%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM860+1 : TPTP v9.3.1. Released v4.1.0.
% 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 : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:10:14 AM UTC 2026
% Result : Theorem 154.49s 41.07s
% Output : Refutation 147.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 23
% Syntax : Number of formulae : 351 ( 67 unt; 0 typ; 9 def)
% Number of atoms : 1272 ( 252 equ; 0 cnn)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 4519 ( 483 ~; 548 |; 57 &;3368 @)
% ( 9 <=>; 54 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 8 con; 0-3 aty)
% Number of variables : 870 ( 9 ^; 846 !; 6 ?; 870 :)
% ( 0 !>; 0 ?*; 0 @-; 9 @+)
% Comments :
%------------------------------------------------------------------------------
thf(minsol_model_ub_decl,type,
minsol_model_ub: $i > $i > $i > $o ).
thf(minsol_model_max_decl,type,
minsol_model_max: $i > $i > $i > $o ).
thf(lesseq_decl,type,
lesseq: $i > $i > $o ).
thf(sum_decl,type,
sum: $i > $i > $i ).
thf(summation_decl,type,
summation: $i > $i ).
thf(max_decl,type,
max: $i > $i > $i ).
thf(ub_decl,type,
ub: $i > $i > $i > $o ).
thf(model_max_decl,type,
model_max: $i > $i > $i > $o ).
thf(model_ub_decl,type,
model_ub: $i > $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk6_decl,type,
sk6: $i ).
thf(sk7_decl,type,
sk7: $i > $i > $i > $i ).
thf(sk8_decl,type,
sk8: $i > $i > $i > $i ).
thf(sk9_decl,type,
sk9: $i > $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ minsol_model_ub ) ) )
=> ( C @ ( B @ ( A @ minsol_model_max ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i] :
( ( B @ ( A @ ( sk1 @ minsol_model_ub ) ) )
=> ( B @ ( A @ ( sk1 @ minsol_model_max ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( A @ ( sk2 @ ( sk1 @ minsol_model_ub ) ) )
=> ( A @ ( sk2 @ ( sk1 @ minsol_model_max ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ minsol_model_max ) ) )
=> ( C @ ( B @ ( A @ minsol_model_ub ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] :
~ ! [B: $i] :
( ( B @ ( A @ ( sk4 @ minsol_model_max ) ) )
=> ( B @ ( A @ ( sk4 @ minsol_model_ub ) ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i] :
~ ( ( A @ ( sk5 @ ( sk4 @ minsol_model_max ) ) )
=> ( A @ ( sk5 @ ( sk4 @ minsol_model_ub ) ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
( ( A @ ( D @ summation @ lesseq ) )
& ( D @ ( B @ ( C @ ub ) ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( D @ ( B @ ( C @ model_max ) ) )
=> ( D @ ( A @ lesseq ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( D @ ( B @ ( C @ model_ub ) ) )
=> ( D @ ( A @ lesseq ) ) ) ) ) ).
thf(3,axiom,
! [A: $i] : ( A @ ( A @ lesseq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lesseq_ref) ).
thf(23,plain,
! [A: $i] : ( A @ ( A @ lesseq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(24,plain,
! [A: $i] : ( A @ ( A @ lesseq ) ),
inference(cnf,[status(esa)],[23]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ lesseq ) )
| ( ( B @ ( A @ max ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',max_1) ).
thf(44,plain,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ lesseq ) )
| ( ( B @ ( A @ max ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(45,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ lesseq ) )
| ( ( B @ ( A @ max ) )
= A ) ),
inference(cnf,[status(esa)],[44]) ).
thf(46,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ lesseq ) )
| ( ( B @ ( A @ max ) )
= A ) ),
inference(lifteq,[status(thm)],[45]) ).
thf(386,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ lesseq ) )
!= ( B @ ( C @ lesseq ) ) )
| ~ $true
| ( ( C @ ( B @ max ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[24,46]) ).
thf(387,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ lesseq ) )
!= ( B @ ( C @ lesseq ) ) )
| ( ( C @ ( B @ max ) )
= B ) ),
inference(simp,[status(thm)],[386]) ).
thf(388,plain,
! [A: $i] :
( ( A @ ( A @ max ) )
= A ),
inference(pattern_uni,[status(thm)],[387:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ model_max ) ) )
<=> ( C @ ( B @ ( A @ max ) @ summation @ lesseq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',model_max_3) ).
thf(57,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ max ) @ summation @ lesseq ) )
=> ( C @ ( B @ ( A @ model_max ) ) ) )
& ( ( C @ ( B @ ( A @ model_max ) ) )
=> ( C @ ( B @ ( A @ max ) @ summation @ lesseq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(58,plain,
( ! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ max ) @ summation @ lesseq ) )
=> ( C @ ( B @ ( A @ model_max ) ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ model_max ) ) )
=> ( C @ ( B @ ( A @ max ) @ summation @ lesseq ) ) ) ),
inference(miniscope,[status(thm)],[57]) ).
thf(59,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ ( D @ model_max ) ) )
| ~ ( F @ ( E @ ( D @ max ) @ summation @ lesseq ) ) )
& ( ( C @ ( B @ ( A @ max ) @ summation @ lesseq ) )
| ~ ( C @ ( B @ ( A @ model_max ) ) ) ) ),
inference(cnf,[status(esa)],[58]) ).
thf(61,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ model_max ) ) )
| ~ ( C @ ( B @ ( A @ max ) @ summation @ lesseq ) ) ),
inference(cnfConj,[status(thm)],[59]) ).
thf(62,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ model_max ) ) )
| ~ ( C @ ( B @ ( A @ max ) @ summation @ lesseq ) ) ),
inference(simp,[status(thm)],[61]) ).
thf(3661,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ lesseq ) )
!= ( D @ ( C @ ( B @ max ) @ summation @ lesseq ) ) )
| ( D @ ( C @ ( B @ model_max ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,62]) ).
thf(3662,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ lesseq ) )
!= ( D @ ( C @ ( B @ max ) @ summation @ lesseq ) ) )
| ( D @ ( C @ ( B @ model_max ) ) ) ),
inference(simp,[status(thm)],[3661]) ).
thf(3663,plain,
! [B: $i,A: $i] : ( B @ ( A @ max ) @ summation @ ( B @ ( A @ model_max ) ) ),
inference(pattern_uni,[status(thm)],[3662:[bind(A,$thf( J @ ( I @ max ) @ summation )),bind(B,$thf( I )),bind(C,$thf( J )),bind(D,$thf( J @ ( I @ max ) @ summation ))]]) ).
thf(3753,plain,
! [B: $i,A: $i] : ( B @ ( A @ max ) @ summation @ ( B @ ( A @ model_max ) ) ),
inference(simp,[status(thm)],[3663]) ).
thf(3796,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ max ) )
!= ( C @ ( B @ max ) ) )
| ( A @ summation @ ( C @ ( B @ model_max ) ) ) ),
inference(paramod_ordered,[status(thm)],[388,3753]) ).
thf(3797,plain,
! [A: $i] : ( A @ summation @ ( A @ ( A @ model_max ) ) ),
inference(pattern_uni,[status(thm)],[3796:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(60,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ max ) @ summation @ lesseq ) )
| ~ ( C @ ( B @ ( A @ model_max ) ) ) ),
inference(cnfConj,[status(thm)],[59]) ).
thf(3811,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ summation @ ( A @ ( A @ model_max ) ) )
!= ( D @ ( C @ ( B @ model_max ) ) ) )
| ( D @ ( C @ ( B @ max ) @ summation @ lesseq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3797,60]) ).
thf(3812,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ summation @ ( A @ ( A @ model_max ) ) )
!= ( D @ ( C @ ( B @ model_max ) ) ) )
| ( D @ ( C @ ( B @ max ) @ summation @ lesseq ) ) ),
inference(simp,[status(thm)],[3811]) ).
thf(3813,plain,
! [A: $i] : ( A @ summation @ ( A @ ( A @ max ) @ summation @ lesseq ) ),
inference(pattern_uni,[status(thm)],[3812:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E )),bind(D,$thf( E @ summation ))]]) ).
thf(3818,plain,
! [A: $i] : ( A @ summation @ ( A @ ( A @ max ) @ summation @ lesseq ) ),
inference(simp,[status(thm)],[3813]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ lesseq ) )
| ( ( B @ ( A @ max ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',max_2) ).
thf(47,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ lesseq ) )
| ( ( B @ ( A @ max ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ lesseq ) )
| ( ( B @ ( A @ max ) )
= B ) ),
inference(cnf,[status(esa)],[47]) ).
thf(49,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ lesseq ) )
| ( ( B @ ( A @ max ) )
= B ) ),
inference(lifteq,[status(thm)],[48]) ).
thf(3897,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ summation @ ( A @ ( A @ max ) @ summation @ lesseq ) )
!= ( C @ ( B @ lesseq ) ) )
| ~ $true
| ( ( C @ ( B @ max ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[3818,49]) ).
thf(3898,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ summation @ ( A @ ( A @ max ) @ summation @ lesseq ) )
!= ( C @ ( B @ lesseq ) ) )
| ( ( C @ ( B @ max ) )
= C ) ),
inference(simp,[status(thm)],[3897]) ).
thf(3899,plain,
! [A: $i] :
( ( A @ summation @ ( A @ ( A @ max ) @ summation @ max ) )
= ( A @ summation ) ),
inference(pattern_uni,[status(thm)],[3898:[bind(A,$thf( G )),bind(B,$thf( G @ ( G @ max ) @ summation )),bind(C,$thf( G @ summation ))]]) ).
thf(3961,plain,
! [A: $i] :
( ( A @ summation @ ( A @ ( A @ max ) @ summation @ max ) )
= ( A @ summation ) ),
inference(simp,[status(thm)],[3899]) ).
thf(5579,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ summation @ ( A @ ( A @ max ) @ summation @ max ) )
!= ( C @ ( B @ max ) ) )
| ( A @ summation @ summation @ ( C @ ( B @ model_max ) ) ) ),
inference(paramod_ordered,[status(thm)],[3961,3753]) ).
thf(5580,plain,
! [A: $i] : ( A @ summation @ summation @ ( A @ summation @ ( A @ ( A @ max ) @ summation @ model_max ) ) ),
inference(pattern_uni,[status(thm)],[5579:[bind(A,$thf( G )),bind(B,$thf( G @ ( G @ max ) @ summation )),bind(C,$thf( G @ summation ))]]) ).
thf(5614,plain,
! [A: $i] : ( A @ summation @ summation @ ( A @ summation @ ( A @ ( A @ max ) @ summation @ model_max ) ) ),
inference(simp,[status(thm)],[5580]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ model_ub ) ) )
<=> ? [D: $i] :
( ( C @ ( D @ summation @ lesseq ) )
& ( D @ ( B @ ( A @ ub ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',model_ub_3) ).
thf(63,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] :
( ( C @ ( D @ summation @ lesseq ) )
& ( D @ ( B @ ( A @ ub ) ) ) )
=> ( C @ ( B @ ( A @ model_ub ) ) ) )
& ( ( C @ ( B @ ( A @ model_ub ) ) )
=> ? [D: $i] :
( ( C @ ( D @ summation @ lesseq ) )
& ( D @ ( B @ ( A @ ub ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(64,plain,
( ! [A: $i,B: $i,C: $i] :
( ? [D: $i] :
( ( C @ ( D @ summation @ lesseq ) )
& ( D @ ( B @ ( A @ ub ) ) ) )
=> ( C @ ( B @ ( A @ model_ub ) ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ model_ub ) ) )
=> ? [D: $i] :
( ( C @ ( D @ summation @ lesseq ) )
& ( D @ ( B @ ( A @ ub ) ) ) ) ) ),
inference(miniscope,[status(thm)],[63]) ).
thf(65,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ ( D @ model_ub ) ) )
| ~ ( F @ ( G @ summation @ lesseq ) )
| ~ ( G @ ( E @ ( D @ ub ) ) ) )
& ( ( C @ ( A @ ( B @ ( C @ sk7 ) ) @ summation @ lesseq ) )
| ~ ( C @ ( B @ ( A @ model_ub ) ) ) )
& ( ( A @ ( B @ ( C @ sk7 ) ) @ ( B @ ( A @ ub ) ) )
| ~ ( C @ ( B @ ( A @ model_ub ) ) ) ) ),
inference(cnf,[status(esa)],[64]) ).
thf(68,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ model_ub ) ) )
| ~ ( C @ ( D @ summation @ lesseq ) )
| ~ ( D @ ( B @ ( A @ ub ) ) ) ),
inference(cnfConj,[status(thm)],[65]) ).
thf(69,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ model_ub ) ) )
| ~ ( C @ ( D @ summation @ lesseq ) )
| ~ ( D @ ( B @ ( A @ ub ) ) ) ),
inference(simp,[status(thm)],[68]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ lesseq ) )
<=> ( B @ summation @ ( A @ summation @ lesseq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',summation_monotone) ).
thf(38,plain,
! [A: $i,B: $i] :
( ( ( B @ summation @ ( A @ summation @ lesseq ) )
=> ( B @ ( A @ lesseq ) ) )
& ( ( B @ ( A @ lesseq ) )
=> ( B @ summation @ ( A @ summation @ lesseq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(39,plain,
( ! [A: $i,B: $i] :
( ( B @ summation @ ( A @ summation @ lesseq ) )
=> ( B @ ( A @ lesseq ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ lesseq ) )
=> ( B @ summation @ ( A @ summation @ lesseq ) ) ) ),
inference(miniscope,[status(thm)],[38]) ).
thf(40,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ lesseq ) )
| ~ ( D @ summation @ ( C @ summation @ lesseq ) ) )
& ( ( B @ summation @ ( A @ summation @ lesseq ) )
| ~ ( B @ ( A @ lesseq ) ) ) ),
inference(cnf,[status(esa)],[39]) ).
thf(42,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ lesseq ) )
| ~ ( B @ summation @ ( A @ summation @ lesseq ) ) ),
inference(cnfConj,[status(thm)],[40]) ).
thf(43,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ lesseq ) )
| ~ ( B @ summation @ ( A @ summation @ lesseq ) ) ),
inference(simp,[status(thm)],[42]) ).
thf(3831,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ summation @ ( A @ ( A @ max ) @ summation @ lesseq ) )
!= ( C @ summation @ ( B @ summation @ lesseq ) ) )
| ( C @ ( B @ lesseq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3818,43]) ).
thf(3832,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ summation @ ( A @ ( A @ max ) @ summation @ lesseq ) )
!= ( C @ summation @ ( B @ summation @ lesseq ) ) )
| ( C @ ( B @ lesseq ) ) ),
inference(simp,[status(thm)],[3831]) ).
thf(3833,plain,
! [A: $i] : ( A @ ( A @ ( A @ max ) @ lesseq ) ),
inference(pattern_uni,[status(thm)],[3832:[bind(A,$thf( E )),bind(B,$thf( E @ ( E @ max ) )),bind(C,$thf( E ))]]) ).
thf(3960,plain,
! [A: $i] : ( A @ ( A @ ( A @ max ) @ lesseq ) ),
inference(simp,[status(thm)],[3833]) ).
thf(4054,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ max ) @ lesseq ) )
!= ( C @ ( B @ lesseq ) ) )
| ~ $true
| ( ( C @ ( B @ max ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[3960,49]) ).
thf(4055,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ max ) @ lesseq ) )
!= ( C @ ( B @ lesseq ) ) )
| ( ( C @ ( B @ max ) )
= C ) ),
inference(simp,[status(thm)],[4054]) ).
thf(4056,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ max ) @ max ) )
= A ),
inference(pattern_uni,[status(thm)],[4055:[bind(A,$thf( E )),bind(B,$thf( E @ ( E @ max ) )),bind(C,$thf( E ))]]) ).
thf(4094,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ max ) @ max ) )
= A ),
inference(simp,[status(thm)],[4056]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ub ) ) )
<=> ( ( C @ ( B @ lesseq ) )
& ( C @ ( A @ lesseq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ub) ).
thf(50,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( B @ lesseq ) )
& ( C @ ( A @ lesseq ) ) )
=> ( C @ ( B @ ( A @ ub ) ) ) )
& ( ( C @ ( B @ ( A @ ub ) ) )
=> ( ( C @ ( B @ lesseq ) )
& ( C @ ( A @ lesseq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(51,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ lesseq ) )
& ( C @ ( A @ lesseq ) ) )
=> ( C @ ( B @ ( A @ ub ) ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ub ) ) )
=> ( ( C @ ( B @ lesseq ) )
& ( C @ ( A @ lesseq ) ) ) ) ),
inference(miniscope,[status(thm)],[50]) ).
thf(52,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ ( D @ ub ) ) )
| ~ ( F @ ( E @ lesseq ) )
| ~ ( F @ ( D @ lesseq ) ) )
& ( ( C @ ( B @ lesseq ) )
| ~ ( C @ ( B @ ( A @ ub ) ) ) )
& ( ( C @ ( A @ lesseq ) )
| ~ ( C @ ( B @ ( A @ ub ) ) ) ) ),
inference(cnf,[status(esa)],[51]) ).
thf(55,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ub ) ) )
| ~ ( C @ ( B @ lesseq ) )
| ~ ( C @ ( A @ lesseq ) ) ),
inference(cnfConj,[status(thm)],[52]) ).
thf(56,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ub ) ) )
| ~ ( C @ ( B @ lesseq ) )
| ~ ( C @ ( A @ lesseq ) ) ),
inference(simp,[status(thm)],[55]) ).
thf(4203,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ max ) @ max ) )
!= ( C @ ( B @ max ) ) )
| ( A @ summation @ ( C @ ( B @ model_max ) ) ) ),
inference(paramod_ordered,[status(thm)],[4094,3753]) ).
thf(4204,plain,
! [A: $i] : ( A @ summation @ ( A @ ( A @ ( A @ max ) @ model_max ) ) ),
inference(pattern_uni,[status(thm)],[4203:[bind(A,$thf( E )),bind(B,$thf( E @ ( E @ max ) )),bind(C,$thf( E ))]]) ).
thf(4222,plain,
! [A: $i] : ( A @ summation @ ( A @ ( A @ ( A @ max ) @ model_max ) ) ),
inference(simp,[status(thm)],[4204]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ minsol_model_ub ) ) )
<=> ( C @ ( B @ ( A @ minsol_model_max ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',max_is_ub_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ minsol_model_ub ) ) )
<=> ( C @ ( B @ ( A @ minsol_model_max ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(16,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ minsol_model_max ) ) )
=> ( C @ ( B @ ( A @ minsol_model_ub ) ) ) )
& ( ( C @ ( B @ ( A @ minsol_model_ub ) ) )
=> ( C @ ( B @ ( A @ minsol_model_max ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(17,plain,
~ ( ! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ minsol_model_max ) ) )
=> ( C @ ( B @ ( A @ minsol_model_ub ) ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ minsol_model_ub ) ) )
=> ( C @ ( B @ ( A @ minsol_model_max ) ) ) ) ),
inference(miniscope,[status(thm)],[16]) ).
thf(18,plain,
( ( ~ ( sk6 @ ( sk5 @ ( sk4 @ minsol_model_ub ) ) )
| ~ ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_max ) ) ) )
& ( ( sk6 @ ( sk5 @ ( sk4 @ minsol_model_max ) ) )
| ~ ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_max ) ) ) )
& ( ~ ( sk6 @ ( sk5 @ ( sk4 @ minsol_model_ub ) ) )
| ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_ub ) ) ) )
& ( ( sk6 @ ( sk5 @ ( sk4 @ minsol_model_max ) ) )
| ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_ub ) ) ) ) ),
inference(cnf,[status(esa)],[17]) ).
thf(19,plain,
( ( sk6 @ ( sk5 @ ( sk4 @ minsol_model_max ) ) )
| ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_ub ) ) ) ),
inference(cnfConj,[status(thm)],[18]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ minsol_model_max ) ) )
<=> ( ! [D: $i] :
( ( D @ ( B @ ( A @ model_max ) ) )
=> ( D @ ( C @ lesseq ) ) )
& ( C @ ( B @ ( A @ model_max ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minsol_model_max) ).
thf(70,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ! [D: $i] :
( ( D @ ( B @ ( A @ model_max ) ) )
=> ( D @ ( C @ lesseq ) ) )
& ( C @ ( B @ ( A @ model_max ) ) ) )
=> ( C @ ( B @ ( A @ minsol_model_max ) ) ) )
& ( ( C @ ( B @ ( A @ minsol_model_max ) ) )
=> ( ! [D: $i] :
( ( D @ ( B @ ( A @ model_max ) ) )
=> ( D @ ( C @ lesseq ) ) )
& ( C @ ( B @ ( A @ model_max ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(71,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( D @ ( B @ ( A @ model_max ) ) )
=> ( D @ ( C @ lesseq ) ) )
& ( C @ ( B @ ( A @ model_max ) ) ) )
=> ( C @ ( B @ ( A @ minsol_model_max ) ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ minsol_model_max ) ) )
=> ( ! [D: $i] :
( ( D @ ( B @ ( A @ model_max ) ) )
=> ( D @ ( C @ lesseq ) ) )
& ( C @ ( B @ ( A @ model_max ) ) ) ) ) ),
inference(miniscope,[status(thm)],[70]) ).
thf(72,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( G @ ( F @ ( E @ minsol_model_max ) ) )
| ~ ( E @ ( F @ ( G @ sk8 ) ) @ ( G @ lesseq ) )
| ~ ( G @ ( F @ ( E @ model_max ) ) ) )
& ( ( G @ ( F @ ( E @ minsol_model_max ) ) )
| ( E @ ( F @ ( G @ sk8 ) ) @ ( F @ ( E @ model_max ) ) )
| ~ ( G @ ( F @ ( E @ model_max ) ) ) )
& ( ( D @ ( C @ lesseq ) )
| ~ ( D @ ( B @ ( A @ model_max ) ) )
| ~ ( C @ ( B @ ( A @ minsol_model_max ) ) ) )
& ( ( C @ ( B @ ( A @ model_max ) ) )
| ~ ( C @ ( B @ ( A @ minsol_model_max ) ) ) ) ),
inference(cnf,[status(esa)],[71]) ).
thf(74,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ lesseq ) )
| ~ ( D @ ( B @ ( A @ model_max ) ) )
| ~ ( C @ ( B @ ( A @ minsol_model_max ) ) ) ),
inference(cnfConj,[status(thm)],[72]) ).
thf(5449,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk6 @ ( sk5 @ ( sk4 @ minsol_model_max ) ) )
!= ( C @ ( B @ ( A @ minsol_model_max ) ) ) )
| ( D @ ( C @ lesseq ) )
| ~ ( D @ ( B @ ( A @ model_max ) ) )
| ~ $true
| ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_ub ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,74]) ).
thf(5450,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk6 @ ( sk5 @ ( sk4 @ minsol_model_max ) ) )
!= ( C @ ( B @ ( A @ minsol_model_max ) ) ) )
| ( D @ ( C @ lesseq ) )
| ~ ( D @ ( B @ ( A @ model_max ) ) )
| ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_ub ) ) ) ),
inference(simp,[status(thm)],[5449]) ).
thf(5451,plain,
! [A: $i] :
( ( A @ ( sk6 @ lesseq ) )
| ~ ( A @ ( sk5 @ ( sk4 @ model_max ) ) )
| ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_ub ) ) ) ),
inference(pattern_uni,[status(thm)],[5450:[bind(A,$thf( sk4 )),bind(B,$thf( sk5 )),bind(C,$thf( sk6 ))]]) ).
thf(5482,plain,
! [A: $i] :
( ( A @ ( sk6 @ lesseq ) )
| ~ ( A @ ( sk5 @ ( sk4 @ model_max ) ) )
| ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_ub ) ) ) ),
inference(simp,[status(thm)],[5451]) ).
thf(5693,plain,
! [B: $i,A: $i] :
( ( ( A @ summation @ ( A @ ( A @ ( A @ max ) @ model_max ) ) )
!= ( B @ ( sk5 @ ( sk4 @ model_max ) ) ) )
| ( B @ ( sk6 @ lesseq ) )
| ~ $true
| ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_ub ) ) ) ),
inference(paramod_ordered,[status(thm)],[4222,5482]) ).
thf(5694,plain,
! [B: $i,A: $i] :
( ( ( A @ summation @ ( A @ ( A @ ( A @ max ) @ model_max ) ) )
!= ( B @ ( sk5 @ ( sk4 @ model_max ) ) ) )
| ( B @ ( sk6 @ lesseq ) )
| ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_ub ) ) ) ),
inference(simp,[status(thm)],[5693]) ).
thf(5705,plain,
! [B: $i,A: $i] :
( ( ( A @ summation )
!= B )
| ( A != sk5 )
| ( ( A @ ( A @ max ) )
!= sk4 )
| ( B @ ( sk6 @ lesseq ) )
| ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_ub ) ) ) ),
inference(simp,[status(thm)],[5694]) ).
thf(5709,plain,
( ( ( sk5 @ ( sk5 @ max ) )
!= sk4 )
| ( sk5 @ summation @ ( sk6 @ lesseq ) )
| ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_ub ) ) ) ),
inference(simp,[status(thm)],[5705]) ).
thf(6515,plain,
( ( sk5 != sk4 )
| ( sk5 @ summation @ ( sk6 @ lesseq ) )
| ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_ub ) ) ) ),
inference(rewrite,[status(thm)],[5709,388]) ).
thf(5675,plain,
! [B: $i,A: $i] :
( ( ( A @ summation @ ( A @ ( A @ model_max ) ) )
!= ( B @ ( sk5 @ ( sk4 @ model_max ) ) ) )
| ( B @ ( sk6 @ lesseq ) )
| ~ $true
| ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_ub ) ) ) ),
inference(paramod_ordered,[status(thm)],[3797,5482]) ).
thf(5676,plain,
! [B: $i,A: $i] :
( ( ( A @ summation @ ( A @ ( A @ model_max ) ) )
!= ( B @ ( sk5 @ ( sk4 @ model_max ) ) ) )
| ( B @ ( sk6 @ lesseq ) )
| ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_ub ) ) ) ),
inference(simp,[status(thm)],[5675]) ).
thf(5704,plain,
! [B: $i,A: $i] :
( ( ( A @ summation )
!= B )
| ( A != sk5 )
| ( A != sk4 )
| ( B @ ( sk6 @ lesseq ) )
| ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_ub ) ) ) ),
inference(simp,[status(thm)],[5676]) ).
thf(5708,plain,
( ( sk5 != sk4 )
| ( sk4 @ summation @ ( sk6 @ lesseq ) )
| ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_ub ) ) ) ),
inference(simp,[status(thm)],[5704]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ lesseq ) )
| ( B @ ( A @ lesseq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lesseq_total) ).
thf(30,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ lesseq ) )
| ( B @ ( A @ lesseq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ lesseq ) )
| ( B @ ( A @ lesseq ) ) ),
inference(cnf,[status(esa)],[30]) ).
thf(2241,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ lesseq ) )
!= ( D @ ( C @ lesseq ) ) )
| ( D @ ( C @ ( B @ ub ) ) )
| ~ $true
| ~ ( D @ ( B @ lesseq ) ) ),
inference(paramod_ordered,[status(thm)],[24,56]) ).
thf(2242,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ lesseq ) )
!= ( D @ ( C @ lesseq ) ) )
| ( D @ ( C @ ( B @ ub ) ) )
| ~ ( D @ ( B @ lesseq ) ) ),
inference(simp,[status(thm)],[2241]) ).
thf(2243,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ub ) ) )
| ~ ( A @ ( B @ lesseq ) ) ),
inference(pattern_uni,[status(thm)],[2242:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).
thf(54,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ lesseq ) )
| ~ ( C @ ( B @ ( A @ ub ) ) ) ),
inference(cnfConj,[status(thm)],[52]) ).
thf(2400,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ub ) ) )
!= ( E @ ( D @ ( C @ ub ) ) ) )
| ( E @ ( D @ lesseq ) )
| ~ $true
| ~ ( A @ ( B @ lesseq ) ) ),
inference(paramod_ordered,[status(thm)],[2243,54]) ).
thf(2401,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ub ) ) )
!= ( E @ ( D @ ( C @ ub ) ) ) )
| ( E @ ( D @ lesseq ) )
| ~ ( A @ ( B @ lesseq ) ) ),
inference(simp,[status(thm)],[2400]) ).
thf(2402,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ lesseq ) )
| ~ ( A @ ( B @ lesseq ) ) ),
inference(pattern_uni,[status(thm)],[2401:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A )),bind(E,$thf( A ))]]) ).
thf(2442,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ lesseq ) )
!= ( C @ ( D @ lesseq ) ) )
| ( C @ ( C @ lesseq ) )
| ~ $true
| ( A @ ( B @ lesseq ) ) ),
inference(paramod_ordered,[status(thm)],[31,2402]) ).
thf(2443,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ lesseq ) )
!= ( C @ ( D @ lesseq ) ) )
| ( C @ ( C @ lesseq ) )
| ( A @ ( B @ lesseq ) ) ),
inference(simp,[status(thm)],[2442]) ).
thf(2444,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ lesseq ) )
| ( A @ ( B @ lesseq ) ) ),
inference(pattern_uni,[status(thm)],[2443:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(2884,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ lesseq ) )
!= ( C @ ( D @ lesseq ) ) )
| ( C @ ( C @ lesseq ) )
| ~ $true
| ( B @ ( B @ lesseq ) ) ),
inference(paramod_ordered,[status(thm)],[2444,2402]) ).
thf(2885,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ lesseq ) )
!= ( C @ ( D @ lesseq ) ) )
| ( C @ ( C @ lesseq ) )
| ( B @ ( B @ lesseq ) ) ),
inference(simp,[status(thm)],[2884]) ).
thf(2886,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ lesseq ) )
| ( B @ ( B @ lesseq ) ) ),
inference(pattern_uni,[status(thm)],[2885:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ lesseq ) )
<=> ( B @ ( C @ sum ) @ ( A @ ( C @ sum ) @ lesseq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_monotone_1) ).
thf(32,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ sum ) @ ( A @ ( C @ sum ) @ lesseq ) )
=> ( B @ ( A @ lesseq ) ) )
& ( ( B @ ( A @ lesseq ) )
=> ( B @ ( C @ sum ) @ ( A @ ( C @ sum ) @ lesseq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(33,plain,
( ! [A: $i,B: $i] :
( ? [C: $i] : ( B @ ( C @ sum ) @ ( A @ ( C @ sum ) @ lesseq ) )
=> ( B @ ( A @ lesseq ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ lesseq ) )
=> ! [C: $i] : ( B @ ( C @ sum ) @ ( A @ ( C @ sum ) @ lesseq ) ) ) ),
inference(miniscope,[status(thm)],[32]) ).
thf(34,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ lesseq ) )
| ~ ( E @ ( F @ sum ) @ ( D @ ( F @ sum ) @ lesseq ) ) )
& ( ( B @ ( C @ sum ) @ ( A @ ( C @ sum ) @ lesseq ) )
| ~ ( B @ ( A @ lesseq ) ) ) ),
inference(cnf,[status(esa)],[33]) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ lesseq ) )
| ~ ( B @ ( C @ sum ) @ ( A @ ( C @ sum ) @ lesseq ) ) ),
inference(cnfConj,[status(thm)],[34]) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ lesseq ) )
| ~ ( B @ ( C @ sum ) @ ( A @ ( C @ sum ) @ lesseq ) ) ),
inference(simp,[status(thm)],[36]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ lesseq ) )
& ( B @ ( A @ lesseq ) ) )
=> ( C @ ( A @ lesseq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lesseq_trans) ).
thf(25,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ lesseq ) )
& ( B @ ( A @ lesseq ) ) )
=> ( C @ ( A @ lesseq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(21,plain,
( ( sk6 @ ( sk5 @ ( sk4 @ minsol_model_max ) ) )
| ~ ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_max ) ) ) ),
inference(cnfConj,[status(thm)],[18]) ).
thf(73,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ model_max ) ) )
| ~ ( C @ ( B @ ( A @ minsol_model_max ) ) ) ),
inference(cnfConj,[status(thm)],[72]) ).
thf(5062,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk6 @ ( sk5 @ ( sk4 @ minsol_model_max ) ) )
!= ( C @ ( B @ ( A @ minsol_model_max ) ) ) )
| ( C @ ( B @ ( A @ model_max ) ) )
| ~ $true
| ~ ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_max ) ) ) ),
inference(paramod_ordered,[status(thm)],[21,73]) ).
thf(5063,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk6 @ ( sk5 @ ( sk4 @ minsol_model_max ) ) )
!= ( C @ ( B @ ( A @ minsol_model_max ) ) ) )
| ( C @ ( B @ ( A @ model_max ) ) )
| ~ ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_max ) ) ) ),
inference(simp,[status(thm)],[5062]) ).
thf(5064,plain,
( ( sk6 @ ( sk5 @ ( sk4 @ model_max ) ) )
| ~ ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_max ) ) ) ),
inference(pattern_uni,[status(thm)],[5063:[bind(A,$thf( sk4 )),bind(B,$thf( sk5 )),bind(C,$thf( sk6 ))]]) ).
thf(20,plain,
( ~ ( sk6 @ ( sk5 @ ( sk4 @ minsol_model_ub ) ) )
| ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_ub ) ) ) ),
inference(cnfConj,[status(thm)],[18]) ).
thf(76,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ minsol_model_max ) ) )
| ~ ( A @ ( B @ ( C @ sk8 ) ) @ ( C @ lesseq ) )
| ~ ( C @ ( B @ ( A @ model_max ) ) ) ),
inference(cnfConj,[status(thm)],[72]) ).
thf(78,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ minsol_model_max ) ) )
| ~ ( A @ ( B @ ( C @ sk8 ) ) @ ( C @ lesseq ) )
| ~ ( C @ ( B @ ( A @ model_max ) ) ) ),
inference(simp,[status(thm)],[76]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ lesseq ) )
& ( B @ ( A @ lesseq ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lesseq_antisymmetric) ).
thf(27,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ lesseq ) )
& ( B @ ( A @ lesseq ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ lesseq ) )
| ~ ( B @ ( A @ lesseq ) ) ),
inference(cnf,[status(esa)],[27]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ lesseq ) )
| ~ ( B @ ( A @ lesseq ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[28]) ).
thf(41,plain,
! [B: $i,A: $i] :
( ( B @ summation @ ( A @ summation @ lesseq ) )
| ~ ( B @ ( A @ lesseq ) ) ),
inference(cnfConj,[status(thm)],[40]) ).
thf(139,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ lesseq ) )
!= ( D @ ( C @ lesseq ) ) )
| ( D @ summation @ ( C @ summation @ lesseq ) )
| ~ $true
| ( A @ ( B @ lesseq ) ) ),
inference(paramod_ordered,[status(thm)],[31,41]) ).
thf(140,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ lesseq ) )
!= ( D @ ( C @ lesseq ) ) )
| ( D @ summation @ ( C @ summation @ lesseq ) )
| ( A @ ( B @ lesseq ) ) ),
inference(simp,[status(thm)],[139]) ).
thf(141,plain,
! [B: $i,A: $i] :
( ( B @ summation @ ( A @ summation @ lesseq ) )
| ( A @ ( B @ lesseq ) ) ),
inference(pattern_uni,[status(thm)],[140:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(177,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ lesseq ) )
!= ( D @ ( C @ lesseq ) ) )
| ( D @ summation @ ( C @ summation @ lesseq ) )
| ~ $true
| ( B @ summation @ ( A @ summation @ lesseq ) ) ),
inference(paramod_ordered,[status(thm)],[141,41]) ).
thf(178,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ lesseq ) )
!= ( D @ ( C @ lesseq ) ) )
| ( D @ summation @ ( C @ summation @ lesseq ) )
| ( B @ summation @ ( A @ summation @ lesseq ) ) ),
inference(simp,[status(thm)],[177]) ).
thf(179,plain,
! [B: $i,A: $i] :
( ( A @ summation @ ( B @ summation @ lesseq ) )
| ( B @ summation @ ( A @ summation @ lesseq ) ) ),
inference(pattern_uni,[status(thm)],[178:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(5701,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ max ) @ summation @ ( B @ ( A @ model_max ) ) )
!= ( C @ ( sk5 @ ( sk4 @ model_max ) ) ) )
| ( C @ ( sk6 @ lesseq ) )
| ~ $true
| ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_ub ) ) ) ),
inference(paramod_ordered,[status(thm)],[3753,5482]) ).
thf(5702,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ max ) @ summation @ ( B @ ( A @ model_max ) ) )
!= ( C @ ( sk5 @ ( sk4 @ model_max ) ) ) )
| ( C @ ( sk6 @ lesseq ) )
| ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_ub ) ) ) ),
inference(simp,[status(thm)],[5701]) ).
thf(5703,plain,
( ( sk5 @ ( sk4 @ max ) @ summation @ ( sk6 @ lesseq ) )
| ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_ub ) ) ) ),
inference(pattern_uni,[status(thm)],[5702:[bind(A,$thf( sk4 )),bind(B,$thf( sk5 )),bind(C,$thf( sk5 @ ( sk4 @ max ) @ summation ))]]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ minsol_model_ub ) ) )
<=> ( ! [D: $i] :
( ( D @ ( B @ ( A @ model_ub ) ) )
=> ( D @ ( C @ lesseq ) ) )
& ( C @ ( B @ ( A @ model_ub ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minsol_model_ub) ).
thf(79,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ! [D: $i] :
( ( D @ ( B @ ( A @ model_ub ) ) )
=> ( D @ ( C @ lesseq ) ) )
& ( C @ ( B @ ( A @ model_ub ) ) ) )
=> ( C @ ( B @ ( A @ minsol_model_ub ) ) ) )
& ( ( C @ ( B @ ( A @ minsol_model_ub ) ) )
=> ( ! [D: $i] :
( ( D @ ( B @ ( A @ model_ub ) ) )
=> ( D @ ( C @ lesseq ) ) )
& ( C @ ( B @ ( A @ model_ub ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(80,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( D @ ( B @ ( A @ model_ub ) ) )
=> ( D @ ( C @ lesseq ) ) )
& ( C @ ( B @ ( A @ model_ub ) ) ) )
=> ( C @ ( B @ ( A @ minsol_model_ub ) ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ minsol_model_ub ) ) )
=> ( ! [D: $i] :
( ( D @ ( B @ ( A @ model_ub ) ) )
=> ( D @ ( C @ lesseq ) ) )
& ( C @ ( B @ ( A @ model_ub ) ) ) ) ) ),
inference(miniscope,[status(thm)],[79]) ).
thf(81,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( G @ ( F @ ( E @ minsol_model_ub ) ) )
| ~ ( E @ ( F @ ( G @ sk9 ) ) @ ( G @ lesseq ) )
| ~ ( G @ ( F @ ( E @ model_ub ) ) ) )
& ( ( G @ ( F @ ( E @ minsol_model_ub ) ) )
| ( E @ ( F @ ( G @ sk9 ) ) @ ( F @ ( E @ model_ub ) ) )
| ~ ( G @ ( F @ ( E @ model_ub ) ) ) )
& ( ( D @ ( C @ lesseq ) )
| ~ ( D @ ( B @ ( A @ model_ub ) ) )
| ~ ( C @ ( B @ ( A @ minsol_model_ub ) ) ) )
& ( ( C @ ( B @ ( A @ model_ub ) ) )
| ~ ( C @ ( B @ ( A @ minsol_model_ub ) ) ) ) ),
inference(cnf,[status(esa)],[80]) ).
thf(82,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ model_ub ) ) )
| ~ ( C @ ( B @ ( A @ minsol_model_ub ) ) ) ),
inference(cnfConj,[status(thm)],[81]) ).
thf(6561,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_ub ) ) )
!= ( C @ ( B @ ( A @ minsol_model_ub ) ) ) )
| ( C @ ( B @ ( A @ model_ub ) ) )
| ~ $true
| ( sk5 @ ( sk4 @ max ) @ summation @ ( sk6 @ lesseq ) ) ),
inference(paramod_ordered,[status(thm)],[5703,82]) ).
thf(6562,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_ub ) ) )
!= ( C @ ( B @ ( A @ minsol_model_ub ) ) ) )
| ( C @ ( B @ ( A @ model_ub ) ) )
| ( sk5 @ ( sk4 @ max ) @ summation @ ( sk6 @ lesseq ) ) ),
inference(simp,[status(thm)],[6561]) ).
thf(6563,plain,
( ( sk3 @ ( sk2 @ ( sk1 @ model_ub ) ) )
| ( sk5 @ ( sk4 @ max ) @ summation @ ( sk6 @ lesseq ) ) ),
inference(pattern_uni,[status(thm)],[6562:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 ))]]) ).
thf(66,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ sk7 ) ) @ ( B @ ( A @ ub ) ) )
| ~ ( C @ ( B @ ( A @ model_ub ) ) ) ),
inference(cnfConj,[status(thm)],[65]) ).
thf(6670,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ ( sk1 @ model_ub ) ) )
!= ( C @ ( B @ ( A @ model_ub ) ) ) )
| ( A @ ( B @ ( C @ sk7 ) ) @ ( B @ ( A @ ub ) ) )
| ~ $true
| ( sk5 @ ( sk4 @ max ) @ summation @ ( sk6 @ lesseq ) ) ),
inference(paramod_ordered,[status(thm)],[6563,66]) ).
thf(6671,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ ( sk1 @ model_ub ) ) )
!= ( C @ ( B @ ( A @ model_ub ) ) ) )
| ( A @ ( B @ ( C @ sk7 ) ) @ ( B @ ( A @ ub ) ) )
| ( sk5 @ ( sk4 @ max ) @ summation @ ( sk6 @ lesseq ) ) ),
inference(simp,[status(thm)],[6670]) ).
thf(6672,plain,
( ( sk1 @ ( sk2 @ ( sk3 @ sk7 ) ) @ ( sk2 @ ( sk1 @ ub ) ) )
| ( sk5 @ ( sk4 @ max ) @ summation @ ( sk6 @ lesseq ) ) ),
inference(pattern_uni,[status(thm)],[6671:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 ))]]) ).
thf(8932,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( sk3 @ sk7 ) ) @ ( sk2 @ ( sk1 @ ub ) ) )
!= ( C @ ( B @ ( A @ ub ) ) ) )
| ( C @ ( B @ lesseq ) )
| ~ $true
| ( sk5 @ ( sk4 @ max ) @ summation @ ( sk6 @ lesseq ) ) ),
inference(paramod_ordered,[status(thm)],[6672,54]) ).
thf(8933,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( sk3 @ sk7 ) ) @ ( sk2 @ ( sk1 @ ub ) ) )
!= ( C @ ( B @ ( A @ ub ) ) ) )
| ( C @ ( B @ lesseq ) )
| ( sk5 @ ( sk4 @ max ) @ summation @ ( sk6 @ lesseq ) ) ),
inference(simp,[status(thm)],[8932]) ).
thf(8934,plain,
( ( sk1 @ ( sk2 @ ( sk3 @ sk7 ) ) @ ( sk2 @ lesseq ) )
| ( sk5 @ ( sk4 @ max ) @ summation @ ( sk6 @ lesseq ) ) ),
inference(pattern_uni,[status(thm)],[8933:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( sk1 @ ( sk2 @ ( sk3 @ sk7 ) ) ))]]) ).
thf(22,plain,
( ~ ( sk6 @ ( sk5 @ ( sk4 @ minsol_model_ub ) ) )
| ~ ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_max ) ) ) ),
inference(cnfConj,[status(thm)],[18]) ).
thf(479,plain,
! [B: $i,A: $i] :
( ( B != sk1 )
| ~ ( sk6 @ ( sk5 @ ( sk4 @ minsol_model_ub ) ) )
| ~ ( sk3 @ ( sk2 @ ( A @ minsol_model_max ) ) )
| ~ ( A @ ( B @ lesseq ) )
| ~ ( B @ ( A @ lesseq ) ) ),
inference(paramod_ordered,[status(thm)],[29,22]) ).
thf(480,plain,
! [A: $i] :
( ~ ( sk6 @ ( sk5 @ ( sk4 @ minsol_model_ub ) ) )
| ~ ( sk3 @ ( sk2 @ ( A @ minsol_model_max ) ) )
| ~ ( A @ ( sk1 @ lesseq ) )
| ~ ( sk1 @ ( A @ lesseq ) ) ),
inference(pattern_uni,[status(thm)],[479:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(4625,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ summation @ ( A @ ( A @ ( A @ max ) @ model_max ) ) )
!= ( D @ ( C @ ( B @ model_max ) ) ) )
| ( D @ ( C @ ( B @ max ) @ summation @ lesseq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4222,60]) ).
thf(4626,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ summation @ ( A @ ( A @ ( A @ max ) @ model_max ) ) )
!= ( D @ ( C @ ( B @ model_max ) ) ) )
| ( D @ ( C @ ( B @ max ) @ summation @ lesseq ) ) ),
inference(simp,[status(thm)],[4625]) ).
thf(4627,plain,
! [A: $i] : ( A @ summation @ ( A @ ( A @ ( A @ max ) @ max ) @ summation @ lesseq ) ),
inference(pattern_uni,[status(thm)],[4626:[bind(A,$thf( G )),bind(B,$thf( G @ ( G @ max ) )),bind(C,$thf( G )),bind(D,$thf( G @ summation ))]]) ).
thf(4657,plain,
! [A: $i] : ( A @ summation @ ( A @ ( A @ ( A @ max ) @ max ) @ summation @ lesseq ) ),
inference(simp,[status(thm)],[4627]) ).
thf(5880,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ summation @ ( A @ ( A @ ( A @ max ) @ max ) @ summation @ lesseq ) )
!= ( C @ summation @ ( B @ summation @ lesseq ) ) )
| ( C @ ( B @ lesseq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4657,43]) ).
thf(5881,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ summation @ ( A @ ( A @ ( A @ max ) @ max ) @ summation @ lesseq ) )
!= ( C @ summation @ ( B @ summation @ lesseq ) ) )
| ( C @ ( B @ lesseq ) ) ),
inference(simp,[status(thm)],[5880]) ).
thf(5882,plain,
! [A: $i] : ( A @ ( A @ ( A @ ( A @ max ) @ max ) @ lesseq ) ),
inference(pattern_uni,[status(thm)],[5881:[bind(A,$thf( E )),bind(B,$thf( E @ ( E @ ( E @ max ) @ max ) )),bind(C,$thf( E ))]]) ).
thf(5960,plain,
! [A: $i] : ( A @ ( A @ ( A @ ( A @ max ) @ max ) @ lesseq ) ),
inference(simp,[status(thm)],[5882]) ).
thf(6049,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ ( A @ max ) @ max ) @ lesseq ) )
!= ( C @ ( B @ lesseq ) ) )
| ~ $true
| ( ( C @ ( B @ max ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[5960,49]) ).
thf(6050,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ ( A @ max ) @ max ) @ lesseq ) )
!= ( C @ ( B @ lesseq ) ) )
| ( ( C @ ( B @ max ) )
= C ) ),
inference(simp,[status(thm)],[6049]) ).
thf(6051,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ ( A @ max ) @ max ) @ max ) )
= A ),
inference(pattern_uni,[status(thm)],[6050:[bind(A,$thf( E )),bind(B,$thf( E @ ( E @ ( E @ max ) @ max ) )),bind(C,$thf( E ))]]) ).
thf(6108,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ ( A @ max ) @ max ) @ max ) )
= A ),
inference(simp,[status(thm)],[6051]) ).
thf(7130,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ ( A @ max ) @ max ) @ max ) )
!= ( C @ ( B @ max ) ) )
| ( A @ summation @ ( C @ ( B @ model_max ) ) ) ),
inference(paramod_ordered,[status(thm)],[6108,3753]) ).
thf(7131,plain,
! [A: $i] : ( A @ summation @ ( A @ ( A @ ( A @ ( A @ max ) @ max ) @ model_max ) ) ),
inference(pattern_uni,[status(thm)],[7130:[bind(A,$thf( E )),bind(B,$thf( E @ ( E @ ( E @ max ) @ max ) )),bind(C,$thf( E ))]]) ).
thf(7194,plain,
! [A: $i] : ( A @ summation @ ( A @ ( A @ ( A @ ( A @ max ) @ max ) @ model_max ) ) ),
inference(simp,[status(thm)],[7131]) ).
thf(3882,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ summation @ ( A @ ( A @ max ) @ summation @ lesseq ) )
!= ( B @ ( C @ lesseq ) ) )
| ( B @ ( B @ ( C @ ub ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3818,2243]) ).
thf(3883,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ summation @ ( A @ ( A @ max ) @ summation @ lesseq ) )
!= ( B @ ( C @ lesseq ) ) )
| ( B @ ( B @ ( C @ ub ) ) ) ),
inference(simp,[status(thm)],[3882]) ).
thf(3884,plain,
! [A: $i] : ( A @ summation @ ( A @ summation @ ( A @ ( A @ max ) @ summation @ ub ) ) ),
inference(pattern_uni,[status(thm)],[3883:[bind(A,$thf( G )),bind(B,$thf( G @ summation )),bind(C,$thf( G @ ( G @ max ) @ summation ))]]) ).
thf(3955,plain,
! [A: $i] : ( A @ summation @ ( A @ summation @ ( A @ ( A @ max ) @ summation @ ub ) ) ),
inference(simp,[status(thm)],[3884]) ).
thf(6558,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_ub ) ) )
!= ( C @ ( B @ ( A @ minsol_model_ub ) ) ) )
| ( C @ ( B @ ( A @ model_ub ) ) )
| ~ $true
| ( sk5 != sk4 )
| ( sk4 @ summation @ ( sk6 @ lesseq ) ) ),
inference(paramod_ordered,[status(thm)],[5708,82]) ).
thf(6559,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_ub ) ) )
!= ( C @ ( B @ ( A @ minsol_model_ub ) ) ) )
| ( C @ ( B @ ( A @ model_ub ) ) )
| ( sk5 != sk4 )
| ( sk4 @ summation @ ( sk6 @ lesseq ) ) ),
inference(simp,[status(thm)],[6558]) ).
thf(6560,plain,
( ( sk3 @ ( sk2 @ ( sk1 @ model_ub ) ) )
| ( sk5 != sk4 )
| ( sk4 @ summation @ ( sk6 @ lesseq ) ) ),
inference(pattern_uni,[status(thm)],[6559:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 ))]]) ).
thf(3885,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ summation @ ( A @ ( A @ max ) @ summation @ lesseq ) )
!= ( C @ ( B @ lesseq ) ) )
| ( C @ summation @ ( B @ summation @ lesseq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3818,41]) ).
thf(3886,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ summation @ ( A @ ( A @ max ) @ summation @ lesseq ) )
!= ( C @ ( B @ lesseq ) ) )
| ( C @ summation @ ( B @ summation @ lesseq ) ) ),
inference(simp,[status(thm)],[3885]) ).
thf(3887,plain,
! [A: $i] : ( A @ summation @ summation @ ( A @ ( A @ max ) @ summation @ summation @ lesseq ) ),
inference(pattern_uni,[status(thm)],[3886:[bind(A,$thf( G )),bind(B,$thf( G @ ( G @ max ) @ summation )),bind(C,$thf( G @ summation ))]]) ).
thf(3957,plain,
! [A: $i] : ( A @ summation @ summation @ ( A @ ( A @ max ) @ summation @ summation @ lesseq ) ),
inference(simp,[status(thm)],[3887]) ).
thf(4404,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ summation @ summation @ ( A @ ( A @ max ) @ summation @ summation @ lesseq ) )
!= ( C @ ( B @ lesseq ) ) )
| ( C @ summation @ ( B @ summation @ lesseq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3957,41]) ).
thf(4405,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ summation @ summation @ ( A @ ( A @ max ) @ summation @ summation @ lesseq ) )
!= ( C @ ( B @ lesseq ) ) )
| ( C @ summation @ ( B @ summation @ lesseq ) ) ),
inference(simp,[status(thm)],[4404]) ).
thf(4406,plain,
! [A: $i] : ( A @ summation @ summation @ summation @ ( A @ ( A @ max ) @ summation @ summation @ summation @ lesseq ) ),
inference(pattern_uni,[status(thm)],[4405:[bind(A,$thf( I )),bind(B,$thf( I @ ( I @ max ) @ summation @ summation )),bind(C,$thf( I @ summation @ summation ))]]) ).
thf(4488,plain,
! [A: $i] : ( A @ summation @ summation @ summation @ ( A @ ( A @ max ) @ summation @ summation @ summation @ lesseq ) ),
inference(simp,[status(thm)],[4406]) ).
thf(4947,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ summation @ summation @ summation @ ( A @ ( A @ max ) @ summation @ summation @ summation @ lesseq ) )
!= ( C @ ( B @ lesseq ) ) )
| ( C @ summation @ ( B @ summation @ lesseq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4488,41]) ).
thf(4948,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ summation @ summation @ summation @ ( A @ ( A @ max ) @ summation @ summation @ summation @ lesseq ) )
!= ( C @ ( B @ lesseq ) ) )
| ( C @ summation @ ( B @ summation @ lesseq ) ) ),
inference(simp,[status(thm)],[4947]) ).
thf(4949,plain,
! [A: $i] : ( A @ summation @ summation @ summation @ summation @ ( A @ ( A @ max ) @ summation @ summation @ summation @ summation @ lesseq ) ),
inference(pattern_uni,[status(thm)],[4948:[bind(A,$thf( K )),bind(B,$thf( K @ ( K @ max ) @ summation @ summation @ summation )),bind(C,$thf( K @ summation @ summation @ summation ))]]) ).
thf(5034,plain,
! [A: $i] : ( A @ summation @ summation @ summation @ summation @ ( A @ ( A @ max ) @ summation @ summation @ summation @ summation @ lesseq ) ),
inference(simp,[status(thm)],[4949]) ).
thf(201,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( B @ summation @ ( A @ summation @ lesseq ) )
!= ( A @ ( B @ lesseq ) ) )
| ( A @ ( B @ lesseq ) ) ),
inference(eqfactor_ordered,[status(thm)],[141]) ).
thf(203,plain,
! [B: $i,A: $i] :
( ( ( B @ summation )
!= A )
| ( ( A @ summation )
!= B )
| ( A @ ( B @ lesseq ) ) ),
inference(simp,[status(thm)],[201]) ).
thf(208,plain,
! [A: $i] :
( ( ( A @ summation @ summation )
!= A )
| ( A @ ( A @ summation @ lesseq ) ) ),
inference(simp,[status(thm)],[203]) ).
thf(721,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ summation @ lesseq ) )
!= ( sk1 @ ( B @ lesseq ) ) )
| ~ ( sk6 @ ( sk5 @ ( sk4 @ minsol_model_ub ) ) )
| ~ ( sk3 @ ( sk2 @ ( B @ minsol_model_max ) ) )
| ~ ( B @ ( sk1 @ lesseq ) )
| ~ $true
| ( ( A @ summation @ summation )
!= A ) ),
inference(paramod_ordered,[status(thm)],[208,480]) ).
thf(722,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ summation @ lesseq ) )
!= ( sk1 @ ( B @ lesseq ) ) )
| ~ ( sk6 @ ( sk5 @ ( sk4 @ minsol_model_ub ) ) )
| ~ ( sk3 @ ( sk2 @ ( B @ minsol_model_max ) ) )
| ~ ( B @ ( sk1 @ lesseq ) )
| ( ( A @ summation @ summation )
!= A ) ),
inference(simp,[status(thm)],[721]) ).
thf(723,plain,
( ~ ( sk6 @ ( sk5 @ ( sk4 @ minsol_model_ub ) ) )
| ~ ( sk3 @ ( sk2 @ ( sk1 @ summation @ minsol_model_max ) ) )
| ~ ( sk1 @ summation @ ( sk1 @ lesseq ) )
| ( ( sk1 @ summation @ summation )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[722:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 @ summation ))]]) ).
thf(1309,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk1 @ summation @ summation ) )
| ~ ( sk6 @ ( sk5 @ ( sk4 @ minsol_model_ub ) ) )
| ~ ( sk3 @ ( sk2 @ ( sk1 @ summation @ minsol_model_max ) ) )
| ~ ( sk1 @ summation @ ( sk1 @ lesseq ) )
| ( B != sk1 )
| ~ ( A @ ( B @ lesseq ) )
| ~ ( B @ ( A @ lesseq ) ) ),
inference(paramod_ordered,[status(thm)],[29,723]) ).
thf(1310,plain,
! [A: $i] :
( ~ ( sk6 @ ( sk5 @ ( sk4 @ minsol_model_ub ) ) )
| ~ ( sk3 @ ( sk2 @ ( sk1 @ summation @ minsol_model_max ) ) )
| ~ ( sk1 @ summation @ ( sk1 @ lesseq ) )
| ( A != sk1 )
| ~ ( sk1 @ summation @ summation @ ( A @ lesseq ) )
| ~ ( A @ ( sk1 @ summation @ summation @ lesseq ) ) ),
inference(pattern_uni,[status(thm)],[1309:[bind(A,$thf( sk1 @ summation @ summation )),bind(B,$thf( B ))]]) ).
thf(1387,plain,
( ~ ( sk6 @ ( sk5 @ ( sk4 @ minsol_model_ub ) ) )
| ~ ( sk3 @ ( sk2 @ ( sk1 @ summation @ minsol_model_max ) ) )
| ~ ( sk1 @ summation @ ( sk1 @ lesseq ) )
| ~ ( sk1 @ summation @ summation @ ( sk1 @ lesseq ) )
| ~ ( sk1 @ ( sk1 @ summation @ summation @ lesseq ) ) ),
inference(simp,[status(thm)],[1310]) ).
thf(1236,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ lesseq ) )
!= ( D @ ( C @ lesseq ) ) )
| ~ $true
| ( ( D @ ( C @ max ) )
= D )
| ( A @ ( B @ lesseq ) ) ),
inference(paramod_ordered,[status(thm)],[31,49]) ).
thf(1237,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ lesseq ) )
!= ( D @ ( C @ lesseq ) ) )
| ( ( D @ ( C @ max ) )
= D )
| ( A @ ( B @ lesseq ) ) ),
inference(simp,[status(thm)],[1236]) ).
thf(1238,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ max ) )
= B )
| ( A @ ( B @ lesseq ) ) ),
inference(pattern_uni,[status(thm)],[1237:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(53,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ lesseq ) )
| ~ ( C @ ( B @ ( A @ ub ) ) ) ),
inference(cnfConj,[status(thm)],[52]) ).
thf(8929,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( sk3 @ sk7 ) ) @ ( sk2 @ ( sk1 @ ub ) ) )
!= ( C @ ( B @ ( A @ ub ) ) ) )
| ( C @ ( A @ lesseq ) )
| ~ $true
| ( sk5 @ ( sk4 @ max ) @ summation @ ( sk6 @ lesseq ) ) ),
inference(paramod_ordered,[status(thm)],[6672,53]) ).
thf(8930,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( sk3 @ sk7 ) ) @ ( sk2 @ ( sk1 @ ub ) ) )
!= ( C @ ( B @ ( A @ ub ) ) ) )
| ( C @ ( A @ lesseq ) )
| ( sk5 @ ( sk4 @ max ) @ summation @ ( sk6 @ lesseq ) ) ),
inference(simp,[status(thm)],[8929]) ).
thf(8931,plain,
( ( sk1 @ ( sk2 @ ( sk3 @ sk7 ) ) @ ( sk1 @ lesseq ) )
| ( sk5 @ ( sk4 @ max ) @ summation @ ( sk6 @ lesseq ) ) ),
inference(pattern_uni,[status(thm)],[8930:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( sk1 @ ( sk2 @ ( sk3 @ sk7 ) ) ))]]) ).
thf(3851,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ summation @ ( A @ ( A @ max ) @ summation @ lesseq ) )
!= ( B @ ( C @ lesseq ) ) )
| ~ $true
| ( ( C @ ( B @ max ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[3818,46]) ).
thf(3852,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ summation @ ( A @ ( A @ max ) @ summation @ lesseq ) )
!= ( B @ ( C @ lesseq ) ) )
| ( ( C @ ( B @ max ) )
= B ) ),
inference(simp,[status(thm)],[3851]) ).
thf(3853,plain,
! [A: $i] :
( ( A @ ( A @ max ) @ summation @ ( A @ summation @ max ) )
= ( A @ summation ) ),
inference(pattern_uni,[status(thm)],[3852:[bind(A,$thf( G )),bind(B,$thf( G @ summation )),bind(C,$thf( G @ ( G @ max ) @ summation ))]]) ).
thf(3937,plain,
! [A: $i] :
( ( A @ ( A @ max ) @ summation @ ( A @ summation @ max ) )
= ( A @ summation ) ),
inference(simp,[status(thm)],[3853]) ).
thf(5142,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ max ) @ summation @ ( A @ summation @ max ) )
!= ( C @ ( B @ max ) ) )
| ( A @ summation @ summation @ ( C @ ( B @ model_max ) ) ) ),
inference(paramod_ordered,[status(thm)],[3937,3753]) ).
thf(5143,plain,
! [A: $i] : ( A @ summation @ summation @ ( A @ ( A @ max ) @ summation @ ( A @ summation @ model_max ) ) ),
inference(pattern_uni,[status(thm)],[5142:[bind(A,$thf( G )),bind(B,$thf( G @ summation )),bind(C,$thf( G @ ( G @ max ) @ summation ))]]) ).
thf(5166,plain,
! [A: $i] : ( A @ summation @ summation @ ( A @ ( A @ max ) @ summation @ ( A @ summation @ model_max ) ) ),
inference(simp,[status(thm)],[5143]) ).
thf(75,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ minsol_model_max ) ) )
| ( A @ ( B @ ( C @ sk8 ) ) @ ( B @ ( A @ model_max ) ) )
| ~ ( C @ ( B @ ( A @ model_max ) ) ) ),
inference(cnfConj,[status(thm)],[72]) ).
thf(77,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ minsol_model_max ) ) )
| ( A @ ( B @ ( C @ sk8 ) ) @ ( B @ ( A @ model_max ) ) )
| ~ ( C @ ( B @ ( A @ model_max ) ) ) ),
inference(simp,[status(thm)],[75]) ).
thf(1287,plain,
! [A: $i] :
( ( ( A @ ( A @ lesseq ) )
!= ( sk1 @ summation @ ( sk1 @ lesseq ) ) )
| ~ ( sk6 @ ( sk5 @ ( sk4 @ minsol_model_ub ) ) )
| ~ ( sk3 @ ( sk2 @ ( sk1 @ summation @ minsol_model_max ) ) )
| ~ $true
| ( ( sk1 @ summation @ summation )
!= sk1 ) ),
inference(paramod_ordered,[status(thm)],[24,723]) ).
thf(1288,plain,
! [A: $i] :
( ( ( A @ ( A @ lesseq ) )
!= ( sk1 @ summation @ ( sk1 @ lesseq ) ) )
| ~ ( sk6 @ ( sk5 @ ( sk4 @ minsol_model_ub ) ) )
| ~ ( sk3 @ ( sk2 @ ( sk1 @ summation @ minsol_model_max ) ) )
| ( ( sk1 @ summation @ summation )
!= sk1 ) ),
inference(simp,[status(thm)],[1287]) ).
thf(1385,plain,
! [A: $i] :
( ( A
!= ( sk1 @ summation ) )
| ( A != sk1 )
| ~ ( sk6 @ ( sk5 @ ( sk4 @ minsol_model_ub ) ) )
| ~ ( sk3 @ ( sk2 @ ( sk1 @ summation @ minsol_model_max ) ) )
| ( ( sk1 @ summation @ summation )
!= sk1 ) ),
inference(simp,[status(thm)],[1288]) ).
thf(1394,plain,
( ( ( sk1 @ summation )
!= sk1 )
| ~ ( sk6 @ ( sk5 @ ( sk4 @ minsol_model_ub ) ) )
| ~ ( sk3 @ ( sk2 @ ( sk1 @ summation @ minsol_model_max ) ) )
| ( ( sk1 @ summation @ summation )
!= sk1 ) ),
inference(simp,[status(thm)],[1385]) ).
thf(1457,plain,
( ( sk1 != sk1 )
| ( ( sk1 @ summation @ summation )
!= ( sk1 @ summation ) )
| ( ( sk1 @ summation )
!= sk1 )
| ~ ( sk6 @ ( sk5 @ ( sk4 @ minsol_model_ub ) ) )
| ~ ( sk3 @ ( sk2 @ ( sk1 @ summation @ minsol_model_max ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[1394]) ).
thf(1459,plain,
( ( ( sk1 @ summation )
!= sk1 )
| ( ( sk1 @ summation )
!= sk1 )
| ~ ( sk6 @ ( sk5 @ ( sk4 @ minsol_model_ub ) ) )
| ~ ( sk3 @ ( sk2 @ ( sk1 @ summation @ minsol_model_max ) ) ) ),
inference(simp,[status(thm)],[1457]) ).
thf(1477,plain,
( ( ( sk1 @ summation )
!= sk1 )
| ~ ( sk6 @ ( sk5 @ ( sk4 @ minsol_model_ub ) ) )
| ~ ( sk3 @ ( sk2 @ ( sk1 @ summation @ minsol_model_max ) ) ) ),
inference(simp,[status(thm)],[1459]) ).
thf(1802,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk1 @ summation ) )
| ( A != sk1 )
| ~ ( sk6 @ ( sk5 @ ( sk4 @ minsol_model_ub ) ) )
| ~ ( sk3 @ ( sk2 @ ( sk1 @ summation @ minsol_model_max ) ) )
| ~ ( A @ ( B @ lesseq ) )
| ~ ( B @ ( A @ lesseq ) ) ),
inference(paramod_ordered,[status(thm)],[29,1477]) ).
thf(1803,plain,
! [A: $i] :
( ( A != sk1 )
| ~ ( sk6 @ ( sk5 @ ( sk4 @ minsol_model_ub ) ) )
| ~ ( sk3 @ ( sk2 @ ( sk1 @ summation @ minsol_model_max ) ) )
| ~ ( A @ ( sk1 @ summation @ lesseq ) )
| ~ ( sk1 @ summation @ ( A @ lesseq ) ) ),
inference(pattern_uni,[status(thm)],[1802:[bind(A,$thf( A )),bind(B,$thf( sk1 @ summation ))]]) ).
thf(1814,plain,
( ~ ( sk6 @ ( sk5 @ ( sk4 @ minsol_model_ub ) ) )
| ~ ( sk3 @ ( sk2 @ ( sk1 @ summation @ minsol_model_max ) ) )
| ~ ( sk1 @ ( sk1 @ summation @ lesseq ) )
| ~ ( sk1 @ summation @ ( sk1 @ lesseq ) ) ),
inference(simp,[status(thm)],[1803]) ).
thf(1239,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ lesseq ) )
!= ( D @ ( C @ lesseq ) ) )
| ~ $true
| ( ( D @ ( C @ max ) )
= D )
| ( B @ ( A @ lesseq ) ) ),
inference(paramod_ordered,[status(thm)],[31,49]) ).
thf(1240,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ lesseq ) )
!= ( D @ ( C @ lesseq ) ) )
| ( ( D @ ( C @ max ) )
= D )
| ( B @ ( A @ lesseq ) ) ),
inference(simp,[status(thm)],[1239]) ).
thf(1241,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ max ) )
= A )
| ( B @ ( A @ lesseq ) ) ),
inference(pattern_uni,[status(thm)],[1240:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(180,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ summation @ ( A @ summation @ lesseq ) )
!= ( D @ ( C @ lesseq ) ) )
| ( D @ summation @ ( C @ summation @ lesseq ) )
| ~ $true
| ( A @ ( B @ lesseq ) ) ),
inference(paramod_ordered,[status(thm)],[141,41]) ).
thf(181,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ summation @ ( A @ summation @ lesseq ) )
!= ( D @ ( C @ lesseq ) ) )
| ( D @ summation @ ( C @ summation @ lesseq ) )
| ( A @ ( B @ lesseq ) ) ),
inference(simp,[status(thm)],[180]) ).
thf(182,plain,
! [B: $i,A: $i] :
( ( B @ summation @ summation @ ( A @ summation @ summation @ lesseq ) )
| ( A @ ( B @ lesseq ) ) ),
inference(pattern_uni,[status(thm)],[181:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E @ summation )),bind(D,$thf( F @ summation ))]]) ).
thf(205,plain,
! [B: $i,A: $i] :
( ( B @ summation @ summation @ ( A @ summation @ summation @ lesseq ) )
| ( A @ ( B @ lesseq ) ) ),
inference(simp,[status(thm)],[182]) ).
thf(443,plain,
! [B: $i,A: $i] :
( ( B != sk2 )
| ( sk6 @ ( sk5 @ ( sk4 @ minsol_model_max ) ) )
| ~ ( sk3 @ ( A @ ( sk1 @ minsol_model_max ) ) )
| ~ ( A @ ( B @ lesseq ) )
| ~ ( B @ ( A @ lesseq ) ) ),
inference(paramod_ordered,[status(thm)],[29,21]) ).
thf(444,plain,
! [A: $i] :
( ( sk6 @ ( sk5 @ ( sk4 @ minsol_model_max ) ) )
| ~ ( sk3 @ ( A @ ( sk1 @ minsol_model_max ) ) )
| ~ ( A @ ( sk2 @ lesseq ) )
| ~ ( sk2 @ ( A @ lesseq ) ) ),
inference(pattern_uni,[status(thm)],[443:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ sum ) @ ( A @ ( C @ sum ) @ lesseq ) )
| ~ ( B @ ( A @ lesseq ) ) ),
inference(cnfConj,[status(thm)],[34]) ).
thf(4061,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ max ) @ lesseq ) )
!= ( C @ ( B @ lesseq ) ) )
| ( C @ ( D @ sum ) @ ( B @ ( D @ sum ) @ lesseq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3960,35]) ).
thf(4062,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ max ) @ lesseq ) )
!= ( C @ ( B @ lesseq ) ) )
| ( C @ ( D @ sum ) @ ( B @ ( D @ sum ) @ lesseq ) ) ),
inference(simp,[status(thm)],[4061]) ).
thf(4063,plain,
! [B: $i,A: $i] : ( B @ ( A @ sum ) @ ( B @ ( B @ max ) @ ( A @ sum ) @ lesseq ) ),
inference(pattern_uni,[status(thm)],[4062:[bind(A,$thf( F )),bind(B,$thf( F @ ( F @ max ) )),bind(C,$thf( F )),bind(D,$thf( D ))]]) ).
thf(4096,plain,
! [B: $i,A: $i] : ( B @ ( A @ sum ) @ ( B @ ( B @ max ) @ ( A @ sum ) @ lesseq ) ),
inference(simp,[status(thm)],[4063]) ).
thf(5399,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk6 @ ( sk5 @ ( sk4 @ model_max ) ) )
!= ( D @ ( B @ ( A @ model_max ) ) ) )
| ( D @ ( C @ lesseq ) )
| ~ $true
| ~ ( C @ ( B @ ( A @ minsol_model_max ) ) )
| ~ ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_max ) ) ) ),
inference(paramod_ordered,[status(thm)],[5064,74]) ).
thf(5400,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk6 @ ( sk5 @ ( sk4 @ model_max ) ) )
!= ( D @ ( B @ ( A @ model_max ) ) ) )
| ( D @ ( C @ lesseq ) )
| ~ ( C @ ( B @ ( A @ minsol_model_max ) ) )
| ~ ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_max ) ) ) ),
inference(simp,[status(thm)],[5399]) ).
thf(5401,plain,
! [A: $i] :
( ( sk6 @ ( A @ lesseq ) )
| ~ ( A @ ( sk5 @ ( sk4 @ minsol_model_max ) ) )
| ~ ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_max ) ) ) ),
inference(pattern_uni,[status(thm)],[5400:[bind(A,$thf( sk4 )),bind(B,$thf( sk5 )),bind(C,$thf( C )),bind(D,$thf( sk6 ))]]) ).
thf(5490,plain,
! [A: $i] :
( ( sk6 @ ( A @ lesseq ) )
| ~ ( A @ ( sk5 @ ( sk4 @ minsol_model_max ) ) )
| ~ ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_max ) ) ) ),
inference(simp,[status(thm)],[5401]) ).
thf(8274,plain,
! [A: $i] :
( ~ $true
| ( ( A @ ( sk5 @ ( sk4 @ minsol_model_max ) ) )
!= ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_max ) ) ) )
| ( sk6 @ ( A @ lesseq ) )
| ~ ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_max ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[5490]) ).
thf(8276,plain,
! [A: $i] :
( ( A != sk3 )
| ( sk5 != sk2 )
| ( sk4 != sk1 )
| ~ ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_max ) ) )
| ( sk6 @ ( A @ lesseq ) ) ),
inference(simp,[status(thm)],[8274]) ).
thf(8286,plain,
( ( sk5 != sk2 )
| ( sk4 != sk1 )
| ~ ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_max ) ) )
| ( sk6 @ ( sk3 @ lesseq ) ) ),
inference(simp,[status(thm)],[8276]) ).
thf(142,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ lesseq ) )
!= ( D @ ( C @ lesseq ) ) )
| ( D @ summation @ ( C @ summation @ lesseq ) )
| ~ $true
| ( B @ ( A @ lesseq ) ) ),
inference(paramod_ordered,[status(thm)],[31,41]) ).
thf(143,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ lesseq ) )
!= ( D @ ( C @ lesseq ) ) )
| ( D @ summation @ ( C @ summation @ lesseq ) )
| ( B @ ( A @ lesseq ) ) ),
inference(simp,[status(thm)],[142]) ).
thf(144,plain,
! [B: $i,A: $i] :
( ( A @ summation @ ( B @ summation @ lesseq ) )
| ( B @ ( A @ lesseq ) ) ),
inference(pattern_uni,[status(thm)],[143:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(84,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ minsol_model_ub ) ) )
| ( A @ ( B @ ( C @ sk9 ) ) @ ( B @ ( A @ model_ub ) ) )
| ~ ( C @ ( B @ ( A @ model_ub ) ) ) ),
inference(cnfConj,[status(thm)],[81]) ).
thf(86,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ minsol_model_ub ) ) )
| ( A @ ( B @ ( C @ sk9 ) ) @ ( B @ ( A @ model_ub ) ) )
| ~ ( C @ ( B @ ( A @ model_ub ) ) ) ),
inference(simp,[status(thm)],[84]) ).
thf(404,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ lesseq ) )
!= ( C @ ( D @ lesseq ) ) )
| ~ $true
| ( ( D @ ( C @ max ) )
= C )
| ( A @ ( B @ lesseq ) ) ),
inference(paramod_ordered,[status(thm)],[31,46]) ).
thf(405,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ lesseq ) )
!= ( C @ ( D @ lesseq ) ) )
| ( ( D @ ( C @ max ) )
= C )
| ( A @ ( B @ lesseq ) ) ),
inference(simp,[status(thm)],[404]) ).
thf(406,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ max ) )
= B )
| ( A @ ( B @ lesseq ) ) ),
inference(pattern_uni,[status(thm)],[405:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(5059,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk6 @ ( sk5 @ ( sk4 @ minsol_model_max ) ) )
!= ( C @ ( B @ ( A @ minsol_model_max ) ) ) )
| ( C @ ( B @ ( A @ model_max ) ) )
| ~ $true
| ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_ub ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,73]) ).
thf(5060,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk6 @ ( sk5 @ ( sk4 @ minsol_model_max ) ) )
!= ( C @ ( B @ ( A @ minsol_model_max ) ) ) )
| ( C @ ( B @ ( A @ model_max ) ) )
| ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_ub ) ) ) ),
inference(simp,[status(thm)],[5059]) ).
thf(5061,plain,
( ( sk6 @ ( sk5 @ ( sk4 @ model_max ) ) )
| ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_ub ) ) ) ),
inference(pattern_uni,[status(thm)],[5060:[bind(A,$thf( sk4 )),bind(B,$thf( sk5 )),bind(C,$thf( sk6 ))]]) ).
thf(5266,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk6 @ ( sk5 @ ( sk4 @ model_max ) ) )
!= ( C @ ( B @ ( A @ model_max ) ) ) )
| ( C @ ( B @ ( A @ max ) @ summation @ lesseq ) )
| ~ $true
| ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_ub ) ) ) ),
inference(paramod_ordered,[status(thm)],[5061,60]) ).
thf(5267,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk6 @ ( sk5 @ ( sk4 @ model_max ) ) )
!= ( C @ ( B @ ( A @ model_max ) ) ) )
| ( C @ ( B @ ( A @ max ) @ summation @ lesseq ) )
| ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_ub ) ) ) ),
inference(simp,[status(thm)],[5266]) ).
thf(5268,plain,
( ( sk6 @ ( sk5 @ ( sk4 @ max ) @ summation @ lesseq ) )
| ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_ub ) ) ) ),
inference(pattern_uni,[status(thm)],[5267:[bind(A,$thf( sk4 )),bind(B,$thf( sk5 )),bind(C,$thf( sk6 ))]]) ).
thf(6570,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_ub ) ) )
!= ( C @ ( B @ ( A @ minsol_model_ub ) ) ) )
| ( C @ ( B @ ( A @ model_ub ) ) )
| ~ $true
| ( sk6 @ ( sk5 @ ( sk4 @ max ) @ summation @ lesseq ) ) ),
inference(paramod_ordered,[status(thm)],[5268,82]) ).
thf(6571,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_ub ) ) )
!= ( C @ ( B @ ( A @ minsol_model_ub ) ) ) )
| ( C @ ( B @ ( A @ model_ub ) ) )
| ( sk6 @ ( sk5 @ ( sk4 @ max ) @ summation @ lesseq ) ) ),
inference(simp,[status(thm)],[6570]) ).
thf(6572,plain,
( ( sk3 @ ( sk2 @ ( sk1 @ model_ub ) ) )
| ( sk6 @ ( sk5 @ ( sk4 @ max ) @ summation @ lesseq ) ) ),
inference(pattern_uni,[status(thm)],[6571:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 ))]]) ).
thf(4015,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ max ) @ lesseq ) )
!= ( B @ ( C @ lesseq ) ) )
| ~ $true
| ( ( C @ ( B @ max ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[3960,46]) ).
thf(4016,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ max ) @ lesseq ) )
!= ( B @ ( C @ lesseq ) ) )
| ( ( C @ ( B @ max ) )
= B ) ),
inference(simp,[status(thm)],[4015]) ).
thf(4017,plain,
! [A: $i] :
( ( A @ ( A @ max ) @ ( A @ max ) )
= A ),
inference(pattern_uni,[status(thm)],[4016:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ ( E @ max ) ))]]) ).
thf(4107,plain,
! [A: $i] :
( ( A @ ( A @ max ) @ ( A @ max ) )
= A ),
inference(simp,[status(thm)],[4017]) ).
thf(5284,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk6 @ ( sk5 @ ( sk4 @ model_max ) ) )
!= ( C @ ( B @ ( A @ model_max ) ) ) )
| ( C @ ( B @ ( A @ max ) @ summation @ lesseq ) )
| ~ $true
| ~ ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_max ) ) ) ),
inference(paramod_ordered,[status(thm)],[5064,60]) ).
thf(5285,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk6 @ ( sk5 @ ( sk4 @ model_max ) ) )
!= ( C @ ( B @ ( A @ model_max ) ) ) )
| ( C @ ( B @ ( A @ max ) @ summation @ lesseq ) )
| ~ ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_max ) ) ) ),
inference(simp,[status(thm)],[5284]) ).
thf(5286,plain,
( ( sk6 @ ( sk5 @ ( sk4 @ max ) @ summation @ lesseq ) )
| ~ ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_max ) ) ) ),
inference(pattern_uni,[status(thm)],[5285:[bind(A,$thf( sk4 )),bind(B,$thf( sk5 )),bind(C,$thf( sk6 ))]]) ).
thf(4290,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ max ) @ ( A @ max ) )
!= ( C @ ( B @ max ) ) )
| ( A @ summation @ ( C @ ( B @ model_max ) ) ) ),
inference(paramod_ordered,[status(thm)],[4107,3753]) ).
thf(4291,plain,
! [A: $i] : ( A @ summation @ ( A @ ( A @ max ) @ ( A @ model_max ) ) ),
inference(pattern_uni,[status(thm)],[4290:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ ( E @ max ) ))]]) ).
thf(4304,plain,
! [A: $i] : ( A @ summation @ ( A @ ( A @ max ) @ ( A @ model_max ) ) ),
inference(simp,[status(thm)],[4291]) ).
thf(5840,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ summation @ ( A @ ( A @ ( A @ max ) @ max ) @ summation @ lesseq ) )
!= ( C @ ( B @ lesseq ) ) )
| ( C @ summation @ ( B @ summation @ lesseq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4657,41]) ).
thf(5841,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ summation @ ( A @ ( A @ ( A @ max ) @ max ) @ summation @ lesseq ) )
!= ( C @ ( B @ lesseq ) ) )
| ( C @ summation @ ( B @ summation @ lesseq ) ) ),
inference(simp,[status(thm)],[5840]) ).
thf(5842,plain,
! [A: $i] : ( A @ summation @ summation @ ( A @ ( A @ ( A @ max ) @ max ) @ summation @ summation @ lesseq ) ),
inference(pattern_uni,[status(thm)],[5841:[bind(A,$thf( I )),bind(B,$thf( I @ ( I @ ( I @ max ) @ max ) @ summation )),bind(C,$thf( I @ summation ))]]) ).
thf(5952,plain,
! [A: $i] : ( A @ summation @ summation @ ( A @ ( A @ ( A @ max ) @ max ) @ summation @ summation @ lesseq ) ),
inference(simp,[status(thm)],[5842]) ).
thf(6555,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_ub ) ) )
!= ( C @ ( B @ ( A @ minsol_model_ub ) ) ) )
| ( C @ ( B @ ( A @ model_ub ) ) )
| ~ $true
| ( sk5 != sk4 )
| ( sk5 @ summation @ ( sk6 @ lesseq ) ) ),
inference(paramod_ordered,[status(thm)],[6515,82]) ).
thf(6556,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_ub ) ) )
!= ( C @ ( B @ ( A @ minsol_model_ub ) ) ) )
| ( C @ ( B @ ( A @ model_ub ) ) )
| ( sk5 != sk4 )
| ( sk5 @ summation @ ( sk6 @ lesseq ) ) ),
inference(simp,[status(thm)],[6555]) ).
thf(6557,plain,
( ( sk3 @ ( sk2 @ ( sk1 @ model_ub ) ) )
| ( sk5 != sk4 )
| ( sk5 @ summation @ ( sk6 @ lesseq ) ) ),
inference(pattern_uni,[status(thm)],[6556:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 ))]]) ).
thf(2794,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ lesseq ) )
!= ( D @ summation @ ( C @ summation @ lesseq ) ) )
| ( D @ ( C @ lesseq ) )
| ~ $true
| ( A @ ( B @ lesseq ) ) ),
inference(paramod_ordered,[status(thm)],[2444,43]) ).
thf(2795,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ lesseq ) )
!= ( D @ summation @ ( C @ summation @ lesseq ) ) )
| ( D @ ( C @ lesseq ) )
| ( A @ ( B @ lesseq ) ) ),
inference(simp,[status(thm)],[2794]) ).
thf(2796,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ lesseq ) )
| ( A @ ( B @ summation @ lesseq ) ) ),
inference(pattern_uni,[status(thm)],[2795:[bind(A,$thf( A )),bind(B,$thf( E @ summation )),bind(C,$thf( E )),bind(D,$thf( E ))]]) ).
thf(2942,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ lesseq ) )
| ( A @ ( B @ summation @ lesseq ) ) ),
inference(simp,[status(thm)],[2796]) ).
thf(2373,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ lesseq ) )
!= ( B @ ( C @ lesseq ) ) )
| ( B @ ( B @ ( C @ ub ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,2243]) ).
thf(2374,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ lesseq ) )
!= ( B @ ( C @ lesseq ) ) )
| ( B @ ( B @ ( C @ ub ) ) ) ),
inference(simp,[status(thm)],[2373]) ).
thf(2375,plain,
! [A: $i] : ( A @ ( A @ ( A @ ub ) ) ),
inference(pattern_uni,[status(thm)],[2374:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(5452,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk6 @ ( sk5 @ ( sk4 @ model_max ) ) )
!= ( D @ ( B @ ( A @ model_max ) ) ) )
| ( D @ ( C @ lesseq ) )
| ~ $true
| ~ ( C @ ( B @ ( A @ minsol_model_max ) ) )
| ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_ub ) ) ) ),
inference(paramod_ordered,[status(thm)],[5061,74]) ).
thf(5453,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk6 @ ( sk5 @ ( sk4 @ model_max ) ) )
!= ( D @ ( B @ ( A @ model_max ) ) ) )
| ( D @ ( C @ lesseq ) )
| ~ ( C @ ( B @ ( A @ minsol_model_max ) ) )
| ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_ub ) ) ) ),
inference(simp,[status(thm)],[5452]) ).
thf(5454,plain,
! [A: $i] :
( ( sk6 @ ( A @ lesseq ) )
| ~ ( A @ ( sk5 @ ( sk4 @ minsol_model_max ) ) )
| ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_ub ) ) ) ),
inference(pattern_uni,[status(thm)],[5453:[bind(A,$thf( sk4 )),bind(B,$thf( sk5 )),bind(C,$thf( C )),bind(D,$thf( sk6 ))]]) ).
thf(5484,plain,
! [A: $i] :
( ( sk6 @ ( A @ lesseq ) )
| ~ ( A @ ( sk5 @ ( sk4 @ minsol_model_max ) ) )
| ( sk3 @ ( sk2 @ ( sk1 @ minsol_model_ub ) ) ) ),
inference(simp,[status(thm)],[5454]) ).
thf(407,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ lesseq ) )
!= ( C @ ( D @ lesseq ) ) )
| ~ $true
| ( ( D @ ( C @ max ) )
= C )
| ( B @ ( A @ lesseq ) ) ),
inference(paramod_ordered,[status(thm)],[31,46]) ).
thf(408,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ lesseq ) )
!= ( C @ ( D @ lesseq ) ) )
| ( ( D @ ( C @ max ) )
= C )
| ( B @ ( A @ lesseq ) ) ),
inference(simp,[status(thm)],[407]) ).
thf(409,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ max ) )
= A )
| ( B @ ( A @ lesseq ) ) ),
inference(pattern_uni,[status(thm)],[408:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(4826,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ summation @ ( A @ ( A @ max ) @ ( A @ model_max ) ) )
!= ( D @ ( C @ ( B @ model_max ) ) ) )
| ( D @ ( C @ ( B @ max ) @ summation @ lesseq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4304,60]) ).
thf(4827,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ summation @ ( A @ ( A @ max ) @ ( A @ model_max ) ) )
!= ( D @ ( C @ ( B @ model_max ) ) ) )
| ( D @ ( C @ ( B @ max ) @ summation @ lesseq ) ) ),
inference(simp,[status(thm)],[4826]) ).
thf(4828,plain,
! [A: $i] : ( A @ summation @ ( A @ ( A @ max ) @ ( A @ max ) @ summation @ lesseq ) ),
inference(pattern_uni,[status(thm)],[4827:[bind(A,$thf( G )),bind(B,$thf( G )),bind(C,$thf( G @ ( G @ max ) )),bind(D,$thf( G @ summation ))]]) ).
thf(4864,plain,
! [A: $i] : ( A @ summation @ ( A @ ( A @ max ) @ ( A @ max ) @ summation @ lesseq ) ),
inference(simp,[status(thm)],[4828]) ).
thf(6389,plain,
! [A: $i] : ( A @ summation @ ( A @ summation @ lesseq ) ),
inference(rewrite,[status(thm)],[4864,4107]) ).
thf(67,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ ( C @ sk7 ) ) @ summation @ lesseq ) )
| ~ ( C @ ( B @ ( A @ model_ub ) ) ) ),
inference(cnfConj,[status(thm)],[65]) ).
thf(6025,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ ( A @ max ) @ max ) @ lesseq ) )
!= ( B @ ( C @ lesseq ) ) )
| ( B @ ( B @ ( C @ ub ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5960,2243]) ).
thf(6026,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ ( A @ max ) @ max ) @ lesseq ) )
!= ( B @ ( C @ lesseq ) ) )
| ( B @ ( B @ ( C @ ub ) ) ) ),
inference(simp,[status(thm)],[6025]) ).
thf(6027,plain,
! [A: $i] : ( A @ ( A @ ( A @ ( A @ ( A @ max ) @ max ) @ ub ) ) ),
inference(pattern_uni,[status(thm)],[6026:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ ( E @ ( E @ max ) @ max ) ))]]) ).
thf(6105,plain,
! [A: $i] : ( A @ ( A @ ( A @ ( A @ ( A @ max ) @ max ) @ ub ) ) ),
inference(simp,[status(thm)],[6027]) ).
thf(85,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ minsol_model_ub ) ) )
| ~ ( A @ ( B @ ( C @ sk9 ) ) @ ( C @ lesseq ) )
| ~ ( C @ ( B @ ( A @ model_ub ) ) ) ),
inference(cnfConj,[status(thm)],[81]) ).
thf(87,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ minsol_model_ub ) ) )
| ~ ( A @ ( B @ ( C @ sk9 ) ) @ ( C @ lesseq ) )
| ~ ( C @ ( B @ ( A @ model_ub ) ) ) ),
inference(simp,[status(thm)],[85]) ).
thf(1293,plain,
! [A: $i] :
( ( ( A @ ( A @ summation @ lesseq ) )
!= ( sk1 @ summation @ ( sk1 @ lesseq ) ) )
| ~ ( sk6 @ ( sk5 @ ( sk4 @ minsol_model_ub ) ) )
| ~ ( sk3 @ ( sk2 @ ( sk1 @ summation @ minsol_model_max ) ) )
| ~ $true
| ( ( sk1 @ summation @ summation )
!= sk1 )
| ( ( A @ summation @ summation )
!= A ) ),
inference(paramod_ordered,[status(thm)],[208,723]) ).
thf(1294,plain,
! [A: $i] :
( ( ( A @ ( A @ summation @ lesseq ) )
!= ( sk1 @ summation @ ( sk1 @ lesseq ) ) )
| ~ ( sk6 @ ( sk5 @ ( sk4 @ minsol_model_ub ) ) )
| ~ ( sk3 @ ( sk2 @ ( sk1 @ summation @ minsol_model_max ) ) )
| ( ( sk1 @ summation @ summation )
!= sk1 )
| ( ( A @ summation @ summation )
!= A ) ),
inference(simp,[status(thm)],[1293]) ).
thf(1384,plain,
! [A: $i] :
( ( A
!= ( sk1 @ summation ) )
| ( ( A @ summation )
!= sk1 )
| ~ ( sk6 @ ( sk5 @ ( sk4 @ minsol_model_ub ) ) )
| ~ ( sk3 @ ( sk2 @ ( sk1 @ summation @ minsol_model_max ) ) )
| ( ( sk1 @ summation @ summation )
!= sk1 )
| ( ( A @ summation @ summation )
!= A ) ),
inference(simp,[status(thm)],[1294]) ).
thf(1393,plain,
( ( ( sk1 @ summation @ summation )
!= sk1 )
| ~ ( sk6 @ ( sk5 @ ( sk4 @ minsol_model_ub ) ) )
| ~ ( sk3 @ ( sk2 @ ( sk1 @ summation @ minsol_model_max ) ) )
| ( ( sk1 @ summation @ summation )
!= sk1 )
| ( ( sk1 @ summation @ summation @ summation )
!= ( sk1 @ summation ) ) ),
inference(simp,[status(thm)],[1384]) ).
thf(8696,plain,
( ~ ( sk6 @ ( sk5 @ ( sk4 @ minsol_model_ub ) ) )
| ~ ( sk3 @ ( sk2 @ ( sk1 @ summation @ minsol_model_max ) ) )
| ( ( sk1 @ summation @ summation )
!= sk1 )
| ( ( sk1 @ summation @ summation @ summation )
!= ( sk1 @ summation ) ) ),
inference(simp,[status(thm)],[1393]) ).
thf(8697,plain,
( ~ ( sk6 @ ( sk5 @ ( sk4 @ minsol_model_ub ) ) )
| ~ ( sk3 @ ( sk2 @ ( sk1 @ summation @ minsol_model_max ) ) )
| ( ( sk1 @ summation @ summation )
!= sk1 )
| ( ( sk1 @ summation @ summation )
!= sk1 ) ),
inference(simp,[status(thm)],[8696]) ).
thf(8825,plain,
( ~ ( sk6 @ ( sk5 @ ( sk4 @ minsol_model_ub ) ) )
| ~ ( sk3 @ ( sk2 @ ( sk1 @ summation @ minsol_model_max ) ) )
| ( ( sk1 @ summation @ summation )
!= sk1 ) ),
inference(simp,[status(thm)],[8697]) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ lesseq ) )
| ~ ( C @ ( B @ lesseq ) )
| ~ ( B @ ( A @ lesseq ) ) ),
inference(cnf,[status(esa)],[25]) ).
thf(112,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ lesseq ) )
!= ( E @ ( D @ lesseq ) ) )
| ( E @ ( C @ lesseq ) )
| ~ $true
| ~ ( D @ ( C @ lesseq ) )
| ( A @ ( B @ lesseq ) ) ),
inference(paramod_ordered,[status(thm)],[31,26]) ).
thf(113,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ lesseq ) )
!= ( E @ ( D @ lesseq ) ) )
| ( E @ ( C @ lesseq ) )
| ~ ( D @ ( C @ lesseq ) )
| ( A @ ( B @ lesseq ) ) ),
inference(simp,[status(thm)],[112]) ).
thf(114,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ lesseq ) )
| ~ ( A @ ( C @ lesseq ) )
| ( A @ ( B @ lesseq ) ) ),
inference(pattern_uni,[status(thm)],[113:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).
thf(2445,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ lesseq ) )
!= ( C @ ( D @ lesseq ) ) )
| ( C @ ( C @ lesseq ) )
| ~ $true
| ( B @ ( A @ lesseq ) ) ),
inference(paramod_ordered,[status(thm)],[31,2402]) ).
thf(2446,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ lesseq ) )
!= ( C @ ( D @ lesseq ) ) )
| ( C @ ( C @ lesseq ) )
| ( B @ ( A @ lesseq ) ) ),
inference(simp,[status(thm)],[2445]) ).
thf(2447,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ lesseq ) )
| ( B @ ( A @ lesseq ) ) ),
inference(pattern_uni,[status(thm)],[2446:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(183,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ lesseq ) )
!= ( D @ summation @ ( C @ summation @ lesseq ) ) )
| ( D @ ( C @ lesseq ) )
| ~ $true
| ( B @ summation @ ( A @ summation @ lesseq ) ) ),
inference(paramod_ordered,[status(thm)],[141,43]) ).
thf(184,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ lesseq ) )
!= ( D @ summation @ ( C @ summation @ lesseq ) ) )
| ( D @ ( C @ lesseq ) )
| ( B @ summation @ ( A @ summation @ lesseq ) ) ),
inference(simp,[status(thm)],[183]) ).
thf(185,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ lesseq ) )
| ( A @ summation @ summation @ ( B @ summation @ summation @ lesseq ) ) ),
inference(pattern_uni,[status(thm)],[184:[bind(A,$thf( F @ summation )),bind(B,$thf( E @ summation )),bind(C,$thf( E )),bind(D,$thf( F ))]]) ).
thf(207,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ lesseq ) )
| ( A @ summation @ summation @ ( B @ summation @ summation @ lesseq ) ) ),
inference(simp,[status(thm)],[185]) ).
thf(124,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ lesseq ) )
!= ( F @ ( E @ lesseq ) ) )
| ( F @ ( D @ lesseq ) )
| ~ $true
| ~ ( E @ ( D @ lesseq ) )
| ~ ( C @ ( B @ lesseq ) )
| ~ ( B @ ( A @ lesseq ) ) ),
inference(paramod_ordered,[status(thm)],[26,26]) ).
thf(125,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ lesseq ) )
!= ( F @ ( E @ lesseq ) ) )
| ( F @ ( D @ lesseq ) )
| ~ ( E @ ( D @ lesseq ) )
| ~ ( C @ ( B @ lesseq ) )
| ~ ( B @ ( A @ lesseq ) ) ),
inference(simp,[status(thm)],[124]) ).
thf(126,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ lesseq ) )
| ~ ( A @ ( D @ lesseq ) )
| ~ ( C @ ( B @ lesseq ) )
| ~ ( B @ ( A @ lesseq ) ) ),
inference(pattern_uni,[status(thm)],[125:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( C ))]]) ).
thf(441,plain,
! [B: $i,A: $i] :
( ( B != sk1 )
| ( sk6 @ ( sk5 @ ( sk4 @ minsol_model_max ) ) )
| ~ ( sk3 @ ( sk2 @ ( A @ minsol_model_max ) ) )
| ~ ( A @ ( B @ lesseq ) )
| ~ ( B @ ( A @ lesseq ) ) ),
inference(paramod_ordered,[status(thm)],[29,21]) ).
thf(442,plain,
! [A: $i] :
( ( sk6 @ ( sk5 @ ( sk4 @ minsol_model_max ) ) )
| ~ ( sk3 @ ( sk2 @ ( A @ minsol_model_max ) ) )
| ~ ( A @ ( sk1 @ lesseq ) )
| ~ ( sk1 @ ( A @ lesseq ) ) ),
inference(pattern_uni,[status(thm)],[441:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(4039,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ max ) @ lesseq ) )
!= ( B @ ( C @ lesseq ) ) )
| ( B @ ( B @ ( C @ ub ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3960,2243]) ).
thf(4040,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ max ) @ lesseq ) )
!= ( B @ ( C @ lesseq ) ) )
| ( B @ ( B @ ( C @ ub ) ) ) ),
inference(simp,[status(thm)],[4039]) ).
thf(4041,plain,
! [A: $i] : ( A @ ( A @ ( A @ ( A @ max ) @ ub ) ) ),
inference(pattern_uni,[status(thm)],[4040:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ ( E @ max ) ))]]) ).
thf(4088,plain,
! [A: $i] : ( A @ ( A @ ( A @ ( A @ max ) @ ub ) ) ),
inference(simp,[status(thm)],[4041]) ).
thf(2448,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ lesseq ) )
!= ( D @ summation @ ( C @ summation @ lesseq ) ) )
| ( D @ ( C @ lesseq ) )
| ~ $true
| ~ ( A @ ( B @ lesseq ) ) ),
inference(paramod_ordered,[status(thm)],[2402,43]) ).
thf(2449,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ lesseq ) )
!= ( D @ summation @ ( C @ summation @ lesseq ) ) )
| ( D @ ( C @ lesseq ) )
| ~ ( A @ ( B @ lesseq ) ) ),
inference(simp,[status(thm)],[2448]) ).
thf(2450,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ lesseq ) )
| ~ ( B @ summation @ ( A @ lesseq ) ) ),
inference(pattern_uni,[status(thm)],[2449:[bind(A,$thf( E @ summation )),bind(B,$thf( B )),bind(C,$thf( E )),bind(D,$thf( E ))]]) ).
thf(2563,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ lesseq ) )
| ~ ( B @ summation @ ( A @ lesseq ) ) ),
inference(simp,[status(thm)],[2450]) ).
thf(83,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ lesseq ) )
| ~ ( D @ ( B @ ( A @ model_ub ) ) )
| ~ ( C @ ( B @ ( A @ minsol_model_ub ) ) ) ),
inference(cnfConj,[status(thm)],[81]) ).
thf(5992,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ ( A @ max ) @ max ) @ lesseq ) )
!= ( B @ ( C @ lesseq ) ) )
| ~ $true
| ( ( C @ ( B @ max ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[5960,46]) ).
thf(5993,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ ( A @ max ) @ max ) @ lesseq ) )
!= ( B @ ( C @ lesseq ) ) )
| ( ( C @ ( B @ max ) )
= B ) ),
inference(simp,[status(thm)],[5992]) ).
thf(5994,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ max ) @ max ) @ ( A @ max ) )
= A ),
inference(pattern_uni,[status(thm)],[5993:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ ( E @ ( E @ max ) @ max ) ))]]) ).
thf(6141,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ max ) @ max ) @ ( A @ max ) )
= A ),
inference(simp,[status(thm)],[5994]) ).
thf(138127,plain,
$false,
inference(e,[status(thm)],[5614,69,4094,56,6515,5708,24,2886,37,25,5064,2444,20,46,57,78,29,179,8934,480,7194,3955,74,60,6560,5034,1387,38,70,21,1238,8931,141,388,53,5166,77,2243,3937,41,73,1814,1241,205,2402,32,444,4657,5960,22,27,44,6108,54,4096,8286,144,49,5703,86,406,6572,3957,208,4107,5286,66,5482,1477,4304,35,6672,5952,6557,2942,63,2375,5484,409,50,6389,67,3818,16,4222,31,4488,3961,6105,43,5490,87,8825,3797,26,114,23,2447,207,82,30,19,5268,6563,126,79,5061,47,62,442,4088,2563,83,6141,3753,3960]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM860+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.12 % 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
% 0.22/0.47 % Computer : n015.cluster.edu
% 0.22/0.47 % Model : x86_64 x86_64
% 0.22/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.47 % Memory : 8046.5625MB
% 0.22/0.47 % OS : Linux 6.8.0-71-generic
% 0.22/0.47 % CPULimit : 300
% 0.22/0.47 % WCLimit : 300
% 0.22/0.47 % DateTime : Sat Sep 26 04:17:28 UTC 2026
% 0.22/0.47 % CPUTime :
% 0.22/0.47 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
% 0.98/0.96 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.53/1.14 % [INFO] Parsing done (177ms).
% 1.53/1.16 % [INFO] Running in sequential loop mode.
% 2.52/1.73 % [INFO] eprover registered as external prover.
% 2.52/1.74 % [INFO] Scanning for conjecture ...
% 2.71/1.84 % [INFO] Found a conjecture (or negated_conjecture) and 13 axioms. Running axiom selection ...
% 2.71/1.87 % [INFO] Axiom selection finished. Selected 13 axioms (removed 0 axioms).
% 2.94/1.91 % [INFO] Problem is first-order (TPTP FOF).
% 2.94/1.91 % [INFO] Type checking passed.
% 2.94/1.92 % [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 ...
% 154.49/41.07 % External prover 'e' found a proof!
% 154.49/41.07 % [INFO] Killing All external provers ...
% 154.49/41.07 % Time passed: 40461ms (effective reasoning time: 39906ms)
% 154.49/41.07 % Solved by 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)>
% 154.49/41.07 % Axioms used in derivation (13): summation_monotone, lesseq_ref, max_1, lesseq_trans, model_max_3, max_2, model_ub_3, ub, lesseq_total, sum_monotone_1, minsol_model_max, lesseq_antisymmetric, minsol_model_ub
% 154.49/41.07 % No. of inferences in proof: 342
% 154.49/41.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 40461 ms resp. 39906 ms w/o parsing
% 147.83/41.24 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 147.83/41.24 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------