%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO652-1 : 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 : n002.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 09:45:06 AM UTC 2026
% Result : Unsatisfiable 5.91s 7.61s
% Output : Refutation 6.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 23
% Syntax : Number of formulae : 47 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 585 ( 0 equ; 0 cnn)
% Maximal formula atoms : 19 ( 12 avg)
% Number of connectives : 3438 ( 500 ~; 538 |; 0 &;2400 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 19 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 : 140 ( 0 ^; 140 !; 0 ?; 140 :)
% 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(18,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_61) ).
thf(57,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(20,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_91) ).
thf(61,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(3,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_16) ).
thf(28,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(22,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_44) ).
thf(65,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)],[22]) ).
thf(16,axiom,
~ ( '0' @ ( z @ f @ 'LE' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_99) ).
thf(53,plain,
~ ( '0' @ ( z @ f @ 'LE' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_181) ).
thf(41,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(19,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_68) ).
thf(59,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(14,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_3) ).
thf(49,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)],[14]) ).
thf(9,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5) ).
thf(39,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(7,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_191) ).
thf(35,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)],[7]) ).
thf(21,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_183) ).
thf(63,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(23,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_100) ).
thf(67,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(11,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_96) ).
thf(43,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_50) ).
thf(47,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(1,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_35) ).
thf(24,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_74) ).
thf(37,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(12,axiom,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_17) ).
thf(45,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_141) ).
thf(32,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(6,axiom,
! [A: $i] : ( '0' @ s @ ( A @ f @ 'LE' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_199) ).
thf(34,plain,
! [A: $i] : ( '0' @ s @ ( A @ f @ 'LE' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(2,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_133) ).
thf(26,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(17,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_76) ).
thf(55,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(4,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/sandbox/benchmark/theBenchmark.p',clause_149) ).
thf(30,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)],[4]) ).
thf(15,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_45) ).
thf(51,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(72,plain,
$false,
inference(e,[status(thm)],[57,61,28,65,53,41,59,49,39,35,63,67,43,47,24,37,45,32,34,26,55,30,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO652-1 : 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
% 0.13/5.61 % Computer : n002.cluster.edu
% 0.13/5.61 % Model : x86_64 x86_64
% 0.13/5.61 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.61 % Memory : 8046.5625MB
% 0.13/5.61 % OS : Linux 6.8.0-71-generic
% 0.13/5.61 % CPULimit : 300
% 0.13/5.61 % WCLimit : 300
% 0.13/5.61 % DateTime : Sat Sep 26 19:45:43 UTC 2026
% 0.13/5.62 % CPUTime :
% 0.13/5.62 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
% 0.18/5.92 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.99/6.07 % [INFO] Parsing done (151ms).
% 0.99/6.08 % [INFO] Running in sequential loop mode.
% 1.69/6.28 % [INFO] eprover registered as external prover.
% 1.69/6.29 % [INFO] Scanning for conjecture ...
% 1.94/6.34 % [INFO] 23 axioms and no conjecture found.
% 2.41/6.50 % [INFO] Problem is propositional (TPTP CNF).
% 2.41/6.51 % [INFO] Type checking passed.
% 2.41/6.52 % [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 ...
% 5.91/7.60 % External prover 'e' found a proof!
% 5.91/7.60 % [INFO] Killing All external provers ...
% 5.91/7.61 % Time passed: 1895ms (effective reasoning time: 1524ms)
% 5.91/7.61 % Axioms used in derivation (23): clause_76, clause_16, clause_149, clause_183, clause_141, clause_44, clause_96, clause_199, clause_3, clause_17, clause_99, clause_191, clause_5, clause_45, clause_100, clause_133, clause_181, clause_74, clause_91, clause_50, clause_61, clause_35, clause_68
% 5.91/7.61 % No. of inferences in proof: 47
% 5.91/7.61 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1895 ms resp. 1524 ms w/o parsing
% 6.23/7.71 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.23/7.71 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------