%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO631-1 : TPTP v9.3.1. Released v7.1.0.
% 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 : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:45:04 AM UTC 2026
% Result : Unsatisfiable 114.10s 36.67s
% Output : Refutation 115.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 57
% Syntax : Number of formulae : 536 ( 74 unt; 0 typ; 0 def)
% Number of atoms : 2498 ( 386 equ; 0 cnn)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 18009 (1098 ~;1562 |; 0 &;15349 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 1021 ( 0 ^;1021 !; 0 ?;1021 :)
% Comments :
%------------------------------------------------------------------------------
thf('E_decl',type,
'E': $i > $i > $o ).
thf(s_decl,type,
s: $i > $i ).
thf('0_decl',type,
'0': $i ).
thf(f_decl,type,
f: $i > $i ).
thf(g_decl,type,
g: $i > $i ).
thf(iLEQ_decl,type,
iLEQ: $i > $i > $o ).
thf('LE_decl',type,
'LE': $i > $i > $o ).
thf(6,axiom,
! [A: $i] : ( A @ ( A @ iLEQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_18_06) ).
thf(67,plain,
! [A: $i] : ( A @ ( A @ iLEQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( ( '0' @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_23_21) ).
thf(90,plain,
! [B: $i,A: $i] :
( ( '0' @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(91,plain,
! [B: $i,A: $i] :
( ( '0' @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(cnf,[status(esa)],[90]) ).
thf(31,axiom,
! [B: $i,A: $i] :
( ( '0' @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ ( A @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_56_31) ).
thf(107,plain,
! [B: $i,A: $i] :
( ( '0' @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ ( A @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(108,plain,
! [B: $i,A: $i] :
( ( '0' @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ ( A @ f @ 'LE' ) ) ),
inference(cnf,[status(esa)],[107]) ).
thf(52,axiom,
! [A: $i] :
~ ( '0' @ ( A @ f @ 'LE' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_38_52) ).
thf(140,plain,
! [A: $i] :
~ ( '0' @ ( A @ f @ 'LE' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(141,plain,
! [A: $i] :
~ ( '0' @ ( A @ f @ 'LE' ) ),
inference(polarity_switch,[status(thm)],[140]) ).
thf(320,plain,
! [B: $i,A: $i] :
( $false
| ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ ( A @ f @ 'LE' ) ) ),
inference(rewrite,[status(thm)],[108,141]) ).
thf(321,plain,
! [B: $i,A: $i] :
( ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ ( A @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[320]) ).
thf(922,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ s @ ( C @ f @ 'LE' ) ) )
| ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ ( C @ iLEQ ) )
| ~ $true
| ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[91,321]) ).
thf(923,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ s @ ( C @ f @ 'LE' ) ) )
| ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ ( C @ iLEQ ) )
| ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[922]) ).
thf(924,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ ( B @ iLEQ ) )
| ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(pattern_uni,[status(thm)],[923:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(999,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ ( B @ iLEQ ) )
| ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[924]) ).
thf(16134,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ ( C @ iLEQ ) )
| ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ $true
| ~ ( '0' @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[67,999]) ).
thf(16135,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ ( C @ iLEQ ) )
| ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[16134]) ).
thf(16136,plain,
! [B: $i,A: $i] :
( ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(pattern_uni,[status(thm)],[16135:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(16216,plain,
! [B: $i,A: $i] :
( ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[16136]) ).
thf(51,axiom,
! [A: $i] :
~ ( '0' @ ( A @ g @ f @ 'LE' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_36_51) ).
thf(138,plain,
! [A: $i] :
~ ( '0' @ ( A @ g @ f @ 'LE' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(27,axiom,
! [A: $i] : ( A @ ( A @ iLEQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_37_27) ).
thf(101,plain,
! [A: $i] : ( A @ ( A @ iLEQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(39,axiom,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_49_39) ).
thf(120,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(121,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(cnf,[status(esa)],[120]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_48_04) ).
thf(63,plain,
! [B: $i,A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(64,plain,
! [B: $i,A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(cnf,[status(esa)],[63]) ).
thf(209,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( C @ ( B @ iLEQ ) )
| ~ $true
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[121,64]) ).
thf(210,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( C @ ( B @ iLEQ ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[209]) ).
thf(211,plain,
! [B: $i,A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[210:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(216,plain,
! [B: $i,A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[211]) ).
thf(241,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ $true
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[67,216]) ).
thf(242,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[241]) ).
thf(243,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[242:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_10_13) ).
thf(78,plain,
! [B: $i,A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(79,plain,
! [B: $i,A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(cnf,[status(esa)],[78]) ).
thf(543,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( C @ ( B @ iLEQ ) )
| ~ $true
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[243,79]) ).
thf(544,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( C @ ( B @ iLEQ ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[543]) ).
thf(545,plain,
! [B: $i,A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[544:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(602,plain,
! [B: $i,A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[545]) ).
thf(862,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ $true
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[67,602]) ).
thf(863,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[862]) ).
thf(864,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[863:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_26_19) ).
thf(87,plain,
! [B: $i,A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(88,plain,
! [B: $i,A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(cnf,[status(esa)],[87]) ).
thf(1450,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( C @ ( B @ iLEQ ) )
| ~ $true
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[864,88]) ).
thf(1451,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( C @ ( B @ iLEQ ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[1450]) ).
thf(1452,plain,
! [B: $i,A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[1451:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(1527,plain,
! [B: $i,A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[1452]) ).
thf(3402,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ $true
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[67,1527]) ).
thf(3403,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[3402]) ).
thf(3404,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[3403:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(45,axiom,
! [B: $i,A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_54_45) ).
thf(128,plain,
! [B: $i,A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(129,plain,
! [B: $i,A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(cnf,[status(esa)],[128]) ).
thf(5981,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( C @ ( B @ iLEQ ) )
| ~ $true
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[3404,129]) ).
thf(5982,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( C @ ( B @ iLEQ ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[5981]) ).
thf(5983,plain,
! [B: $i,A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[5982:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(6162,plain,
! [B: $i,A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[5983]) ).
thf(6281,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ $true
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[67,6162]) ).
thf(6282,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[6281]) ).
thf(6283,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[6282:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(237,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ ( C @ f @ 'LE' ) ) )
| ~ $true
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[216,141]) ).
thf(238,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ ( C @ f @ 'LE' ) ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[237]) ).
thf(249,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s )
!= '0' )
| ( ( B @ f )
!= ( C @ f ) )
| ~ ( B @ ( A @ iLEQ ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[238]) ).
thf(36,axiom,
! [B: $i,A: $i] :
( ( '0' @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_0_36) ).
thf(115,plain,
! [B: $i,A: $i] :
( ( '0' @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( '0' @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_8_03) ).
thf(61,plain,
! [B: $i,A: $i] :
( ( '0' @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ( '0' @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(cnf,[status(esa)],[61]) ).
thf(163,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ ( C @ f @ 'LE' ) ) )
| ~ $true
| ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[62,141]) ).
thf(164,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ ( C @ f @ 'LE' ) ) )
| ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[163]) ).
thf(170,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s )
!= '0' )
| ( ( B @ f )
!= ( C @ f ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[164]) ).
thf(395,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s )
!= '0' )
| ( B != C )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[170]) ).
thf(440,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ s )
!= '0' )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[395]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_11_16) ).
thf(83,plain,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(84,plain,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(cnf,[status(esa)],[83]) ).
thf(5,axiom,
! [A: $i] :
~ ( A @ g @ f @ ( A @ f @ 'E' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_19_05) ).
thf(65,plain,
! [A: $i] :
~ ( A @ g @ f @ ( A @ f @ 'E' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(66,plain,
! [A: $i] :
~ ( A @ g @ f @ ( A @ f @ 'E' ) ),
inference(polarity_switch,[status(thm)],[65]) ).
thf(1036,plain,
! [A: $i] :
( $false
| ~ ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(rewrite,[status(thm)],[84,66]) ).
thf(1037,plain,
! [A: $i] :
( ~ ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[1036]) ).
thf(1038,plain,
! [A: $i] :
( ~ $true
| ( ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) )
!= ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(eqfactor_ordered,[status(thm)],[1037]) ).
thf(1040,plain,
! [A: $i] :
( ( ( A @ g @ f )
!= ( A @ f ) )
| ( ( '0' @ s @ s @ s @ s @ s @ s )
!= ( '0' @ s @ s @ s @ s @ s @ s ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[1038]) ).
thf(1041,plain,
! [A: $i] :
( ( ( A @ g @ f )
!= ( A @ f ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[1040]) ).
thf(2,axiom,
! [A: $i] : ( A @ g @ ( A @ iLEQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3_02) ).
thf(60,plain,
! [A: $i] : ( A @ g @ ( A @ iLEQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(116,plain,
! [B: $i,A: $i] :
( ( '0' @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(cnf,[status(esa)],[115]) ).
thf(4555,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ g @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ $true
| ~ ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[60,116]) ).
thf(4556,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ g @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[4555]) ).
thf(4557,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(pattern_uni,[status(thm)],[4556:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ g ))]]) ).
thf(4739,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[4557]) ).
thf(851,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ g @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ $true
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[60,602]) ).
thf(852,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ g @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[851]) ).
thf(853,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[852:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ g ))]]) ).
thf(895,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[853]) ).
thf(1447,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ $true
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[67,88]) ).
thf(1448,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[1447]) ).
thf(1449,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(pattern_uni,[status(thm)],[1448:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(13010,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ $true
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[895,1449]) ).
thf(13011,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[13010]) ).
thf(13012,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[13011:[bind(A,$thf( C )),bind(B,$thf( C @ g ))]]) ).
thf(13079,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[13012]) ).
thf(6004,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ $true
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[67,129]) ).
thf(6005,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[6004]) ).
thf(6006,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(pattern_uni,[status(thm)],[6005:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(13097,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ $true
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[13079,6006]) ).
thf(13098,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[13097]) ).
thf(13099,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[13098:[bind(A,$thf( C )),bind(B,$thf( C @ g ))]]) ).
thf(13317,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[13099]) ).
thf(53,axiom,
! [A: $i] :
~ ( A @ g @ f @ ( A @ f @ 'E' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_7_53) ).
thf(142,plain,
! [A: $i] :
~ ( A @ g @ f @ ( A @ f @ 'E' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(1,axiom,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_27_01) ).
thf(58,plain,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(59,plain,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(cnf,[status(esa)],[58]) ).
thf(152,plain,
! [A: $i] :
( $false
| ~ ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(rewrite,[status(thm)],[59,66]) ).
thf(153,plain,
! [A: $i] :
( ~ ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[152]) ).
thf(906,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ ( C @ f @ 'LE' ) ) )
| ~ $true
| ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[91,141]) ).
thf(907,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ ( C @ f @ 'LE' ) ) )
| ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[906]) ).
thf(987,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s )
!= '0' )
| ( ( B @ f )
!= ( C @ f ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[907]) ).
thf(1151,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s )
!= '0' )
| ( B != C )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[987]) ).
thf(1243,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s )
!= '0' )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[1151]) ).
thf(35,axiom,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_30_35) ).
thf(113,plain,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(114,plain,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(cnf,[status(esa)],[113]) ).
thf(296,plain,
! [A: $i] :
( $false
| ~ ( A @ g @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(rewrite,[status(thm)],[114,66]) ).
thf(297,plain,
! [A: $i] :
( ~ ( A @ g @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[296]) ).
thf(298,plain,
! [A: $i] :
( ~ $true
| ( ( A @ g @ f @ ( '0' @ s @ 'E' ) )
!= ( A @ f @ ( '0' @ s @ 'E' ) ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(eqfactor_ordered,[status(thm)],[297]) ).
thf(300,plain,
! [A: $i] :
( ( ( A @ g @ f )
!= ( A @ f ) )
| ( ( '0' @ s )
!= ( '0' @ s ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[298]) ).
thf(301,plain,
! [A: $i] :
( ( ( A @ g @ f )
!= ( A @ f ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[300]) ).
thf(4608,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ $true
| ~ ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[67,116]) ).
thf(4609,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[4608]) ).
thf(4610,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(pattern_uni,[status(thm)],[4609:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_29_12) ).
thf(76,plain,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(77,plain,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) ) ),
inference(cnf,[status(esa)],[76]) ).
thf(365,plain,
! [A: $i] :
( $false
| ~ ( A @ g @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) ) ),
inference(rewrite,[status(thm)],[77,66]) ).
thf(366,plain,
! [A: $i] :
( ~ ( A @ g @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[365]) ).
thf(367,plain,
! [A: $i] :
( ~ $true
| ( ( A @ g @ f @ ( '0' @ s @ s @ s @ 'E' ) )
!= ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) ) ),
inference(eqfactor_ordered,[status(thm)],[366]) ).
thf(369,plain,
! [A: $i] :
( ( ( A @ g @ f )
!= ( A @ f ) )
| ( ( '0' @ s @ s @ s )
!= ( '0' @ s @ s @ s ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[367]) ).
thf(370,plain,
! [A: $i] :
( ( ( A @ g @ f )
!= ( A @ f ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[369]) ).
thf(389,plain,
! [A: $i] :
( ( ( A @ g )
!= A )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[370]) ).
thf(23,axiom,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_40_23) ).
thf(94,plain,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(95,plain,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(cnf,[status(esa)],[94]) ).
thf(2327,plain,
! [A: $i] :
( $false
| ~ ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(rewrite,[status(thm)],[95,66]) ).
thf(2328,plain,
! [A: $i] :
( ~ ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[2327]) ).
thf(50,axiom,
! [B: $i,A: $i] :
( ( '0' @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_51_50) ).
thf(136,plain,
! [B: $i,A: $i] :
( ( '0' @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(137,plain,
! [B: $i,A: $i] :
( ( '0' @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(cnf,[status(esa)],[136]) ).
thf(6513,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ g @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ $true
| ~ ( '0' @ s @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[60,137]) ).
thf(6514,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ g @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[6513]) ).
thf(6515,plain,
! [A: $i] :
( ( '0' @ s @ s @ ( A @ g @ f @ 'LE' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(pattern_uni,[status(thm)],[6514:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ g ))]]) ).
thf(6713,plain,
! [A: $i] :
( ( '0' @ s @ s @ ( A @ g @ f @ 'LE' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[6515]) ).
thf(187,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( D @ f @ 'LE' ) )
| ( D @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( D @ ( C @ iLEQ ) )
| ~ $true
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[64,64]) ).
thf(188,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( D @ f @ 'LE' ) )
| ( D @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( D @ ( C @ iLEQ ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[187]) ).
thf(196,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s )
!= ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s ) )
| ( ( B @ f )
!= ( C @ f ) )
| ~ ( D @ ( C @ iLEQ ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( D @ f @ 'LE' ) )
| ( D @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[188]) ).
thf(947,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ $true
| ~ ( '0' @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[67,91]) ).
thf(948,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[947]) ).
thf(949,plain,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(pattern_uni,[status(thm)],[948:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(154,plain,
! [A: $i] :
( ~ $true
| ( ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
!= ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(eqfactor_ordered,[status(thm)],[153]) ).
thf(156,plain,
! [A: $i] :
( ( ( A @ g @ f )
!= ( A @ f ) )
| ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s )
!= ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[154]) ).
thf(157,plain,
! [A: $i] :
( ( ( A @ g @ f )
!= ( A @ f ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[156]) ).
thf(246,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ g @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ $true
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[60,216]) ).
thf(247,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ g @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[246]) ).
thf(248,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[247:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ g ))]]) ).
thf(252,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[248]) ).
thf(564,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ g @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ $true
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[60,79]) ).
thf(565,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ g @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[564]) ).
thf(566,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(pattern_uni,[status(thm)],[565:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ g ))]]) ).
thf(607,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[566]) ).
thf(23320,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ g @ f @ 'LE' ) )
| ( B @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ $true
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[252,607]) ).
thf(23321,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ g @ f @ 'LE' ) )
| ( B @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[23320]) ).
thf(23322,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ g @ f @ 'LE' ) )
| ( A @ g @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[23321:[bind(A,$thf( C )),bind(B,$thf( C @ g ))]]) ).
thf(23716,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ g @ f @ 'LE' ) )
| ( A @ g @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[23322]) ).
thf(23893,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ g @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ $true
| ( A @ g @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[23716,1449]) ).
thf(23894,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ g @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[23893]) ).
thf(23895,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ g @ f @ 'LE' ) )
| ( A @ g @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[23894:[bind(A,$thf( D )),bind(B,$thf( D @ g @ g ))]]) ).
thf(24045,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ g @ f @ 'LE' ) )
| ( A @ g @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[23895]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5_11) ).
thf(74,plain,
! [B: $i,A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(75,plain,
! [B: $i,A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(cnf,[status(esa)],[74]) ).
thf(264,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ s @ s @ ( D @ f @ 'LE' ) )
| ( D @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( D @ ( C @ iLEQ ) )
| ~ $true
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[64,75]) ).
thf(265,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ s @ s @ ( D @ f @ 'LE' ) )
| ( D @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( D @ ( C @ iLEQ ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[264]) ).
thf(284,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s )
!= ( '0' @ s @ s @ s @ s @ s @ s ) )
| ( ( B @ f )
!= ( C @ f ) )
| ~ ( D @ ( C @ iLEQ ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( '0' @ s @ s @ s @ s @ s @ ( D @ f @ 'LE' ) )
| ( D @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[265]) ).
thf(572,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ $true
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[67,79]) ).
thf(573,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[572]) ).
thf(574,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(pattern_uni,[status(thm)],[573:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(2244,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ g @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( ( '0' @ s )
!= '0' )
| ~ $true
| ~ ( '0' @ s @ s @ ( B @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[60,1243]) ).
thf(2245,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ g @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( ( '0' @ s )
!= '0' )
| ~ ( '0' @ s @ s @ ( B @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[2244]) ).
thf(2246,plain,
! [A: $i] :
( ( ( '0' @ s )
!= '0' )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ g @ f @ ( '0' @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[2245:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ g ))]]) ).
thf(2281,plain,
! [A: $i] :
( ( ( '0' @ s )
!= '0' )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ g @ f @ ( '0' @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[2246]) ).
thf(337,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ g @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( C @ f @ ( '0' @ 'E' ) )
| ~ $true
| ~ ( '0' @ s @ ( B @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[60,321]) ).
thf(338,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ g @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( C @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( B @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[337]) ).
thf(339,plain,
! [A: $i] :
( ( A @ g @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ f @ 'LE' ) ) ),
inference(pattern_uni,[status(thm)],[338:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ g ))]]) ).
thf(346,plain,
! [A: $i] :
( ( A @ g @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[339]) ).
thf(954,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ s @ ( C @ f @ 'LE' ) ) )
| ( C @ g @ f @ ( '0' @ 'E' ) )
| ~ $true
| ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[91,346]) ).
thf(955,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ s @ ( C @ f @ 'LE' ) ) )
| ( C @ g @ f @ ( '0' @ 'E' ) )
| ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[954]) ).
thf(956,plain,
! [B: $i,A: $i] :
( ( B @ g @ f @ ( '0' @ 'E' ) )
| ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(pattern_uni,[status(thm)],[955:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(48,axiom,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_55_48) ).
thf(132,plain,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(6496,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ s @ s @ ( C @ f @ 'LE' ) ) )
| ( ( '0' @ s )
!= '0' )
| ~ $true
| ( C @ g @ f @ ( '0' @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[137,2281]) ).
thf(6497,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ s @ s @ ( C @ f @ 'LE' ) ) )
| ( ( '0' @ s )
!= '0' )
| ( C @ g @ f @ ( '0' @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[6496]) ).
thf(6498,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s )
!= '0' )
| ( B @ g @ f @ ( '0' @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(pattern_uni,[status(thm)],[6497:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(20,axiom,
! [A: $i] : ( A @ ( A @ iLEQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_35_20) ).
thf(89,plain,
! [A: $i] : ( A @ ( A @ iLEQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(54,axiom,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_31_54) ).
thf(144,plain,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(145,plain,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(cnf,[status(esa)],[144]) ).
thf(7334,plain,
! [A: $i] :
( $false
| ~ ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(rewrite,[status(thm)],[145,66]) ).
thf(7335,plain,
! [A: $i] :
( ~ ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[7334]) ).
thf(7336,plain,
! [A: $i] :
( ~ $true
| ( ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
!= ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(eqfactor_ordered,[status(thm)],[7335]) ).
thf(7337,plain,
! [A: $i] :
( ( ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
!= ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[7336]) ).
thf(6868,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ ( A @ g @ f @ 'LE' ) )
!= ( '0' @ ( B @ f @ 'LE' ) ) )
| ~ $true
| ( A @ g @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[6713,141]) ).
thf(6869,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ ( A @ g @ f @ 'LE' ) )
!= ( '0' @ ( B @ f @ 'LE' ) ) )
| ( A @ g @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[6868]) ).
thf(6999,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s )
!= '0' )
| ( ( A @ g @ f )
!= ( B @ f ) )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[6869]) ).
thf(10995,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s )
!= '0' )
| ( ( A @ g )
!= B )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[6999]) ).
thf(11195,plain,
! [A: $i] :
( ( ( '0' @ s @ s )
!= '0' )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[10995]) ).
thf(904,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ ( C @ f @ 'LE' ) ) )
| ( ( '0' @ s @ s @ s )
!= '0' )
| ( ( D @ f )
!= ( E @ f ) )
| ~ ( D @ ( C @ iLEQ ) )
| ~ $true
| ( D @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[91,170]) ).
thf(905,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ ( C @ f @ 'LE' ) ) )
| ( ( '0' @ s @ s @ s )
!= '0' )
| ( ( D @ f )
!= ( E @ f ) )
| ~ ( D @ ( C @ iLEQ ) )
| ( D @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[904]) ).
thf(981,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s )
!= ( '0' @ s ) )
| ( ( B @ f )
!= ( C @ f ) )
| ( ( '0' @ s @ s @ s )
!= '0' )
| ( ( D @ f )
!= ( E @ f ) )
| ~ ( D @ ( C @ iLEQ ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( D @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[905]) ).
thf(2255,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( ( '0' @ s )
!= '0' )
| ~ $true
| ~ ( '0' @ s @ s @ ( B @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[67,1243]) ).
thf(2256,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( ( '0' @ s )
!= '0' )
| ~ ( '0' @ s @ s @ ( B @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[2255]) ).
thf(2257,plain,
! [A: $i] :
( ( ( '0' @ s )
!= '0' )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[2256:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(6558,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ s @ s @ ( C @ f @ 'LE' ) ) )
| ( ( '0' @ s )
!= '0' )
| ~ $true
| ( C @ f @ ( '0' @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[137,2257]) ).
thf(6559,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ s @ s @ ( C @ f @ 'LE' ) ) )
| ( ( '0' @ s )
!= '0' )
| ( C @ f @ ( '0' @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[6558]) ).
thf(6560,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s )
!= '0' )
| ( B @ f @ ( '0' @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(pattern_uni,[status(thm)],[6559:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(24182,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( ( '0' @ s )
!= '0' )
| ( C @ g @ f @ ( '0' @ s @ 'E' ) )
| ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ $true
| ~ ( '0' @ s @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[67,6498]) ).
thf(24183,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( ( '0' @ s )
!= '0' )
| ( C @ g @ f @ ( '0' @ s @ 'E' ) )
| ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[24182]) ).
thf(24184,plain,
! [A: $i] :
( ( ( '0' @ s )
!= '0' )
| ( A @ g @ f @ ( '0' @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(pattern_uni,[status(thm)],[24183:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(17,axiom,
! [A: $i] : ( A @ g @ ( A @ iLEQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1_17) ).
thf(85,plain,
! [A: $i] : ( A @ g @ ( A @ iLEQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(28,axiom,
! [A: $i] :
~ ( A @ g @ f @ ( A @ f @ 'E' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_14_28) ).
thf(102,plain,
! [A: $i] :
~ ( A @ g @ f @ ( A @ f @ 'E' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(37,axiom,
! [A: $i] :
~ ( A @ g @ f @ ( A @ f @ 'E' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_33_37) ).
thf(117,plain,
! [A: $i] :
~ ( A @ g @ f @ ( A @ f @ 'E' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_44_07) ).
thf(68,plain,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(69,plain,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(cnf,[status(esa)],[68]) ).
thf(219,plain,
! [A: $i] :
( $false
| ~ ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(rewrite,[status(thm)],[69,66]) ).
thf(220,plain,
! [A: $i] :
( ~ ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[219]) ).
thf(32,axiom,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_42_32) ).
thf(109,plain,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(110,plain,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(cnf,[status(esa)],[109]) ).
thf(3602,plain,
! [A: $i] :
( $false
| ~ ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(rewrite,[status(thm)],[110,66]) ).
thf(3603,plain,
! [A: $i] :
( ~ ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[3602]) ).
thf(1042,plain,
! [A: $i] :
( ( ( A @ g )
!= A )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[1041]) ).
thf(302,plain,
! [A: $i] :
( ( ( A @ g )
!= A )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[301]) ).
thf(546,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ ( C @ f @ 'LE' ) ) )
| ~ $true
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[79,141]) ).
thf(547,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ ( C @ f @ 'LE' ) ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[546]) ).
thf(598,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s )
!= '0' )
| ( ( B @ f )
!= ( C @ f ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[547]) ).
thf(6899,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ ( A @ g @ f @ 'LE' ) )
!= ( '0' @ s @ s @ ( B @ f @ 'LE' ) ) )
| ( ( '0' @ s )
!= '0' )
| ~ $true
| ( B @ f @ ( '0' @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[6713,2257]) ).
thf(6900,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ ( A @ g @ f @ 'LE' ) )
!= ( '0' @ s @ s @ ( B @ f @ 'LE' ) ) )
| ( ( '0' @ s )
!= '0' )
| ( B @ f @ ( '0' @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[6899]) ).
thf(6901,plain,
! [A: $i] :
( ( ( '0' @ s )
!= '0' )
| ( A @ g @ f @ ( '0' @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(pattern_uni,[status(thm)],[6900:[bind(A,$thf( C )),bind(B,$thf( C @ g ))]]) ).
thf(7084,plain,
! [A: $i] :
( ( ( '0' @ s )
!= '0' )
| ( A @ g @ f @ ( '0' @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[6901]) ).
thf(8,axiom,
! [A: $i] : ( A @ ( A @ iLEQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_21_08) ).
thf(70,plain,
! [A: $i] : ( A @ ( A @ iLEQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(22,axiom,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_20_22) ).
thf(92,plain,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(192,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ ( C @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ ( D @ f @ 'LE' ) )
| ( D @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( D @ ( C @ iLEQ ) )
| ~ $true
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[64,62]) ).
thf(193,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ ( C @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ ( D @ f @ 'LE' ) )
| ( D @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( D @ ( C @ iLEQ ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[192]) ).
thf(197,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s )
!= ( '0' @ s @ s @ s @ s ) )
| ( ( B @ f )
!= ( C @ f ) )
| ~ ( D @ ( C @ iLEQ ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( '0' @ s @ s @ s @ ( D @ f @ 'LE' ) )
| ( D @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[193]) ).
thf(2329,plain,
! [A: $i] :
( ~ $true
| ( ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) )
!= ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(eqfactor_ordered,[status(thm)],[2328]) ).
thf(2331,plain,
! [A: $i] :
( ( ( A @ g @ f )
!= ( A @ f ) )
| ( ( '0' @ s @ s @ s @ s @ s )
!= ( '0' @ s @ s @ s @ s @ s ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[2329]) ).
thf(2332,plain,
! [A: $i] :
( ( ( A @ g @ f )
!= ( A @ f ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[2331]) ).
thf(1180,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ s @ s @ ( C @ f @ 'LE' ) ) )
| ( ( '0' @ s )
!= '0' )
| ( ( D @ f )
!= ( E @ f ) )
| ~ ( D @ ( C @ iLEQ ) )
| ~ $true
| ( D @ f @ ( '0' @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[62,987]) ).
thf(1181,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ s @ s @ ( C @ f @ 'LE' ) ) )
| ( ( '0' @ s )
!= '0' )
| ( ( D @ f )
!= ( E @ f ) )
| ~ ( D @ ( C @ iLEQ ) )
| ( D @ f @ ( '0' @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[1180]) ).
thf(1195,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s )
!= ( '0' @ s @ s ) )
| ( ( B @ f )
!= ( C @ f ) )
| ( ( '0' @ s )
!= '0' )
| ( ( D @ f )
!= ( E @ f ) )
| ~ ( D @ ( C @ iLEQ ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( D @ f @ ( '0' @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[1181]) ).
thf(260,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ ( C @ f @ 'LE' ) ) )
| ~ $true
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[75,141]) ).
thf(261,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ ( C @ f @ 'LE' ) ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[260]) ).
thf(283,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s )
!= '0' )
| ( ( B @ f )
!= ( C @ f ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[261]) ).
thf(961,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) ) )
| ( ( '0' @ s @ s @ s @ s @ s )
!= '0' )
| ( ( D @ f )
!= ( E @ f ) )
| ~ ( D @ ( C @ iLEQ ) )
| ~ $true
| ( D @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[91,283]) ).
thf(962,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) ) )
| ( ( '0' @ s @ s @ s @ s @ s )
!= '0' )
| ( ( D @ f )
!= ( E @ f ) )
| ~ ( D @ ( C @ iLEQ ) )
| ( D @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[961]) ).
thf(974,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s )
!= ( '0' @ s ) )
| ( ( B @ f )
!= ( C @ f ) )
| ( ( '0' @ s @ s @ s @ s @ s )
!= '0' )
| ( ( D @ f )
!= ( E @ f ) )
| ~ ( D @ ( C @ iLEQ ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( D @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[962]) ).
thf(221,plain,
! [A: $i] :
( ~ $true
| ( ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
!= ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(eqfactor_ordered,[status(thm)],[220]) ).
thf(223,plain,
! [A: $i] :
( ( ( A @ g @ f )
!= ( A @ f ) )
| ( ( '0' @ s @ s @ s @ s @ s @ s @ s )
!= ( '0' @ s @ s @ s @ s @ s @ s @ s ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[221]) ).
thf(224,plain,
! [A: $i] :
( ( ( A @ g @ f )
!= ( A @ f ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[223]) ).
thf(3373,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ g @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ $true
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[60,1527]) ).
thf(3374,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ g @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[3373]) ).
thf(3375,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[3374:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ g ))]]) ).
thf(3526,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[3375]) ).
thf(10290,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ $true
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[3526,6006]) ).
thf(10291,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[10290]) ).
thf(10292,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[10291:[bind(A,$thf( C )),bind(B,$thf( C @ g ))]]) ).
thf(10330,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[10292]) ).
thf(133,plain,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) ) ),
inference(cnf,[status(esa)],[132]) ).
thf(1529,plain,
! [A: $i] :
( $false
| ~ ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) ) ),
inference(rewrite,[status(thm)],[133,66]) ).
thf(1530,plain,
! [A: $i] :
( ~ ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[1529]) ).
thf(1531,plain,
! [A: $i] :
( ~ $true
| ( ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
!= ( A @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) ) ),
inference(eqfactor_ordered,[status(thm)],[1530]) ).
thf(1533,plain,
! [A: $i] :
( ( ( A @ g @ f )
!= ( A @ f ) )
| ( ( '0' @ s @ s @ s @ s )
!= ( '0' @ s @ s @ s @ s ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[1531]) ).
thf(1534,plain,
! [A: $i] :
( ( ( A @ g @ f )
!= ( A @ f ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[1533]) ).
thf(1424,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ g @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ $true
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[60,88]) ).
thf(1425,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ g @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[1424]) ).
thf(1426,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(pattern_uni,[status(thm)],[1425:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ g ))]]) ).
thf(1520,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[1426]) ).
thf(23830,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ g @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( B @ g @ f @ 'LE' ) )
| ( B @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ $true
| ( A @ g @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[23716,1520]) ).
thf(23831,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ g @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( B @ g @ f @ 'LE' ) )
| ( B @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[23830]) ).
thf(23832,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ g @ g @ f @ 'LE' ) )
| ( A @ g @ g @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[23831:[bind(A,$thf( D )),bind(B,$thf( D @ g @ g ))]]) ).
thf(24044,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ g @ g @ f @ 'LE' ) )
| ( A @ g @ g @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[23832]) ).
thf(93,plain,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(cnf,[status(esa)],[92]) ).
thf(534,plain,
! [A: $i] :
( $false
| ~ ( A @ g @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(rewrite,[status(thm)],[93,66]) ).
thf(535,plain,
! [A: $i] :
( ~ ( A @ g @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[534]) ).
thf(536,plain,
! [A: $i] :
( ~ $true
| ( ( A @ g @ f @ ( '0' @ s @ s @ 'E' ) )
!= ( A @ f @ ( '0' @ s @ s @ 'E' ) ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(eqfactor_ordered,[status(thm)],[535]) ).
thf(537,plain,
! [A: $i] :
( ( ( A @ g @ f @ ( '0' @ s @ s @ 'E' ) )
!= ( A @ f @ ( '0' @ s @ s @ 'E' ) ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[536]) ).
thf(1039,plain,
! [A: $i] :
( ( ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) )
!= ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[1038]) ).
thf(24,axiom,
! [A: $i] :
~ ( A @ g @ f @ ( A @ f @ 'E' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_53_24) ).
thf(96,plain,
! [A: $i] :
~ ( A @ g @ f @ ( A @ f @ 'E' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2_25) ).
thf(98,plain,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(99,plain,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
inference(cnf,[status(esa)],[98]) ).
thf(253,plain,
! [A: $i] :
( $false
| ~ ( A @ g @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
inference(rewrite,[status(thm)],[99,66]) ).
thf(254,plain,
! [A: $i] :
( ~ ( A @ g @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[253]) ).
thf(255,plain,
! [A: $i] :
( ~ $true
| ( ( A @ g @ f @ ( '0' @ 'E' ) )
!= ( A @ f @ ( '0' @ 'E' ) ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
inference(eqfactor_ordered,[status(thm)],[254]) ).
thf(256,plain,
! [A: $i] :
( ( ( A @ g @ f @ ( '0' @ 'E' ) )
!= ( A @ f @ ( '0' @ 'E' ) ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[255]) ).
thf(326,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( C @ f @ ( '0' @ 'E' ) )
| ~ $true
| ~ ( '0' @ s @ ( B @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[67,321]) ).
thf(327,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( C @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( B @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[326]) ).
thf(328,plain,
! [A: $i] :
( ( A @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ f @ 'LE' ) ) ),
inference(pattern_uni,[status(thm)],[327:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(42,axiom,
! [A: $i] :
~ ( A @ g @ f @ ( A @ f @ 'E' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_25_42) ).
thf(124,plain,
! [A: $i] :
~ ( A @ g @ f @ ( A @ f @ 'E' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(225,plain,
! [A: $i] :
( ( ( A @ g )
!= A )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[224]) ).
thf(7338,plain,
! [A: $i] :
( ( ( A @ g @ f )
!= ( A @ f ) )
| ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s )
!= ( '0' @ s @ s @ s @ s @ s @ s @ s @ s ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[7336]) ).
thf(7339,plain,
! [A: $i] :
( ( ( A @ g @ f )
!= ( A @ f ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[7338]) ).
thf(7340,plain,
! [A: $i] :
( ( ( A @ g )
!= A )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[7339]) ).
thf(931,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ g @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ $true
| ~ ( '0' @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[60,91]) ).
thf(932,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ g @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[931]) ).
thf(933,plain,
! [A: $i] :
( ( '0' @ s @ ( A @ g @ f @ 'LE' ) )
| ( A @ g @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(pattern_uni,[status(thm)],[932:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ g ))]]) ).
thf(1002,plain,
! [A: $i] :
( ( '0' @ s @ ( A @ g @ f @ 'LE' ) )
| ( A @ g @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[933]) ).
thf(1083,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ ( A @ g @ f @ 'LE' ) )
!= ( '0' @ s @ ( B @ f @ 'LE' ) ) )
| ( B @ f @ ( '0' @ 'E' ) )
| ~ $true
| ( A @ g @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[1002,328]) ).
thf(1084,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ ( A @ g @ f @ 'LE' ) )
!= ( '0' @ s @ ( B @ f @ 'LE' ) ) )
| ( B @ f @ ( '0' @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[1083]) ).
thf(1085,plain,
! [A: $i] :
( ( A @ g @ f @ ( '0' @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(pattern_uni,[status(thm)],[1084:[bind(A,$thf( C )),bind(B,$thf( C @ g ))]]) ).
thf(1150,plain,
! [A: $i] :
( ( A @ g @ f @ ( '0' @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[1085]) ).
thf(2387,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s )
!= ( '0' @ s ) )
| ( ( B @ f )
!= ( C @ f ) )
| ( ( '0' @ s )
!= '0' )
| ( ( D @ f )
!= ( E @ f ) )
| ~ ( D @ ( C @ iLEQ ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( D @ f @ ( '0' @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[1195]) ).
thf(49,axiom,
! [A: $i] :
~ ( A @ g @ f @ ( A @ f @ 'E' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_15_49) ).
thf(134,plain,
! [A: $i] :
~ ( A @ g @ f @ ( A @ f @ 'E' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(10,axiom,
! [A: $i] : ( A @ g @ ( A @ iLEQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_28_10) ).
thf(73,plain,
! [A: $i] : ( A @ g @ ( A @ iLEQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(30,axiom,
! [A: $i] :
~ ( A @ g @ f @ ( A @ f @ 'E' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_43_30) ).
thf(105,plain,
! [A: $i] :
~ ( A @ g @ f @ ( A @ f @ 'E' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(3604,plain,
! [A: $i] :
( ~ $true
| ( ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
!= ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(eqfactor_ordered,[status(thm)],[3603]) ).
thf(3606,plain,
! [A: $i] :
( ( ( A @ g @ f )
!= ( A @ f ) )
| ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s )
!= ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[3604]) ).
thf(3607,plain,
! [A: $i] :
( ( ( A @ g @ f )
!= ( A @ f ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[3606]) ).
thf(56,axiom,
! [A: $i] : ( A @ g @ ( A @ iLEQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_22_56) ).
thf(148,plain,
! [A: $i] : ( A @ g @ ( A @ iLEQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(6527,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ ( C @ f @ 'LE' ) ) )
| ~ $true
| ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[137,141]) ).
thf(6528,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ ( C @ f @ 'LE' ) ) )
| ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[6527]) ).
thf(6646,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s )
!= '0' )
| ( ( B @ f )
!= ( C @ f ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[6528]) ).
thf(26259,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s )
!= '0' )
| ( B != C )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[6646]) ).
thf(26605,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s )
!= '0' )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[26259]) ).
thf(57,axiom,
! [A: $i] : ( A @ ( A @ iLEQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_24_57) ).
thf(149,plain,
! [A: $i] : ( A @ ( A @ iLEQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(189,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ $true
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[67,64]) ).
thf(190,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[189]) ).
thf(191,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(pattern_uni,[status(thm)],[190:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(1535,plain,
! [A: $i] :
( ( ( A @ g )
!= A )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[1534]) ).
thf(1399,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ ( C @ f @ 'LE' ) ) )
| ~ $true
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[88,141]) ).
thf(1400,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ ( C @ f @ 'LE' ) ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[1399]) ).
thf(1488,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s )
!= '0' )
| ( ( B @ f )
!= ( C @ f ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[1400]) ).
thf(257,plain,
! [A: $i] :
( ( ( A @ g @ f )
!= ( A @ f ) )
| ( '0' != '0' )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[255]) ).
thf(258,plain,
! [A: $i] :
( ( ( A @ g @ f )
!= ( A @ f ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[257]) ).
thf(259,plain,
! [A: $i] :
( ( ( A @ g )
!= A )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[258]) ).
thf(9,axiom,
! [A: $i] :
~ ( A @ g @ f @ ( A @ f @ 'E' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_41_09) ).
thf(71,plain,
! [A: $i] :
~ ( A @ g @ f @ ( A @ f @ 'E' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(538,plain,
! [A: $i] :
( ( ( A @ g @ f )
!= ( A @ f ) )
| ( ( '0' @ s @ s )
!= ( '0' @ s @ s ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[536]) ).
thf(539,plain,
! [A: $i] :
( ( ( A @ g @ f )
!= ( A @ f ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[538]) ).
thf(540,plain,
! [A: $i] :
( ( ( A @ g )
!= A )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[539]) ).
thf(18,axiom,
! [A: $i] : ( A @ g @ ( A @ iLEQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_16_18) ).
thf(86,plain,
! [A: $i] : ( A @ g @ ( A @ iLEQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(160,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ g @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ $true
| ~ ( '0' @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[60,62]) ).
thf(161,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ g @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[160]) ).
thf(162,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(pattern_uni,[status(thm)],[161:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ g ))]]) ).
thf(172,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[162]) ).
thf(6838,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ ( A @ g @ f @ 'LE' ) )
!= ( '0' @ s @ s @ ( B @ f @ 'LE' ) ) )
| ( ( '0' @ s )
!= '0' )
| ~ $true
| ( B @ g @ f @ ( '0' @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[6713,2281]) ).
thf(6839,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ ( A @ g @ f @ 'LE' ) )
!= ( '0' @ s @ s @ ( B @ f @ 'LE' ) ) )
| ( ( '0' @ s )
!= '0' )
| ( B @ g @ f @ ( '0' @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[6838]) ).
thf(6840,plain,
! [A: $i] :
( ( ( '0' @ s )
!= '0' )
| ( A @ g @ g @ f @ ( '0' @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(pattern_uni,[status(thm)],[6839:[bind(A,$thf( C )),bind(B,$thf( C @ g ))]]) ).
thf(7077,plain,
! [A: $i] :
( ( ( '0' @ s )
!= '0' )
| ( A @ g @ g @ f @ ( '0' @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[6840]) ).
thf(18413,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ $true
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[252,574]) ).
thf(18414,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[18413]) ).
thf(18415,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[18414:[bind(A,$thf( C )),bind(B,$thf( C @ g ))]]) ).
thf(18515,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[18415]) ).
thf(18635,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ $true
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[18515,1449]) ).
thf(18636,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[18635]) ).
thf(18637,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[18636:[bind(A,$thf( C )),bind(B,$thf( C @ g ))]]) ).
thf(18827,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[18637]) ).
thf(28595,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( ( '0' @ s @ s )
!= '0' )
| ~ $true
| ~ ( '0' @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[67,26605]) ).
thf(28596,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( ( '0' @ s @ s )
!= '0' )
| ~ ( '0' @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[28595]) ).
thf(28597,plain,
! [A: $i] :
( ( ( '0' @ s @ s )
!= '0' )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[28596:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(16137,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ iLEQ ) )
!= ( D @ ( C @ iLEQ ) ) )
| ( D @ f @ ( '0' @ 'E' ) )
| ~ $true
| ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ ( B @ iLEQ ) )
| ~ ( '0' @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[67,999]) ).
thf(16138,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ iLEQ ) )
!= ( D @ ( C @ iLEQ ) ) )
| ( D @ f @ ( '0' @ 'E' ) )
| ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ ( B @ iLEQ ) )
| ~ ( '0' @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[16137]) ).
thf(16139,plain,
! [B: $i,A: $i] :
( ( A @ f @ ( '0' @ 'E' ) )
| ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ ( B @ iLEQ ) )
| ~ ( '0' @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(pattern_uni,[status(thm)],[16138:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).
thf(239,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( D @ f @ 'LE' ) )
| ( D @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( D @ ( C @ iLEQ ) )
| ~ $true
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[216,64]) ).
thf(240,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( D @ f @ 'LE' ) )
| ( D @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( D @ ( C @ iLEQ ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[239]) ).
thf(251,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s )
!= ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s ) )
| ( ( B @ f )
!= ( C @ f ) )
| ~ ( D @ ( C @ iLEQ ) )
| ~ ( B @ ( A @ iLEQ ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( D @ f @ 'LE' ) )
| ( D @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[240]) ).
thf(1070,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ ( A @ g @ f @ 'LE' ) )
!= ( '0' @ s @ ( B @ f @ 'LE' ) ) )
| ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ ( B @ iLEQ ) )
| ~ $true
| ( A @ g @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[1002,321]) ).
thf(1071,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ ( A @ g @ f @ 'LE' ) )
!= ( '0' @ s @ ( B @ f @ 'LE' ) ) )
| ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ ( B @ iLEQ ) )
| ( A @ g @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[1070]) ).
thf(1072,plain,
! [B: $i,A: $i] :
( ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ ( B @ g @ iLEQ ) )
| ( B @ g @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(pattern_uni,[status(thm)],[1071:[bind(A,$thf( D )),bind(B,$thf( D @ g ))]]) ).
thf(1149,plain,
! [B: $i,A: $i] :
( ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ ( B @ g @ iLEQ ) )
| ( B @ g @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[1072]) ).
thf(155,plain,
! [A: $i] :
( ( ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
!= ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[154]) ).
thf(185,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ ( C @ f @ 'LE' ) ) )
| ~ $true
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[64,141]) ).
thf(186,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ ( C @ f @ 'LE' ) ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[185]) ).
thf(198,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s )
!= '0' )
| ( ( B @ f )
!= ( C @ f ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[186]) ).
thf(46,axiom,
! [A: $i] : ( A @ ( A @ iLEQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_39_46) ).
thf(130,plain,
! [A: $i] : ( A @ ( A @ iLEQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(299,plain,
! [A: $i] :
( ( ( A @ g @ f @ ( '0' @ s @ 'E' ) )
!= ( A @ f @ ( '0' @ s @ 'E' ) ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[298]) ).
thf(226,plain,
! [A: $i] :
( ( ( A @ g )
!= A )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[157]) ).
thf(14,axiom,
! [A: $i] :
~ ( A @ g @ f @ ( A @ f @ 'E' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_9_14) ).
thf(80,plain,
! [A: $i] :
~ ( A @ g @ f @ ( A @ f @ 'E' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(165,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ $true
| ~ ( '0' @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[67,62]) ).
thf(166,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[165]) ).
thf(167,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(pattern_uni,[status(thm)],[166:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(938,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ s @ ( C @ f @ 'LE' ) ) )
| ( C @ f @ ( '0' @ 'E' ) )
| ~ $true
| ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[91,328]) ).
thf(939,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ s @ ( C @ f @ 'LE' ) ) )
| ( C @ f @ ( '0' @ 'E' ) )
| ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[938]) ).
thf(940,plain,
! [B: $i,A: $i] :
( ( B @ f @ ( '0' @ 'E' ) )
| ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(pattern_uni,[status(thm)],[939:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(3574,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( C @ f @ ( '0' @ 'E' ) )
| ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ $true
| ~ ( '0' @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[67,940]) ).
thf(3575,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( C @ f @ ( '0' @ 'E' ) )
| ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[3574]) ).
thf(3576,plain,
! [A: $i] :
( ( A @ f @ ( '0' @ 'E' ) )
| ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(pattern_uni,[status(thm)],[3575:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(34,axiom,
! [A: $i] : ( A @ ( A @ iLEQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_12_34) ).
thf(112,plain,
! [A: $i] : ( A @ ( A @ iLEQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(41,axiom,
! [A: $i] : ( A @ ( A @ iLEQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4_41) ).
thf(123,plain,
! [A: $i] : ( A @ ( A @ iLEQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(2333,plain,
! [A: $i] :
( ( ( A @ g )
!= A )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[2332]) ).
thf(6575,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ $true
| ~ ( '0' @ s @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[67,137]) ).
thf(6576,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[6575]) ).
thf(6577,plain,
! [A: $i] :
( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(pattern_uni,[status(thm)],[6576:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(275,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ s @ s @ ( D @ f @ 'LE' ) )
| ( D @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( D @ ( C @ iLEQ ) )
| ~ $true
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[216,75]) ).
thf(276,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ s @ s @ ( D @ f @ 'LE' ) )
| ( D @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( D @ ( C @ iLEQ ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[275]) ).
thf(282,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s )
!= ( '0' @ s @ s @ s @ s @ s @ s ) )
| ( ( B @ f )
!= ( C @ f ) )
| ~ ( D @ ( C @ iLEQ ) )
| ~ ( B @ ( A @ iLEQ ) )
| ( '0' @ s @ s @ s @ s @ s @ ( D @ f @ 'LE' ) )
| ( D @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[276]) ).
thf(266,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) )
| ~ $true
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[67,75]) ).
thf(267,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[266]) ).
thf(268,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(pattern_uni,[status(thm)],[267:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(7157,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) )
| ~ $true
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[6283,268]) ).
thf(7158,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[7157]) ).
thf(7159,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[7158:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(3608,plain,
! [A: $i] :
( ( ( A @ g )
!= A )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[3607]) ).
thf(194,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( D @ f @ 'LE' ) )
| ( D @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( D @ ( C @ iLEQ ) )
| ~ $true
| ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[62,64]) ).
thf(195,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( D @ f @ 'LE' ) )
| ( D @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( D @ ( C @ iLEQ ) )
| ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[194]) ).
thf(199,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s )
!= ( '0' @ s @ s @ s ) )
| ( ( B @ f )
!= ( C @ f ) )
| ~ ( D @ ( C @ iLEQ ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( D @ f @ 'LE' ) )
| ( D @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[195]) ).
thf(44,axiom,
! [A: $i] : ( A @ g @ ( A @ iLEQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_17_44) ).
thf(127,plain,
! [A: $i] : ( A @ g @ ( A @ iLEQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(9855,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ g @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( ( '0' @ s @ s @ s )
!= '0' )
| ~ $true
| ~ ( '0' @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[60,440]) ).
thf(9856,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ g @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( ( '0' @ s @ s @ s )
!= '0' )
| ~ ( '0' @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[9855]) ).
thf(9857,plain,
! [A: $i] :
( ( ( '0' @ s @ s @ s )
!= '0' )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[9856:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ g ))]]) ).
thf(9930,plain,
! [A: $i] :
( ( ( '0' @ s @ s @ s )
!= '0' )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[9857]) ).
thf(1098,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ ( A @ g @ f @ 'LE' ) )
!= ( '0' @ s @ ( B @ f @ 'LE' ) ) )
| ( B @ g @ f @ ( '0' @ 'E' ) )
| ~ $true
| ( A @ g @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[1002,346]) ).
thf(1099,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ ( A @ g @ f @ 'LE' ) )
!= ( '0' @ s @ ( B @ f @ 'LE' ) ) )
| ( B @ g @ f @ ( '0' @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[1098]) ).
thf(1100,plain,
! [A: $i] :
( ( A @ g @ g @ f @ ( '0' @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(pattern_uni,[status(thm)],[1099:[bind(A,$thf( C )),bind(B,$thf( C @ g ))]]) ).
thf(1140,plain,
! [A: $i] :
( ( A @ g @ g @ f @ ( '0' @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[1100]) ).
thf(19937,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( ( '0' @ s )
!= '0' )
| ( C @ f @ ( '0' @ s @ 'E' ) )
| ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ $true
| ~ ( '0' @ s @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[67,6560]) ).
thf(19938,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( ( '0' @ s )
!= '0' )
| ( C @ f @ ( '0' @ s @ 'E' ) )
| ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[19937]) ).
thf(19939,plain,
! [A: $i] :
( ( ( '0' @ s )
!= '0' )
| ( A @ f @ ( '0' @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(pattern_uni,[status(thm)],[19938:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(5952,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ g @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ $true
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[60,129]) ).
thf(5953,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ g @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[5952]) ).
thf(5954,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(pattern_uni,[status(thm)],[5953:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ g ))]]) ).
thf(6161,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[5954]) ).
thf(244,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ ( C @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ ( D @ f @ 'LE' ) )
| ( D @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( D @ ( C @ iLEQ ) )
| ~ $true
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[216,62]) ).
thf(245,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ ( C @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ ( D @ f @ 'LE' ) )
| ( D @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( D @ ( C @ iLEQ ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[244]) ).
thf(250,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s )
!= ( '0' @ s @ s @ s @ s ) )
| ( ( B @ f )
!= ( C @ f ) )
| ~ ( D @ ( C @ iLEQ ) )
| ~ ( B @ ( A @ iLEQ ) )
| ( '0' @ s @ s @ s @ ( D @ f @ 'LE' ) )
| ( D @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[245]) ).
thf(29,axiom,
! [A: $i] : ( A @ g @ ( A @ iLEQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_45_29) ).
thf(104,plain,
! [A: $i] : ( A @ g @ ( A @ iLEQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(368,plain,
! [A: $i] :
( ( ( A @ g @ f @ ( '0' @ s @ s @ s @ 'E' ) )
!= ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[367]) ).
thf(168,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ ( C @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ ( D @ f @ 'LE' ) )
| ( D @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( D @ ( C @ iLEQ ) )
| ~ $true
| ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[62,62]) ).
thf(169,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ ( B @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ ( C @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ ( D @ f @ 'LE' ) )
| ( D @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( D @ ( C @ iLEQ ) )
| ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[168]) ).
thf(171,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s )
!= ( '0' @ s @ s @ s ) )
| ( ( B @ f )
!= ( C @ f ) )
| ~ ( D @ ( C @ iLEQ ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( '0' @ s @ s @ s @ ( D @ f @ 'LE' ) )
| ( D @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[169]) ).
thf(2330,plain,
! [A: $i] :
( ( ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) )
!= ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[2329]) ).
thf(4444,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( C @ g @ f @ ( '0' @ 'E' ) )
| ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ $true
| ~ ( '0' @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[67,956]) ).
thf(4445,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( C @ g @ f @ ( '0' @ 'E' ) )
| ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[4444]) ).
thf(4446,plain,
! [A: $i] :
( ( A @ g @ f @ ( '0' @ 'E' ) )
| ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(pattern_uni,[status(thm)],[4445:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(15,axiom,
! [A: $i] : ( A @ g @ ( A @ iLEQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_32_15) ).
thf(82,plain,
! [A: $i] : ( A @ g @ ( A @ iLEQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(279,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ g @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) )
| ~ $true
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[60,75]) ).
thf(280,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ g @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[279]) ).
thf(281,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(pattern_uni,[status(thm)],[280:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ g ))]]) ).
thf(290,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[281]) ).
thf(38,axiom,
! [A: $i] : ( A @ g @ ( A @ iLEQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6_38) ).
thf(119,plain,
! [A: $i] : ( A @ g @ ( A @ iLEQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(55,axiom,
! [A: $i] :
~ ( A @ g @ f @ ( A @ f @ 'E' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_34_55) ).
thf(146,plain,
! [A: $i] :
~ ( A @ g @ f @ ( A @ f @ 'E' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(15412,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( B @ g @ f @ 'LE' ) )
| ( B @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ $true
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[895,1520]) ).
thf(15413,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( B @ g @ f @ 'LE' ) )
| ( B @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[15412]) ).
thf(15414,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ g @ f @ 'LE' ) )
| ( A @ g @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[15413:[bind(A,$thf( C )),bind(B,$thf( C @ g ))]]) ).
thf(15690,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ g @ f @ 'LE' ) )
| ( A @ g @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[15414]) ).
thf(43,axiom,
! [A: $i] : ( A @ g @ ( A @ iLEQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_46_43) ).
thf(126,plain,
! [A: $i] : ( A @ g @ ( A @ iLEQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(1532,plain,
! [A: $i] :
( ( ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
!= ( A @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[1531]) ).
thf(3605,plain,
! [A: $i] :
( ( ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
!= ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[3604]) ).
thf(6913,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ ( A @ g @ f @ 'LE' ) )
!= ( '0' @ s @ s @ ( B @ f @ 'LE' ) ) )
| ( B @ f @ ( '0' @ 'E' ) )
| ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ $true
| ( A @ g @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[6713,3576]) ).
thf(6914,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ ( A @ g @ f @ 'LE' ) )
!= ( '0' @ s @ s @ ( B @ f @ 'LE' ) ) )
| ( B @ f @ ( '0' @ 'E' ) )
| ( B @ f @ ( '0' @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[6913]) ).
thf(6915,plain,
! [A: $i] :
( ( A @ g @ f @ ( '0' @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(pattern_uni,[status(thm)],[6914:[bind(A,$thf( C )),bind(B,$thf( C @ g ))]]) ).
thf(7035,plain,
! [A: $i] :
( ( A @ g @ f @ ( '0' @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[6915]) ).
thf(47,axiom,
! [A: $i] : ( A @ g @ ( A @ iLEQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_47_47) ).
thf(131,plain,
! [A: $i] : ( A @ g @ ( A @ iLEQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(182,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ g @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ $true
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(paramod_ordered,[status(thm)],[60,64]) ).
thf(183,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ g @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[182]) ).
thf(184,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(pattern_uni,[status(thm)],[183:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ g ))]]) ).
thf(200,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[184]) ).
thf(18580,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( B @ g @ f @ 'LE' ) )
| ( B @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ $true
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[18515,1520]) ).
thf(18581,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( B @ g @ f @ 'LE' ) )
| ( B @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[18580]) ).
thf(18582,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ g @ f @ 'LE' ) )
| ( A @ g @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[18581:[bind(A,$thf( C )),bind(B,$thf( C @ g ))]]) ).
thf(18826,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( A @ g @ g @ f @ 'LE' ) )
| ( A @ g @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[18582]) ).
thf(40,axiom,
! [A: $i] : ( A @ ( A @ iLEQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_52_40) ).
thf(122,plain,
! [A: $i] : ( A @ ( A @ iLEQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(212,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( C @ ( B @ iLEQ ) )
| ~ $true
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[121,62]) ).
thf(213,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ s @ s @ s @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( C @ ( B @ iLEQ ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[212]) ).
thf(215,plain,
! [C: $i,B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s )
!= ( '0' @ s @ s @ s @ s ) )
| ( ( A @ f )
!= ( B @ f ) )
| ~ ( C @ ( B @ iLEQ ) )
| ( '0' @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[213]) ).
thf(9878,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( ( '0' @ s @ s @ s )
!= '0' )
| ~ $true
| ~ ( '0' @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[67,440]) ).
thf(9879,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( ( '0' @ s @ s @ s )
!= '0' )
| ~ ( '0' @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[9878]) ).
thf(9880,plain,
! [A: $i] :
( ( ( '0' @ s @ s @ s )
!= '0' )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[9879:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(6244,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ g @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ~ $true
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[60,6162]) ).
thf(6245,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ g @ ( A @ iLEQ ) )
!= ( C @ ( B @ iLEQ ) ) )
| ( '0' @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'LE' ) )
| ( C @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[6244]) ).
thf(6246,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[6245:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ g ))]]) ).
thf(6404,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ ( A @ g @ f @ 'LE' ) )
| ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[6246]) ).
thf(222,plain,
! [A: $i] :
( ( ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
!= ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[221]) ).
thf(207,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( B @ f @ 'LE' ) ) )
| ~ $true
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[121,141]) ).
thf(208,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( B @ f @ 'LE' ) ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[207]) ).
thf(214,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s )
!= '0' )
| ( ( A @ f )
!= ( B @ f ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[208]) ).
thf(5223,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
!= ( C @ f @ ( '0' @ 'E' ) ) )
| ~ ( C @ g @ f @ ( '0' @ 'E' ) )
| ~ $true
| ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s )
!= '0' )
| ( ( A @ f )
!= ( B @ f ) ) ),
inference(paramod_ordered,[status(thm)],[214,254]) ).
thf(5224,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
!= ( C @ f @ ( '0' @ 'E' ) ) )
| ~ ( C @ g @ f @ ( '0' @ 'E' ) )
| ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s )
!= '0' )
| ( ( A @ f )
!= ( B @ f ) ) ),
inference(simp,[status(thm)],[5223]) ).
thf(5296,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ f )
!= ( C @ f ) )
| ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s )
!= '0' )
| ~ ( C @ g @ f @ ( '0' @ 'E' ) )
| ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s )
!= '0' )
| ( A != B ) ),
inference(simp,[status(thm)],[5224]) ).
thf(5518,plain,
! [B: $i,A: $i] :
( ( ( A @ f )
!= ( B @ f ) )
| ~ ( B @ g @ f @ ( '0' @ 'E' ) )
| ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s )
!= '0' ) ),
inference(simp,[status(thm)],[5296]) ).
thf(5647,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
!= ( D @ g @ f @ ( '0' @ 'E' ) ) )
| ( ( C @ f )
!= ( D @ f ) )
| ~ $true
| ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s )
!= '0' )
| ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s )
!= '0' )
| ( ( A @ f )
!= ( B @ f ) ) ),
inference(paramod_ordered,[status(thm)],[214,5518]) ).
thf(5648,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'E' ) )
!= ( D @ g @ f @ ( '0' @ 'E' ) ) )
| ( ( C @ f )
!= ( D @ f ) )
| ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s )
!= '0' )
| ( ( A @ f )
!= ( B @ f ) ) ),
inference(simp,[status(thm)],[5647]) ).
thf(5655,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ f )
!= ( D @ g @ f ) )
| ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s )
!= '0' )
| ( C != D )
| ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s )
!= '0' )
| ( A != B ) ),
inference(simp,[status(thm)],[5648]) ).
thf(5662,plain,
! [B: $i,A: $i] :
( ( ( A @ f )
!= ( B @ g @ f ) )
| ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s )
!= '0' ) ),
inference(simp,[status(thm)],[5655]) ).
thf(5910,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ g ) )
| ( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s )
!= '0' ) ),
inference(simp,[status(thm)],[5662]) ).
thf(5911,plain,
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s )
!= '0' ),
inference(simp,[status(thm)],[5910]) ).
thf(26,axiom,
! [A: $i] : ( A @ ( A @ iLEQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_50_26) ).
thf(100,plain,
! [A: $i] : ( A @ ( A @ iLEQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(33,axiom,
! [A: $i] : ( A @ ( A @ iLEQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_13_33) ).
thf(111,plain,
! [A: $i] : ( A @ ( A @ iLEQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(45434,plain,
$false,
inference(e,[status(thm)],[16216,138,101,6283,249,88,115,6162,120,440,1041,4739,13317,142,153,1243,301,4610,389,2328,6713,6006,196,949,157,24045,284,78,216,321,121,574,2281,61,956,132,6498,89,7337,11195,74,602,981,116,243,6560,24184,85,102,60,117,220,366,3603,1042,302,598,7084,137,297,70,92,197,65,2332,1195,974,224,252,10330,1534,141,24044,537,1039,96,256,109,328,124,225,7340,1150,1530,2387,129,1002,134,73,128,105,23716,3607,148,26605,64,149,191,1535,1488,259,1520,3404,71,144,540,86,172,13079,7077,2257,76,98,113,18827,28597,16139,535,140,91,66,251,895,1149,155,198,130,299,226,7339,80,167,3576,112,123,2333,6577,63,282,7159,3608,67,199,370,127,864,9930,1140,19939,6161,250,539,87,104,368,258,171,75,2330,18515,4446,346,82,290,119,58,999,146,1527,15690,107,268,79,94,283,126,136,1532,3605,7035,131,200,62,7335,607,18826,68,254,122,940,83,215,1037,9880,6404,1449,222,5911,100,90,111,3526]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO631-1 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.07 % 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
% 0.12/0.38 % Computer : n014.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sat Sep 26 19:40:31 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 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
% 0.90/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.45/1.23 % [INFO] Parsing done (242ms).
% 1.45/1.24 % [INFO] Running in sequential loop mode.
% 2.25/1.63 % [INFO] eprover registered as external prover.
% 2.25/1.64 % [INFO] Scanning for conjecture ...
% 2.44/1.72 % [INFO] 57 axioms and no conjecture found.
% 2.64/1.84 % [INFO] Problem is propositional (TPTP CNF).
% 2.64/1.85 % [INFO] Type checking passed.
% 2.64/1.85 % [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 ...
% 114.10/36.67 % External prover 'e' found a proof!
% 114.10/36.67 % [INFO] Killing All external provers ...
% 114.10/36.67 % Time passed: 36136ms (effective reasoning time: 35422ms)
% 114.10/36.67 % Axioms used in derivation (57): clause_55_48, clause_44_07, clause_17_44, clause_50_26, clause_39_46, clause_47_47, clause_4_41, clause_16_18, clause_37_27, clause_45_29, clause_7_53, clause_30_35, clause_35_20, clause_46_43, clause_27_01, clause_18_06, clause_22_56, clause_14_28, clause_24_57, clause_12_34, clause_1_17, clause_29_12, clause_28_10, clause_0_36, clause_2_25, clause_34_55, clause_25_42, clause_8_03, clause_40_23, clause_52_40, clause_20_22, clause_6_38, clause_15_49, clause_31_54, clause_56_31, clause_51_50, clause_42_32, clause_53_24, clause_11_16, clause_38_52, clause_41_09, clause_13_33, clause_48_04, clause_32_15, clause_19_05, clause_21_08, clause_23_21, clause_26_19, clause_43_30, clause_54_45, clause_10_13, clause_9_14, clause_36_51, clause_33_37, clause_49_39, clause_5_11, clause_3_02
% 114.10/36.67 % No. of inferences in proof: 536
% 114.10/36.67 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 36136 ms resp. 35422 ms w/o parsing
% 115.16/36.97 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 115.16/36.98 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------