TSTP Solution File: SYO633-1 by Leo-III-SAT---1.7.10
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : SYO633-1 : TPTP v8.1.2. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n006.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 11:05:27 EDT 2024
% Result : Unsatisfiable 10.38s 2.87s
% Output : Refutation 10.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 12
% Syntax : Number of formulae : 57 ( 14 unt; 5 typ; 0 def)
% Number of atoms : 170 ( 5 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 1180 ( 130 ~; 108 |; 0 &; 942 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 13 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 143 ( 0 ^ 143 !; 0 ?; 143 :)
% 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('\'AP\'_type',type,
'\'AP\'': $i > $i > $i ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ D ) ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4_12) ).
thf(32,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ D ) ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(33,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ D ) ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(cnf,[status(esa)],[32]) ).
thf(4,axiom,
! [A: $i] : ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6_04) ).
thf(20,plain,
! [A: $i] : ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [A: $i] : ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_8_05) ).
thf(21,plain,
! [A: $i] : ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1_10) ).
thf(28,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(cnf,[status(esa)],[28]) ).
thf(151,plain,
! [A: $i] :
( ~ $true
| ~ $true
| ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(rewrite,[status(thm)],[29,20,21]) ).
thf(152,plain,
! [A: $i] : ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(simp,[status(thm)],[151]) ).
thf(809,plain,
! [A: $i] :
( ~ $true
| ~ $true
| ~ $true
| ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(rewrite,[status(thm)],[33,20,21,152]) ).
thf(810,plain,
! [A: $i] : ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) ),
inference(simp,[status(thm)],[809]) ).
thf(9,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ E ) ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_12_09) ).
thf(26,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ E ) ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(27,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ E ) ) @ ( s @ '\'0\'' ) ) ),
inference(cnf,[status(esa)],[26]) ).
thf(442,plain,
! [B: $i,A: $i] :
( ~ $true
| ~ $true
| ~ $true
| ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ B ) ) @ ( s @ '\'0\'' ) ) ),
inference(rewrite,[status(thm)],[27,20,21,152]) ).
thf(443,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ B ) ) @ ( s @ '\'0\'' ) ) ),
inference(simp,[status(thm)],[442]) ).
thf(819,plain,
! [C: $i,B: $i,A: $i] :
( ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ C ) ) @ ( s @ '\'0\'' ) )
| ( ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
!= ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[810,443]) ).
thf(820,plain,
! [A: $i] : ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ A ) ) @ ( s @ '\'0\'' ) ),
inference(pattern_uni,[status(thm)],[819:[bind(A,$thf( E )),bind(B,$thf( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ E )),bind(C,$thf( C ))]]) ).
thf(831,plain,
! [A: $i] : ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ A ) ) @ ( s @ '\'0\'' ) ),
inference(simp,[status(thm)],[820]) ).
thf(7,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ E ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ F ) ) @ '\'0\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2_07) ).
thf(23,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ E ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ F ) ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(24,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ E ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ F ) ) @ '\'0\'' ) ),
inference(cnf,[status(esa)],[23]) ).
thf(395,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ $true
| ~ $true
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ '\'0\'' ) )
| ~ $true
| ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ C ) ) @ '\'0\'' ) ),
inference(rewrite,[status(thm)],[24,20,21,152]) ).
thf(396,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ C ) ) @ '\'0\'' ) ),
inference(simp,[status(thm)],[395]) ).
thf(3,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ E ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( f @ F ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5_03) ).
thf(18,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ E ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( f @ F ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(19,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ E ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( f @ F ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[18]) ).
thf(36,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ $true
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ D ) @ '\'0\'' )
| ~ $true ),
inference(rewrite,[status(thm)],[19,20,21]) ).
thf(37,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ D ) @ '\'0\'' ) ),
inference(simp,[status(thm)],[36]) ).
thf(155,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ $true
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(rewrite,[status(thm)],[37,152]) ).
thf(156,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(simp,[status(thm)],[155]) ).
thf(158,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(simp,[status(thm)],[156]) ).
thf(450,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ E ) @ '\'0\'' )
| ( ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ B ) ) @ ( s @ '\'0\'' ) )
!= ( '\'E\'' @ ( f @ D ) @ ( s @ '\'0\'' ) ) ) ),
inference(paramod_ordered,[status(thm)],[443,158]) ).
thf(451,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(pattern_uni,[status(thm)],[450:[bind(A,$thf( A )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ G )),bind(E,$thf( E ))]]) ).
thf(468,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(simp,[status(thm)],[451]) ).
thf(494,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ '\'0\'' )
| ( ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) )
!= ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[468]) ).
thf(505,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(pattern_uni,[status(thm)],[494:[bind(A,$thf( B ))]]) ).
thf(524,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(simp,[status(thm)],[505]) ).
thf(814,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ C ) @ '\'0\'' )
| ( ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
!= ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[810,524]) ).
thf(815,plain,
! [A: $i] :
~ ( '\'E\'' @ ( f @ A ) @ '\'0\'' ),
inference(pattern_uni,[status(thm)],[814:[bind(A,$thf( E )),bind(B,$thf( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ E )),bind(C,$thf( C ))]]) ).
thf(839,plain,
! [A: $i] :
~ ( '\'E\'' @ ( f @ A ) @ '\'0\'' ),
inference(simp,[status(thm)],[815]) ).
thf(840,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ '\'0\'' ) )
| $false ),
inference(rewrite,[status(thm)],[396,839]) ).
thf(841,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
inference(simp,[status(thm)],[840]) ).
thf(861,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
inference(simp,[status(thm)],[841]) ).
thf(919,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ( ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
!= ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[810,861]) ).
thf(920,plain,
! [A: $i] :
~ ( '\'E\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ),
inference(pattern_uni,[status(thm)],[919:[bind(A,$thf( E )),bind(B,$thf( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ E )),bind(C,$thf( C ))]]) ).
thf(945,plain,
! [A: $i] :
~ ( '\'E\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ),
inference(simp,[status(thm)],[920]) ).
thf(948,plain,
$false,
inference(rewrite,[status(thm)],[831,945]) ).
thf(949,plain,
$false,
inference(simp,[status(thm)],[948]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO633-1 : TPTP v8.1.2. Released v7.1.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon May 6 20:12:09 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.96/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.18/0.97 % [INFO] Parsing done (121ms).
% 1.18/0.98 % [INFO] Running in sequential loop mode.
% 1.66/1.17 % [INFO] nitpick registered as external prover.
% 1.66/1.18 % [INFO] Scanning for conjecture ...
% 1.66/1.21 % [INFO] 13 axioms and no conjecture found.
% 1.85/1.27 % [INFO] Problem is propositional (TPTP CNF).
% 1.85/1.27 % [INFO] Type checking passed.
% 2.01/1.27 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 10.38/2.86 % [INFO] Killing All external provers ...
% 10.38/2.86 % Time passed: 2337ms (effective reasoning time: 1881ms)
% 10.38/2.86 % Axioms used in derivation (7): clause_12_09, clause_4_12, clause_5_03, clause_2_07, clause_6_04, clause_1_10, clause_8_05
% 10.38/2.87 % No. of inferences in proof: 52
% 10.38/2.87 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2337 ms resp. 1881 ms w/o parsing
% 10.62/2.93 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.62/2.93 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------