%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO658-1 : 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 : n014.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 09:45:07 AM UTC 2026
% Result : Unsatisfiable 6.86s 3.17s
% Output : Refutation 7.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 34
% Syntax : Number of formulae : 69 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 493 ( 0 equ; 0 cnn)
% Maximal formula atoms : 13 ( 7 avg)
% Number of connectives : 3172 ( 390 ~; 424 |; 0 &;2358 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 13 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 102 ( 0 ^; 102 !; 0 ?; 102 :)
% 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(iLEQ_decl,type,
iLEQ: $i > $i > $o ).
thf('LE_decl',type,
'LE': $i > $i > $o ).
thf(s_decl,type,
s: $i > $i ).
thf(z_decl,type,
z: $i ).
thf(28,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_129) ).
thf(88,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)],[28]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_142) ).
thf(56,plain,
! [B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(2,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_75) ).
thf(37,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)],[2]) ).
thf(23,axiom,
! [B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_29) ).
thf(78,plain,
! [B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(26,axiom,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( 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_16) ).
thf(84,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( 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)],[26]) ).
thf(21,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_151) ).
thf(74,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)],[21]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_140) ).
thf(60,plain,
! [B: $i,A: $i] :
( ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_71) ).
thf(70,plain,
! [B: $i,A: $i] :
( ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(30,axiom,
! [B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_65) ).
thf(92,plain,
! [B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( 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_4) ).
thf(53,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( 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)],[10]) ).
thf(32,axiom,
! [B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_162) ).
thf(96,plain,
! [B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( 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_81) ).
thf(41,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( 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)],[4]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_139) ).
thf(66,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(11,axiom,
! [A: $i] : ( '0' @ s @ s @ ( A @ f @ 'LE' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_72) ).
thf(55,plain,
! [A: $i] : ( '0' @ s @ s @ ( A @ f @ 'LE' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_78) ).
thf(51,plain,
! [B: $i,A: $i] :
( ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(31,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_122) ).
thf(94,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)],[31]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_150) ).
thf(45,plain,
! [B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_41) ).
thf(64,plain,
! [B: $i,A: $i] :
( ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(8,axiom,
~ ( '0' @ ( z @ f @ 'LE' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_87) ).
thf(49,plain,
~ ( '0' @ ( z @ f @ 'LE' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(27,axiom,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_109) ).
thf(86,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(22,axiom,
! [B: $i,A: $i] :
( ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_174) ).
thf(76,plain,
! [B: $i,A: $i] :
( ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(3,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_104) ).
thf(39,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)],[3]) ).
thf(33,axiom,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_93) ).
thf(98,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(24,axiom,
! [B: $i,A: $i] :
( ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_40) ).
thf(80,plain,
! [B: $i,A: $i] :
( ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(1,axiom,
! [B: $i,A: $i] :
( ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_167) ).
thf(35,plain,
! [B: $i,A: $i] :
( ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_30) ).
thf(72,plain,
! [B: $i,A: $i] :
( ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_36) ).
thf(43,plain,
! [B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_108) ).
thf(58,plain,
! [B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_130) ).
thf(82,plain,
! [B: $i,A: $i] :
( ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(7,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_141) ).
thf(47,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)],[7]) ).
thf(18,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_51) ).
thf(68,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)],[18]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_80) ).
thf(62,plain,
! [B: $i,A: $i] :
( ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(29,axiom,
! [B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_55) ).
thf(90,plain,
! [B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(34,axiom,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_134) ).
thf(100,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(125,plain,
$false,
inference(e,[status(thm)],[88,56,37,78,84,74,60,70,92,53,96,41,66,55,51,94,45,64,49,86,76,39,98,80,35,72,43,58,82,47,68,62,90,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO658-1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.07 % 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
% 0.13/0.39 % Computer : n014.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sat Sep 26 19:43:31 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 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
% 0.88/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.45/1.27 % [INFO] Parsing done (285ms).
% 1.45/1.29 % [INFO] Running in sequential loop mode.
% 2.37/1.69 % [INFO] eprover registered as external prover.
% 2.55/1.70 % [INFO] Scanning for conjecture ...
% 2.55/1.79 % [INFO] 34 axioms and no conjecture found.
% 2.96/1.93 % [INFO] Problem is propositional (TPTP CNF).
% 2.96/1.94 % [INFO] Type checking passed.
% 2.96/1.95 % [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 ...
% 6.86/3.17 % External prover 'e' found a proof!
% 6.86/3.17 % [INFO] Killing All external provers ...
% 6.86/3.17 % Time passed: 2623ms (effective reasoning time: 1870ms)
% 6.86/3.17 % Axioms used in derivation (34): clause_108, clause_93, clause_41, clause_65, clause_80, clause_78, clause_141, clause_174, clause_140, clause_129, clause_36, clause_51, clause_30, clause_87, clause_16, clause_122, clause_142, clause_71, clause_109, clause_75, clause_130, clause_55, clause_134, clause_4, clause_162, clause_151, clause_29, clause_150, clause_40, clause_167, clause_139, clause_72, clause_81, clause_104
% 6.86/3.17 % No. of inferences in proof: 69
% 6.86/3.17 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2623 ms resp. 1870 ms w/o parsing
% 7.11/3.27 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.11/3.27 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------