TSTP Solution File: ITP012^2 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP012^2 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %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 : Tue May 7 07:46:46 EDT 2024
% Result : Theorem 6.82s 2.74s
% Output : Refutation 7.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 89
% Syntax : Number of formulae : 152 ( 58 unt; 28 typ; 0 def)
% Number of atoms : 559 ( 103 equ; 0 cnn)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 1423 ( 80 ~; 64 |; 49 &;1070 @)
% ( 0 <=>; 160 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 4 ( 2 usr)
% Number of type conns : 25 ( 25 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 26 usr; 14 con; 0-2 aty)
% Number of variables : 194 ( 0 ^ 190 !; 4 ?; 194 :)
% Comments :
%------------------------------------------------------------------------------
thf(del_type,type,
del: $tType ).
thf(bool_type,type,
bool: del ).
thf(arr_type,type,
arr: del > del > del ).
thf(mem_type,type,
mem: $i > del > $o ).
thf(ap_type,type,
ap: $i > $i > $i ).
thf(lam_type,type,
lam: del > ( $i > $i ) > $i ).
thf(p_type,type,
p: $i > $o ).
thf(inj__o_type,type,
inj__o: $o > $i ).
thf(c_2Ebool_2ET_type,type,
c_2Ebool_2ET: $i ).
thf(c_2Ebool_2E_3F_type,type,
c_2Ebool_2E_3F: del > $i ).
thf(ty_2Einteger_2Eint_type,type,
ty_2Einteger_2Eint: del ).
thf(tp__ty_2Einteger_2Eint_type,type,
tp__ty_2Einteger_2Eint: $tType ).
thf(inj__ty_2Einteger_2Eint_type,type,
inj__ty_2Einteger_2Eint: tp__ty_2Einteger_2Eint > $i ).
thf(surj__ty_2Einteger_2Eint_type,type,
surj__ty_2Einteger_2Eint: $i > tp__ty_2Einteger_2Eint ).
thf(c_2Einteger_2Eint__sub_type,type,
c_2Einteger_2Eint__sub: $i ).
thf(fo__c_2Einteger_2Eint__sub_type,type,
fo__c_2Einteger_2Eint__sub: tp__ty_2Einteger_2Eint > tp__ty_2Einteger_2Eint > tp__ty_2Einteger_2Eint ).
thf(c_2Einteger_2Eint__add_type,type,
c_2Einteger_2Eint__add: $i ).
thf(fo__c_2Einteger_2Eint__add_type,type,
fo__c_2Einteger_2Eint__add: tp__ty_2Einteger_2Eint > tp__ty_2Einteger_2Eint > tp__ty_2Einteger_2Eint ).
thf(c_2Einteger_2Eint__neg_type,type,
c_2Einteger_2Eint__neg: $i ).
thf(fo__c_2Einteger_2Eint__neg_type,type,
fo__c_2Einteger_2Eint__neg: tp__ty_2Einteger_2Eint > tp__ty_2Einteger_2Eint ).
thf(c_2Einteger_2Eint__divides_type,type,
c_2Einteger_2Eint__divides: $i ).
thf(c_2Ebool_2EF_type,type,
c_2Ebool_2EF: $i ).
thf(c_2Emin_2E_3D_3D_3E_type,type,
c_2Emin_2E_3D_3D_3E: $i ).
thf(c_2Ebool_2E_5C_2F_type,type,
c_2Ebool_2E_5C_2F: $i ).
thf(c_2Ebool_2E_2F_5C_type,type,
c_2Ebool_2E_2F_5C: $i ).
thf(c_2Ebool_2E_7E_type,type,
c_2Ebool_2E_7E: $i ).
thf(c_2Emin_2E_3D_type,type,
c_2Emin_2E_3D: del > $i ).
thf(c_2Ebool_2E_21_type,type,
c_2Ebool_2E_21: del > $i ).
thf(30,axiom,
! [A: tp__ty_2Einteger_2Eint] :
( ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__neg @ A ) )
= ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stp_eq_fo_c_2Einteger_2Eint__neg) ).
thf(120,plain,
! [A: tp__ty_2Einteger_2Eint] :
( ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__neg @ A ) )
= ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(9,axiom,
! [A: del] : ( mem @ ( c_2Emin_2E_3D @ A ) @ ( arr @ A @ ( arr @ A @ bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Emin_2E_3D) ).
thf(78,plain,
! [A: del] : ( mem @ ( c_2Emin_2E_3D @ A ) @ ( arr @ A @ ( arr @ A @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(19,axiom,
! [A: tp__ty_2Einteger_2Eint,B: tp__ty_2Einteger_2Eint] :
( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ A ) ) @ ( inj__ty_2Einteger_2Eint @ B ) ) )
= ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ A ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_thm_2Einteger_2Eint__sub) ).
thf(97,plain,
! [A: tp__ty_2Einteger_2Eint,B: tp__ty_2Einteger_2Eint] :
( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ A ) ) @ ( inj__ty_2Einteger_2Eint @ B ) ) )
= ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ A ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(37,axiom,
! [A: tp__ty_2Einteger_2Eint,B: tp__ty_2Einteger_2Eint,C: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ A ) ) @ ( inj__ty_2Einteger_2Eint @ B ) ) )
=> ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ A ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ C ) ) @ ( inj__ty_2Einteger_2Eint @ B ) ) ) )
= ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ A ) ) @ ( inj__ty_2Einteger_2Eint @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Einteger_2EINT__DIVIDES__RADD) ).
thf(141,plain,
! [A: tp__ty_2Einteger_2Eint,B: tp__ty_2Einteger_2Eint,C: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ A ) ) @ ( inj__ty_2Einteger_2Eint @ B ) ) )
=> ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ A ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ C ) ) @ ( inj__ty_2Einteger_2Eint @ B ) ) ) )
= ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ A ) ) @ ( inj__ty_2Einteger_2Eint @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(33,axiom,
! [A: $i] :
( ( mem @ A @ ty_2Einteger_2Eint )
=> ( A
= ( inj__ty_2Einteger_2Eint @ ( surj__ty_2Einteger_2Eint @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stp_iso_mem_ty_2Einteger_2Eint) ).
thf(129,plain,
! [A: $i] :
( ( mem @ A @ ty_2Einteger_2Eint )
=> ( A
= ( inj__ty_2Einteger_2Eint @ ( surj__ty_2Einteger_2Eint @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(21,axiom,
! [A: tp__ty_2Einteger_2Eint] : ( mem @ ( inj__ty_2Einteger_2Eint @ A ) @ ty_2Einteger_2Eint ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stp_inj_mem_ty_2Einteger_2Eint) ).
thf(103,plain,
! [A: tp__ty_2Einteger_2Eint] : ( mem @ ( inj__ty_2Einteger_2Eint @ A ) @ ty_2Einteger_2Eint ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(1,conjecture,
! [A: tp__ty_2Einteger_2Eint,B: tp__ty_2Einteger_2Eint,C: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ A ) ) @ ( inj__ty_2Einteger_2Eint @ B ) ) )
=> ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ A ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ C ) ) @ ( inj__ty_2Einteger_2Eint @ B ) ) ) )
= ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ A ) ) @ ( inj__ty_2Einteger_2Eint @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Einteger_2EINT__DIVIDES__RSUB) ).
thf(2,negated_conjecture,
~ ! [A: tp__ty_2Einteger_2Eint,B: tp__ty_2Einteger_2Eint,C: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ A ) ) @ ( inj__ty_2Einteger_2Eint @ B ) ) )
=> ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ A ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ C ) ) @ ( inj__ty_2Einteger_2Eint @ B ) ) ) )
= ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ A ) ) @ ( inj__ty_2Einteger_2Eint @ C ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(63,plain,
~ ! [A: tp__ty_2Einteger_2Eint,B: tp__ty_2Einteger_2Eint,C: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ A ) ) @ ( inj__ty_2Einteger_2Eint @ B ) ) )
=> ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ A ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ C ) ) @ ( inj__ty_2Einteger_2Eint @ B ) ) ) )
= ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ A ) ) @ ( inj__ty_2Einteger_2Eint @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(27,axiom,
~ ( p @ c_2Ebool_2EF ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_false_p) ).
thf(114,plain,
~ ( p @ c_2Ebool_2EF ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(4,axiom,
! [A: del] : ( mem @ ( c_2Ebool_2E_3F @ A ) @ ( arr @ ( arr @ A @ bool ) @ bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2E_3F) ).
thf(69,plain,
! [A: del] : ( mem @ ( c_2Ebool_2E_3F @ A ) @ ( arr @ ( arr @ A @ bool ) @ bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(36,axiom,
! [A: tp__ty_2Einteger_2Eint] :
( ( surj__ty_2Einteger_2Eint @ ( inj__ty_2Einteger_2Eint @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stp_inj_surj_ty_2Einteger_2Eint) ).
thf(138,plain,
! [A: tp__ty_2Einteger_2Eint] :
( ( surj__ty_2Einteger_2Eint @ ( inj__ty_2Einteger_2Eint @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(16,axiom,
mem @ c_2Einteger_2Eint__neg @ ( arr @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Einteger_2Eint__neg) ).
thf(88,plain,
mem @ c_2Einteger_2Eint__neg @ ( arr @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(51,axiom,
! [A: del,B: $i > $i,C: $i] :
( ( mem @ C @ A )
=> ( ( ap @ ( lam @ A @ B ) @ C )
= ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',beta) ).
thf(184,plain,
! [A: del,B: $i > $i,C: $i] :
( ( mem @ C @ A )
=> ( ( ap @ ( lam @ A @ B ) @ C )
= ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(25,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ! [C: $i] :
( ( mem @ C @ bool )
=> ( ( ( p @ A )
= ( ( p @ B )
= ( p @ C ) ) )
= ( ( ( p @ A )
| ( p @ B )
| ( p @ C ) )
& ( ( p @ A )
| ~ ( p @ C )
| ~ ( p @ B ) )
& ( ( p @ B )
| ~ ( p @ C )
| ~ ( p @ A ) )
& ( ( p @ C )
| ~ ( p @ B )
| ~ ( p @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Esat_2Edc__eq) ).
thf(110,plain,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ! [C: $i] :
( ( mem @ C @ bool )
=> ( ( ( p @ A )
= ( ( p @ B )
= ( p @ C ) ) )
= ( ( ( p @ A )
| ( p @ B )
| ( p @ C ) )
& ( ( p @ A )
| ~ ( p @ C )
| ~ ( p @ B ) )
& ( ( p @ B )
| ~ ( p @ C )
| ~ ( p @ A ) )
& ( ( p @ C )
| ~ ( p @ B )
| ~ ( p @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(42,axiom,
! [A: del,B: $i] :
( ( mem @ B @ ( arr @ A @ bool ) )
=> ! [C: $i] :
( ( mem @ C @ ( arr @ A @ bool ) )
=> ( ( ! [D: $i] :
( ( mem @ D @ A )
=> ( ( p @ ( ap @ B @ D ) )
& ( p @ ( ap @ C @ D ) ) ) ) )
= ( ! [D: $i] :
( ( mem @ D @ A )
=> ( p @ ( ap @ B @ D ) ) )
& ! [D: $i] :
( ( mem @ D @ A )
=> ( p @ ( ap @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ebool_2EFORALL__AND__THM) ).
thf(157,plain,
! [A: del,B: $i] :
( ( mem @ B @ ( arr @ A @ bool ) )
=> ! [C: $i] :
( ( mem @ C @ ( arr @ A @ bool ) )
=> ( ( ! [D: $i] :
( ( mem @ D @ A )
=> ( ( p @ ( ap @ B @ D ) )
& ( p @ ( ap @ C @ D ) ) ) ) )
= ( ! [D: $i] :
( ( mem @ D @ A )
=> ( p @ ( ap @ B @ D ) ) )
& ! [D: $i] :
( ( mem @ D @ A )
=> ( p @ ( ap @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(48,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ( ~ ( p @ A )
=> ( ( p @ A )
=> $false ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ebool_2EF__IMP) ).
thf(179,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(61,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( ~ ( ( p @ A )
| ( p @ B ) )
=> $false )
= ( ( ( p @ A )
=> $false )
=> ( ~ ( p @ B )
=> $false ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Esat_2EOR__DUAL2) ).
thf(211,plain,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( ( p @ A )
| ( p @ B ) )
= ( ~ ( p @ A )
=> ( p @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(23,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ( A
= ( inj__o @ ( p @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stp_iso_mem_o) ).
thf(106,plain,
! [A: $i] :
( ( mem @ A @ bool )
=> ( A
= ( inj__o @ ( p @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(12,axiom,
mem @ c_2Ebool_2E_5C_2F @ ( arr @ bool @ ( arr @ bool @ bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2E_5C_2F) ).
thf(84,plain,
mem @ c_2Ebool_2E_5C_2F @ ( arr @ bool @ ( arr @ bool @ bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(34,axiom,
! [A: del,B: $i] :
( ( mem @ B @ ( arr @ A @ bool ) )
=> ( ( ~ ! [C: $i] :
( ( mem @ C @ A )
=> ( p @ ( ap @ B @ C ) ) ) )
= ( ? [C: $i] :
( ( mem @ C @ A )
& ~ ( p @ ( ap @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ebool_2ENOT__FORALL__THM) ).
thf(132,plain,
! [A: del,B: $i] :
( ( mem @ B @ ( arr @ A @ bool ) )
=> ( ( ~ ! [C: $i] :
( ( mem @ C @ A )
=> ( p @ ( ap @ B @ C ) ) ) )
= ( ? [C: $i] :
( ( mem @ C @ A )
& ~ ( p @ ( ap @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(17,axiom,
! [A: $o] :
( ( p @ ( inj__o @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stp_inj_surj_o) ).
thf(89,plain,
! [A: $o] :
( ( p @ ( inj__o @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(28,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ( ( ( $true
= ( p @ A ) )
= ( p @ A ) )
& ( ( ( p @ A )
= $true )
= ( p @ A ) )
& ( ( $false
= ( p @ A ) )
= ( ~ ( p @ A ) ) )
& ( ( ( p @ A )
= $false )
= ( ~ ( p @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ebool_2EEQ__CLAUSES) ).
thf(116,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(29,axiom,
! [A: tp__ty_2Einteger_2Eint,B: tp__ty_2Einteger_2Eint] :
( ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__add @ A @ B ) )
= ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ A ) ) @ ( inj__ty_2Einteger_2Eint @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stp_eq_fo_c_2Einteger_2Eint__add) ).
thf(117,plain,
! [A: tp__ty_2Einteger_2Eint,B: tp__ty_2Einteger_2Eint] :
( ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__add @ A @ B ) )
= ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ A ) ) @ ( inj__ty_2Einteger_2Eint @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(13,axiom,
mem @ c_2Ebool_2ET @ bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2ET) ).
thf(85,plain,
mem @ c_2Ebool_2ET @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(43,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ! [C: $i] :
( ( mem @ C @ bool )
=> ( ( ( p @ A )
= ( ( p @ B )
| ( p @ C ) ) )
= ( ( ( p @ A )
| ~ ( p @ B ) )
& ( ( p @ A )
| ~ ( p @ C ) )
& ( ( p @ B )
| ( p @ C )
| ~ ( p @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Esat_2Edc__disj) ).
thf(160,plain,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ! [C: $i] :
( ( mem @ C @ bool )
=> ( ( ( p @ A )
= ( ( p @ B )
| ( p @ C ) ) )
= ( ( ( p @ A )
| ~ ( p @ B ) )
& ( ( p @ A )
| ~ ( p @ C ) )
& ( ( p @ B )
| ( p @ C )
| ~ ( p @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(53,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ( ( ~ ( p @ A )
=> $false )
=> ( ( ( p @ A )
=> $false )
=> $false ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Esat_2EAND__INV2) ).
thf(192,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(24,axiom,
mem @ c_2Einteger_2Eint__divides @ ( arr @ ty_2Einteger_2Eint @ ( arr @ ty_2Einteger_2Eint @ bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Einteger_2Eint__divides) ).
thf(109,plain,
mem @ c_2Einteger_2Eint__divides @ ( arr @ ty_2Einteger_2Eint @ ( arr @ ty_2Einteger_2Eint @ bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(8,axiom,
mem @ c_2Einteger_2Eint__add @ ( arr @ ty_2Einteger_2Eint @ ( arr @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Einteger_2Eint__add) ).
thf(77,plain,
mem @ c_2Einteger_2Eint__add @ ( arr @ ty_2Einteger_2Eint @ ( arr @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(54,axiom,
! [A: tp__ty_2Einteger_2Eint,B: tp__ty_2Einteger_2Eint] :
( ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ A ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ B ) ) ) )
= ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ A ) ) @ ( inj__ty_2Einteger_2Eint @ B ) ) ) )
& ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ A ) ) ) @ ( inj__ty_2Einteger_2Eint @ B ) ) )
= ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ A ) ) @ ( inj__ty_2Einteger_2Eint @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Einteger_2EINT__DIVIDES__NEG) ).
thf(193,plain,
! [A: tp__ty_2Einteger_2Eint,B: tp__ty_2Einteger_2Eint] :
( ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ A ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ B ) ) ) )
= ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ A ) ) @ ( inj__ty_2Einteger_2Eint @ B ) ) ) )
& ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ A ) ) ) @ ( inj__ty_2Einteger_2Eint @ B ) ) )
= ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ A ) ) @ ( inj__ty_2Einteger_2Eint @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(22,axiom,
mem @ c_2Einteger_2Eint__sub @ ( arr @ ty_2Einteger_2Eint @ ( arr @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Einteger_2Eint__sub) ).
thf(105,plain,
mem @ c_2Einteger_2Eint__sub @ ( arr @ ty_2Einteger_2Eint @ ( arr @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(58,axiom,
! [A: del,B: del,C: $i] :
( ( mem @ C @ ( arr @ A @ B ) )
=> ! [D: $i] :
( ( mem @ D @ A )
=> ( mem @ ( ap @ C @ D ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_tp) ).
thf(205,plain,
! [A: del,B: del,C: $i] :
( ( mem @ C @ ( arr @ A @ B ) )
=> ! [D: $i] :
( ( mem @ D @ A )
=> ( mem @ ( ap @ C @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(45,axiom,
( ! [A: $i] :
( ( mem @ A @ bool )
=> ( ( ~ ~ ( p @ A ) )
= ( p @ A ) ) )
& ( ~ $true = $false )
& ( ~ $false = $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ebool_2ENOT__CLAUSES) ).
thf(166,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(39,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ! [C: $i] :
( ( mem @ C @ bool )
=> ( ( ( p @ A )
| ( p @ B )
| ( p @ C ) )
= ( ( p @ A )
| ( p @ B )
| ( p @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ebool_2EDISJ__ASSOC) ).
thf(148,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(49,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ( ( ( $true
=> ( p @ A ) )
= ( p @ A ) )
& ( ( ( p @ A )
=> $true )
= $true )
& ( ( $false
=> ( p @ A ) )
= $true )
& ( ( ( p @ A )
=> ( p @ A ) )
= $true )
& ( ( ( p @ A )
=> $false )
= ( ~ ( p @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ebool_2EIMP__CLAUSES) ).
thf(180,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(40,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( ( ~ ( ( p @ A )
& ( p @ B ) ) )
= ( ~ ( p @ A )
| ~ ( p @ B ) ) )
& ( ( ~ ( ( p @ A )
| ( p @ B ) ) )
= ( ~ ( p @ A )
& ~ ( p @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ebool_2EDE__MORGAN__THM) ).
thf(149,plain,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( ( ~ ( ( p @ A )
& ( p @ B ) ) )
= ( ~ ( p @ A )
| ~ ( p @ B ) ) )
& ( ( ~ ( ( p @ A )
| ( p @ B ) ) )
= ( ~ ( p @ A )
& ~ ( p @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(47,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ A ) @ B ) )
= ( ( p @ A )
=> ( p @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_imp_p) ).
thf(176,plain,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ A ) @ B ) )
= ( ( p @ A )
=> ( p @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(57,axiom,
p @ c_2Ebool_2ET,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_true_p) ).
thf(204,plain,
p @ c_2Ebool_2ET,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(5,axiom,
mem @ c_2Ebool_2EF @ bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2EF) ).
thf(71,plain,
mem @ c_2Ebool_2EF @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(50,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ( ( p @ ( ap @ c_2Ebool_2E_7E @ A ) )
= ( ~ ( p @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_neg_p) ).
thf(181,plain,
! [A: $i] :
( ( mem @ A @ bool )
=> ( ( p @ ( ap @ c_2Ebool_2E_7E @ A ) )
= ( ~ ( p @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(14,axiom,
mem @ c_2Ebool_2E_7E @ ( arr @ bool @ bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2E_7E) ).
thf(86,plain,
mem @ c_2Ebool_2E_7E @ ( arr @ bool @ bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(52,axiom,
! [A: del,B: del,C: $i] :
( ( mem @ C @ ( arr @ A @ B ) )
=> ! [D: $i] :
( ( mem @ D @ ( arr @ A @ B ) )
=> ( ! [E: $i] :
( ( mem @ E @ A )
=> ( ( ap @ C @ E )
= ( ap @ D @ E ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcext) ).
thf(187,plain,
! [A: del,B: del,C: $i] :
( ( mem @ C @ ( arr @ A @ B ) )
=> ! [D: $i] :
( ( mem @ D @ ( arr @ A @ B ) )
=> ( ! [E: $i] :
( ( mem @ E @ A )
=> ( ( ap @ C @ E )
= ( ap @ D @ E ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(26,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ( ( p @ A )
=> ( ~ ( p @ A )
=> $false ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Esat_2EAND__INV__IMP) ).
thf(113,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(35,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( ( p @ A )
= ( ~ ( p @ B ) ) )
= ( ( ( p @ A )
| ( p @ B ) )
& ( ~ ( p @ B )
| ~ ( p @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Esat_2Edc__neg) ).
thf(135,plain,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( ( p @ A )
= ( ~ ( p @ B ) ) )
= ( ( ( p @ A )
| ( p @ B ) )
& ( ~ ( p @ B )
| ~ ( p @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(10,axiom,
! [A: del,B: del,C: $i > $i] :
( ! [D: $i] :
( ( mem @ D @ A )
=> ( mem @ ( C @ D ) @ B ) )
=> ( mem @ ( lam @ A @ C ) @ ( arr @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lam_tp) ).
thf(80,plain,
! [A: del,B: del,C: $i > $i] :
( ! [D: $i] :
( ( mem @ D @ A )
=> ( mem @ ( C @ D ) @ B ) )
=> ( mem @ ( lam @ A @ C ) @ ( arr @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(46,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( ( p @ A )
=> ( p @ B ) )
=> ( ( ( p @ B )
=> ( p @ A ) )
=> ( ( p @ A )
= ( p @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ebool_2EIMP__ANTISYM__AX) ).
thf(167,plain,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( ( p @ A )
=> ( p @ B ) )
=> ( ( ( p @ B )
=> ( p @ A ) )
=> ( ( p @ A )
= ( p @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(31,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ A ) @ B ) )
= ( ( p @ A )
| ( p @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_or_p) ).
thf(123,plain,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ A ) @ B ) )
= ( ( p @ A )
| ( p @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(38,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ A ) @ B ) )
= ( ( p @ A )
& ( p @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_and_p) ).
thf(145,plain,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ A ) @ B ) )
= ( ( p @ A )
& ( p @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(41,axiom,
! [A: del,B: $i] :
( ( mem @ B @ ( arr @ A @ bool ) )
=> ( ( p @ ( ap @ ( c_2Ebool_2E_3F @ A ) @ B ) )
= ( ? [C: $i] :
( ( mem @ C @ A )
& ( p @ ( ap @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_ex_p) ).
thf(154,plain,
! [A: del,B: $i] :
( ( mem @ B @ ( arr @ A @ bool ) )
=> ( ( p @ ( ap @ ( c_2Ebool_2E_3F @ A ) @ B ) )
= ( ? [C: $i] :
( ( mem @ C @ A )
& ( p @ ( ap @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(6,axiom,
! [A: $o] : ( mem @ ( inj__o @ A ) @ bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stp_inj_mem_o) ).
thf(72,plain,
! [A: $o] : ( mem @ ( inj__o @ A ) @ bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(15,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ebool_2ETRUTH) ).
thf(87,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(56,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ( ( ( p @ A )
=> $false )
=> ~ ( p @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ebool_2EIMP__F) ).
thf(203,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(7,axiom,
! [A: del] : ( mem @ ( c_2Ebool_2E_21 @ A ) @ ( arr @ ( arr @ A @ bool ) @ bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2E_21) ).
thf(75,plain,
! [A: del] : ( mem @ ( c_2Ebool_2E_21 @ A ) @ ( arr @ ( arr @ A @ bool ) @ bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(59,axiom,
! [A: del,B: $i] :
( ( mem @ B @ ( arr @ A @ bool ) )
=> ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ A ) @ B ) )
= ( ! [C: $i] :
( ( mem @ C @ A )
=> ( p @ ( ap @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_all_p) ).
thf(207,plain,
! [A: del,B: $i] :
( ( mem @ B @ ( arr @ A @ bool ) )
=> ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ A ) @ B ) )
= ( ! [C: $i] :
( ( mem @ C @ A )
=> ( p @ ( ap @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(62,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ! [C: $i] :
( ( mem @ C @ bool )
=> ( ( ( p @ A )
= ( ( p @ B )
& ( p @ C ) ) )
= ( ( ( p @ A )
| ~ ( p @ B )
| ~ ( p @ C ) )
& ( ( p @ B )
| ~ ( p @ A ) )
& ( ( p @ C )
| ~ ( p @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Esat_2Edc__conj) ).
thf(214,plain,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ! [C: $i] :
( ( mem @ C @ bool )
=> ( ( ( p @ A )
= ( ( p @ B )
& ( p @ C ) ) )
= ( ( ( p @ A )
| ~ ( p @ B )
| ~ ( p @ C ) )
& ( ( p @ B )
| ~ ( p @ A ) )
& ( ( p @ C )
| ~ ( p @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(60,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ( ( ~ ~ ( p @ A ) )
= ( p @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Esat_2ENOT__NOT) ).
thf(210,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(32,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( ~ ( ~ ( p @ A )
| ( p @ B ) )
=> $false )
= ( ( p @ A )
=> ( ~ ( p @ B )
=> $false ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Esat_2EOR__DUAL3) ).
thf(126,plain,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( ~ ( p @ A )
| ( p @ B ) )
= ( ( p @ A )
=> ( p @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(18,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ! [C: $i] :
( ( mem @ C @ bool )
=> ( ( ( p @ A )
= ( ( p @ B )
=> ( p @ C ) ) )
= ( ( ( p @ A )
| ( p @ B ) )
& ( ( p @ A )
| ~ ( p @ C ) )
& ( ~ ( p @ B )
| ( p @ C )
| ~ ( p @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Esat_2Edc__imp) ).
thf(94,plain,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ! [C: $i] :
( ( mem @ C @ bool )
=> ( ( ( p @ A )
= ( ( p @ B )
=> ( p @ C ) ) )
= ( ( ( p @ A )
| ( p @ B ) )
& ( ( p @ A )
| ~ ( p @ C ) )
& ( ~ ( p @ B )
| ( p @ C )
| ~ ( p @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(3,axiom,
mem @ c_2Ebool_2E_2F_5C @ ( arr @ bool @ ( arr @ bool @ bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2E_2F_5C) ).
thf(68,plain,
mem @ c_2Ebool_2E_2F_5C @ ( arr @ bool @ ( arr @ bool @ bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(44,axiom,
! [A: tp__ty_2Einteger_2Eint,B: tp__ty_2Einteger_2Eint] :
( ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__sub @ A @ B ) )
= ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ A ) ) @ ( inj__ty_2Einteger_2Eint @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stp_eq_fo_c_2Einteger_2Eint__sub) ).
thf(163,plain,
! [A: tp__ty_2Einteger_2Eint,B: tp__ty_2Einteger_2Eint] :
( ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__sub @ A @ B ) )
= ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ A ) ) @ ( inj__ty_2Einteger_2Eint @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(55,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( ( p @ A )
| ( p @ B ) )
= ( ( p @ B )
| ( p @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ebool_2EDISJ__SYM) ).
thf(200,plain,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( ( p @ A )
| ( p @ B ) )
= ( ( p @ B )
| ( p @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(11,axiom,
mem @ c_2Emin_2E_3D_3D_3E @ ( arr @ bool @ ( arr @ bool @ bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Emin_2E_3D_3D_3E) ).
thf(83,plain,
mem @ c_2Emin_2E_3D_3D_3E @ ( arr @ bool @ ( arr @ bool @ bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(20,axiom,
! [A: del,B: $i] :
( ( mem @ B @ A )
=> ! [C: $i] :
( ( mem @ C @ A )
=> ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ B ) @ C ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_eq_p) ).
thf(100,plain,
! [A: del,B: $i] :
( ( mem @ B @ A )
=> ! [C: $i] :
( ( mem @ C @ A )
=> ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ B ) @ C ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(417,plain,
$false,
inference(cvc4,[status(thm)],[120,78,97,141,129,103,63,114,69,138,88,184,110,157,179,211,106,84,132,89,116,117,85,160,192,109,77,193,105,205,166,148,180,149,176,204,71,181,86,187,113,135,80,167,123,145,154,72,87,203,75,207,214,210,126,94,68,163,200,83,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : ITP012^2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.13/0.16 % Command : run_Leo-III %s %d
% 0.17/0.37 % Computer : n015.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Mon May 6 14:45:09 EDT 2024
% 0.17/0.37 % CPUTime :
% 0.80/0.82 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.46/1.02 % [INFO] Parsing done (198ms).
% 1.46/1.03 % [INFO] Running in sequential loop mode.
% 1.85/1.25 % [INFO] eprover registered as external prover.
% 1.85/1.25 % [INFO] cvc4 registered as external prover.
% 1.85/1.26 % [INFO] Scanning for conjecture ...
% 2.02/1.33 % [INFO] Found a conjecture and 60 axioms. Running axiom selection ...
% 2.17/1.39 % [INFO] Axiom selection finished. Selected 60 axioms (removed 0 axioms).
% 2.45/1.47 % [INFO] Problem is higher-order (TPTP THF).
% 2.52/1.49 % [INFO] Type checking passed.
% 2.52/1.49 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 6.82/2.74 % External prover 'cvc4' found a proof!
% 6.82/2.74 % [INFO] Killing All external provers ...
% 6.82/2.74 % Time passed: 2241ms (effective reasoning time: 1704ms)
% 6.82/2.74 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 6.82/2.74 % Axioms used in derivation (60): stp_inj_mem_ty_2Einteger_2Eint, conj_thm_2Esat_2EOR__DUAL3, conj_thm_2Ebool_2ETRUTH, stp_eq_fo_c_2Einteger_2Eint__add, stp_inj_surj_ty_2Einteger_2Eint, lam_tp, mem_c_2Ebool_2ET, mem_c_2Ebool_2E_3F, conj_thm_2Einteger_2EINT__DIVIDES__RADD, ax_neg_p, mem_c_2Ebool_2E_2F_5C, stp_inj_surj_o, conj_thm_2Esat_2EAND__INV2, conj_thm_2Ebool_2EIMP__CLAUSES, mem_c_2Einteger_2Eint__divides, conj_thm_2Ebool_2EEQ__CLAUSES, ax_imp_p, ax_eq_p, conj_thm_2Ebool_2EDISJ__SYM, funcext, conj_thm_2Ebool_2ENOT__FORALL__THM, mem_c_2Ebool_2E_21, conj_thm_2Esat_2Edc__conj, conj_thm_2Esat_2ENOT__NOT, stp_eq_fo_c_2Einteger_2Eint__sub, conj_thm_2Ebool_2EDISJ__ASSOC, conj_thm_2Einteger_2EINT__DIVIDES__NEG, ax_true_p, mem_c_2Einteger_2Eint__sub, ax_and_p, conj_thm_2Ebool_2ENOT__CLAUSES, conj_thm_2Esat_2Edc__imp, stp_iso_mem_ty_2Einteger_2Eint, mem_c_2Emin_2E_3D, conj_thm_2Esat_2EAND__INV__IMP, stp_eq_fo_c_2Einteger_2Eint__neg, conj_thm_2Ebool_2EDE__MORGAN__THM, mem_c_2Ebool_2E_7E, mem_c_2Ebool_2EF, mem_c_2Einteger_2Eint__neg, conj_thm_2Esat_2Edc__eq, ax_or_p, ax_all_p, conj_thm_2Ebool_2EF__IMP, ax_thm_2Einteger_2Eint__sub, conj_thm_2Esat_2EOR__DUAL2, ax_ex_p, ap_tp, conj_thm_2Ebool_2EFORALL__AND__THM, mem_c_2Einteger_2Eint__add, conj_thm_2Esat_2Edc__neg, beta, mem_c_2Ebool_2E_5C_2F, ax_false_p, conj_thm_2Esat_2Edc__disj, stp_iso_mem_o, mem_c_2Emin_2E_3D_3D_3E, conj_thm_2Ebool_2EIMP__F, stp_inj_mem_o, conj_thm_2Ebool_2EIMP__ANTISYM__AX
% 6.82/2.74 % No. of inferences in proof: 124
% 6.82/2.74 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2241 ms resp. 1704 ms w/o parsing
% 7.99/2.82 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.99/2.82 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------