TSTP Solution File: ITP012^2 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP012^2 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n008.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 03:14:48 EDT 2023
% Result : Theorem 1.03s 1.24s
% Output : Proof 1.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ITP012^2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.00/0.15 % Command : do_cvc5 %s %d
% 0.14/0.36 % Computer : n008.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 15:52:02 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.20/0.50 %----Proving TH0
% 0.20/0.51 %------------------------------------------------------------------------------
% 0.20/0.51 % File : ITP012^2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.20/0.51 % Domain : Interactive Theorem Proving
% 0.20/0.51 % Problem : HOL4 set theory export of thm_2Einteger_2EINT__DIVIDES__RSUB.p, bushy mode
% 0.20/0.51 % Version : [BG+19] axioms.
% 0.20/0.51 % English :
% 0.20/0.51
% 0.20/0.51 % Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% 0.20/0.51 % : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% 0.20/0.51 % Source : [BG+19]
% 0.20/0.51 % Names : thm_2Einteger_2EINT__DIVIDES__RSUB.p [Gau19]
% 0.20/0.51 % : HL405501^2.p [TPAP]
% 0.20/0.51
% 0.20/0.51 % Status : Theorem
% 0.20/0.51 % Rating : 0.54 v8.1.0, 0.36 v7.5.0
% 0.20/0.51 % Syntax : Number of formulae : 90 ( 10 unt; 29 typ; 0 def)
% 0.20/0.51 % Number of atoms : 425 ( 12 equ; 0 cnn)
% 0.20/0.51 % Maximal formula atoms : 21 ( 6 avg)
% 0.20/0.51 % Number of connectives : 803 ( 47 ~; 34 |; 29 &; 550 @)
% 0.20/0.51 % ( 48 <=>; 95 =>; 0 <=; 0 <~>)
% 0.20/0.51 % Maximal formula depth : 15 ( 8 avg)
% 0.20/0.51 % Number of types : 4 ( 2 usr)
% 0.20/0.51 % Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% 0.20/0.51 % Number of symbols : 35 ( 32 usr; 20 con; 0-2 aty)
% 0.20/0.51 % Number of variables : 101 ( 0 ^; 99 !; 2 ?; 101 :)
% 0.20/0.51 % SPC : TH0_THM_EQU_NAR
% 0.20/0.51
% 0.20/0.51 % Comments :
% 0.20/0.51 % Bugfixes : v7.5.0 - Bugfixes in axioms and export.
% 0.20/0.51 %------------------------------------------------------------------------------
% 0.20/0.51 %------------------------------------------------------------------------------
% 0.20/0.51 thf(del_tp,type,
% 0.20/0.51 del: $tType ).
% 0.20/0.51
% 0.20/0.51 thf(bool,type,
% 0.20/0.51 bool: del ).
% 0.20/0.51
% 0.20/0.51 thf(ind,type,
% 0.20/0.51 ind: del ).
% 0.20/0.51
% 0.20/0.51 thf(arr,type,
% 0.20/0.51 arr: del > del > del ).
% 0.20/0.51
% 0.20/0.51 thf(mem,type,
% 0.20/0.51 mem: $i > del > $o ).
% 0.20/0.51
% 0.20/0.51 thf(ap,type,
% 0.20/0.51 ap: $i > $i > $i ).
% 0.20/0.51
% 0.20/0.51 thf(lam,type,
% 0.20/0.51 lam: del > ( $i > $i ) > $i ).
% 0.20/0.51
% 0.20/0.51 thf(p,type,
% 0.20/0.51 p: $i > $o ).
% 0.20/0.51
% 0.20/0.51 thf(stp_inj_o,type,
% 0.20/0.51 inj__o: $o > $i ).
% 0.20/0.51
% 0.20/0.51 thf(stp_inj_surj_o,axiom,
% 0.20/0.51 ! [X: $o] :
% 0.20/0.51 ( ( p @ ( inj__o @ X ) )
% 0.20/0.51 = X ) ).
% 0.20/0.51
% 0.20/0.51 thf(stp_inj_mem_o,axiom,
% 0.20/0.51 ! [X: $o] : ( mem @ ( inj__o @ X ) @ bool ) ).
% 0.20/0.51
% 0.20/0.51 thf(stp_iso_mem_o,axiom,
% 0.20/0.51 ! [X: $i] :
% 0.20/0.51 ( ( mem @ X @ bool )
% 0.20/0.51 => ( X
% 0.20/0.51 = ( inj__o @ ( p @ X ) ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(ap_tp,axiom,
% 0.20/0.51 ! [A: del,B: del,F: $i] :
% 0.20/0.51 ( ( mem @ F @ ( arr @ A @ B ) )
% 0.20/0.51 => ! [X: $i] :
% 0.20/0.51 ( ( mem @ X @ A )
% 0.20/0.51 => ( mem @ ( ap @ F @ X ) @ B ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(lam_tp,axiom,
% 0.20/0.51 ! [A: del,B: del,F: $i > $i] :
% 0.20/0.51 ( ! [X: $i] :
% 0.20/0.51 ( ( mem @ X @ A )
% 0.20/0.51 => ( mem @ ( F @ X ) @ B ) )
% 0.20/0.51 => ( mem @ ( lam @ A @ F ) @ ( arr @ A @ B ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(funcext,axiom,
% 0.20/0.51 ! [A: del,B: del,F: $i] :
% 0.20/0.51 ( ( mem @ F @ ( arr @ A @ B ) )
% 0.20/0.51 => ! [G: $i] :
% 0.20/0.51 ( ( mem @ G @ ( arr @ A @ B ) )
% 0.20/0.51 => ( ! [X: $i] :
% 0.20/0.51 ( ( mem @ X @ A )
% 0.20/0.51 => ( ( ap @ F @ X )
% 0.20/0.51 = ( ap @ G @ X ) ) )
% 0.20/0.51 => ( F = G ) ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(beta,axiom,
% 0.20/0.51 ! [A: del,F: $i > $i,X: $i] :
% 0.20/0.51 ( ( mem @ X @ A )
% 0.20/0.51 => ( ( ap @ ( lam @ A @ F ) @ X )
% 0.20/0.51 = ( F @ X ) ) ) ).
% 0.20/0.51
% 0.20/0.51 %------------------------------------------------------------------------------
% 0.20/0.51 %------------------------------------------------------------------------------
% 0.20/0.51 thf(tp_c_2Ebool_2ET,type,
% 0.20/0.51 c_2Ebool_2ET: $i ).
% 0.20/0.51
% 0.20/0.51 thf(mem_c_2Ebool_2ET,axiom,
% 0.20/0.51 mem @ c_2Ebool_2ET @ bool ).
% 0.20/0.51
% 0.20/0.51 thf(ax_true_p,axiom,
% 0.20/0.51 p @ c_2Ebool_2ET ).
% 0.20/0.51
% 0.20/0.51 thf(tp_c_2Ebool_2E_3F,type,
% 0.20/0.51 c_2Ebool_2E_3F: del > $i ).
% 0.20/0.51
% 0.20/0.51 thf(mem_c_2Ebool_2E_3F,axiom,
% 0.20/0.51 ! [A_27a: del] : ( mem @ ( c_2Ebool_2E_3F @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(ax_ex_p,axiom,
% 0.20/0.51 ! [A: del,Q: $i] :
% 0.20/0.51 ( ( mem @ Q @ ( arr @ A @ bool ) )
% 0.20/0.51 => ( ( p @ ( ap @ ( c_2Ebool_2E_3F @ A ) @ Q ) )
% 0.20/0.51 <=> ? [X: $i] :
% 0.20/0.51 ( ( mem @ X @ A )
% 0.20/0.51 & ( p @ ( ap @ Q @ X ) ) ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(tp_ty_2Einteger_2Eint,type,
% 0.20/0.51 ty_2Einteger_2Eint: del ).
% 0.20/0.51
% 0.20/0.51 thf(stp_ty_2Einteger_2Eint,type,
% 0.20/0.51 tp__ty_2Einteger_2Eint: $tType ).
% 0.20/0.51
% 0.20/0.51 thf(stp_inj_ty_2Einteger_2Eint,type,
% 0.20/0.51 inj__ty_2Einteger_2Eint: tp__ty_2Einteger_2Eint > $i ).
% 0.20/0.51
% 0.20/0.51 thf(stp_surj_ty_2Einteger_2Eint,type,
% 0.20/0.51 surj__ty_2Einteger_2Eint: $i > tp__ty_2Einteger_2Eint ).
% 0.20/0.51
% 0.20/0.51 thf(stp_inj_surj_ty_2Einteger_2Eint,axiom,
% 0.20/0.51 ! [X: tp__ty_2Einteger_2Eint] :
% 0.20/0.51 ( ( surj__ty_2Einteger_2Eint @ ( inj__ty_2Einteger_2Eint @ X ) )
% 0.20/0.51 = X ) ).
% 0.20/0.51
% 0.20/0.51 thf(stp_inj_mem_ty_2Einteger_2Eint,axiom,
% 0.20/0.51 ! [X: tp__ty_2Einteger_2Eint] : ( mem @ ( inj__ty_2Einteger_2Eint @ X ) @ ty_2Einteger_2Eint ) ).
% 0.20/0.51
% 0.20/0.51 thf(stp_iso_mem_ty_2Einteger_2Eint,axiom,
% 0.20/0.51 ! [X: $i] :
% 0.20/0.51 ( ( mem @ X @ ty_2Einteger_2Eint )
% 0.20/0.51 => ( X
% 0.20/0.51 = ( inj__ty_2Einteger_2Eint @ ( surj__ty_2Einteger_2Eint @ X ) ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(tp_c_2Einteger_2Eint__sub,type,
% 0.20/0.51 c_2Einteger_2Eint__sub: $i ).
% 0.20/0.51
% 0.20/0.51 thf(mem_c_2Einteger_2Eint__sub,axiom,
% 0.20/0.51 mem @ c_2Einteger_2Eint__sub @ ( arr @ ty_2Einteger_2Eint @ ( arr @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(stp_fo_c_2Einteger_2Eint__sub,type,
% 0.20/0.51 fo__c_2Einteger_2Eint__sub: tp__ty_2Einteger_2Eint > tp__ty_2Einteger_2Eint > tp__ty_2Einteger_2Eint ).
% 0.20/0.51
% 0.20/0.51 thf(stp_eq_fo_c_2Einteger_2Eint__sub,axiom,
% 0.20/0.51 ! [X0: tp__ty_2Einteger_2Eint,X1: tp__ty_2Einteger_2Eint] :
% 0.20/0.51 ( ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__sub @ X0 @ X1 ) )
% 0.20/0.51 = ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ X0 ) ) @ ( inj__ty_2Einteger_2Eint @ X1 ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(tp_c_2Einteger_2Eint__add,type,
% 0.20/0.51 c_2Einteger_2Eint__add: $i ).
% 0.20/0.51
% 0.20/0.51 thf(mem_c_2Einteger_2Eint__add,axiom,
% 0.20/0.51 mem @ c_2Einteger_2Eint__add @ ( arr @ ty_2Einteger_2Eint @ ( arr @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(stp_fo_c_2Einteger_2Eint__add,type,
% 0.20/0.51 fo__c_2Einteger_2Eint__add: tp__ty_2Einteger_2Eint > tp__ty_2Einteger_2Eint > tp__ty_2Einteger_2Eint ).
% 0.20/0.51
% 0.20/0.51 thf(stp_eq_fo_c_2Einteger_2Eint__add,axiom,
% 0.20/0.51 ! [X0: tp__ty_2Einteger_2Eint,X1: tp__ty_2Einteger_2Eint] :
% 0.20/0.51 ( ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__add @ X0 @ X1 ) )
% 0.20/0.51 = ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ X0 ) ) @ ( inj__ty_2Einteger_2Eint @ X1 ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(tp_c_2Einteger_2Eint__neg,type,
% 0.20/0.51 c_2Einteger_2Eint__neg: $i ).
% 0.20/0.51
% 0.20/0.51 thf(mem_c_2Einteger_2Eint__neg,axiom,
% 0.20/0.51 mem @ c_2Einteger_2Eint__neg @ ( arr @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ).
% 0.20/0.51
% 0.20/0.51 thf(stp_fo_c_2Einteger_2Eint__neg,type,
% 0.20/0.51 fo__c_2Einteger_2Eint__neg: tp__ty_2Einteger_2Eint > tp__ty_2Einteger_2Eint ).
% 0.20/0.51
% 0.20/0.51 thf(stp_eq_fo_c_2Einteger_2Eint__neg,axiom,
% 0.20/0.51 ! [X0: tp__ty_2Einteger_2Eint] :
% 0.20/0.51 ( ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__neg @ X0 ) )
% 0.20/0.51 = ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ X0 ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(tp_c_2Einteger_2Eint__divides,type,
% 0.20/0.51 c_2Einteger_2Eint__divides: $i ).
% 0.20/0.51
% 0.20/0.51 thf(mem_c_2Einteger_2Eint__divides,axiom,
% 0.20/0.51 mem @ c_2Einteger_2Eint__divides @ ( arr @ ty_2Einteger_2Eint @ ( arr @ ty_2Einteger_2Eint @ bool ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(tp_c_2Ebool_2EF,type,
% 0.20/0.51 c_2Ebool_2EF: $i ).
% 0.20/0.51
% 0.20/0.51 thf(mem_c_2Ebool_2EF,axiom,
% 0.20/0.51 mem @ c_2Ebool_2EF @ bool ).
% 0.20/0.51
% 0.20/0.51 thf(ax_false_p,axiom,
% 0.20/0.51 ~ ( p @ c_2Ebool_2EF ) ).
% 0.20/0.51
% 0.20/0.51 thf(tp_c_2Emin_2E_3D_3D_3E,type,
% 0.20/0.51 c_2Emin_2E_3D_3D_3E: $i ).
% 0.20/0.51
% 0.20/0.51 thf(mem_c_2Emin_2E_3D_3D_3E,axiom,
% 0.20/0.51 mem @ c_2Emin_2E_3D_3D_3E @ ( arr @ bool @ ( arr @ bool @ bool ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(ax_imp_p,axiom,
% 0.20/0.51 ! [Q: $i] :
% 0.20/0.51 ( ( mem @ Q @ bool )
% 0.20/0.51 => ! [R: $i] :
% 0.20/0.51 ( ( mem @ R @ bool )
% 0.20/0.51 => ( ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ Q ) @ R ) )
% 0.20/0.51 <=> ( ( p @ Q )
% 0.20/0.51 => ( p @ R ) ) ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(tp_c_2Ebool_2E_5C_2F,type,
% 0.20/0.51 c_2Ebool_2E_5C_2F: $i ).
% 0.20/0.51
% 0.20/0.51 thf(mem_c_2Ebool_2E_5C_2F,axiom,
% 0.20/0.51 mem @ c_2Ebool_2E_5C_2F @ ( arr @ bool @ ( arr @ bool @ bool ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(ax_or_p,axiom,
% 0.20/0.51 ! [Q: $i] :
% 0.20/0.51 ( ( mem @ Q @ bool )
% 0.20/0.51 => ! [R: $i] :
% 0.20/0.51 ( ( mem @ R @ bool )
% 0.20/0.51 => ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ Q ) @ R ) )
% 0.20/0.51 <=> ( ( p @ Q )
% 0.20/0.51 | ( p @ R ) ) ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(tp_c_2Ebool_2E_2F_5C,type,
% 0.20/0.51 c_2Ebool_2E_2F_5C: $i ).
% 0.20/0.51
% 0.20/0.51 thf(mem_c_2Ebool_2E_2F_5C,axiom,
% 0.20/0.51 mem @ c_2Ebool_2E_2F_5C @ ( arr @ bool @ ( arr @ bool @ bool ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(ax_and_p,axiom,
% 0.20/0.51 ! [Q: $i] :
% 0.20/0.51 ( ( mem @ Q @ bool )
% 0.20/0.51 => ! [R: $i] :
% 0.20/0.51 ( ( mem @ R @ bool )
% 0.20/0.51 => ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ Q ) @ R ) )
% 0.20/0.51 <=> ( ( p @ Q )
% 0.20/0.51 & ( p @ R ) ) ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(tp_c_2Ebool_2E_7E,type,
% 0.20/0.51 c_2Ebool_2E_7E: $i ).
% 0.20/0.51
% 0.20/0.51 thf(mem_c_2Ebool_2E_7E,axiom,
% 0.20/0.51 mem @ c_2Ebool_2E_7E @ ( arr @ bool @ bool ) ).
% 0.20/0.51
% 0.20/0.51 thf(ax_neg_p,axiom,
% 0.20/0.51 ! [Q: $i] :
% 0.20/0.51 ( ( mem @ Q @ bool )
% 0.20/0.51 => ( ( p @ ( ap @ c_2Ebool_2E_7E @ Q ) )
% 0.20/0.51 <=> ~ ( p @ Q ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(tp_c_2Emin_2E_3D,type,
% 0.20/0.51 c_2Emin_2E_3D: del > $i ).
% 0.20/0.51
% 0.20/0.51 thf(mem_c_2Emin_2E_3D,axiom,
% 0.20/0.51 ! [A_27a: del] : ( mem @ ( c_2Emin_2E_3D @ A_27a ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(ax_eq_p,axiom,
% 0.20/0.51 ! [A: del,X: $i] :
% 0.20/0.51 ( ( mem @ X @ A )
% 0.20/0.51 => ! [Y: $i] :
% 0.20/0.51 ( ( mem @ Y @ A )
% 0.20/0.51 => ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ X ) @ Y ) )
% 0.20/0.51 <=> ( X = Y ) ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(tp_c_2Ebool_2E_21,type,
% 0.20/0.51 c_2Ebool_2E_21: del > $i ).
% 0.20/0.51
% 0.20/0.51 thf(mem_c_2Ebool_2E_21,axiom,
% 0.20/0.51 ! [A_27a: del] : ( mem @ ( c_2Ebool_2E_21 @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(ax_all_p,axiom,
% 0.20/0.51 ! [A: del,Q: $i] :
% 0.20/0.51 ( ( mem @ Q @ ( arr @ A @ bool ) )
% 0.20/0.51 => ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ A ) @ Q ) )
% 0.20/0.51 <=> ! [X: $i] :
% 0.20/0.51 ( ( mem @ X @ A )
% 0.20/0.51 => ( p @ ( ap @ Q @ X ) ) ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(conj_thm_2Ebool_2ETRUTH,axiom,
% 0.20/0.51 $true ).
% 0.20/0.51
% 0.20/0.51 thf(conj_thm_2Ebool_2EIMP__ANTISYM__AX,axiom,
% 0.20/0.51 ! [V0t1: $i] :
% 0.20/0.51 ( ( mem @ V0t1 @ bool )
% 0.20/0.51 => ! [V1t2: $i] :
% 0.20/0.51 ( ( mem @ V1t2 @ bool )
% 0.20/0.51 => ( ( ( p @ V0t1 )
% 0.20/0.51 => ( p @ V1t2 ) )
% 0.20/0.51 => ( ( ( p @ V1t2 )
% 0.20/0.51 => ( p @ V0t1 ) )
% 0.20/0.51 => ( ( p @ V0t1 )
% 0.20/0.51 <=> ( p @ V1t2 ) ) ) ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(conj_thm_2Ebool_2EIMP__F,axiom,
% 0.20/0.51 ! [V0t: $i] :
% 0.20/0.51 ( ( mem @ V0t @ bool )
% 0.20/0.51 => ( ( ( p @ V0t )
% 0.20/0.51 => $false )
% 0.20/0.51 => ~ ( p @ V0t ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(conj_thm_2Ebool_2EF__IMP,axiom,
% 0.20/0.51 ! [V0t: $i] :
% 0.20/0.51 ( ( mem @ V0t @ bool )
% 0.20/0.51 => ( ~ ( p @ V0t )
% 0.20/0.51 => ( ( p @ V0t )
% 0.20/0.51 => $false ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(conj_thm_2Ebool_2EIMP__CLAUSES,axiom,
% 0.20/0.51 ! [V0t: $i] :
% 0.20/0.51 ( ( mem @ V0t @ bool )
% 0.20/0.51 => ( ( ( $true
% 0.20/0.51 => ( p @ V0t ) )
% 0.20/0.51 <=> ( p @ V0t ) )
% 0.20/0.51 & ( ( ( p @ V0t )
% 0.20/0.51 => $true )
% 0.20/0.51 <=> $true )
% 0.20/0.51 & ( ( $false
% 0.20/0.51 => ( p @ V0t ) )
% 0.20/0.51 <=> $true )
% 0.20/0.51 & ( ( ( p @ V0t )
% 0.20/0.51 => ( p @ V0t ) )
% 0.20/0.51 <=> $true )
% 0.20/0.51 & ( ( ( p @ V0t )
% 0.20/0.51 => $false )
% 0.20/0.51 <=> ~ ( p @ V0t ) ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(conj_thm_2Ebool_2ENOT__CLAUSES,axiom,
% 0.20/0.51 ( ! [V0t: $i] :
% 0.20/0.51 ( ( mem @ V0t @ bool )
% 0.20/0.51 => ( ~ ~ ( p @ V0t )
% 0.20/0.51 <=> ( p @ V0t ) ) )
% 0.20/0.51 & ( ~ $true
% 0.20/0.51 <=> $false )
% 0.20/0.51 & ( ~ $false
% 0.20/0.51 <=> $true ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(conj_thm_2Ebool_2EEQ__CLAUSES,axiom,
% 0.20/0.51 ! [V0t: $i] :
% 0.20/0.51 ( ( mem @ V0t @ bool )
% 0.20/0.51 => ( ( ( $true
% 0.20/0.51 <=> ( p @ V0t ) )
% 0.20/0.51 <=> ( p @ V0t ) )
% 0.20/0.51 & ( ( ( p @ V0t )
% 0.20/0.51 <=> $true )
% 0.20/0.51 <=> ( p @ V0t ) )
% 0.20/0.51 & ( ( $false
% 0.20/0.51 <=> ( p @ V0t ) )
% 0.20/0.51 <=> ~ ( p @ V0t ) )
% 0.20/0.51 & ( ( ( p @ V0t )
% 0.20/0.51 <=> $false )
% 0.20/0.51 <=> ~ ( p @ V0t ) ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(conj_thm_2Ebool_2ENOT__FORALL__THM,axiom,
% 0.20/0.51 ! [A_27a: del,V0P: $i] :
% 0.20/0.51 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 0.20/0.51 => ( ~ ! [V1x: $i] :
% 0.20/0.51 ( ( mem @ V1x @ A_27a )
% 0.20/0.51 => ( p @ ( ap @ V0P @ V1x ) ) )
% 0.20/0.51 <=> ? [V2x: $i] :
% 0.20/0.51 ( ( mem @ V2x @ A_27a )
% 0.20/0.51 & ~ ( p @ ( ap @ V0P @ V2x ) ) ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(conj_thm_2Ebool_2EFORALL__AND__THM,axiom,
% 0.20/0.51 ! [A_27a: del,V0P: $i] :
% 0.20/0.51 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 0.20/0.51 => ! [V1Q: $i] :
% 0.20/0.51 ( ( mem @ V1Q @ ( arr @ A_27a @ bool ) )
% 0.20/0.51 => ( ! [V2x: $i] :
% 0.20/0.51 ( ( mem @ V2x @ A_27a )
% 0.20/0.51 => ( ( p @ ( ap @ V0P @ V2x ) )
% 0.20/0.51 & ( p @ ( ap @ V1Q @ V2x ) ) ) )
% 0.20/0.51 <=> ( ! [V3x: $i] :
% 0.20/0.51 ( ( mem @ V3x @ A_27a )
% 0.20/0.51 => ( p @ ( ap @ V0P @ V3x ) ) )
% 0.20/0.51 & ! [V4x: $i] :
% 0.20/0.51 ( ( mem @ V4x @ A_27a )
% 0.20/0.51 => ( p @ ( ap @ V1Q @ V4x ) ) ) ) ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(conj_thm_2Ebool_2EDISJ__ASSOC,axiom,
% 0.20/0.51 ! [V0A: $i] :
% 0.20/0.51 ( ( mem @ V0A @ bool )
% 0.20/0.51 => ! [V1B: $i] :
% 0.20/0.51 ( ( mem @ V1B @ bool )
% 0.20/0.51 => ! [V2C: $i] :
% 0.20/0.51 ( ( mem @ V2C @ bool )
% 0.20/0.51 => ( ( ( p @ V0A )
% 0.20/0.51 | ( p @ V1B )
% 0.20/0.51 | ( p @ V2C ) )
% 0.20/0.51 <=> ( ( p @ V0A )
% 0.20/0.51 | ( p @ V1B )
% 0.20/0.51 | ( p @ V2C ) ) ) ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(conj_thm_2Ebool_2EDISJ__SYM,axiom,
% 0.20/0.51 ! [V0A: $i] :
% 0.20/0.51 ( ( mem @ V0A @ bool )
% 0.20/0.51 => ! [V1B: $i] :
% 0.20/0.51 ( ( mem @ V1B @ bool )
% 0.20/0.51 => ( ( ( p @ V0A )
% 0.20/0.51 | ( p @ V1B ) )
% 0.20/0.51 <=> ( ( p @ V1B )
% 0.20/0.51 | ( p @ V0A ) ) ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(conj_thm_2Ebool_2EDE__MORGAN__THM,axiom,
% 0.20/0.51 ! [V0A: $i] :
% 0.20/0.51 ( ( mem @ V0A @ bool )
% 0.20/0.51 => ! [V1B: $i] :
% 0.20/0.51 ( ( mem @ V1B @ bool )
% 0.20/0.51 => ( ( ~ ( ( p @ V0A )
% 0.20/0.51 & ( p @ V1B ) )
% 0.20/0.51 <=> ( ~ ( p @ V0A )
% 0.20/0.51 | ~ ( p @ V1B ) ) )
% 0.20/0.51 & ( ~ ( ( p @ V0A )
% 0.20/0.51 | ( p @ V1B ) )
% 0.20/0.51 <=> ( ~ ( p @ V0A )
% 0.20/0.51 & ~ ( p @ V1B ) ) ) ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(ax_thm_2Einteger_2Eint__sub,axiom,
% 0.20/0.51 ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint] :
% 0.20/0.51 ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) )
% 0.20/0.51 = ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(conj_thm_2Einteger_2EINT__DIVIDES__RADD,axiom,
% 0.20/0.51 ! [V0p: tp__ty_2Einteger_2Eint,V1q: tp__ty_2Einteger_2Eint,V2r: tp__ty_2Einteger_2Eint] :
% 0.20/0.51 ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ V0p ) ) @ ( inj__ty_2Einteger_2Eint @ V1q ) ) )
% 0.20/0.51 => ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ V0p ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V2r ) ) @ ( inj__ty_2Einteger_2Eint @ V1q ) ) ) )
% 0.20/0.51 <=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ V0p ) ) @ ( inj__ty_2Einteger_2Eint @ V2r ) ) ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(conj_thm_2Einteger_2EINT__DIVIDES__NEG,axiom,
% 0.20/0.51 ! [V0p: tp__ty_2Einteger_2Eint,V1q: tp__ty_2Einteger_2Eint] :
% 0.20/0.51 ( ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ V0p ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ V1q ) ) ) )
% 0.20/0.51 <=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ V0p ) ) @ ( inj__ty_2Einteger_2Eint @ V1q ) ) ) )
% 0.20/0.51 & ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ V0p ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1q ) ) )
% 0.20/0.51 <=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ V0p ) ) @ ( inj__ty_2Einteger_2Eint @ V1q ) ) ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(conj_thm_2Esat_2ENOT__NOT,axiom,
% 0.20/0.51 ! [V0t: $i] :
% 0.20/0.51 ( ( mem @ V0t @ bool )
% 0.20/0.51 => ( ~ ~ ( p @ V0t )
% 0.20/0.51 <=> ( p @ V0t ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(conj_thm_2Esat_2EAND__INV__IMP,axiom,
% 0.20/0.51 ! [V0A: $i] :
% 0.20/0.51 ( ( mem @ V0A @ bool )
% 0.20/0.51 => ( ( p @ V0A )
% 0.20/0.51 => ( ~ ( p @ V0A )
% 0.20/0.51 => $false ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(conj_thm_2Esat_2EOR__DUAL2,axiom,
% 0.20/0.51 ! [V0A: $i] :
% 0.20/0.51 ( ( mem @ V0A @ bool )
% 0.20/0.51 => ! [V1B: $i] :
% 0.20/0.51 ( ( mem @ V1B @ bool )
% 0.20/0.51 => ( ( ~ ( ( p @ V0A )
% 0.20/0.51 | ( p @ V1B ) )
% 0.20/0.51 => $false )
% 0.20/0.51 <=> ( ( ( p @ V0A )
% 0.20/0.51 => $false )
% 0.20/0.51 => ( ~ ( p @ V1B )
% 0.20/0.51 => $false ) ) ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(conj_thm_2Esat_2EOR__DUAL3,axiom,
% 0.20/0.51 ! [V0A: $i] :
% 0.20/0.51 ( ( mem @ V0A @ bool )
% 0.20/0.51 => ! [V1B: $i] :
% 0.20/0.51 ( ( mem @ V1B @ bool )
% 0.20/0.51 => ( ( ~ ( ~ ( p @ V0A )
% 0.20/0.51 | ( p @ V1B ) )
% 0.20/0.51 => $false )
% 0.20/0.51 <=> ( ( p @ V0A )
% 0.20/0.51 => ( ~ ( p @ V1B )
% 0.20/0.51 => $false ) ) ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(conj_thm_2Esat_2EAND__INV2,axiom,
% 0.20/0.51 ! [V0A: $i] :
% 0.20/0.51 ( ( mem @ V0A @ bool )
% 0.20/0.51 => ( ( ~ ( p @ V0A )
% 0.20/0.51 => $false )
% 0.20/0.51 => ( ( ( p @ V0A )
% 0.20/0.51 => $false )
% 0.20/0.51 => $false ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(conj_thm_2Esat_2Edc__eq,axiom,
% 0.20/0.51 ! [V0p: $i] :
% 0.20/0.51 ( ( mem @ V0p @ bool )
% 0.20/0.51 => ! [V1q: $i] :
% 0.20/0.51 ( ( mem @ V1q @ bool )
% 0.20/0.51 => ! [V2r: $i] :
% 0.20/0.51 ( ( mem @ V2r @ bool )
% 0.20/0.53 => ( ( ( p @ V0p )
% 0.20/0.53 <=> ( ( p @ V1q )
% 0.20/0.53 <=> ( p @ V2r ) ) )
% 0.20/0.53 <=> ( ( ( p @ V0p )
% 0.20/0.53 | ( p @ V1q )
% 0.20/0.53 | ( p @ V2r ) )
% 0.20/0.53 & ( ( p @ V0p )
% 0.20/0.53 | ~ ( p @ V2r )
% 0.20/0.53 | ~ ( p @ V1q ) )
% 0.20/0.53 & ( ( p @ V1q )
% 0.20/0.53 | ~ ( p @ V2r )
% 0.20/0.53 | ~ ( p @ V0p ) )
% 0.20/0.53 & ( ( p @ V2r )
% 0.20/0.53 | ~ ( p @ V1q )
% 0.20/0.53 | ~ ( p @ V0p ) ) ) ) ) ) ) ).
% 0.20/0.53
% 0.20/0.53 thf(conj_thm_2Esat_2Edc__conj,axiom,
% 0.20/0.53 ! [V0p: $i] :
% 0.20/0.53 ( ( mem @ V0p @ bool )
% 0.20/0.53 => ! [V1q: $i] :
% 0.20/0.53 ( ( mem @ V1q @ bool )
% 0.20/0.53 => ! [V2r: $i] :
% 0.20/0.53 ( ( mem @ V2r @ bool )
% 0.20/0.53 => ( ( ( p @ V0p )
% 0.20/0.53 <=> ( ( p @ V1q )
% 0.20/0.53 & ( p @ V2r ) ) )
% 0.20/0.53 <=> ( ( ( p @ V0p )
% 0.20/0.53 | ~ ( p @ V1q )
% 0.20/0.53 | ~ ( p @ V2r ) )
% 0.20/0.53 & ( ( p @ V1q )
% 0.20/0.53 | ~ ( p @ V0p ) )
% 0.20/0.53 & ( ( p @ V2r )
% 0.20/0.53 | ~ ( p @ V0p ) ) ) ) ) ) ) ).
% 0.20/0.53
% 0.20/0.53 thf(conj_thm_2Esat_2Edc__disj,axiom,
% 0.20/0.53 ! [V0p: $i] :
% 0.20/0.53 ( ( mem @ V0p @ bool )
% 0.20/0.53 => ! [V1q: $i] :
% 0.20/0.53 ( ( mem @ V1q @ bool )
% 0.20/0.53 => ! [V2r: $i] :
% 0.20/0.53 ( ( mem @ V2r @ bool )
% 0.20/0.53 => ( ( ( p @ V0p )
% 0.20/0.53 <=> ( ( p @ V1q )
% 0.20/0.53 | ( p @ V2r ) ) )
% 0.20/0.53 <=> ( ( ( p @ V0p )
% 0.20/0.53 | ~ ( p @ V1q ) )
% 0.20/0.53 & ( ( p @ V0p )
% 0.20/0.53 | ~ ( p @ V2r ) )
% 0.20/0.53 & ( ( p @ V1q )
% 0.20/0.53 | ( p @ V2r )
% 0.20/0.53 | ~ ( p @ V0p ) ) ) ) ) ) ) ).
% 0.20/0.53
% 0.20/0.53 thf(conj_thm_2Esat_2Edc__imp,axiom,
% 0.20/0.53 ! [V0p: $i] :
% 0.20/0.53 ( ( mem @ V0p @ bool )
% 0.20/0.53 => ! [V1q: $i] :
% 0.20/0.53 ( ( mem @ V1q @ bool )
% 0.20/0.53 => ! [V2r: $i] :
% 0.20/0.53 ( ( mem @ V2r @ bool )
% 0.20/0.53 => ( ( ( p @ V0p )
% 0.20/0.53 <=> ( ( p @ V1q )
% 0.20/0.53 => ( p @ V2r ) ) )
% 0.20/0.53 <=> ( ( ( p @ V0p )
% 0.20/0.53 | ( p @ V1q ) )
% 0.20/0.53 & ( ( p @ V0p )
% 0.20/0.53 | ~ ( p @ V2r ) )
% 0.20/0.53 & ( ~ ( p @ V1q )
% 0.20/0.53 | ( p @ V2r )
% 0.20/0.53 | ~ ( p @ V0p ) ) ) ) ) ) ) ).
% 0.20/0.53
% 0.20/0.53 thf(conj_thm_2Esat_2Edc__neg,axiom,
% 0.20/0.53 ! [V0p: $i] :
% 0.20/0.53 ( ( mem @ V0p @ bool )
% 0.20/0.53 => ! [V1q: $i] :
% 0.20/0.53 ( ( mem @ V1q @ bool )
% 0.20/0.53 => ( ( ( p @ V0p )
% 0.20/0.53 <=> ~ ( p @ V1q ) )
% 0.20/0.53 <=> ( ( ( p @ V0p )
% 0.20/0.53 | ( p @ V1q ) )
% 0.20/0.53 & ( ~ ( p @ V1q )
% 0.20/0.53 | ~ ( p @ V0p ) ) ) ) ) ) ).
% 0.20/0.53
% 0.20/0.53 thf(conj_thm_2Einteger_2EINT__DIVIDES__RSUB,conjecture,
% 0.20/0.53 ! [V0p: tp__ty_2Einteger_2Eint,V1q: tp__ty_2Einteger_2Eint,V2r: tp__ty_2Einteger_2Eint] :
% 0.20/0.53 ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ V0p ) ) @ ( inj__ty_2Einteger_2Eint @ V1q ) ) )
% 0.20/0.53 => ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ V0p ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ V2r ) ) @ ( inj__ty_2Einteger_2Eint @ V1q ) ) ) )
% 0.20/0.53 <=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ V0p ) ) @ ( inj__ty_2Einteger_2Eint @ V2r ) ) ) ) ) ).
% 0.20/0.53
% 0.20/0.53 %------------------------------------------------------------------------------
% 0.20/0.53 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.BYZS5JYp3o/cvc5---1.0.5_30592.p...
% 0.20/0.53 (declare-sort $$unsorted 0)
% 0.20/0.53 (declare-sort tptp.del 0)
% 0.20/0.53 (declare-fun tptp.bool () tptp.del)
% 0.20/0.53 (declare-fun tptp.ind () tptp.del)
% 0.20/0.53 (declare-fun tptp.arr (tptp.del tptp.del) tptp.del)
% 0.20/0.53 (declare-fun tptp.mem ($$unsorted tptp.del) Bool)
% 0.20/0.53 (declare-fun tptp.ap ($$unsorted $$unsorted) $$unsorted)
% 0.20/0.53 (declare-fun tptp.lam (tptp.del (-> $$unsorted $$unsorted)) $$unsorted)
% 0.20/0.53 (declare-fun tptp.p ($$unsorted) Bool)
% 0.20/0.53 (declare-fun tptp.inj__o (Bool) $$unsorted)
% 0.20/0.53 (assert (forall ((X Bool)) (= (@ tptp.p (@ tptp.inj__o X)) X)))
% 0.20/0.53 (assert (forall ((X Bool)) (@ (@ tptp.mem (@ tptp.inj__o X)) tptp.bool)))
% 0.20/0.53 (assert (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) tptp.bool) (= X (@ tptp.inj__o (@ tptp.p X))))))
% 0.20/0.53 (assert (forall ((A tptp.del) (B tptp.del) (F $$unsorted)) (=> (@ (@ tptp.mem F) (@ (@ tptp.arr A) B)) (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) A) (@ (@ tptp.mem (@ (@ tptp.ap F) X)) B))))))
% 0.20/0.53 (assert (forall ((A tptp.del) (B tptp.del) (F (-> $$unsorted $$unsorted))) (=> (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) A) (@ (@ tptp.mem (@ F X)) B))) (@ (@ tptp.mem (@ (@ tptp.lam A) F)) (@ (@ tptp.arr A) B)))))
% 0.20/0.53 (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 $$unsorted)) (=> (@ (@ tptp.mem X) A) (= (@ (@ tptp.ap F) X) (@ (@ tptp.ap G) X)))) (= F G)))))))
% 0.20/0.53 (assert (forall ((A tptp.del) (F (-> $$unsorted $$unsorted)) (X $$unsorted)) (=> (@ (@ tptp.mem X) A) (= (@ (@ tptp.ap (@ (@ tptp.lam A) F)) X) (@ F X)))))
% 0.20/0.53 (declare-fun tptp.c_2Ebool_2ET () $$unsorted)
% 0.20/0.53 (assert (@ (@ tptp.mem tptp.c_2Ebool_2ET) tptp.bool))
% 0.20/0.53 (assert (@ tptp.p tptp.c_2Ebool_2ET))
% 0.20/0.53 (declare-fun tptp.c_2Ebool_2E_3F (tptp.del) $$unsorted)
% 0.20/0.53 (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))))
% 0.20/0.53 (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))))))))
% 0.20/0.53 (declare-fun tptp.ty_2Einteger_2Eint () tptp.del)
% 0.20/0.53 (declare-sort tptp.tp__ty_2Einteger_2Eint 0)
% 0.20/0.53 (declare-fun tptp.inj__ty_2Einteger_2Eint (tptp.tp__ty_2Einteger_2Eint) $$unsorted)
% 0.20/0.53 (declare-fun tptp.surj__ty_2Einteger_2Eint ($$unsorted) tptp.tp__ty_2Einteger_2Eint)
% 0.20/0.53 (assert (forall ((X tptp.tp__ty_2Einteger_2Eint)) (= (@ tptp.surj__ty_2Einteger_2Eint (@ tptp.inj__ty_2Einteger_2Eint X)) X)))
% 0.20/0.53 (assert (forall ((X tptp.tp__ty_2Einteger_2Eint)) (@ (@ tptp.mem (@ tptp.inj__ty_2Einteger_2Eint X)) tptp.ty_2Einteger_2Eint)))
% 0.20/0.53 (assert (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) tptp.ty_2Einteger_2Eint) (= X (@ tptp.inj__ty_2Einteger_2Eint (@ tptp.surj__ty_2Einteger_2Eint X))))))
% 0.20/0.53 (declare-fun tptp.c_2Einteger_2Eint__sub () $$unsorted)
% 0.20/0.53 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Einteger_2Eint))) (@ (@ tptp.mem tptp.c_2Einteger_2Eint__sub) (@ _let_1 (@ _let_1 tptp.ty_2Einteger_2Eint)))))
% 0.20/0.53 (declare-fun tptp.fo__c_2Einteger_2Eint__sub (tptp.tp__ty_2Einteger_2Eint tptp.tp__ty_2Einteger_2Eint) tptp.tp__ty_2Einteger_2Eint)
% 0.20/0.53 (assert (forall ((X0 tptp.tp__ty_2Einteger_2Eint) (X1 tptp.tp__ty_2Einteger_2Eint)) (= (@ tptp.inj__ty_2Einteger_2Eint (@ (@ tptp.fo__c_2Einteger_2Eint__sub X0) X1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Einteger_2Eint__sub) (@ tptp.inj__ty_2Einteger_2Eint X0))) (@ tptp.inj__ty_2Einteger_2Eint X1)))))
% 0.20/0.53 (declare-fun tptp.c_2Einteger_2Eint__add () $$unsorted)
% 0.20/0.53 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Einteger_2Eint))) (@ (@ tptp.mem tptp.c_2Einteger_2Eint__add) (@ _let_1 (@ _let_1 tptp.ty_2Einteger_2Eint)))))
% 0.20/0.53 (declare-fun tptp.fo__c_2Einteger_2Eint__add (tptp.tp__ty_2Einteger_2Eint tptp.tp__ty_2Einteger_2Eint) tptp.tp__ty_2Einteger_2Eint)
% 0.20/0.53 (assert (forall ((X0 tptp.tp__ty_2Einteger_2Eint) (X1 tptp.tp__ty_2Einteger_2Eint)) (= (@ tptp.inj__ty_2Einteger_2Eint (@ (@ tptp.fo__c_2Einteger_2Eint__add X0) X1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Einteger_2Eint__add) (@ tptp.inj__ty_2Einteger_2Eint X0))) (@ tptp.inj__ty_2Einteger_2Eint X1)))))
% 0.20/0.53 (declare-fun tptp.c_2Einteger_2Eint__neg () $$unsorted)
% 0.20/0.53 (assert (@ (@ tptp.mem tptp.c_2Einteger_2Eint__neg) (@ (@ tptp.arr tptp.ty_2Einteger_2Eint) tptp.ty_2Einteger_2Eint)))
% 0.20/0.53 (declare-fun tptp.fo__c_2Einteger_2Eint__neg (tptp.tp__ty_2Einteger_2Eint) tptp.tp__ty_2Einteger_2Eint)
% 0.20/0.53 (assert (forall ((X0 tptp.tp__ty_2Einteger_2Eint)) (= (@ tptp.inj__ty_2Einteger_2Eint (@ tptp.fo__c_2Einteger_2Eint__neg X0)) (@ (@ tptp.ap tptp.c_2Einteger_2Eint__neg) (@ tptp.inj__ty_2Einteger_2Eint X0)))))
% 0.20/0.53 (declare-fun tptp.c_2Einteger_2Eint__divides () $$unsorted)
% 0.20/0.53 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Einteger_2Eint))) (@ (@ tptp.mem tptp.c_2Einteger_2Eint__divides) (@ _let_1 (@ _let_1 tptp.bool)))))
% 0.20/0.53 (declare-fun tptp.c_2Ebool_2EF () $$unsorted)
% 0.20/0.53 (assert (@ (@ tptp.mem tptp.c_2Ebool_2EF) tptp.bool))
% 0.20/0.53 (assert (not (@ tptp.p tptp.c_2Ebool_2EF)))
% 0.20/0.53 (declare-fun tptp.c_2Emin_2E_3D_3D_3E () $$unsorted)
% 0.20/0.53 (assert (let ((_let_1 (@ tptp.arr tptp.bool))) (@ (@ tptp.mem tptp.c_2Emin_2E_3D_3D_3E) (@ _let_1 (@ _let_1 tptp.bool)))))
% 0.20/0.53 (assert (forall ((Q $$unsorted)) (=> (@ (@ tptp.mem Q) tptp.bool) (forall ((R $$unsorted)) (=> (@ (@ tptp.mem R) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) Q)) R)) (=> (@ tptp.p Q) (@ tptp.p R))))))))
% 0.20/0.53 (declare-fun tptp.c_2Ebool_2E_5C_2F () $$unsorted)
% 0.20/0.53 (assert (let ((_let_1 (@ tptp.arr tptp.bool))) (@ (@ tptp.mem tptp.c_2Ebool_2E_5C_2F) (@ _let_1 (@ _let_1 tptp.bool)))))
% 0.20/0.53 (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))))))))
% 0.20/0.53 (declare-fun tptp.c_2Ebool_2E_2F_5C () $$unsorted)
% 0.20/0.53 (assert (let ((_let_1 (@ tptp.arr tptp.bool))) (@ (@ tptp.mem tptp.c_2Ebool_2E_2F_5C) (@ _let_1 (@ _let_1 tptp.bool)))))
% 0.20/0.53 (assert (forall ((Q $$unsorted)) (=> (@ (@ tptp.mem Q) tptp.bool) (forall ((R $$unsorted)) (=> (@ (@ tptp.mem R) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) Q)) R)) (and (@ tptp.p Q) (@ tptp.p R))))))))
% 0.20/0.53 (declare-fun tptp.c_2Ebool_2E_7E () $$unsorted)
% 0.20/0.53 (assert (@ (@ tptp.mem tptp.c_2Ebool_2E_7E) (@ (@ tptp.arr tptp.bool) tptp.bool)))
% 0.20/0.53 (assert (forall ((Q $$unsorted)) (=> (@ (@ tptp.mem Q) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap tptp.c_2Ebool_2E_7E) Q)) (not (@ tptp.p Q))))))
% 0.20/0.53 (declare-fun tptp.c_2Emin_2E_3D (tptp.del) $$unsorted)
% 0.20/0.53 (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))))))
% 0.20/0.53 (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)))))))
% 0.20/0.53 (declare-fun tptp.c_2Ebool_2E_21 (tptp.del) $$unsorted)
% 0.20/0.53 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Ebool_2E_21 A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool))))
% 0.20/0.53 (assert (forall ((A tptp.del) (Q $$unsorted)) (=> (@ (@ tptp.mem Q) (@ (@ tptp.arr A) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A)) Q)) (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) A) (@ tptp.p (@ (@ tptp.ap Q) X))))))))
% 0.20/0.53 (assert true)
% 0.20/0.53 (assert (forall ((V0t1 $$unsorted)) (=> (@ (@ tptp.mem V0t1) tptp.bool) (forall ((V1t2 $$unsorted)) (let ((_let_1 (@ tptp.p V1t2))) (let ((_let_2 (@ tptp.p V0t1))) (=> (@ (@ tptp.mem V1t2) tptp.bool) (=> (=> _let_2 _let_1) (=> (=> _let_1 _let_2) (= _let_2 _let_1))))))))))
% 0.20/0.53 (assert (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (=> (=> _let_1 false) (not _let_1))))))
% 0.20/0.53 (assert (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (=> (not _let_1) (=> _let_1 false))))))
% 0.20/0.53 (assert (forall ((V0t $$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)))))))
% 0.20/0.53 (assert (and (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (= (not (not _let_1)) _let_1)))) (= (not true) false) (= (not false) true)))
% 0.20/0.53 (assert (forall ((V0t $$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)))))))
% 0.20/0.53 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (= (not (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (@ tptp.p (@ (@ tptp.ap V0P) V1x))))) (exists ((V2x $$unsorted)) (and (@ (@ tptp.mem V2x) A_27a) (not (@ tptp.p (@ (@ tptp.ap V0P) V2x)))))))))
% 0.20/0.53 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) (@ (@ tptp.arr A_27a) tptp.bool)) (= (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (and (@ tptp.p (@ (@ tptp.ap V0P) V2x)) (@ tptp.p (@ (@ tptp.ap V1Q) V2x))))) (and (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (@ tptp.p (@ (@ tptp.ap V0P) V3x)))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (@ tptp.p (@ (@ tptp.ap V1Q) V4x)))))))))))
% 0.20/0.53 (assert (forall ((V0A $$unsorted)) (=> (@ (@ tptp.mem V0A) tptp.bool) (forall ((V1B $$unsorted)) (=> (@ (@ tptp.mem V1B) tptp.bool) (forall ((V2C $$unsorted)) (let ((_let_1 (or (@ tptp.p V0A) (@ tptp.p V1B) (@ tptp.p V2C)))) (=> (@ (@ tptp.mem V2C) tptp.bool) (= _let_1 _let_1)))))))))
% 0.20/0.53 (assert (forall ((V0A $$unsorted)) (=> (@ (@ tptp.mem V0A) tptp.bool) (forall ((V1B $$unsorted)) (let ((_let_1 (@ tptp.p V0A))) (let ((_let_2 (@ tptp.p V1B))) (=> (@ (@ tptp.mem V1B) tptp.bool) (= (or _let_1 _let_2) (or _let_2 _let_1)))))))))
% 0.20/0.53 (assert (forall ((V0A $$unsorted)) (=> (@ (@ tptp.mem V0A) tptp.bool) (forall ((V1B $$unsorted)) (let ((_let_1 (@ tptp.p V1B))) (let ((_let_2 (not _let_1))) (let ((_let_3 (@ tptp.p V0A))) (let ((_let_4 (not _let_3))) (=> (@ (@ tptp.mem V1B) tptp.bool) (and (= (not (and _let_3 _let_1)) (or _let_4 _let_2)) (= (not (or _let_3 _let_1)) (and _let_4 _let_2))))))))))))
% 0.20/0.53 (assert (forall ((V0x tptp.tp__ty_2Einteger_2Eint) (V1y tptp.tp__ty_2Einteger_2Eint)) (let ((_let_1 (@ tptp.inj__ty_2Einteger_2Eint V1y))) (let ((_let_2 (@ tptp.inj__ty_2Einteger_2Eint V0x))) (= (@ tptp.surj__ty_2Einteger_2Eint (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Einteger_2Eint__sub) _let_2)) _let_1)) (@ tptp.surj__ty_2Einteger_2Eint (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Einteger_2Eint__add) _let_2)) (@ (@ tptp.ap tptp.c_2Einteger_2Eint__neg) _let_1))))))))
% 0.20/0.53 (assert (forall ((V0p tptp.tp__ty_2Einteger_2Eint) (V1q tptp.tp__ty_2Einteger_2Eint) (V2r tptp.tp__ty_2Einteger_2Eint)) (let ((_let_1 (@ tptp.inj__ty_2Einteger_2Eint V2r))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Einteger_2Eint__divides) (@ tptp.inj__ty_2Einteger_2Eint V0p))))) (let ((_let_3 (@ tptp.inj__ty_2Einteger_2Eint V1q))) (=> (@ tptp.p (@ _let_2 _let_3)) (= (@ tptp.p (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Einteger_2Eint__add) _let_1)) _let_3))) (@ tptp.p (@ _let_2 _let_1)))))))))
% 0.20/0.53 (assert (forall ((V0p tptp.tp__ty_2Einteger_2Eint) (V1q tptp.tp__ty_2Einteger_2Eint)) (let ((_let_1 (@ tptp.inj__ty_2Einteger_2Eint V1q))) (let ((_let_2 (@ tptp.inj__ty_2Einteger_2Eint V0p))) (let ((_let_3 (@ tptp.ap tptp.c_2Einteger_2Eint__divides))) (let ((_let_4 (@ tptp.ap (@ _let_3 _let_2)))) (let ((_let_5 (@ tptp.p (@ _let_4 _let_1)))) (let ((_let_6 (@ tptp.ap tptp.c_2Einteger_2Eint__neg))) (and (= (@ tptp.p (@ _let_4 (@ _let_6 _let_1))) _let_5) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ _let_6 _let_2))) _let_1)) _let_5))))))))))
% 0.20/0.53 (assert (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (= (not (not _let_1)) _let_1)))))
% 0.20/0.53 (assert (forall ((V0A $$unsorted)) (let ((_let_1 (@ tptp.p V0A))) (=> (@ (@ tptp.mem V0A) tptp.bool) (=> _let_1 (=> (not _let_1) false))))))
% 0.20/0.53 (assert (forall ((V0A $$unsorted)) (=> (@ (@ tptp.mem V0A) tptp.bool) (forall ((V1B $$unsorted)) (let ((_let_1 (@ tptp.p V1B))) (let ((_let_2 (@ tptp.p V0A))) (=> (@ (@ tptp.mem V1B) tptp.bool) (= (=> (not (or _let_2 _let_1)) false) (=> (=> _let_2 false) (=> (not _let_1) false))))))))))
% 0.20/0.53 (assert (forall ((V0A $$unsorted)) (=> (@ (@ tptp.mem V0A) tptp.bool) (forall ((V1B $$unsorted)) (let ((_let_1 (@ tptp.p V1B))) (let ((_let_2 (@ tptp.p V0A))) (=> (@ (@ tptp.mem V1B) tptp.bool) (= (=> (not (or (not _let_2) _let_1)) false) (=> _let_2 (=> (not _let_1) false))))))))))
% 0.20/0.53 (assert (forall ((V0A $$unsorted)) (let ((_let_1 (@ tptp.p V0A))) (=> (@ (@ tptp.mem V0A) tptp.bool) (=> (=> (not _let_1) false) (=> (=> _let_1 false) false))))))
% 0.20/0.53 (assert (forall ((V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) tptp.bool) (forall ((V1q $$unsorted)) (=> (@ (@ tptp.mem V1q) tptp.bool) (forall ((V2r $$unsorted)) (let ((_let_1 (@ tptp.p V0p))) (let ((_let_2 (not _let_1))) (let ((_let_3 (@ tptp.p V1q))) (let ((_let_4 (not _let_3))) (let ((_let_5 (@ tptp.p V2r))) (let ((_let_6 (not _let_5))) (=> (@ (@ tptp.mem V2r) tptp.bool) (= (= _let_1 (= _let_3 _let_5)) (and (or _let_1 _let_3 _let_5) (or _let_1 _let_6 _let_4) (or _let_3 _let_6 _let_2) (or _let_5 _let_4 _let_2))))))))))))))))
% 1.03/1.24 (assert (forall ((V0p $$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))))))))))))))
% 1.03/1.24 (assert (forall ((V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) tptp.bool) (forall ((V1q $$unsorted)) (=> (@ (@ tptp.mem V1q) tptp.bool) (forall ((V2r $$unsorted)) (let ((_let_1 (@ tptp.p V0p))) (let ((_let_2 (@ tptp.p V2r))) (let ((_let_3 (@ tptp.p V1q))) (=> (@ (@ tptp.mem V2r) tptp.bool) (= (= _let_1 (or _let_3 _let_2)) (and (or _let_1 (not _let_3)) (or _let_1 (not _let_2)) (or _let_3 _let_2 (not _let_1))))))))))))))
% 1.03/1.24 (assert (forall ((V0p $$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))))))))))))))
% 1.03/1.24 (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))))))))))))
% 1.03/1.24 (assert (not (forall ((V0p tptp.tp__ty_2Einteger_2Eint) (V1q tptp.tp__ty_2Einteger_2Eint) (V2r tptp.tp__ty_2Einteger_2Eint)) (let ((_let_1 (@ tptp.inj__ty_2Einteger_2Eint V2r))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Einteger_2Eint__divides) (@ tptp.inj__ty_2Einteger_2Eint V0p))))) (let ((_let_3 (@ tptp.inj__ty_2Einteger_2Eint V1q))) (=> (@ tptp.p (@ _let_2 _let_3)) (= (@ tptp.p (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Einteger_2Eint__sub) _let_1)) _let_3))) (@ tptp.p (@ _let_2 _let_1))))))))))
% 1.03/1.24 (set-info :filename cvc5---1.0.5_30592)
% 1.03/1.24 (check-sat-assuming ( true ))
% 1.03/1.24 ------- get file name : TPTP file name is ITP012^2
% 1.03/1.24 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_30592.smt2...
% 1.03/1.24 --- Run --ho-elim --full-saturate-quant at 10...
% 1.03/1.24 % SZS status Theorem for ITP012^2
% 1.03/1.24 % SZS output start Proof for ITP012^2
% 1.03/1.24 (
% 1.03/1.24 (let ((_let_1 (not (forall ((V0p tptp.tp__ty_2Einteger_2Eint) (V1q tptp.tp__ty_2Einteger_2Eint) (V2r tptp.tp__ty_2Einteger_2Eint)) (let ((_let_1 (@ tptp.inj__ty_2Einteger_2Eint V2r))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Einteger_2Eint__divides) (@ tptp.inj__ty_2Einteger_2Eint V0p))))) (let ((_let_3 (@ tptp.inj__ty_2Einteger_2Eint V1q))) (=> (@ tptp.p (@ _let_2 _let_3)) (= (@ tptp.p (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Einteger_2Eint__sub) _let_1)) _let_3))) (@ tptp.p (@ _let_2 _let_1))))))))))) (let ((_let_2 (forall ((V0p tptp.tp__ty_2Einteger_2Eint) (V1q tptp.tp__ty_2Einteger_2Eint)) (let ((_let_1 (@ tptp.inj__ty_2Einteger_2Eint V1q))) (let ((_let_2 (@ tptp.inj__ty_2Einteger_2Eint V0p))) (let ((_let_3 (@ tptp.ap tptp.c_2Einteger_2Eint__divides))) (let ((_let_4 (@ tptp.ap (@ _let_3 _let_2)))) (let ((_let_5 (@ tptp.p (@ _let_4 _let_1)))) (let ((_let_6 (@ tptp.ap tptp.c_2Einteger_2Eint__neg))) (and (= (@ tptp.p (@ _let_4 (@ _let_6 _let_1))) _let_5) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ _let_6 _let_2))) _let_1)) _let_5))))))))))) (let ((_let_3 (forall ((V0p tptp.tp__ty_2Einteger_2Eint) (V1q tptp.tp__ty_2Einteger_2Eint) (V2r tptp.tp__ty_2Einteger_2Eint)) (let ((_let_1 (@ tptp.inj__ty_2Einteger_2Eint V2r))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Einteger_2Eint__divides) (@ tptp.inj__ty_2Einteger_2Eint V0p))))) (let ((_let_3 (@ tptp.inj__ty_2Einteger_2Eint V1q))) (=> (@ tptp.p (@ _let_2 _let_3)) (= (@ tptp.p (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Einteger_2Eint__add) _let_1)) _let_3))) (@ tptp.p (@ _let_2 _let_1)))))))))) (let ((_let_4 (forall ((V0x tptp.tp__ty_2Einteger_2Eint) (V1y tptp.tp__ty_2Einteger_2Eint)) (let ((_let_1 (@ tptp.inj__ty_2Einteger_2Eint V1y))) (let ((_let_2 (@ tptp.inj__ty_2Einteger_2Eint V0x))) (= (@ tptp.surj__ty_2Einteger_2Eint (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Einteger_2Eint__sub) _let_2)) _let_1)) (@ tptp.surj__ty_2Einteger_2Eint (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Einteger_2Eint__add) _let_2)) (@ (@ tptp.ap tptp.c_2Einteger_2Eint__neg) _let_1))))))))) (let ((_let_5 (@ tptp.arr tptp.bool))) (let ((_let_6 (@ _let_5 tptp.bool))) (let ((_let_7 (@ _let_5 _let_6))) (let ((_let_8 (@ tptp.arr tptp.ty_2Einteger_2Eint))) (let ((_let_9 (forall ((X0 tptp.tp__ty_2Einteger_2Eint)) (= (@ tptp.inj__ty_2Einteger_2Eint (@ tptp.fo__c_2Einteger_2Eint__neg X0)) (@ (@ tptp.ap tptp.c_2Einteger_2Eint__neg) (@ tptp.inj__ty_2Einteger_2Eint X0)))))) (let ((_let_10 (@ _let_8 tptp.ty_2Einteger_2Eint))) (let ((_let_11 (@ _let_8 _let_10))) (let ((_let_12 (@ (@ tptp.mem tptp.c_2Einteger_2Eint__add) _let_11))) (let ((_let_13 (forall ((X0 tptp.tp__ty_2Einteger_2Eint) (X1 tptp.tp__ty_2Einteger_2Eint)) (= (@ tptp.inj__ty_2Einteger_2Eint (@ (@ tptp.fo__c_2Einteger_2Eint__sub X0) X1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Einteger_2Eint__sub) (@ tptp.inj__ty_2Einteger_2Eint X0))) (@ tptp.inj__ty_2Einteger_2Eint X1)))))) (let ((_let_14 (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) tptp.ty_2Einteger_2Eint) (= X (@ tptp.inj__ty_2Einteger_2Eint (@ tptp.surj__ty_2Einteger_2Eint X))))))) (let ((_let_15 (forall ((X tptp.tp__ty_2Einteger_2Eint)) (@ (@ tptp.mem (@ tptp.inj__ty_2Einteger_2Eint X)) tptp.ty_2Einteger_2Eint)))) (let ((_let_16 (forall ((X tptp.tp__ty_2Einteger_2Eint)) (= (@ tptp.surj__ty_2Einteger_2Eint (@ tptp.inj__ty_2Einteger_2Eint X)) X)))) (let ((_let_17 (forall ((A tptp.del) (B tptp.del) (F $$unsorted)) (=> (@ (@ tptp.mem F) (@ (@ tptp.arr A) B)) (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) A) (@ (@ tptp.mem (@ (@ tptp.ap F) X)) B))))))) (let ((_let_18 (ho_26 (ho_25 k_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_33) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_32))) (let ((_let_19 (ho_21 k_20 _let_18))) (let ((_let_20 (ho_21 k_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_32))) (let ((_let_21 (ho_21 k_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_33))) (let ((_let_22 (ho_10 k_9 tptp.c_2Einteger_2Eint__sub))) (let ((_let_23 (ho_11 (ho_10 k_9 (ho_11 _let_22 _let_21)) _let_20))) (let ((_let_24 (= _let_23 _let_19))) (let ((_let_25 (ho_10 k_9 tptp.c_2Einteger_2Eint__neg))) (let ((_let_26 (ho_11 _let_25 _let_20))) (let ((_let_27 (ho_11 (ho_10 k_9 tptp.c_2Einteger_2Eint__add) _let_21))) (let ((_let_28 (ho_10 k_9 _let_27))) (let ((_let_29 (ho_11 _let_28 _let_26))) (let ((_let_30 (ho_23 k_22 _let_29))) (let ((_let_31 (= _let_30 (ho_23 k_22 _let_23)))) (let ((_let_32 (= _let_18 (ho_23 k_22 _let_19)))) (let ((_let_33 (ho_26 k_28 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_32))) (let ((_let_34 (ho_21 k_20 _let_33))) (let ((_let_35 (= _let_26 _let_34))) (let ((_let_36 (= _let_29 (ho_21 k_20 _let_30)))) (let ((_let_37 (ho_10 k_9 tptp.c_2Einteger_2Eint__divides))) (let ((_let_38 (ho_10 k_9 (ho_11 _let_37 (ho_21 k_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_31))))) (let ((_let_39 (ho_5 k_4 (ho_11 _let_38 _let_23)))) (let ((_let_40 (ho_11 _let_28 _let_34))) (let ((_let_41 (ho_5 k_4 (ho_11 _let_38 _let_40)))) (let ((_let_42 (forall ((X0 tptp.tp__ty_2Einteger_2Eint) (X1 tptp.tp__ty_2Einteger_2Eint)) (= (ho_11 (ho_10 k_9 (ho_11 (ho_10 k_9 tptp.c_2Einteger_2Eint__sub) (ho_21 k_20 X0))) (ho_21 k_20 X1)) (ho_21 k_20 (ho_26 (ho_25 k_24 X0) X1)))))) (let ((_let_43 (EQ_RESOLVE (ASSUME :args (_let_13)) (PREPROCESS :args ((= _let_13 _let_42)))))) (let ((_let_44 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_43 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_33 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_32 QUANTIFIERS_INST_E_MATCHING ((ho_11 (ho_10 k_9 (ho_11 _let_22 (ho_21 k_20 X0))) (ho_21 k_20 X1))))) :args (_let_42))) _let_43 :args (_let_24 false _let_42)))) (let ((_let_45 (forall ((V0x tptp.tp__ty_2Einteger_2Eint) (V1y tptp.tp__ty_2Einteger_2Eint)) (let ((_let_1 (ho_21 k_20 V1y))) (let ((_let_2 (ho_21 k_20 V0x))) (= (ho_23 k_22 (ho_11 (ho_10 k_9 (ho_11 (ho_10 k_9 tptp.c_2Einteger_2Eint__add) _let_2)) (ho_11 (ho_10 k_9 tptp.c_2Einteger_2Eint__neg) _let_1))) (ho_23 k_22 (ho_11 (ho_10 k_9 (ho_11 (ho_10 k_9 tptp.c_2Einteger_2Eint__sub) _let_2)) _let_1)))))))) (let ((_let_46 (EQ_RESOLVE (ASSUME :args (_let_4)) (PREPROCESS :args ((= _let_4 _let_45)))))) (let ((_let_47 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_46 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_33 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_32 QUANTIFIERS_INST_E_MATCHING ((ho_11 (ho_10 k_9 (ho_11 _let_22 (ho_21 k_20 V0x))) (ho_21 k_20 V1y))))) :args (_let_45))) _let_46 :args (_let_31 false _let_45)))) (let ((_let_48 (forall ((X tptp.tp__ty_2Einteger_2Eint)) (= X (ho_23 k_22 (ho_21 k_20 X)))))) (let ((_let_49 (EQ_RESOLVE (ASSUME :args (_let_16)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((X tptp.tp__ty_2Einteger_2Eint)) (= X (@ tptp.surj__ty_2Einteger_2Eint (@ tptp.inj__ty_2Einteger_2Eint X)))) _let_48))))))) (let ((_let_50 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (_let_18 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_48))) _let_49 :args (_let_32 false _let_48)))) (let ((_let_51 (forall ((X0 tptp.tp__ty_2Einteger_2Eint)) (= (ho_11 (ho_10 k_9 tptp.c_2Einteger_2Eint__neg) (ho_21 k_20 X0)) (ho_21 k_20 (ho_26 k_28 X0)))))) (let ((_let_52 (EQ_RESOLVE (ASSUME :args (_let_9)) (PREPROCESS :args ((= _let_9 _let_51)))))) (let ((_let_53 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_52 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_32 QUANTIFIERS_INST_E_MATCHING ((ho_11 _let_25 (ho_21 k_20 X0))))) :args (_let_51))) _let_52 :args (_let_35 false _let_51)))) (let ((_let_54 (ho_8 (ho_7 k_6 _let_29) tptp.ty_2Einteger_2Eint))) (let ((_let_55 (not _let_54))) (let ((_let_56 (or _let_55 _let_36))) (let ((_let_57 (forall ((X $$unsorted)) (or (not (ho_8 (ho_7 k_6 X) tptp.ty_2Einteger_2Eint)) (= X (ho_21 k_20 (ho_23 k_22 X))))))) (let ((_let_58 (EQ_RESOLVE (ASSUME :args (_let_14)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((X $$unsorted)) (or (not (@ (@ tptp.mem X) tptp.ty_2Einteger_2Eint)) (= X (@ tptp.inj__ty_2Einteger_2Eint (@ tptp.surj__ty_2Einteger_2Eint X))))) _let_57))))))) (let ((_let_59 (ho_8 (ho_7 k_6 _let_40) tptp.ty_2Einteger_2Eint))) (let ((_let_60 (ho_8 (ho_7 k_6 _let_34) tptp.ty_2Einteger_2Eint))) (let ((_let_61 (not _let_60))) (let ((_let_62 (ho_13 k_12 tptp.ty_2Einteger_2Eint))) (let ((_let_63 (ho_14 _let_62 tptp.ty_2Einteger_2Eint))) (let ((_let_64 (ho_8 (ho_7 k_6 _let_27) _let_63))) (let ((_let_65 (not _let_64))) (let ((_let_66 (or _let_65 _let_61 _let_59))) (let ((_let_67 (forall ((A tptp.del) (B tptp.del) (F $$unsorted) (BOUND_VARIABLE_1528 $$unsorted)) (or (not (ho_8 (ho_7 k_6 F) (ho_14 (ho_13 k_12 A) B))) (not (ho_8 (ho_7 k_6 BOUND_VARIABLE_1528) A)) (ho_8 (ho_7 k_6 (ho_11 (ho_10 k_9 F) BOUND_VARIABLE_1528)) B))))) (let ((_let_68 (EQ_RESOLVE (ASSUME :args (_let_17)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((A tptp.del) (B tptp.del) (F $$unsorted) (BOUND_VARIABLE_1528 $$unsorted)) (or (not (@ (@ tptp.mem F) (@ (@ tptp.arr A) B))) (not (@ (@ tptp.mem BOUND_VARIABLE_1528) A)) (@ (@ tptp.mem (@ (@ tptp.ap F) BOUND_VARIABLE_1528)) B))) _let_67))))))) (let ((_let_69 (_let_67))) (let ((_let_70 (forall ((X tptp.tp__ty_2Einteger_2Eint)) (ho_8 (ho_7 k_6 (ho_21 k_20 X)) tptp.ty_2Einteger_2Eint)))) (let ((_let_71 (EQ_RESOLVE (ASSUME :args (_let_15)) (PREPROCESS :args ((= _let_15 _let_70)))))) (let ((_let_72 (_let_70))) (let ((_let_73 ((ho_21 k_20 X)))) (let ((_let_74 (ho_8 (ho_7 k_6 _let_21) tptp.ty_2Einteger_2Eint))) (let ((_let_75 (not _let_74))) (let ((_let_76 (ho_8 (ho_7 k_6 tptp.c_2Einteger_2Eint__add) (ho_14 _let_62 _let_63)))) (let ((_let_77 (not _let_76))) (let ((_let_78 (or _let_77 _let_75 _let_64))) (let ((_let_79 (not _let_35))) (let ((_let_80 (and _let_35 _let_59))) (let ((_let_81 (ASSUME :args (_let_59)))) (let ((_let_82 (APPLY_UF ho_11))) (let ((_let_83 (ASSUME :args (_let_35)))) (let ((_let_84 (SYMM _let_83))) (let ((_let_85 (REFL :args (_let_28)))) (let ((_let_86 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_56)) :args ((or _let_55 _let_36 (not _let_56)))) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_80)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_81 _let_83) (SCOPE (TRUE_ELIM (TRANS (CONG (CONG (REFL :args (k_6)) (CONG _let_85 (SYMM _let_84) :args _let_82) :args (APPLY_UF ho_7)) (REFL :args (tptp.ty_2Einteger_2Eint)) :args (APPLY_UF ho_8)) (TRUE_INTRO _let_81))) :args (_let_59 _let_35))) :args (_let_35 _let_59))) :args (true _let_80)) :args ((or _let_54 _let_79 (not _let_59)))) _let_53 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_66)) :args ((or _let_65 _let_61 _let_59 (not _let_66)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_78)) :args ((or _let_77 _let_75 _let_64 (not _let_78)))) (EQ_RESOLVE (ASSUME :args (_let_12)) (PREPROCESS :args ((= _let_12 _let_76)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_71 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_33 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_73)) :args _let_72)) _let_71 :args (_let_74 false _let_70)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_68 :args (tptp.ty_2Einteger_2Eint _let_63 tptp.c_2Einteger_2Eint__add _let_21 QUANTIFIERS_INST_E_MATCHING ((not (= (ho_8 (ho_7 k_6 F) (ho_14 (ho_13 k_12 A) B)) false)) (not (= (ho_8 (ho_7 k_6 BOUND_VARIABLE_1528) A) false))))) :args _let_69)) _let_68 :args (_let_78 false _let_67)) :args (_let_64 false _let_76 false _let_74 false _let_78)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_71 :args (_let_33 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_73)) :args _let_72)) _let_71 :args (_let_60 false _let_70)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_68 :args (tptp.ty_2Einteger_2Eint tptp.ty_2Einteger_2Eint _let_27 _let_34 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_69)) _let_68 :args (_let_66 false _let_67)) :args (_let_59 false _let_64 false _let_60 false _let_66)) :args (_let_54 false _let_35 false _let_59)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_58 :args (_let_29 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_23 k_22 X)))) :args (_let_57))) _let_58 :args (_let_56 false _let_57)) :args (_let_36 false _let_54 false _let_56)))) (let ((_let_87 (ho_5 k_4 (ho_11 _let_38 _let_21)))) (let ((_let_88 (= _let_87 _let_39))) (let ((_let_89 (ho_5 k_4 (ho_11 _let_38 _let_20)))) (let ((_let_90 (not _let_89))) (let ((_let_91 (or _let_90 _let_88))) (let ((_let_92 (forall ((V0p tptp.tp__ty_2Einteger_2Eint) (V1q tptp.tp__ty_2Einteger_2Eint) (V2r tptp.tp__ty_2Einteger_2Eint)) (let ((_let_1 (ho_21 k_20 V1q))) (let ((_let_2 (ho_21 k_20 V2r))) (let ((_let_3 (ho_10 k_9 (ho_11 (ho_10 k_9 tptp.c_2Einteger_2Eint__divides) (ho_21 k_20 V0p))))) (or (not (ho_5 k_4 (ho_11 _let_3 _let_1))) (= (ho_5 k_4 (ho_11 _let_3 _let_2)) (ho_5 k_4 (ho_11 _let_3 (ho_11 (ho_10 k_9 (ho_11 (ho_10 k_9 tptp.c_2Einteger_2Eint__sub) _let_2)) _let_1))))))))))) (let ((_let_93 (not _let_91))) (let ((_let_94 (not _let_92))) (let ((_let_95 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((V0p tptp.tp__ty_2Einteger_2Eint) (V1q tptp.tp__ty_2Einteger_2Eint) (V2r tptp.tp__ty_2Einteger_2Eint)) (let ((_let_1 (@ tptp.inj__ty_2Einteger_2Eint V2r))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Einteger_2Eint__divides) (@ tptp.inj__ty_2Einteger_2Eint V0p))))) (let ((_let_3 (@ tptp.inj__ty_2Einteger_2Eint V1q))) (or (not (@ tptp.p (@ _let_2 _let_3))) (= (@ tptp.p (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Einteger_2Eint__sub) _let_1)) _let_3))) (@ tptp.p (@ _let_2 _let_1))))))))) _let_94))))))) (let ((_let_96 (or))) (let ((_let_97 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_95) :args (_let_94))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_94) _let_92))) (REFL :args (_let_93)) :args _let_96)) _let_95 :args (_let_93 true _let_92)))) (let ((_let_98 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_91 1)) _let_97 :args ((not _let_88) true _let_91)))) (let 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(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 $$unsorted)) (and (@ (@ tptp.mem X) A) (@ tptp.p (@ (@ tptp.ap Q) X))))))) _let_16 _let_15 _let_14 (@ (@ tptp.mem tptp.c_2Einteger_2Eint__sub) _let_11) _let_13 _let_12 (forall ((X0 tptp.tp__ty_2Einteger_2Eint) (X1 tptp.tp__ty_2Einteger_2Eint)) (= (@ tptp.inj__ty_2Einteger_2Eint (@ (@ tptp.fo__c_2Einteger_2Eint__add X0) X1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Einteger_2Eint__add) (@ tptp.inj__ty_2Einteger_2Eint X0))) (@ tptp.inj__ty_2Einteger_2Eint X1)))) (@ (@ tptp.mem tptp.c_2Einteger_2Eint__neg) _let_10) _let_9 (@ (@ tptp.mem tptp.c_2Einteger_2Eint__divides) (@ _let_8 (@ _let_8 tptp.bool))) (@ (@ tptp.mem tptp.c_2Ebool_2EF) tptp.bool) (not (@ tptp.p tptp.c_2Ebool_2EF)) (@ (@ tptp.mem tptp.c_2Emin_2E_3D_3D_3E) _let_7) (forall ((Q $$unsorted)) (=> (@ (@ tptp.mem Q) tptp.bool) (forall ((R $$unsorted)) (=> (@ (@ tptp.mem R) 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((_let_2 (@ tptp.p V1B))) (=> (@ (@ tptp.mem V1B) tptp.bool) (= (or _let_1 _let_2) (or _let_2 _let_1)))))))) (forall ((V0A $$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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.03/1.25 )
% 1.03/1.25 % SZS output end Proof for ITP012^2
% 1.03/1.25 % cvc5---1.0.5 exiting
% 1.03/1.25 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------