TSTP Solution File: PHI007^5 by Leo-III---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : PHI007^5 : TPTP v8.2.0. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n003.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 02:18:27 EDT 2024
% Result : Theorem 92.06s 26.95s
% Output : Refutation 92.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 70
% Syntax : Number of formulae : 418 ( 92 unt; 60 typ; 0 def)
% Number of atoms : 1418 ( 310 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 3884 ( 672 ~; 303 |; 2 &;2594 @)
% ( 0 <=>; 313 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 624 ( 624 >; 0 *; 0 +; 0 <<)
% Number of symbols : 62 ( 59 usr; 43 con; 0-3 aty)
% Number of variables : 1210 ( 502 ^ 621 !; 87 ?;1210 :)
% Comments :
%------------------------------------------------------------------------------
thf(qML_mu_type,type,
qML_mu: $tType ).
thf(qML_i_type,type,
qML_i: $tType ).
thf(inconsistency_G_type,type,
inconsistency_G: qML_mu > qML_i > $o ).
thf(incons1905966852QML_mu_type,type,
incons1905966852QML_mu: qML_mu > qML_i > $o ).
thf(inconsistency_P_type,type,
inconsistency_P: ( qML_mu > qML_i > $o ) > qML_i > $o ).
thf(incons1389517216QML_mu_type,type,
incons1389517216QML_mu: ( qML_mu > qML_i > $o ) > qML_mu > qML_i > $o ).
thf(qML_r_type,type,
qML_r: qML_i > qML_i > $o ).
thf(sk1_type,type,
sk1: ( qML_mu > qML_i > $o ) > ( qML_mu > qML_i > $o ) > qML_i > qML_i ).
thf(sk3_type,type,
sk3: qML_mu ).
thf(sk4_type,type,
sk4: qML_i ).
thf(sk5_type,type,
sk5: qML_mu ).
thf(sk6_type,type,
sk6: qML_i ).
thf(sk7_type,type,
sk7: qML_mu ).
thf(sk8_type,type,
sk8: qML_i ).
thf(sk9_type,type,
sk9: qML_mu ).
thf(sk10_type,type,
sk10: qML_i ).
thf(sk11_type,type,
sk11: qML_mu > qML_i > $o ).
thf(sk12_type,type,
sk12: qML_mu > qML_i > $o ).
thf(sk13_type,type,
sk13: qML_mu ).
thf(sk14_type,type,
sk14: qML_i ).
thf(sk15_type,type,
sk15: qML_mu ).
thf(sk16_type,type,
sk16: qML_i ).
thf(sk17_type,type,
sk17: qML_mu > qML_i > $o ).
thf(sk20_type,type,
sk20: qML_mu > qML_i > $o ).
thf(sk21_type,type,
sk21: qML_mu ).
thf(sk22_type,type,
sk22: qML_i ).
thf(sk23_type,type,
sk23: qML_mu ).
thf(sk24_type,type,
sk24: qML_i ).
thf(sk26_type,type,
sk26: qML_mu ).
thf(sk27_type,type,
sk27: qML_i ).
thf(sk28_type,type,
sk28: qML_mu ).
thf(sk29_type,type,
sk29: qML_i ).
thf(sk30_type,type,
sk30: qML_mu ).
thf(sk31_type,type,
sk31: qML_i ).
thf(sk34_type,type,
sk34: qML_mu ).
thf(sk35_type,type,
sk35: qML_i ).
thf(sk37_type,type,
sk37: qML_i ).
thf(sk43_type,type,
sk43: qML_i ).
thf(sk55_type,type,
sk55: qML_i ).
thf(sk59_type,type,
sk59: qML_i ).
thf(sk62_type,type,
sk62: qML_mu > qML_i > $o ).
thf(sk64_type,type,
sk64: qML_mu > qML_i > $o ).
thf(sk67_type,type,
sk67: qML_mu > qML_i > $o ).
thf(sk76_type,type,
sk76: qML_i ).
thf(sk89_type,type,
sk89: qML_i ).
thf(sk120_type,type,
sk120: qML_i ).
thf(sk122_type,type,
sk122: qML_i ).
thf(sk126_type,type,
sk126: qML_mu > qML_i > $o ).
thf(sk132_type,type,
sk132: qML_mu > qML_i > $o ).
thf(sk133_type,type,
sk133: qML_mu > qML_i > $o ).
thf(sk134_type,type,
sk134: qML_mu > qML_i > $o ).
thf(sk140_type,type,
sk140: qML_mu > qML_i > $o ).
thf(sk144_type,type,
sk144: qML_i ).
thf(sk149_type,type,
sk149: qML_i ).
thf(sk350_type,type,
sk350: qML_mu ).
thf(sk351_type,type,
sk351: qML_i ).
thf(sk352_type,type,
sk352: qML_mu ).
thf(sk353_type,type,
sk353: qML_i ).
thf(sk354_type,type,
sk354: qML_mu ).
thf(sk355_type,type,
sk355: qML_i ).
thf(9,axiom,
( inconsistency_G
= ( ^ [A: qML_mu,B: qML_i] :
! [C: qML_mu > qML_i > $o] :
( ( inconsistency_P @ C @ B )
=> ( C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_G__def) ).
thf(27,plain,
( inconsistency_G
= ( ^ [A: qML_mu,B: qML_i] :
! [C: qML_mu > qML_i > $o] :
( ( inconsistency_P @ C @ B )
=> ( C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(28,plain,
( inconsistency_G
= ( ^ [A: qML_mu,B: qML_i] :
! [C: qML_mu > qML_i > $o] :
( ( inconsistency_P @ C @ B )
=> ( C @ A @ B ) ) ) ),
inference(lifteq,[status(thm)],[27]) ).
thf(34,plain,
! [B: qML_i,A: qML_mu] :
( ( inconsistency_G @ A @ B )
= ( ! [C: qML_mu > qML_i > $o] :
( ( inconsistency_P @ C @ B )
=> ( C @ A @ B ) ) ) ),
inference(func_ext,[status(esa)],[28]) ).
thf(10,axiom,
( incons1905966852QML_mu
= ( ^ [A: qML_mu,B: qML_i] :
! [C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ A @ B )
=> ! [D: qML_i] :
( ( qML_r @ B @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_NE__def) ).
thf(29,plain,
( incons1905966852QML_mu
= ( ^ [A: qML_mu,B: qML_i] :
! [C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ A @ B )
=> ! [D: qML_i] :
( ( qML_r @ B @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(30,plain,
( incons1905966852QML_mu
= ( ^ [A: qML_mu,B: qML_i] :
! [C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ A @ B )
=> ! [D: qML_i] :
( ( qML_r @ B @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) ) ) ),
inference(lifteq,[status(thm)],[29]) ).
thf(8,axiom,
! [A: qML_i] : ( inconsistency_P @ incons1905966852QML_mu @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_A5) ).
thf(25,plain,
! [A: qML_i] : ( inconsistency_P @ incons1905966852QML_mu @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(26,plain,
! [A: qML_i] : ( inconsistency_P @ incons1905966852QML_mu @ A ),
inference(cnf,[status(esa)],[25]) ).
thf(6,axiom,
! [A: qML_i] : ( inconsistency_P @ inconsistency_G @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_A3) ).
thf(21,plain,
! [A: qML_i] : ( inconsistency_P @ inconsistency_G @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(22,plain,
! [A: qML_i] : ( inconsistency_P @ inconsistency_G @ A ),
inference(cnf,[status(esa)],[21]) ).
thf(35,plain,
! [A: qML_i] :
( ( inconsistency_P
@ ^ [B: qML_mu,C: qML_i] :
! [D: qML_mu > qML_i > $o] :
( ( inconsistency_P @ D @ C )
=> ( D @ B @ C ) )
@ A )
| ( inconsistency_G != inconsistency_G ) ),
inference(paramod_ordered,[status(thm)],[28,22]) ).
thf(36,plain,
! [A: qML_i] :
( inconsistency_P
@ ^ [B: qML_mu,C: qML_i] :
! [D: qML_mu > qML_i > $o] :
( ( inconsistency_P @ D @ C )
=> ( D @ B @ C ) )
@ A ),
inference(pattern_uni,[status(thm)],[35:[]]) ).
thf(3,axiom,
! [A: qML_i,B: qML_mu > qML_i > $o] :
( ( inconsistency_P
@ ^ [C: qML_mu,D: qML_i] :
~ ( B @ C @ D )
@ A )
=> ~ ( inconsistency_P @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_A1a) ).
thf(13,plain,
! [A: qML_i,B: qML_mu > qML_i > $o] :
( ( inconsistency_P
@ ^ [C: qML_mu,D: qML_i] :
~ ( B @ C @ D )
@ A )
=> ~ ( inconsistency_P @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(14,plain,
! [B: qML_mu > qML_i > $o,A: qML_i] :
( ~ ( inconsistency_P
@ ^ [C: qML_mu,D: qML_i] :
~ ( B @ C @ D )
@ A )
| ~ ( inconsistency_P @ B @ A ) ),
inference(cnf,[status(esa)],[13]) ).
thf(46,plain,
! [C: qML_mu > qML_i > $o,B: qML_i,A: qML_i] :
( ~ ( inconsistency_P
@ ^ [D: qML_mu,E: qML_i] :
~ ( C @ D @ E )
@ B )
| ( ( inconsistency_P
@ ^ [D: qML_mu,E: qML_i] :
! [F: qML_mu > qML_i > $o] :
( ( inconsistency_P @ F @ E )
=> ( F @ D @ E ) )
@ A )
!= ( inconsistency_P @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[36,14]) ).
thf(47,plain,
! [A: qML_i] :
~ ( inconsistency_P
@ ^ [B: qML_mu,C: qML_i] :
~ ! [D: qML_mu > qML_i > $o] :
( ( inconsistency_P @ D @ C )
=> ( D @ B @ C ) )
@ A ),
inference(pattern_uni,[status(thm)],[46:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( ^ [D: qML_mu] : ^ [E: qML_i] : ! [F: qML_mu > qML_i > $o] : ( ( inconsistency_P @ F @ E ) => ( F @ D @ E ) ) ))]]) ).
thf(199,plain,
! [B: qML_i,A: qML_i] :
( ( inconsistency_P @ incons1905966852QML_mu @ A )
!= ( inconsistency_P
@ ^ [C: qML_mu,D: qML_i] :
~ ! [E: qML_mu > qML_i > $o] :
( ( inconsistency_P @ E @ D )
=> ( E @ C @ D ) )
@ B ) ),
inference(paramod_ordered,[status(thm)],[26,47]) ).
thf(202,plain,
! [B: qML_i,A: qML_i] :
( ( incons1905966852QML_mu
!= ( ^ [C: qML_mu,D: qML_i] :
~ ! [E: qML_mu > qML_i > $o] :
( ( inconsistency_P @ E @ D )
=> ( E @ C @ D ) ) ) )
| ( A != B ) ),
inference(simp,[status(thm)],[199]) ).
thf(205,plain,
( incons1905966852QML_mu
!= ( ^ [A: qML_mu,B: qML_i] :
~ ! [C: qML_mu > qML_i > $o] :
( ( inconsistency_P @ C @ B )
=> ( C @ A @ B ) ) ) ),
inference(simp,[status(thm)],[202]) ).
thf(209,plain,
( ( ( ^ [A: qML_mu,B: qML_i] :
! [C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ A @ B )
=> ! [D: qML_i] :
( ( qML_r @ B @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) ) )
!= ( ^ [A: qML_mu,B: qML_i] :
~ ! [C: qML_mu > qML_i > $o] :
( ( inconsistency_P @ C @ B )
=> ( C @ A @ B ) ) ) )
| ( incons1905966852QML_mu != incons1905966852QML_mu ) ),
inference(paramod_ordered,[status(thm)],[30,205]) ).
thf(210,plain,
( ( ^ [A: qML_mu,B: qML_i] :
! [C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ A @ B )
=> ! [D: qML_i] :
( ( qML_r @ B @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) ) )
!= ( ^ [A: qML_mu,B: qML_i] :
~ ! [C: qML_mu > qML_i > $o] :
( ( inconsistency_P @ C @ B )
=> ( C @ A @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[209:[]]) ).
thf(406,plain,
( ( ! [A: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ A @ sk23 @ sk24 )
=> ! [B: qML_i] :
( ( qML_r @ sk24 @ B )
=> ? [C: qML_mu] : ( A @ C @ B ) ) ) )
!= ( ~ ! [A: qML_mu > qML_i > $o] :
( ( inconsistency_P @ A @ sk24 )
=> ( A @ sk23 @ sk24 ) ) ) ),
inference(func_ext,[status(esa)],[210]) ).
thf(859,plain,
! [B: qML_i,A: qML_mu] :
( ( ( ~ ( inconsistency_G @ A @ B ) )
!= ( ! [C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ sk23 @ sk24 )
=> ! [D: qML_i] :
( ( qML_r @ sk24 @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) ) ) )
| ( ( ! [C: qML_mu > qML_i > $o] :
( ( inconsistency_P @ C @ B )
=> ( C @ A @ B ) ) )
!= ( ! [C: qML_mu > qML_i > $o] :
( ( inconsistency_P @ C @ sk24 )
=> ( C @ sk23 @ sk24 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[34,406]) ).
thf(860,plain,
( ( ~ ( inconsistency_G @ sk23 @ sk24 ) )
!= ( ! [A: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ A @ sk23 @ sk24 )
=> ! [B: qML_i] :
( ( qML_r @ sk24 @ B )
=> ? [C: qML_mu] : ( A @ C @ B ) ) ) ) ),
inference(pattern_uni,[status(thm)],[859:[bind(A,$thf( sk23 )),bind(B,$thf( sk24 ))]]) ).
thf(872,plain,
( ~ ~ ( inconsistency_G @ sk23 @ sk24 )
| ~ ! [A: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ A @ sk23 @ sk24 )
=> ! [B: qML_i] :
( ( qML_r @ sk24 @ B )
=> ? [C: qML_mu] : ( A @ C @ B ) ) ) ),
inference(bool_ext,[status(thm)],[860]) ).
thf(892,plain,
( ( qML_r @ sk24 @ sk76 )
| ( inconsistency_G @ sk23 @ sk24 ) ),
inference(cnf,[status(esa)],[872]) ).
thf(68,plain,
! [B: qML_i,A: qML_mu] :
( ( incons1905966852QML_mu @ A @ B )
= ( ! [C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ A @ B )
=> ! [D: qML_i] :
( ( qML_r @ B @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) ) ) ),
inference(func_ext,[status(esa)],[30]) ).
thf(40,plain,
! [C: qML_mu > qML_i > $o,B: qML_i,A: qML_i] :
( ~ ( inconsistency_P
@ ^ [D: qML_mu,E: qML_i] :
~ ( C @ D @ E )
@ B )
| ( ( inconsistency_P @ inconsistency_G @ A )
!= ( inconsistency_P @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[22,14]) ).
thf(41,plain,
! [A: qML_i] :
~ ( inconsistency_P
@ ^ [B: qML_mu,C: qML_i] :
~ ( inconsistency_G @ B @ C )
@ A ),
inference(pattern_uni,[status(thm)],[40:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( inconsistency_G ))]]) ).
thf(59,plain,
! [B: qML_i,A: qML_i] :
( ( inconsistency_P @ incons1905966852QML_mu @ A )
!= ( inconsistency_P
@ ^ [C: qML_mu,D: qML_i] :
~ ( inconsistency_G @ C @ D )
@ B ) ),
inference(paramod_ordered,[status(thm)],[26,41]) ).
thf(62,plain,
! [B: qML_i,A: qML_i] :
( ( incons1905966852QML_mu
!= ( ^ [C: qML_mu,D: qML_i] :
~ ( inconsistency_G @ C @ D ) ) )
| ( A != B ) ),
inference(simp,[status(thm)],[59]) ).
thf(65,plain,
( incons1905966852QML_mu
!= ( ^ [A: qML_mu,B: qML_i] :
~ ( inconsistency_G @ A @ B ) ) ),
inference(simp,[status(thm)],[62]) ).
thf(78,plain,
( ( ( ^ [A: qML_mu,B: qML_i] :
! [C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ A @ B )
=> ! [D: qML_i] :
( ( qML_r @ B @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) ) )
!= ( ^ [A: qML_mu,B: qML_i] :
~ ( inconsistency_G @ A @ B ) ) )
| ( incons1905966852QML_mu != incons1905966852QML_mu ) ),
inference(paramod_ordered,[status(thm)],[30,65]) ).
thf(79,plain,
( ( ^ [A: qML_mu,B: qML_i] :
! [C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ A @ B )
=> ! [D: qML_i] :
( ( qML_r @ B @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) ) )
!= ( ^ [A: qML_mu,B: qML_i] :
~ ( inconsistency_G @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[78:[]]) ).
thf(402,plain,
( ( ! [A: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ A @ sk21 @ sk22 )
=> ! [B: qML_i] :
( ( qML_r @ sk22 @ B )
=> ? [C: qML_mu] : ( A @ C @ B ) ) ) )
!= ( ~ ( inconsistency_G @ sk21 @ sk22 ) ) ),
inference(func_ext,[status(esa)],[79]) ).
thf(753,plain,
! [B: qML_i,A: qML_mu] :
( ( ( ~ ! [C: qML_mu > qML_i > $o] :
( ( inconsistency_P @ C @ B )
=> ( C @ A @ B ) ) )
!= ( ! [C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ sk21 @ sk22 )
=> ! [D: qML_i] :
( ( qML_r @ sk22 @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) ) ) )
| ( ( inconsistency_G @ A @ B )
!= ( inconsistency_G @ sk21 @ sk22 ) ) ),
inference(paramod_ordered,[status(thm)],[34,402]) ).
thf(754,plain,
( ( ~ ! [A: qML_mu > qML_i > $o] :
( ( inconsistency_P @ A @ sk22 )
=> ( A @ sk21 @ sk22 ) ) )
!= ( ! [A: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ A @ sk21 @ sk22 )
=> ! [B: qML_i] :
( ( qML_r @ sk22 @ B )
=> ? [C: qML_mu] : ( A @ C @ B ) ) ) ) ),
inference(pattern_uni,[status(thm)],[753:[bind(A,$thf( sk21 )),bind(B,$thf( sk22 ))]]) ).
thf(1205,plain,
! [B: qML_i,A: qML_mu] :
( ( ( incons1905966852QML_mu @ A @ B )
!= ( ~ ! [C: qML_mu > qML_i > $o] :
( ( inconsistency_P @ C @ sk22 )
=> ( C @ sk21 @ sk22 ) ) ) )
| ( ( ! [C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ A @ B )
=> ! [D: qML_i] :
( ( qML_r @ B @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) ) )
!= ( ! [C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ sk21 @ sk22 )
=> ! [D: qML_i] :
( ( qML_r @ sk22 @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[68,754]) ).
thf(1206,plain,
( ( incons1905966852QML_mu @ sk21 @ sk22 )
!= ( ~ ! [A: qML_mu > qML_i > $o] :
( ( inconsistency_P @ A @ sk22 )
=> ( A @ sk21 @ sk22 ) ) ) ),
inference(pattern_uni,[status(thm)],[1205:[bind(A,$thf( sk21 )),bind(B,$thf( sk22 ))]]) ).
thf(1449,plain,
( ( incons1905966852QML_mu @ sk21 @ sk22 )
| ~ ! [A: qML_mu > qML_i > $o] :
( ( inconsistency_P @ A @ sk22 )
=> ( A @ sk21 @ sk22 ) ) ),
inference(bool_ext,[status(thm)],[1206]) ).
thf(1469,plain,
( ~ ( sk133 @ sk21 @ sk22 )
| ( incons1905966852QML_mu @ sk21 @ sk22 ) ),
inference(cnf,[status(esa)],[1449]) ).
thf(208,plain,
( ( incons1905966852QML_mu @ sk13 @ sk14 )
!= ( ~ ! [A: qML_mu > qML_i > $o] :
( ( inconsistency_P @ A @ sk14 )
=> ( A @ sk13 @ sk14 ) ) ) ),
inference(func_ext,[status(esa)],[205]) ).
thf(756,plain,
! [B: qML_i,A: qML_mu] :
( ( ( ~ ( inconsistency_G @ A @ B ) )
!= ( incons1905966852QML_mu @ sk13 @ sk14 ) )
| ( ( ! [C: qML_mu > qML_i > $o] :
( ( inconsistency_P @ C @ B )
=> ( C @ A @ B ) ) )
!= ( ! [C: qML_mu > qML_i > $o] :
( ( inconsistency_P @ C @ sk14 )
=> ( C @ sk13 @ sk14 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[34,208]) ).
thf(757,plain,
( ( incons1905966852QML_mu @ sk13 @ sk14 )
!= ( ~ ( inconsistency_G @ sk13 @ sk14 ) ) ),
inference(pattern_uni,[status(thm)],[756:[bind(A,$thf( sk13 )),bind(B,$thf( sk14 ))]]) ).
thf(1189,plain,
! [B: qML_i,A: qML_mu] :
( ( ( ! [C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ A @ B )
=> ! [D: qML_i] :
( ( qML_r @ B @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) ) )
!= ( ~ ( inconsistency_G @ sk13 @ sk14 ) ) )
| ( ( incons1905966852QML_mu @ A @ B )
!= ( incons1905966852QML_mu @ sk13 @ sk14 ) ) ),
inference(paramod_ordered,[status(thm)],[68,757]) ).
thf(1190,plain,
( ( ! [A: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ A @ sk13 @ sk14 )
=> ! [B: qML_i] :
( ( qML_r @ sk14 @ B )
=> ? [C: qML_mu] : ( A @ C @ B ) ) ) )
!= ( ~ ( inconsistency_G @ sk13 @ sk14 ) ) ),
inference(pattern_uni,[status(thm)],[1189:[bind(A,$thf( sk13 )),bind(B,$thf( sk14 ))]]) ).
thf(215,plain,
( ( incons1905966852QML_mu @ sk13 @ sk14 )
| ~ ! [A: qML_mu > qML_i > $o] :
( ( inconsistency_P @ A @ sk14 )
=> ( A @ sk13 @ sk14 ) ) ),
inference(bool_ext,[status(thm)],[208]) ).
thf(220,plain,
( ( inconsistency_P @ sk17 @ sk14 )
| ( incons1905966852QML_mu @ sk13 @ sk14 ) ),
inference(cnf,[status(esa)],[215]) ).
thf(43,plain,
! [C: qML_mu > qML_i > $o,B: qML_i,A: qML_i] :
( ~ ( inconsistency_P
@ ^ [D: qML_mu,E: qML_i] :
~ ( C @ D @ E )
@ B )
| ( ( inconsistency_P @ incons1905966852QML_mu @ A )
!= ( inconsistency_P @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[26,14]) ).
thf(44,plain,
! [A: qML_i] :
~ ( inconsistency_P
@ ^ [B: qML_mu,C: qML_i] :
~ ( incons1905966852QML_mu @ B @ C )
@ A ),
inference(pattern_uni,[status(thm)],[43:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( incons1905966852QML_mu ))]]) ).
thf(539,plain,
! [A: qML_i] :
( ( incons1905966852QML_mu @ sk13 @ sk14 )
| ( ( inconsistency_P @ sk17 @ sk14 )
!= ( inconsistency_P
@ ^ [B: qML_mu,C: qML_i] :
~ ( incons1905966852QML_mu @ B @ C )
@ A ) ) ),
inference(paramod_ordered,[status(thm)],[220,44]) ).
thf(543,plain,
! [A: qML_i] :
( ( incons1905966852QML_mu @ sk13 @ sk14 )
| ( sk17
!= ( ^ [B: qML_mu,C: qML_i] :
~ ( incons1905966852QML_mu @ B @ C ) ) )
| ( sk14 != A ) ),
inference(simp,[status(thm)],[539]) ).
thf(555,plain,
( ( incons1905966852QML_mu @ sk13 @ sk14 )
| ( sk17
!= ( ^ [A: qML_mu,B: qML_i] :
~ ( incons1905966852QML_mu @ A @ B ) ) ) ),
inference(simp,[status(thm)],[543]) ).
thf(71,plain,
! [A: qML_i] :
( ( inconsistency_P
@ ^ [B: qML_mu,C: qML_i] :
! [D: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ D @ B @ C )
=> ! [E: qML_i] :
( ( qML_r @ C @ E )
=> ? [F: qML_mu] : ( D @ F @ E ) ) )
@ A )
| ( incons1905966852QML_mu != incons1905966852QML_mu ) ),
inference(paramod_ordered,[status(thm)],[30,26]) ).
thf(72,plain,
! [A: qML_i] :
( inconsistency_P
@ ^ [B: qML_mu,C: qML_i] :
! [D: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ D @ B @ C )
=> ! [E: qML_i] :
( ( qML_r @ C @ E )
=> ? [F: qML_mu] : ( D @ F @ E ) ) )
@ A ),
inference(pattern_uni,[status(thm)],[71:[]]) ).
thf(475,plain,
! [C: qML_mu > qML_i > $o,B: qML_i,A: qML_i] :
( ~ ( inconsistency_P
@ ^ [D: qML_mu,E: qML_i] :
~ ( C @ D @ E )
@ B )
| ( ( inconsistency_P
@ ^ [D: qML_mu,E: qML_i] :
! [F: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ F @ D @ E )
=> ! [G: qML_i] :
( ( qML_r @ E @ G )
=> ? [H: qML_mu] : ( F @ H @ G ) ) )
@ A )
!= ( inconsistency_P @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[72,14]) ).
thf(476,plain,
! [A: qML_i] :
~ ( inconsistency_P
@ ^ [B: qML_mu,C: qML_i] :
~ ! [D: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ D @ B @ C )
=> ! [E: qML_i] :
( ( qML_r @ C @ E )
=> ? [F: qML_mu] : ( D @ F @ E ) ) )
@ A ),
inference(pattern_uni,[status(thm)],[475:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( ^ [D: qML_mu] : ^ [E: qML_i] : ! [F: qML_mu > qML_i > $o] : ( ( incons1389517216QML_mu @ F @ D @ E ) => ! [G: qML_i] : ( ( qML_r @ E @ G ) => ? [H: qML_mu] : ( F @ H @ G ) ) ) ))]]) ).
thf(504,plain,
! [B: qML_i,A: qML_i] :
( ( inconsistency_P @ inconsistency_G @ A )
!= ( inconsistency_P
@ ^ [C: qML_mu,D: qML_i] :
~ ! [E: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ E @ C @ D )
=> ! [F: qML_i] :
( ( qML_r @ D @ F )
=> ? [G: qML_mu] : ( E @ G @ F ) ) )
@ B ) ),
inference(paramod_ordered,[status(thm)],[22,476]) ).
thf(510,plain,
! [B: qML_i,A: qML_i] :
( ( inconsistency_G
!= ( ^ [C: qML_mu,D: qML_i] :
~ ! [E: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ E @ C @ D )
=> ! [F: qML_i] :
( ( qML_r @ D @ F )
=> ? [G: qML_mu] : ( E @ G @ F ) ) ) ) )
| ( A != B ) ),
inference(simp,[status(thm)],[504]) ).
thf(520,plain,
( inconsistency_G
!= ( ^ [A: qML_mu,B: qML_i] :
~ ! [C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ A @ B )
=> ! [D: qML_i] :
( ( qML_r @ B @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) ) ) ),
inference(simp,[status(thm)],[510]) ).
thf(525,plain,
( ( inconsistency_G @ sk30 @ sk31 )
!= ( ~ ! [A: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ A @ sk30 @ sk31 )
=> ! [B: qML_i] :
( ( qML_r @ sk31 @ B )
=> ? [C: qML_mu] : ( A @ C @ B ) ) ) ) ),
inference(func_ext,[status(esa)],[520]) ).
thf(1207,plain,
! [B: qML_i,A: qML_mu] :
( ( ( ~ ( incons1905966852QML_mu @ A @ B ) )
!= ( inconsistency_G @ sk30 @ sk31 ) )
| ( ( ! [C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ A @ B )
=> ! [D: qML_i] :
( ( qML_r @ B @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) ) )
!= ( ! [C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ sk30 @ sk31 )
=> ! [D: qML_i] :
( ( qML_r @ sk31 @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[68,525]) ).
thf(1208,plain,
( ( ~ ( incons1905966852QML_mu @ sk30 @ sk31 ) )
!= ( inconsistency_G @ sk30 @ sk31 ) ),
inference(pattern_uni,[status(thm)],[1207:[bind(A,$thf( sk30 )),bind(B,$thf( sk31 ))]]) ).
thf(1280,plain,
( ~ ( incons1905966852QML_mu @ sk30 @ sk31 )
| ( inconsistency_G @ sk30 @ sk31 ) ),
inference(bool_ext,[status(thm)],[1208]) ).
thf(1295,plain,
( ( inconsistency_G @ sk30 @ sk31 )
| ~ ( incons1905966852QML_mu @ sk30 @ sk31 ) ),
inference(cnf,[status(esa)],[1280]) ).
thf(82,plain,
! [B: qML_i,A: qML_i] :
( ( inconsistency_P
@ ^ [C: qML_mu,D: qML_i] :
! [E: qML_mu > qML_i > $o] :
( ( inconsistency_P @ E @ D )
=> ( E @ C @ D ) )
@ A )
!= ( inconsistency_P
@ ^ [C: qML_mu,D: qML_i] :
~ ( incons1905966852QML_mu @ C @ D )
@ B ) ),
inference(paramod_ordered,[status(thm)],[36,44]) ).
thf(85,plain,
! [B: qML_i,A: qML_i] :
( ( ( ^ [C: qML_mu,D: qML_i] :
! [E: qML_mu > qML_i > $o] :
( ( inconsistency_P @ E @ D )
=> ( E @ C @ D ) ) )
!= ( ^ [C: qML_mu,D: qML_i] :
~ ( incons1905966852QML_mu @ C @ D ) ) )
| ( A != B ) ),
inference(simp,[status(thm)],[82]) ).
thf(88,plain,
( ( ^ [A: qML_mu,B: qML_i] :
! [C: qML_mu > qML_i > $o] :
( ( inconsistency_P @ C @ B )
=> ( C @ A @ B ) ) )
!= ( ^ [A: qML_mu,B: qML_i] :
~ ( incons1905966852QML_mu @ A @ B ) ) ),
inference(simp,[status(thm)],[85]) ).
thf(11,axiom,
( incons1389517216QML_mu
= ( ^ [A: qML_mu > qML_i > $o,B: qML_mu,C: qML_i] :
! [D: qML_mu > qML_i > $o] :
( ( D @ B @ C )
=> ! [E: qML_i] :
( ( qML_r @ C @ E )
=> ! [F: qML_mu] :
( ( A @ F @ E )
=> ( D @ F @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_ess__def) ).
thf(31,plain,
( incons1389517216QML_mu
= ( ^ [A: qML_mu > qML_i > $o,B: qML_mu,C: qML_i] :
! [D: qML_mu > qML_i > $o] :
( ( D @ B @ C )
=> ! [E: qML_i] :
( ( qML_r @ C @ E )
=> ! [F: qML_mu] :
( ( A @ F @ E )
=> ( D @ F @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(32,plain,
( incons1389517216QML_mu
= ( ^ [A: qML_mu > qML_i > $o,B: qML_mu,C: qML_i] :
! [D: qML_mu > qML_i > $o] :
( ( D @ B @ C )
=> ! [E: qML_i] :
( ( qML_r @ C @ E )
=> ! [F: qML_mu] :
( ( A @ F @ E )
=> ( D @ F @ E ) ) ) ) ) ),
inference(lifteq,[status(thm)],[31]) ).
thf(122,plain,
! [A: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ A )
= ( ^ [B: qML_mu,C: qML_i] :
! [D: qML_mu > qML_i > $o] :
( ( D @ B @ C )
=> ! [E: qML_i] :
( ( qML_r @ C @ E )
=> ! [F: qML_mu] :
( ( A @ F @ E )
=> ( D @ F @ E ) ) ) ) ) ),
inference(func_ext,[status(esa)],[32]) ).
thf(60,plain,
! [B: qML_i,A: qML_i] :
( ( inconsistency_P
@ ^ [C: qML_mu,D: qML_i] :
! [E: qML_mu > qML_i > $o] :
( ( inconsistency_P @ E @ D )
=> ( E @ C @ D ) )
@ A )
!= ( inconsistency_P
@ ^ [C: qML_mu,D: qML_i] :
~ ( inconsistency_G @ C @ D )
@ B ) ),
inference(paramod_ordered,[status(thm)],[36,41]) ).
thf(63,plain,
! [B: qML_i,A: qML_i] :
( ( ( ^ [C: qML_mu,D: qML_i] :
! [E: qML_mu > qML_i > $o] :
( ( inconsistency_P @ E @ D )
=> ( E @ C @ D ) ) )
!= ( ^ [C: qML_mu,D: qML_i] :
~ ( inconsistency_G @ C @ D ) ) )
| ( A != B ) ),
inference(simp,[status(thm)],[60]) ).
thf(66,plain,
( ( ^ [A: qML_mu,B: qML_i] :
! [C: qML_mu > qML_i > $o] :
( ( inconsistency_P @ C @ B )
=> ( C @ A @ B ) ) )
!= ( ^ [A: qML_mu,B: qML_i] :
~ ( inconsistency_G @ A @ B ) ) ),
inference(simp,[status(thm)],[63]) ).
thf(969,plain,
! [A: qML_mu > qML_i > $o] :
( ( ( incons1389517216QML_mu @ A )
!= ( ^ [B: qML_mu,C: qML_i] :
~ ( inconsistency_G @ B @ C ) ) )
| ( ( ^ [B: qML_mu,C: qML_i] :
! [D: qML_mu > qML_i > $o] :
( ( D @ B @ C )
=> ! [E: qML_i] :
( ( qML_r @ C @ E )
=> ! [F: qML_mu] :
( ( A @ F @ E )
=> ( D @ F @ E ) ) ) ) )
!= ( ^ [B: qML_mu,C: qML_i] :
! [D: qML_mu > qML_i > $o] :
( ( inconsistency_P @ D @ C )
=> ( D @ B @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[122,66]) ).
thf(977,plain,
! [A: qML_mu > qML_i > $o] :
( ( ( incons1389517216QML_mu @ A )
!= ( ^ [B: qML_mu,C: qML_i] :
~ ( inconsistency_G @ B @ C ) ) )
| ( ( ^ [B: qML_mu,C: qML_i,D: qML_mu > qML_i > $o] :
( ( D @ B @ C )
=> ! [E: qML_i] :
( ( qML_r @ C @ E )
=> ! [F: qML_mu] :
( ( A @ F @ E )
=> ( D @ F @ E ) ) ) ) )
!= ( ^ [B: qML_mu,C: qML_i,D: qML_mu > qML_i > $o] :
( ( inconsistency_P @ D @ C )
=> ( D @ B @ C ) ) ) ) ),
inference(simp,[status(thm)],[969]) ).
thf(81,plain,
! [B: qML_i,A: qML_i] :
( ( inconsistency_P @ inconsistency_G @ A )
!= ( inconsistency_P
@ ^ [C: qML_mu,D: qML_i] :
~ ( incons1905966852QML_mu @ C @ D )
@ B ) ),
inference(paramod_ordered,[status(thm)],[22,44]) ).
thf(84,plain,
! [B: qML_i,A: qML_i] :
( ( inconsistency_G
!= ( ^ [C: qML_mu,D: qML_i] :
~ ( incons1905966852QML_mu @ C @ D ) ) )
| ( A != B ) ),
inference(simp,[status(thm)],[81]) ).
thf(87,plain,
( inconsistency_G
!= ( ^ [A: qML_mu,B: qML_i] :
~ ( incons1905966852QML_mu @ A @ B ) ) ),
inference(simp,[status(thm)],[84]) ).
thf(102,plain,
( ( inconsistency_G @ sk5 @ sk6 )
!= ( ~ ( incons1905966852QML_mu @ sk5 @ sk6 ) ) ),
inference(func_ext,[status(esa)],[87]) ).
thf(118,plain,
( ~ ( inconsistency_G @ sk5 @ sk6 )
| ~ ~ ( incons1905966852QML_mu @ sk5 @ sk6 ) ),
inference(bool_ext,[status(thm)],[102]) ).
thf(120,plain,
( ( incons1905966852QML_mu @ sk5 @ sk6 )
| ~ ( inconsistency_G @ sk5 @ sk6 ) ),
inference(cnf,[status(esa)],[118]) ).
thf(478,plain,
! [B: qML_i,A: qML_i] :
( ( inconsistency_P
@ ^ [C: qML_mu,D: qML_i] :
! [E: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ E @ C @ D )
=> ! [F: qML_i] :
( ( qML_r @ D @ F )
=> ? [G: qML_mu] : ( E @ G @ F ) ) )
@ A )
!= ( inconsistency_P
@ ^ [C: qML_mu,D: qML_i] :
~ ( incons1905966852QML_mu @ C @ D )
@ B ) ),
inference(paramod_ordered,[status(thm)],[72,44]) ).
thf(485,plain,
! [B: qML_i,A: qML_i] :
( ( ( ^ [C: qML_mu,D: qML_i] :
! [E: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ E @ C @ D )
=> ! [F: qML_i] :
( ( qML_r @ D @ F )
=> ? [G: qML_mu] : ( E @ G @ F ) ) ) )
!= ( ^ [C: qML_mu,D: qML_i] :
~ ( incons1905966852QML_mu @ C @ D ) ) )
| ( A != B ) ),
inference(simp,[status(thm)],[478]) ).
thf(492,plain,
( ( ^ [A: qML_mu,B: qML_i] :
! [C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ A @ B )
=> ! [D: qML_i] :
( ( qML_r @ B @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) ) )
!= ( ^ [A: qML_mu,B: qML_i] :
~ ( incons1905966852QML_mu @ A @ B ) ) ),
inference(simp,[status(thm)],[485]) ).
thf(496,plain,
( ( ! [A: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ A @ sk26 @ sk27 )
=> ! [B: qML_i] :
( ( qML_r @ sk27 @ B )
=> ? [C: qML_mu] : ( A @ C @ B ) ) ) )
!= ( ~ ( incons1905966852QML_mu @ sk26 @ sk27 ) ) ),
inference(func_ext,[status(esa)],[492]) ).
thf(643,plain,
( ~ ! [A: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ A @ sk26 @ sk27 )
=> ! [B: qML_i] :
( ( qML_r @ sk27 @ B )
=> ? [C: qML_mu] : ( A @ C @ B ) ) )
| ~ ~ ( incons1905966852QML_mu @ sk26 @ sk27 ) ),
inference(bool_ext,[status(thm)],[496]) ).
thf(655,plain,
( ( incons1905966852QML_mu @ sk26 @ sk27 )
| ( qML_r @ sk27 @ sk43 ) ),
inference(cnf,[status(esa)],[643]) ).
thf(507,plain,
! [B: qML_i,A: qML_i] :
( ( inconsistency_P
@ ^ [C: qML_mu,D: qML_i] :
! [E: qML_mu > qML_i > $o] :
( ( inconsistency_P @ E @ D )
=> ( E @ C @ D ) )
@ A )
!= ( inconsistency_P
@ ^ [C: qML_mu,D: qML_i] :
~ ! [E: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ E @ C @ D )
=> ! [F: qML_i] :
( ( qML_r @ D @ F )
=> ? [G: qML_mu] : ( E @ G @ F ) ) )
@ B ) ),
inference(paramod_ordered,[status(thm)],[36,476]) ).
thf(511,plain,
! [B: qML_i,A: qML_i] :
( ( ( ^ [C: qML_mu,D: qML_i] :
! [E: qML_mu > qML_i > $o] :
( ( inconsistency_P @ E @ D )
=> ( E @ C @ D ) ) )
!= ( ^ [C: qML_mu,D: qML_i] :
~ ! [E: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ E @ C @ D )
=> ! [F: qML_i] :
( ( qML_r @ D @ F )
=> ? [G: qML_mu] : ( E @ G @ F ) ) ) ) )
| ( A != B ) ),
inference(simp,[status(thm)],[507]) ).
thf(521,plain,
( ( ^ [A: qML_mu,B: qML_i] :
! [C: qML_mu > qML_i > $o] :
( ( inconsistency_P @ C @ B )
=> ( C @ A @ B ) ) )
!= ( ^ [A: qML_mu,B: qML_i] :
~ ! [C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ A @ B )
=> ! [D: qML_i] :
( ( qML_r @ B @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) ) ) ),
inference(simp,[status(thm)],[511]) ).
thf(619,plain,
( ( ! [A: qML_mu > qML_i > $o] :
( ( inconsistency_P @ A @ sk35 )
=> ( A @ sk34 @ sk35 ) ) )
!= ( ~ ! [A: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ A @ sk34 @ sk35 )
=> ! [B: qML_i] :
( ( qML_r @ sk35 @ B )
=> ? [C: qML_mu] : ( A @ C @ B ) ) ) ) ),
inference(func_ext,[status(esa)],[521]) ).
thf(1172,plain,
! [B: qML_i,A: qML_mu] :
( ( ( ~ ( incons1905966852QML_mu @ A @ B ) )
!= ( ! [C: qML_mu > qML_i > $o] :
( ( inconsistency_P @ C @ sk35 )
=> ( C @ sk34 @ sk35 ) ) ) )
| ( ( ! [C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ A @ B )
=> ! [D: qML_i] :
( ( qML_r @ B @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) ) )
!= ( ! [C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ sk34 @ sk35 )
=> ! [D: qML_i] :
( ( qML_r @ sk35 @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[68,619]) ).
thf(1173,plain,
( ( ~ ( incons1905966852QML_mu @ sk34 @ sk35 ) )
!= ( ! [A: qML_mu > qML_i > $o] :
( ( inconsistency_P @ A @ sk35 )
=> ( A @ sk34 @ sk35 ) ) ) ),
inference(pattern_uni,[status(thm)],[1172:[bind(A,$thf( sk34 )),bind(B,$thf( sk35 ))]]) ).
thf(39,plain,
! [C: qML_mu > qML_i > $o,B: qML_i,A: qML_i] :
( ~ ( inconsistency_P @ C @ B )
| ( ( inconsistency_P @ inconsistency_G @ A )
!= ( inconsistency_P
@ ^ [D: qML_mu,E: qML_i] :
~ ( C @ D @ E )
@ B ) ) ),
inference(paramod_ordered,[status(thm)],[22,14]) ).
thf(51,plain,
! [C: qML_mu > qML_i > $o,B: qML_i,A: qML_i] :
( ~ ( inconsistency_P @ C @ B )
| ( inconsistency_G
!= ( ^ [D: qML_mu,E: qML_i] :
~ ( C @ D @ E ) ) )
| ( A != B ) ),
inference(simp,[status(thm)],[39]) ).
thf(56,plain,
! [B: qML_mu > qML_i > $o,A: qML_i] :
( ~ ( inconsistency_P @ B @ A )
| ( inconsistency_G
!= ( ^ [C: qML_mu,D: qML_i] :
~ ( B @ C @ D ) ) ) ),
inference(simp,[status(thm)],[51]) ).
thf(746,plain,
! [B: qML_i,A: qML_mu] :
( ( ( ! [C: qML_mu > qML_i > $o] :
( ( inconsistency_P @ C @ B )
=> ( C @ A @ B ) ) )
!= ( ~ ( incons1905966852QML_mu @ sk5 @ sk6 ) ) )
| ( ( inconsistency_G @ A @ B )
!= ( inconsistency_G @ sk5 @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[34,102]) ).
thf(747,plain,
( ( ! [A: qML_mu > qML_i > $o] :
( ( inconsistency_P @ A @ sk6 )
=> ( A @ sk5 @ sk6 ) ) )
!= ( ~ ( incons1905966852QML_mu @ sk5 @ sk6 ) ) ),
inference(pattern_uni,[status(thm)],[746:[bind(A,$thf( sk5 )),bind(B,$thf( sk6 ))]]) ).
thf(5,axiom,
! [A: qML_i,B: qML_mu > qML_i > $o,C: qML_mu > qML_i > $o] :
( ( ( inconsistency_P @ B @ A )
& ! [D: qML_i] :
( ( qML_r @ A @ D )
=> ! [E: qML_mu] :
( ( B @ E @ D )
=> ( C @ E @ D ) ) ) )
=> ( inconsistency_P @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_A2) ).
thf(17,plain,
! [A: qML_i,B: qML_mu > qML_i > $o,C: qML_mu > qML_i > $o] :
( ( ( inconsistency_P @ B @ A )
& ! [D: qML_i] :
( ( qML_r @ A @ D )
=> ! [E: qML_mu] :
( ( B @ E @ D )
=> ( C @ E @ D ) ) ) )
=> ( inconsistency_P @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(18,plain,
! [C: qML_mu > qML_i > $o,B: qML_mu > qML_i > $o,A: qML_i] :
( ~ ( inconsistency_P @ B @ A )
| ~ ( C @ ( sk2 @ C @ B @ A ) @ ( sk1 @ C @ B @ A ) )
| ( inconsistency_P @ C @ A ) ),
inference(cnf,[status(esa)],[17]) ).
thf(136,plain,
! [D: qML_mu > qML_i > $o,C: qML_mu > qML_i > $o,B: qML_i,A: qML_i] :
( ~ ( inconsistency_P @ C @ B )
| ( inconsistency_P @ D @ B )
| ( ( inconsistency_P @ incons1905966852QML_mu @ A )
!= ( D @ ( sk2 @ D @ C @ B ) @ ( sk1 @ D @ C @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[26,18]) ).
thf(161,plain,
! [C: qML_mu > qML_i > qML_i,B: qML_mu > qML_i > $o,A: qML_i] :
( ~ ( inconsistency_P @ B @ A )
| ( inconsistency_P
@ ^ [D: qML_mu,E: qML_i] : ( inconsistency_P @ incons1905966852QML_mu @ ( C @ D @ E ) )
@ A ) ),
inference(pre_uni,[status(thm)],[136:[bind(A,$thf( F @ ( sk2 @ ^ [F: qML_mu] : ^ [G: qML_i] : ( inconsistency_P @ incons1905966852QML_mu @ ( F @ F @ G ) ) @ C @ B ) @ ( sk1 @ ^ [F: qML_mu] : ^ [G: qML_i] : ( inconsistency_P @ incons1905966852QML_mu @ ( F @ F @ G ) ) @ C @ B ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( ^ [F: qML_mu] : ^ [G: qML_i] : ( inconsistency_P @ incons1905966852QML_mu @ ( F @ F @ G ) ) ))]]) ).
thf(164,plain,
! [C: qML_mu > qML_i > qML_i,B: qML_mu > qML_i > $o,A: qML_i] :
( ~ ( inconsistency_P @ B @ A )
| ( inconsistency_P
@ ^ [D: qML_mu,E: qML_i] : ( inconsistency_P @ incons1905966852QML_mu @ ( C @ D @ E ) )
@ A ) ),
inference(simp,[status(thm)],[161]) ).
thf(4100,plain,
! [B: qML_mu > qML_i > $o,A: qML_i] :
( ~ ( inconsistency_P @ B @ A )
| ( inconsistency_P
@ ^ [C: qML_mu,D: qML_i] : $true
@ A ) ),
inference(rewrite,[status(thm)],[164,26]) ).
thf(4138,plain,
! [C: qML_mu > qML_i > $o,B: qML_i,A: qML_i] :
( ( inconsistency_P
@ ^ [D: qML_mu,E: qML_i] : $true
@ B )
| ( ( inconsistency_P @ inconsistency_G @ A )
!= ( inconsistency_P @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[22,4100]) ).
thf(4139,plain,
! [A: qML_i] :
( inconsistency_P
@ ^ [B: qML_mu,C: qML_i] : $true
@ A ),
inference(pattern_uni,[status(thm)],[4138:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( inconsistency_G ))]]) ).
thf(42,plain,
! [C: qML_mu > qML_i > $o,B: qML_i,A: qML_i] :
( ~ ( inconsistency_P @ C @ B )
| ( ( inconsistency_P @ incons1905966852QML_mu @ A )
!= ( inconsistency_P
@ ^ [D: qML_mu,E: qML_i] :
~ ( C @ D @ E )
@ B ) ) ),
inference(paramod_ordered,[status(thm)],[26,14]) ).
thf(49,plain,
! [C: qML_mu > qML_i > $o,B: qML_i,A: qML_i] :
( ~ ( inconsistency_P @ C @ B )
| ( incons1905966852QML_mu
!= ( ^ [D: qML_mu,E: qML_i] :
~ ( C @ D @ E ) ) )
| ( A != B ) ),
inference(simp,[status(thm)],[42]) ).
thf(54,plain,
! [B: qML_mu > qML_i > $o,A: qML_i] :
( ~ ( inconsistency_P @ B @ A )
| ( incons1905966852QML_mu
!= ( ^ [C: qML_mu,D: qML_i] :
~ ( B @ C @ D ) ) ) ),
inference(simp,[status(thm)],[49]) ).
thf(4226,plain,
! [C: qML_mu > qML_i > $o,B: qML_i,A: qML_i] :
( ( incons1905966852QML_mu
!= ( ^ [D: qML_mu,E: qML_i] :
~ ( C @ D @ E ) ) )
| ( ( inconsistency_P
@ ^ [D: qML_mu,E: qML_i] : $true
@ A )
!= ( inconsistency_P @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4139,54]) ).
thf(4227,plain,
( incons1905966852QML_mu
!= ( ^ [A: qML_mu,B: qML_i] : ~ $true ) ),
inference(pattern_uni,[status(thm)],[4226:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( ^ [D: qML_mu] : ^ [E: qML_i] : $true ))]]) ).
thf(4247,plain,
( incons1905966852QML_mu
!= ( ^ [A: qML_mu,B: qML_i] : $false ) ),
inference(simp,[status(thm)],[4227]) ).
thf(77,plain,
( ( incons1905966852QML_mu @ sk3 @ sk4 )
!= ( ~ ( inconsistency_G @ sk3 @ sk4 ) ) ),
inference(func_ext,[status(esa)],[65]) ).
thf(115,plain,
( ( incons1905966852QML_mu @ sk3 @ sk4 )
| ~ ( inconsistency_G @ sk3 @ sk4 ) ),
inference(bool_ext,[status(thm)],[77]) ).
thf(117,plain,
( ~ ( inconsistency_G @ sk3 @ sk4 )
| ( incons1905966852QML_mu @ sk3 @ sk4 ) ),
inference(cnf,[status(esa)],[115]) ).
thf(744,plain,
! [B: qML_i,A: qML_mu] :
( ~ ! [C: qML_mu > qML_i > $o] :
( ( inconsistency_P @ C @ B )
=> ( C @ A @ B ) )
| ( incons1905966852QML_mu @ sk3 @ sk4 )
| ( ( inconsistency_G @ A @ B )
!= ( inconsistency_G @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[34,117]) ).
thf(745,plain,
( ~ ! [A: qML_mu > qML_i > $o] :
( ( inconsistency_P @ A @ sk4 )
=> ( A @ sk3 @ sk4 ) )
| ( incons1905966852QML_mu @ sk3 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[744:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(793,plain,
( ( incons1905966852QML_mu @ sk3 @ sk4 )
| ( inconsistency_P @ sk64 @ sk4 ) ),
inference(cnf,[status(esa)],[745]) ).
thf(1506,plain,
! [B: qML_mu > qML_i > $o,A: qML_i] :
( ( incons1905966852QML_mu @ sk3 @ sk4 )
| ( inconsistency_G
!= ( ^ [C: qML_mu,D: qML_i] :
~ ( B @ C @ D ) ) )
| ( ( inconsistency_P @ sk64 @ sk4 )
!= ( inconsistency_P @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[793,56]) ).
thf(1507,plain,
( ( incons1905966852QML_mu @ sk3 @ sk4 )
| ( inconsistency_G
!= ( ^ [A: qML_mu,B: qML_i] :
~ ( sk64 @ A @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[1506:[bind(A,$thf( sk4 )),bind(B,$thf( sk64 ))]]) ).
thf(7,axiom,
! [A: qML_i,B: qML_mu > qML_i > $o] :
( ( inconsistency_P @ B @ A )
=> ! [C: qML_i] :
( ( qML_r @ A @ C )
=> ( inconsistency_P @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_A4) ).
thf(23,plain,
! [A: qML_i,B: qML_mu > qML_i > $o] :
( ( inconsistency_P @ B @ A )
=> ! [C: qML_i] :
( ( qML_r @ A @ C )
=> ( inconsistency_P @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(24,plain,
! [C: qML_i,B: qML_mu > qML_i > $o,A: qML_i] :
( ~ ( inconsistency_P @ B @ A )
| ~ ( qML_r @ A @ C )
| ( inconsistency_P @ B @ C ) ),
inference(cnf,[status(esa)],[23]) ).
thf(45,plain,
! [C: qML_mu > qML_i > $o,B: qML_i,A: qML_i] :
( ~ ( inconsistency_P @ C @ B )
| ( ( inconsistency_P
@ ^ [D: qML_mu,E: qML_i] :
! [F: qML_mu > qML_i > $o] :
( ( inconsistency_P @ F @ E )
=> ( F @ D @ E ) )
@ A )
!= ( inconsistency_P
@ ^ [D: qML_mu,E: qML_i] :
~ ( C @ D @ E )
@ B ) ) ),
inference(paramod_ordered,[status(thm)],[36,14]) ).
thf(50,plain,
! [C: qML_mu > qML_i > $o,B: qML_i,A: qML_i] :
( ~ ( inconsistency_P @ C @ B )
| ( ( ^ [D: qML_mu,E: qML_i] :
! [F: qML_mu > qML_i > $o] :
( ( inconsistency_P @ F @ E )
=> ( F @ D @ E ) ) )
!= ( ^ [D: qML_mu,E: qML_i] :
~ ( C @ D @ E ) ) )
| ( A != B ) ),
inference(simp,[status(thm)],[45]) ).
thf(55,plain,
! [B: qML_mu > qML_i > $o,A: qML_i] :
( ~ ( inconsistency_P @ B @ A )
| ( ( ^ [C: qML_mu,D: qML_i] :
! [E: qML_mu > qML_i > $o] :
( ( inconsistency_P @ E @ D )
=> ( E @ C @ D ) ) )
!= ( ^ [C: qML_mu,D: qML_i] :
~ ( B @ C @ D ) ) ) ),
inference(simp,[status(thm)],[50]) ).
thf(4232,plain,
! [C: qML_mu > qML_i > $o,B: qML_i,A: qML_i] :
( ( ( ^ [D: qML_mu,E: qML_i] :
! [F: qML_mu > qML_i > $o] :
( ( inconsistency_P @ F @ E )
=> ( F @ D @ E ) ) )
!= ( ^ [D: qML_mu,E: qML_i] :
~ ( C @ D @ E ) ) )
| ( ( inconsistency_P
@ ^ [D: qML_mu,E: qML_i] : $true
@ A )
!= ( inconsistency_P @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4139,55]) ).
thf(4233,plain,
( ( ^ [A: qML_mu,B: qML_i] :
! [C: qML_mu > qML_i > $o] :
( ( inconsistency_P @ C @ B )
=> ( C @ A @ B ) ) )
!= ( ^ [A: qML_mu,B: qML_i] : ~ $true ) ),
inference(pattern_uni,[status(thm)],[4232:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( ^ [D: qML_mu] : ^ [E: qML_i] : $true ))]]) ).
thf(4249,plain,
( ( ^ [A: qML_mu,B: qML_i] :
! [C: qML_mu > qML_i > $o] :
( ( inconsistency_P @ C @ B )
=> ( C @ A @ B ) ) )
!= ( ^ [A: qML_mu,B: qML_i] : $false ) ),
inference(simp,[status(thm)],[4233]) ).
thf(48,plain,
! [B: qML_mu > qML_i > $o,A: qML_i] :
( ~ ( inconsistency_P @ B @ A )
| ( ( inconsistency_P
@ ^ [C: qML_mu,D: qML_i] :
~ ( B @ C @ D )
@ A )
!= ( inconsistency_P @ B @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[14]) ).
thf(52,plain,
! [B: qML_mu > qML_i > $o,A: qML_i] :
( ~ ( inconsistency_P @ B @ A )
| ( ( inconsistency_P
@ ^ [C: qML_mu,D: qML_i] :
~ ( B @ C @ D )
@ A )
!= ( inconsistency_P @ B @ A ) ) ),
inference(simp,[status(thm)],[48]) ).
thf(110,plain,
( ( ! [A: qML_mu > qML_i > $o] :
( ( inconsistency_P @ A @ sk10 )
=> ( A @ sk9 @ sk10 ) ) )
!= ( ~ ( incons1905966852QML_mu @ sk9 @ sk10 ) ) ),
inference(func_ext,[status(esa)],[88]) ).
thf(137,plain,
! [C: qML_mu > qML_i > $o,B: qML_mu > qML_i > $o,A: qML_i] :
( ~ ( inconsistency_G @ sk3 @ sk4 )
| ~ ( inconsistency_P @ B @ A )
| ( inconsistency_P @ C @ A )
| ( ( C @ ( sk2 @ C @ B @ A ) @ ( sk1 @ C @ B @ A ) )
!= ( incons1905966852QML_mu @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[117,18]) ).
thf(157,plain,
! [B: qML_mu > qML_i > $o,A: qML_i] :
( ~ ( inconsistency_G @ sk3 @ sk4 )
| ~ ( inconsistency_P @ B @ A )
| ( inconsistency_P
@ ^ [C: qML_mu,D: qML_i] : ( incons1905966852QML_mu @ sk3 @ sk4 )
@ A ) ),
inference(pre_uni,[status(thm)],[137:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( ^ [D: qML_mu] : ^ [E: qML_i] : ( incons1905966852QML_mu @ sk3 @ sk4 ) ))]]) ).
thf(20,plain,
! [C: qML_mu > qML_i > $o,B: qML_mu > qML_i > $o,A: qML_i] :
( ~ ( inconsistency_P @ B @ A )
| ( qML_r @ A @ ( sk1 @ C @ B @ A ) )
| ( inconsistency_P @ C @ A ) ),
inference(cnf,[status(esa)],[17]) ).
thf(990,plain,
! [B: qML_i,A: qML_mu] :
( ( ( inconsistency_G @ A @ B )
!= ( ~ ! [C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ sk34 @ sk35 )
=> ! [D: qML_i] :
( ( qML_r @ sk35 @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) ) ) )
| ( ( ! [C: qML_mu > qML_i > $o] :
( ( inconsistency_P @ C @ B )
=> ( C @ A @ B ) ) )
!= ( ! [C: qML_mu > qML_i > $o] :
( ( inconsistency_P @ C @ sk35 )
=> ( C @ sk34 @ sk35 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[34,619]) ).
thf(991,plain,
( ( inconsistency_G @ sk34 @ sk35 )
!= ( ~ ! [A: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ A @ sk34 @ sk35 )
=> ! [B: qML_i] :
( ( qML_r @ sk35 @ B )
=> ? [C: qML_mu] : ( A @ C @ B ) ) ) ) ),
inference(pattern_uni,[status(thm)],[990:[bind(A,$thf( sk34 )),bind(B,$thf( sk35 ))]]) ).
thf(1213,plain,
! [B: qML_i,A: qML_mu] :
( ( ( ~ ( incons1905966852QML_mu @ A @ B ) )
!= ( inconsistency_G @ sk34 @ sk35 ) )
| ( ( ! [C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ A @ B )
=> ! [D: qML_i] :
( ( qML_r @ B @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) ) )
!= ( ! [C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ sk34 @ sk35 )
=> ! [D: qML_i] :
( ( qML_r @ sk35 @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[68,991]) ).
thf(1214,plain,
( ( ~ ( incons1905966852QML_mu @ sk34 @ sk35 ) )
!= ( inconsistency_G @ sk34 @ sk35 ) ),
inference(pattern_uni,[status(thm)],[1213:[bind(A,$thf( sk34 )),bind(B,$thf( sk35 ))]]) ).
thf(1300,plain,
( ~ ~ ( incons1905966852QML_mu @ sk34 @ sk35 )
| ~ ( inconsistency_G @ sk34 @ sk35 ) ),
inference(bool_ext,[status(thm)],[1214]) ).
thf(1319,plain,
( ~ ( inconsistency_G @ sk34 @ sk35 )
| ( incons1905966852QML_mu @ sk34 @ sk35 ) ),
inference(cnf,[status(esa)],[1300]) ).
thf(4206,plain,
! [C: qML_mu > qML_i > $o,B: qML_i,A: qML_i] :
( ( inconsistency_G
!= ( ^ [D: qML_mu,E: qML_i] :
~ ( C @ D @ E ) ) )
| ( ( inconsistency_P
@ ^ [D: qML_mu,E: qML_i] : $true
@ A )
!= ( inconsistency_P @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4139,56]) ).
thf(4207,plain,
( inconsistency_G
!= ( ^ [A: qML_mu,B: qML_i] : ~ $true ) ),
inference(pattern_uni,[status(thm)],[4206:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( ^ [D: qML_mu] : ^ [E: qML_i] : $true ))]]) ).
thf(4251,plain,
( inconsistency_G
!= ( ^ [A: qML_mu,B: qML_i] : $false ) ),
inference(simp,[status(thm)],[4207]) ).
thf(4270,plain,
inconsistency_G @ sk352 @ sk353,
inference(func_ext,[status(esa)],[4251]) ).
thf(735,plain,
! [B: qML_i,A: qML_mu] :
( ( incons1905966852QML_mu @ sk5 @ sk6 )
| ~ ! [C: qML_mu > qML_i > $o] :
( ( inconsistency_P @ C @ B )
=> ( C @ A @ B ) )
| ( ( inconsistency_G @ A @ B )
!= ( inconsistency_G @ sk5 @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[34,120]) ).
thf(736,plain,
( ( incons1905966852QML_mu @ sk5 @ sk6 )
| ~ ! [A: qML_mu > qML_i > $o] :
( ( inconsistency_P @ A @ sk6 )
=> ( A @ sk5 @ sk6 ) ) ),
inference(pattern_uni,[status(thm)],[735:[bind(A,$thf( sk5 )),bind(B,$thf( sk6 ))]]) ).
thf(781,plain,
( ( inconsistency_P @ sk62 @ sk6 )
| ( incons1905966852QML_mu @ sk5 @ sk6 ) ),
inference(cnf,[status(esa)],[736]) ).
thf(1378,plain,
! [A: qML_i] :
( ( incons1905966852QML_mu @ sk5 @ sk6 )
| ( ( inconsistency_P @ sk62 @ sk6 )
!= ( inconsistency_P
@ ^ [B: qML_mu,C: qML_i] :
~ ( incons1905966852QML_mu @ B @ C )
@ A ) ) ),
inference(paramod_ordered,[status(thm)],[781,44]) ).
thf(1390,plain,
! [A: qML_i] :
( ( incons1905966852QML_mu @ sk5 @ sk6 )
| ( sk62
!= ( ^ [B: qML_mu,C: qML_i] :
~ ( incons1905966852QML_mu @ B @ C ) ) )
| ( sk6 != A ) ),
inference(simp,[status(thm)],[1378]) ).
thf(1398,plain,
( ( incons1905966852QML_mu @ sk5 @ sk6 )
| ( sk62
!= ( ^ [A: qML_mu,B: qML_i] :
~ ( incons1905966852QML_mu @ A @ B ) ) ) ),
inference(simp,[status(thm)],[1390]) ).
thf(4265,plain,
incons1905966852QML_mu @ sk350 @ sk351,
inference(func_ext,[status(esa)],[4247]) ).
thf(758,plain,
! [B: qML_i,A: qML_mu] :
( ( ( ! [C: qML_mu > qML_i > $o] :
( ( inconsistency_P @ C @ B )
=> ( C @ A @ B ) ) )
!= ( ~ ! [C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ sk30 @ sk31 )
=> ! [D: qML_i] :
( ( qML_r @ sk31 @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) ) ) )
| ( ( inconsistency_G @ A @ B )
!= ( inconsistency_G @ sk30 @ sk31 ) ) ),
inference(paramod_ordered,[status(thm)],[34,525]) ).
thf(759,plain,
( ( ! [A: qML_mu > qML_i > $o] :
( ( inconsistency_P @ A @ sk31 )
=> ( A @ sk30 @ sk31 ) ) )
!= ( ~ ! [A: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ A @ sk30 @ sk31 )
=> ! [B: qML_i] :
( ( qML_r @ sk31 @ B )
=> ? [C: qML_mu] : ( A @ C @ B ) ) ) ) ),
inference(pattern_uni,[status(thm)],[758:[bind(A,$thf( sk30 )),bind(B,$thf( sk31 ))]]) ).
thf(1216,plain,
! [B: qML_i,A: qML_mu] :
( ( ( ~ ( incons1905966852QML_mu @ A @ B ) )
!= ( ! [C: qML_mu > qML_i > $o] :
( ( inconsistency_P @ C @ sk31 )
=> ( C @ sk30 @ sk31 ) ) ) )
| ( ( ! [C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ A @ B )
=> ! [D: qML_i] :
( ( qML_r @ B @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) ) )
!= ( ! [C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ sk30 @ sk31 )
=> ! [D: qML_i] :
( ( qML_r @ sk31 @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[68,759]) ).
thf(1217,plain,
( ( ~ ( incons1905966852QML_mu @ sk30 @ sk31 ) )
!= ( ! [A: qML_mu > qML_i > $o] :
( ( inconsistency_P @ A @ sk31 )
=> ( A @ sk30 @ sk31 ) ) ) ),
inference(pattern_uni,[status(thm)],[1216:[bind(A,$thf( sk30 )),bind(B,$thf( sk31 ))]]) ).
thf(1471,plain,
( ~ ~ ( incons1905966852QML_mu @ sk30 @ sk31 )
| ~ ! [A: qML_mu > qML_i > $o] :
( ( inconsistency_P @ A @ sk31 )
=> ( A @ sk30 @ sk31 ) ) ),
inference(bool_ext,[status(thm)],[1217]) ).
thf(1494,plain,
( ( inconsistency_P @ sk134 @ sk31 )
| ( incons1905966852QML_mu @ sk30 @ sk31 ) ),
inference(cnf,[status(esa)],[1471]) ).
thf(105,plain,
( ( ! [A: qML_mu > qML_i > $o] :
( ( inconsistency_P @ A @ sk8 )
=> ( A @ sk7 @ sk8 ) ) )
!= ( ~ ( inconsistency_G @ sk7 @ sk8 ) ) ),
inference(func_ext,[status(esa)],[66]) ).
thf(184,plain,
( ~ ! [A: qML_mu > qML_i > $o] :
( ( inconsistency_P @ A @ sk8 )
=> ( A @ sk7 @ sk8 ) )
| ~ ~ ( inconsistency_G @ sk7 @ sk8 ) ),
inference(bool_ext,[status(thm)],[105]) ).
thf(187,plain,
( ( inconsistency_G @ sk7 @ sk8 )
| ( inconsistency_P @ sk11 @ sk8 ) ),
inference(cnf,[status(esa)],[184]) ).
thf(1099,plain,
! [B: qML_mu > qML_i > $o,A: qML_i] :
( ( inconsistency_G @ sk7 @ sk8 )
| ( inconsistency_G
!= ( ^ [C: qML_mu,D: qML_i] :
~ ( B @ C @ D ) ) )
| ( ( inconsistency_P @ sk11 @ sk8 )
!= ( inconsistency_P @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[187,56]) ).
thf(1100,plain,
( ( inconsistency_G @ sk7 @ sk8 )
| ( inconsistency_G
!= ( ^ [A: qML_mu,B: qML_i] :
~ ( sk11 @ A @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[1099:[bind(A,$thf( sk8 )),bind(B,$thf( sk11 ))]]) ).
thf(200,plain,
! [B: qML_i,A: qML_i] :
( ( inconsistency_P @ inconsistency_G @ A )
!= ( inconsistency_P
@ ^ [C: qML_mu,D: qML_i] :
~ ! [E: qML_mu > qML_i > $o] :
( ( inconsistency_P @ E @ D )
=> ( E @ C @ D ) )
@ B ) ),
inference(paramod_ordered,[status(thm)],[22,47]) ).
thf(203,plain,
! [B: qML_i,A: qML_i] :
( ( inconsistency_G
!= ( ^ [C: qML_mu,D: qML_i] :
~ ! [E: qML_mu > qML_i > $o] :
( ( inconsistency_P @ E @ D )
=> ( E @ C @ D ) ) ) )
| ( A != B ) ),
inference(simp,[status(thm)],[200]) ).
thf(206,plain,
( inconsistency_G
!= ( ^ [A: qML_mu,B: qML_i] :
~ ! [C: qML_mu > qML_i > $o] :
( ( inconsistency_P @ C @ B )
=> ( C @ A @ B ) ) ) ),
inference(simp,[status(thm)],[203]) ).
thf(211,plain,
( ( inconsistency_G @ sk15 @ sk16 )
!= ( ~ ! [A: qML_mu > qML_i > $o] :
( ( inconsistency_P @ A @ sk16 )
=> ( A @ sk15 @ sk16 ) ) ) ),
inference(func_ext,[status(esa)],[206]) ).
thf(119,plain,
( ( inconsistency_G @ sk5 @ sk6 )
| ~ ( incons1905966852QML_mu @ sk5 @ sk6 ) ),
inference(bool_ext,[status(thm)],[102]) ).
thf(121,plain,
( ~ ( incons1905966852QML_mu @ sk5 @ sk6 )
| ( inconsistency_G @ sk5 @ sk6 ) ),
inference(cnf,[status(esa)],[119]) ).
thf(1168,plain,
! [B: qML_i,A: qML_mu] :
( ( ( ~ ! [C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ A @ B )
=> ! [D: qML_i] :
( ( qML_r @ B @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) ) )
!= ( ! [C: qML_mu > qML_i > $o] :
( ( inconsistency_P @ C @ sk10 )
=> ( C @ sk9 @ sk10 ) ) ) )
| ( ( incons1905966852QML_mu @ A @ B )
!= ( incons1905966852QML_mu @ sk9 @ sk10 ) ) ),
inference(paramod_ordered,[status(thm)],[68,110]) ).
thf(1169,plain,
( ( ~ ! [A: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ A @ sk9 @ sk10 )
=> ! [B: qML_i] :
( ( qML_r @ sk10 @ B )
=> ? [C: qML_mu] : ( A @ C @ B ) ) ) )
!= ( ! [A: qML_mu > qML_i > $o] :
( ( inconsistency_P @ A @ sk10 )
=> ( A @ sk9 @ sk10 ) ) ) ),
inference(pattern_uni,[status(thm)],[1168:[bind(A,$thf( sk9 )),bind(B,$thf( sk10 ))]]) ).
thf(2861,plain,
! [A: qML_mu > qML_i > $o] :
( ( ( incons1389517216QML_mu @ A )
!= ( ^ [B: qML_mu,C: qML_i] :
~ ( inconsistency_G @ B @ C ) ) )
| ( ( ^ [B: qML_mu,C: qML_i,D: qML_mu > qML_i > $o] : ( D @ B @ C ) )
!= ( ^ [B: qML_mu,C: qML_i,D: qML_mu > qML_i > $o] : ( inconsistency_P @ D @ C ) ) )
| ( ( ^ [B: qML_mu,C: qML_i,D: qML_mu > qML_i > $o] :
! [E: qML_i] :
( ( qML_r @ C @ E )
=> ! [F: qML_mu] :
( ( A @ F @ E )
=> ( D @ F @ E ) ) ) )
!= ( ^ [B: qML_mu,C: qML_i,D: qML_mu > qML_i > $o] : ( D @ B @ C ) ) ) ),
inference(simp,[status(thm)],[977]) ).
thf(1183,plain,
! [B: qML_i,A: qML_mu] :
( ( ( ~ ! [C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ A @ B )
=> ! [D: qML_i] :
( ( qML_r @ B @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) ) )
!= ( inconsistency_G @ sk5 @ sk6 ) )
| ( ( incons1905966852QML_mu @ A @ B )
!= ( incons1905966852QML_mu @ sk5 @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[68,102]) ).
thf(1184,plain,
( ( ~ ! [A: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ A @ sk5 @ sk6 )
=> ! [B: qML_i] :
( ( qML_r @ sk6 @ B )
=> ? [C: qML_mu] : ( A @ C @ B ) ) ) )
!= ( inconsistency_G @ sk5 @ sk6 ) ),
inference(pattern_uni,[status(thm)],[1183:[bind(A,$thf( sk5 )),bind(B,$thf( sk6 ))]]) ).
thf(1607,plain,
( ~ ! [A: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ A @ sk5 @ sk6 )
=> ! [B: qML_i] :
( ( qML_r @ sk6 @ B )
=> ? [C: qML_mu] : ( A @ C @ B ) ) )
| ( inconsistency_G @ sk5 @ sk6 ) ),
inference(bool_ext,[status(thm)],[1184]) ).
thf(1622,plain,
( ( inconsistency_G @ sk5 @ sk6 )
| ( qML_r @ sk6 @ sk144 ) ),
inference(cnf,[status(esa)],[1607]) ).
thf(114,plain,
( ~ ( incons1905966852QML_mu @ sk3 @ sk4 )
| ~ ~ ( inconsistency_G @ sk3 @ sk4 ) ),
inference(bool_ext,[status(thm)],[77]) ).
thf(116,plain,
( ( inconsistency_G @ sk3 @ sk4 )
| ~ ( incons1905966852QML_mu @ sk3 @ sk4 ) ),
inference(cnf,[status(esa)],[114]) ).
thf(189,plain,
( ~ ! [A: qML_mu > qML_i > $o] :
( ( inconsistency_P @ A @ sk10 )
=> ( A @ sk9 @ sk10 ) )
| ~ ~ ( incons1905966852QML_mu @ sk9 @ sk10 ) ),
inference(bool_ext,[status(thm)],[110]) ).
thf(195,plain,
( ( incons1905966852QML_mu @ sk9 @ sk10 )
| ( inconsistency_P @ sk12 @ sk10 ) ),
inference(cnf,[status(esa)],[189]) ).
thf(411,plain,
! [A: qML_i] :
( ( incons1905966852QML_mu @ sk9 @ sk10 )
| ( ( inconsistency_P @ sk12 @ sk10 )
!= ( inconsistency_P
@ ^ [B: qML_mu,C: qML_i] :
~ ( inconsistency_G @ B @ C )
@ A ) ) ),
inference(paramod_ordered,[status(thm)],[195,41]) ).
thf(422,plain,
! [A: qML_i] :
( ( incons1905966852QML_mu @ sk9 @ sk10 )
| ( sk12
!= ( ^ [B: qML_mu,C: qML_i] :
~ ( inconsistency_G @ B @ C ) ) )
| ( sk10 != A ) ),
inference(simp,[status(thm)],[411]) ).
thf(428,plain,
( ( incons1905966852QML_mu @ sk9 @ sk10 )
| ( sk12
!= ( ^ [A: qML_mu,B: qML_i] :
~ ( inconsistency_G @ A @ B ) ) ) ),
inference(simp,[status(thm)],[422]) ).
thf(828,plain,
( ~ ! [A: qML_mu > qML_i > $o] :
( ( inconsistency_P @ A @ sk6 )
=> ( A @ sk5 @ sk6 ) )
| ~ ~ ( incons1905966852QML_mu @ sk5 @ sk6 ) ),
inference(bool_ext,[status(thm)],[747]) ).
thf(849,plain,
( ( incons1905966852QML_mu @ sk5 @ sk6 )
| ( inconsistency_P @ sk67 @ sk6 ) ),
inference(cnf,[status(esa)],[828]) ).
thf(69,plain,
( ( incons1905966852QML_mu = inconsistency_G )
| ( ( ^ [A: qML_mu,B: qML_i] :
! [C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ A @ B )
=> ! [D: qML_i] :
( ( qML_r @ B @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) ) )
!= ( ^ [A: qML_mu,B: qML_i] :
! [C: qML_mu > qML_i > $o] :
( ( inconsistency_P @ C @ B )
=> ( C @ A @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[30,28]) ).
thf(74,plain,
( ( incons1905966852QML_mu = inconsistency_G )
| ( ( ^ [A: qML_mu,B: qML_i,C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ A @ B )
=> ! [D: qML_i] :
( ( qML_r @ B @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) ) )
!= ( ^ [A: qML_mu,B: qML_i,C: qML_mu > qML_i > $o] :
( ( inconsistency_P @ C @ B )
=> ( C @ A @ B ) ) ) ) ),
inference(simp,[status(thm)],[69]) ).
thf(738,plain,
! [B: qML_i,A: qML_mu] :
( ( ( inconsistency_G @ A @ B )
!= ( ~ ( incons1905966852QML_mu @ sk9 @ sk10 ) ) )
| ( ( ! [C: qML_mu > qML_i > $o] :
( ( inconsistency_P @ C @ B )
=> ( C @ A @ B ) ) )
!= ( ! [C: qML_mu > qML_i > $o] :
( ( inconsistency_P @ C @ sk10 )
=> ( C @ sk9 @ sk10 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[34,110]) ).
thf(739,plain,
( ( inconsistency_G @ sk9 @ sk10 )
!= ( ~ ( incons1905966852QML_mu @ sk9 @ sk10 ) ) ),
inference(pattern_uni,[status(thm)],[738:[bind(A,$thf( sk9 )),bind(B,$thf( sk10 ))]]) ).
thf(798,plain,
( ~ ( inconsistency_G @ sk9 @ sk10 )
| ~ ~ ( incons1905966852QML_mu @ sk9 @ sk10 ) ),
inference(bool_ext,[status(thm)],[739]) ).
thf(815,plain,
( ( incons1905966852QML_mu @ sk9 @ sk10 )
| ~ ( inconsistency_G @ sk9 @ sk10 ) ),
inference(cnf,[status(esa)],[798]) ).
thf(1559,plain,
! [B: qML_i,A: qML_mu] :
( ( incons1905966852QML_mu @ sk9 @ sk10 )
| ~ ! [C: qML_mu > qML_i > $o] :
( ( inconsistency_P @ C @ B )
=> ( C @ A @ B ) )
| ( ( inconsistency_G @ A @ B )
!= ( inconsistency_G @ sk9 @ sk10 ) ) ),
inference(paramod_ordered,[status(thm)],[34,815]) ).
thf(1560,plain,
( ( incons1905966852QML_mu @ sk9 @ sk10 )
| ~ ! [A: qML_mu > qML_i > $o] :
( ( inconsistency_P @ A @ sk10 )
=> ( A @ sk9 @ sk10 ) ) ),
inference(pattern_uni,[status(thm)],[1559:[bind(A,$thf( sk9 )),bind(B,$thf( sk10 ))]]) ).
thf(1604,plain,
( ~ ( sk140 @ sk9 @ sk10 )
| ( incons1905966852QML_mu @ sk9 @ sk10 ) ),
inference(cnf,[status(esa)],[1560]) ).
thf(1198,plain,
! [B: qML_i,A: qML_mu] :
( ( ( incons1905966852QML_mu @ A @ B )
!= ( ~ ! [C: qML_mu > qML_i > $o] :
( ( inconsistency_P @ C @ sk24 )
=> ( C @ sk23 @ sk24 ) ) ) )
| ( ( ! [C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ A @ B )
=> ! [D: qML_i] :
( ( qML_r @ B @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) ) )
!= ( ! [C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ sk23 @ sk24 )
=> ! [D: qML_i] :
( ( qML_r @ sk24 @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[68,406]) ).
thf(1199,plain,
( ( incons1905966852QML_mu @ sk23 @ sk24 )
!= ( ~ ! [A: qML_mu > qML_i > $o] :
( ( inconsistency_P @ A @ sk24 )
=> ( A @ sk23 @ sk24 ) ) ) ),
inference(pattern_uni,[status(thm)],[1198:[bind(A,$thf( sk23 )),bind(B,$thf( sk24 ))]]) ).
thf(1470,plain,
( ( inconsistency_P @ sk133 @ sk22 )
| ( incons1905966852QML_mu @ sk21 @ sk22 ) ),
inference(cnf,[status(esa)],[1449]) ).
thf(1046,plain,
! [B: qML_mu > qML_i > $o,A: qML_i] :
( ( inconsistency_G @ sk7 @ sk8 )
| ( incons1905966852QML_mu
!= ( ^ [C: qML_mu,D: qML_i] :
~ ( B @ C @ D ) ) )
| ( ( inconsistency_P @ sk11 @ sk8 )
!= ( inconsistency_P @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[187,54]) ).
thf(1047,plain,
( ( inconsistency_G @ sk7 @ sk8 )
| ( incons1905966852QML_mu
!= ( ^ [A: qML_mu,B: qML_i] :
~ ( sk11 @ A @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[1046:[bind(A,$thf( sk8 )),bind(B,$thf( sk11 ))]]) ).
thf(1222,plain,
! [B: qML_i,A: qML_mu] :
( ( ( incons1905966852QML_mu @ A @ B )
!= ( ~ ( inconsistency_G @ sk23 @ sk24 ) ) )
| ( ( ! [C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ A @ B )
=> ! [D: qML_i] :
( ( qML_r @ B @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) ) )
!= ( ! [C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ sk23 @ sk24 )
=> ! [D: qML_i] :
( ( qML_r @ sk24 @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[68,860]) ).
thf(1223,plain,
( ( incons1905966852QML_mu @ sk23 @ sk24 )
!= ( ~ ( inconsistency_G @ sk23 @ sk24 ) ) ),
inference(pattern_uni,[status(thm)],[1222:[bind(A,$thf( sk23 )),bind(B,$thf( sk24 ))]]) ).
thf(817,plain,
( ~ ( incons1905966852QML_mu @ sk13 @ sk14 )
| ~ ~ ( inconsistency_G @ sk13 @ sk14 ) ),
inference(bool_ext,[status(thm)],[757]) ).
thf(825,plain,
( ( inconsistency_G @ sk13 @ sk14 )
| ~ ( incons1905966852QML_mu @ sk13 @ sk14 ) ),
inference(cnf,[status(esa)],[817]) ).
thf(419,plain,
! [A: qML_i] :
( ( incons1905966852QML_mu @ sk9 @ sk10 )
| ( ( inconsistency_P @ sk12 @ sk10 )
!= ( inconsistency_P
@ ^ [B: qML_mu,C: qML_i] :
~ ( incons1905966852QML_mu @ B @ C )
@ A ) ) ),
inference(paramod_ordered,[status(thm)],[195,44]) ).
thf(423,plain,
! [A: qML_i] :
( ( incons1905966852QML_mu @ sk9 @ sk10 )
| ( sk12
!= ( ^ [B: qML_mu,C: qML_i] :
~ ( incons1905966852QML_mu @ B @ C ) ) )
| ( sk10 != A ) ),
inference(simp,[status(thm)],[419]) ).
thf(429,plain,
( ( incons1905966852QML_mu @ sk9 @ sk10 )
| ( sk12
!= ( ^ [A: qML_mu,B: qML_i] :
~ ( incons1905966852QML_mu @ A @ B ) ) ) ),
inference(simp,[status(thm)],[423]) ).
thf(33,plain,
! [A: qML_mu] :
( ( inconsistency_G @ A )
= ( ^ [B: qML_i] :
! [C: qML_mu > qML_i > $o] :
( ( inconsistency_P @ C @ B )
=> ( C @ A @ B ) ) ) ),
inference(func_ext,[status(esa)],[28]) ).
thf(145,plain,
! [C: qML_mu > qML_i > $o,B: qML_mu > qML_i > $o,A: qML_i] :
( ~ ( inconsistency_P @ B @ A )
| ( inconsistency_P @ C @ A )
| ( ( C @ ( sk2 @ C @ B @ A ) @ ( sk1 @ C @ B @ A ) )
!= ( ~ ( inconsistency_P @ C @ A ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[18]) ).
thf(160,plain,
! [C: qML_mu > qML_i > $o,B: qML_mu > qML_i > $o,A: qML_i] :
( ( inconsistency_P @ C @ A )
| ~ ( inconsistency_P @ B @ A )
| ( ( C @ ( sk2 @ C @ B @ A ) @ ( sk1 @ C @ B @ A ) )
!= ( ~ ( inconsistency_P @ C @ A ) ) ) ),
inference(simp,[status(thm)],[145]) ).
thf(1369,plain,
! [B: qML_mu > qML_i > $o,A: qML_i] :
( ( incons1905966852QML_mu @ sk5 @ sk6 )
| ( inconsistency_G
!= ( ^ [C: qML_mu,D: qML_i] :
~ ( B @ C @ D ) ) )
| ( ( inconsistency_P @ sk62 @ sk6 )
!= ( inconsistency_P @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[781,56]) ).
thf(1370,plain,
( ( incons1905966852QML_mu @ sk5 @ sk6 )
| ( inconsistency_G
!= ( ^ [A: qML_mu,B: qML_i] :
~ ( sk62 @ A @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[1369:[bind(A,$thf( sk6 )),bind(B,$thf( sk62 ))]]) ).
thf(4,axiom,
! [A: qML_i,B: qML_mu > qML_i > $o] :
( ~ ( inconsistency_P @ B @ A )
=> ( inconsistency_P
@ ^ [C: qML_mu,D: qML_i] :
~ ( B @ C @ D )
@ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_A1b) ).
thf(15,plain,
! [A: qML_i,B: qML_mu > qML_i > $o] :
( ~ ( inconsistency_P @ B @ A )
=> ( inconsistency_P
@ ^ [C: qML_mu,D: qML_i] :
~ ( B @ C @ D )
@ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(16,plain,
! [B: qML_mu > qML_i > $o,A: qML_i] :
( ( inconsistency_P @ B @ A )
| ( inconsistency_P
@ ^ [C: qML_mu,D: qML_i] :
~ ( B @ C @ D )
@ A ) ),
inference(cnf,[status(esa)],[15]) ).
thf(133,plain,
! [E: qML_mu > qML_i > $o,D: qML_mu > qML_i > $o,C: qML_i,B: qML_mu > qML_i > $o,A: qML_i] :
( ( inconsistency_P @ B @ A )
| ~ ( inconsistency_P @ D @ C )
| ( inconsistency_P @ E @ C )
| ( ( inconsistency_P
@ ^ [F: qML_mu,G: qML_i] :
~ ( B @ F @ G )
@ A )
!= ( E @ ( sk2 @ E @ D @ C ) @ ( sk1 @ E @ D @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[16,18]) ).
thf(162,plain,
! [D: qML_mu > qML_i > qML_mu > qML_i > $o,C: qML_mu > qML_i > qML_i,B: qML_mu > qML_i > $o,A: qML_i] :
( ( inconsistency_P
@ ( D
@ ( sk2
@ ^ [E: qML_mu,F: qML_i] :
( inconsistency_P
@ ^ [G: qML_mu,H: qML_i] :
~ ( D @ E @ F @ G @ H )
@ ( C @ E @ F ) )
@ B
@ A )
@ ( sk1
@ ^ [E: qML_mu,F: qML_i] :
( inconsistency_P
@ ^ [G: qML_mu,H: qML_i] :
~ ( D @ E @ F @ G @ H )
@ ( C @ E @ F ) )
@ B
@ A ) )
@ ( C
@ ( sk2
@ ^ [E: qML_mu,F: qML_i] :
( inconsistency_P
@ ^ [G: qML_mu,H: qML_i] :
~ ( D @ E @ F @ G @ H )
@ ( C @ E @ F ) )
@ B
@ A )
@ ( sk1
@ ^ [E: qML_mu,F: qML_i] :
( inconsistency_P
@ ^ [G: qML_mu,H: qML_i] :
~ ( D @ E @ F @ G @ H )
@ ( C @ E @ F ) )
@ B
@ A ) ) )
| ~ ( inconsistency_P @ B @ A )
| ( inconsistency_P
@ ^ [E: qML_mu,F: qML_i] :
( inconsistency_P
@ ^ [G: qML_mu,H: qML_i] :
~ ( D @ E @ F @ G @ H )
@ ( C @ E @ F ) )
@ A ) ),
inference(pre_uni,[status(thm)],[133:[bind(A,$thf( G @ ( sk2 @ ^ [H: qML_mu] : ^ [I: qML_i] : ( inconsistency_P @ ^ [J: qML_mu] : ^ [K: qML_i] : ~ ( H @ H @ I @ J @ K ) @ ( G @ H @ I ) ) @ D @ C ) @ ( sk1 @ ^ [H: qML_mu] : ^ [I: qML_i] : ( inconsistency_P @ ^ [J: qML_mu] : ^ [K: qML_i] : ~ ( H @ H @ I @ J @ K ) @ ( G @ H @ I ) ) @ D @ C ) )),bind(B,$thf( H @ ( sk2 @ ^ [H: qML_mu] : ^ [I: qML_i] : ( inconsistency_P @ ^ [J: qML_mu] : ^ [K: qML_i] : ~ ( H @ H @ I @ J @ K ) @ ( G @ H @ I ) ) @ D @ C ) @ ( sk1 @ ^ [H: qML_mu] : ^ [I: qML_i] : ( inconsistency_P @ ^ [J: qML_mu] : ^ [K: qML_i] : ~ ( H @ H @ I @ J @ K ) @ ( G @ H @ I ) ) @ D @ C ) )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( ^ [H: qML_mu] : ^ [I: qML_i] : ( inconsistency_P @ ^ [J: qML_mu] : ^ [K: qML_i] : ~ ( H @ H @ I @ J @ K ) @ ( G @ H @ I ) ) ))]]) ).
thf(165,plain,
! [D: qML_mu > qML_i > qML_mu > qML_i > $o,C: qML_mu > qML_i > qML_i,B: qML_mu > qML_i > $o,A: qML_i] :
( ( inconsistency_P
@ ( D
@ ( sk2
@ ^ [E: qML_mu,F: qML_i] :
( inconsistency_P
@ ^ [G: qML_mu,H: qML_i] :
~ ( D @ E @ F @ G @ H )
@ ( C @ E @ F ) )
@ B
@ A )
@ ( sk1
@ ^ [E: qML_mu,F: qML_i] :
( inconsistency_P
@ ^ [G: qML_mu,H: qML_i] :
~ ( D @ E @ F @ G @ H )
@ ( C @ E @ F ) )
@ B
@ A ) )
@ ( C
@ ( sk2
@ ^ [E: qML_mu,F: qML_i] :
( inconsistency_P
@ ^ [G: qML_mu,H: qML_i] :
~ ( D @ E @ F @ G @ H )
@ ( C @ E @ F ) )
@ B
@ A )
@ ( sk1
@ ^ [E: qML_mu,F: qML_i] :
( inconsistency_P
@ ^ [G: qML_mu,H: qML_i] :
~ ( D @ E @ F @ G @ H )
@ ( C @ E @ F ) )
@ B
@ A ) ) )
| ~ ( inconsistency_P @ B @ A )
| ( inconsistency_P
@ ^ [E: qML_mu,F: qML_i] :
( inconsistency_P
@ ^ [G: qML_mu,H: qML_i] :
~ ( D @ E @ F @ G @ H )
@ ( C @ E @ F ) )
@ A ) ),
inference(simp,[status(thm)],[162]) ).
thf(506,plain,
! [B: qML_i,A: qML_i] :
( ( inconsistency_P @ incons1905966852QML_mu @ A )
!= ( inconsistency_P
@ ^ [C: qML_mu,D: qML_i] :
~ ! [E: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ E @ C @ D )
=> ! [F: qML_i] :
( ( qML_r @ D @ F )
=> ? [G: qML_mu] : ( E @ G @ F ) ) )
@ B ) ),
inference(paramod_ordered,[status(thm)],[26,476]) ).
thf(515,plain,
! [B: qML_i,A: qML_i] :
( ( incons1905966852QML_mu
!= ( ^ [C: qML_mu,D: qML_i] :
~ ! [E: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ E @ C @ D )
=> ! [F: qML_i] :
( ( qML_r @ D @ F )
=> ? [G: qML_mu] : ( E @ G @ F ) ) ) ) )
| ( A != B ) ),
inference(simp,[status(thm)],[506]) ).
thf(519,plain,
( incons1905966852QML_mu
!= ( ^ [A: qML_mu,B: qML_i] :
~ ! [C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ A @ B )
=> ! [D: qML_i] :
( ( qML_r @ B @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) ) ) ),
inference(simp,[status(thm)],[515]) ).
thf(522,plain,
( ( incons1905966852QML_mu @ sk28 @ sk29 )
!= ( ~ ! [A: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ A @ sk28 @ sk29 )
=> ! [B: qML_i] :
( ( qML_r @ sk29 @ B )
=> ? [C: qML_mu] : ( A @ C @ B ) ) ) ) ),
inference(func_ext,[status(esa)],[519]) ).
thf(530,plain,
! [A: qML_i] :
( ( incons1905966852QML_mu @ sk13 @ sk14 )
| ( ( inconsistency_P @ sk17 @ sk14 )
!= ( inconsistency_P
@ ^ [B: qML_mu,C: qML_i] :
~ ( inconsistency_G @ B @ C )
@ A ) ) ),
inference(paramod_ordered,[status(thm)],[220,41]) ).
thf(547,plain,
! [A: qML_i] :
( ( incons1905966852QML_mu @ sk13 @ sk14 )
| ( sk17
!= ( ^ [B: qML_mu,C: qML_i] :
~ ( inconsistency_G @ B @ C ) ) )
| ( sk14 != A ) ),
inference(simp,[status(thm)],[530]) ).
thf(551,plain,
( ( incons1905966852QML_mu @ sk13 @ sk14 )
| ( sk17
!= ( ^ [A: qML_mu,B: qML_i] :
~ ( inconsistency_G @ A @ B ) ) ) ),
inference(simp,[status(thm)],[547]) ).
thf(1175,plain,
! [B: qML_i,A: qML_mu] :
( ~ ! [C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ A @ B )
=> ! [D: qML_i] :
( ( qML_r @ B @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) )
| ( inconsistency_G @ sk5 @ sk6 )
| ( ( incons1905966852QML_mu @ A @ B )
!= ( incons1905966852QML_mu @ sk5 @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[68,121]) ).
thf(1176,plain,
( ~ ! [A: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ A @ sk5 @ sk6 )
=> ! [B: qML_i] :
( ( qML_r @ sk6 @ B )
=> ? [C: qML_mu] : ( A @ C @ B ) ) )
| ( inconsistency_G @ sk5 @ sk6 ) ),
inference(pattern_uni,[status(thm)],[1175:[bind(A,$thf( sk5 )),bind(B,$thf( sk6 ))]]) ).
thf(1259,plain,
( ( inconsistency_G @ sk5 @ sk6 )
| ( qML_r @ sk6 @ sk120 ) ),
inference(cnf,[status(esa)],[1176]) ).
thf(1493,plain,
( ~ ( sk134 @ sk30 @ sk31 )
| ( incons1905966852QML_mu @ sk30 @ sk31 ) ),
inference(cnf,[status(esa)],[1471]) ).
thf(124,plain,
! [C: qML_i,B: qML_mu,A: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ A @ B @ C )
= ( ! [D: qML_mu > qML_i > $o] :
( ( D @ B @ C )
=> ! [E: qML_i] :
( ( qML_r @ C @ E )
=> ! [F: qML_mu] :
( ( A @ F @ E )
=> ( D @ F @ E ) ) ) ) ) ),
inference(func_ext,[status(esa)],[32]) ).
thf(1003,plain,
( ( inconsistency_G @ sk34 @ sk35 )
| ~ ! [A: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ A @ sk34 @ sk35 )
=> ! [B: qML_i] :
( ( qML_r @ sk35 @ B )
=> ? [C: qML_mu] : ( A @ C @ B ) ) ) ),
inference(bool_ext,[status(thm)],[991]) ).
thf(1016,plain,
( ( qML_r @ sk35 @ sk89 )
| ( inconsistency_G @ sk34 @ sk35 ) ),
inference(cnf,[status(esa)],[1003]) ).
thf(1191,plain,
! [B: qML_i,A: qML_mu] :
( ( ( ! [C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ A @ B )
=> ! [D: qML_i] :
( ( qML_r @ B @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) ) )
!= ( ~ ( inconsistency_G @ sk3 @ sk4 ) ) )
| ( ( incons1905966852QML_mu @ A @ B )
!= ( incons1905966852QML_mu @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[68,77]) ).
thf(1192,plain,
( ( ! [A: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ A @ sk3 @ sk4 )
=> ! [B: qML_i] :
( ( qML_r @ sk4 @ B )
=> ? [C: qML_mu] : ( A @ C @ B ) ) ) )
!= ( ~ ( inconsistency_G @ sk3 @ sk4 ) ) ),
inference(pattern_uni,[status(thm)],[1191:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(1322,plain,
( ( incons1905966852QML_mu @ sk23 @ sk24 )
| ~ ( inconsistency_G @ sk23 @ sk24 ) ),
inference(bool_ext,[status(thm)],[1223]) ).
thf(1333,plain,
( ~ ( inconsistency_G @ sk23 @ sk24 )
| ( incons1905966852QML_mu @ sk23 @ sk24 ) ),
inference(cnf,[status(esa)],[1322]) ).
thf(230,plain,
! [A: qML_i] :
( ( inconsistency_G @ sk7 @ sk8 )
| ( ( inconsistency_P @ sk11 @ sk8 )
!= ( inconsistency_P
@ ^ [B: qML_mu,C: qML_i] :
~ ( incons1905966852QML_mu @ B @ C )
@ A ) ) ),
inference(paramod_ordered,[status(thm)],[187,44]) ).
thf(232,plain,
! [A: qML_i] :
( ( inconsistency_G @ sk7 @ sk8 )
| ( sk11
!= ( ^ [B: qML_mu,C: qML_i] :
~ ( incons1905966852QML_mu @ B @ C ) ) )
| ( sk8 != A ) ),
inference(simp,[status(thm)],[230]) ).
thf(237,plain,
( ( inconsistency_G @ sk7 @ sk8 )
| ( sk11
!= ( ^ [A: qML_mu,B: qML_i] :
~ ( incons1905966852QML_mu @ A @ B ) ) ) ),
inference(simp,[status(thm)],[232]) ).
thf(392,plain,
( ( inconsistency_G @ sk15 @ sk16 )
| ~ ! [A: qML_mu > qML_i > $o] :
( ( inconsistency_P @ A @ sk16 )
=> ( A @ sk15 @ sk16 ) ) ),
inference(bool_ext,[status(thm)],[211]) ).
thf(398,plain,
( ~ ( sk20 @ sk15 @ sk16 )
| ( inconsistency_G @ sk15 @ sk16 ) ),
inference(cnf,[status(esa)],[392]) ).
thf(1201,plain,
! [B: qML_i,A: qML_mu] :
( ( ( ! [C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ A @ B )
=> ! [D: qML_i] :
( ( qML_r @ B @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) ) )
!= ( ~ ! [C: qML_mu > qML_i > $o] :
( ( inconsistency_P @ C @ sk14 )
=> ( C @ sk13 @ sk14 ) ) ) )
| ( ( incons1905966852QML_mu @ A @ B )
!= ( incons1905966852QML_mu @ sk13 @ sk14 ) ) ),
inference(paramod_ordered,[status(thm)],[68,208]) ).
thf(1202,plain,
( ( ! [A: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ A @ sk13 @ sk14 )
=> ! [B: qML_i] :
( ( qML_r @ sk14 @ B )
=> ? [C: qML_mu] : ( A @ C @ B ) ) ) )
!= ( ~ ! [A: qML_mu > qML_i > $o] :
( ( inconsistency_P @ A @ sk14 )
=> ( A @ sk13 @ sk14 ) ) ) ),
inference(pattern_uni,[status(thm)],[1201:[bind(A,$thf( sk13 )),bind(B,$thf( sk14 ))]]) ).
thf(792,plain,
( ( incons1905966852QML_mu @ sk3 @ sk4 )
| ~ ( sk64 @ sk3 @ sk4 ) ),
inference(cnf,[status(esa)],[745]) ).
thf(1651,plain,
! [B: qML_i,A: qML_mu] :
( ( ( ~ ! [C: qML_mu > qML_i > $o] :
( ( inconsistency_P @ C @ B )
=> ( C @ A @ B ) ) )
!= ( ! [C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ sk3 @ sk4 )
=> ! [D: qML_i] :
( ( qML_r @ sk4 @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) ) ) )
| ( ( inconsistency_G @ A @ B )
!= ( inconsistency_G @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[34,1192]) ).
thf(1652,plain,
( ( ~ ! [A: qML_mu > qML_i > $o] :
( ( inconsistency_P @ A @ sk4 )
=> ( A @ sk3 @ sk4 ) ) )
!= ( ! [A: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ A @ sk3 @ sk4 )
=> ! [B: qML_i] :
( ( qML_r @ sk4 @ B )
=> ? [C: qML_mu] : ( A @ C @ B ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1651:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(1832,plain,
! [B: qML_i,A: qML_mu] :
( ( ( incons1905966852QML_mu @ A @ B )
!= ( ~ ! [C: qML_mu > qML_i > $o] :
( ( inconsistency_P @ C @ sk4 )
=> ( C @ sk3 @ sk4 ) ) ) )
| ( ( ! [C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ A @ B )
=> ! [D: qML_i] :
( ( qML_r @ B @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) ) )
!= ( ! [C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ sk3 @ sk4 )
=> ! [D: qML_i] :
( ( qML_r @ sk4 @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[68,1652]) ).
thf(1833,plain,
( ( incons1905966852QML_mu @ sk3 @ sk4 )
!= ( ~ ! [A: qML_mu > qML_i > $o] :
( ( inconsistency_P @ A @ sk4 )
=> ( A @ sk3 @ sk4 ) ) ) ),
inference(pattern_uni,[status(thm)],[1832:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(818,plain,
( ( incons1905966852QML_mu @ sk13 @ sk14 )
| ~ ( inconsistency_G @ sk13 @ sk14 ) ),
inference(bool_ext,[status(thm)],[757]) ).
thf(826,plain,
( ~ ( inconsistency_G @ sk13 @ sk14 )
| ( incons1905966852QML_mu @ sk13 @ sk14 ) ),
inference(cnf,[status(esa)],[818]) ).
thf(1515,plain,
! [A: qML_i] :
( ( incons1905966852QML_mu @ sk3 @ sk4 )
| ( ( inconsistency_P @ sk64 @ sk4 )
!= ( inconsistency_P
@ ^ [B: qML_mu,C: qML_i] :
~ ( incons1905966852QML_mu @ B @ C )
@ A ) ) ),
inference(paramod_ordered,[status(thm)],[793,44]) ).
thf(1527,plain,
! [A: qML_i] :
( ( incons1905966852QML_mu @ sk3 @ sk4 )
| ( sk64
!= ( ^ [B: qML_mu,C: qML_i] :
~ ( incons1905966852QML_mu @ B @ C ) ) )
| ( sk4 != A ) ),
inference(simp,[status(thm)],[1515]) ).
thf(1535,plain,
( ( incons1905966852QML_mu @ sk3 @ sk4 )
| ( sk64
!= ( ^ [A: qML_mu,B: qML_i] :
~ ( incons1905966852QML_mu @ A @ B ) ) ) ),
inference(simp,[status(thm)],[1527]) ).
thf(1,conjecture,
$false,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ $false,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(12,plain,
~ $false,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1321,plain,
( ~ ( incons1905966852QML_mu @ sk23 @ sk24 )
| ~ ~ ( inconsistency_G @ sk23 @ sk24 ) ),
inference(bool_ext,[status(thm)],[1223]) ).
thf(1332,plain,
( ( inconsistency_G @ sk23 @ sk24 )
| ~ ( incons1905966852QML_mu @ sk23 @ sk24 ) ),
inference(cnf,[status(esa)],[1321]) ).
thf(219,plain,
( ~ ( sk17 @ sk13 @ sk14 )
| ( incons1905966852QML_mu @ sk13 @ sk14 ) ),
inference(cnf,[status(esa)],[215]) ).
thf(1042,plain,
! [B: qML_mu > qML_i > $o,A: qML_i] :
( ( incons1905966852QML_mu @ sk13 @ sk14 )
| ( incons1905966852QML_mu
!= ( ^ [C: qML_mu,D: qML_i] :
~ ( B @ C @ D ) ) )
| ( ( inconsistency_P @ sk17 @ sk14 )
!= ( inconsistency_P @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[220,54]) ).
thf(1043,plain,
( ( incons1905966852QML_mu @ sk13 @ sk14 )
| ( incons1905966852QML_mu
!= ( ^ [A: qML_mu,B: qML_i] :
~ ( sk17 @ A @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[1042:[bind(A,$thf( sk14 )),bind(B,$thf( sk17 ))]]) ).
thf(97,plain,
! [B: qML_mu > qML_i > $o,A: qML_i] :
( ( inconsistency_P @ B @ A )
| ( ( inconsistency_P
@ ^ [C: qML_mu,D: qML_i] :
~ ( B @ C @ D )
@ A )
!= ( inconsistency_P @ B @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[16]) ).
thf(98,plain,
! [B: qML_mu > qML_i > $o,A: qML_i] :
( ( inconsistency_P @ B @ A )
| ( ( inconsistency_P
@ ^ [C: qML_mu,D: qML_i] :
~ ( B @ C @ D )
@ A )
!= ( inconsistency_P @ B @ A ) ) ),
inference(simp,[status(thm)],[97]) ).
thf(799,plain,
( ( inconsistency_G @ sk9 @ sk10 )
| ~ ( incons1905966852QML_mu @ sk9 @ sk10 ) ),
inference(bool_ext,[status(thm)],[739]) ).
thf(816,plain,
( ~ ( incons1905966852QML_mu @ sk9 @ sk10 )
| ( inconsistency_G @ sk9 @ sk10 ) ),
inference(cnf,[status(esa)],[799]) ).
thf(222,plain,
! [A: qML_i] :
( ( inconsistency_G @ sk7 @ sk8 )
| ( ( inconsistency_P @ sk11 @ sk8 )
!= ( inconsistency_P
@ ^ [B: qML_mu,C: qML_i] :
~ ( inconsistency_G @ B @ C )
@ A ) ) ),
inference(paramod_ordered,[status(thm)],[187,41]) ).
thf(235,plain,
! [A: qML_i] :
( ( inconsistency_G @ sk7 @ sk8 )
| ( sk11
!= ( ^ [B: qML_mu,C: qML_i] :
~ ( inconsistency_G @ B @ C ) ) )
| ( sk8 != A ) ),
inference(simp,[status(thm)],[222]) ).
thf(240,plain,
( ( inconsistency_G @ sk7 @ sk8 )
| ( sk11
!= ( ^ [A: qML_mu,B: qML_i] :
~ ( inconsistency_G @ A @ B ) ) ) ),
inference(simp,[status(thm)],[235]) ).
thf(848,plain,
( ( incons1905966852QML_mu @ sk5 @ sk6 )
| ~ ( sk67 @ sk5 @ sk6 ) ),
inference(cnf,[status(esa)],[828]) ).
thf(964,plain,
! [A: qML_mu > qML_i > $o] :
( ( ( incons1389517216QML_mu @ A )
!= ( ^ [B: qML_mu,C: qML_i] :
~ ( incons1905966852QML_mu @ B @ C ) ) )
| ( ( ^ [B: qML_mu,C: qML_i] :
! [D: qML_mu > qML_i > $o] :
( ( D @ B @ C )
=> ! [E: qML_i] :
( ( qML_r @ C @ E )
=> ! [F: qML_mu] :
( ( A @ F @ E )
=> ( D @ F @ E ) ) ) ) )
!= ( ^ [B: qML_mu,C: qML_i] :
! [D: qML_mu > qML_i > $o] :
( ( inconsistency_P @ D @ C )
=> ( D @ B @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[122,88]) ).
thf(983,plain,
! [A: qML_mu > qML_i > $o] :
( ( ( incons1389517216QML_mu @ A )
!= ( ^ [B: qML_mu,C: qML_i] :
~ ( incons1905966852QML_mu @ B @ C ) ) )
| ( ( ^ [B: qML_mu,C: qML_i,D: qML_mu > qML_i > $o] :
( ( D @ B @ C )
=> ! [E: qML_i] :
( ( qML_r @ C @ E )
=> ! [F: qML_mu] :
( ( A @ F @ E )
=> ( D @ F @ E ) ) ) ) )
!= ( ^ [B: qML_mu,C: qML_i,D: qML_mu > qML_i > $o] :
( ( inconsistency_P @ D @ C )
=> ( D @ B @ C ) ) ) ) ),
inference(simp,[status(thm)],[964]) ).
thf(129,plain,
( ~ ( inconsistency_G @ sk3 @ sk4 )
| ( inconsistency_G @ sk5 @ sk6 )
| ( ( incons1905966852QML_mu @ sk5 @ sk6 )
!= ( incons1905966852QML_mu @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[117,102]) ).
thf(130,plain,
( ( inconsistency_G @ sk5 @ sk6 )
| ~ ( inconsistency_G @ sk3 @ sk4 )
| ( sk5 != sk3 )
| ( sk6 != sk4 ) ),
inference(simp,[status(thm)],[129]) ).
thf(399,plain,
( ( inconsistency_P @ sk20 @ sk16 )
| ( inconsistency_G @ sk15 @ sk16 ) ),
inference(cnf,[status(esa)],[392]) ).
thf(1426,plain,
( ( incons1905966852QML_mu @ sk23 @ sk24 )
| ~ ! [A: qML_mu > qML_i > $o] :
( ( inconsistency_P @ A @ sk24 )
=> ( A @ sk23 @ sk24 ) ) ),
inference(bool_ext,[status(thm)],[1199]) ).
thf(1445,plain,
( ( inconsistency_P @ sk132 @ sk24 )
| ( incons1905966852QML_mu @ sk23 @ sk24 ) ),
inference(cnf,[status(esa)],[1426]) ).
thf(780,plain,
( ~ ( sk62 @ sk5 @ sk6 )
| ( incons1905966852QML_mu @ sk5 @ sk6 ) ),
inference(cnf,[status(esa)],[736]) ).
thf(1112,plain,
! [B: qML_mu > qML_i > $o,A: qML_i] :
( ( incons1905966852QML_mu @ sk9 @ sk10 )
| ( inconsistency_G
!= ( ^ [C: qML_mu,D: qML_i] :
~ ( B @ C @ D ) ) )
| ( ( inconsistency_P @ sk12 @ sk10 )
!= ( inconsistency_P @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[195,56]) ).
thf(1113,plain,
( ( incons1905966852QML_mu @ sk9 @ sk10 )
| ( inconsistency_G
!= ( ^ [A: qML_mu,B: qML_i] :
~ ( sk12 @ A @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[1112:[bind(A,$thf( sk10 )),bind(B,$thf( sk12 ))]]) ).
thf(1101,plain,
! [B: qML_mu > qML_i > $o,A: qML_i] :
( ( inconsistency_G @ sk15 @ sk16 )
| ( inconsistency_G
!= ( ^ [C: qML_mu,D: qML_i] :
~ ( B @ C @ D ) ) )
| ( ( inconsistency_P @ sk20 @ sk16 )
!= ( inconsistency_P @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[399,56]) ).
thf(1102,plain,
( ( inconsistency_G @ sk15 @ sk16 )
| ( inconsistency_G
!= ( ^ [A: qML_mu,B: qML_i] :
~ ( sk20 @ A @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[1101:[bind(A,$thf( sk16 )),bind(B,$thf( sk20 ))]]) ).
thf(702,plain,
! [A: qML_i] :
( ( inconsistency_G @ sk15 @ sk16 )
| ( ( inconsistency_P @ sk20 @ sk16 )
!= ( inconsistency_P
@ ^ [B: qML_mu,C: qML_i] :
~ ( inconsistency_G @ B @ C )
@ A ) ) ),
inference(paramod_ordered,[status(thm)],[399,41]) ).
thf(714,plain,
! [A: qML_i] :
( ( inconsistency_G @ sk15 @ sk16 )
| ( sk20
!= ( ^ [B: qML_mu,C: qML_i] :
~ ( inconsistency_G @ B @ C ) ) )
| ( sk16 != A ) ),
inference(simp,[status(thm)],[702]) ).
thf(722,plain,
( ( inconsistency_G @ sk15 @ sk16 )
| ( sk20
!= ( ^ [A: qML_mu,B: qML_i] :
~ ( inconsistency_G @ A @ B ) ) ) ),
inference(simp,[status(thm)],[714]) ).
thf(1165,plain,
! [B: qML_i,A: qML_mu] :
( ( ( ~ ! [C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ A @ B )
=> ! [D: qML_i] :
( ( qML_r @ B @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) ) )
!= ( ! [C: qML_mu > qML_i > $o] :
( ( inconsistency_P @ C @ sk6 )
=> ( C @ sk5 @ sk6 ) ) ) )
| ( ( incons1905966852QML_mu @ A @ B )
!= ( incons1905966852QML_mu @ sk5 @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[68,747]) ).
thf(1166,plain,
( ( ~ ! [A: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ A @ sk5 @ sk6 )
=> ! [B: qML_i] :
( ( qML_r @ sk6 @ B )
=> ? [C: qML_mu] : ( A @ C @ B ) ) ) )
!= ( ! [A: qML_mu > qML_i > $o] :
( ( inconsistency_P @ A @ sk6 )
=> ( A @ sk5 @ sk6 ) ) ) ),
inference(pattern_uni,[status(thm)],[1165:[bind(A,$thf( sk5 )),bind(B,$thf( sk6 ))]]) ).
thf(1196,plain,
! [B: qML_i,A: qML_mu] :
( ( ( incons1905966852QML_mu @ A @ B )
!= ( ~ ( inconsistency_G @ sk21 @ sk22 ) ) )
| ( ( ! [C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ A @ B )
=> ! [D: qML_i] :
( ( qML_r @ B @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) ) )
!= ( ! [C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ sk21 @ sk22 )
=> ! [D: qML_i] :
( ( qML_r @ sk22 @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[68,402]) ).
thf(1197,plain,
( ( incons1905966852QML_mu @ sk21 @ sk22 )
!= ( ~ ( inconsistency_G @ sk21 @ sk22 ) ) ),
inference(pattern_uni,[status(thm)],[1196:[bind(A,$thf( sk21 )),bind(B,$thf( sk22 ))]]) ).
thf(1267,plain,
( ( incons1905966852QML_mu @ sk21 @ sk22 )
| ~ ( inconsistency_G @ sk21 @ sk22 ) ),
inference(bool_ext,[status(thm)],[1197]) ).
thf(1277,plain,
( ~ ( inconsistency_G @ sk21 @ sk22 )
| ( incons1905966852QML_mu @ sk21 @ sk22 ) ),
inference(cnf,[status(esa)],[1267]) ).
thf(123,plain,
! [B: qML_mu,A: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ A @ B )
= ( ^ [C: qML_i] :
! [D: qML_mu > qML_i > $o] :
( ( D @ B @ C )
=> ! [E: qML_i] :
( ( qML_r @ C @ E )
=> ! [F: qML_mu] :
( ( A @ F @ E )
=> ( D @ F @ E ) ) ) ) ) ),
inference(func_ext,[status(esa)],[32]) ).
thf(194,plain,
( ( incons1905966852QML_mu @ sk9 @ sk10 )
| ~ ( sk12 @ sk9 @ sk10 ) ),
inference(cnf,[status(esa)],[189]) ).
thf(1048,plain,
! [B: qML_mu > qML_i > $o,A: qML_i] :
( ( inconsistency_G @ sk15 @ sk16 )
| ( incons1905966852QML_mu
!= ( ^ [C: qML_mu,D: qML_i] :
~ ( B @ C @ D ) ) )
| ( ( inconsistency_P @ sk20 @ sk16 )
!= ( inconsistency_P @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[399,54]) ).
thf(1049,plain,
( ( inconsistency_G @ sk15 @ sk16 )
| ( incons1905966852QML_mu
!= ( ^ [A: qML_mu,B: qML_i] :
~ ( sk20 @ A @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[1048:[bind(A,$thf( sk16 )),bind(B,$thf( sk20 ))]]) ).
thf(1366,plain,
! [A: qML_i] :
( ( incons1905966852QML_mu @ sk5 @ sk6 )
| ( ( inconsistency_P @ sk62 @ sk6 )
!= ( inconsistency_P
@ ^ [B: qML_mu,C: qML_i] :
~ ( inconsistency_G @ B @ C )
@ A ) ) ),
inference(paramod_ordered,[status(thm)],[781,41]) ).
thf(1392,plain,
! [A: qML_i] :
( ( incons1905966852QML_mu @ sk5 @ sk6 )
| ( sk62
!= ( ^ [B: qML_mu,C: qML_i] :
~ ( inconsistency_G @ B @ C ) ) )
| ( sk6 != A ) ),
inference(simp,[status(thm)],[1366]) ).
thf(1400,plain,
( ( incons1905966852QML_mu @ sk5 @ sk6 )
| ( sk62
!= ( ^ [A: qML_mu,B: qML_i] :
~ ( inconsistency_G @ A @ B ) ) ) ),
inference(simp,[status(thm)],[1392]) ).
thf(1605,plain,
( ( inconsistency_P @ sk140 @ sk10 )
| ( incons1905966852QML_mu @ sk9 @ sk10 ) ),
inference(cnf,[status(esa)],[1560]) ).
thf(1367,plain,
! [B: qML_mu > qML_i > $o,A: qML_i] :
( ( incons1905966852QML_mu @ sk5 @ sk6 )
| ( incons1905966852QML_mu
!= ( ^ [C: qML_mu,D: qML_i] :
~ ( B @ C @ D ) ) )
| ( ( inconsistency_P @ sk62 @ sk6 )
!= ( inconsistency_P @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[781,54]) ).
thf(1368,plain,
( ( incons1905966852QML_mu @ sk5 @ sk6 )
| ( incons1905966852QML_mu
!= ( ^ [A: qML_mu,B: qML_i] :
~ ( sk62 @ A @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[1367:[bind(A,$thf( sk6 )),bind(B,$thf( sk62 ))]]) ).
thf(67,plain,
! [A: qML_mu] :
( ( incons1905966852QML_mu @ A )
= ( ^ [B: qML_i] :
! [C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ A @ B )
=> ! [D: qML_i] :
( ( qML_r @ B @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) ) ) ),
inference(func_ext,[status(esa)],[30]) ).
thf(1177,plain,
! [B: qML_i,A: qML_mu] :
( ( inconsistency_G @ sk3 @ sk4 )
| ~ ! [C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ A @ B )
=> ! [D: qML_i] :
( ( qML_r @ B @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) )
| ( ( incons1905966852QML_mu @ A @ B )
!= ( incons1905966852QML_mu @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[68,116]) ).
thf(1178,plain,
( ( inconsistency_G @ sk3 @ sk4 )
| ~ ! [A: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ A @ sk3 @ sk4 )
=> ! [B: qML_i] :
( ( qML_r @ sk4 @ B )
=> ? [C: qML_mu] : ( A @ C @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[1177:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(1262,plain,
( ( qML_r @ sk4 @ sk122 )
| ( inconsistency_G @ sk3 @ sk4 ) ),
inference(cnf,[status(esa)],[1178]) ).
thf(1334,plain,
( ~ ~ ( incons1905966852QML_mu @ sk34 @ sk35 )
| ~ ! [A: qML_mu > qML_i > $o] :
( ( inconsistency_P @ A @ sk35 )
=> ( A @ sk34 @ sk35 ) ) ),
inference(bool_ext,[status(thm)],[1173]) ).
thf(1358,plain,
( ( inconsistency_P @ sk126 @ sk35 )
| ( incons1905966852QML_mu @ sk34 @ sk35 ) ),
inference(cnf,[status(esa)],[1334]) ).
thf(3233,plain,
! [D: qML_mu > qML_i > $o,C: qML_i,B: qML_mu > qML_i > $o,A: qML_i] :
( ~ ( inconsistency_G @ sk3 @ sk4 )
| ~ ( inconsistency_P @ B @ A )
| ( inconsistency_G
!= ( ^ [E: qML_mu,F: qML_i] :
~ ( D @ E @ F ) ) )
| ( ( inconsistency_P
@ ^ [E: qML_mu,F: qML_i] : ( incons1905966852QML_mu @ sk3 @ sk4 )
@ A )
!= ( inconsistency_P @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[157,56]) ).
thf(3234,plain,
! [B: qML_mu > qML_i > $o,A: qML_i] :
( ~ ( inconsistency_G @ sk3 @ sk4 )
| ~ ( inconsistency_P @ B @ A )
| ( inconsistency_G
!= ( ^ [C: qML_mu,D: qML_i] :
~ ( incons1905966852QML_mu @ sk3 @ sk4 ) ) ) ),
inference(pattern_uni,[status(thm)],[3233:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( ^ [E: qML_mu] : ^ [F: qML_i] : ( incons1905966852QML_mu @ sk3 @ sk4 ) ))]]) ).
thf(3492,plain,
! [C: qML_mu > qML_i > $o,B: qML_i,A: qML_i] :
( ~ ( inconsistency_G @ sk3 @ sk4 )
| ( inconsistency_G
!= ( ^ [D: qML_mu,E: qML_i] :
~ ( incons1905966852QML_mu @ sk3 @ sk4 ) ) )
| ( ( inconsistency_P @ inconsistency_G @ A )
!= ( inconsistency_P @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[22,3234]) ).
thf(3493,plain,
( ~ ( inconsistency_G @ sk3 @ sk4 )
| ( inconsistency_G
!= ( ^ [A: qML_mu,B: qML_i] :
~ ( incons1905966852QML_mu @ sk3 @ sk4 ) ) ) ),
inference(pattern_uni,[status(thm)],[3492:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( inconsistency_G ))]]) ).
thf(1093,plain,
! [B: qML_mu > qML_i > $o,A: qML_i] :
( ( incons1905966852QML_mu @ sk13 @ sk14 )
| ( inconsistency_G
!= ( ^ [C: qML_mu,D: qML_i] :
~ ( B @ C @ D ) ) )
| ( ( inconsistency_P @ sk17 @ sk14 )
!= ( inconsistency_P @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[220,56]) ).
thf(1094,plain,
( ( incons1905966852QML_mu @ sk13 @ sk14 )
| ( inconsistency_G
!= ( ^ [A: qML_mu,B: qML_i] :
~ ( sk17 @ A @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[1093:[bind(A,$thf( sk14 )),bind(B,$thf( sk17 ))]]) ).
thf(708,plain,
! [A: qML_i] :
( ( inconsistency_G @ sk15 @ sk16 )
| ( ( inconsistency_P @ sk20 @ sk16 )
!= ( inconsistency_P
@ ^ [B: qML_mu,C: qML_i] :
~ ( incons1905966852QML_mu @ B @ C )
@ A ) ) ),
inference(paramod_ordered,[status(thm)],[399,44]) ).
thf(718,plain,
! [A: qML_i] :
( ( inconsistency_G @ sk15 @ sk16 )
| ( sk20
!= ( ^ [B: qML_mu,C: qML_i] :
~ ( incons1905966852QML_mu @ B @ C ) ) )
| ( sk16 != A ) ),
inference(simp,[status(thm)],[708]) ).
thf(727,plain,
( ( inconsistency_G @ sk15 @ sk16 )
| ( sk20
!= ( ^ [A: qML_mu,B: qML_i] :
~ ( incons1905966852QML_mu @ A @ B ) ) ) ),
inference(simp,[status(thm)],[718]) ).
thf(1266,plain,
( ~ ( incons1905966852QML_mu @ sk21 @ sk22 )
| ~ ~ ( inconsistency_G @ sk21 @ sk22 ) ),
inference(bool_ext,[status(thm)],[1197]) ).
thf(1276,plain,
( ( inconsistency_G @ sk21 @ sk22 )
| ~ ( incons1905966852QML_mu @ sk21 @ sk22 ) ),
inference(cnf,[status(esa)],[1266]) ).
thf(1624,plain,
( ~ ! [A: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ A @ sk13 @ sk14 )
=> ! [B: qML_i] :
( ( qML_r @ sk14 @ B )
=> ? [C: qML_mu] : ( A @ C @ B ) ) )
| ~ ~ ( inconsistency_G @ sk13 @ sk14 ) ),
inference(bool_ext,[status(thm)],[1190]) ).
thf(1646,plain,
( ( inconsistency_G @ sk13 @ sk14 )
| ( qML_r @ sk14 @ sk149 ) ),
inference(cnf,[status(esa)],[1624]) ).
thf(4224,plain,
! [B: qML_i,A: qML_i] :
( ( inconsistency_P
@ ^ [C: qML_mu,D: qML_i] : $true
@ A )
!= ( inconsistency_P
@ ^ [C: qML_mu,D: qML_i] :
~ ( inconsistency_G @ C @ D )
@ B ) ),
inference(paramod_ordered,[status(thm)],[4139,41]) ).
thf(4238,plain,
! [B: qML_i,A: qML_i] :
( ( ( ^ [C: qML_mu,D: qML_i] :
~ ( inconsistency_G @ C @ D ) )
!= ( ^ [C: qML_mu,D: qML_i] : $true ) )
| ( A != B ) ),
inference(simp,[status(thm)],[4224]) ).
thf(4250,plain,
( ( ^ [A: qML_mu,B: qML_i] :
~ ( inconsistency_G @ A @ B ) )
!= ( ^ [A: qML_mu,B: qML_i] : $true ) ),
inference(simp,[status(thm)],[4238]) ).
thf(186,plain,
( ( inconsistency_G @ sk7 @ sk8 )
| ~ ( sk11 @ sk7 @ sk8 ) ),
inference(cnf,[status(esa)],[184]) ).
thf(624,plain,
( ~ ! [A: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ A @ sk21 @ sk22 )
=> ! [B: qML_i] :
( ( qML_r @ sk22 @ B )
=> ? [C: qML_mu] : ( A @ C @ B ) ) )
| ~ ~ ( inconsistency_G @ sk21 @ sk22 ) ),
inference(bool_ext,[status(thm)],[402]) ).
thf(632,plain,
( ( inconsistency_G @ sk21 @ sk22 )
| ( qML_r @ sk22 @ sk37 ) ),
inference(cnf,[status(esa)],[624]) ).
thf(4225,plain,
! [B: qML_i,A: qML_i] :
( ( inconsistency_P
@ ^ [C: qML_mu,D: qML_i] : $true
@ A )
!= ( inconsistency_P
@ ^ [C: qML_mu,D: qML_i] :
~ ( incons1905966852QML_mu @ C @ D )
@ B ) ),
inference(paramod_ordered,[status(thm)],[4139,44]) ).
thf(4246,plain,
! [B: qML_i,A: qML_i] :
( ( ( ^ [C: qML_mu,D: qML_i] :
~ ( incons1905966852QML_mu @ C @ D ) )
!= ( ^ [C: qML_mu,D: qML_i] : $true ) )
| ( A != B ) ),
inference(simp,[status(thm)],[4225]) ).
thf(4261,plain,
( ( ^ [A: qML_mu,B: qML_i] :
~ ( incons1905966852QML_mu @ A @ B ) )
!= ( ^ [A: qML_mu,B: qML_i] : $true ) ),
inference(simp,[status(thm)],[4246]) ).
thf(1061,plain,
! [B: qML_mu > qML_i > $o,A: qML_i] :
( ( incons1905966852QML_mu @ sk9 @ sk10 )
| ( incons1905966852QML_mu
!= ( ^ [C: qML_mu,D: qML_i] :
~ ( B @ C @ D ) ) )
| ( ( inconsistency_P @ sk12 @ sk10 )
!= ( inconsistency_P @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[195,54]) ).
thf(1062,plain,
( ( incons1905966852QML_mu @ sk9 @ sk10 )
| ( incons1905966852QML_mu
!= ( ^ [A: qML_mu,B: qML_i] :
~ ( sk12 @ A @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[1061:[bind(A,$thf( sk10 )),bind(B,$thf( sk12 ))]]) ).
thf(1211,plain,
! [B: qML_i,A: qML_mu] :
( ( ( ~ ! [C: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ C @ A @ B )
=> ! [D: qML_i] :
( ( qML_r @ B @ D )
=> ? [E: qML_mu] : ( C @ E @ D ) ) ) )
!= ( inconsistency_G @ sk9 @ sk10 ) )
| ( ( incons1905966852QML_mu @ A @ B )
!= ( incons1905966852QML_mu @ sk9 @ sk10 ) ) ),
inference(paramod_ordered,[status(thm)],[68,739]) ).
thf(1212,plain,
( ( ~ ! [A: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ A @ sk9 @ sk10 )
=> ! [B: qML_i] :
( ( qML_r @ sk10 @ B )
=> ? [C: qML_mu] : ( A @ C @ B ) ) ) )
!= ( inconsistency_G @ sk9 @ sk10 ) ),
inference(pattern_uni,[status(thm)],[1211:[bind(A,$thf( sk9 )),bind(B,$thf( sk10 ))]]) ).
thf(669,plain,
( ( incons1905966852QML_mu @ sk28 @ sk29 )
| ~ ! [A: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ A @ sk28 @ sk29 )
=> ! [B: qML_i] :
( ( qML_r @ sk29 @ B )
=> ? [C: qML_mu] : ( A @ C @ B ) ) ) ),
inference(bool_ext,[status(thm)],[522]) ).
thf(684,plain,
( ( qML_r @ sk29 @ sk55 )
| ( incons1905966852QML_mu @ sk28 @ sk29 ) ),
inference(cnf,[status(esa)],[669]) ).
thf(1444,plain,
( ~ ( sk132 @ sk23 @ sk24 )
| ( incons1905966852QML_mu @ sk23 @ sk24 ) ),
inference(cnf,[status(esa)],[1426]) ).
thf(19,plain,
! [C: qML_mu > qML_i > $o,B: qML_mu > qML_i > $o,A: qML_i] :
( ~ ( inconsistency_P @ B @ A )
| ( B @ ( sk2 @ C @ B @ A ) @ ( sk1 @ C @ B @ A ) )
| ( inconsistency_P @ C @ A ) ),
inference(cnf,[status(esa)],[17]) ).
thf(687,plain,
( ( inconsistency_G @ sk30 @ sk31 )
| ~ ! [A: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ A @ sk30 @ sk31 )
=> ! [B: qML_i] :
( ( qML_r @ sk31 @ B )
=> ? [C: qML_mu] : ( A @ C @ B ) ) ) ),
inference(bool_ext,[status(thm)],[525]) ).
thf(696,plain,
( ( qML_r @ sk31 @ sk59 )
| ( inconsistency_G @ sk30 @ sk31 ) ),
inference(cnf,[status(esa)],[687]) ).
thf(3177,plain,
! [A: qML_mu > qML_i > $o] :
( ( ( incons1389517216QML_mu @ A )
!= ( ^ [B: qML_mu,C: qML_i] :
~ ( incons1905966852QML_mu @ B @ C ) ) )
| ( ( ^ [B: qML_mu,C: qML_i,D: qML_mu > qML_i > $o] : ( D @ B @ C ) )
!= ( ^ [B: qML_mu,C: qML_i,D: qML_mu > qML_i > $o] : ( inconsistency_P @ D @ C ) ) )
| ( ( ^ [B: qML_mu,C: qML_i,D: qML_mu > qML_i > $o] :
! [E: qML_i] :
( ( qML_r @ C @ E )
=> ! [F: qML_mu] :
( ( A @ F @ E )
=> ( D @ F @ E ) ) ) )
!= ( ^ [B: qML_mu,C: qML_i,D: qML_mu > qML_i > $o] : ( D @ B @ C ) ) ) ),
inference(simp,[status(thm)],[983]) ).
thf(1503,plain,
! [A: qML_i] :
( ( incons1905966852QML_mu @ sk3 @ sk4 )
| ( ( inconsistency_P @ sk64 @ sk4 )
!= ( inconsistency_P
@ ^ [B: qML_mu,C: qML_i] :
~ ( inconsistency_G @ B @ C )
@ A ) ) ),
inference(paramod_ordered,[status(thm)],[793,41]) ).
thf(1529,plain,
! [A: qML_i] :
( ( incons1905966852QML_mu @ sk3 @ sk4 )
| ( sk64
!= ( ^ [B: qML_mu,C: qML_i] :
~ ( inconsistency_G @ B @ C ) ) )
| ( sk4 != A ) ),
inference(simp,[status(thm)],[1503]) ).
thf(1537,plain,
( ( incons1905966852QML_mu @ sk3 @ sk4 )
| ( sk64
!= ( ^ [A: qML_mu,B: qML_i] :
~ ( inconsistency_G @ A @ B ) ) ) ),
inference(simp,[status(thm)],[1529]) ).
thf(1357,plain,
( ~ ( sk126 @ sk34 @ sk35 )
| ( incons1905966852QML_mu @ sk34 @ sk35 ) ),
inference(cnf,[status(esa)],[1334]) ).
thf(1279,plain,
( ~ ~ ( incons1905966852QML_mu @ sk30 @ sk31 )
| ~ ( inconsistency_G @ sk30 @ sk31 ) ),
inference(bool_ext,[status(thm)],[1208]) ).
thf(1299,plain,
( ~ ( inconsistency_G @ sk30 @ sk31 )
| ( incons1905966852QML_mu @ sk30 @ sk31 ) ),
inference(cnf,[status(esa)],[1279]) ).
thf(1504,plain,
! [B: qML_mu > qML_i > $o,A: qML_i] :
( ( incons1905966852QML_mu @ sk3 @ sk4 )
| ( incons1905966852QML_mu
!= ( ^ [C: qML_mu,D: qML_i] :
~ ( B @ C @ D ) ) )
| ( ( inconsistency_P @ sk64 @ sk4 )
!= ( inconsistency_P @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[793,54]) ).
thf(1505,plain,
( ( incons1905966852QML_mu @ sk3 @ sk4 )
| ( incons1905966852QML_mu
!= ( ^ [A: qML_mu,B: qML_i] :
~ ( sk64 @ A @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[1504:[bind(A,$thf( sk4 )),bind(B,$thf( sk64 ))]]) ).
thf(1301,plain,
( ~ ( incons1905966852QML_mu @ sk34 @ sk35 )
| ( inconsistency_G @ sk34 @ sk35 ) ),
inference(bool_ext,[status(thm)],[1214]) ).
thf(1320,plain,
( ( inconsistency_G @ sk34 @ sk35 )
| ~ ( incons1905966852QML_mu @ sk34 @ sk35 ) ),
inference(cnf,[status(esa)],[1301]) ).
thf(4273,plain,
~ ~ ( inconsistency_G @ sk354 @ sk355 ),
inference(func_ext,[status(esa)],[4250]) ).
thf(4274,plain,
inconsistency_G @ sk354 @ sk355,
inference(cnf,[status(esa)],[4273]) ).
thf(5374,plain,
$false,
inference(e,[status(thm)],[892,1469,1190,555,1295,88,977,120,655,1173,56,747,4247,1507,24,25,4249,52,14,110,619,157,20,1319,4270,1398,4265,1494,1100,29,492,211,121,1169,2861,1622,116,428,849,74,206,1604,1206,117,793,1199,1470,220,102,1047,1223,825,28,429,33,1217,160,21,1370,165,815,65,522,757,551,519,1259,1493,124,77,476,1214,1016,1192,13,41,1333,237,105,205,398,1202,792,17,32,34,1833,402,22,44,1652,826,1535,27,4251,12,54,1332,187,406,219,4139,1043,98,208,816,240,848,520,66,521,983,130,399,1445,780,1113,1102,722,1166,1208,1277,123,754,194,1049,525,18,1400,1605,739,1368,67,16,1262,31,1358,3493,1094,991,727,72,87,759,1276,1646,4250,186,55,632,781,23,4261,1062,26,1212,684,1444,36,30,19,210,195,1197,696,79,3177,860,1537,1357,47,15,68,1299,1505,1320,1184,496,122,4274]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : PHI007^5 : TPTP v8.2.0. Released v6.4.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n003.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat May 18 14:42:53 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.95/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.19/0.97 % [INFO] Parsing done (112ms).
% 1.19/0.98 % [INFO] Running in sequential loop mode.
% 1.69/1.20 % [INFO] eprover registered as external prover.
% 1.69/1.20 % [INFO] cvc4 registered as external prover.
% 1.69/1.20 % [INFO] Scanning for conjecture ...
% 1.86/1.25 % [INFO] Found a conjecture (or negated_conjecture) and 9 axioms. Running axiom selection ...
% 1.94/1.27 % [INFO] Axiom selection finished. Selected 9 axioms (removed 0 axioms).
% 1.94/1.30 % [INFO] Problem is higher-order (TPTP THF).
% 1.94/1.30 % [INFO] Type checking passed.
% 1.94/1.31 % [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 ...
% 92.06/26.95 % External prover 'e' found a proof!
% 92.06/26.95 % [INFO] Killing All external provers ...
% 92.06/26.95 % Time passed: 26427ms (effective reasoning time: 25967ms)
% 92.06/26.95 % 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)>
% 92.06/26.95 % Axioms used in derivation (9): fact_7_NE__def, fact_8_ess__def, fact_1_A1b, fact_4_A4, fact_2_A2, fact_0_A1a, fact_6_G__def, fact_3_A3, fact_5_A5
% 92.06/26.95 % No. of inferences in proof: 358
% 92.06/26.95 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 26427 ms resp. 25967 ms w/o parsing
% 92.06/27.07 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 92.06/27.07 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------