%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO646-1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : 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 09:45:05 AM UTC 2026
% Result : Unsatisfiable 109.51s 60.95s
% Output : Refutation 110.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 7
% Syntax : Number of formulae : 72 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 660 ( 11 equ; 0 cnn)
% Maximal formula atoms : 34 ( 9 avg)
% Number of connectives : 3722 ( 510 ~; 566 |; 0 &;2646 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 44 ( 15 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 190 ( 0 ^; 190 !; 0 ?; 190 :)
% Comments :
%------------------------------------------------------------------------------
thf('E_decl',type,
'E': $i > $i > $o ).
thf(f_decl,type,
f: $i > $i ).
thf(suc_decl,type,
suc: $i > $i ).
thf(iLEQ_decl,type,
iLEQ: $i > $i > $o ).
thf('0_decl',type,
'0': $i ).
thf(151,axiom,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1548) ).
thf(547,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(548,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(cnf,[status(esa)],[547]) ).
thf(137,axiom,
! [A: $i] : ( A @ f @ ( '0' @ 'E' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1543) ).
thf(520,plain,
! [A: $i] : ( A @ f @ ( '0' @ 'E' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(743,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ $true
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[548,520]) ).
thf(744,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[743]) ).
thf(124,axiom,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1558) ).
thf(494,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)],[124]) ).
thf(495,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
inference(cnf,[status(esa)],[494]) ).
thf(741,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[495,520]) ).
thf(742,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[741]) ).
thf(243,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_891) ).
thf(731,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(732,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(cnf,[status(esa)],[731]) ).
thf(89672,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( E @ suc @ iLEQ ) )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( E @ suc @ ( D @ suc @ iLEQ ) )
| ~ $true
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(rewrite,[status(thm)],[732,520]) ).
thf(89673,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( E @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(simp,[status(thm)],[89672]) ).
thf(89700,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( E @ suc @ ( D @ suc @ iLEQ ) )
!= ( A @ suc @ ( C @ suc @ iLEQ ) ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(eqfactor_ordered,[status(thm)],[89673]) ).
thf(89705,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) ) ),
inference(pattern_uni,[status(thm)],[89700:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(89712,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) ) ),
inference(simp,[status(thm)],[89705]) ).
thf(89738,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ( ( C @ suc @ ( B @ suc @ iLEQ ) )
!= ( A @ suc @ ( C @ suc @ iLEQ ) ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) ) ),
inference(eqfactor_ordered,[status(thm)],[89712]) ).
thf(89743,plain,
! [A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(pattern_uni,[status(thm)],[89738:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(89748,plain,
! [A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(simp,[status(thm)],[89743]) ).
thf(89750,plain,
! [B: $i,A: $i] :
( ( ( A @ suc @ ( A @ suc @ iLEQ ) )
!= ( B @ suc @ ( B @ suc @ iLEQ ) ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ $true
| ( A @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[742,89748]) ).
thf(89751,plain,
! [B: $i,A: $i] :
( ( ( A @ suc @ ( A @ suc @ iLEQ ) )
!= ( B @ suc @ ( B @ suc @ iLEQ ) ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[89750]) ).
thf(89752,plain,
! [A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[89751:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(89756,plain,
! [A: $i] : ( A @ suc @ f @ ( A @ f @ 'E' ) ),
inference(simp,[status(thm)],[89752]) ).
thf(89771,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ $true ),
inference(rewrite,[status(thm)],[744,89756]) ).
thf(89772,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[89771]) ).
thf(93,axiom,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_806) ).
thf(432,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(433,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(cnf,[status(esa)],[432]) ).
thf(87864,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ $true
| ~ $true
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ $true
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ $true ),
inference(rewrite,[status(thm)],[433,520]) ).
thf(87865,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[87864]) ).
thf(31,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( E @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( E @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1238) ).
thf(308,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( E @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( E @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(309,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( E @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( E @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(cnf,[status(esa)],[308]) ).
thf(750,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( E @ suc @ suc @ f @ ( E @ f @ 'E' ) )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ $true
| ~ $true
| ~ $true
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( E @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ $true
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ $true
| ~ $true
| ~ $true
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ $true
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ $true ),
inference(rewrite,[status(thm)],[309,520]) ).
thf(751,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( E @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[750]) ).
thf(811,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( D @ suc @ ( E @ suc @ iLEQ ) )
!= ( A @ suc @ ( B @ suc @ iLEQ ) ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( E @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(eqfactor_ordered,[status(thm)],[751]) ).
thf(819,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[811:[bind(A,$thf( D )),bind(B,$thf( E ))]]) ).
thf(830,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[819]) ).
thf(876,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ( ( C @ suc @ ( A @ suc @ iLEQ ) )
!= ( B @ suc @ ( C @ suc @ iLEQ ) ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) ) ),
inference(eqfactor_ordered,[status(thm)],[830]) ).
thf(885,plain,
! [A: $i] :
( ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[876:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(888,plain,
! [A: $i] :
( ~ ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[885]) ).
thf(88283,plain,
! [B: $i,A: $i] :
( ( ( A @ suc @ ( A @ suc @ iLEQ ) )
!= ( B @ suc @ ( B @ suc @ iLEQ ) ) )
| ~ $true
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[87865,888]) ).
thf(88284,plain,
! [B: $i,A: $i] :
( ( ( A @ suc @ ( A @ suc @ iLEQ ) )
!= ( B @ suc @ ( B @ suc @ iLEQ ) ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[88283]) ).
thf(88285,plain,
! [A: $i] :
( ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[88284:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(88701,plain,
! [A: $i] :
( ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[88285]) ).
thf(89761,plain,
! [A: $i] :
( ~ $true
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(rewrite,[status(thm)],[88701,89756]) ).
thf(89762,plain,
! [A: $i] :
~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) ),
inference(simp,[status(thm)],[89761]) ).
thf(89784,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| $false ),
inference(rewrite,[status(thm)],[89772,89762]) ).
thf(89785,plain,
! [A: $i] : ( A @ suc @ ( A @ suc @ iLEQ ) ),
inference(simp,[status(thm)],[89784]) ).
thf(116,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ( E @ suc @ suc @ f @ ( E @ f @ 'E' ) )
| ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_0) ).
thf(478,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ( E @ suc @ suc @ f @ ( E @ f @ 'E' ) )
| ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(479,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ( E @ suc @ suc @ f @ ( E @ f @ 'E' ) )
| ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(cnf,[status(esa)],[478]) ).
thf(89317,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ( E @ suc @ suc @ f @ ( E @ f @ 'E' ) )
| ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ $true
| ~ $true
| ~ ( E @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ $true
| ~ $true
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ $true
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(rewrite,[status(thm)],[479,520]) ).
thf(89318,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ( E @ suc @ suc @ f @ ( E @ f @ 'E' ) )
| ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( E @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[89317]) ).
thf(89773,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ( E @ suc @ suc @ f @ ( E @ f @ 'E' ) )
| ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ $true
| ~ $true
| ~ ( E @ suc @ ( C @ suc @ iLEQ ) )
| ~ $true
| ~ $true
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ $true ),
inference(rewrite,[status(thm)],[89318,89756]) ).
thf(89774,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ( E @ suc @ suc @ f @ ( E @ f @ 'E' ) )
| ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( E @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(simp,[status(thm)],[89773]) ).
thf(89919,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( $false
| $false
| $false
| $false
| $false
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( E @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(rewrite,[status(thm)],[89774,89762]) ).
thf(89920,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( E @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(simp,[status(thm)],[89919]) ).
thf(89930,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ suc @ ( A @ suc @ iLEQ ) )
!= ( E @ suc @ ( F @ suc @ iLEQ ) ) )
| ~ $true
| ~ ( F @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) ) ),
inference(paramod_ordered,[status(thm)],[89785,89920]) ).
thf(89931,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ suc @ ( A @ suc @ iLEQ ) )
!= ( E @ suc @ ( F @ suc @ iLEQ ) ) )
| ~ ( F @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) ) ),
inference(simp,[status(thm)],[89930]) ).
thf(89932,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) ) ),
inference(pattern_uni,[status(thm)],[89931:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( A ))]]) ).
thf(89966,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( B @ suc @ ( A @ suc @ iLEQ ) )
!= ( C @ suc @ ( B @ suc @ iLEQ ) ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) ) ),
inference(eqfactor_ordered,[status(thm)],[89932]) ).
thf(89969,plain,
! [B: $i,A: $i] :
( ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(pattern_uni,[status(thm)],[89966:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(89972,plain,
! [B: $i,A: $i] :
( ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(simp,[status(thm)],[89969]) ).
thf(89978,plain,
! [B: $i,A: $i] :
( ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ $true ),
inference(rewrite,[status(thm)],[89972,89785]) ).
thf(89979,plain,
! [B: $i,A: $i] :
~ ( A @ suc @ ( B @ suc @ iLEQ ) ),
inference(simp,[status(thm)],[89978]) ).
thf(89980,plain,
$false,
inference(rewrite,[status(thm)],[89785,89979]) ).
thf(89981,plain,
$false,
inference(simp,[status(thm)],[89980]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO646-1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.15/0.40 % Computer : n009.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Sat Sep 26 19:41:59 UTC 2026
% 0.15/0.40 % CPUTime :
% 0.15/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.90/1.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.75/1.53 % [INFO] Parsing done (528ms).
% 2.75/1.54 % [INFO] Running in sequential loop mode.
% 3.97/1.96 % [INFO] eprover registered as external prover.
% 3.97/1.96 % [INFO] Scanning for conjecture ...
% 4.69/2.15 % [INFO] 247 axioms and no conjecture found.
% 7.05/3.12 % [INFO] Problem is propositional (TPTP CNF).
% 7.27/3.15 % [INFO] Type checking passed.
% 7.27/3.16 % [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 ...
% 109.51/60.95 % [INFO] Killing All external provers ...
% 109.51/60.95 % Time passed: 60398ms (effective reasoning time: 59398ms)
% 109.51/60.95 % Axioms used in derivation (7): clause_1238, clause_1548, clause_1543, clause_0, clause_806, clause_1558, clause_891
% 109.51/60.95 % No. of inferences in proof: 72
% 109.51/60.95 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 60398 ms resp. 59398 ms w/o parsing
% 110.01/61.06 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 110.01/61.06 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------