%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO685-1 : 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 : n015.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 09:45:11 AM UTC 2026
% Result : Unsatisfiable 6.35s 3.07s
% Output : Refutation 6.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 47
% Syntax : Number of formulae : 95 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 505 ( 0 equ; 0 cnn)
% Maximal formula atoms : 9 ( 5 avg)
% Number of connectives : 3534 ( 372 ~; 410 |; 0 &;2752 @)
% ( 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 : 9 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 132 ( 0 ^; 132 !; 0 ?; 132 :)
% 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(iLEQ_decl,type,
iLEQ: $i > $i > $o ).
thf('LE_decl',type,
'LE': $i > $i > $o ).
thf(z_decl,type,
z: $i ).
thf(21,axiom,
! [B: $i,A: $i] :
( ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_175) ).
thf(88,plain,
! [B: $i,A: $i] :
( ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(37,axiom,
! [B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_34) ).
thf(120,plain,
! [B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_169) ).
thf(56,plain,
! [B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(16,axiom,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( A @ suc @ suc @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_93) ).
thf(78,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( A @ suc @ suc @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(23,axiom,
! [A: $i] :
( ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ suc @ suc @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_52) ).
thf(92,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ suc @ suc @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_74) ).
thf(64,plain,
! [B: $i,A: $i] :
( ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(36,axiom,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( 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_44) ).
thf(118,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( 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)],[36]) ).
thf(33,axiom,
! [B: $i,A: $i] :
( ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_105) ).
thf(112,plain,
! [B: $i,A: $i] :
( ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(1,axiom,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( 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_143) ).
thf(48,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( 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)],[1]) ).
thf(2,axiom,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_130) ).
thf(50,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,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_184) ).
thf(72,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)],[13]) ).
thf(29,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_168) ).
thf(104,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)],[29]) ).
thf(3,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_125) ).
thf(52,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)],[3]) ).
thf(32,axiom,
! [B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_87) ).
thf(110,plain,
! [B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(30,axiom,
! [B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_192) ).
thf(106,plain,
! [B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(19,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_86) ).
thf(84,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)],[19]) ).
thf(43,axiom,
! [B: $i,A: $i] :
( ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_73) ).
thf(132,plain,
! [B: $i,A: $i] :
( ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(35,axiom,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_113) ).
thf(116,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_94) ).
thf(74,plain,
! [B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_28) ).
thf(60,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(28,axiom,
! [B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_31) ).
thf(102,plain,
! [B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_55) ).
thf(70,plain,
! [B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(46,axiom,
! [B: $i,A: $i] :
( ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_183) ).
thf(137,plain,
! [B: $i,A: $i] :
( ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(39,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/sandbox2/benchmark/theBenchmark.p',clause_19) ).
thf(124,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)],[39]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_36) ).
thf(96,plain,
! [B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(44,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/sandbox2/benchmark/theBenchmark.p',clause_204) ).
thf(134,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)],[44]) ).
thf(41,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_11) ).
thf(128,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)],[41]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( 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_61) ).
thf(54,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( 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)],[4]) ).
thf(20,axiom,
~ ( '0' @ ( z @ f @ 'LE' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_96) ).
thf(86,plain,
~ ( '0' @ ( z @ f @ 'LE' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(15,axiom,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( A @ suc @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_191) ).
thf(76,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( A @ suc @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(26,axiom,
! [B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_194) ).
thf(98,plain,
! [B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_190) ).
thf(66,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(31,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_30) ).
thf(108,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)],[31]) ).
thf(42,axiom,
! [B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_9) ).
thf(130,plain,
! [B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( 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_40) ).
thf(80,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( 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)],[17]) ).
thf(34,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_116) ).
thf(114,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)],[34]) ).
thf(47,axiom,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_173) ).
thf(139,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_208) ).
thf(58,plain,
! [B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(18,axiom,
! [A: $i] :
( ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_95) ).
thf(82,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(24,axiom,
! [B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_154) ).
thf(94,plain,
! [B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(40,axiom,
! [B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_115) ).
thf(126,plain,
! [B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(45,axiom,
! [A: $i] : ( '0' @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_53) ).
thf(136,plain,
! [A: $i] : ( '0' @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_79) ).
thf(68,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(8,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_97) ).
thf(62,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)],[8]) ).
thf(22,axiom,
! [B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_49) ).
thf(90,plain,
! [B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(38,axiom,
! [A: $i] :
( ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ suc @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_111) ).
thf(122,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ suc @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(27,axiom,
! [B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_181) ).
thf(100,plain,
! [B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(144,plain,
$false,
inference(e,[status(thm)],[88,120,56,78,92,64,118,112,48,50,72,104,52,110,106,84,132,116,74,60,102,70,137,124,96,134,128,54,86,76,98,66,108,130,80,114,139,58,82,94,126,136,68,62,90,122,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO685-1 : 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
% 0.15/0.42 % Computer : n015.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sat Sep 26 19:49:14 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 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
% 0.84/1.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.32/1.28 % [INFO] Parsing done (280ms).
% 1.71/1.30 % [INFO] Running in sequential loop mode.
% 2.38/1.71 % [INFO] eprover registered as external prover.
% 2.38/1.72 % [INFO] Scanning for conjecture ...
% 2.60/1.81 % [INFO] 47 axioms and no conjecture found.
% 2.81/1.96 % [INFO] Problem is propositional (TPTP CNF).
% 2.81/1.97 % [INFO] Type checking passed.
% 2.81/1.97 % [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 ...
% 6.35/3.07 % External prover 'e' found a proof!
% 6.35/3.07 % [INFO] Killing All external provers ...
% 6.35/3.07 % Time passed: 2506ms (effective reasoning time: 1765ms)
% 6.35/3.07 % Axioms used in derivation (47): clause_169, clause_175, clause_113, clause_74, clause_130, clause_55, clause_73, clause_168, clause_115, clause_191, clause_49, clause_105, clause_125, clause_204, clause_116, clause_111, clause_34, clause_190, clause_93, clause_52, clause_184, clause_30, clause_87, clause_181, clause_194, clause_183, clause_53, clause_9, clause_97, clause_86, clause_19, clause_31, clause_173, clause_61, clause_79, clause_44, clause_96, clause_36, clause_208, clause_95, clause_40, clause_11, clause_192, clause_28, clause_143, clause_154, clause_94
% 6.35/3.07 % No. of inferences in proof: 95
% 6.35/3.07 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2506 ms resp. 1765 ms w/o parsing
% 6.71/3.19 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.71/3.19 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------