TSTP Solution File: SWW097+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWW097+1 : TPTP v8.1.2. Released v5.2.0.
% 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 : Fri May 19 12:21:41 EDT 2023
% Result : Theorem 167.06s 30.60s
% Output : Refutation 167.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 87
% Syntax : Number of formulae : 367 ( 136 unt; 42 typ; 0 def)
% Number of atoms : 720 ( 440 equ; 0 cnn)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 2911 ( 323 ~; 227 |; 91 &;2215 @)
% ( 5 <=>; 50 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 61 ( 61 >; 0 *; 0 +; 0 <<)
% Number of symbols : 45 ( 42 usr; 10 con; 0-3 aty)
% Number of variables : 437 ( 0 ^; 409 !; 28 ?; 437 :)
% Comments :
%------------------------------------------------------------------------------
thf(lazy_and1_type,type,
lazy_and1: $i > $i > $i ).
thf(lazy_and2_type,type,
lazy_and2: $i > $i > $i ).
thf(f2_type,type,
f2: $i > $i > $i > $i ).
thf(lazy_impl_type,type,
lazy_impl: $i > $i > $i ).
thf(prop_type,type,
prop: $i > $i ).
thf(impl_type,type,
impl: $i > $i > $i ).
thf(f6_type,type,
f6: $i > $i > $i ).
thf(f5_type,type,
f5: $i > $i > $i ).
thf(not2_type,type,
not2: $i > $i ).
thf(false2_type,type,
false2: $i ).
thf(f1_type,type,
f1: $i > $i > $i > $i ).
thf(f4_type,type,
f4: $i > $i > $i > $i ).
thf(apply_type,type,
apply: $i > $i > $i ).
thf(f3_type,type,
f3: $i > $i > $i > $i ).
thf(f7_type,type,
f7: $i > $i ).
thf(d_type,type,
d: $i > $o ).
thf(phi_type,type,
phi: $i > $i ).
thf(err_type,type,
err: $i ).
thf(false_type,type,
false: $i ).
thf(true_type,type,
true: $i ).
thf(bool_type,type,
bool: $i > $o ).
thf(or1_type,type,
or1: $i > $i > $i ).
thf(not1_type,type,
not1: $i > $i ).
thf(and2_type,type,
and2: $i > $i > $i ).
thf(forallprefers_type,type,
forallprefers: $i > $i > $o ).
thf(and1_type,type,
and1: $i > $i > $i ).
thf(exists1_type,type,
exists1: $i > $i ).
thf(existsprefers_type,type,
existsprefers: $i > $i > $o ).
thf(exists2_type,type,
exists2: $i > $i ).
thf(or2_type,type,
or2: $i > $i > $i ).
thf(false1_type,type,
false1: $i ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i > $i > $i ).
thf(sk4_type,type,
sk4: $i > $i ).
thf(sk5_type,type,
sk5: $i > $i > $o ).
thf(sk6_type,type,
sk6: $i > $i > $o ).
thf(sk7_type,type,
sk7: $i > $i ).
thf(sk8_type,type,
sk8: $i > $i > $i ).
thf(sk11_type,type,
sk11: $i ).
thf(sk12_type,type,
sk12: $i > $i > $i ).
thf(sk13_type,type,
sk13: $i > $i > $i ).
thf(45,axiom,
! [A: $i] :
( ( lazy_and1 @ false @ A )
= false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lazy_and1_axiom2) ).
thf(242,plain,
! [A: $i] :
( ( lazy_and1 @ false @ A )
= false ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(243,plain,
! [A: $i] :
( ( lazy_and1 @ false @ A )
= false ),
inference(cnf,[status(esa)],[242]) ).
thf(244,plain,
! [A: $i] :
( ( lazy_and1 @ false @ A )
= false ),
inference(lifteq,[status(thm)],[243]) ).
thf(11,axiom,
! [A: $i] :
( ( lazy_impl @ false @ A )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lazy_impl_axiom2) ).
thf(79,plain,
! [A: $i] :
( ( lazy_impl @ false @ A )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(80,plain,
! [A: $i] :
( ( lazy_impl @ false @ A )
= true ),
inference(cnf,[status(esa)],[79]) ).
thf(81,plain,
! [A: $i] :
( ( lazy_impl @ false @ A )
= true ),
inference(lifteq,[status(thm)],[80]) ).
thf(43,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( ( lazy_and2 @ A @ B )
= ( phi @ ( f2 @ A @ B @ C ) ) )
& ~ ? [D: $i] : ( forallprefers @ ( f2 @ A @ B @ D ) @ ( f2 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_lazy_and2) ).
thf(234,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( ( lazy_and2 @ A @ B )
= ( phi @ ( f2 @ A @ B @ C ) ) )
& ~ ? [D: $i] : ( forallprefers @ ( f2 @ A @ B @ D ) @ ( f2 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(236,plain,
! [B: $i,A: $i] :
( ( lazy_and2 @ A @ B )
= ( phi @ ( f2 @ A @ B @ ( sk13 @ B @ A ) ) ) ),
inference(cnf,[status(esa)],[234]) ).
thf(237,plain,
! [B: $i,A: $i] :
( ( lazy_and2 @ A @ B )
= ( phi @ ( f2 @ A @ B @ ( sk13 @ B @ A ) ) ) ),
inference(lifteq,[status(thm)],[236]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( f2 @ A @ B @ C )
= ( lazy_impl @ ( prop @ C ) @ ( impl @ ( lazy_impl @ A @ ( impl @ B @ C ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_f2) ).
thf(50,plain,
! [A: $i,B: $i,C: $i] :
( ( f2 @ A @ B @ C )
= ( lazy_impl @ ( prop @ C ) @ ( impl @ ( lazy_impl @ A @ ( impl @ B @ C ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(51,plain,
! [C: $i,B: $i,A: $i] :
( ( f2 @ A @ B @ C )
= ( lazy_impl @ ( prop @ C ) @ ( impl @ ( lazy_impl @ A @ ( impl @ B @ C ) ) @ C ) ) ),
inference(cnf,[status(esa)],[50]) ).
thf(52,plain,
! [C: $i,B: $i,A: $i] :
( ( f2 @ A @ B @ C )
= ( lazy_impl @ ( prop @ C ) @ ( impl @ ( lazy_impl @ A @ ( impl @ B @ C ) ) @ C ) ) ),
inference(lifteq,[status(thm)],[51]) ).
thf(1045,plain,
! [B: $i,A: $i] :
( ( lazy_and2 @ A @ B )
= ( phi @ ( lazy_impl @ ( prop @ ( sk13 @ B @ A ) ) @ ( impl @ ( lazy_impl @ A @ ( impl @ B @ ( sk13 @ B @ A ) ) ) @ ( sk13 @ B @ A ) ) ) ) ),
inference(rewrite,[status(thm)],[237,52]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( lazy_and1 @ A @ B )
= ( lazy_and2 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lazy_and1_lazy_and2) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( lazy_and1 @ A @ B )
= ( lazy_and2 @ A @ B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(47,plain,
~ ! [A: $i,B: $i] :
( ( lazy_and1 @ A @ B )
= ( lazy_and2 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(48,plain,
( ( lazy_and1 @ sk1 @ sk2 )
!= ( lazy_and2 @ sk1 @ sk2 ) ),
inference(cnf,[status(esa)],[47]) ).
thf(49,plain,
( ( lazy_and2 @ sk1 @ sk2 )
!= ( lazy_and1 @ sk1 @ sk2 ) ),
inference(lifteq,[status(thm)],[48]) ).
thf(1075,plain,
! [B: $i,A: $i] :
( ( ( phi @ ( lazy_impl @ ( prop @ ( sk13 @ B @ A ) ) @ ( impl @ ( lazy_impl @ A @ ( impl @ B @ ( sk13 @ B @ A ) ) ) @ ( sk13 @ B @ A ) ) ) )
!= ( lazy_and1 @ sk1 @ sk2 ) )
| ( ( lazy_and2 @ A @ B )
!= ( lazy_and2 @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[1045,49]) ).
thf(1076,plain,
( ( phi @ ( lazy_impl @ ( prop @ ( sk13 @ sk2 @ sk1 ) ) @ ( impl @ ( lazy_impl @ sk1 @ ( impl @ sk2 @ ( sk13 @ sk2 @ sk1 ) ) ) @ ( sk13 @ sk2 @ sk1 ) ) ) )
!= ( lazy_and1 @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[1075:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(1174,plain,
! [A: $i] :
( ( ( phi @ ( lazy_impl @ ( prop @ ( sk13 @ sk2 @ sk1 ) ) @ ( impl @ true @ ( sk13 @ sk2 @ sk1 ) ) ) )
!= ( lazy_and1 @ sk1 @ sk2 ) )
| ( ( lazy_impl @ false @ A )
!= ( lazy_impl @ sk1 @ ( impl @ sk2 @ ( sk13 @ sk2 @ sk1 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[81,1076]) ).
thf(1192,plain,
! [A: $i] :
( ( ( phi @ ( lazy_impl @ ( prop @ ( sk13 @ sk2 @ sk1 ) ) @ ( impl @ true @ ( sk13 @ sk2 @ sk1 ) ) ) )
!= ( lazy_and1 @ sk1 @ sk2 ) )
| ( sk1 != false )
| ( A
!= ( impl @ sk2 @ ( sk13 @ sk2 @ sk1 ) ) ) ),
inference(simp,[status(thm)],[1174]) ).
thf(1217,plain,
( ( ( phi @ ( lazy_impl @ ( prop @ ( sk13 @ sk2 @ sk1 ) ) @ ( impl @ true @ ( sk13 @ sk2 @ sk1 ) ) ) )
!= ( lazy_and1 @ sk1 @ sk2 ) )
| ( sk1 != false ) ),
inference(simp,[status(thm)],[1192]) ).
thf(3024,plain,
! [A: $i] :
( ( ( phi @ ( lazy_impl @ ( prop @ ( sk13 @ sk2 @ sk1 ) ) @ ( impl @ true @ ( sk13 @ sk2 @ sk1 ) ) ) )
!= false )
| ( sk1 != false )
| ( ( lazy_and1 @ false @ A )
!= ( lazy_and1 @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[244,1217]) ).
thf(3084,plain,
! [A: $i] :
( ( ( phi @ ( lazy_impl @ ( prop @ ( sk13 @ sk2 @ sk1 ) ) @ ( impl @ true @ ( sk13 @ sk2 @ sk1 ) ) ) )
!= false )
| ( sk1 != false )
| ( sk1 != false )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[3024]) ).
thf(3107,plain,
( ( ( phi @ ( lazy_impl @ ( prop @ ( sk13 @ sk2 @ sk1 ) ) @ ( impl @ true @ ( sk13 @ sk2 @ sk1 ) ) ) )
!= false )
| ( sk1 != false ) ),
inference(simp,[status(thm)],[3084]) ).
thf(5,axiom,
! [A: $i] :
( ( not2 @ A )
= ( impl @ A @ false2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_not2) ).
thf(56,plain,
! [A: $i] :
( ( not2 @ A )
= ( impl @ A @ false2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(57,plain,
! [A: $i] :
( ( not2 @ A )
= ( impl @ A @ false2 ) ),
inference(cnf,[status(esa)],[56]) ).
thf(58,plain,
! [A: $i] :
( ( impl @ A @ false2 )
= ( not2 @ A ) ),
inference(lifteq,[status(thm)],[57]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( f6 @ A @ B )
= ( lazy_impl @ ( prop @ B ) @ ( impl @ ( f5 @ A @ B ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_f6) ).
thf(53,plain,
! [A: $i,B: $i] :
( ( f6 @ A @ B )
= ( lazy_impl @ ( prop @ B ) @ ( impl @ ( f5 @ A @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ( f6 @ A @ B )
= ( lazy_impl @ ( prop @ B ) @ ( impl @ ( f5 @ A @ B ) @ B ) ) ),
inference(cnf,[status(esa)],[53]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ( f6 @ A @ B )
= ( lazy_impl @ ( prop @ B ) @ ( impl @ ( f5 @ A @ B ) @ B ) ) ),
inference(lifteq,[status(thm)],[54]) ).
thf(260,plain,
! [C: $i,B: $i,A: $i] :
( ( ( lazy_impl @ ( prop @ C ) @ ( not2 @ A ) )
= ( f6 @ B @ C ) )
| ( ( impl @ A @ false2 )
!= ( impl @ ( f5 @ B @ C ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[58,55]) ).
thf(261,plain,
! [A: $i] :
( ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( f5 @ A @ false2 ) ) )
= ( f6 @ A @ false2 ) ),
inference(pattern_uni,[status(thm)],[260:[bind(A,$thf( f5 @ D @ false2 )),bind(B,$thf( D )),bind(C,$thf( false2 ))]]) ).
thf(262,plain,
! [A: $i] :
( ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( f5 @ A @ false2 ) ) )
= ( f6 @ A @ false2 ) ),
inference(simp,[status(thm)],[261]) ).
thf(27,axiom,
! [A: $i] :
? [B: $i] :
( ( ( exists2 @ A )
= ( phi @ ( f6 @ A @ B ) ) )
& ~ ? [C: $i] : ( forallprefers @ ( f6 @ A @ C ) @ ( f6 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_exists2) ).
thf(160,plain,
! [A: $i] :
? [B: $i] :
( ( ( exists2 @ A )
= ( phi @ ( f6 @ A @ B ) ) )
& ~ ? [C: $i] : ( forallprefers @ ( f6 @ A @ C ) @ ( f6 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(161,plain,
! [B: $i,A: $i] :
~ ( forallprefers @ ( f6 @ A @ B ) @ ( f6 @ A @ ( sk7 @ A ) ) ),
inference(cnf,[status(esa)],[160]) ).
thf(373,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( forallprefers @ ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( f5 @ A @ false2 ) ) ) @ ( f6 @ B @ ( sk7 @ B ) ) )
| ( ( f6 @ A @ false2 )
!= ( f6 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[262,161]) ).
thf(374,plain,
! [A: $i] :
~ ( forallprefers @ ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( f5 @ A @ false2 ) ) ) @ ( f6 @ A @ ( sk7 @ A ) ) ),
inference(pattern_uni,[status(thm)],[373:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( false2 ))]]) ).
thf(387,plain,
! [B: $i,A: $i] :
( ~ ( forallprefers @ true @ ( f6 @ B @ ( sk7 @ B ) ) )
| ( ( lazy_impl @ false @ A )
!= ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( f5 @ B @ false2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[81,374]) ).
thf(392,plain,
! [B: $i,A: $i] :
( ~ ( forallprefers @ true @ ( f6 @ B @ ( sk7 @ B ) ) )
| ( ( prop @ false2 )
!= false )
| ( A
!= ( not2 @ ( f5 @ B @ false2 ) ) ) ),
inference(simp,[status(thm)],[387]) ).
thf(399,plain,
! [A: $i] :
( ~ ( forallprefers @ true @ ( f6 @ A @ ( sk7 @ A ) ) )
| ( ( prop @ false2 )
!= false ) ),
inference(simp,[status(thm)],[392]) ).
thf(411,plain,
! [B: $i,A: $i] :
( ~ ( forallprefers @ true @ ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( f5 @ A @ false2 ) ) ) )
| ( ( prop @ false2 )
!= false )
| ( ( f6 @ A @ false2 )
!= ( f6 @ B @ ( sk7 @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[262,399]) ).
thf(413,plain,
! [B: $i,A: $i] :
( ~ ( forallprefers @ true @ ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( f5 @ A @ false2 ) ) ) )
| ( ( prop @ false2 )
!= false )
| ( A != B )
| ( ( sk7 @ B )
!= false2 ) ),
inference(simp,[status(thm)],[411]) ).
thf(415,plain,
! [A: $i] :
( ~ ( forallprefers @ true @ ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( f5 @ A @ false2 ) ) ) )
| ( ( prop @ false2 )
!= false )
| ( ( sk7 @ A )
!= false2 ) ),
inference(simp,[status(thm)],[413]) ).
thf(615,plain,
! [B: $i,A: $i] :
( ~ ( forallprefers @ true @ true )
| ( ( prop @ false2 )
!= false )
| ( ( sk7 @ B )
!= false2 )
| ( ( lazy_impl @ false @ A )
!= ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( f5 @ B @ false2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[81,415]) ).
thf(625,plain,
! [B: $i,A: $i] :
( ~ ( forallprefers @ true @ true )
| ( ( prop @ false2 )
!= false )
| ( ( sk7 @ B )
!= false2 )
| ( ( prop @ false2 )
!= false )
| ( A
!= ( not2 @ ( f5 @ B @ false2 ) ) ) ),
inference(simp,[status(thm)],[615]) ).
thf(629,plain,
! [A: $i] :
( ~ ( forallprefers @ true @ true )
| ( ( prop @ false2 )
!= false )
| ( ( sk7 @ A )
!= false2 ) ),
inference(simp,[status(thm)],[625]) ).
thf(13,axiom,
! [A: $i] :
( ( bool @ A )
<=> ( ( A = false )
| ( A = true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_bool) ).
thf(85,plain,
! [A: $i] :
( ( ( bool @ A )
=> ( ( A = false )
| ( A = true ) ) )
& ( ( ( A = false )
| ( A = true ) )
=> ( bool @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(86,plain,
( ! [A: $i] :
( ( bool @ A )
=> ( ( A = false )
| ( A = true ) ) )
& ! [A: $i] :
( ( ( A = false )
| ( A = true ) )
=> ( bool @ A ) ) ),
inference(miniscope,[status(thm)],[85]) ).
thf(89,plain,
! [A: $i] :
( ~ ( bool @ A )
| ( A = false )
| ( A = true ) ),
inference(cnf,[status(esa)],[86]) ).
thf(94,plain,
! [A: $i] :
( ( A = false )
| ( A = true )
| ~ ( bool @ A ) ),
inference(lifteq,[status(thm)],[89]) ).
thf(20,axiom,
( ( d @ true )
& ( d @ false )
& ( d @ err ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',false_true_err_in_d) ).
thf(119,plain,
( ( d @ true )
& ( d @ false )
& ( d @ err ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(122,plain,
d @ true,
inference(cnf,[status(esa)],[119]) ).
thf(10,axiom,
! [A: $i] :
( ( ( d @ A )
& ( ( phi @ A )
= A ) )
| ( ~ ( d @ A )
& ( ( phi @ A )
= err ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_phi) ).
thf(71,plain,
! [A: $i] :
( ( ( d @ A )
& ( ( phi @ A )
= A ) )
| ( ~ ( d @ A )
& ( ( phi @ A )
= err ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(74,plain,
! [A: $i] :
( ( ( phi @ A )
= A )
| ~ ( d @ A ) ),
inference(cnf,[status(esa)],[71]) ).
thf(77,plain,
! [A: $i] :
( ( ( phi @ A )
= A )
| ~ ( d @ A ) ),
inference(lifteq,[status(thm)],[74]) ).
thf(803,plain,
! [A: $i] :
( ( ( phi @ A )
= A )
| ( ( d @ true )
!= ( d @ A ) ) ),
inference(paramod_ordered,[status(thm)],[122,77]) ).
thf(804,plain,
( ( phi @ true )
= true ),
inference(pattern_uni,[status(thm)],[803:[bind(A,$thf( true ))]]) ).
thf(46,axiom,
! [A: $i] :
( ( lazy_and1 @ true @ A )
= ( phi @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lazy_and1_axiom3) ).
thf(245,plain,
! [A: $i] :
( ( lazy_and1 @ true @ A )
= ( phi @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(246,plain,
! [A: $i] :
( ( lazy_and1 @ true @ A )
= ( phi @ A ) ),
inference(cnf,[status(esa)],[245]) ).
thf(247,plain,
! [A: $i] :
( ( lazy_and1 @ true @ A )
= ( phi @ A ) ),
inference(lifteq,[status(thm)],[246]) ).
thf(34,axiom,
! [A: $i] :
( ( ( prop @ A )
= false )
<=> ~ ( bool @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop_false) ).
thf(199,plain,
! [A: $i] :
( ( ( ( prop @ A )
= false )
=> ~ ( bool @ A ) )
& ( ~ ( bool @ A )
=> ( ( prop @ A )
= false ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(200,plain,
( ! [A: $i] :
( ( ( prop @ A )
= false )
=> ~ ( bool @ A ) )
& ! [A: $i] :
( ~ ( bool @ A )
=> ( ( prop @ A )
= false ) ) ),
inference(miniscope,[status(thm)],[199]) ).
thf(201,plain,
! [A: $i] :
( ( bool @ A )
| ( ( prop @ A )
= false ) ),
inference(cnf,[status(esa)],[200]) ).
thf(203,plain,
! [A: $i] :
( ( ( prop @ A )
= false )
| ( bool @ A ) ),
inference(lifteq,[status(thm)],[201]) ).
thf(204,plain,
! [A: $i] :
( ( ( prop @ A )
= false )
| ( bool @ A ) ),
inference(simp,[status(thm)],[203]) ).
thf(1173,plain,
! [A: $i] :
( ( ( lazy_and1 @ sk1 @ sk2 )
!= ( phi @ true ) )
| ( ( lazy_impl @ false @ A )
!= ( lazy_impl @ ( prop @ ( sk13 @ sk2 @ sk1 ) ) @ ( impl @ ( lazy_impl @ sk1 @ ( impl @ sk2 @ ( sk13 @ sk2 @ sk1 ) ) ) @ ( sk13 @ sk2 @ sk1 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[81,1076]) ).
thf(1202,plain,
! [A: $i] :
( ( ( lazy_and1 @ sk1 @ sk2 )
!= ( phi @ true ) )
| ( ( prop @ ( sk13 @ sk2 @ sk1 ) )
!= false )
| ( A
!= ( impl @ ( lazy_impl @ sk1 @ ( impl @ sk2 @ ( sk13 @ sk2 @ sk1 ) ) ) @ ( sk13 @ sk2 @ sk1 ) ) ) ),
inference(simp,[status(thm)],[1173]) ).
thf(1222,plain,
( ( ( lazy_and1 @ sk1 @ sk2 )
!= ( phi @ true ) )
| ( ( prop @ ( sk13 @ sk2 @ sk1 ) )
!= false ) ),
inference(simp,[status(thm)],[1202]) ).
thf(1231,plain,
( ( ( lazy_and1 @ sk1 @ sk2 )
!= true )
| ( ( prop @ ( sk13 @ sk2 @ sk1 ) )
!= false ) ),
inference(rewrite,[status(thm)],[1222,804]) ).
thf(1234,plain,
! [A: $i] :
( ( bool @ A )
| ( ( lazy_and1 @ sk1 @ sk2 )
!= true )
| ( ( prop @ A )
!= ( prop @ ( sk13 @ sk2 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[204,1231]) ).
thf(1235,plain,
( ( bool @ ( sk13 @ sk2 @ sk1 ) )
| ( ( lazy_and1 @ sk1 @ sk2 )
!= true ) ),
inference(pattern_uni,[status(thm)],[1234:[bind(A,$thf( sk13 @ sk2 @ sk1 ))]]) ).
thf(1240,plain,
! [A: $i] :
( ( bool @ ( sk13 @ sk2 @ sk1 ) )
| ( ( phi @ A )
!= true )
| ( ( lazy_and1 @ true @ A )
!= ( lazy_and1 @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[247,1235]) ).
thf(1246,plain,
! [A: $i] :
( ( bool @ ( sk13 @ sk2 @ sk1 ) )
| ( ( phi @ A )
!= true )
| ( sk1 != true )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[1240]) ).
thf(1248,plain,
( ( bool @ ( sk13 @ sk2 @ sk1 ) )
| ( ( phi @ sk2 )
!= true )
| ( sk1 != true ) ),
inference(simp,[status(thm)],[1246]) ).
thf(2098,plain,
( ( bool @ ( sk13 @ sk2 @ sk1 ) )
| ( sk1 != true )
| ( ( phi @ sk2 )
!= ( phi @ true ) ) ),
inference(paramod_ordered,[status(thm)],[804,1248]) ).
thf(2127,plain,
( ( bool @ ( sk13 @ sk2 @ sk1 ) )
| ( sk1 != true )
| ( sk2 != true ) ),
inference(simp,[status(thm)],[2098]) ).
thf(2462,plain,
! [A: $i] :
( ( A = false )
| ~ ( bool @ A )
| ( bool @ ( sk13 @ sk2 @ sk1 ) )
| ( sk2 != true )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[94,2127]) ).
thf(2463,plain,
( ( sk1 = false )
| ~ ( bool @ sk1 )
| ( bool @ ( sk13 @ sk2 @ sk1 ) )
| ( sk2 != true ) ),
inference(pattern_uni,[status(thm)],[2462:[bind(A,$thf( sk1 ))]]) ).
thf(30,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( ( or2 @ A @ B )
= ( phi @ ( f3 @ A @ B @ C ) ) )
& ~ ? [D: $i] : ( forallprefers @ ( f3 @ A @ B @ D ) @ ( f3 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_or2) ).
thf(169,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( ( or2 @ A @ B )
= ( phi @ ( f3 @ A @ B @ C ) ) )
& ~ ? [D: $i] : ( forallprefers @ ( f3 @ A @ B @ D ) @ ( f3 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(171,plain,
! [B: $i,A: $i] :
( ( or2 @ A @ B )
= ( phi @ ( f3 @ A @ B @ ( sk8 @ B @ A ) ) ) ),
inference(cnf,[status(esa)],[169]) ).
thf(172,plain,
! [B: $i,A: $i] :
( ( or2 @ A @ B )
= ( phi @ ( f3 @ A @ B @ ( sk8 @ B @ A ) ) ) ),
inference(lifteq,[status(thm)],[171]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( f3 @ A @ B @ C )
= ( lazy_impl @ ( prop @ C ) @ ( impl @ ( impl @ A @ C ) @ ( impl @ ( impl @ B @ C ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_f3) ).
thf(65,plain,
! [A: $i,B: $i,C: $i] :
( ( f3 @ A @ B @ C )
= ( lazy_impl @ ( prop @ C ) @ ( impl @ ( impl @ A @ C ) @ ( impl @ ( impl @ B @ C ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(66,plain,
! [C: $i,B: $i,A: $i] :
( ( f3 @ A @ B @ C )
= ( lazy_impl @ ( prop @ C ) @ ( impl @ ( impl @ A @ C ) @ ( impl @ ( impl @ B @ C ) @ C ) ) ) ),
inference(cnf,[status(esa)],[65]) ).
thf(67,plain,
! [C: $i,B: $i,A: $i] :
( ( f3 @ A @ B @ C )
= ( lazy_impl @ ( prop @ C ) @ ( impl @ ( impl @ A @ C ) @ ( impl @ ( impl @ B @ C ) @ C ) ) ) ),
inference(lifteq,[status(thm)],[66]) ).
thf(481,plain,
! [B: $i,A: $i] :
( ( or2 @ A @ B )
= ( phi @ ( lazy_impl @ ( prop @ ( sk8 @ B @ A ) ) @ ( impl @ ( impl @ A @ ( sk8 @ B @ A ) ) @ ( impl @ ( impl @ B @ ( sk8 @ B @ A ) ) @ ( sk8 @ B @ A ) ) ) ) ) ),
inference(rewrite,[status(thm)],[172,67]) ).
thf(162,plain,
! [A: $i] :
( ( exists2 @ A )
= ( phi @ ( f6 @ A @ ( sk7 @ A ) ) ) ),
inference(cnf,[status(esa)],[160]) ).
thf(163,plain,
! [A: $i] :
( ( exists2 @ A )
= ( phi @ ( f6 @ A @ ( sk7 @ A ) ) ) ),
inference(lifteq,[status(thm)],[162]) ).
thf(319,plain,
! [C: $i,B: $i,A: $i] :
( ( ( phi @ ( lazy_impl @ ( prop @ B ) @ ( impl @ ( f5 @ A @ B ) @ B ) ) )
= ( exists2 @ C ) )
| ( ( f6 @ A @ B )
!= ( f6 @ C @ ( sk7 @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[55,163]) ).
thf(320,plain,
! [A: $i] :
( ( phi @ ( lazy_impl @ ( prop @ ( sk7 @ A ) ) @ ( impl @ ( f5 @ A @ ( sk7 @ A ) ) @ ( sk7 @ A ) ) ) )
= ( exists2 @ A ) ),
inference(pattern_uni,[status(thm)],[319:[bind(A,$thf( D )),bind(B,$thf( sk7 @ D )),bind(C,$thf( D ))]]) ).
thf(333,plain,
! [A: $i] :
( ( phi @ ( lazy_impl @ ( prop @ ( sk7 @ A ) ) @ ( impl @ ( f5 @ A @ ( sk7 @ A ) ) @ ( sk7 @ A ) ) ) )
= ( exists2 @ A ) ),
inference(simp,[status(thm)],[320]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( forallprefers @ A @ B )
<=> ( ( ~ ( d @ A )
& ( d @ B ) )
| ( ( d @ A )
& ( d @ B )
& ~ ( bool @ A )
& ( bool @ B ) )
| ( ( A = false )
& ( B = true ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_forallprefers) ).
thf(173,plain,
! [A: $i,B: $i] :
( ( ( forallprefers @ A @ B )
=> ( ( ~ ( d @ A )
& ( d @ B ) )
| ( ( d @ A )
& ( d @ B )
& ~ ( bool @ A )
& ( bool @ B ) )
| ( ( A = false )
& ( B = true ) ) ) )
& ( ( ( ~ ( d @ A )
& ( d @ B ) )
| ( ( d @ A )
& ( d @ B )
& ~ ( bool @ A )
& ( bool @ B ) )
| ( ( A = false )
& ( B = true ) ) )
=> ( forallprefers @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(174,plain,
( ! [A: $i,B: $i] :
( ( forallprefers @ A @ B )
=> ( ( ~ ( d @ A )
& ( d @ B ) )
| ( ( d @ A )
& ( d @ B )
& ~ ( bool @ A )
& ( bool @ B ) )
| ( ( A = false )
& ( B = true ) ) ) )
& ! [A: $i,B: $i] :
( ( ( ~ ( d @ A )
& ( d @ B ) )
| ( ( d @ A )
& ( d @ B )
& ~ ( bool @ A )
& ( bool @ B ) )
| ( ( A = false )
& ( B = true ) ) )
=> ( forallprefers @ A @ B ) ) ),
inference(miniscope,[status(thm)],[173]) ).
thf(182,plain,
! [B: $i,A: $i] :
( ( A != false )
| ( B != true )
| ( forallprefers @ A @ B ) ),
inference(cnf,[status(esa)],[174]) ).
thf(190,plain,
! [B: $i,A: $i] :
( ( A != false )
| ( B != true )
| ( forallprefers @ A @ B ) ),
inference(lifteq,[status(thm)],[182]) ).
thf(191,plain,
forallprefers @ false @ true,
inference(simp,[status(thm)],[190]) ).
thf(38,axiom,
? [A: $i] :
( ( false2
= ( phi @ ( f7 @ A ) ) )
& ~ ? [B: $i] : ( forallprefers @ ( f7 @ B ) @ ( f7 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_false2) ).
thf(218,plain,
? [A: $i] :
( ( false2
= ( phi @ ( f7 @ A ) ) )
& ~ ? [B: $i] : ( forallprefers @ ( f7 @ B ) @ ( f7 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(219,plain,
! [A: $i] :
~ ( forallprefers @ ( f7 @ A ) @ ( f7 @ sk11 ) ),
inference(cnf,[status(esa)],[218]) ).
thf(248,plain,
! [A: $i] :
( ( forallprefers @ ( f7 @ A ) @ ( f7 @ sk11 ) )
!= ( forallprefers @ false @ true ) ),
inference(paramod_ordered,[status(thm)],[191,219]) ).
thf(249,plain,
! [A: $i] :
( ( ( f7 @ A )
!= false )
| ( ( f7 @ sk11 )
!= true ) ),
inference(simp,[status(thm)],[248]) ).
thf(37,axiom,
( ( not1 @ true )
= false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not1_axiom3) ).
thf(216,plain,
( ( not1 @ true )
= false ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(217,plain,
( ( not1 @ true )
= false ),
inference(lifteq,[status(thm)],[216]) ).
thf(120,plain,
d @ err,
inference(cnf,[status(esa)],[119]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ~ ( bool @ A )
=> ( ( lazy_impl @ A @ B )
= ( phi @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lazy_impl_axiom1) ).
thf(153,plain,
! [A: $i,B: $i] :
( ~ ( bool @ A )
=> ( ( lazy_impl @ A @ B )
= ( phi @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(618,plain,
! [B: $i,A: $i] :
( ~ ( forallprefers @ true @ ( f6 @ A @ false2 ) )
| ( ( prop @ false2 )
!= false )
| ( ( sk7 @ B )
!= false2 )
| ( ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( f5 @ A @ false2 ) ) )
!= ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( f5 @ B @ false2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[262,415]) ).
thf(619,plain,
! [A: $i] :
( ~ ( forallprefers @ true @ ( f6 @ A @ false2 ) )
| ( ( prop @ false2 )
!= false )
| ( ( sk7 @ A )
!= false2 ) ),
inference(pattern_uni,[status(thm)],[618:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(15,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( ( and2 @ A @ B )
= ( phi @ ( f1 @ A @ B @ C ) ) )
& ~ ? [D: $i] : ( forallprefers @ ( f1 @ A @ B @ D ) @ ( f1 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_and2) ).
thf(98,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( ( and2 @ A @ B )
= ( phi @ ( f1 @ A @ B @ C ) ) )
& ~ ? [D: $i] : ( forallprefers @ ( f1 @ A @ B @ D ) @ ( f1 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(99,plain,
! [C: $i,B: $i,A: $i] :
~ ( forallprefers @ ( f1 @ A @ B @ C ) @ ( f1 @ A @ B @ ( sk3 @ B @ A ) ) ),
inference(cnf,[status(esa)],[98]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( f1 @ A @ B @ C )
= ( lazy_impl @ ( prop @ C ) @ ( impl @ ( impl @ A @ ( impl @ B @ C ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_f1) ).
thf(59,plain,
! [A: $i,B: $i,C: $i] :
( ( f1 @ A @ B @ C )
= ( lazy_impl @ ( prop @ C ) @ ( impl @ ( impl @ A @ ( impl @ B @ C ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(60,plain,
! [C: $i,B: $i,A: $i] :
( ( f1 @ A @ B @ C )
= ( lazy_impl @ ( prop @ C ) @ ( impl @ ( impl @ A @ ( impl @ B @ C ) ) @ C ) ) ),
inference(cnf,[status(esa)],[59]) ).
thf(61,plain,
! [C: $i,B: $i,A: $i] :
( ( f1 @ A @ B @ C )
= ( lazy_impl @ ( prop @ C ) @ ( impl @ ( impl @ A @ ( impl @ B @ C ) ) @ C ) ) ),
inference(lifteq,[status(thm)],[60]) ).
thf(2466,plain,
! [C: $i,B: $i,A: $i] :
~ ( forallprefers @ ( lazy_impl @ ( prop @ C ) @ ( impl @ ( impl @ A @ ( impl @ B @ C ) ) @ C ) ) @ ( lazy_impl @ ( prop @ ( sk3 @ B @ A ) ) @ ( impl @ ( impl @ A @ ( impl @ B @ ( sk3 @ B @ A ) ) ) @ ( sk3 @ B @ A ) ) ) ),
inference(rewrite,[status(thm)],[99,61]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( ( bool @ A )
& ~ ( bool @ B ) )
=> ( ( and1 @ A @ B )
= ( phi @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and1_axiom2) ).
thf(196,plain,
! [A: $i,B: $i] :
( ( ( bool @ A )
& ~ ( bool @ B ) )
=> ( ( and1 @ A @ B )
= ( phi @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(39,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( ( f5 @ A @ B )
= ( phi @ ( f4 @ A @ C @ B ) ) )
& ~ ? [D: $i] : ( forallprefers @ ( f4 @ A @ D @ B ) @ ( f4 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_f5) ).
thf(222,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( ( f5 @ A @ B )
= ( phi @ ( f4 @ A @ C @ B ) ) )
& ~ ? [D: $i] : ( forallprefers @ ( f4 @ A @ D @ B ) @ ( f4 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(224,plain,
! [B: $i,A: $i] :
( ( f5 @ A @ B )
= ( phi @ ( f4 @ A @ ( sk12 @ B @ A ) @ B ) ) ),
inference(cnf,[status(esa)],[222]) ).
thf(225,plain,
! [B: $i,A: $i] :
( ( f5 @ A @ B )
= ( phi @ ( f4 @ A @ ( sk12 @ B @ A ) @ B ) ) ),
inference(lifteq,[status(thm)],[224]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( f4 @ A @ B @ C )
= ( impl @ ( apply @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_f4) ).
thf(62,plain,
! [A: $i,B: $i,C: $i] :
( ( f4 @ A @ B @ C )
= ( impl @ ( apply @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(63,plain,
! [C: $i,B: $i,A: $i] :
( ( f4 @ A @ B @ C )
= ( impl @ ( apply @ A @ B ) @ C ) ),
inference(cnf,[status(esa)],[62]) ).
thf(64,plain,
! [C: $i,B: $i,A: $i] :
( ( f4 @ A @ B @ C )
= ( impl @ ( apply @ A @ B ) @ C ) ),
inference(lifteq,[status(thm)],[63]) ).
thf(532,plain,
! [B: $i,A: $i] :
( ( f5 @ A @ B )
= ( phi @ ( impl @ ( apply @ A @ ( sk12 @ B @ A ) ) @ B ) ) ),
inference(rewrite,[status(thm)],[225,64]) ).
thf(547,plain,
! [C: $i,B: $i,A: $i] :
( ( ( phi @ ( not2 @ A ) )
= ( f5 @ B @ C ) )
| ( ( impl @ A @ false2 )
!= ( impl @ ( apply @ B @ ( sk12 @ C @ B ) ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[58,532]) ).
thf(548,plain,
! [A: $i] :
( ( phi @ ( not2 @ ( apply @ A @ ( sk12 @ false2 @ A ) ) ) )
= ( f5 @ A @ false2 ) ),
inference(pattern_uni,[status(thm)],[547:[bind(A,$thf( apply @ G @ ( sk12 @ false2 @ G ) )),bind(B,$thf( G )),bind(C,$thf( false2 ))]]) ).
thf(567,plain,
! [A: $i] :
( ( phi @ ( not2 @ ( apply @ A @ ( sk12 @ false2 @ A ) ) ) )
= ( f5 @ A @ false2 ) ),
inference(simp,[status(thm)],[548]) ).
thf(582,plain,
! [B: $i,A: $i] :
( ( ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( phi @ ( not2 @ ( apply @ A @ ( sk12 @ false2 @ A ) ) ) ) ) )
= ( f6 @ B @ false2 ) )
| ( ( f5 @ A @ false2 )
!= ( f5 @ B @ false2 ) ) ),
inference(paramod_ordered,[status(thm)],[567,262]) ).
thf(583,plain,
! [A: $i] :
( ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( phi @ ( not2 @ ( apply @ A @ ( sk12 @ false2 @ A ) ) ) ) ) )
= ( f6 @ A @ false2 ) ),
inference(pattern_uni,[status(thm)],[582:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(948,plain,
! [B: $i,A: $i] :
( ( ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( phi @ ( not2 @ ( apply @ A @ ( sk12 @ false2 @ A ) ) ) ) ) )
= ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( f5 @ B @ false2 ) ) ) )
| ( ( f6 @ A @ false2 )
!= ( f6 @ B @ false2 ) ) ),
inference(paramod_ordered,[status(thm)],[583,262]) ).
thf(949,plain,
! [A: $i] :
( ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( phi @ ( not2 @ ( apply @ A @ ( sk12 @ false2 @ A ) ) ) ) ) )
= ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( f5 @ A @ false2 ) ) ) ),
inference(pattern_uni,[status(thm)],[948:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(26,axiom,
! [A: $i] :
( ( bool @ A )
=> ( ( and1 @ false @ A )
= false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and1_axiom3) ).
thf(157,plain,
! [A: $i] :
( ( bool @ A )
=> ( ( and1 @ false @ A )
= false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(88,plain,
! [A: $i] :
( ( A != true )
| ( bool @ A ) ),
inference(cnf,[status(esa)],[86]) ).
thf(92,plain,
! [A: $i] :
( ( A != true )
| ( bool @ A ) ),
inference(lifteq,[status(thm)],[88]) ).
thf(93,plain,
bool @ true,
inference(simp,[status(thm)],[92]) ).
thf(202,plain,
! [A: $i] :
( ( ( prop @ A )
!= false )
| ~ ( bool @ A ) ),
inference(cnf,[status(esa)],[200]) ).
thf(205,plain,
! [A: $i] :
( ( ( prop @ A )
!= false )
| ~ ( bool @ A ) ),
inference(lifteq,[status(thm)],[202]) ).
thf(283,plain,
! [A: $i] :
( ( ( prop @ A )
!= false )
| ( ( bool @ true )
!= ( bool @ A ) ) ),
inference(paramod_ordered,[status(thm)],[93,205]) ).
thf(284,plain,
( ( prop @ true )
!= false ),
inference(pattern_uni,[status(thm)],[283:[bind(A,$thf( true ))]]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( existsprefers @ A @ B )
<=> ( ( ~ ( d @ A )
& ( d @ B ) )
| ( ( d @ A )
& ( d @ B )
& ~ ( bool @ A )
& ( bool @ B ) )
| ( ( A = true )
& ( B = false ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_existsprefers) ).
thf(134,plain,
! [A: $i,B: $i] :
( ( ( existsprefers @ A @ B )
=> ( ( ~ ( d @ A )
& ( d @ B ) )
| ( ( d @ A )
& ( d @ B )
& ~ ( bool @ A )
& ( bool @ B ) )
| ( ( A = true )
& ( B = false ) ) ) )
& ( ( ( ~ ( d @ A )
& ( d @ B ) )
| ( ( d @ A )
& ( d @ B )
& ~ ( bool @ A )
& ( bool @ B ) )
| ( ( A = true )
& ( B = false ) ) )
=> ( existsprefers @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(135,plain,
( ! [A: $i,B: $i] :
( ( existsprefers @ A @ B )
=> ( ( ~ ( d @ A )
& ( d @ B ) )
| ( ( d @ A )
& ( d @ B )
& ~ ( bool @ A )
& ( bool @ B ) )
| ( ( A = true )
& ( B = false ) ) ) )
& ! [A: $i,B: $i] :
( ( ( ~ ( d @ A )
& ( d @ B ) )
| ( ( d @ A )
& ( d @ B )
& ~ ( bool @ A )
& ( bool @ B ) )
| ( ( A = true )
& ( B = false ) ) )
=> ( existsprefers @ A @ B ) ) ),
inference(miniscope,[status(thm)],[134]) ).
thf(145,plain,
! [B: $i,A: $i] :
( ( A != true )
| ( B != false )
| ( existsprefers @ A @ B ) ),
inference(cnf,[status(esa)],[135]) ).
thf(151,plain,
! [B: $i,A: $i] :
( ( A != true )
| ( B != false )
| ( existsprefers @ A @ B ) ),
inference(lifteq,[status(thm)],[145]) ).
thf(152,plain,
existsprefers @ true @ false,
inference(simp,[status(thm)],[151]) ).
thf(75,plain,
! [A: $i] :
( ( ( phi @ A )
= A )
| ( ( phi @ A )
= err ) ),
inference(cnf,[status(esa)],[71]) ).
thf(78,plain,
! [A: $i] :
( ( ( phi @ A )
= A )
| ( ( phi @ A )
= err ) ),
inference(lifteq,[status(thm)],[75]) ).
thf(28,axiom,
! [A: $i] :
( ( bool @ A )
=> ( ( and1 @ true @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and1_axiom4) ).
thf(164,plain,
! [A: $i] :
( ( bool @ A )
=> ( ( and1 @ true @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(87,plain,
! [A: $i] :
( ( A != false )
| ( bool @ A ) ),
inference(cnf,[status(esa)],[86]) ).
thf(90,plain,
! [A: $i] :
( ( A != false )
| ( bool @ A ) ),
inference(lifteq,[status(thm)],[87]) ).
thf(91,plain,
bool @ false,
inference(simp,[status(thm)],[90]) ).
thf(16,axiom,
! [A: $i] :
( ( bool @ A )
=> ( ( impl @ true @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',impl_axiom4) ).
thf(102,plain,
! [A: $i] :
( ( bool @ A )
=> ( ( impl @ true @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(103,plain,
! [A: $i] :
( ~ ( bool @ A )
| ( ( impl @ true @ A )
= A ) ),
inference(cnf,[status(esa)],[102]) ).
thf(104,plain,
! [A: $i] :
( ( ( impl @ true @ A )
= A )
| ~ ( bool @ A ) ),
inference(lifteq,[status(thm)],[103]) ).
thf(2768,plain,
! [A: $i] :
( ( ( impl @ true @ A )
= A )
| ( ( bool @ false )
!= ( bool @ A ) ) ),
inference(paramod_ordered,[status(thm)],[91,104]) ).
thf(2769,plain,
( ( impl @ true @ false )
= false ),
inference(pattern_uni,[status(thm)],[2768:[bind(A,$thf( false ))]]) ).
thf(121,plain,
d @ false,
inference(cnf,[status(esa)],[119]) ).
thf(749,plain,
! [A: $i] :
( ( ( phi @ A )
= A )
| ( ( d @ false )
!= ( d @ A ) ) ),
inference(paramod_ordered,[status(thm)],[121,77]) ).
thf(750,plain,
( ( phi @ false )
= false ),
inference(pattern_uni,[status(thm)],[749:[bind(A,$thf( false ))]]) ).
thf(3468,plain,
( ( sk1 != false )
| ( ( phi @ ( lazy_impl @ ( prop @ ( sk13 @ sk2 @ sk1 ) ) @ ( impl @ true @ ( sk13 @ sk2 @ sk1 ) ) ) )
!= ( phi @ false ) ) ),
inference(paramod_ordered,[status(thm)],[750,3107]) ).
thf(3519,plain,
( ( sk1 != false )
| ( ( lazy_impl @ ( prop @ ( sk13 @ sk2 @ sk1 ) ) @ ( impl @ true @ ( sk13 @ sk2 @ sk1 ) ) )
!= false ) ),
inference(simp,[status(thm)],[3468]) ).
thf(3840,plain,
( ( sk1 != false )
| ( ( lazy_impl @ ( prop @ ( sk13 @ sk2 @ sk1 ) ) @ false )
!= false )
| ( ( impl @ true @ ( sk13 @ sk2 @ sk1 ) )
!= ( impl @ true @ false ) ) ),
inference(paramod_ordered,[status(thm)],[2769,3519]) ).
thf(3877,plain,
( ( sk1 != false )
| ( ( lazy_impl @ ( prop @ ( sk13 @ sk2 @ sk1 ) ) @ false )
!= false )
| ( true != true )
| ( ( sk13 @ sk2 @ sk1 )
!= false ) ),
inference(simp,[status(thm)],[3840]) ).
thf(3887,plain,
( ( sk1 != false )
| ( ( lazy_impl @ ( prop @ ( sk13 @ sk2 @ sk1 ) ) @ false )
!= false )
| ( ( sk13 @ sk2 @ sk1 )
!= false ) ),
inference(simp,[status(thm)],[3877]) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ~ ( bool @ A )
=> ( ( lazy_and1 @ A @ B )
= ( phi @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lazy_and1_axiom1) ).
thf(238,plain,
! [A: $i,B: $i] :
( ~ ( bool @ A )
=> ( ( lazy_and1 @ A @ B )
= ( phi @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(223,plain,
! [C: $i,B: $i,A: $i] :
~ ( forallprefers @ ( f4 @ A @ C @ B ) @ ( f4 @ A @ ( sk12 @ B @ A ) @ B ) ),
inference(cnf,[status(esa)],[222]) ).
thf(3409,plain,
! [C: $i,B: $i,A: $i] :
~ ( forallprefers @ ( impl @ ( apply @ A @ C ) @ B ) @ ( impl @ ( apply @ A @ ( sk12 @ B @ A ) ) @ B ) ),
inference(rewrite,[status(thm)],[223,64]) ).
thf(3419,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( forallprefers @ ( not2 @ A ) @ ( impl @ ( apply @ B @ ( sk12 @ C @ B ) ) @ C ) )
| ( ( impl @ A @ false2 )
!= ( impl @ ( apply @ B @ D ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[58,3409]) ).
thf(3420,plain,
! [B: $i,A: $i] :
~ ( forallprefers @ ( not2 @ ( apply @ A @ B ) ) @ ( impl @ ( apply @ A @ ( sk12 @ false2 @ A ) ) @ false2 ) ),
inference(pattern_uni,[status(thm)],[3419:[bind(A,$thf( apply @ E @ F )),bind(B,$thf( E )),bind(C,$thf( false2 )),bind(D,$thf( F ))]]) ).
thf(3449,plain,
! [B: $i,A: $i] :
~ ( forallprefers @ ( not2 @ ( apply @ A @ B ) ) @ ( impl @ ( apply @ A @ ( sk12 @ false2 @ A ) ) @ false2 ) ),
inference(simp,[status(thm)],[3420]) ).
thf(3569,plain,
! [B: $i,A: $i] :
~ ( forallprefers @ ( not2 @ ( apply @ A @ B ) ) @ ( not2 @ ( apply @ A @ ( sk12 @ false2 @ A ) ) ) ),
inference(rewrite,[status(thm)],[3449,58]) ).
thf(12,axiom,
! [A: $i] :
( ( bool @ A )
=> ( ( or1 @ false @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or1_axiom4) ).
thf(82,plain,
! [A: $i] :
( ( bool @ A )
=> ( ( or1 @ false @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(83,plain,
! [A: $i] :
( ~ ( bool @ A )
| ( ( or1 @ false @ A )
= A ) ),
inference(cnf,[status(esa)],[82]) ).
thf(84,plain,
! [A: $i] :
( ( ( or1 @ false @ A )
= A )
| ~ ( bool @ A ) ),
inference(lifteq,[status(thm)],[83]) ).
thf(220,plain,
( false2
= ( phi @ ( f7 @ sk11 ) ) ),
inference(cnf,[status(esa)],[218]) ).
thf(221,plain,
( ( phi @ ( f7 @ sk11 ) )
= false2 ),
inference(lifteq,[status(thm)],[220]) ).
thf(23,axiom,
! [A: $i] :
? [B: $i] :
( ( ( exists1 @ A )
= ( phi @ ( apply @ A @ B ) ) )
& ~ ? [C: $i] : ( existsprefers @ ( apply @ A @ C ) @ ( apply @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exists1_axiom1) ).
thf(130,plain,
! [A: $i] :
? [B: $i] :
( ( ( exists1 @ A )
= ( phi @ ( apply @ A @ B ) ) )
& ~ ? [C: $i] : ( existsprefers @ ( apply @ A @ C ) @ ( apply @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(132,plain,
! [A: $i] :
( ( exists1 @ A )
= ( phi @ ( apply @ A @ ( sk4 @ A ) ) ) ),
inference(cnf,[status(esa)],[130]) ).
thf(133,plain,
! [A: $i] :
( ( exists1 @ A )
= ( phi @ ( apply @ A @ ( sk4 @ A ) ) ) ),
inference(lifteq,[status(thm)],[132]) ).
thf(19,axiom,
( ( true != false )
& ( true != err )
& ( false != err ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distinct_false_true_err) ).
thf(112,plain,
( ( true != false )
& ( true != err )
& ( false != err ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(113,plain,
false != err,
inference(cnf,[status(esa)],[112]) ).
thf(116,plain,
false != err,
inference(lifteq,[status(thm)],[113]) ).
thf(35,axiom,
! [A: $i] :
( ( bool @ A )
=> ( ( impl @ false @ A )
= true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',impl_axiom3) ).
thf(206,plain,
! [A: $i] :
( ( bool @ A )
=> ( ( impl @ false @ A )
= true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(170,plain,
! [C: $i,B: $i,A: $i] :
~ ( forallprefers @ ( f3 @ A @ B @ C ) @ ( f3 @ A @ B @ ( sk8 @ B @ A ) ) ),
inference(cnf,[status(esa)],[169]) ).
thf(3229,plain,
! [C: $i,B: $i,A: $i] :
~ ( forallprefers @ ( lazy_impl @ ( prop @ C ) @ ( impl @ ( impl @ A @ C ) @ ( impl @ ( impl @ B @ C ) @ C ) ) ) @ ( lazy_impl @ ( prop @ ( sk8 @ B @ A ) ) @ ( impl @ ( impl @ A @ ( sk8 @ B @ A ) ) @ ( impl @ ( impl @ B @ ( sk8 @ B @ A ) ) @ ( sk8 @ B @ A ) ) ) ) ),
inference(rewrite,[status(thm)],[170,67]) ).
thf(114,plain,
true != err,
inference(cnf,[status(esa)],[112]) ).
thf(117,plain,
true != err,
inference(lifteq,[status(thm)],[114]) ).
thf(73,plain,
! [A: $i] :
( ( d @ A )
| ( ( phi @ A )
= err ) ),
inference(cnf,[status(esa)],[71]) ).
thf(76,plain,
! [A: $i] :
( ( ( phi @ A )
= err )
| ( d @ A ) ),
inference(lifteq,[status(thm)],[73]) ).
thf(285,plain,
! [A: $i] :
( ( d @ A )
| ( err = false2 )
| ( ( phi @ A )
!= ( phi @ ( f7 @ sk11 ) ) ) ),
inference(paramod_ordered,[status(thm)],[76,221]) ).
thf(286,plain,
( ( d @ ( f7 @ sk11 ) )
| ( err = false2 ) ),
inference(pattern_uni,[status(thm)],[285:[bind(A,$thf( f7 @ sk11 ))]]) ).
thf(289,plain,
( ( d @ ( f7 @ sk11 ) )
| ( d @ false2 )
| ( err != err ) ),
inference(paramod_ordered,[status(thm)],[286,120]) ).
thf(290,plain,
( ( d @ ( f7 @ sk11 ) )
| ( d @ false2 ) ),
inference(pattern_uni,[status(thm)],[289:[]]) ).
thf(379,plain,
( ( d @ false2 )
| ( ( d @ ( f7 @ sk11 ) )
!= ( d @ false2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[290]) ).
thf(381,plain,
( ( d @ false2 )
| ( ( f7 @ sk11 )
!= false2 ) ),
inference(simp,[status(thm)],[379]) ).
thf(9,axiom,
! [A: $i] :
( ( f7 @ A )
= ( lazy_impl @ ( prop @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_f7) ).
thf(68,plain,
! [A: $i] :
( ( f7 @ A )
= ( lazy_impl @ ( prop @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(69,plain,
! [A: $i] :
( ( f7 @ A )
= ( lazy_impl @ ( prop @ A ) @ A ) ),
inference(cnf,[status(esa)],[68]) ).
thf(70,plain,
! [A: $i] :
( ( lazy_impl @ ( prop @ A ) @ A )
= ( f7 @ A ) ),
inference(lifteq,[status(thm)],[69]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ~ ( bool @ A )
=> ( ( impl @ A @ B )
= ( phi @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',impl_axiom1) ).
thf(192,plain,
! [A: $i,B: $i] :
( ~ ( bool @ A )
=> ( ( impl @ A @ B )
= ( phi @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(1232,plain,
! [A: $i] :
( ( ( phi @ A )
!= true )
| ( ( prop @ ( sk13 @ sk2 @ sk1 ) )
!= false )
| ( ( lazy_and1 @ true @ A )
!= ( lazy_and1 @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[247,1231]) ).
thf(1236,plain,
! [A: $i] :
( ( ( phi @ A )
!= true )
| ( ( prop @ ( sk13 @ sk2 @ sk1 ) )
!= false )
| ( sk1 != true )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[1232]) ).
thf(1238,plain,
( ( ( phi @ sk2 )
!= true )
| ( ( prop @ ( sk13 @ sk2 @ sk1 ) )
!= false )
| ( sk1 != true ) ),
inference(simp,[status(thm)],[1236]) ).
thf(41,axiom,
false1 = false,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_false1) ).
thf(229,plain,
false1 = false,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(14,axiom,
! [A: $i] :
( ~ ( bool @ A )
=> ( ( not1 @ A )
= ( phi @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not1_axiom1) ).
thf(95,plain,
! [A: $i] :
( ~ ( bool @ A )
=> ( ( not1 @ A )
= ( phi @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(96,plain,
! [A: $i] :
( ( bool @ A )
| ( ( not1 @ A )
= ( phi @ A ) ) ),
inference(cnf,[status(esa)],[95]) ).
thf(97,plain,
! [A: $i] :
( ( ( not1 @ A )
= ( phi @ A ) )
| ( bool @ A ) ),
inference(lifteq,[status(thm)],[96]) ).
thf(1026,plain,
! [A: $i] :
( ( ( or1 @ false @ A )
= A )
| ( ( bool @ true )
!= ( bool @ A ) ) ),
inference(paramod_ordered,[status(thm)],[93,84]) ).
thf(1027,plain,
( ( or1 @ false @ true )
= true ),
inference(pattern_uni,[status(thm)],[1026:[bind(A,$thf( true ))]]) ).
thf(18,axiom,
! [A: $i] :
( ( lazy_impl @ true @ A )
= ( phi @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lazy_impl_axiom3) ).
thf(109,plain,
! [A: $i] :
( ( lazy_impl @ true @ A )
= ( phi @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(2464,plain,
! [A: $i] :
( ( A = false )
| ~ ( bool @ A )
| ( bool @ ( sk13 @ sk2 @ sk1 ) )
| ( sk1 != true )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[94,2127]) ).
thf(2465,plain,
( ( sk2 = false )
| ~ ( bool @ sk2 )
| ( bool @ ( sk13 @ sk2 @ sk1 ) )
| ( sk1 != true ) ),
inference(pattern_uni,[status(thm)],[2464:[bind(A,$thf( sk2 ))]]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( ( bool @ A )
& ~ ( bool @ B ) )
=> ( ( or1 @ A @ B )
= ( phi @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or1_axiom2) ).
thf(127,plain,
! [A: $i,B: $i] :
( ( ( bool @ A )
& ~ ( bool @ B ) )
=> ( ( or1 @ A @ B )
= ( phi @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(128,plain,
! [B: $i,A: $i] :
( ~ ( bool @ A )
| ( bool @ B )
| ( ( or1 @ A @ B )
= ( phi @ B ) ) ),
inference(cnf,[status(esa)],[127]) ).
thf(129,plain,
! [B: $i,A: $i] :
( ( ( or1 @ A @ B )
= ( phi @ B ) )
| ~ ( bool @ A )
| ( bool @ B ) ),
inference(lifteq,[status(thm)],[128]) ).
thf(568,plain,
! [B: $i,A: $i] :
( ~ ( forallprefers @ ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( phi @ ( not2 @ ( apply @ A @ ( sk12 @ false2 @ A ) ) ) ) ) ) @ ( f6 @ B @ ( sk7 @ B ) ) )
| ( ( f5 @ A @ false2 )
!= ( f5 @ B @ false2 ) ) ),
inference(paramod_ordered,[status(thm)],[567,374]) ).
thf(569,plain,
! [A: $i] :
~ ( forallprefers @ ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( phi @ ( not2 @ ( apply @ A @ ( sk12 @ false2 @ A ) ) ) ) ) ) @ ( f6 @ A @ ( sk7 @ A ) ) ),
inference(pattern_uni,[status(thm)],[568:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(383,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( forallprefers @ ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( f5 @ C @ false2 ) ) ) @ ( lazy_impl @ ( prop @ B ) @ ( impl @ ( f5 @ A @ B ) @ B ) ) )
| ( ( f6 @ A @ B )
!= ( f6 @ C @ ( sk7 @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[55,374]) ).
thf(384,plain,
! [A: $i] :
~ ( forallprefers @ ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( f5 @ A @ false2 ) ) ) @ ( lazy_impl @ ( prop @ ( sk7 @ A ) ) @ ( impl @ ( f5 @ A @ ( sk7 @ A ) ) @ ( sk7 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[383:[bind(A,$thf( D )),bind(B,$thf( sk7 @ D )),bind(C,$thf( D ))]]) ).
thf(398,plain,
! [A: $i] :
~ ( forallprefers @ ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( f5 @ A @ false2 ) ) ) @ ( lazy_impl @ ( prop @ ( sk7 @ A ) ) @ ( impl @ ( f5 @ A @ ( sk7 @ A ) ) @ ( sk7 @ A ) ) ) ),
inference(simp,[status(thm)],[384]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ~ ( bool @ A )
=> ( ( or1 @ A @ B )
= ( phi @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or1_axiom1) ).
thf(105,plain,
! [A: $i,B: $i] :
( ~ ( bool @ A )
=> ( ( or1 @ A @ B )
= ( phi @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(2764,plain,
! [A: $i] :
( ( ( impl @ true @ A )
= A )
| ( ( bool @ true )
!= ( bool @ A ) ) ),
inference(paramod_ordered,[status(thm)],[93,104]) ).
thf(2765,plain,
( ( impl @ true @ true )
= true ),
inference(pattern_uni,[status(thm)],[2764:[bind(A,$thf( true ))]]) ).
thf(3844,plain,
( ( sk1 != false )
| ( ( lazy_impl @ ( prop @ ( sk13 @ sk2 @ sk1 ) ) @ true )
!= false )
| ( ( impl @ true @ ( sk13 @ sk2 @ sk1 ) )
!= ( impl @ true @ true ) ) ),
inference(paramod_ordered,[status(thm)],[2765,3519]) ).
thf(3882,plain,
( ( sk1 != false )
| ( ( lazy_impl @ ( prop @ ( sk13 @ sk2 @ sk1 ) ) @ true )
!= false )
| ( true != true )
| ( ( sk13 @ sk2 @ sk1 )
!= true ) ),
inference(simp,[status(thm)],[3844]) ).
thf(3890,plain,
( ( sk1 != false )
| ( ( lazy_impl @ ( prop @ ( sk13 @ sk2 @ sk1 ) ) @ true )
!= false )
| ( ( sk13 @ sk2 @ sk1 )
!= true ) ),
inference(simp,[status(thm)],[3882]) ).
thf(1482,plain,
! [A: $i] :
( ( A = false )
| ~ ( bool @ A )
| ( ( lazy_and2 @ sk1 @ true )
!= ( lazy_and1 @ sk1 @ sk2 ) )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[94,49]) ).
thf(1483,plain,
( ( sk2 = false )
| ~ ( bool @ sk2 )
| ( ( lazy_and2 @ sk1 @ true )
!= ( lazy_and1 @ sk1 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[1482:[bind(A,$thf( sk2 ))]]) ).
thf(693,plain,
! [A: $i] :
( ( ( phi @ A )
= A )
| ( ( phi @ A )
!= ( phi @ A ) )
| ( err != A ) ),
inference(eqfactor_ordered,[status(thm)],[78]) ).
thf(694,plain,
( ( phi @ err )
= err ),
inference(pattern_uni,[status(thm)],[693:[bind(A,$thf( err ))]]) ).
thf(115,plain,
true != false,
inference(cnf,[status(esa)],[112]) ).
thf(118,plain,
true != false,
inference(lifteq,[status(thm)],[115]) ).
thf(367,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( forallprefers @ ( f6 @ C @ D ) @ ( lazy_impl @ ( prop @ B ) @ ( impl @ ( f5 @ A @ B ) @ B ) ) )
| ( ( f6 @ A @ B )
!= ( f6 @ C @ ( sk7 @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[55,161]) ).
thf(368,plain,
! [B: $i,A: $i] :
~ ( forallprefers @ ( f6 @ B @ A ) @ ( lazy_impl @ ( prop @ ( sk7 @ B ) ) @ ( impl @ ( f5 @ B @ ( sk7 @ B ) ) @ ( sk7 @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[367:[bind(A,$thf( E )),bind(B,$thf( sk7 @ E )),bind(C,$thf( E ))]]) ).
thf(377,plain,
! [B: $i,A: $i] :
~ ( forallprefers @ ( f6 @ B @ A ) @ ( lazy_impl @ ( prop @ ( sk7 @ B ) ) @ ( impl @ ( f5 @ B @ ( sk7 @ B ) ) @ ( sk7 @ B ) ) ) ),
inference(simp,[status(thm)],[368]) ).
thf(230,plain,
false1 = false,
inference(lifteq,[status(thm)],[229]) ).
thf(1079,plain,
! [C: $i,B: $i,A: $i] :
( ( ( phi @ ( lazy_impl @ ( prop @ ( sk13 @ C @ B ) ) @ ( impl @ true @ ( sk13 @ C @ B ) ) ) )
= ( lazy_and2 @ B @ C ) )
| ( ( lazy_impl @ false @ A )
!= ( lazy_impl @ B @ ( impl @ C @ ( sk13 @ C @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[81,1045]) ).
thf(1080,plain,
! [A: $i] :
( ( phi @ ( lazy_impl @ ( prop @ ( sk13 @ A @ false ) ) @ ( impl @ true @ ( sk13 @ A @ false ) ) ) )
= ( lazy_and2 @ false @ A ) ),
inference(pattern_uni,[status(thm)],[1079:[bind(A,$thf( impl @ F @ ( sk13 @ F @ false ) )),bind(B,$thf( false )),bind(C,$thf( F ))]]) ).
thf(1149,plain,
! [A: $i] :
( ( phi @ ( lazy_impl @ ( prop @ ( sk13 @ A @ false ) ) @ ( impl @ true @ ( sk13 @ A @ false ) ) ) )
= ( lazy_and2 @ false @ A ) ),
inference(simp,[status(thm)],[1080]) ).
thf(106,plain,
! [A: $i] :
( ~ ( bool @ A )
=> ! [B: $i] :
( ( or1 @ A @ B )
= ( phi @ A ) ) ),
inference(miniscope,[status(thm)],[105]) ).
thf(107,plain,
! [B: $i,A: $i] :
( ( bool @ A )
| ( ( or1 @ A @ B )
= ( phi @ A ) ) ),
inference(cnf,[status(esa)],[106]) ).
thf(108,plain,
! [B: $i,A: $i] :
( ( ( or1 @ A @ B )
= ( phi @ A ) )
| ( bool @ A ) ),
inference(lifteq,[status(thm)],[107]) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( ( bool @ A )
& ~ ( bool @ B ) )
=> ( ( impl @ A @ B )
= ( phi @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',impl_axiom2) ).
thf(226,plain,
! [A: $i,B: $i] :
( ( ( bool @ A )
& ~ ( bool @ B ) )
=> ( ( impl @ A @ B )
= ( phi @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(29,axiom,
( ( not1 @ false )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not1_axiom2) ).
thf(167,plain,
( ( not1 @ false )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(721,plain,
( ( d @ ( f7 @ sk11 ) )
| ( ( phi @ false2 )
= err )
| ( err != err ) ),
inference(paramod_ordered,[status(thm)],[286,694]) ).
thf(722,plain,
( ( d @ ( f7 @ sk11 ) )
| ( ( phi @ false2 )
= err ) ),
inference(pattern_uni,[status(thm)],[721:[]]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ~ ( bool @ A )
=> ( ( and1 @ A @ B )
= ( phi @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and1_axiom1) ).
thf(123,plain,
! [A: $i,B: $i] :
( ~ ( bool @ A )
=> ( ( and1 @ A @ B )
= ( phi @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(110,plain,
! [A: $i] :
( ( lazy_impl @ true @ A )
= ( phi @ A ) ),
inference(cnf,[status(esa)],[109]) ).
thf(111,plain,
! [A: $i] :
( ( lazy_impl @ true @ A )
= ( phi @ A ) ),
inference(lifteq,[status(thm)],[110]) ).
thf(1098,plain,
! [C: $i,B: $i,A: $i] :
( ( ( phi @ ( lazy_impl @ ( prop @ ( sk13 @ C @ B ) ) @ ( impl @ ( phi @ A ) @ ( sk13 @ C @ B ) ) ) )
= ( lazy_and2 @ B @ C ) )
| ( ( lazy_impl @ true @ A )
!= ( lazy_impl @ B @ ( impl @ C @ ( sk13 @ C @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[111,1045]) ).
thf(1099,plain,
! [A: $i] :
( ( phi @ ( lazy_impl @ ( prop @ ( sk13 @ A @ true ) ) @ ( impl @ ( phi @ ( impl @ A @ ( sk13 @ A @ true ) ) ) @ ( sk13 @ A @ true ) ) ) )
= ( lazy_and2 @ true @ A ) ),
inference(pattern_uni,[status(thm)],[1098:[bind(A,$thf( impl @ F @ ( sk13 @ F @ true ) )),bind(B,$thf( true )),bind(C,$thf( F ))]]) ).
thf(1134,plain,
! [A: $i] :
( ( phi @ ( lazy_impl @ ( prop @ ( sk13 @ A @ true ) ) @ ( impl @ ( phi @ ( impl @ A @ ( sk13 @ A @ true ) ) ) @ ( sk13 @ A @ true ) ) ) )
= ( lazy_and2 @ true @ A ) ),
inference(simp,[status(thm)],[1099]) ).
thf(36,axiom,
! [A: $i] :
( ( ( prop @ A )
= true )
<=> ( bool @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop_true) ).
thf(209,plain,
! [A: $i] :
( ( ( ( prop @ A )
= true )
=> ( bool @ A ) )
& ( ( bool @ A )
=> ( ( prop @ A )
= true ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(1024,plain,
! [A: $i] :
( ( ( or1 @ false @ A )
= A )
| ( ( bool @ false )
!= ( bool @ A ) ) ),
inference(paramod_ordered,[status(thm)],[91,84]) ).
thf(1025,plain,
( ( or1 @ false @ false )
= false ),
inference(pattern_uni,[status(thm)],[1024:[bind(A,$thf( false ))]]) ).
thf(281,plain,
! [A: $i] :
( ( ( prop @ A )
!= false )
| ( ( bool @ false )
!= ( bool @ A ) ) ),
inference(paramod_ordered,[status(thm)],[91,205]) ).
thf(282,plain,
( ( prop @ false )
!= false ),
inference(pattern_uni,[status(thm)],[281:[bind(A,$thf( false ))]]) ).
thf(1980,plain,
( ( ( prop @ ( sk13 @ sk2 @ sk1 ) )
!= false )
| ( sk1 != true )
| ( ( phi @ sk2 )
!= ( phi @ true ) ) ),
inference(paramod_ordered,[status(thm)],[804,1238]) ).
thf(2012,plain,
( ( ( prop @ ( sk13 @ sk2 @ sk1 ) )
!= false )
| ( sk1 != true )
| ( sk2 != true ) ),
inference(simp,[status(thm)],[1980]) ).
thf(718,plain,
( ( err = false2 )
| ( ( phi @ ( f7 @ sk11 ) )
!= ( phi @ err ) ) ),
inference(paramod_ordered,[status(thm)],[221,694]) ).
thf(739,plain,
( ( err = false2 )
| ( ( f7 @ sk11 )
!= err ) ),
inference(simp,[status(thm)],[718]) ).
thf(369,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( forallprefers @ ( lazy_impl @ ( prop @ B ) @ ( impl @ ( f5 @ A @ B ) @ B ) ) @ ( f6 @ C @ ( sk7 @ C ) ) )
| ( ( f6 @ A @ B )
!= ( f6 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[55,161]) ).
thf(370,plain,
! [B: $i,A: $i] :
~ ( forallprefers @ ( lazy_impl @ ( prop @ B ) @ ( impl @ ( f5 @ A @ B ) @ B ) ) @ ( f6 @ A @ ( sk7 @ A ) ) ),
inference(pattern_uni,[status(thm)],[369:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(42,axiom,
! [A: $i] :
( ( bool @ A )
=> ( ( or1 @ true @ A )
= true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or1_axiom3) ).
thf(231,plain,
! [A: $i] :
( ( bool @ A )
=> ( ( or1 @ true @ A )
= true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(235,plain,
! [C: $i,B: $i,A: $i] :
~ ( forallprefers @ ( f2 @ A @ B @ C ) @ ( f2 @ A @ B @ ( sk13 @ B @ A ) ) ),
inference(cnf,[status(esa)],[234]) ).
thf(3589,plain,
! [C: $i,B: $i,A: $i] :
~ ( forallprefers @ ( lazy_impl @ ( prop @ C ) @ ( impl @ ( lazy_impl @ A @ ( impl @ B @ C ) ) @ C ) ) @ ( lazy_impl @ ( prop @ ( sk13 @ B @ A ) ) @ ( impl @ ( lazy_impl @ A @ ( impl @ B @ ( sk13 @ B @ A ) ) ) @ ( sk13 @ B @ A ) ) ) ),
inference(rewrite,[status(thm)],[235,52]) ).
thf(1480,plain,
! [A: $i] :
( ( A = false )
| ~ ( bool @ A )
| ( ( lazy_and2 @ true @ sk2 )
!= ( lazy_and1 @ sk1 @ sk2 ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[94,49]) ).
thf(1481,plain,
( ( sk1 = false )
| ~ ( bool @ sk1 )
| ( ( lazy_and2 @ true @ sk2 )
!= ( lazy_and1 @ sk1 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[1480:[bind(A,$thf( sk1 ))]]) ).
thf(2719,plain,
( ( sk1 = false )
| ( ( lazy_and2 @ true @ sk2 )
!= ( lazy_and1 @ sk1 @ sk2 ) )
| ( ( bool @ sk1 )
!= ( bool @ true ) ) ),
inference(paramod_ordered,[status(thm)],[93,1481]) ).
thf(2743,plain,
( ( sk1 = false )
| ( ( lazy_and2 @ true @ sk2 )
!= ( lazy_and1 @ sk1 @ sk2 ) )
| ( sk1 != true ) ),
inference(simp,[status(thm)],[2719]) ).
thf(1974,plain,
( ( true != false2 )
| ( ( prop @ ( sk13 @ sk2 @ sk1 ) )
!= false )
| ( sk1 != true )
| ( ( phi @ ( f7 @ sk11 ) )
!= ( phi @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[221,1238]) ).
thf(2009,plain,
( ( true != false2 )
| ( ( prop @ ( sk13 @ sk2 @ sk1 ) )
!= false )
| ( sk1 != true )
| ( ( f7 @ sk11 )
!= sk2 ) ),
inference(simp,[status(thm)],[1974]) ).
thf(2647,plain,
! [B: $i,A: $i] :
( ( ( phi @ ( lazy_impl @ ( prop @ ( sk7 @ A ) ) @ ( impl @ ( f5 @ A @ ( sk7 @ A ) ) @ ( sk7 @ A ) ) ) )
= ( phi @ ( f6 @ B @ ( sk7 @ B ) ) ) )
| ( ( exists2 @ A )
!= ( exists2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[333,163]) ).
thf(2648,plain,
! [A: $i] :
( ( phi @ ( lazy_impl @ ( prop @ ( sk7 @ A ) ) @ ( impl @ ( f5 @ A @ ( sk7 @ A ) ) @ ( sk7 @ A ) ) ) )
= ( phi @ ( f6 @ A @ ( sk7 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[2647:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(535,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( lazy_impl @ ( prop @ D ) @ ( impl @ ( phi @ ( impl @ ( apply @ A @ ( sk12 @ B @ A ) ) @ B ) ) @ D ) )
= ( f6 @ C @ D ) )
| ( ( f5 @ A @ B )
!= ( f5 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[532,55]) ).
thf(536,plain,
! [B: $i,A: $i] :
( ( lazy_impl @ ( prop @ B ) @ ( impl @ ( phi @ ( impl @ ( apply @ A @ ( sk12 @ B @ A ) ) @ B ) ) @ B ) )
= ( f6 @ A @ B ) ),
inference(pattern_uni,[status(thm)],[535:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(168,plain,
( ( not1 @ false )
= true ),
inference(lifteq,[status(thm)],[167]) ).
thf(100,plain,
! [B: $i,A: $i] :
( ( and2 @ A @ B )
= ( phi @ ( f1 @ A @ B @ ( sk3 @ B @ A ) ) ) ),
inference(cnf,[status(esa)],[98]) ).
thf(101,plain,
! [B: $i,A: $i] :
( ( and2 @ A @ B )
= ( phi @ ( f1 @ A @ B @ ( sk3 @ B @ A ) ) ) ),
inference(lifteq,[status(thm)],[100]) ).
thf(437,plain,
! [B: $i,A: $i] :
( ( and2 @ A @ B )
= ( phi @ ( lazy_impl @ ( prop @ ( sk3 @ B @ A ) ) @ ( impl @ ( impl @ A @ ( impl @ B @ ( sk3 @ B @ A ) ) ) @ ( sk3 @ B @ A ) ) ) ) ),
inference(rewrite,[status(thm)],[101,61]) ).
thf(124,plain,
! [A: $i] :
( ~ ( bool @ A )
=> ! [B: $i] :
( ( and1 @ A @ B )
= ( phi @ A ) ) ),
inference(miniscope,[status(thm)],[123]) ).
thf(125,plain,
! [B: $i,A: $i] :
( ( bool @ A )
| ( ( and1 @ A @ B )
= ( phi @ A ) ) ),
inference(cnf,[status(esa)],[124]) ).
thf(126,plain,
! [B: $i,A: $i] :
( ( ( and1 @ A @ B )
= ( phi @ A ) )
| ( bool @ A ) ),
inference(lifteq,[status(thm)],[125]) ).
thf(136,plain,
! [B: $i,A: $i] :
( ~ ( existsprefers @ A @ B )
| ~ ( sk5 @ A @ B )
| ~ ( bool @ A )
| ( sk6 @ A @ B ) ),
inference(cnf,[status(esa)],[135]) ).
thf(131,plain,
! [B: $i,A: $i] :
~ ( existsprefers @ ( apply @ A @ B ) @ ( apply @ A @ ( sk4 @ A ) ) ),
inference(cnf,[status(esa)],[130]) ).
thf(68503,plain,
$false,
inference(cvc4,[status(thm)],[3107,629,2463,234,481,333,249,217,120,247,56,153,52,619,2466,196,949,157,93,284,152,78,216,164,3887,238,121,3569,84,61,221,133,116,206,3229,117,85,381,102,70,192,1238,1217,160,229,65,97,583,1027,2769,53,169,109,77,1231,2465,173,129,569,3409,134,205,398,105,244,750,3890,1483,161,64,694,191,3519,286,204,59,118,71,49,804,219,81,377,230,245,98,76,567,91,1149,108,130,399,2765,226,167,1076,722,374,112,123,1134,209,1025,282,95,2012,739,50,67,199,370,1235,127,231,3589,218,2743,104,1481,55,2009,2648,536,290,119,58,82,1045,1248,168,262,242,79,437,532,94,415,126,136,2127,163,68,62,131,47,111,122,222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW097+1 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n003.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Thu May 18 22:13:31 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.94/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.21/0.98 % [INFO] Parsing done (129ms).
% 1.21/0.99 % [INFO] Running in sequential loop mode.
% 1.76/1.18 % [INFO] eprover registered as external prover.
% 1.76/1.18 % [INFO] cvc4 registered as external prover.
% 1.76/1.18 % [INFO] Scanning for conjecture ...
% 1.97/1.24 % [INFO] Found a conjecture and 44 axioms. Running axiom selection ...
% 2.11/1.29 % [INFO] Axiom selection finished. Selected 44 axioms (removed 0 axioms).
% 2.11/1.34 % [INFO] Problem is first-order (TPTP FOF).
% 2.38/1.34 % [INFO] Type checking passed.
% 2.38/1.34 % [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 ...
% 167.06/30.59 % External prover 'cvc4' found a proof!
% 167.06/30.59 % [INFO] Killing All external provers ...
% 167.06/30.59 % Time passed: 30064ms (effective reasoning time: 29604ms)
% 167.06/30.59 % 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)>
% 167.06/30.59 % Axioms used in derivation (44): or1_axiom2, def_or2, distinct_false_true_err, def_f3, prop_false, impl_axiom1, def_f5, lazy_impl_axiom1, def_f7, def_existsprefers, not1_axiom2, lazy_impl_axiom3, lazy_and1_axiom1, and1_axiom3, false_true_err_in_d, impl_axiom4, def_f4, def_f6, and1_axiom4, prop_true, or1_axiom3, or1_axiom4, def_false2, not1_axiom3, lazy_and1_axiom3, def_exists2, def_false1, and1_axiom1, impl_axiom2, def_f2, exists1_axiom1, def_not2, def_bool, def_f1, and1_axiom2, def_lazy_and2, impl_axiom3, def_phi, def_and2, not1_axiom1, lazy_and1_axiom2, or1_axiom1, def_forallprefers, lazy_impl_axiom2
% 167.06/30.59 % No. of inferences in proof: 325
% 167.06/30.60 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 30064 ms resp. 29604 ms w/o parsing
% 167.19/30.72 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 167.19/30.72 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------