TSTP Solution File: PHI004^1 by Leo-III---1.7.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : PHI004^1 : TPTP v8.2.0. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n025.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 21 02:18:25 EDT 2024
% Result : Theorem 121.48s 23.57s
% Output : Refutation 121.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 49
% Syntax : Number of formulae : 268 ( 84 unt; 32 typ; 11 def)
% Number of atoms : 870 ( 175 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 2024 ( 305 ~; 177 |; 13 &;1441 @)
% ( 0 <=>; 88 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 436 ( 436 >; 0 *; 0 +; 0 <<)
% Number of symbols : 39 ( 36 usr; 21 con; 0-3 aty)
% Number of variables : 866 ( 581 ^ 275 !; 10 ?; 866 :)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
thf(mnot_type,type,
mnot: ( $i > $o ) > $i > $o ).
thf(mnot_def,definition,
( mnot
= ( ^ [A: $i > $o,B: $i] :
~ ( A @ B ) ) ) ).
thf(mand_type,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mand_def,definition,
( mand
= ( ^ [A: $i > $o,B: $i > $o,C: $i] :
( ( A @ C )
& ( B @ C ) ) ) ) ).
thf(mimplies_type,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mimplies_def,definition,
( mimplies
= ( ^ [A: $i > $o,B: $i > $o,C: $i] :
( ( A @ C )
=> ( B @ C ) ) ) ) ).
thf(mequiv_type,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mequiv_def,definition,
( mequiv
= ( ^ [A: $i > $o,B: $i > $o,C: $i] :
( ( A @ C )
= ( B @ C ) ) ) ) ).
thf(mforall_ind_type,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(mforall_ind_def,definition,
( mforall_ind
= ( ^ [A: mu > $i > $o,B: $i] :
! [C: mu] : ( A @ C @ B ) ) ) ).
thf(mforall_indset_type,type,
mforall_indset: ( ( mu > $i > $o ) > $i > $o ) > $i > $o ).
thf(mforall_indset_def,definition,
( mforall_indset
= ( ^ [A: ( mu > $i > $o ) > $i > $o,B: $i] :
! [C: mu > $i > $o] : ( A @ C @ B ) ) ) ).
thf(rel_type,type,
rel: $i > $i > $o ).
thf(mbox_type,type,
mbox: ( $i > $o ) > $i > $o ).
thf(mbox_def,definition,
( mbox
= ( mbox_generic @ rel ) ) ).
thf(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf(mvalid_def,definition,
( mvalid
= ( '!' @ $i ) ) ).
thf(positive_type,type,
positive: ( mu > $i > $o ) > $i > $o ).
thf(god_type,type,
god: mu > $i > $o ).
thf(god_def,definition,
( god
= ( ^ [A: mu] :
( mforall_indset
@ ^ [B: mu > $i > $o] : ( mimplies @ ( positive @ B ) @ ( B @ A ) ) ) ) ) ).
thf(essence_type,type,
essence: ( mu > $i > $o ) > mu > $i > $o ).
thf(essence_def,definition,
( essence
= ( ^ [A: mu > $i > $o,B: mu] :
( mand @ ( A @ B )
@ ( mforall_indset
@ ^ [C: mu > $i > $o] :
( mimplies @ ( C @ B )
@ ( mbox
@ ( mforall_ind
@ ^ [D: mu] : ( mimplies @ ( A @ D ) @ ( C @ D ) ) ) ) ) ) ) ) ) ).
thf(necessary_existence_type,type,
necessary_existence: mu > $i > $o ).
thf(necessary_existence_def,definition,
( necessary_existence
= ( ^ [A: mu] :
( mforall_indset
@ ^ [B: mu > $i > $o] : ( mimplies @ ( essence @ B @ A ) @ ( mbox @ ( mexists_ind @ B ) ) ) ) ) ) ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: mu ).
thf(sk3_type,type,
sk3: $o ).
thf(sk4_type,type,
sk4: mu > $i > $o ).
thf(sk5_type,type,
sk5: mu > $i > $o ).
thf(sk6_type,type,
sk6: $i ).
thf(sk7_type,type,
sk7: mu ).
thf(sk8_type,type,
sk8: ( mu > $i > $o ) > ( mu > $i > $o ) > $i > $i ).
thf(sk11_type,type,
sk11: $i > ( mu > $i > $o ) > $i ).
thf(sk64_type,type,
sk64: mu ).
thf(sk65_type,type,
sk65: $i ).
thf(sk69_type,type,
sk69: $i ).
thf(sk73_type,type,
sk73: $i ).
thf(sk74_type,type,
sk74: mu ).
thf(sk79_type,type,
sk79: $i ).
thf(sk81_type,type,
sk81: $i ).
thf(sk83_type,type,
sk83: $i ).
thf(sk91_type,type,
sk91: $i ).
thf(1,conjecture,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] : ( mimplies @ ( god @ A ) @ ( essence @ god @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thmT2) ).
thf(2,negated_conjecture,
~ ( mvalid
@ ( mforall_ind
@ ^ [A: mu] : ( mimplies @ ( god @ A ) @ ( essence @ god @ A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
~ ! [A: $i,B: mu] :
( ! [C: mu > $i > $o] :
( ( positive @ C @ A )
=> ( C @ B @ A ) )
=> ( ! [C: mu > $i > $o] :
( ( positive @ C @ A )
=> ( C @ B @ A ) )
& ! [C: mu > $i > $o] :
( ( C @ B @ A )
=> ! [D: $i] :
( ~ ( rel @ A @ D )
| ! [E: mu] :
( ! [F: mu > $i > $o] :
( ( positive @ F @ D )
=> ( F @ E @ D ) )
=> ( C @ E @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,plain,
( sk3
| ( sk5 @ sk2 @ sk1 ) ),
inference(cnf,[status(esa)],[8]) ).
thf(13,plain,
( ( positive @ sk4 @ sk1 )
| ~ sk3 ),
inference(cnf,[status(esa)],[8]) ).
thf(15,plain,
! [A: mu > $i > $o] :
( ~ ( positive @ A @ sk1 )
| ( A @ sk2 @ sk1 ) ),
inference(cnf,[status(esa)],[8]) ).
thf(11,plain,
( ~ ( sk4 @ sk2 @ sk1 )
| ~ sk3 ),
inference(cnf,[status(esa)],[8]) ).
thf(72,plain,
! [A: mu > $i > $o] :
( ~ ( positive @ A @ sk1 )
| ~ sk3
| ( ( A @ sk2 @ sk1 )
!= ( sk4 @ sk2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[15,11]) ).
thf(97,plain,
( ~ ( positive @ sk4 @ sk1 )
| ~ sk3 ),
inference(pre_uni,[status(thm)],[72:[bind(A,$thf( sk4 ))]]) ).
thf(168,plain,
( ~ sk3
| ( ( positive @ sk4 @ sk1 )
!= ( positive @ sk4 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[13,97]) ).
thf(169,plain,
~ sk3,
inference(pattern_uni,[status(thm)],[168:[]]) ).
thf(184,plain,
( $false
| ( sk5 @ sk2 @ sk1 ) ),
inference(rewrite,[status(thm)],[10,169]) ).
thf(185,plain,
sk5 @ sk2 @ sk1,
inference(simp,[status(thm)],[184]) ).
thf(3,axiom,
( mvalid
@ ( mforall_indset
@ ^ [A: mu > $i > $o] :
( mequiv
@ ( positive
@ ^ [B: mu] : ( mnot @ ( A @ B ) ) )
@ ( mnot @ ( positive @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axA1) ).
thf(17,plain,
! [A: $i,B: mu > $i > $o] :
( ( positive
@ ^ [C: mu,D: $i] :
~ ( B @ C @ D )
@ A )
= ( ~ ( positive @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(18,plain,
! [B: mu > $i > $o,A: $i] :
( ( positive
@ ^ [C: mu,D: $i] :
~ ( B @ C @ D )
@ A )
= ( ~ ( positive @ B @ A ) ) ),
inference(cnf,[status(esa)],[17]) ).
thf(19,plain,
! [B: mu > $i > $o,A: $i] :
( ( positive
@ ^ [C: mu,D: $i] :
~ ( B @ C @ D )
@ A )
= ( ~ ( positive @ B @ A ) ) ),
inference(lifteq,[status(thm)],[18]) ).
thf(77,plain,
! [C: mu > $i > $o,B: mu > $i > $o,A: $i] :
( ( positive @ B @ A )
| ( C @ sk2 @ sk1 )
| ( ( positive
@ ^ [D: mu,E: $i] :
~ ( B @ D @ E )
@ A )
!= ( positive @ C @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[19,15]) ).
thf(78,plain,
! [A: mu > $i > $o] :
( ( positive @ A @ sk1 )
| ~ ( A @ sk2 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[77:[bind(A,$thf( sk1 )),bind(B,$thf( D )),bind(C,$thf( ^ [E: mu] : ^ [F: $i] : ~ ( D @ E @ F ) ))]]) ).
thf(110,plain,
! [A: mu > $i > $o] :
( ~ ( A @ sk2 @ sk1 )
| ( positive @ A @ sk1 ) ),
inference(cnf,[status(esa)],[78]) ).
thf(111,plain,
! [A: mu > $i > $o] :
( ~ ( A @ sk2 @ sk1 )
| ( positive @ A @ sk1 ) ),
inference(simp,[status(thm)],[110]) ).
thf(2863,plain,
! [A: mu > $i > $o] :
( ( positive @ A @ sk1 )
| ( ( sk5 @ sk2 @ sk1 )
!= ( A @ sk2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[185,111]) ).
thf(2993,plain,
positive @ sk5 @ sk1,
inference(pre_uni,[status(thm)],[2863:[bind(A,$thf( sk5 ))]]) ).
thf(90,plain,
( ~ ( positive
@ ^ [A: mu,B: $i] : $false
@ sk1 )
| $false ),
inference(prim_subst,[status(thm)],[15:[bind(A,$thf( ^ [B: mu] : ^ [C: $i] : $false ))]]) ).
thf(119,plain,
~ ( positive
@ ^ [A: mu,B: $i] : $false
@ sk1 ),
inference(simp,[status(thm)],[90]) ).
thf(129,plain,
! [A: mu > $i > $o] :
( ~ ( positive @ A @ sk1 )
| ( ( A @ sk2 @ sk1 )
!= ( positive
@ ^ [B: mu,C: $i] : $false
@ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[15,119]) ).
thf(133,plain,
~ ( positive
@ ^ [A: mu] :
( positive
@ ^ [B: mu,C: $i] : $false )
@ sk1 ),
inference(pre_uni,[status(thm)],[129:[bind(A,$thf( ^ [B: mu] : ( positive @ ^ [C: mu] : ^ [D: $i] : $false ) ))]]) ).
thf(3077,plain,
( ( positive @ sk5 @ sk1 )
!= ( positive
@ ^ [A: mu] :
( positive
@ ^ [B: mu,C: $i] : $false )
@ sk1 ) ),
inference(paramod_ordered,[status(thm)],[2993,133]) ).
thf(3133,plain,
( ( sk5
!= ( ^ [A: mu] :
( positive
@ ^ [B: mu,C: $i] : $false ) ) )
| ( sk1 != sk1 ) ),
inference(simp,[status(thm)],[3077]) ).
thf(3153,plain,
( sk5
!= ( ^ [A: mu] :
( positive
@ ^ [B: mu,C: $i] : $false ) ) ),
inference(simp,[status(thm)],[3133]) ).
thf(3069,plain,
( ( positive @ sk5 @ sk1 )
!= ( positive
@ ^ [A: mu,B: $i] : $false
@ sk1 ) ),
inference(paramod_ordered,[status(thm)],[2993,119]) ).
thf(3112,plain,
( ( sk5
!= ( ^ [A: mu,B: $i] : $false ) )
| ( sk1 != sk1 ) ),
inference(simp,[status(thm)],[3069]) ).
thf(3148,plain,
( sk5
!= ( ^ [A: mu,B: $i] : $false ) ),
inference(simp,[status(thm)],[3112]) ).
thf(9,plain,
! [A: mu > $i > $o] :
( sk3
| ~ ( positive @ A @ sk6 )
| ( A @ sk7 @ sk6 ) ),
inference(cnf,[status(esa)],[8]) ).
thf(16,plain,
! [A: mu > $i > $o] :
( sk3
| ~ ( positive @ A @ sk6 )
| ( A @ sk7 @ sk6 ) ),
inference(simp,[status(thm)],[9]) ).
thf(192,plain,
! [A: mu > $i > $o] :
( $false
| ~ ( positive @ A @ sk6 )
| ( A @ sk7 @ sk6 ) ),
inference(rewrite,[status(thm)],[16,169]) ).
thf(193,plain,
! [A: mu > $i > $o] :
( ~ ( positive @ A @ sk6 )
| ( A @ sk7 @ sk6 ) ),
inference(simp,[status(thm)],[192]) ).
thf(12,plain,
( sk3
| ~ ( sk5 @ sk7 @ sk6 ) ),
inference(cnf,[status(esa)],[8]) ).
thf(188,plain,
( $false
| ~ ( sk5 @ sk7 @ sk6 ) ),
inference(rewrite,[status(thm)],[12,169]) ).
thf(189,plain,
~ ( sk5 @ sk7 @ sk6 ),
inference(simp,[status(thm)],[188]) ).
thf(261,plain,
! [A: mu > $i > $o] :
( ~ ( positive @ A @ sk6 )
| ( ( A @ sk7 @ sk6 )
!= ( sk5 @ sk7 @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[193,189]) ).
thf(266,plain,
~ ( positive
@ ^ [A: mu] : ( sk5 @ sk7 )
@ sk6 ),
inference(pre_uni,[status(thm)],[261:[bind(A,$thf( ^ [B: mu] : ( sk5 @ sk7 ) ))]]) ).
thf(573,plain,
! [A: mu > $i > $o] :
( ~ ( positive @ A @ sk6 )
| ( ( A @ sk7 @ sk6 )
!= ( positive
@ ^ [B: mu] : ( sk5 @ sk7 )
@ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[193,266]) ).
thf(583,plain,
~ ( positive
@ ^ [A: mu,B: $i] :
( positive
@ ^ [C: mu] : ( sk5 @ A )
@ sk6 )
@ sk6 ),
inference(pre_uni,[status(thm)],[573:[bind(A,$thf( ^ [B: mu] : ^ [C: $i] : ( positive @ ^ [D: mu] : ( sk5 @ B ) @ sk6 ) ))]]) ).
thf(2127,plain,
! [A: mu > $i > $o] :
( ~ ( positive @ A @ sk6 )
| ( ( A @ sk7 @ sk6 )
!= ( positive
@ ^ [B: mu,C: $i] :
( positive
@ ^ [D: mu] : ( sk5 @ B )
@ sk6 )
@ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[193,583]) ).
thf(2164,plain,
~ ( positive
@ ^ [A: mu,B: $i] :
( positive
@ ^ [C: mu,D: $i] :
( positive
@ ^ [E: mu] : ( sk5 @ C )
@ B )
@ B )
@ sk6 ),
inference(pre_uni,[status(thm)],[2127:[bind(A,$thf( ^ [B: mu] : ^ [C: $i] : ( positive @ ^ [D: mu] : ^ [E: $i] : ( positive @ ^ [F: mu] : ( sk5 @ D ) @ C ) @ C ) ))]]) ).
thf(5,axiom,
mvalid @ ( positive @ god ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axA3) ).
thf(24,plain,
! [A: $i] :
( positive
@ ^ [B: mu,C: $i] :
! [D: mu > $i > $o] :
( ( positive @ D @ C )
=> ( D @ B @ C ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(25,plain,
! [A: $i] :
( positive
@ ^ [B: mu,C: $i] :
! [D: mu > $i > $o] :
( ( positive @ D @ C )
=> ( D @ B @ C ) )
@ A ),
inference(cnf,[status(esa)],[24]) ).
thf(265,plain,
~ ( positive
@ ^ [A: mu,B: $i] : ( sk5 @ A @ sk6 )
@ sk6 ),
inference(pre_uni,[status(thm)],[261:[bind(A,$thf( ^ [B: mu] : ^ [C: $i] : ( sk5 @ B @ sk6 ) ))]]) ).
thf(554,plain,
! [A: $i] :
( ( positive
@ ^ [B: mu,C: $i] :
! [D: mu > $i > $o] :
( ( positive @ D @ C )
=> ( D @ B @ C ) )
@ A )
!= ( positive
@ ^ [B: mu,C: $i] : ( sk5 @ B @ sk6 )
@ sk6 ) ),
inference(paramod_ordered,[status(thm)],[25,265]) ).
thf(560,plain,
! [A: $i] :
( ( ( ^ [B: mu,C: $i] :
! [D: mu > $i > $o] :
( ( positive @ D @ C )
=> ( D @ B @ C ) ) )
!= ( ^ [B: mu,C: $i] : ( sk5 @ B @ sk6 ) ) )
| ( A != sk6 ) ),
inference(simp,[status(thm)],[554]) ).
thf(569,plain,
( ( ^ [A: mu,B: $i] :
! [C: mu > $i > $o] :
( ( positive @ C @ B )
=> ( C @ A @ B ) ) )
!= ( ^ [A: mu,B: $i] : ( sk5 @ A @ sk6 ) ) ),
inference(simp,[status(thm)],[560]) ).
thf(2991,plain,
( positive
@ ^ [A: mu,B: $i] : ( sk5 @ A @ sk1 )
@ sk1 ),
inference(pre_uni,[status(thm)],[2863:[bind(A,$thf( ^ [B: mu] : ^ [C: $i] : ( sk5 @ B @ sk1 ) ))]]) ).
thf(3774,plain,
( ( positive
@ ^ [A: mu,B: $i] : ( sk5 @ A @ sk1 )
@ sk1 )
!= ( positive
@ ^ [A: mu,B: $i] : $false
@ sk1 ) ),
inference(paramod_ordered,[status(thm)],[2991,119]) ).
thf(3849,plain,
( ( ( ^ [A: mu,B: $i] : ( sk5 @ A @ sk1 ) )
!= ( ^ [A: mu,B: $i] : $false ) )
| ( sk1 != sk1 ) ),
inference(simp,[status(thm)],[3774]) ).
thf(3859,plain,
( ( ^ [A: mu,B: $i] : ( sk5 @ A @ sk1 ) )
!= ( ^ [A: mu,B: $i] : $false ) ),
inference(simp,[status(thm)],[3849]) ).
thf(3871,plain,
sk5 @ sk74 @ sk1,
inference(func_ext,[status(esa)],[3859]) ).
thf(3876,plain,
! [A: mu > $i > $o] :
( ( positive @ A @ sk1 )
| ( ( sk5 @ sk74 @ sk1 )
!= ( A @ sk2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[3871,111]) ).
thf(3881,plain,
( positive
@ ^ [A: mu] : ( sk5 @ sk74 )
@ sk1 ),
inference(pre_uni,[status(thm)],[3876:[bind(A,$thf( ^ [B: mu] : ( sk5 @ sk74 ) ))]]) ).
thf(4706,plain,
( ( positive
@ ^ [A: mu] : ( sk5 @ sk74 )
@ sk1 )
!= ( positive
@ ^ [A: mu,B: $i] : $false
@ sk1 ) ),
inference(paramod_ordered,[status(thm)],[3881,119]) ).
thf(4747,plain,
( ( ( ^ [A: mu] : ( sk5 @ sk74 ) )
!= ( ^ [A: mu,B: $i] : $false ) )
| ( sk1 != sk1 ) ),
inference(simp,[status(thm)],[4706]) ).
thf(4751,plain,
( ( ^ [A: mu] : ( sk5 @ sk74 ) )
!= ( ^ [A: mu,B: $i] : $false ) ),
inference(simp,[status(thm)],[4747]) ).
thf(4763,plain,
sk5 @ sk74 @ sk91,
inference(func_ext,[status(esa)],[4751]) ).
thf(3821,plain,
! [A: mu > $i > $o] :
( ( positive @ A @ sk1 )
| ( ( positive
@ ^ [B: mu,C: $i] : ( sk5 @ B @ sk1 )
@ sk1 )
!= ( A @ sk2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[2991,111]) ).
thf(3836,plain,
( positive
@ ^ [A: mu,B: $i] :
( positive
@ ^ [C: mu,D: $i] : ( sk5 @ C @ B )
@ B )
@ sk1 ),
inference(pre_uni,[status(thm)],[3821:[bind(A,$thf( ^ [B: mu] : ^ [C: $i] : ( positive @ ^ [D: mu] : ^ [E: $i] : ( sk5 @ D @ C ) @ C ) ))]]) ).
thf(2945,plain,
( ~ $true
| ( positive
@ ^ [A: mu,B: $i] : $true
@ sk1 ) ),
inference(prim_subst,[status(thm)],[111:[bind(A,$thf( ^ [B: mu] : ^ [C: $i] : $true ))]]) ).
thf(3006,plain,
( positive
@ ^ [A: mu,B: $i] : $true
@ sk1 ),
inference(simp,[status(thm)],[2945]) ).
thf(146,plain,
! [A: mu > $i > $o] :
( ~ ( positive @ A @ sk1 )
| ( ( A @ sk2 @ sk1 )
!= ( positive
@ ^ [B: mu] :
( positive
@ ^ [C: mu,D: $i] : $false )
@ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[15,133]) ).
thf(155,plain,
~ ( positive
@ ^ [A: mu] :
( positive
@ ^ [B: mu] :
( positive
@ ^ [C: mu,D: $i] : $false ) )
@ sk1 ),
inference(pre_uni,[status(thm)],[146:[bind(A,$thf( ^ [B: mu] : ( positive @ ^ [C: mu] : ( positive @ ^ [D: mu] : ^ [E: $i] : $false ) ) ))]]) ).
thf(3432,plain,
( ( positive
@ ^ [A: mu] :
( positive
@ ^ [B: mu] :
( positive
@ ^ [C: mu,D: $i] : $false ) )
@ sk1 )
!= ( positive
@ ^ [A: mu,B: $i] : $true
@ sk1 ) ),
inference(paramod_ordered,[status(thm)],[3006,155]) ).
thf(3488,plain,
( ( ( ^ [A: mu] :
( positive
@ ^ [B: mu] :
( positive
@ ^ [C: mu,D: $i] : $false ) ) )
!= ( ^ [A: mu,B: $i] : $true ) )
| ( sk1 != sk1 ) ),
inference(simp,[status(thm)],[3432]) ).
thf(3502,plain,
( ( ^ [A: mu] :
( positive
@ ^ [B: mu] :
( positive
@ ^ [C: mu,D: $i] : $false ) ) )
!= ( ^ [A: mu,B: $i] : $true ) ),
inference(simp,[status(thm)],[3488]) ).
thf(552,plain,
! [A: mu > $i > $o] :
( ~ ( positive @ A @ sk6 )
| ( ( A @ sk7 @ sk6 )
!= ( positive
@ ^ [B: mu,C: $i] : ( sk5 @ B @ sk6 )
@ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[193,265]) ).
thf(565,plain,
~ ( positive
@ ^ [A: mu,B: $i] :
( positive
@ ^ [C: mu,D: $i] : ( sk5 @ C @ B )
@ B )
@ sk6 ),
inference(pre_uni,[status(thm)],[552:[bind(A,$thf( ^ [B: mu] : ^ [C: $i] : ( positive @ ^ [D: mu] : ^ [E: $i] : ( sk5 @ D @ C ) @ C ) ))]]) ).
thf(33,plain,
! [C: mu > $i > $o,B: $i,A: $i] :
( ~ ( positive @ C @ B )
| ( ( positive
@ ^ [D: mu,E: $i] :
! [F: mu > $i > $o] :
( ( positive @ F @ E )
=> ( F @ D @ E ) )
@ A )
!= ( positive
@ ^ [D: mu,E: $i] :
~ ( C @ D @ E )
@ B ) ) ),
inference(paramod_ordered,[status(thm)],[25,19]) ).
thf(35,plain,
! [C: mu > $i > $o,B: $i,A: $i] :
( ~ ( positive @ C @ B )
| ( ( ^ [D: mu,E: $i] :
! [F: mu > $i > $o] :
( ( positive @ F @ E )
=> ( F @ D @ E ) ) )
!= ( ^ [D: mu,E: $i] :
~ ( C @ D @ E ) ) )
| ( A != B ) ),
inference(simp,[status(thm)],[33]) ).
thf(37,plain,
! [B: mu > $i > $o,A: $i] :
( ~ ( positive @ B @ A )
| ( ( ^ [C: mu,D: $i] :
! [E: mu > $i > $o] :
( ( positive @ E @ D )
=> ( E @ C @ D ) ) )
!= ( ^ [C: mu,D: $i] :
~ ( B @ C @ D ) ) ) ),
inference(simp,[status(thm)],[35]) ).
thf(267,plain,
~ ( positive @ sk5 @ sk6 ),
inference(pre_uni,[status(thm)],[261:[bind(A,$thf( sk5 ))]]) ).
thf(291,plain,
! [A: mu > $i > $o] :
( ~ ( positive @ A @ sk6 )
| ( ( A @ sk7 @ sk6 )
!= ( positive @ sk5 @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[193,267]) ).
thf(299,plain,
~ ( positive
@ ^ [A: mu] : ( positive @ sk5 )
@ sk6 ),
inference(pre_uni,[status(thm)],[291:[bind(A,$thf( ^ [B: mu] : ( positive @ sk5 ) ))]]) ).
thf(625,plain,
! [A: $i] :
( ( positive
@ ^ [B: mu,C: $i] :
! [D: mu > $i > $o] :
( ( positive @ D @ C )
=> ( D @ B @ C ) )
@ A )
!= ( positive
@ ^ [B: mu] : ( positive @ sk5 )
@ sk6 ) ),
inference(paramod_ordered,[status(thm)],[25,299]) ).
thf(632,plain,
! [A: $i] :
( ( ( ^ [B: mu,C: $i] :
! [D: mu > $i > $o] :
( ( positive @ D @ C )
=> ( D @ B @ C ) ) )
!= ( ^ [B: mu] : ( positive @ sk5 ) ) )
| ( A != sk6 ) ),
inference(simp,[status(thm)],[625]) ).
thf(638,plain,
( ( ^ [A: mu,B: $i] :
! [C: mu > $i > $o] :
( ( positive @ C @ B )
=> ( C @ A @ B ) ) )
!= ( ^ [A: mu] : ( positive @ sk5 ) ) ),
inference(simp,[status(thm)],[632]) ).
thf(4,axiom,
( mvalid
@ ( mforall_indset
@ ^ [A: mu > $i > $o] :
( mforall_indset
@ ^ [B: mu > $i > $o] :
( mimplies
@ ( mand @ ( positive @ A )
@ ( mbox
@ ( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( A @ C ) @ ( B @ C ) ) ) ) )
@ ( positive @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axA2) ).
thf(20,plain,
! [A: $i,B: mu > $i > $o,C: mu > $i > $o] :
( ( ( positive @ B @ A )
& ! [D: $i] :
( ~ ( rel @ A @ D )
| ! [E: mu] :
( ( B @ E @ D )
=> ( C @ E @ D ) ) ) )
=> ( positive @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(32,plain,
! [C: $i,B: mu > $i > $o,A: $i] :
( ~ ( positive @ B @ A )
| ( ( positive
@ ^ [D: mu,E: $i] :
~ ( B @ D @ E )
@ A )
!= ( positive
@ ^ [D: mu,E: $i] :
! [F: mu > $i > $o] :
( ( positive @ F @ E )
=> ( F @ D @ E ) )
@ C ) ) ),
inference(paramod_ordered,[status(thm)],[19,25]) ).
thf(34,plain,
! [C: $i,B: mu > $i > $o,A: $i] :
( ~ ( positive @ B @ A )
| ( ( ^ [D: mu,E: $i] :
~ ( B @ D @ E ) )
!= ( ^ [D: mu,E: $i] :
! [F: mu > $i > $o] :
( ( positive @ F @ E )
=> ( F @ D @ E ) ) ) )
| ( A != C ) ),
inference(simp,[status(thm)],[32]) ).
thf(36,plain,
! [B: $i,A: mu > $i > $o] :
( ~ ( positive @ A @ B )
| ( ( ^ [C: mu,D: $i] :
~ ( A @ C @ D ) )
!= ( ^ [C: mu,D: $i] :
! [E: mu > $i > $o] :
( ( positive @ E @ D )
=> ( E @ C @ D ) ) ) ) ),
inference(simp,[status(thm)],[34]) ).
thf(46,plain,
! [B: $i,A: mu > $i > $o] :
( ( ( ~ ( A @ ( sk10 @ B @ A ) @ ( sk11 @ B @ A ) ) )
!= ( ! [C: mu > $i > $o] :
( ( positive @ C @ ( sk11 @ B @ A ) )
=> ( C @ ( sk10 @ B @ A ) @ ( sk11 @ B @ A ) ) ) ) )
| ~ ( positive @ A @ B ) ),
inference(func_ext,[status(esa)],[36]) ).
thf(80,plain,
! [A: mu > $i > $o] :
( ~ ( positive @ A @ sk1 )
| ( ( A @ sk2 @ sk1 )
!= ( ~ ( positive @ A @ sk1 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[15]) ).
thf(93,plain,
! [A: mu > $i > $o] :
( ~ ( positive @ A @ sk1 )
| ( ( A @ sk2 @ sk1 )
!= ( ~ ( positive @ A @ sk1 ) ) ) ),
inference(simp,[status(thm)],[80]) ).
thf(205,plain,
! [A: mu > $i > $o] :
( ~ ( positive @ A @ sk6 )
| ( ( A @ sk7 @ sk6 )
!= sk3 ) ),
inference(paramod_ordered,[status(thm)],[193,169]) ).
thf(226,plain,
~ ( positive
@ ^ [A: mu,B: $i] : sk3
@ sk6 ),
inference(pre_uni,[status(thm)],[205:[bind(A,$thf( ^ [B: mu] : ^ [C: $i] : sk3 ))]]) ).
thf(271,plain,
~ ( positive
@ ^ [A: mu,B: $i] : $false
@ sk6 ),
inference(rewrite,[status(thm)],[226,169]) ).
thf(272,plain,
! [A: mu > $i > $o] :
( ~ ( positive @ A @ sk6 )
| ( ( A @ sk7 @ sk6 )
!= ( positive
@ ^ [B: mu,C: $i] : $false
@ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[193,271]) ).
thf(284,plain,
~ ( positive
@ ^ [A: mu] :
( positive
@ ^ [B: mu,C: $i] : $false )
@ sk6 ),
inference(pre_uni,[status(thm)],[272:[bind(A,$thf( ^ [B: mu] : ( positive @ ^ [C: mu] : ^ [D: $i] : $false ) ))]]) ).
thf(3445,plain,
! [A: mu > $i > $o] :
( ( positive @ A @ sk1 )
| ( ( positive
@ ^ [B: mu,C: $i] : $true
@ sk1 )
!= ( A @ sk2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[3006,111]) ).
thf(3470,plain,
( positive
@ ^ [A: mu] :
( positive
@ ^ [B: mu,C: $i] : $true )
@ sk1 ),
inference(pre_uni,[status(thm)],[3445:[bind(A,$thf( ^ [B: mu] : ( positive @ ^ [C: mu] : ^ [D: $i] : $true ) ))]]) ).
thf(585,plain,
~ ( positive
@ ^ [A: mu] :
( positive
@ ^ [B: mu] : ( sk5 @ A ) )
@ sk6 ),
inference(pre_uni,[status(thm)],[573:[bind(A,$thf( ^ [B: mu] : ( positive @ ^ [C: mu] : ( sk5 @ B ) ) ))]]) ).
thf(1076,plain,
! [A: $i] :
( ( positive
@ ^ [B: mu,C: $i] :
! [D: mu > $i > $o] :
( ( positive @ D @ C )
=> ( D @ B @ C ) )
@ A )
!= ( positive
@ ^ [B: mu] :
( positive
@ ^ [C: mu] : ( sk5 @ B ) )
@ sk6 ) ),
inference(paramod_ordered,[status(thm)],[25,585]) ).
thf(1094,plain,
! [A: $i] :
( ( ( ^ [B: mu,C: $i] :
! [D: mu > $i > $o] :
( ( positive @ D @ C )
=> ( D @ B @ C ) ) )
!= ( ^ [B: mu] :
( positive
@ ^ [C: mu] : ( sk5 @ B ) ) ) )
| ( A != sk6 ) ),
inference(simp,[status(thm)],[1076]) ).
thf(1100,plain,
( ( ^ [A: mu,B: $i] :
! [C: mu > $i > $o] :
( ( positive @ C @ B )
=> ( C @ A @ B ) ) )
!= ( ^ [A: mu] :
( positive
@ ^ [B: mu] : ( sk5 @ A ) ) ) ),
inference(simp,[status(thm)],[1094]) ).
thf(7,axiom,
mvalid @ ( positive @ necessary_existence ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axA5) ).
thf(28,plain,
! [A: $i] :
( positive
@ ^ [B: mu,C: $i] :
! [D: mu > $i > $o] :
( ( ( D @ B @ C )
& ! [E: mu > $i > $o] :
( ( E @ B @ C )
=> ! [F: $i] :
( ~ ( rel @ C @ F )
| ! [G: mu] :
( ( D @ G @ F )
=> ( E @ G @ F ) ) ) ) )
=> ! [E: $i] :
( ~ ( rel @ C @ E )
| ? [F: mu] : ( D @ F @ E ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(29,plain,
! [A: $i] :
( positive
@ ^ [B: mu,C: $i] :
! [D: mu > $i > $o] :
( ( ( D @ B @ C )
& ! [E: mu > $i > $o] :
( ( E @ B @ C )
=> ! [F: $i] :
( ~ ( rel @ C @ F )
| ! [G: mu] :
( ( D @ G @ F )
=> ( E @ G @ F ) ) ) ) )
=> ! [E: $i] :
( ~ ( rel @ C @ E )
| ? [F: mu] : ( D @ F @ E ) ) )
@ A ),
inference(cnf,[status(esa)],[28]) ).
thf(14,plain,
( sk3
| ( rel @ sk1 @ sk6 ) ),
inference(cnf,[status(esa)],[8]) ).
thf(186,plain,
( $false
| ( rel @ sk1 @ sk6 ) ),
inference(rewrite,[status(thm)],[14,169]) ).
thf(187,plain,
rel @ sk1 @ sk6,
inference(simp,[status(thm)],[186]) ).
thf(2910,plain,
! [A: mu > $i > $o] :
( ( positive @ A @ sk1 )
| ( ( rel @ sk1 @ sk6 )
!= ( A @ sk2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[187,111]) ).
thf(2950,plain,
( positive
@ ^ [A: mu,B: $i] : ( rel @ B @ sk6 )
@ sk1 ),
inference(pre_uni,[status(thm)],[2910:[bind(A,$thf( ^ [B: mu] : ^ [C: $i] : ( rel @ C @ sk6 ) ))]]) ).
thf(575,plain,
! [A: $i] :
( ( positive
@ ^ [B: mu,C: $i] :
! [D: mu > $i > $o] :
( ( positive @ D @ C )
=> ( D @ B @ C ) )
@ A )
!= ( positive
@ ^ [B: mu] : ( sk5 @ sk7 )
@ sk6 ) ),
inference(paramod_ordered,[status(thm)],[25,266]) ).
thf(587,plain,
! [A: $i] :
( ( ( ^ [B: mu,C: $i] :
! [D: mu > $i > $o] :
( ( positive @ D @ C )
=> ( D @ B @ C ) ) )
!= ( ^ [B: mu] : ( sk5 @ sk7 ) ) )
| ( A != sk6 ) ),
inference(simp,[status(thm)],[575]) ).
thf(591,plain,
( ( ^ [A: mu,B: $i] :
! [C: mu > $i > $o] :
( ( positive @ C @ B )
=> ( C @ A @ B ) ) )
!= ( ^ [A: mu] : ( sk5 @ sk7 ) ) ),
inference(simp,[status(thm)],[587]) ).
thf(1046,plain,
! [A: $i] :
( ( positive
@ ^ [B: mu,C: $i] :
! [D: mu > $i > $o] :
( ( positive @ D @ C )
=> ( D @ B @ C ) )
@ A )
!= ( positive
@ ^ [B: mu,C: $i] :
( positive
@ ^ [D: mu,E: $i] : ( sk5 @ D @ C )
@ C )
@ sk6 ) ),
inference(paramod_ordered,[status(thm)],[25,565]) ).
thf(1054,plain,
! [A: $i] :
( ( ( ^ [B: mu,C: $i] :
! [D: mu > $i > $o] :
( ( positive @ D @ C )
=> ( D @ B @ C ) ) )
!= ( ^ [B: mu,C: $i] :
( positive
@ ^ [D: mu,E: $i] : ( sk5 @ D @ C )
@ C ) ) )
| ( A != sk6 ) ),
inference(simp,[status(thm)],[1046]) ).
thf(1072,plain,
( ( ^ [A: mu,B: $i] :
! [C: mu > $i > $o] :
( ( positive @ C @ B )
=> ( C @ A @ B ) ) )
!= ( ^ [A: mu,B: $i] :
( positive
@ ^ [C: mu,D: $i] : ( sk5 @ C @ B )
@ B ) ) ),
inference(simp,[status(thm)],[1054]) ).
thf(85,plain,
! [B: mu > $i > $o,A: mu > $i > $o] :
( ~ ( positive
@ ^ [C: mu,D: $i] :
( ( A @ C @ D )
| ( B @ C @ D ) )
@ sk1 )
| ( A @ sk2 @ sk1 )
| ( B @ sk2 @ sk1 ) ),
inference(prim_subst,[status(thm)],[15:[bind(A,$thf( ^ [D: mu] : ^ [E: $i] : ( ( B @ D @ E ) | ( C @ D @ E ) ) ))]]) ).
thf(115,plain,
! [B: mu > $i > $o,A: mu > $i > $o] :
( ( A @ sk2 @ sk1 )
| ( B @ sk2 @ sk1 )
| ~ ( positive
@ ^ [C: mu,D: $i] :
( ( A @ C @ D )
| ( B @ C @ D ) )
@ sk1 ) ),
inference(cnf,[status(esa)],[85]) ).
thf(116,plain,
! [B: mu > $i > $o,A: mu > $i > $o] :
( ( A @ sk2 @ sk1 )
| ( B @ sk2 @ sk1 )
| ~ ( positive
@ ^ [C: mu,D: $i] :
( ( A @ C @ D )
| ( B @ C @ D ) )
@ sk1 ) ),
inference(simp,[status(thm)],[115]) ).
thf(89,plain,
( ~ ( positive @ sk4 @ sk1 )
| ( sk4 @ sk2 @ sk1 ) ),
inference(prim_subst,[status(thm)],[15:[bind(A,$thf( sk4 ))]]) ).
thf(293,plain,
! [A: $i] :
( ( positive
@ ^ [B: mu,C: $i] :
! [D: mu > $i > $o] :
( ( positive @ D @ C )
=> ( D @ B @ C ) )
@ A )
!= ( positive @ sk5 @ sk6 ) ),
inference(paramod_ordered,[status(thm)],[25,267]) ).
thf(296,plain,
! [A: $i] :
( ( ( ^ [B: mu,C: $i] :
! [D: mu > $i > $o] :
( ( positive @ D @ C )
=> ( D @ B @ C ) ) )
!= sk5 )
| ( A != sk6 ) ),
inference(simp,[status(thm)],[293]) ).
thf(302,plain,
( ( ^ [A: mu,B: $i] :
! [C: mu > $i > $o] :
( ( positive @ C @ B )
=> ( C @ A @ B ) ) )
!= sk5 ),
inference(simp,[status(thm)],[296]) ).
thf(3674,plain,
( ( positive
@ ^ [A: mu] :
( positive
@ ^ [B: mu,C: $i] : $false )
@ sk1 )
!= ( positive
@ ^ [A: mu,B: $i] : ( rel @ B @ sk6 )
@ sk1 ) ),
inference(paramod_ordered,[status(thm)],[2950,133]) ).
thf(3733,plain,
( ( ( ^ [A: mu] :
( positive
@ ^ [B: mu,C: $i] : $false ) )
!= ( ^ [A: mu,B: $i] : ( rel @ B @ sk6 ) ) )
| ( sk1 != sk1 ) ),
inference(simp,[status(thm)],[3674]) ).
thf(3752,plain,
( ( ^ [A: mu] :
( positive
@ ^ [B: mu,C: $i] : $false ) )
!= ( ^ [A: mu,B: $i] : ( rel @ B @ sk6 ) ) ),
inference(simp,[status(thm)],[3733]) ).
thf(21,plain,
! [C: mu > $i > $o,B: mu > $i > $o,A: $i] :
( ~ ( positive @ B @ A )
| ~ ( C @ ( sk9 @ C @ B @ A ) @ ( sk8 @ C @ B @ A ) )
| ( positive @ C @ A ) ),
inference(cnf,[status(esa)],[20]) ).
thf(23,plain,
! [C: mu > $i > $o,B: mu > $i > $o,A: $i] :
( ~ ( positive @ B @ A )
| ( rel @ A @ ( sk8 @ C @ B @ A ) )
| ( positive @ C @ A ) ),
inference(cnf,[status(esa)],[20]) ).
thf(1727,plain,
! [D: mu > $i > $o,C: mu > $i > $o,B: $i,A: $i] :
( ( rel @ B @ ( sk8 @ D @ C @ B ) )
| ( positive @ D @ B )
| ( ( positive
@ ^ [E: mu,F: $i] :
! [G: mu > $i > $o] :
( ( positive @ G @ F )
=> ( G @ E @ F ) )
@ A )
!= ( positive @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[25,23]) ).
thf(1728,plain,
! [B: mu > $i > $o,A: $i] :
( ( rel @ A
@ ( sk8 @ B
@ ^ [C: mu,D: $i] :
! [E: mu > $i > $o] :
( ( positive @ E @ D )
=> ( E @ C @ D ) )
@ A ) )
| ( positive @ B @ A ) ),
inference(pattern_uni,[status(thm)],[1727:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( ^ [E: mu] : ^ [F: $i] : ! [G: mu > $i > $o] : ( ( positive @ G @ F ) => ( G @ E @ F ) ) )),bind(D,$thf( D ))]]) ).
thf(1779,plain,
! [B: mu > $i > $o,A: $i] :
( ( rel @ A
@ ( sk8 @ B
@ ^ [C: mu,D: $i] :
! [E: mu > $i > $o] :
( ( positive @ E @ D )
=> ( E @ C @ D ) )
@ A ) )
| ( positive @ B @ A ) ),
inference(simp,[status(thm)],[1728]) ).
thf(1836,plain,
! [B: mu > $i > $o,A: $i] :
( ( rel @ A
@ ( sk8 @ B
@ ^ [C: mu,D: $i] :
! [E: mu > $i > $o] :
( ( positive @ E @ D )
=> ( E @ C @ D ) )
@ A ) )
| ( ( positive @ B @ A )
!= ( positive
@ ^ [C: mu,D: $i] :
( positive
@ ^ [E: mu,F: $i] : ( sk5 @ E @ D )
@ D )
@ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[1779,565]) ).
thf(1837,plain,
( rel @ sk6
@ ( sk8
@ ^ [A: mu,B: $i] :
( positive
@ ^ [C: mu,D: $i] : ( sk5 @ C @ B )
@ B )
@ ^ [A: mu,B: $i] :
! [C: mu > $i > $o] :
( ( positive @ C @ B )
=> ( C @ A @ B ) )
@ sk6 ) ),
inference(pattern_uni,[status(thm)],[1836:[bind(A,$thf( sk6 )),bind(B,$thf( ^ [C: mu] : ^ [D: $i] : ( positive @ ^ [E: mu] : ^ [F: $i] : ( sk5 @ E @ D ) @ D ) ))]]) ).
thf(339,plain,
! [D: mu > $i > $o,C: mu > $i > $o,B: mu > $i > $o,A: $i] :
( ( C @ sk2 @ sk1 )
| ( D @ sk2 @ sk1 )
| ( positive @ B @ A )
| ( ( positive
@ ^ [E: mu,F: $i] :
~ ( B @ E @ F )
@ A )
!= ( positive
@ ^ [E: mu,F: $i] :
( ( C @ E @ F )
| ( D @ E @ F ) )
@ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[19,116]) ).
thf(391,plain,
! [D: mu > $i > $o,C: mu > $i > $o,B: mu > $i > $o,A: $i] :
( ( C @ sk2 @ sk1 )
| ( D @ sk2 @ sk1 )
| ( positive @ B @ A )
| ( ( ^ [E: mu,F: $i] :
~ ( B @ E @ F ) )
!= ( ^ [E: mu,F: $i] :
( ( C @ E @ F )
| ( D @ E @ F ) ) ) )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[339]) ).
thf(420,plain,
! [C: mu > $i > $o,B: mu > $i > $o,A: mu > $i > $o] :
( ( B @ sk2 @ sk1 )
| ( C @ sk2 @ sk1 )
| ( positive @ A @ sk1 )
| ( ( ^ [D: mu,E: $i] :
~ ( A @ D @ E ) )
!= ( ^ [D: mu,E: $i] :
( ( B @ D @ E )
| ( C @ D @ E ) ) ) ) ),
inference(simp,[status(thm)],[391]) ).
thf(682,plain,
! [E: mu > $i > $o,D: mu > $i > $o,C: mu > $i > $o,B: mu > $i > $o,A: mu > $i > $o] :
( ( B @ sk2 @ sk1 )
| ( C @ sk2 @ sk1 )
| ( ( ^ [F: mu,G: $i] :
~ ( A @ F @ G ) )
!= ( ^ [F: mu,G: $i] :
( ( B @ F @ G )
| ( C @ F @ G ) ) ) )
| ( D @ sk2 @ sk1 )
| ( E @ sk2 @ sk1 )
| ( ( positive @ A @ sk1 )
!= ( positive
@ ^ [F: mu,G: $i] :
( ( D @ F @ G )
| ( E @ F @ G ) )
@ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[420,116]) ).
thf(683,plain,
! [D: mu > $i > $o,C: mu > $i > $o,B: mu > $i > $o,A: mu > $i > $o] :
( ( A @ sk2 @ sk1 )
| ( B @ sk2 @ sk1 )
| ( ( ^ [E: mu,F: $i] :
~ ( ( C @ E @ F )
| ( D @ E @ F ) ) )
!= ( ^ [E: mu,F: $i] :
( ( A @ E @ F )
| ( B @ E @ F ) ) ) )
| ( C @ sk2 @ sk1 )
| ( D @ sk2 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[682:[bind(A,$thf( ^ [H: mu] : ^ [I: $i] : ( ( F @ H @ I ) | ( G @ H @ I ) ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( F )),bind(E,$thf( G ))]]) ).
thf(842,plain,
! [D: mu > $i > $o,C: mu > $i > $o,B: mu > $i > $o,A: mu > $i > $o] :
( ( A @ sk2 @ sk1 )
| ( B @ sk2 @ sk1 )
| ( ( ^ [E: mu,F: $i] :
~ ( ( C @ E @ F )
| ( D @ E @ F ) ) )
!= ( ^ [E: mu,F: $i] :
( ( A @ E @ F )
| ( B @ E @ F ) ) ) )
| ( C @ sk2 @ sk1 )
| ( D @ sk2 @ sk1 ) ),
inference(simp,[status(thm)],[683]) ).
thf(3405,plain,
( ( positive
@ ^ [A: mu] :
( positive
@ ^ [B: mu,C: $i] : $false )
@ sk1 )
!= ( positive
@ ^ [A: mu,B: $i] : $true
@ sk1 ) ),
inference(paramod_ordered,[status(thm)],[3006,133]) ).
thf(3487,plain,
( ( ( ^ [A: mu] :
( positive
@ ^ [B: mu,C: $i] : $false ) )
!= ( ^ [A: mu,B: $i] : $true ) )
| ( sk1 != sk1 ) ),
inference(simp,[status(thm)],[3405]) ).
thf(3501,plain,
( ( ^ [A: mu] :
( positive
@ ^ [B: mu,C: $i] : $false ) )
!= ( ^ [A: mu,B: $i] : $true ) ),
inference(simp,[status(thm)],[3487]) ).
thf(3518,plain,
~ ( positive
@ ^ [A: mu,B: $i] : $false
@ sk69 ),
inference(func_ext,[status(esa)],[3501]) ).
thf(126,plain,
! [A: $i] :
( ( positive
@ ^ [B: mu,C: $i] :
! [D: mu > $i > $o] :
( ( positive @ D @ C )
=> ( D @ B @ C ) )
@ A )
!= ( positive
@ ^ [B: mu,C: $i] : $false
@ sk1 ) ),
inference(paramod_ordered,[status(thm)],[25,119]) ).
thf(137,plain,
! [A: $i] :
( ( ( ^ [B: mu,C: $i] :
! [D: mu > $i > $o] :
( ( positive @ D @ C )
=> ( D @ B @ C ) ) )
!= ( ^ [B: mu,C: $i] : $false ) )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[126]) ).
thf(141,plain,
( ( ^ [A: mu,B: $i] :
! [C: mu > $i > $o] :
( ( positive @ C @ B )
=> ( C @ A @ B ) ) )
!= ( ^ [A: mu,B: $i] : $false ) ),
inference(simp,[status(thm)],[137]) ).
thf(3097,plain,
( ( positive @ sk5 @ sk1 )
!= ( positive
@ ^ [A: mu] :
( positive
@ ^ [B: mu] :
( positive
@ ^ [C: mu,D: $i] : $false ) )
@ sk1 ) ),
inference(paramod_ordered,[status(thm)],[2993,155]) ).
thf(3111,plain,
( ( sk5
!= ( ^ [A: mu] :
( positive
@ ^ [B: mu] :
( positive
@ ^ [C: mu,D: $i] : $false ) ) ) )
| ( sk1 != sk1 ) ),
inference(simp,[status(thm)],[3097]) ).
thf(3147,plain,
( sk5
!= ( ^ [A: mu] :
( positive
@ ^ [B: mu] :
( positive
@ ^ [C: mu,D: $i] : $false ) ) ) ),
inference(simp,[status(thm)],[3111]) ).
thf(1856,plain,
! [B: mu > $i > $o,A: $i] :
( ( rel @ A
@ ( sk8 @ B
@ ^ [C: mu,D: $i] :
! [E: mu > $i > $o] :
( ( positive @ E @ D )
=> ( E @ C @ D ) )
@ A ) )
| ( ( positive @ B @ A )
!= ( positive @ sk5 @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[1779,267]) ).
thf(1857,plain,
( rel @ sk6
@ ( sk8 @ sk5
@ ^ [A: mu,B: $i] :
! [C: mu > $i > $o] :
( ( positive @ C @ B )
=> ( C @ A @ B ) )
@ sk6 ) ),
inference(pattern_uni,[status(thm)],[1856:[bind(A,$thf( sk6 )),bind(B,$thf( sk5 ))]]) ).
thf(1073,plain,
! [A: mu > $i > $o] :
( ~ ( positive @ A @ sk6 )
| ( ( A @ sk7 @ sk6 )
!= ( positive
@ ^ [B: mu] :
( positive
@ ^ [C: mu] : ( sk5 @ B ) )
@ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[193,585]) ).
thf(1086,plain,
~ ( positive
@ ^ [A: mu] :
( positive
@ ^ [B: mu] :
( positive
@ ^ [C: mu] : ( sk5 @ B ) ) )
@ sk6 ),
inference(pre_uni,[status(thm)],[1073:[bind(A,$thf( ^ [B: mu] : ( positive @ ^ [C: mu] : ( positive @ ^ [D: mu] : ( sk5 @ C ) ) ) ))]]) ).
thf(2992,plain,
( positive
@ ^ [A: mu] : ( sk5 @ sk2 )
@ sk1 ),
inference(pre_uni,[status(thm)],[2863:[bind(A,$thf( ^ [B: mu] : ( sk5 @ sk2 ) ))]]) ).
thf(3887,plain,
( ( positive
@ ^ [A: mu] : ( sk5 @ sk2 )
@ sk1 )
!= ( positive
@ ^ [A: mu,B: $i] : $false
@ sk1 ) ),
inference(paramod_ordered,[status(thm)],[2992,119]) ).
thf(3950,plain,
( ( ( ^ [A: mu] : ( sk5 @ sk2 ) )
!= ( ^ [A: mu,B: $i] : $false ) )
| ( sk1 != sk1 ) ),
inference(simp,[status(thm)],[3887]) ).
thf(3982,plain,
( ( ^ [A: mu] : ( sk5 @ sk2 ) )
!= ( ^ [A: mu,B: $i] : $false ) ),
inference(simp,[status(thm)],[3950]) ).
thf(3985,plain,
sk5 @ sk2 @ sk79,
inference(func_ext,[status(esa)],[3982]) ).
thf(4605,plain,
( ( positive
@ ^ [A: mu,B: $i] :
( positive
@ ^ [C: mu,D: $i] : ( sk5 @ C @ B )
@ B )
@ sk1 )
!= ( positive
@ ^ [A: mu,B: $i] : $false
@ sk1 ) ),
inference(paramod_ordered,[status(thm)],[3836,119]) ).
thf(4638,plain,
( ( ( ^ [A: mu,B: $i] :
( positive
@ ^ [C: mu,D: $i] : ( sk5 @ C @ B )
@ B ) )
!= ( ^ [A: mu,B: $i] : $false ) )
| ( sk1 != sk1 ) ),
inference(simp,[status(thm)],[4605]) ).
thf(4657,plain,
( ( ^ [A: mu,B: $i] :
( positive
@ ^ [C: mu,D: $i] : ( sk5 @ C @ B )
@ B ) )
!= ( ^ [A: mu,B: $i] : $false ) ),
inference(simp,[status(thm)],[4638]) ).
thf(41,plain,
! [C: $i,B: mu > $i > $o,A: $i] :
( ~ ( positive @ B @ A )
| ( ( positive
@ ^ [D: mu,E: $i] :
~ ( B @ D @ E )
@ A )
!= ( positive
@ ^ [D: mu,E: $i] :
! [F: mu > $i > $o] :
( ( ( F @ D @ E )
& ! [G: mu > $i > $o] :
( ( G @ D @ E )
=> ! [H: $i] :
( ~ ( rel @ E @ H )
| ! [I: mu] :
( ( F @ I @ H )
=> ( G @ I @ H ) ) ) ) )
=> ! [G: $i] :
( ~ ( rel @ E @ G )
| ? [H: mu] : ( F @ H @ G ) ) )
@ C ) ) ),
inference(paramod_ordered,[status(thm)],[19,29]) ).
thf(43,plain,
! [C: $i,B: mu > $i > $o,A: $i] :
( ~ ( positive @ B @ A )
| ( ( ^ [D: mu,E: $i] :
~ ( B @ D @ E ) )
!= ( ^ [D: mu,E: $i] :
! [F: mu > $i > $o] :
( ( ( F @ D @ E )
& ! [G: mu > $i > $o] :
( ( G @ D @ E )
=> ! [H: $i] :
( ~ ( rel @ E @ H )
| ! [I: mu] :
( ( F @ I @ H )
=> ( G @ I @ H ) ) ) ) )
=> ! [G: $i] :
( ~ ( rel @ E @ G )
| ? [H: mu] : ( F @ H @ G ) ) ) ) )
| ( A != C ) ),
inference(simp,[status(thm)],[41]) ).
thf(45,plain,
! [B: $i,A: mu > $i > $o] :
( ~ ( positive @ A @ B )
| ( ( ^ [C: mu,D: $i] :
~ ( A @ C @ D ) )
!= ( ^ [C: mu,D: $i] :
! [E: mu > $i > $o] :
( ( ( E @ C @ D )
& ! [F: mu > $i > $o] :
( ( F @ C @ D )
=> ! [G: $i] :
( ~ ( rel @ D @ G )
| ! [H: mu] :
( ( E @ H @ G )
=> ( F @ H @ G ) ) ) ) )
=> ! [F: $i] :
( ~ ( rel @ D @ F )
| ? [G: mu] : ( E @ G @ F ) ) ) ) ) ),
inference(simp,[status(thm)],[43]) ).
thf(584,plain,
~ ( positive
@ ^ [A: mu] :
( positive
@ ^ [B: mu] : ( sk5 @ sk7 ) )
@ sk6 ),
inference(pre_uni,[status(thm)],[573:[bind(A,$thf( ^ [B: mu] : ( positive @ ^ [C: mu] : ( sk5 @ sk7 ) ) ))]]) ).
thf(2218,plain,
! [A: mu > $i > $o] :
( ~ ( positive @ A @ sk6 )
| ( ( A @ sk7 @ sk6 )
!= ( positive
@ ^ [B: mu] :
( positive
@ ^ [C: mu] : ( sk5 @ sk7 ) )
@ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[193,584]) ).
thf(2253,plain,
~ ( positive
@ ^ [A: mu] :
( positive
@ ^ [B: mu] :
( positive
@ ^ [C: mu] : ( sk5 @ A ) ) )
@ sk6 ),
inference(pre_uni,[status(thm)],[2218:[bind(A,$thf( ^ [B: mu] : ( positive @ ^ [C: mu] : ( positive @ ^ [D: mu] : ( sk5 @ B ) ) ) ))]]) ).
thf(1832,plain,
! [B: mu > $i > $o,A: $i] :
( ( rel @ A
@ ( sk8 @ B
@ ^ [C: mu,D: $i] :
! [E: mu > $i > $o] :
( ( positive @ E @ D )
=> ( E @ C @ D ) )
@ A ) )
| ( ( positive @ B @ A )
!= ( positive
@ ^ [C: mu,D: $i] : $false
@ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[1779,119]) ).
thf(1833,plain,
( rel @ sk1
@ ( sk8
@ ^ [A: mu,B: $i] : $false
@ ^ [A: mu,B: $i] :
! [C: mu > $i > $o] :
( ( positive @ C @ B )
=> ( C @ A @ B ) )
@ sk1 ) ),
inference(pattern_uni,[status(thm)],[1832:[bind(A,$thf( sk1 )),bind(B,$thf( ^ [C: mu] : ^ [D: $i] : $false ))]]) ).
thf(22,plain,
! [C: mu > $i > $o,B: mu > $i > $o,A: $i] :
( ~ ( positive @ B @ A )
| ( B @ ( sk9 @ C @ B @ A ) @ ( sk8 @ C @ B @ A ) )
| ( positive @ C @ A ) ),
inference(cnf,[status(esa)],[20]) ).
thf(40,plain,
! [C: mu > $i > $o,B: $i,A: $i] :
( ~ ( positive @ C @ B )
| ( ( positive
@ ^ [D: mu,E: $i] :
! [F: mu > $i > $o] :
( ( ( F @ D @ E )
& ! [G: mu > $i > $o] :
( ( G @ D @ E )
=> ! [H: $i] :
( ~ ( rel @ E @ H )
| ! [I: mu] :
( ( F @ I @ H )
=> ( G @ I @ H ) ) ) ) )
=> ! [G: $i] :
( ~ ( rel @ E @ G )
| ? [H: mu] : ( F @ H @ G ) ) )
@ A )
!= ( positive
@ ^ [D: mu,E: $i] :
~ ( C @ D @ E )
@ B ) ) ),
inference(paramod_ordered,[status(thm)],[29,19]) ).
thf(42,plain,
! [C: mu > $i > $o,B: $i,A: $i] :
( ~ ( positive @ C @ B )
| ( ( ^ [D: mu,E: $i] :
! [F: mu > $i > $o] :
( ( ( F @ D @ E )
& ! [G: mu > $i > $o] :
( ( G @ D @ E )
=> ! [H: $i] :
( ~ ( rel @ E @ H )
| ! [I: mu] :
( ( F @ I @ H )
=> ( G @ I @ H ) ) ) ) )
=> ! [G: $i] :
( ~ ( rel @ E @ G )
| ? [H: mu] : ( F @ H @ G ) ) ) )
!= ( ^ [D: mu,E: $i] :
~ ( C @ D @ E ) ) )
| ( A != B ) ),
inference(simp,[status(thm)],[40]) ).
thf(44,plain,
! [B: mu > $i > $o,A: $i] :
( ~ ( positive @ B @ A )
| ( ( ^ [C: mu,D: $i] :
! [E: mu > $i > $o] :
( ( ( E @ C @ D )
& ! [F: mu > $i > $o] :
( ( F @ C @ D )
=> ! [G: $i] :
( ~ ( rel @ D @ G )
| ! [H: mu] :
( ( E @ H @ G )
=> ( F @ H @ G ) ) ) ) )
=> ! [F: $i] :
( ~ ( rel @ D @ F )
| ? [G: mu] : ( E @ G @ F ) ) ) )
!= ( ^ [C: mu,D: $i] :
~ ( B @ C @ D ) ) ) ),
inference(simp,[status(thm)],[42]) ).
thf(3663,plain,
( ( positive
@ ^ [A: mu,B: $i] : ( rel @ B @ sk6 )
@ sk1 )
!= ( positive
@ ^ [A: mu,B: $i] : $false
@ sk1 ) ),
inference(paramod_ordered,[status(thm)],[2950,119]) ).
thf(3732,plain,
( ( ( ^ [A: mu,B: $i] : ( rel @ B @ sk6 ) )
!= ( ^ [A: mu,B: $i] : $false ) )
| ( sk1 != sk1 ) ),
inference(simp,[status(thm)],[3663]) ).
thf(3751,plain,
( ( ^ [A: mu,B: $i] : ( rel @ B @ sk6 ) )
!= ( ^ [A: mu,B: $i] : $false ) ),
inference(simp,[status(thm)],[3732]) ).
thf(3758,plain,
rel @ sk73 @ sk6,
inference(func_ext,[status(esa)],[3751]) ).
thf(6,axiom,
( mvalid
@ ( mforall_indset
@ ^ [A: mu > $i > $o] : ( mimplies @ ( positive @ A ) @ ( mbox @ ( positive @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axA4) ).
thf(26,plain,
! [A: $i,B: mu > $i > $o] :
( ( positive @ B @ A )
=> ! [C: $i] :
( ~ ( rel @ A @ C )
| ( positive @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(27,plain,
! [C: $i,B: mu > $i > $o,A: $i] :
( ~ ( positive @ B @ A )
| ~ ( rel @ A @ C )
| ( positive @ B @ C ) ),
inference(cnf,[status(esa)],[26]) ).
thf(3383,plain,
sk5 @ sk64 @ sk65,
inference(func_ext,[status(esa)],[3148]) ).
thf(3647,plain,
( ( sk5 @ sk64 @ sk65 )
!= ( sk5 @ sk7 @ sk6 ) ),
inference(paramod_ordered,[status(thm)],[3383,189]) ).
thf(3651,plain,
( ( sk64 != sk7 )
| ( sk65 != sk6 ) ),
inference(simp,[status(thm)],[3647]) ).
thf(143,plain,
! [A: $i] :
( ( positive
@ ^ [B: mu,C: $i] :
! [D: mu > $i > $o] :
( ( positive @ D @ C )
=> ( D @ B @ C ) )
@ A )
!= ( positive
@ ^ [B: mu] :
( positive
@ ^ [C: mu,D: $i] : $false )
@ sk1 ) ),
inference(paramod_ordered,[status(thm)],[25,133]) ).
thf(153,plain,
! [A: $i] :
( ( ( ^ [B: mu,C: $i] :
! [D: mu > $i > $o] :
( ( positive @ D @ C )
=> ( D @ B @ C ) ) )
!= ( ^ [B: mu] :
( positive
@ ^ [C: mu,D: $i] : $false ) ) )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[143]) ).
thf(159,plain,
( ( ^ [A: mu,B: $i] :
! [C: mu > $i > $o] :
( ( positive @ C @ B )
=> ( C @ A @ B ) ) )
!= ( ^ [A: mu] :
( positive
@ ^ [B: mu,C: $i] : $false ) ) ),
inference(simp,[status(thm)],[153]) ).
thf(1852,plain,
! [B: mu > $i > $o,A: $i] :
( ( rel @ A
@ ( sk8 @ B
@ ^ [C: mu,D: $i] :
! [E: mu > $i > $o] :
( ( positive @ E @ D )
=> ( E @ C @ D ) )
@ A ) )
| ( ( positive @ B @ A )
!= ( positive
@ ^ [C: mu,D: $i] : $false
@ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[1779,271]) ).
thf(1853,plain,
( rel @ sk6
@ ( sk8
@ ^ [A: mu,B: $i] : $false
@ ^ [A: mu,B: $i] :
! [C: mu > $i > $o] :
( ( positive @ C @ B )
=> ( C @ A @ B ) )
@ sk6 ) ),
inference(pattern_uni,[status(thm)],[1852:[bind(A,$thf( sk6 )),bind(B,$thf( ^ [C: mu] : ^ [D: $i] : $false ))]]) ).
thf(595,plain,
! [A: mu > $i > $o] :
( ~ ( positive @ A @ sk6 )
| ( ( A @ sk7 @ sk6 )
!= ( positive
@ ^ [B: mu] :
( positive
@ ^ [C: mu,D: $i] : $false )
@ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[193,284]) ).
thf(616,plain,
~ ( positive
@ ^ [A: mu] :
( positive
@ ^ [B: mu] :
( positive
@ ^ [C: mu,D: $i] : $false ) )
@ sk6 ),
inference(pre_uni,[status(thm)],[595:[bind(A,$thf( ^ [B: mu] : ( positive @ ^ [C: mu] : ( positive @ ^ [D: mu] : ^ [E: $i] : $false ) ) ))]]) ).
thf(623,plain,
! [A: mu > $i > $o] :
( ~ ( positive @ A @ sk6 )
| ( ( A @ sk7 @ sk6 )
!= ( positive
@ ^ [B: mu] : ( positive @ sk5 )
@ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[193,299]) ).
thf(631,plain,
~ ( positive
@ ^ [A: mu] :
( positive
@ ^ [B: mu] : ( positive @ sk5 ) )
@ sk6 ),
inference(pre_uni,[status(thm)],[623:[bind(A,$thf( ^ [B: mu] : ( positive @ ^ [C: mu] : ( positive @ sk5 ) ) ))]]) ).
thf(3785,plain,
( ( positive
@ ^ [A: mu,B: $i] : ( sk5 @ A @ sk1 )
@ sk1 )
!= ( positive
@ ^ [A: mu] :
( positive
@ ^ [B: mu,C: $i] : $false )
@ sk1 ) ),
inference(paramod_ordered,[status(thm)],[2991,133]) ).
thf(3851,plain,
( ( ( ^ [A: mu,B: $i] : ( sk5 @ A @ sk1 ) )
!= ( ^ [A: mu] :
( positive
@ ^ [B: mu,C: $i] : $false ) ) )
| ( sk1 != sk1 ) ),
inference(simp,[status(thm)],[3785]) ).
thf(3861,plain,
( ( ^ [A: mu,B: $i] : ( sk5 @ A @ sk1 ) )
!= ( ^ [A: mu] :
( positive
@ ^ [B: mu,C: $i] : $false ) ) ),
inference(simp,[status(thm)],[3851]) ).
thf(563,plain,
~ ( positive
@ ^ [A: mu,B: $i] :
( positive
@ ^ [C: mu,D: $i] : ( sk5 @ C @ B )
@ sk6 )
@ sk6 ),
inference(pre_uni,[status(thm)],[552:[bind(A,$thf( ^ [B: mu] : ^ [C: $i] : ( positive @ ^ [D: mu] : ^ [E: $i] : ( sk5 @ D @ C ) @ sk6 ) ))]]) ).
thf(3100,plain,
( ( positive @ sk5 @ sk6 )
!= ( positive @ sk5 @ sk1 ) ),
inference(paramod_ordered,[status(thm)],[2993,267]) ).
thf(3139,plain,
( ( sk5 != sk5 )
| ( sk6 != sk1 ) ),
inference(simp,[status(thm)],[3100]) ).
thf(3142,plain,
sk6 != sk1,
inference(simp,[status(thm)],[3139]) ).
thf(564,plain,
~ ( positive
@ ^ [A: mu] :
( positive
@ ^ [B: mu,C: $i] : ( sk5 @ B @ sk6 ) )
@ sk6 ),
inference(pre_uni,[status(thm)],[552:[bind(A,$thf( ^ [B: mu] : ( positive @ ^ [C: mu] : ^ [D: $i] : ( sk5 @ C @ sk6 ) ) ))]]) ).
thf(2080,plain,
! [A: mu > $i > $o] :
( ~ ( positive @ A @ sk6 )
| ( ( A @ sk7 @ sk6 )
!= ( positive
@ ^ [B: mu] :
( positive
@ ^ [C: mu,D: $i] : ( sk5 @ C @ sk6 ) )
@ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[193,564]) ).
thf(2107,plain,
~ ( positive
@ ^ [A: mu,B: $i] :
( positive
@ ^ [C: mu] :
( positive
@ ^ [D: mu,E: $i] : ( sk5 @ D @ B ) )
@ B )
@ sk6 ),
inference(pre_uni,[status(thm)],[2080:[bind(A,$thf( ^ [B: mu] : ^ [C: $i] : ( positive @ ^ [D: mu] : ( positive @ ^ [E: mu] : ^ [F: $i] : ( sk5 @ E @ C ) ) @ C ) ))]]) ).
thf(4246,plain,
( ( positive
@ ^ [A: mu] :
( positive
@ ^ [B: mu,C: $i] : $true )
@ sk1 )
!= ( positive
@ ^ [A: mu,B: $i] : $false
@ sk1 ) ),
inference(paramod_ordered,[status(thm)],[3470,119]) ).
thf(4292,plain,
( ( ( ^ [A: mu] :
( positive
@ ^ [B: mu,C: $i] : $true ) )
!= ( ^ [A: mu,B: $i] : $false ) )
| ( sk1 != sk1 ) ),
inference(simp,[status(thm)],[4246]) ).
thf(4319,plain,
( ( ^ [A: mu] :
( positive
@ ^ [B: mu,C: $i] : $true ) )
!= ( ^ [A: mu,B: $i] : $false ) ),
inference(simp,[status(thm)],[4292]) ).
thf(3109,plain,
! [A: mu > $i > $o] :
( ( positive @ A @ sk1 )
| ( ( positive @ sk5 @ sk1 )
!= ( A @ sk2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[2993,111]) ).
thf(3129,plain,
( positive
@ ^ [A: mu] : ( positive @ sk5 )
@ sk1 ),
inference(pre_uni,[status(thm)],[3109:[bind(A,$thf( ^ [B: mu] : ( positive @ sk5 ) ))]]) ).
thf(4324,plain,
( positive
@ ^ [A: mu,B: $i] : $true
@ sk83 ),
inference(func_ext,[status(esa)],[4319]) ).
thf(49,plain,
! [C: $i,B: mu > $i > $o,A: $i] :
( ( ( ^ [D: mu,E: $i] :
~ ( B @ D @ E ) )
!= ( ^ [D: mu,E: $i] :
! [F: mu > $i > $o] :
( ( positive @ F @ E )
=> ( F @ D @ E ) ) ) )
| ( ( positive
@ ^ [D: mu,E: $i] :
! [F: mu > $i > $o] :
( ( ( F @ D @ E )
& ! [G: mu > $i > $o] :
( ( G @ D @ E )
=> ! [H: $i] :
( ~ ( rel @ E @ H )
| ! [I: mu] :
( ( F @ I @ H )
=> ( G @ I @ H ) ) ) ) )
=> ! [G: $i] :
( ~ ( rel @ E @ G )
| ? [H: mu] : ( F @ H @ G ) ) )
@ A )
!= ( positive @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[29,36]) ).
thf(50,plain,
( ( ^ [A: mu,B: $i] :
~ ! [C: mu > $i > $o] :
( ( ( C @ A @ B )
& ! [D: mu > $i > $o] :
( ( D @ A @ B )
=> ! [E: $i] :
( ~ ( rel @ B @ E )
| ! [F: mu] :
( ( C @ F @ E )
=> ( D @ F @ E ) ) ) ) )
=> ! [D: $i] :
( ~ ( rel @ B @ D )
| ? [E: mu] : ( C @ E @ D ) ) ) )
!= ( ^ [A: mu,B: $i] :
! [C: mu > $i > $o] :
( ( positive @ C @ B )
=> ( C @ A @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[49:[bind(A,$thf( A )),bind(B,$thf( ^ [D: mu] : ^ [E: $i] : ! [F: mu > $i > $o] : ( ( ( F @ D @ E ) & ! [G: mu > $i > $o] : ( ( G @ D @ E ) => ! [H: $i] : ( ~ ( rel @ E @ H ) | ! [I: mu] : ( ( F @ I @ H ) => ( G @ I @ H ) ) ) ) ) => ! [G: $i] : ( ~ ( rel @ E @ G ) | ? [H: mu] : ( F @ H @ G ) ) ) )),bind(C,$thf( A ))]]) ).
thf(2030,plain,
! [A: mu > $i > $o] :
( ~ ( positive @ A @ sk6 )
| ( ( A @ sk7 @ sk6 )
!= ( positive
@ ^ [B: mu,C: $i] :
( positive
@ ^ [D: mu,E: $i] : ( sk5 @ D @ C )
@ sk6 )
@ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[193,563]) ).
thf(2056,plain,
~ ( positive
@ ^ [A: mu,B: $i] :
( positive
@ ^ [C: mu,D: $i] :
( positive
@ ^ [E: mu,F: $i] : ( sk5 @ E @ D )
@ B )
@ B )
@ sk6 ),
inference(pre_uni,[status(thm)],[2030:[bind(A,$thf( ^ [B: mu] : ^ [C: $i] : ( positive @ ^ [D: mu] : ^ [E: $i] : ( positive @ ^ [F: mu] : ^ [G: $i] : ( sk5 @ F @ E ) @ C ) @ C ) ))]]) ).
thf(4001,plain,
( ( positive
@ ^ [A: mu] : ( positive @ sk5 )
@ sk1 )
!= ( positive
@ ^ [A: mu,B: $i] : $false
@ sk1 ) ),
inference(paramod_ordered,[status(thm)],[3129,119]) ).
thf(4069,plain,
( ( ( ^ [A: mu] : ( positive @ sk5 ) )
!= ( ^ [A: mu,B: $i] : $false ) )
| ( sk1 != sk1 ) ),
inference(simp,[status(thm)],[4001]) ).
thf(4089,plain,
( ( ^ [A: mu] : ( positive @ sk5 ) )
!= ( ^ [A: mu,B: $i] : $false ) ),
inference(simp,[status(thm)],[4069]) ).
thf(4098,plain,
positive @ sk5 @ sk81,
inference(func_ext,[status(esa)],[4089]) ).
thf(4136,plain,
( ( positive @ sk5 @ sk81 )
!= ( positive @ sk5 @ sk6 ) ),
inference(paramod_ordered,[status(thm)],[4098,267]) ).
thf(4158,plain,
( ( sk5 != sk5 )
| ( sk81 != sk6 ) ),
inference(simp,[status(thm)],[4136]) ).
thf(4193,plain,
sk81 != sk6,
inference(simp,[status(thm)],[4158]) ).
thf(1043,plain,
! [A: mu > $i > $o] :
( ~ ( positive @ A @ sk6 )
| ( ( A @ sk7 @ sk6 )
!= ( positive
@ ^ [B: mu,C: $i] :
( positive
@ ^ [D: mu,E: $i] : ( sk5 @ D @ C )
@ C )
@ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[193,565]) ).
thf(1065,plain,
~ ( positive
@ ^ [A: mu] :
( positive
@ ^ [B: mu,C: $i] :
( positive
@ ^ [D: mu,E: $i] : ( sk5 @ D @ C )
@ C ) )
@ sk6 ),
inference(pre_uni,[status(thm)],[1043:[bind(A,$thf( ^ [B: mu] : ( positive @ ^ [C: mu] : ^ [D: $i] : ( positive @ ^ [E: mu] : ^ [F: $i] : ( sk5 @ E @ D ) @ D ) ) ))]]) ).
thf(1828,plain,
! [B: mu > $i > $o,A: $i] :
( ( rel @ A
@ ( sk8 @ B
@ ^ [C: mu,D: $i] :
! [E: mu > $i > $o] :
( ( positive @ E @ D )
=> ( E @ C @ D ) )
@ A ) )
| ( ( positive @ B @ A )
!= ( positive
@ ^ [C: mu] :
( positive
@ ^ [D: mu] : ( sk5 @ C ) )
@ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[1779,585]) ).
thf(1829,plain,
( rel @ sk6
@ ( sk8
@ ^ [A: mu] :
( positive
@ ^ [B: mu] : ( sk5 @ A ) )
@ ^ [A: mu,B: $i] :
! [C: mu > $i > $o] :
( ( positive @ C @ B )
=> ( C @ A @ B ) )
@ sk6 ) ),
inference(pattern_uni,[status(thm)],[1828:[bind(A,$thf( sk6 )),bind(B,$thf( ^ [C: mu] : ( positive @ ^ [D: mu] : ( sk5 @ C ) ) ))]]) ).
thf(5942,plain,
$false,
inference(e,[status(thm)],[3153,3148,2164,193,569,4763,185,3836,3502,24,565,37,25,638,189,20,46,93,284,3470,1100,29,2950,591,4751,1072,116,265,89,133,302,28,3752,21,1837,583,842,3518,169,141,420,3147,1857,1086,266,1779,3985,4657,45,17,2253,3871,584,1833,22,44,3758,2991,27,3751,3651,159,187,1853,616,271,631,3006,3861,155,563,299,3142,267,3881,2107,4319,3129,4324,50,585,2056,2992,4089,26,3383,3501,3859,23,8,119,4098,36,19,564,3982,4193,1065,1829,15,111,2993]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : PHI004^1 : TPTP v8.2.0. Released v6.1.0.
% 0.11/0.14 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n025.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat May 18 14:47:39 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.98/1.02 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.58/1.29 % [INFO] Parsing done (266ms).
% 1.58/1.31 % [INFO] Running in sequential loop mode.
% 2.35/1.70 % [INFO] eprover registered as external prover.
% 2.35/1.70 % [INFO] cvc4 registered as external prover.
% 2.35/1.71 % [INFO] Scanning for conjecture ...
% 2.61/1.86 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 2.61/1.90 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 2.61/1.91 % [INFO] Problem is higher-order (TPTP THF).
% 2.88/1.91 % [INFO] Type checking passed.
% 2.88/1.92 % [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 ...
% 121.48/23.56 % External prover 'e' found a proof!
% 121.48/23.56 % [INFO] Killing All external provers ...
% 121.48/23.56 % Time passed: 23057ms (effective reasoning time: 22250ms)
% 121.48/23.56 % 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)>
% 121.48/23.56 % Axioms used in derivation (5): axA3, axA1, axA5, axA2, axA4
% 121.48/23.56 % No. of inferences in proof: 225
% 121.48/23.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 23057 ms resp. 22250 ms w/o parsing
% 121.48/23.67 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 121.48/23.67 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------