TSTP Solution File: SWW102+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWW102+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n007.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 12:21:43 EDT 2023
% Result : Theorem 4.68s 2.09s
% Output : Refutation 4.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 76
% Syntax : Number of formulae : 123 ( 32 unt; 31 typ; 0 def)
% Number of atoms : 221 ( 109 equ; 0 cnn)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 691 ( 57 ~; 17 |; 67 &; 505 @)
% ( 5 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 47 ( 47 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 31 usr; 6 con; 0-3 aty)
% Number of variables : 153 ( 0 ^; 125 !; 28 ?; 153 :)
% Comments :
%------------------------------------------------------------------------------
thf(not1_type,type,
not1: $i > $i ).
thf(not2_type,type,
not2: $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(f1_type,type,
f1: $i > $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(f4_type,type,
f4: $i > $i > $i > $i ).
thf(apply_type,type,
apply: $i > $i > $i ).
thf(lazy_and2_type,type,
lazy_and2: $i > $i > $i ).
thf(forallprefers_type,type,
forallprefers: $i > $i > $o ).
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(or2_type,type,
or2: $i > $i > $i ).
thf(and2_type,type,
and2: $i > $i > $i ).
thf(false2_type,type,
false2: $i ).
thf(false1_type,type,
false1: $i ).
thf(24,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(138,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)],[24]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ~ ( bool @ A )
=> ( ( lazy_impl @ A @ B )
= ( phi @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lazy_impl_axiom1) ).
thf(165,plain,
! [A: $i,B: $i] :
( ~ ( bool @ A )
=> ( ( lazy_impl @ A @ B )
= ( phi @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
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(180,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(26,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(146,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)],[26]) ).
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(227,plain,
! [A: $i,B: $i] :
( ( ( bool @ A )
& ~ ( bool @ B ) )
=> ( ( impl @ A @ B )
= ( phi @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(36,axiom,
! [A: $i] :
( ( lazy_and1 @ true @ A )
= ( phi @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lazy_and1_axiom3) ).
thf(217,plain,
! [A: $i] :
( ( lazy_and1 @ true @ A )
= ( phi @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(19,axiom,
( ( d @ true )
& ( d @ false )
& ( d @ err ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',false_true_err_in_d) ).
thf(120,plain,
( ( d @ true )
& ( d @ false )
& ( d @ err ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(5,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(56,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)],[5]) ).
thf(25,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(142,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)],[25]) ).
thf(16,axiom,
! [A: $i] :
( ( ( prop @ A )
= true )
<=> ( bool @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop_true) ).
thf(106,plain,
! [A: $i] :
( ( ( ( prop @ A )
= true )
=> ( bool @ A ) )
& ( ( bool @ A )
=> ( ( prop @ A )
= true ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(43,axiom,
! [A: $i] :
( ( not2 @ A )
= ( impl @ A @ false2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_not2) ).
thf(238,plain,
! [A: $i] :
( ( not2 @ A )
= ( impl @ A @ false2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(12,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)],[12]) ).
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(116,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(41,axiom,
false1 = false,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_false1) ).
thf(233,plain,
false1 = false,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(37,axiom,
! [A: $i] :
( ( bool @ A )
=> ( ( impl @ false @ A )
= true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',impl_axiom3) ).
thf(220,plain,
! [A: $i] :
( ( bool @ A )
=> ( ( impl @ false @ A )
= true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ~ ( bool @ A )
=> ( ( or1 @ A @ B )
= ( phi @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or1_axiom1) ).
thf(92,plain,
! [A: $i,B: $i] :
( ~ ( bool @ A )
=> ( ( or1 @ A @ B )
= ( phi @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(8,axiom,
! [A: $i] :
( ( ( d @ A )
& ( ( phi @ A )
= A ) )
| ( ~ ( d @ A )
& ( ( phi @ A )
= err ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_phi) ).
thf(65,plain,
! [A: $i] :
( ( ( d @ A )
& ( ( phi @ A )
= A ) )
| ( ~ ( d @ A )
& ( ( phi @ A )
= err ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
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(28,axiom,
! [A: $i] :
( ( bool @ A )
=> ( ( and1 @ false @ A )
= false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and1_axiom3) ).
thf(169,plain,
! [A: $i] :
( ( bool @ A )
=> ( ( and1 @ false @ A )
= false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ~ ( bool @ A )
=> ( ( and1 @ A @ B )
= ( phi @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and1_axiom1) ).
thf(124,plain,
! [A: $i,B: $i] :
( ~ ( bool @ A )
=> ( ( and1 @ A @ B )
= ( phi @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(14,axiom,
! [A: $i] :
( ( lazy_impl @ true @ A )
= ( phi @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lazy_impl_axiom3) ).
thf(96,plain,
! [A: $i] :
( ( lazy_impl @ true @ A )
= ( phi @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(9,axiom,
! [A: $i] :
( ( lazy_impl @ false @ A )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lazy_impl_axiom2) ).
thf(73,plain,
! [A: $i] :
( ( lazy_impl @ false @ A )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( ( bool @ A )
& ~ ( bool @ B ) )
=> ( ( or1 @ A @ B )
= ( phi @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or1_axiom2) ).
thf(128,plain,
! [A: $i,B: $i] :
( ( ( bool @ A )
& ~ ( bool @ B ) )
=> ( ( or1 @ A @ B )
= ( phi @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(45,axiom,
( ( not1 @ false )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not1_axiom2) ).
thf(244,plain,
( ( not1 @ false )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
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(176,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(6,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(59,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)],[6]) ).
thf(29,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(172,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)],[29]) ).
thf(17,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(113,plain,
! [A: $i,B: $i,C: $i] :
( ( f4 @ A @ B @ C )
= ( impl @ ( apply @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(40,axiom,
! [A: $i] :
( ( bool @ A )
=> ( ( and1 @ true @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and1_axiom4) ).
thf(230,plain,
! [A: $i] :
( ( bool @ A )
=> ( ( and1 @ true @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(10,axiom,
! [A: $i] :
( ( bool @ A )
=> ( ( or1 @ false @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or1_axiom4) ).
thf(76,plain,
! [A: $i] :
( ( bool @ A )
=> ( ( or1 @ false @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
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(223,plain,
? [A: $i] :
( ( false2
= ( phi @ ( f7 @ A ) ) )
& ~ ? [B: $i] : ( forallprefers @ ( f7 @ B ) @ ( f7 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(23,axiom,
! [A: $i] :
( ( lazy_and1 @ false @ A )
= false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lazy_and1_axiom2) ).
thf(135,plain,
! [A: $i] :
( ( lazy_and1 @ false @ A )
= false ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(44,axiom,
! [A: $i] :
( ~ ( bool @ A )
=> ( ( not1 @ A )
= ( phi @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not1_axiom1) ).
thf(241,plain,
! [A: $i] :
( ~ ( bool @ A )
=> ( ( not1 @ A )
= ( phi @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
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(32,axiom,
! [A: $i,B: $i] :
( ~ ( bool @ A )
=> ( ( impl @ A @ B )
= ( phi @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',impl_axiom1) ).
thf(199,plain,
! [A: $i,B: $i] :
( ~ ( bool @ A )
=> ( ( impl @ A @ B )
= ( phi @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(15,axiom,
( ( true != false )
& ( true != err )
& ( false != err ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distinct_false_true_err) ).
thf(99,plain,
( ( true != false )
& ( true != err )
& ( false != err ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(33,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(203,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)],[33]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( ( bool @ A )
& ~ ( bool @ B ) )
=> ( ( and1 @ A @ B )
= ( phi @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and1_axiom2) ).
thf(207,plain,
! [A: $i,B: $i] :
( ( ( bool @ A )
& ~ ( bool @ B ) )
=> ( ( and1 @ A @ B )
= ( phi @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(42,axiom,
! [A: $i] :
( ( bool @ A )
=> ( ( or1 @ true @ A )
= true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or1_axiom3) ).
thf(235,plain,
! [A: $i] :
( ( bool @ A )
=> ( ( or1 @ true @ A )
= true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(46,axiom,
( ( not1 @ true )
= false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not1_axiom3) ).
thf(246,plain,
( ( not1 @ true )
= false ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(35,axiom,
! [A: $i] :
( ( ( prop @ A )
= false )
<=> ~ ( bool @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop_false) ).
thf(210,plain,
! [A: $i] :
( ( ( ( prop @ A )
= false )
=> ~ ( bool @ A ) )
& ( ~ ( bool @ A )
=> ( ( prop @ A )
= false ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(11,axiom,
! [A: $i] :
( ( bool @ A )
<=> ( ( A = false )
| ( A = true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_bool) ).
thf(79,plain,
! [A: $i] :
( ( ( bool @ A )
=> ( ( A = false )
| ( A = true ) ) )
& ( ( ( A = false )
| ( A = true ) )
=> ( bool @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(7,axiom,
! [A: $i] :
( ( f7 @ A )
= ( lazy_impl @ ( prop @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_f7) ).
thf(62,plain,
! [A: $i] :
( ( f7 @ A )
= ( lazy_impl @ ( prop @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ~ ( bool @ A )
=> ( ( lazy_and1 @ A @ B )
= ( phi @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lazy_and1_axiom1) ).
thf(131,plain,
! [A: $i,B: $i] :
( ~ ( bool @ A )
=> ( ( lazy_and1 @ A @ B )
= ( phi @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(1,conjecture,
! [A: $i] :
( ( not1 @ A )
= ( not2 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not1_not2) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( not1 @ A )
= ( not2 @ A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(47,plain,
~ ! [A: $i] :
( ( not1 @ A )
= ( not2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(248,plain,
$false,
inference(cvc4,[status(thm)],[138,165,180,146,227,217,120,56,142,106,238,89,116,233,220,92,65,53,169,124,96,73,128,244,176,59,172,113,230,76,223,135,241,50,199,99,203,207,235,246,210,79,62,131,47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW102+1 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n007.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Thu May 18 22:14:54 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.86/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.19/0.98 % [INFO] Parsing done (138ms).
% 1.19/0.99 % [INFO] Running in sequential loop mode.
% 1.83/1.20 % [INFO] eprover registered as external prover.
% 1.83/1.20 % [INFO] cvc4 registered as external prover.
% 1.89/1.20 % [INFO] Scanning for conjecture ...
% 1.97/1.26 % [INFO] Found a conjecture and 44 axioms. Running axiom selection ...
% 1.97/1.31 % [INFO] Axiom selection finished. Selected 44 axioms (removed 0 axioms).
% 2.28/1.37 % [INFO] Problem is first-order (TPTP FOF).
% 2.28/1.38 % [INFO] Type checking passed.
% 2.28/1.38 % [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 ...
% 4.68/2.09 % External prover 'cvc4' found a proof!
% 4.68/2.09 % [INFO] Killing All external provers ...
% 4.68/2.09 % Time passed: 1565ms (effective reasoning time: 1092ms)
% 4.68/2.09 % 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)>
% 4.68/2.09 % 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
% 4.68/2.09 % No. of inferences in proof: 92
% 4.68/2.09 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1565 ms resp. 1092 ms w/o parsing
% 4.68/2.14 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.68/2.14 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------