TSTP Solution File: ITP011^2 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP011^2 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n003.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 03:14:39 EDT 2023
% Result : Timeout 299.68s 300.17s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : ITP011^2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.13/0.15 % Command : do_cvc5 %s %d
% 0.15/0.36 % Computer : n003.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sun Aug 27 11:40:24 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.21/0.52 %----Proving TH0
% 0.21/0.53 %------------------------------------------------------------------------------
% 0.21/0.53 % File : ITP011^2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.21/0.53 % Domain : Interactive Theorem Proving
% 0.21/0.53 % Problem : HOL4 set theory export of thm_2Equotient__option_2EOPTION__REL__def.p, bushy mode
% 0.21/0.53 % Version : [BG+19] axioms.
% 0.21/0.53 % English :
% 0.21/0.53
% 0.21/0.53 % Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% 0.21/0.53 % : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% 0.21/0.53 % Source : [BG+19]
% 0.21/0.53 % Names : thm_2Equotient__option_2EOPTION__REL__def.p [Gau19]
% 0.21/0.53 % : HL405001^2.p [TPAP]
% 0.21/0.53
% 0.21/0.53 % Status : Theorem
% 0.21/0.53 % Rating : 0.69 v8.1.0, 0.55 v7.5.0
% 0.21/0.53 % Syntax : Number of formulae : 74 ( 5 unt; 28 typ; 0 def)
% 0.21/0.53 % Number of atoms : 399 ( 30 equ; 0 cnn)
% 0.21/0.53 % Maximal formula atoms : 69 ( 8 avg)
% 0.21/0.53 % Number of connectives : 839 ( 11 ~; 7 |; 48 &; 659 @)
% 0.21/0.53 % ( 41 <=>; 73 =>; 0 <=; 0 <~>)
% 0.21/0.53 % Maximal formula depth : 34 ( 8 avg)
% 0.21/0.53 % Number of types : 3 ( 1 usr)
% 0.21/0.53 % Number of type conns : 29 ( 29 >; 0 *; 0 +; 0 <<)
% 0.21/0.53 % Number of symbols : 35 ( 32 usr; 15 con; 0-2 aty)
% 0.21/0.53 % Number of variables : 101 ( 0 ^; 97 !; 4 ?; 101 :)
% 0.21/0.53 % SPC : TH0_THM_EQU_NAR
% 0.21/0.53
% 0.21/0.53 % Comments :
% 0.21/0.53 % Bugfixes : v7.5.0 - Bugfixes in axioms and export.
% 0.21/0.53 %------------------------------------------------------------------------------
% 0.21/0.53 %------------------------------------------------------------------------------
% 0.21/0.53 thf(del_tp,type,
% 0.21/0.53 del: $tType ).
% 0.21/0.53
% 0.21/0.53 thf(bool,type,
% 0.21/0.53 bool: del ).
% 0.21/0.53
% 0.21/0.53 thf(ind,type,
% 0.21/0.53 ind: del ).
% 0.21/0.53
% 0.21/0.53 thf(arr,type,
% 0.21/0.53 arr: del > del > del ).
% 0.21/0.53
% 0.21/0.53 thf(mem,type,
% 0.21/0.53 mem: $i > del > $o ).
% 0.21/0.53
% 0.21/0.53 thf(ap,type,
% 0.21/0.53 ap: $i > $i > $i ).
% 0.21/0.53
% 0.21/0.53 thf(lam,type,
% 0.21/0.53 lam: del > ( $i > $i ) > $i ).
% 0.21/0.53
% 0.21/0.53 thf(p,type,
% 0.21/0.53 p: $i > $o ).
% 0.21/0.53
% 0.21/0.53 thf(stp_inj_o,type,
% 0.21/0.53 inj__o: $o > $i ).
% 0.21/0.53
% 0.21/0.53 thf(stp_inj_surj_o,axiom,
% 0.21/0.53 ! [X: $o] :
% 0.21/0.53 ( ( p @ ( inj__o @ X ) )
% 0.21/0.53 = X ) ).
% 0.21/0.53
% 0.21/0.53 thf(stp_inj_mem_o,axiom,
% 0.21/0.53 ! [X: $o] : ( mem @ ( inj__o @ X ) @ bool ) ).
% 0.21/0.53
% 0.21/0.53 thf(stp_iso_mem_o,axiom,
% 0.21/0.53 ! [X: $i] :
% 0.21/0.53 ( ( mem @ X @ bool )
% 0.21/0.53 => ( X
% 0.21/0.53 = ( inj__o @ ( p @ X ) ) ) ) ).
% 0.21/0.53
% 0.21/0.53 thf(ap_tp,axiom,
% 0.21/0.53 ! [A: del,B: del,F: $i] :
% 0.21/0.53 ( ( mem @ F @ ( arr @ A @ B ) )
% 0.21/0.53 => ! [X: $i] :
% 0.21/0.53 ( ( mem @ X @ A )
% 0.21/0.53 => ( mem @ ( ap @ F @ X ) @ B ) ) ) ).
% 0.21/0.53
% 0.21/0.53 thf(lam_tp,axiom,
% 0.21/0.53 ! [A: del,B: del,F: $i > $i] :
% 0.21/0.53 ( ! [X: $i] :
% 0.21/0.53 ( ( mem @ X @ A )
% 0.21/0.53 => ( mem @ ( F @ X ) @ B ) )
% 0.21/0.53 => ( mem @ ( lam @ A @ F ) @ ( arr @ A @ B ) ) ) ).
% 0.21/0.53
% 0.21/0.53 thf(funcext,axiom,
% 0.21/0.53 ! [A: del,B: del,F: $i] :
% 0.21/0.53 ( ( mem @ F @ ( arr @ A @ B ) )
% 0.21/0.53 => ! [G: $i] :
% 0.21/0.53 ( ( mem @ G @ ( arr @ A @ B ) )
% 0.21/0.53 => ( ! [X: $i] :
% 0.21/0.53 ( ( mem @ X @ A )
% 0.21/0.53 => ( ( ap @ F @ X )
% 0.21/0.53 = ( ap @ G @ X ) ) )
% 0.21/0.53 => ( F = G ) ) ) ) ).
% 0.21/0.53
% 0.21/0.53 thf(beta,axiom,
% 0.21/0.53 ! [A: del,F: $i > $i,X: $i] :
% 0.21/0.53 ( ( mem @ X @ A )
% 0.21/0.53 => ( ( ap @ ( lam @ A @ F ) @ X )
% 0.21/0.53 = ( F @ X ) ) ) ).
% 0.21/0.53
% 0.21/0.53 %------------------------------------------------------------------------------
% 0.21/0.53 %------------------------------------------------------------------------------
% 0.21/0.53 thf(tp_ty_2Eoption_2Eoption,type,
% 0.21/0.53 ty_2Eoption_2Eoption: del > del ).
% 0.21/0.53
% 0.21/0.53 thf(tp_c_2Eoption_2EOPTION__JOIN,type,
% 0.21/0.53 c_2Eoption_2EOPTION__JOIN: del > $i ).
% 0.21/0.53
% 0.21/0.53 thf(mem_c_2Eoption_2EOPTION__JOIN,axiom,
% 0.21/0.53 ! [A_27a: del] : ( mem @ ( c_2Eoption_2EOPTION__JOIN @ A_27a ) @ ( arr @ ( ty_2Eoption_2Eoption @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) ).
% 0.21/0.53
% 0.21/0.53 thf(tp_c_2Eoption_2EOPTION__MAP,type,
% 0.21/0.53 c_2Eoption_2EOPTION__MAP: del > del > $i ).
% 0.21/0.53
% 0.21/0.53 thf(mem_c_2Eoption_2EOPTION__MAP,axiom,
% 0.21/0.53 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Eoption_2EOPTION__MAP @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) ) ).
% 0.21/0.53
% 0.21/0.53 thf(tp_c_2Eoption_2Eoption__CASE,type,
% 0.21/0.53 c_2Eoption_2Eoption__CASE: del > del > $i ).
% 0.21/0.53
% 0.21/0.53 thf(mem_c_2Eoption_2Eoption__CASE,axiom,
% 0.21/0.53 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Eoption_2Eoption__CASE @ A_27a @ A_27b ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ ( arr @ A_27b @ ( arr @ ( arr @ A_27a @ A_27b ) @ A_27b ) ) ) ) ).
% 0.21/0.53
% 0.21/0.53 thf(tp_c_2Emin_2E_3D_3D_3E,type,
% 0.21/0.53 c_2Emin_2E_3D_3D_3E: $i ).
% 0.21/0.53
% 0.21/0.53 thf(mem_c_2Emin_2E_3D_3D_3E,axiom,
% 0.21/0.53 mem @ c_2Emin_2E_3D_3D_3E @ ( arr @ bool @ ( arr @ bool @ bool ) ) ).
% 0.21/0.53
% 0.21/0.53 thf(ax_imp_p,axiom,
% 0.21/0.53 ! [Q: $i] :
% 0.21/0.53 ( ( mem @ Q @ bool )
% 0.21/0.53 => ! [R: $i] :
% 0.21/0.53 ( ( mem @ R @ bool )
% 0.21/0.53 => ( ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ Q ) @ R ) )
% 0.21/0.53 <=> ( ( p @ Q )
% 0.21/0.53 => ( p @ R ) ) ) ) ) ).
% 0.21/0.53
% 0.21/0.53 thf(tp_c_2Eoption_2EIS__NONE,type,
% 0.21/0.53 c_2Eoption_2EIS__NONE: del > $i ).
% 0.21/0.53
% 0.21/0.53 thf(mem_c_2Eoption_2EIS__NONE,axiom,
% 0.21/0.53 ! [A_27a: del] : ( mem @ ( c_2Eoption_2EIS__NONE @ A_27a ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ bool ) ) ).
% 0.21/0.53
% 0.21/0.53 thf(tp_c_2Ebool_2EF,type,
% 0.21/0.53 c_2Ebool_2EF: $i ).
% 0.21/0.53
% 0.21/0.53 thf(mem_c_2Ebool_2EF,axiom,
% 0.21/0.53 mem @ c_2Ebool_2EF @ bool ).
% 0.21/0.53
% 0.21/0.53 thf(ax_false_p,axiom,
% 0.21/0.53 ~ ( p @ c_2Ebool_2EF ) ).
% 0.21/0.53
% 0.21/0.53 thf(tp_c_2Ebool_2ET,type,
% 0.21/0.53 c_2Ebool_2ET: $i ).
% 0.21/0.53
% 0.21/0.53 thf(mem_c_2Ebool_2ET,axiom,
% 0.21/0.53 mem @ c_2Ebool_2ET @ bool ).
% 0.21/0.53
% 0.21/0.53 thf(ax_true_p,axiom,
% 0.21/0.53 p @ c_2Ebool_2ET ).
% 0.21/0.53
% 0.21/0.53 thf(tp_c_2Eoption_2EIS__SOME,type,
% 0.21/0.53 c_2Eoption_2EIS__SOME: del > $i ).
% 0.21/0.53
% 0.21/0.53 thf(mem_c_2Eoption_2EIS__SOME,axiom,
% 0.21/0.53 ! [A_27a: del] : ( mem @ ( c_2Eoption_2EIS__SOME @ A_27a ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ bool ) ) ).
% 0.21/0.53
% 0.21/0.53 thf(tp_c_2Ebool_2E_7E,type,
% 0.21/0.53 c_2Ebool_2E_7E: $i ).
% 0.21/0.53
% 0.21/0.53 thf(mem_c_2Ebool_2E_7E,axiom,
% 0.21/0.53 mem @ c_2Ebool_2E_7E @ ( arr @ bool @ bool ) ).
% 0.21/0.53
% 0.21/0.53 thf(ax_neg_p,axiom,
% 0.21/0.53 ! [Q: $i] :
% 0.21/0.53 ( ( mem @ Q @ bool )
% 0.21/0.53 => ( ( p @ ( ap @ c_2Ebool_2E_7E @ Q ) )
% 0.21/0.53 <=> ~ ( p @ Q ) ) ) ).
% 0.21/0.53
% 0.21/0.53 thf(tp_c_2Eoption_2ETHE,type,
% 0.21/0.53 c_2Eoption_2ETHE: del > $i ).
% 0.21/0.53
% 0.21/0.53 thf(mem_c_2Eoption_2ETHE,axiom,
% 0.21/0.53 ! [A_27a: del] : ( mem @ ( c_2Eoption_2ETHE @ A_27a ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ A_27a ) ) ).
% 0.21/0.53
% 0.21/0.53 thf(tp_c_2Eoption_2ESOME,type,
% 0.21/0.53 c_2Eoption_2ESOME: del > $i ).
% 0.21/0.53
% 0.21/0.53 thf(mem_c_2Eoption_2ESOME,axiom,
% 0.21/0.53 ! [A_27a: del] : ( mem @ ( c_2Eoption_2ESOME @ A_27a ) @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) ).
% 0.21/0.53
% 0.21/0.53 thf(tp_c_2Ebool_2E_3F,type,
% 0.21/0.53 c_2Ebool_2E_3F: del > $i ).
% 0.21/0.53
% 0.21/0.53 thf(mem_c_2Ebool_2E_3F,axiom,
% 0.21/0.53 ! [A_27a: del] : ( mem @ ( c_2Ebool_2E_3F @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ).
% 0.21/0.53
% 0.21/0.53 thf(ax_ex_p,axiom,
% 0.21/0.53 ! [A: del,Q: $i] :
% 0.21/0.53 ( ( mem @ Q @ ( arr @ A @ bool ) )
% 0.21/0.53 => ( ( p @ ( ap @ ( c_2Ebool_2E_3F @ A ) @ Q ) )
% 0.21/0.53 <=> ? [X: $i] :
% 0.21/0.53 ( ( mem @ X @ A )
% 0.21/0.53 & ( p @ ( ap @ Q @ X ) ) ) ) ) ).
% 0.21/0.53
% 0.21/0.53 thf(tp_c_2Eoption_2ENONE,type,
% 0.21/0.53 c_2Eoption_2ENONE: del > $i ).
% 0.21/0.53
% 0.21/0.53 thf(mem_c_2Eoption_2ENONE,axiom,
% 0.21/0.53 ! [A_27a: del] : ( mem @ ( c_2Eoption_2ENONE @ A_27a ) @ ( ty_2Eoption_2Eoption @ A_27a ) ) ).
% 0.21/0.53
% 0.21/0.53 thf(tp_c_2Ebool_2E_2F_5C,type,
% 0.21/0.53 c_2Ebool_2E_2F_5C: $i ).
% 0.21/0.53
% 0.21/0.53 thf(mem_c_2Ebool_2E_2F_5C,axiom,
% 0.21/0.53 mem @ c_2Ebool_2E_2F_5C @ ( arr @ bool @ ( arr @ bool @ bool ) ) ).
% 0.21/0.53
% 0.21/0.53 thf(ax_and_p,axiom,
% 0.21/0.53 ! [Q: $i] :
% 0.21/0.53 ( ( mem @ Q @ bool )
% 0.21/0.53 => ! [R: $i] :
% 0.21/0.53 ( ( mem @ R @ bool )
% 0.21/0.53 => ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ Q ) @ R ) )
% 0.21/0.53 <=> ( ( p @ Q )
% 0.21/0.53 & ( p @ R ) ) ) ) ) ).
% 0.21/0.53
% 0.21/0.53 thf(tp_c_2Ebool_2E_5C_2F,type,
% 0.21/0.53 c_2Ebool_2E_5C_2F: $i ).
% 0.21/0.53
% 0.21/0.53 thf(mem_c_2Ebool_2E_5C_2F,axiom,
% 0.21/0.53 mem @ c_2Ebool_2E_5C_2F @ ( arr @ bool @ ( arr @ bool @ bool ) ) ).
% 0.21/0.53
% 0.21/0.53 thf(ax_or_p,axiom,
% 0.21/0.53 ! [Q: $i] :
% 0.21/0.53 ( ( mem @ Q @ bool )
% 0.21/0.53 => ! [R: $i] :
% 0.21/0.53 ( ( mem @ R @ bool )
% 0.21/0.53 => ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ Q ) @ R ) )
% 0.21/0.53 <=> ( ( p @ Q )
% 0.21/0.53 | ( p @ R ) ) ) ) ) ).
% 0.21/0.53
% 0.21/0.53 thf(tp_c_2Eoption_2EOPTREL,type,
% 0.21/0.53 c_2Eoption_2EOPTREL: del > del > $i ).
% 0.21/0.53
% 0.21/0.53 thf(mem_c_2Eoption_2EOPTREL,axiom,
% 0.21/0.53 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Eoption_2EOPTREL @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27b ) @ bool ) ) ) ) ).
% 0.21/0.53
% 0.21/0.53 thf(tp_c_2Emin_2E_3D,type,
% 0.21/0.53 c_2Emin_2E_3D: del > $i ).
% 0.21/0.53
% 0.21/0.53 thf(mem_c_2Emin_2E_3D,axiom,
% 0.21/0.53 ! [A_27a: del] : ( mem @ ( c_2Emin_2E_3D @ A_27a ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) ).
% 0.21/0.53
% 0.21/0.53 thf(ax_eq_p,axiom,
% 0.21/0.53 ! [A: del,X: $i] :
% 0.21/0.53 ( ( mem @ X @ A )
% 0.21/0.53 => ! [Y: $i] :
% 0.21/0.53 ( ( mem @ Y @ A )
% 0.21/0.53 => ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ X ) @ Y ) )
% 0.21/0.53 <=> ( X = Y ) ) ) ) ).
% 0.21/0.53
% 0.21/0.53 thf(tp_c_2Ebool_2E_21,type,
% 0.21/0.53 c_2Ebool_2E_21: del > $i ).
% 0.21/0.53
% 0.21/0.53 thf(mem_c_2Ebool_2E_21,axiom,
% 0.21/0.53 ! [A_27a: del] : ( mem @ ( c_2Ebool_2E_21 @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ).
% 0.21/0.53
% 0.21/0.53 thf(ax_all_p,axiom,
% 0.21/0.53 ! [A: del,Q: $i] :
% 0.21/0.53 ( ( mem @ Q @ ( arr @ A @ bool ) )
% 0.21/0.53 => ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ A ) @ Q ) )
% 0.21/0.53 <=> ! [X: $i] :
% 0.21/0.53 ( ( mem @ X @ A )
% 0.21/0.53 => ( p @ ( ap @ Q @ X ) ) ) ) ) ).
% 0.21/0.53
% 0.21/0.53 thf(conj_thm_2Ebool_2ETRUTH,axiom,
% 0.21/0.53 $true ).
% 0.21/0.53
% 0.21/0.53 thf(conj_thm_2Ebool_2EIMP__ANTISYM__AX,axiom,
% 0.21/0.53 ! [V0t1: $i] :
% 0.21/0.53 ( ( mem @ V0t1 @ bool )
% 0.21/0.53 => ! [V1t2: $i] :
% 0.21/0.53 ( ( mem @ V1t2 @ bool )
% 0.21/0.53 => ( ( ( p @ V0t1 )
% 0.21/0.53 => ( p @ V1t2 ) )
% 0.21/0.53 => ( ( ( p @ V1t2 )
% 0.21/0.53 => ( p @ V0t1 ) )
% 0.21/0.53 => ( ( p @ V0t1 )
% 0.21/0.53 <=> ( p @ V1t2 ) ) ) ) ) ) ).
% 0.21/0.53
% 0.21/0.53 thf(conj_thm_2Ebool_2EFALSITY,axiom,
% 0.21/0.53 ! [V0t: $i] :
% 0.21/0.53 ( ( mem @ V0t @ bool )
% 0.21/0.53 => ( $false
% 0.21/0.53 => ( p @ V0t ) ) ) ).
% 0.21/0.53
% 0.21/0.53 thf(conj_thm_2Ebool_2EEXISTS__SIMP,axiom,
% 0.21/0.53 ! [A_27a: del,V0t: $i] :
% 0.21/0.53 ( ( mem @ V0t @ bool )
% 0.21/0.53 => ( ? [V1x: $i] :
% 0.21/0.53 ( ( mem @ V1x @ A_27a )
% 0.21/0.53 & ( p @ V0t ) )
% 0.21/0.53 <=> ( p @ V0t ) ) ) ).
% 0.21/0.53
% 0.21/0.53 thf(conj_thm_2Ebool_2EAND__CLAUSES,axiom,
% 0.21/0.53 ! [V0t: $i] :
% 0.21/0.53 ( ( mem @ V0t @ bool )
% 0.21/0.53 => ( ( ( $true
% 0.21/0.53 & ( p @ V0t ) )
% 0.21/0.53 <=> ( p @ V0t ) )
% 0.21/0.53 & ( ( ( p @ V0t )
% 0.21/0.53 & $true )
% 0.21/0.53 <=> ( p @ V0t ) )
% 0.21/0.53 & ( ( $false
% 0.21/0.53 & ( p @ V0t ) )
% 0.21/0.53 <=> $false )
% 0.21/0.53 & ( ( ( p @ V0t )
% 0.21/0.53 & $false )
% 0.21/0.53 <=> $false )
% 0.21/0.53 & ( ( ( p @ V0t )
% 0.21/0.53 & ( p @ V0t ) )
% 0.21/0.53 <=> ( p @ V0t ) ) ) ) ).
% 0.21/0.53
% 0.21/0.53 thf(conj_thm_2Ebool_2EOR__CLAUSES,axiom,
% 0.21/0.53 ! [V0t: $i] :
% 0.21/0.53 ( ( mem @ V0t @ bool )
% 0.21/0.53 => ( ( ( $true
% 0.21/0.53 | ( p @ V0t ) )
% 0.21/0.53 <=> $true )
% 0.21/0.53 & ( ( ( p @ V0t )
% 0.21/0.53 | $true )
% 0.21/0.53 <=> $true )
% 0.21/0.53 & ( ( $false
% 0.21/0.53 | ( p @ V0t ) )
% 0.21/0.53 <=> ( p @ V0t ) )
% 0.21/0.53 & ( ( ( p @ V0t )
% 0.21/0.53 | $false )
% 0.21/0.53 <=> ( p @ V0t ) )
% 0.21/0.53 & ( ( ( p @ V0t )
% 0.21/0.53 | ( p @ V0t ) )
% 0.21/0.53 <=> ( p @ V0t ) ) ) ) ).
% 0.21/0.53
% 0.21/0.53 thf(conj_thm_2Ebool_2ENOT__CLAUSES,axiom,
% 0.21/0.53 ( ! [V0t: $i] :
% 0.21/0.53 ( ( mem @ V0t @ bool )
% 0.21/0.53 => ( ~ ~ ( p @ V0t )
% 0.21/0.53 <=> ( p @ V0t ) ) )
% 0.21/0.53 & ( ~ $true
% 0.21/0.53 <=> $false )
% 0.21/0.53 & ( ~ $false
% 0.21/0.53 <=> $true ) ) ).
% 0.21/0.53
% 0.21/0.53 thf(conj_thm_2Ebool_2EREFL__CLAUSE,axiom,
% 0.21/0.53 ! [A_27a: del,V0x: $i] :
% 0.21/0.53 ( ( mem @ V0x @ A_27a )
% 0.21/0.53 => ( ( V0x = V0x )
% 0.21/0.53 <=> $true ) ) ).
% 0.21/0.53
% 0.21/0.53 thf(conj_thm_2Ebool_2EEQ__CLAUSES,axiom,
% 0.21/0.53 ! [V0t: $i] :
% 0.21/0.53 ( ( mem @ V0t @ bool )
% 0.21/0.53 => ( ( ( $true
% 0.21/0.53 <=> ( p @ V0t ) )
% 0.21/0.53 <=> ( p @ V0t ) )
% 0.21/0.53 & ( ( ( p @ V0t )
% 0.21/0.53 <=> $true )
% 0.21/0.53 <=> ( p @ V0t ) )
% 0.21/0.53 & ( ( $false
% 0.21/0.53 <=> ( p @ V0t ) )
% 0.21/0.53 <=> ~ ( p @ V0t ) )
% 0.21/0.53 & ( ( ( p @ V0t )
% 0.21/0.53 <=> $false )
% 0.21/0.53 <=> ~ ( p @ V0t ) ) ) ) ).
% 0.21/0.53
% 0.21/0.53 thf(conj_thm_2Eoption_2Eoption__CLAUSES,axiom,
% 0.21/0.53 ! [A_27a: del,A_27b: del,V0e: $i] :
% 0.21/0.53 ( ( mem @ V0e @ A_27b )
% 0.21/0.53 => ! [V1f: $i] :
% 0.21/0.53 ( ( mem @ V1f @ ( arr @ A_27a @ A_27b ) )
% 0.21/0.53 => ! [V2e: $i] :
% 0.21/0.53 ( ( mem @ V2e @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 0.21/0.53 => ( ! [V3x: $i] :
% 0.21/0.53 ( ( mem @ V3x @ A_27a )
% 0.21/0.53 => ! [V4y: $i] :
% 0.21/0.53 ( ( mem @ V4y @ A_27a )
% 0.21/0.53 => ( ( ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V3x )
% 0.21/0.53 = ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V4y ) )
% 0.21/0.53 <=> ( V3x = V4y ) ) ) )
% 0.21/0.53 & ! [V5x: $i] :
% 0.21/0.53 ( ( mem @ V5x @ A_27a )
% 0.21/0.53 => ( ( ap @ ( c_2Eoption_2ETHE @ A_27a ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V5x ) )
% 0.21/0.53 = V5x ) )
% 0.21/0.53 & ! [V6x: $i] :
% 0.21/0.53 ( ( mem @ V6x @ A_27a )
% 0.21/0.53 => ( ( c_2Eoption_2ENONE @ A_27a )
% 0.21/0.53 != ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V6x ) ) )
% 0.21/0.53 & ! [V7x: $i] :
% 0.21/0.53 ( ( mem @ V7x @ A_27a )
% 0.21/0.53 => ( ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V7x )
% 0.21/0.53 != ( c_2Eoption_2ENONE @ A_27a ) ) )
% 0.21/0.53 & ! [V8x: $i] :
% 0.21/0.53 ( ( mem @ V8x @ A_27a )
% 0.21/0.53 => ( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27a ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V8x ) ) )
% 0.21/0.53 <=> $true ) )
% 0.21/0.53 & ( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27a ) @ ( c_2Eoption_2ENONE @ A_27a ) ) )
% 0.21/0.53 <=> $false )
% 0.21/0.53 & ! [V9x: $i] :
% 0.21/0.53 ( ( mem @ V9x @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 0.21/0.53 => ( ( p @ ( ap @ ( c_2Eoption_2EIS__NONE @ A_27a ) @ V9x ) )
% 0.21/0.53 <=> ( V9x
% 0.21/0.53 = ( c_2Eoption_2ENONE @ A_27a ) ) ) )
% 0.21/0.53 & ! [V10x: $i] :
% 0.21/0.53 ( ( mem @ V10x @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 0.21/0.53 => ( ~ ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27a ) @ V10x ) )
% 0.21/0.53 <=> ( V10x
% 0.21/0.53 = ( c_2Eoption_2ENONE @ A_27a ) ) ) )
% 0.21/0.53 & ! [V11x: $i] :
% 0.21/0.53 ( ( mem @ V11x @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 0.21/0.53 => ( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27a ) @ V11x ) )
% 0.21/0.53 => ( ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ ( ap @ ( c_2Eoption_2ETHE @ A_27a ) @ V11x ) )
% 0.21/0.53 = V11x ) ) )
% 0.21/0.53 & ! [V12x: $i] :
% 0.21/0.53 ( ( mem @ V12x @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 0.21/0.53 => ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A_27a @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ V12x ) @ ( c_2Eoption_2ENONE @ A_27a ) ) @ ( c_2Eoption_2ESOME @ A_27a ) )
% 0.21/0.53 = V12x ) )
% 0.21/0.53 & ! [V13x: $i] :
% 0.21/0.53 ( ( mem @ V13x @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 0.21/0.53 => ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A_27a @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ V13x ) @ V13x ) @ ( c_2Eoption_2ESOME @ A_27a ) )
% 0.21/0.53 = V13x ) )
% 0.21/0.53 & ! [V14x: $i] :
% 0.21/0.53 ( ( mem @ V14x @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 0.21/0.53 => ( ( p @ ( ap @ ( c_2Eoption_2EIS__NONE @ A_27a ) @ V14x ) )
% 0.21/0.53 => ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A_27a @ A_27b ) @ V14x ) @ V0e ) @ V1f )
% 0.21/0.53 = V0e ) ) )
% 0.21/0.53 & ! [V15x: $i] :
% 0.21/0.53 ( ( mem @ V15x @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 0.21/0.53 => ( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27a ) @ V15x ) )
% 0.21/0.53 => ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A_27a @ A_27b ) @ V15x ) @ V0e ) @ V1f )
% 0.21/0.53 = ( ap @ V1f @ ( ap @ ( c_2Eoption_2ETHE @ A_27a ) @ V15x ) ) ) ) )
% 0.21/0.53 & ! [V16x: $i] :
% 0.21/0.53 ( ( mem @ V16x @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 0.21/0.53 => ( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27a ) @ V16x ) )
% 0.21/0.53 => ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A_27a @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ V16x ) @ V2e ) @ ( c_2Eoption_2ESOME @ A_27a ) )
% 0.21/0.53 = V16x ) ) )
% 0.21/0.53 & ! [V17v: $i] :
% 0.21/0.53 ( ( mem @ V17v @ A_27b )
% 0.21/0.53 => ! [V18f: $i] :
% 0.21/0.53 ( ( mem @ V18f @ ( arr @ A_27a @ A_27b ) )
% 0.21/0.53 => ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A_27a @ A_27b ) @ ( c_2Eoption_2ENONE @ A_27a ) ) @ V17v ) @ V18f )
% 0.21/0.53 = V17v ) ) )
% 0.21/0.53 & ! [V19x: $i] :
% 0.21/0.53 ( ( mem @ V19x @ A_27a )
% 0.21/0.53 => ! [V20v: $i] :
% 0.21/0.53 ( ( mem @ V20v @ A_27b )
% 0.21/0.53 => ! [V21f: $i] :
% 0.21/0.53 ( ( mem @ V21f @ ( arr @ A_27a @ A_27b ) )
% 0.21/0.53 => ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A_27a @ A_27b ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V19x ) ) @ V20v ) @ V21f )
% 0.21/0.53 = ( ap @ V21f @ V19x ) ) ) ) )
% 0.21/0.55 & ! [V22f: $i] :
% 0.21/0.55 ( ( mem @ V22f @ ( arr @ A_27a @ A_27b ) )
% 0.21/0.55 => ! [V23x: $i] :
% 0.21/0.55 ( ( mem @ V23x @ A_27a )
% 0.21/0.55 => ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ A_27a @ A_27b ) @ V22f ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V23x ) )
% 0.21/0.55 = ( ap @ ( c_2Eoption_2ESOME @ A_27b ) @ ( ap @ V22f @ V23x ) ) ) ) )
% 0.21/0.55 & ! [V24f: $i] :
% 0.21/0.55 ( ( mem @ V24f @ ( arr @ A_27a @ A_27b ) )
% 0.21/0.55 => ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ A_27a @ A_27b ) @ V24f ) @ ( c_2Eoption_2ENONE @ A_27a ) )
% 0.21/0.55 = ( c_2Eoption_2ENONE @ A_27b ) ) )
% 0.21/0.55 & ( ( ap @ ( c_2Eoption_2EOPTION__JOIN @ A_27a ) @ ( c_2Eoption_2ENONE @ ( ty_2Eoption_2Eoption @ A_27a ) ) )
% 0.21/0.55 = ( c_2Eoption_2ENONE @ A_27a ) )
% 0.21/0.55 & ! [V25x: $i] :
% 0.21/0.55 ( ( mem @ V25x @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 0.21/0.55 => ( ( ap @ ( c_2Eoption_2EOPTION__JOIN @ A_27a ) @ ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ V25x ) )
% 0.21/0.55 = V25x ) ) ) ) ) ) ).
% 0.21/0.55
% 0.21/0.55 thf(ax_thm_2Eoption_2EOPTREL__def,axiom,
% 0.21/0.55 ! [A_27a: del,A_27b: del,V0R: $i] :
% 0.21/0.55 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 0.21/0.55 => ! [V1x: $i] :
% 0.21/0.55 ( ( mem @ V1x @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 0.21/0.55 => ! [V2y: $i] :
% 0.21/0.55 ( ( mem @ V2y @ ( ty_2Eoption_2Eoption @ A_27b ) )
% 0.21/0.55 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTREL @ A_27a @ A_27b ) @ V0R ) @ V1x ) @ V2y ) )
% 0.21/0.55 <=> ( ( ( V1x
% 0.21/0.55 = ( c_2Eoption_2ENONE @ A_27a ) )
% 0.21/0.55 & ( V2y
% 0.21/0.55 = ( c_2Eoption_2ENONE @ A_27b ) ) )
% 0.21/0.55 | ? [V3x0: $i] :
% 0.21/0.55 ( ( mem @ V3x0 @ A_27a )
% 0.21/0.55 & ? [V4y0: $i] :
% 0.21/0.55 ( ( mem @ V4y0 @ A_27b )
% 0.21/0.55 & ( V1x
% 0.21/0.55 = ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V3x0 ) )
% 0.21/0.55 & ( V2y
% 0.21/0.55 = ( ap @ ( c_2Eoption_2ESOME @ A_27b ) @ V4y0 ) )
% 0.21/0.55 & ( p @ ( ap @ ( ap @ V0R @ V3x0 ) @ V4y0 ) ) ) ) ) ) ) ) ) ).
% 0.21/0.55
% 0.21/0.55 thf(conj_thm_2Equotient__option_2EOPTION__REL__def,conjecture,
% 0.21/0.55 ! [A_27a: del,V0R: $i] :
% 0.21/0.55 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.21/0.55 => ! [V1x: $i] :
% 0.21/0.55 ( ( mem @ V1x @ A_27a )
% 0.21/0.55 => ! [V2y: $i] :
% 0.21/0.55 ( ( mem @ V2y @ A_27a )
% 0.21/0.55 => ( ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTREL @ A_27a @ A_27a ) @ V0R ) @ ( c_2Eoption_2ENONE @ A_27a ) ) @ ( c_2Eoption_2ENONE @ A_27a ) ) )
% 0.21/0.55 <=> $true )
% 0.21/0.55 & ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTREL @ A_27a @ A_27a ) @ V0R ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V1x ) ) @ ( c_2Eoption_2ENONE @ A_27a ) ) )
% 0.21/0.55 <=> $false )
% 0.21/0.55 & ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTREL @ A_27a @ A_27a ) @ V0R ) @ ( c_2Eoption_2ENONE @ A_27a ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V2y ) ) )
% 0.21/0.55 <=> $false )
% 0.21/0.55 & ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTREL @ A_27a @ A_27a ) @ V0R ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V1x ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V2y ) ) )
% 0.21/0.55 <=> ( p @ ( ap @ ( ap @ V0R @ V1x ) @ V2y ) ) ) ) ) ) ) ).
% 0.21/0.55
% 0.21/0.55 %------------------------------------------------------------------------------
% 0.21/0.55 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.GGTqd8w4mf/cvc5---1.0.5_24528.p...
% 0.21/0.55 (declare-sort $$unsorted 0)
% 0.21/0.55 (declare-sort tptp.del 0)
% 0.21/0.55 (declare-fun tptp.bool () tptp.del)
% 0.21/0.55 (declare-fun tptp.ind () tptp.del)
% 0.21/0.55 (declare-fun tptp.arr (tptp.del tptp.del) tptp.del)
% 0.21/0.55 (declare-fun tptp.mem ($$unsorted tptp.del) Bool)
% 0.21/0.55 (declare-fun tptp.ap ($$unsorted $$unsorted) $$unsorted)
% 0.21/0.55 (declare-fun tptp.lam (tptp.del (-> $$unsorted $$unsorted)) $$unsorted)
% 0.21/0.55 (declare-fun tptp.p ($$unsorted) Bool)
% 0.21/0.55 (declare-fun tptp.inj__o (Bool) $$unsorted)
% 0.21/0.55 (assert (forall ((X Bool)) (= (@ tptp.p (@ tptp.inj__o X)) X)))
% 0.21/0.55 (assert (forall ((X Bool)) (@ (@ tptp.mem (@ tptp.inj__o X)) tptp.bool)))
% 0.21/0.55 (assert (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) tptp.bool) (= X (@ tptp.inj__o (@ tptp.p X))))))
% 0.21/0.55 (assert (forall ((A tptp.del) (B tptp.del) (F $$unsorted)) (=> (@ (@ tptp.mem F) (@ (@ tptp.arr A) B)) (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) A) (@ (@ tptp.mem (@ (@ tptp.ap F) X)) B))))))
% 0.21/0.55 (assert (forall ((A tptp.del) (B tptp.del) (F (-> $$unsorted $$unsorted))) (=> (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) A) (@ (@ tptp.mem (@ F X)) B))) (@ (@ tptp.mem (@ (@ tptp.lam A) F)) (@ (@ tptp.arr A) B)))))
% 0.21/0.55 (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 $$unsorted)) (=> (@ (@ tptp.mem X) A) (= (@ (@ tptp.ap F) X) (@ (@ tptp.ap G) X)))) (= F G)))))))
% 0.21/0.55 (assert (forall ((A tptp.del) (F (-> $$unsorted $$unsorted)) (X $$unsorted)) (=> (@ (@ tptp.mem X) A) (= (@ (@ tptp.ap (@ (@ tptp.lam A) F)) X) (@ F X)))))
% 0.21/0.55 (declare-fun tptp.ty_2Eoption_2Eoption (tptp.del) tptp.del)
% 0.21/0.55 (declare-fun tptp.c_2Eoption_2EOPTION__JOIN (tptp.del) $$unsorted)
% 0.21/0.55 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.ty_2Eoption_2Eoption A_27a))) (@ (@ tptp.mem (@ tptp.c_2Eoption_2EOPTION__JOIN A_27a)) (@ (@ tptp.arr (@ tptp.ty_2Eoption_2Eoption _let_1)) _let_1)))))
% 0.21/0.55 (declare-fun tptp.c_2Eoption_2EOPTION__MAP (tptp.del tptp.del) $$unsorted)
% 0.21/0.55 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Eoption_2EOPTION__MAP A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) A_27b)) (@ (@ tptp.arr (@ tptp.ty_2Eoption_2Eoption A_27a)) (@ tptp.ty_2Eoption_2Eoption A_27b))))))
% 0.21/0.55 (declare-fun tptp.c_2Eoption_2Eoption__CASE (tptp.del tptp.del) $$unsorted)
% 0.21/0.55 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Eoption_2Eoption__CASE A_27a) A_27b)) (@ (@ tptp.arr (@ tptp.ty_2Eoption_2Eoption A_27a)) (@ (@ tptp.arr A_27b) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) A_27b)) A_27b))))))
% 0.21/0.55 (declare-fun tptp.c_2Emin_2E_3D_3D_3E () $$unsorted)
% 0.21/0.55 (assert (let ((_let_1 (@ tptp.arr tptp.bool))) (@ (@ tptp.mem tptp.c_2Emin_2E_3D_3D_3E) (@ _let_1 (@ _let_1 tptp.bool)))))
% 0.21/0.55 (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))))))))
% 0.21/0.55 (declare-fun tptp.c_2Eoption_2EIS__NONE (tptp.del) $$unsorted)
% 0.21/0.55 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Eoption_2EIS__NONE A_27a)) (@ (@ tptp.arr (@ tptp.ty_2Eoption_2Eoption A_27a)) tptp.bool))))
% 0.21/0.55 (declare-fun tptp.c_2Ebool_2EF () $$unsorted)
% 0.21/0.55 (assert (@ (@ tptp.mem tptp.c_2Ebool_2EF) tptp.bool))
% 0.21/0.55 (assert (not (@ tptp.p tptp.c_2Ebool_2EF)))
% 0.21/0.55 (declare-fun tptp.c_2Ebool_2ET () $$unsorted)
% 0.21/0.55 (assert (@ (@ tptp.mem tptp.c_2Ebool_2ET) tptp.bool))
% 0.21/0.55 (assert (@ tptp.p tptp.c_2Ebool_2ET))
% 0.21/0.55 (declare-fun tptp.c_2Eoption_2EIS__SOME (tptp.del) $$unsorted)
% 0.21/0.55 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Eoption_2EIS__SOME A_27a)) (@ (@ tptp.arr (@ tptp.ty_2Eoption_2Eoption A_27a)) tptp.bool))))
% 0.21/0.55 (declare-fun tptp.c_2Ebool_2E_7E () $$unsorted)
% 0.21/0.55 (assert (@ (@ tptp.mem tptp.c_2Ebool_2E_7E) (@ (@ tptp.arr tptp.bool) tptp.bool)))
% 0.21/0.55 (assert (forall ((Q $$unsorted)) (=> (@ (@ tptp.mem Q) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap tptp.c_2Ebool_2E_7E) Q)) (not (@ tptp.p Q))))))
% 0.21/0.55 (declare-fun tptp.c_2Eoption_2ETHE (tptp.del) $$unsorted)
% 0.21/0.55 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Eoption_2ETHE A_27a)) (@ (@ tptp.arr (@ tptp.ty_2Eoption_2Eoption A_27a)) A_27a))))
% 0.21/0.55 (declare-fun tptp.c_2Eoption_2ESOME (tptp.del) $$unsorted)
% 0.21/0.55 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Eoption_2ESOME A_27a)) (@ (@ tptp.arr A_27a) (@ tptp.ty_2Eoption_2Eoption A_27a)))))
% 0.21/0.55 (declare-fun tptp.c_2Ebool_2E_3F (tptp.del) $$unsorted)
% 0.21/0.55 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Ebool_2E_3F A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool))))
% 0.21/0.55 (assert (forall ((A tptp.del) (Q $$unsorted)) (=> (@ (@ tptp.mem Q) (@ (@ tptp.arr A) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F A)) Q)) (exists ((X $$unsorted)) (and (@ (@ tptp.mem X) A) (@ tptp.p (@ (@ tptp.ap Q) X))))))))
% 0.21/0.55 (declare-fun tptp.c_2Eoption_2ENONE (tptp.del) $$unsorted)
% 0.21/0.55 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Eoption_2ENONE A_27a)) (@ tptp.ty_2Eoption_2Eoption A_27a))))
% 0.21/0.55 (declare-fun tptp.c_2Ebool_2E_2F_5C () $$unsorted)
% 0.21/0.55 (assert (let ((_let_1 (@ tptp.arr tptp.bool))) (@ (@ tptp.mem tptp.c_2Ebool_2E_2F_5C) (@ _let_1 (@ _let_1 tptp.bool)))))
% 0.21/0.55 (assert (forall ((Q $$unsorted)) (=> (@ (@ tptp.mem Q) tptp.bool) (forall ((R $$unsorted)) (=> (@ (@ tptp.mem R) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) Q)) R)) (and (@ tptp.p Q) (@ tptp.p R))))))))
% 0.21/0.55 (declare-fun tptp.c_2Ebool_2E_5C_2F () $$unsorted)
% 0.21/0.55 (assert (let ((_let_1 (@ tptp.arr tptp.bool))) (@ (@ tptp.mem tptp.c_2Ebool_2E_5C_2F) (@ _let_1 (@ _let_1 tptp.bool)))))
% 0.21/0.55 (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))))))))
% 0.21/0.55 (declare-fun tptp.c_2Eoption_2EOPTREL (tptp.del tptp.del) $$unsorted)
% 0.21/0.55 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Eoption_2EOPTREL A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (@ (@ tptp.arr (@ tptp.ty_2Eoption_2Eoption A_27a)) (@ (@ tptp.arr (@ tptp.ty_2Eoption_2Eoption A_27b)) tptp.bool))))))
% 0.21/0.55 (declare-fun tptp.c_2Emin_2E_3D (tptp.del) $$unsorted)
% 0.21/0.55 (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))))))
% 0.21/0.55 (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)))))))
% 0.21/0.55 (declare-fun tptp.c_2Ebool_2E_21 (tptp.del) $$unsorted)
% 0.21/0.55 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Ebool_2E_21 A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool))))
% 0.21/0.55 (assert (forall ((A tptp.del) (Q $$unsorted)) (=> (@ (@ tptp.mem Q) (@ (@ tptp.arr A) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A)) Q)) (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) A) (@ tptp.p (@ (@ tptp.ap Q) X))))))))
% 0.21/0.55 (assert true)
% 0.21/0.55 (assert (forall ((V0t1 $$unsorted)) (=> (@ (@ tptp.mem V0t1) tptp.bool) (forall ((V1t2 $$unsorted)) (let ((_let_1 (@ tptp.p V1t2))) (let ((_let_2 (@ tptp.p V0t1))) (=> (@ (@ tptp.mem V1t2) tptp.bool) (=> (=> _let_2 _let_1) (=> (=> _let_1 _let_2) (= _let_2 _let_1))))))))))
% 0.21/0.55 (assert (forall ((V0t $$unsorted)) (=> (@ (@ tptp.mem V0t) tptp.bool) (=> false (@ tptp.p V0t)))))
% 0.21/0.55 (assert (forall ((A_27a tptp.del) (V0t $$unsorted)) (=> (@ (@ tptp.mem V0t) tptp.bool) (= (exists ((V1x $$unsorted)) (and (@ (@ tptp.mem V1x) A_27a) (@ tptp.p V0t))) (@ tptp.p V0t)))))
% 0.21/0.55 (assert (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (and (= (and true _let_1) _let_1) (= (and _let_1 true) _let_1) (= (and false _let_1) false) (= (and _let_1 false) false) (= (and _let_1 _let_1) _let_1))))))
% 0.21/0.55 (assert (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (and (= (or true _let_1) true) (= (or _let_1 true) true) (= (or false _let_1) _let_1) (= (or _let_1 false) _let_1) (= (or _let_1 _let_1) _let_1))))))
% 0.21/0.55 (assert (and (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (= (not (not _let_1)) _let_1)))) (= (not true) false) (= (not false) true)))
% 0.21/0.55 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (= (= V0x V0x) true))))
% 0.21/0.55 (assert (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (let ((_let_2 (not _let_1))) (=> (@ (@ tptp.mem V0t) tptp.bool) (and (= (= true _let_1) _let_1) (= (= _let_1 true) _let_1) (= (= false _let_1) _let_2) (= (= _let_1 false) _let_2)))))))
% 0.21/0.55 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0e $$unsorted)) (=> (@ (@ tptp.mem V0e) A_27b) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V2e $$unsorted)) (let ((_let_1 (@ tptp.c_2Eoption_2ENONE A_27a))) (let ((_let_2 (@ tptp.ty_2Eoption_2Eoption A_27a))) (=> (@ (@ tptp.mem V2e) _let_2) (and (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (forall ((V4y $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)))) (=> (@ (@ tptp.mem V4y) A_27a) (= (= (@ _let_1 V3x) (@ _let_1 V4y)) (= V3x V4y))))))) (forall ((V5x $$unsorted)) (=> (@ (@ tptp.mem V5x) A_27a) (= (@ (@ tptp.ap (@ tptp.c_2Eoption_2ETHE A_27a)) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V5x)) V5x))) (forall ((V6x $$unsorted)) (=> (@ (@ tptp.mem V6x) A_27a) (not (= (@ tptp.c_2Eoption_2ENONE A_27a) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V6x))))) (forall ((V7x $$unsorted)) (=> (@ (@ tptp.mem V7x) A_27a) (not (= (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V7x) (@ tptp.c_2Eoption_2ENONE A_27a))))) (forall ((V8x $$unsorted)) (=> (@ (@ tptp.mem V8x) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eoption_2EIS__SOME A_27a)) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V8x))) true))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eoption_2EIS__SOME A_27a)) _let_1)) false) (forall ((V9x $$unsorted)) (=> (@ (@ tptp.mem V9x) (@ tptp.ty_2Eoption_2Eoption A_27a)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eoption_2EIS__NONE A_27a)) V9x)) (= V9x (@ tptp.c_2Eoption_2ENONE A_27a))))) (forall ((V10x $$unsorted)) (=> (@ (@ tptp.mem V10x) (@ tptp.ty_2Eoption_2Eoption A_27a)) (= (not (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eoption_2EIS__SOME A_27a)) V10x))) (= V10x (@ tptp.c_2Eoption_2ENONE A_27a))))) (forall ((V11x $$unsorted)) (=> (@ (@ tptp.mem V11x) (@ tptp.ty_2Eoption_2Eoption A_27a)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eoption_2EIS__SOME A_27a)) V11x)) (= (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ETHE A_27a)) V11x)) V11x)))) (forall ((V12x $$unsorted)) (let ((_let_1 (@ tptp.ty_2Eoption_2Eoption A_27a))) (=> (@ (@ tptp.mem V12x) _let_1) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2Eoption__CASE A_27a) _let_1)) V12x)) (@ tptp.c_2Eoption_2ENONE A_27a))) (@ tptp.c_2Eoption_2ESOME A_27a)) V12x)))) (forall ((V13x $$unsorted)) (let ((_let_1 (@ tptp.ty_2Eoption_2Eoption A_27a))) (=> (@ (@ tptp.mem V13x) _let_1) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2Eoption__CASE A_27a) _let_1)) V13x)) V13x)) (@ tptp.c_2Eoption_2ESOME A_27a)) V13x)))) (forall ((V14x $$unsorted)) (=> (@ (@ tptp.mem V14x) (@ tptp.ty_2Eoption_2Eoption A_27a)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eoption_2EIS__NONE A_27a)) V14x)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2Eoption__CASE A_27a) A_27b)) V14x)) V0e)) V1f) V0e)))) (forall ((V15x $$unsorted)) (=> (@ (@ tptp.mem V15x) (@ tptp.ty_2Eoption_2Eoption A_27a)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eoption_2EIS__SOME A_27a)) V15x)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2Eoption__CASE A_27a) A_27b)) V15x)) V0e)) V1f) (@ (@ tptp.ap V1f) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ETHE A_27a)) V15x)))))) (forall ((V16x $$unsorted)) (let ((_let_1 (@ tptp.ty_2Eoption_2Eoption A_27a))) (=> (@ (@ tptp.mem V16x) _let_1) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eoption_2EIS__SOME A_27a)) V16x)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2Eoption__CASE A_27a) _let_1)) V16x)) V2e)) (@ tptp.c_2Eoption_2ESOME A_27a)) V16x))))) (forall ((V17v $$unsorted)) (=> (@ (@ tptp.mem V17v) A_27b) (forall ((V18f $$unsorted)) (=> (@ (@ tptp.mem V18f) (@ (@ tptp.arr A_27a) A_27b)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2Eoption__CASE A_27a) A_27b)) (@ tptp.c_2Eoption_2ENONE A_27a))) V17v)) V18f) V17v))))) (forall ((V19x $$unsorted)) (=> (@ (@ tptp.mem V19x) A_27a) (forall ((V20v $$unsorted)) (=> (@ (@ tptp.mem V20v) A_27b) (forall ((V21f $$unsorted)) (=> (@ (@ tptp.mem V21f) (@ (@ tptp.arr A_27a) A_27b)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ /export/starexec/sandbox2/solver/bin/do_THM_THF: line 35: 27241 Alarm clock ( read result; case "$result" in
% 299.68/300.17 unsat)
% 299.68/300.17 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 299.68/300.17 ;;
% 299.68/300.17 sat)
% 299.68/300.17 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 299.68/300.17 ;;
% 299.68/300.17 esac; exit 1 )
% 299.68/300.18 (@ tptp.c_2Eoption_2Eoption__CASE A_27a) A_27b)) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V19x))) V20v)) V21f) (@ (@ tptp.ap V21f) V19x)))))))) (forall ((V22f $$unsorted)) (=> (@ (@ tptp.mem V22f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V23x $$unsorted)) (=> (@ (@ tptp.mem V23x) A_27a) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2EOPTION__MAP A_27a) A_27b)) V22f)) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V23x)) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27b)) (@ (@ tptp.ap V22f) V23x))))))) (forall ((V24f $$unsorted)) (=> (@ (@ tptp.mem V24f) (@ (@ tptp.arr A_27a) A_27b)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2EOPTION__MAP A_27a) A_27b)) V24f)) (@ tptp.c_2Eoption_2ENONE A_27a)) (@ tptp.c_2Eoption_2ENONE A_27b)))) (= (@ (@ tptp.ap (@ tptp.c_2Eoption_2EOPTION__JOIN A_27a)) (@ tptp.c_2Eoption_2ENONE _let_2)) _let_1) (forall ((V25x $$unsorted)) (let ((_let_1 (@ tptp.ty_2Eoption_2Eoption A_27a))) (=> (@ (@ tptp.mem V25x) _let_1) (= (@ (@ tptp.ap (@ tptp.c_2Eoption_2EOPTION__JOIN A_27a)) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME _let_1)) V25x)) V25x))))))))))))))
% 299.68/300.18 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R $$unsorted)) (=> (@ (@ tptp.mem V0R) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) (@ tptp.ty_2Eoption_2Eoption A_27a)) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) (@ tptp.ty_2Eoption_2Eoption A_27b)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2EOPTREL A_27a) A_27b)) V0R)) V1x)) V2y)) (or (and (= V1x (@ tptp.c_2Eoption_2ENONE A_27a)) (= V2y (@ tptp.c_2Eoption_2ENONE A_27b))) (exists ((V3x0 $$unsorted)) (and (@ (@ tptp.mem V3x0) A_27a) (exists ((V4y0 $$unsorted)) (and (@ (@ tptp.mem V4y0) A_27b) (= V1x (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V3x0)) (= V2y (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27b)) V4y0)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V3x0)) V4y0)))))))))))))))
% 299.68/300.18 (assert (not (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)))) (let ((_let_2 (@ _let_1 V2y))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2EOPTREL A_27a) A_27a)) V0R)))) (let ((_let_4 (@ tptp.ap (@ _let_3 (@ _let_1 V1x))))) (let ((_let_5 (@ tptp.c_2Eoption_2ENONE A_27a))) (let ((_let_6 (@ tptp.ap (@ _let_3 _let_5)))) (=> (@ (@ tptp.mem V2y) A_27a) (and (= (@ tptp.p (@ _let_6 _let_5)) true) (= (@ tptp.p (@ _let_4 _let_5)) false) (= (@ tptp.p (@ _let_6 _let_2)) false) (= (@ tptp.p (@ _let_4 _let_2)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V1x)) V2y)))))))))))))))))))
% 299.68/300.18 (set-info :filename cvc5---1.0.5_24528)
% 299.68/300.18 (check-sat-assuming ( true ))
% 299.68/300.18 ------- get file name : TPTP file name is ITP011^2
% 299.68/300.18 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_24528.smt2...
% 299.68/300.18 --- Run --ho-elim --full-saturate-quant at 10...
% 299.68/300.18 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
% 299.68/300.18 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10...
% 299.68/300.18 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5...
% 299.68/300.18 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5...
% 299.68/300.18 --- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 10...
% 299.68/300.18 --- Run --no-ho-matching --full-saturate-quant --macros-quant-mode=all at 10...
% 299.68/300.18 --- Run --ho-elim --full-saturate-quant --enum-inst-interleave at 10...
% 299.68/300.18 --- Run --no-ho-matching --full-saturate-quant --ho-elim-store-ax at 10...
% 299.68/300.18 --- Run --ho-elim --no-ho-elim-store-ax --full-saturate-quant...
% 299.68/300.18 % cvc5---1.0.5 exiting
% 299.68/300.18 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------