%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO668-1 : TPTP v9.3.1. Released v7.3.0.
% 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 : n017.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 09:45:09 AM UTC 2026
% Result : Unsatisfiable 8.39s 3.87s
% Output : Refutation 8.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 35
% Syntax : Number of formulae : 71 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 317 ( 0 equ; 0 cnn)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 2336 ( 218 ~; 246 |; 0 &;1872 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 68 ( 0 ^; 68 !; 0 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
thf('E_decl',type,
'E': $i > $i > $o ).
thf('0_decl',type,
'0': $i ).
thf(f_decl,type,
f: $i > $i ).
thf(suc_decl,type,
suc: $i > $i ).
thf('LE_decl',type,
'LE': $i > $i > $o ).
thf(s_decl,type,
s: $i > $i ).
thf(z_decl,type,
z: $i ).
thf(34,axiom,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ suc @ suc @ suc @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_82) ).
thf(101,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ suc @ suc @ suc @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(11,axiom,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_39) ).
thf(56,plain,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(4,axiom,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ suc @ suc @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_37) ).
thf(42,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ suc @ suc @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
! [A: $i] :
( ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_35) ).
thf(52,plain,
! [A: $i] :
( ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(25,axiom,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ suc @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3) ).
thf(84,plain,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ suc @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(13,axiom,
! [A: $i] :
( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ suc @ suc @ suc @ suc @ suc @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_21) ).
thf(60,plain,
! [A: $i] :
( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ suc @ suc @ suc @ suc @ suc @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(32,axiom,
! [A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_43) ).
thf(97,plain,
! [A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(15,axiom,
! [A: $i] :
( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2) ).
thf(64,plain,
! [A: $i] :
( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_88) ).
thf(44,plain,
! [A: $i] :
( ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(21,axiom,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ suc @ suc @ suc @ suc @ suc @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5) ).
thf(76,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ suc @ suc @ suc @ suc @ suc @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(23,axiom,
! [A: $i] :
( ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_60) ).
thf(80,plain,
! [A: $i] :
( ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(8,axiom,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ suc @ suc @ suc @ suc @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_17) ).
thf(50,plain,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ suc @ suc @ suc @ suc @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_41) ).
thf(72,plain,
! [A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(3,axiom,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_27) ).
thf(40,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,axiom,
! [A: $i] :
( ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_31) ).
thf(36,plain,
! [A: $i] :
( ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(6,axiom,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ suc @ suc @ suc @ suc @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_74) ).
thf(46,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ suc @ suc @ suc @ suc @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(30,axiom,
! [A: $i] :
( ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_50) ).
thf(93,plain,
! [A: $i] :
( ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(22,axiom,
! [A: $i] :
( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ suc @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_83) ).
thf(78,plain,
! [A: $i] :
( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ suc @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(28,axiom,
! [A: $i] :
( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ suc @ suc @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_10) ).
thf(89,plain,
! [A: $i] :
( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ suc @ suc @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(20,axiom,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ suc @ suc @ suc @ suc @ suc @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_20) ).
thf(74,plain,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ suc @ suc @ suc @ suc @ suc @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(2,axiom,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ suc @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_101) ).
thf(38,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ suc @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(18,axiom,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ suc @ suc @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_87) ).
thf(70,plain,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ suc @ suc @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_40) ).
thf(54,plain,
! [A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(26,axiom,
! [A: $i] : ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_102) ).
thf(86,plain,
! [A: $i] : ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(35,axiom,
~ ( '0' @ ( z @ f @ 'LE' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_48) ).
thf(103,plain,
~ ( '0' @ ( z @ f @ 'LE' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(29,axiom,
! [A: $i] :
( ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_19) ).
thf(91,plain,
! [A: $i] :
( ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(16,axiom,
! [A: $i] :
( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ suc @ suc @ suc @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_76) ).
thf(66,plain,
! [A: $i] :
( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ suc @ suc @ suc @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_18) ).
thf(48,plain,
! [A: $i] :
( ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(31,axiom,
! [A: $i] :
( ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_59) ).
thf(95,plain,
! [A: $i] :
( ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(33,axiom,
! [A: $i] :
( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ suc @ suc @ suc @ suc @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_73) ).
thf(99,plain,
! [A: $i] :
( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ suc @ suc @ suc @ suc @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(27,axiom,
! [A: $i] :
( ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_32) ).
thf(87,plain,
! [A: $i] :
( ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_45) ).
thf(58,plain,
! [A: $i] :
( ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(24,axiom,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ suc @ suc @ suc @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_56) ).
thf(82,plain,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ suc @ suc @ suc @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_25) ).
thf(68,plain,
! [A: $i] :
( ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_53) ).
thf(62,plain,
! [A: $i] :
( ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(108,plain,
$false,
inference(e,[status(thm)],[101,56,42,52,84,60,97,64,44,76,80,50,72,40,36,46,93,78,89,74,38,70,54,86,103,91,66,48,95,99,87,58,82,68,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO668-1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.08 % 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
% 0.14/0.41 % Computer : n017.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sat Sep 26 19:39:49 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 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
% 1.21/1.20 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.06/1.53 % [INFO] Parsing done (329ms).
% 2.06/1.55 % [INFO] Running in sequential loop mode.
% 3.27/2.15 % [INFO] eprover registered as external prover.
% 3.52/2.16 % [INFO] Scanning for conjecture ...
% 3.60/2.28 % [INFO] 35 axioms and no conjecture found.
% 4.02/2.49 % [INFO] Problem is propositional (TPTP CNF).
% 4.31/2.50 % [INFO] Type checking passed.
% 4.31/2.51 % [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 ...
% 8.39/3.87 % External prover 'e' found a proof!
% 8.39/3.87 % [INFO] Killing All external provers ...
% 8.39/3.87 % Time passed: 3310ms (effective reasoning time: 2306ms)
% 8.39/3.87 % Axioms used in derivation (35): clause_5, clause_83, clause_45, clause_53, clause_48, clause_37, clause_25, clause_18, clause_40, clause_17, clause_87, clause_27, clause_2, clause_76, clause_41, clause_82, clause_56, clause_20, clause_60, clause_74, clause_43, clause_102, clause_59, clause_19, clause_31, clause_101, clause_10, clause_50, clause_21, clause_32, clause_73, clause_39, clause_3, clause_35, clause_88
% 8.39/3.87 % No. of inferences in proof: 71
% 8.39/3.87 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 3310 ms resp. 2306 ms w/o parsing
% 8.70/4.00 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.70/4.00 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------