%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO667-1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/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 09:45:08 AM UTC 2026
% Result : Unsatisfiable 6.13s 3.27s
% Output : Refutation 6.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 29
% Syntax : Number of formulae : 59 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 233 ( 0 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 1622 ( 152 ~; 174 |; 0 &;1296 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 10 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 : 56 ( 0 ^; 56 !; 0 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
thf('E_decl',type,
'E': $i > $i > $o ).
thf(s_decl,type,
s: $i > $i ).
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(z_decl,type,
z: $i ).
thf(14,axiom,
! [A: $i] :
( ~ ( 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/sandbox2/benchmark/theBenchmark.p',clause_4) ).
thf(56,plain,
! [A: $i] :
( ~ ( 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)],[14]) ).
thf(7,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/sandbox2/benchmark/theBenchmark.p',clause_27) ).
thf(42,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)],[7]) ).
thf(12,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/sandbox2/benchmark/theBenchmark.p',clause_21) ).
thf(52,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)],[12]) ).
thf(9,axiom,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ suc @ suc @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_19) ).
thf(46,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)],[9]) ).
thf(25,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/sandbox2/benchmark/theBenchmark.p',clause_32) ).
thf(77,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)],[25]) ).
thf(23,axiom,
~ ( '0' @ ( z @ f @ 'LE' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_25) ).
thf(73,plain,
~ ( '0' @ ( z @ f @ 'LE' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(8,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/sandbox2/benchmark/theBenchmark.p',clause_41) ).
thf(44,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)],[8]) ).
thf(27,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/sandbox2/benchmark/theBenchmark.p',clause_38) ).
thf(81,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)],[27]) ).
thf(19,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/sandbox2/benchmark/theBenchmark.p',clause_40) ).
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)],[19]) ).
thf(10,axiom,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_13) ).
thf(48,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(11,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/sandbox2/benchmark/theBenchmark.p',clause_30) ).
thf(50,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)],[11]) ).
thf(6,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/sandbox2/benchmark/theBenchmark.p',clause_24) ).
thf(40,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)],[6]) ).
thf(26,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/sandbox2/benchmark/theBenchmark.p',clause_43) ).
thf(79,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)],[26]) ).
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/sandbox2/benchmark/theBenchmark.p',clause_6) ).
thf(83,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(16,axiom,
! [A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_23) ).
thf(60,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)],[16]) ).
thf(29,axiom,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_20) ).
thf(85,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)],[29]) ).
thf(5,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 @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_49) ).
thf(38,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 @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(21,axiom,
! [A: $i] : ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_51) ).
thf(70,plain,
! [A: $i] : ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(18,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/sandbox2/benchmark/theBenchmark.p',clause_42) ).
thf(64,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)],[18]) ).
thf(2,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/sandbox2/benchmark/theBenchmark.p',clause_33) ).
thf(32,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)],[2]) ).
thf(3,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/sandbox2/benchmark/theBenchmark.p',clause_37) ).
thf(34,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)],[3]) ).
thf(22,axiom,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ suc @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
thf(71,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)],[22]) ).
thf(13,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/sandbox2/benchmark/theBenchmark.p',clause_2) ).
thf(54,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)],[13]) ).
thf(24,axiom,
! [A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_22) ).
thf(75,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)],[24]) ).
thf(15,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' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_14) ).
thf(58,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' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(4,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/sandbox2/benchmark/theBenchmark.p',clause_8) ).
thf(36,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)],[4]) ).
thf(1,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/sandbox2/benchmark/theBenchmark.p',clause_44) ).
thf(30,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)],[1]) ).
thf(20,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/sandbox2/benchmark/theBenchmark.p',clause_29) ).
thf(68,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)],[20]) ).
thf(17,axiom,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ suc @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_50) ).
thf(62,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)],[17]) ).
thf(90,plain,
$false,
inference(e,[status(thm)],[56,42,52,46,77,73,44,81,66,48,50,40,79,83,60,85,38,70,64,32,34,71,54,75,58,36,30,68,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO667-1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.13/0.41 % Computer : n017.cluster.edu
% 0.13/0.41 % Model : x86_64 x86_64
% 0.13/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.41 % Memory : 8046.5625MB
% 0.13/0.41 % OS : Linux 6.8.0-71-generic
% 0.13/0.41 % CPULimit : 300
% 0.13/0.41 % WCLimit : 300
% 0.13/0.41 % DateTime : Sat Sep 26 19:39:35 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.31/1.16 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.06/1.52 % [INFO] Parsing done (348ms).
% 2.06/1.54 % [INFO] Running in sequential loop mode.
% 3.30/2.14 % [INFO] eprover registered as external prover.
% 3.30/2.15 % [INFO] Scanning for conjecture ...
% 3.59/2.23 % [INFO] 29 axioms and no conjecture found.
% 3.79/2.35 % [INFO] Problem is propositional (TPTP CNF).
% 3.79/2.36 % [INFO] Type checking passed.
% 3.79/2.36 % [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 ...
% 6.13/3.27 % External prover 'e' found a proof!
% 6.13/3.27 % [INFO] Killing All external provers ...
% 6.13/3.27 % Time passed: 2674ms (effective reasoning time: 1720ms)
% 6.13/3.27 % Axioms used in derivation (29): clause_23, clause_43, clause_37, clause_25, clause_29, clause_6, clause_40, clause_33, clause_49, clause_38, clause_30, clause_27, clause_2, clause_41, clause_8, clause_20, clause_42, clause_19, clause_14, clause_50, clause_21, clause_4, clause_44, clause_32, clause_13, clause_24, clause_51, clause_22, clause_3
% 6.13/3.27 % No. of inferences in proof: 59
% 6.13/3.27 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2674 ms resp. 1720 ms w/o parsing
% 6.37/3.36 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.37/3.36 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------