%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : PUZ039-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n011.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 08:21:12 AM UTC 2026
% Result : Unsatisfiable 107.26s 29.83s
% Output : Refutation 108.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 44
% Syntax : Number of formulae : 217 ( 163 unt; 0 typ; 0 def)
% Number of atoms : 311 ( 310 equ; 0 cnn)
% Maximal formula atoms : 13 ( 1 avg)
% Number of connectives : 13446 ( 114 ~; 94 |; 0 &;13238 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 11 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 3 con; 0-12 aty)
% Number of variables : 2079 ( 0 ^;2079 !; 0 ?;2079 :)
% Comments :
%------------------------------------------------------------------------------
thf(state_decl,type,
state: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(v4_decl,type,
v4: $i > $i > $i ).
thf(s_decl,type,
s: $i > $i ).
thf(o_decl,type,
o: $i ).
thf(true_decl,type,
true: $i ).
thf(ifeq_decl,type,
ifeq: $i > $i > $i > $i > $i ).
thf(h_decl,type,
h: $i > $i > $i ).
thf(e1_decl,type,
e1: $i > $i > $i ).
thf(s3_decl,type,
s3: $i > $i > $i ).
thf(v3_decl,type,
v3: $i > $i > $i ).
thf(e2_decl,type,
e2: $i > $i > $i ).
thf(s4_decl,type,
s4: $i > $i > $i ).
thf(v1_decl,type,
v1: $i > $i > $i ).
thf(v2_decl,type,
v2: $i > $i > $i ).
thf(bb_decl,type,
bb: $i > $i > $i ).
thf(s2_decl,type,
s2: $i > $i > $i ).
thf(s1_decl,type,
s1: $i > $i > $i ).
thf(35,axiom,
( ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_state) ).
thf(114,plain,
( ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(115,plain,
( ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
= true ),
inference(lifteq,[status(thm)],[114]) ).
thf(4,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( J @ s @ ( I @ e1 ) @ ( K @ ( J @ ( I @ s3 ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( J @ ( I @ e1 ) @ ( K @ ( J @ s @ ( I @ s3 ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_left) ).
thf(52,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( J @ s @ ( I @ e1 ) @ ( K @ ( J @ ( I @ s3 ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( J @ ( I @ e1 ) @ ( K @ ( J @ s @ ( I @ s3 ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(53,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( J @ s @ ( I @ e1 ) @ ( K @ ( J @ ( I @ s3 ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( J @ ( I @ e1 ) @ ( K @ ( J @ s @ ( I @ s3 ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(lifteq,[status(thm)],[52]) ).
thf(258,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
!= ( L @ ( J @ ( I @ e1 ) @ ( K @ ( J @ s @ ( I @ s3 ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( true @ ( L @ ( J @ s @ ( I @ e1 ) @ ( K @ ( J @ ( I @ s3 ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[115,53]) ).
thf(259,plain,
( ( true @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[258:[bind(A,$thf( o @ s @ ( o @ bb ) )),bind(B,$thf( o @ ( o @ v1 ) )),bind(C,$thf( o @ s @ s @ s @ ( o @ v2 ) )),bind(D,$thf( o @ ( o @ s @ s @ v3 ) )),bind(E,$thf( o @ s @ s @ s @ ( o @ s @ s @ v4 ) )),bind(F,$thf( o @ s @ ( o @ s @ s @ h ) )),bind(G,$thf( o @ s @ ( o @ s @ s @ s @ s1 ) )),bind(H,$thf( o @ s @ s @ ( o @ s @ s @ s @ s2 ) )),bind(I,$thf( o @ s @ s @ s @ s )),bind(J,$thf( o )),bind(K,$thf( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) )),bind(L,$thf( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) ))]]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
thf(48,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(49,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
inference(lifteq,[status(thm)],[48]) ).
thf(294,plain,
( ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
= true ),
inference(rewrite,[status(thm)],[259,49]) ).
thf(11,axiom,
! [N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( K @ e2 ) @ ( N @ ( M @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( N @ ( M @ e2 ) @ ( L @ ( K @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',swap_blanks) ).
thf(66,plain,
! [N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( K @ e2 ) @ ( N @ ( M @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( N @ ( M @ e2 ) @ ( L @ ( K @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(67,plain,
! [N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( K @ e2 ) @ ( N @ ( M @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( N @ ( M @ e2 ) @ ( L @ ( K @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(lifteq,[status(thm)],[66]) ).
thf(146,plain,
! [Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( true @ ( L @ ( K @ e2 ) @ ( N @ ( M @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( N @ ( M @ e2 ) @ ( L @ ( K @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
!= ( Q @ ( P @ ( O @ ( O @ ifeq ) ) ) ) )
| ( true = P ) ),
inference(paramod_ordered,[status(thm)],[67,49]) ).
thf(148,plain,
! [Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true != Q )
| ( ( L @ ( K @ e2 ) @ ( N @ ( M @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) )
!= P )
| ( true != O )
| ( ( N @ ( M @ e2 ) @ ( L @ ( K @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) )
!= O )
| ( true = P ) ),
inference(simp,[status(thm)],[146]) ).
thf(150,plain,
! [N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( N @ ( M @ e2 ) @ ( L @ ( K @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) )
!= true )
| ( ( L @ ( K @ e2 ) @ ( N @ ( M @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) )
= true ) ),
inference(simp,[status(thm)],[148]) ).
thf(301,plain,
! [N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
!= ( N @ ( M @ e2 ) @ ( L @ ( K @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) )
| ( true != true )
| ( ( L @ ( K @ e2 ) @ ( N @ ( M @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[294,150]) ).
thf(302,plain,
! [N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
!= ( N @ ( M @ e2 ) @ ( L @ ( K @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( L @ ( K @ e2 ) @ ( N @ ( M @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) )
= true ) ),
inference(simp,[status(thm)],[301]) ).
thf(303,plain,
( ( o @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[302:[bind(A,$thf( o @ s @ ( o @ bb ) )),bind(B,$thf( o @ ( o @ v1 ) )),bind(C,$thf( o @ s @ s @ s @ ( o @ v2 ) )),bind(D,$thf( o @ ( o @ s @ s @ v3 ) )),bind(E,$thf( o @ s @ s @ s @ ( o @ s @ s @ v4 ) )),bind(F,$thf( o @ s @ ( o @ s @ s @ h ) )),bind(G,$thf( o @ s @ ( o @ s @ s @ s @ s1 ) )),bind(H,$thf( o @ s @ s @ ( o @ s @ s @ s @ s2 ) )),bind(I,$thf( o @ ( o @ s @ s @ s @ s @ s3 ) )),bind(J,$thf( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) )),bind(K,$thf( o @ s @ s @ s @ s )),bind(L,$thf( o @ s )),bind(M,$thf( o @ s @ s @ s @ s )),bind(N,$thf( o @ s @ s @ s ))]]) ).
thf(18,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( F @ ( E @ s @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ v4 ) @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( F @ ( E @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ s @ v4 ) @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v4_up) ).
thf(80,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( F @ ( E @ s @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ v4 ) @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( F @ ( E @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ s @ v4 ) @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(81,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( F @ ( E @ s @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ v4 ) @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( F @ ( E @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ s @ v4 ) @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(lifteq,[status(thm)],[80]) ).
thf(4248,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( o @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
!= ( L @ ( F @ ( E @ s @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ v4 ) @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( true @ ( true @ ( true @ ( L @ ( F @ ( E @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ s @ v4 ) @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[303,81]) ).
thf(4249,plain,
( ( true @ ( true @ ( true @ ( o @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ e1 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[4248:[bind(A,$thf( o @ s @ ( o @ bb ) )),bind(B,$thf( o @ ( o @ v1 ) )),bind(C,$thf( o @ s @ s @ s @ ( o @ v2 ) )),bind(D,$thf( o @ ( o @ s @ s @ v3 ) )),bind(E,$thf( o @ s @ s )),bind(F,$thf( o @ s @ s @ s )),bind(G,$thf( o @ s @ ( o @ s @ s @ h ) )),bind(H,$thf( o @ s @ ( o @ s @ s @ s @ s1 ) )),bind(I,$thf( o @ s @ s @ ( o @ s @ s @ s @ s2 ) )),bind(J,$thf( o @ ( o @ s @ s @ s @ s @ s3 ) )),bind(K,$thf( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) )),bind(L,$thf( o @ s @ ( o @ s @ s @ s @ s @ e2 ) ))]]) ).
thf(8,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( K @ ( J @ e1 ) @ ( K @ s @ ( J @ s4 ) @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( K @ s @ ( J @ e1 ) @ ( K @ ( J @ s4 ) @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s4_right) ).
thf(60,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( K @ ( J @ e1 ) @ ( K @ s @ ( J @ s4 ) @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( K @ s @ ( J @ e1 ) @ ( K @ ( J @ s4 ) @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(61,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( K @ ( J @ e1 ) @ ( K @ s @ ( J @ s4 ) @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( K @ s @ ( J @ e1 ) @ ( K @ ( J @ s4 ) @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(lifteq,[status(thm)],[60]) ).
thf(1208,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( o @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
!= ( L @ ( K @ s @ ( J @ e1 ) @ ( K @ ( J @ s4 ) @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( true @ ( L @ ( K @ ( J @ e1 ) @ ( K @ s @ ( J @ s4 ) @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[303,61]) ).
thf(1209,plain,
( ( true @ ( o @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[1208:[bind(A,$thf( o @ s @ ( o @ bb ) )),bind(B,$thf( o @ ( o @ v1 ) )),bind(C,$thf( o @ s @ s @ s @ ( o @ v2 ) )),bind(D,$thf( o @ ( o @ s @ s @ v3 ) )),bind(E,$thf( o @ s @ s @ s @ ( o @ s @ s @ v4 ) )),bind(F,$thf( o @ s @ ( o @ s @ s @ h ) )),bind(G,$thf( o @ s @ ( o @ s @ s @ s @ s1 ) )),bind(H,$thf( o @ s @ s @ ( o @ s @ s @ s @ s2 ) )),bind(I,$thf( o @ ( o @ s @ s @ s @ s @ s3 ) )),bind(J,$thf( o @ s @ s @ s @ s )),bind(K,$thf( o @ s @ s )),bind(L,$thf( o @ s @ ( o @ s @ s @ s @ s @ e2 ) ))]]) ).
thf(1384,plain,
( ( o @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
= true ),
inference(rewrite,[status(thm)],[1209,49]) ).
thf(1427,plain,
! [N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( o @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
!= ( N @ ( M @ e2 ) @ ( L @ ( K @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) )
| ( true != true )
| ( ( L @ ( K @ e2 ) @ ( N @ ( M @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[1384,150]) ).
thf(1428,plain,
! [N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( o @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
!= ( N @ ( M @ e2 ) @ ( L @ ( K @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( L @ ( K @ e2 ) @ ( N @ ( M @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) )
= true ) ),
inference(simp,[status(thm)],[1427]) ).
thf(1429,plain,
( ( o @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[1428:[bind(A,$thf( o @ s @ ( o @ bb ) )),bind(B,$thf( o @ ( o @ v1 ) )),bind(C,$thf( o @ s @ s @ s @ ( o @ v2 ) )),bind(D,$thf( o @ ( o @ s @ s @ v3 ) )),bind(E,$thf( o @ s @ s @ s @ ( o @ s @ s @ v4 ) )),bind(F,$thf( o @ s @ ( o @ s @ s @ h ) )),bind(G,$thf( o @ s @ ( o @ s @ s @ s @ s1 ) )),bind(H,$thf( o @ s @ s @ ( o @ s @ s @ s @ s2 ) )),bind(I,$thf( o @ ( o @ s @ s @ s @ s @ s3 ) )),bind(J,$thf( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) )),bind(K,$thf( o @ s @ s @ s @ s )),bind(L,$thf( o @ s @ s )),bind(M,$thf( o @ s @ s @ s @ s )),bind(N,$thf( o @ s ))]]) ).
thf(34,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( H @ ( G @ e1 ) @ ( K @ ( J @ ( I @ ( H @ s @ ( G @ s1 ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( H @ s @ ( G @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ s1 ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_right) ).
thf(112,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( H @ ( G @ e1 ) @ ( K @ ( J @ ( I @ ( H @ s @ ( G @ s1 ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( H @ s @ ( G @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ s1 ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(12,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( D @ ( C @ s @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ v2 ) @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( D @ ( C @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ s @ v2 ) @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v2_up) ).
thf(68,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( D @ ( C @ s @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ v2 ) @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( D @ ( C @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ s @ v2 ) @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(69,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( D @ ( C @ s @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ v2 ) @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( D @ ( C @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ s @ v2 ) @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(lifteq,[status(thm)],[68]) ).
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] :
( ( true @ ( B @ s @ ( A @ s @ s @ e2 ) @ ( B @ ( A @ s @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( B @ s @ ( A @ e2 ) @ ( B @ ( A @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_up) ).
thf(88,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( B @ s @ ( A @ s @ s @ e2 ) @ ( B @ ( A @ s @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( B @ s @ ( A @ e2 ) @ ( B @ ( A @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(38,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( I @ s @ ( H @ e1 ) @ ( K @ ( J @ ( I @ ( H @ s2 ) @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( I @ ( H @ e1 ) @ ( K @ ( J @ ( I @ s @ ( H @ s2 ) @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_left) ).
thf(120,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( I @ s @ ( H @ e1 ) @ ( K @ ( J @ ( I @ ( H @ s2 ) @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( I @ ( H @ e1 ) @ ( K @ ( J @ ( I @ s @ ( H @ s2 ) @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(6,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( K @ s @ ( J @ e1 ) @ ( K @ ( J @ s4 ) @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( K @ ( J @ e1 ) @ ( K @ s @ ( J @ s4 ) @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s4_left) ).
thf(56,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( K @ s @ ( J @ e1 ) @ ( K @ ( J @ s4 ) @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( K @ ( J @ e1 ) @ ( K @ s @ ( J @ s4 ) @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(156,plain,
! [N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
!= ( N @ ( M @ e2 ) @ ( L @ ( K @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) )
| ( true != true )
| ( ( L @ ( K @ e2 ) @ ( N @ ( M @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[115,150]) ).
thf(157,plain,
! [N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
!= ( N @ ( M @ e2 ) @ ( L @ ( K @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( L @ ( K @ e2 ) @ ( N @ ( M @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) )
= true ) ),
inference(simp,[status(thm)],[156]) ).
thf(158,plain,
( ( o @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[157:[bind(A,$thf( o @ s @ ( o @ bb ) )),bind(B,$thf( o @ ( o @ v1 ) )),bind(C,$thf( o @ s @ s @ s @ ( o @ v2 ) )),bind(D,$thf( o @ ( o @ s @ s @ v3 ) )),bind(E,$thf( o @ s @ s @ s @ ( o @ s @ s @ v4 ) )),bind(F,$thf( o @ s @ ( o @ s @ s @ h ) )),bind(G,$thf( o @ s @ ( o @ s @ s @ s @ s1 ) )),bind(H,$thf( o @ s @ s @ ( o @ s @ s @ s @ s2 ) )),bind(I,$thf( o @ s @ ( o @ s @ s @ s @ s @ s3 ) )),bind(J,$thf( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) )),bind(K,$thf( o @ s @ s @ s @ s )),bind(L,$thf( o )),bind(M,$thf( o @ s @ s @ s @ s )),bind(N,$thf( o @ s @ s @ s ))]]) ).
thf(1242,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( o @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
!= ( L @ ( K @ s @ ( J @ e1 ) @ ( K @ ( J @ s4 ) @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( true @ ( L @ ( K @ ( J @ e1 ) @ ( K @ s @ ( J @ s4 ) @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[158,61]) ).
thf(1243,plain,
( ( true @ ( o @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[1242:[bind(A,$thf( o @ s @ ( o @ bb ) )),bind(B,$thf( o @ ( o @ v1 ) )),bind(C,$thf( o @ s @ s @ s @ ( o @ v2 ) )),bind(D,$thf( o @ ( o @ s @ s @ v3 ) )),bind(E,$thf( o @ s @ s @ s @ ( o @ s @ s @ v4 ) )),bind(F,$thf( o @ s @ ( o @ s @ s @ h ) )),bind(G,$thf( o @ s @ ( o @ s @ s @ s @ s1 ) )),bind(H,$thf( o @ s @ s @ ( o @ s @ s @ s @ s2 ) )),bind(I,$thf( o @ s @ ( o @ s @ s @ s @ s @ s3 ) )),bind(J,$thf( o @ s @ s @ s @ s )),bind(K,$thf( o @ s @ s )),bind(L,$thf( o @ ( o @ s @ s @ s @ s @ e2 ) ))]]) ).
thf(1648,plain,
( ( o @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
= true ),
inference(rewrite,[status(thm)],[1243,49]) ).
thf(1696,plain,
! [N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( o @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
!= ( N @ ( M @ e2 ) @ ( L @ ( K @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) )
| ( true != true )
| ( ( L @ ( K @ e2 ) @ ( N @ ( M @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[1648,150]) ).
thf(1697,plain,
! [N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( o @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
!= ( N @ ( M @ e2 ) @ ( L @ ( K @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( L @ ( K @ e2 ) @ ( N @ ( M @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) )
= true ) ),
inference(simp,[status(thm)],[1696]) ).
thf(1698,plain,
( ( o @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[1697:[bind(A,$thf( o @ s @ ( o @ bb ) )),bind(B,$thf( o @ ( o @ v1 ) )),bind(C,$thf( o @ s @ s @ s @ ( o @ v2 ) )),bind(D,$thf( o @ ( o @ s @ s @ v3 ) )),bind(E,$thf( o @ s @ s @ s @ ( o @ s @ s @ v4 ) )),bind(F,$thf( o @ s @ ( o @ s @ s @ h ) )),bind(G,$thf( o @ s @ ( o @ s @ s @ s @ s1 ) )),bind(H,$thf( o @ s @ s @ ( o @ s @ s @ s @ s2 ) )),bind(I,$thf( o @ s @ ( o @ s @ s @ s @ s @ s3 ) )),bind(J,$thf( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) )),bind(K,$thf( o @ s @ s @ s @ s )),bind(L,$thf( o @ s @ s )),bind(M,$thf( o @ s @ s @ s @ s )),bind(N,$thf( o ))]]) ).
thf(15,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( E @ ( D @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ s @ v3 ) @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( E @ ( D @ s @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ v3 ) @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v3_down) ).
thf(74,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( E @ ( D @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ s @ v3 ) @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( E @ ( D @ s @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ v3 ) @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(75,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( E @ ( D @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ s @ v3 ) @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( E @ ( D @ s @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ v3 ) @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(lifteq,[status(thm)],[74]) ).
thf(3120,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( o @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
!= ( L @ ( E @ ( D @ s @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ v3 ) @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( true @ ( L @ ( E @ ( D @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ s @ v3 ) @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[1698,75]) ).
thf(3121,plain,
( ( true @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ ( o @ s @ s @ e1 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[3120:[bind(A,$thf( o @ s @ ( o @ bb ) )),bind(B,$thf( o @ ( o @ v1 ) )),bind(C,$thf( o @ s @ s @ s @ ( o @ v2 ) )),bind(D,$thf( o @ s @ s )),bind(E,$thf( o )),bind(F,$thf( o @ s @ s @ s @ ( o @ s @ s @ v4 ) )),bind(G,$thf( o @ s @ ( o @ s @ s @ h ) )),bind(H,$thf( o @ s @ ( o @ s @ s @ s @ s1 ) )),bind(I,$thf( o @ s @ s @ ( o @ s @ s @ s @ s2 ) )),bind(J,$thf( o @ s @ ( o @ s @ s @ s @ s @ s3 ) )),bind(K,$thf( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) )),bind(L,$thf( o @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) ))]]) ).
thf(3600,plain,
( ( o @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ ( o @ s @ s @ e1 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
= true ),
inference(rewrite,[status(thm)],[3121,49]) ).
thf(3,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( G @ s @ s @ ( F @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ h ) @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( G @ ( F @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ s @ ( F @ h ) @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_left) ).
thf(50,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( G @ s @ s @ ( F @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ h ) @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( G @ ( F @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ s @ ( F @ h ) @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(51,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( G @ s @ s @ ( F @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ h ) @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( G @ ( F @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ s @ ( F @ h ) @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(lifteq,[status(thm)],[50]) ).
thf(3628,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( o @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ ( o @ s @ s @ e1 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
!= ( L @ ( G @ ( F @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ s @ ( F @ h ) @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( true @ ( L @ ( G @ s @ s @ ( F @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ h ) @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[3600,51]) ).
thf(3629,plain,
( ( true @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ s @ ( o @ s @ s @ e1 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[3628:[bind(A,$thf( o @ s @ ( o @ bb ) )),bind(B,$thf( o @ ( o @ v1 ) )),bind(C,$thf( o @ s @ s @ s @ ( o @ v2 ) )),bind(D,$thf( o @ ( o @ s @ s @ s @ v3 ) )),bind(E,$thf( o @ s @ s @ s @ ( o @ s @ s @ v4 ) )),bind(F,$thf( o @ s @ s )),bind(G,$thf( o )),bind(H,$thf( o @ s @ ( o @ s @ s @ s @ s1 ) )),bind(I,$thf( o @ s @ s @ ( o @ s @ s @ s @ s2 ) )),bind(J,$thf( o @ s @ ( o @ s @ s @ s @ s @ s3 ) )),bind(K,$thf( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) )),bind(L,$thf( o @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) ))]]) ).
thf(7329,plain,
( ( o @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ s @ ( o @ s @ s @ e1 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
= true ),
inference(rewrite,[status(thm)],[3629,49]) ).
thf(7420,plain,
! [N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( o @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ s @ ( o @ s @ s @ e1 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
!= ( N @ ( M @ e2 ) @ ( L @ ( K @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) )
| ( true != true )
| ( ( L @ ( K @ e2 ) @ ( N @ ( M @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[7329,150]) ).
thf(7421,plain,
! [N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( o @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ s @ ( o @ s @ s @ e1 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
!= ( N @ ( M @ e2 ) @ ( L @ ( K @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( L @ ( K @ e2 ) @ ( N @ ( M @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) )
= true ) ),
inference(simp,[status(thm)],[7420]) ).
thf(7422,plain,
( ( o @ s @ s @ ( o @ s @ s @ e2 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[7421:[bind(A,$thf( o @ s @ ( o @ bb ) )),bind(B,$thf( o @ ( o @ v1 ) )),bind(C,$thf( o @ s @ s @ s @ ( o @ v2 ) )),bind(D,$thf( o @ ( o @ s @ s @ s @ v3 ) )),bind(E,$thf( o @ s @ s @ s @ ( o @ s @ s @ v4 ) )),bind(F,$thf( o @ ( o @ s @ s @ h ) )),bind(G,$thf( o @ s @ ( o @ s @ s @ s @ s1 ) )),bind(H,$thf( o @ s @ s @ ( o @ s @ s @ s @ s2 ) )),bind(I,$thf( o @ s @ ( o @ s @ s @ s @ s @ s3 ) )),bind(J,$thf( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) )),bind(K,$thf( o @ s @ s )),bind(L,$thf( o @ s @ s )),bind(M,$thf( o @ s @ s @ s @ s )),bind(N,$thf( o @ s @ s ))]]) ).
thf(33,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( I @ ( H @ e1 ) @ ( K @ ( J @ ( I @ ( H @ s @ s2 ) @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( I @ ( H @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ s2 ) @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_down) ).
thf(110,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( I @ ( H @ e1 ) @ ( K @ ( J @ ( I @ ( H @ s @ s2 ) @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( I @ ( H @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ s2 ) @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(3065,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
!= ( L @ ( E @ ( D @ s @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ v3 ) @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( true @ ( L @ ( E @ ( D @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ s @ v3 ) @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[115,75]) ).
thf(3066,plain,
( ( true @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ ( o @ s @ s @ e1 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[3065:[bind(A,$thf( o @ s @ ( o @ bb ) )),bind(B,$thf( o @ ( o @ v1 ) )),bind(C,$thf( o @ s @ s @ s @ ( o @ v2 ) )),bind(D,$thf( o @ s @ s )),bind(E,$thf( o )),bind(F,$thf( o @ s @ s @ s @ ( o @ s @ s @ v4 ) )),bind(G,$thf( o @ s @ ( o @ s @ s @ h ) )),bind(H,$thf( o @ s @ ( o @ s @ s @ s @ s1 ) )),bind(I,$thf( o @ s @ s @ ( o @ s @ s @ s @ s2 ) )),bind(J,$thf( o @ s @ ( o @ s @ s @ s @ s @ s3 ) )),bind(K,$thf( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) )),bind(L,$thf( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) ))]]) ).
thf(3211,plain,
( ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ ( o @ s @ s @ e1 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
= true ),
inference(rewrite,[status(thm)],[3066,49]) ).
thf(3278,plain,
! [N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ ( o @ s @ s @ e1 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
!= ( N @ ( M @ e2 ) @ ( L @ ( K @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) )
| ( true != true )
| ( ( L @ ( K @ e2 ) @ ( N @ ( M @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[3211,150]) ).
thf(3279,plain,
! [N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ ( o @ s @ s @ e1 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
!= ( N @ ( M @ e2 ) @ ( L @ ( K @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( L @ ( K @ e2 ) @ ( N @ ( M @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) )
= true ) ),
inference(simp,[status(thm)],[3278]) ).
thf(3280,plain,
( ( o @ ( o @ s @ s @ e2 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[3279:[bind(A,$thf( o @ s @ ( o @ bb ) )),bind(B,$thf( o @ ( o @ v1 ) )),bind(C,$thf( o @ s @ s @ s @ ( o @ v2 ) )),bind(D,$thf( o @ ( o @ s @ s @ s @ v3 ) )),bind(E,$thf( o @ s @ s @ s @ ( o @ s @ s @ v4 ) )),bind(F,$thf( o @ s @ ( o @ s @ s @ h ) )),bind(G,$thf( o @ s @ ( o @ s @ s @ s @ s1 ) )),bind(H,$thf( o @ s @ s @ ( o @ s @ s @ s @ s2 ) )),bind(I,$thf( o @ s @ ( o @ s @ s @ s @ s @ s3 ) )),bind(J,$thf( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) )),bind(K,$thf( o @ s @ s )),bind(L,$thf( o )),bind(M,$thf( o @ s @ s @ s @ s )),bind(N,$thf( o @ s @ s @ s ))]]) ).
thf(24,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( H @ s @ ( G @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ s1 ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( H @ ( G @ e1 ) @ ( K @ ( J @ ( I @ ( H @ s @ ( G @ s1 ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_left) ).
thf(92,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( H @ s @ ( G @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ s1 ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( H @ ( G @ e1 ) @ ( K @ ( J @ ( I @ ( H @ s @ ( G @ s1 ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(93,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( H @ s @ ( G @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ s1 ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( H @ ( G @ e1 ) @ ( K @ ( J @ ( I @ ( H @ s @ ( G @ s1 ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(lifteq,[status(thm)],[92]) ).
thf(57,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( K @ s @ ( J @ e1 ) @ ( K @ ( J @ s4 ) @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( K @ ( J @ e1 ) @ ( K @ s @ ( J @ s4 ) @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(lifteq,[status(thm)],[56]) ).
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] :
( ( true @ ( G @ s @ ( F @ e2 ) @ ( G @ ( F @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ s @ h ) @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( G @ s @ ( F @ s @ e2 ) @ ( G @ ( F @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ h ) @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_down) ).
thf(78,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( G @ s @ ( F @ e2 ) @ ( G @ ( F @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ s @ h ) @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( G @ s @ ( F @ s @ e2 ) @ ( G @ ( F @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ h ) @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(31,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( I @ ( H @ e1 ) @ ( K @ ( J @ ( I @ s @ ( H @ s2 ) @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( I @ s @ ( H @ e1 ) @ ( K @ ( J @ ( I @ ( H @ s2 ) @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_right) ).
thf(106,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( I @ ( H @ e1 ) @ ( K @ ( J @ ( I @ s @ ( H @ s2 ) @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( I @ s @ ( H @ e1 ) @ ( K @ ( J @ ( I @ ( H @ s2 ) @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(20,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( B @ s @ ( A @ e2 ) @ ( B @ ( A @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( B @ s @ ( A @ s @ s @ e2 ) @ ( B @ ( A @ s @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_down) ).
thf(84,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( B @ s @ ( A @ e2 ) @ ( B @ ( A @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( B @ s @ ( A @ s @ s @ e2 ) @ ( B @ ( A @ s @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(44,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( D @ ( C @ s @ e2 ) @ ( D @ ( C @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ s @ ( C @ v2 ) @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( D @ s @ ( C @ s @ e2 ) @ ( D @ s @ ( C @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ v2 ) @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v2_right) ).
thf(132,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( D @ ( C @ s @ e2 ) @ ( D @ ( C @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ s @ ( C @ v2 ) @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( D @ s @ ( C @ s @ e2 ) @ ( D @ s @ ( C @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ v2 ) @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(3674,plain,
! [N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( o @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ ( o @ s @ s @ e1 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
!= ( N @ ( M @ e2 ) @ ( L @ ( K @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) )
| ( true != true )
| ( ( L @ ( K @ e2 ) @ ( N @ ( M @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[3600,150]) ).
thf(3675,plain,
! [N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( o @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ ( o @ s @ s @ e1 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
!= ( N @ ( M @ e2 ) @ ( L @ ( K @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( L @ ( K @ e2 ) @ ( N @ ( M @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) )
= true ) ),
inference(simp,[status(thm)],[3674]) ).
thf(3676,plain,
( ( o @ ( o @ s @ s @ e2 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[3675:[bind(A,$thf( o @ s @ ( o @ bb ) )),bind(B,$thf( o @ ( o @ v1 ) )),bind(C,$thf( o @ s @ s @ s @ ( o @ v2 ) )),bind(D,$thf( o @ ( o @ s @ s @ s @ v3 ) )),bind(E,$thf( o @ s @ s @ s @ ( o @ s @ s @ v4 ) )),bind(F,$thf( o @ s @ ( o @ s @ s @ h ) )),bind(G,$thf( o @ s @ ( o @ s @ s @ s @ s1 ) )),bind(H,$thf( o @ s @ s @ ( o @ s @ s @ s @ s2 ) )),bind(I,$thf( o @ s @ ( o @ s @ s @ s @ s @ s3 ) )),bind(J,$thf( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) )),bind(K,$thf( o @ s @ s )),bind(L,$thf( o )),bind(M,$thf( o @ s @ s @ s @ s )),bind(N,$thf( o @ s @ s ))]]) ).
thf(89,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( B @ s @ ( A @ s @ s @ e2 ) @ ( B @ ( A @ s @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( B @ s @ ( A @ e2 ) @ ( B @ ( A @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(lifteq,[status(thm)],[88]) ).
thf(36,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( C @ ( B @ s @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ v1 ) @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( C @ ( B @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ s @ v1 ) @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v1_up) ).
thf(116,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( C @ ( B @ s @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ v1 ) @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( C @ ( B @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ s @ v1 ) @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(682,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
!= ( L @ ( K @ ( J @ e1 ) @ ( K @ s @ ( J @ s4 ) @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( true @ ( L @ ( K @ s @ ( J @ e1 ) @ ( K @ ( J @ s4 ) @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[294,57]) ).
thf(683,plain,
( ( true @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[682:[bind(A,$thf( o @ s @ ( o @ bb ) )),bind(B,$thf( o @ ( o @ v1 ) )),bind(C,$thf( o @ s @ s @ s @ ( o @ v2 ) )),bind(D,$thf( o @ ( o @ s @ s @ v3 ) )),bind(E,$thf( o @ s @ s @ s @ ( o @ s @ s @ v4 ) )),bind(F,$thf( o @ s @ ( o @ s @ s @ h ) )),bind(G,$thf( o @ s @ ( o @ s @ s @ s @ s1 ) )),bind(H,$thf( o @ s @ s @ ( o @ s @ s @ s @ s2 ) )),bind(I,$thf( o @ ( o @ s @ s @ s @ s @ s3 ) )),bind(J,$thf( o @ s @ s @ s @ s )),bind(K,$thf( o @ s )),bind(L,$thf( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) ))]]) ).
thf(901,plain,
( ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
= true ),
inference(rewrite,[status(thm)],[683,49]) ).
thf(916,plain,
! [N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
!= ( N @ ( M @ e2 ) @ ( L @ ( K @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) )
| ( true != true )
| ( ( L @ ( K @ e2 ) @ ( N @ ( M @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[901,150]) ).
thf(917,plain,
! [N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
!= ( N @ ( M @ e2 ) @ ( L @ ( K @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( L @ ( K @ e2 ) @ ( N @ ( M @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) )
= true ) ),
inference(simp,[status(thm)],[916]) ).
thf(918,plain,
( ( o @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[917:[bind(A,$thf( o @ s @ ( o @ bb ) )),bind(B,$thf( o @ ( o @ v1 ) )),bind(C,$thf( o @ s @ s @ s @ ( o @ v2 ) )),bind(D,$thf( o @ ( o @ s @ s @ v3 ) )),bind(E,$thf( o @ s @ s @ s @ ( o @ s @ s @ v4 ) )),bind(F,$thf( o @ s @ ( o @ s @ s @ h ) )),bind(G,$thf( o @ s @ ( o @ s @ s @ s @ s1 ) )),bind(H,$thf( o @ s @ s @ ( o @ s @ s @ s @ s2 ) )),bind(I,$thf( o @ ( o @ s @ s @ s @ s @ s3 ) )),bind(J,$thf( o @ s @ ( o @ s @ s @ s @ s @ s4 ) )),bind(K,$thf( o @ s @ s @ s @ s )),bind(L,$thf( o @ s @ s )),bind(M,$thf( o @ s @ s @ s @ s )),bind(N,$thf( o @ s @ s @ s ))]]) ).
thf(4284,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( o @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
!= ( L @ ( F @ ( E @ s @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ v4 ) @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( true @ ( true @ ( true @ ( L @ ( F @ ( E @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ s @ v4 ) @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[918,81]) ).
thf(4285,plain,
( ( true @ ( true @ ( true @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ e1 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[4284:[bind(A,$thf( o @ s @ ( o @ bb ) )),bind(B,$thf( o @ ( o @ v1 ) )),bind(C,$thf( o @ s @ s @ s @ ( o @ v2 ) )),bind(D,$thf( o @ ( o @ s @ s @ v3 ) )),bind(E,$thf( o @ s @ s )),bind(F,$thf( o @ s @ s @ s )),bind(G,$thf( o @ s @ ( o @ s @ s @ h ) )),bind(H,$thf( o @ s @ ( o @ s @ s @ s @ s1 ) )),bind(I,$thf( o @ s @ s @ ( o @ s @ s @ s @ s2 ) )),bind(J,$thf( o @ ( o @ s @ s @ s @ s @ s3 ) )),bind(K,$thf( o @ s @ ( o @ s @ s @ s @ s @ s4 ) )),bind(L,$thf( o @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) ))]]) ).
thf(85,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( B @ s @ ( A @ e2 ) @ ( B @ ( A @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( B @ s @ ( A @ s @ s @ e2 ) @ ( B @ ( A @ s @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(lifteq,[status(thm)],[84]) ).
thf(29,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( C @ s @ ( B @ s @ e2 ) @ ( C @ s @ ( B @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ v1 ) @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( C @ ( B @ s @ e2 ) @ ( C @ ( B @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ s @ ( B @ v1 ) @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v1_left) ).
thf(102,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( C @ s @ ( B @ s @ e2 ) @ ( C @ s @ ( B @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ v1 ) @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( C @ ( B @ s @ e2 ) @ ( C @ ( B @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ s @ ( B @ v1 ) @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(23,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( I @ ( H @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ s2 ) @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( I @ ( H @ e1 ) @ ( K @ ( J @ ( I @ ( H @ s @ s2 ) @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_up) ).
thf(90,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( I @ ( H @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ s2 ) @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( I @ ( H @ e1 ) @ ( K @ ( J @ ( I @ ( H @ s @ s2 ) @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(91,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( I @ ( H @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ s2 ) @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( I @ ( H @ e1 ) @ ( K @ ( J @ ( I @ ( H @ s @ s2 ) @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(lifteq,[status(thm)],[90]) ).
thf(3866,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( o @ ( o @ s @ s @ e2 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
!= ( L @ ( I @ ( H @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ s2 ) @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( true @ ( true @ ( true @ ( L @ ( I @ ( H @ e1 ) @ ( K @ ( J @ ( I @ ( H @ s @ s2 ) @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[3676,91]) ).
thf(3867,plain,
( ( true @ ( true @ ( true @ ( o @ ( o @ s @ s @ e2 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ e1 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[3866:[bind(A,$thf( o @ s @ ( o @ bb ) )),bind(B,$thf( o @ ( o @ v1 ) )),bind(C,$thf( o @ s @ s @ s @ ( o @ v2 ) )),bind(D,$thf( o @ ( o @ s @ s @ s @ v3 ) )),bind(E,$thf( o @ s @ s @ s @ ( o @ s @ s @ v4 ) )),bind(F,$thf( o @ s @ ( o @ s @ s @ h ) )),bind(G,$thf( o @ s @ ( o @ s @ s @ s @ s1 ) )),bind(H,$thf( o @ s @ s @ s )),bind(I,$thf( o @ s @ s )),bind(J,$thf( o @ s @ ( o @ s @ s @ s @ s @ s3 ) )),bind(K,$thf( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) )),bind(L,$thf( o @ ( o @ s @ s @ e2 ) ))]]) ).
thf(13,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( G @ s @ ( F @ s @ e2 ) @ ( G @ ( F @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ h ) @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( G @ s @ ( F @ e2 ) @ ( G @ ( F @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ s @ h ) @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_up) ).
thf(70,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( G @ s @ ( F @ s @ e2 ) @ ( G @ ( F @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ h ) @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( G @ s @ ( F @ e2 ) @ ( G @ ( F @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ s @ h ) @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(1,negated_conjecture,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( o @ s @ s @ ( o @ s @ s @ v4 ) @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) )
!= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_state) ).
thf(45,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( o @ s @ s @ ( o @ s @ s @ v4 ) @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) )
!= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(46,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( o @ s @ s @ ( o @ s @ s @ v4 ) @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) )
!= true ),
inference(polarity_switch,[status(thm)],[45]) ).
thf(47,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( o @ s @ s @ ( o @ s @ s @ v4 ) @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) )
!= true ),
inference(lifteq,[status(thm)],[46]) ).
thf(134,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
!= ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( o @ s @ s @ ( o @ s @ s @ v4 ) @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[115,47]) ).
thf(135,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
!= ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( o @ s @ s @ ( o @ s @ s @ v4 ) @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[134]) ).
thf(136,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) )
!= K )
| ( ( o @ ( o @ s @ s @ s @ s @ e1 ) )
!= J )
| ( ( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) )
!= I )
| ( ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) )
!= H )
| ( ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) )
!= G )
| ( ( o @ s @ ( o @ s @ s @ s @ s1 ) )
!= F )
| ( ( o @ s @ ( o @ s @ s @ h ) )
!= E )
| ( ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) )
!= ( o @ s @ s @ ( o @ s @ s @ v4 ) ) )
| ( ( o @ ( o @ s @ s @ v3 ) )
!= D )
| ( ( o @ s @ s @ s @ ( o @ v2 ) )
!= C )
| ( ( o @ ( o @ v1 ) )
!= B )
| ( ( o @ s @ ( o @ bb ) )
!= A ) ),
inference(simp,[status(thm)],[135]) ).
thf(137,plain,
( ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) )
!= ( o @ s @ s @ ( o @ s @ s @ v4 ) ) ),
inference(simp,[status(thm)],[136]) ).
thf(10,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( C @ ( B @ s @ e2 ) @ ( C @ ( B @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ s @ ( B @ v1 ) @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( C @ s @ ( B @ s @ e2 ) @ ( C @ s @ ( B @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ v1 ) @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v1_right) ).
thf(64,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( C @ ( B @ s @ e2 ) @ ( C @ ( B @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ s @ ( B @ v1 ) @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( C @ s @ ( B @ s @ e2 ) @ ( C @ s @ ( B @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ v1 ) @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(65,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( C @ ( B @ s @ e2 ) @ ( C @ ( B @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ s @ ( B @ v1 ) @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( C @ s @ ( B @ s @ e2 ) @ ( C @ s @ ( B @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ v1 ) @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(lifteq,[status(thm)],[64]) ).
thf(166,plain,
! [Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( L @ ( K @ e2 ) @ ( N @ ( M @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) )
!= ( Y @ ( X @ ( W @ ( V @ ( U @ ( T @ ( S @ ( o @ s @ s @ ( o @ s @ s @ v4 ) @ ( R @ ( Q @ ( P @ ( O @ state ) ) ) ) ) ) ) ) ) ) ) ) )
| ( true != true )
| ( ( N @ ( M @ e2 ) @ ( L @ ( K @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) )
!= true ) ),
inference(paramod_ordered,[status(thm)],[150,47]) ).
thf(167,plain,
! [Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( L @ ( K @ e2 ) @ ( N @ ( M @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) )
!= ( Y @ ( X @ ( W @ ( V @ ( U @ ( T @ ( S @ ( o @ s @ s @ ( o @ s @ s @ v4 ) @ ( R @ ( Q @ ( P @ ( O @ state ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( N @ ( M @ e2 ) @ ( L @ ( K @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) )
!= true ) ),
inference(simp,[status(thm)],[166]) ).
thf(168,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( K @ ( J @ e2 ) @ ( M @ ( L @ e1 ) @ ( I @ ( H @ ( G @ ( F @ ( E @ ( o @ s @ s @ ( o @ s @ s @ v4 ) @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) )
!= true ),
inference(pattern_uni,[status(thm)],[167:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( o @ s @ s @ ( o @ s @ s @ v4 ) )),bind(F,$thf( F )),bind(G,$thf( G )),bind(H,$thf( H )),bind(I,$thf( I )),bind(J,$thf( J )),bind(K,$thf( ZH )),bind(L,$thf( ZI )),bind(M,$thf( ZF )),bind(N,$thf( ZG )),bind(O,$thf( A )),bind(P,$thf( B )),bind(Q,$thf( C )),bind(R,$thf( D )),bind(S,$thf( F )),bind(T,$thf( G )),bind(U,$thf( H )),bind(V,$thf( I )),bind(W,$thf( J )),bind(X,$thf( ZG @ ( ZF @ e1 ) )),bind(Y,$thf( ZI @ ( ZH @ e2 ) ))]]) ).
thf(169,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( K @ ( J @ e2 ) @ ( M @ ( L @ e1 ) @ ( I @ ( H @ ( G @ ( F @ ( E @ ( o @ s @ s @ ( o @ s @ s @ v4 ) @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) )
!= true ),
inference(simp,[status(thm)],[168]) ).
thf(138,plain,
( ( ( o @ s @ s @ s )
!= ( o @ s @ s ) )
| ( ( o @ s @ s )
!= ( o @ s @ s ) ) ),
inference(simp,[status(thm)],[137]) ).
thf(139,plain,
( ( o @ s @ s @ s )
!= ( o @ s @ s ) ),
inference(simp,[status(thm)],[138]) ).
thf(140,plain,
( ( o @ s @ s )
!= ( o @ s ) ),
inference(simp,[status(thm)],[139]) ).
thf(141,plain,
( ( o @ s )
!= o ),
inference(simp,[status(thm)],[140]) ).
thf(40,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( J @ ( I @ e1 ) @ ( K @ ( J @ s @ ( I @ s3 ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( J @ s @ ( I @ e1 ) @ ( K @ ( J @ ( I @ s3 ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_right) ).
thf(124,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( J @ ( I @ e1 ) @ ( K @ ( J @ s @ ( I @ s3 ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( J @ s @ ( I @ e1 ) @ ( K @ ( J @ ( I @ s3 ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(16,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( J @ ( I @ s @ e1 ) @ ( K @ ( J @ ( I @ s3 ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( J @ ( I @ e1 ) @ ( K @ ( J @ ( I @ s @ s3 ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_up) ).
thf(76,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( J @ ( I @ s @ e1 ) @ ( K @ ( J @ ( I @ s3 ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( J @ ( I @ e1 ) @ ( K @ ( J @ ( I @ s @ s3 ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(77,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( J @ ( I @ s @ e1 ) @ ( K @ ( J @ ( I @ s3 ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( J @ ( I @ e1 ) @ ( K @ ( J @ ( I @ s @ s3 ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(lifteq,[status(thm)],[76]) ).
thf(26,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( K @ ( J @ s @ e1 ) @ ( K @ ( J @ s4 ) @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( K @ ( J @ e1 ) @ ( K @ ( J @ s @ s4 ) @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s4_up) ).
thf(96,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( K @ ( J @ s @ e1 ) @ ( K @ ( J @ s4 ) @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( K @ ( J @ e1 ) @ ( K @ ( J @ s @ s4 ) @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(14,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( D @ s @ ( C @ s @ e2 ) @ ( D @ s @ ( C @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ v2 ) @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( D @ ( C @ s @ e2 ) @ ( D @ ( C @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ s @ ( C @ v2 ) @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v2_left) ).
thf(72,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( D @ s @ ( C @ s @ e2 ) @ ( D @ s @ ( C @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ v2 ) @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( D @ ( C @ s @ e2 ) @ ( D @ ( C @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ s @ ( C @ v2 ) @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(73,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( D @ s @ ( C @ s @ e2 ) @ ( D @ s @ ( C @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ v2 ) @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( D @ ( C @ s @ e2 ) @ ( D @ ( C @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ s @ ( C @ v2 ) @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(lifteq,[status(thm)],[72]) ).
thf(42,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( C @ ( B @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ s @ v1 ) @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( C @ ( B @ s @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ v1 ) @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v1_down) ).
thf(128,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( C @ ( B @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ s @ v1 ) @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( C @ ( B @ s @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ v1 ) @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(144,plain,
! [N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
!= ( L @ ( K @ e2 ) @ ( N @ ( M @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( true @ ( true @ ( true @ ( N @ ( M @ e2 ) @ ( L @ ( K @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[115,67]) ).
thf(145,plain,
( ( true @ ( true @ ( true @ ( o @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[144:[bind(A,$thf( o @ s @ ( o @ bb ) )),bind(B,$thf( o @ ( o @ v1 ) )),bind(C,$thf( o @ s @ s @ s @ ( o @ v2 ) )),bind(D,$thf( o @ ( o @ s @ s @ v3 ) )),bind(E,$thf( o @ s @ s @ s @ ( o @ s @ s @ v4 ) )),bind(F,$thf( o @ s @ ( o @ s @ s @ h ) )),bind(G,$thf( o @ s @ ( o @ s @ s @ s @ s1 ) )),bind(H,$thf( o @ s @ s @ ( o @ s @ s @ s @ s2 ) )),bind(I,$thf( o @ s @ ( o @ s @ s @ s @ s @ s3 ) )),bind(J,$thf( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) )),bind(K,$thf( o @ s @ s @ s @ s )),bind(L,$thf( o @ s @ s @ s )),bind(M,$thf( o @ s @ s @ s @ s )),bind(N,$thf( o ))]]) ).
thf(244,plain,
( ( true @ ( true @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[145,158]) ).
thf(5,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( E @ s @ ( D @ s @ e2 ) @ ( E @ s @ ( D @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ v3 ) @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( E @ ( D @ s @ e2 ) @ ( E @ ( D @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ s @ ( D @ v3 ) @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v3_left) ).
thf(54,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( E @ s @ ( D @ s @ e2 ) @ ( E @ s @ ( D @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ v3 ) @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( E @ ( D @ s @ e2 ) @ ( E @ ( D @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ s @ ( D @ v3 ) @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(55,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( E @ s @ ( D @ s @ e2 ) @ ( E @ s @ ( D @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ v3 ) @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( E @ ( D @ s @ e2 ) @ ( E @ ( D @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ s @ ( D @ v3 ) @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(lifteq,[status(thm)],[54]) ).
thf(396,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( o @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
!= ( E @ s @ ( D @ s @ e2 ) @ ( E @ s @ ( D @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ v3 ) @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( true @ ( true @ ( true @ ( E @ ( D @ s @ e2 ) @ ( E @ ( D @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ s @ ( D @ v3 ) @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[303,55]) ).
thf(416,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( o @ s @ ( o @ s @ s @ s @ s @ e2 ) )
!= ( E @ s @ ( D @ s @ e2 ) ) )
| ( ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e1 ) )
!= ( E @ s @ ( D @ e1 ) ) )
| ( ( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) )
!= K )
| ( ( o @ ( o @ s @ s @ s @ s @ s3 ) )
!= J )
| ( ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) )
!= I )
| ( ( o @ s @ ( o @ s @ s @ s @ s1 ) )
!= H )
| ( ( o @ s @ ( o @ s @ s @ h ) )
!= G )
| ( ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) )
!= F )
| ( ( o @ ( o @ s @ s @ v3 ) )
!= ( E @ ( D @ v3 ) ) )
| ( ( o @ s @ s @ s @ ( o @ v2 ) )
!= C )
| ( ( o @ ( o @ v1 ) )
!= B )
| ( ( o @ s @ ( o @ bb ) )
!= A )
| ( ( true @ ( true @ ( true @ ( E @ ( D @ s @ e2 ) @ ( E @ ( D @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ s @ ( D @ v3 ) @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[396]) ).
thf(425,plain,
! [B: $i,A: $i] :
( ( ( o @ s @ ( o @ s @ s @ s @ s @ e2 ) )
!= ( B @ s @ ( A @ s @ e2 ) ) )
| ( ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e1 ) )
!= ( B @ s @ ( A @ e1 ) ) )
| ( ( o @ ( o @ s @ s @ v3 ) )
!= ( B @ ( A @ v3 ) ) )
| ( ( true @ ( true @ ( true @ ( B @ ( A @ s @ e2 ) @ ( B @ ( A @ e1 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( B @ s @ ( A @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[416]) ).
thf(265,plain,
! [O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
!= ( true @ ( O @ ( M @ s @ ( L @ e1 ) @ ( N @ ( M @ ( L @ s3 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( O @ ( M @ ( L @ e1 ) @ ( N @ ( M @ s @ ( L @ s3 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) ) )
| ( B = true ) ),
inference(paramod_ordered,[status(thm)],[49,53]) ).
thf(281,plain,
! [O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C != true )
| ( B
!= ( O @ ( M @ s @ ( L @ e1 ) @ ( N @ ( M @ ( L @ s3 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ state ) ) ) ) ) ) ) ) ) ) ) ) )
| ( A != true )
| ( A
!= ( O @ ( M @ ( L @ e1 ) @ ( N @ ( M @ s @ ( L @ s3 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ state ) ) ) ) ) ) ) ) ) ) ) ) )
| ( B = true ) ),
inference(simp,[status(thm)],[265]) ).
thf(286,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( L @ ( J @ ( I @ e1 ) @ ( K @ ( J @ s @ ( I @ s3 ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) )
!= true )
| ( ( L @ ( J @ s @ ( I @ e1 ) @ ( K @ ( J @ ( I @ s3 ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) )
= true ) ),
inference(simp,[status(thm)],[281]) ).
thf(7,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( E @ ( D @ s @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ v3 ) @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( E @ ( D @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ s @ v3 ) @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v3_up) ).
thf(58,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( E @ ( D @ s @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ v3 ) @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( E @ ( D @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ s @ v3 ) @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(59,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( E @ ( D @ s @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ v3 ) @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( E @ ( D @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ s @ v3 ) @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(lifteq,[status(thm)],[58]) ).
thf(37,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( B @ s @ s @ ( A @ s @ e2 ) @ ( B @ s @ s @ ( A @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( B @ ( A @ s @ e2 ) @ ( B @ ( A @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ s @ ( A @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_left) ).
thf(118,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( B @ s @ s @ ( A @ s @ e2 ) @ ( B @ s @ s @ ( A @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( B @ ( A @ s @ e2 ) @ ( B @ ( A @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ s @ ( A @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(71,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( G @ s @ ( F @ s @ e2 ) @ ( G @ ( F @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ h ) @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( G @ s @ ( F @ e2 ) @ ( G @ ( F @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ s @ h ) @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(lifteq,[status(thm)],[70]) ).
thf(21,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( J @ ( I @ e1 ) @ ( K @ ( J @ ( I @ s @ s3 ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( J @ ( I @ s @ e1 ) @ ( K @ ( J @ ( I @ s3 ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_down) ).
thf(86,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( J @ ( I @ e1 ) @ ( K @ ( J @ ( I @ s @ s3 ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( J @ ( I @ s @ e1 ) @ ( K @ ( J @ ( I @ s3 ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(27,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( F @ ( E @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ s @ v4 ) @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( F @ ( E @ s @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ v4 ) @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v4_down) ).
thf(98,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( F @ ( E @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ s @ v4 ) @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( F @ ( E @ s @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ v4 ) @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(194,plain,
! [ZA: $i,Z: $i,Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( L @ ( K @ e2 ) @ ( N @ ( M @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) )
!= ( Y @ ( X @ e2 ) @ ( ZA @ ( Z @ e1 ) @ ( W @ ( V @ ( U @ ( T @ ( S @ ( o @ s @ s @ ( o @ s @ s @ v4 ) @ ( R @ ( Q @ ( P @ ( O @ state ) ) ) ) ) ) ) ) ) ) ) ) )
| ( true != true )
| ( ( N @ ( M @ e2 ) @ ( L @ ( K @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) )
!= true ) ),
inference(paramod_ordered,[status(thm)],[150,169]) ).
thf(195,plain,
! [ZA: $i,Z: $i,Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( L @ ( K @ e2 ) @ ( N @ ( M @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) )
!= ( Y @ ( X @ e2 ) @ ( ZA @ ( Z @ e1 ) @ ( W @ ( V @ ( U @ ( T @ ( S @ ( o @ s @ s @ ( o @ s @ s @ v4 ) @ ( R @ ( Q @ ( P @ ( O @ state ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( N @ ( M @ e2 ) @ ( L @ ( K @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) )
!= true ) ),
inference(simp,[status(thm)],[194]) ).
thf(196,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( M @ ( L @ e2 ) @ ( K @ ( J @ e1 ) @ ( I @ ( H @ ( G @ ( F @ ( E @ ( o @ s @ s @ ( o @ s @ s @ v4 ) @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) )
!= true ),
inference(pattern_uni,[status(thm)],[195:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( o @ s @ s @ ( o @ s @ s @ v4 ) )),bind(F,$thf( F )),bind(G,$thf( G )),bind(H,$thf( H )),bind(I,$thf( I )),bind(J,$thf( J )),bind(K,$thf( K )),bind(L,$thf( L )),bind(M,$thf( M )),bind(N,$thf( N )),bind(O,$thf( A )),bind(P,$thf( B )),bind(Q,$thf( C )),bind(R,$thf( D )),bind(S,$thf( F )),bind(T,$thf( G )),bind(U,$thf( H )),bind(V,$thf( I )),bind(W,$thf( J )),bind(X,$thf( K )),bind(Y,$thf( L )),bind(Z,$thf( M )),bind(ZA,$thf( N ))]]) ).
thf(198,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( M @ ( L @ e2 ) @ ( K @ ( J @ e1 ) @ ( I @ ( H @ ( G @ ( F @ ( E @ ( o @ s @ s @ ( o @ s @ s @ v4 ) @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) )
!= true ),
inference(simp,[status(thm)],[196]) ).
thf(32,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( H @ ( G @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ s1 ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( H @ ( G @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ s @ s1 ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_up) ).
thf(108,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( H @ ( G @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ s1 ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( H @ ( G @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ s @ s1 ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(43,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( G @ ( F @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ s @ ( F @ h ) @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( G @ s @ s @ ( F @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ h ) @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_right) ).
thf(130,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( G @ ( F @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ s @ ( F @ h ) @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( G @ s @ s @ ( F @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ h ) @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(3837,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( o @ ( o @ s @ s @ e2 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
!= ( L @ ( J @ s @ ( I @ e1 ) @ ( K @ ( J @ ( I @ s3 ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( true @ ( true @ ( true @ ( L @ ( J @ ( I @ e1 ) @ ( K @ ( J @ s @ ( I @ s3 ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[3676,53]) ).
thf(3838,plain,
( ( true @ ( true @ ( true @ ( o @ ( o @ s @ s @ e2 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[3837:[bind(A,$thf( o @ s @ ( o @ bb ) )),bind(B,$thf( o @ ( o @ v1 ) )),bind(C,$thf( o @ s @ s @ s @ ( o @ v2 ) )),bind(D,$thf( o @ ( o @ s @ s @ s @ v3 ) )),bind(E,$thf( o @ s @ s @ s @ ( o @ s @ s @ v4 ) )),bind(F,$thf( o @ s @ ( o @ s @ s @ h ) )),bind(G,$thf( o @ s @ ( o @ s @ s @ s @ s1 ) )),bind(H,$thf( o @ s @ s @ ( o @ s @ s @ s @ s2 ) )),bind(I,$thf( o @ s @ s @ s @ s )),bind(J,$thf( o @ s )),bind(K,$thf( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) )),bind(L,$thf( o @ ( o @ s @ s @ e2 ) ))]]) ).
thf(3015,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( o @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
!= ( L @ ( I @ ( H @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ s2 ) @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( true @ ( true @ ( true @ ( L @ ( I @ ( H @ e1 ) @ ( K @ ( J @ ( I @ ( H @ s @ s2 ) @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[1384,91]) ).
thf(3016,plain,
( ( true @ ( true @ ( true @ ( o @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ e1 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[3015:[bind(A,$thf( o @ s @ ( o @ bb ) )),bind(B,$thf( o @ ( o @ v1 ) )),bind(C,$thf( o @ s @ s @ s @ ( o @ v2 ) )),bind(D,$thf( o @ ( o @ s @ s @ v3 ) )),bind(E,$thf( o @ s @ s @ s @ ( o @ s @ s @ v4 ) )),bind(F,$thf( o @ s @ ( o @ s @ s @ h ) )),bind(G,$thf( o @ s @ ( o @ s @ s @ s @ s1 ) )),bind(H,$thf( o @ s @ s @ s )),bind(I,$thf( o @ s @ s )),bind(J,$thf( o @ ( o @ s @ s @ s @ s @ s3 ) )),bind(K,$thf( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) )),bind(L,$thf( o @ s @ ( o @ s @ s @ s @ s @ e2 ) ))]]) ).
thf(2966,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( o @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
!= ( L @ ( I @ ( H @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ s2 ) @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( true @ ( true @ ( true @ ( L @ ( I @ ( H @ e1 ) @ ( K @ ( J @ ( I @ ( H @ s @ s2 ) @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[1648,91]) ).
thf(2967,plain,
( ( true @ ( true @ ( true @ ( o @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ e1 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[2966:[bind(A,$thf( o @ s @ ( o @ bb ) )),bind(B,$thf( o @ ( o @ v1 ) )),bind(C,$thf( o @ s @ s @ s @ ( o @ v2 ) )),bind(D,$thf( o @ ( o @ s @ s @ v3 ) )),bind(E,$thf( o @ s @ s @ s @ ( o @ s @ s @ v4 ) )),bind(F,$thf( o @ s @ ( o @ s @ s @ h ) )),bind(G,$thf( o @ s @ ( o @ s @ s @ s @ s1 ) )),bind(H,$thf( o @ s @ s @ s )),bind(I,$thf( o @ s @ s )),bind(J,$thf( o @ s @ ( o @ s @ s @ s @ s @ s3 ) )),bind(K,$thf( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) )),bind(L,$thf( o @ ( o @ s @ s @ s @ s @ e2 ) ))]]) ).
thf(9,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( F @ ( E @ s @ e2 ) @ ( F @ ( E @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ s @ ( E @ v4 ) @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( F @ s @ ( E @ s @ e2 ) @ ( F @ s @ ( E @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ v4 ) @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v4_right) ).
thf(62,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( F @ ( E @ s @ e2 ) @ ( F @ ( E @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ s @ ( E @ v4 ) @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( F @ s @ ( E @ s @ e2 ) @ ( F @ s @ ( E @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ v4 ) @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
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] :
( ( true @ ( F @ ( E @ s @ e2 ) @ ( F @ ( E @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ s @ ( E @ v4 ) @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( F @ s @ ( E @ s @ e2 ) @ ( F @ s @ ( E @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ v4 ) @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(lifteq,[status(thm)],[62]) ).
thf(25,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( K @ ( J @ e1 ) @ ( K @ ( J @ s @ s4 ) @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( K @ ( J @ s @ e1 ) @ ( K @ ( J @ s4 ) @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s4_down) ).
thf(94,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( K @ ( J @ e1 ) @ ( K @ ( J @ s @ s4 ) @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( K @ ( J @ s @ e1 ) @ ( K @ ( J @ s4 ) @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(95,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( K @ ( J @ e1 ) @ ( K @ ( J @ s @ s4 ) @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( K @ ( J @ s @ e1 ) @ ( K @ ( J @ s4 ) @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(lifteq,[status(thm)],[94]) ).
thf(4271,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( o @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
!= ( L @ ( F @ ( E @ s @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ v4 ) @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( true @ ( true @ ( true @ ( L @ ( F @ ( E @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ s @ v4 ) @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[158,81]) ).
thf(4272,plain,
( ( true @ ( true @ ( true @ ( o @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ e1 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[4271:[bind(A,$thf( o @ s @ ( o @ bb ) )),bind(B,$thf( o @ ( o @ v1 ) )),bind(C,$thf( o @ s @ s @ s @ ( o @ v2 ) )),bind(D,$thf( o @ ( o @ s @ s @ v3 ) )),bind(E,$thf( o @ s @ s )),bind(F,$thf( o @ s @ s @ s )),bind(G,$thf( o @ s @ ( o @ s @ s @ h ) )),bind(H,$thf( o @ s @ ( o @ s @ s @ s @ s1 ) )),bind(I,$thf( o @ s @ s @ ( o @ s @ s @ s @ s2 ) )),bind(J,$thf( o @ s @ ( o @ s @ s @ s @ s @ s3 ) )),bind(K,$thf( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) )),bind(L,$thf( o @ ( o @ s @ s @ s @ s @ e2 ) ))]]) ).
thf(1678,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( o @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
!= ( L @ ( J @ s @ ( I @ e1 ) @ ( K @ ( J @ ( I @ s3 ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( true @ ( true @ ( true @ ( L @ ( J @ ( I @ e1 ) @ ( K @ ( J @ s @ ( I @ s3 ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[1648,53]) ).
thf(1679,plain,
( ( true @ ( true @ ( true @ ( o @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[1678:[bind(A,$thf( o @ s @ ( o @ bb ) )),bind(B,$thf( o @ ( o @ v1 ) )),bind(C,$thf( o @ s @ s @ s @ ( o @ v2 ) )),bind(D,$thf( o @ ( o @ s @ s @ v3 ) )),bind(E,$thf( o @ s @ s @ s @ ( o @ s @ s @ v4 ) )),bind(F,$thf( o @ s @ ( o @ s @ s @ h ) )),bind(G,$thf( o @ s @ ( o @ s @ s @ s @ s1 ) )),bind(H,$thf( o @ s @ s @ ( o @ s @ s @ s @ s2 ) )),bind(I,$thf( o @ s @ s @ s @ s )),bind(J,$thf( o @ s )),bind(K,$thf( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) )),bind(L,$thf( o @ ( o @ s @ s @ s @ s @ e2 ) ))]]) ).
thf(3237,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ ( o @ s @ s @ e1 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
!= ( L @ ( G @ ( F @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ s @ ( F @ h ) @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( true @ ( L @ ( G @ s @ s @ ( F @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ h ) @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[3211,51]) ).
thf(3238,plain,
( ( true @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ s @ ( o @ s @ s @ e1 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[3237:[bind(A,$thf( o @ s @ ( o @ bb ) )),bind(B,$thf( o @ ( o @ v1 ) )),bind(C,$thf( o @ s @ s @ s @ ( o @ v2 ) )),bind(D,$thf( o @ ( o @ s @ s @ s @ v3 ) )),bind(E,$thf( o @ s @ s @ s @ ( o @ s @ s @ v4 ) )),bind(F,$thf( o @ s @ s )),bind(G,$thf( o )),bind(H,$thf( o @ s @ ( o @ s @ s @ s @ s1 ) )),bind(I,$thf( o @ s @ s @ ( o @ s @ s @ s @ s2 ) )),bind(J,$thf( o @ s @ ( o @ s @ s @ s @ s @ s3 ) )),bind(K,$thf( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) )),bind(L,$thf( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) ))]]) ).
thf(6366,plain,
( ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ s @ ( o @ s @ s @ e1 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
= true ),
inference(rewrite,[status(thm)],[3238,49]) ).
thf(6455,plain,
! [N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ s @ ( o @ s @ s @ e1 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
!= ( N @ ( M @ e2 ) @ ( L @ ( K @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) )
| ( true != true )
| ( ( L @ ( K @ e2 ) @ ( N @ ( M @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[6366,150]) ).
thf(6456,plain,
! [N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ s @ ( o @ s @ s @ e1 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
!= ( N @ ( M @ e2 ) @ ( L @ ( K @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( L @ ( K @ e2 ) @ ( N @ ( M @ e1 ) @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) )
= true ) ),
inference(simp,[status(thm)],[6455]) ).
thf(6457,plain,
( ( o @ s @ s @ ( o @ s @ s @ e2 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[6456:[bind(A,$thf( o @ s @ ( o @ bb ) )),bind(B,$thf( o @ ( o @ v1 ) )),bind(C,$thf( o @ s @ s @ s @ ( o @ v2 ) )),bind(D,$thf( o @ ( o @ s @ s @ s @ v3 ) )),bind(E,$thf( o @ s @ s @ s @ ( o @ s @ s @ v4 ) )),bind(F,$thf( o @ ( o @ s @ s @ h ) )),bind(G,$thf( o @ s @ ( o @ s @ s @ s @ s1 ) )),bind(H,$thf( o @ s @ s @ ( o @ s @ s @ s @ s2 ) )),bind(I,$thf( o @ s @ ( o @ s @ s @ s @ s @ s3 ) )),bind(J,$thf( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) )),bind(K,$thf( o @ s @ s )),bind(L,$thf( o @ s @ s )),bind(M,$thf( o @ s @ s @ s @ s )),bind(N,$thf( o @ s @ s @ s ))]]) ).
thf(6700,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( o @ s @ s @ ( o @ s @ s @ e2 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
!= ( L @ ( F @ ( E @ s @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ v4 ) @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( true @ ( true @ ( true @ ( L @ ( F @ ( E @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ s @ v4 ) @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[6457,81]) ).
thf(6701,plain,
( ( true @ ( true @ ( true @ ( o @ s @ s @ ( o @ s @ s @ e2 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ e1 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[6700:[bind(A,$thf( o @ s @ ( o @ bb ) )),bind(B,$thf( o @ ( o @ v1 ) )),bind(C,$thf( o @ s @ s @ s @ ( o @ v2 ) )),bind(D,$thf( o @ ( o @ s @ s @ s @ v3 ) )),bind(E,$thf( o @ s @ s )),bind(F,$thf( o @ s @ s @ s )),bind(G,$thf( o @ ( o @ s @ s @ h ) )),bind(H,$thf( o @ s @ ( o @ s @ s @ s @ s1 ) )),bind(I,$thf( o @ s @ s @ ( o @ s @ s @ s @ s2 ) )),bind(J,$thf( o @ s @ ( o @ s @ s @ s @ s @ s3 ) )),bind(K,$thf( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) )),bind(L,$thf( o @ s @ s @ ( o @ s @ s @ e2 ) ))]]) ).
thf(87,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( J @ ( I @ e1 ) @ ( K @ ( J @ ( I @ s @ s3 ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( J @ ( I @ s @ e1 ) @ ( K @ ( J @ ( I @ s3 ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(lifteq,[status(thm)],[86]) ).
thf(30,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( B @ ( A @ s @ e2 ) @ ( B @ ( A @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ s @ ( A @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( B @ s @ s @ ( A @ s @ e2 ) @ ( B @ s @ s @ ( A @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_right) ).
thf(104,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( B @ ( A @ s @ e2 ) @ ( B @ ( A @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ s @ ( A @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( B @ s @ s @ ( A @ s @ e2 ) @ ( B @ s @ s @ ( A @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(19,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( E @ ( D @ s @ e2 ) @ ( E @ ( D @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ s @ ( D @ v3 ) @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( E @ s @ ( D @ s @ e2 ) @ ( E @ s @ ( D @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ v3 ) @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v3_right) ).
thf(82,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( E @ ( D @ s @ e2 ) @ ( E @ ( D @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ s @ ( D @ v3 ) @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( E @ s @ ( D @ s @ e2 ) @ ( E @ s @ ( D @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ v3 ) @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(2955,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
!= ( L @ ( I @ ( H @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ s2 ) @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( true @ ( true @ ( true @ ( L @ ( I @ ( H @ e1 ) @ ( K @ ( J @ ( I @ ( H @ s @ s2 ) @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[901,91]) ).
thf(2956,plain,
( ( true @ ( true @ ( true @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ e1 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[2955:[bind(A,$thf( o @ s @ ( o @ bb ) )),bind(B,$thf( o @ ( o @ v1 ) )),bind(C,$thf( o @ s @ s @ s @ ( o @ v2 ) )),bind(D,$thf( o @ ( o @ s @ s @ v3 ) )),bind(E,$thf( o @ s @ s @ s @ ( o @ s @ s @ v4 ) )),bind(F,$thf( o @ s @ ( o @ s @ s @ h ) )),bind(G,$thf( o @ s @ ( o @ s @ s @ s @ s1 ) )),bind(H,$thf( o @ s @ s @ s )),bind(I,$thf( o @ s @ s )),bind(J,$thf( o @ ( o @ s @ s @ s @ s @ s3 ) )),bind(K,$thf( o @ s @ ( o @ s @ s @ s @ s @ s4 ) )),bind(L,$thf( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e2 ) ))]]) ).
thf(4177,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( o @ ( o @ s @ s @ e2 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ s @ e1 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) )
!= ( L @ ( F @ ( E @ s @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ v4 ) @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( true @ ( true @ ( true @ ( L @ ( F @ ( E @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ s @ v4 ) @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[3280,81]) ).
thf(4178,plain,
( ( true @ ( true @ ( true @ ( o @ ( o @ s @ s @ e2 ) @ ( o @ s @ s @ s @ ( o @ s @ s @ e1 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) @ ( o @ s @ ( o @ s @ s @ s @ s @ s3 ) @ ( o @ s @ s @ ( o @ s @ s @ s @ s2 ) @ ( o @ s @ ( o @ s @ s @ s @ s1 ) @ ( o @ s @ ( o @ s @ s @ h ) @ ( o @ s @ s @ s @ ( o @ s @ s @ s @ v4 ) @ ( o @ ( o @ s @ s @ s @ v3 ) @ ( o @ s @ s @ s @ ( o @ v2 ) @ ( o @ ( o @ v1 ) @ ( o @ s @ ( o @ bb ) @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[4177:[bind(A,$thf( o @ s @ ( o @ bb ) )),bind(B,$thf( o @ ( o @ v1 ) )),bind(C,$thf( o @ s @ s @ s @ ( o @ v2 ) )),bind(D,$thf( o @ ( o @ s @ s @ s @ v3 ) )),bind(E,$thf( o @ s @ s )),bind(F,$thf( o @ s @ s @ s )),bind(G,$thf( o @ s @ ( o @ s @ s @ h ) )),bind(H,$thf( o @ s @ ( o @ s @ s @ s @ s1 ) )),bind(I,$thf( o @ s @ s @ ( o @ s @ s @ s @ s2 ) )),bind(J,$thf( o @ s @ ( o @ s @ s @ s @ s @ s3 ) )),bind(K,$thf( o @ s @ s @ ( o @ s @ s @ s @ s @ s4 ) )),bind(L,$thf( o @ ( o @ s @ s @ e2 ) ))]]) ).
thf(79,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( G @ s @ ( F @ e2 ) @ ( G @ ( F @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ s @ h ) @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( G @ s @ ( F @ s @ e2 ) @ ( G @ ( F @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ h ) @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(lifteq,[status(thm)],[78]) ).
thf(41,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( D @ ( C @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ s @ v2 ) @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( D @ ( C @ s @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ v2 ) @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v2_down) ).
thf(126,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( D @ ( C @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ s @ v2 ) @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( D @ ( C @ s @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ v2 ) @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(39,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( F @ s @ ( E @ s @ e2 ) @ ( F @ s @ ( E @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ v4 ) @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( F @ ( E @ s @ e2 ) @ ( F @ ( E @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ s @ ( E @ v4 ) @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v4_left) ).
thf(122,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( F @ s @ ( E @ s @ e2 ) @ ( F @ s @ ( E @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ v4 ) @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( F @ ( E @ s @ e2 ) @ ( F @ ( E @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ s @ ( E @ v4 ) @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(83,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( E @ ( D @ s @ e2 ) @ ( E @ ( D @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ s @ ( D @ v3 ) @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( E @ s @ ( D @ s @ e2 ) @ ( E @ s @ ( D @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ v3 ) @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(lifteq,[status(thm)],[82]) ).
thf(28,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( H @ ( G @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ s @ s1 ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( H @ ( G @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ s1 ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_down) ).
thf(100,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( L @ ( H @ ( G @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ s @ s1 ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ( true @ ( L @ ( H @ ( G @ s @ e1 ) @ ( K @ ( J @ ( I @ ( H @ ( G @ s1 ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(10154,plain,
$false,
inference(e,[status(thm)],[4249,1429,112,69,88,115,120,56,7422,52,110,3280,93,57,78,106,84,61,132,3676,89,116,4285,3211,74,60,85,102,3867,70,137,92,65,3600,7329,53,169,141,124,77,901,96,73,128,244,1648,425,1698,45,64,286,59,118,71,54,49,86,81,76,98,303,140,91,66,198,108,130,3838,3016,2967,80,48,63,95,150,4272,50,67,1679,6457,6701,72,87,104,158,139,55,114,58,82,75,2956,51,6366,4178,79,94,294,126,918,1384,47,68,62,90,122,83,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ039-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.15/0.61 % Computer : n011.cluster.edu
% 0.15/0.61 % Model : x86_64 x86_64
% 0.15/0.61 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.61 % Memory : 8046.5625MB
% 0.15/0.61 % OS : Linux 6.8.0-71-generic
% 0.15/0.61 % CPULimit : 300
% 0.15/0.61 % WCLimit : 300
% 0.15/0.61 % DateTime : Sat Sep 26 05:07:29 UTC 2026
% 0.15/0.61 % CPUTime :
% 0.15/0.61 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.18/0.95 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.96/1.11 % [INFO] Parsing done (157ms).
% 0.96/1.12 % [INFO] Running in sequential loop mode.
% 1.80/1.34 % [INFO] eprover registered as external prover.
% 1.80/1.34 % [INFO] Scanning for conjecture ...
% 2.07/1.43 % [INFO] Found a conjecture (or negated_conjecture) and 43 axioms. Running axiom selection ...
% 2.07/1.50 % [INFO] Axiom selection finished. Selected 43 axioms (removed 0 axioms).
% 2.45/1.57 % [INFO] Problem is propositional (TPTP CNF).
% 2.45/1.57 % [INFO] Type checking passed.
% 2.45/1.58 % [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 ...
% 107.26/29.82 % External prover 'e' found a proof!
% 107.26/29.82 % [INFO] Killing All external provers ...
% 107.26/29.82 % Time passed: 29103ms (effective reasoning time: 28700ms)
% 107.26/29.83 % Axioms used in derivation (43): v1_down, ifeq_axiom, s2_right, v4_up, v3_left, v1_up, v2_down, s3_left, v2_left, s4_up, s4_left, b_up, s1_left, v3_right, v2_up, b_right, s3_down, v3_down, h_right, s2_down, s1_right, s1_up, v2_right, h_left, s1_down, b_left, h_up, v4_right, s3_right, v1_right, s2_up, h_down, v1_left, initial_state, v3_up, v4_down, v4_left, s3_up, s4_right, s2_left, swap_blanks, s4_down, b_down
% 107.26/29.83 % No. of inferences in proof: 217
% 107.26/29.83 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 29103 ms resp. 28700 ms w/o parsing
% 108.60/30.11 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 108.60/30.12 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------