%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SYO689-1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n012.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 : Fri Sep 25 03:51:56 PM UTC 2026
% Result : Unsatisfiable 1.94s 0.95s
% Output : CNFRefutation 1.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 22
% Syntax : Number of formulae : 145 ( 15 unt; 0 def)
% Number of atoms : 746 ( 0 equ)
% Maximal formula atoms : 17 ( 5 avg)
% Number of connectives : 1230 ( 629 ~; 601 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 7 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-1 aty)
% Number of variables : 238 ( 0 sgn 238 !; 0 ?; 192 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( iLEQ(suc(X0),suc(X0))
| ~ 'E'(s(s(s(s('0')))),f(suc(X0)))
| ~ 'E'(s(s(s(s('0')))),f(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1581) ).
fof(f2,axiom,
! [X0] :
( iLEQ(suc(X0),suc(X0))
| ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1218) ).
fof(f3,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ 'E'(s('0'),f(X3))
| ~ 'E'(s('0'),f(X5))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X4)))
| ~ 'E'(s('0'),f(suc(X5)))
| ~ iLEQ(suc(X1),suc(X4))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X5),suc(X0))
| ~ iLEQ(suc(X0),suc(X3))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(X4))
| ~ iLEQ(suc(X3),suc(X2))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_327) ).
fof(f4,axiom,
! [X0] : 'LE'(f(X0),s(s(s(s(s('0')))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_583) ).
fof(f5,axiom,
! [X0] :
( 'LE'(f(X0),s('0'))
| 'E'(s('0'),f(X0))
| ~ 'LE'(f(X0),s(s('0'))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_740) ).
fof(f6,axiom,
! [X0] :
( 'LE'(f(X0),s(s('0')))
| 'E'(s(s('0')),f(suc(X0)))
| ~ 'LE'(f(suc(X0)),s(s(s('0')))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_388) ).
fof(f7,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ 'E'(s(s(s('0'))),f(suc(X4)))
| ~ iLEQ(suc(X0),suc(X5))
| ~ iLEQ(suc(X3),suc(X2))
| ~ 'E'(s(s(s('0'))),f(suc(X0)))
| ~ 'E'(s(s(s('0'))),f(suc(X2)))
| ~ 'E'(s(s(s('0'))),f(X4))
| ~ 'E'(s(s(s('0'))),f(suc(X5)))
| ~ iLEQ(suc(X5),suc(X4))
| ~ iLEQ(suc(X1),suc(X0))
| ~ 'E'(s(s(s('0'))),f(X5))
| ~ 'E'(s(s(s('0'))),f(suc(X3)))
| ~ 'E'(s(s(s('0'))),f(X1))
| ~ iLEQ(suc(X4),suc(X3))
| ~ 'E'(s(s(s('0'))),f(X3))
| ~ 'E'(s(s(s('0'))),f(X2))
| ~ 'E'(s(s(s('0'))),f(suc(X1)))
| ~ 'E'(s(s(s('0'))),f(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_657) ).
fof(f8,axiom,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'('0',f(X0))
| ~ 'LE'(f(X0),s('0')) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_328) ).
fof(f9,axiom,
! [X0] :
( 'LE'(f(X0),s(s('0')))
| 'E'(s(s('0')),f(X0))
| ~ 'LE'(f(X0),s(s(s('0')))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1314) ).
fof(f10,axiom,
! [X0] :
( iLEQ(suc(X0),suc(X0))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2293) ).
fof(f11,axiom,
~ 'LE'(f(z),'0'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1092) ).
fof(f12,axiom,
! [X0] :
( 'LE'(f(X0),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(X0))
| ~ 'LE'(f(X0),s(s(s(s('0'))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1230) ).
fof(f13,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ 'E'('0',f(X2))
| ~ iLEQ(suc(X4),suc(X0))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(suc(X4)))
| ~ 'E'('0',f(suc(X0)))
| ~ iLEQ(suc(X2),suc(X4))
| ~ iLEQ(suc(X0),suc(X5))
| ~ 'E'('0',f(X5))
| ~ 'E'('0',f(suc(X5)))
| ~ 'E'('0',f(suc(X3)))
| ~ 'E'('0',f(X4))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(X3))
| ~ iLEQ(suc(X3),suc(X1))
| ~ 'E'('0',f(suc(X2)))
| ~ iLEQ(suc(X1),suc(X2))
| ~ 'E'('0',f(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_421) ).
fof(f14,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ 'E'(s(s(s(s('0')))),f(X2))
| ~ 'E'(s(s(s(s('0')))),f(suc(X3)))
| ~ 'E'(s(s(s(s('0')))),f(X5))
| ~ 'E'(s(s(s(s('0')))),f(suc(X1)))
| ~ iLEQ(suc(X5),suc(X1))
| ~ 'E'(s(s(s(s('0')))),f(suc(X5)))
| ~ 'E'(s(s(s(s('0')))),f(suc(X4)))
| ~ iLEQ(suc(X3),suc(X4))
| ~ 'E'(s(s(s(s('0')))),f(X1))
| ~ iLEQ(suc(X2),suc(X0))
| ~ 'E'(s(s(s(s('0')))),f(X4))
| ~ 'E'(s(s(s(s('0')))),f(X3))
| ~ 'E'(s(s(s(s('0')))),f(suc(X2)))
| ~ iLEQ(suc(X0),suc(X3))
| ~ iLEQ(suc(X1),suc(X2))
| ~ 'E'(s(s(s(s('0')))),f(suc(X0)))
| ~ 'E'(s(s(s(s('0')))),f(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1514) ).
fof(f15,axiom,
! [X0] :
( iLEQ(suc(X0),suc(X0))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1329) ).
fof(f16,axiom,
! [X0] :
( 'LE'(f(X0),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(suc(X0)))
| ~ 'LE'(f(suc(X0)),s(s(s(s('0'))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1935) ).
fof(f17,axiom,
! [X0] :
( 'LE'(f(X0),s(s(s(s('0')))))
| 'E'(s(s(s(s('0')))),f(X0))
| ~ 'LE'(f(X0),s(s(s(s(s('0')))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2115) ).
fof(f18,axiom,
! [X0] :
( iLEQ(suc(X0),suc(X0))
| ~ 'E'(s(s(s('0'))),f(suc(X0)))
| ~ 'E'(s(s(s('0'))),f(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2227) ).
fof(f19,axiom,
! [X0] :
( 'LE'(f(X0),s('0'))
| 'E'(s('0'),f(suc(X0)))
| ~ 'LE'(f(suc(X0)),s(s('0'))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1440) ).
fof(f20,axiom,
! [X0] :
( 'LE'(f(X0),s(s(s(s('0')))))
| 'E'(s(s(s(s('0')))),f(suc(X0)))
| ~ 'LE'(f(suc(X0)),s(s(s(s(s('0')))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2050) ).
fof(f21,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ iLEQ(suc(X2),suc(X5))
| ~ 'E'(s(s('0')),f(X4))
| ~ 'E'(s(s('0')),f(suc(X2)))
| ~ 'E'(s(s('0')),f(suc(X5)))
| ~ iLEQ(suc(X0),suc(X2))
| ~ 'E'(s(s('0')),f(suc(X0)))
| ~ iLEQ(suc(X4),suc(X1))
| ~ 'E'(s(s('0')),f(X5))
| ~ iLEQ(suc(X3),suc(X0))
| ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(suc(X4)))
| ~ iLEQ(suc(X1),suc(X3))
| ~ 'E'(s(s('0')),f(suc(X3)))
| ~ 'E'(s(s('0')),f(X3))
| ~ 'E'(s(s('0')),f(X2))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1712) ).
fof(f22,axiom,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'('0',f(suc(X0)))
| ~ 'LE'(f(suc(X0)),s('0')) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_113) ).
tcf(c_71,plain,
! [X0: $i] :
( iLEQ(suc(X0),suc(X0))
| ~ 'E'(s(s(s(s('0')))),f(X0))
| ~ 'E'(s(s(s(s('0')))),f(suc(X0))) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_72,plain,
! [X0: $i] :
( iLEQ(suc(X0),suc(X0))
| ~ 'E'(s(s('0')),f(X0))
| ~ 'E'(s(s('0')),f(suc(X0))) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ 'E'(s('0'),f(X5))
| ~ 'E'(s('0'),f(X4))
| ~ 'E'(s('0'),f(X3))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(X0))
| ~ iLEQ(suc(X5),suc(X0))
| ~ iLEQ(suc(X3),suc(X2))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X1),suc(X4))
| ~ iLEQ(suc(X0),suc(X3))
| ~ 'E'(s('0'),f(suc(X5)))
| ~ 'E'(s('0'),f(suc(X4)))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(suc(X0))) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_74,plain,
! [X0: $i] : 'LE'(f(X0),s(s(s(s(s('0')))))),
inference(cnf_transformation,[],[f4]) ).
tcf(c_75,plain,
! [X0: $i] :
( 'LE'(f(X0),s('0'))
| 'E'(s('0'),f(X0))
| ~ 'LE'(f(X0),s(s('0'))) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_76,plain,
! [X0: $i] :
( 'LE'(f(X0),s(s('0')))
| 'E'(s(s('0')),f(suc(X0)))
| ~ 'LE'(f(suc(X0)),s(s(s('0')))) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ iLEQ(suc(X5),suc(X4))
| ~ iLEQ(suc(X4),suc(X3))
| ~ iLEQ(suc(X3),suc(X2))
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X5))
| ~ 'E'(s(s(s('0'))),f(X5))
| ~ 'E'(s(s(s('0'))),f(X4))
| ~ 'E'(s(s(s('0'))),f(X3))
| ~ 'E'(s(s(s('0'))),f(X2))
| ~ 'E'(s(s(s('0'))),f(X1))
| ~ 'E'(s(s(s('0'))),f(X0))
| ~ 'E'(s(s(s('0'))),f(suc(X5)))
| ~ 'E'(s(s(s('0'))),f(suc(X4)))
| ~ 'E'(s(s(s('0'))),f(suc(X3)))
| ~ 'E'(s(s(s('0'))),f(suc(X2)))
| ~ 'E'(s(s(s('0'))),f(suc(X1)))
| ~ 'E'(s(s(s('0'))),f(suc(X0))) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_78,plain,
! [X0: $i] :
( 'LE'(f(X0),'0')
| 'E'('0',f(X0))
| ~ 'LE'(f(X0),s('0')) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_79,plain,
! [X0: $i] :
( 'LE'(f(X0),s(s('0')))
| 'E'(s(s('0')),f(X0))
| ~ 'LE'(f(X0),s(s(s('0')))) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_80,plain,
! [X0: $i] :
( iLEQ(suc(X0),suc(X0))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X0))) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_81,plain,
~ 'LE'(f(z),'0'),
inference(cnf_transformation,[],[f11]) ).
tcf(c_82,plain,
! [X0: $i] :
( 'LE'(f(X0),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(X0))
| ~ 'LE'(f(X0),s(s(s(s('0'))))) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ 'E'('0',f(X5))
| ~ 'E'('0',f(X4))
| ~ 'E'('0',f(X3))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X5)))
| ~ 'E'('0',f(suc(X4)))
| ~ 'E'('0',f(suc(X3)))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(suc(X0)))
| ~ iLEQ(suc(X5),suc(X2))
| ~ iLEQ(suc(X4),suc(X0))
| ~ iLEQ(suc(X3),suc(X4))
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ iLEQ(suc(X5),suc(X1))
| ~ iLEQ(suc(X3),suc(X4))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X3))
| ~ 'E'(s(s(s(s('0')))),f(X5))
| ~ 'E'(s(s(s(s('0')))),f(X4))
| ~ 'E'(s(s(s(s('0')))),f(X3))
| ~ 'E'(s(s(s(s('0')))),f(X2))
| ~ 'E'(s(s(s(s('0')))),f(X1))
| ~ 'E'(s(s(s(s('0')))),f(X0))
| ~ 'E'(s(s(s(s('0')))),f(suc(X5)))
| ~ 'E'(s(s(s(s('0')))),f(suc(X4)))
| ~ 'E'(s(s(s(s('0')))),f(suc(X3)))
| ~ 'E'(s(s(s(s('0')))),f(suc(X2)))
| ~ 'E'(s(s(s(s('0')))),f(suc(X1)))
| ~ 'E'(s(s(s(s('0')))),f(suc(X0))) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_85,plain,
! [X0: $i] :
( iLEQ(suc(X0),suc(X0))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X0))) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_86,plain,
! [X0: $i] :
( 'LE'(f(X0),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(suc(X0)))
| ~ 'LE'(f(suc(X0)),s(s(s(s('0'))))) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_87,plain,
! [X0: $i] :
( 'LE'(f(X0),s(s(s(s('0')))))
| 'E'(s(s(s(s('0')))),f(X0))
| ~ 'LE'(f(X0),s(s(s(s(s('0')))))) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_88,plain,
! [X0: $i] :
( iLEQ(suc(X0),suc(X0))
| ~ 'E'(s(s(s('0'))),f(X0))
| ~ 'E'(s(s(s('0'))),f(suc(X0))) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_89,plain,
! [X0: $i] :
( 'LE'(f(X0),s('0'))
| 'E'(s('0'),f(suc(X0)))
| ~ 'LE'(f(suc(X0)),s(s('0'))) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_90,plain,
! [X0: $i] :
( 'LE'(f(X0),s(s(s(s('0')))))
| 'E'(s(s(s(s('0')))),f(suc(X0)))
| ~ 'LE'(f(suc(X0)),s(s(s(s(s('0')))))) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ iLEQ(suc(X4),suc(X1))
| ~ iLEQ(suc(X3),suc(X0))
| ~ iLEQ(suc(X2),suc(X5))
| ~ iLEQ(suc(X1),suc(X3))
| ~ iLEQ(suc(X0),suc(X2))
| ~ 'E'(s(s('0')),f(X5))
| ~ 'E'(s(s('0')),f(X4))
| ~ 'E'(s(s('0')),f(X3))
| ~ 'E'(s(s('0')),f(X2))
| ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(X0))
| ~ 'E'(s(s('0')),f(suc(X5)))
| ~ 'E'(s(s('0')),f(suc(X4)))
| ~ 'E'(s(s('0')),f(suc(X3)))
| ~ 'E'(s(s('0')),f(suc(X2)))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(suc(X0))) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_92,plain,
! [X0: $i] :
( 'LE'(f(X0),'0')
| 'E'('0',f(suc(X0)))
| ~ 'LE'(f(suc(X0)),s('0')) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_114,plain,
! [X0: $i] :
( 'LE'(f(X0),s(s(s(s('0')))))
| 'E'(s(s(s(s('0')))),f(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_87,c_74,c_87]) ).
tcf(c_121,plain,
! [X0: $i] :
( 'LE'(f(X0),s(s(s(s('0')))))
| 'E'(s(s(s(s('0')))),f(suc(X0))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_90,c_74]) ).
tcf(c_637,plain,
! [X0_iProver_f_1: iProver_f_1] :
( 'LE'(f(X0_iProver_f_1),s(s(s(s('0')))))
| 'E'(s(s(s(s('0')))),f(suc(X0_iProver_f_1))) ),
inference(subtyping,[status(esa)],[c_121]) ).
tcf(c_638,plain,
! [X0_iProver_f_1: iProver_f_1] :
( 'LE'(f(X0_iProver_f_1),s(s(s(s('0')))))
| 'E'(s(s(s(s('0')))),f(X0_iProver_f_1)) ),
inference(subtyping,[status(esa)],[c_114]) ).
tcf(c_639,plain,
! [X0_iProver_f_1: iProver_f_1,X1_iProver_f_1: iProver_f_1,X2_iProver_f_1: iProver_f_1,X3_iProver_f_1: iProver_f_1,X4_iProver_f_1: iProver_f_1,X5_iProver_f_1: iProver_f_1] :
( ~ iLEQ(suc(X5_iProver_f_1),suc(X2_iProver_f_1))
| ~ iLEQ(suc(X3_iProver_f_1),suc(X0_iProver_f_1))
| ~ iLEQ(suc(X2_iProver_f_1),suc(X3_iProver_f_1))
| ~ iLEQ(suc(X1_iProver_f_1),suc(X4_iProver_f_1))
| ~ iLEQ(suc(X0_iProver_f_1),suc(X1_iProver_f_1))
| ~ 'E'(s(s('0')),f(X5_iProver_f_1))
| ~ 'E'(s(s('0')),f(X4_iProver_f_1))
| ~ 'E'(s(s('0')),f(X3_iProver_f_1))
| ~ 'E'(s(s('0')),f(X2_iProver_f_1))
| ~ 'E'(s(s('0')),f(X1_iProver_f_1))
| ~ 'E'(s(s('0')),f(X0_iProver_f_1))
| ~ 'E'(s(s('0')),f(suc(X5_iProver_f_1)))
| ~ 'E'(s(s('0')),f(suc(X4_iProver_f_1)))
| ~ 'E'(s(s('0')),f(suc(X3_iProver_f_1)))
| ~ 'E'(s(s('0')),f(suc(X2_iProver_f_1)))
| ~ 'E'(s(s('0')),f(suc(X1_iProver_f_1)))
| ~ 'E'(s(s('0')),f(suc(X0_iProver_f_1))) ),
inference(subtyping,[status(esa)],[c_91]) ).
tcf(c_640,plain,
! [X0_iProver_f_1: iProver_f_1,X1_iProver_f_1: iProver_f_1,X2_iProver_f_1: iProver_f_1,X3_iProver_f_1: iProver_f_1,X4_iProver_f_1: iProver_f_1,X5_iProver_f_1: iProver_f_1] :
( ~ iLEQ(suc(X5_iProver_f_1),suc(X2_iProver_f_1))
| ~ iLEQ(suc(X3_iProver_f_1),suc(X0_iProver_f_1))
| ~ iLEQ(suc(X2_iProver_f_1),suc(X3_iProver_f_1))
| ~ iLEQ(suc(X1_iProver_f_1),suc(X4_iProver_f_1))
| ~ iLEQ(suc(X0_iProver_f_1),suc(X1_iProver_f_1))
| ~ 'E'(s(s(s(s('0')))),f(X5_iProver_f_1))
| ~ 'E'(s(s(s(s('0')))),f(X4_iProver_f_1))
| ~ 'E'(s(s(s(s('0')))),f(X3_iProver_f_1))
| ~ 'E'(s(s(s(s('0')))),f(X2_iProver_f_1))
| ~ 'E'(s(s(s(s('0')))),f(X1_iProver_f_1))
| ~ 'E'(s(s(s(s('0')))),f(X0_iProver_f_1))
| ~ 'E'(s(s(s(s('0')))),f(suc(X5_iProver_f_1)))
| ~ 'E'(s(s(s(s('0')))),f(suc(X4_iProver_f_1)))
| ~ 'E'(s(s(s(s('0')))),f(suc(X3_iProver_f_1)))
| ~ 'E'(s(s(s(s('0')))),f(suc(X2_iProver_f_1)))
| ~ 'E'(s(s(s(s('0')))),f(suc(X1_iProver_f_1)))
| ~ 'E'(s(s(s(s('0')))),f(suc(X0_iProver_f_1))) ),
inference(subtyping,[status(esa)],[c_84]) ).
tcf(c_641,plain,
! [X0_iProver_f_1: iProver_f_1,X1_iProver_f_1: iProver_f_1,X2_iProver_f_1: iProver_f_1,X3_iProver_f_1: iProver_f_1,X4_iProver_f_1: iProver_f_1,X5_iProver_f_1: iProver_f_1] :
( ~ 'E'('0',f(X5_iProver_f_1))
| ~ 'E'('0',f(X4_iProver_f_1))
| ~ 'E'('0',f(X3_iProver_f_1))
| ~ 'E'('0',f(X2_iProver_f_1))
| ~ 'E'('0',f(X1_iProver_f_1))
| ~ 'E'('0',f(X0_iProver_f_1))
| ~ 'E'('0',f(suc(X5_iProver_f_1)))
| ~ 'E'('0',f(suc(X4_iProver_f_1)))
| ~ 'E'('0',f(suc(X3_iProver_f_1)))
| ~ 'E'('0',f(suc(X2_iProver_f_1)))
| ~ 'E'('0',f(suc(X1_iProver_f_1)))
| ~ 'E'('0',f(suc(X0_iProver_f_1)))
| ~ iLEQ(suc(X5_iProver_f_1),suc(X2_iProver_f_1))
| ~ iLEQ(suc(X4_iProver_f_1),suc(X0_iProver_f_1))
| ~ iLEQ(suc(X3_iProver_f_1),suc(X4_iProver_f_1))
| ~ iLEQ(suc(X2_iProver_f_1),suc(X3_iProver_f_1))
| ~ iLEQ(suc(X0_iProver_f_1),suc(X1_iProver_f_1)) ),
inference(subtyping,[status(esa)],[c_83]) ).
tcf(c_642,plain,
! [X0_iProver_f_1: iProver_f_1] :
( 'LE'(f(X0_iProver_f_1),'0')
| 'E'('0',f(suc(X0_iProver_f_1)))
| ~ 'LE'(f(suc(X0_iProver_f_1)),s('0')) ),
inference(subtyping,[status(esa)],[c_92]) ).
tcf(c_643,plain,
! [X0_iProver_f_1: iProver_f_1] :
( 'LE'(f(X0_iProver_f_1),s('0'))
| 'E'(s('0'),f(suc(X0_iProver_f_1)))
| ~ 'LE'(f(suc(X0_iProver_f_1)),s(s('0'))) ),
inference(subtyping,[status(esa)],[c_89]) ).
tcf(c_644,plain,
! [X0_iProver_f_1: iProver_f_1] :
( iLEQ(suc(X0_iProver_f_1),suc(X0_iProver_f_1))
| ~ 'E'(s(s(s('0'))),f(X0_iProver_f_1))
| ~ 'E'(s(s(s('0'))),f(suc(X0_iProver_f_1))) ),
inference(subtyping,[status(esa)],[c_88]) ).
tcf(c_645,plain,
! [X0_iProver_f_1: iProver_f_1] :
( 'LE'(f(X0_iProver_f_1),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(suc(X0_iProver_f_1)))
| ~ 'LE'(f(suc(X0_iProver_f_1)),s(s(s(s('0'))))) ),
inference(subtyping,[status(esa)],[c_86]) ).
tcf(c_646,plain,
! [X0_iProver_f_1: iProver_f_1] :
( iLEQ(suc(X0_iProver_f_1),suc(X0_iProver_f_1))
| ~ 'E'(s('0'),f(X0_iProver_f_1))
| ~ 'E'(s('0'),f(suc(X0_iProver_f_1))) ),
inference(subtyping,[status(esa)],[c_85]) ).
tcf(c_647,plain,
! [X0_iProver_f_1: iProver_f_1] :
( 'LE'(f(X0_iProver_f_1),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(X0_iProver_f_1))
| ~ 'LE'(f(X0_iProver_f_1),s(s(s(s('0'))))) ),
inference(subtyping,[status(esa)],[c_82]) ).
tcf(c_648,plain,
~ 'LE'(f(z),'0'),
inference(subtyping,[status(esa)],[c_81]) ).
tcf(c_649,plain,
! [X0_iProver_f_1: iProver_f_1] :
( iLEQ(suc(X0_iProver_f_1),suc(X0_iProver_f_1))
| ~ 'E'('0',f(X0_iProver_f_1))
| ~ 'E'('0',f(suc(X0_iProver_f_1))) ),
inference(subtyping,[status(esa)],[c_80]) ).
tcf(c_650,plain,
! [X0_iProver_f_1: iProver_f_1] :
( 'LE'(f(X0_iProver_f_1),s(s('0')))
| 'E'(s(s('0')),f(X0_iProver_f_1))
| ~ 'LE'(f(X0_iProver_f_1),s(s(s('0')))) ),
inference(subtyping,[status(esa)],[c_79]) ).
tcf(c_651,plain,
! [X0_iProver_f_1: iProver_f_1] :
( 'LE'(f(X0_iProver_f_1),'0')
| 'E'('0',f(X0_iProver_f_1))
| ~ 'LE'(f(X0_iProver_f_1),s('0')) ),
inference(subtyping,[status(esa)],[c_78]) ).
tcf(c_652,plain,
! [X0_iProver_f_1: iProver_f_1,X1_iProver_f_1: iProver_f_1,X2_iProver_f_1: iProver_f_1,X3_iProver_f_1: iProver_f_1,X4_iProver_f_1: iProver_f_1,X5_iProver_f_1: iProver_f_1] :
( ~ iLEQ(suc(X5_iProver_f_1),suc(X3_iProver_f_1))
| ~ iLEQ(suc(X3_iProver_f_1),suc(X4_iProver_f_1))
| ~ iLEQ(suc(X2_iProver_f_1),suc(X0_iProver_f_1))
| ~ iLEQ(suc(X1_iProver_f_1),suc(X5_iProver_f_1))
| ~ iLEQ(suc(X0_iProver_f_1),suc(X1_iProver_f_1))
| ~ 'E'(s(s(s('0'))),f(X5_iProver_f_1))
| ~ 'E'(s(s(s('0'))),f(X4_iProver_f_1))
| ~ 'E'(s(s(s('0'))),f(X3_iProver_f_1))
| ~ 'E'(s(s(s('0'))),f(X2_iProver_f_1))
| ~ 'E'(s(s(s('0'))),f(X1_iProver_f_1))
| ~ 'E'(s(s(s('0'))),f(X0_iProver_f_1))
| ~ 'E'(s(s(s('0'))),f(suc(X5_iProver_f_1)))
| ~ 'E'(s(s(s('0'))),f(suc(X4_iProver_f_1)))
| ~ 'E'(s(s(s('0'))),f(suc(X3_iProver_f_1)))
| ~ 'E'(s(s(s('0'))),f(suc(X2_iProver_f_1)))
| ~ 'E'(s(s(s('0'))),f(suc(X1_iProver_f_1)))
| ~ 'E'(s(s(s('0'))),f(suc(X0_iProver_f_1))) ),
inference(subtyping,[status(esa)],[c_77]) ).
tcf(c_653,plain,
! [X0_iProver_f_1: iProver_f_1] :
( 'LE'(f(X0_iProver_f_1),s(s('0')))
| 'E'(s(s('0')),f(suc(X0_iProver_f_1)))
| ~ 'LE'(f(suc(X0_iProver_f_1)),s(s(s('0')))) ),
inference(subtyping,[status(esa)],[c_76]) ).
tcf(c_654,plain,
! [X0_iProver_f_1: iProver_f_1] :
( 'LE'(f(X0_iProver_f_1),s('0'))
| 'E'(s('0'),f(X0_iProver_f_1))
| ~ 'LE'(f(X0_iProver_f_1),s(s('0'))) ),
inference(subtyping,[status(esa)],[c_75]) ).
tcf(c_655,plain,
! [X0_iProver_f_1: iProver_f_1,X1_iProver_f_1: iProver_f_1,X2_iProver_f_1: iProver_f_1,X3_iProver_f_1: iProver_f_1,X4_iProver_f_1: iProver_f_1,X5_iProver_f_1: iProver_f_1] :
( ~ 'E'(s('0'),f(X5_iProver_f_1))
| ~ 'E'(s('0'),f(X4_iProver_f_1))
| ~ 'E'(s('0'),f(X3_iProver_f_1))
| ~ 'E'(s('0'),f(X2_iProver_f_1))
| ~ 'E'(s('0'),f(X1_iProver_f_1))
| ~ 'E'(s('0'),f(X0_iProver_f_1))
| ~ iLEQ(suc(X5_iProver_f_1),suc(X0_iProver_f_1))
| ~ iLEQ(suc(X4_iProver_f_1),suc(X2_iProver_f_1))
| ~ iLEQ(suc(X3_iProver_f_1),suc(X5_iProver_f_1))
| ~ iLEQ(suc(X2_iProver_f_1),suc(X3_iProver_f_1))
| ~ iLEQ(suc(X0_iProver_f_1),suc(X1_iProver_f_1))
| ~ 'E'(s('0'),f(suc(X5_iProver_f_1)))
| ~ 'E'(s('0'),f(suc(X4_iProver_f_1)))
| ~ 'E'(s('0'),f(suc(X3_iProver_f_1)))
| ~ 'E'(s('0'),f(suc(X2_iProver_f_1)))
| ~ 'E'(s('0'),f(suc(X1_iProver_f_1)))
| ~ 'E'(s('0'),f(suc(X0_iProver_f_1))) ),
inference(subtyping,[status(esa)],[c_73]) ).
tcf(c_656,plain,
! [X0_iProver_f_1: iProver_f_1] :
( iLEQ(suc(X0_iProver_f_1),suc(X0_iProver_f_1))
| ~ 'E'(s(s('0')),f(X0_iProver_f_1))
| ~ 'E'(s(s('0')),f(suc(X0_iProver_f_1))) ),
inference(subtyping,[status(esa)],[c_72]) ).
tcf(c_657,plain,
! [X0_iProver_f_1: iProver_f_1] :
( iLEQ(suc(X0_iProver_f_1),suc(X0_iProver_f_1))
| ~ 'E'(s(s(s(s('0')))),f(X0_iProver_f_1))
| ~ 'E'(s(s(s(s('0')))),f(suc(X0_iProver_f_1))) ),
inference(subtyping,[status(esa)],[c_71]) ).
tcf(c_658,plain,
( 'LE'(f(z),'0')
| 'E'('0',f(z))
| ~ 'LE'(f(z),s('0')) ),
inference(instantiation,[status(thm)],[c_651]) ).
tcf(c_663,plain,
( 'LE'(f(z),s('0'))
| 'E'(s('0'),f(z))
| ~ 'LE'(f(z),s(s('0'))) ),
inference(instantiation,[status(thm)],[c_654]) ).
tcf(c_665,plain,
( 'LE'(f(z),s('0'))
| 'E'(s('0'),f(suc(z)))
| ~ 'LE'(f(suc(z)),s(s('0'))) ),
inference(instantiation,[status(thm)],[c_643]) ).
tcf(c_666,plain,
( 'LE'(f(z),s(s('0')))
| 'E'(s(s('0')),f(z))
| ~ 'LE'(f(z),s(s(s('0')))) ),
inference(instantiation,[status(thm)],[c_650]) ).
tcf(c_710,plain,
( 'E'('0',f(z))
| ~ 'LE'(f(z),s('0')) ),
inference(resolution,[status(thm)],[c_651,c_648]) ).
tcf(c_746,plain,
! [X0_iProver_f_1: iProver_f_1,X1_iProver_f_1: iProver_f_1,X2_iProver_f_1: iProver_f_1,X3_iProver_f_1: iProver_f_1] :
( ~ 'E'('0',f(X3_iProver_f_1))
| ~ 'E'('0',f(X2_iProver_f_1))
| ~ 'E'('0',f(X1_iProver_f_1))
| ~ 'E'('0',f(X0_iProver_f_1))
| ~ 'E'('0',f(suc(X3_iProver_f_1)))
| ~ 'E'('0',f(suc(X2_iProver_f_1)))
| ~ 'E'('0',f(suc(X1_iProver_f_1)))
| ~ 'E'('0',f(suc(X0_iProver_f_1)))
| ~ iLEQ(suc(X3_iProver_f_1),suc(X2_iProver_f_1))
| ~ iLEQ(suc(X2_iProver_f_1),suc(X0_iProver_f_1))
| ~ iLEQ(suc(X0_iProver_f_1),suc(X1_iProver_f_1))
| ~ iLEQ(suc(X0_iProver_f_1),suc(X0_iProver_f_1)) ),
inference(factoring,[status(thm)],[c_641]) ).
tcf(c_747,plain,
! [X0_iProver_f_1: iProver_f_1,X1_iProver_f_1: iProver_f_1,X2_iProver_f_1: iProver_f_1,X3_iProver_f_1: iProver_f_1] :
( ~ 'E'('0',f(X3_iProver_f_1))
| ~ 'E'('0',f(X2_iProver_f_1))
| ~ 'E'('0',f(X1_iProver_f_1))
| ~ 'E'('0',f(X0_iProver_f_1))
| ~ 'E'('0',f(suc(X3_iProver_f_1)))
| ~ 'E'('0',f(suc(X2_iProver_f_1)))
| ~ 'E'('0',f(suc(X1_iProver_f_1)))
| ~ 'E'('0',f(suc(X0_iProver_f_1)))
| ~ iLEQ(suc(X3_iProver_f_1),suc(X2_iProver_f_1))
| ~ iLEQ(suc(X2_iProver_f_1),suc(X0_iProver_f_1))
| ~ iLEQ(suc(X0_iProver_f_1),suc(X1_iProver_f_1)) ),
inference(global_subsumption_just,[status(thm)],[c_746,c_649,c_746]) ).
tcf(c_778,plain,
! [X0_iProver_f_1: iProver_f_1,X1_iProver_f_1: iProver_f_1] :
( ~ 'E'('0',f(X1_iProver_f_1))
| ~ 'E'('0',f(X0_iProver_f_1))
| ~ 'E'('0',f(suc(X1_iProver_f_1)))
| ~ 'E'('0',f(suc(X0_iProver_f_1)))
| ~ iLEQ(suc(X0_iProver_f_1),suc(X1_iProver_f_1))
| ~ iLEQ(suc(X0_iProver_f_1),suc(X0_iProver_f_1)) ),
inference(factoring,[status(thm)],[c_747]) ).
tcf(c_779,plain,
! [X0_iProver_f_1: iProver_f_1,X1_iProver_f_1: iProver_f_1] :
( ~ 'E'('0',f(X1_iProver_f_1))
| ~ 'E'('0',f(X0_iProver_f_1))
| ~ 'E'('0',f(suc(X1_iProver_f_1)))
| ~ 'E'('0',f(suc(X0_iProver_f_1)))
| ~ iLEQ(suc(X0_iProver_f_1),suc(X1_iProver_f_1)) ),
inference(global_subsumption_just,[status(thm)],[c_778,c_649,c_778]) ).
tcf(c_799,plain,
! [X0_iProver_f_1: iProver_f_1] :
( ~ 'E'('0',f(X0_iProver_f_1))
| ~ 'E'('0',f(suc(X0_iProver_f_1))) ),
inference(resolution,[status(thm)],[c_779,c_649]) ).
tcf(c_803,plain,
! [X0_iProver_f_1: iProver_f_1] :
( 'LE'(f(X0_iProver_f_1),'0')
| ~ 'E'('0',f(X0_iProver_f_1))
| ~ 'LE'(f(suc(X0_iProver_f_1)),s('0')) ),
inference(resolution,[status(thm)],[c_799,c_642]) ).
tcf(c_808,plain,
( ~ 'E'('0',f(z))
| ~ 'LE'(f(suc(z)),s('0')) ),
inference(resolution,[status(thm)],[c_803,c_648]) ).
tcf(c_811,plain,
( 'E'(s('0'),f(suc(z)))
| ~ 'E'('0',f(z))
| ~ 'LE'(f(suc(z)),s(s('0'))) ),
inference(resolution,[status(thm)],[c_808,c_654]) ).
tcf(c_812,plain,
( 'E'(s('0'),f(suc(z)))
| ~ 'LE'(f(suc(z)),s(s('0'))) ),
inference(global_subsumption_just,[status(thm)],[c_811,c_81,c_658,c_665,c_811]) ).
tcf(c_837,plain,
! [X0_iProver_f_1: iProver_f_1,X1_iProver_f_1: iProver_f_1,X2_iProver_f_1: iProver_f_1,X3_iProver_f_1: iProver_f_1] :
( ~ iLEQ(suc(X3_iProver_f_1),suc(X0_iProver_f_1))
| ~ iLEQ(suc(X1_iProver_f_1),suc(X2_iProver_f_1))
| ~ iLEQ(suc(X0_iProver_f_1),suc(X1_iProver_f_1))
| ~ iLEQ(suc(X0_iProver_f_1),suc(X0_iProver_f_1))
| ~ 'E'(s(s('0')),f(X3_iProver_f_1))
| ~ 'E'(s(s('0')),f(X2_iProver_f_1))
| ~ 'E'(s(s('0')),f(X1_iProver_f_1))
| ~ 'E'(s(s('0')),f(X0_iProver_f_1))
| ~ 'E'(s(s('0')),f(suc(X3_iProver_f_1)))
| ~ 'E'(s(s('0')),f(suc(X2_iProver_f_1)))
| ~ 'E'(s(s('0')),f(suc(X1_iProver_f_1)))
| ~ 'E'(s(s('0')),f(suc(X0_iProver_f_1))) ),
inference(factoring,[status(thm)],[c_639]) ).
tcf(c_838,plain,
! [X0_iProver_f_1: iProver_f_1,X1_iProver_f_1: iProver_f_1,X2_iProver_f_1: iProver_f_1,X3_iProver_f_1: iProver_f_1] :
( ~ iLEQ(suc(X3_iProver_f_1),suc(X0_iProver_f_1))
| ~ iLEQ(suc(X1_iProver_f_1),suc(X2_iProver_f_1))
| ~ iLEQ(suc(X0_iProver_f_1),suc(X1_iProver_f_1))
| ~ 'E'(s(s('0')),f(suc(X0_iProver_f_1)))
| ~ 'E'(s(s('0')),f(suc(X1_iProver_f_1)))
| ~ 'E'(s(s('0')),f(suc(X2_iProver_f_1)))
| ~ 'E'(s(s('0')),f(suc(X3_iProver_f_1)))
| ~ 'E'(s(s('0')),f(X0_iProver_f_1))
| ~ 'E'(s(s('0')),f(X1_iProver_f_1))
| ~ 'E'(s(s('0')),f(X2_iProver_f_1))
| ~ 'E'(s(s('0')),f(X3_iProver_f_1)) ),
inference(global_subsumption_just,[status(thm)],[c_837,c_656,c_837]) ).
tcf(c_839,plain,
! [X0_iProver_f_1: iProver_f_1,X1_iProver_f_1: iProver_f_1,X2_iProver_f_1: iProver_f_1,X3_iProver_f_1: iProver_f_1] :
( ~ iLEQ(suc(X3_iProver_f_1),suc(X0_iProver_f_1))
| ~ iLEQ(suc(X1_iProver_f_1),suc(X2_iProver_f_1))
| ~ iLEQ(suc(X0_iProver_f_1),suc(X1_iProver_f_1))
| ~ 'E'(s(s('0')),f(X3_iProver_f_1))
| ~ 'E'(s(s('0')),f(X2_iProver_f_1))
| ~ 'E'(s(s('0')),f(X1_iProver_f_1))
| ~ 'E'(s(s('0')),f(X0_iProver_f_1))
| ~ 'E'(s(s('0')),f(suc(X3_iProver_f_1)))
| ~ 'E'(s(s('0')),f(suc(X2_iProver_f_1)))
| ~ 'E'(s(s('0')),f(suc(X1_iProver_f_1)))
| ~ 'E'(s(s('0')),f(suc(X0_iProver_f_1))) ),
inference(renaming,[status(thm)],[c_838]) ).
tcf(c_885,plain,
! [X0_iProver_f_1: iProver_f_1] :
( 'LE'(f(suc(X0_iProver_f_1)),s(s('0')))
| 'E'(s(s('0')),f(suc(X0_iProver_f_1)))
| ~ 'LE'(f(suc(X0_iProver_f_1)),s(s(s('0')))) ),
inference(instantiation,[status(thm)],[c_650]) ).
tcf(c_886,plain,
( 'LE'(f(suc(z)),s(s('0')))
| 'E'(s(s('0')),f(suc(z)))
| ~ 'LE'(f(suc(z)),s(s(s('0')))) ),
inference(instantiation,[status(thm)],[c_885]) ).
tcf(c_887,plain,
! [X0_iProver_f_1: iProver_f_1] :
( 'LE'(f(suc(X0_iProver_f_1)),s(s('0')))
| 'E'(s(s('0')),f(suc(suc(X0_iProver_f_1))))
| ~ 'LE'(f(suc(suc(X0_iProver_f_1))),s(s(s('0')))) ),
inference(instantiation,[status(thm)],[c_653]) ).
tcf(c_888,plain,
( 'LE'(f(suc(z)),s(s('0')))
| 'E'(s(s('0')),f(suc(suc(z))))
| ~ 'LE'(f(suc(suc(z))),s(s(s('0')))) ),
inference(instantiation,[status(thm)],[c_887]) ).
tcf(c_917,plain,
! [X0_iProver_f_1: iProver_f_1,X1_iProver_f_1: iProver_f_1] :
( ~ iLEQ(suc(X0_iProver_f_1),suc(X1_iProver_f_1))
| ~ iLEQ(suc(X0_iProver_f_1),suc(X0_iProver_f_1))
| ~ 'E'(s(s('0')),f(X1_iProver_f_1))
| ~ 'E'(s(s('0')),f(X0_iProver_f_1))
| ~ 'E'(s(s('0')),f(suc(X1_iProver_f_1)))
| ~ 'E'(s(s('0')),f(suc(X0_iProver_f_1))) ),
inference(factoring,[status(thm)],[c_839]) ).
tcf(c_918,plain,
! [X0_iProver_f_1: iProver_f_1,X1_iProver_f_1: iProver_f_1] :
( ~ iLEQ(suc(X0_iProver_f_1),suc(X1_iProver_f_1))
| ~ 'E'(s(s('0')),f(suc(X0_iProver_f_1)))
| ~ 'E'(s(s('0')),f(suc(X1_iProver_f_1)))
| ~ 'E'(s(s('0')),f(X0_iProver_f_1))
| ~ 'E'(s(s('0')),f(X1_iProver_f_1)) ),
inference(global_subsumption_just,[status(thm)],[c_917,c_656,c_917]) ).
tcf(c_919,plain,
! [X0_iProver_f_1: iProver_f_1,X1_iProver_f_1: iProver_f_1] :
( ~ iLEQ(suc(X0_iProver_f_1),suc(X1_iProver_f_1))
| ~ 'E'(s(s('0')),f(X1_iProver_f_1))
| ~ 'E'(s(s('0')),f(X0_iProver_f_1))
| ~ 'E'(s(s('0')),f(suc(X1_iProver_f_1)))
| ~ 'E'(s(s('0')),f(suc(X0_iProver_f_1))) ),
inference(renaming,[status(thm)],[c_918]) ).
tcf(c_933,plain,
! [X0_iProver_f_1: iProver_f_1] :
( ~ 'E'(s(s('0')),f(X0_iProver_f_1))
| ~ 'E'(s(s('0')),f(suc(X0_iProver_f_1))) ),
inference(resolution,[status(thm)],[c_919,c_656]) ).
tcf(c_934,plain,
( ~ 'E'(s(s('0')),f(z))
| ~ 'E'(s(s('0')),f(suc(z))) ),
inference(instantiation,[status(thm)],[c_933]) ).
tcf(c_937,plain,
! [X0_iProver_f_1: iProver_f_1] :
( 'LE'(f(X0_iProver_f_1),s(s('0')))
| ~ 'E'(s(s('0')),f(X0_iProver_f_1))
| ~ 'LE'(f(suc(X0_iProver_f_1)),s(s(s('0')))) ),
inference(resolution,[status(thm)],[c_933,c_653]) ).
tcf(c_960,plain,
! [X0_iProver_f_1: iProver_f_1,X1_iProver_f_1: iProver_f_1,X2_iProver_f_1: iProver_f_1,X3_iProver_f_1: iProver_f_1] :
( ~ 'E'(s('0'),f(X3_iProver_f_1))
| ~ 'E'(s('0'),f(X2_iProver_f_1))
| ~ 'E'(s('0'),f(X1_iProver_f_1))
| ~ 'E'(s('0'),f(X0_iProver_f_1))
| ~ iLEQ(suc(X3_iProver_f_1),suc(X2_iProver_f_1))
| ~ iLEQ(suc(X2_iProver_f_1),suc(X0_iProver_f_1))
| ~ iLEQ(suc(X0_iProver_f_1),suc(X1_iProver_f_1))
| ~ iLEQ(suc(X0_iProver_f_1),suc(X0_iProver_f_1))
| ~ 'E'(s('0'),f(suc(X3_iProver_f_1)))
| ~ 'E'(s('0'),f(suc(X2_iProver_f_1)))
| ~ 'E'(s('0'),f(suc(X1_iProver_f_1)))
| ~ 'E'(s('0'),f(suc(X0_iProver_f_1))) ),
inference(factoring,[status(thm)],[c_655]) ).
tcf(c_961,plain,
! [X0_iProver_f_1: iProver_f_1,X1_iProver_f_1: iProver_f_1,X2_iProver_f_1: iProver_f_1,X3_iProver_f_1: iProver_f_1] :
( ~ 'E'(s('0'),f(X3_iProver_f_1))
| ~ 'E'(s('0'),f(X2_iProver_f_1))
| ~ 'E'(s('0'),f(X1_iProver_f_1))
| ~ 'E'(s('0'),f(X0_iProver_f_1))
| ~ iLEQ(suc(X3_iProver_f_1),suc(X2_iProver_f_1))
| ~ iLEQ(suc(X2_iProver_f_1),suc(X0_iProver_f_1))
| ~ iLEQ(suc(X0_iProver_f_1),suc(X1_iProver_f_1))
| ~ 'E'(s('0'),f(suc(X0_iProver_f_1)))
| ~ 'E'(s('0'),f(suc(X1_iProver_f_1)))
| ~ 'E'(s('0'),f(suc(X2_iProver_f_1)))
| ~ 'E'(s('0'),f(suc(X3_iProver_f_1))) ),
inference(global_subsumption_just,[status(thm)],[c_960,c_646,c_960]) ).
tcf(c_962,plain,
! [X0_iProver_f_1: iProver_f_1,X1_iProver_f_1: iProver_f_1,X2_iProver_f_1: iProver_f_1,X3_iProver_f_1: iProver_f_1] :
( ~ 'E'(s('0'),f(X3_iProver_f_1))
| ~ 'E'(s('0'),f(X2_iProver_f_1))
| ~ 'E'(s('0'),f(X1_iProver_f_1))
| ~ 'E'(s('0'),f(X0_iProver_f_1))
| ~ iLEQ(suc(X3_iProver_f_1),suc(X2_iProver_f_1))
| ~ iLEQ(suc(X2_iProver_f_1),suc(X0_iProver_f_1))
| ~ iLEQ(suc(X0_iProver_f_1),suc(X1_iProver_f_1))
| ~ 'E'(s('0'),f(suc(X3_iProver_f_1)))
| ~ 'E'(s('0'),f(suc(X2_iProver_f_1)))
| ~ 'E'(s('0'),f(suc(X1_iProver_f_1)))
| ~ 'E'(s('0'),f(suc(X0_iProver_f_1))) ),
inference(renaming,[status(thm)],[c_961]) ).
tcf(c_1007,plain,
! [X0_iProver_f_1: iProver_f_1,X1_iProver_f_1: iProver_f_1] :
( ~ 'E'(s('0'),f(X1_iProver_f_1))
| ~ 'E'(s('0'),f(X0_iProver_f_1))
| ~ iLEQ(suc(X0_iProver_f_1),suc(X1_iProver_f_1))
| ~ iLEQ(suc(X0_iProver_f_1),suc(X0_iProver_f_1))
| ~ 'E'(s('0'),f(suc(X1_iProver_f_1)))
| ~ 'E'(s('0'),f(suc(X0_iProver_f_1))) ),
inference(factoring,[status(thm)],[c_962]) ).
tcf(c_1008,plain,
! [X0_iProver_f_1: iProver_f_1,X1_iProver_f_1: iProver_f_1] :
( ~ 'E'(s('0'),f(X1_iProver_f_1))
| ~ 'E'(s('0'),f(X0_iProver_f_1))
| ~ iLEQ(suc(X0_iProver_f_1),suc(X1_iProver_f_1))
| ~ 'E'(s('0'),f(suc(X0_iProver_f_1)))
| ~ 'E'(s('0'),f(suc(X1_iProver_f_1))) ),
inference(global_subsumption_just,[status(thm)],[c_1007,c_646,c_1007]) ).
tcf(c_1009,plain,
! [X0_iProver_f_1: iProver_f_1,X1_iProver_f_1: iProver_f_1] :
( ~ 'E'(s('0'),f(X1_iProver_f_1))
| ~ 'E'(s('0'),f(X0_iProver_f_1))
| ~ iLEQ(suc(X0_iProver_f_1),suc(X1_iProver_f_1))
| ~ 'E'(s('0'),f(suc(X1_iProver_f_1)))
| ~ 'E'(s('0'),f(suc(X0_iProver_f_1))) ),
inference(renaming,[status(thm)],[c_1008]) ).
tcf(c_1026,plain,
! [X0_iProver_f_1: iProver_f_1] :
( ~ 'E'(s('0'),f(X0_iProver_f_1))
| ~ 'E'(s('0'),f(suc(X0_iProver_f_1))) ),
inference(resolution,[status(thm)],[c_1009,c_646]) ).
tcf(c_1030,plain,
! [X0_iProver_f_1: iProver_f_1] :
( 'LE'(f(X0_iProver_f_1),s('0'))
| ~ 'E'(s('0'),f(X0_iProver_f_1))
| ~ 'LE'(f(suc(X0_iProver_f_1)),s(s('0'))) ),
inference(resolution,[status(thm)],[c_1026,c_643]) ).
tcf(c_1032,plain,
( ~ 'E'(s('0'),f(z))
| ~ 'LE'(f(suc(z)),s(s('0'))) ),
inference(resolution,[status(thm)],[c_1026,c_812]) ).
tcf(c_1035,plain,
( ~ 'E'(s('0'),f(z))
| ~ 'E'(s(s('0')),f(suc(z)))
| ~ 'LE'(f(suc(suc(z))),s(s(s('0')))) ),
inference(resolution,[status(thm)],[c_1032,c_937]) ).
tcf(c_1036,plain,
( 'E'(s(s('0')),f(suc(z)))
| ~ 'E'(s('0'),f(z))
| ~ 'LE'(f(suc(z)),s(s(s('0')))) ),
inference(resolution,[status(thm)],[c_1032,c_650]) ).
tcf(c_1040,plain,
( ~ 'E'('0',f(z))
| ~ 'E'(s('0'),f(suc(z)))
| ~ 'LE'(f(suc(suc(z))),s(s('0'))) ),
inference(resolution,[status(thm)],[c_1030,c_808]) ).
tcf(c_1054,plain,
( ~ 'E'('0',f(z))
| ~ 'E'(s('0'),f(suc(z)))
| ~ 'E'(s(s('0')),f(suc(suc(z))))
| ~ 'LE'(f(suc(suc(suc(z)))),s(s(s('0')))) ),
inference(resolution,[status(thm)],[c_1040,c_937]) ).
tcf(c_1055,plain,
( 'E'(s(s('0')),f(suc(suc(z))))
| ~ 'E'('0',f(z))
| ~ 'E'(s('0'),f(suc(z)))
| ~ 'LE'(f(suc(suc(z))),s(s(s('0')))) ),
inference(resolution,[status(thm)],[c_1040,c_650]) ).
tcf(c_1056,plain,
( 'E'(s(s('0')),f(suc(suc(z))))
| ~ 'E'('0',f(z))
| ~ 'LE'(f(suc(suc(z))),s(s(s('0')))) ),
inference(global_subsumption_just,[status(thm)],[c_1055,c_812,c_888,c_1055]) ).
tcf(c_1068,plain,
( ~ 'E'('0',f(z))
| ~ 'E'(s(s('0')),f(suc(z)))
| ~ 'LE'(f(suc(suc(z))),s(s(s('0')))) ),
inference(resolution,[status(thm)],[c_1056,c_933]) ).
tcf(c_1112,plain,
! [X0_iProver_f_1: iProver_f_1,X1_iProver_f_1: iProver_f_1,X2_iProver_f_1: iProver_f_1,X3_iProver_f_1: iProver_f_1] :
( ~ iLEQ(suc(X3_iProver_f_1),suc(X0_iProver_f_1))
| ~ iLEQ(suc(X1_iProver_f_1),suc(X2_iProver_f_1))
| ~ iLEQ(suc(X0_iProver_f_1),suc(X1_iProver_f_1))
| ~ iLEQ(suc(X0_iProver_f_1),suc(X0_iProver_f_1))
| ~ 'E'(s(s(s(s('0')))),f(X3_iProver_f_1))
| ~ 'E'(s(s(s(s('0')))),f(X2_iProver_f_1))
| ~ 'E'(s(s(s(s('0')))),f(X1_iProver_f_1))
| ~ 'E'(s(s(s(s('0')))),f(X0_iProver_f_1))
| ~ 'E'(s(s(s(s('0')))),f(suc(X3_iProver_f_1)))
| ~ 'E'(s(s(s(s('0')))),f(suc(X2_iProver_f_1)))
| ~ 'E'(s(s(s(s('0')))),f(suc(X1_iProver_f_1)))
| ~ 'E'(s(s(s(s('0')))),f(suc(X0_iProver_f_1))) ),
inference(factoring,[status(thm)],[c_640]) ).
tcf(c_1113,plain,
! [X0_iProver_f_1: iProver_f_1,X1_iProver_f_1: iProver_f_1,X2_iProver_f_1: iProver_f_1,X3_iProver_f_1: iProver_f_1] :
( ~ iLEQ(suc(X3_iProver_f_1),suc(X0_iProver_f_1))
| ~ iLEQ(suc(X1_iProver_f_1),suc(X2_iProver_f_1))
| ~ iLEQ(suc(X0_iProver_f_1),suc(X1_iProver_f_1))
| ~ 'E'(s(s(s(s('0')))),f(suc(X0_iProver_f_1)))
| ~ 'E'(s(s(s(s('0')))),f(suc(X1_iProver_f_1)))
| ~ 'E'(s(s(s(s('0')))),f(suc(X2_iProver_f_1)))
| ~ 'E'(s(s(s(s('0')))),f(suc(X3_iProver_f_1)))
| ~ 'E'(s(s(s(s('0')))),f(X0_iProver_f_1))
| ~ 'E'(s(s(s(s('0')))),f(X1_iProver_f_1))
| ~ 'E'(s(s(s(s('0')))),f(X2_iProver_f_1))
| ~ 'E'(s(s(s(s('0')))),f(X3_iProver_f_1)) ),
inference(global_subsumption_just,[status(thm)],[c_1112,c_657,c_1112]) ).
tcf(c_1114,plain,
! [X0_iProver_f_1: iProver_f_1,X1_iProver_f_1: iProver_f_1,X2_iProver_f_1: iProver_f_1,X3_iProver_f_1: iProver_f_1] :
( ~ iLEQ(suc(X3_iProver_f_1),suc(X0_iProver_f_1))
| ~ iLEQ(suc(X1_iProver_f_1),suc(X2_iProver_f_1))
| ~ iLEQ(suc(X0_iProver_f_1),suc(X1_iProver_f_1))
| ~ 'E'(s(s(s(s('0')))),f(X3_iProver_f_1))
| ~ 'E'(s(s(s(s('0')))),f(X2_iProver_f_1))
| ~ 'E'(s(s(s(s('0')))),f(X1_iProver_f_1))
| ~ 'E'(s(s(s(s('0')))),f(X0_iProver_f_1))
| ~ 'E'(s(s(s(s('0')))),f(suc(X3_iProver_f_1)))
| ~ 'E'(s(s(s(s('0')))),f(suc(X2_iProver_f_1)))
| ~ 'E'(s(s(s(s('0')))),f(suc(X1_iProver_f_1)))
| ~ 'E'(s(s(s(s('0')))),f(suc(X0_iProver_f_1))) ),
inference(renaming,[status(thm)],[c_1113]) ).
tcf(c_1181,plain,
! [X0_iProver_f_1: iProver_f_1,X1_iProver_f_1: iProver_f_1] :
( ~ iLEQ(suc(X0_iProver_f_1),suc(X1_iProver_f_1))
| ~ iLEQ(suc(X0_iProver_f_1),suc(X0_iProver_f_1))
| ~ 'E'(s(s(s(s('0')))),f(X1_iProver_f_1))
| ~ 'E'(s(s(s(s('0')))),f(X0_iProver_f_1))
| ~ 'E'(s(s(s(s('0')))),f(suc(X1_iProver_f_1)))
| ~ 'E'(s(s(s(s('0')))),f(suc(X0_iProver_f_1))) ),
inference(factoring,[status(thm)],[c_1114]) ).
tcf(c_1182,plain,
! [X0_iProver_f_1: iProver_f_1,X1_iProver_f_1: iProver_f_1] :
( ~ iLEQ(suc(X0_iProver_f_1),suc(X1_iProver_f_1))
| ~ 'E'(s(s(s(s('0')))),f(suc(X0_iProver_f_1)))
| ~ 'E'(s(s(s(s('0')))),f(suc(X1_iProver_f_1)))
| ~ 'E'(s(s(s(s('0')))),f(X0_iProver_f_1))
| ~ 'E'(s(s(s(s('0')))),f(X1_iProver_f_1)) ),
inference(global_subsumption_just,[status(thm)],[c_1181,c_657,c_1181]) ).
tcf(c_1183,plain,
! [X0_iProver_f_1: iProver_f_1,X1_iProver_f_1: iProver_f_1] :
( ~ iLEQ(suc(X0_iProver_f_1),suc(X1_iProver_f_1))
| ~ 'E'(s(s(s(s('0')))),f(X1_iProver_f_1))
| ~ 'E'(s(s(s(s('0')))),f(X0_iProver_f_1))
| ~ 'E'(s(s(s(s('0')))),f(suc(X1_iProver_f_1)))
| ~ 'E'(s(s(s(s('0')))),f(suc(X0_iProver_f_1))) ),
inference(renaming,[status(thm)],[c_1182]) ).
tcf(c_1196,plain,
! [X0_iProver_f_1: iProver_f_1] :
( ~ 'E'(s(s(s(s('0')))),f(X0_iProver_f_1))
| ~ 'E'(s(s(s(s('0')))),f(suc(X0_iProver_f_1))) ),
inference(resolution,[status(thm)],[c_1183,c_657]) ).
tcf(c_1200,plain,
! [X0_iProver_f_1: iProver_f_1] :
( 'LE'(f(X0_iProver_f_1),s(s(s(s('0')))))
| ~ 'E'(s(s(s(s('0')))),f(X0_iProver_f_1)) ),
inference(resolution,[status(thm)],[c_1196,c_637]) ).
tcf(c_1202,plain,
! [X0_iProver_f_1: iProver_f_1] : 'LE'(f(X0_iProver_f_1),s(s(s(s('0'))))),
inference(global_subsumption_just,[status(thm)],[c_1200,c_638,c_1200]) ).
tcf(c_1231,plain,
! [X0_iProver_f_1: iProver_f_1,X1_iProver_f_1: iProver_f_1,X2_iProver_f_1: iProver_f_1,X3_iProver_f_1: iProver_f_1] :
( ~ iLEQ(suc(X2_iProver_f_1),suc(X3_iProver_f_1))
| ~ iLEQ(suc(X1_iProver_f_1),suc(X2_iProver_f_1))
| ~ iLEQ(suc(X0_iProver_f_1),suc(X1_iProver_f_1))
| ~ iLEQ(suc(X0_iProver_f_1),suc(X0_iProver_f_1))
| ~ 'E'(s(s(s('0'))),f(X3_iProver_f_1))
| ~ 'E'(s(s(s('0'))),f(X2_iProver_f_1))
| ~ 'E'(s(s(s('0'))),f(X1_iProver_f_1))
| ~ 'E'(s(s(s('0'))),f(X0_iProver_f_1))
| ~ 'E'(s(s(s('0'))),f(suc(X3_iProver_f_1)))
| ~ 'E'(s(s(s('0'))),f(suc(X2_iProver_f_1)))
| ~ 'E'(s(s(s('0'))),f(suc(X1_iProver_f_1)))
| ~ 'E'(s(s(s('0'))),f(suc(X0_iProver_f_1))) ),
inference(factoring,[status(thm)],[c_652]) ).
tcf(c_1232,plain,
! [X0_iProver_f_1: iProver_f_1,X1_iProver_f_1: iProver_f_1,X2_iProver_f_1: iProver_f_1,X3_iProver_f_1: iProver_f_1] :
( ~ iLEQ(suc(X2_iProver_f_1),suc(X3_iProver_f_1))
| ~ iLEQ(suc(X1_iProver_f_1),suc(X2_iProver_f_1))
| ~ iLEQ(suc(X0_iProver_f_1),suc(X1_iProver_f_1))
| ~ 'E'(s(s(s('0'))),f(suc(X0_iProver_f_1)))
| ~ 'E'(s(s(s('0'))),f(suc(X1_iProver_f_1)))
| ~ 'E'(s(s(s('0'))),f(suc(X2_iProver_f_1)))
| ~ 'E'(s(s(s('0'))),f(suc(X3_iProver_f_1)))
| ~ 'E'(s(s(s('0'))),f(X0_iProver_f_1))
| ~ 'E'(s(s(s('0'))),f(X1_iProver_f_1))
| ~ 'E'(s(s(s('0'))),f(X2_iProver_f_1))
| ~ 'E'(s(s(s('0'))),f(X3_iProver_f_1)) ),
inference(global_subsumption_just,[status(thm)],[c_1231,c_644,c_1231]) ).
tcf(c_1233,plain,
! [X0_iProver_f_1: iProver_f_1,X1_iProver_f_1: iProver_f_1,X2_iProver_f_1: iProver_f_1,X3_iProver_f_1: iProver_f_1] :
( ~ iLEQ(suc(X2_iProver_f_1),suc(X3_iProver_f_1))
| ~ iLEQ(suc(X1_iProver_f_1),suc(X2_iProver_f_1))
| ~ iLEQ(suc(X0_iProver_f_1),suc(X1_iProver_f_1))
| ~ 'E'(s(s(s('0'))),f(X3_iProver_f_1))
| ~ 'E'(s(s(s('0'))),f(X2_iProver_f_1))
| ~ 'E'(s(s(s('0'))),f(X1_iProver_f_1))
| ~ 'E'(s(s(s('0'))),f(X0_iProver_f_1))
| ~ 'E'(s(s(s('0'))),f(suc(X3_iProver_f_1)))
| ~ 'E'(s(s(s('0'))),f(suc(X2_iProver_f_1)))
| ~ 'E'(s(s(s('0'))),f(suc(X1_iProver_f_1)))
| ~ 'E'(s(s(s('0'))),f(suc(X0_iProver_f_1))) ),
inference(renaming,[status(thm)],[c_1232]) ).
tcf(c_1257,plain,
! [X0_iProver_f_1: iProver_f_1,X1_iProver_f_1: iProver_f_1] :
( ~ iLEQ(suc(X0_iProver_f_1),suc(X1_iProver_f_1))
| ~ iLEQ(suc(X0_iProver_f_1),suc(X0_iProver_f_1))
| ~ 'E'(s(s(s('0'))),f(X1_iProver_f_1))
| ~ 'E'(s(s(s('0'))),f(X0_iProver_f_1))
| ~ 'E'(s(s(s('0'))),f(suc(X1_iProver_f_1)))
| ~ 'E'(s(s(s('0'))),f(suc(X0_iProver_f_1))) ),
inference(factoring,[status(thm)],[c_1233]) ).
tcf(c_1258,plain,
! [X0_iProver_f_1: iProver_f_1,X1_iProver_f_1: iProver_f_1] :
( ~ iLEQ(suc(X0_iProver_f_1),suc(X1_iProver_f_1))
| ~ 'E'(s(s(s('0'))),f(suc(X0_iProver_f_1)))
| ~ 'E'(s(s(s('0'))),f(suc(X1_iProver_f_1)))
| ~ 'E'(s(s(s('0'))),f(X0_iProver_f_1))
| ~ 'E'(s(s(s('0'))),f(X1_iProver_f_1)) ),
inference(global_subsumption_just,[status(thm)],[c_1257,c_644,c_1257]) ).
tcf(c_1259,plain,
! [X0_iProver_f_1: iProver_f_1,X1_iProver_f_1: iProver_f_1] :
( ~ iLEQ(suc(X0_iProver_f_1),suc(X1_iProver_f_1))
| ~ 'E'(s(s(s('0'))),f(X1_iProver_f_1))
| ~ 'E'(s(s(s('0'))),f(X0_iProver_f_1))
| ~ 'E'(s(s(s('0'))),f(suc(X1_iProver_f_1)))
| ~ 'E'(s(s(s('0'))),f(suc(X0_iProver_f_1))) ),
inference(renaming,[status(thm)],[c_1258]) ).
tcf(c_1268,plain,
! [X0_iProver_f_1: iProver_f_1] :
( ~ 'E'(s(s(s('0'))),f(X0_iProver_f_1))
| ~ 'E'(s(s(s('0'))),f(suc(X0_iProver_f_1))) ),
inference(resolution,[status(thm)],[c_1259,c_644]) ).
tcf(c_1272,plain,
! [X0_iProver_f_1: iProver_f_1] :
( 'LE'(f(X0_iProver_f_1),s(s(s('0'))))
| ~ 'E'(s(s(s('0'))),f(X0_iProver_f_1))
| ~ 'LE'(f(suc(X0_iProver_f_1)),s(s(s(s('0'))))) ),
inference(resolution,[status(thm)],[c_1268,c_645]) ).
tcf(c_1274,plain,
! [X0_iProver_f_1: iProver_f_1] :
( 'LE'(f(X0_iProver_f_1),s(s(s('0'))))
| ~ 'LE'(f(suc(X0_iProver_f_1)),s(s(s(s('0'))))) ),
inference(global_subsumption_just,[status(thm)],[c_1272,c_647,c_1202,c_1272]) ).
tcf(c_1285,plain,
! [X0_iProver_f_1: iProver_f_1] : 'LE'(f(X0_iProver_f_1),s(s(s('0')))),
inference(forward_subsumption_resolution,[status(thm)],[c_1274,c_1202]) ).
tcf(c_1287,plain,
'LE'(f(z),s(s(s('0')))),
inference(instantiation,[status(thm)],[c_1285]) ).
tcf(c_1290,plain,
( ~ 'E'('0',f(z))
| ~ 'E'(s(s('0')),f(suc(z))) ),
inference(resolution,[status(thm)],[c_1285,c_1068]) ).
tcf(c_1291,plain,
( ~ 'E'(s('0'),f(z))
| ~ 'E'(s(s('0')),f(suc(z))) ),
inference(resolution,[status(thm)],[c_1285,c_1035]) ).
tcf(c_1292,plain,
~ 'E'(s(s('0')),f(suc(z))),
inference(global_subsumption_just,[status(thm)],[c_1290,c_663,c_666,c_710,c_934,c_1287,c_1291,c_1290]) ).
tcf(c_1294,plain,
( ~ 'E'('0',f(z))
| ~ 'E'(s('0'),f(suc(z)))
| ~ 'E'(s(s('0')),f(suc(suc(z)))) ),
inference(resolution,[status(thm)],[c_1285,c_1054]) ).
tcf(c_1296,plain,
( 'LE'(f(z),s(s('0')))
| ~ 'LE'(f(suc(z)),s(s(s('0')))) ),
inference(resolution,[status(thm)],[c_1292,c_653]) ).
tcf(c_1297,plain,
( ~ 'E'(s('0'),f(z))
| ~ 'LE'(f(suc(z)),s(s(s('0')))) ),
inference(resolution,[status(thm)],[c_1292,c_1036]) ).
tcf(c_1302,plain,
'LE'(f(z),s(s('0'))),
inference(forward_subsumption_resolution,[status(thm)],[c_1296,c_1285]) ).
tcf(c_1307,plain,
~ 'E'(s('0'),f(z)),
inference(forward_subsumption_resolution,[status(thm)],[c_1297,c_1285]) ).
tcf(c_1313,plain,
( 'LE'(f(suc(z)),s(s('0')))
| ~ 'E'('0',f(z))
| ~ 'E'(s('0'),f(suc(z)))
| ~ 'LE'(f(suc(suc(z))),s(s(s('0')))) ),
inference(resolution,[status(thm)],[c_1294,c_653]) ).
tcf(c_1314,plain,
( ~ 'E'(s('0'),f(suc(z)))
| ~ 'LE'(f(suc(suc(z))),s(s(s('0')))) ),
inference(global_subsumption_just,[status(thm)],[c_1313,c_81,c_658,c_663,c_1056,c_1294,c_1302,c_1307]) ).
tcf(c_1319,plain,
~ 'E'(s('0'),f(suc(z))),
inference(forward_subsumption_resolution,[status(thm)],[c_1314,c_1285]) ).
tcf(c_1325,plain,
~ 'LE'(f(suc(z)),s(s('0'))),
inference(resolution,[status(thm)],[c_1319,c_812]) ).
tcf(c_1329,plain,
( 'E'(s(s('0')),f(suc(z)))
| ~ 'LE'(f(suc(z)),s(s(s('0')))) ),
inference(resolution,[status(thm)],[c_1325,c_650]) ).
tcf(c_1330,plain,
~ 'LE'(f(suc(z)),s(s(s('0')))),
inference(global_subsumption_just,[status(thm)],[c_1329,c_81,c_658,c_663,c_811,c_886,c_1292,c_1302,c_1307,c_1319]) ).
tcf(c_1333,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1330,c_1285]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SYO689-1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Fri Sep 25 03:24:11 UTC 2026
% 0.02/0.29 % CPUTime :
% 0.02/0.29 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.02/0.31 Running first-order theorem proving
% 0.02/0.31 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/0.32
% 0.02/0.32 % ======== iProver multi-core TPTP/SMT =========
% 0.02/0.32
% 0.02/0.32 % Detected problem language: tptp
% 0.06/0.33 % Proving...
% 1.94/0.95 % SZS status Started for theBenchmark.p
% 1.94/0.95 % SZS status Unsatisfiable for theBenchmark.p
% 1.94/0.95
% 1.94/0.95 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.94/0.95
% 1.94/0.95 % ------ iProver source info
% 1.94/0.95
% 1.94/0.95 % git: date: 2026-07-19 20:42:38 +0200
% 1.94/0.95 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.94/0.95 % git: non_committed_changes: false
% 1.94/0.95
% 1.94/0.95 % ------ Parsing...% successful
% 1.94/0.95
% 1.94/0.95
% 1.94/0.95 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.94/0.95
% 1.94/0.95 % ------ Preprocessing... sf_s rm: 1 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.94/0.95
% 1.94/0.95 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.94/0.95 % ------ Proving...
% 1.94/0.95 % ------ Problem Properties
% 1.94/0.95
% 1.94/0.95 %
% 1.94/0.95 % clauses 21
% 1.94/0.95 % conjectures 0
% 1.94/0.95 % EPR 0
% 1.94/0.95 % Horn 11
% 1.94/0.95 % unary 1
% 1.94/0.95 % binary 2
% 1.94/0.95 % lits 129
% 1.94/0.95 % lits eq 0
% 1.94/0.95 % fd_pure 0
% 1.94/0.95 % fd_pseudo 0
% 1.94/0.95 % fd_cond 0
% 1.94/0.95 % fd_pseudo_cond 0
% 1.94/0.95 % AC symbols 0
% 1.94/0.95
% 1.94/0.95 % ------ Input Options Time Limit: Unbounded
% 1.94/0.95
% 1.94/0.95
% 1.94/0.95 % ------
% 1.94/0.95 % Current options:
% 1.94/0.95 % ------
% 1.94/0.95
% 1.94/0.95
% 1.94/0.95 %
% 1.94/0.95
% 1.94/0.95 % ------ Proving...
% 1.94/0.95 %
% 1.94/0.95
% 1.94/0.95 % SZS status Unsatisfiable for theBenchmark.p
% 1.94/0.95
% 1.94/0.95 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.94/0.95
% 1.94/0.95
%------------------------------------------------------------------------------