%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO671-1 : 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 : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:45:09 AM UTC 2026
% Result : Unsatisfiable 10.48s 4.64s
% Output : Refutation 11.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 41
% Syntax : Number of formulae : 83 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 713 ( 0 equ; 0 cnn)
% Maximal formula atoms : 14 ( 8 avg)
% Number of connectives : 4586 ( 584 ~; 630 |; 0 &;3372 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 15 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 : 176 ( 0 ^; 176 !; 0 ?; 176 :)
% 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(38,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_67) ).
thf(115,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_20) ).
thf(56,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_66) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(6,axiom,
! [A: $i] :
( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ suc @ suc @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_217) ).
thf(52,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)],[6]) ).
thf(41,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_18) ).
thf(121,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)],[41]) ).
thf(25,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_144) ).
thf(89,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_123) ).
thf(44,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,axiom,
! [A: $i] : ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_421) ).
thf(62,plain,
! [A: $i] : ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(15,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/sandbox/benchmark/theBenchmark.p',clause_37) ).
thf(69,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)],[15]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_82) ).
thf(101,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_206) ).
thf(46,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(27,axiom,
! [A: $i] :
( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_261) ).
thf(93,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)],[27]) ).
thf(23,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_72) ).
thf(85,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)],[23]) ).
thf(10,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_326) ).
thf(60,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)],[10]) ).
thf(39,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_266) ).
thf(117,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_311) ).
thf(65,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_340) ).
thf(97,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(35,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_110) ).
thf(109,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_94) ).
thf(77,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_232) ).
thf(73,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(33,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_205) ).
thf(105,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(16,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_86) ).
thf(71,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)],[16]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_350) ).
thf(54,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(37,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_77) ).
thf(113,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(21,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_60) ).
thf(81,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)],[21]) ).
thf(32,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_189) ).
thf(103,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(26,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_146) ).
thf(91,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(4,axiom,
! [A: $i] :
( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ suc @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_183) ).
thf(48,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)],[4]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_219) ).
thf(63,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(28,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_116) ).
thf(95,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)],[28]) ).
thf(5,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/sandbox/benchmark/theBenchmark.p',clause_26) ).
thf(50,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)],[5]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_83) ).
thf(67,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(30,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_353) ).
thf(99,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)],[30]) ).
thf(24,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/sandbox/benchmark/theBenchmark.p',clause_91) ).
thf(87,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)],[24]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_49) ).
thf(75,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(40,axiom,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_307) ).
thf(119,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_16) ).
thf(58,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(34,axiom,
~ ( '0' @ ( z @ f @ 'LE' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_211) ).
thf(107,plain,
~ ( '0' @ ( z @ f @ 'LE' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(20,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_351) ).
thf(79,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(36,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_138) ).
thf(111,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)],[36]) ).
thf(22,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_61) ).
thf(83,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(131,plain,
$false,
inference(e,[status(thm)],[115,56,42,52,121,89,44,62,69,101,46,93,85,60,117,65,97,109,77,73,105,71,54,113,81,103,91,48,63,95,50,67,99,87,75,119,58,107,79,111,83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYO671-1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.11 % 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
% 0.20/0.75 % Computer : n009.cluster.edu
% 0.20/0.75 % Model : x86_64 x86_64
% 0.20/0.75 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.75 % Memory : 8046.5625MB
% 0.20/0.75 % OS : Linux 6.8.0-71-generic
% 0.20/0.75 % CPULimit : 300
% 0.20/0.75 % WCLimit : 300
% 0.20/0.75 % DateTime : Sat Sep 26 19:44:31 UTC 2026
% 0.20/0.75 % CPUTime :
% 0.20/0.75 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.27/1.55 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.10/1.97 % [INFO] Parsing done (418ms).
% 2.10/1.99 % [INFO] Running in sequential loop mode.
% 3.23/2.41 % [INFO] eprover registered as external prover.
% 3.23/2.42 % [INFO] Scanning for conjecture ...
% 3.44/2.55 % [INFO] 41 axioms and no conjecture found.
% 4.18/2.80 % [INFO] Problem is propositional (TPTP CNF).
% 4.18/2.82 % [INFO] Type checking passed.
% 4.18/2.83 % [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 ...
% 10.48/4.63 % External prover 'e' found a proof!
% 10.48/4.64 % [INFO] Killing All external provers ...
% 10.48/4.64 % Time passed: 3687ms (effective reasoning time: 2642ms)
% 10.48/4.64 % Axioms used in derivation (41): clause_261, clause_350, clause_83, clause_189, clause_91, clause_18, clause_205, clause_110, clause_94, clause_266, clause_49, clause_206, clause_116, clause_146, clause_67, clause_82, clause_16, clause_353, clause_138, clause_217, clause_340, clause_307, clause_351, clause_20, clause_60, clause_26, clause_144, clause_232, clause_211, clause_183, clause_37, clause_311, clause_326, clause_86, clause_66, clause_123, clause_61, clause_72, clause_421, clause_77, clause_219
% 10.48/4.64 % No. of inferences in proof: 83
% 10.48/4.64 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 3687 ms resp. 2642 ms w/o parsing
% 11.20/4.81 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 11.20/4.82 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------