TSTP Solution File: SYO634-1 by Leo-III---1.7.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SYO634-1 : TPTP v8.2.0. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 08:57:46 EDT 2024
% Result : Unsatisfiable 5.12s 2.10s
% Output : Refutation 5.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 29
% Syntax : Number of formulae : 53 ( 9 unt; 6 typ; 0 def)
% Number of atoms : 283 ( 0 equ; 0 cnn)
% Maximal formula atoms : 11 ( 6 avg)
% Number of connectives : 3432 ( 238 ~; 236 |; 0 &;2958 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 38 ( 24 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 278 ( 0 ^ 278 !; 0 ?; 278 :)
% Comments :
%------------------------------------------------------------------------------
thf('\'E\'_type',type,
'\'E\'': $i > $i > $o ).
thf(f_type,type,
f: $i > $i ).
thf(s_type,type,
s: $i > $i ).
thf('\'0\'_type',type,
'\'0\'': $i ).
thf('\'LEQ\'_type',type,
'\'LEQ\'': $i > $i > $o ).
thf('\'AP\'_type',type,
'\'AP\'': $i > $i > $i ).
thf(21,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ E ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) )
| ( '\'LEQ\'' @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ F ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_22_21) ).
thf(61,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ E ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) )
| ( '\'LEQ\'' @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ F ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(23,axiom,
! [B: $i,A: $i] : ( '\'LEQ\'' @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) @ A ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_19_23) ).
thf(65,plain,
! [B: $i,A: $i] : ( '\'LEQ\'' @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) @ A ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(17,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ E ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ F ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ G ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ H ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( f @ I ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ J ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ K ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3_17) ).
thf(53,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ E ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ F ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ G ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ H ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( f @ I ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ J ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ K ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(15,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ E ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ F ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ G ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) )
| ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) ) @ H ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_18_15) ).
thf(49,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ E ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ F ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ G ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) )
| ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) ) @ H ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(9,axiom,
! [A: $i] : ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_17_09) ).
thf(39,plain,
! [A: $i] : ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(7,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ E ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ F ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ G ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) )
| ( '\'LEQ\'' @ ( '\'AP\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ H ) @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) ) @ H ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5_07) ).
thf(35,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ E ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ F ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ G ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) )
| ( '\'LEQ\'' @ ( '\'AP\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ H ) @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) ) @ H ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(22,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ E ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ F ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ G ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ H ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( f @ I ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ J ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) )
| ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) ) @ K ) ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_10_22) ).
thf(63,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ E ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ F ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ G ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ H ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( f @ I ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ J ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) )
| ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) ) @ K ) ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) )
| ( '\'LEQ\'' @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7_05) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) )
| ( '\'LEQ\'' @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(16,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) )
| ( '\'LEQ\'' @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ E ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2_16) ).
thf(51,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) )
| ( '\'LEQ\'' @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ E ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_12_14) ).
thf(47,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(11,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ E ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ F ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ G ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( f @ H ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ I ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) )
| ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) ) @ J ) ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_8_11) ).
thf(42,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ E ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ F ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ G ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( f @ H ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ I ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) )
| ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) ) @ J ) ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_21_01) ).
thf(24,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ E ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ F ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) )
| ( '\'LEQ\'' @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ G ) @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) ) @ G ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_20_08) ).
thf(37,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ E ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ F ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) )
| ( '\'LEQ\'' @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ G ) @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) ) @ G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(13,axiom,
! [B: $i,A: $i] : ( '\'LEQ\'' @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) @ A ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6_13) ).
thf(46,plain,
! [B: $i,A: $i] : ( '\'LEQ\'' @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) @ A ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(19,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ E ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ F ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( f @ G ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ H ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) )
| ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) ) @ I ) ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_0_19) ).
thf(57,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ E ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ F ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( f @ G ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ H ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) )
| ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) ) @ I ) ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(4,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ E ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ F ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( f @ G ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ H ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) )
| ( '\'LEQ\'' @ ( '\'AP\'' @ ( s @ ( s @ '\'0\'' ) ) @ I ) @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) ) @ I ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4_04) ).
thf(29,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ E ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ F ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( f @ G ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ H ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) )
| ( '\'LEQ\'' @ ( '\'AP\'' @ ( s @ ( s @ '\'0\'' ) ) @ I ) @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) ) @ I ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [A: $i] : ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_11_03) ).
thf(28,plain,
! [A: $i] : ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1_06) ).
thf(33,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(12,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ E ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ F ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) )
| ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) ) @ G ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_9_12) ).
thf(44,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ E ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ F ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) )
| ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) ) @ G ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(20,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ E ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_15_20) ).
thf(59,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ E ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(10,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ E ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ F ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ G ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( f @ H ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ I ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) )
| ( '\'LEQ\'' @ ( '\'AP\'' @ ( s @ '\'0\'' ) @ J ) @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) ) @ J ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_16_10) ).
thf(40,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ E ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ F ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ G ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( f @ H ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ I ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) )
| ( '\'LEQ\'' @ ( '\'AP\'' @ ( s @ '\'0\'' ) @ J ) @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) ) @ J ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(2,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ E ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ F ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ G ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ H ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( f @ I ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ J ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) )
| ( '\'LEQ\'' @ ( '\'AP\'' @ '\'0\'' @ K ) @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) ) @ K ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_14_02) ).
thf(26,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ E ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ F ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ G ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ H ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( f @ I ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ J ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) )
| ( '\'LEQ\'' @ ( '\'AP\'' @ '\'0\'' @ K ) @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) ) @ K ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(18,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) )
| ( '\'LEQ\'' @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) @ D ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_13_18) ).
thf(55,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) ) )
| ( '\'LEQ\'' @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ) @ D ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(66,plain,
$false,
inference(e,[status(thm)],[61,65,53,49,39,35,63,31,51,47,42,24,37,46,57,29,28,33,44,59,40,26,55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO634-1 : TPTP v8.2.0. Released v7.1.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n020.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon May 20 10:04:09 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.98/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.42/1.03 % [INFO] Parsing done (168ms).
% 1.42/1.04 % [INFO] Running in sequential loop mode.
% 1.93/1.27 % [INFO] eprover registered as external prover.
% 1.93/1.27 % [INFO] cvc4 registered as external prover.
% 1.93/1.27 % [INFO] Scanning for conjecture ...
% 2.19/1.32 % [INFO] 23 axioms and no conjecture found.
% 2.42/1.42 % [INFO] Problem is propositional (TPTP CNF).
% 2.42/1.42 % [INFO] Type checking passed.
% 2.42/1.43 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 5.12/2.09 % External prover 'e' found a proof!
% 5.12/2.09 % [INFO] Killing All external provers ...
% 5.12/2.09 % Time passed: 1571ms (effective reasoning time: 1049ms)
% 5.12/2.10 % Axioms used in derivation (23): clause_2_16, clause_7_05, clause_1_06, clause_3_17, clause_15_20, clause_6_13, clause_9_12, clause_22_21, clause_17_09, clause_18_15, clause_16_10, clause_20_08, clause_5_07, clause_0_19, clause_10_22, clause_4_04, clause_21_01, clause_14_02, clause_19_23, clause_13_18, clause_8_11, clause_11_03, clause_12_14
% 5.12/2.10 % No. of inferences in proof: 47
% 5.12/2.10 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1571 ms resp. 1049 ms w/o parsing
% 5.29/2.21 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.29/2.21 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------