%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO691-1.001 : 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 : n004.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 09:45:13 AM UTC 2026
% Result : Unsatisfiable 17.07s 5.39s
% Output : Refutation 14.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 7
% Syntax : Number of formulae : 127 ( 38 unt; 0 typ; 0 def)
% Number of atoms : 404 ( 85 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 2666 ( 245 ~; 167 |; 0 &;2254 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 504 ( 0 ^; 504 !; 0 ?; 504 :)
% Comments :
%------------------------------------------------------------------------------
thf(seq_decl,type,
seq: $i > $i > $i > $o ).
thf(succ_decl,type,
succ: $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(top_decl,type,
top: $i > $i > $o ).
thf(f_decl,type,
f: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(step_decl,type,
step: $i > $i > $o ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ step ) )
| ~ ( B @ ( A @ top ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rewrite_top) ).
thf(11,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ step ) )
| ~ ( B @ ( A @ top ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ step ) )
| ~ ( B @ ( A @ top ) ) ),
inference(cnf,[status(esa)],[11]) ).
thf(6,axiom,
! [A: $i] : ( A @ ( A @ ( zero @ seq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rewrite_sequence_zero) ).
thf(17,plain,
! [A: $i] : ( A @ ( A @ ( zero @ seq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ succ @ seq ) ) )
| ~ ( D @ ( C @ step ) )
| ~ ( C @ ( B @ ( A @ seq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rewrite_sequence_succ) ).
thf(18,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ succ @ seq ) ) )
| ~ ( D @ ( C @ step ) )
| ~ ( C @ ( B @ ( A @ seq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(19,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ succ @ seq ) ) )
| ~ ( D @ ( C @ step ) )
| ~ ( C @ ( B @ ( A @ seq ) ) ) ),
inference(cnf,[status(esa)],[18]) ).
thf(1,negated_conjecture,
! [A: $i] :
~ ( A @ ( A @ ( zero @ succ @ succ @ succ @ succ @ succ @ seq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(8,plain,
! [A: $i] :
~ ( A @ ( A @ ( zero @ succ @ succ @ succ @ succ @ succ @ seq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(9,plain,
! [A: $i] :
~ ( A @ ( A @ ( zero @ succ @ succ @ succ @ succ @ succ @ seq ) ) ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(24,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ succ @ seq ) ) )
!= ( E @ ( E @ ( zero @ succ @ succ @ succ @ succ @ succ @ seq ) ) ) )
| ~ $true
| ~ ( D @ ( C @ step ) )
| ~ ( C @ ( B @ ( A @ seq ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,9]) ).
thf(25,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ succ @ seq ) ) )
!= ( E @ ( E @ ( zero @ succ @ succ @ succ @ succ @ succ @ seq ) ) ) )
| ~ ( D @ ( C @ step ) )
| ~ ( C @ ( B @ ( A @ seq ) ) ) ),
inference(simp,[status(thm)],[24]) ).
thf(26,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ step ) )
| ~ ( A @ ( B @ ( zero @ succ @ succ @ succ @ succ @ seq ) ) ) ),
inference(pattern_uni,[status(thm)],[25:[bind(A,$thf( zero @ succ @ succ @ succ @ succ )),bind(B,$thf( D )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( D ))]]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ step ) )
| ~ ( A @ ( B @ ( zero @ succ @ succ @ succ @ succ @ seq ) ) ) ),
inference(simp,[status(thm)],[26]) ).
thf(36,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ succ @ seq ) ) )
!= ( E @ ( F @ ( zero @ succ @ succ @ succ @ succ @ seq ) ) ) )
| ~ ( F @ ( E @ step ) )
| ~ $true
| ~ ( D @ ( C @ step ) )
| ~ ( C @ ( B @ ( A @ seq ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,34]) ).
thf(37,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ succ @ seq ) ) )
!= ( E @ ( F @ ( zero @ succ @ succ @ succ @ succ @ seq ) ) ) )
| ~ ( F @ ( E @ step ) )
| ~ ( D @ ( C @ step ) )
| ~ ( C @ ( B @ ( A @ seq ) ) ) ),
inference(simp,[status(thm)],[36]) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ step ) )
| ~ ( C @ ( B @ step ) )
| ~ ( B @ ( A @ ( zero @ succ @ succ @ succ @ seq ) ) ) ),
inference(pattern_uni,[status(thm)],[37:[bind(A,$thf( zero @ succ @ succ @ succ )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( D )),bind(F,$thf( B ))]]) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ step ) )
| ~ ( C @ ( B @ step ) )
| ~ ( B @ ( A @ ( zero @ succ @ succ @ succ @ seq ) ) ) ),
inference(simp,[status(thm)],[38]) ).
thf(169,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( zero @ seq ) ) )
!= ( C @ ( B @ ( zero @ succ @ succ @ succ @ seq ) ) ) )
| ~ ( B @ ( D @ step ) )
| ~ ( D @ ( C @ step ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17,42]) ).
thf(170,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( zero @ seq ) ) )
!= ( C @ ( B @ ( zero @ succ @ succ @ succ @ seq ) ) ) )
| ~ ( B @ ( D @ step ) )
| ~ ( D @ ( C @ step ) ) ),
inference(simp,[status(thm)],[169]) ).
thf(172,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A != C )
| ( A != B )
| ( ( zero @ succ @ succ @ succ )
!= zero )
| ~ ( B @ ( D @ step ) )
| ~ ( D @ ( C @ step ) ) ),
inference(simp,[status(thm)],[170]) ).
thf(181,plain,
! [B: $i,A: $i] :
( ( ( zero @ succ @ succ @ succ )
!= zero )
| ~ ( A @ ( B @ step ) )
| ~ ( B @ ( A @ step ) ) ),
inference(simp,[status(thm)],[172]) ).
thf(509,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ step ) )
!= ( D @ ( C @ step ) ) )
| ( ( zero @ succ @ succ @ succ )
!= zero )
| ~ ( C @ ( D @ step ) )
| ~ $true
| ~ ( B @ ( A @ top ) ) ),
inference(paramod_ordered,[status(thm)],[12,181]) ).
thf(510,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ step ) )
!= ( D @ ( C @ step ) ) )
| ( ( zero @ succ @ succ @ succ )
!= zero )
| ~ ( C @ ( D @ step ) )
| ~ ( B @ ( A @ top ) ) ),
inference(simp,[status(thm)],[509]) ).
thf(511,plain,
! [B: $i,A: $i] :
( ( ( zero @ succ @ succ @ succ )
!= zero )
| ~ ( A @ ( B @ step ) )
| ~ ( B @ ( A @ top ) ) ),
inference(pattern_uni,[status(thm)],[510:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( zero @ seq ) ) )
!= ( B @ ( C @ ( zero @ succ @ succ @ succ @ succ @ seq ) ) ) )
| ~ ( C @ ( B @ step ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17,34]) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( zero @ seq ) ) )
!= ( B @ ( C @ ( zero @ succ @ succ @ succ @ succ @ seq ) ) ) )
| ~ ( C @ ( B @ step ) ) ),
inference(simp,[status(thm)],[39]) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ( A != B )
| ( A != C )
| ( ( zero @ succ @ succ @ succ @ succ )
!= zero )
| ~ ( C @ ( B @ step ) ) ),
inference(simp,[status(thm)],[40]) ).
thf(43,plain,
! [A: $i] :
( ( ( zero @ succ @ succ @ succ @ succ )
!= zero )
| ~ ( A @ ( A @ step ) ) ),
inference(simp,[status(thm)],[41]) ).
thf(54,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ step ) )
!= ( C @ ( C @ step ) ) )
| ( ( zero @ succ @ succ @ succ @ succ )
!= zero )
| ~ $true
| ~ ( B @ ( A @ top ) ) ),
inference(paramod_ordered,[status(thm)],[12,43]) ).
thf(55,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ step ) )
!= ( C @ ( C @ step ) ) )
| ( ( zero @ succ @ succ @ succ @ succ )
!= zero )
| ~ ( B @ ( A @ top ) ) ),
inference(simp,[status(thm)],[54]) ).
thf(56,plain,
! [A: $i] :
( ( ( zero @ succ @ succ @ succ @ succ )
!= zero )
| ~ ( A @ ( A @ top ) ) ),
inference(pattern_uni,[status(thm)],[55:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(57,plain,
! [A: $i] :
( ( ( zero @ succ @ succ @ succ @ succ )
!= zero )
| ~ ( A @ ( A @ top ) ) ),
inference(simp,[status(thm)],[56]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] : ( A @ ( a @ ( a @ ( B @ f ) @ f ) @ ( C @ f ) @ f ) @ ( a @ ( C @ f ) @ ( B @ ( a @ ( A @ f ) @ f ) @ f ) @ top ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_1) ).
thf(10,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( a @ ( a @ ( B @ f ) @ f ) @ ( C @ f ) @ f ) @ ( a @ ( C @ f ) @ ( B @ ( a @ ( A @ f ) @ f ) @ f ) @ top ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(44,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( a @ ( a @ ( B @ f ) @ f ) @ ( C @ f ) @ f ) @ ( a @ ( C @ f ) @ ( B @ ( a @ ( A @ f ) @ f ) @ f ) @ top ) )
!= ( E @ ( D @ top ) ) )
| ( E @ ( D @ step ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10,12]) ).
thf(45,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( a @ ( a @ ( B @ f ) @ f ) @ ( C @ f ) @ f ) @ ( a @ ( C @ f ) @ ( B @ ( a @ ( A @ f ) @ f ) @ f ) @ top ) )
!= ( E @ ( D @ top ) ) )
| ( E @ ( D @ step ) ) ),
inference(simp,[status(thm)],[44]) ).
thf(46,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( a @ ( a @ ( C @ f ) @ f ) @ ( B @ f ) @ f ) @ ( a @ ( B @ f ) @ ( C @ ( a @ ( A @ f ) @ f ) @ f ) @ step ) ),
inference(pattern_uni,[status(thm)],[45:[bind(A,$thf( O )),bind(B,$thf( T )),bind(C,$thf( P )),bind(D,$thf( a @ ( P @ f ) @ ( T @ ( a @ ( O @ f ) @ f ) @ f ) )),bind(E,$thf( O @ ( a @ ( a @ ( T @ f ) @ f ) @ ( P @ f ) @ f ) ))]]) ).
thf(53,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( a @ ( a @ ( C @ f ) @ f ) @ ( B @ f ) @ f ) @ ( a @ ( B @ f ) @ ( C @ ( a @ ( A @ f ) @ f ) @ f ) @ step ) ),
inference(simp,[status(thm)],[46]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ f ) @ ( C @ ( A @ f ) @ step ) )
| ~ ( B @ ( A @ step ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rewrite_left) ).
thf(13,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ f ) @ ( C @ ( A @ f ) @ step ) )
| ~ ( B @ ( A @ step ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(14,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ f ) @ ( C @ ( A @ f ) @ step ) )
| ~ ( B @ ( A @ step ) ) ),
inference(cnf,[status(esa)],[13]) ).
thf(82,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( a @ ( a @ ( C @ f ) @ f ) @ ( B @ f ) @ f ) @ ( a @ ( B @ f ) @ ( C @ ( a @ ( A @ f ) @ f ) @ f ) @ step ) )
!= ( E @ ( D @ step ) ) )
| ( F @ ( E @ f ) @ ( F @ ( D @ f ) @ step ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[53,14]) ).
thf(83,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( a @ ( a @ ( C @ f ) @ f ) @ ( B @ f ) @ f ) @ ( a @ ( B @ f ) @ ( C @ ( a @ ( A @ f ) @ f ) @ f ) @ step ) )
!= ( E @ ( D @ step ) ) )
| ( F @ ( E @ f ) @ ( F @ ( D @ f ) @ step ) ) ),
inference(simp,[status(thm)],[82]) ).
thf(84,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( a @ ( a @ ( D @ f ) @ f ) @ ( C @ f ) @ f ) @ f ) @ ( A @ ( a @ ( C @ f ) @ ( D @ ( a @ ( B @ f ) @ f ) @ f ) @ f ) @ step ) ),
inference(pattern_uni,[status(thm)],[83:[bind(A,$thf( P )),bind(B,$thf( Q )),bind(C,$thf( U )),bind(D,$thf( a @ ( Q @ f ) @ ( U @ ( a @ ( P @ f ) @ f ) @ f ) )),bind(E,$thf( P @ ( a @ ( a @ ( U @ f ) @ f ) @ ( Q @ f ) @ f ) )),bind(F,$thf( F ))]]) ).
thf(94,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( a @ ( a @ ( D @ f ) @ f ) @ ( C @ f ) @ f ) @ f ) @ ( A @ ( a @ ( C @ f ) @ ( D @ ( a @ ( B @ f ) @ f ) @ f ) @ f ) @ step ) ),
inference(simp,[status(thm)],[84]) ).
thf(106,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( a @ ( a @ ( D @ f ) @ f ) @ ( C @ f ) @ f ) @ f ) @ ( A @ ( a @ ( C @ f ) @ ( D @ ( a @ ( B @ f ) @ f ) @ f ) @ f ) @ step ) )
!= ( F @ ( E @ step ) ) )
| ( G @ ( F @ f ) @ ( G @ ( E @ f ) @ step ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[94,14]) ).
thf(107,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( a @ ( a @ ( D @ f ) @ f ) @ ( C @ f ) @ f ) @ f ) @ ( A @ ( a @ ( C @ f ) @ ( D @ ( a @ ( B @ f ) @ f ) @ f ) @ f ) @ step ) )
!= ( F @ ( E @ step ) ) )
| ( G @ ( F @ f ) @ ( G @ ( E @ f ) @ step ) ) ),
inference(simp,[status(thm)],[106]) ).
thf(108,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( a @ ( a @ ( E @ f ) @ f ) @ ( D @ f ) @ f ) @ f ) @ f ) @ ( A @ ( B @ ( a @ ( D @ f ) @ ( E @ ( a @ ( C @ f ) @ f ) @ f ) @ f ) @ f ) @ step ) ),
inference(pattern_uni,[status(thm)],[107:[bind(A,$thf( S )),bind(B,$thf( U )),bind(C,$thf( V )),bind(D,$thf( Z )),bind(E,$thf( S @ ( a @ ( V @ f ) @ ( Z @ ( a @ ( U @ f ) @ f ) @ f ) @ f ) )),bind(F,$thf( S @ ( U @ ( a @ ( a @ ( Z @ f ) @ f ) @ ( V @ f ) @ f ) @ f ) )),bind(G,$thf( G ))]]) ).
thf(121,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( a @ ( a @ ( E @ f ) @ f ) @ ( D @ f ) @ f ) @ f ) @ f ) @ ( A @ ( B @ ( a @ ( D @ f ) @ ( E @ ( a @ ( C @ f ) @ f ) @ f ) @ f ) @ f ) @ step ) ),
inference(simp,[status(thm)],[108]) ).
thf(30,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ succ @ seq ) ) )
!= ( G @ ( F @ ( E @ seq ) ) ) )
| ( H @ ( F @ ( E @ succ @ seq ) ) )
| ~ ( H @ ( G @ step ) )
| ~ $true
| ~ ( D @ ( C @ step ) )
| ~ ( C @ ( B @ ( A @ seq ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,19]) ).
thf(31,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ succ @ seq ) ) )
!= ( G @ ( F @ ( E @ seq ) ) ) )
| ( H @ ( F @ ( E @ succ @ seq ) ) )
| ~ ( H @ ( G @ step ) )
| ~ ( D @ ( C @ step ) )
| ~ ( C @ ( B @ ( A @ seq ) ) ) ),
inference(simp,[status(thm)],[30]) ).
thf(32,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( E @ succ @ succ @ seq ) ) )
| ~ ( D @ ( C @ step ) )
| ~ ( C @ ( B @ step ) )
| ~ ( B @ ( A @ ( E @ seq ) ) ) ),
inference(pattern_uni,[status(thm)],[31:[bind(A,$thf( I )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( I @ succ )),bind(F,$thf( B )),bind(G,$thf( D ))]]) ).
thf(33,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( E @ succ @ succ @ seq ) ) )
| ~ ( D @ ( C @ step ) )
| ~ ( C @ ( B @ step ) )
| ~ ( B @ ( A @ ( E @ seq ) ) ) ),
inference(simp,[status(thm)],[32]) ).
thf(171,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ( ( A @ ( C @ step ) )
!= ( C @ ( B @ step ) ) )
| ~ ( C @ ( B @ step ) )
| ~ ( B @ ( A @ ( zero @ succ @ succ @ succ @ seq ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[42]) ).
thf(173,plain,
! [A: $i] :
( ~ ( A @ ( A @ step ) )
| ~ ( A @ ( A @ ( zero @ succ @ succ @ succ @ seq ) ) ) ),
inference(pattern_uni,[status(thm)],[171:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(222,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( zero @ seq ) ) )
!= ( B @ ( B @ ( zero @ succ @ succ @ succ @ seq ) ) ) )
| ~ ( B @ ( B @ step ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17,173]) ).
thf(223,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( zero @ seq ) ) )
!= ( B @ ( B @ ( zero @ succ @ succ @ succ @ seq ) ) ) )
| ~ ( B @ ( B @ step ) ) ),
inference(simp,[status(thm)],[222]) ).
thf(225,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( A != B )
| ( ( zero @ succ @ succ @ succ )
!= zero )
| ~ ( B @ ( B @ step ) ) ),
inference(simp,[status(thm)],[223]) ).
thf(229,plain,
! [A: $i] :
( ( ( zero @ succ @ succ @ succ )
!= zero )
| ~ ( A @ ( A @ step ) ) ),
inference(simp,[status(thm)],[225]) ).
thf(90,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( a @ ( a @ ( C @ f ) @ f ) @ ( B @ f ) @ f ) @ ( a @ ( B @ f ) @ ( C @ ( a @ ( A @ f ) @ f ) @ f ) @ step ) )
!= ( E @ ( D @ step ) ) )
| ~ $true
| ~ ( D @ ( E @ ( zero @ succ @ succ @ succ @ succ @ seq ) ) ) ),
inference(paramod_ordered,[status(thm)],[53,34]) ).
thf(91,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( a @ ( a @ ( C @ f ) @ f ) @ ( B @ f ) @ f ) @ ( a @ ( B @ f ) @ ( C @ ( a @ ( A @ f ) @ f ) @ f ) @ step ) )
!= ( E @ ( D @ step ) ) )
| ~ ( D @ ( E @ ( zero @ succ @ succ @ succ @ succ @ seq ) ) ) ),
inference(simp,[status(thm)],[90]) ).
thf(92,plain,
! [C: $i,B: $i,A: $i] :
~ ( a @ ( B @ f ) @ ( C @ ( a @ ( A @ f ) @ f ) @ f ) @ ( A @ ( a @ ( a @ ( C @ f ) @ f ) @ ( B @ f ) @ f ) @ ( zero @ succ @ succ @ succ @ succ @ seq ) ) ),
inference(pattern_uni,[status(thm)],[91:[bind(A,$thf( O )),bind(B,$thf( P )),bind(C,$thf( T )),bind(D,$thf( a @ ( P @ f ) @ ( T @ ( a @ ( O @ f ) @ f ) @ f ) )),bind(E,$thf( O @ ( a @ ( a @ ( T @ f ) @ f ) @ ( P @ f ) @ f ) ))]]) ).
thf(96,plain,
! [C: $i,B: $i,A: $i] :
~ ( a @ ( B @ f ) @ ( C @ ( a @ ( A @ f ) @ f ) @ f ) @ ( A @ ( a @ ( a @ ( C @ f ) @ f ) @ ( B @ f ) @ f ) @ ( zero @ succ @ succ @ succ @ succ @ seq ) ) ),
inference(simp,[status(thm)],[92]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ f ) @ ( A @ ( C @ f ) @ step ) )
| ~ ( B @ ( A @ step ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rewrite_right) ).
thf(15,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ f ) @ ( A @ ( C @ f ) @ step ) )
| ~ ( B @ ( A @ step ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(16,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ f ) @ ( A @ ( C @ f ) @ step ) )
| ~ ( B @ ( A @ step ) ) ),
inference(cnf,[status(esa)],[15]) ).
thf(291,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( a @ ( a @ ( C @ f ) @ f ) @ ( B @ f ) @ f ) @ ( a @ ( B @ f ) @ ( C @ ( a @ ( A @ f ) @ f ) @ f ) @ step ) )
!= ( E @ ( D @ step ) ) )
| ( E @ ( F @ f ) @ ( D @ ( F @ f ) @ step ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[53,16]) ).
thf(292,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( a @ ( a @ ( C @ f ) @ f ) @ ( B @ f ) @ f ) @ ( a @ ( B @ f ) @ ( C @ ( a @ ( A @ f ) @ f ) @ f ) @ step ) )
!= ( E @ ( D @ step ) ) )
| ( E @ ( F @ f ) @ ( D @ ( F @ f ) @ step ) ) ),
inference(simp,[status(thm)],[291]) ).
thf(293,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( a @ ( a @ ( D @ f ) @ f ) @ ( C @ f ) @ f ) @ ( A @ f ) @ ( a @ ( C @ f ) @ ( D @ ( a @ ( B @ f ) @ f ) @ f ) @ ( A @ f ) @ step ) ),
inference(pattern_uni,[status(thm)],[292:[bind(A,$thf( P )),bind(B,$thf( Q )),bind(C,$thf( U )),bind(D,$thf( a @ ( Q @ f ) @ ( U @ ( a @ ( P @ f ) @ f ) @ f ) )),bind(E,$thf( P @ ( a @ ( a @ ( U @ f ) @ f ) @ ( Q @ f ) @ f ) )),bind(F,$thf( F ))]]) ).
thf(300,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( a @ ( a @ ( D @ f ) @ f ) @ ( C @ f ) @ f ) @ ( A @ f ) @ ( a @ ( C @ f ) @ ( D @ ( a @ ( B @ f ) @ f ) @ f ) @ ( A @ f ) @ step ) ),
inference(simp,[status(thm)],[293]) ).
thf(329,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( a @ ( a @ ( D @ f ) @ f ) @ ( C @ f ) @ f ) @ ( A @ f ) @ ( a @ ( C @ f ) @ ( D @ ( a @ ( B @ f ) @ f ) @ f ) @ ( A @ f ) @ step ) )
!= ( F @ ( E @ step ) ) )
| ~ $true
| ~ ( E @ ( F @ ( zero @ succ @ succ @ succ @ succ @ seq ) ) ) ),
inference(paramod_ordered,[status(thm)],[300,34]) ).
thf(330,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( a @ ( a @ ( D @ f ) @ f ) @ ( C @ f ) @ f ) @ ( A @ f ) @ ( a @ ( C @ f ) @ ( D @ ( a @ ( B @ f ) @ f ) @ f ) @ ( A @ f ) @ step ) )
!= ( F @ ( E @ step ) ) )
| ~ ( E @ ( F @ ( zero @ succ @ succ @ succ @ succ @ seq ) ) ) ),
inference(simp,[status(thm)],[329]) ).
thf(331,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( a @ ( C @ f ) @ ( D @ ( a @ ( B @ f ) @ f ) @ f ) @ ( A @ f ) @ ( B @ ( a @ ( a @ ( D @ f ) @ f ) @ ( C @ f ) @ f ) @ ( A @ f ) @ ( zero @ succ @ succ @ succ @ succ @ seq ) ) ),
inference(pattern_uni,[status(thm)],[330:[bind(A,$thf( Q )),bind(B,$thf( T )),bind(C,$thf( U )),bind(D,$thf( Y )),bind(E,$thf( a @ ( U @ f ) @ ( Y @ ( a @ ( T @ f ) @ f ) @ f ) @ ( Q @ f ) )),bind(F,$thf( T @ ( a @ ( a @ ( Y @ f ) @ f ) @ ( U @ f ) @ f ) @ ( Q @ f ) ))]]) ).
thf(343,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( a @ ( C @ f ) @ ( D @ ( a @ ( B @ f ) @ f ) @ f ) @ ( A @ f ) @ ( B @ ( a @ ( a @ ( D @ f ) @ f ) @ ( C @ f ) @ f ) @ ( A @ f ) @ ( zero @ succ @ succ @ succ @ succ @ seq ) ) ),
inference(simp,[status(thm)],[331]) ).
thf(321,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( a @ ( a @ ( D @ f ) @ f ) @ ( C @ f ) @ f ) @ ( A @ f ) @ ( a @ ( C @ f ) @ ( D @ ( a @ ( B @ f ) @ f ) @ f ) @ ( A @ f ) @ step ) )
!= ( F @ ( E @ step ) ) )
| ( F @ ( G @ f ) @ ( E @ ( G @ f ) @ step ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[300,16]) ).
thf(322,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( a @ ( a @ ( D @ f ) @ f ) @ ( C @ f ) @ f ) @ ( A @ f ) @ ( a @ ( C @ f ) @ ( D @ ( a @ ( B @ f ) @ f ) @ f ) @ ( A @ f ) @ step ) )
!= ( F @ ( E @ step ) ) )
| ( F @ ( G @ f ) @ ( E @ ( G @ f ) @ step ) ) ),
inference(simp,[status(thm)],[321]) ).
thf(323,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( C @ ( a @ ( a @ ( E @ f ) @ f ) @ ( D @ f ) @ f ) @ ( B @ f ) @ ( A @ f ) @ ( a @ ( D @ f ) @ ( E @ ( a @ ( C @ f ) @ f ) @ f ) @ ( B @ f ) @ ( A @ f ) @ step ) ),
inference(pattern_uni,[status(thm)],[322:[bind(A,$thf( R )),bind(B,$thf( U )),bind(C,$thf( V )),bind(D,$thf( Z )),bind(E,$thf( a @ ( V @ f ) @ ( Z @ ( a @ ( U @ f ) @ f ) @ f ) @ ( R @ f ) )),bind(F,$thf( U @ ( a @ ( a @ ( Z @ f ) @ f ) @ ( V @ f ) @ f ) @ ( R @ f ) )),bind(G,$thf( G ))]]) ).
thf(340,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( C @ ( a @ ( a @ ( E @ f ) @ f ) @ ( D @ f ) @ f ) @ ( B @ f ) @ ( A @ f ) @ ( a @ ( D @ f ) @ ( E @ ( a @ ( C @ f ) @ f ) @ f ) @ ( B @ f ) @ ( A @ f ) @ step ) ),
inference(simp,[status(thm)],[323]) ).
thf(409,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( a @ ( a @ ( E @ f ) @ f ) @ ( D @ f ) @ f ) @ ( B @ f ) @ ( A @ f ) @ ( a @ ( D @ f ) @ ( E @ ( a @ ( C @ f ) @ f ) @ f ) @ ( B @ f ) @ ( A @ f ) @ step ) )
!= ( G @ ( F @ step ) ) )
| ~ $true
| ~ ( F @ ( G @ ( zero @ succ @ succ @ succ @ succ @ seq ) ) ) ),
inference(paramod_ordered,[status(thm)],[340,34]) ).
thf(410,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( a @ ( a @ ( E @ f ) @ f ) @ ( D @ f ) @ f ) @ ( B @ f ) @ ( A @ f ) @ ( a @ ( D @ f ) @ ( E @ ( a @ ( C @ f ) @ f ) @ f ) @ ( B @ f ) @ ( A @ f ) @ step ) )
!= ( G @ ( F @ step ) ) )
| ~ ( F @ ( G @ ( zero @ succ @ succ @ succ @ succ @ seq ) ) ) ),
inference(simp,[status(thm)],[409]) ).
thf(411,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
~ ( a @ ( D @ f ) @ ( E @ ( a @ ( C @ f ) @ f ) @ f ) @ ( B @ f ) @ ( A @ f ) @ ( C @ ( a @ ( a @ ( E @ f ) @ f ) @ ( D @ f ) @ f ) @ ( B @ f ) @ ( A @ f ) @ ( zero @ succ @ succ @ succ @ succ @ seq ) ) ),
inference(pattern_uni,[status(thm)],[410:[bind(A,$thf( T )),bind(B,$thf( V )),bind(C,$thf( Y )),bind(D,$thf( Z )),bind(E,$thf( ZD )),bind(F,$thf( a @ ( Z @ f ) @ ( ZD @ ( a @ ( Y @ f ) @ f ) @ f ) @ ( V @ f ) @ ( T @ f ) )),bind(G,$thf( Y @ ( a @ ( a @ ( ZD @ f ) @ f ) @ ( Z @ f ) @ f ) @ ( V @ f ) @ ( T @ f ) ))]]) ).
thf(423,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
~ ( a @ ( D @ f ) @ ( E @ ( a @ ( C @ f ) @ f ) @ f ) @ ( B @ f ) @ ( A @ f ) @ ( C @ ( a @ ( a @ ( E @ f ) @ f ) @ ( D @ f ) @ f ) @ ( B @ f ) @ ( A @ f ) @ ( zero @ succ @ succ @ succ @ succ @ seq ) ) ),
inference(simp,[status(thm)],[411]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( zero @ seq ) ) )
!= ( B @ ( B @ ( zero @ succ @ succ @ succ @ succ @ succ @ seq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17,9]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( zero @ seq ) ) )
!= ( B @ ( B @ ( zero @ succ @ succ @ succ @ succ @ succ @ seq ) ) ) ),
inference(simp,[status(thm)],[20]) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( A != B )
| ( ( zero @ succ @ succ @ succ @ succ @ succ )
!= zero ) ),
inference(simp,[status(thm)],[21]) ).
thf(23,plain,
( ( zero @ succ @ succ @ succ @ succ @ succ )
!= zero ),
inference(simp,[status(thm)],[22]) ).
thf(282,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( a @ ( a @ ( D @ f ) @ f ) @ ( C @ f ) @ f ) @ f ) @ ( A @ ( a @ ( C @ f ) @ ( D @ ( a @ ( B @ f ) @ f ) @ f ) @ f ) @ step ) )
!= ( F @ ( E @ step ) ) )
| ( F @ ( G @ f ) @ ( E @ ( G @ f ) @ step ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[94,16]) ).
thf(283,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( a @ ( a @ ( D @ f ) @ f ) @ ( C @ f ) @ f ) @ f ) @ ( A @ ( a @ ( C @ f ) @ ( D @ ( a @ ( B @ f ) @ f ) @ f ) @ f ) @ step ) )
!= ( F @ ( E @ step ) ) )
| ( F @ ( G @ f ) @ ( E @ ( G @ f ) @ step ) ) ),
inference(simp,[status(thm)],[282]) ).
thf(284,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( B @ ( C @ ( a @ ( a @ ( E @ f ) @ f ) @ ( D @ f ) @ f ) @ f ) @ ( A @ f ) @ ( B @ ( a @ ( D @ f ) @ ( E @ ( a @ ( C @ f ) @ f ) @ f ) @ f ) @ ( A @ f ) @ step ) ),
inference(pattern_uni,[status(thm)],[283:[bind(A,$thf( S )),bind(B,$thf( U )),bind(C,$thf( V )),bind(D,$thf( Z )),bind(E,$thf( S @ ( a @ ( V @ f ) @ ( Z @ ( a @ ( U @ f ) @ f ) @ f ) @ f ) )),bind(F,$thf( S @ ( U @ ( a @ ( a @ ( Z @ f ) @ f ) @ ( V @ f ) @ f ) @ f ) )),bind(G,$thf( G ))]]) ).
thf(309,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( B @ ( C @ ( a @ ( a @ ( E @ f ) @ f ) @ ( D @ f ) @ f ) @ f ) @ ( A @ f ) @ ( B @ ( a @ ( D @ f ) @ ( E @ ( a @ ( C @ f ) @ f ) @ f ) @ f ) @ ( A @ f ) @ step ) ),
inference(simp,[status(thm)],[284]) ).
thf(373,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( a @ ( a @ ( E @ f ) @ f ) @ ( D @ f ) @ f ) @ f ) @ ( A @ f ) @ ( B @ ( a @ ( D @ f ) @ ( E @ ( a @ ( C @ f ) @ f ) @ f ) @ f ) @ ( A @ f ) @ step ) )
!= ( G @ ( F @ step ) ) )
| ~ $true
| ~ ( F @ ( G @ ( zero @ succ @ succ @ succ @ succ @ seq ) ) ) ),
inference(paramod_ordered,[status(thm)],[309,34]) ).
thf(374,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( a @ ( a @ ( E @ f ) @ f ) @ ( D @ f ) @ f ) @ f ) @ ( A @ f ) @ ( B @ ( a @ ( D @ f ) @ ( E @ ( a @ ( C @ f ) @ f ) @ f ) @ f ) @ ( A @ f ) @ step ) )
!= ( G @ ( F @ step ) ) )
| ~ ( F @ ( G @ ( zero @ succ @ succ @ succ @ succ @ seq ) ) ) ),
inference(simp,[status(thm)],[373]) ).
thf(375,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
~ ( B @ ( a @ ( D @ f ) @ ( E @ ( a @ ( C @ f ) @ f ) @ f ) @ f ) @ ( A @ f ) @ ( B @ ( C @ ( a @ ( a @ ( E @ f ) @ f ) @ ( D @ f ) @ f ) @ f ) @ ( A @ f ) @ ( zero @ succ @ succ @ succ @ succ @ seq ) ) ),
inference(pattern_uni,[status(thm)],[374:[bind(A,$thf( T )),bind(B,$thf( W )),bind(C,$thf( Y )),bind(D,$thf( Z )),bind(E,$thf( ZD )),bind(F,$thf( W @ ( a @ ( Z @ f ) @ ( ZD @ ( a @ ( Y @ f ) @ f ) @ f ) @ f ) @ ( T @ f ) )),bind(G,$thf( W @ ( Y @ ( a @ ( a @ ( ZD @ f ) @ f ) @ ( Z @ f ) @ f ) @ f ) @ ( T @ f ) ))]]) ).
thf(384,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
~ ( B @ ( a @ ( D @ f ) @ ( E @ ( a @ ( C @ f ) @ f ) @ f ) @ f ) @ ( A @ f ) @ ( B @ ( C @ ( a @ ( a @ ( E @ f ) @ f ) @ ( D @ f ) @ f ) @ f ) @ ( A @ f ) @ ( zero @ succ @ succ @ succ @ succ @ seq ) ) ),
inference(simp,[status(thm)],[375]) ).
thf(50,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ step ) )
!= ( D @ ( C @ step ) ) )
| ~ $true
| ~ ( C @ ( D @ ( zero @ succ @ succ @ succ @ succ @ seq ) ) )
| ~ ( B @ ( A @ top ) ) ),
inference(paramod_ordered,[status(thm)],[12,34]) ).
thf(51,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ step ) )
!= ( D @ ( C @ step ) ) )
| ~ ( C @ ( D @ ( zero @ succ @ succ @ succ @ succ @ seq ) ) )
| ~ ( B @ ( A @ top ) ) ),
inference(simp,[status(thm)],[50]) ).
thf(52,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( zero @ succ @ succ @ succ @ succ @ seq ) ) )
| ~ ( B @ ( A @ top ) ) ),
inference(pattern_uni,[status(thm)],[51:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(578,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ step ) )
!= ( C @ ( D @ step ) ) )
| ( ( zero @ succ @ succ @ succ )
!= zero )
| ~ $true
| ~ ( D @ ( C @ top ) )
| ~ ( B @ ( A @ top ) ) ),
inference(paramod_ordered,[status(thm)],[12,511]) ).
thf(579,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ step ) )
!= ( C @ ( D @ step ) ) )
| ( ( zero @ succ @ succ @ succ )
!= zero )
| ~ ( D @ ( C @ top ) )
| ~ ( B @ ( A @ top ) ) ),
inference(simp,[status(thm)],[578]) ).
thf(580,plain,
! [B: $i,A: $i] :
( ( ( zero @ succ @ succ @ succ )
!= zero )
| ~ ( A @ ( B @ top ) )
| ~ ( B @ ( A @ top ) ) ),
inference(pattern_uni,[status(thm)],[579:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(209,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ step ) )
!= ( C @ ( C @ step ) ) )
| ~ $true
| ~ ( C @ ( C @ ( zero @ succ @ succ @ succ @ seq ) ) )
| ~ ( B @ ( A @ top ) ) ),
inference(paramod_ordered,[status(thm)],[12,173]) ).
thf(210,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ step ) )
!= ( C @ ( C @ step ) ) )
| ~ ( C @ ( C @ ( zero @ succ @ succ @ succ @ seq ) ) )
| ~ ( B @ ( A @ top ) ) ),
inference(simp,[status(thm)],[209]) ).
thf(211,plain,
! [A: $i] :
( ~ ( A @ ( A @ ( zero @ succ @ succ @ succ @ seq ) ) )
| ~ ( A @ ( A @ top ) ) ),
inference(pattern_uni,[status(thm)],[210:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(231,plain,
! [A: $i] :
( ~ ( A @ ( A @ ( zero @ succ @ succ @ succ @ seq ) ) )
| ~ ( A @ ( A @ top ) ) ),
inference(simp,[status(thm)],[211]) ).
thf(197,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( a @ ( a @ ( E @ f ) @ f ) @ ( D @ f ) @ f ) @ f ) @ f ) @ ( A @ ( B @ ( a @ ( D @ f ) @ ( E @ ( a @ ( C @ f ) @ f ) @ f ) @ f ) @ f ) @ step ) )
!= ( G @ ( F @ step ) ) )
| ~ $true
| ~ ( F @ ( G @ ( zero @ succ @ succ @ succ @ succ @ seq ) ) ) ),
inference(paramod_ordered,[status(thm)],[121,34]) ).
thf(198,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( a @ ( a @ ( E @ f ) @ f ) @ ( D @ f ) @ f ) @ f ) @ f ) @ ( A @ ( B @ ( a @ ( D @ f ) @ ( E @ ( a @ ( C @ f ) @ f ) @ f ) @ f ) @ f ) @ step ) )
!= ( G @ ( F @ step ) ) )
| ~ ( F @ ( G @ ( zero @ succ @ succ @ succ @ succ @ seq ) ) ) ),
inference(simp,[status(thm)],[197]) ).
thf(199,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( a @ ( D @ f ) @ ( E @ ( a @ ( C @ f ) @ f ) @ f ) @ f ) @ f ) @ ( A @ ( B @ ( C @ ( a @ ( a @ ( E @ f ) @ f ) @ ( D @ f ) @ f ) @ f ) @ f ) @ ( zero @ succ @ succ @ succ @ succ @ seq ) ) ),
inference(pattern_uni,[status(thm)],[198:[bind(A,$thf( U )),bind(B,$thf( W )),bind(C,$thf( Y )),bind(D,$thf( Z )),bind(E,$thf( ZD )),bind(F,$thf( U @ ( W @ ( a @ ( Z @ f ) @ ( ZD @ ( a @ ( Y @ f ) @ f ) @ f ) @ f ) @ f ) )),bind(G,$thf( U @ ( W @ ( Y @ ( a @ ( a @ ( ZD @ f ) @ f ) @ ( Z @ f ) @ f ) @ f ) @ f ) ))]]) ).
thf(203,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( a @ ( D @ f ) @ ( E @ ( a @ ( C @ f ) @ f ) @ f ) @ f ) @ f ) @ ( A @ ( B @ ( C @ ( a @ ( a @ ( E @ f ) @ f ) @ ( D @ f ) @ f ) @ f ) @ f ) @ ( zero @ succ @ succ @ succ @ succ @ seq ) ) ),
inference(simp,[status(thm)],[199]) ).
thf(114,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( a @ ( a @ ( D @ f ) @ f ) @ ( C @ f ) @ f ) @ f ) @ ( A @ ( a @ ( C @ f ) @ ( D @ ( a @ ( B @ f ) @ f ) @ f ) @ f ) @ step ) )
!= ( F @ ( E @ step ) ) )
| ~ $true
| ~ ( E @ ( F @ ( zero @ succ @ succ @ succ @ succ @ seq ) ) ) ),
inference(paramod_ordered,[status(thm)],[94,34]) ).
thf(115,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( a @ ( a @ ( D @ f ) @ f ) @ ( C @ f ) @ f ) @ f ) @ ( A @ ( a @ ( C @ f ) @ ( D @ ( a @ ( B @ f ) @ f ) @ f ) @ f ) @ step ) )
!= ( F @ ( E @ step ) ) )
| ~ ( E @ ( F @ ( zero @ succ @ succ @ succ @ succ @ seq ) ) ) ),
inference(simp,[status(thm)],[114]) ).
thf(116,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( a @ ( C @ f ) @ ( D @ ( a @ ( B @ f ) @ f ) @ f ) @ f ) @ ( A @ ( B @ ( a @ ( a @ ( D @ f ) @ f ) @ ( C @ f ) @ f ) @ f ) @ ( zero @ succ @ succ @ succ @ succ @ seq ) ) ),
inference(pattern_uni,[status(thm)],[115:[bind(A,$thf( R )),bind(B,$thf( T )),bind(C,$thf( U )),bind(D,$thf( Y )),bind(E,$thf( R @ ( a @ ( U @ f ) @ ( Y @ ( a @ ( T @ f ) @ f ) @ f ) @ f ) )),bind(F,$thf( R @ ( T @ ( a @ ( a @ ( Y @ f ) @ f ) @ ( U @ f ) @ f ) @ f ) ))]]) ).
thf(119,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( a @ ( C @ f ) @ ( D @ ( a @ ( B @ f ) @ f ) @ f ) @ f ) @ ( A @ ( B @ ( a @ ( a @ ( D @ f ) @ f ) @ ( C @ f ) @ f ) @ f ) @ ( zero @ succ @ succ @ succ @ succ @ seq ) ) ),
inference(simp,[status(thm)],[116]) ).
thf(326,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( a @ ( a @ ( D @ f ) @ f ) @ ( C @ f ) @ f ) @ ( A @ f ) @ ( a @ ( C @ f ) @ ( D @ ( a @ ( B @ f ) @ f ) @ f ) @ ( A @ f ) @ step ) )
!= ( F @ ( E @ step ) ) )
| ( G @ ( F @ f ) @ ( G @ ( E @ f ) @ step ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[300,14]) ).
thf(327,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( a @ ( a @ ( D @ f ) @ f ) @ ( C @ f ) @ f ) @ ( A @ f ) @ ( a @ ( C @ f ) @ ( D @ ( a @ ( B @ f ) @ f ) @ f ) @ ( A @ f ) @ step ) )
!= ( F @ ( E @ step ) ) )
| ( G @ ( F @ f ) @ ( G @ ( E @ f ) @ step ) ) ),
inference(simp,[status(thm)],[326]) ).
thf(328,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( C @ ( a @ ( a @ ( E @ f ) @ f ) @ ( D @ f ) @ f ) @ ( B @ f ) @ f ) @ ( A @ ( a @ ( D @ f ) @ ( E @ ( a @ ( C @ f ) @ f ) @ f ) @ ( B @ f ) @ f ) @ step ) ),
inference(pattern_uni,[status(thm)],[327:[bind(A,$thf( R )),bind(B,$thf( U )),bind(C,$thf( V )),bind(D,$thf( Z )),bind(E,$thf( a @ ( V @ f ) @ ( Z @ ( a @ ( U @ f ) @ f ) @ f ) @ ( R @ f ) )),bind(F,$thf( U @ ( a @ ( a @ ( Z @ f ) @ f ) @ ( V @ f ) @ f ) @ ( R @ f ) )),bind(G,$thf( G ))]]) ).
thf(341,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( C @ ( a @ ( a @ ( E @ f ) @ f ) @ ( D @ f ) @ f ) @ ( B @ f ) @ f ) @ ( A @ ( a @ ( D @ f ) @ ( E @ ( a @ ( C @ f ) @ f ) @ f ) @ ( B @ f ) @ f ) @ step ) ),
inference(simp,[status(thm)],[328]) ).
thf(461,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( a @ ( a @ ( E @ f ) @ f ) @ ( D @ f ) @ f ) @ ( B @ f ) @ f ) @ ( A @ ( a @ ( D @ f ) @ ( E @ ( a @ ( C @ f ) @ f ) @ f ) @ ( B @ f ) @ f ) @ step ) )
!= ( G @ ( F @ step ) ) )
| ~ $true
| ~ ( F @ ( G @ ( zero @ succ @ succ @ succ @ succ @ seq ) ) ) ),
inference(paramod_ordered,[status(thm)],[341,34]) ).
thf(462,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( a @ ( a @ ( E @ f ) @ f ) @ ( D @ f ) @ f ) @ ( B @ f ) @ f ) @ ( A @ ( a @ ( D @ f ) @ ( E @ ( a @ ( C @ f ) @ f ) @ f ) @ ( B @ f ) @ f ) @ step ) )
!= ( G @ ( F @ step ) ) )
| ~ ( F @ ( G @ ( zero @ succ @ succ @ succ @ succ @ seq ) ) ) ),
inference(simp,[status(thm)],[461]) ).
thf(463,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( a @ ( D @ f ) @ ( E @ ( a @ ( C @ f ) @ f ) @ f ) @ ( B @ f ) @ f ) @ ( A @ ( C @ ( a @ ( a @ ( E @ f ) @ f ) @ ( D @ f ) @ f ) @ ( B @ f ) @ f ) @ ( zero @ succ @ succ @ succ @ succ @ seq ) ) ),
inference(pattern_uni,[status(thm)],[462:[bind(A,$thf( U )),bind(B,$thf( V )),bind(C,$thf( Y )),bind(D,$thf( Z )),bind(E,$thf( ZD )),bind(F,$thf( U @ ( a @ ( Z @ f ) @ ( ZD @ ( a @ ( Y @ f ) @ f ) @ f ) @ ( V @ f ) @ f ) )),bind(G,$thf( U @ ( Y @ ( a @ ( a @ ( ZD @ f ) @ f ) @ ( Z @ f ) @ f ) @ ( V @ f ) @ f ) ))]]) ).
thf(478,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( a @ ( D @ f ) @ ( E @ ( a @ ( C @ f ) @ f ) @ f ) @ ( B @ f ) @ f ) @ ( A @ ( C @ ( a @ ( a @ ( E @ f ) @ f ) @ ( D @ f ) @ f ) @ ( B @ f ) @ f ) @ ( zero @ succ @ succ @ succ @ succ @ seq ) ) ),
inference(simp,[status(thm)],[463]) ).
thf(237,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ step ) )
!= ( C @ ( C @ step ) ) )
| ( ( zero @ succ @ succ @ succ )
!= zero )
| ~ $true
| ~ ( B @ ( A @ top ) ) ),
inference(paramod_ordered,[status(thm)],[12,229]) ).
thf(238,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ step ) )
!= ( C @ ( C @ step ) ) )
| ( ( zero @ succ @ succ @ succ )
!= zero )
| ~ ( B @ ( A @ top ) ) ),
inference(simp,[status(thm)],[237]) ).
thf(239,plain,
! [A: $i] :
( ( ( zero @ succ @ succ @ succ )
!= zero )
| ~ ( A @ ( A @ top ) ) ),
inference(pattern_uni,[status(thm)],[238:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(254,plain,
! [A: $i] :
( ( ( zero @ succ @ succ @ succ )
!= zero )
| ~ ( A @ ( A @ top ) ) ),
inference(simp,[status(thm)],[239]) ).
thf(851,plain,
$false,
inference(e,[status(thm)],[511,42,57,121,33,229,96,343,423,16,23,15,10,384,340,52,14,9,53,173,13,34,17,12,181,580,18,11,43,231,203,8,119,478,300,19,341,94,254,309]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO691-1.001 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.08 % 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
% 0.18/0.63 % Computer : n004.cluster.edu
% 0.18/0.63 % Model : x86_64 x86_64
% 0.18/0.63 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.63 % Memory : 8046.5625MB
% 0.18/0.63 % OS : Linux 6.8.0-71-generic
% 0.18/0.63 % CPULimit : 300
% 0.18/0.63 % WCLimit : 300
% 0.18/0.63 % DateTime : Sat Sep 26 19:46:53 UTC 2026
% 0.20/0.63 % CPUTime :
% 0.20/0.63 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
% 1.02/1.25 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.39/1.43 % [INFO] Parsing done (176ms).
% 1.39/1.44 % [INFO] Running in sequential loop mode.
% 1.98/1.85 % [INFO] eprover registered as external prover.
% 1.98/1.86 % [INFO] Scanning for conjecture ...
% 2.20/1.94 % [INFO] Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ...
% 2.20/1.98 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 2.20/1.99 % [INFO] Problem is propositional (TPTP CNF).
% 2.20/2.00 % [INFO] Type checking passed.
% 2.20/2.00 % [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 ...
% 17.07/5.38 % External prover 'e' found a proof!
% 17.07/5.38 % [INFO] Killing All external provers ...
% 17.07/5.38 % Time passed: 4615ms (effective reasoning time: 3939ms)
% 17.07/5.39 % Axioms used in derivation (6): rewrite_right, rewrite_top, rule_1, rewrite_sequence_succ, rewrite_sequence_zero, rewrite_left
% 17.07/5.39 % No. of inferences in proof: 127
% 17.07/5.39 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4615 ms resp. 3939 ms w/o parsing
% 14.78/5.49 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 14.78/5.50 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------