%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW102+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:09:34 AM UTC 2026
% Result : Theorem 2.49s 11.76s
% Output : Refutation 2.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 45
% Syntax : Number of formulae : 92 ( 32 unt; 0 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 : 0 ( 0 >; 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_decl,type,
not1: $i > $i ).
thf(not2_decl,type,
not2: $i > $i ).
thf(f2_decl,type,
f2: $i > $i > $i > $i ).
thf(lazy_impl_decl,type,
lazy_impl: $i > $i > $i ).
thf(prop_decl,type,
prop: $i > $i ).
thf(impl_decl,type,
impl: $i > $i > $i ).
thf(f6_decl,type,
f6: $i > $i > $i ).
thf(f5_decl,type,
f5: $i > $i > $i ).
thf(f1_decl,type,
f1: $i > $i > $i > $i ).
thf(f3_decl,type,
f3: $i > $i > $i > $i ).
thf(f7_decl,type,
f7: $i > $i ).
thf(d_decl,type,
d: $i > $o ).
thf(phi_decl,type,
phi: $i > $i ).
thf(err_decl,type,
err: $i ).
thf(false_decl,type,
false: $i ).
thf(true_decl,type,
true: $i ).
thf(bool_decl,type,
bool: $i > $o ).
thf(or1_decl,type,
or1: $i > $i > $i ).
thf(f4_decl,type,
f4: $i > $i > $i > $i ).
thf(apply_decl,type,
apply: $i > $i > $i ).
thf(lazy_and2_decl,type,
lazy_and2: $i > $i > $i ).
thf(forallprefers_decl,type,
forallprefers: $i > $i > $o ).
thf(and1_decl,type,
and1: $i > $i > $i ).
thf(lazy_and1_decl,type,
lazy_and1: $i > $i > $i ).
thf(exists1_decl,type,
exists1: $i > $i ).
thf(existsprefers_decl,type,
existsprefers: $i > $i > $o ).
thf(exists2_decl,type,
exists2: $i > $i ).
thf(or2_decl,type,
or2: $i > $i > $i ).
thf(and2_decl,type,
and2: $i > $i > $i ).
thf(false2_decl,type,
false2: $i ).
thf(false1_decl,type,
false1: $i ).
thf(18,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ~ ? [D: $i] : ( C @ ( B @ ( A @ f2 ) ) @ ( D @ ( B @ ( A @ f2 ) ) @ forallprefers ) )
& ( ( B @ ( A @ lazy_and2 ) )
= ( C @ ( B @ ( A @ f2 ) ) @ phi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_lazy_and2) ).
thf(120,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ~ ? [D: $i] : ( C @ ( B @ ( A @ f2 ) ) @ ( D @ ( B @ ( A @ f2 ) ) @ forallprefers ) )
& ( ( B @ ( A @ lazy_and2 ) )
= ( C @ ( B @ ( A @ f2 ) ) @ phi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ f1 ) ) )
= ( C @ ( C @ ( B @ impl ) @ ( A @ impl ) @ impl ) @ ( C @ prop @ lazy_impl ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_f1) ).
thf(56,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ f1 ) ) )
= ( C @ ( C @ ( B @ impl ) @ ( A @ impl ) @ impl ) @ ( C @ prop @ lazy_impl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ~ ( A @ bool )
=> ( ( B @ ( A @ lazy_impl ) )
= ( A @ phi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lazy_impl_axiom1) ).
thf(174,plain,
! [A: $i,B: $i] :
( ~ ( A @ bool )
=> ( ( B @ ( A @ lazy_impl ) )
= ( A @ phi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(19,axiom,
( ( err @ d )
& ( false @ d )
& ( true @ d ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',false_true_err_in_d) ).
thf(125,plain,
( ( err @ d )
& ( false @ d )
& ( true @ d ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(46,axiom,
( ( true @ not1 )
= false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not1_axiom3) ).
thf(261,plain,
( ( true @ not1 )
= false ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ ( false @ lazy_impl ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lazy_impl_axiom2) ).
thf(74,plain,
! [A: $i] :
( ( A @ ( false @ lazy_impl ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ~ ( A @ bool )
=> ( ( B @ ( A @ lazy_and1 ) )
= ( A @ phi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lazy_and1_axiom1) ).
thf(137,plain,
! [A: $i,B: $i] :
( ~ ( A @ bool )
=> ( ( B @ ( A @ lazy_and1 ) )
= ( A @ phi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(8,axiom,
! [A: $i] :
( ( ( ( A @ phi )
= err )
& ~ ( A @ d ) )
| ( ( ( A @ phi )
= A )
& ( A @ d ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_phi) ).
thf(65,plain,
! [A: $i] :
( ( ( ( A @ phi )
= err )
& ~ ( A @ d ) )
| ( ( ( A @ phi )
= A )
& ( A @ d ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(25,axiom,
! [A: $i] :
? [B: $i] :
( ~ ? [C: $i] : ( B @ ( A @ apply ) @ ( C @ ( A @ apply ) @ existsprefers ) )
& ( ( A @ exists1 )
= ( B @ ( A @ apply ) @ phi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exists1_axiom1) ).
thf(149,plain,
! [A: $i] :
? [B: $i] :
( ~ ? [C: $i] : ( B @ ( A @ apply ) @ ( C @ ( A @ apply ) @ existsprefers ) )
& ( ( A @ exists1 )
= ( B @ ( A @ apply ) @ phi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ bool )
=> ( ( A @ ( true @ impl ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',impl_axiom4) ).
thf(91,plain,
! [A: $i] :
( ( A @ bool )
=> ( ( A @ ( true @ impl ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ f2 ) ) )
= ( C @ ( C @ ( B @ impl ) @ ( A @ lazy_impl ) @ impl ) @ ( C @ prop @ lazy_impl ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_f2) ).
thf(50,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ f2 ) ) )
= ( C @ ( C @ ( B @ impl ) @ ( A @ lazy_impl ) @ impl ) @ ( C @ prop @ lazy_impl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ existsprefers ) )
<=> ( ( ( B = false )
& ( A = true ) )
| ( ( B @ bool )
& ~ ( A @ bool )
& ( B @ d )
& ( A @ d ) )
| ( ( B @ d )
& ~ ( A @ d ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_existsprefers) ).
thf(154,plain,
! [A: $i,B: $i] :
( ( ( ( ( B = false )
& ( A = true ) )
| ( ( B @ bool )
& ~ ( A @ bool )
& ( B @ d )
& ( A @ d ) )
| ( ( B @ d )
& ~ ( A @ d ) ) )
=> ( B @ ( A @ existsprefers ) ) )
& ( ( B @ ( A @ existsprefers ) )
=> ( ( ( B = false )
& ( A = true ) )
| ( ( B @ bool )
& ~ ( A @ bool )
& ( B @ d )
& ( A @ d ) )
| ( ( B @ d )
& ~ ( A @ d ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(30,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ~ ? [D: $i] : ( C @ ( B @ ( A @ f3 ) ) @ ( D @ ( B @ ( A @ f3 ) ) @ forallprefers ) )
& ( ( B @ ( A @ or2 ) )
= ( C @ ( B @ ( A @ f3 ) ) @ phi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_or2) ).
thf(186,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ~ ? [D: $i] : ( C @ ( B @ ( A @ f3 ) ) @ ( D @ ( B @ ( A @ f3 ) ) @ forallprefers ) )
& ( ( B @ ( A @ or2 ) )
= ( C @ ( B @ ( A @ f3 ) ) @ phi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(33,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ~ ? [D: $i] : ( C @ ( B @ ( A @ f1 ) ) @ ( D @ ( B @ ( A @ f1 ) ) @ forallprefers ) )
& ( ( B @ ( A @ and2 ) )
= ( C @ ( B @ ( A @ f1 ) ) @ phi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_and2) ).
thf(215,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ~ ? [D: $i] : ( C @ ( B @ ( A @ f1 ) ) @ ( D @ ( B @ ( A @ f1 ) ) @ forallprefers ) )
& ( ( B @ ( A @ and2 ) )
= ( C @ ( B @ ( A @ f1 ) ) @ phi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(15,axiom,
( ( false != err )
& ( true != err )
& ( true != false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distinct_false_true_err) ).
thf(101,plain,
( ( false != err )
& ( true != err )
& ( true != false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(37,axiom,
! [A: $i] :
( ( A @ bool )
=> ( ( A @ ( false @ impl ) )
= true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',impl_axiom3) ).
thf(234,plain,
! [A: $i] :
( ( A @ bool )
=> ( ( A @ ( false @ impl ) )
= true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ~ ( A @ bool )
=> ( ( B @ ( A @ impl ) )
= ( A @ phi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',impl_axiom1) ).
thf(211,plain,
! [A: $i,B: $i] :
( ~ ( A @ bool )
=> ( ( B @ ( A @ impl ) )
= ( A @ phi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(43,axiom,
! [A: $i] :
( ( A @ not2 )
= ( false2 @ ( A @ impl ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_not2) ).
thf(253,plain,
! [A: $i] :
( ( A @ not2 )
= ( false2 @ ( A @ impl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(41,axiom,
false1 = false,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_false1) ).
thf(248,plain,
false1 = false,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ f4 ) ) )
= ( C @ ( B @ ( A @ apply ) @ impl ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_f4) ).
thf(117,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ f4 ) ) )
= ( C @ ( B @ ( A @ apply ) @ impl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ bool )
& ( A @ bool ) )
=> ( ( B @ ( A @ and1 ) )
= ( B @ phi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and1_axiom2) ).
thf(220,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ bool )
& ( A @ bool ) )
=> ( ( B @ ( A @ and1 ) )
= ( B @ phi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ f6 ) )
= ( B @ ( B @ ( A @ f5 ) @ impl ) @ ( B @ prop @ lazy_impl ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_f6) ).
thf(53,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ f6 ) )
= ( B @ ( B @ ( A @ f5 ) @ impl ) @ ( B @ prop @ lazy_impl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(23,axiom,
! [A: $i] :
( ( A @ ( false @ lazy_and1 ) )
= false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lazy_and1_axiom2) ).
thf(141,plain,
! [A: $i] :
( ( A @ ( false @ lazy_and1 ) )
= false ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ bool )
=> ( ( A @ ( false @ or1 ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or1_axiom4) ).
thf(77,plain,
! [A: $i] :
( ( A @ bool )
=> ( ( A @ ( false @ or1 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(16,axiom,
! [A: $i] :
( ( ( A @ prop )
= true )
<=> ( A @ bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop_true) ).
thf(109,plain,
! [A: $i] :
( ( ( A @ bool )
=> ( ( A @ prop )
= true ) )
& ( ( ( A @ prop )
= true )
=> ( A @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(44,axiom,
! [A: $i] :
( ~ ( A @ bool )
=> ( ( A @ not1 )
= ( A @ phi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not1_axiom1) ).
thf(256,plain,
! [A: $i] :
( ~ ( A @ bool )
=> ( ( A @ not1 )
= ( A @ phi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ bool )
& ( A @ bool ) )
=> ( ( B @ ( A @ or1 ) )
= ( B @ phi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or1_axiom2) ).
thf(134,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ bool )
& ( A @ bool ) )
=> ( ( B @ ( A @ or1 ) )
= ( B @ phi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(38,axiom,
? [A: $i] :
( ~ ? [B: $i] : ( A @ f7 @ ( B @ f7 @ forallprefers ) )
& ( false2
= ( A @ f7 @ phi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_false2) ).
thf(237,plain,
? [A: $i] :
( ~ ? [B: $i] : ( A @ f7 @ ( B @ f7 @ forallprefers ) )
& ( false2
= ( A @ f7 @ phi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ forallprefers ) )
<=> ( ( ( B = true )
& ( A = false ) )
| ( ( B @ bool )
& ~ ( A @ bool )
& ( B @ d )
& ( A @ d ) )
| ( ( B @ d )
& ~ ( A @ d ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_forallprefers) ).
thf(191,plain,
! [A: $i,B: $i] :
( ( ( ( ( B = true )
& ( A = false ) )
| ( ( B @ bool )
& ~ ( A @ bool )
& ( B @ d )
& ( A @ d ) )
| ( ( B @ d )
& ~ ( A @ d ) ) )
=> ( B @ ( A @ forallprefers ) ) )
& ( ( B @ ( A @ forallprefers ) )
=> ( ( ( B = true )
& ( A = false ) )
| ( ( B @ bool )
& ~ ( A @ bool )
& ( B @ d )
& ( A @ d ) )
| ( ( B @ d )
& ~ ( A @ d ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ f3 ) ) )
= ( C @ ( C @ ( B @ impl ) @ impl ) @ ( C @ ( A @ impl ) @ impl ) @ ( C @ prop @ lazy_impl ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_f3) ).
thf(59,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ f3 ) ) )
= ( C @ ( C @ ( B @ impl ) @ impl ) @ ( C @ ( A @ impl ) @ impl ) @ ( C @ prop @ lazy_impl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(45,axiom,
( ( false @ not1 )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not1_axiom2) ).
thf(259,plain,
( ( false @ not1 )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(24,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ~ ? [D: $i] : ( B @ ( C @ ( A @ f4 ) ) @ ( B @ ( D @ ( A @ f4 ) ) @ forallprefers ) )
& ( ( B @ ( A @ f5 ) )
= ( B @ ( C @ ( A @ f4 ) ) @ phi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_f5) ).
thf(144,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ~ ? [D: $i] : ( B @ ( C @ ( A @ f4 ) ) @ ( B @ ( D @ ( A @ f4 ) ) @ forallprefers ) )
& ( ( B @ ( A @ f5 ) )
= ( B @ ( C @ ( A @ f4 ) ) @ phi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(29,axiom,
! [A: $i] :
? [B: $i] :
( ~ ? [C: $i] : ( B @ ( A @ f6 ) @ ( C @ ( A @ f6 ) @ forallprefers ) )
& ( ( A @ exists2 )
= ( B @ ( A @ f6 ) @ phi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_exists2) ).
thf(181,plain,
! [A: $i] :
? [B: $i] :
( ~ ? [C: $i] : ( B @ ( A @ f6 ) @ ( C @ ( A @ f6 ) @ forallprefers ) )
& ( ( A @ exists2 )
= ( B @ ( A @ f6 ) @ phi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(40,axiom,
! [A: $i] :
( ( A @ bool )
=> ( ( A @ ( true @ and1 ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and1_axiom4) ).
thf(245,plain,
! [A: $i] :
( ( A @ bool )
=> ( ( A @ ( true @ and1 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ ( true @ lazy_impl ) )
= ( A @ phi ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lazy_impl_axiom3) ).
thf(98,plain,
! [A: $i] :
( ( A @ ( true @ lazy_impl ) )
= ( A @ phi ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ~ ( A @ bool )
=> ( ( B @ ( A @ and1 ) )
= ( A @ phi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and1_axiom1) ).
thf(130,plain,
! [A: $i,B: $i] :
( ~ ( A @ bool )
=> ( ( B @ ( A @ and1 ) )
= ( A @ phi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(35,axiom,
! [A: $i] :
( ( ( A @ prop )
= false )
<=> ~ ( A @ bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop_false) ).
thf(223,plain,
! [A: $i] :
( ( ~ ( A @ bool )
=> ( ( A @ prop )
= false ) )
& ( ( ( A @ prop )
= false )
=> ~ ( A @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ bool )
<=> ( ( A = true )
| ( A = false ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_bool) ).
thf(80,plain,
! [A: $i] :
( ( ( ( A = true )
| ( A = false ) )
=> ( A @ bool ) )
& ( ( A @ bool )
=> ( ( A = true )
| ( A = false ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(42,axiom,
! [A: $i] :
( ( A @ bool )
=> ( ( A @ ( true @ or1 ) )
= true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or1_axiom3) ).
thf(250,plain,
! [A: $i] :
( ( A @ bool )
=> ( ( A @ ( true @ or1 ) )
= true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(36,axiom,
! [A: $i] :
( ( A @ ( true @ lazy_and1 ) )
= ( A @ phi ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lazy_and1_axiom3) ).
thf(231,plain,
! [A: $i] :
( ( A @ ( true @ lazy_and1 ) )
= ( A @ phi ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ bool )
& ( A @ bool ) )
=> ( ( B @ ( A @ impl ) )
= ( B @ phi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',impl_axiom2) ).
thf(242,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ bool )
& ( A @ bool ) )
=> ( ( B @ ( A @ impl ) )
= ( B @ phi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ~ ( A @ bool )
=> ( ( B @ ( A @ or1 ) )
= ( A @ phi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or1_axiom1) ).
thf(94,plain,
! [A: $i,B: $i] :
( ~ ( A @ bool )
=> ( ( B @ ( A @ or1 ) )
= ( A @ phi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(1,conjecture,
! [A: $i] :
( ( A @ not1 )
= ( A @ not2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not1_not2) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( A @ not1 )
= ( A @ not2 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(47,plain,
~ ! [A: $i] :
( ( A @ not1 )
= ( A @ not2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ f7 )
= ( A @ ( A @ prop @ lazy_impl ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_f7) ).
thf(62,plain,
! [A: $i] :
( ( A @ f7 )
= ( A @ ( A @ prop @ lazy_impl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(28,axiom,
! [A: $i] :
( ( A @ bool )
=> ( ( A @ ( false @ and1 ) )
= false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and1_axiom3) ).
thf(178,plain,
! [A: $i] :
( ( A @ bool )
=> ( ( A @ ( false @ and1 ) )
= false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(263,plain,
$false,
inference(e,[status(thm)],[120,56,174,125,261,74,137,65,149,91,50,154,186,215,101,234,211,253,248,117,220,53,141,77,109,256,134,237,191,59,259,144,181,245,98,130,223,80,250,231,242,94,47,62,178]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWW102+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.07/10.55 % Computer : n012.cluster.edu
% 0.07/10.55 % Model : x86_64 x86_64
% 0.07/10.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/10.55 % Memory : 8046.5625MB
% 0.07/10.55 % OS : Linux 6.8.0-71-generic
% 0.07/10.55 % CPULimit : 300
% 0.07/10.55 % WCLimit : 300
% 0.07/10.55 % DateTime : Sat Sep 26 15:24:02 UTC 2026
% 0.07/10.55 % CPUTime :
% 0.07/10.55 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.09/10.83 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.09/10.94 % [INFO] Parsing done (108ms).
% 0.09/10.94 % [INFO] Running in sequential loop mode.
% 1.04/11.13 % [INFO] eprover registered as external prover.
% 1.04/11.13 % [INFO] Scanning for conjecture ...
% 1.04/11.18 % [INFO] Found a conjecture (or negated_conjecture) and 44 axioms. Running axiom selection ...
% 1.20/11.22 % [INFO] Axiom selection finished. Selected 44 axioms (removed 0 axioms).
% 1.20/11.26 % [INFO] Problem is first-order (TPTP FOF).
% 1.20/11.27 % [INFO] Type checking passed.
% 1.20/11.27 % [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 ...
% 2.49/11.75 % External prover 'e' found a proof!
% 2.49/11.75 % [INFO] Killing All external provers ...
% 2.49/11.76 % Time passed: 1126ms (effective reasoning time: 808ms)
% 2.49/11.76 % 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)>
% 2.49/11.76 % 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
% 2.49/11.76 % No. of inferences in proof: 92
% 2.49/11.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1126 ms resp. 808 ms w/o parsing
% 2.81/11.80 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.81/11.80 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------