TSTP Solution File: ITP021^2 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP021^2 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n014.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 03:16:26 EDT 2023
% Result : Theorem 4.01s 4.23s
% Output : Proof 4.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ITP021^2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n014.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 15:00:46 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.49 %----Proving TH0
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 % File : ITP021^2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.21/0.50 % Domain : Interactive Theorem Proving
% 0.21/0.50 % Problem : HOL4 set theory export of thm_2Eextreal_2Emax__le.p, bushy mode
% 0.21/0.50 % Version : [BG+19] axioms.
% 0.21/0.50 % English :
% 0.21/0.50
% 0.21/0.50 % Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% 0.21/0.50 % : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% 0.21/0.50 % Source : [BG+19]
% 0.21/0.50 % Names : thm_2Eextreal_2Emax__le.p [Gau19]
% 0.21/0.50 % : HL410001^2.p [TPAP]
% 0.21/0.50
% 0.21/0.50 % Status : Theorem
% 0.21/0.50 % Rating : 0.69 v8.1.0, 0.73 v7.5.0
% 0.21/0.50 % Syntax : Number of formulae : 83 ( 8 unt; 25 typ; 0 def)
% 0.21/0.50 % Number of atoms : 395 ( 14 equ; 0 cnn)
% 0.21/0.50 % Maximal formula atoms : 21 ( 6 avg)
% 0.21/0.50 % Number of connectives : 733 ( 46 ~; 36 |; 27 &; 488 @)
% 0.21/0.50 % ( 43 <=>; 93 =>; 0 <=; 0 <~>)
% 0.21/0.50 % Maximal formula depth : 15 ( 8 avg)
% 0.21/0.50 % Number of types : 4 ( 2 usr)
% 0.21/0.50 % Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% 0.21/0.50 % Number of symbols : 31 ( 28 usr; 18 con; 0-2 aty)
% 0.21/0.50 % Number of variables : 93 ( 0 ^; 93 !; 0 ?; 93 :)
% 0.21/0.50 % SPC : TH0_THM_EQU_NAR
% 0.21/0.50
% 0.21/0.50 % Comments :
% 0.21/0.50 % Bugfixes : v7.5.0 - Bugfixes in axioms and export.
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 thf(del_tp,type,
% 0.21/0.50 del: $tType ).
% 0.21/0.50
% 0.21/0.50 thf(bool,type,
% 0.21/0.50 bool: del ).
% 0.21/0.50
% 0.21/0.50 thf(ind,type,
% 0.21/0.50 ind: del ).
% 0.21/0.50
% 0.21/0.50 thf(arr,type,
% 0.21/0.50 arr: del > del > del ).
% 0.21/0.50
% 0.21/0.50 thf(mem,type,
% 0.21/0.50 mem: $i > del > $o ).
% 0.21/0.50
% 0.21/0.50 thf(ap,type,
% 0.21/0.50 ap: $i > $i > $i ).
% 0.21/0.50
% 0.21/0.50 thf(lam,type,
% 0.21/0.50 lam: del > ( $i > $i ) > $i ).
% 0.21/0.50
% 0.21/0.50 thf(p,type,
% 0.21/0.50 p: $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(stp_inj_o,type,
% 0.21/0.50 inj__o: $o > $i ).
% 0.21/0.50
% 0.21/0.50 thf(stp_inj_surj_o,axiom,
% 0.21/0.50 ! [X: $o] :
% 0.21/0.50 ( ( p @ ( inj__o @ X ) )
% 0.21/0.50 = X ) ).
% 0.21/0.50
% 0.21/0.50 thf(stp_inj_mem_o,axiom,
% 0.21/0.50 ! [X: $o] : ( mem @ ( inj__o @ X ) @ bool ) ).
% 0.21/0.50
% 0.21/0.50 thf(stp_iso_mem_o,axiom,
% 0.21/0.50 ! [X: $i] :
% 0.21/0.50 ( ( mem @ X @ bool )
% 0.21/0.50 => ( X
% 0.21/0.50 = ( inj__o @ ( p @ X ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(ap_tp,axiom,
% 0.21/0.50 ! [A: del,B: del,F: $i] :
% 0.21/0.50 ( ( mem @ F @ ( arr @ A @ B ) )
% 0.21/0.50 => ! [X: $i] :
% 0.21/0.50 ( ( mem @ X @ A )
% 0.21/0.50 => ( mem @ ( ap @ F @ X ) @ B ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(lam_tp,axiom,
% 0.21/0.50 ! [A: del,B: del,F: $i > $i] :
% 0.21/0.50 ( ! [X: $i] :
% 0.21/0.50 ( ( mem @ X @ A )
% 0.21/0.50 => ( mem @ ( F @ X ) @ B ) )
% 0.21/0.50 => ( mem @ ( lam @ A @ F ) @ ( arr @ A @ B ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(funcext,axiom,
% 0.21/0.50 ! [A: del,B: del,F: $i] :
% 0.21/0.50 ( ( mem @ F @ ( arr @ A @ B ) )
% 0.21/0.50 => ! [G: $i] :
% 0.21/0.50 ( ( mem @ G @ ( arr @ A @ B ) )
% 0.21/0.50 => ( ! [X: $i] :
% 0.21/0.50 ( ( mem @ X @ A )
% 0.21/0.50 => ( ( ap @ F @ X )
% 0.21/0.50 = ( ap @ G @ X ) ) )
% 0.21/0.50 => ( F = G ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(beta,axiom,
% 0.21/0.50 ! [A: del,F: $i > $i,X: $i] :
% 0.21/0.50 ( ( mem @ X @ A )
% 0.21/0.50 => ( ( ap @ ( lam @ A @ F ) @ X )
% 0.21/0.50 = ( F @ X ) ) ) ).
% 0.21/0.50
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 thf(tp_c_2Ebool_2ET,type,
% 0.21/0.50 c_2Ebool_2ET: $i ).
% 0.21/0.50
% 0.21/0.50 thf(mem_c_2Ebool_2ET,axiom,
% 0.21/0.50 mem @ c_2Ebool_2ET @ bool ).
% 0.21/0.50
% 0.21/0.50 thf(ax_true_p,axiom,
% 0.21/0.50 p @ c_2Ebool_2ET ).
% 0.21/0.50
% 0.21/0.50 thf(tp_ty_2Eextreal_2Eextreal,type,
% 0.21/0.50 ty_2Eextreal_2Eextreal: del ).
% 0.21/0.50
% 0.21/0.50 thf(stp_ty_2Eextreal_2Eextreal,type,
% 0.21/0.50 tp__ty_2Eextreal_2Eextreal: $tType ).
% 0.21/0.50
% 0.21/0.50 thf(stp_inj_ty_2Eextreal_2Eextreal,type,
% 0.21/0.50 inj__ty_2Eextreal_2Eextreal: tp__ty_2Eextreal_2Eextreal > $i ).
% 0.21/0.50
% 0.21/0.50 thf(stp_surj_ty_2Eextreal_2Eextreal,type,
% 0.21/0.50 surj__ty_2Eextreal_2Eextreal: $i > tp__ty_2Eextreal_2Eextreal ).
% 0.21/0.50
% 0.21/0.50 thf(stp_inj_surj_ty_2Eextreal_2Eextreal,axiom,
% 0.21/0.50 ! [X: tp__ty_2Eextreal_2Eextreal] :
% 0.21/0.50 ( ( surj__ty_2Eextreal_2Eextreal @ ( inj__ty_2Eextreal_2Eextreal @ X ) )
% 0.21/0.50 = X ) ).
% 0.21/0.50
% 0.21/0.50 thf(stp_inj_mem_ty_2Eextreal_2Eextreal,axiom,
% 0.21/0.50 ! [X: tp__ty_2Eextreal_2Eextreal] : ( mem @ ( inj__ty_2Eextreal_2Eextreal @ X ) @ ty_2Eextreal_2Eextreal ) ).
% 0.21/0.50
% 0.21/0.50 thf(stp_iso_mem_ty_2Eextreal_2Eextreal,axiom,
% 0.21/0.50 ! [X: $i] :
% 0.21/0.50 ( ( mem @ X @ ty_2Eextreal_2Eextreal )
% 0.21/0.50 => ( X
% 0.21/0.50 = ( inj__ty_2Eextreal_2Eextreal @ ( surj__ty_2Eextreal_2Eextreal @ X ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(tp_c_2Eextreal_2Eextreal__le,type,
% 0.21/0.50 c_2Eextreal_2Eextreal__le: $i ).
% 0.21/0.50
% 0.21/0.50 thf(mem_c_2Eextreal_2Eextreal__le,axiom,
% 0.21/0.50 mem @ c_2Eextreal_2Eextreal__le @ ( arr @ ty_2Eextreal_2Eextreal @ ( arr @ ty_2Eextreal_2Eextreal @ bool ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(tp_c_2Ebool_2ECOND,type,
% 0.21/0.50 c_2Ebool_2ECOND: del > $i ).
% 0.21/0.50
% 0.21/0.50 thf(mem_c_2Ebool_2ECOND,axiom,
% 0.21/0.50 ! [A_27a: del] : ( mem @ ( c_2Ebool_2ECOND @ A_27a ) @ ( arr @ bool @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(tp_c_2Eextreal_2Eextreal__max,type,
% 0.21/0.50 c_2Eextreal_2Eextreal__max: $i ).
% 0.21/0.50
% 0.21/0.50 thf(mem_c_2Eextreal_2Eextreal__max,axiom,
% 0.21/0.50 mem @ c_2Eextreal_2Eextreal__max @ ( arr @ ty_2Eextreal_2Eextreal @ ( arr @ ty_2Eextreal_2Eextreal @ ty_2Eextreal_2Eextreal ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(stp_fo_c_2Eextreal_2Eextreal__max,type,
% 0.21/0.50 fo__c_2Eextreal_2Eextreal__max: tp__ty_2Eextreal_2Eextreal > tp__ty_2Eextreal_2Eextreal > tp__ty_2Eextreal_2Eextreal ).
% 0.21/0.50
% 0.21/0.50 thf(stp_eq_fo_c_2Eextreal_2Eextreal__max,axiom,
% 0.21/0.50 ! [X0: tp__ty_2Eextreal_2Eextreal,X1: tp__ty_2Eextreal_2Eextreal] :
% 0.21/0.50 ( ( inj__ty_2Eextreal_2Eextreal @ ( fo__c_2Eextreal_2Eextreal__max @ X0 @ X1 ) )
% 0.21/0.50 = ( ap @ ( ap @ c_2Eextreal_2Eextreal__max @ ( inj__ty_2Eextreal_2Eextreal @ X0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X1 ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(tp_c_2Ebool_2EF,type,
% 0.21/0.50 c_2Ebool_2EF: $i ).
% 0.21/0.50
% 0.21/0.50 thf(mem_c_2Ebool_2EF,axiom,
% 0.21/0.50 mem @ c_2Ebool_2EF @ bool ).
% 0.21/0.50
% 0.21/0.50 thf(ax_false_p,axiom,
% 0.21/0.50 ~ ( p @ c_2Ebool_2EF ) ).
% 0.21/0.50
% 0.21/0.50 thf(tp_c_2Emin_2E_3D_3D_3E,type,
% 0.21/0.50 c_2Emin_2E_3D_3D_3E: $i ).
% 0.21/0.50
% 0.21/0.50 thf(mem_c_2Emin_2E_3D_3D_3E,axiom,
% 0.21/0.50 mem @ c_2Emin_2E_3D_3D_3E @ ( arr @ bool @ ( arr @ bool @ bool ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(ax_imp_p,axiom,
% 0.21/0.50 ! [Q: $i] :
% 0.21/0.50 ( ( mem @ Q @ bool )
% 0.21/0.50 => ! [R: $i] :
% 0.21/0.50 ( ( mem @ R @ bool )
% 0.21/0.50 => ( ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ Q ) @ R ) )
% 0.21/0.50 <=> ( ( p @ Q )
% 0.21/0.50 => ( p @ R ) ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(tp_c_2Ebool_2E_5C_2F,type,
% 0.21/0.50 c_2Ebool_2E_5C_2F: $i ).
% 0.21/0.50
% 0.21/0.50 thf(mem_c_2Ebool_2E_5C_2F,axiom,
% 0.21/0.50 mem @ c_2Ebool_2E_5C_2F @ ( arr @ bool @ ( arr @ bool @ bool ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(ax_or_p,axiom,
% 0.21/0.50 ! [Q: $i] :
% 0.21/0.50 ( ( mem @ Q @ bool )
% 0.21/0.50 => ! [R: $i] :
% 0.21/0.50 ( ( mem @ R @ bool )
% 0.21/0.50 => ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ Q ) @ R ) )
% 0.21/0.50 <=> ( ( p @ Q )
% 0.21/0.50 | ( p @ R ) ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(tp_c_2Ebool_2E_2F_5C,type,
% 0.21/0.50 c_2Ebool_2E_2F_5C: $i ).
% 0.21/0.50
% 0.21/0.50 thf(mem_c_2Ebool_2E_2F_5C,axiom,
% 0.21/0.50 mem @ c_2Ebool_2E_2F_5C @ ( arr @ bool @ ( arr @ bool @ bool ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(ax_and_p,axiom,
% 0.21/0.50 ! [Q: $i] :
% 0.21/0.50 ( ( mem @ Q @ bool )
% 0.21/0.50 => ! [R: $i] :
% 0.21/0.50 ( ( mem @ R @ bool )
% 0.21/0.50 => ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ Q ) @ R ) )
% 0.21/0.50 <=> ( ( p @ Q )
% 0.21/0.50 & ( p @ R ) ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(tp_c_2Ebool_2E_7E,type,
% 0.21/0.50 c_2Ebool_2E_7E: $i ).
% 0.21/0.50
% 0.21/0.50 thf(mem_c_2Ebool_2E_7E,axiom,
% 0.21/0.50 mem @ c_2Ebool_2E_7E @ ( arr @ bool @ bool ) ).
% 0.21/0.50
% 0.21/0.50 thf(ax_neg_p,axiom,
% 0.21/0.50 ! [Q: $i] :
% 0.21/0.50 ( ( mem @ Q @ bool )
% 0.21/0.50 => ( ( p @ ( ap @ c_2Ebool_2E_7E @ Q ) )
% 0.21/0.50 <=> ~ ( p @ Q ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(tp_c_2Emin_2E_3D,type,
% 0.21/0.50 c_2Emin_2E_3D: del > $i ).
% 0.21/0.50
% 0.21/0.50 thf(mem_c_2Emin_2E_3D,axiom,
% 0.21/0.50 ! [A_27a: del] : ( mem @ ( c_2Emin_2E_3D @ A_27a ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(ax_eq_p,axiom,
% 0.21/0.50 ! [A: del,X: $i] :
% 0.21/0.50 ( ( mem @ X @ A )
% 0.21/0.50 => ! [Y: $i] :
% 0.21/0.50 ( ( mem @ Y @ A )
% 0.21/0.50 => ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ X ) @ Y ) )
% 0.21/0.50 <=> ( X = Y ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(tp_c_2Ebool_2E_21,type,
% 0.21/0.50 c_2Ebool_2E_21: del > $i ).
% 0.21/0.50
% 0.21/0.50 thf(mem_c_2Ebool_2E_21,axiom,
% 0.21/0.50 ! [A_27a: del] : ( mem @ ( c_2Ebool_2E_21 @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(ax_all_p,axiom,
% 0.21/0.50 ! [A: del,Q: $i] :
% 0.21/0.50 ( ( mem @ Q @ ( arr @ A @ bool ) )
% 0.21/0.50 => ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ A ) @ Q ) )
% 0.21/0.50 <=> ! [X: $i] :
% 0.21/0.50 ( ( mem @ X @ A )
% 0.21/0.50 => ( p @ ( ap @ Q @ X ) ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(conj_thm_2Ebool_2ETRUTH,axiom,
% 0.21/0.50 $true ).
% 0.21/0.50
% 0.21/0.50 thf(conj_thm_2Ebool_2EIMP__ANTISYM__AX,axiom,
% 0.21/0.50 ! [V0t1: $i] :
% 0.21/0.50 ( ( mem @ V0t1 @ bool )
% 0.21/0.50 => ! [V1t2: $i] :
% 0.21/0.50 ( ( mem @ V1t2 @ bool )
% 0.21/0.50 => ( ( ( p @ V0t1 )
% 0.21/0.50 => ( p @ V1t2 ) )
% 0.21/0.50 => ( ( ( p @ V1t2 )
% 0.21/0.50 => ( p @ V0t1 ) )
% 0.21/0.50 => ( ( p @ V0t1 )
% 0.21/0.50 <=> ( p @ V1t2 ) ) ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(conj_thm_2Ebool_2EFALSITY,axiom,
% 0.21/0.50 ! [V0t: $i] :
% 0.21/0.50 ( ( mem @ V0t @ bool )
% 0.21/0.50 => ( $false
% 0.21/0.50 => ( p @ V0t ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(conj_thm_2Ebool_2EEXCLUDED__MIDDLE,axiom,
% 0.21/0.50 ! [V0t: $i] :
% 0.21/0.50 ( ( mem @ V0t @ bool )
% 0.21/0.50 => ( ( p @ V0t )
% 0.21/0.50 | ~ ( p @ V0t ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(conj_thm_2Ebool_2EIMP__F,axiom,
% 0.21/0.50 ! [V0t: $i] :
% 0.21/0.50 ( ( mem @ V0t @ bool )
% 0.21/0.50 => ( ( ( p @ V0t )
% 0.21/0.50 => $false )
% 0.21/0.50 => ~ ( p @ V0t ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(conj_thm_2Ebool_2EF__IMP,axiom,
% 0.21/0.50 ! [V0t: $i] :
% 0.21/0.50 ( ( mem @ V0t @ bool )
% 0.21/0.50 => ( ~ ( p @ V0t )
% 0.21/0.50 => ( ( p @ V0t )
% 0.21/0.50 => $false ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(conj_thm_2Ebool_2EIMP__CLAUSES,axiom,
% 0.21/0.50 ! [V0t: $i] :
% 0.21/0.50 ( ( mem @ V0t @ bool )
% 0.21/0.50 => ( ( ( $true
% 0.21/0.50 => ( p @ V0t ) )
% 0.21/0.50 <=> ( p @ V0t ) )
% 0.21/0.50 & ( ( ( p @ V0t )
% 0.21/0.50 => $true )
% 0.21/0.50 <=> $true )
% 0.21/0.50 & ( ( $false
% 0.21/0.50 => ( p @ V0t ) )
% 0.21/0.50 <=> $true )
% 0.21/0.50 & ( ( ( p @ V0t )
% 0.21/0.50 => ( p @ V0t ) )
% 0.21/0.50 <=> $true )
% 0.21/0.50 & ( ( ( p @ V0t )
% 0.21/0.50 => $false )
% 0.21/0.50 <=> ~ ( p @ V0t ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(conj_thm_2Ebool_2ENOT__CLAUSES,axiom,
% 0.21/0.50 ( ! [V0t: $i] :
% 0.21/0.50 ( ( mem @ V0t @ bool )
% 0.21/0.50 => ( ~ ~ ( p @ V0t )
% 0.21/0.50 <=> ( p @ V0t ) ) )
% 0.21/0.50 & ( ~ $true
% 0.21/0.50 <=> $false )
% 0.21/0.50 & ( ~ $false
% 0.21/0.50 <=> $true ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(conj_thm_2Ebool_2EEQ__SYM__EQ,axiom,
% 0.21/0.50 ! [A_27a: del,V0x: $i] :
% 0.21/0.50 ( ( mem @ V0x @ A_27a )
% 0.21/0.50 => ! [V1y: $i] :
% 0.21/0.50 ( ( mem @ V1y @ A_27a )
% 0.21/0.50 => ( ( V0x = V1y )
% 0.21/0.50 <=> ( V1y = V0x ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(conj_thm_2Ebool_2EEQ__CLAUSES,axiom,
% 0.21/0.50 ! [V0t: $i] :
% 0.21/0.50 ( ( mem @ V0t @ bool )
% 0.21/0.50 => ( ( ( $true
% 0.21/0.50 <=> ( p @ V0t ) )
% 0.21/0.50 <=> ( p @ V0t ) )
% 0.21/0.50 & ( ( ( p @ V0t )
% 0.21/0.50 <=> $true )
% 0.21/0.50 <=> ( p @ V0t ) )
% 0.21/0.50 & ( ( $false
% 0.21/0.50 <=> ( p @ V0t ) )
% 0.21/0.50 <=> ~ ( p @ V0t ) )
% 0.21/0.50 & ( ( ( p @ V0t )
% 0.21/0.50 <=> $false )
% 0.21/0.50 <=> ~ ( p @ V0t ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(conj_thm_2Ebool_2ECOND__CLAUSES,axiom,
% 0.21/0.50 ! [A_27a: del,V0t1: $i] :
% 0.21/0.50 ( ( mem @ V0t1 @ A_27a )
% 0.21/0.50 => ! [V1t2: $i] :
% 0.21/0.50 ( ( mem @ V1t2 @ A_27a )
% 0.21/0.50 => ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ c_2Ebool_2ET ) @ V0t1 ) @ V1t2 )
% 0.21/0.50 = V0t1 )
% 0.21/0.50 & ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ c_2Ebool_2EF ) @ V0t1 ) @ V1t2 )
% 0.21/0.50 = V1t2 ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(conj_thm_2Ebool_2EDISJ__ASSOC,axiom,
% 0.21/0.50 ! [V0A: $i] :
% 0.21/0.50 ( ( mem @ V0A @ bool )
% 0.21/0.50 => ! [V1B: $i] :
% 0.21/0.50 ( ( mem @ V1B @ bool )
% 0.21/0.50 => ! [V2C: $i] :
% 0.21/0.50 ( ( mem @ V2C @ bool )
% 0.21/0.50 => ( ( ( p @ V0A )
% 0.21/0.50 | ( p @ V1B )
% 0.21/0.50 | ( p @ V2C ) )
% 0.21/0.50 <=> ( ( p @ V0A )
% 0.21/0.50 | ( p @ V1B )
% 0.21/0.50 | ( p @ V2C ) ) ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(conj_thm_2Ebool_2EDISJ__SYM,axiom,
% 0.21/0.50 ! [V0A: $i] :
% 0.21/0.50 ( ( mem @ V0A @ bool )
% 0.21/0.50 => ! [V1B: $i] :
% 0.21/0.50 ( ( mem @ V1B @ bool )
% 0.21/0.50 => ( ( ( p @ V0A )
% 0.21/0.50 | ( p @ V1B ) )
% 0.21/0.50 <=> ( ( p @ V1B )
% 0.21/0.50 | ( p @ V0A ) ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(conj_thm_2Ebool_2EDE__MORGAN__THM,axiom,
% 0.21/0.50 ! [V0A: $i] :
% 0.21/0.50 ( ( mem @ V0A @ bool )
% 0.21/0.50 => ! [V1B: $i] :
% 0.21/0.50 ( ( mem @ V1B @ bool )
% 0.21/0.50 => ( ( ~ ( ( p @ V0A )
% 0.21/0.50 & ( p @ V1B ) )
% 0.21/0.50 <=> ( ~ ( p @ V0A )
% 0.21/0.50 | ~ ( p @ V1B ) ) )
% 0.21/0.50 & ( ~ ( ( p @ V0A )
% 0.21/0.50 | ( p @ V1B ) )
% 0.21/0.50 <=> ( ~ ( p @ V0A )
% 0.21/0.50 & ~ ( p @ V1B ) ) ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(conj_thm_2Eextreal_2Ele__trans,axiom,
% 0.21/0.50 ! [V0x: tp__ty_2Eextreal_2Eextreal,V1y: tp__ty_2Eextreal_2Eextreal,V2z: tp__ty_2Eextreal_2Eextreal] :
% 0.21/0.50 ( ( ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ V0x ) ) @ ( inj__ty_2Eextreal_2Eextreal @ V1y ) ) )
% 0.21/0.50 & ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ V1y ) ) @ ( inj__ty_2Eextreal_2Eextreal @ V2z ) ) ) )
% 0.21/0.50 => ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ V0x ) ) @ ( inj__ty_2Eextreal_2Eextreal @ V2z ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(conj_thm_2Eextreal_2Ele__total,axiom,
% 0.21/0.50 ! [V0x: tp__ty_2Eextreal_2Eextreal,V1y: tp__ty_2Eextreal_2Eextreal] :
% 0.21/0.50 ( ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ V0x ) ) @ ( inj__ty_2Eextreal_2Eextreal @ V1y ) ) )
% 0.21/0.50 | ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ V1y ) ) @ ( inj__ty_2Eextreal_2Eextreal @ V0x ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(ax_thm_2Eextreal_2Eextreal__max__def,axiom,
% 0.21/0.50 ! [V0x: tp__ty_2Eextreal_2Eextreal,V1y: tp__ty_2Eextreal_2Eextreal] :
% 0.21/0.50 ( ( surj__ty_2Eextreal_2Eextreal @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__max @ ( inj__ty_2Eextreal_2Eextreal @ V0x ) ) @ ( inj__ty_2Eextreal_2Eextreal @ V1y ) ) )
% 0.21/0.50 = ( surj__ty_2Eextreal_2Eextreal @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Eextreal_2Eextreal ) @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ V0x ) ) @ ( inj__ty_2Eextreal_2Eextreal @ V1y ) ) ) @ ( inj__ty_2Eextreal_2Eextreal @ V1y ) ) @ ( inj__ty_2Eextreal_2Eextreal @ V0x ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(conj_thm_2Esat_2ENOT__NOT,axiom,
% 0.21/0.50 ! [V0t: $i] :
% 0.21/0.50 ( ( mem @ V0t @ bool )
% 0.21/0.50 => ( ~ ~ ( p @ V0t )
% 0.21/0.50 <=> ( p @ V0t ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(conj_thm_2Esat_2EAND__INV__IMP,axiom,
% 0.21/0.50 ! [V0A: $i] :
% 0.21/0.50 ( ( mem @ V0A @ bool )
% 0.21/0.50 => ( ( p @ V0A )
% 0.21/0.50 => ( ~ ( p @ V0A )
% 0.21/0.50 => $false ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(conj_thm_2Esat_2EOR__DUAL2,axiom,
% 0.21/0.50 ! [V0A: $i] :
% 0.21/0.50 ( ( mem @ V0A @ bool )
% 0.21/0.50 => ! [V1B: $i] :
% 0.21/0.50 ( ( mem @ V1B @ bool )
% 0.21/0.50 => ( ( ~ ( ( p @ V0A )
% 0.21/0.50 | ( p @ V1B ) )
% 0.21/0.50 => $false )
% 0.21/0.50 <=> ( ( ( p @ V0A )
% 0.21/0.50 => $false )
% 0.21/0.50 => ( ~ ( p @ V1B )
% 0.21/0.50 => $false ) ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(conj_thm_2Esat_2EOR__DUAL3,axiom,
% 0.21/0.50 ! [V0A: $i] :
% 0.21/0.50 ( ( mem @ V0A @ bool )
% 0.21/0.50 => ! [V1B: $i] :
% 0.21/0.50 ( ( mem @ V1B @ bool )
% 0.21/0.50 => ( ( ~ ( ~ ( p @ V0A )
% 0.21/0.50 | ( p @ V1B ) )
% 0.21/0.50 => $false )
% 0.21/0.50 <=> ( ( p @ V0A )
% 0.21/0.50 => ( ~ ( p @ V1B )
% 0.21/0.50 => $false ) ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(conj_thm_2Esat_2EAND__INV2,axiom,
% 0.21/0.50 ! [V0A: $i] :
% 0.21/0.50 ( ( mem @ V0A @ bool )
% 0.21/0.50 => ( ( ~ ( p @ V0A )
% 0.21/0.50 => $false )
% 0.21/0.50 => ( ( ( p @ V0A )
% 0.21/0.50 => $false )
% 0.21/0.50 => $false ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(conj_thm_2Esat_2Edc__eq,axiom,
% 0.21/0.50 ! [V0p: $i] :
% 0.21/0.50 ( ( mem @ V0p @ bool )
% 0.21/0.50 => ! [V1q: $i] :
% 0.21/0.50 ( ( mem @ V1q @ bool )
% 0.21/0.50 => ! [V2r: $i] :
% 0.21/0.50 ( ( mem @ V2r @ bool )
% 0.21/0.50 => ( ( ( p @ V0p )
% 0.21/0.50 <=> ( ( p @ V1q )
% 0.21/0.50 <=> ( p @ V2r ) ) )
% 0.21/0.50 <=> ( ( ( p @ V0p )
% 0.21/0.50 | ( p @ V1q )
% 0.21/0.50 | ( p @ V2r ) )
% 0.21/0.50 & ( ( p @ V0p )
% 0.21/0.50 | ~ ( p @ V2r )
% 0.21/0.50 | ~ ( p @ V1q ) )
% 0.21/0.50 & ( ( p @ V1q )
% 0.21/0.50 | ~ ( p @ V2r )
% 0.21/0.50 | ~ ( p @ V0p ) )
% 0.21/0.50 & ( ( p @ V2r )
% 0.21/0.50 | ~ ( p @ V1q )
% 0.21/0.50 | ~ ( p @ V0p ) ) ) ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(conj_thm_2Esat_2Edc__conj,axiom,
% 0.21/0.50 ! [V0p: $i] :
% 0.21/0.50 ( ( mem @ V0p @ bool )
% 0.21/0.50 => ! [V1q: $i] :
% 0.21/0.50 ( ( mem @ V1q @ bool )
% 0.21/0.50 => ! [V2r: $i] :
% 0.21/0.50 ( ( mem @ V2r @ bool )
% 0.21/0.50 => ( ( ( p @ V0p )
% 0.21/0.50 <=> ( ( p @ V1q )
% 0.21/0.50 & ( p @ V2r ) ) )
% 0.21/0.50 <=> ( ( ( p @ V0p )
% 0.21/0.50 | ~ ( p @ V1q )
% 0.21/0.50 | ~ ( p @ V2r ) )
% 0.21/0.50 & ( ( p @ V1q )
% 0.21/0.50 | ~ ( p @ V0p ) )
% 0.21/0.50 & ( ( p @ V2r )
% 0.21/0.50 | ~ ( p @ V0p ) ) ) ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(conj_thm_2Esat_2Edc__disj,axiom,
% 0.21/0.50 ! [V0p: $i] :
% 0.21/0.50 ( ( mem @ V0p @ bool )
% 0.21/0.50 => ! [V1q: $i] :
% 0.21/0.50 ( ( mem @ V1q @ bool )
% 0.21/0.50 => ! [V2r: $i] :
% 0.21/0.50 ( ( mem @ V2r @ bool )
% 0.21/0.50 => ( ( ( p @ V0p )
% 0.21/0.50 <=> ( ( p @ V1q )
% 0.21/0.50 | ( p @ V2r ) ) )
% 0.21/0.50 <=> ( ( ( p @ V0p )
% 0.21/0.50 | ~ ( p @ V1q ) )
% 0.21/0.50 & ( ( p @ V0p )
% 0.21/0.50 | ~ ( p @ V2r ) )
% 0.21/0.52 & ( ( p @ V1q )
% 0.21/0.52 | ( p @ V2r )
% 0.21/0.52 | ~ ( p @ V0p ) ) ) ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(conj_thm_2Esat_2Edc__imp,axiom,
% 0.21/0.52 ! [V0p: $i] :
% 0.21/0.52 ( ( mem @ V0p @ bool )
% 0.21/0.52 => ! [V1q: $i] :
% 0.21/0.52 ( ( mem @ V1q @ bool )
% 0.21/0.52 => ! [V2r: $i] :
% 0.21/0.52 ( ( mem @ V2r @ bool )
% 0.21/0.52 => ( ( ( p @ V0p )
% 0.21/0.52 <=> ( ( p @ V1q )
% 0.21/0.52 => ( p @ V2r ) ) )
% 0.21/0.52 <=> ( ( ( p @ V0p )
% 0.21/0.52 | ( p @ V1q ) )
% 0.21/0.52 & ( ( p @ V0p )
% 0.21/0.52 | ~ ( p @ V2r ) )
% 0.21/0.52 & ( ~ ( p @ V1q )
% 0.21/0.52 | ( p @ V2r )
% 0.21/0.52 | ~ ( p @ V0p ) ) ) ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(conj_thm_2Esat_2Edc__neg,axiom,
% 0.21/0.52 ! [V0p: $i] :
% 0.21/0.52 ( ( mem @ V0p @ bool )
% 0.21/0.52 => ! [V1q: $i] :
% 0.21/0.52 ( ( mem @ V1q @ bool )
% 0.21/0.52 => ( ( ( p @ V0p )
% 0.21/0.52 <=> ~ ( p @ V1q ) )
% 0.21/0.52 <=> ( ( ( p @ V0p )
% 0.21/0.52 | ( p @ V1q ) )
% 0.21/0.52 & ( ~ ( p @ V1q )
% 0.21/0.52 | ~ ( p @ V0p ) ) ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(conj_thm_2Eextreal_2Emax__le,conjecture,
% 0.21/0.52 ! [V0z: tp__ty_2Eextreal_2Eextreal,V1x: tp__ty_2Eextreal_2Eextreal,V2y: tp__ty_2Eextreal_2Eextreal] :
% 0.21/0.52 ( ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__max @ ( inj__ty_2Eextreal_2Eextreal @ V1x ) ) @ ( inj__ty_2Eextreal_2Eextreal @ V2y ) ) ) @ ( inj__ty_2Eextreal_2Eextreal @ V0z ) ) )
% 0.21/0.52 <=> ( ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ V1x ) ) @ ( inj__ty_2Eextreal_2Eextreal @ V0z ) ) )
% 0.21/0.52 & ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ V2y ) ) @ ( inj__ty_2Eextreal_2Eextreal @ V0z ) ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 %------------------------------------------------------------------------------
% 0.21/0.52 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.a6HA6ExNVV/cvc5---1.0.5_19323.p...
% 0.21/0.52 (declare-sort $$unsorted 0)
% 0.21/0.52 (declare-sort tptp.del 0)
% 0.21/0.52 (declare-fun tptp.bool () tptp.del)
% 0.21/0.52 (declare-fun tptp.ind () tptp.del)
% 0.21/0.52 (declare-fun tptp.arr (tptp.del tptp.del) tptp.del)
% 0.21/0.52 (declare-fun tptp.mem ($$unsorted tptp.del) Bool)
% 0.21/0.52 (declare-fun tptp.ap ($$unsorted $$unsorted) $$unsorted)
% 0.21/0.52 (declare-fun tptp.lam (tptp.del (-> $$unsorted $$unsorted)) $$unsorted)
% 0.21/0.52 (declare-fun tptp.p ($$unsorted) Bool)
% 0.21/0.52 (declare-fun tptp.inj__o (Bool) $$unsorted)
% 0.21/0.52 (assert (forall ((X Bool)) (= (@ tptp.p (@ tptp.inj__o X)) X)))
% 0.21/0.52 (assert (forall ((X Bool)) (@ (@ tptp.mem (@ tptp.inj__o X)) tptp.bool)))
% 0.21/0.52 (assert (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) tptp.bool) (= X (@ tptp.inj__o (@ tptp.p X))))))
% 0.21/0.52 (assert (forall ((A tptp.del) (B tptp.del) (F $$unsorted)) (=> (@ (@ tptp.mem F) (@ (@ tptp.arr A) B)) (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) A) (@ (@ tptp.mem (@ (@ tptp.ap F) X)) B))))))
% 0.21/0.52 (assert (forall ((A tptp.del) (B tptp.del) (F (-> $$unsorted $$unsorted))) (=> (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) A) (@ (@ tptp.mem (@ F X)) B))) (@ (@ tptp.mem (@ (@ tptp.lam A) F)) (@ (@ tptp.arr A) B)))))
% 0.21/0.52 (assert (forall ((A tptp.del) (B tptp.del) (F $$unsorted)) (=> (@ (@ tptp.mem F) (@ (@ tptp.arr A) B)) (forall ((G $$unsorted)) (=> (@ (@ tptp.mem G) (@ (@ tptp.arr A) B)) (=> (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) A) (= (@ (@ tptp.ap F) X) (@ (@ tptp.ap G) X)))) (= F G)))))))
% 0.21/0.52 (assert (forall ((A tptp.del) (F (-> $$unsorted $$unsorted)) (X $$unsorted)) (=> (@ (@ tptp.mem X) A) (= (@ (@ tptp.ap (@ (@ tptp.lam A) F)) X) (@ F X)))))
% 0.21/0.52 (declare-fun tptp.c_2Ebool_2ET () $$unsorted)
% 0.21/0.52 (assert (@ (@ tptp.mem tptp.c_2Ebool_2ET) tptp.bool))
% 0.21/0.52 (assert (@ tptp.p tptp.c_2Ebool_2ET))
% 0.21/0.52 (declare-fun tptp.ty_2Eextreal_2Eextreal () tptp.del)
% 0.21/0.52 (declare-sort tptp.tp__ty_2Eextreal_2Eextreal 0)
% 0.21/0.52 (declare-fun tptp.inj__ty_2Eextreal_2Eextreal (tptp.tp__ty_2Eextreal_2Eextreal) $$unsorted)
% 0.21/0.52 (declare-fun tptp.surj__ty_2Eextreal_2Eextreal ($$unsorted) tptp.tp__ty_2Eextreal_2Eextreal)
% 0.21/0.52 (assert (forall ((X tptp.tp__ty_2Eextreal_2Eextreal)) (= (@ tptp.surj__ty_2Eextreal_2Eextreal (@ tptp.inj__ty_2Eextreal_2Eextreal X)) X)))
% 0.21/0.52 (assert (forall ((X tptp.tp__ty_2Eextreal_2Eextreal)) (@ (@ tptp.mem (@ tptp.inj__ty_2Eextreal_2Eextreal X)) tptp.ty_2Eextreal_2Eextreal)))
% 0.21/0.52 (assert (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) tptp.ty_2Eextreal_2Eextreal) (= X (@ tptp.inj__ty_2Eextreal_2Eextreal (@ tptp.surj__ty_2Eextreal_2Eextreal X))))))
% 0.21/0.52 (declare-fun tptp.c_2Eextreal_2Eextreal__le () $$unsorted)
% 0.21/0.52 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Eextreal_2Eextreal))) (@ (@ tptp.mem tptp.c_2Eextreal_2Eextreal__le) (@ _let_1 (@ _let_1 tptp.bool)))))
% 0.21/0.52 (declare-fun tptp.c_2Ebool_2ECOND (tptp.del) $$unsorted)
% 0.21/0.52 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Ebool_2ECOND A_27a)) (@ (@ tptp.arr tptp.bool) (@ _let_1 (@ _let_1 A_27a)))))))
% 0.21/0.52 (declare-fun tptp.c_2Eextreal_2Eextreal__max () $$unsorted)
% 0.21/0.52 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Eextreal_2Eextreal))) (@ (@ tptp.mem tptp.c_2Eextreal_2Eextreal__max) (@ _let_1 (@ _let_1 tptp.ty_2Eextreal_2Eextreal)))))
% 0.21/0.52 (declare-fun tptp.fo__c_2Eextreal_2Eextreal__max (tptp.tp__ty_2Eextreal_2Eextreal tptp.tp__ty_2Eextreal_2Eextreal) tptp.tp__ty_2Eextreal_2Eextreal)
% 0.21/0.52 (assert (forall ((X0 tptp.tp__ty_2Eextreal_2Eextreal) (X1 tptp.tp__ty_2Eextreal_2Eextreal)) (= (@ tptp.inj__ty_2Eextreal_2Eextreal (@ (@ tptp.fo__c_2Eextreal_2Eextreal__max X0) X1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eextreal_2Eextreal__max) (@ tptp.inj__ty_2Eextreal_2Eextreal X0))) (@ tptp.inj__ty_2Eextreal_2Eextreal X1)))))
% 0.21/0.52 (declare-fun tptp.c_2Ebool_2EF () $$unsorted)
% 0.21/0.52 (assert (@ (@ tptp.mem tptp.c_2Ebool_2EF) tptp.bool))
% 0.21/0.52 (assert (not (@ tptp.p tptp.c_2Ebool_2EF)))
% 0.21/0.52 (declare-fun tptp.c_2Emin_2E_3D_3D_3E () $$unsorted)
% 0.21/0.52 (assert (let ((_let_1 (@ tptp.arr tptp.bool))) (@ (@ tptp.mem tptp.c_2Emin_2E_3D_3D_3E) (@ _let_1 (@ _let_1 tptp.bool)))))
% 0.21/0.52 (assert (forall ((Q $$unsorted)) (=> (@ (@ tptp.mem Q) tptp.bool) (forall ((R $$unsorted)) (=> (@ (@ tptp.mem R) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) Q)) R)) (=> (@ tptp.p Q) (@ tptp.p R))))))))
% 0.21/0.52 (declare-fun tptp.c_2Ebool_2E_5C_2F () $$unsorted)
% 0.21/0.52 (assert (let ((_let_1 (@ tptp.arr tptp.bool))) (@ (@ tptp.mem tptp.c_2Ebool_2E_5C_2F) (@ _let_1 (@ _let_1 tptp.bool)))))
% 0.21/0.52 (assert (forall ((Q $$unsorted)) (=> (@ (@ tptp.mem Q) tptp.bool) (forall ((R $$unsorted)) (=> (@ (@ tptp.mem R) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_5C_2F) Q)) R)) (or (@ tptp.p Q) (@ tptp.p R))))))))
% 0.21/0.52 (declare-fun tptp.c_2Ebool_2E_2F_5C () $$unsorted)
% 0.21/0.52 (assert (let ((_let_1 (@ tptp.arr tptp.bool))) (@ (@ tptp.mem tptp.c_2Ebool_2E_2F_5C) (@ _let_1 (@ _let_1 tptp.bool)))))
% 0.21/0.52 (assert (forall ((Q $$unsorted)) (=> (@ (@ tptp.mem Q) tptp.bool) (forall ((R $$unsorted)) (=> (@ (@ tptp.mem R) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) Q)) R)) (and (@ tptp.p Q) (@ tptp.p R))))))))
% 0.21/0.52 (declare-fun tptp.c_2Ebool_2E_7E () $$unsorted)
% 0.21/0.52 (assert (@ (@ tptp.mem tptp.c_2Ebool_2E_7E) (@ (@ tptp.arr tptp.bool) tptp.bool)))
% 0.21/0.52 (assert (forall ((Q $$unsorted)) (=> (@ (@ tptp.mem Q) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap tptp.c_2Ebool_2E_7E) Q)) (not (@ tptp.p Q))))))
% 0.21/0.52 (declare-fun tptp.c_2Emin_2E_3D (tptp.del) $$unsorted)
% 0.21/0.52 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Emin_2E_3D A_27a)) (@ _let_1 (@ _let_1 tptp.bool))))))
% 0.21/0.52 (assert (forall ((A tptp.del) (X $$unsorted)) (=> (@ (@ tptp.mem X) A) (forall ((Y $$unsorted)) (=> (@ (@ tptp.mem Y) A) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A)) X)) Y)) (= X Y)))))))
% 0.21/0.52 (declare-fun tptp.c_2Ebool_2E_21 (tptp.del) $$unsorted)
% 0.21/0.52 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Ebool_2E_21 A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool))))
% 0.21/0.52 (assert (forall ((A tptp.del) (Q $$unsorted)) (=> (@ (@ tptp.mem Q) (@ (@ tptp.arr A) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A)) Q)) (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) A) (@ tptp.p (@ (@ tptp.ap Q) X))))))))
% 0.21/0.52 (assert true)
% 0.21/0.52 (assert (forall ((V0t1 $$unsorted)) (=> (@ (@ tptp.mem V0t1) tptp.bool) (forall ((V1t2 $$unsorted)) (let ((_let_1 (@ tptp.p V1t2))) (let ((_let_2 (@ tptp.p V0t1))) (=> (@ (@ tptp.mem V1t2) tptp.bool) (=> (=> _let_2 _let_1) (=> (=> _let_1 _let_2) (= _let_2 _let_1))))))))))
% 0.21/0.52 (assert (forall ((V0t $$unsorted)) (=> (@ (@ tptp.mem V0t) tptp.bool) (=> false (@ tptp.p V0t)))))
% 0.21/0.52 (assert (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (or _let_1 (not _let_1))))))
% 0.21/0.52 (assert (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (=> (=> _let_1 false) (not _let_1))))))
% 0.21/0.52 (assert (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (=> (not _let_1) (=> _let_1 false))))))
% 0.21/0.52 (assert (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (and (= (=> true _let_1) _let_1) (= (=> _let_1 true) true) (= (=> false _let_1) true) (= (=> _let_1 _let_1) true) (= (=> _let_1 false) (not _let_1)))))))
% 0.21/0.52 (assert (and (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (= (not (not _let_1)) _let_1)))) (= (not true) false) (= (not false) true)))
% 0.21/0.52 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1y $$unsorted)) (=> (@ (@ tptp.mem V1y) A_27a) (= (= V0x V1y) (= V1y V0x)))))))
% 0.21/0.52 (assert (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (let ((_let_2 (not _let_1))) (=> (@ (@ tptp.mem V0t) tptp.bool) (and (= (= true _let_1) _let_1) (= (= _let_1 true) _let_1) (= (= false _let_1) _let_2) (= (= _let_1 false) _let_2)))))))
% 0.21/0.52 (assert (forall ((A_27a tptp.del) (V0t1 $$unsorted)) (=> (@ (@ tptp.mem V0t1) A_27a) (forall ((V1t2 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Ebool_2ECOND A_27a)))) (=> (@ (@ tptp.mem V1t2) A_27a) (and (= (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 tptp.c_2Ebool_2ET)) V0t1)) V1t2) V0t1) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 tptp.c_2Ebool_2EF)) V0t1)) V1t2) V1t2))))))))
% 0.21/0.52 (assert (forall ((V0A $$unsorted)) (=> (@ (@ tptp.mem V0A) tptp.bool) (forall ((V1B $$unsorted)) (=> (@ (@ tptp.mem V1B) tptp.bool) (forall ((V2C $$unsorted)) (let ((_let_1 (or (@ tptp.p V0A) (@ tptp.p V1B) (@ tptp.p V2C)))) (=> (@ (@ tptp.mem V2C) tptp.bool) (= _let_1 _let_1)))))))))
% 0.21/0.52 (assert (forall ((V0A $$unsorted)) (=> (@ (@ tptp.mem V0A) tptp.bool) (forall ((V1B $$unsorted)) (let ((_let_1 (@ tptp.p V0A))) (let ((_let_2 (@ tptp.p V1B))) (=> (@ (@ tptp.mem V1B) tptp.bool) (= (or _let_1 _let_2) (or _let_2 _let_1)))))))))
% 0.21/0.52 (assert (forall ((V0A $$unsorted)) (=> (@ (@ tptp.mem V0A) tptp.bool) (forall ((V1B $$unsorted)) (let ((_let_1 (@ tptp.p V1B))) (let ((_let_2 (not _let_1))) (let ((_let_3 (@ tptp.p V0A))) (let ((_let_4 (not _let_3))) (=> (@ (@ tptp.mem V1B) tptp.bool) (and (= (not (and _let_3 _let_1)) (or _let_4 _let_2)) (= (not (or _let_3 _let_1)) (and _let_4 _let_2))))))))))))
% 0.21/0.52 (assert (forall ((V0x tptp.tp__ty_2Eextreal_2Eextreal) (V1y tptp.tp__ty_2Eextreal_2Eextreal) (V2z tptp.tp__ty_2Eextreal_2Eextreal)) (let ((_let_1 (@ tptp.inj__ty_2Eextreal_2Eextreal V2z))) (let ((_let_2 (@ tptp.ap tptp.c_2Eextreal_2Eextreal__le))) (let ((_let_3 (@ tptp.ap (@ _let_2 (@ tptp.inj__ty_2Eextreal_2Eextreal V0x))))) (let ((_let_4 (@ tptp.inj__ty_2Eextreal_2Eextreal V1y))) (=> (and (@ tptp.p (@ _let_3 _let_4)) (@ tptp.p (@ (@ tptp.ap (@ _let_2 _let_4)) _let_1))) (@ tptp.p (@ _let_3 _let_1)))))))))
% 0.21/0.52 (assert (forall ((V0x tptp.tp__ty_2Eextreal_2Eextreal) (V1y tptp.tp__ty_2Eextreal_2Eextreal)) (let ((_let_1 (@ tptp.inj__ty_2Eextreal_2Eextreal V0x))) (let ((_let_2 (@ tptp.inj__ty_2Eextreal_2Eextreal V1y))) (let ((_let_3 (@ tptp.ap tptp.c_2Eextreal_2Eextreal__le))) (or (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))
% 0.21/0.52 (assert (forall ((V0x tptp.tp__ty_2Eextreal_2Eextreal) (V1y tptp.tp__ty_2Eextreal_2Eextreal)) (let ((_let_1 (@ tptp.inj__ty_2Eextreal_2Eextreal V0x))) (let ((_let_2 (@ tptp.inj__ty_2Eextreal_2Eextreal V1y))) (= (@ tptp.surj__ty_2Eextreal_2Eextreal (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eextreal_2Eextreal__max) _let_1)) _let_2)) (@ tptp.surj__ty_2Eextreal_2Eextreal (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Eextreal_2Eextreal)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eextreal_2Eextreal__le) _let_1)) _let_2))) _let_2)) _let_1)))))))
% 4.01/4.23 (assert (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (= (not (not _let_1)) _let_1)))))
% 4.01/4.23 (assert (forall ((V0A $$unsorted)) (let ((_let_1 (@ tptp.p V0A))) (=> (@ (@ tptp.mem V0A) tptp.bool) (=> _let_1 (=> (not _let_1) false))))))
% 4.01/4.23 (assert (forall ((V0A $$unsorted)) (=> (@ (@ tptp.mem V0A) tptp.bool) (forall ((V1B $$unsorted)) (let ((_let_1 (@ tptp.p V1B))) (let ((_let_2 (@ tptp.p V0A))) (=> (@ (@ tptp.mem V1B) tptp.bool) (= (=> (not (or _let_2 _let_1)) false) (=> (=> _let_2 false) (=> (not _let_1) false))))))))))
% 4.01/4.23 (assert (forall ((V0A $$unsorted)) (=> (@ (@ tptp.mem V0A) tptp.bool) (forall ((V1B $$unsorted)) (let ((_let_1 (@ tptp.p V1B))) (let ((_let_2 (@ tptp.p V0A))) (=> (@ (@ tptp.mem V1B) tptp.bool) (= (=> (not (or (not _let_2) _let_1)) false) (=> _let_2 (=> (not _let_1) false))))))))))
% 4.01/4.23 (assert (forall ((V0A $$unsorted)) (let ((_let_1 (@ tptp.p V0A))) (=> (@ (@ tptp.mem V0A) tptp.bool) (=> (=> (not _let_1) false) (=> (=> _let_1 false) false))))))
% 4.01/4.23 (assert (forall ((V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) tptp.bool) (forall ((V1q $$unsorted)) (=> (@ (@ tptp.mem V1q) tptp.bool) (forall ((V2r $$unsorted)) (let ((_let_1 (@ tptp.p V0p))) (let ((_let_2 (not _let_1))) (let ((_let_3 (@ tptp.p V1q))) (let ((_let_4 (not _let_3))) (let ((_let_5 (@ tptp.p V2r))) (let ((_let_6 (not _let_5))) (=> (@ (@ tptp.mem V2r) tptp.bool) (= (= _let_1 (= _let_3 _let_5)) (and (or _let_1 _let_3 _let_5) (or _let_1 _let_6 _let_4) (or _let_3 _let_6 _let_2) (or _let_5 _let_4 _let_2))))))))))))))))
% 4.01/4.23 (assert (forall ((V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) tptp.bool) (forall ((V1q $$unsorted)) (=> (@ (@ tptp.mem V1q) tptp.bool) (forall ((V2r $$unsorted)) (let ((_let_1 (@ tptp.p V0p))) (let ((_let_2 (not _let_1))) (let ((_let_3 (@ tptp.p V2r))) (let ((_let_4 (@ tptp.p V1q))) (=> (@ (@ tptp.mem V2r) tptp.bool) (= (= _let_1 (and _let_4 _let_3)) (and (or _let_1 (not _let_4) (not _let_3)) (or _let_4 _let_2) (or _let_3 _let_2))))))))))))))
% 4.01/4.23 (assert (forall ((V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) tptp.bool) (forall ((V1q $$unsorted)) (=> (@ (@ tptp.mem V1q) tptp.bool) (forall ((V2r $$unsorted)) (let ((_let_1 (@ tptp.p V0p))) (let ((_let_2 (@ tptp.p V2r))) (let ((_let_3 (@ tptp.p V1q))) (=> (@ (@ tptp.mem V2r) tptp.bool) (= (= _let_1 (or _let_3 _let_2)) (and (or _let_1 (not _let_3)) (or _let_1 (not _let_2)) (or _let_3 _let_2 (not _let_1))))))))))))))
% 4.01/4.23 (assert (forall ((V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) tptp.bool) (forall ((V1q $$unsorted)) (=> (@ (@ tptp.mem V1q) tptp.bool) (forall ((V2r $$unsorted)) (let ((_let_1 (@ tptp.p V0p))) (let ((_let_2 (@ tptp.p V2r))) (let ((_let_3 (@ tptp.p V1q))) (=> (@ (@ tptp.mem V2r) tptp.bool) (= (= _let_1 (=> _let_3 _let_2)) (and (or _let_1 _let_3) (or _let_1 (not _let_2)) (or (not _let_3) _let_2 (not _let_1))))))))))))))
% 4.01/4.23 (assert (forall ((V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) tptp.bool) (forall ((V1q $$unsorted)) (let ((_let_1 (@ tptp.p V0p))) (let ((_let_2 (@ tptp.p V1q))) (let ((_let_3 (not _let_2))) (=> (@ (@ tptp.mem V1q) tptp.bool) (= (= _let_1 _let_3) (and (or _let_1 _let_2) (or _let_3 (not _let_1))))))))))))
% 4.01/4.23 (assert (not (forall ((V0z tptp.tp__ty_2Eextreal_2Eextreal) (V1x tptp.tp__ty_2Eextreal_2Eextreal) (V2y tptp.tp__ty_2Eextreal_2Eextreal)) (let ((_let_1 (@ tptp.inj__ty_2Eextreal_2Eextreal V0z))) (let ((_let_2 (@ tptp.inj__ty_2Eextreal_2Eextreal V2y))) (let ((_let_3 (@ tptp.ap tptp.c_2Eextreal_2Eextreal__le))) (let ((_let_4 (@ tptp.inj__ty_2Eextreal_2Eextreal V1x))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eextreal_2Eextreal__max) _let_4)) _let_2))) _let_1)) (and (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_4)) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))))
% 4.01/4.23 (set-info :filename cvc5---1.0.5_19323)
% 4.01/4.23 (check-sat-assuming ( true ))
% 4.01/4.23 ------- get file name : TPTP file name is ITP021^2
% 4.01/4.23 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_19323.smt2...
% 4.01/4.23 --- Run --ho-elim --full-saturate-quant at 10...
% 4.01/4.23 % SZS status Theorem for ITP021^2
% 4.01/4.23 % SZS output start Proof for ITP021^2
% 4.07/4.25 (
% 4.07/4.25 (let ((_let_1 (not (forall ((V0z tptp.tp__ty_2Eextreal_2Eextreal) (V1x tptp.tp__ty_2Eextreal_2Eextreal) (V2y tptp.tp__ty_2Eextreal_2Eextreal)) (let ((_let_1 (@ tptp.inj__ty_2Eextreal_2Eextreal V0z))) (let ((_let_2 (@ tptp.inj__ty_2Eextreal_2Eextreal V2y))) (let ((_let_3 (@ tptp.ap tptp.c_2Eextreal_2Eextreal__le))) (let ((_let_4 (@ tptp.inj__ty_2Eextreal_2Eextreal V1x))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eextreal_2Eextreal__max) _let_4)) _let_2))) _let_1)) (and (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_4)) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))))) (let ((_let_2 (forall ((V0x tptp.tp__ty_2Eextreal_2Eextreal) (V1y tptp.tp__ty_2Eextreal_2Eextreal)) (let ((_let_1 (@ tptp.inj__ty_2Eextreal_2Eextreal V0x))) (let ((_let_2 (@ tptp.inj__ty_2Eextreal_2Eextreal V1y))) (= (@ tptp.surj__ty_2Eextreal_2Eextreal (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eextreal_2Eextreal__max) _let_1)) _let_2)) (@ tptp.surj__ty_2Eextreal_2Eextreal (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Eextreal_2Eextreal)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eextreal_2Eextreal__le) _let_1)) _let_2))) _let_2)) _let_1)))))))) (let ((_let_3 (forall ((V0x tptp.tp__ty_2Eextreal_2Eextreal) (V1y tptp.tp__ty_2Eextreal_2Eextreal)) (let ((_let_1 (@ tptp.inj__ty_2Eextreal_2Eextreal V0x))) (let ((_let_2 (@ tptp.inj__ty_2Eextreal_2Eextreal V1y))) (let ((_let_3 (@ tptp.ap tptp.c_2Eextreal_2Eextreal__le))) (or (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))) (let ((_let_4 (forall ((V0x tptp.tp__ty_2Eextreal_2Eextreal) (V1y tptp.tp__ty_2Eextreal_2Eextreal) (V2z tptp.tp__ty_2Eextreal_2Eextreal)) (let ((_let_1 (@ tptp.inj__ty_2Eextreal_2Eextreal V2z))) (let ((_let_2 (@ tptp.ap tptp.c_2Eextreal_2Eextreal__le))) (let ((_let_3 (@ tptp.ap (@ _let_2 (@ tptp.inj__ty_2Eextreal_2Eextreal V0x))))) (let ((_let_4 (@ tptp.inj__ty_2Eextreal_2Eextreal V1y))) (=> (and (@ tptp.p (@ _let_3 _let_4)) (@ tptp.p (@ (@ tptp.ap (@ _let_2 _let_4)) _let_1))) (@ tptp.p (@ _let_3 _let_1)))))))))) (let ((_let_5 (forall ((A_27a tptp.del) (V0t1 $$unsorted)) (=> (@ (@ tptp.mem V0t1) A_27a) (forall ((V1t2 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Ebool_2ECOND A_27a)))) (=> (@ (@ tptp.mem V1t2) A_27a) (and (= (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 tptp.c_2Ebool_2ET)) V0t1)) V1t2) V0t1) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 tptp.c_2Ebool_2EF)) V0t1)) V1t2) V1t2))))))))) (let ((_let_6 (@ tptp.arr tptp.bool))) (let ((_let_7 (@ _let_6 tptp.bool))) (let ((_let_8 (@ _let_6 _let_7))) (let ((_let_9 (not (@ tptp.p tptp.c_2Ebool_2EF)))) (let ((_let_10 (@ (@ tptp.mem tptp.c_2Ebool_2EF) tptp.bool))) (let ((_let_11 (forall ((X0 tptp.tp__ty_2Eextreal_2Eextreal) (X1 tptp.tp__ty_2Eextreal_2Eextreal)) (= (@ tptp.inj__ty_2Eextreal_2Eextreal (@ (@ tptp.fo__c_2Eextreal_2Eextreal__max X0) X1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eextreal_2Eextreal__max) (@ tptp.inj__ty_2Eextreal_2Eextreal X0))) (@ tptp.inj__ty_2Eextreal_2Eextreal X1)))))) (let ((_let_12 (@ tptp.arr tptp.ty_2Eextreal_2Eextreal))) (let ((_let_13 (@ (@ tptp.mem tptp.c_2Eextreal_2Eextreal__max) (@ _let_12 (@ _let_12 tptp.ty_2Eextreal_2Eextreal))))) (let ((_let_14 (@ (@ tptp.mem tptp.c_2Eextreal_2Eextreal__le) (@ _let_12 (@ _let_12 tptp.bool))))) (let ((_let_15 (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) tptp.ty_2Eextreal_2Eextreal) (= X (@ tptp.inj__ty_2Eextreal_2Eextreal (@ tptp.surj__ty_2Eextreal_2Eextreal X))))))) (let ((_let_16 (forall ((X tptp.tp__ty_2Eextreal_2Eextreal)) (@ (@ tptp.mem (@ tptp.inj__ty_2Eextreal_2Eextreal X)) tptp.ty_2Eextreal_2Eextreal)))) (let ((_let_17 (forall ((X tptp.tp__ty_2Eextreal_2Eextreal)) (= (@ tptp.surj__ty_2Eextreal_2Eextreal (@ tptp.inj__ty_2Eextreal_2Eextreal X)) X)))) (let ((_let_18 (@ tptp.p tptp.c_2Ebool_2ET))) (let ((_let_19 (@ (@ tptp.mem tptp.c_2Ebool_2ET) tptp.bool))) (let ((_let_20 (forall ((A tptp.del) (B tptp.del) (F $$unsorted)) (=> (@ (@ tptp.mem F) (@ (@ tptp.arr A) B)) (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) A) (@ (@ tptp.mem (@ (@ tptp.ap F) X)) B))))))) (let ((_let_21 (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) tptp.bool) (= X (@ tptp.inj__o (@ tptp.p X))))))) (let ((_let_22 (ho_19 k_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_31))) (let ((_let_23 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_31 (ho_21 k_20 _let_22)))) (let ((_let_24 (ho_25 k_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30))) (let ((_let_25 (ho_26 _let_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_31))) (let ((_let_26 (ho_19 k_18 _let_25))) (let ((_let_27 (ho_19 k_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30))) (let ((_let_28 (ho_10 k_9 tptp.c_2Eextreal_2Eextreal__max))) (let ((_let_29 (ho_11 _let_28 _let_27))) (let ((_let_30 (ho_10 k_9 _let_29))) (let ((_let_31 (ho_11 _let_30 _let_22))) (let ((_let_32 (= _let_31 _let_26))) (let ((_let_33 (ho_10 k_9 tptp.c_2Eextreal_2Eextreal__le))) (let ((_let_34 (ho_11 _let_33 _let_27))) (let ((_let_35 (ho_10 k_9 _let_34))) (let ((_let_36 (ho_11 _let_35 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_let_112)) _let_111 :args (_let_419 false _let_110)) :args (_let_413 false _let_208 false _let_417 false _let_419)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_331 :args (_let_171 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_333)) :args _let_332)) _let_331 :args (_let_415 false _let_330)) :args (_let_182 false _let_413 false _let_415)) _let_212 _let_98 _let_412 _let_96 _let_90 _let_321 _let_89 _let_75 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_71 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_31 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29 QUANTIFIERS_INST_E_MATCHING _let_97)) :args _let_72)) _let_71 :args (_let_176 false _let_70)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_71 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29 QUANTIFIERS_INST_E_MATCHING _let_97)) :args _let_72)) _let_71 :args (_let_173 false _let_70)) _let_69 _let_64 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_61 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_63)) :args _let_62)) _let_61 :args (_let_170 false _let_60)) _let_316 _let_59 _let_314 (REORDERING (CNF_OR_POS :args (_let_168)) :args ((or _let_167 _let_137 _let_166 (not _let_168)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_410 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_31 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_411)) _let_410 :args (_let_168 false _let_409)) _let_408 _let_162 (REORDERING (CNF_OR_POS :args (_let_165)) :args ((or _let_55 _let_164 (not _let_165)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_93 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_31 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_94)) _let_93 :args (_let_165 false _let_92)) (EQUIV_ELIM2 _let_203) (REORDERING (CNF_AND_POS :args (_let_156 1)) :args ((or _let_55 _let_163))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_57 _let_250 _let_252 _let_383 _let_385 _let_387 _let_388 _let_268 _let_270 _let_389 _let_390 _let_392 _let_394 _let_341 _let_399 _let_401 _let_403 _let_405 _let_291 _let_295 _let_297 _let_300 _let_310) :args (_let_56 _let_245 _let_191 _let_32 _let_38 BOOLEAN_TERM_VARIABLE_5855 _let_39 _let_177 _let_312 BOOLEAN_TERM_VARIABLE_6129 _let_186 _let_40 _let_195 BOOLEAN_TERM_VARIABLE_12001 _let_200 BOOLEAN_TERM_VARIABLE_12034 _let_46 _let_199 _let_198 _let_50 _let_215 _let_148 _let_201)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS _let_311 (CONG _let_308 (TRANS _let_307 (CONG (TRANS _let_305 (CONG _let_274 (TRANS (CONG _let_303 (TRANS _let_297 _let_407 (CONG _let_282 (TRANS (CONG _let_278 (TRANS (CONG (CONG _let_274 (CONG (CONG _let_274 _let_406 :args _let_260) _let_267 :args _let_258) :args _let_260) _let_287 :args _let_258) _let_400) :args _let_264) _let_398 _let_392) :args _let_261) _let_393) :args _let_258) _let_397) :args _let_260) _let_396) _let_259 :args _let_258) _let_386 _let_384 _let_251) :args _let_249) _let_248)) :args (_let_56 _let_39 BOOLEAN_TERM_VARIABLE_5855 BOOLEAN_TERM_VARIABLE_6129 _let_186 _let_191 _let_201 BOOLEAN_TERM_VARIABLE_12034 _let_46 BOOLEAN_TERM_VARIABLE_12001 _let_200 _let_195 _let_199 _let_198 _let_148 _let_177 _let_312 _let_215 _let_50 _let_38 _let_32 _let_40 _let_245)) :args ((not (and _let_56 _let_245 _let_191 _let_32 _let_38 BOOLEAN_TERM_VARIABLE_5855 _let_39 _let_177 _let_312 BOOLEAN_TERM_VARIABLE_6129 _let_186 _let_40 _let_195 BOOLEAN_TERM_VARIABLE_12001 _let_200 BOOLEAN_TERM_VARIABLE_12034 _let_46 _let_199 _let_198 _let_50 _let_215 _let_148 _let_201)) SB_LITERAL))) (CONG _let_247 _let_246 _let_382 _let_243 _let_242 _let_241 _let_240 _let_381 _let_380 _let_379 _let_377 _let_237 _let_376 _let_375 _let_374 _let_235 _let_234 _let_373 _let_372 _let_230 _let_371 _let_370 _let_369 :args _let_82)) :args ((or _let_228 _let_53 _let_227 _let_226 BOOLEAN_TERM_VARIABLE_5957 _let_368 _let_367 _let_366 _let_365 _let_222 _let_221 _let_220 _let_364 _let_363 _let_219 _let_218 _let_362 BOOLEAN_TERM_VARIABLE_22241 _let_216 _let_361 _let_335 _let_360 _let_359))) _let_358 _let_355 _let_147 _let_354 _let_349 _let_344 _let_326 _let_124 _let_325 _let_96 _let_324 _let_90 _let_321 _let_89 _let_75 _let_69 _let_317 _let_316 _let_59 _let_57 (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_57 _let_250 _let_252 _let_255 _let_256 _let_262 _let_265 _let_268 _let_270 _let_280 _let_285 _let_289 _let_291 _let_295 _let_297 _let_300 _let_310) :args (_let_56 _let_245 _let_23 _let_32 _let_38 BOOLEAN_TERM_VARIABLE_5855 _let_39 BOOLEAN_TERM_VARIABLE_6164 _let_181 _let_40 _let_45 BOOLEAN_TERM_VARIABLE_12034 _let_46 _let_49 BOOLEAN_TERM_VARIABLE_22241 _let_50 _let_51)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS _let_311 (CONG _let_308 (TRANS _let_307 (CONG (TRANS _let_305 (CONG _let_274 (CONG _let_303 (TRANS _let_297 (CONG _let_282 (TRANS _let_302 _let_299 _let_296 _let_294 _let_284) :args _let_261) (CONG _let_282 _let_280 :args _let_261) _let_283) :args _let_258) :args _let_260)) _let_259 :args _let_258) _let_257 (CONG _let_85 (TRANS (TRUE_INTRO _let_255) _let_254) :args _let_84) _let_251) :args _let_249) _let_248)) :args (_let_56 _let_39 BOOLEAN_TERM_VARIABLE_5855 BOOLEAN_TERM_VARIABLE_6164 _let_181 _let_23 _let_49 BOOLEAN_TERM_VARIABLE_12034 _let_46 _let_45 _let_51 BOOLEAN_TERM_VARIABLE_22241 _let_50 _let_38 _let_32 _let_40 _let_245)) :args ((not (and _let_56 _let_245 _let_23 _let_32 _let_38 BOOLEAN_TERM_VARIABLE_5855 _let_39 BOOLEAN_TERM_VARIABLE_6164 _let_181 _let_40 _let_45 BOOLEAN_TERM_VARIABLE_12034 _let_46 _let_49 BOOLEAN_TERM_VARIABLE_22241 _let_50 _let_51)) SB_LITERAL))) (CONG _let_247 _let_246 _let_244 _let_243 _let_242 _let_241 _let_240 (REFL :args _let_239) _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_230 _let_229 :args _let_82)) :args ((or _let_228 _let_53 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213))) _let_153 _let_147 _let_133 _let_124 _let_212 _let_98 _let_96 _let_90 _let_89 _let_75 _let_69 _let_64 _let_59 _let_57 (CNF_EQUIV_NEG2 :args _let_204) _let_162 (EQUIV_ELIM1 _let_203) (CNF_AND_NEG :args (_let_156)) _let_190 :args ((or _let_167 _let_202) false _let_201 false _let_148 false _let_50 false _let_186 false _let_200 false _let_199 false _let_198 false _let_46 false _let_195 false BOOLEAN_TERM_VARIABLE_12034 false BOOLEAN_TERM_VARIABLE_12001 false _let_40 false _let_177 false _let_39 false _let_38 false _let_32 false _let_191 true BOOLEAN_TERM_VARIABLE_5957 false BOOLEAN_TERM_VARIABLE_5855 false _let_56 true BOOLEAN_TERM_VARIABLE_22241 false _let_51 false _let_50 false _let_49 false _let_46 false _let_181 false _let_45 false BOOLEAN_TERM_VARIABLE_12034 false _let_40 false _let_39 false _let_38 false _let_32 false _let_23 false BOOLEAN_TERM_VARIABLE_5855 false _let_56 true _let_53 true _let_157 false BOOLEAN_TERM_VARIABLE_6164 false _let_156 false BOOLEAN_TERM_VARIABLE_6129)) _let_190 :args (_let_167 true BOOLEAN_TERM_VARIABLE_22241 false _let_188 false _let_51 false _let_50 false _let_186 false _let_49 false _let_185 false _let_183 false _let_46 false _let_182 false _let_181 false _let_45 false _let_180 false BOOLEAN_TERM_VARIABLE_12034 false _let_40 false _let_177 false _let_39 false _let_38 false _let_176 false _let_173 false _let_32 false _let_23 false _let_170 true BOOLEAN_TERM_VARIABLE_5957 false BOOLEAN_TERM_VARIABLE_5855 true _let_169 false _let_137 false _let_168 false _let_53 true _let_157 false _let_164 false _let_165 true BOOLEAN_TERM_VARIABLE_6164 true _let_156 true _let_55 false BOOLEAN_TERM_VARIABLE_6129)))) (let ((_let_461 (MACRO_RESOLUTION_TRUST _let_408 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_156 0)) :args ((or _let_155 _let_163))) _let_460 :args (_let_163 true _let_155)) _let_162 :args (_let_53 true _let_156 true _let_157)))) (let ((_let_462 (ASSUME :args _let_378))) (let ((_let_463 (CONG _let_85 (TRANS (FALSE_INTRO _let_462) _let_404) :args _let_84))) (let ((_let_464 (CONG _let_273 (TRANS _let_386 _let_463 _let_402) :args _let_258))) (let ((_let_465 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_314 _let_401 _let_403 _let_462 _let_385 _let_387 _let_388 _let_250 _let_252 _let_268 _let_270 _let_389 _let_390 _let_392 _let_394 _let_341 _let_399 _let_405 _let_291 _let_295 _let_297 _let_300 _let_457) :args (_let_313 _let_53 _let_191 _let_32 _let_38 BOOLEAN_TERM_VARIABLE_5855 _let_39 _let_177 _let_312 _let_186 _let_366 _let_40 _let_195 BOOLEAN_TERM_VARIABLE_12001 _let_200 BOOLEAN_TERM_VARIABLE_12034 _let_46 _let_199 _let_198 _let_50 _let_215 _let_148 _let_201)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS _let_459 (CONG _let_308 (TRANS (CONG (CONG _let_274 (SYMM _let_304) :args _let_260) _let_259 :args _let_258) (CONG (TRANS (CONG _let_274 (TRANS _let_304 (CONG _let_303 (TRANS _let_297 _let_407 (CONG _let_282 (TRANS (CONG _let_278 (TRANS (CONG (CONG _let_274 (CONG (TRANS (CONG _let_274 (TRANS _let_406 (SYMM _let_464)) :args _let_260) (CONG _let_274 _let_464 :args _let_260)) _let_267 :args _let_258) :args _let_260) _let_287 :args _let_258) _let_400) :args _let_264) _let_398 _let_392) :args _let_261) _let_393) :args _let_258) _let_397) :args _let_260) _let_396) _let_259 :args _let_258) _let_386 _let_463 _let_402) :args _let_249) _let_445)) :args (_let_313 _let_177 _let_312 _let_366 _let_186 _let_191 _let_201 _let_39 BOOLEAN_TERM_VARIABLE_5855 BOOLEAN_TERM_VARIABLE_12034 _let_46 BOOLEAN_TERM_VARIABLE_12001 _let_200 _let_195 _let_199 _let_198 _let_148 _let_215 _let_50 _let_38 _let_32 _let_40 _let_53)) :args ((not (and _let_313 _let_53 _let_191 _let_32 _let_38 BOOLEAN_TERM_VARIABLE_5855 _let_39 _let_177 _let_312 _let_186 _let_366 _let_40 _let_195 BOOLEAN_TERM_VARIABLE_12001 _let_200 BOOLEAN_TERM_VARIABLE_12034 _let_46 _let_199 _let_198 _let_50 _let_215 _let_148 _let_201)) SB_LITERAL))) (CONG _let_444 _let_443 _let_382 _let_243 _let_242 _let_241 _let_240 _let_381 _let_380 _let_377 (MACRO_SR_PRED_INTRO :args ((= (not _let_366) BOOLEAN_TERM_VARIABLE_6129))) _let_237 _let_376 _let_375 _let_374 _let_235 _let_234 _let_373 _let_372 _let_230 _let_371 _let_370 _let_369 :args _let_82)) :args ((or _let_169 _let_245 _let_227 _let_226 BOOLEAN_TERM_VARIABLE_5957 _let_368 BOOLEAN_TERM_VARIABLE_6129 _let_367 _let_365 _let_222 _let_221 _let_220 _let_364 _let_363 _let_219 _let_218 _let_362 BOOLEAN_TERM_VARIABLE_22241 _let_216 _let_361 _let_335 _let_360 _let_359))) _let_314 _let_461 _let_89 _let_59 _let_316 _let_321 (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 _let_189) _let_460 :args (_let_366 true _let_155)) _let_354 _let_317 _let_69 _let_75 _let_90 _let_349 _let_324 _let_124 _let_96 _let_325 _let_147 _let_344 _let_326 _let_355 _let_358 :args (BOOLEAN_TERM_VARIABLE_22241 true _let_169 false _let_53 false _let_39 false BOOLEAN_TERM_VARIABLE_5855 true BOOLEAN_TERM_VARIABLE_5957 false _let_177 true BOOLEAN_TERM_VARIABLE_6129 false _let_186 false _let_191 false _let_32 false _let_38 false _let_40 false _let_200 false BOOLEAN_TERM_VARIABLE_12001 false _let_46 false BOOLEAN_TERM_VARIABLE_12034 false _let_195 false _let_50 false _let_199 false _let_198 false _let_148 false _let_201)))) (let ((_let_466 (not _let_137))) (let ((_let_467 (or _let_466 _let_202 _let_155))) (let ((_let_468 (and _let_53 _let_23 _let_32 _let_38 BOOLEAN_TERM_VARIABLE_5855 _let_39 _let_40 _let_45 BOOLEAN_TERM_VARIABLE_12034 _let_46 _let_49 BOOLEAN_TERM_VARIABLE_22241 _let_50 _let_51))) (let ((_let_469 (CONG _let_274 (CONG _let_273 (TRANS (SYMM _let_251) _let_288 _let_271) :args _let_258) :args _let_260))) (let ((_let_470 (CONG (SYMM _let_469) _let_267 :args _let_258))) (let ((_let_471 (CONG _let_274 (SYMM _let_470) :args _let_260))) (let ((_let_472 (CONG _let_278 (TRANS (CONG (SYMM _let_471) _let_267 :args _let_258) _let_266) :args _let_264))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_468)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_457 _let_297 _let_300 _let_295 _let_291 _let_289 _let_252 _let_268 _let_270 _let_250 _let_285 _let_265 _let_280 _let_262) (SCOPE (TRUE_ELIM (TRANS (CONG _let_308 (TRANS (CONG (TRANS (CONG _let_274 (CONG _let_303 (TRANS (CONG _let_282 (TRANS (SYMM _let_263) (SYMM _let_472) _let_280) :args _let_261) (CONG _let_282 (TRANS _let_281 _let_472 (CONG _let_278 (TRANS (SYMM _let_286) (CONG (TRANS _let_471 (CONG _let_274 (TRANS _let_470 (CONG (TRANS _let_469 (CONG _let_274 (CONG _let_273 (TRANS _let_272 _let_269 (CONG _let_85 (TRANS _let_253 (SYMM _let_290)) :args _let_84) _let_292) :args _let_258) :args _let_260)) _let_267 :args _let_258)) :args _let_260)) _let_287 :args _let_258)) :args _let_264)) :args _let_261) (CONG _let_282 (TRANS (SYMM _let_296) (CONG _let_278 _let_297 :args _let_264) _let_301) :args _let_261) _let_298) :args _let_258) :args _let_260) _let_306) _let_259 :args _let_258) (CONG _let_305 _let_259 :args _let_258)) :args _let_249) _let_458)) :args (_let_53 _let_32 _let_40 _let_38 _let_50 BOOLEAN_TERM_VARIABLE_22241 BOOLEAN_TERM_VARIABLE_5855 BOOLEAN_TERM_VARIABLE_12034 _let_46 _let_39 _let_51 _let_49 _let_45 _let_23))) :args (_let_53 _let_23 _let_32 _let_38 BOOLEAN_TERM_VARIABLE_5855 _let_39 _let_40 _let_45 BOOLEAN_TERM_VARIABLE_12034 _let_46 _let_49 BOOLEAN_TERM_VARIABLE_22241 _let_50 _let_51))) :args (true _let_468)) :args ((or _let_55 _let_245 _let_227 _let_226 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_467)) :args ((or _let_155 _let_202 _let_466 (not _let_467)))) _let_460 (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 _let_138) _let_465 :args (_let_137 false BOOLEAN_TERM_VARIABLE_22241)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_410 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_31 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_411)) _let_410 :args (_let_467 false _let_409)) :args (_let_202 true _let_155 false _let_137 false _let_467)) _let_465 _let_461 _let_153 _let_147 _let_133 _let_124 _let_98 _let_96 _let_90 _let_89 _let_75 _let_69 _let_64 _let_59 :args (false true _let_55 false BOOLEAN_TERM_VARIABLE_22241 false _let_53 false _let_51 false _let_50 false _let_49 false _let_46 false _let_45 false BOOLEAN_TERM_VARIABLE_12034 false _let_40 false _let_39 false _let_38 false _let_32 false _let_23 false BOOLEAN_TERM_VARIABLE_5855)) :args ((forall ((X Bool)) (= (@ tptp.p (@ tptp.inj__o X)) X)) (forall ((X Bool)) (@ (@ tptp.mem (@ tptp.inj__o X)) tptp.bool)) _let_21 _let_20 (forall ((A tptp.del) (B tptp.del) (F (-> $$unsorted $$unsorted))) (=> (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) A) (@ (@ tptp.mem (@ F X)) B))) (@ (@ tptp.mem (@ (@ tptp.lam A) F)) (@ (@ tptp.arr A) B)))) (forall ((A tptp.del) (B tptp.del) (F $$unsorted)) (=> (@ (@ tptp.mem F) (@ (@ tptp.arr A) B)) (forall ((G $$unsorted)) (=> (@ (@ tptp.mem G) (@ (@ tptp.arr A) B)) (=> (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) A) (= (@ (@ tptp.ap F) X) (@ (@ tptp.ap G) X)))) (= F G)))))) (forall ((A tptp.del) (F (-> $$unsorted $$unsorted)) (X $$unsorted)) (=> (@ (@ tptp.mem X) A) (= (@ (@ tptp.ap (@ (@ tptp.lam A) F)) X) (@ F X)))) _let_19 _let_18 _let_17 _let_16 _let_15 _let_14 (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Ebool_2ECOND A_27a)) (@ (@ tptp.arr tptp.bool) (@ _let_1 (@ _let_1 A_27a)))))) _let_13 _let_11 _let_10 _let_9 (@ (@ tptp.mem tptp.c_2Emin_2E_3D_3D_3E) _let_8) (forall ((Q $$unsorted)) (=> (@ (@ tptp.mem Q) tptp.bool) (forall ((R $$unsorted)) (=> (@ (@ tptp.mem R) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) Q)) R)) (=> (@ tptp.p Q) (@ tptp.p R))))))) (@ (@ tptp.mem tptp.c_2Ebool_2E_5C_2F) _let_8) (forall ((Q $$unsorted)) (=> (@ (@ tptp.mem Q) tptp.bool) (forall ((R $$unsorted)) (=> (@ (@ tptp.mem R) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_5C_2F) Q)) R)) (or (@ tptp.p Q) (@ tptp.p R))))))) (@ (@ tptp.mem tptp.c_2Ebool_2E_2F_5C) _let_8) (forall ((Q $$unsorted)) (=> (@ (@ tptp.mem Q) tptp.bool) (forall ((R $$unsorted)) (=> (@ (@ tptp.mem R) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) Q)) R)) (and (@ tptp.p Q) (@ tptp.p R))))))) (@ (@ tptp.mem tptp.c_2Ebool_2E_7E) _let_7) (forall ((Q $$unsorted)) (=> (@ (@ tptp.mem Q) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap tptp.c_2Ebool_2E_7E) Q)) (not (@ tptp.p Q))))) (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Emin_2E_3D A_27a)) (@ _let_1 (@ _let_1 tptp.bool))))) (forall ((A tptp.del) (X $$unsorted)) (=> (@ (@ tptp.mem X) A) (forall ((Y $$unsorted)) (=> (@ (@ tptp.mem Y) A) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A)) X)) Y)) (= X Y)))))) (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Ebool_2E_21 A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool))) (forall ((A tptp.del) (Q $$unsorted)) (=> (@ (@ tptp.mem Q) (@ (@ tptp.arr A) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A)) Q)) (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) A) (@ tptp.p (@ (@ tptp.ap Q) X))))))) true (forall ((V0t1 $$unsorted)) (=> (@ (@ tptp.mem V0t1) tptp.bool) (forall ((V1t2 $$unsorted)) (let ((_let_1 (@ tptp.p V1t2))) (let ((_let_2 (@ tptp.p V0t1))) (=> (@ (@ tptp.mem V1t2) tptp.bool) (=> (=> _let_2 _let_1) (=> (=> _let_1 _let_2) (= _let_2 _let_1))))))))) (forall ((V0t $$unsorted)) (=> (@ (@ tptp.mem V0t) tptp.bool) (=> false (@ tptp.p V0t)))) (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (or _let_1 (not _let_1))))) (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (=> (=> _let_1 false) (not _let_1))))) (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (=> (not _let_1) (=> _let_1 false))))) (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (and (= (=> true _let_1) _let_1) (= (=> _let_1 true) true) (= (=> false _let_1) true) (= (=> _let_1 _let_1) true) (= (=> _let_1 false) (not _let_1)))))) (and (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (= (not (not _let_1)) _let_1)))) (= (not true) false) (= (not false) true)) (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1y $$unsorted)) (=> (@ (@ tptp.mem V1y) A_27a) (= (= V0x V1y) (= V1y V0x)))))) (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (let ((_let_2 (not _let_1))) (=> (@ (@ tptp.mem V0t) tptp.bool) (and (= (= true _let_1) _let_1) (= (= _let_1 true) _let_1) (= (= false _let_1) _let_2) (= (= _let_1 false) _let_2)))))) _let_5 (forall ((V0A $$unsorted)) (=> (@ (@ tptp.mem V0A) tptp.bool) (forall ((V1B $$unsorted)) (=> (@ (@ tptp.mem V1B) tptp.bool) (forall ((V2C $$unsorted)) (let ((_let_1 (or (@ tptp.p V0A) (@ tptp.p V1B) (@ tptp.p V2C)))) (=> (@ (@ tptp.mem V2C) tptp.bool) (= _let_1 _let_1)))))))) (forall ((V0A $$unsorted)) (=> (@ (@ tptp.mem V0A) tptp.bool) (forall ((V1B $$unsorted)) (let ((_let_1 (@ tptp.p V0A))) (let ((_let_2 (@ tptp.p V1B))) (=> (@ (@ tptp.mem V1B) tptp.bool) (= (or _let_1 _let_2) (or _let_2 _let_1)))))))) (forall ((V0A $$unsorted)) (=> (@ (@ tptp.mem V0A) tptp.bool) (forall ((V1B $$unsorted)) (let ((_let_1 (@ tptp.p V1B))) (let ((_let_2 (not _let_1))) (let ((_let_3 (@ tptp.p V0A))) (let ((_let_4 (not _let_3))) (=> (@ (@ tptp.mem V1B) tptp.bool) (and (= (not (and _let_3 _let_1)) (or _let_4 _let_2)) (= (not (or _let_3 _let_1)) (and _let_4 _let_2))))))))))) _let_4 _let_3 _let_2 (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (= (not (not _let_1)) _let_1)))) (forall ((V0A $$unsorted)) (let ((_let_1 (@ tptp.p V0A))) (=> (@ (@ tptp.mem V0A) tptp.bool) (=> _let_1 (=> (not _let_1) false))))) (forall ((V0A $$unsorted)) (=> (@ (@ tptp.mem V0A) tptp.bool) (forall ((V1B $$unsorted)) (let ((_let_1 (@ tptp.p V1B))) (let ((_let_2 (@ tptp.p V0A))) (=> (@ (@ tptp.mem V1B) tptp.bool) (= (=> (not (or _let_2 _let_1)) false) (=> (=> _let_2 false) (=> (not _let_1) false))))))))) (forall ((V0A $$unsorted)) (=> (@ (@ tptp.mem V0A) tptp.bool) (forall ((V1B $$unsorted)) (let ((_let_1 (@ tptp.p V1B))) (let ((_let_2 (@ tptp.p V0A))) (=> (@ (@ tptp.mem V1B) tptp.bool) (= (=> (not (or (not _let_2) _let_1)) false) (=> _let_2 (=> (not _let_1) false))))))))) (forall ((V0A $$unsorted)) (let ((_let_1 (@ tptp.p V0A))) (=> (@ (@ tptp.mem V0A) tptp.bool) (=> (=> (not _let_1) false) (=> (=> _let_1 false) false))))) (forall ((V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) tptp.bool) (forall ((V1q $$unsorted)) (=> (@ (@ tptp.mem V1q) tptp.bool) (forall ((V2r $$unsorted)) (let ((_let_1 (@ tptp.p V0p))) (let ((_let_2 (not _let_1))) (let ((_let_3 (@ tptp.p V1q))) (let ((_let_4 (not _let_3))) (let ((_let_5 (@ tptp.p V2r))) (let ((_let_6 (not _let_5))) (=> (@ (@ tptp.mem V2r) tptp.bool) (= (= _let_1 (= _let_3 _let_5)) (and (or _let_1 _let_3 _let_5) (or _let_1 _let_6 _let_4) (or _let_3 _let_6 _let_2) (or _let_5 _let_4 _let_2))))))))))))))) (forall ((V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) tptp.bool) (forall ((V1q $$unsorted)) (=> (@ (@ tptp.mem V1q) tptp.bool) (forall ((V2r $$unsorted)) (let ((_let_1 (@ tptp.p V0p))) (let ((_let_2 (not _let_1))) (let ((_let_3 (@ tptp.p V2r))) (let ((_let_4 (@ tptp.p V1q))) (=> (@ (@ tptp.mem V2r) tptp.bool) (= (= _let_1 (and _let_4 _let_3)) (and (or _let_1 (not _let_4) (not _let_3)) (or _let_4 _let_2) (or _let_3 _let_2))))))))))))) (forall ((V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) tptp.bool) (forall ((V1q $$unsorted)) (=> (@ (@ tptp.mem V1q) tptp.bool) (forall ((V2r $$unsorted)) (let ((_let_1 (@ tptp.p V0p))) (let ((_let_2 (@ tptp.p V2r))) (let ((_let_3 (@ tptp.p V1q))) (=> (@ (@ tptp.mem V2r) tptp.bool) (= (= _let_1 (or _let_3 _let_2)) (and (or _let_1 (not _let_3)) (or _let_1 (not _let_2)) (or _let_3 _let_2 (not _let_1))))))))))))) (forall ((V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) tptp.bool) (forall ((V1q $$unsorted)) (=> (@ (@ tptp.mem V1q) tptp.bool) (forall ((V2r $$unsorted)) (let ((_let_1 (@ tptp.p V0p))) (let ((_let_2 (@ tptp.p V2r))) (let ((_let_3 (@ tptp.p V1q))) (=> (@ (@ tptp.mem V2r) tptp.bool) (= (= _let_1 (=> _let_3 _let_2)) (and (or _let_1 _let_3) (or _let_1 (not _let_2)) (or (not _let_3) _let_2 (not _let_1))))))))))))) (forall ((V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) tptp.bool) (forall ((V1q $$unsorted)) (let ((_let_1 (@ tptp.p V0p))) (let ((_let_2 (@ tptp.p V1q))) (let ((_let_3 (not _let_2))) (=> (@ (@ tptp.mem V1q) tptp.bool) (= (= _let_1 _let_3) (and (or _let_1 _let_2) (or _let_3 (not _let_1))))))))))) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 4.07/4.26 )
% 4.07/4.26 % SZS output end Proof for ITP021^2
% 4.07/4.26 % cvc5---1.0.5 exiting
% 4.14/4.26 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------