/0.62 ! [A2: bounde472938360z_real,B2: bounde472938360z_real,A3: bounde472938360z_real,B3: bounde472938360z_real] :
% 0.26/0.62 ( ( ( produc784663575z_real @ A2 @ B2 )
% 0.26/0.62 = ( produc784663575z_real @ A3 @ B3 ) )
% 0.26/0.62 = ( ( A2 = A3 )
% 0.26/0.62 & ( B2 = B3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % old.prod.inject
% 0.26/0.62 thf(fact_69_old_Oprod_Oinject,axiom,
% 0.26/0.62 ! [A2: denota610675952t_unit,B2: produc866628903_sc_sz,A3: denota610675952t_unit,B3: produc866628903_sc_sz] :
% 0.26/0.62 ( ( ( produc789536734_sc_sz @ A2 @ B2 )
% 0.26/0.62 = ( produc789536734_sc_sz @ A3 @ B3 ) )
% 0.26/0.62 = ( ( A2 = A3 )
% 0.26/0.62 & ( B2 = B3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % old.prod.inject
% 0.26/0.62 thf(fact_70_prod_Oinject,axiom,
% 0.26/0.62 ! [X1: finite1398487019real_c,X22: finite1398487019real_c,Y1: finite1398487019real_c,Y22: finite1398487019real_c] :
% 0.26/0.62 ( ( ( produc394644079real_c @ X1 @ X22 )
% 0.26/0.62 = ( produc394644079real_c @ Y1 @ Y22 ) )
% 0.26/0.62 = ( ( X1 = Y1 )
% 0.26/0.62 & ( X22 = Y22 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % prod.inject
% 0.26/0.62 thf(fact_71_prod_Oinject,axiom,
% 0.26/0.62 ! [X1: list_f1238882004_sc_sz,X22: list_f1238882004_sc_sz,Y1: list_f1238882004_sc_sz,Y22: list_f1238882004_sc_sz] :
% 0.26/0.62 ( ( ( produc1822718231_sc_sz @ X1 @ X22 )
% 0.26/0.62 = ( produc1822718231_sc_sz @ Y1 @ Y22 ) )
% 0.26/0.62 = ( ( X1 = Y1 )
% 0.26/0.62 & ( X22 = Y22 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % prod.inject
% 0.26/0.62 thf(fact_72_prod_Oinject,axiom,
% 0.26/0.62 ! [X1: set_Fi291318197eal_sz,X22: set_Fi291318197eal_sz,Y1: set_Fi291318197eal_sz,Y22: set_Fi291318197eal_sz] :
% 0.26/0.62 ( ( ( produc1235791063eal_sz @ X1 @ X22 )
% 0.26/0.62 = ( produc1235791063eal_sz @ Y1 @ Y22 ) )
% 0.26/0.62 = ( ( X1 = Y1 )
% 0.26/0.62 & ( X22 = Y22 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % prod.inject
% 0.26/0.62 thf(fact_73_prod_Oinject,axiom,
% 0.26/0.62 ! [X1: bounde472938360z_real,X22: bounde472938360z_real,Y1: bounde472938360z_real,Y22: bounde472938360z_real] :
% 0.26/0.62 ( ( ( produc784663575z_real @ X1 @ X22 )
% 0.26/0.62 = ( produc784663575z_real @ Y1 @ Y22 ) )
% 0.26/0.62 = ( ( X1 = Y1 )
% 0.26/0.62 & ( X22 = Y22 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % prod.inject
% 0.26/0.62 thf(fact_74_prod_Oinject,axiom,
% 0.26/0.62 ! [X1: denota610675952t_unit,X22: produc866628903_sc_sz,Y1: denota610675952t_unit,Y22: produc866628903_sc_sz] :
% 0.26/0.62 ( ( ( produc789536734_sc_sz @ X1 @ X22 )
% 0.26/0.62 = ( produc789536734_sc_sz @ Y1 @ Y22 ) )
% 0.26/0.62 = ( ( X1 = Y1 )
% 0.26/0.62 & ( X22 = Y22 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % prod.inject
% 0.26/0.62 thf(fact_75_trm_Oinject_I3_J,axiom,
% 0.26/0.62 ! [X31: a,X32: c > trm_a_c,Y31: a,Y32: c > trm_a_c] :
% 0.26/0.62 ( ( ( function_a_c @ X31 @ X32 )
% 0.26/0.62 = ( function_a_c @ Y31 @ Y32 ) )
% 0.26/0.62 = ( ( X31 = Y31 )
% 0.26/0.63 & ( X32 = Y32 ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % trm.inject(3)
% 0.26/0.63 thf(fact_76_trm_Oinject_I3_J,axiom,
% 0.26/0.63 ! [X31: sf,X32: sz > trm_sf_sz,Y31: sf,Y32: sz > trm_sf_sz] :
% 0.26/0.63 ( ( ( function_sf_sz @ X31 @ X32 )
% 0.26/0.63 = ( function_sf_sz @ Y31 @ Y32 ) )
% 0.26/0.63 = ( ( X31 = Y31 )
% 0.26/0.63 & ( X32 = Y32 ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % trm.inject(3)
% 0.26/0.63 thf(fact_77_trm_Oinject_I4_J,axiom,
% 0.26/0.63 ! [X41: trm_sf_sz,X42: trm_sf_sz,Y41: trm_sf_sz,Y42: trm_sf_sz] :
% 0.26/0.63 ( ( ( plus_sf_sz @ X41 @ X42 )
% 0.26/0.63 = ( plus_sf_sz @ Y41 @ Y42 ) )
% 0.26/0.63 = ( ( X41 = Y41 )
% 0.26/0.63 & ( X42 = Y42 ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % trm.inject(4)
% 0.26/0.63 thf(fact_78_trm_Oinject_I4_J,axiom,
% 0.26/0.63 ! [X41: trm_a_c,X42: trm_a_c,Y41: trm_a_c,Y42: trm_a_c] :
% 0.26/0.63 ( ( ( plus_a_c @ X41 @ X42 )
% 0.26/0.63 = ( plus_a_c @ Y41 @ Y42 ) )
% 0.26/0.63 = ( ( X41 = Y41 )
% 0.26/0.63 & ( X42 = Y42 ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % trm.inject(4)
% 0.26/0.63 thf(fact_79_trm_Oinject_I5_J,axiom,
% 0.26/0.63 ! [X51: trm_a_c,X52: trm_a_c,Y51: trm_a_c,Y52: trm_a_c] :
% 0.26/0.63 ( ( ( times_a_c @ X51 @ X52 )
% 0.26/0.63 = ( times_a_c @ Y51 @ Y52 ) )
% 0.26/0.63 = ( ( X51 = Y51 )
% 0.26/0.63 & ( X52 = Y52 ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % trm.inject(5)
% 0.26/0.63 thf(fact_80_trm_Oinject_I5_J,axiom,
% 0.26/0.63 ! [X51: trm_sf_sz,X52: trm_sf_sz,Y51: trm_sf_sz,Y52: trm_sf_sz] :
% 0.26/0.63 ( ( ( times_sf_sz @ X51 @ X52 )
% 0.26/0.63 = ( times_sf_sz @ Y51 @ Y52 ) )
% 0.26/0.63 = ( ( X51 = Y51 )
% 0.26/0.63 & ( X52 = Y52 ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % trm.inject(5)
% 0.26/0.63 thf(fact_81_mem__Collect__eq,axiom,
% 0.26/0.63 ! [A2: finite824932053eal_sz,P: finite824932053eal_sz > $o] :
% 0.26/0.63 ( ( member1693951742eal_sz @ A2 @ ( collec1002602816eal_sz @ P ) )
% 0.26/0.63 = ( P @ A2 ) ) ).
% 0.26/0.63
% 0.26/0.63 % mem_Collect_eq
% 0.26/0.63 thf(fact_82_mem__Collect__eq,axiom,
% 0.26/0.63 ! [A2: produc1821101996_sc_sz,P: produc1821101996_sc_sz > $o] :
% 0.26/0.63 ( ( member1057565379_sc_sz @ A2 @ ( collec1199592193_sc_sz @ P ) )
% 0.26/0.63 = ( P @ A2 ) ) ).
% 0.26/0.63
% 0.26/0.63 % mem_Collect_eq
% 0.26/0.63 thf(fact_83_mem__Collect__eq,axiom,
% 0.26/0.63 ! [A2: trm_sf_sz,P: trm_sf_sz > $o] :
% 0.26/0.63 ( ( member_trm_sf_sz @ A2 @ ( collect_trm_sf_sz @ P ) )
% 0.26/0.63 = ( P @ A2 ) ) ).
% 0.26/0.63
% 0.26/0.63 % mem_Collect_eq
% 0.26/0.63 thf(fact_84_mem__Collect__eq,axiom,
% 0.26/0.63 ! [A2: trm_a_c,P: trm_a_c > $o] :
% 0.26/0.63 ( ( member_trm_a_c @ A2 @ ( collect_trm_a_c @ P ) )
% 0.26/0.63 = ( P @ A2 ) ) ).
% 0.26/0.63
% 0.26/0.63 % mem_Collect_eq
% 0.26/0.63 thf(fact_85_mem__Collect__eq,axiom,
% 0.26/0.63 ! [A2: a,P: a > $o] :
% 0.26/0.63 ( ( member_a @ A2 @ ( collect_a @ P ) )
% 0.26/0.63 = ( P @ A2 ) ) ).
% 0.26/0.63
% 0.26/0.63 % mem_Collect_eq
% 0.26/0.63 thf(fact_86_mem__Collect__eq,axiom,
% 0.26/0.63 ! [A2: sum_su737395349um_b_c,P: sum_su737395349um_b_c > $o] :
% 0.26/0.63 ( ( member1893232190um_b_c @ A2 @ ( collec2086029184um_b_c @ P ) )
% 0.26/0.63 = ( P @ A2 ) ) ).
% 0.26/0.63
% 0.26/0.63 % mem_Collect_eq
% 0.26/0.63 thf(fact_87_Collect__mem__eq,axiom,
% 0.26/0.63 ! [A: set_Fi291318197eal_sz] :
% 0.26/0.63 ( ( collec1002602816eal_sz
% 0.26/0.63 @ ^ [X2: finite824932053eal_sz] : ( member1693951742eal_sz @ X2 @ A ) )
% 0.26/0.63 = A ) ).
% 0.26/0.63
% 0.26/0.63 % Collect_mem_eq
% 0.26/0.63 thf(fact_88_Collect__mem__eq,axiom,
% 0.26/0.63 ! [A: set_Pr1169339874_sc_sz] :
% 0.26/0.63 ( ( collec1199592193_sc_sz
% 0.26/0.63 @ ^ [X2: produc1821101996_sc_sz] : ( member1057565379_sc_sz @ X2 @ A ) )
% 0.26/0.63 = A ) ).
% 0.26/0.63
% 0.26/0.63 % Collect_mem_eq
% 0.26/0.63 thf(fact_89_Collect__mem__eq,axiom,
% 0.26/0.63 ! [A: set_trm_sf_sz] :
% 0.26/0.63 ( ( collect_trm_sf_sz
% 0.26/0.63 @ ^ [X2: trm_sf_sz] : ( member_trm_sf_sz @ X2 @ A ) )
% 0.26/0.63 = A ) ).
% 0.26/0.63
% 0.26/0.63 % Collect_mem_eq
% 0.26/0.63 thf(fact_90_Collect__mem__eq,axiom,
% 0.26/0.63 ! [A: set_trm_a_c] :
% 0.26/0.63 ( ( collect_trm_a_c
% 0.26/0.63 @ ^ [X2: trm_a_c] : ( member_trm_a_c @ X2 @ A ) )
% 0.26/0.63 = A ) ).
% 0.26/0.63
% 0.26/0.63 % Collect_mem_eq
% 0.26/0.63 thf(fact_91_Collect__mem__eq,axiom,
% 0.26/0.63 ! [A: set_a] :
% 0.26/0.63 ( ( collect_a
% 0.26/0.63 @ ^ [X2: a] : ( member_a @ X2 @ A ) )
% 0.26/0.63 = A ) ).
% 0.26/0.63
% 0.26/0.63 % Collect_mem_eq
% 0.26/0.63 thf(fact_92_Collect__mem__eq,axiom,
% 0.26/0.63 ! [A: set_Su1783761653um_b_c] :
% 0.26/0.63 ( ( collec2086029184um_b_c
% 0.26/0.63 @ ^ [X2: sum_su737395349um_b_c] : ( member1893232190um_b_c @ X2 @ A ) )
% 0.26/0.63 = A ) ).
% 0.26/0.63
% 0.26/0.63 % Collect_mem_eq
% 0.26/0.63 thf(fact_93_Collect__cong,axiom,
% 0.26/0.63 ! [P: finite824932053eal_sz > $o,Q: finite824932053eal_sz > $o] :
% 0.26/0.63 ( ! [X3: finite824932053eal_sz] :
% 0.26/0.63 ( ( P @ X3 )
% 0.26/0.63 = ( Q @ X3 ) )
% 0.26/0.63 => ( ( collec1002602816eal_sz @ P )
% 0.26/0.63 = ( collec1002602816eal_sz @ Q ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % Collect_cong
% 0.26/0.63 thf(fact_94_Collect__cong,axiom,
% 0.26/0.63 ! [P: produc1821101996_sc_sz > $o,Q: produc1821101996_sc_sz > $o] :
% 0.26/0.63 ( ! [X3: produc1821101996_sc_sz] :
% 0.26/0.63 ( ( P @ X3 )
% 0.26/0.63 = ( Q @ X3 ) )
% 0.26/0.63 => ( ( collec1199592193_sc_sz @ P )
% 0.26/0.63 = ( collec1199592193_sc_sz @ Q ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % Collect_cong
% 0.26/0.63 thf(fact_95_Collect__cong,axiom,
% 0.26/0.63 ! [P: trm_sf_sz > $o,Q: trm_sf_sz > $o] :
% 0.26/0.63 ( ! [X3: trm_sf_sz] :
% 0.26/0.63 ( ( P @ X3 )
% 0.26/0.63 = ( Q @ X3 ) )
% 0.26/0.63 => ( ( collect_trm_sf_sz @ P )
% 0.26/0.63 = ( collect_trm_sf_sz @ Q ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % Collect_cong
% 0.26/0.63 thf(fact_96_Collect__cong,axiom,
% 0.26/0.63 ! [P: trm_a_c > $o,Q: trm_a_c > $o] :
% 0.26/0.63 ( ! [X3: trm_a_c] :
% 0.26/0.63 ( ( P @ X3 )
% 0.26/0.63 = ( Q @ X3 ) )
% 0.26/0.63 => ( ( collect_trm_a_c @ P )
% 0.26/0.63 = ( collect_trm_a_c @ Q ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % Collect_cong
% 0.26/0.63 thf(fact_97_Collect__cong,axiom,
% 0.26/0.63 ! [P: a > $o,Q: a > $o] :
% 0.26/0.63 ( ! [X3: a] :
% 0.26/0.63 ( ( P @ X3 )
% 0.26/0.63 = ( Q @ X3 ) )
% 0.26/0.63 => ( ( collect_a @ P )
% 0.26/0.63 = ( collect_a @ Q ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % Collect_cong
% 0.26/0.63 thf(fact_98_Collect__cong,axiom,
% 0.26/0.63 ! [P: sum_su737395349um_b_c > $o,Q: sum_su737395349um_b_c > $o] :
% 0.26/0.63 ( ! [X3: sum_su737395349um_b_c] :
% 0.26/0.63 ( ( P @ X3 )
% 0.26/0.63 = ( Q @ X3 ) )
% 0.26/0.63 => ( ( collec2086029184um_b_c @ P )
% 0.26/0.63 = ( collec2086029184um_b_c @ Q ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % Collect_cong
% 0.26/0.63 thf(fact_99_agree__sub,axiom,
% 0.26/0.63 ! [A: set_Sum_sum_sz_sz,B: set_Sum_sum_sz_sz,Nu: produc1149990247eal_sz,Omega: produc1149990247eal_sz] :
% 0.26/0.63 ( ( ord_le1110131657_sz_sz @ A @ B )
% 0.26/0.63 => ( ( denota102713844ree_sz @ Nu @ Omega @ B )
% 0.26/0.63 => ( denota102713844ree_sz @ Nu @ Omega @ A ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % agree_sub
% 0.26/0.63 thf(fact_100_agree__sub,axiom,
% 0.26/0.63 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c,Nu: produc190496183real_c,Omega: produc190496183real_c] :
% 0.26/0.63 ( ( ord_le1772180283um_c_c @ A @ B )
% 0.26/0.63 => ( ( denota1997846518gree_c @ Nu @ Omega @ B )
% 0.26/0.63 => ( denota1997846518gree_c @ Nu @ Omega @ A ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % agree_sub
% 0.26/0.63 thf(fact_101_agree__supset,axiom,
% 0.26/0.63 ! [B: set_Sum_sum_sz_sz,A: set_Sum_sum_sz_sz,Nu: produc1149990247eal_sz,Nu2: produc1149990247eal_sz] :
% 0.26/0.63 ( ( ord_le1110131657_sz_sz @ B @ A )
% 0.26/0.63 => ( ( denota102713844ree_sz @ Nu @ Nu2 @ A )
% 0.26/0.63 => ( denota102713844ree_sz @ Nu @ Nu2 @ B ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % agree_supset
% 0.26/0.63 thf(fact_102_agree__supset,axiom,
% 0.26/0.63 ! [B: set_Sum_sum_c_c,A: set_Sum_sum_c_c,Nu: produc190496183real_c,Nu2: produc190496183real_c] :
% 0.26/0.63 ( ( ord_le1772180283um_c_c @ B @ A )
% 0.26/0.63 => ( ( denota1997846518gree_c @ Nu @ Nu2 @ A )
% 0.26/0.63 => ( denota1997846518gree_c @ Nu @ Nu2 @ B ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % agree_supset
% 0.26/0.63 thf(fact_103_old_Oprod_Oinducts,axiom,
% 0.26/0.63 ! [P: produc190496183real_c > $o,Prod: produc190496183real_c] :
% 0.26/0.63 ( ! [A4: finite1398487019real_c,B4: finite1398487019real_c] : ( P @ ( produc394644079real_c @ A4 @ B4 ) )
% 0.26/0.63 => ( P @ Prod ) ) ).
% 0.26/0.63
% 0.26/0.63 % old.prod.inducts
% 0.26/0.63 thf(fact_104_old_Oprod_Oinducts,axiom,
% 0.26/0.63 ! [P: produc866628903_sc_sz > $o,Prod: produc866628903_sc_sz] :
% 0.26/0.63 ( ! [A4: list_f1238882004_sc_sz,B4: list_f1238882004_sc_sz] : ( P @ ( produc1822718231_sc_sz @ A4 @ B4 ) )
% 0.26/0.63 => ( P @ Prod ) ) ).
% 0.26/0.63
% 0.26/0.63 % old.prod.inducts
% 0.26/0.63 thf(fact_105_old_Oprod_Oinducts,axiom,
% 0.26/0.63 ! [P: produc1241881959eal_sz > $o,Prod: produc1241881959eal_sz] :
% 0.26/0.63 ( ! [A4: set_Fi291318197eal_sz,B4: set_Fi291318197eal_sz] : ( P @ ( produc1235791063eal_sz @ A4 @ B4 ) )
% 0.26/0.63 => ( P @ Prod ) ) ).
% 0.26/0.63
% 0.26/0.63 % old.prod.inducts
% 0.26/0.63 thf(fact_106_old_Oprod_Oinducts,axiom,
% 0.26/0.63 ! [P: produc1892666919z_real > $o,Prod: produc1892666919z_real] :
% 0.26/0.63 ( ! [A4: bounde472938360z_real,B4: bounde472938360z_real] : ( P @ ( produc784663575z_real @ A4 @ B4 ) )
% 0.26/0.63 => ( P @ Prod ) ) ).
% 0.26/0.63
% 0.26/0.63 % old.prod.inducts
% 0.26/0.63 thf(fact_107_old_Oprod_Oinducts,axiom,
% 0.26/0.63 ! [P: produc1821101996_sc_sz > $o,Prod: produc1821101996_sc_sz] :
% 0.26/0.63 ( ! [A4: denota610675952t_unit,B4: produc866628903_sc_sz] : ( P @ ( produc789536734_sc_sz @ A4 @ B4 ) )
% 0.26/0.63 => ( P @ Prod ) ) ).
% 0.26/0.63
% 0.26/0.63 % old.prod.inducts
% 0.26/0.63 thf(fact_108_old_Oprod_Oexhaust,axiom,
% 0.26/0.63 ! [Y: produc190496183real_c] :
% 0.26/0.63 ~ ! [A4: finite1398487019real_c,B4: finite1398487019real_c] :
% 0.26/0.63 ( Y
% 0.26/0.63 != ( produc394644079real_c @ A4 @ B4 ) ) ).
% 0.26/0.63
% 0.26/0.63 % old.prod.exhaust
% 0.26/0.63 thf(fact_109_old_Oprod_Oexhaust,axiom,
% 0.26/0.63 ! [Y: produc866628903_sc_sz] :
% 0.26/0.63 ~ ! [A4: list_f1238882004_sc_sz,B4: list_f1238882004_sc_sz] :
% 0.26/0.63 ( Y
% 0.26/0.63 != ( produc1822718231_sc_sz @ A4 @ B4 ) ) ).
% 0.26/0.63
% 0.26/0.63 % old.prod.exhaust
% 0.26/0.63 thf(fact_110_old_Oprod_Oexhaust,axiom,
% 0.26/0.63 ! [Y: produc1241881959eal_sz] :
% 0.26/0.63 ~ ! [A4: set_Fi291318197eal_sz,B4: set_Fi291318197eal_sz] :
% 0.26/0.63 ( Y
% 0.26/0.63 != ( produc1235791063eal_sz @ A4 @ B4 ) ) ).
% 0.26/0.63
% 0.26/0.63 % old.prod.exhaust
% 0.26/0.63 thf(fact_111_old_Oprod_Oexhaust,axiom,
% 0.26/0.63 ! [Y: produc1892666919z_real] :
% 0.26/0.63 ~ ! [A4: bounde472938360z_real,B4: bounde472938360z_real] :
% 0.26/0.63 ( Y
% 0.26/0.63 != ( produc784663575z_real @ A4 @ B4 ) ) ).
% 0.26/0.63
% 0.26/0.63 % old.prod.exhaust
% 0.26/0.63 thf(fact_112_old_Oprod_Oexhaust,axiom,
% 0.26/0.63 ! [Y: produc1821101996_sc_sz] :
% 0.26/0.63 ~ ! [A4: denota610675952t_unit,B4: produc866628903_sc_sz] :
% 0.26/0.63 ( Y
% 0.26/0.63 != ( produc789536734_sc_sz @ A4 @ B4 ) ) ).
% 0.26/0.63
% 0.26/0.63 % old.prod.exhaust
% 0.26/0.63 thf(fact_113_Pair__inject,axiom,
% 0.26/0.63 ! [A2: finite1398487019real_c,B2: finite1398487019real_c,A3: finite1398487019real_c,B3: finite1398487019real_c] :
% 0.26/0.63 ( ( ( produc394644079real_c @ A2 @ B2 )
% 0.26/0.63 = ( produc394644079real_c @ A3 @ B3 ) )
% 0.26/0.63 => ~ ( ( A2 = A3 )
% 0.26/0.63 => ( B2 != B3 ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % Pair_inject
% 0.26/0.63 thf(fact_114_Pair__inject,axiom,
% 0.26/0.63 ! [A2: list_f1238882004_sc_sz,B2: list_f1238882004_sc_sz,A3: list_f1238882004_sc_sz,B3: list_f1238882004_sc_sz] :
% 0.26/0.63 ( ( ( produc1822718231_sc_sz @ A2 @ B2 )
% 0.26/0.63 = ( produc1822718231_sc_sz @ A3 @ B3 ) )
% 0.26/0.63 => ~ ( ( A2 = A3 )
% 0.26/0.63 => ( B2 != B3 ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % Pair_inject
% 0.26/0.63 thf(fact_115_Pair__inject,axiom,
% 0.26/0.63 ! [A2: set_Fi291318197eal_sz,B2: set_Fi291318197eal_sz,A3: set_Fi291318197eal_sz,B3: set_Fi291318197eal_sz] :
% 0.26/0.63 ( ( ( produc1235791063eal_sz @ A2 @ B2 )
% 0.26/0.63 = ( produc1235791063eal_sz @ A3 @ B3 ) )
% 0.26/0.63 => ~ ( ( A2 = A3 )
% 0.26/0.63 => ( B2 != B3 ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % Pair_inject
% 0.26/0.63 thf(fact_116_Pair__inject,axiom,
% 0.26/0.63 ! [A2: bounde472938360z_real,B2: bounde472938360z_real,A3: bounde472938360z_real,B3: bounde472938360z_real] :
% 0.26/0.63 ( ( ( produc784663575z_real @ A2 @ B2 )
% 0.26/0.63 = ( produc784663575z_real @ A3 @ B3 ) )
% 0.26/0.63 => ~ ( ( A2 = A3 )
% 0.26/0.63 => ( B2 != B3 ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % Pair_inject
% 0.26/0.63 thf(fact_117_Pair__inject,axiom,
% 0.26/0.63 ! [A2: denota610675952t_unit,B2: produc866628903_sc_sz,A3: denota610675952t_unit,B3: produc866628903_sc_sz] :
% 0.26/0.63 ( ( ( produc789536734_sc_sz @ A2 @ B2 )
% 0.26/0.63 = ( produc789536734_sc_sz @ A3 @ B3 ) )
% 0.26/0.63 => ~ ( ( A2 = A3 )
% 0.26/0.63 => ( B2 != B3 ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % Pair_inject
% 0.26/0.63 thf(fact_118_prod__cases,axiom,
% 0.26/0.63 ! [P: produc190496183real_c > $o,P2: produc190496183real_c] :
% 0.26/0.63 ( ! [A4: finite1398487019real_c,B4: finite1398487019real_c] : ( P @ ( produc394644079real_c @ A4 @ B4 ) )
% 0.26/0.63 => ( P @ P2 ) ) ).
% 0.26/0.63
% 0.26/0.63 % prod_cases
% 0.26/0.63 thf(fact_119_prod__cases,axiom,
% 0.26/0.63 ! [P: produc866628903_sc_sz > $o,P2: produc866628903_sc_sz] :
% 0.26/0.63 ( ! [A4: list_f1238882004_sc_sz,B4: list_f1238882004_sc_sz] : ( P @ ( produc1822718231_sc_sz @ A4 @ B4 ) )
% 0.26/0.63 => ( P @ P2 ) ) ).
% 0.26/0.63
% 0.26/0.63 % prod_cases
% 0.26/0.63 thf(fact_120_prod__cases,axiom,
% 0.26/0.63 ! [P: produc1241881959eal_sz > $o,P2: produc1241881959eal_sz] :
% 0.26/0.63 ( ! [A4: set_Fi291318197eal_sz,B4: set_Fi291318197eal_sz] : ( P @ ( produc1235791063eal_sz @ A4 @ B4 ) )
% 0.26/0.63 => ( P @ P2 ) ) ).
% 0.26/0.63
% 0.26/0.63 % prod_cases
% 0.26/0.63 thf(fact_121_prod__cases,axiom,
% 0.26/0.63 ! [P: produc1892666919z_real > $o,P2: produc1892666919z_real] :
% 0.26/0.63 ( ! [A4: bounde472938360z_real,B4: bounde472938360z_real] : ( P @ ( produc784663575z_real @ A4 @ B4 ) )
% 0.26/0.63 => ( P @ P2 ) ) ).
% 0.26/0.63
% 0.26/0.63 % prod_cases
% 0.26/0.63 thf(fact_122_prod__cases,axiom,
% 0.26/0.63 ! [P: produc1821101996_sc_sz > $o,P2: produc1821101996_sc_sz] :
% 0.26/0.63 ( ! [A4: denota610675952t_unit,B4: produc866628903_sc_sz] : ( P @ ( produc789536734_sc_sz @ A4 @ B4 ) )
% 0.26/0.63 => ( P @ P2 ) ) ).
% 0.26/0.63
% 0.26/0.63 % prod_cases
% 0.26/0.63 thf(fact_123_surj__pair,axiom,
% 0.26/0.63 ! [P2: produc190496183real_c] :
% 0.26/0.63 ? [X3: finite1398487019real_c,Y3: finite1398487019real_c] :
% 0.26/0.63 ( P2
% 0.26/0.63 = ( produc394644079real_c @ X3 @ Y3 ) ) ).
% 0.26/0.63
% 0.26/0.63 % surj_pair
% 0.26/0.63 thf(fact_124_surj__pair,axiom,
% 0.26/0.63 ! [P2: produc866628903_sc_sz] :
% 0.26/0.63 ? [X3: list_f1238882004_sc_sz,Y3: list_f1238882004_sc_sz] :
% 0.26/0.63 ( P2
% 0.26/0.63 = ( produc1822718231_sc_sz @ X3 @ Y3 ) ) ).
% 0.26/0.63
% 0.26/0.63 % surj_pair
% 0.26/0.63 thf(fact_125_surj__pair,axiom,
% 0.26/0.63 ! [P2: produc1241881959eal_sz] :
% 0.26/0.63 ? [X3: set_Fi291318197eal_sz,Y3: set_Fi291318197eal_sz] :
% 0.26/0.63 ( P2
% 0.26/0.63 = ( produc1235791063eal_sz @ X3 @ Y3 ) ) ).
% 0.26/0.63
% 0.26/0.63 % surj_pair
% 0.26/0.63 thf(fact_126_surj__pair,axiom,
% 0.26/0.63 ! [P2: produc1892666919z_real] :
% 0.26/0.63 ? [X3: bounde472938360z_real,Y3: bounde472938360z_real] :
% 0.26/0.63 ( P2
% 0.26/0.63 = ( produc784663575z_real @ X3 @ Y3 ) ) ).
% 0.26/0.63
% 0.26/0.63 % surj_pair
% 0.26/0.63 thf(fact_127_surj__pair,axiom,
% 0.26/0.63 ! [P2: produc1821101996_sc_sz] :
% 0.26/0.63 ? [X3: denota610675952t_unit,Y3: produc866628903_sc_sz] :
% 0.26/0.63 ( P2
% 0.26/0.63 = ( produc789536734_sc_sz @ X3 @ Y3 ) ) ).
% 0.26/0.63
% 0.26/0.63 % surj_pair
% 0.26/0.63 thf(fact_128_prod__induct3,axiom,
% 0.26/0.63 ! [P: produc1821101996_sc_sz > $o,X: produc1821101996_sc_sz] :
% 0.26/0.63 ( ! [A4: denota610675952t_unit,B4: list_f1238882004_sc_sz,C: list_f1238882004_sc_sz] : ( P @ ( produc789536734_sc_sz @ A4 @ ( produc1822718231_sc_sz @ B4 @ C ) ) )
% 0.26/0.63 => ( P @ X ) ) ).
% 0.26/0.63
% 0.26/0.63 % prod_induct3
% 0.26/0.63 thf(fact_129_prod__cases3,axiom,
% 0.26/0.63 ! [Y: produc1821101996_sc_sz] :
% 0.26/0.63 ~ ! [A4: denota610675952t_unit,B4: list_f1238882004_sc_sz,C: list_f1238882004_sc_sz] :
% 0.26/0.63 ( Y
% 0.26/0.63 != ( produc789536734_sc_sz @ A4 @ ( produc1822718231_sc_sz @ B4 @ C ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % prod_cases3
% 0.26/0.63 thf(fact_130_fst__conv,axiom,
% 0.26/0.63 ! [X1: list_f1238882004_sc_sz,X22: list_f1238882004_sc_sz] :
% 0.26/0.63 ( ( produc548504323_sc_sz @ ( produc1822718231_sc_sz @ X1 @ X22 ) )
% 0.26/0.63 = X1 ) ).
% 0.26/0.63
% 0.26/0.63 % fst_conv
% 0.26/0.63 thf(fact_131_fst__conv,axiom,
% 0.26/0.63 ! [X1: set_Fi291318197eal_sz,X22: set_Fi291318197eal_sz] :
% 0.26/0.63 ( ( produc286845635eal_sz @ ( produc1235791063eal_sz @ X1 @ X22 ) )
% 0.26/0.63 = X1 ) ).
% 0.26/0.63
% 0.26/0.63 % fst_conv
% 0.26/0.63 thf(fact_132_fst__conv,axiom,
% 0.26/0.63 ! [X1: bounde472938360z_real,X22: bounde472938360z_real] :
% 0.26/0.63 ( ( produc870616579z_real @ ( produc784663575z_real @ X1 @ X22 ) )
% 0.26/0.63 = X1 ) ).
% 0.26/0.63
% 0.26/0.63 % fst_conv
% 0.26/0.63 thf(fact_133_fst__conv,axiom,
% 0.26/0.63 ! [X1: finite824932053eal_sz,X22: finite824932053eal_sz] :
% 0.26/0.63 ( ( produc1111759555eal_sz @ ( produc1308130519eal_sz @ X1 @ X22 ) )
% 0.26/0.63 = X1 ) ).
% 0.26/0.63
% 0.26/0.63 % fst_conv
% 0.26/0.63 thf(fact_134_fst__conv,axiom,
% 0.26/0.63 ! [X1: denota610675952t_unit,X22: produc866628903_sc_sz] :
% 0.26/0.63 ( ( produc1503602930_sc_sz @ ( produc789536734_sc_sz @ X1 @ X22 ) )
% 0.26/0.63 = X1 ) ).
% 0.26/0.63
% 0.26/0.63 % fst_conv
% 0.26/0.63 thf(fact_135_fst__conv,axiom,
% 0.26/0.63 ! [X1: finite1398487019real_c,X22: finite1398487019real_c] :
% 0.26/0.63 ( ( produc2010422875real_c @ ( produc394644079real_c @ X1 @ X22 ) )
% 0.26/0.63 = X1 ) ).
% 0.26/0.63
% 0.26/0.63 % fst_conv
% 0.26/0.63 thf(fact_136_fst__eqD,axiom,
% 0.26/0.63 ! [X: list_f1238882004_sc_sz,Y: list_f1238882004_sc_sz,A2: list_f1238882004_sc_sz] :
% 0.26/0.63 ( ( ( produc548504323_sc_sz @ ( produc1822718231_sc_sz @ X @ Y ) )
% 0.26/0.63 = A2 )
% 0.26/0.63 => ( X = A2 ) ) ).
% 0.26/0.63
% 0.26/0.63 % fst_eqD
% 0.26/0.63 thf(fact_137_fst__eqD,axiom,
% 0.26/0.63 ! [X: set_Fi291318197eal_sz,Y: set_Fi291318197eal_sz,A2: set_Fi291318197eal_sz] :
% 0.26/0.63 ( ( ( produc286845635eal_sz @ ( produc1235791063eal_sz @ X @ Y ) )
% 0.26/0.63 = A2 )
% 0.26/0.63 => ( X = A2 ) ) ).
% 0.26/0.63
% 0.26/0.63 % fst_eqD
% 0.26/0.63 thf(fact_138_fst__eqD,axiom,
% 0.26/0.63 ! [X: bounde472938360z_real,Y: bounde472938360z_real,A2: bounde472938360z_real] :
% 0.26/0.63 ( ( ( produc870616579z_real @ ( produc784663575z_real @ X @ Y ) )
% 0.26/0.63 = A2 )
% 0.26/0.63 => ( X = A2 ) ) ).
% 0.26/0.63
% 0.26/0.63 % fst_eqD
% 0.26/0.63 thf(fact_139_fst__eqD,axiom,
% 0.26/0.63 ! [X: finite824932053eal_sz,Y: finite824932053eal_sz,A2: finite824932053eal_sz] :
% 0.26/0.63 ( ( ( produc1111759555eal_sz @ ( produc1308130519eal_sz @ X @ Y ) )
% 0.26/0.63 = A2 )
% 0.26/0.63 => ( X = A2 ) ) ).
% 0.26/0.63
% 0.26/0.63 % fst_eqD
% 0.26/0.63 thf(fact_140_fst__eqD,axiom,
% 0.26/0.63 ! [X: denota610675952t_unit,Y: produc866628903_sc_sz,A2: denota610675952t_unit] :
% 0.26/0.63 ( ( ( produc1503602930_sc_sz @ ( produc789536734_sc_sz @ X @ Y ) )
% 0.26/0.63 = A2 )
% 0.26/0.63 => ( X = A2 ) ) ).
% 0.26/0.63
% 0.26/0.63 % fst_eqD
% 0.26/0.63 thf(fact_141_fst__eqD,axiom,
% 0.26/0.63 ! [X: finite1398487019real_c,Y: finite1398487019real_c,A2: finite1398487019real_c] :
% 0.26/0.63 ( ( ( produc2010422875real_c @ ( produc394644079real_c @ X @ Y ) )
% 0.26/0.63 = A2 )
% 0.26/0.63 => ( X = A2 ) ) ).
% 0.26/0.63
% 0.26/0.63 % fst_eqD
% 0.26/0.63 thf(fact_142_snd__conv,axiom,
% 0.26/0.63 ! [X1: list_f1238882004_sc_sz,X22: list_f1238882004_sc_sz] :
% 0.26/0.63 ( ( produc4753477_sc_sz @ ( produc1822718231_sc_sz @ X1 @ X22 ) )
% 0.26/0.63 = X22 ) ).
% 0.26/0.63
% 0.26/0.63 % snd_conv
% 0.26/0.63 thf(fact_143_snd__conv,axiom,
% 0.26/0.63 ! [X1: set_Fi291318197eal_sz,X22: set_Fi291318197eal_sz] :
% 0.26/0.63 ( ( produc1746886149eal_sz @ ( produc1235791063eal_sz @ X1 @ X22 ) )
% 0.26/0.63 = X22 ) ).
% 0.26/0.63
% 0.26/0.63 % snd_conv
% 0.26/0.63 thf(fact_144_snd__conv,axiom,
% 0.26/0.63 ! [X1: bounde472938360z_real,X22: bounde472938360z_real] :
% 0.26/0.63 ( ( produc1422611269z_real @ ( produc784663575z_real @ X1 @ X22 ) )
% 0.26/0.63 = X22 ) ).
% 0.26/0.63
% 0.26/0.63 % snd_conv
% 0.26/0.63 thf(fact_145_snd__conv,axiom,
% 0.26/0.63 ! [X1: finite824932053eal_sz,X22: finite824932053eal_sz] :
% 0.26/0.63 ( ( produc1269210629eal_sz @ ( produc1308130519eal_sz @ X1 @ X22 ) )
% 0.26/0.63 = X22 ) ).
% 0.26/0.63
% 0.26/0.63 % snd_conv
% 0.26/0.63 thf(fact_146_snd__conv,axiom,
% 0.26/0.63 ! [X1: denota610675952t_unit,X22: produc866628903_sc_sz] :
% 0.26/0.63 ( ( produc974239792_sc_sz @ ( produc789536734_sc_sz @ X1 @ X22 ) )
% 0.26/0.63 = X22 ) ).
% 0.26/0.63
% 0.26/0.63 % snd_conv
% 0.26/0.63 thf(fact_147_snd__conv,axiom,
% 0.26/0.63 ! [X1: finite1398487019real_c,X22: finite1398487019real_c] :
% 0.26/0.63 ( ( produc314122909real_c @ ( produc394644079real_c @ X1 @ X22 ) )
% 0.26/0.63 = X22 ) ).
% 0.26/0.63
% 0.26/0.63 % snd_conv
% 0.26/0.63 thf(fact_148_snd__eqD,axiom,
% 0.26/0.63 ! [X: list_f1238882004_sc_sz,Y: list_f1238882004_sc_sz,A2: list_f1238882004_sc_sz] :
% 0.26/0.63 ( ( ( produc4753477_sc_sz @ ( produc1822718231_sc_sz @ X @ Y ) )
% 0.26/0.63 = A2 )
% 0.26/0.63 => ( Y = A2 ) ) ).
% 0.26/0.63
% 0.26/0.63 % snd_eqD
% 0.26/0.63 thf(fact_149_snd__eqD,axiom,
% 0.26/0.63 ! [X: set_Fi291318197eal_sz,Y: set_Fi291318197eal_sz,A2: set_Fi291318197eal_sz] :
% 0.26/0.63 ( ( ( produc1746886149eal_sz @ ( produc1235791063eal_sz @ X @ Y ) )
% 0.26/0.63 = A2 )
% 0.26/0.63 => ( Y = A2 ) ) ).
% 0.26/0.63
% 0.26/0.63 % snd_eqD
% 0.26/0.63 thf(fact_150_snd__eqD,axiom,
% 0.26/0.63 ! [X: bounde472938360z_real,Y: bounde472938360z_real,A2: bounde472938360z_real] :
% 0.26/0.63 ( ( ( produc1422611269z_real @ ( produc784663575z_real @ X @ Y ) )
% 0.26/0.63 = A2 )
% 0.26/0.63 => ( Y = A2 ) ) ).
% 0.26/0.63
% 0.26/0.63 % snd_eqD
% 0.26/0.63 thf(fact_151_snd__eqD,axiom,
% 0.26/0.63 ! [X: finite824932053eal_sz,Y: finite824932053eal_sz,A2: finite824932053eal_sz] :
% 0.26/0.63 ( ( ( produc1269210629eal_sz @ ( produc1308130519eal_sz @ X @ Y ) )
% 0.26/0.63 = A2 )
% 0.26/0.63 => ( Y = A2 ) ) ).
% 0.26/0.63
% 0.26/0.63 % snd_eqD
% 0.26/0.63 thf(fact_152_snd__eqD,axiom,
% 0.26/0.63 ! [X: denota610675952t_unit,Y: produc866628903_sc_sz,A2: produc866628903_sc_sz] :
% 0.26/0.63 ( ( ( produc974239792_sc_sz @ ( produc789536734_sc_sz @ X @ Y ) )
% 0.26/0.63 = A2 )
% 0.26/0.63 => ( Y = A2 ) ) ).
% 0.26/0.63
% 0.26/0.63 % snd_eqD
% 0.26/0.63 thf(fact_153_snd__eqD,axiom,
% 0.26/0.63 ! [X: finite1398487019real_c,Y: finite1398487019real_c,A2: finite1398487019real_c] :
% 0.26/0.63 ( ( ( produc314122909real_c @ ( produc394644079real_c @ X @ Y ) )
% 0.26/0.63 = A2 )
% 0.26/0.63 => ( Y = A2 ) ) ).
% 0.26/0.63
% 0.26/0.63 % snd_eqD
% 0.26/0.63 thf(fact_154_prod__eq__iff,axiom,
% 0.26/0.63 ( ( ^ [Y4: produc1149990247eal_sz,Z: produc1149990247eal_sz] : ( Y4 = Z ) )
% 0.26/0.63 = ( ^ [S2: produc1149990247eal_sz,T: produc1149990247eal_sz] :
% 0.26/0.63 ( ( ( produc1111759555eal_sz @ S2 )
% 0.26/0.63 = ( produc1111759555eal_sz @ T ) )
% 0.26/0.63 & ( ( produc1269210629eal_sz @ S2 )
% 0.26/0.63 = ( produc1269210629eal_sz @ T ) ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % prod_eq_iff
% 0.26/0.63 thf(fact_155_prod__eq__iff,axiom,
% 0.26/0.63 ( ( ^ [Y4: produc1821101996_sc_sz,Z: produc1821101996_sc_sz] : ( Y4 = Z ) )
% 0.26/0.63 = ( ^ [S2: produc1821101996_sc_sz,T: produc1821101996_sc_sz] :
% 0.26/0.63 ( ( ( produc1503602930_sc_sz @ S2 )
% 0.26/0.63 = ( produc1503602930_sc_sz @ T ) )
% 0.26/0.63 & ( ( produc974239792_sc_sz @ S2 )
% 0.26/0.63 = ( produc974239792_sc_sz @ T ) ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % prod_eq_iff
% 0.26/0.63 thf(fact_156_prod__eq__iff,axiom,
% 0.26/0.63 ( ( ^ [Y4: produc190496183real_c,Z: produc190496183real_c] : ( Y4 = Z ) )
% 0.26/0.63 = ( ^ [S2: produc190496183real_c,T: produc190496183real_c] :
% 0.26/0.63 ( ( ( produc2010422875real_c @ S2 )
% 0.26/0.63 = ( produc2010422875real_c @ T ) )
% 0.26/0.63 & ( ( produc314122909real_c @ S2 )
% 0.26/0.63 = ( produc314122909real_c @ T ) ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % prod_eq_iff
% 0.26/0.63 thf(fact_157_prod_Oexpand,axiom,
% 0.26/0.63 ! [Prod: produc1149990247eal_sz,Prod2: produc1149990247eal_sz] :
% 0.26/0.63 ( ( ( ( produc1111759555eal_sz @ Prod )
% 0.26/0.63 = ( produc1111759555eal_sz @ Prod2 ) )
% 0.26/0.63 & ( ( produc1269210629eal_sz @ Prod )
% 0.26/0.63 = ( produc1269210629eal_sz @ Prod2 ) ) )
% 0.26/0.63 => ( Prod = Prod2 ) ) ).
% 0.26/0.63
% 0.26/0.63 % prod.expand
% 0.26/0.63 thf(fact_158_prod_Oexpand,axiom,
% 0.26/0.63 ! [Prod: produc1821101996_sc_sz,Prod2: produc1821101996_sc_sz] :
% 0.26/0.63 ( ( ( ( produc1503602930_sc_sz @ Prod )
% 0.26/0.63 = ( produc1503602930_sc_sz @ Prod2 ) )
% 0.26/0.63 & ( ( produc974239792_sc_sz @ Prod )
% 0.26/0.63 = ( produc974239792_sc_sz @ Prod2 ) ) )
% 0.26/0.63 => ( Prod = Prod2 ) ) ).
% 0.26/0.63
% 0.26/0.63 % prod.expand
% 0.26/0.63 thf(fact_159_prod_Oexpand,axiom,
% 0.26/0.63 ! [Prod: produc190496183real_c,Prod2: produc190496183real_c] :
% 0.26/0.63 ( ( ( ( produc2010422875real_c @ Prod )
% 0.26/0.63 = ( produc2010422875real_c @ Prod2 ) )
% 0.26/0.63 & ( ( produc314122909real_c @ Prod )
% 0.26/0.63 = ( produc314122909real_c @ Prod2 ) ) )
% 0.26/0.63 => ( Prod = Prod2 ) ) ).
% 0.26/0.63
% 0.26/0.63 % prod.expand
% 0.26/0.63 thf(fact_160_prod__eqI,axiom,
% 0.26/0.63 ! [P2: produc1149990247eal_sz,Q2: produc1149990247eal_sz] :
% 0.26/0.63 ( ( ( produc1111759555eal_sz @ P2 )
% 0.26/0.63 = ( produc1111759555eal_sz @ Q2 ) )
% 0.26/0.63 => ( ( ( produc1269210629eal_sz @ P2 )
% 0.26/0.63 = ( produc1269210629eal_sz @ Q2 ) )
% 0.26/0.63 => ( P2 = Q2 ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % prod_eqI
% 0.26/0.63 thf(fact_161_prod__eqI,axiom,
% 0.26/0.63 ! [P2: produc1821101996_sc_sz,Q2: produc1821101996_sc_sz] :
% 0.26/0.63 ( ( ( produc1503602930_sc_sz @ P2 )
% 0.26/0.63 = ( produc1503602930_sc_sz @ Q2 ) )
% 0.26/0.63 => ( ( ( produc974239792_sc_sz @ P2 )
% 0.26/0.63 = ( produc974239792_sc_sz @ Q2 ) )
% 0.26/0.63 => ( P2 = Q2 ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % prod_eqI
% 0.26/0.63 thf(fact_162_prod__eqI,axiom,
% 0.26/0.63 ! [P2: produc190496183real_c,Q2: produc190496183real_c] :
% 0.26/0.63 ( ( ( produc2010422875real_c @ P2 )
% 0.26/0.63 = ( produc2010422875real_c @ Q2 ) )
% 0.26/0.63 => ( ( ( produc314122909real_c @ P2 )
% 0.26/0.63 = ( produc314122909real_c @ Q2 ) )
% 0.26/0.63 => ( P2 = Q2 ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % prod_eqI
% 0.26/0.63 thf(fact_163_dfree__Fun,axiom,
% 0.26/0.63 ! [Args: c > trm_a_c,I: a] :
% 0.26/0.63 ( ! [I4: c] : ( dfree_a_c @ ( Args @ I4 ) )
% 0.26/0.63 => ( dfree_a_c @ ( function_a_c @ I @ Args ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % dfree_Fun
% 0.26/0.63 thf(fact_164_dfree__Fun,axiom,
% 0.26/0.63 ! [Args: sz > trm_sf_sz,I: sf] :
% 0.26/0.63 ( ! [I4: sz] : ( dfree_sf_sz @ ( Args @ I4 ) )
% 0.26/0.63 => ( dfree_sf_sz @ ( function_sf_sz @ I @ Args ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % dfree_Fun
% 0.26/0.63 thf(fact_165_dfree_Odfree__Plus,axiom,
% 0.26/0.63 ! [Theta_1: trm_sf_sz,Theta_2: trm_sf_sz] :
% 0.26/0.63 ( ( dfree_sf_sz @ Theta_1 )
% 0.26/0.63 => ( ( dfree_sf_sz @ Theta_2 )
% 0.26/0.63 => ( dfree_sf_sz @ ( plus_sf_sz @ Theta_1 @ Theta_2 ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % dfree.dfree_Plus
% 0.26/0.63 thf(fact_166_dfree_Odfree__Plus,axiom,
% 0.26/0.63 ! [Theta_1: trm_a_c,Theta_2: trm_a_c] :
% 0.26/0.63 ( ( dfree_a_c @ Theta_1 )
% 0.26/0.63 => ( ( dfree_a_c @ Theta_2 )
% 0.26/0.63 => ( dfree_a_c @ ( plus_a_c @ Theta_1 @ Theta_2 ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % dfree.dfree_Plus
% 0.26/0.63 thf(fact_167_dfree__Times,axiom,
% 0.26/0.63 ! [Theta_1: trm_a_c,Theta_2: trm_a_c] :
% 0.26/0.63 ( ( dfree_a_c @ Theta_1 )
% 0.26/0.63 => ( ( dfree_a_c @ Theta_2 )
% 0.26/0.63 => ( dfree_a_c @ ( times_a_c @ Theta_1 @ Theta_2 ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % dfree_Times
% 0.26/0.63 thf(fact_168_dfree__Times,axiom,
% 0.26/0.63 ! [Theta_1: trm_sf_sz,Theta_2: trm_sf_sz] :
% 0.26/0.63 ( ( dfree_sf_sz @ Theta_1 )
% 0.26/0.63 => ( ( dfree_sf_sz @ Theta_2 )
% 0.26/0.63 => ( dfree_sf_sz @ ( times_sf_sz @ Theta_1 @ Theta_2 ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % dfree_Times
% 0.26/0.63 thf(fact_169_trm_Odistinct_I23_J,axiom,
% 0.26/0.63 ! [X31: a,X32: c > trm_a_c,X41: trm_a_c,X42: trm_a_c] :
% 0.26/0.63 ( ( function_a_c @ X31 @ X32 )
% 0.26/0.63 != ( plus_a_c @ X41 @ X42 ) ) ).
% 0.26/0.63
% 0.26/0.63 % trm.distinct(23)
% 0.26/0.63 thf(fact_170_trm_Odistinct_I23_J,axiom,
% 0.26/0.63 ! [X31: sf,X32: sz > trm_sf_sz,X41: trm_sf_sz,X42: trm_sf_sz] :
% 0.26/0.63 ( ( function_sf_sz @ X31 @ X32 )
% 0.26/0.63 != ( plus_sf_sz @ X41 @ X42 ) ) ).
% 0.26/0.63
% 0.26/0.63 % trm.distinct(23)
% 0.26/0.63 thf(fact_171_trm_Odistinct_I25_J,axiom,
% 0.26/0.63 ! [X31: a,X32: c > trm_a_c,X51: trm_a_c,X52: trm_a_c] :
% 0.26/0.63 ( ( function_a_c @ X31 @ X32 )
% 0.26/0.63 != ( times_a_c @ X51 @ X52 ) ) ).
% 0.26/0.63
% 0.26/0.63 % trm.distinct(25)
% 0.26/0.63 thf(fact_172_trm_Odistinct_I25_J,axiom,
% 0.26/0.63 ! [X31: sf,X32: sz > trm_sf_sz,X51: trm_sf_sz,X52: trm_sf_sz] :
% 0.26/0.63 ( ( function_sf_sz @ X31 @ X32 )
% 0.26/0.63 != ( times_sf_sz @ X51 @ X52 ) ) ).
% 0.26/0.63
% 0.26/0.63 % trm.distinct(25)
% 0.26/0.63 thf(fact_173_trm_Odistinct_I31_J,axiom,
% 0.26/0.63 ! [X41: trm_sf_sz,X42: trm_sf_sz,X51: trm_sf_sz,X52: trm_sf_sz] :
% 0.26/0.63 ( ( plus_sf_sz @ X41 @ X42 )
% 0.26/0.63 != ( times_sf_sz @ X51 @ X52 ) ) ).
% 0.26/0.63
% 0.26/0.63 % trm.distinct(31)
% 0.26/0.63 thf(fact_174_trm_Odistinct_I31_J,axiom,
% 0.26/0.63 ! [X41: trm_a_c,X42: trm_a_c,X51: trm_a_c,X52: trm_a_c] :
% 0.26/0.63 ( ( plus_a_c @ X41 @ X42 )
% 0.26/0.63 != ( times_a_c @ X51 @ X52 ) ) ).
% 0.26/0.63
% 0.26/0.63 % trm.distinct(31)
% 0.26/0.63 thf(fact_175_surjective__pairing,axiom,
% 0.26/0.63 ! [T3: produc866628903_sc_sz] :
% 0.26/0.63 ( T3
% 0.26/0.63 = ( produc1822718231_sc_sz @ ( produc548504323_sc_sz @ T3 ) @ ( produc4753477_sc_sz @ T3 ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % surjective_pairing
% 0.26/0.63 thf(fact_176_surjective__pairing,axiom,
% 0.26/0.63 ! [T3: produc1241881959eal_sz] :
% 0.26/0.63 ( T3
% 0.26/0.63 = ( produc1235791063eal_sz @ ( produc286845635eal_sz @ T3 ) @ ( produc1746886149eal_sz @ T3 ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % surjective_pairing
% 0.26/0.63 thf(fact_177_surjective__pairing,axiom,
% 0.26/0.63 ! [T3: produc1892666919z_real] :
% 0.26/0.63 ( T3
% 0.26/0.63 = ( produc784663575z_real @ ( produc870616579z_real @ T3 ) @ ( produc1422611269z_real @ T3 ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % surjective_pairing
% 0.26/0.63 thf(fact_178_surjective__pairing,axiom,
% 0.26/0.63 ! [T3: produc1149990247eal_sz] :
% 0.26/0.63 ( T3
% 0.26/0.63 = ( produc1308130519eal_sz @ ( produc1111759555eal_sz @ T3 ) @ ( produc1269210629eal_sz @ T3 ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % surjective_pairing
% 0.26/0.63 thf(fact_179_surjective__pairing,axiom,
% 0.26/0.63 ! [T3: produc1821101996_sc_sz] :
% 0.26/0.63 ( T3
% 0.26/0.63 = ( produc789536734_sc_sz @ ( produc1503602930_sc_sz @ T3 ) @ ( produc974239792_sc_sz @ T3 ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % surjective_pairing
% 0.26/0.63 thf(fact_180_surjective__pairing,axiom,
% 0.26/0.63 ! [T3: produc190496183real_c] :
% 0.26/0.63 ( T3
% 0.26/0.63 = ( produc394644079real_c @ ( produc2010422875real_c @ T3 ) @ ( produc314122909real_c @ T3 ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % surjective_pairing
% 0.26/0.63 thf(fact_181_prod_Oexhaust__sel,axiom,
% 0.26/0.63 ! [Prod: produc866628903_sc_sz] :
% 0.26/0.63 ( Prod
% 0.26/0.63 = ( produc1822718231_sc_sz @ ( produc548504323_sc_sz @ Prod ) @ ( produc4753477_sc_sz @ Prod ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % prod.exhaust_sel
% 0.26/0.63 thf(fact_182_prod_Oexhaust__sel,axiom,
% 0.26/0.63 ! [Prod: produc1241881959eal_sz] :
% 0.26/0.63 ( Prod
% 0.26/0.63 = ( produc1235791063eal_sz @ ( produc286845635eal_sz @ Prod ) @ ( produc1746886149eal_sz @ Prod ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % prod.exhaust_sel
% 0.26/0.63 thf(fact_183_prod_Oexhaust__sel,axiom,
% 0.26/0.63 ! [Prod: produc1892666919z_real] :
% 0.26/0.63 ( Prod
% 0.26/0.63 = ( produc784663575z_real @ ( produc870616579z_real @ Prod ) @ ( produc1422611269z_real @ Prod ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % prod.exhaust_sel
% 0.26/0.63 thf(fact_184_prod_Oexhaust__sel,axiom,
% 0.26/0.63 ! [Prod: produc1149990247eal_sz] :
% 0.26/0.63 ( Prod
% 0.26/0.63 = ( produc1308130519eal_sz @ ( produc1111759555eal_sz @ Prod ) @ ( produc1269210629eal_sz @ Prod ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % prod.exhaust_sel
% 0.26/0.63 thf(fact_185_prod_Oexhaust__sel,axiom,
% 0.26/0.63 ! [Prod: produc1821101996_sc_sz] :
% 0.26/0.63 ( Prod
% 0.26/0.63 = ( produc789536734_sc_sz @ ( produc1503602930_sc_sz @ Prod ) @ ( produc974239792_sc_sz @ Prod ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % prod.exhaust_sel
% 0.26/0.63 thf(fact_186_prod_Oexhaust__sel,axiom,
% 0.26/0.63 ! [Prod: produc190496183real_c] :
% 0.26/0.63 ( Prod
% 0.26/0.63 = ( produc394644079real_c @ ( produc2010422875real_c @ Prod ) @ ( produc314122909real_c @ Prod ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % prod.exhaust_sel
% 0.26/0.63 thf(fact_187_Pair__le,axiom,
% 0.26/0.63 ! [A2: set_a,B2: set_a,C2: set_a,D: set_a] :
% 0.26/0.63 ( ( ord_le486764743_set_a @ ( produc1928581911_set_a @ A2 @ B2 ) @ ( produc1928581911_set_a @ C2 @ D ) )
% 0.26/0.63 = ( ( ord_less_eq_set_a @ A2 @ C2 )
% 0.26/0.63 & ( ord_less_eq_set_a @ B2 @ D ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % Pair_le
% 0.26/0.63 thf(fact_188_Pair__le,axiom,
% 0.26/0.63 ! [A2: set_a,B2: a > $o,C2: set_a,D: a > $o] :
% 0.26/0.63 ( ( ord_le501349868_a_a_o @ ( produc634809990_a_a_o @ A2 @ B2 ) @ ( produc634809990_a_a_o @ C2 @ D ) )
% 0.26/0.63 = ( ( ord_less_eq_set_a @ A2 @ C2 )
% 0.26/0.63 & ( ord_less_eq_a_o @ B2 @ D ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % Pair_le
% 0.26/0.63 thf(fact_189_Pair__le,axiom,
% 0.26/0.63 ! [A2: a > $o,B2: set_a,C2: a > $o,D: set_a] :
% 0.26/0.63 ( ( ord_le72828020_set_a @ ( produc1916559302_set_a @ A2 @ B2 ) @ ( produc1916559302_set_a @ C2 @ D ) )
% 0.26/0.63 = ( ( ord_less_eq_a_o @ A2 @ C2 )
% 0.26/0.63 & ( ord_less_eq_set_a @ B2 @ D ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % Pair_le
% 0.26/0.63 thf(fact_190_Pair__le,axiom,
% 0.26/0.63 ! [A2: finite1398487019real_c,B2: finite1398487019real_c,C2: finite1398487019real_c,D: finite1398487019real_c] :
% 0.26/0.63 ( ( ord_le850691415real_c @ ( produc394644079real_c @ A2 @ B2 ) @ ( produc394644079real_c @ C2 @ D ) )
% 0.26/0.63 = ( ( ord_le775706699real_c @ A2 @ C2 )
% 0.26/0.63 & ( ord_le775706699real_c @ B2 @ D ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % Pair_le
% 0.26/0.63 thf(fact_191_Pair__le,axiom,
% 0.26/0.63 ! [A2: a > $o,B2: a > $o,C2: a > $o,D: a > $o] :
% 0.26/0.63 ( ( ord_le1883211903_o_a_o @ ( product_Pair_a_o_a_o @ A2 @ B2 ) @ ( product_Pair_a_o_a_o @ C2 @ D ) )
% 0.26/0.63 = ( ( ord_less_eq_a_o @ A2 @ C2 )
% 0.26/0.63 & ( ord_less_eq_a_o @ B2 @ D ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % Pair_le
% 0.26/0.63 thf(fact_192_Pair__le,axiom,
% 0.26/0.63 ! [A2: set_Fi291318197eal_sz,B2: set_Fi291318197eal_sz,C2: set_Fi291318197eal_sz,D: set_Fi291318197eal_sz] :
% 0.26/0.63 ( ( ord_le978883847eal_sz @ ( produc1235791063eal_sz @ A2 @ B2 ) @ ( produc1235791063eal_sz @ C2 @ D ) )
% 0.26/0.63 = ( ( ord_le41263445eal_sz @ A2 @ C2 )
% 0.26/0.63 & ( ord_le41263445eal_sz @ B2 @ D ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % Pair_le
% 0.26/0.63 thf(fact_193_Pair__le,axiom,
% 0.26/0.63 ! [A2: set_a,B2: trm_sf_sz > trm_sf_sz > $o,C2: set_a,D: trm_sf_sz > trm_sf_sz > $o] :
% 0.26/0.63 ( ( ord_le1884788375f_sz_o @ ( produc1174558183f_sz_o @ A2 @ B2 ) @ ( produc1174558183f_sz_o @ C2 @ D ) )
% 0.26/0.63 = ( ( ord_less_eq_set_a @ A2 @ C2 )
% 0.26/0.63 & ( ord_le8515534f_sz_o @ B2 @ D ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % Pair_le
% 0.26/0.63 thf(fact_194_Pair__le,axiom,
% 0.26/0.63 ! [A2: trm_sf_sz > trm_sf_sz > $o,B2: set_a,C2: trm_sf_sz > trm_sf_sz > $o,D: set_a] :
% 0.26/0.63 ( ( ord_le1643089911_set_a @ ( produc1543226183_set_a @ A2 @ B2 ) @ ( produc1543226183_set_a @ C2 @ D ) )
% 0.26/0.63 = ( ( ord_le8515534f_sz_o @ A2 @ C2 )
% 0.26/0.63 & ( ord_less_eq_set_a @ B2 @ D ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % Pair_le
% 0.26/0.63 thf(fact_195_Pair__le,axiom,
% 0.26/0.63 ! [A2: trm_sf_sz > trm_sf_sz > $o,B2: a > $o,C2: trm_sf_sz > trm_sf_sz > $o,D: a > $o] :
% 0.26/0.63 ( ( ord_le2132572860_o_a_o @ ( produc1152932438_o_a_o @ A2 @ B2 ) @ ( produc1152932438_o_a_o @ C2 @ D ) )
% 0.26/0.63 = ( ( ord_le8515534f_sz_o @ A2 @ C2 )
% 0.26/0.63 & ( ord_less_eq_a_o @ B2 @ D ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % Pair_le
% 0.26/0.63 thf(fact_196_Pair__le,axiom,
% 0.26/0.63 ! [A2: a > $o,B2: trm_sf_sz > trm_sf_sz > $o,C2: a > $o,D: trm_sf_sz > trm_sf_sz > $o] :
% 0.26/0.63 ( ( ord_le472894788f_sz_o @ ( produc593159062f_sz_o @ A2 @ B2 ) @ ( produc593159062f_sz_o @ C2 @ D ) )
% 0.26/0.63 = ( ( ord_less_eq_a_o @ A2 @ C2 )
% 0.26/0.63 & ( ord_le8515534f_sz_o @ B2 @ D ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % Pair_le
% 0.26/0.63 thf(fact_197_directional__derivative__def,axiom,
% 0.26/0.63 ( denota2112424896_a_b_c
% 0.26/0.63 = ( ^ [I5: denota231621370t_unit,T: trm_a_c,V2: produc190496183real_c] : ( denota229585092_a_b_c @ I5 @ T @ ( produc2010422875real_c @ V2 ) @ ( produc314122909real_c @ V2 ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % directional_derivative_def
% 0.26/0.63 thf(fact_198_directional__derivative__def,axiom,
% 0.26/0.63 ( denota453121236_sc_sz
% 0.26/0.63 = ( ^ [I5: denota610675952t_unit,T: trm_sf_sz,V2: produc1149990247eal_sz] : ( denota1979904720_sc_sz @ I5 @ T @ ( produc1111759555eal_sz @ V2 ) @ ( produc1269210629eal_sz @ V2 ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % directional_derivative_def
% 0.26/0.63 thf(fact_199_raw__interp__inverse,axiom,
% 0.26/0.63 ! [X: freche2095075217_sc_sz] :
% 0.26/0.63 ( ( freche1784963216_sc_sz @ ( freche1421597129_sc_sz @ X ) )
% 0.26/0.63 = X ) ).
% 0.26/0.63
% 0.26/0.63 % raw_interp_inverse
% 0.26/0.63 thf(fact_200_type__definition__strm,axiom,
% 0.26/0.63 type_d1238563341rm_a_c @ frechet_raw_term_a_c @ freche665377492rm_a_c @ ( collect_trm_a_c @ dfree_a_c ) ).
% 0.26/0.63
% 0.26/0.63 % type_definition_strm
% 0.26/0.63 thf(fact_201_type__definition__strm,axiom,
% 0.26/0.63 type_d46389773_sf_sz @ freche782854530_sf_sz @ freche1046279700_sf_sz @ ( collect_trm_sf_sz @ dfree_sf_sz ) ).
% 0.26/0.63
% 0.26/0.63 % type_definition_strm
% 0.26/0.63 thf(fact_202_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.26/0.63 ! [P: list_f1238882004_sc_sz > list_f1238882004_sc_sz > $o,X: list_f1238882004_sc_sz,Y: list_f1238882004_sc_sz,A2: produc866628903_sc_sz] :
% 0.26/0.63 ( ( P @ X @ Y )
% 0.26/0.63 => ( ( A2
% 0.26/0.63 = ( produc1822718231_sc_sz @ X @ Y ) )
% 0.26/0.63 => ( P @ ( produc548504323_sc_sz @ A2 ) @ ( produc4753477_sc_sz @ A2 ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % BNF_Greatest_Fixpoint.subst_Pair
% 0.26/0.63 thf(fact_203_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.26/0.63 ! [P: set_Fi291318197eal_sz > set_Fi291318197eal_sz > $o,X: set_Fi291318197eal_sz,Y: set_Fi291318197eal_sz,A2: produc1241881959eal_sz] :
% 0.26/0.63 ( ( P @ X @ Y )
% 0.26/0.63 => ( ( A2
% 0.26/0.63 = ( produc1235791063eal_sz @ X @ Y ) )
% 0.26/0.63 => ( P @ ( produc286845635eal_sz @ A2 ) @ ( produc1746886149eal_sz @ A2 ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % BNF_Greatest_Fixpoint.subst_Pair
% 0.26/0.63 thf(fact_204_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.26/0.63 ! [P: bounde472938360z_real > bounde472938360z_real > $o,X: bounde472938360z_real,Y: bounde472938360z_real,A2: produc1892666919z_real] :
% 0.26/0.63 ( ( P @ X @ Y )
% 0.26/0.63 => ( ( A2
% 0.26/0.63 = ( produc784663575z_real @ X @ Y ) )
% 0.26/0.63 => ( P @ ( produc870616579z_real @ A2 ) @ ( produc1422611269z_real @ A2 ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % BNF_Greatest_Fixpoint.subst_Pair
% 0.26/0.63 thf(fact_205_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.26/0.63 ! [P: finite824932053eal_sz > finite824932053eal_sz > $o,X: finite824932053eal_sz,Y: finite824932053eal_sz,A2: produc1149990247eal_sz] :
% 0.26/0.63 ( ( P @ X @ Y )
% 0.26/0.63 => ( ( A2
% 0.26/0.63 = ( produc1308130519eal_sz @ X @ Y ) )
% 0.26/0.63 => ( P @ ( produc1111759555eal_sz @ A2 ) @ ( produc1269210629eal_sz @ A2 ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % BNF_Greatest_Fixpoint.subst_Pair
% 0.26/0.63 thf(fact_206_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.26/0.63 ! [P: denota610675952t_unit > produc866628903_sc_sz > $o,X: denota610675952t_unit,Y: produc866628903_sc_sz,A2: produc1821101996_sc_sz] :
% 0.26/0.63 ( ( P @ X @ Y )
% 0.26/0.63 => ( ( A2
% 0.26/0.63 = ( produc789536734_sc_sz @ X @ Y ) )
% 0.26/0.63 => ( P @ ( produc1503602930_sc_sz @ A2 ) @ ( produc974239792_sc_sz @ A2 ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % BNF_Greatest_Fixpoint.subst_Pair
% 0.26/0.63 thf(fact_207_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.26/0.63 ! [P: finite1398487019real_c > finite1398487019real_c > $o,X: finite1398487019real_c,Y: finite1398487019real_c,A2: produc190496183real_c] :
% 0.26/0.63 ( ( P @ X @ Y )
% 0.26/0.63 => ( ( A2
% 0.26/0.63 = ( produc394644079real_c @ X @ Y ) )
% 0.26/0.63 => ( P @ ( produc2010422875real_c @ A2 ) @ ( produc314122909real_c @ A2 ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % BNF_Greatest_Fixpoint.subst_Pair
% 0.26/0.63 thf(fact_208_conjI__realizer,axiom,
% 0.26/0.63 ! [P: list_f1238882004_sc_sz > $o,P2: list_f1238882004_sc_sz,Q: list_f1238882004_sc_sz > $o,Q2: list_f1238882004_sc_sz] :
% 0.26/0.63 ( ( P @ P2 )
% 0.26/0.63 => ( ( Q @ Q2 )
% 0.26/0.63 => ( ( P @ ( produc548504323_sc_sz @ ( produc1822718231_sc_sz @ P2 @ Q2 ) ) )
% 0.26/0.63 & ( Q @ ( produc4753477_sc_sz @ ( produc1822718231_sc_sz @ P2 @ Q2 ) ) ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % conjI_realizer
% 0.26/0.63 thf(fact_209_conjI__realizer,axiom,
% 0.26/0.63 ! [P: set_Fi291318197eal_sz > $o,P2: set_Fi291318197eal_sz,Q: set_Fi291318197eal_sz > $o,Q2: set_Fi291318197eal_sz] :
% 0.26/0.63 ( ( P @ P2 )
% 0.26/0.63 => ( ( Q @ Q2 )
% 0.26/0.63 => ( ( P @ ( produc286845635eal_sz @ ( produc1235791063eal_sz @ P2 @ Q2 ) ) )
% 0.26/0.63 & ( Q @ ( produc1746886149eal_sz @ ( produc1235791063eal_sz @ P2 @ Q2 ) ) ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % conjI_realizer
% 0.26/0.63 thf(fact_210_conjI__realizer,axiom,
% 0.26/0.63 ! [P: bounde472938360z_real > $o,P2: bounde472938360z_real,Q: bounde472938360z_real > $o,Q2: bounde472938360z_real] :
% 0.26/0.63 ( ( P @ P2 )
% 0.26/0.63 => ( ( Q @ Q2 )
% 0.26/0.63 => ( ( P @ ( produc870616579z_real @ ( produc784663575z_real @ P2 @ Q2 ) ) )
% 0.26/0.63 & ( Q @ ( produc1422611269z_real @ ( produc784663575z_real @ P2 @ Q2 ) ) ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % conjI_realizer
% 0.26/0.63 thf(fact_211_conjI__realizer,axiom,
% 0.26/0.63 ! [P: finite824932053eal_sz > $o,P2: finite824932053eal_sz,Q: finite824932053eal_sz > $o,Q2: finite824932053eal_sz] :
% 0.26/0.63 ( ( P @ P2 )
% 0.26/0.63 => ( ( Q @ Q2 )
% 0.26/0.63 => ( ( P @ ( produc1111759555eal_sz @ ( produc1308130519eal_sz @ P2 @ Q2 ) ) )
% 0.26/0.63 & ( Q @ ( produc1269210629eal_sz @ ( produc1308130519eal_sz @ P2 @ Q2 ) ) ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % conjI_realizer
% 0.26/0.63 thf(fact_212_conjI__realizer,axiom,
% 0.26/0.63 ! [P: denota610675952t_unit > $o,P2: denota610675952t_unit,Q: produc866628903_sc_sz > $o,Q2: produc866628903_sc_sz] :
% 0.26/0.63 ( ( P @ P2 )
% 0.26/0.63 => ( ( Q @ Q2 )
% 0.26/0.63 => ( ( P @ ( produc1503602930_sc_sz @ ( produc789536734_sc_sz @ P2 @ Q2 ) ) )
% 0.26/0.63 & ( Q @ ( produc974239792_sc_sz @ ( produc789536734_sc_sz @ P2 @ Q2 ) ) ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % conjI_realizer
% 0.26/0.63 thf(fact_213_conjI__realizer,axiom,
% 0.26/0.63 ! [P: finite1398487019real_c > $o,P2: finite1398487019real_c,Q: finite1398487019real_c > $o,Q2: finite1398487019real_c] :
% 0.26/0.63 ( ( P @ P2 )
% 0.26/0.63 => ( ( Q @ Q2 )
% 0.26/0.63 => ( ( P @ ( produc2010422875real_c @ ( produc394644079real_c @ P2 @ Q2 ) ) )
% 0.26/0.63 & ( Q @ ( produc314122909real_c @ ( produc394644079real_c @ P2 @ Q2 ) ) ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % conjI_realizer
% 0.26/0.63 thf(fact_214_exI__realizer,axiom,
% 0.26/0.63 ! [P: list_f1238882004_sc_sz > list_f1238882004_sc_sz > $o,Y: list_f1238882004_sc_sz,X: list_f1238882004_sc_sz] :
% 0.26/0.63 ( ( P @ Y @ X )
% 0.26/0.63 => ( P @ ( produc4753477_sc_sz @ ( produc1822718231_sc_sz @ X @ Y ) ) @ ( produc548504323_sc_sz @ ( produc1822718231_sc_sz @ X @ Y ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % exI_realizer
% 0.26/0.63 thf(fact_215_exI__realizer,axiom,
% 0.26/0.63 ! [P: set_Fi291318197eal_sz > set_Fi291318197eal_sz > $o,Y: set_Fi291318197eal_sz,X: set_Fi291318197eal_sz] :
% 0.26/0.63 ( ( P @ Y @ X )
% 0.26/0.63 => ( P @ ( produc1746886149eal_sz @ ( produc1235791063eal_sz @ X @ Y ) ) @ ( produc286845635eal_sz @ ( produc1235791063eal_sz @ X @ Y ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % exI_realizer
% 0.26/0.63 thf(fact_216_exI__realizer,axiom,
% 0.26/0.63 ! [P: bounde472938360z_real > bounde472938360z_real > $o,Y: bounde472938360z_real,X: bounde472938360z_real] :
% 0.26/0.63 ( ( P @ Y @ X )
% 0.26/0.63 => ( P @ ( produc1422611269z_real @ ( produc784663575z_real @ X @ Y ) ) @ ( produc870616579z_real @ ( produc784663575z_real @ X @ Y ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % exI_realizer
% 0.26/0.63 thf(fact_217_exI__realizer,axiom,
% 0.26/0.63 ! [P: finite824932053eal_sz > finite824932053eal_sz > $o,Y: finite824932053eal_sz,X: finite824932053eal_sz] :
% 0.26/0.63 ( ( P @ Y @ X )
% 0.26/0.63 => ( P @ ( produc1269210629eal_sz @ ( produc1308130519eal_sz @ X @ Y ) ) @ ( produc1111759555eal_sz @ ( produc1308130519eal_sz @ X @ Y ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % exI_realizer
% 0.26/0.63 thf(fact_218_exI__realizer,axiom,
% 0.26/0.63 ! [P: produc866628903_sc_sz > denota610675952t_unit > $o,Y: produc866628903_sc_sz,X: denota610675952t_unit] :
% 0.26/0.63 ( ( P @ Y @ X )
% 0.26/0.63 => ( P @ ( produc974239792_sc_sz @ ( produc789536734_sc_sz @ X @ Y ) ) @ ( produc1503602930_sc_sz @ ( produc789536734_sc_sz @ X @ Y ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % exI_realizer
% 0.26/0.63 thf(fact_219_exI__realizer,axiom,
% 0.26/0.63 ! [P: finite1398487019real_c > finite1398487019real_c > $o,Y: finite1398487019real_c,X: finite1398487019real_c] :
% 0.26/0.63 ( ( P @ Y @ X )
% 0.26/0.63 => ( P @ ( produc314122909real_c @ ( produc394644079real_c @ X @ Y ) ) @ ( produc2010422875real_c @ ( produc394644079real_c @ X @ Y ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % exI_realizer
% 0.26/0.63 thf(fact_220_less__eq__prod__def,axiom,
% 0.26/0.63 ( ord_le850691415real_c
% 0.26/0.63 = ( ^ [X2: produc190496183real_c,Y2: produc190496183real_c] :
% 0.26/0.63 ( ( ord_le775706699real_c @ ( produc2010422875real_c @ X2 ) @ ( produc2010422875real_c @ Y2 ) )
% 0.26/0.63 & ( ord_le775706699real_c @ ( produc314122909real_c @ X2 ) @ ( produc314122909real_c @ Y2 ) ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % less_eq_prod_def
% 0.26/0.63 thf(fact_221_less__eq__prod__def,axiom,
% 0.26/0.63 ( ord_le486764743_set_a
% 0.26/0.63 = ( ^ [X2: produc1691597095_set_a,Y2: produc1691597095_set_a] :
% 0.26/0.63 ( ( ord_less_eq_set_a @ ( produc1926412547_set_a @ X2 ) @ ( produc1926412547_set_a @ Y2 ) )
% 0.26/0.63 & ( ord_less_eq_set_a @ ( produc918972485_set_a @ X2 ) @ ( produc918972485_set_a @ Y2 ) ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % less_eq_prod_def
% 0.26/0.63 thf(fact_222_less__eq__prod__def,axiom,
% 0.26/0.63 ( ord_le501349868_a_a_o
% 0.26/0.63 = ( ^ [X2: produc1989635468_a_a_o,Y2: produc1989635468_a_a_o] :
% 0.26/0.63 ( ( ord_less_eq_set_a @ ( produc1911461786_a_a_o @ X2 ) @ ( produc1911461786_a_a_o @ Y2 ) )
% 0.26/0.63 & ( ord_less_eq_a_o @ ( produc23639768_a_a_o @ X2 ) @ ( produc23639768_a_a_o @ Y2 ) ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % less_eq_prod_def
% 0.26/0.63 thf(fact_223_less__eq__prod__def,axiom,
% 0.26/0.63 ( ord_le72828020_set_a
% 0.26/0.63 = ( ^ [X2: produc1561113620_set_a,Y2: produc1561113620_set_a] :
% 0.26/0.63 ( ( ord_less_eq_a_o @ ( produc1045727450_set_a @ X2 ) @ ( produc1045727450_set_a @ Y2 ) )
% 0.26/0.63 & ( ord_less_eq_set_a @ ( produc1305389080_set_a @ X2 ) @ ( produc1305389080_set_a @ Y2 ) ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % less_eq_prod_def
% 0.26/0.63 thf(fact_224_less__eq__prod__def,axiom,
% 0.26/0.63 ( ord_le473656583eal_sz
% 0.26/0.63 = ( ^ [X2: produc1149990247eal_sz,Y2: produc1149990247eal_sz] :
% 0.26/0.63 ( ( ord_le787639925eal_sz @ ( produc1111759555eal_sz @ X2 ) @ ( produc1111759555eal_sz @ Y2 ) )
% 0.26/0.63 & ( ord_le787639925eal_sz @ ( produc1269210629eal_sz @ X2 ) @ ( produc1269210629eal_sz @ Y2 ) ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % less_eq_prod_def
% 0.26/0.63 thf(fact_225_less__eq__prod__def,axiom,
% 0.26/0.63 ( ord_le1883211903_o_a_o
% 0.26/0.63 = ( ^ [X2: product_prod_a_o_a_o,Y2: product_prod_a_o_a_o] :
% 0.26/0.63 ( ( ord_less_eq_a_o @ ( product_fst_a_o_a_o @ X2 ) @ ( product_fst_a_o_a_o @ Y2 ) )
% 0.26/0.63 & ( ord_less_eq_a_o @ ( product_snd_a_o_a_o @ X2 ) @ ( product_snd_a_o_a_o @ Y2 ) ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % less_eq_prod_def
% 0.26/0.63 thf(fact_226_less__eq__prod__def,axiom,
% 0.26/0.63 ( ord_le1884788375f_sz_o
% 0.26/0.63 = ( ^ [X2: produc1144880887f_sz_o,Y2: produc1144880887f_sz_o] :
% 0.26/0.63 ( ( ord_less_eq_set_a @ ( produc38604755f_sz_o @ X2 ) @ ( produc38604755f_sz_o @ Y2 ) )
% 0.26/0.63 & ( ord_le8515534f_sz_o @ ( produc407510293f_sz_o @ X2 ) @ ( produc407510293f_sz_o @ Y2 ) ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % less_eq_prod_def
% 0.26/0.63 thf(fact_227_less__eq__prod__def,axiom,
% 0.26/0.63 ( ord_le1643089911_set_a
% 0.26/0.63 = ( ^ [X2: produc903182423_set_a,Y2: produc903182423_set_a] :
% 0.26/0.63 ( ( ord_le8515534f_sz_o @ ( produc407272755_set_a @ X2 ) @ ( produc407272755_set_a @ Y2 ) )
% 0.26/0.63 & ( ord_less_eq_set_a @ ( produc776178293_set_a @ X2 ) @ ( produc776178293_set_a @ Y2 ) ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % less_eq_prod_def
% 0.26/0.63 thf(fact_228_less__eq__prod__def,axiom,
% 0.26/0.63 ( ord_le2132572860_o_a_o
% 0.26/0.63 = ( ^ [X2: produc1065634396_o_a_o,Y2: produc1065634396_o_a_o] :
% 0.26/0.63 ( ( ord_le8515534f_sz_o @ ( produc2013638506_o_a_o @ X2 ) @ ( produc2013638506_o_a_o @ Y2 ) )
% 0.26/0.63 & ( ord_less_eq_a_o @ ( produc1630531752_o_a_o @ X2 ) @ ( produc1630531752_o_a_o @ Y2 ) ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % less_eq_prod_def
% 0.26/0.63 thf(fact_229_less__eq__prod__def,axiom,
% 0.26/0.63 ( ord_le472894788f_sz_o
% 0.26/0.63 = ( ^ [X2: produc1553439972f_sz_o,Y2: produc1553439972f_sz_o] :
% 0.26/0.63 ( ( ord_less_eq_a_o @ ( produc1453865130f_sz_o @ X2 ) @ ( produc1453865130f_sz_o @ Y2 ) )
% 0.26/0.63 & ( ord_le8515534f_sz_o @ ( produc1070758376f_sz_o @ X2 ) @ ( produc1070758376f_sz_o @ Y2 ) ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % less_eq_prod_def
% 0.26/0.63 thf(fact_230_Iagree__sub,axiom,
% 0.26/0.63 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,I3: denota231621370t_unit,J: denota231621370t_unit] :
% 0.26/0.63 ( ( ord_le929608341um_b_c @ A @ B )
% 0.26/0.63 => ( ( denota69106024_a_b_c @ I3 @ J @ B )
% 0.26/0.63 => ( denota69106024_a_b_c @ I3 @ J @ A ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % Iagree_sub
% 0.26/0.63 thf(fact_231_subset__Collect__iff,axiom,
% 0.26/0.63 ! [B: set_Fi291318197eal_sz,A: set_Fi291318197eal_sz,P: finite824932053eal_sz > $o] :
% 0.26/0.63 ( ( ord_le41263445eal_sz @ B @ A )
% 0.26/0.63 => ( ( ord_le41263445eal_sz @ B
% 0.26/0.63 @ ( collec1002602816eal_sz
% 0.26/0.63 @ ^ [X2: finite824932053eal_sz] :
% 0.26/0.63 ( ( member1693951742eal_sz @ X2 @ A )
% 0.26/0.63 & ( P @ X2 ) ) ) )
% 0.26/0.63 = ( ! [X2: finite824932053eal_sz] :
% 0.26/0.63 ( ( member1693951742eal_sz @ X2 @ B )
% 0.26/0.63 => ( P @ X2 ) ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % subset_Collect_iff
% 0.26/0.63 thf(fact_232_subset__Collect__iff,axiom,
% 0.26/0.63 ! [B: set_Pr1169339874_sc_sz,A: set_Pr1169339874_sc_sz,P: produc1821101996_sc_sz > $o] :
% 0.26/0.63 ( ( ord_le1230423618_sc_sz @ B @ A )
% 0.26/0.63 => ( ( ord_le1230423618_sc_sz @ B
% 0.26/0.63 @ ( collec1199592193_sc_sz
% 0.26/0.63 @ ^ [X2: produc1821101996_sc_sz] :
% 0.26/0.63 ( ( member1057565379_sc_sz @ X2 @ A )
% 0.26/0.63 & ( P @ X2 ) ) ) )
% 0.26/0.63 = ( ! [X2: produc1821101996_sc_sz] :
% 0.26/0.63 ( ( member1057565379_sc_sz @ X2 @ B )
% 0.26/0.63 => ( P @ X2 ) ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % subset_Collect_iff
% 0.26/0.63 thf(fact_233_subset__Collect__iff,axiom,
% 0.26/0.63 ! [B: set_trm_sf_sz,A: set_trm_sf_sz,P: trm_sf_sz > $o] :
% 0.26/0.63 ( ( ord_le1697056455_sf_sz @ B @ A )
% 0.26/0.63 => ( ( ord_le1697056455_sf_sz @ B
% 0.26/0.63 @ ( collect_trm_sf_sz
% 0.26/0.63 @ ^ [X2: trm_sf_sz] :
% 0.26/0.63 ( ( member_trm_sf_sz @ X2 @ A )
% 0.26/0.63 & ( P @ X2 ) ) ) )
% 0.26/0.63 = ( ! [X2: trm_sf_sz] :
% 0.26/0.63 ( ( member_trm_sf_sz @ X2 @ B )
% 0.26/0.63 => ( P @ X2 ) ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % subset_Collect_iff
% 0.26/0.63 thf(fact_234_subset__Collect__iff,axiom,
% 0.26/0.63 ! [B: set_trm_a_c,A: set_trm_a_c,P: trm_a_c > $o] :
% 0.26/0.63 ( ( ord_le1369644495rm_a_c @ B @ A )
% 0.26/0.63 => ( ( ord_le1369644495rm_a_c @ B
% 0.26/0.63 @ ( collect_trm_a_c
% 0.26/0.63 @ ^ [X2: trm_a_c] :
% 0.26/0.63 ( ( member_trm_a_c @ X2 @ A )
% 0.26/0.63 & ( P @ X2 ) ) ) )
% 0.26/0.63 = ( ! [X2: trm_a_c] :
% 0.26/0.63 ( ( member_trm_a_c @ X2 @ B )
% 0.26/0.63 => ( P @ X2 ) ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % subset_Collect_iff
% 0.26/0.63 thf(fact_235_subset__Collect__iff,axiom,
% 0.26/0.63 ! [B: set_a,A: set_a,P: a > $o] :
% 0.26/0.63 ( ( ord_less_eq_set_a @ B @ A )
% 0.26/0.63 => ( ( ord_less_eq_set_a @ B
% 0.26/0.63 @ ( collect_a
% 0.26/0.63 @ ^ [X2: a] :
% 0.26/0.63 ( ( member_a @ X2 @ A )
% 0.26/0.63 & ( P @ X2 ) ) ) )
% 0.26/0.63 = ( ! [X2: a] :
% 0.26/0.63 ( ( member_a @ X2 @ B )
% 0.26/0.63 => ( P @ X2 ) ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % subset_Collect_iff
% 0.26/0.63 thf(fact_236_subset__Collect__iff,axiom,
% 0.26/0.63 ! [B: set_Su1783761653um_b_c,A: set_Su1783761653um_b_c,P: sum_su737395349um_b_c > $o] :
% 0.26/0.63 ( ( ord_le929608341um_b_c @ B @ A )
% 0.26/0.63 => ( ( ord_le929608341um_b_c @ B
% 0.26/0.63 @ ( collec2086029184um_b_c
% 0.26/0.63 @ ^ [X2: sum_su737395349um_b_c] :
% 0.26/0.63 ( ( member1893232190um_b_c @ X2 @ A )
% 0.26/0.63 & ( P @ X2 ) ) ) )
% 0.26/0.63 = ( ! [X2: sum_su737395349um_b_c] :
% 0.26/0.63 ( ( member1893232190um_b_c @ X2 @ B )
% 0.26/0.63 => ( P @ X2 ) ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % subset_Collect_iff
% 0.26/0.63 thf(fact_237_subset__CollectI,axiom,
% 0.26/0.63 ! [B: set_Fi291318197eal_sz,A: set_Fi291318197eal_sz,Q: finite824932053eal_sz > $o,P: finite824932053eal_sz > $o] :
% 0.26/0.63 ( ( ord_le41263445eal_sz @ B @ A )
% 0.26/0.63 => ( ! [X3: finite824932053eal_sz] :
% 0.26/0.63 ( ( member1693951742eal_sz @ X3 @ B )
% 0.26/0.63 => ( ( Q @ X3 )
% 0.26/0.63 => ( P @ X3 ) ) )
% 0.26/0.63 => ( ord_le41263445eal_sz
% 0.26/0.63 @ ( collec1002602816eal_sz
% 0.26/0.63 @ ^ [X2: finite824932053eal_sz] :
% 0.26/0.63 ( ( member1693951742eal_sz @ X2 @ B )
% 0.26/0.63 & ( Q @ X2 ) ) )
% 0.26/0.63 @ ( collec1002602816eal_sz
% 0.26/0.63 @ ^ [X2: finite824932053eal_sz] :
% 0.26/0.63 ( ( member1693951742eal_sz @ X2 @ A )
% 0.26/0.63 & ( P @ X2 ) ) ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % subset_CollectI
% 0.26/0.63 thf(fact_238_subset__CollectI,axiom,
% 0.26/0.63 ! [B: set_Pr1169339874_sc_sz,A: set_Pr1169339874_sc_sz,Q: produc1821101996_sc_sz > $o,P: produc1821101996_sc_sz > $o] :
% 0.26/0.63 ( ( ord_le1230423618_sc_sz @ B @ A )
% 0.26/0.63 => ( ! [X3: produc1821101996_sc_sz] :
% 0.26/0.63 ( ( member1057565379_sc_sz @ X3 @ B )
% 0.26/0.63 => ( ( Q @ X3 )
% 0.26/0.63 => ( P @ X3 ) ) )
% 0.26/0.63 => ( ord_le1230423618_sc_sz
% 0.26/0.63 @ ( collec1199592193_sc_sz
% 0.26/0.63 @ ^ [X2: produc1821101996_sc_sz] :
% 0.26/0.63 ( ( member1057565379_sc_sz @ X2 @ B )
% 0.26/0.63 & ( Q @ X2 ) ) )
% 0.26/0.63 @ ( collec1199592193_sc_sz
% 0.26/0.63 @ ^ [X2: produc1821101996_sc_sz] :
% 0.26/0.63 ( ( member1057565379_sc_sz @ X2 @ A )
% 0.26/0.63 & ( P @ X2 ) ) ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % subset_CollectI
% 0.26/0.63 thf(fact_239_subset__CollectI,axiom,
% 0.26/0.63 ! [B: set_trm_sf_sz,A: set_trm_sf_sz,Q: trm_sf_sz > $o,P: trm_sf_sz > $o] :
% 0.26/0.63 ( ( ord_le1697056455_sf_sz @ B @ A )
% 0.26/0.63 => ( ! [X3: trm_sf_sz] :
% 0.26/0.63 ( ( member_trm_sf_sz @ X3 @ B )
% 0.26/0.63 => ( ( Q @ X3 )
% 0.26/0.63 => ( P @ X3 ) ) )
% 0.26/0.63 => ( ord_le1697056455_sf_sz
% 0.26/0.63 @ ( collect_trm_sf_sz
% 0.26/0.63 @ ^ [X2: trm_sf_sz] :
% 0.26/0.63 ( ( member_trm_sf_sz @ X2 @ B )
% 0.26/0.63 & ( Q @ X2 ) ) )
% 0.26/0.63 @ ( collect_trm_sf_sz
% 0.26/0.63 @ ^ [X2: trm_sf_sz] :
% 0.26/0.63 ( ( member_trm_sf_sz @ X2 @ A )
% 0.26/0.63 & ( P @ X2 ) ) ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % subset_CollectI
% 0.26/0.63 thf(fact_240_subset__CollectI,axiom,
% 0.26/0.63 ! [B: set_trm_a_c,A: set_trm_a_c,Q: trm_a_c > $o,P: trm_a_c > $o] :
% 0.26/0.63 ( ( ord_le1369644495rm_a_c @ B @ A )
% 0.26/0.63 => ( ! [X3: trm_a_c] :
% 0.26/0.63 ( ( member_trm_a_c @ X3 @ B )
% 0.26/0.63 => ( ( Q @ X3 )
% 0.26/0.63 => ( P @ X3 ) ) )
% 0.26/0.63 => ( ord_le1369644495rm_a_c
% 0.26/0.63 @ ( collect_trm_a_c
% 0.26/0.63 @ ^ [X2: trm_a_c] :
% 0.26/0.63 ( ( member_trm_a_c @ X2 @ B )
% 0.26/0.63 & ( Q @ X2 ) ) )
% 0.26/0.63 @ ( collect_trm_a_c
% 0.26/0.63 @ ^ [X2: trm_a_c] :
% 0.26/0.63 ( ( member_trm_a_c @ X2 @ A )
% 0.26/0.63 & ( P @ X2 ) ) ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % subset_CollectI
% 0.26/0.63 thf(fact_241_subset__CollectI,axiom,
% 0.26/0.63 ! [B: set_a,A: set_a,Q: a > $o,P: a > $o] :
% 0.26/0.63 ( ( ord_less_eq_set_a @ B @ A )
% 0.26/0.63 => ( ! [X3: a] :
% 0.26/0.63 ( ( member_a @ X3 @ B )
% 0.26/0.63 => ( ( Q @ X3 )
% 0.26/0.63 => ( P @ X3 ) ) )
% 0.26/0.63 => ( ord_less_eq_set_a
% 0.26/0.63 @ ( collect_a
% 0.26/0.63 @ ^ [X2: a] :
% 0.26/0.63 ( ( member_a @ X2 @ B )
% 0.26/0.63 & ( Q @ X2 ) ) )
% 0.26/0.63 @ ( collect_a
% 0.26/0.63 @ ^ [X2: a] :
% 0.26/0.63 ( ( member_a @ X2 @ A )
% 0.26/0.63 & ( P @ X2 ) ) ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % subset_CollectI
% 0.26/0.63 thf(fact_242_subset__CollectI,axiom,
% 0.26/0.63 ! [B: set_Su1783761653um_b_c,A: set_Su1783761653um_b_c,Q: sum_su737395349um_b_c > $o,P: sum_su737395349um_b_c > $o] :
% 0.26/0.63 ( ( ord_le929608341um_b_c @ B @ A )
% 0.26/0.63 => ( ! [X3: sum_su737395349um_b_c] :
% 0.26/0.63 ( ( member1893232190um_b_c @ X3 @ B )
% 0.26/0.63 => ( ( Q @ X3 )
% 0.26/0.63 => ( P @ X3 ) ) )
% 0.26/0.63 => ( ord_le929608341um_b_c
% 0.26/0.63 @ ( collec2086029184um_b_c
% 0.26/0.63 @ ^ [X2: sum_su737395349um_b_c] :
% 0.26/0.63 ( ( member1893232190um_b_c @ X2 @ B )
% 0.26/0.63 & ( Q @ X2 ) ) )
% 0.26/0.63 @ ( collec2086029184um_b_c
% 0.26/0.63 @ ^ [X2: sum_su737395349um_b_c] :
% 0.26/0.63 ( ( member1893232190um_b_c @ X2 @ A )
% 0.26/0.63 & ( P @ X2 ) ) ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % subset_CollectI
% 0.26/0.63 thf(fact_243_Pair__mono,axiom,
% 0.26/0.63 ! [X: set_a,X4: set_a,Y: set_a,Y5: set_a] :
% 0.26/0.63 ( ( ord_less_eq_set_a @ X @ X4 )
% 0.26/0.63 => ( ( ord_less_eq_set_a @ Y @ Y5 )
% 0.26/0.63 => ( ord_le486764743_set_a @ ( produc1928581911_set_a @ X @ Y ) @ ( produc1928581911_set_a @ X4 @ Y5 ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % Pair_mono
% 0.26/0.63 thf(fact_244_Pair__mono,axiom,
% 0.26/0.63 ! [X: set_a,X4: set_a,Y: a > $o,Y5: a > $o] :
% 0.26/0.63 ( ( ord_less_eq_set_a @ X @ X4 )
% 0.26/0.63 => ( ( ord_less_eq_a_o @ Y @ Y5 )
% 0.26/0.63 => ( ord_le501349868_a_a_o @ ( produc634809990_a_a_o @ X @ Y ) @ ( produc634809990_a_a_o @ X4 @ Y5 ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % Pair_mono
% 0.26/0.63 thf(fact_245_Pair__mono,axiom,
% 0.26/0.63 ! [X: a > $o,X4: a > $o,Y: set_a,Y5: set_a] :
% 0.26/0.63 ( ( ord_less_eq_a_o @ X @ X4 )
% 0.26/0.63 => ( ( ord_less_eq_set_a @ Y @ Y5 )
% 0.26/0.63 => ( ord_le72828020_set_a @ ( produc1916559302_set_a @ X @ Y ) @ ( produc1916559302_set_a @ X4 @ Y5 ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % Pair_mono
% 0.26/0.63 thf(fact_246_Pair__mono,axiom,
% 0.26/0.63 ! [X: finite1398487019real_c,X4: finite1398487019real_c,Y: finite1398487019real_c,Y5: finite1398487019real_c] :
% 0.26/0.63 ( ( ord_le775706699real_c @ X @ X4 )
% 0.26/0.63 => ( ( ord_le775706699real_c @ Y @ Y5 )
% 0.26/0.63 => ( ord_le850691415real_c @ ( produc394644079real_c @ X @ Y ) @ ( produc394644079real_c @ X4 @ Y5 ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % Pair_mono
% 0.26/0.63 thf(fact_247_Pair__mono,axiom,
% 0.26/0.63 ! [X: a > $o,X4: a > $o,Y: a > $o,Y5: a > $o] :
% 0.26/0.63 ( ( ord_less_eq_a_o @ X @ X4 )
% 0.26/0.63 => ( ( ord_less_eq_a_o @ Y @ Y5 )
% 0.26/0.63 => ( ord_le1883211903_o_a_o @ ( product_Pair_a_o_a_o @ X @ Y ) @ ( product_Pair_a_o_a_o @ X4 @ Y5 ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % Pair_mono
% 0.26/0.63 thf(fact_248_Pair__mono,axiom,
% 0.26/0.63 ! [X: set_Fi291318197eal_sz,X4: set_Fi291318197eal_sz,Y: set_Fi291318197eal_sz,Y5: set_Fi291318197eal_sz] :
% 0.26/0.63 ( ( ord_le41263445eal_sz @ X @ X4 )
% 0.26/0.63 => ( ( ord_le41263445eal_sz @ Y @ Y5 )
% 0.26/0.63 => ( ord_le978883847eal_sz @ ( produc1235791063eal_sz @ X @ Y ) @ ( produc1235791063eal_sz @ X4 @ Y5 ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % Pair_mono
% 0.26/0.63 thf(fact_249_Pair__mono,axiom,
% 0.26/0.63 ! [X: set_a,X4: set_a,Y: trm_sf_sz > trm_sf_sz > $o,Y5: trm_sf_sz > trm_sf_sz > $o] :
% 0.26/0.63 ( ( ord_less_eq_set_a @ X @ X4 )
% 0.26/0.63 => ( ( ord_le8515534f_sz_o @ Y @ Y5 )
% 0.26/0.63 => ( ord_le1884788375f_sz_o @ ( produc1174558183f_sz_o @ X @ Y ) @ ( produc1174558183f_sz_o @ X4 @ Y5 ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % Pair_mono
% 0.26/0.63 thf(fact_250_Pair__mono,axiom,
% 0.26/0.63 ! [X: trm_sf_sz > trm_sf_sz > $o,X4: trm_sf_sz > trm_sf_sz > $o,Y: set_a,Y5: set_a] :
% 0.26/0.63 ( ( ord_le8515534f_sz_o @ X @ X4 )
% 0.26/0.63 => ( ( ord_less_eq_set_a @ Y @ Y5 )
% 0.26/0.63 => ( ord_le1643089911_set_a @ ( produc1543226183_set_a @ X @ Y ) @ ( produc1543226183_set_a @ X4 @ Y5 ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % Pair_mono
% 0.26/0.63 thf(fact_251_Pair__mono,axiom,
% 0.26/0.63 ! [X: trm_sf_sz > trm_sf_sz > $o,X4: trm_sf_sz > trm_sf_sz > $o,Y: a > $o,Y5: a > $o] :
% 0.26/0.63 ( ( ord_le8515534f_sz_o @ X @ X4 )
% 0.26/0.63 => ( ( ord_less_eq_a_o @ Y @ Y5 )
% 0.26/0.63 => ( ord_le2132572860_o_a_o @ ( produc1152932438_o_a_o @ X @ Y ) @ ( produc1152932438_o_a_o @ X4 @ Y5 ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % Pair_mono
% 0.26/0.63 thf(fact_252_Pair__mono,axiom,
% 0.26/0.63 ! [X: a > $o,X4: a > $o,Y: trm_sf_sz > trm_sf_sz > $o,Y5: trm_sf_sz > trm_sf_sz > $o] :
% 0.26/0.63 ( ( ord_less_eq_a_o @ X @ X4 )
% 0.26/0.63 => ( ( ord_le8515534f_sz_o @ Y @ Y5 )
% 0.26/0.63 => ( ord_le472894788f_sz_o @ ( produc593159062f_sz_o @ X @ Y ) @ ( produc593159062f_sz_o @ X4 @ Y5 ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % Pair_mono
% 0.26/0.63 thf(fact_253_fst__mono,axiom,
% 0.26/0.63 ! [X: produc1149990247eal_sz,Y: produc1149990247eal_sz] :
% 0.26/0.63 ( ( ord_le473656583eal_sz @ X @ Y )
% 0.26/0.63 => ( ord_le787639925eal_sz @ ( produc1111759555eal_sz @ X ) @ ( produc1111759555eal_sz @ Y ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % fst_mono
% 0.26/0.63 thf(fact_254_fst__mono,axiom,
% 0.26/0.63 ! [X: produc190496183real_c,Y: produc190496183real_c] :
% 0.26/0.63 ( ( ord_le850691415real_c @ X @ Y )
% 0.26/0.63 => ( ord_le775706699real_c @ ( produc2010422875real_c @ X ) @ ( produc2010422875real_c @ Y ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % fst_mono
% 0.26/0.63 thf(fact_255_snd__mono,axiom,
% 0.26/0.63 ! [X: produc1149990247eal_sz,Y: produc1149990247eal_sz] :
% 0.26/0.63 ( ( ord_le473656583eal_sz @ X @ Y )
% 0.26/0.63 => ( ord_le787639925eal_sz @ ( produc1269210629eal_sz @ X ) @ ( produc1269210629eal_sz @ Y ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % snd_mono
% 0.26/0.63 thf(fact_256_snd__mono,axiom,
% 0.26/0.63 ! [X: produc190496183real_c,Y: produc190496183real_c] :
% 0.26/0.63 ( ( ord_le850691415real_c @ X @ Y )
% 0.26/0.63 => ( ord_le775706699real_c @ ( produc314122909real_c @ X ) @ ( produc314122909real_c @ Y ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % snd_mono
% 0.26/0.63 thf(fact_257_exE__realizer_H,axiom,
% 0.26/0.63 ! [P: finite824932053eal_sz > finite824932053eal_sz > $o,P2: produc1149990247eal_sz] :
% 0.26/0.63 ( ( P @ ( produc1269210629eal_sz @ P2 ) @ ( produc1111759555eal_sz @ P2 ) )
% 0.26/0.63 => ~ ! [X3: finite824932053eal_sz,Y3: finite824932053eal_sz] :
% 0.26/0.63 ~ ( P @ Y3 @ X3 ) ) ).
% 0.26/0.63
% 0.26/0.63 % exE_realizer'
% 0.26/0.63 thf(fact_258_exE__realizer_H,axiom,
% 0.26/0.63 ! [P: produc866628903_sc_sz > denota610675952t_unit > $o,P2: produc1821101996_sc_sz] :
% 0.26/0.63 ( ( P @ ( produc974239792_sc_sz @ P2 ) @ ( produc1503602930_sc_sz @ P2 ) )
% 0.26/0.63 => ~ ! [X3: denota610675952t_unit,Y3: produc866628903_sc_sz] :
% 0.26/0.63 ~ ( P @ Y3 @ X3 ) ) ).
% 0.26/0.63
% 0.26/0.63 % exE_realizer'
% 0.26/0.63 thf(fact_259_exE__realizer_H,axiom,
% 0.26/0.63 ! [P: finite1398487019real_c > finite1398487019real_c > $o,P2: produc190496183real_c] :
% 0.26/0.63 ( ( P @ ( produc314122909real_c @ P2 ) @ ( produc2010422875real_c @ P2 ) )
% 0.26/0.63 => ~ ! [X3: finite1398487019real_c,Y3: finite1398487019real_c] :
% 0.26/0.63 ~ ( P @ Y3 @ X3 ) ) ).
% 0.26/0.63
% 0.26/0.63 % exE_realizer'
% 0.26/0.63 thf(fact_260_sum_Oinject_I1_J,axiom,
% 0.26/0.63 ! [X1: a,Y1: a] :
% 0.26/0.63 ( ( ( sum_In2139678582um_b_c @ X1 )
% 0.26/0.63 = ( sum_In2139678582um_b_c @ Y1 ) )
% 0.26/0.63 = ( X1 = Y1 ) ) ).
% 0.26/0.63
% 0.26/0.63 % sum.inject(1)
% 0.26/0.63 thf(fact_261_old_Osum_Oinject_I1_J,axiom,
% 0.26/0.63 ! [A2: a,A3: a] :
% 0.26/0.63 ( ( ( sum_In2139678582um_b_c @ A2 )
% 0.26/0.63 = ( sum_In2139678582um_b_c @ A3 ) )
% 0.26/0.63 = ( A2 = A3 ) ) ).
% 0.26/0.63
% 0.26/0.63 % old.sum.inject(1)
% 0.26/0.63 thf(fact_262_good__interp__inverse,axiom,
% 0.26/0.63 ! [Y: denota231621370t_unit] :
% 0.26/0.63 ( ( member1777622435t_unit @ Y @ ( collec451781861t_unit @ denota258389581_a_b_c ) )
% 0.26/0.63 => ( ( freche1608036107_a_b_c @ ( freche1473475332_a_b_c @ Y ) )
% 0.26/0.63 = Y ) ) ).
% 0.26/0.63
% 0.26/0.63 % good_interp_inverse
% 0.26/0.63 thf(fact_263_good__interp__inverse,axiom,
% 0.26/0.63 ! [Y: denota610675952t_unit] :
% 0.26/0.63 ( ( member754147591t_unit @ Y @ ( collec1767975749t_unit @ denota1579475975_sc_sz ) )
% 0.26/0.63 => ( ( freche1421597129_sc_sz @ ( freche1784963216_sc_sz @ Y ) )
% 0.26/0.63 = Y ) ) ).
% 0.26/0.63
% 0.26/0.63 % good_interp_inverse
% 0.26/0.63 thf(fact_264_f0__def,axiom,
% 0.26/0.63 ( f0_sf_sz
% 0.26/0.63 = ( ^ [F: sf] : ( function_sf_sz @ F @ empty_sz_sf ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % f0_def
% 0.26/0.63 thf(fact_265_subsetI,axiom,
% 0.26/0.63 ! [A: set_Fi291318197eal_sz,B: set_Fi291318197eal_sz] :
% 0.26/0.63 ( ! [X3: finite824932053eal_sz] :
% 0.26/0.63 ( ( member1693951742eal_sz @ X3 @ A )
% 0.26/0.63 => ( member1693951742eal_sz @ X3 @ B ) )
% 0.26/0.63 => ( ord_le41263445eal_sz @ A @ B ) ) ).
% 0.26/0.63
% 0.26/0.63 % subsetI
% 0.26/0.63 thf(fact_266_subsetI,axiom,
% 0.26/0.63 ! [A: set_Pr1169339874_sc_sz,B: set_Pr1169339874_sc_sz] :
% 0.26/0.63 ( ! [X3: produc1821101996_sc_sz] :
% 0.26/0.63 ( ( member1057565379_sc_sz @ X3 @ A )
% 0.26/0.63 => ( member1057565379_sc_sz @ X3 @ B ) )
% 0.26/0.63 => ( ord_le1230423618_sc_sz @ A @ B ) ) ).
% 0.26/0.63
% 0.26/0.63 % subsetI
% 0.26/0.63 thf(fact_267_subsetI,axiom,
% 0.26/0.63 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c] :
% 0.26/0.63 ( ! [X3: sum_su737395349um_b_c] :
% 0.26/0.63 ( ( member1893232190um_b_c @ X3 @ A )
% 0.26/0.63 => ( member1893232190um_b_c @ X3 @ B ) )
% 0.26/0.63 => ( ord_le929608341um_b_c @ A @ B ) ) ).
% 0.26/0.63
% 0.26/0.63 % subsetI
% 0.26/0.63 thf(fact_268_subsetI,axiom,
% 0.26/0.63 ! [A: set_trm_sf_sz,B: set_trm_sf_sz] :
% 0.26/0.63 ( ! [X3: trm_sf_sz] :
% 0.26/0.63 ( ( member_trm_sf_sz @ X3 @ A )
% 0.26/0.63 => ( member_trm_sf_sz @ X3 @ B ) )
% 0.26/0.63 => ( ord_le1697056455_sf_sz @ A @ B ) ) ).
% 0.26/0.63
% 0.26/0.63 % subsetI
% 0.26/0.63 thf(fact_269_subsetI,axiom,
% 0.26/0.63 ! [A: set_trm_a_c,B: set_trm_a_c] :
% 0.26/0.63 ( ! [X3: trm_a_c] :
% 0.26/0.63 ( ( member_trm_a_c @ X3 @ A )
% 0.26/0.63 => ( member_trm_a_c @ X3 @ B ) )
% 0.26/0.63 => ( ord_le1369644495rm_a_c @ A @ B ) ) ).
% 0.26/0.63
% 0.26/0.63 % subsetI
% 0.26/0.63 thf(fact_270_subsetI,axiom,
% 0.26/0.63 ! [A: set_a,B: set_a] :
% 0.26/0.63 ( ! [X3: a] :
% 0.26/0.63 ( ( member_a @ X3 @ A )
% 0.26/0.63 => ( member_a @ X3 @ B ) )
% 0.26/0.63 => ( ord_less_eq_set_a @ A @ B ) ) ).
% 0.26/0.63
% 0.26/0.63 % subsetI
% 0.26/0.63 thf(fact_271_raw__interp__induct,axiom,
% 0.26/0.63 ! [Y: denota231621370t_unit,P: denota231621370t_unit > $o] :
% 0.26/0.63 ( ( member1777622435t_unit @ Y @ ( collec451781861t_unit @ denota258389581_a_b_c ) )
% 0.26/0.63 => ( ! [X3: freche914690577_a_b_c] : ( P @ ( freche1608036107_a_b_c @ X3 ) )
% 0.26/0.63 => ( P @ Y ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % raw_interp_induct
% 0.26/0.63 thf(fact_272_raw__interp__induct,axiom,
% 0.26/0.63 ! [Y: denota610675952t_unit,P: denota610675952t_unit > $o] :
% 0.26/0.63 ( ( member754147591t_unit @ Y @ ( collec1767975749t_unit @ denota1579475975_sc_sz ) )
% 0.26/0.63 => ( ! [X3: freche2095075217_sc_sz] : ( P @ ( freche1421597129_sc_sz @ X3 ) )
% 0.26/0.63 => ( P @ Y ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % raw_interp_induct
% 0.26/0.63 thf(fact_273_raw__interp__cases,axiom,
% 0.26/0.63 ! [Y: denota231621370t_unit] :
% 0.26/0.63 ( ( member1777622435t_unit @ Y @ ( collec451781861t_unit @ denota258389581_a_b_c ) )
% 0.26/0.63 => ~ ! [X3: freche914690577_a_b_c] :
% 0.26/0.63 ( Y
% 0.26/0.63 != ( freche1608036107_a_b_c @ X3 ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % raw_interp_cases
% 0.26/0.63 thf(fact_274_raw__interp__cases,axiom,
% 0.26/0.63 ! [Y: denota610675952t_unit] :
% 0.26/0.63 ( ( member754147591t_unit @ Y @ ( collec1767975749t_unit @ denota1579475975_sc_sz ) )
% 0.26/0.63 => ~ ! [X3: freche2095075217_sc_sz] :
% 0.26/0.63 ( Y
% 0.26/0.63 != ( freche1421597129_sc_sz @ X3 ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % raw_interp_cases
% 0.26/0.63 thf(fact_275_raw__interp,axiom,
% 0.26/0.63 ! [X: freche914690577_a_b_c] : ( member1777622435t_unit @ ( freche1608036107_a_b_c @ X ) @ ( collec451781861t_unit @ denota258389581_a_b_c ) ) ).
% 0.26/0.63
% 0.26/0.63 % raw_interp
% 0.26/0.63 thf(fact_276_raw__interp,axiom,
% 0.26/0.63 ! [X: freche2095075217_sc_sz] : ( member754147591t_unit @ ( freche1421597129_sc_sz @ X ) @ ( collec1767975749t_unit @ denota1579475975_sc_sz ) ) ).
% 0.26/0.63
% 0.26/0.63 % raw_interp
% 0.26/0.63 thf(fact_277_good__interp__cases,axiom,
% 0.26/0.63 ! [X: freche914690577_a_b_c] :
% 0.26/0.63 ~ ! [Y3: denota231621370t_unit] :
% 0.26/0.63 ( ( X
% 0.26/0.63 = ( freche1473475332_a_b_c @ Y3 ) )
% 0.26/0.63 => ~ ( member1777622435t_unit @ Y3 @ ( collec451781861t_unit @ denota258389581_a_b_c ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % good_interp_cases
% 0.26/0.63 thf(fact_278_good__interp__cases,axiom,
% 0.26/0.63 ! [X: freche2095075217_sc_sz] :
% 0.26/0.63 ~ ! [Y3: denota610675952t_unit] :
% 0.26/0.63 ( ( X
% 0.26/0.63 = ( freche1784963216_sc_sz @ Y3 ) )
% 0.26/0.63 => ~ ( member754147591t_unit @ Y3 @ ( collec1767975749t_unit @ denota1579475975_sc_sz ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % good_interp_cases
% 0.26/0.63 thf(fact_279_good__interp__induct,axiom,
% 0.26/0.63 ! [P: freche914690577_a_b_c > $o,X: freche914690577_a_b_c] :
% 0.26/0.63 ( ! [Y3: denota231621370t_unit] :
% 0.26/0.63 ( ( member1777622435t_unit @ Y3 @ ( collec451781861t_unit @ denota258389581_a_b_c ) )
% 0.26/0.63 => ( P @ ( freche1473475332_a_b_c @ Y3 ) ) )
% 0.26/0.63 => ( P @ X ) ) ).
% 0.26/0.63
% 0.26/0.63 % good_interp_induct
% 0.26/0.63 thf(fact_280_good__interp__induct,axiom,
% 0.26/0.63 ! [P: freche2095075217_sc_sz > $o,X: freche2095075217_sc_sz] :
% 0.26/0.63 ( ! [Y3: denota610675952t_unit] :
% 0.26/0.63 ( ( member754147591t_unit @ Y3 @ ( collec1767975749t_unit @ denota1579475975_sc_sz ) )
% 0.26/0.63 => ( P @ ( freche1784963216_sc_sz @ Y3 ) ) )
% 0.26/0.63 => ( P @ X ) ) ).
% 0.26/0.63
% 0.26/0.63 % good_interp_induct
% 0.26/0.63 thf(fact_281_good__interp__inject,axiom,
% 0.26/0.63 ! [X: denota231621370t_unit,Y: denota231621370t_unit] :
% 0.26/0.63 ( ( member1777622435t_unit @ X @ ( collec451781861t_unit @ denota258389581_a_b_c ) )
% 0.26/0.63 => ( ( member1777622435t_unit @ Y @ ( collec451781861t_unit @ denota258389581_a_b_c ) )
% 0.26/0.63 => ( ( ( freche1473475332_a_b_c @ X )
% 0.26/0.63 = ( freche1473475332_a_b_c @ Y ) )
% 0.26/0.63 = ( X = Y ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % good_interp_inject
% 0.26/0.63 thf(fact_282_good__interp__inject,axiom,
% 0.26/0.63 ! [X: denota610675952t_unit,Y: denota610675952t_unit] :
% 0.26/0.63 ( ( member754147591t_unit @ X @ ( collec1767975749t_unit @ denota1579475975_sc_sz ) )
% 0.26/0.63 => ( ( member754147591t_unit @ Y @ ( collec1767975749t_unit @ denota1579475975_sc_sz ) )
% 0.26/0.63 => ( ( ( freche1784963216_sc_sz @ X )
% 0.26/0.63 = ( freche1784963216_sc_sz @ Y ) )
% 0.26/0.63 = ( X = Y ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % good_interp_inject
% 0.26/0.63 thf(fact_283_subset__antisym,axiom,
% 0.26/0.63 ! [A: set_a,B: set_a] :
% 0.26/0.63 ( ( ord_less_eq_set_a @ A @ B )
% 0.26/0.63 => ( ( ord_less_eq_set_a @ B @ A )
% 0.26/0.63 => ( A = B ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % subset_antisym
% 0.26/0.63 thf(fact_284_Collect__mono__iff,axiom,
% 0.26/0.63 ! [P: finite824932053eal_sz > $o,Q: finite824932053eal_sz > $o] :
% 0.26/0.63 ( ( ord_le41263445eal_sz @ ( collec1002602816eal_sz @ P ) @ ( collec1002602816eal_sz @ Q ) )
% 0.26/0.63 = ( ! [X2: finite824932053eal_sz] :
% 0.26/0.63 ( ( P @ X2 )
% 0.26/0.63 => ( Q @ X2 ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % Collect_mono_iff
% 0.26/0.63 thf(fact_285_Collect__mono__iff,axiom,
% 0.26/0.63 ! [P: produc1821101996_sc_sz > $o,Q: produc1821101996_sc_sz > $o] :
% 0.26/0.63 ( ( ord_le1230423618_sc_sz @ ( collec1199592193_sc_sz @ P ) @ ( collec1199592193_sc_sz @ Q ) )
% 0.26/0.63 = ( ! [X2: produc1821101996_sc_sz] :
% 0.26/0.63 ( ( P @ X2 )
% 0.26/0.63 => ( Q @ X2 ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % Collect_mono_iff
% 0.26/0.63 thf(fact_286_Collect__mono__iff,axiom,
% 0.26/0.63 ! [P: trm_sf_sz > $o,Q: trm_sf_sz > $o] :
% 0.26/0.63 ( ( ord_le1697056455_sf_sz @ ( collect_trm_sf_sz @ P ) @ ( collect_trm_sf_sz @ Q ) )
% 0.26/0.63 = ( ! [X2: trm_sf_sz] :
% 0.26/0.63 ( ( P @ X2 )
% 0.26/0.63 => ( Q @ X2 ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % Collect_mono_iff
% 0.26/0.63 thf(fact_287_Collect__mono__iff,axiom,
% 0.26/0.63 ! [P: trm_a_c > $o,Q: trm_a_c > $o] :
% 0.26/0.63 ( ( ord_le1369644495rm_a_c @ ( collect_trm_a_c @ P ) @ ( collect_trm_a_c @ Q ) )
% 0.26/0.63 = ( ! [X2: trm_a_c] :
% 0.26/0.63 ( ( P @ X2 )
% 0.26/0.63 => ( Q @ X2 ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % Collect_mono_iff
% 0.26/0.63 thf(fact_288_Collect__mono__iff,axiom,
% 0.26/0.63 ! [P: a > $o,Q: a > $o] :
% 0.26/0.63 ( ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) )
% 0.26/0.63 = ( ! [X2: a] :
% 0.26/0.63 ( ( P @ X2 )
% 0.26/0.63 => ( Q @ X2 ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % Collect_mono_iff
% 0.26/0.63 thf(fact_289_Collect__mono__iff,axiom,
% 0.26/0.63 ! [P: sum_su737395349um_b_c > $o,Q: sum_su737395349um_b_c > $o] :
% 0.26/0.63 ( ( ord_le929608341um_b_c @ ( collec2086029184um_b_c @ P ) @ ( collec2086029184um_b_c @ Q ) )
% 0.26/0.63 = ( ! [X2: sum_su737395349um_b_c] :
% 0.26/0.63 ( ( P @ X2 )
% 0.26/0.63 => ( Q @ X2 ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % Collect_mono_iff
% 0.26/0.63 thf(fact_290_set__eq__subset,axiom,
% 0.26/0.63 ( ( ^ [Y4: set_a,Z: set_a] : ( Y4 = Z ) )
% 0.26/0.63 = ( ^ [A5: set_a,B5: set_a] :
% 0.26/0.63 ( ( ord_less_eq_set_a @ A5 @ B5 )
% 0.26/0.63 & ( ord_less_eq_set_a @ B5 @ A5 ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % set_eq_subset
% 0.26/0.63 thf(fact_291_subset__trans,axiom,
% 0.26/0.63 ! [A: set_a,B: set_a,C3: set_a] :
% 0.26/0.63 ( ( ord_less_eq_set_a @ A @ B )
% 0.26/0.63 => ( ( ord_less_eq_set_a @ B @ C3 )
% 0.26/0.63 => ( ord_less_eq_set_a @ A @ C3 ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % subset_trans
% 0.26/0.63 thf(fact_292_Collect__mono,axiom,
% 0.26/0.63 ! [P: produc1821101996_sc_sz > $o,Q: produc1821101996_sc_sz > $o] :
% 0.26/0.63 ( ! [X3: produc1821101996_sc_sz] :
% 0.26/0.63 ( ( P @ X3 )
% 0.26/0.63 => ( Q @ X3 ) )
% 0.26/0.63 => ( ord_le1230423618_sc_sz @ ( collec1199592193_sc_sz @ P ) @ ( collec1199592193_sc_sz @ Q ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % Collect_mono
% 0.26/0.63 thf(fact_293_Collect__mono,axiom,
% 0.26/0.63 ! [P: trm_sf_sz > $o,Q: trm_sf_sz > $o] :
% 0.26/0.63 ( ! [X3: trm_sf_sz] :
% 0.26/0.63 ( ( P @ X3 )
% 0.26/0.63 => ( Q @ X3 ) )
% 0.26/0.63 => ( ord_le1697056455_sf_sz @ ( collect_trm_sf_sz @ P ) @ ( collect_trm_sf_sz @ Q ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % Collect_mono
% 0.26/0.63 thf(fact_294_Collect__mono,axiom,
% 0.26/0.63 ! [P: trm_a_c > $o,Q: trm_a_c > $o] :
% 0.26/0.63 ( ! [X3: trm_a_c] :
% 0.26/0.63 ( ( P @ X3 )
% 0.26/0.63 => ( Q @ X3 ) )
% 0.26/0.63 => ( ord_le1369644495rm_a_c @ ( collect_trm_a_c @ P ) @ ( collect_trm_a_c @ Q ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % Collect_mono
% 0.26/0.63 thf(fact_295_Collect__mono,axiom,
% 0.26/0.63 ! [P: a > $o,Q: a > $o] :
% 0.26/0.63 ( ! [X3: a] :
% 0.26/0.63 ( ( P @ X3 )
% 0.26/0.63 => ( Q @ X3 ) )
% 0.26/0.63 => ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % Collect_mono
% 0.26/0.63 thf(fact_296_Collect__mono,axiom,
% 0.26/0.63 ! [P: sum_su737395349um_b_c > $o,Q: sum_su737395349um_b_c > $o] :
% 0.26/0.63 ( ! [X3: sum_su737395349um_b_c] :
% 0.26/0.63 ( ( P @ X3 )
% 0.26/0.63 => ( Q @ X3 ) )
% 0.26/0.63 => ( ord_le929608341um_b_c @ ( collec2086029184um_b_c @ P ) @ ( collec2086029184um_b_c @ Q ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % Collect_mono
% 0.26/0.63 thf(fact_297_subset__iff,axiom,
% 0.26/0.63 ( ord_less_eq_set_a
% 0.26/0.63 = ( ^ [A5: set_a,B5: set_a] :
% 0.26/0.63 ! [T: a] :
% 0.26/0.63 ( ( member_a @ T @ A5 )
% 0.26/0.63 => ( member_a @ T @ B5 ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % subset_iff
% 0.26/0.63 thf(fact_298_subset__eq,axiom,
% 0.26/0.63 ( ord_less_eq_set_a
% 0.26/0.63 = ( ^ [A5: set_a,B5: set_a] :
% 0.26/0.63 ! [X2: a] :
% 0.26/0.63 ( ( member_a @ X2 @ A5 )
% 0.26/0.63 => ( member_a @ X2 @ B5 ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % subset_eq
% 0.26/0.63 thf(fact_299_subsetD,axiom,
% 0.26/0.63 ! [A: set_a,B: set_a,C2: a] :
% 0.26/0.63 ( ( ord_less_eq_set_a @ A @ B )
% 0.26/0.63 => ( ( member_a @ C2 @ A )
% 0.26/0.63 => ( member_a @ C2 @ B ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % subsetD
% 0.26/0.63 thf(fact_300_in__mono,axiom,
% 0.26/0.63 ! [A: set_a,B: set_a,X: a] :
% 0.26/0.63 ( ( ord_less_eq_set_a @ A @ B )
% 0.26/0.63 => ( ( member_a @ X @ A )
% 0.26/0.63 => ( member_a @ X @ B ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % in_mono
% 0.26/0.63 thf(fact_301_Inl__inject,axiom,
% 0.26/0.63 ! [X: a,Y: a] :
% 0.26/0.63 ( ( ( sum_In2139678582um_b_c @ X )
% 0.26/0.63 = ( sum_In2139678582um_b_c @ Y ) )
% 0.26/0.63 => ( X = Y ) ) ).
% 0.26/0.63
% 0.26/0.63 % Inl_inject
% 0.26/0.63 thf(fact_302_Collect__subset,axiom,
% 0.26/0.63 ! [A: set_a,P: a > $o] :
% 0.26/0.63 ( ord_less_eq_set_a
% 0.26/0.63 @ ( collect_a
% 0.26/0.63 @ ^ [X2: a] :
% 0.26/0.63 ( ( member_a @ X2 @ A )
% 0.26/0.63 & ( P @ X2 ) ) )
% 0.26/0.63 @ A ) ).
% 0.26/0.63
% 0.26/0.63 % Collect_subset
% 0.26/0.63 thf(fact_303_Collect__subset,axiom,
% 0.26/0.63 ! [A: set_Su1783761653um_b_c,P: sum_su737395349um_b_c > $o] :
% 0.26/0.63 ( ord_le929608341um_b_c
% 0.26/0.63 @ ( collec2086029184um_b_c
% 0.26/0.63 @ ^ [X2: sum_su737395349um_b_c] :
% 0.26/0.63 ( ( member1893232190um_b_c @ X2 @ A )
% 0.26/0.63 & ( P @ X2 ) ) )
% 0.26/0.63 @ A ) ).
% 0.26/0.63
% 0.26/0.63 % Collect_subset
% 0.26/0.63 thf(fact_304_less__eq__set__def,axiom,
% 0.26/0.63 ( ord_less_eq_set_a
% 0.26/0.63 = ( ^ [A5: set_a,B5: set_a] :
% 0.26/0.63 ( ord_less_eq_a_o
% 0.26/0.63 @ ^ [X2: a] : ( member_a @ X2 @ A5 )
% 0.26/0.63 @ ^ [X2: a] : ( member_a @ X2 @ B5 ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % less_eq_set_def
% 0.26/0.63 thf(fact_305_sterm__determines__frechet,axiom,
% 0.26/0.63 ! [I3: denota231621370t_unit,J: denota231621370t_unit,Theta_12: trm_a_c,Theta_22: trm_a_c,Nu: produc190496183real_c] :
% 0.26/0.63 ( ( denota258389581_a_b_c @ I3 )
% 0.26/0.63 => ( ( denota258389581_a_b_c @ J )
% 0.26/0.63 => ( ( dfree_a_c @ Theta_12 )
% 0.26/0.63 => ( ( dfree_a_c @ Theta_22 )
% 0.26/0.63 => ( ( ( denota2042094639_a_b_c @ I3 @ Theta_12 )
% 0.26/0.63 = ( denota2042094639_a_b_c @ J @ Theta_22 ) )
% 0.26/0.63 => ( ( denota229585092_a_b_c @ I3 @ Theta_12 @ ( produc2010422875real_c @ Nu ) @ ( produc314122909real_c @ Nu ) )
% 0.26/0.63 = ( denota229585092_a_b_c @ J @ Theta_22 @ ( produc2010422875real_c @ Nu ) @ ( produc314122909real_c @ Nu ) ) ) ) ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % sterm_determines_frechet
% 0.26/0.63 thf(fact_306_sterm__determines__frechet,axiom,
% 0.26/0.63 ! [I3: denota610675952t_unit,J: denota610675952t_unit,Theta_12: trm_sf_sz,Theta_22: trm_sf_sz,Nu: produc1149990247eal_sz] :
% 0.26/0.63 ( ( denota1579475975_sc_sz @ I3 )
% 0.26/0.63 => ( ( denota1579475975_sc_sz @ J )
% 0.26/0.63 => ( ( dfree_sf_sz @ Theta_12 )
% 0.26/0.63 => ( ( dfree_sf_sz @ Theta_22 )
% 0.26/0.63 => ( ( ( denota1179238309_sc_sz @ I3 @ Theta_12 )
% 0.26/0.63 = ( denota1179238309_sc_sz @ J @ Theta_22 ) )
% 0.26/0.63 => ( ( denota1979904720_sc_sz @ I3 @ Theta_12 @ ( produc1111759555eal_sz @ Nu ) @ ( produc1269210629eal_sz @ Nu ) )
% 0.26/0.63 = ( denota1979904720_sc_sz @ J @ Theta_22 @ ( produc1111759555eal_sz @ Nu ) @ ( produc1269210629eal_sz @ Nu ) ) ) ) ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % sterm_determines_frechet
% 0.26/0.63 thf(fact_307_type__definition__good__interp,axiom,
% 0.26/0.63 type_d1092523951t_unit @ freche1421597129_sc_sz @ freche1784963216_sc_sz @ ( collec1767975749t_unit @ denota1579475975_sc_sz ) ).
% 0.26/0.63
% 0.26/0.63 % type_definition_good_interp
% 0.26/0.63 thf(fact_308_image2__def,axiom,
% 0.26/0.63 ( bNF_Gr1775200401_sc_sz
% 0.26/0.63 = ( ^ [A5: set_a,F: a > denota610675952t_unit,G: a > produc866628903_sc_sz] :
% 0.26/0.63 ( collec1199592193_sc_sz
% 0.26/0.63 @ ^ [Uu: produc1821101996_sc_sz] :
% 0.26/0.63 ? [A6: a] :
% 0.26/0.63 ( ( Uu
% 0.26/0.63 = ( produc789536734_sc_sz @ ( F @ A6 ) @ ( G @ A6 ) ) )
% 0.26/0.63 & ( member_a @ A6 @ A5 ) ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % image2_def
% 0.26/0.63 thf(fact_309_image2__eqI,axiom,
% 0.26/0.63 ! [B2: denota610675952t_unit,F2: a > denota610675952t_unit,X: a,C2: produc866628903_sc_sz,G2: a > produc866628903_sc_sz,A: set_a] :
% 0.26/0.63 ( ( B2
% 0.26/0.63 = ( F2 @ X ) )
% 0.26/0.63 => ( ( C2
% 0.26/0.63 = ( G2 @ X ) )
% 0.26/0.63 => ( ( member_a @ X @ A )
% 0.26/0.63 => ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ B2 @ C2 ) @ ( bNF_Gr1775200401_sc_sz @ A @ F2 @ G2 ) ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % image2_eqI
% 0.26/0.63 thf(fact_310_coincidence__sterm_H,axiom,
% 0.26/0.63 ! [Theta: trm_a_c,Nu: produc190496183real_c,Nu2: produc190496183real_c,I3: denota231621370t_unit,J: denota231621370t_unit] :
% 0.26/0.63 ( ( dfree_a_c @ Theta )
% 0.26/0.63 => ( ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVT_a_c @ Theta ) )
% 0.26/0.63 => ( ( denota69106024_a_b_c @ I3 @ J
% 0.26/0.63 @ ( collec2086029184um_b_c
% 0.26/0.63 @ ^ [Uu: sum_su737395349um_b_c] :
% 0.26/0.63 ? [X2: a] :
% 0.26/0.63 ( ( Uu
% 0.26/0.63 = ( sum_In2139678582um_b_c @ X2 ) )
% 0.26/0.63 & ( member_a @ X2 @ ( static_SIGT_a_c @ Theta ) ) ) ) )
% 0.26/0.63 => ( ( denota2042094639_a_b_c @ I3 @ Theta @ ( produc2010422875real_c @ Nu ) )
% 0.26/0.63 = ( denota2042094639_a_b_c @ J @ Theta @ ( produc2010422875real_c @ Nu2 ) ) ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % coincidence_sterm'
% 0.26/0.63 thf(fact_311_pred__subset__eq,axiom,
% 0.26/0.63 ! [R: set_a,S3: set_a] :
% 0.26/0.63 ( ( ord_less_eq_a_o
% 0.26/0.63 @ ^ [X2: a] : ( member_a @ X2 @ R )
% 0.26/0.63 @ ^ [X2: a] : ( member_a @ X2 @ S3 ) )
% 0.26/0.63 = ( ord_less_eq_set_a @ R @ S3 ) ) ).
% 0.26/0.63
% 0.26/0.63 % pred_subset_eq
% 0.26/0.63 thf(fact_312_sterm__continuous_H,axiom,
% 0.26/0.63 ! [I3: denota610675952t_unit,Theta: trm_sf_sz,S3: set_Fi291318197eal_sz] :
% 0.26/0.63 ( ( denota1579475975_sc_sz @ I3 )
% 0.26/0.63 => ( ( dfree_sf_sz @ Theta )
% 0.26/0.63 => ( topolo1348430467z_real @ S3 @ ( denota1179238309_sc_sz @ I3 @ Theta ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % sterm_continuous'
% 0.26/0.63 thf(fact_313_agree__func__fvt,axiom,
% 0.26/0.63 ! [Nu: produc1149990247eal_sz,Nu2: produc1149990247eal_sz,F2: sf,Args: sz > trm_sf_sz,I: sz] :
% 0.26/0.63 ( ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVT_sf_sz @ ( function_sf_sz @ F2 @ Args ) ) )
% 0.26/0.63 => ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVT_sf_sz @ ( Args @ I ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % agree_func_fvt
% 0.26/0.63 thf(fact_314_subrelI,axiom,
% 0.26/0.63 ! [R2: set_Pr1169339874_sc_sz,S4: set_Pr1169339874_sc_sz] :
% 0.26/0.63 ( ! [X3: denota610675952t_unit,Y3: produc866628903_sc_sz] :
% 0.26/0.63 ( ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ X3 @ Y3 ) @ R2 )
% 0.26/0.63 => ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ X3 @ Y3 ) @ S4 ) )
% 0.26/0.63 => ( ord_le1230423618_sc_sz @ R2 @ S4 ) ) ).
% 0.26/0.63
% 0.26/0.63 % subrelI
% 0.26/0.63 thf(fact_315_FVDiff__sub,axiom,
% 0.26/0.63 ! [F2: trm_a_c] : ( ord_le1772180283um_c_c @ ( static_FVT_a_c @ F2 ) @ ( static_FVDiff_a_c @ F2 ) ) ).
% 0.26/0.63
% 0.26/0.63 % FVDiff_sub
% 0.26/0.63 thf(fact_316_pred__equals__eq2,axiom,
% 0.26/0.63 ! [R: set_Pr1169339874_sc_sz,S3: set_Pr1169339874_sc_sz] :
% 0.26/0.63 ( ( ( ^ [X2: denota610675952t_unit,Y2: produc866628903_sc_sz] : ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ X2 @ Y2 ) @ R ) )
% 0.26/0.63 = ( ^ [X2: denota610675952t_unit,Y2: produc866628903_sc_sz] : ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ X2 @ Y2 ) @ S3 ) ) )
% 0.26/0.63 = ( R = S3 ) ) ).
% 0.26/0.63
% 0.26/0.63 % pred_equals_eq2
% 0.26/0.63 thf(fact_317_pred__subset__eq2,axiom,
% 0.26/0.63 ! [R: set_Pr1169339874_sc_sz,S3: set_Pr1169339874_sc_sz] :
% 0.26/0.63 ( ( ord_le108471557c_sz_o
% 0.26/0.63 @ ^ [X2: denota610675952t_unit,Y2: produc866628903_sc_sz] : ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ X2 @ Y2 ) @ R )
% 0.26/0.63 @ ^ [X2: denota610675952t_unit,Y2: produc866628903_sc_sz] : ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ X2 @ Y2 ) @ S3 ) )
% 0.26/0.63 = ( ord_le1230423618_sc_sz @ R @ S3 ) ) ).
% 0.26/0.63
% 0.26/0.63 % pred_subset_eq2
% 0.26/0.63 thf(fact_318_sterm__continuous,axiom,
% 0.26/0.63 ! [I3: denota610675952t_unit,Theta: trm_sf_sz] :
% 0.26/0.63 ( ( denota1579475975_sc_sz @ I3 )
% 0.26/0.63 => ( ( dfree_sf_sz @ Theta )
% 0.26/0.63 => ( topolo1348430467z_real @ top_to1873962757eal_sz @ ( denota1179238309_sc_sz @ I3 @ Theta ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % sterm_continuous
% 0.26/0.63 thf(fact_319_continuous__on__cases__le,axiom,
% 0.26/0.63 ! [S4: set_Fi291318197eal_sz,H: finite824932053eal_sz > real,A2: real,F2: finite824932053eal_sz > bounde472938360z_real,G2: finite824932053eal_sz > bounde472938360z_real] :
% 0.26/0.63 ( ( topolo885751137z_real
% 0.26/0.63 @ ( collec1002602816eal_sz
% 0.26/0.63 @ ^ [T: finite824932053eal_sz] :
% 0.26/0.63 ( ( member1693951742eal_sz @ T @ S4 )
% 0.26/0.63 & ( ord_less_eq_real @ ( H @ T ) @ A2 ) ) )
% 0.26/0.63 @ F2 )
% 0.26/0.63 => ( ( topolo885751137z_real
% 0.26/0.63 @ ( collec1002602816eal_sz
% 0.26/0.63 @ ^ [T: finite824932053eal_sz] :
% 0.26/0.63 ( ( member1693951742eal_sz @ T @ S4 )
% 0.26/0.63 & ( ord_less_eq_real @ A2 @ ( H @ T ) ) ) )
% 0.26/0.63 @ G2 )
% 0.26/0.63 => ( ( topolo1348430467z_real @ S4 @ H )
% 0.26/0.63 => ( ! [T4: finite824932053eal_sz] :
% 0.26/0.63 ( ( member1693951742eal_sz @ T4 @ S4 )
% 0.26/0.63 => ( ( ( H @ T4 )
% 0.26/0.63 = A2 )
% 0.26/0.63 => ( ( F2 @ T4 )
% 0.26/0.63 = ( G2 @ T4 ) ) ) )
% 0.26/0.63 => ( topolo885751137z_real @ S4
% 0.26/0.63 @ ^ [T: finite824932053eal_sz] : ( if_Bou1785791806z_real @ ( ord_less_eq_real @ ( H @ T ) @ A2 ) @ ( F2 @ T ) @ ( G2 @ T ) ) ) ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % continuous_on_cases_le
% 0.26/0.63 thf(fact_320_UNIV__I,axiom,
% 0.26/0.63 ! [X: a] : ( member_a @ X @ top_top_set_a ) ).
% 0.26/0.63
% 0.26/0.63 % UNIV_I
% 0.26/0.63 thf(fact_321_UNIV__I,axiom,
% 0.26/0.63 ! [X: finite824932053eal_sz] : ( member1693951742eal_sz @ X @ top_to1873962757eal_sz ) ).
% 0.26/0.63
% 0.26/0.63 % UNIV_I
% 0.26/0.63 thf(fact_322_top_Oextremum__uniqueI,axiom,
% 0.26/0.63 ! [A2: set_Fi291318197eal_sz] :
% 0.26/0.63 ( ( ord_le41263445eal_sz @ top_to1873962757eal_sz @ A2 )
% 0.26/0.63 => ( A2 = top_to1873962757eal_sz ) ) ).
% 0.26/0.63
% 0.26/0.63 % top.extremum_uniqueI
% 0.26/0.63 thf(fact_323_top_Oextremum__unique,axiom,
% 0.26/0.63 ! [A2: set_Fi291318197eal_sz] :
% 0.26/0.63 ( ( ord_le41263445eal_sz @ top_to1873962757eal_sz @ A2 )
% 0.26/0.63 = ( A2 = top_to1873962757eal_sz ) ) ).
% 0.26/0.63
% 0.26/0.63 % top.extremum_unique
% 0.26/0.63 thf(fact_324_top__greatest,axiom,
% 0.26/0.63 ! [A2: set_Fi291318197eal_sz] : ( ord_le41263445eal_sz @ A2 @ top_to1873962757eal_sz ) ).
% 0.26/0.63
% 0.26/0.63 % top_greatest
% 0.26/0.63 thf(fact_325_subset__UNIV,axiom,
% 0.26/0.63 ! [A: set_Fi291318197eal_sz] : ( ord_le41263445eal_sz @ A @ top_to1873962757eal_sz ) ).
% 0.26/0.63
% 0.26/0.63 % subset_UNIV
% 0.26/0.63 thf(fact_326_ids_Oseq__sem_Ocases,axiom,
% 0.26/0.63 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc,X: produc1821101996_sc_sz] :
% 0.26/0.63 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.26/0.63 => ~ ! [I2: denota610675952t_unit,S: produc866628903_sc_sz] :
% 0.26/0.63 ( X
% 0.26/0.63 != ( produc789536734_sc_sz @ I2 @ S ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % ids.seq_sem.cases
% 0.26/0.63 thf(fact_327_UNIV__def,axiom,
% 0.26/0.63 ( top_to524132421um_b_c
% 0.26/0.63 = ( collec2086029184um_b_c
% 0.26/0.63 @ ^ [X2: sum_su737395349um_b_c] : $true ) ) ).
% 0.26/0.63
% 0.26/0.63 % UNIV_def
% 0.26/0.63 thf(fact_328_UNIV__def,axiom,
% 0.26/0.63 ( top_to1873962757eal_sz
% 0.26/0.63 = ( collec1002602816eal_sz
% 0.26/0.63 @ ^ [X2: finite824932053eal_sz] : $true ) ) ).
% 0.26/0.63
% 0.26/0.63 % UNIV_def
% 0.26/0.63 thf(fact_329_UNIV__witness,axiom,
% 0.26/0.63 ? [X3: a] : ( member_a @ X3 @ top_top_set_a ) ).
% 0.26/0.63
% 0.26/0.63 % UNIV_witness
% 0.26/0.63 thf(fact_330_UNIV__witness,axiom,
% 0.26/0.63 ? [X3: finite824932053eal_sz] : ( member1693951742eal_sz @ X3 @ top_to1873962757eal_sz ) ).
% 0.26/0.63
% 0.26/0.63 % UNIV_witness
% 0.26/0.63 thf(fact_331_UNIV__eq__I,axiom,
% 0.26/0.63 ! [A: set_a] :
% 0.26/0.63 ( ! [X3: a] : ( member_a @ X3 @ A )
% 0.26/0.63 => ( top_top_set_a = A ) ) ).
% 0.26/0.63
% 0.26/0.63 % UNIV_eq_I
% 0.26/0.63 thf(fact_332_UNIV__eq__I,axiom,
% 0.26/0.63 ! [A: set_Fi291318197eal_sz] :
% 0.26/0.63 ( ! [X3: finite824932053eal_sz] : ( member1693951742eal_sz @ X3 @ A )
% 0.26/0.63 => ( top_to1873962757eal_sz = A ) ) ).
% 0.26/0.63
% 0.26/0.63 % UNIV_eq_I
% 0.26/0.63 thf(fact_333_top__prod__def,axiom,
% 0.26/0.63 ( top_to1787697847eal_sz
% 0.26/0.63 = ( produc1235791063eal_sz @ top_to1873962757eal_sz @ top_to1873962757eal_sz ) ) ).
% 0.26/0.63
% 0.26/0.63 % top_prod_def
% 0.26/0.63 thf(fact_334_ids_OP__def,axiom,
% 0.26/0.63 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc,P2: sc] :
% 0.26/0.63 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.26/0.63 => ( ( p_sc_sf_sz @ P2 )
% 0.26/0.63 = ( predic913887884_sf_sz @ P2 ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % ids.P_def
% 0.26/0.63 thf(fact_335_frechet__continuous,axiom,
% 0.26/0.63 ! [I3: denota610675952t_unit,Theta: trm_sf_sz] :
% 0.26/0.63 ( ( denota1579475975_sc_sz @ I3 )
% 0.26/0.63 => ( ( dfree_sf_sz @ Theta )
% 0.26/0.63 => ( topolo885751137z_real @ top_to1873962757eal_sz @ ( freche585307148_sc_sz @ ( freche1784963216_sc_sz @ I3 ) @ ( freche1046279700_sf_sz @ Theta ) ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % frechet_continuous
% 0.26/0.63 thf(fact_336_top__empty__eq2,axiom,
% 0.26/0.63 ( top_to1399053141c_sz_o
% 0.26/0.63 = ( ^ [X2: denota610675952t_unit,Y2: produc866628903_sc_sz] : ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ X2 @ Y2 ) @ top_to1499569298_sc_sz ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % top_empty_eq2
% 0.26/0.63 thf(fact_337_top__set__def,axiom,
% 0.26/0.63 ( top_to524132421um_b_c
% 0.26/0.63 = ( collec2086029184um_b_c @ top_to1201357528_b_c_o ) ) ).
% 0.26/0.63
% 0.26/0.63 % top_set_def
% 0.26/0.63 thf(fact_338_top__set__def,axiom,
% 0.26/0.63 ( top_to1873962757eal_sz
% 0.26/0.63 = ( collec1002602816eal_sz @ top_to646513176l_sz_o ) ) ).
% 0.26/0.63
% 0.26/0.63 % top_set_def
% 0.26/0.63 thf(fact_339_Vagree__univ,axiom,
% 0.26/0.63 ! [A2: finite1398487019real_c,B2: finite1398487019real_c,C2: finite1398487019real_c,D: finite1398487019real_c] :
% 0.26/0.63 ( ( denota1997846518gree_c @ ( produc394644079real_c @ A2 @ B2 ) @ ( produc394644079real_c @ C2 @ D ) @ top_to1660572043um_c_c )
% 0.26/0.63 => ( ( A2 = C2 )
% 0.26/0.63 & ( B2 = D ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % Vagree_univ
% 0.26/0.63 thf(fact_340_agree__UNIV__eq,axiom,
% 0.26/0.63 ! [Nu: produc190496183real_c,Omega: produc190496183real_c] :
% 0.26/0.63 ( ( denota1997846518gree_c @ Nu @ Omega @ top_to1660572043um_c_c )
% 0.26/0.63 => ( Nu = Omega ) ) ).
% 0.26/0.63
% 0.26/0.63 % agree_UNIV_eq
% 0.26/0.63 thf(fact_341_ids_Ofrechet__continuous,axiom,
% 0.26/0.63 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc,I3: denota610675952t_unit,Theta: trm_sf_sz] :
% 0.26/0.63 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.26/0.63 => ( ( denota1579475975_sc_sz @ I3 )
% 0.26/0.63 => ( ( dfree_sf_sz @ Theta )
% 0.26/0.63 => ( topolo885751137z_real @ top_to1873962757eal_sz @ ( freche585307148_sc_sz @ ( freche1784963216_sc_sz @ I3 ) @ ( freche1046279700_sf_sz @ Theta ) ) ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % ids.frechet_continuous
% 0.26/0.63 thf(fact_342_frechet__blin,axiom,
% 0.26/0.63 ! [I3: denota610675952t_unit,Theta: trm_sf_sz] :
% 0.26/0.63 ( ( denota1579475975_sc_sz @ I3 )
% 0.26/0.63 => ( ( dfree_sf_sz @ Theta )
% 0.26/0.63 => ( ( ^ [V2: finite824932053eal_sz] : ( bounde397081123z_real @ ( denota1979904720_sc_sz @ I3 @ Theta @ V2 ) ) )
% 0.26/0.63 = ( freche585307148_sc_sz @ ( freche1784963216_sc_sz @ I3 ) @ ( freche1046279700_sf_sz @ Theta ) ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % frechet_blin
% 0.26/0.63 thf(fact_343_continuous__on__const,axiom,
% 0.26/0.63 ! [S4: set_Fi291318197eal_sz,C2: bounde472938360z_real] :
% 0.26/0.63 ( topolo885751137z_real @ S4
% 0.26/0.63 @ ^ [X2: finite824932053eal_sz] : C2 ) ).
% 0.26/0.63
% 0.26/0.63 % continuous_on_const
% 0.26/0.63 thf(fact_344_continuous__on__subset,axiom,
% 0.26/0.63 ! [S4: set_Fi291318197eal_sz,F2: finite824932053eal_sz > bounde472938360z_real,T3: set_Fi291318197eal_sz] :
% 0.26/0.63 ( ( topolo885751137z_real @ S4 @ F2 )
% 0.26/0.63 => ( ( ord_le41263445eal_sz @ T3 @ S4 )
% 0.26/0.63 => ( topolo885751137z_real @ T3 @ F2 ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % continuous_on_subset
% 0.26/0.63 thf(fact_345_continuous__on__Pair,axiom,
% 0.26/0.63 ! [S4: set_Fi291318197eal_sz,F2: finite824932053eal_sz > bounde472938360z_real,G2: finite824932053eal_sz > bounde472938360z_real] :
% 0.26/0.63 ( ( topolo885751137z_real @ S4 @ F2 )
% 0.26/0.63 => ( ( topolo885751137z_real @ S4 @ G2 )
% 0.26/0.63 => ( topolo1027477648z_real @ S4
% 0.26/0.63 @ ^ [X2: finite824932053eal_sz] : ( produc784663575z_real @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % continuous_on_Pair
% 0.26/0.63 thf(fact_346_ids_Ofrechet__blin,axiom,
% 0.26/0.63 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc,I3: denota610675952t_unit,Theta: trm_sf_sz] :
% 0.26/0.63 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.26/0.63 => ( ( denota1579475975_sc_sz @ I3 )
% 0.26/0.63 => ( ( dfree_sf_sz @ Theta )
% 0.26/0.63 => ( ( ^ [V2: finite824932053eal_sz] : ( bounde397081123z_real @ ( denota1979904720_sc_sz @ I3 @ Theta @ V2 ) ) )
% 0.26/0.63 = ( freche585307148_sc_sz @ ( freche1784963216_sc_sz @ I3 ) @ ( freche1046279700_sf_sz @ Theta ) ) ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % ids.frechet_blin
% 0.26/0.63 thf(fact_347_blin__frechet_Oabs__eq,axiom,
% 0.26/0.63 ! [Xb: denota610675952t_unit,Xa: trm_sf_sz,X: finite824932053eal_sz] :
% 0.26/0.63 ( ( bNF_eq1660582207t_unit @ denota1579475975_sc_sz @ Xb @ Xb )
% 0.26/0.63 => ( ( bNF_eq_onp_trm_sf_sz @ dfree_sf_sz @ Xa @ Xa )
% 0.26/0.63 => ( ( freche585307148_sc_sz @ ( freche1784963216_sc_sz @ Xb ) @ ( freche1046279700_sf_sz @ Xa ) @ X )
% 0.26/0.63 = ( bounde397081123z_real @ ( denota1979904720_sc_sz @ Xb @ Xa @ X ) ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % blin_frechet.abs_eq
% 0.26/0.63 thf(fact_348_ids_Oblin__frechet_Oabs__eq,axiom,
% 0.26/0.63 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc,Xb: denota610675952t_unit,Xa: trm_sf_sz,X: finite824932053eal_sz] :
% 0.26/0.63 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.26/0.63 => ( ( bNF_eq1660582207t_unit @ denota1579475975_sc_sz @ Xb @ Xb )
% 0.26/0.63 => ( ( bNF_eq_onp_trm_sf_sz @ dfree_sf_sz @ Xa @ Xa )
% 0.26/0.63 => ( ( freche585307148_sc_sz @ ( freche1784963216_sc_sz @ Xb ) @ ( freche1046279700_sf_sz @ Xa ) @ X )
% 0.26/0.63 = ( bounde397081123z_real @ ( denota1979904720_sc_sz @ Xb @ Xa @ X ) ) ) ) ) ) ).
% 0.26/0.63
% 0.26/0.63 % ids.blin_frechet.abs_eq
% 0.26/0.63 thf(fact_349_Quotient__good__interp,axiom,
% 0.26/0.63 quotie842200089_sc_sz @ ( bNF_eq1660582207t_unit @ denota1579475975_sc_sz ) @ freche1784963216_sc_sz @ freche1421597129_sc_sz @ freche58918398_sc_sz ).
% 0.26/0.63
% 0.26/0.63 % Quotient_good_interp
% 0.26/0.63 thf(fact_350_Quotient__strm,axiom,
% 0.26/0.63 quotie1467858509rm_a_c @ ( bNF_eq_onp_trm_a_c @ dfree_a_c ) @ freche665377492rm_a_c @ frechet_raw_term_a_c @ frechet_cr_strm_a_c ).
% 0.26/0.63
% 0.26/0.63 % Quotient_strm
% 0.26/0.63 thf(fact_351_Quotient__strm,axiom,
% 0.26/0.63 quotie1549861309_sf_sz @ ( bNF_eq_onp_trm_sf_sz @ dfree_sf_sz ) @ freche1046279700_sf_sz @ freche782854530_sf_sz @ freche1244000341_sf_sz ).
% 0.26/0.63
% 0.26/0.63 % Quotient_strm
% 0.26/0.63 thf(fact_352_eq__onp__le__eq,axiom,
% 0.26/0.63 ! [P: denota610675952t_unit > $o] :
% 0.26/0.63 ( ord_le2003534918unit_o @ ( bNF_eq1660582207t_unit @ P )
% 0.26/0.63 @ ^ [Y4: denota610675952t_unit,Z: denota610675952t_unit] : ( Y4 = Z ) ) ).
% 0.26/0.63
% 0.26/0.63 % eq_onp_le_eq
% 0.26/0.63 thf(fact_353_eq__onp__le__eq,axiom,
% 0.26/0.63 ! [P: trm_sf_sz > $o] :
% 0.26/0.63 ( ord_le8515534f_sz_o @ ( bNF_eq_onp_trm_sf_sz @ P )
% 0.26/0.63 @ ^ [Y4: trm_sf_sz,Z: trm_sf_sz] : ( Y4 = Z ) ) ).
% 0.26/0.63
% 0.26/0.63 % eq_onp_le_eq
% 0.26/0.63
% 0.26/0.63 % Helper facts (3)
% 0.26/0.63 thf(help_If_3_1_If_001t__Bounded____Linear____Function__Oblinfun_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_Mt__Real__Oreal_J_T,axiom,
% 0.26/0.63 ! [P: $o] :
% 0.26/0.63 ( ( P = $true )
% 0.26/0.63 | ( P = $false ) ) ).
% 0.26/0.63
% 0.26/0.63 thf(help_If_2_1_If_001t__Bounded____Linear____Function__Oblinfun_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_Mt__Real__Oreal_J_T,axiom,
% 0.26/0.63 ! [X: bounde472938360z_real,Y: bounde472938360z_real] :
% 0.26/0.63 ( ( if_Bou1785791806z_real @ $false @ X @ Y )
% 0.26/0.63 = Y ) ).
% 0.26/0.63
% 0.26/0.63 thf(help_If_1_1_If_001t__Bounded____Linear____Function__Oblinfun_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_Mt__Real__Oreal_J_T,axiom,
% 0.26/0.71 ! [X: bounde472938360z_real,Y: bounde472938360z_real] :
% 0.26/0.71 ( ( if_Bou1785791806z_real @ $true @ X @ Y )
% 0.26/0.71 = X ) ).
% 0.26/0.71
% 0.26/0.71 % Conjectures (1)
% 0.26/0.71 thf(conj_0,conjecture,
% 0.26/0.71 denota1997846518gree_c @ nu @ nu2 @ ( static_FVDiff_a_c @ t2 ) ).
% 0.26/0.71
% 0.26/0.71 %------------------------------------------------------------------------------
% 0.26/0.71 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.Y49uHccraq/cvc5---1.0.5_17543.p...
% 0.26/0.71 (declare-sort $$unsorted 0)
% 0.26/0.71 (declare-sort tptp.set_Pr1169339874_sc_sz 0)
% 0.26/0.71 (declare-sort tptp.produc1821101996_sc_sz 0)
% 0.26/0.71 (declare-sort tptp.produc1892666919z_real 0)
% 0.26/0.71 (declare-sort tptp.produc1241881959eal_sz 0)
% 0.26/0.71 (declare-sort tptp.produc1149990247eal_sz 0)
% 0.26/0.71 (declare-sort tptp.produc190496183real_c 0)
% 0.26/0.71 (declare-sort tptp.produc866628903_sc_sz 0)
% 0.26/0.71 (declare-sort tptp.produc1144880887f_sz_o 0)
% 0.26/0.71 (declare-sort tptp.produc903182423_set_a 0)
% 0.26/0.71 (declare-sort tptp.produc1553439972f_sz_o 0)
% 0.26/0.71 (declare-sort tptp.produc1065634396_o_a_o 0)
% 0.26/0.71 (declare-sort tptp.bounde472938360z_real 0)
% 0.26/0.71 (declare-sort tptp.set_De208295462t_unit 0)
% 0.26/0.71 (declare-sort tptp.set_De455519194t_unit 0)
% 0.26/0.71 (declare-sort tptp.denota610675952t_unit 0)
% 0.26/0.71 (declare-sort tptp.denota231621370t_unit 0)
% 0.26/0.71 (declare-sort tptp.set_Su1783761653um_b_c 0)
% 0.26/0.71 (declare-sort tptp.set_Fi291318197eal_sz 0)
% 0.26/0.71 (declare-sort tptp.freche2095075217_sc_sz 0)
% 0.26/0.71 (declare-sort tptp.produc1691597095_set_a 0)
% 0.26/0.71 (declare-sort tptp.freche914690577_a_b_c 0)
% 0.26/0.71 (declare-sort tptp.produc1989635468_a_a_o 0)
% 0.26/0.71 (declare-sort tptp.produc1561113620_set_a 0)
% 0.26/0.71 (declare-sort tptp.sum_su737395349um_b_c 0)
% 0.26/0.71 (declare-sort tptp.product_prod_a_o_a_o 0)
% 0.26/0.71 (declare-sort tptp.finite824932053eal_sz 0)
% 0.26/0.71 (declare-sort tptp.finite1398487019real_c 0)
% 0.26/0.71 (declare-sort tptp.list_f1238882004_sc_sz 0)
% 0.26/0.71 (declare-sort tptp.frechet_strm_sf_sz 0)
% 0.26/0.71 (declare-sort tptp.set_Sum_sum_sz_sz 0)
% 0.26/0.71 (declare-sort tptp.frechet_strm_a_c 0)
% 0.26/0.71 (declare-sort tptp.set_Sum_sum_c_c 0)
% 0.26/0.71 (declare-sort tptp.set_trm_sf_sz 0)
% 0.26/0.71 (declare-sort tptp.set_trm_a_c 0)
% 0.26/0.71 (declare-sort tptp.formula_sf_sc_sz 0)
% 0.26/0.71 (declare-sort tptp.trm_sf_sz 0)
% 0.26/0.71 (declare-sort tptp.trm_a_c 0)
% 0.26/0.71 (declare-sort tptp.set_a 0)
% 0.26/0.71 (declare-sort tptp.real 0)
% 0.26/0.71 (declare-sort tptp.sz 0)
% 0.26/0.71 (declare-sort tptp.sf 0)
% 0.26/0.71 (declare-sort tptp.sc 0)
% 0.26/0.71 (declare-sort tptp.c 0)
% 0.26/0.71 (declare-sort tptp.a 0)
% 0.26/0.71 (declare-fun tptp.bNF_eq1660582207t_unit ((-> tptp.denota610675952t_unit Bool) tptp.denota610675952t_unit tptp.denota610675952t_unit) Bool)
% 0.26/0.71 (declare-fun tptp.bNF_eq_onp_trm_a_c ((-> tptp.trm_a_c Bool) tptp.trm_a_c tptp.trm_a_c) Bool)
% 0.26/0.71 (declare-fun tptp.bNF_eq_onp_trm_sf_sz ((-> tptp.trm_sf_sz Bool) tptp.trm_sf_sz tptp.trm_sf_sz) Bool)
% 0.26/0.71 (declare-fun tptp.bNF_Gr1775200401_sc_sz (tptp.set_a (-> tptp.a tptp.denota610675952t_unit) (-> tptp.a tptp.produc866628903_sc_sz)) tptp.set_Pr1169339874_sc_sz)
% 0.26/0.71 (declare-fun tptp.bounde397081123z_real ((-> tptp.finite824932053eal_sz tptp.real)) tptp.bounde472938360z_real)
% 0.26/0.71 (declare-fun tptp.denota69106024_a_b_c (tptp.denota231621370t_unit tptp.denota231621370t_unit tptp.set_Su1783761653um_b_c) Bool)
% 0.26/0.71 (declare-fun tptp.denota1997846518gree_c (tptp.produc190496183real_c tptp.produc190496183real_c tptp.set_Sum_sum_c_c) Bool)
% 0.26/0.71 (declare-fun tptp.denota102713844ree_sz (tptp.produc1149990247eal_sz tptp.produc1149990247eal_sz tptp.set_Sum_sum_sz_sz) Bool)
% 0.26/0.71 (declare-fun tptp.denota2112424896_a_b_c (tptp.denota231621370t_unit tptp.trm_a_c tptp.produc190496183real_c) tptp.real)
% 0.26/0.71 (declare-fun tptp.denota453121236_sc_sz (tptp.denota610675952t_unit tptp.trm_sf_sz tptp.produc1149990247eal_sz) tptp.real)
% 0.26/0.71 (declare-fun tptp.denota229585092_a_b_c (tptp.denota231621370t_unit tptp.trm_a_c tptp.finite1398487019real_c tptp.finite1398487019real_c) tptp.real)
% 0.26/0.71 (declare-fun tptp.denota1979904720_sc_sz (tptp.denota610675952t_unit tptp.trm_sf_sz tptp.finite824932053eal_sz tptp.finite824932053eal_sz) tptp.real)
% 0.26/0.71 (declare-fun tptp.denota258389581_a_b_c (tptp.denota231621370t_unit) Bool)
% 0.26/0.71 (declare-fun tptp.denota1579475975_sc_sz (tptp.denota610675952t_unit) Bool)
% 0.26/0.71 (declare-fun tptp.denota2042094639_a_b_c (tptp.denota231621370t_unit tptp.trm_a_c tptp.finite1398487019real_c) tptp.real)
% 0.26/0.71 (declare-fun tptp.denota1179238309_sc_sz (tptp.denota610675952t_unit tptp.trm_sf_sz tptp.finite824932053eal_sz) tptp.real)
% 0.26/0.71 (declare-fun tptp.freche585307148_sc_sz (tptp.freche2095075217_sc_sz tptp.frechet_strm_sf_sz tptp.finite824932053eal_sz) tptp.bounde472938360z_real)
% 0.26/0.71 (declare-fun tptp.freche58918398_sc_sz (tptp.denota610675952t_unit tptp.freche2095075217_sc_sz) Bool)
% 0.26/0.71 (declare-fun tptp.frechet_cr_strm_a_c (tptp.trm_a_c tptp.frechet_strm_a_c) Bool)
% 0.26/0.71 (declare-fun tptp.freche1244000341_sf_sz (tptp.trm_sf_sz tptp.frechet_strm_sf_sz) Bool)
% 0.26/0.71 (declare-fun tptp.freche1473475332_a_b_c (tptp.denota231621370t_unit) tptp.freche914690577_a_b_c)
% 0.26/0.71 (declare-fun tptp.freche1784963216_sc_sz (tptp.denota610675952t_unit) tptp.freche2095075217_sc_sz)
% 0.26/0.71 (declare-fun tptp.freche1608036107_a_b_c (tptp.freche914690577_a_b_c) tptp.denota231621370t_unit)
% 0.26/0.71 (declare-fun tptp.freche1421597129_sc_sz (tptp.freche2095075217_sc_sz) tptp.denota610675952t_unit)
% 0.26/0.71 (declare-fun tptp.frechet_raw_term_a_c (tptp.frechet_strm_a_c) tptp.trm_a_c)
% 0.26/0.71 (declare-fun tptp.freche782854530_sf_sz (tptp.frechet_strm_sf_sz) tptp.trm_sf_sz)
% 0.26/0.71 (declare-fun tptp.freche665377492rm_a_c (tptp.trm_a_c) tptp.frechet_strm_a_c)
% 0.26/0.71 (declare-fun tptp.freche1046279700_sf_sz (tptp.trm_sf_sz) tptp.frechet_strm_sf_sz)
% 0.26/0.71 (declare-fun tptp.ids_sz_sf_sc (tptp.sz tptp.sz tptp.sz tptp.sf tptp.sf tptp.sf tptp.sc tptp.sc tptp.sc tptp.sc) Bool)
% 0.26/0.71 (declare-fun tptp.if_Bou1785791806z_real (Bool tptp.bounde472938360z_real tptp.bounde472938360z_real) tptp.bounde472938360z_real)
% 0.26/0.71 (declare-fun tptp.quotie842200089_sc_sz ((-> tptp.denota610675952t_unit tptp.denota610675952t_unit Bool) (-> tptp.denota610675952t_unit tptp.freche2095075217_sc_sz) (-> tptp.freche2095075217_sc_sz tptp.denota610675952t_unit) (-> tptp.denota610675952t_unit tptp.freche2095075217_sc_sz Bool)) Bool)
% 0.26/0.71 (declare-fun tptp.quotie1467858509rm_a_c ((-> tptp.trm_a_c tptp.trm_a_c Bool) (-> tptp.trm_a_c tptp.frechet_strm_a_c) (-> tptp.frechet_strm_a_c tptp.trm_a_c) (-> tptp.trm_a_c tptp.frechet_strm_a_c Bool)) Bool)
% 0.26/0.71 (declare-fun tptp.quotie1549861309_sf_sz ((-> tptp.trm_sf_sz tptp.trm_sf_sz Bool) (-> tptp.trm_sf_sz tptp.frechet_strm_sf_sz) (-> tptp.frechet_strm_sf_sz tptp.trm_sf_sz) (-> tptp.trm_sf_sz tptp.frechet_strm_sf_sz Bool)) Bool)
% 0.26/0.71 (declare-fun tptp.ord_le2003534918unit_o ((-> tptp.denota610675952t_unit tptp.denota610675952t_unit Bool) (-> tptp.denota610675952t_unit tptp.denota610675952t_unit Bool)) Bool)
% 0.26/0.71 (declare-fun tptp.ord_le108471557c_sz_o ((-> tptp.denota610675952t_unit tptp.produc866628903_sc_sz Bool) (-> tptp.denota610675952t_unit tptp.produc866628903_sc_sz Bool)) Bool)
% 0.26/0.71 (declare-fun tptp.ord_le8515534f_sz_o ((-> tptp.trm_sf_sz tptp.trm_sf_sz Bool) (-> tptp.trm_sf_sz tptp.trm_sf_sz Bool)) Bool)
% 0.26/0.71 (declare-fun tptp.ord_less_eq_a_o ((-> tptp.a Bool) (-> tptp.a Bool)) Bool)
% 0.26/0.71 (declare-fun tptp.ord_le775706699real_c (tptp.finite1398487019real_c tptp.finite1398487019real_c) Bool)
% 0.26/0.71 (declare-fun tptp.ord_le787639925eal_sz (tptp.finite824932053eal_sz tptp.finite824932053eal_sz) Bool)
% 0.26/0.71 (declare-fun tptp.ord_le2132572860_o_a_o (tptp.produc1065634396_o_a_o tptp.produc1065634396_o_a_o) Bool)
% 0.26/0.71 (declare-fun tptp.ord_le1643089911_set_a (tptp.produc903182423_set_a tptp.produc903182423_set_a) Bool)
% 0.26/0.71 (declare-fun tptp.ord_le472894788f_sz_o (tptp.produc1553439972f_sz_o tptp.produc1553439972f_sz_o) Bool)
% 0.26/0.71 (declare-fun tptp.ord_le1883211903_o_a_o (tptp.product_prod_a_o_a_o tptp.product_prod_a_o_a_o) Bool)
% 0.26/0.71 (declare-fun tptp.ord_le72828020_set_a (tptp.produc1561113620_set_a tptp.produc1561113620_set_a) Bool)
% 0.26/0.71 (declare-fun tptp.ord_le850691415real_c (tptp.produc190496183real_c tptp.produc190496183real_c) Bool)
% 0.26/0.71 (declare-fun tptp.ord_le473656583eal_sz (tptp.produc1149990247eal_sz tptp.produc1149990247eal_sz) Bool)
% 0.26/0.71 (declare-fun tptp.ord_le978883847eal_sz (tptp.produc1241881959eal_sz tptp.produc1241881959eal_sz) Bool)
% 0.26/0.71 (declare-fun tptp.ord_le1884788375f_sz_o (tptp.produc1144880887f_sz_o tptp.produc1144880887f_sz_o) Bool)
% 0.26/0.71 (declare-fun tptp.ord_le501349868_a_a_o (tptp.produc1989635468_a_a_o tptp.produc1989635468_a_a_o) Bool)
% 0.26/0.71 (declare-fun tptp.ord_le486764743_set_a (tptp.produc1691597095_set_a tptp.produc1691597095_set_a) Bool)
% 0.26/0.71 (declare-fun tptp.ord_less_eq_real (tptp.real tptp.real) Bool)
% 0.26/0.71 (declare-fun tptp.ord_le41263445eal_sz (tptp.set_Fi291318197eal_sz tptp.set_Fi291318197eal_sz) Bool)
% 0.26/0.71 (declare-fun tptp.ord_le1230423618_sc_sz (tptp.set_Pr1169339874_sc_sz tptp.set_Pr1169339874_sc_sz) Bool)
% 0.26/0.71 (declare-fun tptp.ord_le929608341um_b_c (tptp.set_Su1783761653um_b_c tptp.set_Su1783761653um_b_c) Bool)
% 0.26/0.71 (declare-fun tptp.ord_le1772180283um_c_c (tptp.set_Sum_sum_c_c tptp.set_Sum_sum_c_c) Bool)
% 0.26/0.71 (declare-fun tptp.ord_le1110131657_sz_sz (tptp.set_Sum_sum_sz_sz tptp.set_Sum_sum_sz_sz) Bool)
% 0.26/0.71 (declare-fun tptp.ord_le1369644495rm_a_c (tptp.set_trm_a_c tptp.set_trm_a_c) Bool)
% 0.26/0.71 (declare-fun tptp.ord_le1697056455_sf_sz (tptp.set_trm_sf_sz tptp.set_trm_sf_sz) Bool)
% 0.26/0.71 (declare-fun tptp.ord_less_eq_set_a (tptp.set_a tptp.set_a) Bool)
% 0.26/0.71 (declare-fun tptp.top_to1399053141c_sz_o (tptp.denota610675952t_unit tptp.produc866628903_sc_sz) Bool)
% 0.26/0.71 (declare-fun tptp.top_to646513176l_sz_o (tptp.finite824932053eal_sz) Bool)
% 0.26/0.71 (declare-fun tptp.top_to1201357528_b_c_o (tptp.sum_su737395349um_b_c) Bool)
% 0.26/0.71 (declare-fun tptp.top_to1787697847eal_sz () tptp.produc1241881959eal_sz)
% 0.26/0.71 (declare-fun tptp.top_to1873962757eal_sz () tptp.set_Fi291318197eal_sz)
% 0.26/0.71 (declare-fun tptp.top_to1499569298_sc_sz () tptp.set_Pr1169339874_sc_sz)
% 0.26/0.71 (declare-fun tptp.top_to524132421um_b_c () tptp.set_Su1783761653um_b_c)
% 0.26/0.71 (declare-fun tptp.top_to1660572043um_c_c () tptp.set_Sum_sum_c_c)
% 0.26/0.71 (declare-fun tptp.top_top_set_a () tptp.set_a)
% 0.26/0.71 (declare-fun tptp.produc1152932438_o_a_o ((-> tptp.trm_sf_sz tptp.trm_sf_sz Bool) (-> tptp.a Bool)) tptp.produc1065634396_o_a_o)
% 0.26/0.71 (declare-fun tptp.produc1543226183_set_a ((-> tptp.trm_sf_sz tptp.trm_sf_sz Bool) tptp.set_a) tptp.produc903182423_set_a)
% 0.26/0.71 (declare-fun tptp.produc593159062f_sz_o ((-> tptp.a Bool) (-> tptp.trm_sf_sz tptp.trm_sf_sz Bool)) tptp.produc1553439972f_sz_o)
% 0.26/0.71 (declare-fun tptp.product_Pair_a_o_a_o ((-> tptp.a Bool) (-> tptp.a Bool)) tptp.product_prod_a_o_a_o)
% 0.26/0.71 (declare-fun tptp.produc1916559302_set_a ((-> tptp.a Bool) tptp.set_a) tptp.produc1561113620_set_a)
% 0.26/0.71 (declare-fun tptp.produc784663575z_real (tptp.bounde472938360z_real tptp.bounde472938360z_real) tptp.produc1892666919z_real)
% 0.26/0.71 (declare-fun tptp.produc789536734_sc_sz (tptp.denota610675952t_unit tptp.produc866628903_sc_sz) tptp.produc1821101996_sc_sz)
% 0.26/0.71 (declare-fun tptp.produc394644079real_c (tptp.finite1398487019real_c tptp.finite1398487019real_c) tptp.produc190496183real_c)
% 0.26/0.71 (declare-fun tptp.produc1308130519eal_sz (tptp.finite824932053eal_sz tptp.finite824932053eal_sz) tptp.produc1149990247eal_sz)
% 0.26/0.71 (declare-fun tptp.produc1822718231_sc_sz (tptp.list_f1238882004_sc_sz tptp.list_f1238882004_sc_sz) tptp.produc866628903_sc_sz)
% 0.26/0.71 (declare-fun tptp.produc1235791063eal_sz (tptp.set_Fi291318197eal_sz tptp.set_Fi291318197eal_sz) tptp.produc1241881959eal_sz)
% 0.26/0.71 (declare-fun tptp.produc1174558183f_sz_o (tptp.set_a (-> tptp.trm_sf_sz tptp.trm_sf_sz Bool)) tptp.produc1144880887f_sz_o)
% 0.26/0.71 (declare-fun tptp.produc634809990_a_a_o (tptp.set_a (-> tptp.a Bool)) tptp.produc1989635468_a_a_o)
% 0.26/0.71 (declare-fun tptp.produc1928581911_set_a (tptp.set_a tptp.set_a) tptp.produc1691597095_set_a)
% 0.26/0.71 (declare-fun tptp.produc2013638506_o_a_o (tptp.produc1065634396_o_a_o tptp.trm_sf_sz tptp.trm_sf_sz) Bool)
% 0.26/0.71 (declare-fun tptp.produc407272755_set_a (tptp.produc903182423_set_a tptp.trm_sf_sz tptp.trm_sf_sz) Bool)
% 0.26/0.71 (declare-fun tptp.produc1453865130f_sz_o (tptp.produc1553439972f_sz_o tptp.a) Bool)
% 0.26/0.71 (declare-fun tptp.product_fst_a_o_a_o (tptp.product_prod_a_o_a_o tptp.a) Bool)
% 0.26/0.71 (declare-fun tptp.produc1045727450_set_a (tptp.produc1561113620_set_a tptp.a) Bool)
% 0.26/0.71 (declare-fun tptp.produc870616579z_real (tptp.produc1892666919z_real) tptp.bounde472938360z_real)
% 0.26/0.71 (declare-fun tptp.produc1503602930_sc_sz (tptp.produc1821101996_sc_sz) tptp.denota610675952t_unit)
% 0.26/0.71 (declare-fun tptp.produc2010422875real_c (tptp.produc190496183real_c) tptp.finite1398487019real_c)
% 0.26/0.71 (declare-fun tptp.produc1111759555eal_sz (tptp.produc1149990247eal_sz) tptp.finite824932053eal_sz)
% 0.26/0.71 (declare-fun tptp.produc548504323_sc_sz (tptp.produc866628903_sc_sz) tptp.list_f1238882004_sc_sz)
% 0.26/0.71 (declare-fun tptp.produc286845635eal_sz (tptp.produc1241881959eal_sz) tptp.set_Fi291318197eal_sz)
% 0.26/0.71 (declare-fun tptp.produc38604755f_sz_o (tptp.produc1144880887f_sz_o) tptp.set_a)
% 0.26/0.71 (declare-fun tptp.produc1911461786_a_a_o (tptp.produc1989635468_a_a_o) tptp.set_a)
% 0.26/0.71 (declare-fun tptp.produc1926412547_set_a (tptp.produc1691597095_set_a) tptp.set_a)
% 0.26/0.71 (declare-fun tptp.produc1630531752_o_a_o (tptp.produc1065634396_o_a_o tptp.a) Bool)
% 0.26/0.71 (declare-fun tptp.produc776178293_set_a (tptp.produc903182423_set_a) tptp.set_a)
% 0.26/0.71 (declare-fun tptp.produc1070758376f_sz_o (tptp.produc1553439972f_sz_o tptp.trm_sf_sz tptp.trm_sf_sz) Bool)
% 0.26/0.71 (declare-fun tptp.product_snd_a_o_a_o (tptp.product_prod_a_o_a_o tptp.a) Bool)
% 0.26/0.71 (declare-fun tptp.produc1305389080_set_a (tptp.produc1561113620_set_a) tptp.set_a)
% 0.26/0.71 (declare-fun tptp.produc1422611269z_real (tptp.produc1892666919z_real) tptp.bounde472938360z_real)
% 0.26/0.71 (declare-fun tptp.produc974239792_sc_sz (tptp.produc1821101996_sc_sz) tptp.produc866628903_sc_sz)
% 0.26/0.71 (declare-fun tptp.produc314122909real_c (tptp.produc190496183real_c) tptp.finite1398487019real_c)
% 0.26/0.71 (declare-fun tptp.produc1269210629eal_sz (tptp.produc1149990247eal_sz) tptp.finite824932053eal_sz)
% 0.26/0.71 (declare-fun tptp.produc4753477_sc_sz (tptp.produc866628903_sc_sz) tptp.list_f1238882004_sc_sz)
% 0.26/0.71 (declare-fun tptp.produc1746886149eal_sz (tptp.produc1241881959eal_sz) tptp.set_Fi291318197eal_sz)
% 0.26/0.71 (declare-fun tptp.produc407510293f_sz_o (tptp.produc1144880887f_sz_o tptp.trm_sf_sz tptp.trm_sf_sz) Bool)
% 0.26/0.71 (declare-fun tptp.produc23639768_a_a_o (tptp.produc1989635468_a_a_o tptp.a) Bool)
% 0.26/0.71 (declare-fun tptp.produc918972485_set_a (tptp.produc1691597095_set_a) tptp.set_a)
% 0.26/0.71 (declare-fun tptp.collec451781861t_unit ((-> tptp.denota231621370t_unit Bool)) tptp.set_De455519194t_unit)
% 0.26/0.71 (declare-fun tptp.collec1767975749t_unit ((-> tptp.denota610675952t_unit Bool)) tptp.set_De208295462t_unit)
% 0.26/0.71 (declare-fun tptp.collec1002602816eal_sz ((-> tptp.finite824932053eal_sz Bool)) tptp.set_Fi291318197eal_sz)
% 0.26/0.71 (declare-fun tptp.collec1199592193_sc_sz ((-> tptp.produc1821101996_sc_sz Bool)) tptp.set_Pr1169339874_sc_sz)
% 0.26/0.71 (declare-fun tptp.collec2086029184um_b_c ((-> tptp.sum_su737395349um_b_c Bool)) tptp.set_Su1783761653um_b_c)
% 0.26/0.71 (declare-fun tptp.collect_trm_a_c ((-> tptp.trm_a_c Bool)) tptp.set_trm_a_c)
% 0.26/0.71 (declare-fun tptp.collect_trm_sf_sz ((-> tptp.trm_sf_sz Bool)) tptp.set_trm_sf_sz)
% 0.26/0.71 (declare-fun tptp.collect_a ((-> tptp.a Bool)) tptp.set_a)
% 0.26/0.71 (declare-fun tptp.static_FVDiff_a_c (tptp.trm_a_c) tptp.set_Sum_sum_c_c)
% 0.26/0.71 (declare-fun tptp.static_FVDiff_sf_sz (tptp.trm_sf_sz) tptp.set_Sum_sum_sz_sz)
% 0.26/0.71 (declare-fun tptp.static_FVT_a_c (tptp.trm_a_c) tptp.set_Sum_sum_c_c)
% 0.26/0.71 (declare-fun tptp.static_FVT_sf_sz (tptp.trm_sf_sz) tptp.set_Sum_sum_sz_sz)
% 0.26/0.71 (declare-fun tptp.static_SIGT_a_c (tptp.trm_a_c) tptp.set_a)
% 0.26/0.71 (declare-fun tptp.sum_In2139678582um_b_c (tptp.a) tptp.sum_su737395349um_b_c)
% 0.26/0.71 (declare-fun tptp.predic913887884_sf_sz (tptp.sc) tptp.formula_sf_sc_sz)
% 0.26/0.71 (declare-fun tptp.dfree_a_c (tptp.trm_a_c) Bool)
% 0.26/0.71 (declare-fun tptp.dfree_sf_sz (tptp.trm_sf_sz) Bool)
% 0.26/0.71 (declare-fun tptp.p_sc_sf_sz (tptp.sc) tptp.formula_sf_sc_sz)
% 0.26/0.71 (declare-fun tptp.empty_sz_sf (tptp.sz) tptp.trm_sf_sz)
% 0.26/0.71 (declare-fun tptp.f0_sf_sz (tptp.sf) tptp.trm_sf_sz)
% 0.26/0.71 (declare-fun tptp.function_a_c (tptp.a (-> tptp.c tptp.trm_a_c)) tptp.trm_a_c)
% 0.26/0.71 (declare-fun tptp.function_sf_sz (tptp.sf (-> tptp.sz tptp.trm_sf_sz)) tptp.trm_sf_sz)
% 0.26/0.71 (declare-fun tptp.plus_a_c (tptp.trm_a_c tptp.trm_a_c) tptp.trm_a_c)
% 0.26/0.71 (declare-fun tptp.plus_sf_sz (tptp.trm_sf_sz tptp.trm_sf_sz) tptp.trm_sf_sz)
% 0.26/0.71 (declare-fun tptp.times_a_c (tptp.trm_a_c tptp.trm_a_c) tptp.trm_a_c)
% 0.26/0.71 (declare-fun tptp.times_sf_sz (tptp.trm_sf_sz tptp.trm_sf_sz) tptp.trm_sf_sz)
% 0.26/0.71 (declare-fun tptp.topolo885751137z_real (tptp.set_Fi291318197eal_sz (-> tptp.finite824932053eal_sz tptp.bounde472938360z_real)) Bool)
% 0.26/0.71 (declare-fun tptp.topolo1027477648z_real (tptp.set_Fi291318197eal_sz (-> tptp.finite824932053eal_sz tptp.produc1892666919z_real)) Bool)
% 0.26/0.71 (declare-fun tptp.topolo1348430467z_real (tptp.set_Fi291318197eal_sz (-> tptp.finite824932053eal_sz tptp.real)) Bool)
% 0.26/0.71 (declare-fun tptp.type_d1092523951t_unit ((-> tptp.freche2095075217_sc_sz tptp.denota610675952t_unit) (-> tptp.denota610675952t_unit tptp.freche2095075217_sc_sz) tptp.set_De208295462t_unit) Bool)
% 0.26/0.71 (declare-fun tptp.type_d1238563341rm_a_c ((-> tptp.frechet_strm_a_c tptp.trm_a_c) (-> tptp.trm_a_c tptp.frechet_strm_a_c) tptp.set_trm_a_c) Bool)
% 0.26/0.71 (declare-fun tptp.type_d46389773_sf_sz ((-> tptp.frechet_strm_sf_sz tptp.trm_sf_sz) (-> tptp.trm_sf_sz tptp.frechet_strm_sf_sz) tptp.set_trm_sf_sz) Bool)
% 0.26/0.71 (declare-fun tptp.member1777622435t_unit (tptp.denota231621370t_unit tptp.set_De455519194t_unit) Bool)
% 0.26/0.71 (declare-fun tptp.member754147591t_unit (tptp.denota610675952t_unit tptp.set_De208295462t_unit) Bool)
% 0.26/0.71 (declare-fun tptp.member1693951742eal_sz (tptp.finite824932053eal_sz tptp.set_Fi291318197eal_sz) Bool)
% 0.26/0.71 (declare-fun tptp.member1057565379_sc_sz (tptp.produc1821101996_sc_sz tptp.set_Pr1169339874_sc_sz) Bool)
% 0.26/0.71 (declare-fun tptp.member1893232190um_b_c (tptp.sum_su737395349um_b_c tptp.set_Su1783761653um_b_c) Bool)
% 0.26/0.71 (declare-fun tptp.member_trm_a_c (tptp.trm_a_c tptp.set_trm_a_c) Bool)
% 0.26/0.71 (declare-fun tptp.member_trm_sf_sz (tptp.trm_sf_sz tptp.set_trm_sf_sz) Bool)
% 0.26/0.71 (declare-fun tptp.member_a (tptp.a tptp.set_a) Bool)
% 0.26/0.71 (declare-fun tptp.i () tptp.denota231621370t_unit)
% 0.26/0.71 (declare-fun tptp.j () tptp.denota231621370t_unit)
% 0.26/0.71 (declare-fun tptp.nu () tptp.produc190496183real_c)
% 0.26/0.71 (declare-fun tptp.nu2 () tptp.produc190496183real_c)
% 0.26/0.71 (declare-fun tptp.t1 () tptp.trm_a_c)
% 0.26/0.71 (declare-fun tptp.t2 () tptp.trm_a_c)
% 0.26/0.71 (assert (forall ((Nu tptp.produc1149990247eal_sz) (Nu2 tptp.produc1149990247eal_sz) (T1 tptp.trm_sf_sz) (T2 tptp.trm_sf_sz)) (let ((_let_1 (@ (@ tptp.denota102713844ree_sz Nu) Nu2))) (=> (@ _let_1 (@ tptp.static_FVDiff_sf_sz (@ (@ tptp.plus_sf_sz T1) T2))) (@ _let_1 (@ tptp.static_FVDiff_sf_sz T2))))))
% 0.26/0.71 (assert (forall ((Nu tptp.produc190496183real_c) (Nu2 tptp.produc190496183real_c) (T1 tptp.trm_a_c) (T2 tptp.trm_a_c)) (let ((_let_1 (@ (@ tptp.denota1997846518gree_c Nu) Nu2))) (=> (@ _let_1 (@ tptp.static_FVDiff_a_c (@ (@ tptp.plus_a_c T1) T2))) (@ _let_1 (@ tptp.static_FVDiff_a_c T2))))))
% 0.26/0.71 (assert (@ (@ (@ tptp.denota1997846518gree_c tptp.nu) tptp.nu2) (@ tptp.static_FVDiff_a_c (@ (@ tptp.plus_a_c tptp.t1) tptp.t2))))
% 0.26/0.71 (assert (@ (@ (@ tptp.denota1997846518gree_c tptp.nu) tptp.nu2) (@ tptp.static_FVDiff_a_c tptp.t1)))
% 0.26/0.71 (assert (@ tptp.dfree_a_c tptp.t2))
% 0.26/0.71 (assert (forall ((Nu tptp.produc1149990247eal_sz) (Nu2 tptp.produc1149990247eal_sz) (T1 tptp.trm_sf_sz) (T2 tptp.trm_sf_sz)) (let ((_let_1 (@ (@ tptp.denota102713844ree_sz Nu) Nu2))) (=> (@ _let_1 (@ tptp.static_FVDiff_sf_sz (@ (@ tptp.plus_sf_sz T1) T2))) (@ _let_1 (@ tptp.static_FVDiff_sf_sz T1))))))
% 0.26/0.71 (assert (forall ((Nu tptp.produc190496183real_c) (Nu2 tptp.produc190496183real_c) (T1 tptp.trm_a_c) (T2 tptp.trm_a_c)) (let ((_let_1 (@ (@ tptp.denota1997846518gree_c Nu) Nu2))) (=> (@ _let_1 (@ tptp.static_FVDiff_a_c (@ (@ tptp.plus_a_c T1) T2))) (@ _let_1 (@ tptp.static_FVDiff_a_c T1))))))
% 0.26/0.71 (assert (forall ((A tptp.produc1149990247eal_sz) (B tptp.produc1149990247eal_sz) (V tptp.set_Sum_sum_sz_sz)) (=> (@ (@ (@ tptp.denota102713844ree_sz A) B) V) (@ (@ (@ tptp.denota102713844ree_sz B) A) V))))
% 0.26/0.71 (assert (forall ((A tptp.produc190496183real_c) (B tptp.produc190496183real_c) (V tptp.set_Sum_sum_c_c)) (=> (@ (@ (@ tptp.denota1997846518gree_c A) B) V) (@ (@ (@ tptp.denota1997846518gree_c B) A) V))))
% 0.26/0.71 (assert (forall ((Nu tptp.produc1149990247eal_sz) (A tptp.set_Sum_sum_sz_sz)) (@ (@ (@ tptp.denota102713844ree_sz Nu) Nu) A)))
% 0.26/0.71 (assert (forall ((Nu tptp.produc190496183real_c) (A tptp.set_Sum_sum_c_c)) (@ (@ (@ tptp.denota1997846518gree_c Nu) Nu) A)))
% 0.26/0.71 (assert (@ tptp.dfree_a_c tptp.t1))
% 0.26/0.71 (assert (forall ((X tptp.freche2095075217_sc_sz) (Y tptp.freche2095075217_sc_sz)) (= (= (@ tptp.freche1421597129_sc_sz X) (@ tptp.freche1421597129_sc_sz Y)) (= X Y))))
% 0.26/0.71 (assert (forall ((X tptp.frechet_strm_sf_sz) (Y tptp.frechet_strm_sf_sz)) (= (= (@ tptp.freche782854530_sf_sz X) (@ tptp.freche782854530_sf_sz Y)) (= X Y))))
% 0.26/0.71 (assert (forall ((X tptp.frechet_strm_a_c) (Y tptp.frechet_strm_a_c)) (= (= (@ tptp.frechet_raw_term_a_c X) (@ tptp.frechet_raw_term_a_c Y)) (= X Y))))
% 0.26/0.71 (assert (forall ((Nu tptp.produc1149990247eal_sz) (Nu2 tptp.produc1149990247eal_sz) (T1 tptp.trm_sf_sz) (T2 tptp.trm_sf_sz)) (let ((_let_1 (@ (@ tptp.denota102713844ree_sz Nu) Nu2))) (=> (@ _let_1 (@ tptp.static_FVDiff_sf_sz (@ (@ tptp.times_sf_sz T1) T2))) (@ _let_1 (@ tptp.static_FVDiff_sf_sz T1))))))
% 0.26/0.71 (assert (forall ((Nu tptp.produc190496183real_c) (Nu2 tptp.produc190496183real_c) (T1 tptp.trm_a_c) (T2 tptp.trm_a_c)) (let ((_let_1 (@ (@ tptp.denota1997846518gree_c Nu) Nu2))) (=> (@ _let_1 (@ tptp.static_FVDiff_a_c (@ (@ tptp.times_a_c T1) T2))) (@ _let_1 (@ tptp.static_FVDiff_a_c T1))))))
% 0.26/0.71 (assert (forall ((Nu tptp.produc1149990247eal_sz) (Nu2 tptp.produc1149990247eal_sz) (T1 tptp.trm_sf_sz) (T2 tptp.trm_sf_sz)) (let ((_let_1 (@ (@ tptp.denota102713844ree_sz Nu) Nu2))) (=> (@ _let_1 (@ tptp.static_FVDiff_sf_sz (@ (@ tptp.times_sf_sz T1) T2))) (@ _let_1 (@ tptp.static_FVDiff_sf_sz T2))))))
% 0.26/0.71 (assert (forall ((Nu tptp.produc190496183real_c) (Nu2 tptp.produc190496183real_c) (T1 tptp.trm_a_c) (T2 tptp.trm_a_c)) (let ((_let_1 (@ (@ tptp.denota1997846518gree_c Nu) Nu2))) (=> (@ _let_1 (@ tptp.static_FVDiff_a_c (@ (@ tptp.times_a_c T1) T2))) (@ _let_1 (@ tptp.static_FVDiff_a_c T2))))))
% 0.26/0.71 (assert (forall ((Nu tptp.produc1149990247eal_sz) (Nu2 tptp.produc1149990247eal_sz) (Var tptp.sf) (Args (-> tptp.sz tptp.trm_sf_sz)) (I tptp.sz)) (let ((_let_1 (@ (@ tptp.denota102713844ree_sz Nu) Nu2))) (=> (@ _let_1 (@ tptp.static_FVDiff_sf_sz (@ (@ tptp.function_sf_sz Var) Args))) (@ _let_1 (@ tptp.static_FVDiff_sf_sz (@ Args I)))))))
% 0.26/0.71 (assert (forall ((Nu tptp.produc190496183real_c) (Nu2 tptp.produc190496183real_c) (Var tptp.a) (Args (-> tptp.c tptp.trm_a_c)) (I tptp.c)) (let ((_let_1 (@ (@ tptp.denota1997846518gree_c Nu) Nu2))) (=> (@ _let_1 (@ tptp.static_FVDiff_a_c (@ (@ tptp.function_a_c Var) Args))) (@ _let_1 (@ tptp.static_FVDiff_a_c (@ Args I)))))))
% 0.26/0.71 (assert (= tptp.p_sc_sf_sz tptp.predic913887884_sf_sz))
% 0.26/0.71 (assert (=> (@ (@ (@ tptp.denota1997846518gree_c tptp.nu) tptp.nu2) (@ tptp.static_FVDiff_a_c tptp.t2)) (=> (@ (@ (@ tptp.denota69106024_a_b_c tptp.i) tptp.j) (@ tptp.collec2086029184um_b_c (lambda ((Uu tptp.sum_su737395349um_b_c)) (exists ((X2 tptp.a)) (and (= Uu (@ tptp.sum_In2139678582um_b_c X2)) (@ (@ tptp.member_a X2) (@ tptp.static_SIGT_a_c tptp.t2))))))) (= (@ (@ (@ (@ tptp.denota229585092_a_b_c tptp.i) tptp.t2) (@ tptp.produc2010422875real_c tptp.nu)) (@ tptp.produc314122909real_c tptp.nu)) (@ (@ (@ (@ tptp.denota229585092_a_b_c tptp.j) tptp.t2) (@ tptp.produc2010422875real_c tptp.nu2)) (@ tptp.produc314122909real_c tptp.nu2))))))
% 0.26/0.71 (assert (forall ((X tptp.produc1821101996_sc_sz)) (not (forall ((I2 tptp.denota610675952t_unit) (S tptp.produc866628903_sc_sz)) (not (= X (@ (@ tptp.produc789536734_sc_sz I2) S)))))))
% 0.26/0.71 (assert (forall ((X tptp.frechet_strm_a_c)) (@ (@ tptp.member_trm_a_c (@ tptp.frechet_raw_term_a_c X)) (@ tptp.collect_trm_a_c tptp.dfree_a_c))))
% 0.26/0.71 (assert (forall ((X tptp.frechet_strm_sf_sz)) (@ (@ tptp.member_trm_sf_sz (@ tptp.freche782854530_sf_sz X)) (@ tptp.collect_trm_sf_sz tptp.dfree_sf_sz))))
% 0.26/0.71 (assert (forall ((Y tptp.trm_a_c)) (=> (@ (@ tptp.member_trm_a_c Y) (@ tptp.collect_trm_a_c tptp.dfree_a_c)) (not (forall ((X3 tptp.frechet_strm_a_c)) (not (= Y (@ tptp.frechet_raw_term_a_c X3))))))))
% 0.26/0.71 (assert (forall ((Y tptp.trm_sf_sz)) (=> (@ (@ tptp.member_trm_sf_sz Y) (@ tptp.collect_trm_sf_sz tptp.dfree_sf_sz)) (not (forall ((X3 tptp.frechet_strm_sf_sz)) (not (= Y (@ tptp.freche782854530_sf_sz X3))))))))
% 0.26/0.71 (assert (forall ((Y tptp.trm_a_c) (P (-> tptp.trm_a_c Bool))) (=> (@ (@ tptp.member_trm_a_c Y) (@ tptp.collect_trm_a_c tptp.dfree_a_c)) (=> (forall ((X3 tptp.frechet_strm_a_c)) (@ P (@ tptp.frechet_raw_term_a_c X3))) (@ P Y)))))
% 0.26/0.71 (assert (forall ((Y tptp.trm_sf_sz) (P (-> tptp.trm_sf_sz Bool))) (=> (@ (@ tptp.member_trm_sf_sz Y) (@ tptp.collect_trm_sf_sz tptp.dfree_sf_sz)) (=> (forall ((X3 tptp.frechet_strm_sf_sz)) (@ P (@ tptp.freche782854530_sf_sz X3))) (@ P Y)))))
% 0.26/0.71 (assert (forall ((Theta tptp.trm_a_c) (Nu tptp.produc190496183real_c) (Nu2 tptp.produc190496183real_c) (I3 tptp.denota231621370t_unit)) (let ((_let_1 (@ (@ tptp.denota229585092_a_b_c I3) Theta))) (=> (@ tptp.dfree_a_c Theta) (=> (@ (@ (@ tptp.denota1997846518gree_c Nu) Nu2) (@ tptp.static_FVDiff_a_c Theta)) (= (@ (@ _let_1 (@ tptp.produc2010422875real_c Nu)) (@ tptp.produc314122909real_c Nu)) (@ (@ _let_1 (@ tptp.produc2010422875real_c Nu2)) (@ tptp.produc314122909real_c Nu2))))))))
% 0.26/0.71 (assert (forall ((Theta tptp.trm_sf_sz) (Nu tptp.produc1149990247eal_sz) (Nu2 tptp.produc1149990247eal_sz) (I3 tptp.denota610675952t_unit)) (let ((_let_1 (@ (@ tptp.denota1979904720_sc_sz I3) Theta))) (=> (@ tptp.dfree_sf_sz Theta) (=> (@ (@ (@ tptp.denota102713844ree_sz Nu) Nu2) (@ tptp.static_FVDiff_sf_sz Theta)) (= (@ (@ _let_1 (@ tptp.produc1111759555eal_sz Nu)) (@ tptp.produc1269210629eal_sz Nu)) (@ (@ _let_1 (@ tptp.produc1111759555eal_sz Nu2)) (@ tptp.produc1269210629eal_sz Nu2))))))))
% 0.26/0.71 (assert (@ (@ (@ tptp.denota69106024_a_b_c tptp.i) tptp.j) (@ tptp.collec2086029184um_b_c (lambda ((Uu tptp.sum_su737395349um_b_c)) (exists ((X2 tptp.a)) (and (= Uu (@ tptp.sum_In2139678582um_b_c X2)) (@ (@ tptp.member_a X2) (@ tptp.static_SIGT_a_c (@ (@ tptp.plus_a_c tptp.t1) tptp.t2)))))))))
% 0.26/0.71 (assert (@ (@ (@ tptp.denota69106024_a_b_c tptp.i) tptp.j) (@ tptp.collec2086029184um_b_c (lambda ((Uu tptp.sum_su737395349um_b_c)) (exists ((X2 tptp.a)) (and (= Uu (@ tptp.sum_In2139678582um_b_c X2)) (@ (@ tptp.member_a X2) (@ tptp.static_SIGT_a_c tptp.t1))))))))
% 0.26/0.71 (assert (@ (@ (@ tptp.denota69106024_a_b_c tptp.i) tptp.j) (@ tptp.collec2086029184um_b_c (lambda ((Uu tptp.sum_su737395349um_b_c)) (exists ((X2 tptp.a)) (and (= Uu (@ tptp.sum_In2139678582um_b_c X2)) (@ (@ tptp.member_a X2) (@ tptp.static_SIGT_a_c tptp.t2))))))))
% 0.26/0.71 (assert (=> (@ (@ (@ tptp.denota1997846518gree_c tptp.nu) tptp.nu2) (@ tptp.static_FVDiff_a_c tptp.t1)) (=> (@ (@ (@ tptp.denota69106024_a_b_c tptp.i) tptp.j) (@ tptp.collec2086029184um_b_c (lambda ((Uu tptp.sum_su737395349um_b_c)) (exists ((X2 tptp.a)) (and (= Uu (@ tptp.sum_In2139678582um_b_c X2)) (@ (@ tptp.member_a X2) (@ tptp.static_SIGT_a_c tptp.t1))))))) (= (@ (@ (@ (@ tptp.denota229585092_a_b_c tptp.i) tptp.t1) (@ tptp.produc2010422875real_c tptp.nu)) (@ tptp.produc314122909real_c tptp.nu)) (@ (@ (@ (@ tptp.denota229585092_a_b_c tptp.j) tptp.t1) (@ tptp.produc2010422875real_c tptp.nu2)) (@ tptp.produc314122909real_c tptp.nu2))))))
% 0.26/0.71 (assert (forall ((A tptp.denota231621370t_unit) (B tptp.denota231621370t_unit) (V tptp.set_Su1783761653um_b_c)) (=> (@ (@ (@ tptp.denota69106024_a_b_c A) B) V) (@ (@ (@ tptp.denota69106024_a_b_c B) A) V))))
% 0.26/0.71 (assert (forall ((I3 tptp.denota231621370t_unit) (A tptp.set_Su1783761653um_b_c)) (@ (@ (@ tptp.denota69106024_a_b_c I3) I3) A)))
% 0.26/0.71 (assert (@ (@ tptp.ord_le929608341um_b_c (@ tptp.collec2086029184um_b_c (lambda ((Uu tptp.sum_su737395349um_b_c)) (exists ((X2 tptp.a)) (and (= Uu (@ tptp.sum_In2139678582um_b_c X2)) (@ (@ tptp.member_a X2) (@ tptp.static_SIGT_a_c tptp.t2))))))) (@ tptp.collec2086029184um_b_c (lambda ((Uu tptp.sum_su737395349um_b_c)) (exists ((X2 tptp.a)) (and (= Uu (@ tptp.sum_In2139678582um_b_c X2)) (@ (@ tptp.member_a X2) (@ tptp.static_SIGT_a_c (@ (@ tptp.plus_a_c tptp.t1) tptp.t2)))))))))
% 0.26/0.71 (assert (@ (@ tptp.ord_le929608341um_b_c (@ tptp.collec2086029184um_b_c (lambda ((Uu tptp.sum_su737395349um_b_c)) (exists ((X2 tptp.a)) (and (= Uu (@ tptp.sum_In2139678582um_b_c X2)) (@ (@ tptp.member_a X2) (@ tptp.static_SIGT_a_c tptp.t1))))))) (@ tptp.collec2086029184um_b_c (lambda ((Uu tptp.sum_su737395349um_b_c)) (exists ((X2 tptp.a)) (and (= Uu (@ tptp.sum_In2139678582um_b_c X2)) (@ (@ tptp.member_a X2) (@ tptp.static_SIGT_a_c (@ (@ tptp.plus_a_c tptp.t1) tptp.t2)))))))))
% 0.26/0.71 (assert (forall ((Y tptp.trm_a_c)) (=> (@ (@ tptp.member_trm_a_c Y) (@ tptp.collect_trm_a_c tptp.dfree_a_c)) (= (@ tptp.frechet_raw_term_a_c (@ tptp.freche665377492rm_a_c Y)) Y))))
% 0.26/0.71 (assert (forall ((Y tptp.trm_sf_sz)) (=> (@ (@ tptp.member_trm_sf_sz Y) (@ tptp.collect_trm_sf_sz tptp.dfree_sf_sz)) (= (@ tptp.freche782854530_sf_sz (@ tptp.freche1046279700_sf_sz Y)) Y))))
% 0.26/0.71 (assert (forall ((Prod tptp.produc866628903_sc_sz)) (= (@ (@ tptp.produc1822718231_sc_sz (@ tptp.produc548504323_sc_sz Prod)) (@ tptp.produc4753477_sc_sz Prod)) Prod)))
% 0.26/0.71 (assert (forall ((Prod tptp.produc1241881959eal_sz)) (= (@ (@ tptp.produc1235791063eal_sz (@ tptp.produc286845635eal_sz Prod)) (@ tptp.produc1746886149eal_sz Prod)) Prod)))
% 0.26/0.71 (assert (forall ((Prod tptp.produc1892666919z_real)) (= (@ (@ tptp.produc784663575z_real (@ tptp.produc870616579z_real Prod)) (@ tptp.produc1422611269z_real Prod)) Prod)))
% 0.26/0.71 (assert (forall ((Prod tptp.produc1149990247eal_sz)) (= (@ (@ tptp.produc1308130519eal_sz (@ tptp.produc1111759555eal_sz Prod)) (@ tptp.produc1269210629eal_sz Prod)) Prod)))
% 0.26/0.71 (assert (forall ((Prod tptp.produc1821101996_sc_sz)) (= (@ (@ tptp.produc789536734_sc_sz (@ tptp.produc1503602930_sc_sz Prod)) (@ tptp.produc974239792_sc_sz Prod)) Prod)))
% 0.26/0.71 (assert (forall ((Prod tptp.produc190496183real_c)) (= (@ (@ tptp.produc394644079real_c (@ tptp.produc2010422875real_c Prod)) (@ tptp.produc314122909real_c Prod)) Prod)))
% 0.26/0.71 (assert (= tptp.freche58918398_sc_sz (lambda ((X2 tptp.denota610675952t_unit) (Y2 tptp.freche2095075217_sc_sz)) (= X2 (@ tptp.freche1421597129_sc_sz Y2)))))
% 0.26/0.71 (assert (= tptp.freche1244000341_sf_sz (lambda ((X2 tptp.trm_sf_sz) (Y2 tptp.frechet_strm_sf_sz)) (= X2 (@ tptp.freche782854530_sf_sz Y2)))))
% 0.26/0.71 (assert (= tptp.frechet_cr_strm_a_c (lambda ((X2 tptp.trm_a_c) (Y2 tptp.frechet_strm_a_c)) (= X2 (@ tptp.frechet_raw_term_a_c Y2)))))
% 0.26/0.71 (assert (forall ((A2 tptp.trm_a_c) (B2 tptp.trm_a_c)) (= (@ tptp.dfree_a_c (@ (@ tptp.times_a_c A2) B2)) (and (@ tptp.dfree_a_c A2) (@ tptp.dfree_a_c B2)))))
% 0.26/0.71 (assert (forall ((A2 tptp.trm_sf_sz) (B2 tptp.trm_sf_sz)) (= (@ tptp.dfree_sf_sz (@ (@ tptp.times_sf_sz A2) B2)) (and (@ tptp.dfree_sf_sz A2) (@ tptp.dfree_sf_sz B2)))))
% 0.26/0.71 (assert (forall ((A2 tptp.trm_sf_sz) (B2 tptp.trm_sf_sz)) (= (@ tptp.dfree_sf_sz (@ (@ tptp.plus_sf_sz A2) B2)) (and (@ tptp.dfree_sf_sz A2) (@ tptp.dfree_sf_sz B2)))))
% 0.26/0.71 (assert (forall ((A2 tptp.trm_a_c) (B2 tptp.trm_a_c)) (= (@ tptp.dfree_a_c (@ (@ tptp.plus_a_c A2) B2)) (and (@ tptp.dfree_a_c A2) (@ tptp.dfree_a_c B2)))))
% 0.26/0.71 (assert (forall ((I tptp.a) (Args (-> tptp.c tptp.trm_a_c))) (= (@ tptp.dfree_a_c (@ (@ tptp.function_a_c I) Args)) (forall ((X2 tptp.c)) (@ tptp.dfree_a_c (@ Args X2))))))
% 0.26/0.71 (assert (forall ((I tptp.sf) (Args (-> tptp.sz tptp.trm_sf_sz))) (= (@ tptp.dfree_sf_sz (@ (@ tptp.function_sf_sz I) Args)) (forall ((X2 tptp.sz)) (@ tptp.dfree_sf_sz (@ Args X2))))))
% 0.26/0.71 (assert (forall ((X tptp.frechet_strm_a_c)) (not (forall ((Y3 tptp.trm_a_c)) (=> (= X (@ tptp.freche665377492rm_a_c Y3)) (not (@ (@ tptp.member_trm_a_c Y3) (@ tptp.collect_trm_a_c tptp.dfree_a_c))))))))
% 0.26/0.71 (assert (forall ((X tptp.frechet_strm_sf_sz)) (not (forall ((Y3 tptp.trm_sf_sz)) (=> (= X (@ tptp.freche1046279700_sf_sz Y3)) (not (@ (@ tptp.member_trm_sf_sz Y3) (@ tptp.collect_trm_sf_sz tptp.dfree_sf_sz))))))))
% 0.26/0.71 (assert (forall ((X tptp.frechet_strm_a_c)) (= (@ tptp.freche665377492rm_a_c (@ tptp.frechet_raw_term_a_c X)) X)))
% 0.26/0.71 (assert (forall ((X tptp.frechet_strm_sf_sz)) (= (@ tptp.freche1046279700_sf_sz (@ tptp.freche782854530_sf_sz X)) X)))
% 0.26/0.71 (assert (forall ((X tptp.trm_a_c) (Y tptp.trm_a_c)) (let ((_let_1 (@ tptp.collect_trm_a_c tptp.dfree_a_c))) (=> (@ (@ tptp.member_trm_a_c X) _let_1) (=> (@ (@ tptp.member_trm_a_c Y) _let_1) (= (= (@ tptp.freche665377492rm_a_c X) (@ tptp.freche665377492rm_a_c Y)) (= X Y)))))))
% 0.26/0.71 (assert (forall ((X tptp.trm_sf_sz) (Y tptp.trm_sf_sz)) (let ((_let_1 (@ tptp.collect_trm_sf_sz tptp.dfree_sf_sz))) (=> (@ (@ tptp.member_trm_sf_sz X) _let_1) (=> (@ (@ tptp.member_trm_sf_sz Y) _let_1) (= (= (@ tptp.freche1046279700_sf_sz X) (@ tptp.freche1046279700_sf_sz Y)) (= X Y)))))))
% 0.26/0.71 (assert (forall ((P (-> tptp.frechet_strm_a_c Bool)) (X tptp.frechet_strm_a_c)) (=> (forall ((Y3 tptp.trm_a_c)) (=> (@ (@ tptp.member_trm_a_c Y3) (@ tptp.collect_trm_a_c tptp.dfree_a_c)) (@ P (@ tptp.freche665377492rm_a_c Y3)))) (@ P X))))
% 0.26/0.71 (assert (forall ((P (-> tptp.frechet_strm_sf_sz Bool)) (X tptp.frechet_strm_sf_sz)) (=> (forall ((Y3 tptp.trm_sf_sz)) (=> (@ (@ tptp.member_trm_sf_sz Y3) (@ tptp.collect_trm_sf_sz tptp.dfree_sf_sz)) (@ P (@ tptp.freche1046279700_sf_sz Y3)))) (@ P X))))
% 0.26/0.71 (assert (forall ((A2 tptp.finite1398487019real_c) (B2 tptp.finite1398487019real_c) (A3 tptp.finite1398487019real_c) (B3 tptp.finite1398487019real_c)) (= (= (@ (@ tptp.produc394644079real_c A2) B2) (@ (@ tptp.produc394644079real_c A3) B3)) (and (= A2 A3) (= B2 B3)))))
% 0.26/0.71 (assert (forall ((A2 tptp.list_f1238882004_sc_sz) (B2 tptp.list_f1238882004_sc_sz) (A3 tptp.list_f1238882004_sc_sz) (B3 tptp.list_f1238882004_sc_sz)) (= (= (@ (@ tptp.produc1822718231_sc_sz A2) B2) (@ (@ tptp.produc1822718231_sc_sz A3) B3)) (and (= A2 A3) (= B2 B3)))))
% 0.26/0.71 (assert (forall ((A2 tptp.set_Fi291318197eal_sz) (B2 tptp.set_Fi291318197eal_sz) (A3 tptp.set_Fi291318197eal_sz) (B3 tptp.set_Fi291318197eal_sz)) (= (= (@ (@ tptp.produc1235791063eal_sz A2) B2) (@ (@ tptp.produc1235791063eal_sz A3) B3)) (and (= A2 A3) (= B2 B3)))))
% 0.26/0.71 (assert (forall ((A2 tptp.bounde472938360z_real) (B2 tptp.bounde472938360z_real) (A3 tptp.bounde472938360z_real) (B3 tptp.bounde472938360z_real)) (= (= (@ (@ tptp.produc784663575z_real A2) B2) (@ (@ tptp.produc784663575z_real A3) B3)) (and (= A2 A3) (= B2 B3)))))
% 0.26/0.71 (assert (forall ((A2 tptp.denota610675952t_unit) (B2 tptp.produc866628903_sc_sz) (A3 tptp.denota610675952t_unit) (B3 tptp.produc866628903_sc_sz)) (= (= (@ (@ tptp.produc789536734_sc_sz A2) B2) (@ (@ tptp.produc789536734_sc_sz A3) B3)) (and (= A2 A3) (= B2 B3)))))
% 0.26/0.71 (assert (forall ((X1 tptp.finite1398487019real_c) (X22 tptp.finite1398487019real_c) (Y1 tptp.finite1398487019real_c) (Y22 tptp.finite1398487019real_c)) (= (= (@ (@ tptp.produc394644079real_c X1) X22) (@ (@ tptp.produc394644079real_c Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 0.26/0.71 (assert (forall ((X1 tptp.list_f1238882004_sc_sz) (X22 tptp.list_f1238882004_sc_sz) (Y1 tptp.list_f1238882004_sc_sz) (Y22 tptp.list_f1238882004_sc_sz)) (= (= (@ (@ tptp.produc1822718231_sc_sz X1) X22) (@ (@ tptp.produc1822718231_sc_sz Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 0.26/0.71 (assert (forall ((X1 tptp.set_Fi291318197eal_sz) (X22 tptp.set_Fi291318197eal_sz) (Y1 tptp.set_Fi291318197eal_sz) (Y22 tptp.set_Fi291318197eal_sz)) (= (= (@ (@ tptp.produc1235791063eal_sz X1) X22) (@ (@ tptp.produc1235791063eal_sz Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 0.26/0.71 (assert (forall ((X1 tptp.bounde472938360z_real) (X22 tptp.bounde472938360z_real) (Y1 tptp.bounde472938360z_real) (Y22 tptp.bounde472938360z_real)) (= (= (@ (@ tptp.produc784663575z_real X1) X22) (@ (@ tptp.produc784663575z_real Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 0.26/0.71 (assert (forall ((X1 tptp.denota610675952t_unit) (X22 tptp.produc866628903_sc_sz) (Y1 tptp.denota610675952t_unit) (Y22 tptp.produc866628903_sc_sz)) (= (= (@ (@ tptp.produc789536734_sc_sz X1) X22) (@ (@ tptp.produc789536734_sc_sz Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 0.26/0.71 (assert (forall ((X31 tptp.a) (X32 (-> tptp.c tptp.trm_a_c)) (Y31 tptp.a) (Y32 (-> tptp.c tptp.trm_a_c))) (= (= (@ (@ tptp.function_a_c X31) X32) (@ (@ tptp.function_a_c Y31) Y32)) (and (= X31 Y31) (= X32 Y32)))))
% 0.26/0.71 (assert (forall ((X31 tptp.sf) (X32 (-> tptp.sz tptp.trm_sf_sz)) (Y31 tptp.sf) (Y32 (-> tptp.sz tptp.trm_sf_sz))) (= (= (@ (@ tptp.function_sf_sz X31) X32) (@ (@ tptp.function_sf_sz Y31) Y32)) (and (= X31 Y31) (= X32 Y32)))))
% 0.26/0.71 (assert (forall ((X41 tptp.trm_sf_sz) (X42 tptp.trm_sf_sz) (Y41 tptp.trm_sf_sz) (Y42 tptp.trm_sf_sz)) (= (= (@ (@ tptp.plus_sf_sz X41) X42) (@ (@ tptp.plus_sf_sz Y41) Y42)) (and (= X41 Y41) (= X42 Y42)))))
% 0.26/0.71 (assert (forall ((X41 tptp.trm_a_c) (X42 tptp.trm_a_c) (Y41 tptp.trm_a_c) (Y42 tptp.trm_a_c)) (= (= (@ (@ tptp.plus_a_c X41) X42) (@ (@ tptp.plus_a_c Y41) Y42)) (and (= X41 Y41) (= X42 Y42)))))
% 0.26/0.71 (assert (forall ((X51 tptp.trm_a_c) (X52 tptp.trm_a_c) (Y51 tptp.trm_a_c) (Y52 tptp.trm_a_c)) (= (= (@ (@ tptp.times_a_c X51) X52) (@ (@ tptp.times_a_c Y51) Y52)) (and (= X51 Y51) (= X52 Y52)))))
% 0.26/0.71 (assert (forall ((X51 tptp.trm_sf_sz) (X52 tptp.trm_sf_sz) (Y51 tptp.trm_sf_sz) (Y52 tptp.trm_sf_sz)) (= (= (@ (@ tptp.times_sf_sz X51) X52) (@ (@ tptp.times_sf_sz Y51) Y52)) (and (= X51 Y51) (= X52 Y52)))))
% 0.26/0.71 (assert (forall ((A2 tptp.finite824932053eal_sz) (P (-> tptp.finite824932053eal_sz Bool))) (= (@ (@ tptp.member1693951742eal_sz A2) (@ tptp.collec1002602816eal_sz P)) (@ P A2))))
% 0.26/0.71 (assert (forall ((A2 tptp.produc1821101996_sc_sz) (P (-> tptp.produc1821101996_sc_sz Bool))) (= (@ (@ tptp.member1057565379_sc_sz A2) (@ tptp.collec1199592193_sc_sz P)) (@ P A2))))
% 0.26/0.71 (assert (forall ((A2 tptp.trm_sf_sz) (P (-> tptp.trm_sf_sz Bool))) (= (@ (@ tptp.member_trm_sf_sz A2) (@ tptp.collect_trm_sf_sz P)) (@ P A2))))
% 0.26/0.71 (assert (forall ((A2 tptp.trm_a_c) (P (-> tptp.trm_a_c Bool))) (= (@ (@ tptp.member_trm_a_c A2) (@ tptp.collect_trm_a_c P)) (@ P A2))))
% 0.26/0.71 (assert (forall ((A2 tptp.a) (P (-> tptp.a Bool))) (= (@ (@ tptp.member_a A2) (@ tptp.collect_a P)) (@ P A2))))
% 0.26/0.71 (assert (forall ((A2 tptp.sum_su737395349um_b_c) (P (-> tptp.sum_su737395349um_b_c Bool))) (= (@ (@ tptp.member1893232190um_b_c A2) (@ tptp.collec2086029184um_b_c P)) (@ P A2))))
% 0.26/0.71 (assert (forall ((A tptp.set_Fi291318197eal_sz)) (= (@ tptp.collec1002602816eal_sz (lambda ((X2 tptp.finite824932053eal_sz)) (@ (@ tptp.member1693951742eal_sz X2) A))) A)))
% 0.26/0.71 (assert (forall ((A tptp.set_Pr1169339874_sc_sz)) (= (@ tptp.collec1199592193_sc_sz (lambda ((X2 tptp.produc1821101996_sc_sz)) (@ (@ tptp.member1057565379_sc_sz X2) A))) A)))
% 0.26/0.71 (assert (forall ((A tptp.set_trm_sf_sz)) (= (@ tptp.collect_trm_sf_sz (lambda ((X2 tptp.trm_sf_sz)) (@ (@ tptp.member_trm_sf_sz X2) A))) A)))
% 0.26/0.71 (assert (forall ((A tptp.set_trm_a_c)) (= (@ tptp.collect_trm_a_c (lambda ((X2 tptp.trm_a_c)) (@ (@ tptp.member_trm_a_c X2) A))) A)))
% 0.26/0.71 (assert (forall ((A tptp.set_a)) (= (@ tptp.collect_a (lambda ((X2 tptp.a)) (@ (@ tptp.member_a X2) A))) A)))
% 0.26/0.71 (assert (forall ((A tptp.set_Su1783761653um_b_c)) (= (@ tptp.collec2086029184um_b_c (lambda ((X2 tptp.sum_su737395349um_b_c)) (@ (@ tptp.member1893232190um_b_c X2) A))) A)))
% 0.26/0.71 (assert (forall ((P (-> tptp.finite824932053eal_sz Bool)) (Q (-> tptp.finite824932053eal_sz Bool))) (=> (forall ((X3 tptp.finite824932053eal_sz)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collec1002602816eal_sz P) (@ tptp.collec1002602816eal_sz Q)))))
% 0.26/0.71 (assert (forall ((P (-> tptp.produc1821101996_sc_sz Bool)) (Q (-> tptp.produc1821101996_sc_sz Bool))) (=> (forall ((X3 tptp.produc1821101996_sc_sz)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collec1199592193_sc_sz P) (@ tptp.collec1199592193_sc_sz Q)))))
% 0.26/0.71 (assert (forall ((P (-> tptp.trm_sf_sz Bool)) (Q (-> tptp.trm_sf_sz Bool))) (=> (forall ((X3 tptp.trm_sf_sz)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collect_trm_sf_sz P) (@ tptp.collect_trm_sf_sz Q)))))
% 0.26/0.71 (assert (forall ((P (-> tptp.trm_a_c Bool)) (Q (-> tptp.trm_a_c Bool))) (=> (forall ((X3 tptp.trm_a_c)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collect_trm_a_c P) (@ tptp.collect_trm_a_c Q)))))
% 0.26/0.71 (assert (forall ((P (-> tptp.a Bool)) (Q (-> tptp.a Bool))) (=> (forall ((X3 tptp.a)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collect_a P) (@ tptp.collect_a Q)))))
% 0.26/0.71 (assert (forall ((P (-> tptp.sum_su737395349um_b_c Bool)) (Q (-> tptp.sum_su737395349um_b_c Bool))) (=> (forall ((X3 tptp.sum_su737395349um_b_c)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collec2086029184um_b_c P) (@ tptp.collec2086029184um_b_c Q)))))
% 0.26/0.71 (assert (forall ((A tptp.set_Sum_sum_sz_sz) (B tptp.set_Sum_sum_sz_sz) (Nu tptp.produc1149990247eal_sz) (Omega tptp.produc1149990247eal_sz)) (let ((_let_1 (@ (@ tptp.denota102713844ree_sz Nu) Omega))) (=> (@ (@ tptp.ord_le1110131657_sz_sz A) B) (=> (@ _let_1 B) (@ _let_1 A))))))
% 0.26/0.71 (assert (forall ((A tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c) (Nu tptp.produc190496183real_c) (Omega tptp.produc190496183real_c)) (let ((_let_1 (@ (@ tptp.denota1997846518gree_c Nu) Omega))) (=> (@ (@ tptp.ord_le1772180283um_c_c A) B) (=> (@ _let_1 B) (@ _let_1 A))))))
% 0.26/0.71 (assert (forall ((B tptp.set_Sum_sum_sz_sz) (A tptp.set_Sum_sum_sz_sz) (Nu tptp.produc1149990247eal_sz) (Nu2 tptp.produc1149990247eal_sz)) (let ((_let_1 (@ (@ tptp.denota102713844ree_sz Nu) Nu2))) (=> (@ (@ tptp.ord_le1110131657_sz_sz B) A) (=> (@ _let_1 A) (@ _let_1 B))))))
% 0.26/0.71 (assert (forall ((B tptp.set_Sum_sum_c_c) (A tptp.set_Sum_sum_c_c) (Nu tptp.produc190496183real_c) (Nu2 tptp.produc190496183real_c)) (let ((_let_1 (@ (@ tptp.denota1997846518gree_c Nu) Nu2))) (=> (@ (@ tptp.ord_le1772180283um_c_c B) A) (=> (@ _let_1 A) (@ _let_1 B))))))
% 0.26/0.71 (assert (forall ((P (-> tptp.produc190496183real_c Bool)) (Prod tptp.produc190496183real_c)) (=> (forall ((A4 tptp.finite1398487019real_c) (B4 tptp.finite1398487019real_c)) (@ P (@ (@ tptp.produc394644079real_c A4) B4))) (@ P Prod))))
% 0.26/0.71 (assert (forall ((P (-> tptp.produc866628903_sc_sz Bool)) (Prod tptp.produc866628903_sc_sz)) (=> (forall ((A4 tptp.list_f1238882004_sc_sz) (B4 tptp.list_f1238882004_sc_sz)) (@ P (@ (@ tptp.produc1822718231_sc_sz A4) B4))) (@ P Prod))))
% 0.26/0.71 (assert (forall ((P (-> tptp.produc1241881959eal_sz Bool)) (Prod tptp.produc1241881959eal_sz)) (=> (forall ((A4 tptp.set_Fi291318197eal_sz) (B4 tptp.set_Fi291318197eal_sz)) (@ P (@ (@ tptp.produc1235791063eal_sz A4) B4))) (@ P Prod))))
% 0.26/0.71 (assert (forall ((P (-> tptp.produc1892666919z_real Bool)) (Prod tptp.produc1892666919z_real)) (=> (forall ((A4 tptp.bounde472938360z_real) (B4 tptp.bounde472938360z_real)) (@ P (@ (@ tptp.produc784663575z_real A4) B4))) (@ P Prod))))
% 0.26/0.71 (assert (forall ((P (-> tptp.produc1821101996_sc_sz Bool)) (Prod tptp.produc1821101996_sc_sz)) (=> (forall ((A4 tptp.denota610675952t_unit) (B4 tptp.produc866628903_sc_sz)) (@ P (@ (@ tptp.produc789536734_sc_sz A4) B4))) (@ P Prod))))
% 0.26/0.71 (assert (forall ((Y tptp.produc190496183real_c)) (not (forall ((A4 tptp.finite1398487019real_c) (B4 tptp.finite1398487019real_c)) (not (= Y (@ (@ tptp.produc394644079real_c A4) B4)))))))
% 0.26/0.72 (assert (forall ((Y tptp.produc866628903_sc_sz)) (not (forall ((A4 tptp.list_f1238882004_sc_sz) (B4 tptp.list_f1238882004_sc_sz)) (not (= Y (@ (@ tptp.produc1822718231_sc_sz A4) B4)))))))
% 0.26/0.72 (assert (forall ((Y tptp.produc1241881959eal_sz)) (not (forall ((A4 tptp.set_Fi291318197eal_sz) (B4 tptp.set_Fi291318197eal_sz)) (not (= Y (@ (@ tptp.produc1235791063eal_sz A4) B4)))))))
% 0.26/0.72 (assert (forall ((Y tptp.produc1892666919z_real)) (not (forall ((A4 tptp.bounde472938360z_real) (B4 tptp.bounde472938360z_real)) (not (= Y (@ (@ tptp.produc784663575z_real A4) B4)))))))
% 0.26/0.72 (assert (forall ((Y tptp.produc1821101996_sc_sz)) (not (forall ((A4 tptp.denota610675952t_unit) (B4 tptp.produc866628903_sc_sz)) (not (= Y (@ (@ tptp.produc789536734_sc_sz A4) B4)))))))
% 0.26/0.72 (assert (forall ((A2 tptp.finite1398487019real_c) (B2 tptp.finite1398487019real_c) (A3 tptp.finite1398487019real_c) (B3 tptp.finite1398487019real_c)) (=> (= (@ (@ tptp.produc394644079real_c A2) B2) (@ (@ tptp.produc394644079real_c A3) B3)) (not (=> (= A2 A3) (not (= B2 B3)))))))
% 0.26/0.72 (assert (forall ((A2 tptp.list_f1238882004_sc_sz) (B2 tptp.list_f1238882004_sc_sz) (A3 tptp.list_f1238882004_sc_sz) (B3 tptp.list_f1238882004_sc_sz)) (=> (= (@ (@ tptp.produc1822718231_sc_sz A2) B2) (@ (@ tptp.produc1822718231_sc_sz A3) B3)) (not (=> (= A2 A3) (not (= B2 B3)))))))
% 0.26/0.72 (assert (forall ((A2 tptp.set_Fi291318197eal_sz) (B2 tptp.set_Fi291318197eal_sz) (A3 tptp.set_Fi291318197eal_sz) (B3 tptp.set_Fi291318197eal_sz)) (=> (= (@ (@ tptp.produc1235791063eal_sz A2) B2) (@ (@ tptp.produc1235791063eal_sz A3) B3)) (not (=> (= A2 A3) (not (= B2 B3)))))))
% 0.26/0.72 (assert (forall ((A2 tptp.bounde472938360z_real) (B2 tptp.bounde472938360z_real) (A3 tptp.bounde472938360z_real) (B3 tptp.bounde472938360z_real)) (=> (= (@ (@ tptp.produc784663575z_real A2) B2) (@ (@ tptp.produc784663575z_real A3) B3)) (not (=> (= A2 A3) (not (= B2 B3)))))))
% 0.26/0.72 (assert (forall ((A2 tptp.denota610675952t_unit) (B2 tptp.produc866628903_sc_sz) (A3 tptp.denota610675952t_unit) (B3 tptp.produc866628903_sc_sz)) (=> (= (@ (@ tptp.produc789536734_sc_sz A2) B2) (@ (@ tptp.produc789536734_sc_sz A3) B3)) (not (=> (= A2 A3) (not (= B2 B3)))))))
% 0.26/0.72 (assert (forall ((P (-> tptp.produc190496183real_c Bool)) (P2 tptp.produc190496183real_c)) (=> (forall ((A4 tptp.finite1398487019real_c) (B4 tptp.finite1398487019real_c)) (@ P (@ (@ tptp.produc394644079real_c A4) B4))) (@ P P2))))
% 0.26/0.72 (assert (forall ((P (-> tptp.produc866628903_sc_sz Bool)) (P2 tptp.produc866628903_sc_sz)) (=> (forall ((A4 tptp.list_f1238882004_sc_sz) (B4 tptp.list_f1238882004_sc_sz)) (@ P (@ (@ tptp.produc1822718231_sc_sz A4) B4))) (@ P P2))))
% 0.26/0.72 (assert (forall ((P (-> tptp.produc1241881959eal_sz Bool)) (P2 tptp.produc1241881959eal_sz)) (=> (forall ((A4 tptp.set_Fi291318197eal_sz) (B4 tptp.set_Fi291318197eal_sz)) (@ P (@ (@ tptp.produc1235791063eal_sz A4) B4))) (@ P P2))))
% 0.26/0.72 (assert (forall ((P (-> tptp.produc1892666919z_real Bool)) (P2 tptp.produc1892666919z_real)) (=> (forall ((A4 tptp.bounde472938360z_real) (B4 tptp.bounde472938360z_real)) (@ P (@ (@ tptp.produc784663575z_real A4) B4))) (@ P P2))))
% 0.26/0.72 (assert (forall ((P (-> tptp.produc1821101996_sc_sz Bool)) (P2 tptp.produc1821101996_sc_sz)) (=> (forall ((A4 tptp.denota610675952t_unit) (B4 tptp.produc866628903_sc_sz)) (@ P (@ (@ tptp.produc789536734_sc_sz A4) B4))) (@ P P2))))
% 0.26/0.72 (assert (forall ((P2 tptp.produc190496183real_c)) (exists ((X3 tptp.finite1398487019real_c) (Y3 tptp.finite1398487019real_c)) (= P2 (@ (@ tptp.produc394644079real_c X3) Y3)))))
% 0.26/0.72 (assert (forall ((P2 tptp.produc866628903_sc_sz)) (exists ((X3 tptp.list_f1238882004_sc_sz) (Y3 tptp.list_f1238882004_sc_sz)) (= P2 (@ (@ tptp.produc1822718231_sc_sz X3) Y3)))))
% 0.26/0.72 (assert (forall ((P2 tptp.produc1241881959eal_sz)) (exists ((X3 tptp.set_Fi291318197eal_sz) (Y3 tptp.set_Fi291318197eal_sz)) (= P2 (@ (@ tptp.produc1235791063eal_sz X3) Y3)))))
% 0.26/0.72 (assert (forall ((P2 tptp.produc1892666919z_real)) (exists ((X3 tptp.bounde472938360z_real) (Y3 tptp.bounde472938360z_real)) (= P2 (@ (@ tptp.produc784663575z_real X3) Y3)))))
% 0.26/0.72 (assert (forall ((P2 tptp.produc1821101996_sc_sz)) (exists ((X3 tptp.denota610675952t_unit) (Y3 tptp.produc866628903_sc_sz)) (= P2 (@ (@ tptp.produc789536734_sc_sz X3) Y3)))))
% 0.26/0.72 (assert (forall ((P (-> tptp.produc1821101996_sc_sz Bool)) (X tptp.produc1821101996_sc_sz)) (=> (forall ((A4 tptp.denota610675952t_unit) (B4 tptp.list_f1238882004_sc_sz) (C tptp.list_f1238882004_sc_sz)) (@ P (@ (@ tptp.produc789536734_sc_sz A4) (@ (@ tptp.produc1822718231_sc_sz B4) C)))) (@ P X))))
% 0.26/0.72 (assert (forall ((Y tptp.produc1821101996_sc_sz)) (not (forall ((A4 tptp.denota610675952t_unit) (B4 tptp.list_f1238882004_sc_sz) (C tptp.list_f1238882004_sc_sz)) (not (= Y (@ (@ tptp.produc789536734_sc_sz A4) (@ (@ tptp.produc1822718231_sc_sz B4) C))))))))
% 0.26/0.72 (assert (forall ((X1 tptp.list_f1238882004_sc_sz) (X22 tptp.list_f1238882004_sc_sz)) (= (@ tptp.produc548504323_sc_sz (@ (@ tptp.produc1822718231_sc_sz X1) X22)) X1)))
% 0.26/0.72 (assert (forall ((X1 tptp.set_Fi291318197eal_sz) (X22 tptp.set_Fi291318197eal_sz)) (= (@ tptp.produc286845635eal_sz (@ (@ tptp.produc1235791063eal_sz X1) X22)) X1)))
% 0.26/0.72 (assert (forall ((X1 tptp.bounde472938360z_real) (X22 tptp.bounde472938360z_real)) (= (@ tptp.produc870616579z_real (@ (@ tptp.produc784663575z_real X1) X22)) X1)))
% 0.26/0.72 (assert (forall ((X1 tptp.finite824932053eal_sz) (X22 tptp.finite824932053eal_sz)) (= (@ tptp.produc1111759555eal_sz (@ (@ tptp.produc1308130519eal_sz X1) X22)) X1)))
% 0.26/0.72 (assert (forall ((X1 tptp.denota610675952t_unit) (X22 tptp.produc866628903_sc_sz)) (= (@ tptp.produc1503602930_sc_sz (@ (@ tptp.produc789536734_sc_sz X1) X22)) X1)))
% 0.26/0.72 (assert (forall ((X1 tptp.finite1398487019real_c) (X22 tptp.finite1398487019real_c)) (= (@ tptp.produc2010422875real_c (@ (@ tptp.produc394644079real_c X1) X22)) X1)))
% 0.26/0.72 (assert (forall ((X tptp.list_f1238882004_sc_sz) (Y tptp.list_f1238882004_sc_sz) (A2 tptp.list_f1238882004_sc_sz)) (=> (= (@ tptp.produc548504323_sc_sz (@ (@ tptp.produc1822718231_sc_sz X) Y)) A2) (= X A2))))
% 0.26/0.72 (assert (forall ((X tptp.set_Fi291318197eal_sz) (Y tptp.set_Fi291318197eal_sz) (A2 tptp.set_Fi291318197eal_sz)) (=> (= (@ tptp.produc286845635eal_sz (@ (@ tptp.produc1235791063eal_sz X) Y)) A2) (= X A2))))
% 0.26/0.72 (assert (forall ((X tptp.bounde472938360z_real) (Y tptp.bounde472938360z_real) (A2 tptp.bounde472938360z_real)) (=> (= (@ tptp.produc870616579z_real (@ (@ tptp.produc784663575z_real X) Y)) A2) (= X A2))))
% 0.26/0.72 (assert (forall ((X tptp.finite824932053eal_sz) (Y tptp.finite824932053eal_sz) (A2 tptp.finite824932053eal_sz)) (=> (= (@ tptp.produc1111759555eal_sz (@ (@ tptp.produc1308130519eal_sz X) Y)) A2) (= X A2))))
% 0.26/0.72 (assert (forall ((X tptp.denota610675952t_unit) (Y tptp.produc866628903_sc_sz) (A2 tptp.denota610675952t_unit)) (=> (= (@ tptp.produc1503602930_sc_sz (@ (@ tptp.produc789536734_sc_sz X) Y)) A2) (= X A2))))
% 0.26/0.72 (assert (forall ((X tptp.finite1398487019real_c) (Y tptp.finite1398487019real_c) (A2 tptp.finite1398487019real_c)) (=> (= (@ tptp.produc2010422875real_c (@ (@ tptp.produc394644079real_c X) Y)) A2) (= X A2))))
% 0.26/0.72 (assert (forall ((X1 tptp.list_f1238882004_sc_sz) (X22 tptp.list_f1238882004_sc_sz)) (= (@ tptp.produc4753477_sc_sz (@ (@ tptp.produc1822718231_sc_sz X1) X22)) X22)))
% 0.26/0.72 (assert (forall ((X1 tptp.set_Fi291318197eal_sz) (X22 tptp.set_Fi291318197eal_sz)) (= (@ tptp.produc1746886149eal_sz (@ (@ tptp.produc1235791063eal_sz X1) X22)) X22)))
% 0.26/0.72 (assert (forall ((X1 tptp.bounde472938360z_real) (X22 tptp.bounde472938360z_real)) (= (@ tptp.produc1422611269z_real (@ (@ tptp.produc784663575z_real X1) X22)) X22)))
% 0.26/0.72 (assert (forall ((X1 tptp.finite824932053eal_sz) (X22 tptp.finite824932053eal_sz)) (= (@ tptp.produc1269210629eal_sz (@ (@ tptp.produc1308130519eal_sz X1) X22)) X22)))
% 0.26/0.72 (assert (forall ((X1 tptp.denota610675952t_unit) (X22 tptp.produc866628903_sc_sz)) (= (@ tptp.produc974239792_sc_sz (@ (@ tptp.produc789536734_sc_sz X1) X22)) X22)))
% 0.26/0.72 (assert (forall ((X1 tptp.finite1398487019real_c) (X22 tptp.finite1398487019real_c)) (= (@ tptp.produc314122909real_c (@ (@ tptp.produc394644079real_c X1) X22)) X22)))
% 0.26/0.72 (assert (forall ((X tptp.list_f1238882004_sc_sz) (Y tptp.list_f1238882004_sc_sz) (A2 tptp.list_f1238882004_sc_sz)) (=> (= (@ tptp.produc4753477_sc_sz (@ (@ tptp.produc1822718231_sc_sz X) Y)) A2) (= Y A2))))
% 0.26/0.72 (assert (forall ((X tptp.set_Fi291318197eal_sz) (Y tptp.set_Fi291318197eal_sz) (A2 tptp.set_Fi291318197eal_sz)) (=> (= (@ tptp.produc1746886149eal_sz (@ (@ tptp.produc1235791063eal_sz X) Y)) A2) (= Y A2))))
% 0.26/0.72 (assert (forall ((X tptp.bounde472938360z_real) (Y tptp.bounde472938360z_real) (A2 tptp.bounde472938360z_real)) (=> (= (@ tptp.produc1422611269z_real (@ (@ tptp.produc784663575z_real X) Y)) A2) (= Y A2))))
% 0.26/0.72 (assert (forall ((X tptp.finite824932053eal_sz) (Y tptp.finite824932053eal_sz) (A2 tptp.finite824932053eal_sz)) (=> (= (@ tptp.produc1269210629eal_sz (@ (@ tptp.produc1308130519eal_sz X) Y)) A2) (= Y A2))))
% 0.26/0.72 (assert (forall ((X tptp.denota610675952t_unit) (Y tptp.produc866628903_sc_sz) (A2 tptp.produc866628903_sc_sz)) (=> (= (@ tptp.produc974239792_sc_sz (@ (@ tptp.produc789536734_sc_sz X) Y)) A2) (= Y A2))))
% 0.26/0.72 (assert (forall ((X tptp.finite1398487019real_c) (Y tptp.finite1398487019real_c) (A2 tptp.finite1398487019real_c)) (=> (= (@ tptp.produc314122909real_c (@ (@ tptp.produc394644079real_c X) Y)) A2) (= Y A2))))
% 0.26/0.72 (assert (= (lambda ((Y4 tptp.produc1149990247eal_sz) (Z tptp.produc1149990247eal_sz)) (= Y4 Z)) (lambda ((S2 tptp.produc1149990247eal_sz) (T tptp.produc1149990247eal_sz)) (and (= (@ tptp.produc1111759555eal_sz S2) (@ tptp.produc1111759555eal_sz T)) (= (@ tptp.produc1269210629eal_sz S2) (@ tptp.produc1269210629eal_sz T))))))
% 0.26/0.72 (assert (= (lambda ((Y4 tptp.produc1821101996_sc_sz) (Z tptp.produc1821101996_sc_sz)) (= Y4 Z)) (lambda ((S2 tptp.produc1821101996_sc_sz) (T tptp.produc1821101996_sc_sz)) (and (= (@ tptp.produc1503602930_sc_sz S2) (@ tptp.produc1503602930_sc_sz T)) (= (@ tptp.produc974239792_sc_sz S2) (@ tptp.produc974239792_sc_sz T))))))
% 0.26/0.72 (assert (= (lambda ((Y4 tptp.produc190496183real_c) (Z tptp.produc190496183real_c)) (= Y4 Z)) (lambda ((S2 tptp.produc190496183real_c) (T tptp.produc190496183real_c)) (and (= (@ tptp.produc2010422875real_c S2) (@ tptp.produc2010422875real_c T)) (= (@ tptp.produc314122909real_c S2) (@ tptp.produc314122909real_c T))))))
% 0.26/0.72 (assert (forall ((Prod tptp.produc1149990247eal_sz) (Prod2 tptp.produc1149990247eal_sz)) (=> (and (= (@ tptp.produc1111759555eal_sz Prod) (@ tptp.produc1111759555eal_sz Prod2)) (= (@ tptp.produc1269210629eal_sz Prod) (@ tptp.produc1269210629eal_sz Prod2))) (= Prod Prod2))))
% 0.26/0.72 (assert (forall ((Prod tptp.produc1821101996_sc_sz) (Prod2 tptp.produc1821101996_sc_sz)) (=> (and (= (@ tptp.produc1503602930_sc_sz Prod) (@ tptp.produc1503602930_sc_sz Prod2)) (= (@ tptp.produc974239792_sc_sz Prod) (@ tptp.produc974239792_sc_sz Prod2))) (= Prod Prod2))))
% 0.26/0.72 (assert (forall ((Prod tptp.produc190496183real_c) (Prod2 tptp.produc190496183real_c)) (=> (and (= (@ tptp.produc2010422875real_c Prod) (@ tptp.produc2010422875real_c Prod2)) (= (@ tptp.produc314122909real_c Prod) (@ tptp.produc314122909real_c Prod2))) (= Prod Prod2))))
% 0.26/0.72 (assert (forall ((P2 tptp.produc1149990247eal_sz) (Q2 tptp.produc1149990247eal_sz)) (=> (= (@ tptp.produc1111759555eal_sz P2) (@ tptp.produc1111759555eal_sz Q2)) (=> (= (@ tptp.produc1269210629eal_sz P2) (@ tptp.produc1269210629eal_sz Q2)) (= P2 Q2)))))
% 0.26/0.72 (assert (forall ((P2 tptp.produc1821101996_sc_sz) (Q2 tptp.produc1821101996_sc_sz)) (=> (= (@ tptp.produc1503602930_sc_sz P2) (@ tptp.produc1503602930_sc_sz Q2)) (=> (= (@ tptp.produc974239792_sc_sz P2) (@ tptp.produc974239792_sc_sz Q2)) (= P2 Q2)))))
% 0.26/0.72 (assert (forall ((P2 tptp.produc190496183real_c) (Q2 tptp.produc190496183real_c)) (=> (= (@ tptp.produc2010422875real_c P2) (@ tptp.produc2010422875real_c Q2)) (=> (= (@ tptp.produc314122909real_c P2) (@ tptp.produc314122909real_c Q2)) (= P2 Q2)))))
% 0.26/0.72 (assert (forall ((Args (-> tptp.c tptp.trm_a_c)) (I tptp.a)) (=> (forall ((I4 tptp.c)) (@ tptp.dfree_a_c (@ Args I4))) (@ tptp.dfree_a_c (@ (@ tptp.function_a_c I) Args)))))
% 0.26/0.72 (assert (forall ((Args (-> tptp.sz tptp.trm_sf_sz)) (I tptp.sf)) (=> (forall ((I4 tptp.sz)) (@ tptp.dfree_sf_sz (@ Args I4))) (@ tptp.dfree_sf_sz (@ (@ tptp.function_sf_sz I) Args)))))
% 0.26/0.72 (assert (forall ((Theta_1 tptp.trm_sf_sz) (Theta_2 tptp.trm_sf_sz)) (=> (@ tptp.dfree_sf_sz Theta_1) (=> (@ tptp.dfree_sf_sz Theta_2) (@ tptp.dfree_sf_sz (@ (@ tptp.plus_sf_sz Theta_1) Theta_2))))))
% 0.26/0.72 (assert (forall ((Theta_1 tptp.trm_a_c) (Theta_2 tptp.trm_a_c)) (=> (@ tptp.dfree_a_c Theta_1) (=> (@ tptp.dfree_a_c Theta_2) (@ tptp.dfree_a_c (@ (@ tptp.plus_a_c Theta_1) Theta_2))))))
% 0.26/0.72 (assert (forall ((Theta_1 tptp.trm_a_c) (Theta_2 tptp.trm_a_c)) (=> (@ tptp.dfree_a_c Theta_1) (=> (@ tptp.dfree_a_c Theta_2) (@ tptp.dfree_a_c (@ (@ tptp.times_a_c Theta_1) Theta_2))))))
% 0.26/0.72 (assert (forall ((Theta_1 tptp.trm_sf_sz) (Theta_2 tptp.trm_sf_sz)) (=> (@ tptp.dfree_sf_sz Theta_1) (=> (@ tptp.dfree_sf_sz Theta_2) (@ tptp.dfree_sf_sz (@ (@ tptp.times_sf_sz Theta_1) Theta_2))))))
% 0.26/0.72 (assert (forall ((X31 tptp.a) (X32 (-> tptp.c tptp.trm_a_c)) (X41 tptp.trm_a_c) (X42 tptp.trm_a_c)) (not (= (@ (@ tptp.function_a_c X31) X32) (@ (@ tptp.plus_a_c X41) X42)))))
% 0.26/0.72 (assert (forall ((X31 tptp.sf) (X32 (-> tptp.sz tptp.trm_sf_sz)) (X41 tptp.trm_sf_sz) (X42 tptp.trm_sf_sz)) (not (= (@ (@ tptp.function_sf_sz X31) X32) (@ (@ tptp.plus_sf_sz X41) X42)))))
% 0.26/0.72 (assert (forall ((X31 tptp.a) (X32 (-> tptp.c tptp.trm_a_c)) (X51 tptp.trm_a_c) (X52 tptp.trm_a_c)) (not (= (@ (@ tptp.function_a_c X31) X32) (@ (@ tptp.times_a_c X51) X52)))))
% 0.26/0.72 (assert (forall ((X31 tptp.sf) (X32 (-> tptp.sz tptp.trm_sf_sz)) (X51 tptp.trm_sf_sz) (X52 tptp.trm_sf_sz)) (not (= (@ (@ tptp.function_sf_sz X31) X32) (@ (@ tptp.times_sf_sz X51) X52)))))
% 0.26/0.72 (assert (forall ((X41 tptp.trm_sf_sz) (X42 tptp.trm_sf_sz) (X51 tptp.trm_sf_sz) (X52 tptp.trm_sf_sz)) (not (= (@ (@ tptp.plus_sf_sz X41) X42) (@ (@ tptp.times_sf_sz X51) X52)))))
% 0.26/0.72 (assert (forall ((X41 tptp.trm_a_c) (X42 tptp.trm_a_c) (X51 tptp.trm_a_c) (X52 tptp.trm_a_c)) (not (= (@ (@ tptp.plus_a_c X41) X42) (@ (@ tptp.times_a_c X51) X52)))))
% 0.26/0.72 (assert (forall ((T3 tptp.produc866628903_sc_sz)) (= T3 (@ (@ tptp.produc1822718231_sc_sz (@ tptp.produc548504323_sc_sz T3)) (@ tptp.produc4753477_sc_sz T3)))))
% 0.26/0.72 (assert (forall ((T3 tptp.produc1241881959eal_sz)) (= T3 (@ (@ tptp.produc1235791063eal_sz (@ tptp.produc286845635eal_sz T3)) (@ tptp.produc1746886149eal_sz T3)))))
% 0.26/0.72 (assert (forall ((T3 tptp.produc1892666919z_real)) (= T3 (@ (@ tptp.produc784663575z_real (@ tptp.produc870616579z_real T3)) (@ tptp.produc1422611269z_real T3)))))
% 0.26/0.72 (assert (forall ((T3 tptp.produc1149990247eal_sz)) (= T3 (@ (@ tptp.produc1308130519eal_sz (@ tptp.produc1111759555eal_sz T3)) (@ tptp.produc1269210629eal_sz T3)))))
% 0.26/0.72 (assert (forall ((T3 tptp.produc1821101996_sc_sz)) (= T3 (@ (@ tptp.produc789536734_sc_sz (@ tptp.produc1503602930_sc_sz T3)) (@ tptp.produc974239792_sc_sz T3)))))
% 0.26/0.72 (assert (forall ((T3 tptp.produc190496183real_c)) (= T3 (@ (@ tptp.produc394644079real_c (@ tptp.produc2010422875real_c T3)) (@ tptp.produc314122909real_c T3)))))
% 0.26/0.72 (assert (forall ((Prod tptp.produc866628903_sc_sz)) (= Prod (@ (@ tptp.produc1822718231_sc_sz (@ tptp.produc548504323_sc_sz Prod)) (@ tptp.produc4753477_sc_sz Prod)))))
% 0.26/0.72 (assert (forall ((Prod tptp.produc1241881959eal_sz)) (= Prod (@ (@ tptp.produc1235791063eal_sz (@ tptp.produc286845635eal_sz Prod)) (@ tptp.produc1746886149eal_sz Prod)))))
% 0.26/0.72 (assert (forall ((Prod tptp.produc1892666919z_real)) (= Prod (@ (@ tptp.produc784663575z_real (@ tptp.produc870616579z_real Prod)) (@ tptp.produc1422611269z_real Prod)))))
% 0.26/0.72 (assert (forall ((Prod tptp.produc1149990247eal_sz)) (= Prod (@ (@ tptp.produc1308130519eal_sz (@ tptp.produc1111759555eal_sz Prod)) (@ tptp.produc1269210629eal_sz Prod)))))
% 0.26/0.72 (assert (forall ((Prod tptp.produc1821101996_sc_sz)) (= Prod (@ (@ tptp.produc789536734_sc_sz (@ tptp.produc1503602930_sc_sz Prod)) (@ tptp.produc974239792_sc_sz Prod)))))
% 0.26/0.72 (assert (forall ((Prod tptp.produc190496183real_c)) (= Prod (@ (@ tptp.produc394644079real_c (@ tptp.produc2010422875real_c Prod)) (@ tptp.produc314122909real_c Prod)))))
% 0.26/0.72 (assert (forall ((A2 tptp.set_a) (B2 tptp.set_a) (C2 tptp.set_a) (D tptp.set_a)) (= (@ (@ tptp.ord_le486764743_set_a (@ (@ tptp.produc1928581911_set_a A2) B2)) (@ (@ tptp.produc1928581911_set_a C2) D)) (and (@ (@ tptp.ord_less_eq_set_a A2) C2) (@ (@ tptp.ord_less_eq_set_a B2) D)))))
% 0.26/0.72 (assert (forall ((A2 tptp.set_a) (B2 (-> tptp.a Bool)) (C2 tptp.set_a) (D (-> tptp.a Bool))) (= (@ (@ tptp.ord_le501349868_a_a_o (@ (@ tptp.produc634809990_a_a_o A2) B2)) (@ (@ tptp.produc634809990_a_a_o C2) D)) (and (@ (@ tptp.ord_less_eq_set_a A2) C2) (@ (@ tptp.ord_less_eq_a_o B2) D)))))
% 0.26/0.72 (assert (forall ((A2 (-> tptp.a Bool)) (B2 tptp.set_a) (C2 (-> tptp.a Bool)) (D tptp.set_a)) (= (@ (@ tptp.ord_le72828020_set_a (@ (@ tptp.produc1916559302_set_a A2) B2)) (@ (@ tptp.produc1916559302_set_a C2) D)) (and (@ (@ tptp.ord_less_eq_a_o A2) C2) (@ (@ tptp.ord_less_eq_set_a B2) D)))))
% 0.26/0.72 (assert (forall ((A2 tptp.finite1398487019real_c) (B2 tptp.finite1398487019real_c) (C2 tptp.finite1398487019real_c) (D tptp.finite1398487019real_c)) (= (@ (@ tptp.ord_le850691415real_c (@ (@ tptp.produc394644079real_c A2) B2)) (@ (@ tptp.produc394644079real_c C2) D)) (and (@ (@ tptp.ord_le775706699real_c A2) C2) (@ (@ tptp.ord_le775706699real_c B2) D)))))
% 0.26/0.72 (assert (forall ((A2 (-> tptp.a Bool)) (B2 (-> tptp.a Bool)) (C2 (-> tptp.a Bool)) (D (-> tptp.a Bool))) (= (@ (@ tptp.ord_le1883211903_o_a_o (@ (@ tptp.product_Pair_a_o_a_o A2) B2)) (@ (@ tptp.product_Pair_a_o_a_o C2) D)) (and (@ (@ tptp.ord_less_eq_a_o A2) C2) (@ (@ tptp.ord_less_eq_a_o B2) D)))))
% 0.26/0.72 (assert (forall ((A2 tptp.set_Fi291318197eal_sz) (B2 tptp.set_Fi291318197eal_sz) (C2 tptp.set_Fi291318197eal_sz) (D tptp.set_Fi291318197eal_sz)) (= (@ (@ tptp.ord_le978883847eal_sz (@ (@ tptp.produc1235791063eal_sz A2) B2)) (@ (@ tptp.produc1235791063eal_sz C2) D)) (and (@ (@ tptp.ord_le41263445eal_sz A2) C2) (@ (@ tptp.ord_le41263445eal_sz B2) D)))))
% 0.26/0.72 (assert (forall ((A2 tptp.set_a) (B2 (-> tptp.trm_sf_sz tptp.trm_sf_sz Bool)) (C2 tptp.set_a) (D (-> tptp.trm_sf_sz tptp.trm_sf_sz Bool))) (= (@ (@ tptp.ord_le1884788375f_sz_o (@ (@ tptp.produc1174558183f_sz_o A2) B2)) (@ (@ tptp.produc1174558183f_sz_o C2) D)) (and (@ (@ tptp.ord_less_eq_set_a A2) C2) (@ (@ tptp.ord_le8515534f_sz_o B2) D)))))
% 0.26/0.72 (assert (forall ((A2 (-> tptp.trm_sf_sz tptp.trm_sf_sz Bool)) (B2 tptp.set_a) (C2 (-> tptp.trm_sf_sz tptp.trm_sf_sz Bool)) (D tptp.set_a)) (= (@ (@ tptp.ord_le1643089911_set_a (@ (@ tptp.produc1543226183_set_a A2) B2)) (@ (@ tptp.produc1543226183_set_a C2) D)) (and (@ (@ tptp.ord_le8515534f_sz_o A2) C2) (@ (@ tptp.ord_less_eq_set_a B2) D)))))
% 0.26/0.72 (assert (forall ((A2 (-> tptp.trm_sf_sz tptp.trm_sf_sz Bool)) (B2 (-> tptp.a Bool)) (C2 (-> tptp.trm_sf_sz tptp.trm_sf_sz Bool)) (D (-> tptp.a Bool))) (= (@ (@ tptp.ord_le2132572860_o_a_o (@ (@ tptp.produc1152932438_o_a_o A2) B2)) (@ (@ tptp.produc1152932438_o_a_o C2) D)) (and (@ (@ tptp.ord_le8515534f_sz_o A2) C2) (@ (@ tptp.ord_less_eq_a_o B2) D)))))
% 0.26/0.72 (assert (forall ((A2 (-> tptp.a Bool)) (B2 (-> tptp.trm_sf_sz tptp.trm_sf_sz Bool)) (C2 (-> tptp.a Bool)) (D (-> tptp.trm_sf_sz tptp.trm_sf_sz Bool))) (= (@ (@ tptp.ord_le472894788f_sz_o (@ (@ tptp.produc593159062f_sz_o A2) B2)) (@ (@ tptp.produc593159062f_sz_o C2) D)) (and (@ (@ tptp.ord_less_eq_a_o A2) C2) (@ (@ tptp.ord_le8515534f_sz_o B2) D)))))
% 0.26/0.72 (assert (= tptp.denota2112424896_a_b_c (lambda ((I5 tptp.denota231621370t_unit) (T tptp.trm_a_c) (V2 tptp.produc190496183real_c)) (@ (@ (@ (@ tptp.denota229585092_a_b_c I5) T) (@ tptp.produc2010422875real_c V2)) (@ tptp.produc314122909real_c V2)))))
% 0.26/0.72 (assert (= tptp.denota453121236_sc_sz (lambda ((I5 tptp.denota610675952t_unit) (T tptp.trm_sf_sz) (V2 tptp.produc1149990247eal_sz)) (@ (@ (@ (@ tptp.denota1979904720_sc_sz I5) T) (@ tptp.produc1111759555eal_sz V2)) (@ tptp.produc1269210629eal_sz V2)))))
% 0.26/0.72 (assert (forall ((X tptp.freche2095075217_sc_sz)) (= (@ tptp.freche1784963216_sc_sz (@ tptp.freche1421597129_sc_sz X)) X)))
% 0.26/0.72 (assert (@ (@ (@ tptp.type_d1238563341rm_a_c tptp.frechet_raw_term_a_c) tptp.freche665377492rm_a_c) (@ tptp.collect_trm_a_c tptp.dfree_a_c)))
% 0.26/0.72 (assert (@ (@ (@ tptp.type_d46389773_sf_sz tptp.freche782854530_sf_sz) tptp.freche1046279700_sf_sz) (@ tptp.collect_trm_sf_sz tptp.dfree_sf_sz)))
% 0.26/0.72 (assert (forall ((P (-> tptp.list_f1238882004_sc_sz tptp.list_f1238882004_sc_sz Bool)) (X tptp.list_f1238882004_sc_sz) (Y tptp.list_f1238882004_sc_sz) (A2 tptp.produc866628903_sc_sz)) (=> (@ (@ P X) Y) (=> (= A2 (@ (@ tptp.produc1822718231_sc_sz X) Y)) (@ (@ P (@ tptp.produc548504323_sc_sz A2)) (@ tptp.produc4753477_sc_sz A2))))))
% 0.26/0.72 (assert (forall ((P (-> tptp.set_Fi291318197eal_sz tptp.set_Fi291318197eal_sz Bool)) (X tptp.set_Fi291318197eal_sz) (Y tptp.set_Fi291318197eal_sz) (A2 tptp.produc1241881959eal_sz)) (=> (@ (@ P X) Y) (=> (= A2 (@ (@ tptp.produc1235791063eal_sz X) Y)) (@ (@ P (@ tptp.produc286845635eal_sz A2)) (@ tptp.produc1746886149eal_sz A2))))))
% 0.26/0.72 (assert (forall ((P (-> tptp.bounde472938360z_real tptp.bounde472938360z_real Bool)) (X tptp.bounde472938360z_real) (Y tptp.bounde472938360z_real) (A2 tptp.produc1892666919z_real)) (=> (@ (@ P X) Y) (=> (= A2 (@ (@ tptp.produc784663575z_real X) Y)) (@ (@ P (@ tptp.produc870616579z_real A2)) (@ tptp.produc1422611269z_real A2))))))
% 0.26/0.72 (assert (forall ((P (-> tptp.finite824932053eal_sz tptp.finite824932053eal_sz Bool)) (X tptp.finite824932053eal_sz) (Y tptp.finite824932053eal_sz) (A2 tptp.produc1149990247eal_sz)) (=> (@ (@ P X) Y) (=> (= A2 (@ (@ tptp.produc1308130519eal_sz X) Y)) (@ (@ P (@ tptp.produc1111759555eal_sz A2)) (@ tptp.produc1269210629eal_sz A2))))))
% 0.26/0.72 (assert (forall ((P (-> tptp.denota610675952t_unit tptp.produc866628903_sc_sz Bool)) (X tptp.denota610675952t_unit) (Y tptp.produc866628903_sc_sz) (A2 tptp.produc1821101996_sc_sz)) (=> (@ (@ P X) Y) (=> (= A2 (@ (@ tptp.produc789536734_sc_sz X) Y)) (@ (@ P (@ tptp.produc1503602930_sc_sz A2)) (@ tptp.produc974239792_sc_sz A2))))))
% 0.26/0.72 (assert (forall ((P (-> tptp.finite1398487019real_c tptp.finite1398487019real_c Bool)) (X tptp.finite1398487019real_c) (Y tptp.finite1398487019real_c) (A2 tptp.produc190496183real_c)) (=> (@ (@ P X) Y) (=> (= A2 (@ (@ tptp.produc394644079real_c X) Y)) (@ (@ P (@ tptp.produc2010422875real_c A2)) (@ tptp.produc314122909real_c A2))))))
% 0.26/0.72 (assert (forall ((P (-> tptp.list_f1238882004_sc_sz Bool)) (P2 tptp.list_f1238882004_sc_sz) (Q (-> tptp.list_f1238882004_sc_sz Bool)) (Q2 tptp.list_f1238882004_sc_sz)) (let ((_let_1 (@ (@ tptp.produc1822718231_sc_sz P2) Q2))) (=> (@ P P2) (=> (@ Q Q2) (and (@ P (@ tptp.produc548504323_sc_sz _let_1)) (@ Q (@ tptp.produc4753477_sc_sz _let_1))))))))
% 0.26/0.72 (assert (forall ((P (-> tptp.set_Fi291318197eal_sz Bool)) (P2 tptp.set_Fi291318197eal_sz) (Q (-> tptp.set_Fi291318197eal_sz Bool)) (Q2 tptp.set_Fi291318197eal_sz)) (let ((_let_1 (@ (@ tptp.produc1235791063eal_sz P2) Q2))) (=> (@ P P2) (=> (@ Q Q2) (and (@ P (@ tptp.produc286845635eal_sz _let_1)) (@ Q (@ tptp.produc1746886149eal_sz _let_1))))))))
% 0.26/0.72 (assert (forall ((P (-> tptp.bounde472938360z_real Bool)) (P2 tptp.bounde472938360z_real) (Q (-> tptp.bounde472938360z_real Bool)) (Q2 tptp.bounde472938360z_real)) (let ((_let_1 (@ (@ tptp.produc784663575z_real P2) Q2))) (=> (@ P P2) (=> (@ Q Q2) (and (@ P (@ tptp.produc870616579z_real _let_1)) (@ Q (@ tptp.produc1422611269z_real _let_1))))))))
% 0.26/0.72 (assert (forall ((P (-> tptp.finite824932053eal_sz Bool)) (P2 tptp.finite824932053eal_sz) (Q (-> tptp.finite824932053eal_sz Bool)) (Q2 tptp.finite824932053eal_sz)) (let ((_let_1 (@ (@ tptp.produc1308130519eal_sz P2) Q2))) (=> (@ P P2) (=> (@ Q Q2) (and (@ P (@ tptp.produc1111759555eal_sz _let_1)) (@ Q (@ tptp.produc1269210629eal_sz _let_1))))))))
% 0.26/0.72 (assert (forall ((P (-> tptp.denota610675952t_unit Bool)) (P2 tptp.denota610675952t_unit) (Q (-> tptp.produc866628903_sc_sz Bool)) (Q2 tptp.produc866628903_sc_sz)) (let ((_let_1 (@ (@ tptp.produc789536734_sc_sz P2) Q2))) (=> (@ P P2) (=> (@ Q Q2) (and (@ P (@ tptp.produc1503602930_sc_sz _let_1)) (@ Q (@ tptp.produc974239792_sc_sz _let_1))))))))
% 0.26/0.72 (assert (forall ((P (-> tptp.finite1398487019real_c Bool)) (P2 tptp.finite1398487019real_c) (Q (-> tptp.finite1398487019real_c Bool)) (Q2 tptp.finite1398487019real_c)) (let ((_let_1 (@ (@ tptp.produc394644079real_c P2) Q2))) (=> (@ P P2) (=> (@ Q Q2) (and (@ P (@ tptp.produc2010422875real_c _let_1)) (@ Q (@ tptp.produc314122909real_c _let_1))))))))
% 0.26/0.72 (assert (forall ((P (-> tptp.list_f1238882004_sc_sz tptp.list_f1238882004_sc_sz Bool)) (Y tptp.list_f1238882004_sc_sz) (X tptp.list_f1238882004_sc_sz)) (let ((_let_1 (@ (@ tptp.produc1822718231_sc_sz X) Y))) (=> (@ (@ P Y) X) (@ (@ P (@ tptp.produc4753477_sc_sz _let_1)) (@ tptp.produc548504323_sc_sz _let_1))))))
% 0.26/0.72 (assert (forall ((P (-> tptp.set_Fi291318197eal_sz tptp.set_Fi291318197eal_sz Bool)) (Y tptp.set_Fi291318197eal_sz) (X tptp.set_Fi291318197eal_sz)) (let ((_let_1 (@ (@ tptp.produc1235791063eal_sz X) Y))) (=> (@ (@ P Y) X) (@ (@ P (@ tptp.produc1746886149eal_sz _let_1)) (@ tptp.produc286845635eal_sz _let_1))))))
% 0.26/0.72 (assert (forall ((P (-> tptp.bounde472938360z_real tptp.bounde472938360z_real Bool)) (Y tptp.bounde472938360z_real) (X tptp.bounde472938360z_real)) (let ((_let_1 (@ (@ tptp.produc784663575z_real X) Y))) (=> (@ (@ P Y) X) (@ (@ P (@ tptp.produc1422611269z_real _let_1)) (@ tptp.produc870616579z_real _let_1))))))
% 0.26/0.72 (assert (forall ((P (-> tptp.finite824932053eal_sz tptp.finite824932053eal_sz Bool)) (Y tptp.finite824932053eal_sz) (X tptp.finite824932053eal_sz)) (let ((_let_1 (@ (@ tptp.produc1308130519eal_sz X) Y))) (=> (@ (@ P Y) X) (@ (@ P (@ tptp.produc1269210629eal_sz _let_1)) (@ tptp.produc1111759555eal_sz _let_1))))))
% 0.26/0.72 (assert (forall ((P (-> tptp.produc866628903_sc_sz tptp.denota610675952t_unit Bool)) (Y tptp.produc866628903_sc_sz) (X tptp.denota610675952t_unit)) (let ((_let_1 (@ (@ tptp.produc789536734_sc_sz X) Y))) (=> (@ (@ P Y) X) (@ (@ P (@ tptp.produc974239792_sc_sz _let_1)) (@ tptp.produc1503602930_sc_sz _let_1))))))
% 0.26/0.72 (assert (forall ((P (-> tptp.finite1398487019real_c tptp.finite1398487019real_c Bool)) (Y tptp.finite1398487019real_c) (X tptp.finite1398487019real_c)) (let ((_let_1 (@ (@ tptp.produc394644079real_c X) Y))) (=> (@ (@ P Y) X) (@ (@ P (@ tptp.produc314122909real_c _let_1)) (@ tptp.produc2010422875real_c _let_1))))))
% 0.26/0.72 (assert (= tptp.ord_le850691415real_c (lambda ((X2 tptp.produc190496183real_c) (Y2 tptp.produc190496183real_c)) (and (@ (@ tptp.ord_le775706699real_c (@ tptp.produc2010422875real_c X2)) (@ tptp.produc2010422875real_c Y2)) (@ (@ tptp.ord_le775706699real_c (@ tptp.produc314122909real_c X2)) (@ tptp.produc314122909real_c Y2))))))
% 0.26/0.72 (assert (= tptp.ord_le486764743_set_a (lambda ((X2 tptp.produc1691597095_set_a) (Y2 tptp.produc1691597095_set_a)) (and (@ (@ tptp.ord_less_eq_set_a (@ tptp.produc1926412547_set_a X2)) (@ tptp.produc1926412547_set_a Y2)) (@ (@ tptp.ord_less_eq_set_a (@ tptp.produc918972485_set_a X2)) (@ tptp.produc918972485_set_a Y2))))))
% 0.26/0.72 (assert (= tptp.ord_le501349868_a_a_o (lambda ((X2 tptp.produc1989635468_a_a_o) (Y2 tptp.produc1989635468_a_a_o)) (and (@ (@ tptp.ord_less_eq_set_a (@ tptp.produc1911461786_a_a_o X2)) (@ tptp.produc1911461786_a_a_o Y2)) (@ (@ tptp.ord_less_eq_a_o (@ tptp.produc23639768_a_a_o X2)) (@ tptp.produc23639768_a_a_o Y2))))))
% 0.26/0.72 (assert (= tptp.ord_le72828020_set_a (lambda ((X2 tptp.produc1561113620_set_a) (Y2 tptp.produc1561113620_set_a)) (and (@ (@ tptp.ord_less_eq_a_o (@ tptp.produc1045727450_set_a X2)) (@ tptp.produc1045727450_set_a Y2)) (@ (@ tptp.ord_less_eq_set_a (@ tptp.produc1305389080_set_a X2)) (@ tptp.produc1305389080_set_a Y2))))))
% 0.26/0.72 (assert (= tptp.ord_le473656583eal_sz (lambda ((X2 tptp.produc1149990247eal_sz) (Y2 tptp.produc1149990247eal_sz)) (and (@ (@ tptp.ord_le787639925eal_sz (@ tptp.produc1111759555eal_sz X2)) (@ tptp.produc1111759555eal_sz Y2)) (@ (@ tptp.ord_le787639925eal_sz (@ tptp.produc1269210629eal_sz X2)) (@ tptp.produc1269210629eal_sz Y2))))))
% 0.26/0.72 (assert (= tptp.ord_le1883211903_o_a_o (lambda ((X2 tptp.product_prod_a_o_a_o) (Y2 tptp.product_prod_a_o_a_o)) (and (@ (@ tptp.ord_less_eq_a_o (@ tptp.product_fst_a_o_a_o X2)) (@ tptp.product_fst_a_o_a_o Y2)) (@ (@ tptp.ord_less_eq_a_o (@ tptp.product_snd_a_o_a_o X2)) (@ tptp.product_snd_a_o_a_o Y2))))))
% 0.26/0.72 (assert (= tptp.ord_le1884788375f_sz_o (lambda ((X2 tptp.produc1144880887f_sz_o) (Y2 tptp.produc1144880887f_sz_o)) (and (@ (@ tptp.ord_less_eq_set_a (@ tptp.produc38604755f_sz_o X2)) (@ tptp.produc38604755f_sz_o Y2)) (@ (@ tptp.ord_le8515534f_sz_o (@ tptp.produc407510293f_sz_o X2)) (@ tptp.produc407510293f_sz_o Y2))))))
% 0.26/0.72 (assert (= tptp.ord_le1643089911_set_a (lambda ((X2 tptp.produc903182423_set_a) (Y2 tptp.produc903182423_set_a)) (and (@ (@ tptp.ord_le8515534f_sz_o (@ tptp.produc407272755_set_a X2)) (@ tptp.produc407272755_set_a Y2)) (@ (@ tptp.ord_less_eq_set_a (@ tptp.produc776178293_set_a X2)) (@ tptp.produc776178293_set_a Y2))))))
% 0.26/0.72 (assert (= tptp.ord_le2132572860_o_a_o (lambda ((X2 tptp.produc1065634396_o_a_o) (Y2 tptp.produc1065634396_o_a_o)) (and (@ (@ tptp.ord_le8515534f_sz_o (@ tptp.produc2013638506_o_a_o X2)) (@ tptp.produc2013638506_o_a_o Y2)) (@ (@ tptp.ord_less_eq_a_o (@ tptp.produc1630531752_o_a_o X2)) (@ tptp.produc1630531752_o_a_o Y2))))))
% 0.26/0.72 (assert (= tptp.ord_le472894788f_sz_o (lambda ((X2 tptp.produc1553439972f_sz_o) (Y2 tptp.produc1553439972f_sz_o)) (and (@ (@ tptp.ord_less_eq_a_o (@ tptp.produc1453865130f_sz_o X2)) (@ tptp.produc1453865130f_sz_o Y2)) (@ (@ tptp.ord_le8515534f_sz_o (@ tptp.produc1070758376f_sz_o X2)) (@ tptp.produc1070758376f_sz_o Y2))))))
% 0.26/0.72 (assert (forall ((A tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c) (I3 tptp.denota231621370t_unit) (J tptp.denota231621370t_unit)) (let ((_let_1 (@ (@ tptp.denota69106024_a_b_c I3) J))) (=> (@ (@ tptp.ord_le929608341um_b_c A) B) (=> (@ _let_1 B) (@ _let_1 A))))))
% 0.26/0.72 (assert (forall ((B tptp.set_Fi291318197eal_sz) (A tptp.set_Fi291318197eal_sz) (P (-> tptp.finite824932053eal_sz Bool))) (let ((_let_1 (@ tptp.ord_le41263445eal_sz B))) (=> (@ _let_1 A) (= (@ _let_1 (@ tptp.collec1002602816eal_sz (lambda ((X2 tptp.finite824932053eal_sz)) (and (@ (@ tptp.member1693951742eal_sz X2) A) (@ P X2))))) (forall ((X2 tptp.finite824932053eal_sz)) (=> (@ (@ tptp.member1693951742eal_sz X2) B) (@ P X2))))))))
% 0.26/0.72 (assert (forall ((B tptp.set_Pr1169339874_sc_sz) (A tptp.set_Pr1169339874_sc_sz) (P (-> tptp.produc1821101996_sc_sz Bool))) (let ((_let_1 (@ tptp.ord_le1230423618_sc_sz B))) (=> (@ _let_1 A) (= (@ _let_1 (@ tptp.collec1199592193_sc_sz (lambda ((X2 tptp.produc1821101996_sc_sz)) (and (@ (@ tptp.member1057565379_sc_sz X2) A) (@ P X2))))) (forall ((X2 tptp.produc1821101996_sc_sz)) (=> (@ (@ tptp.member1057565379_sc_sz X2) B) (@ P X2))))))))
% 0.26/0.72 (assert (forall ((B tptp.set_trm_sf_sz) (A tptp.set_trm_sf_sz) (P (-> tptp.trm_sf_sz Bool))) (let ((_let_1 (@ tptp.ord_le1697056455_sf_sz B))) (=> (@ _let_1 A) (= (@ _let_1 (@ tptp.collect_trm_sf_sz (lambda ((X2 tptp.trm_sf_sz)) (and (@ (@ tptp.member_trm_sf_sz X2) A) (@ P X2))))) (forall ((X2 tptp.trm_sf_sz)) (=> (@ (@ tptp.member_trm_sf_sz X2) B) (@ P X2))))))))
% 0.26/0.72 (assert (forall ((B tptp.set_trm_a_c) (A tptp.set_trm_a_c) (P (-> tptp.trm_a_c Bool))) (let ((_let_1 (@ tptp.ord_le1369644495rm_a_c B))) (=> (@ _let_1 A) (= (@ _let_1 (@ tptp.collect_trm_a_c (lambda ((X2 tptp.trm_a_c)) (and (@ (@ tptp.member_trm_a_c X2) A) (@ P X2))))) (forall ((X2 tptp.trm_a_c)) (=> (@ (@ tptp.member_trm_a_c X2) B) (@ P X2))))))))
% 0.26/0.72 (assert (forall ((B tptp.set_a) (A tptp.set_a) (P (-> tptp.a Bool))) (let ((_let_1 (@ tptp.ord_less_eq_set_a B))) (=> (@ _let_1 A) (= (@ _let_1 (@ tptp.collect_a (lambda ((X2 tptp.a)) (and (@ (@ tptp.member_a X2) A) (@ P X2))))) (forall ((X2 tptp.a)) (=> (@ (@ tptp.member_a X2) B) (@ P X2))))))))
% 0.26/0.72 (assert (forall ((B tptp.set_Su1783761653um_b_c) (A tptp.set_Su1783761653um_b_c) (P (-> tptp.sum_su737395349um_b_c Bool))) (let ((_let_1 (@ tptp.ord_le929608341um_b_c B))) (=> (@ _let_1 A) (= (@ _let_1 (@ tptp.collec2086029184um_b_c (lambda ((X2 tptp.sum_su737395349um_b_c)) (and (@ (@ tptp.member1893232190um_b_c X2) A) (@ P X2))))) (forall ((X2 tptp.sum_su737395349um_b_c)) (=> (@ (@ tptp.member1893232190um_b_c X2) B) (@ P X2))))))))
% 0.26/0.72 (assert (forall ((B tptp.set_Fi291318197eal_sz) (A tptp.set_Fi291318197eal_sz) (Q (-> tptp.finite824932053eal_sz Bool)) (P (-> tptp.finite824932053eal_sz Bool))) (=> (@ (@ tptp.ord_le41263445eal_sz B) A) (=> (forall ((X3 tptp.finite824932053eal_sz)) (=> (@ (@ tptp.member1693951742eal_sz X3) B) (=> (@ Q X3) (@ P X3)))) (@ (@ tptp.ord_le41263445eal_sz (@ tptp.collec1002602816eal_sz (lambda ((X2 tptp.finite824932053eal_sz)) (and (@ (@ tptp.member1693951742eal_sz X2) B) (@ Q X2))))) (@ tptp.collec1002602816eal_sz (lambda ((X2 tptp.finite824932053eal_sz)) (and (@ (@ tptp.member1693951742eal_sz X2) A) (@ P X2)))))))))
% 0.26/0.72 (assert (forall ((B tptp.set_Pr1169339874_sc_sz) (A tptp.set_Pr1169339874_sc_sz) (Q (-> tptp.produc1821101996_sc_sz Bool)) (P (-> tptp.produc1821101996_sc_sz Bool))) (=> (@ (@ tptp.ord_le1230423618_sc_sz B) A) (=> (forall ((X3 tptp.produc1821101996_sc_sz)) (=> (@ (@ tptp.member1057565379_sc_sz X3) B) (=> (@ Q X3) (@ P X3)))) (@ (@ tptp.ord_le1230423618_sc_sz (@ tptp.collec1199592193_sc_sz (lambda ((X2 tptp.produc1821101996_sc_sz)) (and (@ (@ tptp.member1057565379_sc_sz X2) B) (@ Q X2))))) (@ tptp.collec1199592193_sc_sz (lambda ((X2 tptp.produc1821101996_sc_sz)) (and (@ (@ tptp.member1057565379_sc_sz X2) A) (@ P X2)))))))))
% 0.26/0.72 (assert (forall ((B tptp.set_trm_sf_sz) (A tptp.set_trm_sf_sz) (Q (-> tptp.trm_sf_sz Bool)) (P (-> tptp.trm_sf_sz Bool))) (=> (@ (@ tptp.ord_le1697056455_sf_sz B) A) (=> (forall ((X3 tptp.trm_sf_sz)) (=> (@ (@ tptp.member_trm_sf_sz X3) B) (=> (@ Q X3) (@ P X3)))) (@ (@ tptp.ord_le1697056455_sf_sz (@ tptp.collect_trm_sf_sz (lambda ((X2 tptp.trm_sf_sz)) (and (@ (@ tptp.member_trm_sf_sz X2) B) (@ Q X2))))) (@ tptp.collect_trm_sf_sz (lambda ((X2 tptp.trm_sf_sz)) (and (@ (@ tptp.member_trm_sf_sz X2) A) (@ P X2)))))))))
% 0.26/0.72 (assert (forall ((B tptp.set_trm_a_c) (A tptp.set_trm_a_c) (Q (-> tptp.trm_a_c Bool)) (P (-> tptp.trm_a_c Bool))) (=> (@ (@ tptp.ord_le1369644495rm_a_c B) A) (=> (forall ((X3 tptp.trm_a_c)) (=> (@ (@ tptp.member_trm_a_c X3) B) (=> (@ Q X3) (@ P X3)))) (@ (@ tptp.ord_le1369644495rm_a_c (@ tptp.collect_trm_a_c (lambda ((X2 tptp.trm_a_c)) (and (@ (@ tptp.member_trm_a_c X2) B) (@ Q X2))))) (@ tptp.collect_trm_a_c (lambda ((X2 tptp.trm_a_c)) (and (@ (@ tptp.member_trm_a_c X2) A) (@ P X2)))))))))
% 0.26/0.72 (assert (forall ((B tptp.set_a) (A tptp.set_a) (Q (-> tptp.a Bool)) (P (-> tptp.a Bool))) (=> (@ (@ tptp.ord_less_eq_set_a B) A) (=> (forall ((X3 tptp.a)) (=> (@ (@ tptp.member_a X3) B) (=> (@ Q X3) (@ P X3)))) (@ (@ tptp.ord_less_eq_set_a (@ tptp.collect_a (lambda ((X2 tptp.a)) (and (@ (@ tptp.member_a X2) B) (@ Q X2))))) (@ tptp.collect_a (lambda ((X2 tptp.a)) (and (@ (@ tptp.member_a X2) A) (@ P X2)))))))))
% 0.26/0.72 (assert (forall ((B tptp.set_Su1783761653um_b_c) (A tptp.set_Su1783761653um_b_c) (Q (-> tptp.sum_su737395349um_b_c Bool)) (P (-> tptp.sum_su737395349um_b_c Bool))) (=> (@ (@ tptp.ord_le929608341um_b_c B) A) (=> (forall ((X3 tptp.sum_su737395349um_b_c)) (=> (@ (@ tptp.member1893232190um_b_c X3) B) (=> (@ Q X3) (@ P X3)))) (@ (@ tptp.ord_le929608341um_b_c (@ tptp.collec2086029184um_b_c (lambda ((X2 tptp.sum_su737395349um_b_c)) (and (@ (@ tptp.member1893232190um_b_c X2) B) (@ Q X2))))) (@ tptp.collec2086029184um_b_c (lambda ((X2 tptp.sum_su737395349um_b_c)) (and (@ (@ tptp.member1893232190um_b_c X2) A) (@ P X2)))))))))
% 0.26/0.72 (assert (forall ((X tptp.set_a) (X4 tptp.set_a) (Y tptp.set_a) (Y5 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a X) X4) (=> (@ (@ tptp.ord_less_eq_set_a Y) Y5) (@ (@ tptp.ord_le486764743_set_a (@ (@ tptp.produc1928581911_set_a X) Y)) (@ (@ tptp.produc1928581911_set_a X4) Y5))))))
% 0.26/0.72 (assert (forall ((X tptp.set_a) (X4 tptp.set_a) (Y (-> tptp.a Bool)) (Y5 (-> tptp.a Bool))) (=> (@ (@ tptp.ord_less_eq_set_a X) X4) (=> (@ (@ tptp.ord_less_eq_a_o Y) Y5) (@ (@ tptp.ord_le501349868_a_a_o (@ (@ tptp.produc634809990_a_a_o X) Y)) (@ (@ tptp.produc634809990_a_a_o X4) Y5))))))
% 0.26/0.72 (assert (forall ((X (-> tptp.a Bool)) (X4 (-> tptp.a Bool)) (Y tptp.set_a) (Y5 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_a_o X) X4) (=> (@ (@ tptp.ord_less_eq_set_a Y) Y5) (@ (@ tptp.ord_le72828020_set_a (@ (@ tptp.produc1916559302_set_a X) Y)) (@ (@ tptp.produc1916559302_set_a X4) Y5))))))
% 0.26/0.72 (assert (forall ((X tptp.finite1398487019real_c) (X4 tptp.finite1398487019real_c) (Y tptp.finite1398487019real_c) (Y5 tptp.finite1398487019real_c)) (=> (@ (@ tptp.ord_le775706699real_c X) X4) (=> (@ (@ tptp.ord_le775706699real_c Y) Y5) (@ (@ tptp.ord_le850691415real_c (@ (@ tptp.produc394644079real_c X) Y)) (@ (@ tptp.produc394644079real_c X4) Y5))))))
% 0.26/0.72 (assert (forall ((X (-> tptp.a Bool)) (X4 (-> tptp.a Bool)) (Y (-> tptp.a Bool)) (Y5 (-> tptp.a Bool))) (=> (@ (@ tptp.ord_less_eq_a_o X) X4) (=> (@ (@ tptp.ord_less_eq_a_o Y) Y5) (@ (@ tptp.ord_le1883211903_o_a_o (@ (@ tptp.product_Pair_a_o_a_o X) Y)) (@ (@ tptp.product_Pair_a_o_a_o X4) Y5))))))
% 0.26/0.72 (assert (forall ((X tptp.set_Fi291318197eal_sz) (X4 tptp.set_Fi291318197eal_sz) (Y tptp.set_Fi291318197eal_sz) (Y5 tptp.set_Fi291318197eal_sz)) (=> (@ (@ tptp.ord_le41263445eal_sz X) X4) (=> (@ (@ tptp.ord_le41263445eal_sz Y) Y5) (@ (@ tptp.ord_le978883847eal_sz (@ (@ tptp.produc1235791063eal_sz X) Y)) (@ (@ tptp.produc1235791063eal_sz X4) Y5))))))
% 0.26/0.72 (assert (forall ((X tptp.set_a) (X4 tptp.set_a) (Y (-> tptp.trm_sf_sz tptp.trm_sf_sz Bool)) (Y5 (-> tptp.trm_sf_sz tptp.trm_sf_sz Bool))) (=> (@ (@ tptp.ord_less_eq_set_a X) X4) (=> (@ (@ tptp.ord_le8515534f_sz_o Y) Y5) (@ (@ tptp.ord_le1884788375f_sz_o (@ (@ tptp.produc1174558183f_sz_o X) Y)) (@ (@ tptp.produc1174558183f_sz_o X4) Y5))))))
% 0.26/0.72 (assert (forall ((X (-> tptp.trm_sf_sz tptp.trm_sf_sz Bool)) (X4 (-> tptp.trm_sf_sz tptp.trm_sf_sz Bool)) (Y tptp.set_a) (Y5 tptp.set_a)) (=> (@ (@ tptp.ord_le8515534f_sz_o X) X4) (=> (@ (@ tptp.ord_less_eq_set_a Y) Y5) (@ (@ tptp.ord_le1643089911_set_a (@ (@ tptp.produc1543226183_set_a X) Y)) (@ (@ tptp.produc1543226183_set_a X4) Y5))))))
% 0.26/0.72 (assert (forall ((X (-> tptp.trm_sf_sz tptp.trm_sf_sz Bool)) (X4 (-> tptp.trm_sf_sz tptp.trm_sf_sz Bool)) (Y (-> tptp.a Bool)) (Y5 (-> tptp.a Bool))) (=> (@ (@ tptp.ord_le8515534f_sz_o X) X4) (=> (@ (@ tptp.ord_less_eq_a_o Y) Y5) (@ (@ tptp.ord_le2132572860_o_a_o (@ (@ tptp.produc1152932438_o_a_o X) Y)) (@ (@ tptp.produc1152932438_o_a_o X4) Y5))))))
% 0.26/0.72 (assert (forall ((X (-> tptp.a Bool)) (X4 (-> tptp.a Bool)) (Y (-> tptp.trm_sf_sz tptp.trm_sf_sz Bool)) (Y5 (-> tptp.trm_sf_sz tptp.trm_sf_sz Bool))) (=> (@ (@ tptp.ord_less_eq_a_o X) X4) (=> (@ (@ tptp.ord_le8515534f_sz_o Y) Y5) (@ (@ tptp.ord_le472894788f_sz_o (@ (@ tptp.produc593159062f_sz_o X) Y)) (@ (@ tptp.produc593159062f_sz_o X4) Y5))))))
% 0.26/0.72 (assert (forall ((X tptp.produc1149990247eal_sz) (Y tptp.produc1149990247eal_sz)) (=> (@ (@ tptp.ord_le473656583eal_sz X) Y) (@ (@ tptp.ord_le787639925eal_sz (@ tptp.produc1111759555eal_sz X)) (@ tptp.produc1111759555eal_sz Y)))))
% 0.26/0.72 (assert (forall ((X tptp.produc190496183real_c) (Y tptp.produc190496183real_c)) (=> (@ (@ tptp.ord_le850691415real_c X) Y) (@ (@ tptp.ord_le775706699real_c (@ tptp.produc2010422875real_c X)) (@ tptp.produc2010422875real_c Y)))))
% 0.26/0.72 (assert (forall ((X tptp.produc1149990247eal_sz) (Y tptp.produc1149990247eal_sz)) (=> (@ (@ tptp.ord_le473656583eal_sz X) Y) (@ (@ tptp.ord_le787639925eal_sz (@ tptp.produc1269210629eal_sz X)) (@ tptp.produc1269210629eal_sz Y)))))
% 0.26/0.72 (assert (forall ((X tptp.produc190496183real_c) (Y tptp.produc190496183real_c)) (=> (@ (@ tptp.ord_le850691415real_c X) Y) (@ (@ tptp.ord_le775706699real_c (@ tptp.produc314122909real_c X)) (@ tptp.produc314122909real_c Y)))))
% 0.26/0.72 (assert (forall ((P (-> tptp.finite824932053eal_sz tptp.finite824932053eal_sz Bool)) (P2 tptp.produc1149990247eal_sz)) (=> (@ (@ P (@ tptp.produc1269210629eal_sz P2)) (@ tptp.produc1111759555eal_sz P2)) (not (forall ((X3 tptp.finite824932053eal_sz) (Y3 tptp.finite824932053eal_sz)) (not (@ (@ P Y3) X3)))))))
% 0.26/0.72 (assert (forall ((P (-> tptp.produc866628903_sc_sz tptp.denota610675952t_unit Bool)) (P2 tptp.produc1821101996_sc_sz)) (=> (@ (@ P (@ tptp.produc974239792_sc_sz P2)) (@ tptp.produc1503602930_sc_sz P2)) (not (forall ((X3 tptp.denota610675952t_unit) (Y3 tptp.produc866628903_sc_sz)) (not (@ (@ P Y3) X3)))))))
% 0.26/0.72 (assert (forall ((P (-> tptp.finite1398487019real_c tptp.finite1398487019real_c Bool)) (P2 tptp.produc190496183real_c)) (=> (@ (@ P (@ tptp.produc314122909real_c P2)) (@ tptp.produc2010422875real_c P2)) (not (forall ((X3 tptp.finite1398487019real_c) (Y3 tptp.finite1398487019real_c)) (not (@ (@ P Y3) X3)))))))
% 0.26/0.72 (assert (forall ((X1 tptp.a) (Y1 tptp.a)) (= (= (@ tptp.sum_In2139678582um_b_c X1) (@ tptp.sum_In2139678582um_b_c Y1)) (= X1 Y1))))
% 0.26/0.72 (assert (forall ((A2 tptp.a) (A3 tptp.a)) (= (= (@ tptp.sum_In2139678582um_b_c A2) (@ tptp.sum_In2139678582um_b_c A3)) (= A2 A3))))
% 0.26/0.72 (assert (forall ((Y tptp.denota231621370t_unit)) (=> (@ (@ tptp.member1777622435t_unit Y) (@ tptp.collec451781861t_unit tptp.denota258389581_a_b_c)) (= (@ tptp.freche1608036107_a_b_c (@ tptp.freche1473475332_a_b_c Y)) Y))))
% 0.26/0.72 (assert (forall ((Y tptp.denota610675952t_unit)) (=> (@ (@ tptp.member754147591t_unit Y) (@ tptp.collec1767975749t_unit tptp.denota1579475975_sc_sz)) (= (@ tptp.freche1421597129_sc_sz (@ tptp.freche1784963216_sc_sz Y)) Y))))
% 0.26/0.72 (assert (= tptp.f0_sf_sz (lambda ((F tptp.sf)) (@ (@ tptp.function_sf_sz F) tptp.empty_sz_sf))))
% 0.26/0.72 (assert (forall ((A tptp.set_Fi291318197eal_sz) (B tptp.set_Fi291318197eal_sz)) (=> (forall ((X3 tptp.finite824932053eal_sz)) (let ((_let_1 (@ tptp.member1693951742eal_sz X3))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.ord_le41263445eal_sz A) B))))
% 0.26/0.72 (assert (forall ((A tptp.set_Pr1169339874_sc_sz) (B tptp.set_Pr1169339874_sc_sz)) (=> (forall ((X3 tptp.produc1821101996_sc_sz)) (let ((_let_1 (@ tptp.member1057565379_sc_sz X3))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.ord_le1230423618_sc_sz A) B))))
% 0.26/0.72 (assert (forall ((A tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c)) (=> (forall ((X3 tptp.sum_su737395349um_b_c)) (let ((_let_1 (@ tptp.member1893232190um_b_c X3))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.ord_le929608341um_b_c A) B))))
% 0.26/0.72 (assert (forall ((A tptp.set_trm_sf_sz) (B tptp.set_trm_sf_sz)) (=> (forall ((X3 tptp.trm_sf_sz)) (let ((_let_1 (@ tptp.member_trm_sf_sz X3))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.ord_le1697056455_sf_sz A) B))))
% 0.26/0.72 (assert (forall ((A tptp.set_trm_a_c) (B tptp.set_trm_a_c)) (=> (forall ((X3 tptp.trm_a_c)) (let ((_let_1 (@ tptp.member_trm_a_c X3))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.ord_le1369644495rm_a_c A) B))))
% 0.26/0.72 (assert (forall ((A tptp.set_a) (B tptp.set_a)) (=> (forall ((X3 tptp.a)) (let ((_let_1 (@ tptp.member_a X3))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.ord_less_eq_set_a A) B))))
% 0.26/0.72 (assert (forall ((Y tptp.denota231621370t_unit) (P (-> tptp.denota231621370t_unit Bool))) (=> (@ (@ tptp.member1777622435t_unit Y) (@ tptp.collec451781861t_unit tptp.denota258389581_a_b_c)) (=> (forall ((X3 tptp.freche914690577_a_b_c)) (@ P (@ tptp.freche1608036107_a_b_c X3))) (@ P Y)))))
% 0.26/0.72 (assert (forall ((Y tptp.denota610675952t_unit) (P (-> tptp.denota610675952t_unit Bool))) (=> (@ (@ tptp.member754147591t_unit Y) (@ tptp.collec1767975749t_unit tptp.denota1579475975_sc_sz)) (=> (forall ((X3 tptp.freche2095075217_sc_sz)) (@ P (@ tptp.freche1421597129_sc_sz X3))) (@ P Y)))))
% 0.26/0.72 (assert (forall ((Y tptp.denota231621370t_unit)) (=> (@ (@ tptp.member1777622435t_unit Y) (@ tptp.collec451781861t_unit tptp.denota258389581_a_b_c)) (not (forall ((X3 tptp.freche914690577_a_b_c)) (not (= Y (@ tptp.freche1608036107_a_b_c X3))))))))
% 0.26/0.72 (assert (forall ((Y tptp.denota610675952t_unit)) (=> (@ (@ tptp.member754147591t_unit Y) (@ tptp.collec1767975749t_unit tptp.denota1579475975_sc_sz)) (not (forall ((X3 tptp.freche2095075217_sc_sz)) (not (= Y (@ tptp.freche1421597129_sc_sz X3))))))))
% 0.26/0.72 (assert (forall ((X tptp.freche914690577_a_b_c)) (@ (@ tptp.member1777622435t_unit (@ tptp.freche1608036107_a_b_c X)) (@ tptp.collec451781861t_unit tptp.denota258389581_a_b_c))))
% 0.26/0.72 (assert (forall ((X tptp.freche2095075217_sc_sz)) (@ (@ tptp.member754147591t_unit (@ tptp.freche1421597129_sc_sz X)) (@ tptp.collec1767975749t_unit tptp.denota1579475975_sc_sz))))
% 0.26/0.72 (assert (forall ((X tptp.freche914690577_a_b_c)) (not (forall ((Y3 tptp.denota231621370t_unit)) (=> (= X (@ tptp.freche1473475332_a_b_c Y3)) (not (@ (@ tptp.member1777622435t_unit Y3) (@ tptp.collec451781861t_unit tptp.denota258389581_a_b_c))))))))
% 0.26/0.72 (assert (forall ((X tptp.freche2095075217_sc_sz)) (not (forall ((Y3 tptp.denota610675952t_unit)) (=> (= X (@ tptp.freche1784963216_sc_sz Y3)) (not (@ (@ tptp.member754147591t_unit Y3) (@ tptp.collec1767975749t_unit tptp.denota1579475975_sc_sz))))))))
% 0.26/0.72 (assert (forall ((P (-> tptp.freche914690577_a_b_c Bool)) (X tptp.freche914690577_a_b_c)) (=> (forall ((Y3 tptp.denota231621370t_unit)) (=> (@ (@ tptp.member1777622435t_unit Y3) (@ tptp.collec451781861t_unit tptp.denota258389581_a_b_c)) (@ P (@ tptp.freche1473475332_a_b_c Y3)))) (@ P X))))
% 0.26/0.72 (assert (forall ((P (-> tptp.freche2095075217_sc_sz Bool)) (X tptp.freche2095075217_sc_sz)) (=> (forall ((Y3 tptp.denota610675952t_unit)) (=> (@ (@ tptp.member754147591t_unit Y3) (@ tptp.collec1767975749t_unit tptp.denota1579475975_sc_sz)) (@ P (@ tptp.freche1784963216_sc_sz Y3)))) (@ P X))))
% 0.26/0.72 (assert (forall ((X tptp.denota231621370t_unit) (Y tptp.denota231621370t_unit)) (let ((_let_1 (@ tptp.collec451781861t_unit tptp.denota258389581_a_b_c))) (=> (@ (@ tptp.member1777622435t_unit X) _let_1) (=> (@ (@ tptp.member1777622435t_unit Y) _let_1) (= (= (@ tptp.freche1473475332_a_b_c X) (@ tptp.freche1473475332_a_b_c Y)) (= X Y)))))))
% 0.26/0.72 (assert (forall ((X tptp.denota610675952t_unit) (Y tptp.denota610675952t_unit)) (let ((_let_1 (@ tptp.collec1767975749t_unit tptp.denota1579475975_sc_sz))) (=> (@ (@ tptp.member754147591t_unit X) _let_1) (=> (@ (@ tptp.member754147591t_unit Y) _let_1) (= (= (@ tptp.freche1784963216_sc_sz X) (@ tptp.freche1784963216_sc_sz Y)) (= X Y)))))))
% 0.26/0.72 (assert (forall ((A tptp.set_a) (B tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a A) B) (=> (@ (@ tptp.ord_less_eq_set_a B) A) (= A B)))))
% 0.26/0.72 (assert (forall ((P (-> tptp.finite824932053eal_sz Bool)) (Q (-> tptp.finite824932053eal_sz Bool))) (= (@ (@ tptp.ord_le41263445eal_sz (@ tptp.collec1002602816eal_sz P)) (@ tptp.collec1002602816eal_sz Q)) (forall ((X2 tptp.finite824932053eal_sz)) (=> (@ P X2) (@ Q X2))))))
% 0.26/0.72 (assert (forall ((P (-> tptp.produc1821101996_sc_sz Bool)) (Q (-> tptp.produc1821101996_sc_sz Bool))) (= (@ (@ tptp.ord_le1230423618_sc_sz (@ tptp.collec1199592193_sc_sz P)) (@ tptp.collec1199592193_sc_sz Q)) (forall ((X2 tptp.produc1821101996_sc_sz)) (=> (@ P X2) (@ Q X2))))))
% 0.26/0.72 (assert (forall ((P (-> tptp.trm_sf_sz Bool)) (Q (-> tptp.trm_sf_sz Bool))) (= (@ (@ tptp.ord_le1697056455_sf_sz (@ tptp.collect_trm_sf_sz P)) (@ tptp.collect_trm_sf_sz Q)) (forall ((X2 tptp.trm_sf_sz)) (=> (@ P X2) (@ Q X2))))))
% 0.26/0.72 (assert (forall ((P (-> tptp.trm_a_c Bool)) (Q (-> tptp.trm_a_c Bool))) (= (@ (@ tptp.ord_le1369644495rm_a_c (@ tptp.collect_trm_a_c P)) (@ tptp.collect_trm_a_c Q)) (forall ((X2 tptp.trm_a_c)) (=> (@ P X2) (@ Q X2))))))
% 0.26/0.72 (assert (forall ((P (-> tptp.a Bool)) (Q (-> tptp.a Bool))) (= (@ (@ tptp.ord_less_eq_set_a (@ tptp.collect_a P)) (@ tptp.collect_a Q)) (forall ((X2 tptp.a)) (=> (@ P X2) (@ Q X2))))))
% 0.26/0.72 (assert (forall ((P (-> tptp.sum_su737395349um_b_c Bool)) (Q (-> tptp.sum_su737395349um_b_c Bool))) (= (@ (@ tptp.ord_le929608341um_b_c (@ tptp.collec2086029184um_b_c P)) (@ tptp.collec2086029184um_b_c Q)) (forall ((X2 tptp.sum_su737395349um_b_c)) (=> (@ P X2) (@ Q X2))))))
% 0.26/0.72 (assert (= (lambda ((Y4 tptp.set_a) (Z tptp.set_a)) (= Y4 Z)) (lambda ((A5 tptp.set_a) (B5 tptp.set_a)) (and (@ (@ tptp.ord_less_eq_set_a A5) B5) (@ (@ tptp.ord_less_eq_set_a B5) A5)))))
% 0.26/0.72 (assert (forall ((A tptp.set_a) (B tptp.set_a) (C3 tptp.set_a)) (let ((_let_1 (@ tptp.ord_less_eq_set_a A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_a B) C3) (@ _let_1 C3))))))
% 0.26/0.72 (assert (forall ((P (-> tptp.produc1821101996_sc_sz Bool)) (Q (-> tptp.produc1821101996_sc_sz Bool))) (=> (forall ((X3 tptp.produc1821101996_sc_sz)) (=> (@ P X3) (@ Q X3))) (@ (@ tptp.ord_le1230423618_sc_sz (@ tptp.collec1199592193_sc_sz P)) (@ tptp.collec1199592193_sc_sz Q)))))
% 0.26/0.72 (assert (forall ((P (-> tptp.trm_sf_sz Bool)) (Q (-> tptp.trm_sf_sz Bool))) (=> (forall ((X3 tptp.trm_sf_sz)) (=> (@ P X3) (@ Q X3))) (@ (@ tptp.ord_le1697056455_sf_sz (@ tptp.collect_trm_sf_sz P)) (@ tptp.collect_trm_sf_sz Q)))))
% 0.26/0.72 (assert (forall ((P (-> tptp.trm_a_c Bool)) (Q (-> tptp.trm_a_c Bool))) (=> (forall ((X3 tptp.trm_a_c)) (=> (@ P X3) (@ Q X3))) (@ (@ tptp.ord_le1369644495rm_a_c (@ tptp.collect_trm_a_c P)) (@ tptp.collect_trm_a_c Q)))))
% 0.26/0.72 (assert (forall ((P (-> tptp.a Bool)) (Q (-> tptp.a Bool))) (=> (forall ((X3 tptp.a)) (=> (@ P X3) (@ Q X3))) (@ (@ tptp.ord_less_eq_set_a (@ tptp.collect_a P)) (@ tptp.collect_a Q)))))
% 0.26/0.72 (assert (forall ((P (-> tptp.sum_su737395349um_b_c Bool)) (Q (-> tptp.sum_su737395349um_b_c Bool))) (=> (forall ((X3 tptp.sum_su737395349um_b_c)) (=> (@ P X3) (@ Q X3))) (@ (@ tptp.ord_le929608341um_b_c (@ tptp.collec2086029184um_b_c P)) (@ tptp.collec2086029184um_b_c Q)))))
% 0.26/0.72 (assert (= tptp.ord_less_eq_set_a (lambda ((A5 tptp.set_a) (B5 tptp.set_a)) (forall ((T tptp.a)) (let ((_let_1 (@ tptp.member_a T))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))
% 0.26/0.72 (assert (= tptp.ord_less_eq_set_a (lambda ((A5 tptp.set_a) (B5 tptp.set_a)) (forall ((X2 tptp.a)) (let ((_let_1 (@ tptp.member_a X2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))
% 0.26/0.72 (assert (forall ((A tptp.set_a) (B tptp.set_a) (C2 tptp.a)) (let ((_let_1 (@ tptp.member_a C2))) (=> (@ (@ tptp.ord_less_eq_set_a A) B) (=> (@ _let_1 A) (@ _let_1 B))))))
% 0.26/0.72 (assert (forall ((A tptp.set_a) (B tptp.set_a) (X tptp.a)) (let ((_let_1 (@ tptp.member_a X))) (=> (@ (@ tptp.ord_less_eq_set_a A) B) (=> (@ _let_1 A) (@ _let_1 B))))))
% 0.26/0.72 (assert (forall ((X tptp.a) (Y tptp.a)) (=> (= (@ tptp.sum_In2139678582um_b_c X) (@ tptp.sum_In2139678582um_b_c Y)) (= X Y))))
% 0.26/0.72 (assert (forall ((A tptp.set_a) (P (-> tptp.a Bool))) (@ (@ tptp.ord_less_eq_set_a (@ tptp.collect_a (lambda ((X2 tptp.a)) (and (@ (@ tptp.member_a X2) A) (@ P X2))))) A)))
% 0.26/0.72 (assert (forall ((A tptp.set_Su1783761653um_b_c) (P (-> tptp.sum_su737395349um_b_c Bool))) (@ (@ tptp.ord_le929608341um_b_c (@ tptp.collec2086029184um_b_c (lambda ((X2 tptp.sum_su737395349um_b_c)) (and (@ (@ tptp.member1893232190um_b_c X2) A) (@ P X2))))) A)))
% 0.26/0.72 (assert (= tptp.ord_less_eq_set_a (lambda ((A5 tptp.set_a) (B5 tptp.set_a)) (@ (@ tptp.ord_less_eq_a_o (lambda ((X2 tptp.a)) (@ (@ tptp.member_a X2) A5))) (lambda ((X2 tptp.a)) (@ (@ tptp.member_a X2) B5))))))
% 0.26/0.72 (assert (forall ((I3 tptp.denota231621370t_unit) (J tptp.denota231621370t_unit) (Theta_12 tptp.trm_a_c) (Theta_22 tptp.trm_a_c) (Nu tptp.produc190496183real_c)) (let ((_let_1 (@ tptp.produc314122909real_c Nu))) (let ((_let_2 (@ tptp.produc2010422875real_c Nu))) (=> (@ tptp.denota258389581_a_b_c I3) (=> (@ tptp.denota258389581_a_b_c J) (=> (@ tptp.dfree_a_c Theta_12) (=> (@ tptp.dfree_a_c Theta_22) (=> (= (@ (@ tptp.denota2042094639_a_b_c I3) Theta_12) (@ (@ tptp.denota2042094639_a_b_c J) Theta_22)) (= (@ (@ (@ (@ tptp.denota229585092_a_b_c I3) Theta_12) _let_2) _let_1) (@ (@ (@ (@ tptp.denota229585092_a_b_c J) Theta_22) _let_2) _let_1)))))))))))
% 0.26/0.72 (assert (forall ((I3 tptp.denota610675952t_unit) (J tptp.denota610675952t_unit) (Theta_12 tptp.trm_sf_sz) (Theta_22 tptp.trm_sf_sz) (Nu tptp.produc1149990247eal_sz)) (let ((_let_1 (@ tptp.produc1269210629eal_sz Nu))) (let ((_let_2 (@ tptp.produc1111759555eal_sz Nu))) (=> (@ tptp.denota1579475975_sc_sz I3) (=> (@ tptp.denota1579475975_sc_sz J) (=> (@ tptp.dfree_sf_sz Theta_12) (=> (@ tptp.dfree_sf_sz Theta_22) (=> (= (@ (@ tptp.denota1179238309_sc_sz I3) Theta_12) (@ (@ tptp.denota1179238309_sc_sz J) Theta_22)) (= (@ (@ (@ (@ tptp.denota1979904720_sc_sz I3) Theta_12) _let_2) _let_1) (@ (@ (@ (@ tptp.denota1979904720_sc_sz J) Theta_22) _let_2) _let_1)))))))))))
% 0.26/0.72 (assert (@ (@ (@ tptp.type_d1092523951t_unit tptp.freche1421597129_sc_sz) tptp.freche1784963216_sc_sz) (@ tptp.collec1767975749t_unit tptp.denota1579475975_sc_sz)))
% 0.26/0.72 (assert (= tptp.bNF_Gr1775200401_sc_sz (lambda ((A5 tptp.set_a) (F (-> tptp.a tptp.denota610675952t_unit)) (G (-> tptp.a tptp.produc866628903_sc_sz))) (@ tptp.collec1199592193_sc_sz (lambda ((Uu tptp.produc1821101996_sc_sz)) (exists ((A6 tptp.a)) (and (= Uu (@ (@ tptp.produc789536734_sc_sz (@ F A6)) (@ G A6))) (@ (@ tptp.member_a A6) A5))))))))
% 0.26/0.72 (assert (forall ((B2 tptp.denota610675952t_unit) (F2 (-> tptp.a tptp.denota610675952t_unit)) (X tptp.a) (C2 tptp.produc866628903_sc_sz) (G2 (-> tptp.a tptp.produc866628903_sc_sz)) (A tptp.set_a)) (=> (= B2 (@ F2 X)) (=> (= C2 (@ G2 X)) (=> (@ (@ tptp.member_a X) A) (@ (@ tptp.member1057565379_sc_sz (@ (@ tptp.produc789536734_sc_sz B2) C2)) (@ (@ (@ tptp.bNF_Gr1775200401_sc_sz A) F2) G2)))))))
% 0.26/0.72 (assert (forall ((Theta tptp.trm_a_c) (Nu tptp.produc190496183real_c) (Nu2 tptp.produc190496183real_c) (I3 tptp.denota231621370t_unit) (J tptp.denota231621370t_unit)) (=> (@ tptp.dfree_a_c Theta) (=> (@ (@ (@ tptp.denota1997846518gree_c Nu) Nu2) (@ tptp.static_FVT_a_c Theta)) (=> (@ (@ (@ tptp.denota69106024_a_b_c I3) J) (@ tptp.collec2086029184um_b_c (lambda ((Uu tptp.sum_su737395349um_b_c)) (exists ((X2 tptp.a)) (and (= Uu (@ tptp.sum_In2139678582um_b_c X2)) (@ (@ tptp.member_a X2) (@ tptp.static_SIGT_a_c Theta))))))) (= (@ (@ (@ tptp.denota2042094639_a_b_c I3) Theta) (@ tptp.produc2010422875real_c Nu)) (@ (@ (@ tptp.denota2042094639_a_b_c J) Theta) (@ tptp.produc2010422875real_c Nu2))))))))
% 0.26/0.72 (assert (forall ((R tptp.set_a) (S3 tptp.set_a)) (= (@ (@ tptp.ord_less_eq_a_o (lambda ((X2 tptp.a)) (@ (@ tptp.member_a X2) R))) (lambda ((X2 tptp.a)) (@ (@ tptp.member_a X2) S3))) (@ (@ tptp.ord_less_eq_set_a R) S3))))
% 0.26/0.72 (assert (forall ((I3 tptp.denota610675952t_unit) (Theta tptp.trm_sf_sz) (S3 tptp.set_Fi291318197eal_sz)) (=> (@ tptp.denota1579475975_sc_sz I3) (=> (@ tptp.dfree_sf_sz Theta) (@ (@ tptp.topolo1348430467z_real S3) (@ (@ tptp.denota1179238309_sc_sz I3) Theta))))))
% 0.26/0.72 (assert (forall ((Nu tptp.produc1149990247eal_sz) (Nu2 tptp.produc1149990247eal_sz) (F2 tptp.sf) (Args (-> tptp.sz tptp.trm_sf_sz)) (I tptp.sz)) (let ((_let_1 (@ (@ tptp.denota102713844ree_sz Nu) Nu2))) (=> (@ _let_1 (@ tptp.static_FVT_sf_sz (@ (@ tptp.function_sf_sz F2) Args))) (@ _let_1 (@ tptp.static_FVT_sf_sz (@ Args I)))))))
% 0.26/0.72 (assert (forall ((R2 tptp.set_Pr1169339874_sc_sz) (S4 tptp.set_Pr1169339874_sc_sz)) (=> (forall ((X3 tptp.denota610675952t_unit) (Y3 tptp.produc866628903_sc_sz)) (let ((_let_1 (@ tptp.member1057565379_sc_sz (@ (@ tptp.produc789536734_sc_sz X3) Y3)))) (=> (@ _let_1 R2) (@ _let_1 S4)))) (@ (@ tptp.ord_le1230423618_sc_sz R2) S4))))
% 0.26/0.72 (assert (forall ((F2 tptp.trm_a_c)) (@ (@ tptp.ord_le1772180283um_c_c (@ tptp.static_FVT_a_c F2)) (@ tptp.static_FVDiff_a_c F2))))
% 0.26/0.72 (assert (forall ((R tptp.set_Pr1169339874_sc_sz) (S3 tptp.set_Pr1169339874_sc_sz)) (= (= (lambda ((X2 tptp.denota610675952t_unit) (Y2 tptp.produc866628903_sc_sz)) (@ (@ tptp.member1057565379_sc_sz (@ (@ tptp.produc789536734_sc_sz X2) Y2)) R)) (lambda ((X2 tptp.denota610675952t_unit) (Y2 tptp.produc866628903_sc_sz)) (@ (@ tptp.member1057565379_sc_sz (@ (@ tptp.produc789536734_sc_sz X2) Y2)) S3))) (= R S3))))
% 0.26/0.72 (assert (forall ((R tptp.set_Pr1169339874_sc_sz) (S3 tptp.set_Pr1169339874_sc_sz)) (= (@ (@ tptp.ord_le108471557c_sz_o (lambda ((X2 tptp.denota610675952t_unit) (Y2 tptp.produc866628903_sc_sz)) (@ (@ tptp.member1057565379_sc_sz (@ (@ tptp.produc789536734_sc_sz X2) Y2)) R))) (lambda ((X2 tptp.denota610675952t_unit) (Y2 tptp.produc866628903_sc_sz)) (@ (@ tptp.member1057565379_sc_sz (@ (@ tptp.produc789536734_sc_sz X2) Y2)) S3))) (@ (@ tptp.ord_le1230423618_sc_sz R) S3))))
% 0.26/0.72 (assert (forall ((I3 tptp.denota610675952t_unit) (Theta tptp.trm_sf_sz)) (=> (@ tptp.denota1579475975_sc_sz I3) (=> (@ tptp.dfree_sf_sz Theta) (@ (@ tptp.topolo1348430467z_real tptp.top_to1873962757eal_sz) (@ (@ tptp.denota1179238309_sc_sz I3) Theta))))))
% 0.26/0.72 (assert (forall ((S4 tptp.set_Fi291318197eal_sz) (H (-> tptp.finite824932053eal_sz tptp.real)) (A2 tptp.real) (F2 (-> tptp.finite824932053eal_sz tptp.bounde472938360z_real)) (G2 (-> tptp.finite824932053eal_sz tptp.bounde472938360z_real))) (=> (@ (@ tptp.topolo885751137z_real (@ tptp.collec1002602816eal_sz (lambda ((T tptp.finite824932053eal_sz)) (and (@ (@ tptp.member1693951742eal_sz T) S4) (@ (@ tptp.ord_less_eq_real (@ H T)) A2))))) F2) (=> (@ (@ tptp.topolo885751137z_real (@ tptp.collec1002602816eal_sz (lambda ((T tptp.finite824932053eal_sz)) (and (@ (@ tptp.member1693951742eal_sz T) S4) (@ (@ tptp.ord_less_eq_real A2) (@ H T)))))) G2) (=> (@ (@ tptp.topolo1348430467z_real S4) H) (=> (forall ((T4 tptp.finite824932053eal_sz)) (=> (@ (@ tptp.member1693951742eal_sz T4) S4) (=> (= (@ H T4) A2) (= (@ F2 T4) (@ G2 T4))))) (@ (@ tptp.topolo885751137z_real S4) (lambda ((T tptp.finite824932053eal_sz)) (@ (@ (@ tptp.if_Bou1785791806z_real (@ (@ tptp.ord_less_eq_real (@ H T)) A2)) (@ F2 T)) (@ G2 T))))))))))
% 0.26/0.72 (assert (forall ((X tptp.a)) (@ (@ tptp.member_a X) tptp.top_top_set_a)))
% 0.26/0.72 (assert (forall ((X tptp.finite824932053eal_sz)) (@ (@ tptp.member1693951742eal_sz X) tptp.top_to1873962757eal_sz)))
% 0.26/0.72 (assert (forall ((A2 tptp.set_Fi291318197eal_sz)) (=> (@ (@ tptp.ord_le41263445eal_sz tptp.top_to1873962757eal_sz) A2) (= A2 tptp.top_to1873962757eal_sz))))
% 0.26/0.72 (assert (forall ((A2 tptp.set_Fi291318197eal_sz)) (= (@ (@ tptp.ord_le41263445eal_sz tptp.top_to1873962757eal_sz) A2) (= A2 tptp.top_to1873962757eal_sz))))
% 0.26/0.72 (assert (forall ((A2 tptp.set_Fi291318197eal_sz)) (@ (@ tptp.ord_le41263445eal_sz A2) tptp.top_to1873962757eal_sz)))
% 0.26/0.72 (assert (forall ((A tptp.set_Fi291318197eal_sz)) (@ (@ tptp.ord_le41263445eal_sz A) tptp.top_to1873962757eal_sz)))
% 0.26/0.72 (assert (forall ((Vid1 tptp.sz) (Vid2 tptp.sz) (Vid3 tptp.sz) (Fid1 tptp.sf) (Fid2 tptp.sf) (Fid3 tptp.sf) (Pid1 tptp.sc) (Pid2 tptp.sc) (Pid3 tptp.sc) (Pid4 tptp.sc) (X tptp.produc1821101996_sc_sz)) (=> (@ (@ (@ (@ (@ (@ (@ (@ (@ (@ tptp.ids_sz_sf_sc Vid1) Vid2) Vid3) Fid1) Fid2) Fid3) Pid1) Pid2) Pid3) Pid4) (not (forall ((I2 tptp.denota610675952t_unit) (S tptp.produc866628903_sc_sz)) (not (= X (@ (@ tptp.produc789536734_sc_sz I2) S))))))))
% 0.26/0.72 (assert (= tptp.top_to524132421um_b_c (@ tptp.collec2086029184um_b_c (lambda ((X2 tptp.sum_su737395349um_b_c)) true))))
% 0.26/0.72 (assert (= tptp.top_to1873962757eal_sz (@ tptp.collec1002602816eal_sz (lambda ((X2 tptp.finite824932053eal_sz)) true))))
% 0.26/0.72 (assert (exists ((X3 tptp.a)) (@ (@ tptp.member_a X3) tptp.top_top_set_a)))
% 0.26/0.72 (assert (exists ((X3 tptp.finite824932053eal_sz)) (@ (@ tptp.member1693951742eal_sz X3) tptp.top_to1873962757eal_sz)))
% 0.26/0.72 (assert (forall ((A tptp.set_a)) (=> (forall ((X3 tptp.a)) (@ (@ tptp.member_a X3) A)) (= tptp.top_top_set_a A))))
% 0.26/0.72 (assert (forall ((A tptp.set_Fi291318197eal_sz)) (=> (forall ((X3 tptp.finite824932053eal_sz)) (@ (@ tptp.member1693951742eal_sz X3) A)) (= tptp.top_to1873962757eal_sz A))))
% 0.26/0.72 (assert (= tptp.top_to1787697847eal_sz (@ (@ tptp.produc1235791063eal_sz tptp.top_to1873962757eal_sz) tptp.top_to1873962757eal_sz)))
% 0.26/0.72 (assert (forall ((Vid1 tptp.sz) (Vid2 tptp.sz) (Vid3 tptp.sz) (Fid1 tptp.sf) (Fid2 tptp.sf) (Fid3 tptp.sf) (Pid1 tptp.sc) (Pid2 tptp.sc) (Pid3 tptp.sc) (Pid4 tptp.sc) (P2 tptp.sc)) (=> (@ (@ (@ (@ (@ (@ (@ (@ (@ (@ tptp.ids_sz_sf_sc Vid1) Vid2) Vid3) Fid1) Fid2) Fid3) Pid1) Pid2) Pid3) Pid4) (= (@ tptp.p_sc_sf_sz P2) (@ tptp.predic913887884_sf_sz P2)))))
% 0.26/0.72 (assert (forall ((I3 tptp.denota610675952t_unit) (Theta tptp.trm_sf_sz)) (=> (@ tptp.denota1579475975_sc_sz I3) (=> (@ tptp.dfree_sf_sz Theta) (@ (@ tptp.topolo885751137z_real tptp.top_to1873962757eal_sz) (@ (@ tptp.freche585307148_sc_sz (@ tptp.freche1784963216_sc_sz I3)) (@ tptp.freche1046279700_sf_sz Theta)))))))
% 0.26/0.72 (assert (= tptp.top_to1399053141c_sz_o (lambda ((X2 tptp.denota610675952t_unit) (Y2 tptp.produc866628903_sc_sz)) (@ (@ tptp.member1057565379_sc_sz (@ (@ tptp.produc789536734_sc_sz X2) Y2)) tptp.top_to1499569298_sc_sz))))
% 0.26/0.72 (assert (= tptp.top_to524132421um_b_c (@ tptp.collec2086029184um_b_c tptp.top_to1201357528_b_c_o)))
% 0.26/0.72 (assert (= tptp.top_to1873962757eal_sz (@ tptp.collec1002602816eal_sz tptp.top_to646513176l_sz_o)))
% 0.26/0.72 (assert (forall ((A2 tptp.finite1398487019real_c) (B2 tptp.finite1398487019real_c) (C2 tptp.finite1398487019real_c) (D tptp.finite1398487019real_c)) (=> (@ (@ (@ tptp.denota1997846518gree_c (@ (@ tptp.produc394644079real_c A2) B2)) (@ (@ tptp.produc394644079real_c C2) D)) tptp.top_to1660572043um_c_c) (and (= A2 C2) (= B2 D)))))
% 0.26/0.72 (assert (forall ((Nu tptp.produc190496183real_c) (Omega tptp.produc190496183real_c)) (=> (@ (@ (@ tptp.denota1997846518gree_c Nu) Omega) tptp.top_to1660572043um_c_c) (= Nu Omega))))
% 0.26/0.72 (assert (forall ((Vid1 tptp.sz) (Vid2 tptp.sz) (Vid3 tptp.sz) (Fid1 tptp.sf) (Fid2 tptp.sf) (Fid3 tptp.sf) (Pid1 tptp.sc) (Pid2 tptp.sc) (Pid3 tptp.sc) (Pid4 tptp.sc) (I3 tptp.denota610675952t_unit) (Theta tptp.trm_sf_sz)) (=> (@ (@ (@ (@ (@ (@ (@ (@ (@ (@ tptp.ids_sz_sf_sc Vid1) Vid2) Vid3) Fid1) Fid2) Fid3) Pid1) Pid2) Pid3) Pid4) (=> (@ tptp.denota1579475975_sc_sz I3) (=> (@ tptp.dfree_sf_sz Theta) (@ (@ tptp.topolo885751137z_real tptp.top_to1873962757eal_sz) (@ (@ tptp.freche585307148_sc_sz (@ tptp.freche1784963216_sc_sz I3)) (@ tptp.freche1046279700_sf_sz Theta))))))))
% 0.26/0.72 (assert (forall ((I3 tptp.denota610675952t_unit) (Theta tptp.trm_sf_sz)) (=> (@ tptp.denota1579475975_sc_sz I3) (=> (@ tptp.dfree_sf_sz Theta) (= (lambda ((V2 tptp.finite824932053eal_sz)) (@ tptp.bounde397081123z_real (@ (@ (@ tptp.denota1979904720_sc_sz I3) Theta) V2))) (@ (@ tptp.freche585307148_sc_sz (@ tptp.freche1784963216_sc_sz I3)) (@ tptp.freche1046279700_sf_sz Theta)))))))
% 0.26/0.72 (assert (forall ((S4 tptp.set_Fi291318197eal_sz) (C2 tptp.bounde472938360z_real)) (@ (@ tptp.topolo885751137z_real S4) (lambda ((X2 tptp.finite824932053eal_sz)) C2))))
% 0.26/0.72 (assert (forall ((S4 tptp.set_Fi291318197eal_sz) (F2 (-> tptp.finite824932053eal_sz tptp.bounde472938360z_real)) (T3 tptp.set_Fi291318197eal_sz)) (=> (@ (@ tptp.topolo885751137z_real S4) F2) (=> (@ (@ tptp.ord_le41263445eal_sz T3) S4) (@ (@ tptp.topolo885751137z_real T3) F2)))))
% 0.26/0.72 (assert (forall ((S4 tptp.set_Fi291318197eal_sz) (F2 (-> tptp.finite824932053eal_sz tptp.bounde472938360z_real)) (G2 (-> tptp.finite824932053eal_sz tptp.bounde472938360z_real))) (let ((_let_1 (@ tptp.topolo885751137z_real S4))) (=> (@ _let_1 F2) (=> (@ _let_1 G2) (@ (@ tptp.topolo1027477648z_real S4) (lambda ((X2 tptp.finite824932053eal_sz)) (@ (@ tptp.produc784663575z_real (@ F2 X2)) (@ G2 X2)))))))))
% 0.26/0.72 (assert (forall ((Vid1 tptp.sz) (Vid2 tptp.sz) (Vid3 tptp.sz) (Fid1 tptp.sf) (Fid2 tptp.sf) (Fid3 tptp.sf) (Pid1 tptp.sc) (Pid2 tptp.sc) (Pid3 tptp.sc) (Pid4 tptp.sc) (I3 tptp.denota610675952t_unit) (Theta tptp.trm_sf_sz)) (=> (@ (@ (@ (@ (@ (@ (@ (@ (@ (@ tptp.ids_sz_sf_sc Vid1) Vid2) Vid3) Fid1) Fid2) Fid3) Pid1) Pid2) Pid3) Pid4) (=> (@ tptp.denota1579475975_sc_sz I3) (=> (@ tptp.dfree_sf_sz Theta) (= (lambda ((V2 tptp.finite824932053eal_sz)) (@ tptp.bounde397081123z_real (@ (@ (@ tptp.denota1979904720_sc_sz I3) Theta) V2))) (@ (@ tptp.freche585307148_sc_sz (@ tptp.freche1784963216_sc_sz I3)) (@ tptp.freche1046279700_sf_sz Theta))))))))
% 0.26/0.72 (assert (forall ((Xb tptp.denota610675952t_unit) (Xa tptp.trm_sf_sz) (X tptp.finite824932053eal_sz)) (=> (@ (@ (@ tptp.bNF_eq1660582207t_unit tptp.denota1579475975_sc_sz) Xb) Xb) (=> (@ (@ (@ tptp.bNF_eq_onp_trm_sf_sz tptp.dfree_sf_sz) Xa) Xa) (= (@ (@ (@ tptp.freche585307148_sc_sz (@ tptp.freche1784963216_sc_sz Xb)) (@ tptp.freche1046279700_sf_sz Xa)) X) (@ tptp.bounde397081123z_real (@ (@ (@ tptp.denota1979904720_sc_sz Xb) Xa) X)))))))
% 0.26/0.72 (assert (forall ((Vid1 tptp.sz) (Vid2 tptp.sz) (Vid3 tptp.sz) (Fid1 tptp.sf) (Fid2 tptp.sf) (Fid3 tptp.sf) (Pid1 tptp.sc) (Pid2 tptp.sc) (Pid3 tptp.sc) (Pid4 tptp.sc) (Xb tptp.denota610675952t_unit) (Xa tptp.trm_sf_sz) (X tptp.finite824932053eal_sz)) (=> (@ (@ (@ (@ (@ (@ (@ (@ (@ (@ tptp.ids_sz_sf_sc Vid1) Vid2) Vid3) Fid1) Fid2) Fid3) Pid1) Pid2) Pid3) Pid4) (=> (@ (@ (@ tptp.bNF_eq1660582207t_unit tptp.denota1579475975_sc_sz) Xb) Xb) (=> (@ (@ (@ tptp.bNF_eq_onp_trm_sf_sz tptp.dfree_sf_sz) Xa) Xa) (= (@ (@ (@ tptp.freche585307148_sc_sz (@ tptp.freche1784963216_sc_sz Xb)) (@ tptp.freche1046279700_sf_sz Xa)) X) (@ tptp.bounde397081123z_real (@ (@ (@ tptp.denota1979904720_sc_sz Xb) Xa) X))))))))
% 0.26/0.72 (assert (@ (@ (@ (@ tptp.quotie842200089_sc_sz (@ tptp.bNF_eq1660582207t_unit tptp.denota1579475975_sc_sz)) tptp.freche1784963216_sc_sz) tptp.freche1421597129_sc_sz) tptp.freche58918398_sc_sz))
% 0.26/0.72 (assert (@ (@ (@ (@ tptp.quotie1467858509rm_a_c (@ tptp.bNF_eq_onp_trm_a_c tptp.dfree_a_c)) tptp.freche665377492rm_a_c) tptp.frechet_raw_term_a_c) tptp.frechet_cr_strm_a_c))
% 0.52/1.05 (assert (@ (@ (@ (@ tptp.quotie1549861309_sf_sz (@ tptp.bNF_eq_onp_trm_sf_sz tptp.dfree_sf_sz)) tptp.freche1046279700_sf_sz) tptp.freche782854530_sf_sz) tptp.freche1244000341_sf_sz))
% 0.52/1.05 (assert (forall ((P (-> tptp.denota610675952t_unit Bool))) (@ (@ tptp.ord_le2003534918unit_o (@ tptp.bNF_eq1660582207t_unit P)) (lambda ((Y4 tptp.denota610675952t_unit) (Z tptp.denota610675952t_unit)) (= Y4 Z)))))
% 0.52/1.05 (assert (forall ((P (-> tptp.trm_sf_sz Bool))) (@ (@ tptp.ord_le8515534f_sz_o (@ tptp.bNF_eq_onp_trm_sf_sz P)) (lambda ((Y4 tptp.trm_sf_sz) (Z tptp.trm_sf_sz)) (= Y4 Z)))))
% 0.52/1.05 (assert (forall ((P Bool)) (or (= P true) (= P false))))
% 0.52/1.05 (assert (forall ((X tptp.bounde472938360z_real) (Y tptp.bounde472938360z_real)) (= (@ (@ (@ tptp.if_Bou1785791806z_real false) X) Y) Y)))
% 0.52/1.05 (assert (forall ((X tptp.bounde472938360z_real) (Y tptp.bounde472938360z_real)) (= (@ (@ (@ tptp.if_Bou1785791806z_real true) X) Y) X)))
% 0.52/1.05 (assert (not (@ (@ (@ tptp.denota1997846518gree_c tptp.nu) tptp.nu2) (@ tptp.static_FVDiff_a_c tptp.t2))))
% 0.52/1.05 (set-info :filename cvc5---1.0.5_17543)
% 0.52/1.05 (check-sat-assuming ( true ))
% 0.52/1.05 ------- get file name : TPTP file name is ITP038^1
% 0.52/1.05 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_17543.smt2...
% 0.52/1.05 --- Run --ho-elim --full-saturate-quant at 10...
% 0.52/1.05 % SZS status Theorem for ITP038^1
% 0.52/1.05 % SZS output start Proof for ITP038^1
% 0.52/1.05 (
% 0.52/1.05 (let ((_let_1 (@ (@ tptp.denota1997846518gree_c tptp.nu) tptp.nu2))) (let ((_let_2 (@ _let_1 (@ tptp.static_FVDiff_a_c tptp.t2)))) (let ((_let_3 (not _let_2))) (let ((_let_4 (@ tptp.produc314122909real_c tptp.nu2))) (let ((_let_5 (@ tptp.produc2010422875real_c tptp.nu2))) (let ((_let_6 (@ tptp.denota229585092_a_b_c tptp.j))) (let ((_let_7 (@ tptp.produc314122909real_c tptp.nu))) (let ((_let_8 (@ tptp.produc2010422875real_c tptp.nu))) (let ((_let_9 (@ tptp.denota229585092_a_b_c tptp.i))) (let ((_let_10 (@ (@ tptp.denota69106024_a_b_c tptp.i) tptp.j))) (let ((_let_11 (@ _let_1 (@ tptp.static_FVDiff_a_c tptp.t1)))) (let ((_let_12 (@ _let_1 (@ tptp.static_FVDiff_a_c (@ (@ tptp.plus_a_c tptp.t1) tptp.t2))))) (let ((_let_13 (forall ((Nu tptp.produc190496183real_c) (Nu2 tptp.produc190496183real_c) (T1 tptp.trm_a_c) (T2 tptp.trm_a_c)) (let ((_let_1 (@ (@ tptp.denota1997846518gree_c Nu) Nu2))) (=> (@ _let_1 (@ tptp.static_FVDiff_a_c (@ (@ tptp.plus_a_c T1) T2))) (@ _let_1 (@ tptp.static_FVDiff_a_c T2))))))) (let ((_let_14 (forall ((Nu tptp.produc190496183real_c) (Nu2 tptp.produc190496183real_c) (T1 tptp.trm_a_c) (T2 tptp.trm_a_c)) (let ((_let_1 (ho_284 (ho_283 k_282 Nu) Nu2))) (or (not (ho_285 _let_1 (ho_281 k_280 (ho_262 (ho_261 k_260 T1) T2)))) (ho_285 _let_1 (ho_281 k_280 T2))))))) (let ((_let_15 (ho_284 (ho_283 k_282 tptp.nu) tptp.nu2))) (let ((_let_16 (ho_285 _let_15 (ho_281 k_280 tptp.t2)))) (let ((_let_17 (ho_285 _let_15 (ho_281 k_280 (ho_262 (ho_261 k_260 tptp.t1) tptp.t2))))) (let ((_let_18 (not _let_17))) (let ((_let_19 (or _let_18 _let_16))) (let ((_let_20 (EQ_RESOLVE (ASSUME :args (_let_13)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((Nu tptp.produc190496183real_c) (Nu2 tptp.produc190496183real_c) (T1 tptp.trm_a_c) (T2 tptp.trm_a_c)) (let ((_let_1 (@ (@ tptp.denota1997846518gree_c Nu) Nu2))) (or (not (@ _let_1 (@ tptp.static_FVDiff_a_c (@ (@ tptp.plus_a_c T1) T2)))) (@ _let_1 (@ tptp.static_FVDiff_a_c T2))))) _let_14))))))) (let ((_let_21 (not _let_19))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_20 :args (tptp.nu tptp.nu2 tptp.t1 tptp.t2 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_14))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_19)) :args ((or _let_16 _let_18 _let_21))) (EQ_RESOLVE (ASSUME :args (_let_3)) (PREPROCESS :args ((= _let_3 (not _let_16))))) (EQ_RESOLVE (ASSUME :args (_let_12)) (PREPROCESS :args ((= _let_12 _let_17)))) :args (_let_21 true _let_16 false _let_17)) _let_20 :args (false true _let_19 false _let_14)) :args ((forall ((Nu tptp.produc1149990247eal_sz) (Nu2 tptp.produc1149990247eal_sz) (T1 tptp.trm_sf_sz) (T2 tptp.trm_sf_sz)) (let ((_let_1 (@ (@ tptp.denota102713844ree_sz Nu) Nu2))) (=> (@ _let_1 (@ tptp.static_FVDiff_sf_sz (@ (@ tptp.plus_sf_sz T1) T2))) (@ _let_1 (@ tptp.static_FVDiff_sf_sz T2))))) _let_13 _let_12 _let_11 (@ tptp.dfree_a_c tptp.t2) (forall ((Nu tptp.produc1149990247eal_sz) (Nu2 tptp.produc1149990247eal_sz) (T1 tptp.trm_sf_sz) (T2 tptp.trm_sf_sz)) (let ((_let_1 (@ (@ tptp.denota102713844ree_sz Nu) Nu2))) (=> (@ _let_1 (@ tptp.static_FVDiff_sf_sz (@ (@ tptp.plus_sf_sz T1) T2))) (@ _let_1 (@ tptp.static_FVDiff_sf_sz T1))))) (forall ((Nu tptp.produc190496183real_c) (Nu2 tptp.produc190496183real_c) (T1 tptp.trm_a_c) (T2 tptp.trm_a_c)) (let ((_let_1 (@ (@ tptp.denota1997846518gree_c Nu) Nu2))) (=> (@ _let_1 (@ tptp.static_FVDiff_a_c (@ (@ tptp.plus_a_c T1) T2))) (@ _let_1 (@ tptp.static_FVDiff_a_c T1))))) (forall ((A tptp.produc1149990247eal_sz) (B tptp.produc1149990247eal_sz) (V tptp.set_Sum_sum_sz_sz)) (=> (@ (@ (@ tptp.denota102713844ree_sz A) B) V) (@ (@ (@ tptp.denota102713844ree_sz B) A) V))) (forall ((A tptp.produc190496183real_c) (B tptp.produc190496183real_c) (V tptp.set_Sum_sum_c_c)) (=> (@ (@ (@ tptp.denota1997846518gree_c A) B) V) (@ (@ (@ tptp.denota1997846518gree_c B) A) V))) (forall ((Nu tptp.produc1149990247eal_sz) (A tptp.set_Sum_sum_sz_sz)) (@ (@ (@ tptp.denota102713844ree_sz Nu) Nu) A)) (forall ((Nu tptp.produc190496183real_c) (A tptp.set_Sum_sum_c_c)) (@ (@ (@ tptp.denota1997846518gree_c Nu) Nu) A)) (@ tptp.dfree_a_c tptp.t1) (forall ((X tptp.freche2095075217_sc_sz) (Y tptp.freche2095075217_sc_sz)) (= (= (@ tptp.freche1421597129_sc_sz X) (@ tptp.freche1421597129_sc_sz Y)) (= X Y))) (forall ((X tptp.frechet_strm_sf_sz) (Y tptp.frechet_strm_sf_sz)) (= (= (@ tptp.freche782854530_sf_sz X) (@ tptp.freche782854530_sf_sz Y)) (= X Y))) (forall ((X tptp.frechet_strm_a_c) (Y tptp.frechet_strm_a_c)) (= (= (@ tptp.frechet_raw_term_a_c X) (@ tptp.frechet_raw_term_a_c Y)) (= X Y))) (forall ((Nu tptp.produc1149990247eal_sz) (Nu2 tptp.produc1149990247eal_sz) (T1 tptp.trm_sf_sz) (T2 tptp.trm_sf_sz)) (let ((_let_1 (@ (@ tptp.denota102713844ree_sz Nu) Nu2))) (=> (@ _let_1 (@ tptp.static_FVDiff_sf_sz (@ (@ tptp.times_sf_sz T1) T2))) (@ _let_1 (@ tptp.static_FVDiff_sf_sz T1))))) (forall ((Nu tptp.produc190496183real_c) (Nu2 tptp.produc190496183real_c) (T1 tptp.trm_a_c) (T2 tptp.trm_a_c)) (let ((_let_1 (@ (@ tptp.denota1997846518gree_c Nu) Nu2))) (=> (@ _let_1 (@ tptp.static_FVDiff_a_c (@ (@ tptp.times_a_c T1) T2))) (@ _let_1 (@ tptp.static_FVDiff_a_c T1))))) (forall ((Nu tptp.produc1149990247eal_sz) (Nu2 tptp.produc1149990247eal_sz) (T1 tptp.trm_sf_sz) (T2 tptp.trm_sf_sz)) (let ((_let_1 (@ (@ tptp.denota102713844ree_sz Nu) Nu2))) (=> (@ _let_1 (@ tptp.static_FVDiff_sf_sz (@ (@ tptp.times_sf_sz T1) T2))) (@ _let_1 (@ tptp.static_FVDiff_sf_sz T2))))) (forall ((Nu tptp.produc190496183real_c) (Nu2 tptp.produc190496183real_c) (T1 tptp.trm_a_c) (T2 tptp.trm_a_c)) (let ((_let_1 (@ (@ tptp.denota1997846518gree_c Nu) Nu2))) (=> (@ _let_1 (@ tptp.static_FVDiff_a_c (@ (@ tptp.times_a_c T1) T2))) (@ _let_1 (@ tptp.static_FVDiff_a_c T2))))) (forall ((Nu tptp.produc1149990247eal_sz) (Nu2 tptp.produc1149990247eal_sz) (Var tptp.sf) (Args (-> tptp.sz tptp.trm_sf_sz)) (I tptp.sz)) (let ((_let_1 (@ (@ tptp.denota102713844ree_sz Nu) Nu2))) (=> (@ _let_1 (@ tptp.static_FVDiff_sf_sz (@ (@ tptp.function_sf_sz Var) Args))) (@ _let_1 (@ tptp.static_FVDiff_sf_sz (@ Args I)))))) (forall ((Nu tptp.produc190496183real_c) (Nu2 tptp.produc190496183real_c) (Var tptp.a) (Args (-> tptp.c tptp.trm_a_c)) (I tptp.c)) (let ((_let_1 (@ (@ tptp.denota1997846518gree_c Nu) Nu2))) (=> (@ _let_1 (@ tptp.static_FVDiff_a_c (@ (@ tptp.function_a_c Var) Args))) (@ _let_1 (@ tptp.static_FVDiff_a_c (@ Args I)))))) (= tptp.p_sc_sf_sz tptp.predic913887884_sf_sz) (=> _let_2 (=> (@ _let_10 (@ tptp.collec2086029184um_b_c (lambda ((Uu tptp.sum_su737395349um_b_c)) (exists ((X2 tptp.a)) (and (= Uu (@ tptp.sum_In2139678582um_b_c X2)) (@ (@ tptp.member_a X2) (@ tptp.static_SIGT_a_c tptp.t2))))))) (= (@ (@ (@ _let_9 tptp.t2) _let_8) _let_7) (@ (@ (@ _let_6 tptp.t2) _let_5) _let_4)))) (forall ((X tptp.produc1821101996_sc_sz)) (not (forall ((I2 tptp.denota610675952t_unit) (S tptp.produc866628903_sc_sz)) (not (= X (@ (@ tptp.produc789536734_sc_sz I2) S)))))) (forall ((X tptp.frechet_strm_a_c)) (@ (@ tptp.member_trm_a_c (@ tptp.frechet_raw_term_a_c X)) (@ tptp.collect_trm_a_c tptp.dfree_a_c))) (forall ((X tptp.frechet_strm_sf_sz)) (@ (@ tptp.member_trm_sf_sz (@ tptp.freche782854530_sf_sz X)) (@ tptp.collect_trm_sf_sz tptp.dfree_sf_sz))) (forall ((Y tptp.trm_a_c)) (=> (@ (@ tptp.member_trm_a_c Y) (@ tptp.collect_trm_a_c tptp.dfree_a_c)) (not (forall ((X3 tptp.frechet_strm_a_c)) (not (= Y (@ tptp.frechet_raw_term_a_c X3))))))) (forall ((Y tptp.trm_sf_sz)) (=> (@ (@ tptp.member_trm_sf_sz Y) (@ tptp.collect_trm_sf_sz tptp.dfree_sf_sz)) (not (forall ((X3 tptp.frechet_strm_sf_sz)) (not (= Y (@ tptp.freche782854530_sf_sz X3))))))) (forall ((Y tptp.trm_a_c) (P (-> tptp.trm_a_c Bool))) (=> (@ (@ tptp.member_trm_a_c Y) (@ tptp.collect_trm_a_c tptp.dfree_a_c)) (=> (forall ((X3 tptp.frechet_strm_a_c)) (@ P (@ tptp.frechet_raw_term_a_c X3))) (@ P Y)))) (forall ((Y tptp.trm_sf_sz) (P (-> tptp.trm_sf_sz Bool))) (=> (@ (@ tptp.member_trm_sf_sz Y) (@ tptp.collect_trm_sf_sz tptp.dfree_sf_sz)) (=> (forall ((X3 tptp.frechet_strm_sf_sz)) (@ P (@ tptp.freche782854530_sf_sz X3))) (@ P Y)))) (forall ((Theta tptp.trm_a_c) (Nu tptp.produc190496183real_c) (Nu2 tptp.produc190496183real_c) (I3 tptp.denota231621370t_unit)) (let ((_let_1 (@ (@ tptp.denota229585092_a_b_c I3) Theta))) (=> (@ tptp.dfree_a_c Theta) (=> (@ (@ (@ tptp.denota1997846518gree_c Nu) Nu2) (@ tptp.static_FVDiff_a_c Theta)) (= (@ (@ _let_1 (@ tptp.produc2010422875real_c Nu)) (@ tptp.produc314122909real_c Nu)) (@ (@ _let_1 (@ tptp.produc2010422875real_c Nu2)) (@ tptp.produc314122909real_c Nu2))))))) (forall ((Theta tptp.trm_sf_sz) (Nu tptp.produc1149990247eal_sz) (Nu2 tptp.produc1149990247eal_sz) (I3 tptp.denota610675952t_unit)) (let ((_let_1 (@ (@ tptp.denota1979904720_sc_sz I3) Theta))) (=> (@ tptp.dfree_sf_sz Theta) (=> (@ (@ (@ tptp.denota102713844ree_sz Nu) Nu2) (@ tptp.static_FVDiff_sf_sz Theta)) (= (@ (@ _let_1 (@ tptp.produc1111759555eal_sz Nu)) (@ tptp.produc1269210629eal_sz Nu)) (@ (@ _let_1 (@ tptp.produc1111759555eal_sz Nu2)) (@ tptp.produc1269210629eal_sz Nu2))))))) (@ _let_10 (@ tptp.collec2086029184um_b_c (lambda ((Uu tptp.sum_su737395349um_b_c)) (exists ((X2 tptp.a)) (and (= Uu (@ tptp.sum_In2139678582um_b_c X2)) (@ (@ tptp.member_a X2) (@ tptp.static_SIGT_a_c (@ (@ tptp.plus_a_c tptp.t1) tptp.t2)))))))) (@ _let_10 (@ tptp.collec2086029184um_b_c (lambda ((Uu tptp.sum_su737395349um_b_c)) (exists ((X2 tptp.a)) (and (= Uu (@ tptp.sum_In2139678582um_b_c X2)) (@ (@ tptp.member_a X2) (@ tptp.static_SIGT_a_c tptp.t1))))))) (@ _let_10 (@ tptp.collec2086029184um_b_c (lambda ((Uu tptp.sum_su737395349um_b_c)) (exists ((X2 tptp.a)) (and (= Uu (@ tptp.sum_In2139678582um_b_c X2)) (@ (@ tptp.member_a X2) (@ tptp.static_SIGT_a_c tptp.t2))))))) (=> _let_11 (=> (@ _let_10 (@ tptp.collec2086029184um_b_c (lambda ((Uu tptp.sum_su737395349um_b_c)) (exists ((X2 tptp.a)) (and (= Uu (@ tptp.sum_In2139678582um_b_c X2)) (@ (@ tptp.member_a X2) (@ tptp.static_SIGT_a_c tptp.t1))))))) (= (@ (@ (@ _let_9 tptp.t1) _let_8) _let_7) (@ (@ (@ _let_6 tptp.t1) _let_5) _let_4)))) (forall ((A tptp.denota231621370t_unit) (B tptp.denota231621370t_unit) (V tptp.set_Su1783761653um_b_c)) (=> (@ (@ (@ tptp.denota69106024_a_b_c A) B) V) (@ (@ (@ tptp.denota69106024_a_b_c B) A) V))) (forall ((I3 tptp.denota231621370t_unit) (A tptp.set_Su1783761653um_b_c)) (@ (@ (@ tptp.denota69106024_a_b_c I3) I3) A)) (@ (@ tptp.ord_le929608341um_b_c (@ tptp.collec2086029184um_b_c (lambda ((Uu tptp.sum_su737395349um_b_c)) (exists ((X2 tptp.a)) (and (= Uu (@ tptp.sum_In2139678582um_b_c X2)) (@ (@ tptp.member_a X2) (@ tptp.static_SIGT_a_c tptp.t2))))))) (@ tptp.collec2086029184um_b_c (lambda ((Uu tptp.sum_su737395349um_b_c)) (exists ((X2 tptp.a)) (and (= Uu (@ tptp.sum_In2139678582um_b_c X2)) (@ (@ tptp.member_a X2) (@ tptp.static_SIGT_a_c (@ (@ tptp.plus_a_c tptp.t1) tptp.t2)))))))) (@ (@ tptp.ord_le929608341um_b_c (@ tptp.collec2086029184um_b_c (lambda ((Uu tptp.sum_su737395349um_b_c)) (exists ((X2 tptp.a)) (and (= Uu (@ tptp.sum_In2139678582um_b_c X2)) (@ (@ tptp.member_a X2) (@ tptp.static_SIGT_a_c tptp.t1))))))) (@ tptp.collec2086029184um_b_c (lambda ((Uu tptp.sum_su737395349um_b_c)) (exists ((X2 tptp.a)) (and (= Uu (@ tptp.sum_In2139678582um_b_c X2)) (@ (@ tptp.member_a X2) (@ tptp.static_SIGT_a_c (@ (@ tptp.plus_a_c tptp.t1) tptp.t2)))))))) (forall ((Y tptp.trm_a_c)) (=> (@ (@ tptp.member_trm_a_c Y) (@ tptp.collect_trm_a_c tptp.dfree_a_c)) (= (@ tptp.frechet_raw_term_a_c (@ tptp.freche665377492rm_a_c Y)) Y))) (forall ((Y tptp.trm_sf_sz)) (=> (@ (@ tptp.member_trm_sf_sz Y) (@ tptp.collect_trm_sf_sz tptp.dfree_sf_sz)) (= (@ tptp.freche782854530_sf_sz (@ tptp.freche1046279700_sf_sz Y)) Y))) (forall ((Prod tptp.produc866628903_sc_sz)) (= (@ (@ tptp.produc1822718231_sc_sz (@ tptp.produc548504323_sc_sz Prod)) (@ tptp.produc4753477_sc_sz Prod)) Prod)) (forall ((Prod tptp.produc1241881959eal_sz)) (= (@ (@ tptp.produc1235791063eal_sz (@ tptp.produc286845635eal_sz Prod)) (@ tptp.produc1746886149eal_sz Prod)) Prod)) (forall ((Prod tptp.produc1892666919z_real)) (= (@ (@ tptp.produc784663575z_real (@ tptp.produc870616579z_real Prod)) (@ tptp.produc1422611269z_real Prod)) Prod)) (forall ((Prod tptp.produc1149990247eal_sz)) (= (@ (@ tptp.produc1308130519eal_sz (@ tptp.produc1111759555eal_sz Prod)) (@ tptp.produc1269210629eal_sz Prod)) Prod)) (forall ((Prod tptp.produc1821101996_sc_sz)) (= (@ (@ tptp.produc789536734_sc_sz (@ tptp.produc1503602930_sc_sz Prod)) (@ tptp.produc974239792_sc_sz Prod)) Prod)) (forall ((Prod tptp.produc190496183real_c)) (= (@ (@ tptp.produc394644079real_c (@ tptp.produc2010422875real_c Prod)) (@ tptp.produc314122909real_c Prod)) Prod)) (= tptp.freche58918398_sc_sz (lambda ((X2 tptp.denota610675952t_unit) (Y2 tptp.freche2095075217_sc_sz)) (= X2 (@ tptp.freche1421597129_sc_sz Y2)))) (= tptp.freche1244000341_sf_sz (lambda ((X2 tptp.trm_sf_sz) (Y2 tptp.frechet_strm_sf_sz)) (= X2 (@ tptp.freche782854530_sf_sz Y2)))) (= tptp.frechet_cr_strm_a_c (lambda ((X2 tptp.trm_a_c) (Y2 tptp.frechet_strm_a_c)) (= X2 (@ tptp.frechet_raw_term_a_c Y2)))) (forall ((A2 tptp.trm_a_c) (B2 tptp.trm_a_c)) (= (@ tptp.dfree_a_c (@ (@ tptp.times_a_c A2) B2)) (and (@ tptp.dfree_a_c A2) (@ tptp.dfree_a_c B2)))) (forall ((A2 tptp.trm_sf_sz) (B2 tptp.trm_sf_sz)) (= (@ tptp.dfree_sf_sz (@ (@ tptp.times_sf_sz A2) B2)) (and (@ tptp.dfree_sf_sz A2) (@ tptp.dfree_sf_sz B2)))) (forall ((A2 tptp.trm_sf_sz) (B2 tptp.trm_sf_sz)) (= (@ tptp.dfree_sf_sz (@ (@ tptp.plus_sf_sz A2) B2)) (and (@ tptp.dfree_sf_sz A2) (@ tptp.dfree_sf_sz B2)))) (forall ((A2 tptp.trm_a_c) (B2 tptp.trm_a_c)) (= (@ tptp.dfree_a_c (@ (@ tptp.plus_a_c A2) B2)) (and (@ tptp.dfree_a_c A2) (@ tptp.dfree_a_c B2)))) (forall ((I tptp.a) (Args (-> tptp.c tptp.trm_a_c))) (= (@ tptp.dfree_a_c (@ (@ tptp.function_a_c I) Args)) (forall ((X2 tptp.c)) (@ tptp.dfree_a_c (@ Args X2))))) (forall ((I tptp.sf) (Args (-> tptp.sz tptp.trm_sf_sz))) (= (@ tptp.dfree_sf_sz (@ (@ tptp.function_sf_sz I) Args)) (forall ((X2 tptp.sz)) (@ tptp.dfree_sf_sz (@ Args X2))))) (forall ((X tptp.frechet_strm_a_c)) (not (forall ((Y3 tptp.trm_a_c)) (=> (= X (@ tptp.freche665377492rm_a_c Y3)) (not (@ (@ tptp.member_trm_a_c Y3) (@ tptp.collect_trm_a_c tptp.dfree_a_c))))))) (forall ((X tptp.frechet_strm_sf_sz)) (not (forall ((Y3 tptp.trm_sf_sz)) (=> (= X (@ tptp.freche1046279700_sf_sz Y3)) (not (@ (@ tptp.member_trm_sf_sz Y3) (@ tptp.collect_trm_sf_sz tptp.dfree_sf_sz))))))) (forall ((X tptp.frechet_strm_a_c)) (= (@ tptp.freche665377492rm_a_c (@ tptp.frechet_raw_term_a_c X)) X)) (forall ((X tptp.frechet_strm_sf_sz)) (= (@ tptp.freche1046279700_sf_sz (@ tptp.freche782854530_sf_sz X)) X)) (forall ((X tptp.trm_a_c) (Y tptp.trm_a_c)) (let ((_let_1 (@ tptp.collect_trm_a_c tptp.dfree_a_c))) (=> (@ (@ tptp.member_trm_a_c X) _let_1) (=> (@ (@ tptp.member_trm_a_c Y) _let_1) (= (= (@ tptp.freche665377492rm_a_c X) (@ tptp.freche665377492rm_a_c Y)) (= X Y)))))) (forall ((X tptp.trm_sf_sz) (Y tptp.trm_sf_sz)) (let ((_let_1 (@ tptp.collect_trm_sf_sz tptp.dfree_sf_sz))) (=> (@ (@ tptp.member_trm_sf_sz X) _let_1) (=> (@ (@ tptp.member_trm_sf_sz Y) _let_1) (= (= (@ tptp.freche1046279700_sf_sz X) (@ tptp.freche1046279700_sf_sz Y)) (= X Y)))))) (forall ((P (-> tptp.frechet_strm_a_c Bool)) (X tptp.frechet_strm_a_c)) (=> (forall ((Y3 tptp.trm_a_c)) (=> (@ (@ tptp.member_trm_a_c Y3) (@ tptp.collect_trm_a_c tptp.dfree_a_c)) (@ P (@ tptp.freche665377492rm_a_c Y3)))) (@ P X))) (forall ((P (-> tptp.frechet_strm_sf_sz Bool)) (X tptp.frechet_strm_sf_sz)) (=> (forall ((Y3 tptp.trm_sf_sz)) (=> (@ (@ tptp.member_trm_sf_sz Y3) (@ tptp.collect_trm_sf_sz tptp.dfree_sf_sz)) (@ P (@ tptp.freche1046279700_sf_sz Y3)))) (@ P X))) (forall ((A2 tptp.finite1398487019real_c) (B2 tptp.finite1398487019real_c) (A3 tptp.finite1398487019real_c) (B3 tptp.finite1398487019real_c)) (= (= (@ (@ tptp.produc394644079real_c A2) B2) (@ (@ tptp.produc394644079real_c A3) B3)) (and (= A2 A3) (= B2 B3)))) (forall ((A2 tptp.list_f1238882004_sc_sz) (B2 tptp.list_f1238882004_sc_sz) (A3 tptp.list_f1238882004_sc_sz) (B3 tptp.list_f1238882004_sc_sz)) (= (= (@ (@ tptp.produc1822718231_sc_sz A2) B2) (@ (@ tptp.produc1822718231_sc_sz A3) B3)) (and (= A2 A3) (= B2 B3)))) (forall ((A2 tptp.set_Fi291318197eal_sz) (B2 tptp.set_Fi291318197eal_sz) (A3 tptp.set_Fi291318197eal_sz) (B3 tptp.set_Fi291318197eal_sz)) (= (= (@ (@ tptp.produc1235791063eal_sz A2) B2) (@ (@ tptp.produc1235791063eal_sz A3) B3)) (and (= A2 A3) (= B2 B3)))) (forall ((A2 tptp.bounde472938360z_real) (B2 tptp.bounde472938360z_real) (A3 tptp.bounde472938360z_real) (B3 tptp.bounde472938360z_real)) (= (= (@ (@ tptp.produc784663575z_real A2) B2) (@ (@ tptp.produc784663575z_real A3) B3)) (and (= A2 A3) (= B2 B3)))) (forall ((A2 tptp.denota610675952t_unit) (B2 tptp.produc866628903_sc_sz) (A3 tptp.denota610675952t_unit) (B3 tptp.produc866628903_sc_sz)) (= (= (@ (@ tptp.produc789536734_sc_sz A2) B2) (@ (@ tptp.produc789536734_sc_sz A3) B3)) (and (= A2 A3) (= B2 B3)))) (forall ((X1 tptp.finite1398487019real_c) (X22 tptp.finite1398487019real_c) (Y1 tptp.finite1398487019real_c) (Y22 tptp.finite1398487019real_c)) (= (= (@ (@ tptp.produc394644079real_c X1) X22) (@ (@ tptp.produc394644079real_c Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))) (forall ((X1 tptp.list_f1238882004_sc_sz) (X22 tptp.list_f1238882004_sc_sz) (Y1 tptp.list_f1238882004_sc_sz) (Y22 tptp.list_f1238882004_sc_sz)) (= (= (@ (@ tptp.produc1822718231_sc_sz X1) X22) (@ (@ tptp.produc1822718231_sc_sz Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))) (forall ((X1 tptp.set_Fi291318197eal_sz) (X22 tptp.set_Fi291318197eal_sz) (Y1 tptp.set_Fi291318197eal_sz) (Y22 tptp.set_Fi291318197eal_sz)) (= (= (@ (@ tptp.produc1235791063eal_sz X1) X22) (@ (@ tptp.produc1235791063eal_sz Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))) (forall ((X1 tptp.bounde472938360z_real) (X22 tptp.bounde472938360z_real) (Y1 tptp.bounde472938360z_real) (Y22 tptp.bounde472938360z_real)) (= (= (@ (@ tptp.produc784663575z_real X1) X22) (@ (@ tptp.produc784663575z_real Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))) (forall ((X1 tptp.denota610675952t_unit) (X22 tptp.produc866628903_sc_sz) (Y1 tptp.denota610675952t_unit) (Y22 tptp.produc866628903_sc_sz)) (= (= (@ (@ tptp.produc789536734_sc_sz X1) X22) (@ (@ tptp.produc789536734_sc_sz Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))) (forall ((X31 tptp.a) (X32 (-> tptp.c tptp.trm_a_c)) (Y31 tptp.a) (Y32 (-> tptp.c tptp.trm_a_c))) (= (= (@ (@ tptp.function_a_c X31) X32) (@ (@ tptp.function_a_c Y31) Y32)) (and (= X31 Y31) (= X32 Y32)))) (forall ((X31 tptp.sf) (X32 (-> tptp.sz tptp.trm_sf_sz)) (Y31 tptp.sf) (Y32 (-> tptp.sz tptp.trm_sf_sz))) (= (= (@ (@ tptp.function_sf_sz X31) X32) (@ (@ tptp.function_sf_sz Y31) Y32)) (and (= X31 Y31) (= X32 Y32)))) (forall ((X41 tptp.trm_sf_sz) (X42 tptp.trm_sf_sz) (Y41 tptp.trm_sf_sz) (Y42 tptp.trm_sf_sz)) (= (= (@ (@ tptp.plus_sf_sz X41) X42) (@ (@ tptp.plus_sf_sz Y41) Y42)) (and (= X41 Y41) (= X42 Y42)))) (forall ((X41 tptp.trm_a_c) (X42 tptp.trm_a_c) (Y41 tptp.trm_a_c) (Y42 tptp.trm_a_c)) (= (= (@ (@ tptp.plus_a_c X41) X42) (@ (@ tptp.plus_a_c Y41) Y42)) (and (= X41 Y41) (= X42 Y42)))) (forall ((X51 tptp.trm_a_c) (X52 tptp.trm_a_c) (Y51 tptp.trm_a_c) (Y52 tptp.trm_a_c)) (= (= (@ (@ tptp.times_a_c X51) X52) (@ (@ tptp.times_a_c Y51) Y52)) (and (= X51 Y51) (= X52 Y52)))) (forall ((X51 tptp.trm_sf_sz) (X52 tptp.trm_sf_sz) (Y51 tptp.trm_sf_sz) (Y52 tptp.trm_sf_sz)) (= (= (@ (@ tptp.times_sf_sz X51) X52) (@ (@ tptp.times_sf_sz Y51) Y52)) (and (= X51 Y51) (= X52 Y52)))) (forall ((A2 tptp.finite824932053eal_sz) (P (-> tptp.finite824932053eal_sz Bool))) (= (@ (@ tptp.member1693951742eal_sz A2) (@ tptp.collec1002602816eal_sz P)) (@ P A2))) (forall ((A2 tptp.produc1821101996_sc_sz) (P (-> tptp.produc1821101996_sc_sz Bool))) (= (@ (@ tptp.member1057565379_sc_sz A2) (@ tptp.collec1199592193_sc_sz P)) (@ P A2))) (forall ((A2 tptp.trm_sf_sz) (P (-> tptp.trm_sf_sz Bool))) (= (@ (@ tptp.member_trm_sf_sz A2) (@ tptp.collect_trm_sf_sz P)) (@ P A2))) (forall ((A2 tptp.trm_a_c) (P (-> tptp.trm_a_c Bool))) (= (@ (@ tptp.member_trm_a_c A2) (@ tptp.collect_trm_a_c P)) (@ P A2))) (forall ((A2 tptp.a) (P (-> tptp.a Bool))) (= (@ (@ tptp.member_a A2) (@ tptp.collect_a P)) (@ P A2))) (forall ((A2 tptp.sum_su737395349um_b_c) (P (-> tptp.sum_su737395349um_b_c Bool))) (= (@ (@ tptp.member1893232190um_b_c A2) (@ tptp.collec2086029184um_b_c P)) (@ P A2))) (forall ((A tptp.set_Fi291318197eal_sz)) (= (@ tptp.collec1002602816eal_sz (lambda ((X2 tptp.finite824932053eal_sz)) (@ (@ tptp.member1693951742eal_sz X2) A))) A)) (forall ((A tptp.set_Pr1169339874_sc_sz)) (= (@ tptp.collec1199592193_sc_sz (lambda ((X2 tptp.produc1821101996_sc_sz)) (@ (@ tptp.member1057565379_sc_sz X2) A))) A)) (forall ((A tptp.set_trm_sf_sz)) (= (@ tptp.collect_trm_sf_sz (lambda ((X2 tptp.trm_sf_sz)) (@ (@ tptp.member_trm_sf_sz X2) A))) A)) (forall ((A tptp.set_trm_a_c)) (= (@ tptp.collect_trm_a_c (lambda ((X2 tptp.trm_a_c)) (@ (@ tptp.member_trm_a_c X2) A))) A)) (forall ((A tptp.set_a)) (= (@ tptp.collect_a (lambda ((X2 tptp.a)) (@ (@ tptp.member_a X2) A))) A)) (forall ((A tptp.set_Su1783761653um_b_c)) (= (@ tptp.collec2086029184um_b_c (lambda ((X2 tptp.sum_su737395349um_b_c)) (@ (@ tptp.member1893232190um_b_c X2) A))) A)) (forall ((P (-> tptp.finite824932053eal_sz Bool)) (Q (-> tptp.finite824932053eal_sz Bool))) (=> (forall ((X3 tptp.finite824932053eal_sz)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collec1002602816eal_sz P) (@ tptp.collec1002602816eal_sz Q)))) (forall ((P (-> tptp.produc1821101996_sc_sz Bool)) (Q (-> tptp.produc1821101996_sc_sz Bool))) (=> (forall ((X3 tptp.produc1821101996_sc_sz)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collec1199592193_sc_sz P) (@ tptp.collec1199592193_sc_sz Q)))) (forall ((P (-> tptp.trm_sf_sz Bool)) (Q (-> tptp.trm_sf_sz Bool))) (=> (forall ((X3 tptp.trm_sf_sz)) (= (@ P X3) (@ Q X3))) (= (@ 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tptp.produc866628903_sc_sz)) (=> (forall ((A4 tptp.list_f1238882004_sc_sz) (B4 tptp.list_f1238882004_sc_sz)) (@ P (@ (@ tptp.produc1822718231_sc_sz A4) B4))) (@ P Prod))) (forall ((P (-> tptp.produc1241881959eal_sz Bool)) (Prod tptp.produc1241881959eal_sz)) (=> (forall ((A4 tptp.set_Fi291318197eal_sz) (B4 tptp.set_Fi291318197eal_sz)) (@ P (@ (@ tptp.produc1235791063eal_sz A4) B4))) (@ P Prod))) (forall ((P (-> tptp.produc1892666919z_real Bool)) (Prod tptp.produc1892666919z_real)) (=> (forall ((A4 tptp.bounde472938360z_real) (B4 tptp.bounde472938360z_real)) (@ P (@ (@ tptp.produc784663575z_real A4) B4))) (@ P Prod))) (forall ((P (-> tptp.produc1821101996_sc_sz Bool)) (Prod tptp.produc1821101996_sc_sz)) (=> (forall ((A4 tptp.denota610675952t_unit) (B4 tptp.produc866628903_sc_sz)) (@ P (@ (@ tptp.produc789536734_sc_sz A4) B4))) (@ P Prod))) (forall ((Y tptp.produc190496183real_c)) (not (forall ((A4 tptp.finite1398487019real_c) (B4 tptp.finite1398487019real_c)) (not (= Y (@ (@ 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A3) (not (= B2 B3)))))) (forall ((A2 tptp.list_f1238882004_sc_sz) (B2 tptp.list_f1238882004_sc_sz) (A3 tptp.list_f1238882004_sc_sz) (B3 tptp.list_f1238882004_sc_sz)) (=> (= (@ (@ tptp.produc1822718231_sc_sz A2) B2) (@ (@ tptp.produc1822718231_sc_sz A3) B3)) (not (=> (= A2 A3) (not (= B2 B3)))))) (forall ((A2 tptp.set_Fi291318197eal_sz) (B2 tptp.set_Fi291318197eal_sz) (A3 tptp.set_Fi291318197eal_sz) (B3 tptp.set_Fi291318197eal_sz)) (=> (= (@ (@ tptp.produc1235791063eal_sz A2) B2) (@ (@ tptp.produc1235791063eal_sz A3) B3)) (not (=> (= A2 A3) (not (= B2 B3)))))) (forall ((A2 tptp.bounde472938360z_real) (B2 tptp.bounde472938360z_real) (A3 tptp.bounde472938360z_real) (B3 tptp.bounde472938360z_real)) (=> (= (@ (@ tptp.produc784663575z_real A2) B2) (@ (@ tptp.produc784663575z_real A3) B3)) (not (=> (= A2 A3) (not (= B2 B3)))))) (forall ((A2 tptp.denota610675952t_unit) (B2 tptp.produc866628903_sc_sz) (A3 tptp.denota610675952t_unit) (B3 tptp.produc866628903_sc_sz)) (=> (= (@ (@ tptp.produc789536734_sc_sz A2) B2) (@ (@ tptp.produc789536734_sc_sz A3) B3)) (not (=> (= A2 A3) (not (= B2 B3)))))) (forall ((P (-> tptp.produc190496183real_c Bool)) (P2 tptp.produc190496183real_c)) (=> (forall ((A4 tptp.finite1398487019real_c) (B4 tptp.finite1398487019real_c)) (@ P (@ (@ tptp.produc394644079real_c A4) B4))) (@ P P2))) (forall ((P (-> tptp.produc866628903_sc_sz Bool)) (P2 tptp.produc866628903_sc_sz)) (=> (forall ((A4 tptp.list_f1238882004_sc_sz) (B4 tptp.list_f1238882004_sc_sz)) (@ P (@ (@ tptp.produc1822718231_sc_sz A4) B4))) (@ P P2))) (forall ((P (-> tptp.produc1241881959eal_sz Bool)) (P2 tptp.produc1241881959eal_sz)) (=> (forall ((A4 tptp.set_Fi291318197eal_sz) (B4 tptp.set_Fi291318197eal_sz)) (@ P (@ (@ tptp.produc1235791063eal_sz A4) B4))) (@ P P2))) (forall ((P (-> tptp.produc1892666919z_real Bool)) (P2 tptp.produc1892666919z_real)) (=> (forall ((A4 tptp.bounde472938360z_real) (B4 tptp.bounde472938360z_real)) (@ P (@ (@ tptp.produc784663575z_real A4) B4))) (@ P P2))) (forall ((P (-> tptp.produc1821101996_sc_sz Bool)) (P2 tptp.produc1821101996_sc_sz)) (=> (forall ((A4 tptp.denota610675952t_unit) (B4 tptp.produc866628903_sc_sz)) (@ P (@ (@ tptp.produc789536734_sc_sz A4) B4))) (@ P P2))) (forall ((P2 tptp.produc190496183real_c)) (exists ((X3 tptp.finite1398487019real_c) (Y3 tptp.finite1398487019real_c)) (= P2 (@ (@ tptp.produc394644079real_c X3) Y3)))) (forall ((P2 tptp.produc866628903_sc_sz)) (exists ((X3 tptp.list_f1238882004_sc_sz) (Y3 tptp.list_f1238882004_sc_sz)) (= P2 (@ (@ tptp.produc1822718231_sc_sz X3) Y3)))) (forall ((P2 tptp.produc1241881959eal_sz)) (exists ((X3 tptp.set_Fi291318197eal_sz) (Y3 tptp.set_Fi291318197eal_sz)) (= P2 (@ (@ tptp.produc1235791063eal_sz X3) Y3)))) (forall ((P2 tptp.produc1892666919z_real)) (exists ((X3 tptp.bounde472938360z_real) (Y3 tptp.bounde472938360z_real)) (= P2 (@ (@ tptp.produc784663575z_real X3) Y3)))) (forall ((P2 tptp.produc1821101996_sc_sz)) (exists ((X3 tptp.denota610675952t_unit) (Y3 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tptp.set_Fi291318197eal_sz)) (= (@ tptp.produc1746886149eal_sz (@ (@ tptp.produc1235791063eal_sz X1) X22)) X22)) (forall ((X1 tptp.bounde472938360z_real) (X22 tptp.bounde472938360z_real)) (= (@ tptp.produc1422611269z_real (@ (@ tptp.produc784663575z_real X1) X22)) X22)) (forall ((X1 tptp.finite824932053eal_sz) (X22 tptp.finite824932053eal_sz)) (= (@ tptp.produc1269210629eal_sz (@ (@ tptp.produc1308130519eal_sz X1) X22)) X22)) (forall ((X1 tptp.denota610675952t_unit) (X22 tptp.produc866628903_sc_sz)) (= (@ tptp.produc974239792_sc_sz (@ (@ tptp.produc789536734_sc_sz X1) X22)) X22)) (forall ((X1 tptp.finite1398487019real_c) (X22 tptp.finite1398487019real_c)) (= (@ tptp.produc314122909real_c (@ (@ tptp.produc394644079real_c X1) X22)) X22)) (forall ((X tptp.list_f1238882004_sc_sz) (Y tptp.list_f1238882004_sc_sz) (A2 tptp.list_f1238882004_sc_sz)) (=> (= (@ tptp.produc4753477_sc_sz (@ (@ tptp.produc1822718231_sc_sz X) Y)) A2) (= Y A2))) (forall ((X tptp.set_Fi291318197eal_sz) (Y tptp.set_Fi291318197eal_sz) (A2 tptp.set_Fi291318197eal_sz)) (=> (= (@ tptp.produc1746886149eal_sz (@ (@ tptp.produc1235791063eal_sz X) Y)) A2) (= Y A2))) (forall ((X tptp.bounde472938360z_real) (Y tptp.bounde472938360z_real) (A2 tptp.bounde472938360z_real)) (=> (= (@ tptp.produc1422611269z_real (@ (@ tptp.produc784663575z_real X) Y)) A2) (= Y A2))) (forall ((X tptp.finite824932053eal_sz) (Y tptp.finite824932053eal_sz) (A2 tptp.finite824932053eal_sz)) (=> (= (@ tptp.produc1269210629eal_sz (@ (@ tptp.produc1308130519eal_sz X) Y)) A2) (= Y A2))) (forall ((X tptp.denota610675952t_unit) (Y tptp.produc866628903_sc_sz) (A2 tptp.produc866628903_sc_sz)) (=> (= (@ tptp.produc974239792_sc_sz (@ (@ tptp.produc789536734_sc_sz X) Y)) A2) (= Y A2))) (forall ((X tptp.finite1398487019real_c) (Y tptp.finite1398487019real_c) (A2 tptp.finite1398487019real_c)) (=> (= (@ tptp.produc314122909real_c (@ (@ tptp.produc394644079real_c X) Y)) A2) (= Y A2))) (= (lambda ((Y4 tptp.produc1149990247eal_sz) (Z tptp.produc1149990247eal_sz)) (= Y4 Z)) (lambda ((S2 tptp.produc1149990247eal_sz) (T tptp.produc1149990247eal_sz)) (and (= (@ tptp.produc1111759555eal_sz S2) (@ tptp.produc1111759555eal_sz T)) (= (@ tptp.produc1269210629eal_sz S2) (@ tptp.produc1269210629eal_sz T))))) (= (lambda ((Y4 tptp.produc1821101996_sc_sz) (Z tptp.produc1821101996_sc_sz)) (= Y4 Z)) (lambda ((S2 tptp.produc1821101996_sc_sz) (T tptp.produc1821101996_sc_sz)) (and (= (@ tptp.produc1503602930_sc_sz S2) (@ tptp.produc1503602930_sc_sz T)) (= (@ tptp.produc974239792_sc_sz S2) (@ tptp.produc974239792_sc_sz T))))) (= (lambda ((Y4 tptp.produc190496183real_c) (Z tptp.produc190496183real_c)) (= Y4 Z)) (lambda ((S2 tptp.produc190496183real_c) (T tptp.produc190496183real_c)) (and (= (@ tptp.produc2010422875real_c S2) (@ tptp.produc2010422875real_c T)) (= (@ tptp.produc314122909real_c S2) (@ tptp.produc314122909real_c T))))) (forall ((Prod tptp.produc1149990247eal_sz) (Prod2 tptp.produc1149990247eal_sz)) (=> (and (= (@ tptp.produc1111759555eal_sz Prod) (@ tptp.produc1111759555eal_sz Prod2)) (= (@ tptp.produc1269210629eal_sz Prod) (@ tptp.produc1269210629eal_sz Prod2))) (= Prod Prod2))) (forall ((Prod tptp.produc1821101996_sc_sz) (Prod2 tptp.produc1821101996_sc_sz)) (=> (and (= (@ tptp.produc1503602930_sc_sz Prod) (@ tptp.produc1503602930_sc_sz Prod2)) (= (@ tptp.produc974239792_sc_sz Prod) (@ tptp.produc974239792_sc_sz Prod2))) (= Prod Prod2))) (forall ((Prod tptp.produc190496183real_c) (Prod2 tptp.produc190496183real_c)) (=> (and (= (@ tptp.produc2010422875real_c Prod) (@ tptp.produc2010422875real_c Prod2)) (= (@ tptp.produc314122909real_c Prod) (@ tptp.produc314122909real_c Prod2))) (= Prod Prod2))) (forall ((P2 tptp.produc1149990247eal_sz) (Q2 tptp.produc1149990247eal_sz)) (=> (= (@ tptp.produc1111759555eal_sz P2) (@ tptp.produc1111759555eal_sz Q2)) (=> (= (@ tptp.produc1269210629eal_sz P2) (@ tptp.produc1269210629eal_sz Q2)) (= P2 Q2)))) (forall ((P2 tptp.produc1821101996_sc_sz) (Q2 tptp.produc1821101996_sc_sz)) (=> (= (@ tptp.produc1503602930_sc_sz P2) (@ tptp.produc1503602930_sc_sz Q2)) (=> (= (@ tptp.produc974239792_sc_sz P2) (@ tptp.produc974239792_sc_sz Q2)) (= P2 Q2)))) (forall ((P2 tptp.produc190496183real_c) (Q2 tptp.produc190496183real_c)) (=> (= (@ tptp.produc2010422875real_c P2) (@ tptp.produc2010422875real_c Q2)) (=> (= (@ tptp.produc314122909real_c P2) (@ tptp.produc314122909real_c Q2)) (= P2 Q2)))) (forall ((Args (-> tptp.c tptp.trm_a_c)) (I tptp.a)) (=> (forall ((I4 tptp.c)) (@ tptp.dfree_a_c (@ Args I4))) (@ tptp.dfree_a_c (@ (@ tptp.function_a_c I) Args)))) (forall ((Args (-> tptp.sz tptp.trm_sf_sz)) (I tptp.sf)) (=> (forall ((I4 tptp.sz)) (@ tptp.dfree_sf_sz (@ Args I4))) (@ tptp.dfree_sf_sz (@ (@ tptp.function_sf_sz I) Args)))) (forall ((Theta_1 tptp.trm_sf_sz) (Theta_2 tptp.trm_sf_sz)) (=> (@ tptp.dfree_sf_sz Theta_1) (=> (@ tptp.dfree_sf_sz Theta_2) (@ tptp.dfree_sf_sz (@ (@ tptp.plus_sf_sz Theta_1) Theta_2))))) (forall ((Theta_1 tptp.trm_a_c) (Theta_2 tptp.trm_a_c)) (=> (@ tptp.dfree_a_c Theta_1) (=> (@ tptp.dfree_a_c Theta_2) (@ tptp.dfree_a_c (@ (@ tptp.plus_a_c Theta_1) Theta_2))))) (forall ((Theta_1 tptp.trm_a_c) (Theta_2 tptp.trm_a_c)) (=> (@ tptp.dfree_a_c Theta_1) (=> (@ tptp.dfree_a_c Theta_2) (@ tptp.dfree_a_c (@ (@ tptp.times_a_c Theta_1) Theta_2))))) (forall ((Theta_1 tptp.trm_sf_sz) (Theta_2 tptp.trm_sf_sz)) (=> (@ tptp.dfree_sf_sz Theta_1) (=> (@ tptp.dfree_sf_sz Theta_2) (@ tptp.dfree_sf_sz (@ (@ tptp.times_sf_sz Theta_1) Theta_2))))) (forall ((X31 tptp.a) (X32 (-> tptp.c tptp.trm_a_c)) (X41 tptp.trm_a_c) (X42 tptp.trm_a_c)) (not (= (@ (@ tptp.function_a_c X31) X32) (@ (@ tptp.plus_a_c X41) X42)))) (forall ((X31 tptp.sf) (X32 (-> tptp.sz tptp.trm_sf_sz)) (X41 tptp.trm_sf_sz) (X42 tptp.trm_sf_sz)) (not (= (@ (@ tptp.function_sf_sz X31) X32) (@ (@ tptp.plus_sf_sz X41) X42)))) (forall ((X31 tptp.a) (X32 (-> tptp.c tptp.trm_a_c)) (X51 tptp.trm_a_c) (X52 tptp.trm_a_c)) (not (= (@ (@ tptp.function_a_c X31) X32) (@ (@ tptp.times_a_c X51) X52)))) (forall ((X31 tptp.sf) (X32 (-> tptp.sz tptp.trm_sf_sz)) (X51 tptp.trm_sf_sz) (X52 tptp.trm_sf_sz)) (not (= (@ (@ tptp.function_sf_sz X31) X32) (@ (@ tptp.times_sf_sz X51) X52)))) (forall ((X41 tptp.trm_sf_sz) (X42 tptp.trm_sf_sz) (X51 tptp.trm_sf_sz) (X52 tptp.trm_sf_sz)) (not (= (@ (@ tptp.plus_sf_sz X41) X42) (@ (@ tptp.times_sf_sz X51) X52)))) (forall ((X41 tptp.trm_a_c) (X42 tptp.trm_a_c) (X51 tptp.trm_a_c) (X52 tptp.trm_a_c)) (not (= (@ (@ tptp.plus_a_c X41) X42) (@ (@ tptp.times_a_c X51) X52)))) (forall ((T3 tptp.produc866628903_sc_sz)) (= T3 (@ (@ tptp.produc1822718231_sc_sz (@ tptp.produc548504323_sc_sz T3)) (@ tptp.produc4753477_sc_sz T3)))) (forall ((T3 tptp.produc1241881959eal_sz)) (= T3 (@ (@ tptp.produc1235791063eal_sz (@ tptp.produc286845635eal_sz T3)) (@ tptp.produc1746886149eal_sz T3)))) (forall ((T3 tptp.produc1892666919z_real)) (= T3 (@ (@ tptp.produc784663575z_real (@ tptp.produc870616579z_real T3)) (@ tptp.produc1422611269z_real T3)))) (forall ((T3 tptp.produc1149990247eal_sz)) (= T3 (@ (@ tptp.produc1308130519eal_sz (@ tptp.produc1111759555eal_sz T3)) (@ tptp.produc1269210629eal_sz T3)))) (forall ((T3 tptp.produc1821101996_sc_sz)) (= T3 (@ (@ tptp.produc789536734_sc_sz (@ tptp.produc1503602930_sc_sz T3)) (@ tptp.produc974239792_sc_sz T3)))) (forall ((T3 tptp.produc190496183real_c)) (= T3 (@ (@ tptp.produc394644079real_c (@ tptp.produc2010422875real_c T3)) (@ tptp.produc314122909real_c T3)))) (forall ((Prod tptp.produc866628903_sc_sz)) (= Prod (@ (@ tptp.produc1822718231_sc_sz (@ tptp.produc548504323_sc_sz Prod)) (@ tptp.produc4753477_sc_sz Prod)))) (forall ((Prod tptp.produc1241881959eal_sz)) (= Prod (@ (@ tptp.produc1235791063eal_sz (@ tptp.produc286845635eal_sz Prod)) (@ tptp.produc1746886149eal_sz Prod)))) (forall ((Prod tptp.produc1892666919z_real)) (= Prod (@ (@ tptp.produc784663575z_real (@ tptp.produc870616579z_real Prod)) (@ tptp.produc1422611269z_real Prod)))) (forall ((Prod tptp.produc1149990247eal_sz)) (= Prod (@ (@ tptp.produc1308130519eal_sz (@ tptp.produc1111759555eal_sz Prod)) (@ tptp.produc1269210629eal_sz Prod)))) (forall ((Prod tptp.produc1821101996_sc_sz)) (= Prod (@ (@ tptp.produc789536734_sc_sz (@ tptp.produc1503602930_sc_sz Prod)) (@ tptp.produc974239792_sc_sz Prod)))) (forall ((Prod tptp.produc190496183real_c)) (= Prod (@ (@ tptp.produc394644079real_c (@ tptp.produc2010422875real_c Prod)) (@ tptp.produc314122909real_c Prod)))) (forall ((A2 tptp.set_a) (B2 tptp.set_a) (C2 tptp.set_a) (D tptp.set_a)) (= (@ (@ tptp.ord_le486764743_set_a (@ (@ tptp.produc1928581911_set_a A2) B2)) (@ (@ tptp.produc1928581911_set_a C2) D)) (and (@ (@ tptp.ord_less_eq_set_a A2) C2) (@ (@ tptp.ord_less_eq_set_a B2) D)))) (forall ((A2 tptp.set_a) (B2 (-> tptp.a Bool)) (C2 tptp.set_a) (D (-> tptp.a Bool))) (= (@ (@ tptp.ord_le501349868_a_a_o (@ (@ tptp.produc634809990_a_a_o A2) B2)) (@ (@ tptp.produc634809990_a_a_o C2) D)) (and (@ (@ tptp.ord_less_eq_set_a A2) C2) (@ (@ tptp.ord_less_eq_a_o B2) D)))) (forall ((A2 (-> tptp.a Bool)) (B2 tptp.set_a) (C2 (-> tptp.a Bool)) (D tptp.set_a)) (= (@ (@ tptp.ord_le72828020_set_a (@ (@ tptp.produc1916559302_set_a A2) B2)) (@ (@ tptp.produc1916559302_set_a C2) D)) (and (@ (@ tptp.ord_less_eq_a_o A2) C2) (@ (@ tptp.ord_less_eq_set_a B2) D)))) (forall ((A2 tptp.finite1398487019real_c) (B2 tptp.finite1398487019real_c) (C2 tptp.finite1398487019real_c) (D tptp.finite1398487019real_c)) (= (@ (@ tptp.ord_le850691415real_c (@ (@ tptp.produc394644079real_c A2) B2)) (@ (@ tptp.produc394644079real_c C2) D)) (and (@ (@ tptp.ord_le775706699real_c A2) C2) (@ (@ tptp.ord_le775706699real_c B2) D)))) (forall ((A2 (-> tptp.a Bool)) (B2 (-> tptp.a Bool)) (C2 (-> tptp.a Bool)) (D (-> tptp.a Bool))) (= (@ (@ tptp.ord_le1883211903_o_a_o (@ (@ tptp.product_Pair_a_o_a_o A2) B2)) (@ (@ tptp.product_Pair_a_o_a_o C2) D)) (and (@ (@ tptp.ord_less_eq_a_o A2) C2) (@ (@ tptp.ord_less_eq_a_o B2) D)))) (forall ((A2 tptp.set_Fi291318197eal_sz) (B2 tptp.set_Fi291318197eal_sz) (C2 tptp.set_Fi291318197eal_sz) (D tptp.set_Fi291318197eal_sz)) (= (@ (@ tptp.ord_le978883847eal_sz (@ (@ tptp.produc1235791063eal_sz A2) B2)) (@ (@ tptp.produc1235791063eal_sz C2) D)) (and (@ (@ tptp.ord_le41263445eal_sz A2) C2) (@ (@ tptp.ord_le41263445eal_sz B2) D)))) (forall ((A2 tptp.set_a) (B2 (-> tptp.trm_sf_sz tptp.trm_sf_sz Bool)) (C2 tptp.set_a) (D (-> tptp.trm_sf_sz tptp.trm_sf_sz Bool))) (= (@ (@ tptp.ord_le1884788375f_sz_o (@ (@ tptp.produc1174558183f_sz_o A2) B2)) (@ (@ tptp.produc1174558183f_sz_o C2) D)) (and (@ (@ tptp.ord_less_eq_set_a A2) C2) (@ (@ tptp.ord_le8515534f_sz_o B2) D)))) (forall ((A2 (-> tptp.trm_sf_sz tptp.trm_sf_sz Bool)) (B2 tptp.set_a) (C2 (-> tptp.trm_sf_sz tptp.trm_sf_sz Bool)) (D tptp.set_a)) (= (@ (@ tptp.ord_le1643089911_set_a (@ (@ tptp.produc1543226183_set_a A2) B2)) (@ (@ tptp.produc1543226183_set_a C2) D)) (and (@ (@ tptp.ord_le8515534f_sz_o A2) C2) (@ (@ tptp.ord_less_eq_set_a B2) D)))) (forall ((A2 (-> tptp.trm_sf_sz tptp.trm_sf_sz Bool)) (B2 (-> tptp.a Bool)) (C2 (-> tptp.trm_sf_sz tptp.trm_sf_sz Bool)) (D (-> tptp.a Bool))) (= (@ (@ tptp.ord_le2132572860_o_a_o (@ (@ tptp.produc1152932438_o_a_o A2) B2)) (@ (@ tptp.produc1152932438_o_a_o C2) D)) (and (@ (@ tptp.ord_le8515534f_sz_o A2) C2) (@ (@ tptp.ord_less_eq_a_o B2) D)))) (forall ((A2 (-> tptp.a Bool)) (B2 (-> tptp.trm_sf_sz tptp.trm_sf_sz Bool)) (C2 (-> tptp.a Bool)) (D (-> tptp.trm_sf_sz tptp.trm_sf_sz Bool))) (= (@ (@ tptp.ord_le472894788f_sz_o (@ (@ tptp.produc593159062f_sz_o A2) B2)) (@ (@ tptp.produc593159062f_sz_o C2) D)) (and (@ (@ tptp.ord_less_eq_a_o A2) C2) (@ (@ tptp.ord_le8515534f_sz_o B2) D)))) (= tptp.denota2112424896_a_b_c (lambda ((I5 tptp.denota231621370t_unit) (T tptp.trm_a_c) (V2 tptp.produc190496183real_c)) (@ (@ (@ (@ tptp.denota229585092_a_b_c I5) T) (@ tptp.produc2010422875real_c V2)) (@ tptp.produc314122909real_c V2)))) (= tptp.denota453121236_sc_sz (lambda ((I5 tptp.denota610675952t_unit) (T tptp.trm_sf_sz) (V2 tptp.produc1149990247eal_sz)) (@ (@ (@ (@ tptp.denota1979904720_sc_sz I5) T) (@ tptp.produc1111759555eal_sz V2)) (@ tptp.produc1269210629eal_sz V2)))) (forall ((X tptp.freche2095075217_sc_sz)) (= (@ tptp.freche1784963216_sc_sz (@ tptp.freche1421597129_sc_sz X)) X)) (@ (@ (@ tptp.type_d1238563341rm_a_c tptp.frechet_raw_term_a_c) tptp.freche665377492rm_a_c) (@ tptp.collect_trm_a_c tptp.dfree_a_c)) (@ (@ (@ tptp.type_d46389773_sf_sz tptp.freche782854530_sf_sz) tptp.freche1046279700_sf_sz) (@ tptp.collect_trm_sf_sz tptp.dfree_sf_sz)) (forall ((P (-> tptp.list_f1238882004_sc_sz tptp.list_f1238882004_sc_sz Bool)) (X tptp.list_f1238882004_sc_sz) (Y tptp.list_f1238882004_sc_sz) (A2 tptp.produc866628903_sc_sz)) (=> (@ (@ P X) Y) (=> (= A2 (@ (@ tptp.produc1822718231_sc_sz X) Y)) (@ (@ P (@ tptp.produc548504323_sc_sz A2)) (@ tptp.produc4753477_sc_sz A2))))) (forall ((P (-> tptp.set_Fi291318197eal_sz tptp.set_Fi291318197eal_sz Bool)) (X tptp.set_Fi291318197eal_sz) (Y tptp.set_Fi291318197eal_sz) (A2 tptp.produc1241881959eal_sz)) (=> (@ (@ P X) Y) (=> (= A2 (@ (@ tptp.produc1235791063eal_sz X) Y)) (@ (@ P (@ tptp.produc286845635eal_sz A2)) (@ tptp.produc1746886149eal_sz A2))))) (forall ((P (-> tptp.bounde472938360z_real tptp.bounde472938360z_real Bool)) (X tptp.bounde472938360z_real) (Y tptp.bounde472938360z_real) (A2 tptp.produc1892666919z_real)) (=> (@ (@ P X) Y) (=> (= A2 (@ (@ tptp.produc784663575z_real X) Y)) (@ (@ P (@ tptp.produc870616579z_real A2)) (@ tptp.produc1422611269z_real A2))))) (forall ((P (-> tptp.finite824932053eal_sz tptp.finite824932053eal_sz Bool)) (X tptp.finite824932053eal_sz) (Y tptp.finite824932053eal_sz) (A2 tptp.produc1149990247eal_sz)) (=> (@ (@ P X) Y) (=> (= A2 (@ (@ tptp.produc1308130519eal_sz X) Y)) (@ (@ P (@ tptp.produc1111759555eal_sz A2)) (@ tptp.produc1269210629eal_sz A2))))) (forall ((P (-> tptp.denota610675952t_unit tptp.produc866628903_sc_sz Bool)) (X tptp.denota610675952t_unit) (Y tptp.produc866628903_sc_sz) (A2 tptp.produc1821101996_sc_sz)) (=> (@ (@ P X) Y) (=> (= A2 (@ (@ tptp.produc789536734_sc_sz X) Y)) (@ (@ P (@ tptp.produc1503602930_sc_sz A2)) (@ tptp.produc974239792_sc_sz A2))))) (forall ((P (-> tptp.finite1398487019real_c tptp.finite1398487019real_c Bool)) (X tptp.finite1398487019real_c) (Y tptp.finite1398487019real_c) (A2 tptp.produc190496183real_c)) (=> (@ (@ P X) Y) (=> (= A2 (@ (@ tptp.produc394644079real_c X) Y)) (@ (@ P (@ tptp.produc2010422875real_c A2)) (@ tptp.produc314122909real_c A2))))) (forall ((P (-> tptp.list_f1238882004_sc_sz Bool)) (P2 tptp.list_f1238882004_sc_sz) (Q (-> tptp.list_f1238882004_sc_sz Bool)) (Q2 tptp.list_f1238882004_sc_sz)) (let ((_let_1 (@ (@ tptp.produc1822718231_sc_sz P2) Q2))) (=> (@ P P2) (=> (@ Q Q2) (and (@ P (@ tptp.produc548504323_sc_sz _let_1)) (@ Q (@ tptp.produc4753477_sc_sz _let_1))))))) (forall ((P (-> tptp.set_Fi291318197eal_sz Bool)) (P2 tptp.set_Fi291318197eal_sz) (Q (-> tptp.set_Fi291318197eal_sz Bool)) (Q2 tptp.set_Fi291318197eal_sz)) (let ((_let_1 (@ (@ tptp.produc1235791063eal_sz P2) Q2))) (=> (@ P P2) (=> (@ Q Q2) (and (@ P (@ tptp.produc286845635eal_sz _let_1)) (@ Q (@ tptp.produc1746886149eal_sz _let_1))))))) (forall ((P (-> tptp.bounde472938360z_real Bool)) (P2 tptp.bounde472938360z_real) (Q (-> tptp.bounde472938360z_real Bool)) (Q2 tptp.bounde472938360z_real)) (let ((_let_1 (@ (@ tptp.produc784663575z_real P2) Q2))) (=> (@ P P2) (=> (@ Q Q2) (and (@ P (@ tptp.produc870616579z_real _let_1)) (@ Q (@ tptp.produc1422611269z_real _let_1))))))) (forall ((P (-> tptp.finite824932053eal_sz Bool)) (P2 tptp.finite824932053eal_sz) (Q (-> tptp.finite824932053eal_sz Bool)) (Q2 tptp.finite824932053eal_sz)) (let ((_let_1 (@ (@ tptp.produc1308130519eal_sz P2) Q2))) (=> (@ P P2) (=> (@ Q Q2) (and (@ P (@ tptp.produc1111759555eal_sz _let_1)) (@ Q (@ tptp.produc1269210629eal_sz _let_1))))))) (forall ((P (-> tptp.denota610675952t_unit Bool)) (P2 tptp.denota610675952t_unit) (Q (-> tptp.produc866628903_sc_sz Bool)) (Q2 tptp.produc866628903_sc_sz)) (let ((_let_1 (@ (@ tptp.produc789536734_sc_sz P2) Q2))) (=> (@ P P2) (=> (@ Q Q2) (and (@ P (@ tptp.produc1503602930_sc_sz _let_1)) (@ Q (@ tptp.produc974239792_sc_sz _let_1))))))) (forall ((P (-> tptp.finite1398487019real_c Bool)) (P2 tptp.finite1398487019real_c) (Q (-> tptp.finite1398487019real_c Bool)) (Q2 tptp.finite1398487019real_c)) (let ((_let_1 (@ (@ tptp.produc394644079real_c P2) Q2))) (=> (@ P P2) (=> (@ Q Q2) (and (@ P (@ tptp.produc2010422875real_c _let_1)) (@ Q (@ tptp.produc314122909real_c _let_1))))))) (forall ((P (-> tptp.list_f1238882004_sc_sz tptp.list_f1238882004_sc_sz Bool)) (Y tptp.list_f1238882004_sc_sz) (X tptp.list_f1238882004_sc_sz)) (let ((_let_1 (@ (@ tptp.produc1822718231_sc_sz X) Y))) (=> (@ (@ P Y) X) (@ (@ P (@ tptp.produc4753477_sc_sz _let_1)) (@ tptp.produc548504323_sc_sz _let_1))))) (forall ((P (-> tptp.set_Fi291318197eal_sz tptp.set_Fi291318197eal_sz Bool)) (Y tptp.set_Fi291318197eal_sz) (X tptp.set_Fi291318197eal_sz)) (let ((_let_1 (@ (@ tptp.produc1235791063eal_sz X) Y))) (=> (@ (@ P Y) X) (@ (@ P (@ tptp.produc1746886149eal_sz _let_1)) (@ tptp.produc286845635eal_sz _let_1))))) (forall ((P (-> tptp.bounde472938360z_real tptp.bounde472938360z_real Bool)) (Y tptp.bounde472938360z_real) (X tptp.bounde472938360z_real)) (let ((_let_1 (@ (@ tptp.produc784663575z_real X) Y))) (=> (@ (@ P Y) X) (@ (@ P (@ tptp.produc1422611269z_real _let_1)) (@ tptp.produc870616579z_real _let_1))))) (forall ((P (-> tptp.finite824932053eal_sz tptp.finite824932053eal_sz Bool)) (Y tptp.finite824932053eal_sz) (X tptp.finite824932053eal_sz)) (let ((_let_1 (@ (@ tptp.produc1308130519eal_sz X) Y))) (=> (@ (@ P Y) X) (@ (@ P (@ tptp.produc1269210629eal_sz _let_1)) (@ tptp.produc1111759555eal_sz _let_1))))) (forall ((P (-> tptp.produc866628903_sc_sz tptp.denota610675952t_unit Bool)) (Y tptp.produc866628903_sc_sz) (X tptp.denota610675952t_unit)) (let ((_let_1 (@ (@ tptp.produc789536734_sc_sz X) Y))) (=> (@ (@ P Y) X) (@ (@ P (@ tptp.produc974239792_sc_sz _let_1)) (@ tptp.produc1503602930_sc_sz _let_1))))) (forall ((P (-> tptp.finite1398487019real_c tptp.finite1398487019real_c Bool)) (Y tptp.finite1398487019real_c) (X tptp.finite1398487019real_c)) (let ((_let_1 (@ (@ tptp.produc394644079real_c X) Y))) (=> (@ (@ P Y) X) (@ (@ P (@ tptp.produc314122909real_c _let_1)) (@ tptp.produc2010422875real_c _let_1))))) (= tptp.ord_le850691415real_c (lambda ((X2 tptp.produc190496183real_c) (Y2 tptp.produc190496183real_c)) (and (@ (@ tptp.ord_le775706699real_c (@ tptp.produc2010422875real_c X2)) (@ tptp.produc2010422875real_c Y2)) (@ (@ tptp.ord_le775706699real_c (@ tptp.produc314122909real_c X2)) (@ tptp.produc314122909real_c Y2))))) (= tptp.ord_le486764743_set_a (lambda ((X2 tptp.produc1691597095_set_a) (Y2 tptp.produc1691597095_set_a)) (and (@ (@ tptp.ord_less_eq_set_a (@ tptp.produc1926412547_set_a X2)) (@ tptp.produc1926412547_set_a Y2)) (@ (@ tptp.ord_less_eq_set_a (@ tptp.produc918972485_set_a X2)) (@ tptp.produc918972485_set_a Y2))))) (= tptp.ord_le501349868_a_a_o (lambda ((X2 tptp.produc1989635468_a_a_o) (Y2 tptp.produc1989635468_a_a_o)) (and (@ (@ tptp.ord_less_eq_set_a (@ tptp.produc1911461786_a_a_o X2)) (@ tptp.produc1911461786_a_a_o Y2)) (@ (@ tptp.ord_less_eq_a_o (@ tptp.produc23639768_a_a_o X2)) (@ tptp.produc23639768_a_a_o Y2))))) (= tptp.ord_le72828020_set_a (lambda ((X2 tptp.produc1561113620_set_a) (Y2 tptp.produc1561113620_set_a)) (and (@ (@ tptp.ord_less_eq_a_o (@ tptp.produc1045727450_set_a X2)) (@ tptp.produc1045727450_set_a Y2)) (@ (@ tptp.ord_less_eq_set_a (@ tptp.produc1305389080_set_a X2)) (@ tptp.produc1305389080_set_a Y2))))) (= tptp.ord_le473656583eal_sz (lambda ((X2 tptp.produc1149990247eal_sz) (Y2 tptp.produc1149990247eal_sz)) (and (@ (@ tptp.ord_le787639925eal_sz (@ tptp.produc1111759555eal_sz X2)) (@ tptp.produc1111759555eal_sz Y2)) (@ (@ tptp.ord_le787639925eal_sz (@ tptp.produc1269210629eal_sz X2)) (@ tptp.produc1269210629eal_sz Y2))))) (= tptp.ord_le1883211903_o_a_o (lambda ((X2 tptp.product_prod_a_o_a_o) (Y2 tptp.product_prod_a_o_a_o)) (and (@ (@ tptp.ord_less_eq_a_o (@ tptp.product_fst_a_o_a_o X2)) (@ tptp.product_fst_a_o_a_o Y2)) (@ (@ tptp.ord_less_eq_a_o (@ tptp.product_snd_a_o_a_o X2)) (@ tptp.product_snd_a_o_a_o Y2))))) (= tptp.ord_le1884788375f_sz_o (lambda ((X2 tptp.produc1144880887f_sz_o) (Y2 tptp.produc1144880887f_sz_o)) (and (@ (@ tptp.ord_less_eq_set_a (@ tptp.produc38604755f_sz_o X2)) (@ tptp.produc38604755f_sz_o Y2)) (@ (@ tptp.ord_le8515534f_sz_o (@ tptp.produc407510293f_sz_o X2)) (@ tptp.produc407510293f_sz_o Y2))))) (= tptp.ord_le1643089911_set_a (lambda ((X2 tptp.produc903182423_set_a) (Y2 tptp.produc903182423_set_a)) (and (@ (@ tptp.ord_le8515534f_sz_o (@ tptp.produc407272755_set_a X2)) (@ tptp.produc407272755_set_a Y2)) (@ (@ tptp.ord_less_eq_set_a (@ tptp.produc776178293_set_a X2)) (@ tptp.produc776178293_set_a Y2))))) (= tptp.ord_le2132572860_o_a_o (lambda ((X2 tptp.produc1065634396_o_a_o) (Y2 tptp.produc1065634396_o_a_o)) (and (@ (@ tptp.ord_le8515534f_sz_o (@ tptp.produc2013638506_o_a_o X2)) (@ tptp.produc2013638506_o_a_o Y2)) (@ (@ tptp.ord_less_eq_a_o (@ tptp.produc1630531752_o_a_o X2)) (@ tptp.produc1630531752_o_a_o Y2))))) (= tptp.ord_le472894788f_sz_o (lambda ((X2 tptp.produc1553439972f_sz_o) (Y2 tptp.produc1553439972f_sz_o)) (and (@ (@ tptp.ord_less_eq_a_o (@ tptp.produc1453865130f_sz_o X2)) (@ tptp.produc1453865130f_sz_o Y2)) (@ (@ tptp.ord_le8515534f_sz_o (@ tptp.produc1070758376f_sz_o X2)) (@ tptp.produc1070758376f_sz_o Y2))))) (forall ((A tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c) (I3 tptp.denota231621370t_unit) (J tptp.denota231621370t_unit)) (let ((_let_1 (@ (@ tptp.denota69106024_a_b_c I3) J))) (=> (@ (@ tptp.ord_le929608341um_b_c A) B) (=> (@ _let_1 B) (@ _let_1 A))))) (forall ((B tptp.set_Fi291318197eal_sz) (A tptp.set_Fi291318197eal_sz) (P (-> tptp.finite824932053eal_sz Bool))) (let ((_let_1 (@ tptp.ord_le41263445eal_sz B))) (=> (@ _let_1 A) (= (@ _let_1 (@ tptp.collec1002602816eal_sz (lambda ((X2 tptp.finite824932053eal_sz)) (and (@ (@ tptp.member1693951742eal_sz X2) A) (@ P X2))))) (forall ((X2 tptp.finite824932053eal_sz)) (=> (@ (@ tptp.member1693951742eal_sz X2) B) (@ P X2))))))) (forall ((B tptp.set_Pr1169339874_sc_sz) (A tptp.set_Pr1169339874_sc_sz) (P (-> tptp.produc1821101996_sc_sz Bool))) (let ((_let_1 (@ tptp.ord_le1230423618_sc_sz B))) (=> (@ _let_1 A) (= (@ _let_1 (@ tptp.collec1199592193_sc_sz (lambda ((X2 tptp.produc1821101996_sc_sz)) (and (@ (@ tptp.member1057565379_sc_sz X2) A) (@ P X2))))) (forall ((X2 tptp.produc1821101996_sc_sz)) (=> (@ (@ tptp.member1057565379_sc_sz X2) B) (@ P X2))))))) (forall ((B tptp.set_trm_sf_sz) (A tptp.set_trm_sf_sz) (P (-> tptp.trm_sf_sz Bool))) (let ((_let_1 (@ tptp.ord_le1697056455_sf_sz B))) (=> (@ _let_1 A) (= (@ _let_1 (@ tptp.collect_trm_sf_sz (lambda ((X2 tptp.trm_sf_sz)) (and (@ (@ tptp.member_trm_sf_sz X2) A) (@ P X2))))) (forall ((X2 tptp.trm_sf_sz)) (=> (@ (@ tptp.member_trm_sf_sz X2) B) (@ P X2))))))) (forall ((B tptp.set_trm_a_c) (A tptp.set_trm_a_c) (P (-> tptp.trm_a_c Bool))) (let ((_let_1 (@ tptp.ord_le1369644495rm_a_c B))) (=> (@ _let_1 A) (= (@ _let_1 (@ tptp.collect_trm_a_c (lambda ((X2 tptp.trm_a_c)) (and (@ (@ tptp.member_trm_a_c X2) A) (@ P X2))))) (forall ((X2 tptp.trm_a_c)) (=> (@ (@ tptp.member_trm_a_c X2) B) (@ P X2))))))) (forall ((B tptp.set_a) (A tptp.set_a) (P (-> tptp.a Bool))) (let ((_let_1 (@ tptp.ord_less_eq_set_a B))) (=> (@ _let_1 A) (= (@ _let_1 (@ tptp.collect_a (lambda ((X2 tptp.a)) (and (@ (@ tptp.member_a X2) A) (@ P X2))))) (forall ((X2 tptp.a)) (=> (@ (@ tptp.member_a X2) B) (@ P X2))))))) (forall ((B tptp.set_Su1783761653um_b_c) (A tptp.set_Su1783761653um_b_c) (P (-> tptp.sum_su737395349um_b_c Bool))) (let ((_let_1 (@ tptp.ord_le929608341um_b_c B))) (=> (@ _let_1 A) (= (@ _let_1 (@ tptp.collec2086029184um_b_c (lambda ((X2 tptp.sum_su737395349um_b_c)) (and (@ (@ tptp.member1893232190um_b_c X2) A) (@ P X2))))) (forall ((X2 tptp.sum_su737395349um_b_c)) (=> (@ (@ tptp.member1893232190um_b_c X2) B) (@ P X2))))))) (forall ((B tptp.set_Fi291318197eal_sz) (A tptp.set_Fi291318197eal_sz) (Q (-> tptp.finite824932053eal_sz Bool)) (P (-> tptp.finite824932053eal_sz Bool))) (=> (@ (@ tptp.ord_le41263445eal_sz B) A) (=> (forall ((X3 tptp.finite824932053eal_sz)) (=> (@ (@ tptp.member1693951742eal_sz X3) B) (=> (@ Q X3) (@ P X3)))) (@ (@ tptp.ord_le41263445eal_sz (@ tptp.collec1002602816eal_sz (lambda ((X2 tptp.finite824932053eal_sz)) (and (@ (@ tptp.member1693951742eal_sz X2) B) (@ Q X2))))) (@ tptp.collec1002602816eal_sz (lambda ((X2 tptp.finite824932053eal_sz)) (and (@ (@ tptp.member1693951742eal_sz X2) A) (@ P X2)))))))) (forall ((B tptp.set_Pr1169339874_sc_sz) (A tptp.set_Pr1169339874_sc_sz) (Q (-> tptp.produc1821101996_sc_sz Bool)) (P (-> tptp.produc1821101996_sc_sz Bool))) (=> (@ (@ tptp.ord_le1230423618_sc_sz B) A) (=> (forall ((X3 tptp.produc1821101996_sc_sz)) (=> (@ (@ tptp.member1057565379_sc_sz X3) B) (=> (@ Q X3) (@ P X3)))) (@ (@ tptp.ord_le1230423618_sc_sz (@ tptp.collec1199592193_sc_sz (lambda ((X2 tptp.produc1821101996_sc_sz)) (and (@ (@ tptp.member1057565379_sc_sz X2) B) (@ Q X2))))) (@ tptp.collec1199592193_sc_sz (lambda ((X2 tptp.produc1821101996_sc_sz)) (and (@ (@ tptp.member1057565379_sc_sz X2) A) (@ P X2)))))))) (forall ((B tptp.set_trm_sf_sz) (A tptp.set_trm_sf_sz) (Q (-> tptp.trm_sf_sz Bool)) (P (-> tptp.trm_sf_sz Bool))) (=> (@ (@ tptp.ord_le1697056455_sf_sz B) A) (=> (forall ((X3 tptp.trm_sf_sz)) (=> (@ (@ tptp.member_trm_sf_sz X3) B) (=> (@ Q X3) (@ P X3)))) (@ (@ tptp.ord_le1697056455_sf_sz (@ tptp.collect_trm_sf_sz (lambda ((X2 tptp.trm_sf_sz)) (and (@ (@ tptp.member_trm_sf_sz X2) B) (@ Q X2))))) (@ tptp.collect_trm_sf_sz (lambda ((X2 tptp.trm_sf_sz)) (and (@ (@ tptp.member_trm_sf_sz X2) A) (@ P X2)))))))) (forall ((B tptp.set_trm_a_c) (A tptp.set_trm_a_c) (Q (-> tptp.trm_a_c Bool)) (P (-> tptp.trm_a_c Bool))) (=> (@ (@ tptp.ord_le1369644495rm_a_c B) A) (=> (forall ((X3 tptp.trm_a_c)) (=> (@ (@ tptp.member_trm_a_c X3) B) (=> (@ Q X3) (@ P X3)))) (@ (@ tptp.ord_le1369644495rm_a_c (@ tptp.collect_trm_a_c (lambda ((X2 tptp.trm_a_c)) (and (@ (@ tptp.member_trm_a_c X2) B) (@ Q X2))))) (@ tptp.collect_trm_a_c (lambda ((X2 tptp.trm_a_c)) (and (@ (@ tptp.member_trm_a_c X2) A) (@ P X2)))))))) (forall ((B tptp.set_a) (A tptp.set_a) (Q (-> tptp.a Bool)) (P (-> tptp.a Bool))) (=> (@ (@ tptp.ord_less_eq_set_a B) A) (=> (forall ((X3 tptp.a)) (=> (@ (@ tptp.member_a X3) B) (=> (@ Q X3) (@ P X3)))) (@ (@ tptp.ord_less_eq_set_a (@ tptp.collect_a (lambda ((X2 tptp.a)) (and (@ (@ tptp.member_a X2) B) (@ Q X2))))) (@ tptp.collect_a (lambda ((X2 tptp.a)) (and (@ (@ tptp.member_a X2) A) (@ P X2)))))))) (forall ((B tptp.set_Su1783761653um_b_c) (A tptp.set_Su1783761653um_b_c) (Q (-> tptp.sum_su737395349um_b_c Bool)) (P (-> tptp.sum_su737395349um_b_c Bool))) (=> (@ (@ tptp.ord_le929608341um_b_c B) A) (=> (forall ((X3 tptp.sum_su737395349um_b_c)) (=> (@ (@ tptp.member1893232190um_b_c X3) B) (=> (@ Q X3) (@ P X3)))) (@ (@ tptp.ord_le929608341um_b_c (@ tptp.collec2086029184um_b_c (lambda ((X2 tptp.sum_su737395349um_b_c)) (and (@ (@ tptp.member1893232190um_b_c X2) B) (@ Q X2))))) (@ tptp.collec2086029184um_b_c (lambda ((X2 tptp.sum_su737395349um_b_c)) (and (@ (@ tptp.member1893232190um_b_c X2) A) (@ P X2)))))))) (forall ((X tptp.set_a) (X4 tptp.set_a) (Y tptp.set_a) (Y5 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a X) X4) (=> (@ (@ tptp.ord_less_eq_set_a Y) Y5) (@ (@ tptp.ord_le486764743_set_a (@ (@ tptp.produc1928581911_set_a X) Y)) (@ (@ tptp.produc1928581911_set_a X4) Y5))))) (forall ((X tptp.set_a) (X4 tptp.set_a) (Y (-> tptp.a Bool)) (Y5 (-> tptp.a Bool))) (=> (@ (@ tptp.ord_less_eq_set_a X) X4) (=> (@ (@ tptp.ord_less_eq_a_o Y) Y5) (@ (@ tptp.ord_le501349868_a_a_o (@ (@ tptp.produc634809990_a_a_o X) Y)) (@ (@ tptp.produc634809990_a_a_o X4) Y5))))) (forall ((X (-> tptp.a Bool)) (X4 (-> tptp.a Bool)) (Y tptp.set_a) (Y5 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_a_o X) X4) (=> (@ (@ tptp.ord_less_eq_set_a Y) Y5) (@ (@ tptp.ord_le72828020_set_a (@ (@ tptp.produc1916559302_set_a X) Y)) (@ (@ tptp.produc1916559302_set_a X4) Y5))))) (forall ((X tptp.finite1398487019real_c) (X4 tptp.finite1398487019real_c) (Y tptp.finite1398487019real_c) (Y5 tptp.finite1398487019real_c)) (=> (@ (@ tptp.ord_le775706699real_c X) X4) (=> (@ (@ tptp.ord_le775706699real_c Y) Y5) (@ (@ tptp.ord_le850691415real_c (@ (@ tptp.produc394644079real_c X) Y)) (@ (@ tptp.produc394644079real_c X4) Y5))))) (forall ((X (-> tptp.a Bool)) (X4 (-> tptp.a Bool)) (Y (-> tptp.a Bool)) (Y5 (-> tptp.a Bool))) (=> (@ (@ tptp.ord_less_eq_a_o X) X4) (=> (@ (@ tptp.ord_less_eq_a_o Y) Y5) (@ (@ tptp.ord_le1883211903_o_a_o (@ (@ tptp.product_Pair_a_o_a_o X) Y)) (@ (@ tptp.product_Pair_a_o_a_o X4) Y5))))) (forall ((X tptp.set_Fi291318197eal_sz) (X4 tptp.set_Fi291318197eal_sz) (Y tptp.set_Fi291318197eal_sz) (Y5 tptp.set_Fi291318197eal_sz)) (=> (@ (@ tptp.ord_le41263445eal_sz X) X4) (=> (@ (@ tptp.ord_le41263445eal_sz Y) Y5) (@ (@ tptp.ord_le978883847eal_sz (@ (@ tptp.produc1235791063eal_sz X) Y)) (@ (@ tptp.produc1235791063eal_sz X4) Y5))))) (forall ((X tptp.set_a) (X4 tptp.set_a) (Y (-> tptp.trm_sf_sz tptp.trm_sf_sz Bool)) (Y5 (-> tptp.trm_sf_sz tptp.trm_sf_sz Bool))) (=> (@ (@ tptp.ord_less_eq_set_a X) X4) (=> (@ (@ tptp.ord_le8515534f_sz_o Y) Y5) (@ (@ tptp.ord_le1884788375f_sz_o (@ (@ tptp.produc1174558183f_sz_o X) Y)) (@ (@ tptp.produc1174558183f_sz_o X4) Y5))))) (forall ((X (-> tptp.trm_sf_sz tptp.trm_sf_sz Bool)) (X4 (-> tptp.trm_sf_sz tptp.trm_sf_sz Bool)) (Y tptp.set_a) (Y5 tptp.set_a)) (=> (@ (@ tptp.ord_le8515534f_sz_o X) X4) (=> (@ (@ tptp.ord_less_eq_set_a Y) Y5) (@ (@ tptp.ord_le1643089911_set_a (@ (@ tptp.produc1543226183_set_a X) Y)) (@ (@ tptp.produc1543226183_set_a X4) Y5))))) (forall ((X (-> tptp.trm_sf_sz tptp.trm_sf_sz Bool)) (X4 (-> tptp.trm_sf_sz tptp.trm_sf_sz Bool)) (Y (-> tptp.a Bool)) (Y5 (-> tptp.a Bool))) (=> (@ (@ tptp.ord_le8515534f_sz_o X) X4) (=> (@ (@ tptp.ord_less_eq_a_o Y) Y5) (@ (@ tptp.ord_le2132572860_o_a_o (@ (@ tptp.produc1152932438_o_a_o X) Y)) (@ (@ tptp.produc1152932438_o_a_o X4) Y5))))) (forall ((X (-> tptp.a Bool)) (X4 (-> tptp.a Bool)) (Y (-> tptp.trm_sf_sz tptp.trm_sf_sz Bool)) (Y5 (-> tptp.trm_sf_sz tptp.trm_sf_sz Bool))) (=> (@ (@ tptp.ord_less_eq_a_o X) X4) (=> (@ (@ tptp.ord_le8515534f_sz_o Y) Y5) (@ (@ tptp.ord_le472894788f_sz_o (@ (@ tptp.produc593159062f_sz_o X) Y)) (@ (@ tptp.produc593159062f_sz_o X4) Y5))))) (forall ((X tptp.produc1149990247eal_sz) (Y tptp.produc1149990247eal_sz)) (=> (@ (@ tptp.ord_le473656583eal_sz X) Y) (@ (@ tptp.ord_le787639925eal_sz (@ tptp.produc1111759555eal_sz X)) (@ tptp.produc1111759555eal_sz Y)))) (forall ((X tptp.produc190496183real_c) (Y tptp.produc190496183real_c)) (=> (@ (@ tptp.ord_le850691415real_c X) Y) (@ (@ tptp.ord_le775706699real_c (@ tptp.produc2010422875real_c X)) (@ tptp.produc2010422875real_c Y)))) (forall ((X tptp.produc1149990247eal_sz) (Y tptp.produc1149990247eal_sz)) (=> (@ (@ tptp.ord_le473656583eal_sz X) Y) (@ (@ tptp.ord_le787639925eal_sz (@ tptp.produc1269210629eal_sz X)) (@ tptp.produc1269210629eal_sz Y)))) (forall ((X tptp.produc190496183real_c) (Y tptp.produc190496183real_c)) (=> (@ (@ tptp.ord_le850691415real_c X) Y) (@ (@ tptp.ord_le775706699real_c (@ tptp.produc314122909real_c X)) (@ tptp.produc314122909real_c Y)))) (forall ((P (-> tptp.finite824932053eal_sz tptp.finite824932053eal_sz Bool)) (P2 tptp.produc1149990247eal_sz)) (=> (@ (@ P (@ tptp.produc1269210629eal_sz P2)) (@ tptp.produc1111759555eal_sz P2)) (not (forall ((X3 tptp.finite824932053eal_sz) (Y3 tptp.finite824932053eal_sz)) (not (@ (@ P Y3) X3)))))) (forall ((P (-> tptp.produc866628903_sc_sz tptp.denota610675952t_unit Bool)) (P2 tptp.produc1821101996_sc_sz)) (=> (@ (@ P (@ tptp.produc974239792_sc_sz P2)) (@ tptp.produc1503602930_sc_sz P2)) (not (forall ((X3 tptp.denota610675952t_unit) (Y3 tptp.produc866628903_sc_sz)) (not (@ (@ P Y3) X3)))))) (forall ((P (-> tptp.finite1398487019real_c tptp.finite1398487019real_c Bool)) (P2 tptp.produc190496183real_c)) (=> (@ (@ P (@ tptp.produc314122909real_c P2)) (@ tptp.produc2010422875real_c P2)) (not (forall ((X3 tptp.finite1398487019real_c) (Y3 tptp.finite1398487019real_c)) (not (@ (@ P Y3) X3)))))) (forall ((X1 tptp.a) (Y1 tptp.a)) (= (= (@ tptp.sum_In2139678582um_b_c X1) (@ tptp.sum_In2139678582um_b_c Y1)) (= X1 Y1))) (forall ((A2 tptp.a) (A3 tptp.a)) (= (= (@ tptp.sum_In2139678582um_b_c A2) (@ tptp.sum_In2139678582um_b_c A3)) (= A2 A3))) (forall ((Y tptp.denota231621370t_unit)) (=> (@ (@ tptp.member1777622435t_unit Y) (@ tptp.collec451781861t_unit tptp.denota258389581_a_b_c)) (= (@ tptp.freche1608036107_a_b_c (@ tptp.freche1473475332_a_b_c Y)) Y))) (forall ((Y tptp.denota610675952t_unit)) (=> (@ (@ tptp.member754147591t_unit Y) (@ tptp.collec1767975749t_unit tptp.denota1579475975_sc_sz)) (= (@ tptp.freche1421597129_sc_sz (@ tptp.freche1784963216_sc_sz Y)) Y))) (= tptp.f0_sf_sz (lambda ((F tptp.sf)) (@ (@ tptp.function_sf_sz F) tptp.empty_sz_sf))) (forall ((A tptp.set_Fi291318197eal_sz) (B tptp.set_Fi291318197eal_sz)) (=> (forall ((X3 tptp.finite824932053eal_sz)) (let ((_let_1 (@ tptp.member1693951742eal_sz X3))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.ord_le41263445eal_sz A) B))) (forall ((A tptp.set_Pr1169339874_sc_sz) (B tptp.set_Pr1169339874_sc_sz)) (=> (forall ((X3 tptp.produc1821101996_sc_sz)) (let ((_let_1 (@ tptp.member1057565379_sc_sz X3))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.ord_le1230423618_sc_sz A) B))) (forall ((A tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c)) (=> (forall ((X3 tptp.sum_su737395349um_b_c)) (let ((_let_1 (@ tptp.member1893232190um_b_c X3))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.ord_le929608341um_b_c A) B))) (forall ((A tptp.set_trm_sf_sz) (B tptp.set_trm_sf_sz)) (=> (forall ((X3 tptp.trm_sf_sz)) (let ((_let_1 (@ tptp.member_trm_sf_sz X3))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.ord_le1697056455_sf_sz A) B))) (forall ((A tptp.set_trm_a_c) (B tptp.set_trm_a_c)) (=> (forall ((X3 tptp.trm_a_c)) (let ((_let_1 (@ tptp.member_trm_a_c X3))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.ord_le1369644495rm_a_c A) B))) (forall ((A tptp.set_a) (B tptp.set_a)) (=> (forall ((X3 tptp.a)) (let ((_let_1 (@ tptp.member_a X3))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.ord_less_eq_set_a A) B))) (forall ((Y tptp.denota231621370t_unit) (P (-> tptp.denota231621370t_unit Bool))) (=> (@ (@ tptp.member1777622435t_unit Y) (@ tptp.collec451781861t_unit tptp.denota258389581_a_b_c)) (=> (forall ((X3 tptp.freche914690577_a_b_c)) (@ P (@ tptp.freche1608036107_a_b_c X3))) (@ P Y)))) (forall ((Y tptp.denota610675952t_unit) (P (-> tptp.denota610675952t_unit Bool))) (=> (@ (@ tptp.member754147591t_unit Y) (@ tptp.collec1767975749t_unit tptp.denota1579475975_sc_sz)) (=> (forall ((X3 tptp.freche2095075217_sc_sz)) (@ P (@ tptp.freche1421597129_sc_sz X3))) (@ P Y)))) (forall ((Y tptp.denota231621370t_unit)) (=> (@ (@ tptp.member1777622435t_unit Y) (@ tptp.collec451781861t_unit tptp.denota258389581_a_b_c)) (not (forall ((X3 tptp.freche914690577_a_b_c)) (not (= Y (@ tptp.freche1608036107_a_b_c X3))))))) (forall ((Y tptp.denota610675952t_unit)) (=> (@ (@ tptp.member754147591t_unit Y) (@ tptp.collec1767975749t_unit tptp.denota1579475975_sc_sz)) (not (forall ((X3 tptp.freche2095075217_sc_sz)) (not (= Y (@ tptp.freche1421597129_sc_sz X3))))))) (forall ((X tptp.freche914690577_a_b_c)) (@ (@ tptp.member1777622435t_unit (@ tptp.freche1608036107_a_b_c X)) (@ tptp.collec451781861t_unit tptp.denota258389581_a_b_c))) (forall ((X tptp.freche2095075217_sc_sz)) (@ (@ tptp.member754147591t_unit (@ tptp.freche1421597129_sc_sz X)) (@ tptp.collec1767975749t_unit tptp.denota1579475975_sc_sz))) (forall ((X tptp.freche914690577_a_b_c)) (not (forall ((Y3 tptp.denota231621370t_unit)) (=> (= X (@ tptp.freche1473475332_a_b_c Y3)) (not (@ (@ tptp.member1777622435t_unit Y3) (@ tptp.collec451781861t_unit tptp.denota258389581_a_b_c))))))) (forall ((X tptp.freche2095075217_sc_sz)) (not (forall ((Y3 tptp.denota610675952t_unit)) (=> (= X (@ tptp.freche1784963216_sc_sz Y3)) (not (@ (@ tptp.member754147591t_unit Y3) (@ tptp.collec1767975749t_unit tptp.denota1579475975_sc_sz))))))) (forall ((P (-> tptp.freche914690577_a_b_c Bool)) (X tptp.freche914690577_a_b_c)) (=> (forall ((Y3 tptp.denota231621370t_unit)) (=> (@ (@ tptp.member1777622435t_unit Y3) (@ tptp.collec451781861t_unit tptp.denota258389581_a_b_c)) (@ P (@ tptp.freche1473475332_a_b_c Y3)))) (@ P X))) (forall ((P (-> tptp.freche2095075217_sc_sz Bool)) (X tptp.freche2095075217_sc_sz)) (=> (forall ((Y3 tptp.denota610675952t_unit)) (=> (@ (@ tptp.member754147591t_unit Y3) (@ tptp.collec1767975749t_unit tptp.denota1579475975_sc_sz)) (@ P (@ tptp.freche1784963216_sc_sz Y3)))) (@ P X))) (forall ((X tptp.denota231621370t_unit) (Y tptp.denota231621370t_unit)) (let ((_let_1 (@ tptp.collec451781861t_unit tptp.denota258389581_a_b_c))) (=> (@ (@ tptp.member1777622435t_unit X) _let_1) (=> (@ (@ tptp.member1777622435t_unit Y) _let_1) (= (= (@ tptp.freche1473475332_a_b_c X) (@ tptp.freche1473475332_a_b_c Y)) (= X Y)))))) (forall ((X tptp.denota610675952t_unit) (Y tptp.denota610675952t_unit)) (let ((_let_1 (@ tptp.collec1767975749t_unit tptp.denota1579475975_sc_sz))) (=> (@ (@ tptp.member754147591t_unit X) _let_1) (=> (@ (@ tptp.member754147591t_unit Y) _let_1) (= (= (@ tptp.freche1784963216_sc_sz X) (@ tptp.freche1784963216_sc_sz Y)) (= X Y)))))) (forall ((A tptp.set_a) (B tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a A) B) (=> (@ (@ tptp.ord_less_eq_set_a B) A) (= A B)))) (forall ((P (-> tptp.finite824932053eal_sz Bool)) (Q (-> tptp.finite824932053eal_sz Bool))) (= (@ (@ tptp.ord_le41263445eal_sz (@ tptp.collec1002602816eal_sz P)) (@ tptp.collec1002602816eal_sz Q)) (forall ((X2 tptp.finite824932053eal_sz)) (=> (@ P X2) (@ Q X2))))) (forall ((P (-> tptp.produc1821101996_sc_sz Bool)) (Q (-> tptp.produc1821101996_sc_sz Bool))) (= (@ (@ tptp.ord_le1230423618_sc_sz (@ tptp.collec1199592193_sc_sz P)) (@ tptp.collec1199592193_sc_sz Q)) (forall ((X2 tptp.produc1821101996_sc_sz)) (=> (@ P X2) (@ Q X2))))) (forall ((P (-> tptp.trm_sf_sz Bool)) (Q (-> tptp.trm_sf_sz Bool))) (= (@ (@ tptp.ord_le1697056455_sf_sz (@ tptp.collect_trm_sf_sz P)) (@ tptp.collect_trm_sf_sz Q)) (forall ((X2 tptp.trm_sf_sz)) (=> (@ P X2) (@ Q X2))))) (forall ((P (-> tptp.trm_a_c Bool)) (Q (-> tptp.trm_a_c Bool))) (= (@ (@ tptp.ord_le1369644495rm_a_c (@ tptp.collect_trm_a_c P)) (@ tptp.collect_trm_a_c Q)) (forall ((X2 tptp.trm_a_c)) (=> (@ P X2) (@ Q X2))))) (forall ((P (-> tptp.a Bool)) (Q (-> tptp.a Bool))) (= (@ (@ tptp.ord_less_eq_set_a (@ tptp.collect_a P)) (@ tptp.collect_a Q)) (forall ((X2 tptp.a)) (=> (@ P X2) (@ Q X2))))) (forall ((P (-> tptp.sum_su737395349um_b_c Bool)) (Q (-> tptp.sum_su737395349um_b_c Bool))) (= (@ (@ tptp.ord_le929608341um_b_c (@ tptp.collec2086029184um_b_c P)) (@ tptp.collec2086029184um_b_c Q)) (forall ((X2 tptp.sum_su737395349um_b_c)) (=> (@ P X2) (@ Q X2))))) (= (lambda ((Y4 tptp.set_a) (Z tptp.set_a)) (= Y4 Z)) (lambda ((A5 tptp.set_a) (B5 tptp.set_a)) (and (@ (@ tptp.ord_less_eq_set_a A5) B5) (@ (@ tptp.ord_less_eq_set_a B5) A5)))) (forall ((A tptp.set_a) (B tptp.set_a) (C3 tptp.set_a)) (let ((_let_1 (@ tptp.ord_less_eq_set_a A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_a B) C3) (@ _let_1 C3))))) (forall ((P (-> tptp.produc1821101996_sc_sz Bool)) (Q (-> tptp.produc1821101996_sc_sz Bool))) (=> (forall ((X3 tptp.produc1821101996_sc_sz)) (=> (@ P X3) (@ Q X3))) (@ (@ tptp.ord_le1230423618_sc_sz (@ tptp.collec1199592193_sc_sz P)) (@ tptp.collec1199592193_sc_sz Q)))) (forall ((P (-> tptp.trm_sf_sz Bool)) (Q (-> tptp.trm_sf_sz Bool))) (=> (forall ((X3 tptp.trm_sf_sz)) (=> (@ P X3) (@ Q X3))) (@ (@ tptp.ord_le1697056455_sf_sz (@ tptp.collect_trm_sf_sz P)) (@ tptp.collect_trm_sf_sz Q)))) (forall ((P (-> tptp.trm_a_c Bool)) (Q (-> tptp.trm_a_c Bool))) (=> (forall ((X3 tptp.trm_a_c)) (=> (@ P X3) (@ Q X3))) (@ (@ tptp.ord_le1369644495rm_a_c (@ tptp.collect_trm_a_c P)) (@ tptp.collect_trm_a_c Q)))) (forall ((P (-> tptp.a Bool)) (Q (-> tptp.a Bool))) (=> (forall ((X3 tptp.a)) (=> (@ P X3) (@ Q X3))) (@ (@ tptp.ord_less_eq_set_a (@ tptp.collect_a P)) (@ tptp.collect_a Q)))) (forall ((P (-> tptp.sum_su737395349um_b_c Bool)) (Q (-> tptp.sum_su737395349um_b_c Bool))) (=> (forall ((X3 tptp.sum_su737395349um_b_c)) (=> (@ P X3) (@ Q X3))) (@ (@ tptp.ord_le929608341um_b_c (@ tptp.collec2086029184um_b_c P)) (@ tptp.collec2086029184um_b_c Q)))) (= tptp.ord_less_eq_set_a (lambda ((A5 tptp.set_a) (B5 tptp.set_a)) (forall ((T tptp.a)) (let ((_let_1 (@ tptp.member_a T))) (=> (@ _let_1 A5) (@ _let_1 B5)))))) (= tptp.ord_less_eq_set_a (lambda ((A5 tptp.set_a) (B5 tptp.set_a)) (forall ((X2 tptp.a)) (let ((_let_1 (@ tptp.member_a X2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))) (forall ((A tptp.set_a) (B tptp.set_a) (C2 tptp.a)) (let ((_let_1 (@ tptp.member_a C2))) (=> (@ (@ tptp.ord_less_eq_set_a A) B) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((A tptp.set_a) (B tptp.set_a) (X tptp.a)) (let ((_let_1 (@ tptp.member_a X))) (=> (@ (@ tptp.ord_less_eq_set_a A) B) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((X tptp.a) (Y tptp.a)) (=> (= (@ tptp.sum_In2139678582um_b_c X) (@ tptp.sum_In2139678582um_b_c Y)) (= X Y))) (forall ((A tptp.set_a) (P (-> tptp.a Bool))) (@ (@ tptp.ord_less_eq_set_a (@ tptp.collect_a (lambda ((X2 tptp.a)) (and (@ (@ tptp.member_a X2) A) (@ P X2))))) A)) (forall ((A tptp.set_Su1783761653um_b_c) (P (-> tptp.sum_su737395349um_b_c Bool))) (@ (@ tptp.ord_le929608341um_b_c (@ tptp.collec2086029184um_b_c (lambda ((X2 tptp.sum_su737395349um_b_c)) (and (@ (@ tptp.member1893232190um_b_c X2) A) (@ P X2))))) A)) (= tptp.ord_less_eq_set_a (lambda ((A5 tptp.set_a) (B5 tptp.set_a)) (@ (@ tptp.ord_less_eq_a_o (lambda ((X2 tptp.a)) (@ (@ tptp.member_a X2) A5))) (lambda ((X2 tptp.a)) (@ (@ tptp.member_a X2) B5))))) (forall ((I3 tptp.denota231621370t_unit) (J tptp.denota231621370t_unit) (Theta_12 tptp.trm_a_c) (Theta_22 tptp.trm_a_c) (Nu tptp.produc190496183real_c)) (let ((_let_1 (@ tptp.produc314122909real_c Nu))) (let ((_let_2 (@ tptp.produc2010422875real_c Nu))) (=> (@ tptp.denota258389581_a_b_c I3) (=> (@ tptp.denota258389581_a_b_c J) (=> (@ tptp.dfree_a_c Theta_12) (=> (@ tptp.dfree_a_c Theta_22) (=> (= (@ (@ tptp.denota2042094639_a_b_c I3) Theta_12) (@ (@ tptp.denota2042094639_a_b_c J) Theta_22)) (= (@ (@ (@ (@ tptp.denota229585092_a_b_c I3) Theta_12) _let_2) _let_1) (@ (@ (@ (@ tptp.denota229585092_a_b_c J) Theta_22) _let_2) _let_1)))))))))) (forall ((I3 tptp.denota610675952t_unit) (J tptp.denota610675952t_unit) (Theta_12 tptp.trm_sf_sz) (Theta_22 tptp.trm_sf_sz) (Nu tptp.produc1149990247eal_sz)) (let ((_let_1 (@ tptp.produc1269210629eal_sz Nu))) (let ((_let_2 (@ tptp.produc1111759555eal_sz Nu))) (=> (@ tptp.denota1579475975_sc_sz I3) (=> (@ tptp.denota1579475975_sc_sz J) (=> (@ tptp.dfree_sf_sz Theta_12) (=> (@ tptp.dfree_sf_sz Theta_22) (=> (= (@ (@ tptp.denota1179238309_sc_sz I3) Theta_12) (@ (@ tptp.denota1179238309_sc_sz J) Theta_22)) (= (@ (@ (@ (@ tptp.denota1979904720_sc_sz I3) Theta_12) _let_2) _let_1) (@ (@ (@ (@ tptp.denota1979904720_sc_sz J) Theta_22) _let_2) _let_1)))))))))) (@ (@ (@ tptp.type_d1092523951t_unit tptp.freche1421597129_sc_sz) tptp.freche1784963216_sc_sz) (@ tptp.collec1767975749t_unit tptp.denota1579475975_sc_sz)) (= tptp.bNF_Gr1775200401_sc_sz (lambda ((A5 tptp.set_a) (F (-> tptp.a tptp.denota610675952t_unit)) (G (-> tptp.a tptp.produc866628903_sc_sz))) (@ tptp.collec1199592193_sc_sz (lambda ((Uu tptp.produc1821101996_sc_sz)) (exists ((A6 tptp.a)) (and (= Uu (@ (@ tptp.produc789536734_sc_sz (@ F A6)) (@ G A6))) (@ (@ tptp.member_a A6) A5))))))) (forall ((B2 tptp.denota610675952t_unit) (F2 (-> tptp.a tptp.denota610675952t_unit)) (X tptp.a) (C2 tptp.produc866628903_sc_sz) (G2 (-> tptp.a tptp.produc866628903_sc_sz)) (A tptp.set_a)) (=> (= B2 (@ F2 X)) (=> (= C2 (@ G2 X)) (=> (@ (@ tptp.member_a X) A) (@ (@ tptp.member1057565379_sc_sz (@ (@ tptp.produc789536734_sc_sz B2) C2)) (@ (@ (@ tptp.bNF_Gr1775200401_sc_sz A) F2) G2)))))) (forall ((Theta tptp.trm_a_c) (Nu tptp.produc190496183real_c) (Nu2 tptp.produc190496183real_c) (I3 tptp.denota231621370t_unit) (J tptp.denota231621370t_unit)) (=> (@ tptp.dfree_a_c Theta) (=> (@ (@ (@ tptp.denota1997846518gree_c Nu) Nu2) (@ tptp.static_FVT_a_c Theta)) (=> (@ (@ (@ tptp.denota69106024_a_b_c I3) J) (@ tptp.collec2086029184um_b_c (lambda ((Uu tptp.sum_su737395349um_b_c)) (exists ((X2 tptp.a)) (and (= Uu (@ tptp.sum_In2139678582um_b_c X2)) (@ (@ tptp.member_a X2) (@ tptp.static_SIGT_a_c Theta))))))) (= (@ (@ (@ tptp.denota2042094639_a_b_c I3) Theta) (@ tptp.produc2010422875real_c Nu)) (@ (@ (@ tptp.denota2042094639_a_b_c J) Theta) (@ tptp.produc2010422875real_c Nu2))))))) (forall ((R tptp.set_a) (S3 tptp.set_a)) (= (@ (@ tptp.ord_less_eq_a_o (lambda ((X2 tptp.a)) (@ (@ tptp.member_a X2) R))) (lambda ((X2 tptp.a)) (@ (@ tptp.member_a X2) S3))) (@ (@ tptp.ord_less_eq_set_a R) S3))) (forall ((I3 tptp.denota610675952t_unit) (Theta tptp.trm_sf_sz) (S3 tptp.set_Fi291318197eal_sz)) (=> (@ tptp.denota1579475975_sc_sz I3) (=> (@ tptp.dfree_sf_sz Theta) (@ (@ tptp.topolo1348430467z_real S3) (@ (@ tptp.denota1179238309_sc_sz I3) Theta))))) (forall ((Nu tptp.produc1149990247eal_sz) (Nu2 tptp.produc1149990247eal_sz) (F2 tptp.sf) (Args (-> tptp.sz tptp.trm_sf_sz)) (I tptp.sz)) (let ((_let_1 (@ (@ tptp.denota102713844ree_sz Nu) Nu2))) (=> (@ _let_1 (@ tptp.static_FVT_sf_sz (@ (@ tptp.function_sf_sz F2) Args))) (@ _let_1 (@ tptp.static_FVT_sf_sz (@ Args I)))))) (forall ((R2 tptp.set_Pr1169339874_sc_sz) (S4 tptp.set_Pr1169339874_sc_sz)) (=> (forall ((X3 tptp.denota610675952t_unit) (Y3 tptp.produc866628903_sc_sz)) (let ((_let_1 (@ tptp.member1057565379_sc_sz (@ (@ tptp.produc789536734_sc_sz X3) Y3)))) (=> (@ _let_1 R2) (@ _let_1 S4)))) (@ (@ tptp.ord_le1230423618_sc_sz R2) S4))) (forall ((F2 tptp.trm_a_c)) (@ (@ tptp.ord_le1772180283um_c_c (@ tptp.static_FVT_a_c F2)) (@ tptp.static_FVDiff_a_c F2))) (forall ((R tptp.set_Pr1169339874_sc_sz) (S3 tptp.set_Pr1169339874_sc_sz)) (= (= (lambda ((X2 tptp.denota610675952t_unit) (Y2 tptp.produc866628903_sc_sz)) (@ (@ tptp.member1057565379_sc_sz (@ (@ tptp.produc789536734_sc_sz X2) Y2)) R)) (lambda ((X2 tptp.denota610675952t_unit) (Y2 tptp.produc866628903_sc_sz)) (@ (@ tptp.member1057565379_sc_sz (@ (@ tptp.produc789536734_sc_sz X2) Y2)) S3))) (= R S3))) (forall ((R tptp.set_Pr1169339874_sc_sz) (S3 tptp.set_Pr1169339874_sc_sz)) (= (@ (@ tptp.ord_le108471557c_sz_o (lambda ((X2 tptp.denota610675952t_unit) (Y2 tptp.produc866628903_sc_sz)) (@ (@ tptp.member1057565379_sc_sz (@ (@ tptp.produc789536734_sc_sz X2) Y2)) R))) (lambda ((X2 tptp.denota610675952t_unit) (Y2 tptp.produc866628903_sc_sz)) (@ (@ tptp.member1057565379_sc_sz (@ (@ tptp.produc789536734_sc_sz X2) Y2)) S3))) (@ (@ tptp.ord_le1230423618_sc_sz R) S3))) (forall ((I3 tptp.denota610675952t_unit) (Theta tptp.trm_sf_sz)) (=> (@ tptp.denota1579475975_sc_sz I3) (=> (@ tptp.dfree_sf_sz Theta) (@ (@ tptp.topolo1348430467z_real tptp.top_to1873962757eal_sz) (@ (@ tptp.denota1179238309_sc_sz I3) Theta))))) (forall ((S4 tptp.set_Fi291318197eal_sz) (H (-> tptp.finite824932053eal_sz tptp.real)) (A2 tptp.real) (F2 (-> tptp.finite824932053eal_sz tptp.bounde472938360z_real)) (G2 (-> tptp.finite824932053eal_sz tptp.bounde472938360z_real))) (=> (@ (@ tptp.topolo885751137z_real (@ tptp.collec1002602816eal_sz (lambda ((T tptp.finite824932053eal_sz)) (and (@ (@ tptp.member1693951742eal_sz T) S4) (@ (@ tptp.ord_less_eq_real (@ H T)) A2))))) F2) (=> (@ (@ tptp.topolo885751137z_real (@ tptp.collec1002602816eal_sz (lambda ((T tptp.finite824932053eal_sz)) (and (@ (@ tptp.member1693951742eal_sz T) S4) (@ (@ tptp.ord_less_eq_real A2) (@ H T)))))) G2) (=> (@ (@ tptp.topolo1348430467z_real S4) H) (=> (forall ((T4 tptp.finite824932053eal_sz)) (=> (@ (@ tptp.member1693951742eal_sz T4) S4) (=> (= (@ H T4) A2) (= (@ F2 T4) (@ G2 T4))))) (@ (@ tptp.topolo885751137z_real S4) (lambda ((T tptp.finite824932053eal_sz)) (@ (@ (@ tptp.if_Bou1785791806z_real (@ (@ tptp.ord_less_eq_real (@ H T)) A2)) (@ F2 T)) (@ G2 T))))))))) (forall ((X tptp.a)) (@ (@ tptp.member_a X) tptp.top_top_set_a)) (forall ((X tptp.finite824932053eal_sz)) (@ (@ tptp.member1693951742eal_sz X) tptp.top_to1873962757eal_sz)) (forall ((A2 tptp.set_Fi291318197eal_sz)) (=> (@ (@ tptp.ord_le41263445eal_sz tptp.top_to1873962757eal_sz) A2) (= A2 tptp.top_to1873962757eal_sz))) (forall ((A2 tptp.set_Fi291318197eal_sz)) (= (@ (@ tptp.ord_le41263445eal_sz tptp.top_to1873962757eal_sz) A2) (= A2 tptp.top_to1873962757eal_sz))) (forall ((A2 tptp.set_Fi291318197eal_sz)) (@ (@ tptp.ord_le41263445eal_sz A2) tptp.top_to1873962757eal_sz)) (forall ((A tptp.set_Fi291318197eal_sz)) (@ (@ tptp.ord_le41263445eal_sz A) tptp.top_to1873962757eal_sz)) (forall ((Vid1 tptp.sz) (Vid2 tptp.sz) (Vid3 tptp.sz) (Fid1 tptp.sf) (Fid2 tptp.sf) (Fid3 tptp.sf) (Pid1 tptp.sc) (Pid2 tptp.sc) (Pid3 tptp.sc) (Pid4 tptp.sc) (X tptp.produc1821101996_sc_sz)) (=> (@ (@ (@ (@ (@ (@ (@ (@ (@ (@ tptp.ids_sz_sf_sc Vid1) Vid2) Vid3) Fid1) Fid2) Fid3) Pid1) Pid2) Pid3) Pid4) (not (forall ((I2 tptp.denota610675952t_unit) (S tptp.produc866628903_sc_sz)) (not (= X (@ (@ tptp.produc789536734_sc_sz I2) S))))))) (= tptp.top_to524132421um_b_c (@ tptp.collec2086029184um_b_c (lambda ((X2 tptp.sum_su737395349um_b_c)) true))) (= tptp.top_to1873962757eal_sz (@ tptp.collec1002602816eal_sz (lambda ((X2 tptp.finite824932053eal_sz)) true))) (exists ((X3 tptp.a)) (@ (@ tptp.member_a X3) tptp.top_top_set_a)) (exists ((X3 tptp.finite824932053eal_sz)) (@ (@ tptp.member1693951742eal_sz X3) tptp.top_to1873962757eal_sz)) (forall ((A tptp.set_a)) (=> (forall ((X3 tptp.a)) (@ (@ tptp.member_a X3) A)) (= tptp.top_top_set_a A))) (forall ((A tptp.set_Fi291318197eal_sz)) (=> (forall ((X3 tptp.finite824932053eal_sz)) (@ (@ tptp.member1693951742eal_sz X3) A)) (= tptp.top_to1873962757eal_sz A))) (= tptp.top_to1787697847eal_sz (@ (@ tptp.produc1235791063eal_sz tptp.top_to1873962757eal_sz) tptp.top_to1873962757eal_sz)) (forall ((Vid1 tptp.sz) (Vid2 tptp.sz) (Vid3 tptp.sz) (Fid1 tptp.sf) (Fid2 tptp.sf) (Fid3 tptp.sf) (Pid1 tptp.sc) (Pid2 tptp.sc) (Pid3 tptp.sc) (Pid4 tptp.sc) (P2 tptp.sc)) (=> (@ (@ (@ (@ (@ (@ (@ (@ (@ (@ tptp.ids_sz_sf_sc Vid1) Vid2) Vid3) Fid1) Fid2) Fid3) Pid1) Pid2) Pid3) Pid4) (= (@ tptp.p_sc_sf_sz P2) (@ tptp.predic913887884_sf_sz P2)))) (forall ((I3 tptp.denota610675952t_unit) (Theta tptp.trm_sf_sz)) (=> (@ tptp.denota1579475975_sc_sz I3) (=> (@ tptp.dfree_sf_sz Theta) (@ (@ tptp.topolo885751137z_real tptp.top_to1873962757eal_sz) (@ (@ tptp.freche585307148_sc_sz (@ tptp.freche1784963216_sc_sz I3)) (@ tptp.freche1046279700_sf_sz Theta)))))) (= tptp.top_to1399053141c_sz_o (lambda ((X2 tptp.denota610675952t_unit) (Y2 tptp.produc866628903_sc_sz)) (@ (@ tptp.member1057565379_sc_sz (@ (@ tptp.produc789536734_sc_sz X2) Y2)) tptp.top_to1499569298_sc_sz))) (= tptp.top_to524132421um_b_c (@ tptp.collec2086029184um_b_c tptp.top_to1201357528_b_c_o)) (= tptp.top_to1873962757eal_sz (@ tptp.collec1002602816eal_sz tptp.top_to646513176l_sz_o)) (forall ((A2 tptp.finite1398487019real_c) (B2 tptp.finite1398487019real_c) (C2 tptp.finite1398487019real_c) (D tptp.finite1398487019real_c)) (=> (@ (@ (@ tptp.denota1997846518gree_c (@ (@ tptp.produc394644079real_c A2) B2)) (@ (@ tptp.produc394644079real_c C2) D)) tptp.top_to1660572043um_c_c) (and (= A2 C2) (= B2 D)))) (forall ((Nu tptp.produc190496183real_c) (Omega tptp.produc190496183real_c)) (=> (@ (@ (@ tptp.denota1997846518gree_c Nu) Omega) tptp.top_to1660572043um_c_c) (= Nu Omega))) (forall ((Vid1 tptp.sz) (Vid2 tptp.sz) (Vid3 tptp.sz) (Fid1 tptp.sf) (Fid2 tptp.sf) (Fid3 tptp.sf) (Pid1 tptp.sc) (Pid2 tptp.sc) (Pid3 tptp.sc) (Pid4 tptp.sc) (I3 tptp.denota610675952t_unit) (Theta tptp.trm_sf_sz)) (=> (@ (@ (@ (@ (@ (@ (@ (@ (@ (@ tptp.ids_sz_sf_sc Vid1) Vid2) Vid3) Fid1) Fid2) Fid3) Pid1) Pid2) Pid3) Pid4) (=> (@ tptp.denota1579475975_sc_sz I3) (=> (@ tptp.dfree_sf_sz Theta) (@ (@ tptp.topolo885751137z_real tptp.top_to1873962757eal_sz) (@ (@ tptp.freche585307148_sc_sz (@ tptp.freche1784963216_sc_sz I3)) (@ tptp.freche1046279700_sf_sz Theta))))))) (forall ((I3 tptp.denota610675952t_unit) (Theta tptp.trm_sf_sz)) (=> (@ tptp.denota1579475975_sc_sz I3) (=> (@ tptp.dfree_sf_sz Theta) (= (lambda ((V2 tptp.finite824932053eal_sz)) (@ tptp.bounde397081123z_real (@ (@ (@ tptp.denota1979904720_sc_sz I3) Theta) V2))) (@ (@ tptp.freche585307148_sc_sz (@ tptp.freche1784963216_sc_sz I3)) (@ tptp.freche1046279700_sf_sz Theta)))))) (forall ((S4 tptp.set_Fi291318197eal_sz) (C2 tptp.bounde472938360z_real)) (@ (@ tptp.topolo885751137z_real S4) (lambda ((X2 tptp.finite824932053eal_sz)) C2))) (forall ((S4 tptp.set_Fi291318197eal_sz) (F2 (-> tptp.finite824932053eal_sz tptp.bounde472938360z_real)) (T3 tptp.set_Fi291318197eal_sz)) (=> (@ (@ tptp.topolo885751137z_real S4) F2) (=> (@ (@ tptp.ord_le41263445eal_sz T3) S4) (@ (@ tptp.topolo885751137z_real T3) F2)))) (forall ((S4 tptp.set_Fi291318197eal_sz) (F2 (-> tptp.finite824932053eal_sz tptp.bounde472938360z_real)) (G2 (-> tptp.finite824932053eal_sz tptp.bounde472938360z_real))) (let ((_let_1 (@ tptp.topolo885751137z_real S4))) (=> (@ _let_1 F2) (=> (@ _let_1 G2) (@ (@ tptp.topolo1027477648z_real S4) (lambda ((X2 tptp.finite824932053eal_sz)) (@ (@ tptp.produc784663575z_real (@ F2 X2)) (@ G2 X2)))))))) (forall ((Vid1 tptp.sz) (Vid2 tptp.sz) (Vid3 tptp.sz) (Fid1 tptp.sf) (Fid2 tptp.sf) (Fid3 tptp.sf) (Pid1 tptp.sc) (Pid2 tptp.sc) (Pid3 tptp.sc) (Pid4 tptp.sc) (I3 tptp.denota610675952t_unit) (Theta tptp.trm_sf_sz)) (=> (@ (@ (@ (@ (@ (@ (@ (@ (@ (@ tptp.ids_sz_sf_sc Vid1) Vid2) Vid3) Fid1) Fid2) Fid3) Pid1) Pid2) Pid3) Pid4) (=> (@ tptp.denota1579475975_sc_sz I3) (=> (@ tptp.dfree_sf_sz Theta) (= (lambda ((V2 tptp.finite824932053eal_sz)) (@ tptp.bounde397081123z_real (@ (@ (@ tptp.denota1979904720_sc_sz I3) Theta) V2))) (@ (@ tptp.freche585307148_sc_sz (@ tptp.freche1784963216_sc_sz I3)) (@ tptp.freche1046279700_sf_sz Theta))))))) (forall ((Xb tptp.denota610675952t_unit) (Xa tptp.trm_sf_sz) (X tptp.finite824932053eal_sz)) (=> (@ (@ (@ tptp.bNF_eq1660582207t_unit tptp.denota1579475975_sc_sz) Xb) Xb) (=> (@ (@ (@ tptp.bNF_eq_onp_trm_sf_sz tptp.dfree_sf_sz) Xa) Xa) (= (@ (@ (@ tptp.freche585307148_sc_sz (@ tptp.freche1784963216_sc_sz Xb)) (@ tptp.freche1046279700_sf_sz Xa)) X) (@ tptp.bounde397081123z_real (@ (@ (@ tptp.denota1979904720_sc_sz Xb) Xa) X)))))) (forall ((Vid1 tptp.sz) (Vid2 tptp.sz) (Vid3 tptp.sz) (Fid1 tptp.sf) (Fid2 tptp.sf) (Fid3 tptp.sf) (Pid1 tptp.sc) (Pid2 tptp.sc) (Pid3 tptp.sc) (Pid4 tptp.sc) (Xb tptp.denota610675952t_unit) (Xa tptp.trm_sf_sz) (X tptp.finite824932053eal_sz)) (=> (@ (@ (@ (@ (@ (@ (@ (@ (@ (@ tptp.ids_sz_sf_sc Vid1) Vid2) Vid3) Fid1) Fid2) Fid3) Pid1) Pid2) Pid3) Pid4) (=> (@ (@ (@ tptp.bNF_eq1660582207t_unit tptp.denota1579475975_sc_sz) Xb) Xb) (=> (@ (@ (@ tptp.bNF_eq_onp_trm_sf_sz tptp.dfree_sf_sz) Xa) Xa) (= (@ (@ (@ tptp.freche585307148_sc_sz (@ tptp.freche1784963216_sc_sz Xb)) (@ tptp.freche1046279700_sf_sz Xa)) X) (@ tptp.bounde397081123z_real (@ (@ (@ tptp.denota1979904720_sc_sz Xb) Xa) X))))))) (@ (@ (@ (@ tptp.quotie842200089_sc_sz (@ tptp.bNF_eq1660582207t_unit tptp.denota1579475975_sc_sz)) tptp.freche1784963216_sc_sz) tptp.freche1421597129_sc_sz) tptp.freche58918398_sc_sz) (@ (@ (@ (@ tptp.quotie1467858509rm_a_c (@ tptp.bNF_eq_onp_trm_a_c tptp.dfree_a_c)) tptp.freche665377492rm_a_c) tptp.frechet_raw_term_a_c) tptp.frechet_cr_strm_a_c) (@ (@ (@ (@ tptp.quotie1549861309_sf_sz (@ tptp.bNF_eq_onp_trm_sf_sz tptp.dfree_sf_sz)) tptp.freche1046279700_sf_sz) tptp.freche782854530_sf_sz) tptp.freche1244000341_sf_sz) (forall ((P (-> tptp.denota610675952t_unit Bool))) (@ (@ tptp.ord_le2003534918unit_o (@ tptp.bNF_eq1660582207t_unit P)) (lambda ((Y4 tptp.denota610675952t_unit) (Z tptp.denota610675952t_unit)) (= Y4 Z)))) (forall ((P (-> tptp.trm_sf_sz Bool))) (@ (@ tptp.ord_le8515534f_sz_o (@ tptp.bNF_eq_onp_trm_sf_sz P)) (lambda ((Y4 tptp.trm_sf_sz) (Z tptp.trm_sf_sz)) (= Y4 Z)))) (forall ((P Bool)) (or (= P true) (= P false))) (forall ((X tptp.bounde472938360z_real) (Y tptp.bounde472938360z_real)) (= (@ (@ (@ tptp.if_Bou1785791806z_real false) X) Y) Y)) (forall ((X tptp.bounde472938360z_real) (Y tptp.bounde472938360z_real)) (= (@ (@ (@ tptp.if_Bou1785791806z_real true) X) Y) X)) _let_3 true))))))))))))))))))))))))
% 0.52/1.05 )
% 0.52/1.05 % SZS output end Proof for ITP038^1
% 0.52/1.05 % cvc5---1.0.5 exiting
% 0.52/1.06 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------