TSTP Solution File: ITP010^2 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP010^2 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n015.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 03:14:30 EDT 2023
% Result : Theorem 0.22s 0.53s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ITP010^2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.36 % Computer : n015.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun Aug 27 13:56:39 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.22/0.49 %----Proving TH0
% 0.22/0.49 %------------------------------------------------------------------------------
% 0.22/0.49 % File : ITP010^2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.22/0.49 % Domain : Interactive Theorem Proving
% 0.22/0.49 % Problem : HOL4 set theory export of thm_2Ecardinal_2ECARD__NOT__LE.p, bushy mode
% 0.22/0.49 % Version : [BG+19] axioms.
% 0.22/0.49 % English :
% 0.22/0.49
% 0.22/0.49 % Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% 0.22/0.49 % : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% 0.22/0.49 % Source : [BG+19]
% 0.22/0.49 % Names : thm_2Ecardinal_2ECARD__NOT__LE.p [Gau19]
% 0.22/0.49 % : HL404501^2.p [TPAP]
% 0.22/0.49
% 0.22/0.49 % Status : Theorem
% 0.22/0.49 % Rating : 0.15 v8.1.0, 0.18 v7.5.0
% 0.22/0.49 % Syntax : Number of formulae : 58 ( 4 unt; 18 typ; 0 def)
% 0.22/0.49 % Number of atoms : 264 ( 7 equ; 0 cnn)
% 0.22/0.49 % Maximal formula atoms : 21 ( 6 avg)
% 0.22/0.49 % Number of connectives : 459 ( 29 ~; 14 |; 14 &; 305 @)
% 0.22/0.49 % ( 33 <=>; 64 =>; 0 <=; 0 <~>)
% 0.22/0.49 % Maximal formula depth : 16 ( 8 avg)
% 0.22/0.49 % Number of types : 3 ( 1 usr)
% 0.22/0.49 % Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% 0.22/0.49 % Number of symbols : 25 ( 22 usr; 15 con; 0-2 aty)
% 0.22/0.49 % Number of variables : 65 ( 0 ^; 65 !; 0 ?; 65 :)
% 0.22/0.49 % SPC : TH0_THM_EQU_NAR
% 0.22/0.49
% 0.22/0.49 % Comments :
% 0.22/0.49 % Bugfixes : v7.5.0 - Bugfixes in axioms and export.
% 0.22/0.49 %------------------------------------------------------------------------------
% 0.22/0.49 %------------------------------------------------------------------------------
% 0.22/0.49 thf(del_tp,type,
% 0.22/0.49 del: $tType ).
% 0.22/0.49
% 0.22/0.49 thf(bool,type,
% 0.22/0.49 bool: del ).
% 0.22/0.49
% 0.22/0.49 thf(ind,type,
% 0.22/0.49 ind: del ).
% 0.22/0.49
% 0.22/0.49 thf(arr,type,
% 0.22/0.49 arr: del > del > del ).
% 0.22/0.49
% 0.22/0.49 thf(mem,type,
% 0.22/0.49 mem: $i > del > $o ).
% 0.22/0.49
% 0.22/0.49 thf(ap,type,
% 0.22/0.49 ap: $i > $i > $i ).
% 0.22/0.49
% 0.22/0.49 thf(lam,type,
% 0.22/0.49 lam: del > ( $i > $i ) > $i ).
% 0.22/0.49
% 0.22/0.49 thf(p,type,
% 0.22/0.49 p: $i > $o ).
% 0.22/0.49
% 0.22/0.49 thf(stp_inj_o,type,
% 0.22/0.49 inj__o: $o > $i ).
% 0.22/0.49
% 0.22/0.49 thf(stp_inj_surj_o,axiom,
% 0.22/0.49 ! [X: $o] :
% 0.22/0.49 ( ( p @ ( inj__o @ X ) )
% 0.22/0.49 = X ) ).
% 0.22/0.49
% 0.22/0.49 thf(stp_inj_mem_o,axiom,
% 0.22/0.49 ! [X: $o] : ( mem @ ( inj__o @ X ) @ bool ) ).
% 0.22/0.49
% 0.22/0.49 thf(stp_iso_mem_o,axiom,
% 0.22/0.49 ! [X: $i] :
% 0.22/0.49 ( ( mem @ X @ bool )
% 0.22/0.49 => ( X
% 0.22/0.49 = ( inj__o @ ( p @ X ) ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(ap_tp,axiom,
% 0.22/0.49 ! [A: del,B: del,F: $i] :
% 0.22/0.49 ( ( mem @ F @ ( arr @ A @ B ) )
% 0.22/0.49 => ! [X: $i] :
% 0.22/0.49 ( ( mem @ X @ A )
% 0.22/0.49 => ( mem @ ( ap @ F @ X ) @ B ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(lam_tp,axiom,
% 0.22/0.49 ! [A: del,B: del,F: $i > $i] :
% 0.22/0.49 ( ! [X: $i] :
% 0.22/0.49 ( ( mem @ X @ A )
% 0.22/0.49 => ( mem @ ( F @ X ) @ B ) )
% 0.22/0.49 => ( mem @ ( lam @ A @ F ) @ ( arr @ A @ B ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(funcext,axiom,
% 0.22/0.49 ! [A: del,B: del,F: $i] :
% 0.22/0.49 ( ( mem @ F @ ( arr @ A @ B ) )
% 0.22/0.49 => ! [G: $i] :
% 0.22/0.49 ( ( mem @ G @ ( arr @ A @ B ) )
% 0.22/0.49 => ( ! [X: $i] :
% 0.22/0.49 ( ( mem @ X @ A )
% 0.22/0.49 => ( ( ap @ F @ X )
% 0.22/0.49 = ( ap @ G @ X ) ) )
% 0.22/0.49 => ( F = G ) ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(beta,axiom,
% 0.22/0.49 ! [A: del,F: $i > $i,X: $i] :
% 0.22/0.49 ( ( mem @ X @ A )
% 0.22/0.49 => ( ( ap @ ( lam @ A @ F ) @ X )
% 0.22/0.49 = ( F @ X ) ) ) ).
% 0.22/0.49
% 0.22/0.49 %------------------------------------------------------------------------------
% 0.22/0.49 %------------------------------------------------------------------------------
% 0.22/0.49 thf(tp_c_2Ebool_2ET,type,
% 0.22/0.49 c_2Ebool_2ET: $i ).
% 0.22/0.49
% 0.22/0.49 thf(mem_c_2Ebool_2ET,axiom,
% 0.22/0.49 mem @ c_2Ebool_2ET @ bool ).
% 0.22/0.49
% 0.22/0.49 thf(ax_true_p,axiom,
% 0.22/0.49 p @ c_2Ebool_2ET ).
% 0.22/0.49
% 0.22/0.49 thf(tp_c_2Ecardinal_2Ecardleq,type,
% 0.22/0.49 c_2Ecardinal_2Ecardleq: del > del > $i ).
% 0.22/0.49
% 0.22/0.49 thf(mem_c_2Ecardinal_2Ecardleq,axiom,
% 0.22/0.49 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27b @ bool ) @ bool ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(tp_c_2Ebool_2EF,type,
% 0.22/0.49 c_2Ebool_2EF: $i ).
% 0.22/0.49
% 0.22/0.49 thf(mem_c_2Ebool_2EF,axiom,
% 0.22/0.49 mem @ c_2Ebool_2EF @ bool ).
% 0.22/0.49
% 0.22/0.49 thf(ax_false_p,axiom,
% 0.22/0.49 ~ ( p @ c_2Ebool_2EF ) ).
% 0.22/0.49
% 0.22/0.49 thf(tp_c_2Emin_2E_3D_3D_3E,type,
% 0.22/0.49 c_2Emin_2E_3D_3D_3E: $i ).
% 0.22/0.49
% 0.22/0.49 thf(mem_c_2Emin_2E_3D_3D_3E,axiom,
% 0.22/0.49 mem @ c_2Emin_2E_3D_3D_3E @ ( arr @ bool @ ( arr @ bool @ bool ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(ax_imp_p,axiom,
% 0.22/0.49 ! [Q: $i] :
% 0.22/0.49 ( ( mem @ Q @ bool )
% 0.22/0.49 => ! [R: $i] :
% 0.22/0.49 ( ( mem @ R @ bool )
% 0.22/0.49 => ( ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ Q ) @ R ) )
% 0.22/0.49 <=> ( ( p @ Q )
% 0.22/0.49 => ( p @ R ) ) ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(tp_c_2Ebool_2E_5C_2F,type,
% 0.22/0.49 c_2Ebool_2E_5C_2F: $i ).
% 0.22/0.49
% 0.22/0.49 thf(mem_c_2Ebool_2E_5C_2F,axiom,
% 0.22/0.49 mem @ c_2Ebool_2E_5C_2F @ ( arr @ bool @ ( arr @ bool @ bool ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(ax_or_p,axiom,
% 0.22/0.49 ! [Q: $i] :
% 0.22/0.49 ( ( mem @ Q @ bool )
% 0.22/0.49 => ! [R: $i] :
% 0.22/0.49 ( ( mem @ R @ bool )
% 0.22/0.49 => ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ Q ) @ R ) )
% 0.22/0.49 <=> ( ( p @ Q )
% 0.22/0.49 | ( p @ R ) ) ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(tp_c_2Ebool_2E_2F_5C,type,
% 0.22/0.49 c_2Ebool_2E_2F_5C: $i ).
% 0.22/0.49
% 0.22/0.49 thf(mem_c_2Ebool_2E_2F_5C,axiom,
% 0.22/0.49 mem @ c_2Ebool_2E_2F_5C @ ( arr @ bool @ ( arr @ bool @ bool ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(ax_and_p,axiom,
% 0.22/0.49 ! [Q: $i] :
% 0.22/0.49 ( ( mem @ Q @ bool )
% 0.22/0.49 => ! [R: $i] :
% 0.22/0.49 ( ( mem @ R @ bool )
% 0.22/0.49 => ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ Q ) @ R ) )
% 0.22/0.49 <=> ( ( p @ Q )
% 0.22/0.49 & ( p @ R ) ) ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(tp_c_2Ebool_2E_7E,type,
% 0.22/0.49 c_2Ebool_2E_7E: $i ).
% 0.22/0.49
% 0.22/0.49 thf(mem_c_2Ebool_2E_7E,axiom,
% 0.22/0.49 mem @ c_2Ebool_2E_7E @ ( arr @ bool @ bool ) ).
% 0.22/0.49
% 0.22/0.49 thf(ax_neg_p,axiom,
% 0.22/0.49 ! [Q: $i] :
% 0.22/0.49 ( ( mem @ Q @ bool )
% 0.22/0.49 => ( ( p @ ( ap @ c_2Ebool_2E_7E @ Q ) )
% 0.22/0.49 <=> ~ ( p @ Q ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(tp_c_2Emin_2E_3D,type,
% 0.22/0.49 c_2Emin_2E_3D: del > $i ).
% 0.22/0.49
% 0.22/0.49 thf(mem_c_2Emin_2E_3D,axiom,
% 0.22/0.49 ! [A_27a: del] : ( mem @ ( c_2Emin_2E_3D @ A_27a ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(ax_eq_p,axiom,
% 0.22/0.49 ! [A: del,X: $i] :
% 0.22/0.49 ( ( mem @ X @ A )
% 0.22/0.49 => ! [Y: $i] :
% 0.22/0.49 ( ( mem @ Y @ A )
% 0.22/0.49 => ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ X ) @ Y ) )
% 0.22/0.49 <=> ( X = Y ) ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(tp_c_2Ebool_2E_21,type,
% 0.22/0.49 c_2Ebool_2E_21: del > $i ).
% 0.22/0.49
% 0.22/0.49 thf(mem_c_2Ebool_2E_21,axiom,
% 0.22/0.49 ! [A_27a: del] : ( mem @ ( c_2Ebool_2E_21 @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(ax_all_p,axiom,
% 0.22/0.49 ! [A: del,Q: $i] :
% 0.22/0.49 ( ( mem @ Q @ ( arr @ A @ bool ) )
% 0.22/0.49 => ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ A ) @ Q ) )
% 0.22/0.49 <=> ! [X: $i] :
% 0.22/0.49 ( ( mem @ X @ A )
% 0.22/0.49 => ( p @ ( ap @ Q @ X ) ) ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(conj_thm_2Ebool_2ETRUTH,axiom,
% 0.22/0.49 $true ).
% 0.22/0.49
% 0.22/0.49 thf(conj_thm_2Ebool_2EFALSITY,axiom,
% 0.22/0.49 ! [V0t: $i] :
% 0.22/0.49 ( ( mem @ V0t @ bool )
% 0.22/0.49 => ( $false
% 0.22/0.49 => ( p @ V0t ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(conj_thm_2Ebool_2EFORALL__SIMP,axiom,
% 0.22/0.49 ! [A_27a: del,V0t: $i] :
% 0.22/0.49 ( ( mem @ V0t @ bool )
% 0.22/0.49 => ( ! [V1x: $i] :
% 0.22/0.49 ( ( mem @ V1x @ A_27a )
% 0.22/0.49 => ( p @ V0t ) )
% 0.22/0.49 <=> ( p @ V0t ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(conj_thm_2Ebool_2EIMP__CLAUSES,axiom,
% 0.22/0.49 ! [V0t: $i] :
% 0.22/0.49 ( ( mem @ V0t @ bool )
% 0.22/0.49 => ( ( ( $true
% 0.22/0.49 => ( p @ V0t ) )
% 0.22/0.49 <=> ( p @ V0t ) )
% 0.22/0.49 & ( ( ( p @ V0t )
% 0.22/0.49 => $true )
% 0.22/0.49 <=> $true )
% 0.22/0.49 & ( ( $false
% 0.22/0.49 => ( p @ V0t ) )
% 0.22/0.49 <=> $true )
% 0.22/0.49 & ( ( ( p @ V0t )
% 0.22/0.49 => ( p @ V0t ) )
% 0.22/0.49 <=> $true )
% 0.22/0.49 & ( ( ( p @ V0t )
% 0.22/0.49 => $false )
% 0.22/0.49 <=> ~ ( p @ V0t ) ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(conj_thm_2Ebool_2ENOT__CLAUSES,axiom,
% 0.22/0.49 ( ! [V0t: $i] :
% 0.22/0.49 ( ( mem @ V0t @ bool )
% 0.22/0.49 => ( ~ ~ ( p @ V0t )
% 0.22/0.49 <=> ( p @ V0t ) ) )
% 0.22/0.49 & ( ~ $true
% 0.22/0.49 <=> $false )
% 0.22/0.49 & ( ~ $false
% 0.22/0.49 <=> $true ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(conj_thm_2Ebool_2EREFL__CLAUSE,axiom,
% 0.22/0.49 ! [A_27a: del,V0x: $i] :
% 0.22/0.49 ( ( mem @ V0x @ A_27a )
% 0.22/0.49 => ( ( V0x = V0x )
% 0.22/0.49 <=> $true ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(conj_thm_2Ebool_2EEQ__CLAUSES,axiom,
% 0.22/0.49 ! [V0t: $i] :
% 0.22/0.49 ( ( mem @ V0t @ bool )
% 0.22/0.49 => ( ( ( $true
% 0.22/0.49 <=> ( p @ V0t ) )
% 0.22/0.49 <=> ( p @ V0t ) )
% 0.22/0.49 & ( ( ( p @ V0t )
% 0.22/0.49 <=> $true )
% 0.22/0.49 <=> ( p @ V0t ) )
% 0.22/0.49 & ( ( $false
% 0.22/0.49 <=> ( p @ V0t ) )
% 0.22/0.49 <=> ~ ( p @ V0t ) )
% 0.22/0.49 & ( ( ( p @ V0t )
% 0.22/0.49 <=> $false )
% 0.22/0.49 <=> ~ ( p @ V0t ) ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(conj_thm_2Ecardinal_2ECARD__LE__TOTAL,axiom,
% 0.22/0.49 ! [A_27a: del,A_27b: del,V0s: $i] :
% 0.22/0.49 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 0.22/0.49 => ! [V1t: $i] :
% 0.22/0.49 ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
% 0.22/0.49 => ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27b ) @ V0s ) @ V1t ) )
% 0.22/0.49 | ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27b @ A_27a ) @ V1t ) @ V0s ) ) ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(conj_thm_2Esat_2ENOT__NOT,axiom,
% 0.22/0.50 ! [V0t: $i] :
% 0.22/0.50 ( ( mem @ V0t @ bool )
% 0.22/0.50 => ( ~ ~ ( p @ V0t )
% 0.22/0.50 <=> ( p @ V0t ) ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(conj_thm_2Esat_2EAND__INV__IMP,axiom,
% 0.22/0.50 ! [V0A: $i] :
% 0.22/0.50 ( ( mem @ V0A @ bool )
% 0.22/0.50 => ( ( p @ V0A )
% 0.22/0.50 => ( ~ ( p @ V0A )
% 0.22/0.50 => $false ) ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(conj_thm_2Esat_2EOR__DUAL2,axiom,
% 0.22/0.50 ! [V0A: $i] :
% 0.22/0.50 ( ( mem @ V0A @ bool )
% 0.22/0.50 => ! [V1B: $i] :
% 0.22/0.50 ( ( mem @ V1B @ bool )
% 0.22/0.50 => ( ( ~ ( ( p @ V0A )
% 0.22/0.50 | ( p @ V1B ) )
% 0.22/0.50 => $false )
% 0.22/0.50 <=> ( ( ( p @ V0A )
% 0.22/0.50 => $false )
% 0.22/0.50 => ( ~ ( p @ V1B )
% 0.22/0.50 => $false ) ) ) ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(conj_thm_2Esat_2EOR__DUAL3,axiom,
% 0.22/0.50 ! [V0A: $i] :
% 0.22/0.50 ( ( mem @ V0A @ bool )
% 0.22/0.50 => ! [V1B: $i] :
% 0.22/0.50 ( ( mem @ V1B @ bool )
% 0.22/0.50 => ( ( ~ ( ~ ( p @ V0A )
% 0.22/0.50 | ( p @ V1B ) )
% 0.22/0.50 => $false )
% 0.22/0.50 <=> ( ( p @ V0A )
% 0.22/0.50 => ( ~ ( p @ V1B )
% 0.22/0.50 => $false ) ) ) ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(conj_thm_2Esat_2EAND__INV2,axiom,
% 0.22/0.50 ! [V0A: $i] :
% 0.22/0.50 ( ( mem @ V0A @ bool )
% 0.22/0.50 => ( ( ~ ( p @ V0A )
% 0.22/0.50 => $false )
% 0.22/0.50 => ( ( ( p @ V0A )
% 0.22/0.50 => $false )
% 0.22/0.50 => $false ) ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(conj_thm_2Esat_2Edc__eq,axiom,
% 0.22/0.50 ! [V0p: $i] :
% 0.22/0.50 ( ( mem @ V0p @ bool )
% 0.22/0.50 => ! [V1q: $i] :
% 0.22/0.50 ( ( mem @ V1q @ bool )
% 0.22/0.50 => ! [V2r: $i] :
% 0.22/0.50 ( ( mem @ V2r @ bool )
% 0.22/0.50 => ( ( ( p @ V0p )
% 0.22/0.50 <=> ( ( p @ V1q )
% 0.22/0.50 <=> ( p @ V2r ) ) )
% 0.22/0.50 <=> ( ( ( p @ V0p )
% 0.22/0.50 | ( p @ V1q )
% 0.22/0.50 | ( p @ V2r ) )
% 0.22/0.50 & ( ( p @ V0p )
% 0.22/0.50 | ~ ( p @ V2r )
% 0.22/0.50 | ~ ( p @ V1q ) )
% 0.22/0.50 & ( ( p @ V1q )
% 0.22/0.50 | ~ ( p @ V2r )
% 0.22/0.50 | ~ ( p @ V0p ) )
% 0.22/0.50 & ( ( p @ V2r )
% 0.22/0.50 | ~ ( p @ V1q )
% 0.22/0.50 | ~ ( p @ V0p ) ) ) ) ) ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(conj_thm_2Esat_2Edc__neg,axiom,
% 0.22/0.50 ! [V0p: $i] :
% 0.22/0.50 ( ( mem @ V0p @ bool )
% 0.22/0.50 => ! [V1q: $i] :
% 0.22/0.50 ( ( mem @ V1q @ bool )
% 0.22/0.50 => ( ( ( p @ V0p )
% 0.22/0.50 <=> ~ ( p @ V1q ) )
% 0.22/0.50 <=> ( ( ( p @ V0p )
% 0.22/0.50 | ( p @ V1q ) )
% 0.22/0.50 & ( ~ ( p @ V1q )
% 0.22/0.50 | ~ ( p @ V0p ) ) ) ) ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(conj_thm_2Ecardinal_2ECARD__NOT__LE,conjecture,
% 0.22/0.50 ! [A_27a: del,A_27b: del,V0s: $i] :
% 0.22/0.50 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 0.22/0.50 => ! [V1t: $i] :
% 0.22/0.50 ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
% 0.22/0.50 => ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27b ) @ V0s ) @ V1t ) )
% 0.22/0.50 <=> ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27b ) @ V0s ) @ V1t ) ) ) ) ) ).
% 0.22/0.50
% 0.22/0.50 %------------------------------------------------------------------------------
% 0.22/0.50 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.4lMUw7ObFA/cvc5---1.0.5_1443.p...
% 0.22/0.50 (declare-sort $$unsorted 0)
% 0.22/0.50 (declare-sort tptp.del 0)
% 0.22/0.50 (declare-fun tptp.bool () tptp.del)
% 0.22/0.50 (declare-fun tptp.ind () tptp.del)
% 0.22/0.50 (declare-fun tptp.arr (tptp.del tptp.del) tptp.del)
% 0.22/0.50 (declare-fun tptp.mem ($$unsorted tptp.del) Bool)
% 0.22/0.50 (declare-fun tptp.ap ($$unsorted $$unsorted) $$unsorted)
% 0.22/0.50 (declare-fun tptp.lam (tptp.del (-> $$unsorted $$unsorted)) $$unsorted)
% 0.22/0.50 (declare-fun tptp.p ($$unsorted) Bool)
% 0.22/0.50 (declare-fun tptp.inj__o (Bool) $$unsorted)
% 0.22/0.50 (assert (forall ((X Bool)) (= (@ tptp.p (@ tptp.inj__o X)) X)))
% 0.22/0.50 (assert (forall ((X Bool)) (@ (@ tptp.mem (@ tptp.inj__o X)) tptp.bool)))
% 0.22/0.50 (assert (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) tptp.bool) (= X (@ tptp.inj__o (@ tptp.p X))))))
% 0.22/0.50 (assert (forall ((A tptp.del) (B tptp.del) (F $$unsorted)) (=> (@ (@ tptp.mem F) (@ (@ tptp.arr A) B)) (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) A) (@ (@ tptp.mem (@ (@ tptp.ap F) X)) B))))))
% 0.22/0.50 (assert (forall ((A tptp.del) (B tptp.del) (F (-> $$unsorted $$unsorted))) (=> (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) A) (@ (@ tptp.mem (@ F X)) B))) (@ (@ tptp.mem (@ (@ tptp.lam A) F)) (@ (@ tptp.arr A) B)))))
% 0.22/0.50 (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 $$unsorted)) (=> (@ (@ tptp.mem X) A) (= (@ (@ tptp.ap F) X) (@ (@ tptp.ap G) X)))) (= F G)))))))
% 0.22/0.50 (assert (forall ((A tptp.del) (F (-> $$unsorted $$unsorted)) (X $$unsorted)) (=> (@ (@ tptp.mem X) A) (= (@ (@ tptp.ap (@ (@ tptp.lam A) F)) X) (@ F X)))))
% 0.22/0.50 (declare-fun tptp.c_2Ebool_2ET () $$unsorted)
% 0.22/0.50 (assert (@ (@ tptp.mem tptp.c_2Ebool_2ET) tptp.bool))
% 0.22/0.50 (assert (@ tptp.p tptp.c_2Ebool_2ET))
% 0.22/0.50 (declare-fun tptp.c_2Ecardinal_2Ecardleq (tptp.del tptp.del) $$unsorted)
% 0.22/0.50 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Ecardinal_2Ecardleq A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) (@ (@ tptp.arr (@ (@ tptp.arr A_27b) tptp.bool)) tptp.bool)))))
% 0.22/0.50 (declare-fun tptp.c_2Ebool_2EF () $$unsorted)
% 0.22/0.50 (assert (@ (@ tptp.mem tptp.c_2Ebool_2EF) tptp.bool))
% 0.22/0.50 (assert (not (@ tptp.p tptp.c_2Ebool_2EF)))
% 0.22/0.50 (declare-fun tptp.c_2Emin_2E_3D_3D_3E () $$unsorted)
% 0.22/0.50 (assert (let ((_let_1 (@ tptp.arr tptp.bool))) (@ (@ tptp.mem tptp.c_2Emin_2E_3D_3D_3E) (@ _let_1 (@ _let_1 tptp.bool)))))
% 0.22/0.50 (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))))))))
% 0.22/0.50 (declare-fun tptp.c_2Ebool_2E_5C_2F () $$unsorted)
% 0.22/0.50 (assert (let ((_let_1 (@ tptp.arr tptp.bool))) (@ (@ tptp.mem tptp.c_2Ebool_2E_5C_2F) (@ _let_1 (@ _let_1 tptp.bool)))))
% 0.22/0.50 (assert (forall ((Q $$unsorted)) (=> (@ (@ tptp.mem Q) tptp.bool) (forall ((R $$unsorted)) (=> (@ (@ tptp.mem R) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_5C_2F) Q)) R)) (or (@ tptp.p Q) (@ tptp.p R))))))))
% 0.22/0.50 (declare-fun tptp.c_2Ebool_2E_2F_5C () $$unsorted)
% 0.22/0.50 (assert (let ((_let_1 (@ tptp.arr tptp.bool))) (@ (@ tptp.mem tptp.c_2Ebool_2E_2F_5C) (@ _let_1 (@ _let_1 tptp.bool)))))
% 0.22/0.50 (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))))))))
% 0.22/0.50 (declare-fun tptp.c_2Ebool_2E_7E () $$unsorted)
% 0.22/0.50 (assert (@ (@ tptp.mem tptp.c_2Ebool_2E_7E) (@ (@ tptp.arr tptp.bool) tptp.bool)))
% 0.22/0.50 (assert (forall ((Q $$unsorted)) (=> (@ (@ tptp.mem Q) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap tptp.c_2Ebool_2E_7E) Q)) (not (@ tptp.p Q))))))
% 0.22/0.50 (declare-fun tptp.c_2Emin_2E_3D (tptp.del) $$unsorted)
% 0.22/0.50 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Emin_2E_3D A_27a)) (@ _let_1 (@ _let_1 tptp.bool))))))
% 0.22/0.50 (assert (forall ((A tptp.del) (X $$unsorted)) (=> (@ (@ tptp.mem X) A) (forall ((Y $$unsorted)) (=> (@ (@ tptp.mem Y) A) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A)) X)) Y)) (= X Y)))))))
% 0.22/0.50 (declare-fun tptp.c_2Ebool_2E_21 (tptp.del) $$unsorted)
% 0.22/0.50 (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))))
% 0.22/0.50 (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))))))))
% 0.22/0.50 (assert true)
% 0.22/0.50 (assert (forall ((V0t $$unsorted)) (=> (@ (@ tptp.mem V0t) tptp.bool) (=> false (@ tptp.p V0t)))))
% 0.22/0.50 (assert (forall ((A_27a tptp.del) (V0t $$unsorted)) (=> (@ (@ tptp.mem V0t) tptp.bool) (= (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (@ tptp.p V0t))) (@ tptp.p V0t)))))
% 0.22/0.50 (assert (forall ((V0t $$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)))))))
% 0.22/0.50 (assert (and (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (= (not (not _let_1)) _let_1)))) (= (not true) false) (= (not false) true)))
% 0.22/0.50 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (= (= V0x V0x) true))))
% 0.22/0.53 (assert (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (let ((_let_2 (not _let_1))) (=> (@ (@ tptp.mem V0t) tptp.bool) (and (= (= true _let_1) _let_1) (= (= _let_1 true) _let_1) (= (= false _let_1) _let_2) (= (= _let_1 false) _let_2)))))))
% 0.22/0.53 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27b) tptp.bool)) (or (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecardinal_2Ecardleq A_27a) A_27b)) V0s)) V1t)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecardinal_2Ecardleq A_27b) A_27a)) V1t)) V0s))))))))
% 0.22/0.53 (assert (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (= (not (not _let_1)) _let_1)))))
% 0.22/0.53 (assert (forall ((V0A $$unsorted)) (let ((_let_1 (@ tptp.p V0A))) (=> (@ (@ tptp.mem V0A) tptp.bool) (=> _let_1 (=> (not _let_1) false))))))
% 0.22/0.53 (assert (forall ((V0A $$unsorted)) (=> (@ (@ tptp.mem V0A) tptp.bool) (forall ((V1B $$unsorted)) (let ((_let_1 (@ tptp.p V1B))) (let ((_let_2 (@ tptp.p V0A))) (=> (@ (@ tptp.mem V1B) tptp.bool) (= (=> (not (or _let_2 _let_1)) false) (=> (=> _let_2 false) (=> (not _let_1) false))))))))))
% 0.22/0.53 (assert (forall ((V0A $$unsorted)) (=> (@ (@ tptp.mem V0A) tptp.bool) (forall ((V1B $$unsorted)) (let ((_let_1 (@ tptp.p V1B))) (let ((_let_2 (@ tptp.p V0A))) (=> (@ (@ tptp.mem V1B) tptp.bool) (= (=> (not (or (not _let_2) _let_1)) false) (=> _let_2 (=> (not _let_1) false))))))))))
% 0.22/0.53 (assert (forall ((V0A $$unsorted)) (let ((_let_1 (@ tptp.p V0A))) (=> (@ (@ tptp.mem V0A) tptp.bool) (=> (=> (not _let_1) false) (=> (=> _let_1 false) false))))))
% 0.22/0.53 (assert (forall ((V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) tptp.bool) (forall ((V1q $$unsorted)) (=> (@ (@ tptp.mem V1q) tptp.bool) (forall ((V2r $$unsorted)) (let ((_let_1 (@ tptp.p V0p))) (let ((_let_2 (not _let_1))) (let ((_let_3 (@ tptp.p V1q))) (let ((_let_4 (not _let_3))) (let ((_let_5 (@ tptp.p V2r))) (let ((_let_6 (not _let_5))) (=> (@ (@ tptp.mem V2r) tptp.bool) (= (= _let_1 (= _let_3 _let_5)) (and (or _let_1 _let_3 _let_5) (or _let_1 _let_6 _let_4) (or _let_3 _let_6 _let_2) (or _let_5 _let_4 _let_2))))))))))))))))
% 0.22/0.53 (assert (forall ((V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) tptp.bool) (forall ((V1q $$unsorted)) (let ((_let_1 (@ tptp.p V0p))) (let ((_let_2 (@ tptp.p V1q))) (let ((_let_3 (not _let_2))) (=> (@ (@ tptp.mem V1q) tptp.bool) (= (= _let_1 _let_3) (and (or _let_1 _let_2) (or _let_3 (not _let_1))))))))))))
% 0.22/0.53 (assert (not (forall ((A_27a tptp.del) (A_27b tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (let ((_let_1 (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecardinal_2Ecardleq A_27a) A_27b)) V0s)) V1t))))) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27b) tptp.bool)) (= _let_1 _let_1))))))))
% 0.22/0.53 (set-info :filename cvc5---1.0.5_1443)
% 0.22/0.53 (check-sat-assuming ( true ))
% 0.22/0.53 ------- get file name : TPTP file name is ITP010^2
% 0.22/0.53 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_1443.smt2...
% 0.22/0.53 --- Run --ho-elim --full-saturate-quant at 10...
% 0.22/0.53 % SZS status Theorem for ITP010^2
% 0.22/0.53 % SZS output start Proof for ITP010^2
% 0.22/0.53 (
% 0.22/0.53 (let ((_let_1 (not (forall ((A_27a tptp.del) (A_27b tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (let ((_let_1 (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecardinal_2Ecardleq A_27a) A_27b)) V0s)) V1t))))) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27b) tptp.bool)) (= _let_1 _let_1))))))))) (let ((_let_2 (@ tptp.arr tptp.bool))) (let ((_let_3 (@ _let_2 tptp.bool))) (let ((_let_4 (@ _let_2 _let_3))) (SCOPE (SCOPE (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))) :args ((forall ((X Bool)) (= (@ tptp.p (@ tptp.inj__o X)) X)) (forall ((X Bool)) (@ (@ tptp.mem (@ tptp.inj__o X)) tptp.bool)) (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) tptp.bool) (= X (@ tptp.inj__o (@ tptp.p X))))) (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))))) (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 $$unsorted)) (=> (@ (@ tptp.mem X) A) (= (@ (@ tptp.ap (@ (@ tptp.lam A) F)) X) (@ F X)))) (@ (@ tptp.mem tptp.c_2Ebool_2ET) tptp.bool) (@ tptp.p tptp.c_2Ebool_2ET) (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Ecardinal_2Ecardleq A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) (@ (@ tptp.arr (@ (@ tptp.arr A_27b) tptp.bool)) tptp.bool)))) (@ (@ tptp.mem tptp.c_2Ebool_2EF) tptp.bool) (not (@ tptp.p tptp.c_2Ebool_2EF)) (@ (@ tptp.mem tptp.c_2Emin_2E_3D_3D_3E) _let_4) (forall ((Q $$unsorted)) (=> (@ (@ tptp.mem Q) tptp.bool) (forall ((R $$unsorted)) (=> (@ (@ tptp.mem R) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) Q)) R)) (=> (@ tptp.p Q) (@ tptp.p R))))))) (@ (@ tptp.mem tptp.c_2Ebool_2E_5C_2F) _let_4) (forall ((Q $$unsorted)) (=> (@ (@ tptp.mem Q) tptp.bool) (forall ((R $$unsorted)) (=> (@ (@ tptp.mem R) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_5C_2F) Q)) R)) (or (@ tptp.p Q) (@ tptp.p R))))))) (@ (@ tptp.mem tptp.c_2Ebool_2E_2F_5C) _let_4) (forall ((Q $$unsorted)) (=> (@ (@ tptp.mem Q) tptp.bool) (forall ((R $$unsorted)) (=> (@ (@ tptp.mem R) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) Q)) R)) (and (@ tptp.p Q) (@ tptp.p R))))))) (@ (@ tptp.mem tptp.c_2Ebool_2E_7E) _let_3) (forall ((Q $$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 ((V0t $$unsorted)) (=> (@ (@ tptp.mem V0t) tptp.bool) (=> false (@ tptp.p V0t)))) (forall ((A_27a tptp.del) (V0t $$unsorted)) (=> (@ (@ tptp.mem V0t) tptp.bool) (= (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (@ tptp.p V0t))) (@ tptp.p V0t)))) (forall ((V0t $$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) (= (= V0x V0x) true))) (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (let ((_let_2 (not _let_1))) (=> (@ (@ tptp.mem V0t) tptp.bool) (and (= (= true _let_1) _let_1) (= (= _let_1 true) _let_1) (= (= false _let_1) _let_2) (= (= _let_1 false) _let_2)))))) (forall ((A_27a tptp.del) (A_27b tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27b) tptp.bool)) (or (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecardinal_2Ecardleq A_27a) A_27b)) V0s)) V1t)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecardinal_2Ecardleq A_27b) A_27a)) V1t)) V0s))))))) (forall ((V0t $$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)) (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)))))))
% 0.22/0.54 )
% 0.22/0.54 % SZS output end Proof for ITP010^2
% 0.22/0.54 % cvc5---1.0.5 exiting
% 0.22/0.54 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------