TSTP Solution File: SWW098+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWW098+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n023.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 12:21:42 EDT 2023
% Result : Theorem 196.73s 36.99s
% Output : Refutation 196.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 85
% Syntax : Number of formulae : 356 ( 147 unt; 40 typ; 0 def)
% Number of atoms : 653 ( 396 equ; 0 cnn)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 2574 ( 254 ~; 166 |; 92 &;2005 @)
% ( 5 <=>; 52 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 57 ( 57 >; 0 *; 0 +; 0 <<)
% Number of symbols : 43 ( 40 usr; 10 con; 0-3 aty)
% Number of variables : 428 ( 0 ^; 400 !; 28 ?; 428 :)
% Comments :
%------------------------------------------------------------------------------
thf(or1_type,type,
or1: $i > $i > $i ).
thf(or2_type,type,
or2: $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(not1_type,type,
not1: $i > $i ).
thf(and2_type,type,
and2: $i > $i > $i ).
thf(forallprefers_type,type,
forallprefers: $i > $i > $o ).
thf(lazy_and2_type,type,
lazy_and2: $i > $i > $i ).
thf(and1_type,type,
and1: $i > $i > $i ).
thf(lazy_and1_type,type,
lazy_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(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 > $i ).
thf(sk5_type,type,
sk5: $i > $i > $i ).
thf(sk6_type,type,
sk6: $i > $i ).
thf(sk9_type,type,
sk9: $i > $i ).
thf(sk10_type,type,
sk10: $i ).
thf(sk13_type,type,
sk13: $i > $i > $i ).
thf(45,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(241,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)],[45]) ).
thf(243,plain,
! [B: $i,A: $i] :
( ( or2 @ A @ B )
= ( phi @ ( f3 @ A @ B @ ( sk13 @ B @ A ) ) ) ),
inference(cnf,[status(esa)],[241]) ).
thf(244,plain,
! [B: $i,A: $i] :
( ( or2 @ A @ B )
= ( phi @ ( f3 @ A @ B @ ( sk13 @ B @ A ) ) ) ),
inference(lifteq,[status(thm)],[243]) ).
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(1190,plain,
! [B: $i,A: $i] :
( ( or2 @ A @ B )
= ( phi @ ( lazy_impl @ ( prop @ ( sk13 @ B @ A ) ) @ ( impl @ ( impl @ A @ ( sk13 @ B @ A ) ) @ ( impl @ ( impl @ B @ ( sk13 @ B @ A ) ) @ ( sk13 @ B @ A ) ) ) ) ) ),
inference(rewrite,[status(thm)],[244,67]) ).
thf(16,axiom,
( ( true != false )
& ( true != err )
& ( false != err ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distinct_false_true_err) ).
thf(95,plain,
( ( true != false )
& ( true != err )
& ( false != err ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(98,plain,
true != false,
inference(cnf,[status(esa)],[95]) ).
thf(101,plain,
true != false,
inference(lifteq,[status(thm)],[98]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ~ ( bool @ A )
=> ( ( or1 @ A @ B )
= ( phi @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or1_axiom1) ).
thf(234,plain,
! [A: $i,B: $i] :
( ~ ( bool @ A )
=> ( ( or1 @ A @ B )
= ( phi @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(18,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(109,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)],[18]) ).
thf(111,plain,
! [B: $i,A: $i] :
( ( lazy_and2 @ A @ B )
= ( phi @ ( f2 @ A @ B @ ( sk4 @ B @ A ) ) ) ),
inference(cnf,[status(esa)],[109]) ).
thf(112,plain,
! [B: $i,A: $i] :
( ( lazy_and2 @ A @ B )
= ( phi @ ( f2 @ A @ B @ ( sk4 @ B @ A ) ) ) ),
inference(lifteq,[status(thm)],[111]) ).
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(481,plain,
! [B: $i,A: $i] :
( ( lazy_and2 @ A @ B )
= ( phi @ ( lazy_impl @ ( prop @ ( sk4 @ B @ A ) ) @ ( impl @ ( lazy_impl @ A @ ( impl @ B @ ( sk4 @ B @ A ) ) ) @ ( sk4 @ B @ A ) ) ) ) ),
inference(rewrite,[status(thm)],[112,52]) ).
thf(30,axiom,
( ( not1 @ false )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not1_axiom2) ).
thf(169,plain,
( ( not1 @ false )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(170,plain,
( ( not1 @ false )
= true ),
inference(lifteq,[status(thm)],[169]) ).
thf(19,axiom,
( ( d @ true )
& ( d @ false )
& ( d @ err ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',false_true_err_in_d) ).
thf(113,plain,
( ( d @ true )
& ( d @ false )
& ( d @ err ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(115,plain,
d @ false,
inference(cnf,[status(esa)],[113]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ~ ( bool @ A )
=> ( ( and1 @ A @ B )
= ( phi @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and1_axiom1) ).
thf(117,plain,
! [A: $i,B: $i] :
( ~ ( bool @ A )
=> ( ( and1 @ A @ B )
= ( phi @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(118,plain,
! [A: $i] :
( ~ ( bool @ A )
=> ! [B: $i] :
( ( and1 @ A @ B )
= ( phi @ A ) ) ),
inference(miniscope,[status(thm)],[117]) ).
thf(119,plain,
! [B: $i,A: $i] :
( ( bool @ A )
| ( ( and1 @ A @ B )
= ( phi @ A ) ) ),
inference(cnf,[status(esa)],[118]) ).
thf(120,plain,
! [B: $i,A: $i] :
( ( ( and1 @ A @ B )
= ( phi @ A ) )
| ( bool @ A ) ),
inference(lifteq,[status(thm)],[119]) ).
thf(37,axiom,
( ( not1 @ true )
= false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not1_axiom3) ).
thf(201,plain,
( ( not1 @ true )
= false ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(202,plain,
( ( not1 @ true )
= false ),
inference(lifteq,[status(thm)],[201]) ).
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(1,conjecture,
! [A: $i,B: $i] :
( ( or1 @ A @ B )
= ( or2 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or1_or2) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( or1 @ A @ B )
= ( or2 @ A @ B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(47,plain,
~ ! [A: $i,B: $i] :
( ( or1 @ A @ B )
= ( or2 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(48,plain,
( ( or1 @ sk1 @ sk2 )
!= ( or2 @ sk1 @ sk2 ) ),
inference(cnf,[status(esa)],[47]) ).
thf(49,plain,
( ( or2 @ sk1 @ sk2 )
!= ( or1 @ sk1 @ sk2 ) ),
inference(lifteq,[status(thm)],[48]) ).
thf(1221,plain,
! [B: $i,A: $i] :
( ( ( phi @ ( lazy_impl @ ( prop @ ( sk13 @ B @ A ) ) @ ( impl @ ( impl @ A @ ( sk13 @ B @ A ) ) @ ( impl @ ( impl @ B @ ( sk13 @ B @ A ) ) @ ( sk13 @ B @ A ) ) ) ) )
!= ( or1 @ sk1 @ sk2 ) )
| ( ( or2 @ A @ B )
!= ( or2 @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[1190,49]) ).
thf(1222,plain,
( ( phi @ ( lazy_impl @ ( prop @ ( sk13 @ sk2 @ sk1 ) ) @ ( impl @ ( impl @ sk1 @ ( sk13 @ sk2 @ sk1 ) ) @ ( impl @ ( impl @ sk2 @ ( sk13 @ sk2 @ sk1 ) ) @ ( sk13 @ sk2 @ sk1 ) ) ) ) )
!= ( or1 @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[1221:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
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(185,plain,
! [A: $i,B: $i] :
( ( ( bool @ A )
& ~ ( bool @ B ) )
=> ( ( and1 @ A @ B )
= ( phi @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(116,plain,
d @ true,
inference(cnf,[status(esa)],[113]) ).
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(674,plain,
! [A: $i] :
( ( ( phi @ A )
= A )
| ( ( d @ true )
!= ( d @ A ) ) ),
inference(paramod_ordered,[status(thm)],[116,77]) ).
thf(675,plain,
( ( phi @ true )
= true ),
inference(pattern_uni,[status(thm)],[674:[bind(A,$thf( true ))]]) ).
thf(32,axiom,
! [A: $i] :
( ( bool @ A )
<=> ( ( A = false )
| ( A = true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_bool) ).
thf(175,plain,
! [A: $i] :
( ( ( bool @ A )
=> ( ( A = false )
| ( A = true ) ) )
& ( ( ( A = false )
| ( A = true ) )
=> ( bool @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(176,plain,
( ! [A: $i] :
( ( bool @ A )
=> ( ( A = false )
| ( A = true ) ) )
& ! [A: $i] :
( ( ( A = false )
| ( A = true ) )
=> ( bool @ A ) ) ),
inference(miniscope,[status(thm)],[175]) ).
thf(178,plain,
! [A: $i] :
( ( A != true )
| ( bool @ A ) ),
inference(cnf,[status(esa)],[176]) ).
thf(182,plain,
! [A: $i] :
( ( A != true )
| ( bool @ A ) ),
inference(lifteq,[status(thm)],[178]) ).
thf(183,plain,
bool @ true,
inference(simp,[status(thm)],[182]) ).
thf(17,axiom,
! [A: $i] :
( ( ( prop @ A )
= true )
<=> ( bool @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop_true) ).
thf(102,plain,
! [A: $i] :
( ( ( ( prop @ A )
= true )
=> ( bool @ A ) )
& ( ( bool @ A )
=> ( ( prop @ A )
= true ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(103,plain,
( ! [A: $i] :
( ( ( prop @ A )
= true )
=> ( bool @ A ) )
& ! [A: $i] :
( ( bool @ A )
=> ( ( prop @ A )
= true ) ) ),
inference(miniscope,[status(thm)],[102]) ).
thf(104,plain,
! [A: $i] :
( ~ ( bool @ A )
| ( ( prop @ A )
= true ) ),
inference(cnf,[status(esa)],[103]) ).
thf(106,plain,
! [A: $i] :
( ( ( prop @ A )
= true )
| ~ ( bool @ A ) ),
inference(lifteq,[status(thm)],[104]) ).
thf(107,plain,
! [A: $i] :
( ( ( prop @ A )
= true )
| ~ ( bool @ A ) ),
inference(simp,[status(thm)],[106]) ).
thf(1868,plain,
! [A: $i] :
( ( ( prop @ A )
= true )
| ( ( bool @ true )
!= ( bool @ A ) ) ),
inference(paramod_ordered,[status(thm)],[183,107]) ).
thf(1869,plain,
( ( prop @ true )
= true ),
inference(pattern_uni,[status(thm)],[1868:[bind(A,$thf( true ))]]) ).
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(1954,plain,
! [A: $i] :
( ( ( lazy_impl @ true @ A )
= ( f7 @ A ) )
| ( ( prop @ true )
!= ( prop @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1869,70]) ).
thf(1955,plain,
( ( lazy_impl @ true @ true )
= ( f7 @ true ) ),
inference(pattern_uni,[status(thm)],[1954:[bind(A,$thf( true ))]]) ).
thf(15,axiom,
! [A: $i] :
( ( lazy_impl @ true @ A )
= ( phi @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lazy_impl_axiom3) ).
thf(92,plain,
! [A: $i] :
( ( lazy_impl @ true @ A )
= ( phi @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(93,plain,
! [A: $i] :
( ( lazy_impl @ true @ A )
= ( phi @ A ) ),
inference(cnf,[status(esa)],[92]) ).
thf(94,plain,
! [A: $i] :
( ( lazy_impl @ true @ A )
= ( phi @ A ) ),
inference(lifteq,[status(thm)],[93]) ).
thf(2061,plain,
( ( phi @ true )
= ( f7 @ true ) ),
inference(rewrite,[status(thm)],[1955,94]) ).
thf(2063,plain,
( ( f7 @ true )
= true ),
inference(rewrite,[status(thm)],[675,2061]) ).
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(203,plain,
? [A: $i] :
( ( false2
= ( phi @ ( f7 @ A ) ) )
& ~ ? [B: $i] : ( forallprefers @ ( f7 @ B ) @ ( f7 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(204,plain,
! [A: $i] :
~ ( forallprefers @ ( f7 @ A ) @ ( f7 @ sk10 ) ),
inference(cnf,[status(esa)],[203]) ).
thf(2135,plain,
! [A: $i] :
( ~ ( forallprefers @ true @ ( f7 @ sk10 ) )
| ( ( f7 @ true )
!= ( f7 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2063,204]) ).
thf(2136,plain,
~ ( forallprefers @ true @ ( f7 @ sk10 ) ),
inference(pattern_uni,[status(thm)],[2135:[bind(A,$thf( true ))]]) ).
thf(22,axiom,
! [A: $i] :
( ( lazy_and1 @ false @ A )
= false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lazy_and1_axiom2) ).
thf(125,plain,
! [A: $i] :
( ( lazy_and1 @ false @ A )
= false ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
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(1974,plain,
! [B: $i,A: $i] :
( ( ( lazy_impl @ true @ ( impl @ ( f5 @ A @ B ) @ B ) )
= ( f6 @ A @ B ) )
| ( ( prop @ true )
!= ( prop @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1869,55]) ).
thf(1975,plain,
! [A: $i] :
( ( lazy_impl @ true @ ( impl @ ( f5 @ A @ true ) @ true ) )
= ( f6 @ A @ true ) ),
inference(pattern_uni,[status(thm)],[1974:[bind(A,$thf( A )),bind(B,$thf( true ))]]) ).
thf(2638,plain,
! [A: $i] :
( ( phi @ ( impl @ ( f5 @ A @ true ) @ true ) )
= ( f6 @ A @ true ) ),
inference(rewrite,[status(thm)],[1975,94]) ).
thf(28,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(162,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)],[28]) ).
thf(163,plain,
! [B: $i,A: $i] :
~ ( forallprefers @ ( f6 @ A @ B ) @ ( f6 @ A @ ( sk9 @ A ) ) ),
inference(cnf,[status(esa)],[162]) ).
thf(2702,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( forallprefers @ ( phi @ ( impl @ ( f5 @ A @ true ) @ true ) ) @ ( f6 @ B @ ( sk9 @ B ) ) )
| ( ( f6 @ A @ true )
!= ( f6 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[2638,163]) ).
thf(2703,plain,
! [A: $i] :
~ ( forallprefers @ ( phi @ ( impl @ ( f5 @ A @ true ) @ true ) ) @ ( f6 @ A @ ( sk9 @ A ) ) ),
inference(pattern_uni,[status(thm)],[2702:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( true ))]]) ).
thf(672,plain,
! [A: $i] :
( ( ( phi @ A )
= A )
| ( ( d @ false )
!= ( d @ A ) ) ),
inference(paramod_ordered,[status(thm)],[115,77]) ).
thf(673,plain,
( ( phi @ false )
= false ),
inference(pattern_uni,[status(thm)],[672:[bind(A,$thf( false ))]]) ).
thf(177,plain,
! [A: $i] :
( ( A != false )
| ( bool @ A ) ),
inference(cnf,[status(esa)],[176]) ).
thf(180,plain,
! [A: $i] :
( ( A != false )
| ( bool @ A ) ),
inference(lifteq,[status(thm)],[177]) ).
thf(181,plain,
bool @ false,
inference(simp,[status(thm)],[180]) ).
thf(1904,plain,
! [A: $i] :
( ( ( prop @ A )
= true )
| ( ( bool @ false )
!= ( bool @ A ) ) ),
inference(paramod_ordered,[status(thm)],[181,107]) ).
thf(1905,plain,
( ( prop @ false )
= true ),
inference(pattern_uni,[status(thm)],[1904:[bind(A,$thf( false ))]]) ).
thf(2012,plain,
! [A: $i] :
( ( ( lazy_impl @ true @ A )
= ( f7 @ A ) )
| ( ( prop @ false )
!= ( prop @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1905,70]) ).
thf(2013,plain,
( ( lazy_impl @ true @ false )
= ( f7 @ false ) ),
inference(pattern_uni,[status(thm)],[2012:[bind(A,$thf( false ))]]) ).
thf(2300,plain,
( ( phi @ false )
= ( f7 @ false ) ),
inference(rewrite,[status(thm)],[2013,94]) ).
thf(2301,plain,
( ( f7 @ false )
= false ),
inference(rewrite,[status(thm)],[673,2300]) ).
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(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(34,axiom,
! [A: $i] :
( ( ( prop @ A )
= false )
<=> ~ ( bool @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop_false) ).
thf(188,plain,
! [A: $i] :
( ( ( ( prop @ A )
= false )
=> ~ ( bool @ A ) )
& ( ~ ( bool @ A )
=> ( ( prop @ A )
= false ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(189,plain,
( ! [A: $i] :
( ( ( prop @ A )
= false )
=> ~ ( bool @ A ) )
& ! [A: $i] :
( ~ ( bool @ A )
=> ( ( prop @ A )
= false ) ) ),
inference(miniscope,[status(thm)],[188]) ).
thf(190,plain,
! [A: $i] :
( ( bool @ A )
| ( ( prop @ A )
= false ) ),
inference(cnf,[status(esa)],[189]) ).
thf(192,plain,
! [A: $i] :
( ( ( prop @ A )
= false )
| ( bool @ A ) ),
inference(lifteq,[status(thm)],[190]) ).
thf(193,plain,
! [A: $i] :
( ( ( prop @ A )
= false )
| ( bool @ A ) ),
inference(simp,[status(thm)],[192]) ).
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(1310,plain,
! [A: $i] :
( ( ( or1 @ sk1 @ sk2 )
!= ( phi @ true ) )
| ( ( lazy_impl @ false @ A )
!= ( lazy_impl @ ( prop @ ( sk13 @ sk2 @ sk1 ) ) @ ( impl @ ( impl @ sk1 @ ( sk13 @ sk2 @ sk1 ) ) @ ( impl @ ( impl @ sk2 @ ( sk13 @ sk2 @ sk1 ) ) @ ( sk13 @ sk2 @ sk1 ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[81,1222]) ).
thf(1321,plain,
! [A: $i] :
( ( ( or1 @ sk1 @ sk2 )
!= ( phi @ true ) )
| ( ( prop @ ( sk13 @ sk2 @ sk1 ) )
!= false )
| ( A
!= ( impl @ ( impl @ sk1 @ ( sk13 @ sk2 @ sk1 ) ) @ ( impl @ ( impl @ sk2 @ ( sk13 @ sk2 @ sk1 ) ) @ ( sk13 @ sk2 @ sk1 ) ) ) ) ),
inference(simp,[status(thm)],[1310]) ).
thf(1342,plain,
( ( ( or1 @ sk1 @ sk2 )
!= ( phi @ true ) )
| ( ( prop @ ( sk13 @ sk2 @ sk1 ) )
!= false ) ),
inference(simp,[status(thm)],[1321]) ).
thf(1353,plain,
( ( ( or1 @ sk1 @ sk2 )
!= true )
| ( ( prop @ ( sk13 @ sk2 @ sk1 ) )
!= false ) ),
inference(rewrite,[status(thm)],[1342,675]) ).
thf(1354,plain,
! [A: $i] :
( ( bool @ A )
| ( ( or1 @ sk1 @ sk2 )
!= true )
| ( ( prop @ A )
!= ( prop @ ( sk13 @ sk2 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[193,1353]) ).
thf(1355,plain,
( ( bool @ ( sk13 @ sk2 @ sk1 ) )
| ( ( or1 @ sk1 @ sk2 )
!= true ) ),
inference(pattern_uni,[status(thm)],[1354:[bind(A,$thf( sk13 @ sk2 @ sk1 ))]]) ).
thf(14,axiom,
! [A: $i] :
( ( bool @ A )
=> ( ( impl @ true @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',impl_axiom4) ).
thf(89,plain,
! [A: $i] :
( ( bool @ A )
=> ( ( impl @ true @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(90,plain,
! [A: $i] :
( ~ ( bool @ A )
| ( ( impl @ true @ A )
= A ) ),
inference(cnf,[status(esa)],[89]) ).
thf(91,plain,
! [A: $i] :
( ( ( impl @ true @ A )
= A )
| ~ ( bool @ A ) ),
inference(lifteq,[status(thm)],[90]) ).
thf(1431,plain,
! [A: $i] :
( ( ( or1 @ sk1 @ sk2 )
!= true )
| ( ( impl @ true @ A )
= A )
| ( ( bool @ ( sk13 @ sk2 @ sk1 ) )
!= ( bool @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1355,91]) ).
thf(1432,plain,
( ( ( or1 @ sk1 @ sk2 )
!= true )
| ( ( impl @ true @ ( sk13 @ sk2 @ sk1 ) )
= ( sk13 @ sk2 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[1431:[bind(A,$thf( sk13 @ sk2 @ sk1 ))]]) ).
thf(1787,plain,
! [A: $i] :
( ( ( or1 @ sk1 @ sk2 )
!= true )
| ( ( not2 @ A )
= ( sk13 @ sk2 @ sk1 ) )
| ( ( impl @ A @ false2 )
!= ( impl @ true @ ( sk13 @ sk2 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[58,1432]) ).
thf(1822,plain,
! [A: $i] :
( ( ( not2 @ A )
= ( sk13 @ sk2 @ sk1 ) )
| ( ( or1 @ sk1 @ sk2 )
!= true )
| ( A != true )
| ( ( sk13 @ sk2 @ sk1 )
!= false2 ) ),
inference(simp,[status(thm)],[1787]) ).
thf(1847,plain,
( ( ( sk13 @ sk2 @ sk1 )
= ( not2 @ true ) )
| ( ( or1 @ sk1 @ sk2 )
!= true )
| ( ( sk13 @ sk2 @ sk1 )
!= false2 ) ),
inference(simp,[status(thm)],[1822]) ).
thf(1417,plain,
! [A: $i] :
( ( ( impl @ true @ A )
= A )
| ( ( bool @ true )
!= ( bool @ A ) ) ),
inference(paramod_ordered,[status(thm)],[183,91]) ).
thf(1418,plain,
( ( impl @ true @ true )
= true ),
inference(pattern_uni,[status(thm)],[1417:[bind(A,$thf( true ))]]) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ( ( bool @ A )
& ~ ( bool @ B ) )
=> ( ( or1 @ A @ B )
= ( phi @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or1_axiom2) ).
thf(238,plain,
! [A: $i,B: $i] :
( ( ( bool @ A )
& ~ ( bool @ B ) )
=> ( ( or1 @ A @ B )
= ( phi @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ~ ( bool @ A )
=> ( ( lazy_and1 @ A @ B )
= ( phi @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lazy_and1_axiom1) ).
thf(121,plain,
! [A: $i,B: $i] :
( ~ ( bool @ A )
=> ( ( lazy_and1 @ A @ B )
= ( phi @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(12,axiom,
! [A: $i] :
( ~ ( bool @ A )
=> ( ( not1 @ A )
= ( phi @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not1_axiom1) ).
thf(82,plain,
! [A: $i] :
( ~ ( bool @ A )
=> ( ( not1 @ A )
= ( phi @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(83,plain,
! [A: $i] :
( ( bool @ A )
| ( ( not1 @ A )
= ( phi @ A ) ) ),
inference(cnf,[status(esa)],[82]) ).
thf(84,plain,
! [A: $i] :
( ( ( not1 @ A )
= ( phi @ A ) )
| ( bool @ A ) ),
inference(lifteq,[status(thm)],[83]) ).
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(23,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(128,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)],[23]) ).
thf(130,plain,
! [B: $i,A: $i] :
( ( f5 @ A @ B )
= ( phi @ ( f4 @ A @ ( sk5 @ B @ A ) @ B ) ) ),
inference(cnf,[status(esa)],[128]) ).
thf(131,plain,
! [B: $i,A: $i] :
( ( f5 @ A @ B )
= ( phi @ ( f4 @ A @ ( sk5 @ B @ A ) @ B ) ) ),
inference(lifteq,[status(thm)],[130]) ).
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(866,plain,
! [B: $i,A: $i] :
( ( f5 @ A @ B )
= ( phi @ ( impl @ ( apply @ A @ ( sk5 @ B @ A ) ) @ B ) ) ),
inference(rewrite,[status(thm)],[131,64]) ).
thf(264,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(265,plain,
! [A: $i] :
( ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( f5 @ A @ false2 ) ) )
= ( f6 @ A @ false2 ) ),
inference(pattern_uni,[status(thm)],[264:[bind(A,$thf( f5 @ D @ false2 )),bind(B,$thf( D )),bind(C,$thf( false2 ))]]) ).
thf(266,plain,
! [A: $i] :
( ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( f5 @ A @ false2 ) ) )
= ( f6 @ A @ false2 ) ),
inference(simp,[status(thm)],[265]) ).
thf(349,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( forallprefers @ ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( f5 @ A @ false2 ) ) ) @ ( f6 @ B @ ( sk9 @ B ) ) )
| ( ( f6 @ A @ false2 )
!= ( f6 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[266,163]) ).
thf(350,plain,
! [A: $i] :
~ ( forallprefers @ ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( f5 @ A @ false2 ) ) ) @ ( f6 @ A @ ( sk9 @ A ) ) ),
inference(pattern_uni,[status(thm)],[349:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( false2 ))]]) ).
thf(387,plain,
! [B: $i,A: $i] :
( ~ ( forallprefers @ true @ ( f6 @ B @ ( sk9 @ B ) ) )
| ( ( lazy_impl @ false @ A )
!= ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( f5 @ B @ false2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[81,350]) ).
thf(393,plain,
! [B: $i,A: $i] :
( ~ ( forallprefers @ true @ ( f6 @ B @ ( sk9 @ B ) ) )
| ( ( prop @ false2 )
!= false )
| ( A
!= ( not2 @ ( f5 @ B @ false2 ) ) ) ),
inference(simp,[status(thm)],[387]) ).
thf(400,plain,
! [A: $i] :
( ~ ( forallprefers @ true @ ( f6 @ A @ ( sk9 @ A ) ) )
| ( ( prop @ false2 )
!= false ) ),
inference(simp,[status(thm)],[393]) ).
thf(404,plain,
! [B: $i,A: $i] :
( ~ ( forallprefers @ true @ ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( f5 @ A @ false2 ) ) ) )
| ( ( prop @ false2 )
!= false )
| ( ( f6 @ A @ false2 )
!= ( f6 @ B @ ( sk9 @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[266,400]) ).
thf(408,plain,
! [B: $i,A: $i] :
( ~ ( forallprefers @ true @ ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( f5 @ A @ false2 ) ) ) )
| ( ( prop @ false2 )
!= false )
| ( A != B )
| ( ( sk9 @ B )
!= false2 ) ),
inference(simp,[status(thm)],[404]) ).
thf(411,plain,
! [A: $i] :
( ~ ( forallprefers @ true @ ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( f5 @ A @ false2 ) ) ) )
| ( ( prop @ false2 )
!= false )
| ( ( sk9 @ A )
!= false2 ) ),
inference(simp,[status(thm)],[408]) ).
thf(205,plain,
( false2
= ( phi @ ( f7 @ sk10 ) ) ),
inference(cnf,[status(esa)],[203]) ).
thf(206,plain,
( ( phi @ ( f7 @ sk10 ) )
= false2 ),
inference(lifteq,[status(thm)],[205]) ).
thf(24,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(132,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)],[24]) ).
thf(2370,plain,
! [A: $i] :
( ~ ( forallprefers @ false @ ( f7 @ sk10 ) )
| ( ( f7 @ false )
!= ( f7 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2301,204]) ).
thf(2371,plain,
~ ( forallprefers @ false @ ( f7 @ sk10 ) ),
inference(pattern_uni,[status(thm)],[2370:[bind(A,$thf( false ))]]) ).
thf(133,plain,
! [B: $i,A: $i] :
~ ( existsprefers @ ( apply @ A @ B ) @ ( apply @ A @ ( sk6 @ A ) ) ),
inference(cnf,[status(esa)],[132]) ).
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(269,plain,
! [A: $i] :
( ( d @ A )
| ( err = false2 )
| ( ( phi @ A )
!= ( phi @ ( f7 @ sk10 ) ) ) ),
inference(paramod_ordered,[status(thm)],[76,206]) ).
thf(270,plain,
( ( d @ ( f7 @ sk10 ) )
| ( err = false2 ) ),
inference(pattern_uni,[status(thm)],[269:[bind(A,$thf( f7 @ sk10 ))]]) ).
thf(545,plain,
! [B: $i,A: $i] :
( ~ ( forallprefers @ true @ ( f6 @ A @ false2 ) )
| ( ( prop @ false2 )
!= false )
| ( ( sk9 @ B )
!= false2 )
| ( ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( f5 @ A @ false2 ) ) )
!= ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( f5 @ B @ false2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[266,411]) ).
thf(546,plain,
! [A: $i] :
( ~ ( forallprefers @ true @ ( f6 @ A @ false2 ) )
| ( ( prop @ false2 )
!= false )
| ( ( sk9 @ A )
!= false2 ) ),
inference(pattern_uni,[status(thm)],[545:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(13,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(85,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)],[13]) ).
thf(164,plain,
! [A: $i] :
( ( exists2 @ A )
= ( phi @ ( f6 @ A @ ( sk9 @ A ) ) ) ),
inference(cnf,[status(esa)],[162]) ).
thf(165,plain,
! [A: $i] :
( ( exists2 @ A )
= ( phi @ ( f6 @ A @ ( sk9 @ A ) ) ) ),
inference(lifteq,[status(thm)],[164]) ).
thf(35,axiom,
! [A: $i] :
( ( lazy_and1 @ true @ A )
= ( phi @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lazy_and1_axiom3) ).
thf(195,plain,
! [A: $i] :
( ( lazy_and1 @ true @ A )
= ( phi @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(196,plain,
! [A: $i] :
( ( lazy_and1 @ true @ A )
= ( phi @ A ) ),
inference(cnf,[status(esa)],[195]) ).
thf(197,plain,
! [A: $i] :
( ( lazy_and1 @ true @ A )
= ( phi @ A ) ),
inference(lifteq,[status(thm)],[196]) ).
thf(40,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(210,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)],[40]) ).
thf(211,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)],[210]) ).
thf(217,plain,
! [B: $i,A: $i] :
( ( A != false )
| ( B != true )
| ( forallprefers @ A @ B ) ),
inference(cnf,[status(esa)],[211]) ).
thf(223,plain,
! [B: $i,A: $i] :
( ( A != false )
| ( B != true )
| ( forallprefers @ A @ B ) ),
inference(lifteq,[status(thm)],[217]) ).
thf(224,plain,
forallprefers @ false @ true,
inference(simp,[status(thm)],[223]) ).
thf(256,plain,
! [A: $i] :
( ( forallprefers @ ( f7 @ A ) @ ( f7 @ sk10 ) )
!= ( forallprefers @ false @ true ) ),
inference(paramod_ordered,[status(thm)],[224,204]) ).
thf(257,plain,
! [A: $i] :
( ( ( f7 @ A )
!= false )
| ( ( f7 @ sk10 )
!= true ) ),
inference(simp,[status(thm)],[256]) ).
thf(2373,plain,
! [A: $i] :
( ( ( f7 @ sk10 )
!= true )
| ( ( f7 @ false )
!= ( f7 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2301,257]) ).
thf(2374,plain,
( ( f7 @ sk10 )
!= true ),
inference(pattern_uni,[status(thm)],[2373:[bind(A,$thf( false ))]]) ).
thf(2462,plain,
( ( f7 @ sk10 )
!= ( f7 @ true ) ),
inference(paramod_ordered,[status(thm)],[2063,2374]) ).
thf(2464,plain,
sk10 != true,
inference(simp,[status(thm)],[2462]) ).
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(2655,plain,
! [C: $i,B: $i,A: $i] :
( ( ( phi @ ( impl @ ( phi @ ( impl @ ( apply @ A @ ( sk5 @ B @ A ) ) @ B ) ) @ true ) )
= ( f6 @ C @ true ) )
| ( ( f5 @ A @ B )
!= ( f5 @ C @ true ) ) ),
inference(paramod_ordered,[status(thm)],[866,2638]) ).
thf(2656,plain,
! [A: $i] :
( ( phi @ ( impl @ ( phi @ ( impl @ ( apply @ A @ ( sk5 @ true @ A ) ) @ true ) ) @ true ) )
= ( f6 @ A @ true ) ),
inference(pattern_uni,[status(thm)],[2655:[bind(A,$thf( A )),bind(B,$thf( true )),bind(C,$thf( A ))]]) ).
thf(3253,plain,
! [B: $i,A: $i] :
( ( ( phi @ ( impl @ ( phi @ ( impl @ ( apply @ A @ ( sk5 @ true @ A ) ) @ true ) ) @ true ) )
= ( phi @ ( impl @ ( f5 @ B @ true ) @ true ) ) )
| ( ( f6 @ A @ true )
!= ( f6 @ B @ true ) ) ),
inference(paramod_ordered,[status(thm)],[2656,2638]) ).
thf(3254,plain,
! [A: $i] :
( ( phi @ ( impl @ ( phi @ ( impl @ ( apply @ A @ ( sk5 @ true @ A ) ) @ true ) ) @ true ) )
= ( phi @ ( impl @ ( f5 @ A @ true ) @ true ) ) ),
inference(pattern_uni,[status(thm)],[3253:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(122,plain,
! [A: $i] :
( ~ ( bool @ A )
=> ! [B: $i] :
( ( lazy_and1 @ A @ B )
= ( phi @ A ) ) ),
inference(miniscope,[status(thm)],[121]) ).
thf(123,plain,
! [B: $i,A: $i] :
( ( bool @ A )
| ( ( lazy_and1 @ A @ B )
= ( phi @ A ) ) ),
inference(cnf,[status(esa)],[122]) ).
thf(124,plain,
! [B: $i,A: $i] :
( ( ( lazy_and1 @ A @ B )
= ( phi @ A ) )
| ( bool @ A ) ),
inference(lifteq,[status(thm)],[123]) ).
thf(1445,plain,
! [A: $i] :
( ( ( impl @ true @ A )
= A )
| ( ( bool @ false )
!= ( bool @ A ) ) ),
inference(paramod_ordered,[status(thm)],[181,91]) ).
thf(1446,plain,
( ( impl @ true @ false )
= false ),
inference(pattern_uni,[status(thm)],[1445:[bind(A,$thf( false ))]]) ).
thf(2694,plain,
! [C: $i,B: $i,A: $i] :
( ( ( phi @ ( impl @ ( f5 @ A @ true ) @ true ) )
= ( lazy_impl @ ( prop @ C ) @ ( impl @ ( f5 @ B @ C ) @ C ) ) )
| ( ( f6 @ A @ true )
!= ( f6 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[2638,55]) ).
thf(2695,plain,
! [A: $i] :
( ( lazy_impl @ ( prop @ true ) @ ( impl @ ( f5 @ A @ true ) @ true ) )
= ( phi @ ( impl @ ( f5 @ A @ true ) @ true ) ) ),
inference(pattern_uni,[status(thm)],[2694:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( true ))]]) ).
thf(3059,plain,
! [A: $i] :
( ( lazy_impl @ true @ ( impl @ ( f5 @ A @ true ) @ true ) )
= ( phi @ ( impl @ ( f5 @ A @ true ) @ true ) ) ),
inference(rewrite,[status(thm)],[2695,1869]) ).
thf(2033,plain,
! [B: $i,A: $i] :
( ( ( lazy_impl @ true @ ( impl @ ( f5 @ A @ B ) @ B ) )
= ( f6 @ A @ B ) )
| ( ( prop @ false )
!= ( prop @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1905,55]) ).
thf(2034,plain,
! [A: $i] :
( ( lazy_impl @ true @ ( impl @ ( f5 @ A @ false ) @ false ) )
= ( f6 @ A @ false ) ),
inference(pattern_uni,[status(thm)],[2033:[bind(A,$thf( A )),bind(B,$thf( false ))]]) ).
thf(2766,plain,
! [A: $i] :
( ( phi @ ( impl @ ( f5 @ A @ false ) @ false ) )
= ( f6 @ A @ false ) ),
inference(rewrite,[status(thm)],[2034,94]) ).
thf(2368,plain,
( ( phi @ false )
= false ),
inference(rewrite,[status(thm)],[2300,2301]) ).
thf(551,plain,
! [B: $i,A: $i] :
( ~ ( forallprefers @ true @ ( phi @ A ) )
| ( ( prop @ false2 )
!= false )
| ( ( sk9 @ B )
!= false2 )
| ( ( lazy_impl @ true @ A )
!= ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( f5 @ B @ false2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[94,411]) ).
thf(553,plain,
! [B: $i,A: $i] :
( ~ ( forallprefers @ true @ ( phi @ A ) )
| ( ( prop @ false2 )
!= false )
| ( ( sk9 @ B )
!= false2 )
| ( ( prop @ false2 )
!= true )
| ( A
!= ( not2 @ ( f5 @ B @ false2 ) ) ) ),
inference(simp,[status(thm)],[551]) ).
thf(558,plain,
! [A: $i] :
( ~ ( forallprefers @ true @ ( phi @ ( not2 @ ( f5 @ A @ false2 ) ) ) )
| ( ( prop @ false2 )
!= false )
| ( ( sk9 @ A )
!= false2 )
| ( ( prop @ false2 )
!= true ) ),
inference(simp,[status(thm)],[553]) ).
thf(2787,plain,
! [C: $i,B: $i,A: $i] :
( ( ( phi @ ( impl @ ( phi @ ( impl @ ( apply @ A @ ( sk5 @ B @ A ) ) @ B ) ) @ false ) )
= ( f6 @ C @ false ) )
| ( ( f5 @ A @ B )
!= ( f5 @ C @ false ) ) ),
inference(paramod_ordered,[status(thm)],[866,2766]) ).
thf(2788,plain,
! [A: $i] :
( ( phi @ ( impl @ ( phi @ ( impl @ ( apply @ A @ ( sk5 @ false @ A ) ) @ false ) ) @ false ) )
= ( f6 @ A @ false ) ),
inference(pattern_uni,[status(thm)],[2787:[bind(A,$thf( A )),bind(B,$thf( false )),bind(C,$thf( A ))]]) ).
thf(86,plain,
! [C: $i,B: $i,A: $i] :
~ ( forallprefers @ ( f1 @ A @ B @ C ) @ ( f1 @ A @ B @ ( sk3 @ B @ A ) ) ),
inference(cnf,[status(esa)],[85]) ).
thf(1135,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)],[86,61]) ).
thf(29,axiom,
! [A: $i] :
( ( bool @ A )
=> ( ( and1 @ true @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and1_axiom4) ).
thf(166,plain,
! [A: $i] :
( ( bool @ A )
=> ( ( and1 @ true @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(2826,plain,
! [C: $i,B: $i,A: $i] :
( ( ( phi @ ( impl @ ( f5 @ A @ false ) @ false ) )
= ( lazy_impl @ ( prop @ C ) @ ( impl @ ( f5 @ B @ C ) @ C ) ) )
| ( ( f6 @ A @ false )
!= ( f6 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[2766,55]) ).
thf(2827,plain,
! [A: $i] :
( ( lazy_impl @ ( prop @ false ) @ ( impl @ ( f5 @ A @ false ) @ false ) )
= ( phi @ ( impl @ ( f5 @ A @ false ) @ false ) ) ),
inference(pattern_uni,[status(thm)],[2826:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( false ))]]) ).
thf(3158,plain,
! [A: $i] :
( ( lazy_impl @ true @ ( impl @ ( f5 @ A @ false ) @ false ) )
= ( phi @ ( impl @ ( f5 @ A @ false ) @ false ) ) ),
inference(rewrite,[status(thm)],[2827,1905]) ).
thf(610,plain,
! [A: $i] :
( ( ( phi @ A )
= A )
| ( ( phi @ A )
!= ( phi @ A ) )
| ( err != A ) ),
inference(eqfactor_ordered,[status(thm)],[78]) ).
thf(611,plain,
( ( phi @ err )
= err ),
inference(pattern_uni,[status(thm)],[610:[bind(A,$thf( err ))]]) ).
thf(27,axiom,
! [A: $i] :
( ( bool @ A )
=> ( ( and1 @ false @ A )
= false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and1_axiom3) ).
thf(159,plain,
! [A: $i] :
( ( bool @ A )
=> ( ( and1 @ false @ A )
= false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(114,plain,
d @ err,
inference(cnf,[status(esa)],[113]) ).
thf(273,plain,
( ( d @ ( f7 @ sk10 ) )
| ( d @ false2 )
| ( err != err ) ),
inference(paramod_ordered,[status(thm)],[270,114]) ).
thf(274,plain,
( ( d @ ( f7 @ sk10 ) )
| ( d @ false2 ) ),
inference(pattern_uni,[status(thm)],[273:[]]) ).
thf(230,plain,
false1 = false,
inference(lifteq,[status(thm)],[229]) ).
thf(46,axiom,
! [A: $i] :
( ( bool @ A )
=> ( ( or1 @ true @ A )
= true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or1_axiom3) ).
thf(245,plain,
! [A: $i] :
( ( bool @ A )
=> ( ( or1 @ true @ A )
= true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(129,plain,
! [C: $i,B: $i,A: $i] :
~ ( forallprefers @ ( f4 @ A @ C @ B ) @ ( f4 @ A @ ( sk5 @ B @ A ) @ B ) ),
inference(cnf,[status(esa)],[128]) ).
thf(3457,plain,
! [C: $i,B: $i,A: $i] :
~ ( forallprefers @ ( impl @ ( apply @ A @ C ) @ B ) @ ( impl @ ( apply @ A @ ( sk5 @ B @ A ) ) @ B ) ),
inference(rewrite,[status(thm)],[129,64]) ).
thf(3460,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( forallprefers @ ( not2 @ A ) @ ( impl @ ( apply @ B @ ( sk5 @ C @ B ) ) @ C ) )
| ( ( impl @ A @ false2 )
!= ( impl @ ( apply @ B @ D ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[58,3457]) ).
thf(3461,plain,
! [B: $i,A: $i] :
~ ( forallprefers @ ( not2 @ ( apply @ A @ B ) ) @ ( impl @ ( apply @ A @ ( sk5 @ false2 @ A ) ) @ false2 ) ),
inference(pattern_uni,[status(thm)],[3460:[bind(A,$thf( apply @ E @ F )),bind(B,$thf( E )),bind(C,$thf( false2 )),bind(D,$thf( F ))]]) ).
thf(3486,plain,
! [B: $i,A: $i] :
~ ( forallprefers @ ( not2 @ ( apply @ A @ B ) ) @ ( impl @ ( apply @ A @ ( sk5 @ false2 @ A ) ) @ false2 ) ),
inference(simp,[status(thm)],[3461]) ).
thf(3710,plain,
! [B: $i,A: $i] :
~ ( forallprefers @ ( not2 @ ( apply @ A @ B ) ) @ ( not2 @ ( apply @ A @ ( sk5 @ false2 @ A ) ) ) ),
inference(rewrite,[status(thm)],[3486,58]) ).
thf(497,plain,
! [C: $i,B: $i,A: $i] :
( ( ( phi @ ( lazy_impl @ ( prop @ ( sk4 @ C @ B ) ) @ ( impl @ true @ ( sk4 @ C @ B ) ) ) )
= ( lazy_and2 @ B @ C ) )
| ( ( lazy_impl @ false @ A )
!= ( lazy_impl @ B @ ( impl @ C @ ( sk4 @ C @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[81,481]) ).
thf(498,plain,
! [A: $i] :
( ( phi @ ( lazy_impl @ ( prop @ ( sk4 @ A @ false ) ) @ ( impl @ true @ ( sk4 @ A @ false ) ) ) )
= ( lazy_and2 @ false @ A ) ),
inference(pattern_uni,[status(thm)],[497:[bind(A,$thf( impl @ F @ ( sk4 @ F @ false ) )),bind(B,$thf( false )),bind(C,$thf( F ))]]) ).
thf(535,plain,
! [A: $i] :
( ( phi @ ( lazy_impl @ ( prop @ ( sk4 @ A @ false ) ) @ ( impl @ true @ ( sk4 @ A @ false ) ) ) )
= ( lazy_and2 @ false @ A ) ),
inference(simp,[status(thm)],[498]) ).
thf(877,plain,
! [C: $i,B: $i,A: $i] :
( ( ( phi @ ( not2 @ A ) )
= ( f5 @ B @ C ) )
| ( ( impl @ A @ false2 )
!= ( impl @ ( apply @ B @ ( sk5 @ C @ B ) ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[58,866]) ).
thf(878,plain,
! [A: $i] :
( ( phi @ ( not2 @ ( apply @ A @ ( sk5 @ false2 @ A ) ) ) )
= ( f5 @ A @ false2 ) ),
inference(pattern_uni,[status(thm)],[877:[bind(A,$thf( apply @ G @ ( sk5 @ false2 @ G ) )),bind(B,$thf( G )),bind(C,$thf( false2 ))]]) ).
thf(931,plain,
! [A: $i] :
( ( phi @ ( not2 @ ( apply @ A @ ( sk5 @ false2 @ A ) ) ) )
= ( f5 @ A @ false2 ) ),
inference(simp,[status(thm)],[878]) ).
thf(963,plain,
! [B: $i,A: $i] :
( ( ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( phi @ ( not2 @ ( apply @ A @ ( sk5 @ false2 @ A ) ) ) ) ) )
= ( f6 @ B @ false2 ) )
| ( ( f5 @ A @ false2 )
!= ( f5 @ B @ false2 ) ) ),
inference(paramod_ordered,[status(thm)],[931,266]) ).
thf(964,plain,
! [A: $i] :
( ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( phi @ ( not2 @ ( apply @ A @ ( sk5 @ false2 @ A ) ) ) ) ) )
= ( f6 @ A @ false2 ) ),
inference(pattern_uni,[status(thm)],[963:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ~ ( bool @ A )
=> ( ( lazy_impl @ A @ B )
= ( phi @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lazy_impl_axiom1) ).
thf(155,plain,
! [A: $i,B: $i] :
( ~ ( bool @ A )
=> ( ( lazy_impl @ A @ B )
= ( phi @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(36,axiom,
! [A: $i] :
( ( bool @ A )
=> ( ( impl @ false @ A )
= true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',impl_axiom3) ).
thf(198,plain,
! [A: $i] :
( ( bool @ A )
=> ( ( impl @ false @ A )
= true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(105,plain,
! [A: $i] :
( ( ( prop @ A )
!= true )
| ( bool @ A ) ),
inference(cnf,[status(esa)],[103]) ).
thf(108,plain,
! [A: $i] :
( ( ( prop @ A )
!= true )
| ( bool @ A ) ),
inference(lifteq,[status(thm)],[105]) ).
thf(328,plain,
( ( d @ false2 )
| ( ( d @ ( f7 @ sk10 ) )
!= ( d @ false2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[274]) ).
thf(330,plain,
( ( d @ false2 )
| ( ( f7 @ sk10 )
!= false2 ) ),
inference(simp,[status(thm)],[328]) ).
thf(2834,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( forallprefers @ ( phi @ ( impl @ ( f5 @ A @ false ) @ false ) ) @ ( f6 @ B @ ( sk9 @ B ) ) )
| ( ( f6 @ A @ false )
!= ( f6 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[2766,163]) ).
thf(2835,plain,
! [A: $i] :
~ ( forallprefers @ ( phi @ ( impl @ ( f5 @ A @ false ) @ false ) ) @ ( f6 @ A @ ( sk9 @ A ) ) ),
inference(pattern_uni,[status(thm)],[2834:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( false ))]]) ).
thf(134,plain,
! [A: $i] :
( ( exists1 @ A )
= ( phi @ ( apply @ A @ ( sk6 @ A ) ) ) ),
inference(cnf,[status(esa)],[132]) ).
thf(135,plain,
! [A: $i] :
( ( exists1 @ A )
= ( phi @ ( apply @ A @ ( sk6 @ A ) ) ) ),
inference(lifteq,[status(thm)],[134]) ).
thf(2372,plain,
( ~ ( forallprefers @ true @ false )
| ( ( f7 @ sk10 )
!= ( f7 @ false ) ) ),
inference(paramod_ordered,[status(thm)],[2301,2136]) ).
thf(2390,plain,
( ~ ( forallprefers @ true @ false )
| ( sk10 != false ) ),
inference(simp,[status(thm)],[2372]) ).
thf(1033,plain,
! [B: $i,A: $i] :
( ( ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( phi @ ( not2 @ ( apply @ A @ ( sk5 @ false2 @ A ) ) ) ) ) )
= ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( f5 @ B @ false2 ) ) ) )
| ( ( f6 @ A @ false2 )
!= ( f6 @ B @ false2 ) ) ),
inference(paramod_ordered,[status(thm)],[964,266]) ).
thf(1034,plain,
! [A: $i] :
( ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( phi @ ( not2 @ ( apply @ A @ ( sk5 @ false2 @ A ) ) ) ) ) )
= ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( f5 @ A @ false2 ) ) ) ),
inference(pattern_uni,[status(thm)],[1033:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(191,plain,
! [A: $i] :
( ( ( prop @ A )
!= false )
| ~ ( bool @ A ) ),
inference(cnf,[status(esa)],[189]) ).
thf(194,plain,
! [A: $i] :
( ( ( prop @ A )
!= false )
| ~ ( bool @ A ) ),
inference(lifteq,[status(thm)],[191]) ).
thf(25,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(136,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)],[25]) ).
thf(137,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)],[136]) ).
thf(138,plain,
! [B: $i,A: $i] :
( ( A != true )
| ( B != false )
| ( existsprefers @ A @ B ) ),
inference(cnf,[status(esa)],[137]) ).
thf(149,plain,
! [B: $i,A: $i] :
( ( A != true )
| ( B != false )
| ( existsprefers @ A @ B ) ),
inference(lifteq,[status(thm)],[138]) ).
thf(150,plain,
existsprefers @ true @ false,
inference(simp,[status(thm)],[149]) ).
thf(721,plain,
( ( false = false2 )
| ( ( phi @ ( f7 @ sk10 ) )
!= ( phi @ false ) ) ),
inference(paramod_ordered,[status(thm)],[206,673]) ).
thf(739,plain,
( ( false = false2 )
| ( ( f7 @ sk10 )
!= false ) ),
inference(simp,[status(thm)],[721]) ).
thf(126,plain,
! [A: $i] :
( ( lazy_and1 @ false @ A )
= false ),
inference(cnf,[status(esa)],[125]) ).
thf(127,plain,
! [A: $i] :
( ( lazy_and1 @ false @ A )
= false ),
inference(lifteq,[status(thm)],[126]) ).
thf(110,plain,
! [C: $i,B: $i,A: $i] :
~ ( forallprefers @ ( f2 @ A @ B @ C ) @ ( f2 @ A @ B @ ( sk4 @ B @ A ) ) ),
inference(cnf,[status(esa)],[109]) ).
thf(2468,plain,
! [C: $i,B: $i,A: $i] :
~ ( forallprefers @ ( lazy_impl @ ( prop @ C ) @ ( impl @ ( lazy_impl @ A @ ( impl @ B @ C ) ) @ C ) ) @ ( lazy_impl @ ( prop @ ( sk4 @ B @ A ) ) @ ( impl @ ( lazy_impl @ A @ ( impl @ B @ ( sk4 @ B @ A ) ) ) @ ( sk4 @ B @ A ) ) ) ),
inference(rewrite,[status(thm)],[110,52]) ).
thf(42,axiom,
! [A: $i] :
( ( bool @ A )
=> ( ( or1 @ false @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or1_axiom4) ).
thf(231,plain,
! [A: $i] :
( ( bool @ A )
=> ( ( or1 @ false @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(96,plain,
false != err,
inference(cnf,[status(esa)],[95]) ).
thf(99,plain,
false != err,
inference(lifteq,[status(thm)],[96]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ~ ( bool @ A )
=> ( ( impl @ A @ B )
= ( phi @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',impl_axiom1) ).
thf(171,plain,
! [A: $i,B: $i] :
( ~ ( bool @ A )
=> ( ( impl @ A @ B )
= ( phi @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(2130,plain,
( ( phi @ true )
= true ),
inference(rewrite,[status(thm)],[2061,2063]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( ( bool @ A )
& ~ ( bool @ B ) )
=> ( ( impl @ A @ B )
= ( phi @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',impl_axiom2) ).
thf(207,plain,
! [A: $i,B: $i] :
( ( ( bool @ A )
& ~ ( bool @ B ) )
=> ( ( impl @ A @ B )
= ( phi @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(267,plain,
! [B: $i,A: $i] :
( ( existsprefers @ ( apply @ A @ B ) @ ( apply @ A @ ( sk6 @ A ) ) )
!= ( existsprefers @ true @ false ) ),
inference(paramod_ordered,[status(thm)],[150,133]) ).
thf(268,plain,
! [B: $i,A: $i] :
( ( ( apply @ A @ B )
!= true )
| ( ( apply @ A @ ( sk6 @ A ) )
!= false ) ),
inference(simp,[status(thm)],[267]) ).
thf(87,plain,
! [B: $i,A: $i] :
( ( and2 @ A @ B )
= ( phi @ ( f1 @ A @ B @ ( sk3 @ B @ A ) ) ) ),
inference(cnf,[status(esa)],[85]) ).
thf(88,plain,
! [B: $i,A: $i] :
( ( and2 @ A @ B )
= ( phi @ ( f1 @ A @ B @ ( sk3 @ B @ A ) ) ) ),
inference(lifteq,[status(thm)],[87]) ).
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)],[88,61]) ).
thf(634,plain,
( ( err = false2 )
| ( ( phi @ ( f7 @ sk10 ) )
!= ( phi @ err ) ) ),
inference(paramod_ordered,[status(thm)],[611,206]) ).
thf(644,plain,
( ( err = false2 )
| ( ( f7 @ sk10 )
!= err ) ),
inference(simp,[status(thm)],[634]) ).
thf(1884,plain,
! [A: $i] :
( ( ( or1 @ sk1 @ sk2 )
!= true )
| ( ( prop @ A )
= true )
| ( ( bool @ ( sk13 @ sk2 @ sk1 ) )
!= ( bool @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1355,107]) ).
thf(1885,plain,
( ( ( or1 @ sk1 @ sk2 )
!= true )
| ( ( prop @ ( sk13 @ sk2 @ sk1 ) )
= true ) ),
inference(pattern_uni,[status(thm)],[1884:[bind(A,$thf( sk13 @ sk2 @ sk1 ))]]) ).
thf(549,plain,
! [B: $i,A: $i] :
( ~ ( forallprefers @ true @ true )
| ( ( prop @ false2 )
!= false )
| ( ( sk9 @ B )
!= false2 )
| ( ( lazy_impl @ false @ A )
!= ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( f5 @ B @ false2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[81,411]) ).
thf(556,plain,
! [B: $i,A: $i] :
( ~ ( forallprefers @ true @ true )
| ( ( prop @ false2 )
!= false )
| ( ( sk9 @ B )
!= false2 )
| ( ( prop @ false2 )
!= false )
| ( A
!= ( not2 @ ( f5 @ B @ false2 ) ) ) ),
inference(simp,[status(thm)],[549]) ).
thf(560,plain,
! [A: $i] :
( ~ ( forallprefers @ true @ true )
| ( ( prop @ false2 )
!= false )
| ( ( sk9 @ A )
!= false2 ) ),
inference(simp,[status(thm)],[556]) ).
thf(97,plain,
true != err,
inference(cnf,[status(esa)],[95]) ).
thf(100,plain,
true != err,
inference(lifteq,[status(thm)],[97]) ).
thf(94913,plain,
$false,
inference(cvc4,[status(thm)],[1190,101,234,481,170,115,120,202,56,1222,185,2136,52,125,2703,2301,78,1847,1418,238,121,84,61,866,411,116,206,132,2371,89,133,117,270,546,102,85,201,1355,70,165,92,197,65,224,2464,229,3254,188,53,169,2638,109,124,77,193,1446,3059,2766,266,2368,558,128,2788,1135,166,64,3158,59,204,71,611,49,181,350,159,113,274,81,230,76,245,3710,535,91,964,155,198,108,330,2835,135,2390,241,1034,162,1905,194,150,95,739,67,1432,1869,127,2468,2656,50,1353,175,231,3457,99,931,203,171,2130,55,114,58,207,82,2374,183,210,107,136,268,79,195,437,400,2063,94,644,47,163,68,62,1885,560,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWW098+1 : TPTP v8.1.2. Released v5.2.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n023.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 23:02:15 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.92/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.36/1.01 % [INFO] Parsing done (136ms).
% 1.36/1.02 % [INFO] Running in sequential loop mode.
% 1.97/1.29 % [INFO] eprover registered as external prover.
% 1.97/1.29 % [INFO] cvc4 registered as external prover.
% 1.97/1.30 % [INFO] Scanning for conjecture ...
% 2.13/1.37 % [INFO] Found a conjecture and 44 axioms. Running axiom selection ...
% 2.28/1.43 % [INFO] Axiom selection finished. Selected 44 axioms (removed 0 axioms).
% 2.37/1.49 % [INFO] Problem is first-order (TPTP FOF).
% 2.37/1.49 % [INFO] Type checking passed.
% 2.37/1.50 % [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 ...
% 196.73/36.98 % External prover 'cvc4' found a proof!
% 196.73/36.98 % [INFO] Killing All external provers ...
% 196.73/36.99 % Time passed: 36444ms (effective reasoning time: 35961ms)
% 196.73/36.99 % 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)>
% 196.73/36.99 % 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
% 196.73/36.99 % No. of inferences in proof: 316
% 196.73/36.99 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 36444 ms resp. 35961 ms w/o parsing
% 196.90/37.05 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 196.90/37.05 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------