%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP012^2 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:06:20 AM UTC 2026
% Result : Theorem 13.21s 3.28s
% Output : Refutation 12.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 65
% Syntax : Number of formulae : 219 ( 104 unt; 0 typ; 4 def)
% Number of atoms : 812 ( 218 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 2493 ( 198 ~; 123 |; 51 &;1957 @)
% ( 0 <=>; 164 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 4 ( 2 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 30 usr; 17 con; 0-3 aty)
% Number of variables : 271 ( 3 ^; 260 !; 4 ?; 271 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(del_type,type,
del: $tType ).
thf(tp__ty_2Einteger_2Eint_type,type,
tp__ty_2Einteger_2Eint: $tType ).
thf(bool_decl,type,
bool: del ).
thf(arr_decl,type,
arr: del > del > del ).
thf(mem_decl,type,
mem: $i > del > $o ).
thf(ap_decl,type,
ap: $i > $i > $i ).
thf(lam_decl,type,
lam: del > ( $i > $i ) > $i ).
thf(p_decl,type,
p: $i > $o ).
thf(inj__o_decl,type,
inj__o: $o > $i ).
thf(c_2Ebool_2ET_decl,type,
c_2Ebool_2ET: $i ).
thf(c_2Ebool_2E_3F_decl,type,
c_2Ebool_2E_3F: del > $i ).
thf(ty_2Einteger_2Eint_decl,type,
ty_2Einteger_2Eint: del ).
thf(inj__ty_2Einteger_2Eint_decl,type,
inj__ty_2Einteger_2Eint: tp__ty_2Einteger_2Eint > $i ).
thf(surj__ty_2Einteger_2Eint_decl,type,
surj__ty_2Einteger_2Eint: $i > tp__ty_2Einteger_2Eint ).
thf(c_2Einteger_2Eint__sub_decl,type,
c_2Einteger_2Eint__sub: $i ).
thf(fo__c_2Einteger_2Eint__sub_decl,type,
fo__c_2Einteger_2Eint__sub: tp__ty_2Einteger_2Eint > tp__ty_2Einteger_2Eint > tp__ty_2Einteger_2Eint ).
thf(c_2Einteger_2Eint__add_decl,type,
c_2Einteger_2Eint__add: $i ).
thf(fo__c_2Einteger_2Eint__add_decl,type,
fo__c_2Einteger_2Eint__add: tp__ty_2Einteger_2Eint > tp__ty_2Einteger_2Eint > tp__ty_2Einteger_2Eint ).
thf(c_2Einteger_2Eint__neg_decl,type,
c_2Einteger_2Eint__neg: $i ).
thf(fo__c_2Einteger_2Eint__neg_decl,type,
fo__c_2Einteger_2Eint__neg: tp__ty_2Einteger_2Eint > tp__ty_2Einteger_2Eint ).
thf(c_2Einteger_2Eint__divides_decl,type,
c_2Einteger_2Eint__divides: $i ).
thf(c_2Ebool_2EF_decl,type,
c_2Ebool_2EF: $i ).
thf(c_2Emin_2E_3D_3D_3E_decl,type,
c_2Emin_2E_3D_3D_3E: $i ).
thf(c_2Ebool_2E_5C_2F_decl,type,
c_2Ebool_2E_5C_2F: $i ).
thf(c_2Ebool_2E_2F_5C_decl,type,
c_2Ebool_2E_2F_5C: $i ).
thf(c_2Ebool_2E_7E_decl,type,
c_2Ebool_2E_7E: $i ).
thf(c_2Emin_2E_3D_decl,type,
c_2Emin_2E_3D: del > $i ).
thf(c_2Ebool_2E_21_decl,type,
c_2Ebool_2E_21: del > $i ).
thf(sk1_decl,type,
sk1: tp__ty_2Einteger_2Eint ).
thf(sk2_decl,type,
sk2: tp__ty_2Einteger_2Eint ).
thf(sk3_decl,type,
sk3: tp__ty_2Einteger_2Eint ).
thf(sk4_decl,type,
sk4: ( $i > $i ) > del > del > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: tp__ty_2Einteger_2Eint] :
~ ! [B: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ A ) ) @ ( inj__ty_2Einteger_2Eint @ B ) ) )
=> ! [C: tp__ty_2Einteger_2Eint] :
( ( 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 ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: tp__ty_2Einteger_2Eint] :
~ ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) ) @ ( inj__ty_2Einteger_2Eint @ A ) ) )
=> ! [B: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ B ) ) @ ( inj__ty_2Einteger_2Eint @ A ) ) ) )
= ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) ) @ ( inj__ty_2Einteger_2Eint @ B ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ A ) ) @ ( inj__ty_2Einteger_2Eint @ sk2 ) ) ) )
!= ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) ) @ ( inj__ty_2Einteger_2Eint @ A ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i > $i,B: del,C: del] :
@+[D: $i] :
~ ( ( mem @ D @ C )
=> ( mem @ ( A @ D ) @ B ) ) ) ) ).
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(140,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(141,plain,
! [A: tp__ty_2Einteger_2Eint] :
( ( surj__ty_2Einteger_2Eint @ ( inj__ty_2Einteger_2Eint @ A ) )
= A ),
inference(cnf,[status(esa)],[140]) ).
thf(142,plain,
! [A: tp__ty_2Einteger_2Eint] :
( ( surj__ty_2Einteger_2Eint @ ( inj__ty_2Einteger_2Eint @ A ) )
= A ),
inference(lifteq,[status(thm)],[141]) ).
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(185,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(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(166,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(167,plain,
! [B: tp__ty_2Einteger_2Eint,A: 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(cnf,[status(esa)],[166]) ).
thf(168,plain,
! [B: tp__ty_2Einteger_2Eint,A: 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(lifteq,[status(thm)],[167]) ).
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(64,plain,
~ ! [A: tp__ty_2Einteger_2Eint,B: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ A ) ) @ ( inj__ty_2Einteger_2Eint @ B ) ) )
=> ! [C: tp__ty_2Einteger_2Eint] :
( ( 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(miniscope,[status(thm)],[63]) ).
thf(65,plain,
( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) ) @ ( inj__ty_2Einteger_2Eint @ sk2 ) ) )
& ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ sk3 ) ) @ ( inj__ty_2Einteger_2Eint @ sk2 ) ) ) )
!= ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) ) @ ( inj__ty_2Einteger_2Eint @ sk3 ) ) ) ) ),
inference(cnf,[status(esa)],[64]) ).
thf(67,plain,
( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ sk3 ) ) @ ( inj__ty_2Einteger_2Eint @ sk2 ) ) ) )
!= ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) ) @ ( inj__ty_2Einteger_2Eint @ sk3 ) ) ) ),
inference(cnfConj,[status(thm)],[65]) ).
thf(68,plain,
( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ sk3 ) ) @ ( inj__ty_2Einteger_2Eint @ sk2 ) ) ) )
!= ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) ) @ ( inj__ty_2Einteger_2Eint @ sk3 ) ) ) ),
inference(lifteq,[status(thm)],[67]) ).
thf(235,plain,
( ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ sk3 ) ) @ ( inj__ty_2Einteger_2Eint @ sk2 ) ) )
!= ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) ) @ ( inj__ty_2Einteger_2Eint @ sk3 ) ) ),
inference(simp,[status(thm)],[68]) ).
thf(251,plain,
( ( ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) )
!= ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) ) )
| ( ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ sk3 ) ) @ ( inj__ty_2Einteger_2Eint @ sk2 ) )
!= ( inj__ty_2Einteger_2Eint @ sk3 ) ) ),
inference(simp,[status(thm)],[235]) ).
thf(252,plain,
( ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ sk3 ) ) @ ( inj__ty_2Einteger_2Eint @ sk2 ) )
!= ( inj__ty_2Einteger_2Eint @ sk3 ) ),
inference(simp,[status(thm)],[251]) ).
thf(700,plain,
! [B: tp__ty_2Einteger_2Eint,A: tp__ty_2Einteger_2Eint] :
( ( ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__sub @ A @ B ) )
!= ( inj__ty_2Einteger_2Eint @ sk3 ) )
| ( ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ A ) ) @ ( inj__ty_2Einteger_2Eint @ B ) )
!= ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ sk3 ) ) @ ( inj__ty_2Einteger_2Eint @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[168,252]) ).
thf(701,plain,
( ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__sub @ sk3 @ sk2 ) )
!= ( inj__ty_2Einteger_2Eint @ sk3 ) ),
inference(pattern_uni,[status(thm)],[700:[bind(A,$thf( sk3 )),bind(B,$thf( sk2 ))]]) ).
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(69,plain,
mem @ c_2Ebool_2E_2F_5C @ ( arr @ bool @ ( arr @ bool @ bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(17,axiom,
! [A: $o] :
( ( p @ ( inj__o @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stp_inj_surj_o) ).
thf(91,plain,
! [A: $o] :
( ( p @ ( inj__o @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(92,plain,
( ( p @ ( inj__o @ $true ) )
= $true ),
inference(instance,[status(thm)],[91]) ).
thf(93,plain,
p @ ( inj__o @ $true ),
inference(simp,[status(thm)],[92]) ).
thf(27,axiom,
~ ( p @ c_2Ebool_2EF ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_false_p) ).
thf(116,plain,
~ ( p @ c_2Ebool_2EF ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(117,plain,
~ ( p @ c_2Ebool_2EF ),
inference(polarity_switch,[status(thm)],[116]) ).
thf(245,plain,
( ~ $true
| ( ( p @ ( inj__o @ $true ) )
!= ( p @ c_2Ebool_2EF ) ) ),
inference(paramod_ordered,[status(thm)],[93,117]) ).
thf(246,plain,
( ( p @ ( inj__o @ $true ) )
!= ( p @ c_2Ebool_2EF ) ),
inference(simp,[status(thm)],[245]) ).
thf(249,plain,
( ( inj__o @ $true )
!= c_2Ebool_2EF ),
inference(simp,[status(thm)],[246]) ).
thf(66,plain,
p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) ) @ ( inj__ty_2Einteger_2Eint @ sk2 ) ),
inference(cnfConj,[status(thm)],[65]) ).
thf(94,plain,
( ( p @ ( inj__o @ $false ) )
= $false ),
inference(instance,[status(thm)],[91]) ).
thf(95,plain,
~ ( p @ ( inj__o @ $false ) ),
inference(simp,[status(thm)],[94]) ).
thf(231,plain,
( ~ $true
| ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) ) @ ( inj__ty_2Einteger_2Eint @ sk2 ) ) )
!= ( p @ ( inj__o @ $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[66,95]) ).
thf(232,plain,
( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) ) @ ( inj__ty_2Einteger_2Eint @ sk2 ) ) )
!= ( p @ ( inj__o @ $false ) ) ),
inference(simp,[status(thm)],[231]) ).
thf(234,plain,
( ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) ) @ ( inj__ty_2Einteger_2Eint @ sk2 ) )
!= ( inj__o @ $false ) ),
inference(simp,[status(thm)],[232]) ).
thf(14,axiom,
mem @ c_2Ebool_2E_7E @ ( arr @ bool @ bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2E_7E) ).
thf(88,plain,
mem @ c_2Ebool_2E_7E @ ( arr @ bool @ bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
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(170,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(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(115,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
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(217,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(242,plain,
( ~ $true
| ( ( p @ ( inj__o @ $false ) )
!= ( p @ ( inj__o @ $true ) ) ) ),
inference(paramod_ordered,[status(thm)],[93,95]) ).
thf(243,plain,
( ( p @ ( inj__o @ $false ) )
!= ( p @ ( inj__o @ $true ) ) ),
inference(simp,[status(thm)],[242]) ).
thf(247,plain,
( ( inj__o @ $false )
!= ( inj__o @ $true ) ),
inference(simp,[status(thm)],[243]) ).
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(184,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
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(125,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(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(157,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(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(122,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(123,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(cnf,[status(esa)],[122]) ).
thf(124,plain,
! [A: tp__ty_2Einteger_2Eint] :
( ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ A ) )
= ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__neg @ A ) ) ),
inference(lifteq,[status(thm)],[123]) ).
thf(316,plain,
! [A: tp__ty_2Einteger_2Eint] :
( ( ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__neg @ A ) )
!= ( inj__ty_2Einteger_2Eint @ sk3 ) )
| ( ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ A ) )
!= ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ sk3 ) ) @ ( inj__ty_2Einteger_2Eint @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[124,252]) ).
thf(377,plain,
! [A: tp__ty_2Einteger_2Eint] :
( ( ( fo__c_2Einteger_2Eint__neg @ A )
!= sk3 )
| ( ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ sk3 ) )
!= c_2Einteger_2Eint__neg )
| ( ( inj__ty_2Einteger_2Eint @ A )
!= ( inj__ty_2Einteger_2Eint @ sk2 ) ) ),
inference(simp,[status(thm)],[316]) ).
thf(411,plain,
! [A: tp__ty_2Einteger_2Eint] :
( ( ( fo__c_2Einteger_2Eint__neg @ A )
!= sk3 )
| ( ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ sk3 ) )
!= c_2Einteger_2Eint__neg )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[377]) ).
thf(416,plain,
( ( ( fo__c_2Einteger_2Eint__neg @ sk2 )
!= sk3 )
| ( ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ sk3 ) )
!= c_2Einteger_2Eint__neg ) ),
inference(simp,[status(thm)],[411]) ).
thf(57,axiom,
p @ c_2Ebool_2ET,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_true_p) ).
thf(210,plain,
p @ c_2Ebool_2ET,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(226,plain,
( ~ $true
| ( ( p @ ( inj__o @ $false ) )
!= ( p @ c_2Ebool_2ET ) ) ),
inference(paramod_ordered,[status(thm)],[210,95]) ).
thf(227,plain,
( ( p @ ( inj__o @ $false ) )
!= ( p @ c_2Ebool_2ET ) ),
inference(simp,[status(thm)],[226]) ).
thf(228,plain,
( ( inj__o @ $false )
!= c_2Ebool_2ET ),
inference(simp,[status(thm)],[227]) ).
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(78,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(60,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ( ( ~ ~ ( p @ A ) )
= ( p @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Esat_2ENOT__NOT) ).
thf(216,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
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(211,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(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(105,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(106,plain,
! [A: tp__ty_2Einteger_2Eint] : ( mem @ ( inj__ty_2Einteger_2Eint @ A ) @ ty_2Einteger_2Eint ),
inference(cnf,[status(esa)],[105]) ).
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(147,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(15,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ebool_2ETRUTH) ).
thf(89,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(6,axiom,
! [A: $o] : ( mem @ ( inj__o @ A ) @ bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stp_inj_mem_o) ).
thf(73,plain,
! [A: $o] : ( mem @ ( inj__o @ A ) @ bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(74,plain,
mem @ ( inj__o @ $true ) @ bool,
inference(instance,[status(thm)],[73]) ).
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(206,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(229,plain,
( ~ $true
| ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) ) @ ( inj__ty_2Einteger_2Eint @ sk2 ) ) )
!= ( p @ c_2Ebool_2EF ) ) ),
inference(paramod_ordered,[status(thm)],[66,117]) ).
thf(230,plain,
( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) ) @ ( inj__ty_2Einteger_2Eint @ sk2 ) ) )
!= ( p @ c_2Ebool_2EF ) ),
inference(simp,[status(thm)],[229]) ).
thf(233,plain,
( ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) ) @ ( inj__ty_2Einteger_2Eint @ sk2 ) )
!= c_2Ebool_2EF ),
inference(simp,[status(thm)],[230]) ).
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(85,plain,
mem @ c_2Emin_2E_3D_3D_3E @ ( arr @ bool @ ( arr @ bool @ bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
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(220,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(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(102,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(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(160,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(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(70,plain,
! [A: del] : ( mem @ ( c_2Ebool_2E_3F @ A ) @ ( arr @ ( arr @ A @ bool ) @ bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
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(137,plain,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( ( p @ A )
= ( ~ ( p @ B ) ) )
= ( ( ( p @ A )
| ( p @ B ) )
& ( ~ ( p @ B )
| ~ ( p @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(728,plain,
! [B: tp__ty_2Einteger_2Eint,A: tp__ty_2Einteger_2Eint] :
( ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) ) @ ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__sub @ A @ B ) ) ) )
!= ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) ) @ ( inj__ty_2Einteger_2Eint @ sk3 ) ) ) )
| ( ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ A ) ) @ ( inj__ty_2Einteger_2Eint @ B ) )
!= ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ sk3 ) ) @ ( inj__ty_2Einteger_2Eint @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[168,68]) ).
thf(729,plain,
( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) ) @ ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__sub @ sk3 @ sk2 ) ) ) )
!= ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) ) @ ( inj__ty_2Einteger_2Eint @ sk3 ) ) ) ),
inference(pattern_uni,[status(thm)],[728:[bind(A,$thf( sk3 )),bind(B,$thf( sk2 ))]]) ).
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(197,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
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(188,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(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(169,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
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(76,plain,
! [A: del] : ( mem @ ( c_2Ebool_2E_21 @ A ) @ ( arr @ ( arr @ A @ bool ) @ bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(77,plain,
! [A: del] : ( mem @ ( c_2Ebool_2E_21 @ A ) @ ( arr @ ( arr @ A @ bool ) @ bool ) ),
inference(cnf,[status(esa)],[76]) ).
thf(321,plain,
! [A: tp__ty_2Einteger_2Eint] :
( ( p @ ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__neg @ A ) ) )
| ( ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ A ) )
!= ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) ) @ ( inj__ty_2Einteger_2Eint @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[124,66]) ).
thf(378,plain,
! [A: tp__ty_2Einteger_2Eint] :
( ( p @ ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__neg @ A ) ) )
| ( ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) )
!= c_2Einteger_2Eint__neg )
| ( ( inj__ty_2Einteger_2Eint @ A )
!= ( inj__ty_2Einteger_2Eint @ sk2 ) ) ),
inference(simp,[status(thm)],[321]) ).
thf(1015,plain,
! [A: tp__ty_2Einteger_2Eint] :
( ( ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) )
!= c_2Einteger_2Eint__neg )
| ( ( inj__ty_2Einteger_2Eint @ A )
!= ( inj__ty_2Einteger_2Eint @ sk2 ) )
| ~ $true
| ( ( p @ ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__neg @ A ) ) )
!= ( p @ c_2Ebool_2EF ) ) ),
inference(paramod_ordered,[status(thm)],[378,117]) ).
thf(1016,plain,
! [A: tp__ty_2Einteger_2Eint] :
( ( ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) )
!= c_2Einteger_2Eint__neg )
| ( ( inj__ty_2Einteger_2Eint @ A )
!= ( inj__ty_2Einteger_2Eint @ sk2 ) )
| ( ( p @ ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__neg @ A ) ) )
!= ( p @ c_2Ebool_2EF ) ) ),
inference(simp,[status(thm)],[1015]) ).
thf(1035,plain,
! [A: tp__ty_2Einteger_2Eint] :
( ( ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) )
!= c_2Einteger_2Eint__neg )
| ( A != sk2 )
| ( ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__neg @ A ) )
!= c_2Ebool_2EF ) ),
inference(simp,[status(thm)],[1016]) ).
thf(1075,plain,
( ( ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) )
!= c_2Einteger_2Eint__neg )
| ( ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__neg @ sk2 ) )
!= c_2Ebool_2EF ) ),
inference(simp,[status(thm)],[1035]) ).
thf(970,plain,
( ( fo__c_2Einteger_2Eint__sub @ sk3 @ sk2 )
!= sk3 ),
inference(simp,[status(thm)],[701]) ).
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(96,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(223,plain,
( ~ $true
| ( ( p @ c_2Ebool_2EF )
!= ( p @ c_2Ebool_2ET ) ) ),
inference(paramod_ordered,[status(thm)],[210,117]) ).
thf(224,plain,
( ( p @ c_2Ebool_2EF )
!= ( p @ c_2Ebool_2ET ) ),
inference(simp,[status(thm)],[223]) ).
thf(225,plain,
c_2Ebool_2EF != c_2Ebool_2ET,
inference(simp,[status(thm)],[224]) ).
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(134,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(1000,plain,
! [A: tp__ty_2Einteger_2Eint] :
( ( ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) )
!= c_2Einteger_2Eint__neg )
| ( ( inj__ty_2Einteger_2Eint @ A )
!= ( inj__ty_2Einteger_2Eint @ sk2 ) )
| ~ $true
| ( ( p @ ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__neg @ A ) ) )
!= ( p @ ( inj__o @ $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[378,95]) ).
thf(1001,plain,
! [A: tp__ty_2Einteger_2Eint] :
( ( ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) )
!= c_2Einteger_2Eint__neg )
| ( ( inj__ty_2Einteger_2Eint @ A )
!= ( inj__ty_2Einteger_2Eint @ sk2 ) )
| ( ( p @ ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__neg @ A ) ) )
!= ( p @ ( inj__o @ $false ) ) ) ),
inference(simp,[status(thm)],[1000]) ).
thf(1028,plain,
! [A: tp__ty_2Einteger_2Eint] :
( ( ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) )
!= c_2Einteger_2Eint__neg )
| ( A != sk2 )
| ( ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__neg @ A ) )
!= ( inj__o @ $false ) ) ),
inference(simp,[status(thm)],[1001]) ).
thf(1071,plain,
( ( ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) )
!= c_2Einteger_2Eint__neg )
| ( ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__neg @ sk2 ) )
!= ( inj__o @ $false ) ) ),
inference(simp,[status(thm)],[1028]) ).
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(128,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(237,plain,
( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ sk3 ) ) @ ( inj__ty_2Einteger_2Eint @ sk2 ) ) ) )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) ) @ ( inj__ty_2Einteger_2Eint @ sk3 ) ) ) ),
inference(bool_ext,[status(thm)],[68]) ).
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(180,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(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(191,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(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(118,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(71,plain,
! [A: del] : ( mem @ ( c_2Ebool_2E_3F @ A ) @ ( arr @ ( arr @ A @ bool ) @ bool ) ),
inference(cnf,[status(esa)],[70]) ).
thf(236,plain,
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ sk3 ) ) @ ( inj__ty_2Einteger_2Eint @ sk2 ) ) ) )
| ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) ) @ ( inj__ty_2Einteger_2Eint @ sk3 ) ) ) ),
inference(bool_ext,[status(thm)],[68]) ).
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(86,plain,
mem @ c_2Ebool_2E_5C_2F @ ( arr @ bool @ ( arr @ bool @ bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
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(81,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(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(213,plain,
! [A: del,B: $i] :
( ( mem @ B @ ( arr @ A @ bool ) )
=> ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ A ) @ B ) )
= ( ! [C: $i] :
( ( mem @ C @ A )
=> ( p @ ( ap @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(738,plain,
! [C: tp__ty_2Einteger_2Eint,B: tp__ty_2Einteger_2Eint,A: tp__ty_2Einteger_2Eint] :
( ( mem @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ A ) ) @ ( inj__ty_2Einteger_2Eint @ B ) ) @ ty_2Einteger_2Eint )
| ( ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__sub @ A @ B ) )
!= ( inj__ty_2Einteger_2Eint @ C ) ) ),
inference(paramod_ordered,[status(thm)],[168,106]) ).
thf(739,plain,
! [B: tp__ty_2Einteger_2Eint,A: tp__ty_2Einteger_2Eint] : ( mem @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ A ) ) @ ( inj__ty_2Einteger_2Eint @ B ) ) @ ty_2Einteger_2Eint ),
inference(pattern_uni,[status(thm)],[738:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( fo__c_2Einteger_2Eint__sub @ D @ E ))]]) ).
thf(964,plain,
! [B: tp__ty_2Einteger_2Eint,A: tp__ty_2Einteger_2Eint] : ( mem @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ A ) ) @ ( inj__ty_2Einteger_2Eint @ B ) ) @ ty_2Einteger_2Eint ),
inference(simp,[status(thm)],[739]) ).
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(198,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(23,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ( A
= ( inj__o @ ( p @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stp_iso_mem_o) ).
thf(108,plain,
! [A: $i] :
( ( mem @ A @ bool )
=> ( A
= ( inj__o @ ( p @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(239,plain,
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) ) @ ( inj__ty_2Einteger_2Eint @ sk3 ) ) )
| ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ sk3 ) ) @ ( inj__ty_2Einteger_2Eint @ sk2 ) ) ) )
!= ( p @ c_2Ebool_2ET ) ) ),
inference(paramod_ordered,[status(thm)],[210,68]) ).
thf(241,plain,
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) ) @ ( inj__ty_2Einteger_2Eint @ sk3 ) ) )
| ( ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ sk3 ) ) @ ( inj__ty_2Einteger_2Eint @ sk2 ) ) )
!= c_2Ebool_2ET ) ),
inference(simp,[status(thm)],[239]) ).
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(79,plain,
! [A: del] : ( mem @ ( c_2Emin_2E_3D @ A ) @ ( arr @ A @ ( arr @ A @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(80,plain,
! [A: del] : ( mem @ ( c_2Emin_2E_3D @ A ) @ ( arr @ A @ ( arr @ A @ bool ) ) ),
inference(cnf,[status(esa)],[79]) ).
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(119,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(120,plain,
! [B: tp__ty_2Einteger_2Eint,A: 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(cnf,[status(esa)],[119]) ).
thf(121,plain,
! [B: tp__ty_2Einteger_2Eint,A: 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(lifteq,[status(thm)],[120]) ).
thf(469,plain,
! [C: tp__ty_2Einteger_2Eint,B: tp__ty_2Einteger_2Eint,A: tp__ty_2Einteger_2Eint] :
( ( mem @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ A ) ) @ ( inj__ty_2Einteger_2Eint @ B ) ) @ ty_2Einteger_2Eint )
| ( ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__add @ A @ B ) )
!= ( inj__ty_2Einteger_2Eint @ C ) ) ),
inference(paramod_ordered,[status(thm)],[121,106]) ).
thf(470,plain,
! [B: tp__ty_2Einteger_2Eint,A: tp__ty_2Einteger_2Eint] : ( mem @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ A ) ) @ ( inj__ty_2Einteger_2Eint @ B ) ) @ ty_2Einteger_2Eint ),
inference(pattern_uni,[status(thm)],[469:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( fo__c_2Einteger_2Eint__add @ D @ E ))]]) ).
thf(675,plain,
! [B: tp__ty_2Einteger_2Eint,A: tp__ty_2Einteger_2Eint] : ( mem @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ A ) ) @ ( inj__ty_2Einteger_2Eint @ B ) ) @ ty_2Einteger_2Eint ),
inference(simp,[status(thm)],[470]) ).
thf(336,plain,
! [A: tp__ty_2Einteger_2Eint] :
( ( ( ap @ ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__neg @ A ) ) @ ( inj__ty_2Einteger_2Eint @ sk2 ) )
!= c_2Ebool_2EF )
| ( ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ A ) )
!= ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[124,233]) ).
thf(363,plain,
! [A: tp__ty_2Einteger_2Eint] :
( ( ( ap @ ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__neg @ A ) ) @ ( inj__ty_2Einteger_2Eint @ sk2 ) )
!= c_2Ebool_2EF )
| ( c_2Einteger_2Eint__divides != c_2Einteger_2Eint__neg )
| ( ( inj__ty_2Einteger_2Eint @ A )
!= ( inj__ty_2Einteger_2Eint @ sk1 ) ) ),
inference(simp,[status(thm)],[336]) ).
thf(421,plain,
! [A: tp__ty_2Einteger_2Eint] :
( ( ( ap @ ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__neg @ A ) ) @ ( inj__ty_2Einteger_2Eint @ sk2 ) )
!= c_2Ebool_2EF )
| ( c_2Einteger_2Eint__divides != c_2Einteger_2Eint__neg )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[363]) ).
thf(426,plain,
( ( ( ap @ ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__neg @ sk1 ) ) @ ( inj__ty_2Einteger_2Eint @ sk2 ) )
!= c_2Ebool_2EF )
| ( c_2Einteger_2Eint__divides != c_2Einteger_2Eint__neg ) ),
inference(simp,[status(thm)],[421]) ).
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(209,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
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(112,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(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(150,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(431,plain,
! [C: tp__ty_2Einteger_2Eint,B: tp__ty_2Einteger_2Eint,A: tp__ty_2Einteger_2Eint] :
( ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ A ) ) @ ( inj__ty_2Einteger_2Eint @ B ) ) )
= C )
| ( ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__add @ A @ B ) )
!= ( inj__ty_2Einteger_2Eint @ C ) ) ),
inference(paramod_ordered,[status(thm)],[121,142]) ).
thf(432,plain,
! [B: tp__ty_2Einteger_2Eint,A: tp__ty_2Einteger_2Eint] :
( ( fo__c_2Einteger_2Eint__add @ A @ B )
= ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ A ) ) @ ( inj__ty_2Einteger_2Eint @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[431:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( fo__c_2Einteger_2Eint__add @ D @ E ))]]) ).
thf(673,plain,
! [B: tp__ty_2Einteger_2Eint,A: tp__ty_2Einteger_2Eint] :
( ( fo__c_2Einteger_2Eint__add @ A @ B )
= ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ A ) ) @ ( inj__ty_2Einteger_2Eint @ B ) ) ) ),
inference(simp,[status(thm)],[432]) ).
thf(807,plain,
! [B: tp__ty_2Einteger_2Eint,A: tp__ty_2Einteger_2Eint] :
( ( ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) ) @ ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__sub @ A @ B ) ) )
!= ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) ) @ ( inj__ty_2Einteger_2Eint @ sk3 ) ) )
| ( ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ A ) ) @ ( inj__ty_2Einteger_2Eint @ B ) )
!= ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ sk3 ) ) @ ( inj__ty_2Einteger_2Eint @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[168,235]) ).
thf(808,plain,
( ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) ) @ ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__sub @ sk3 @ sk2 ) ) )
!= ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) ) @ ( inj__ty_2Einteger_2Eint @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[807:[bind(A,$thf( sk3 )),bind(B,$thf( sk2 ))]]) ).
thf(1033,plain,
! [A: tp__ty_2Einteger_2Eint] :
( ( ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) )
!= c_2Einteger_2Eint__neg )
| ( A != sk2 )
| ( ( p @ ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__neg @ A ) ) )
!= ( p @ c_2Ebool_2EF ) ) ),
inference(simp,[status(thm)],[1016]) ).
thf(1074,plain,
( ( ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) )
!= c_2Einteger_2Eint__neg )
| ( ( p @ ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__neg @ sk2 ) ) )
!= ( p @ c_2Ebool_2EF ) ) ),
inference(simp,[status(thm)],[1033]) ).
thf(1218,plain,
( ( ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) )
!= c_2Einteger_2Eint__neg )
| ( p @ ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__neg @ sk2 ) ) ) ),
inference(rewrite,[status(thm)],[1074,117]) ).
thf(5,axiom,
mem @ c_2Ebool_2EF @ bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2EF) ).
thf(72,plain,
mem @ c_2Ebool_2EF @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
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(143,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(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(99,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(13,axiom,
mem @ c_2Ebool_2ET @ bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2ET) ).
thf(87,plain,
mem @ c_2Ebool_2ET @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(75,plain,
mem @ ( inj__o @ $false ) @ bool,
inference(instance,[status(thm)],[73]) ).
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(151,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(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(183,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
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(107,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(259,plain,
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ sk3 ) ) @ ( inj__ty_2Einteger_2Eint @ sk2 ) ) ) )
| ~ $true
| ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) ) @ ( inj__ty_2Einteger_2Eint @ sk3 ) ) )
!= ( p @ c_2Ebool_2ET ) ) ),
inference(paramod_ordered,[status(thm)],[210,236]) ).
thf(260,plain,
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ sk3 ) ) @ ( inj__ty_2Einteger_2Eint @ sk2 ) ) ) )
| ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) ) @ ( inj__ty_2Einteger_2Eint @ sk3 ) ) )
!= ( p @ c_2Ebool_2ET ) ) ),
inference(simp,[status(thm)],[259]) ).
thf(268,plain,
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ sk3 ) ) @ ( inj__ty_2Einteger_2Eint @ sk2 ) ) ) )
| ( ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ sk1 ) ) @ ( inj__ty_2Einteger_2Eint @ sk3 ) )
!= c_2Ebool_2ET ) ),
inference(simp,[status(thm)],[260]) ).
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(131,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(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(163,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(82,plain,
! [C: $i > $i,B: del,A: del] :
( ( ( mem @ ( sk4 @ C @ B @ A ) @ A )
| ( mem @ ( lam @ A @ C ) @ ( arr @ A @ B ) ) )
& ( ~ ( mem @ ( C @ ( sk4 @ C @ B @ A ) ) @ B )
| ( mem @ ( lam @ A @ C ) @ ( arr @ A @ B ) ) ) ),
inference(cnf,[status(esa)],[81]) ).
thf(83,plain,
! [C: $i > $i,B: del,A: del] :
( ( mem @ ( sk4 @ C @ B @ A ) @ A )
| ( mem @ ( lam @ A @ C ) @ ( arr @ A @ B ) ) ),
inference(cnfConj,[status(thm)],[82]) ).
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(90,plain,
mem @ c_2Einteger_2Eint__neg @ ( arr @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
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(111,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(2347,plain,
$false,
inference(e,[status(thm)],[142,185,701,69,249,234,88,170,115,217,247,184,125,157,93,416,228,78,216,211,106,147,89,116,74,206,233,117,85,220,102,160,70,137,729,252,197,188,169,77,1075,970,96,124,225,134,73,105,1071,128,237,166,180,191,118,71,236,86,81,377,76,140,213,91,66,964,198,108,241,80,675,426,209,112,63,150,95,673,808,1218,72,143,99,363,87,75,235,119,378,151,168,183,210,107,268,79,131,163,68,122,83,90,111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ITP012^2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Sep 29 19:26:48 UTC 2026
% 0.08/0.11 % CPUTime :
% 0.08/0.11 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.43/0.40 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.88/0.54 % [INFO] Parsing done (145ms).
% 0.88/0.55 % [INFO] Running in sequential loop mode.
% 1.27/0.74 % [INFO] eprover registered as external prover.
% 1.27/0.74 % [INFO] Scanning for conjecture ...
% 1.48/0.80 % [INFO] Found a conjecture (or negated_conjecture) and 60 axioms. Running axiom selection ...
% 1.48/0.85 % [INFO] Axiom selection finished. Selected 60 axioms (removed 0 axioms).
% 1.72/0.91 % [INFO] Problem is higher-order (TPTP THF).
% 1.72/0.91 % [INFO] Type checking passed.
% 1.72/0.92 % [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 ...
% 13.21/3.27 % External prover 'e' found a proof!
% 13.21/3.27 % [INFO] Killing All external provers ...
% 13.21/3.28 % Time passed: 3088ms (effective reasoning time: 2723ms)
% 13.21/3.28 % 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)>
% 13.21/3.28 % 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
% 13.21/3.28 % No. of inferences in proof: 215
% 13.21/3.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3088 ms resp. 2723 ms w/o parsing
% 12.19/3.37 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.19/3.38 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------