TSTP Solution File: SYO664-1 by Leo-III-SAT---1.7.10
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : SYO664-1 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n027.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 7 11:05:29 EDT 2024
% Result : Unsatisfiable 56.39s 9.11s
% Output : Refutation 56.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 18
% Syntax : Number of formulae : 93 ( 12 unt; 8 typ; 0 def)
% Number of atoms : 412 ( 20 equ; 0 cnn)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 2092 ( 273 ~; 287 |; 0 &;1532 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 115 ( 0 ^ 115 !; 0 ?; 115 :)
% Comments :
%------------------------------------------------------------------------------
thf('\'E\'_type',type,
'\'E\'': $i > $i > $o ).
thf(s_type,type,
s: $i > $i ).
thf('\'0\'_type',type,
'\'0\'': $i ).
thf(f_type,type,
f: $i > $i ).
thf(suc_type,type,
suc: $i > $i ).
thf(iLEQ_type,type,
iLEQ: $i > $i > $o ).
thf('\'LE\'_type',type,
'\'LE\'': $i > $i > $o ).
thf(z_type,type,
z: $i ).
thf(10,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_83) ).
thf(28,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(29,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(cnf,[status(esa)],[28]) ).
thf(5,axiom,
! [A: $i] : ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_58) ).
thf(19,plain,
! [A: $i] : ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(649,plain,
! [A: $i] :
( ~ $true
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(rewrite,[status(thm)],[29,19]) ).
thf(650,plain,
! [A: $i] :
( ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(simp,[status(thm)],[649]) ).
thf(7,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_117) ).
thf(22,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(23,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(cnf,[status(esa)],[22]) ).
thf(654,plain,
! [B: $i,A: $i] :
( ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' )
| ( ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) )
!= ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ '\'0\'' ) ) ) ),
inference(paramod_ordered,[status(thm)],[650,23]) ).
thf(655,plain,
! [A: $i] :
( ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(pattern_uni,[status(thm)],[654:[bind(A,$thf( suc @ C )),bind(B,$thf( C ))]]) ).
thf(657,plain,
! [A: $i] :
( ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(simp,[status(thm)],[655]) ).
thf(2,axiom,
~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_70) ).
thf(13,plain,
~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(14,plain,
~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' ),
inference(polarity_switch,[status(thm)],[13]) ).
thf(741,plain,
! [A: $i] :
( ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( ( '\'LE\'' @ ( f @ A ) @ '\'0\'' )
!= ( '\'LE\'' @ ( f @ z ) @ '\'0\'' ) ) ),
inference(paramod_ordered,[status(thm)],[657,14]) ).
thf(742,plain,
( ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ z ) ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ z ) ) ) ),
inference(pattern_uni,[status(thm)],[741:[bind(A,$thf( z ))]]) ).
thf(3,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_20) ).
thf(15,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(16,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(cnf,[status(esa)],[15]) ).
thf(116,plain,
! [A: $i] :
( ~ $true
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(rewrite,[status(thm)],[16,19]) ).
thf(117,plain,
! [A: $i] :
( ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(simp,[status(thm)],[116]) ).
thf(8,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_94) ).
thf(24,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(25,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(cnf,[status(esa)],[24]) ).
thf(118,plain,
! [B: $i,A: $i] :
( ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' )
| ( ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) )
!= ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ) ),
inference(paramod_ordered,[status(thm)],[117,25]) ).
thf(119,plain,
! [A: $i] :
( ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(pattern_uni,[status(thm)],[118:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(366,plain,
! [A: $i] :
( ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( ( '\'LE\'' @ ( f @ A ) @ '\'0\'' )
!= ( '\'LE\'' @ ( f @ z ) @ '\'0\'' ) ) ),
inference(paramod_ordered,[status(thm)],[119,14]) ).
thf(367,plain,
( ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ z ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ z ) ) ),
inference(pattern_uni,[status(thm)],[366:[bind(A,$thf( z ))]]) ).
thf(651,plain,
! [B: $i,A: $i] :
( ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' )
| ( ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) )
!= ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ) ),
inference(paramod_ordered,[status(thm)],[650,25]) ).
thf(652,plain,
! [A: $i] :
( ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(pattern_uni,[status(thm)],[651:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(659,plain,
! [A: $i] :
( ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( ( '\'LE\'' @ ( f @ A ) @ '\'0\'' )
!= ( '\'LE\'' @ ( f @ z ) @ '\'0\'' ) ) ),
inference(paramod_ordered,[status(thm)],[652,14]) ).
thf(660,plain,
( ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ z ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ z ) ) ),
inference(pattern_uni,[status(thm)],[659:[bind(A,$thf( z ))]]) ).
thf(9,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_50) ).
thf(26,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(27,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(cnf,[status(esa)],[26]) ).
thf(1,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ E ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ E ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ E ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_37) ).
thf(11,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ E ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ E ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ E ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(12,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ E ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ E ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ E ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ E ) ) ) ),
inference(cnf,[status(esa)],[11]) ).
thf(97,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ E ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ E ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ E ) ) )
| ( ( iLEQ @ ( suc @ C ) @ ( suc @ E ) )
!= ( iLEQ @ ( suc @ D ) @ ( suc @ C ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[12]) ).
thf(100,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) ) ),
inference(pattern_uni,[status(thm)],[97:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( E )),bind(D,$thf( E ))]]) ).
thf(106,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) ) ),
inference(simp,[status(thm)],[100]) ).
thf(2134,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
!= ( iLEQ @ ( suc @ C ) @ ( suc @ C ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[106]) ).
thf(2139,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) ) ),
inference(pattern_uni,[status(thm)],[2134:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(2184,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(simp,[status(thm)],[2139]) ).
thf(4041,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( ( iLEQ @ ( suc @ A ) @ ( suc @ A ) )
!= ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[27,2184]) ).
thf(4042,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) ) ),
inference(pattern_uni,[status(thm)],[4041:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(4060,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) ) ),
inference(simp,[status(thm)],[4042]) ).
thf(4070,plain,
! [A: $i] :
( ( '\'E\'' @ '\'0\'' @ ( f @ z ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ z ) ) )
!= ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[660,4060]) ).
thf(4071,plain,
( ( '\'E\'' @ '\'0\'' @ ( f @ z ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ z ) ) ),
inference(pattern_uni,[status(thm)],[4070:[bind(A,$thf( z ))]]) ).
thf(4086,plain,
( ( '\'E\'' @ '\'0\'' @ ( f @ z ) )
| ( ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ z ) )
!= ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ z ) ) ) ),
inference(paramod_ordered,[status(thm)],[367,4071]) ).
thf(4087,plain,
'\'E\'' @ '\'0\'' @ ( f @ z ),
inference(pattern_uni,[status(thm)],[4086:[]]) ).
thf(6,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
thf(20,plain,
! [A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(21,plain,
! [A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(cnf,[status(esa)],[20]) ).
thf(4,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ E ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ E ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ E ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_66) ).
thf(17,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ E ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ E ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ E ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(18,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ E ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ E ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ E ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) ) ),
inference(cnf,[status(esa)],[17]) ).
thf(37,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ E ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ E ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ( ( iLEQ @ ( suc @ A ) @ ( suc @ E ) )
!= ( iLEQ @ ( suc @ C ) @ ( suc @ B ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[18]) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) ) ),
inference(pattern_uni,[status(thm)],[37:[bind(A,$thf( A )),bind(B,$thf( E )),bind(C,$thf( A ))]]) ).
thf(46,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) ) ),
inference(simp,[status(thm)],[40]) ).
thf(52,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
!= ( iLEQ @ ( suc @ A ) @ ( suc @ C ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[46]) ).
thf(55,plain,
! [A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) ) ),
inference(pattern_uni,[status(thm)],[52:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(58,plain,
! [A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(simp,[status(thm)],[55]) ).
thf(375,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( ( iLEQ @ ( suc @ A ) @ ( suc @ A ) )
!= ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[21,58]) ).
thf(376,plain,
! [A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[375:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(386,plain,
! [A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) ) ),
inference(simp,[status(thm)],[376]) ).
thf(4112,plain,
! [A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( ( '\'E\'' @ '\'0\'' @ ( f @ z ) )
!= ( '\'E\'' @ '\'0\'' @ ( f @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[4087,386]) ).
thf(4113,plain,
~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ z ) ) ),
inference(pattern_uni,[status(thm)],[4112:[bind(A,$thf( z ))]]) ).
thf(4136,plain,
( ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ z ) ) ) )
| $false ),
inference(rewrite,[status(thm)],[742,4113]) ).
thf(4137,plain,
'\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ z ) ) ),
inference(simp,[status(thm)],[4136]) ).
thf(4198,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ z ) ) ) )
!= ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4137,4060]) ).
thf(4199,plain,
~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ z ) ) ),
inference(pattern_uni,[status(thm)],[4198:[bind(A,$thf( suc @ z ))]]) ).
thf(121,plain,
! [B: $i,A: $i] :
( ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' )
| ( ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) )
!= ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ '\'0\'' ) ) ) ),
inference(paramod_ordered,[status(thm)],[117,23]) ).
thf(122,plain,
! [A: $i] :
( ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(pattern_uni,[status(thm)],[121:[bind(A,$thf( suc @ C )),bind(B,$thf( C ))]]) ).
thf(124,plain,
! [A: $i] :
( ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(simp,[status(thm)],[122]) ).
thf(555,plain,
! [A: $i] :
( ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( ( '\'LE\'' @ ( f @ A ) @ '\'0\'' )
!= ( '\'LE\'' @ ( f @ z ) @ '\'0\'' ) ) ),
inference(paramod_ordered,[status(thm)],[124,14]) ).
thf(556,plain,
( ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ z ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ z ) ) ) ),
inference(pattern_uni,[status(thm)],[555:[bind(A,$thf( z ))]]) ).
thf(588,plain,
( ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ z ) ) )
| ( ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ z ) ) )
!= ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ z ) ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[556]) ).
thf(590,plain,
( ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ z ) ) )
| ( ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ z ) ) )
!= ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ z ) ) ) ) ),
inference(simp,[status(thm)],[588]) ).
thf(4140,plain,
( $false
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ z ) ) ) ),
inference(rewrite,[status(thm)],[590,4113]) ).
thf(4141,plain,
'\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ z ) ),
inference(simp,[status(thm)],[4140]) ).
thf(4222,plain,
~ $true,
inference(rewrite,[status(thm)],[4199,4141]) ).
thf(4223,plain,
$false,
inference(simp,[status(thm)],[4222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SYO664-1 : TPTP v8.1.2. Released v7.3.0.
% 0.08/0.16 % Command : run_Leo-III %s %d
% 0.16/0.38 % Computer : n027.cluster.edu
% 0.16/0.38 % Model : x86_64 x86_64
% 0.16/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38 % Memory : 8042.1875MB
% 0.16/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38 % CPULimit : 300
% 0.16/0.38 % WCLimit : 300
% 0.16/0.38 % DateTime : Mon May 6 20:15:09 EDT 2024
% 0.16/0.38 % CPUTime :
% 0.93/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.06/1.01 % [INFO] Parsing done (143ms).
% 1.06/1.02 % [INFO] Running in sequential loop mode.
% 1.49/1.27 % [INFO] nitpick registered as external prover.
% 1.49/1.27 % [INFO] Scanning for conjecture ...
% 1.74/1.32 % [INFO] 10 axioms and no conjecture found.
% 1.84/1.40 % [INFO] Problem is propositional (TPTP CNF).
% 1.84/1.40 % [INFO] Type checking passed.
% 1.84/1.40 % [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 ...
% 56.39/9.10 % [INFO] Killing All external provers ...
% 56.39/9.11 % Time passed: 8606ms (effective reasoning time: 8083ms)
% 56.39/9.11 % Axioms used in derivation (10): clause_83, clause_20, clause_37, clause_58, clause_6, clause_70, clause_50, clause_66, clause_117, clause_94
% 56.39/9.11 % No. of inferences in proof: 85
% 56.39/9.11 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 8606 ms resp. 8083 ms w/o parsing
% 56.54/9.24 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 56.54/9.24 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------