TSTP Solution File: SWC119-1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWC119-1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:09:46 EDT 2023
% Result : Unsatisfiable 244.24s 45.64s
% Output : Refutation 244.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 270
% Syntax : Number of formulae : 1584 ( 608 unt; 73 typ; 0 def)
% Number of atoms : 4050 ( 818 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 11458 (2040 ~;1889 |; 0 &;7529 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 82 ( 82 >; 0 *; 0 +; 0 <<)
% Number of symbols : 76 ( 73 usr; 10 con; 0-2 aty)
% Number of variables : 1854 ( 0 ^;1854 !; 0 ?;1854 :)
% Comments :
%------------------------------------------------------------------------------
thf(ssList_type,type,
ssList: $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i ).
thf(nil_type,type,
nil: $i ).
thf(ssItem_type,type,
ssItem: $i > $o ).
thf(sk5_type,type,
sk5: $i ).
thf(neq_type,type,
neq: $i > $i > $o ).
thf(cons_type,type,
cons: $i > $i > $i ).
thf(memberP_type,type,
memberP: $i > $i > $o ).
thf(segmentP_type,type,
segmentP: $i > $i > $o ).
thf(skac3_type,type,
skac3: $i ).
thf(skac2_type,type,
skac2: $i ).
thf(skaf43_type,type,
skaf43: $i > $i > $i ).
thf(leq_type,type,
leq: $i > $i > $o ).
thf(geq_type,type,
geq: $i > $i > $o ).
thf(totalorderedP_type,type,
totalorderedP: $i > $o ).
thf(lt_type,type,
lt: $i > $i > $o ).
thf(gt_type,type,
gt: $i > $i > $o ).
thf(skaf62_type,type,
skaf62: $i > $i ).
thf(app_type,type,
app: $i > $i > $i ).
thf(skaf69_type,type,
skaf69: $i > $i ).
thf(skaf70_type,type,
skaf70: $i > $i ).
thf(strictorderedP_type,type,
strictorderedP: $i > $o ).
thf(cyclefreeP_type,type,
cyclefreeP: $i > $o ).
thf(skaf49_type,type,
skaf49: $i > $i ).
thf(skaf50_type,type,
skaf50: $i > $i ).
thf(singletonP_type,type,
singletonP: $i > $o ).
thf(skaf44_type,type,
skaf44: $i > $i ).
thf(duplicatefreeP_type,type,
duplicatefreeP: $i > $o ).
thf(skaf75_type,type,
skaf75: $i > $i ).
thf(skaf74_type,type,
skaf74: $i > $i ).
thf(skaf76_type,type,
skaf76: $i > $i ).
thf(skaf77_type,type,
skaf77: $i > $i ).
thf(skaf72_type,type,
skaf72: $i > $i ).
thf(skaf79_type,type,
skaf79: $i > $i ).
thf(hd_type,type,
hd: $i > $i ).
thf(frontsegP_type,type,
frontsegP: $i > $i > $o ).
thf(skaf71_type,type,
skaf71: $i > $i ).
thf(skaf73_type,type,
skaf73: $i > $i ).
thf(skaf46_type,type,
skaf46: $i > $i > $i ).
thf(skaf64_type,type,
skaf64: $i > $i ).
thf(tl_type,type,
tl: $i > $i ).
thf(skaf66_type,type,
skaf66: $i > $i ).
thf(skaf67_type,type,
skaf67: $i > $i ).
thf(skaf65_type,type,
skaf65: $i > $i ).
thf(skaf68_type,type,
skaf68: $i > $i ).
thf(skaf45_type,type,
skaf45: $i > $i > $i ).
thf(rearsegP_type,type,
rearsegP: $i > $i > $o ).
thf(strictorderP_type,type,
strictorderP: $i > $o ).
thf(skaf61_type,type,
skaf61: $i > $i ).
thf(skaf59_type,type,
skaf59: $i > $i ).
thf(skaf60_type,type,
skaf60: $i > $i ).
thf(skaf63_type,type,
skaf63: $i > $i ).
thf(skaf51_type,type,
skaf51: $i > $i ).
thf(skaf52_type,type,
skaf52: $i > $i ).
thf(skaf53_type,type,
skaf53: $i > $i ).
thf(skaf57_type,type,
skaf57: $i > $i ).
thf(equalelemsP_type,type,
equalelemsP: $i > $o ).
thf(totalorderP_type,type,
totalorderP: $i > $o ).
thf(skaf56_type,type,
skaf56: $i > $i ).
thf(skaf54_type,type,
skaf54: $i > $i ).
thf(skaf55_type,type,
skaf55: $i > $i ).
thf(skaf58_type,type,
skaf58: $i > $i ).
thf(skaf48_type,type,
skaf48: $i > $i > $i ).
thf(skaf80_type,type,
skaf80: $i > $i ).
thf(skaf47_type,type,
skaf47: $i > $i > $i ).
thf(skaf78_type,type,
skaf78: $i > $i ).
thf(skaf81_type,type,
skaf81: $i > $i ).
thf(skaf83_type,type,
skaf83: $i > $i ).
thf(skaf82_type,type,
skaf82: $i > $i ).
thf(skaf42_type,type,
skaf42: $i > $i > $i ).
thf(92,axiom,
! [A: $i] : ( ssItem @ ( skaf60 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause35) ).
thf(406,plain,
! [A: $i] : ( ssItem @ ( skaf60 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ( totalorderedP @ ( cons @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause113) ).
thf(227,plain,
! [B: $i,A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ( totalorderedP @ ( cons @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(228,plain,
! [B: $i,A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ( totalorderedP @ ( cons @ B @ A ) ) ),
inference(cnf,[status(esa)],[227]) ).
thf(229,plain,
! [B: $i,A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ( totalorderedP @ ( cons @ B @ A ) ) ),
inference(lifteq,[status(thm)],[228]) ).
thf(230,plain,
! [A: $i] :
( ~ ( ssList @ nil )
| ~ ( ssItem @ A )
| ( totalorderedP @ ( cons @ A @ nil ) ) ),
inference(simp,[status(thm)],[229]) ).
thf(41,axiom,
ssList @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause8) ).
thf(287,plain,
ssList @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(696,plain,
! [A: $i] :
( ~ $true
| ~ ( ssItem @ A )
| ( totalorderedP @ ( cons @ A @ nil ) ) ),
inference(rewrite,[status(thm)],[230,287]) ).
thf(697,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( totalorderedP @ ( cons @ A @ nil ) ) ),
inference(simp,[status(thm)],[696]) ).
thf(881,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf60 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[406,697]) ).
thf(882,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf60 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[881:[bind(A,$thf( C )),bind(B,$thf( skaf60 @ C ))]]) ).
thf(892,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf60 @ A ) @ nil ) ),
inference(simp,[status(thm)],[882]) ).
thf(1,negated_conjecture,
ssList @ sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
thf(200,plain,
ssList @ sk1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(43,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( rearsegP @ A @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause58) ).
thf(291,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( rearsegP @ A @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(292,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( rearsegP @ A @ nil ) ),
inference(cnf,[status(esa)],[291]) ).
thf(15488,plain,
! [A: $i] :
( ( rearsegP @ A @ nil )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[200,292]) ).
thf(15489,plain,
rearsegP @ sk1 @ nil,
inference(pattern_uni,[status(thm)],[15488:[bind(A,$thf( sk1 ))]]) ).
thf(50,axiom,
! [A: $i] :
( ~ ( rearsegP @ nil @ A )
| ~ ( ssList @ A )
| ( nil = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause82) ).
thf(308,plain,
! [A: $i] :
( ~ ( rearsegP @ nil @ A )
| ~ ( ssList @ A )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(309,plain,
! [A: $i] :
( ~ ( rearsegP @ nil @ A )
| ~ ( ssList @ A )
| ( nil = A ) ),
inference(cnf,[status(esa)],[308]) ).
thf(310,plain,
! [A: $i] :
( ( nil = A )
| ~ ( rearsegP @ nil @ A )
| ~ ( ssList @ A ) ),
inference(lifteq,[status(thm)],[309]) ).
thf(21491,plain,
! [A: $i] :
( ( nil = A )
| ~ ( rearsegP @ nil @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[200,310]) ).
thf(21492,plain,
( ( nil = sk1 )
| ~ ( rearsegP @ nil @ sk1 ) ),
inference(pattern_uni,[status(thm)],[21491:[bind(A,$thf( sk1 ))]]) ).
thf(126,axiom,
cyclefreeP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause7) ).
thf(480,plain,
cyclefreeP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(26124,plain,
( ~ ( rearsegP @ nil @ sk1 )
| ( cyclefreeP @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[21492,480]) ).
thf(26125,plain,
( ~ ( rearsegP @ nil @ sk1 )
| ( cyclefreeP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[26124:[]]) ).
thf(53957,plain,
( ( cyclefreeP @ sk1 )
| ( ( rearsegP @ nil @ sk1 )
!= ( rearsegP @ sk1 @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[15489,26125]) ).
thf(53986,plain,
( ( cyclefreeP @ sk1 )
| ( nil != sk1 )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[53957]) ).
thf(54031,plain,
( ( cyclefreeP @ sk1 )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[53986]) ).
thf(85,axiom,
! [A: $i] : ( ssItem @ ( skaf69 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause26) ).
thf(394,plain,
! [A: $i] : ( ssItem @ ( skaf69 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(40,axiom,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( neq @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause117) ).
thf(283,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( neq @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(284,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( neq @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A ) ),
inference(cnf,[status(esa)],[283]) ).
thf(285,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( neq @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A ) ),
inference(lifteq,[status(thm)],[284]) ).
thf(286,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ~ ( ssItem @ A ) ),
inference(simp,[status(thm)],[285]) ).
thf(13836,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssItem @ ( skaf69 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[394,286]) ).
thf(13837,plain,
! [A: $i] :
~ ( neq @ ( skaf69 @ A ) @ ( skaf69 @ A ) ),
inference(pattern_uni,[status(thm)],[13836:[bind(A,$thf( C )),bind(B,$thf( skaf69 @ C ))]]) ).
thf(13854,plain,
! [A: $i] :
~ ( neq @ ( skaf69 @ A ) @ ( skaf69 @ A ) ),
inference(simp,[status(thm)],[13837]) ).
thf(22,axiom,
! [A: $i] :
( ~ ( lt @ ( skaf69 @ A ) @ ( skaf70 @ A ) )
| ~ ( ssList @ A )
| ( strictorderedP @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause90) ).
thf(242,plain,
! [A: $i] :
( ~ ( lt @ ( skaf69 @ A ) @ ( skaf70 @ A ) )
| ~ ( ssList @ A )
| ( strictorderedP @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(243,plain,
! [A: $i] :
( ~ ( lt @ ( skaf69 @ A ) @ ( skaf70 @ A ) )
| ~ ( ssList @ A )
| ( strictorderedP @ A ) ),
inference(cnf,[status(esa)],[242]) ).
thf(1236,plain,
! [A: $i] :
( ~ ( lt @ ( skaf69 @ A ) @ ( skaf70 @ A ) )
| ( strictorderedP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[200,243]) ).
thf(1237,plain,
( ~ ( lt @ ( skaf69 @ sk1 ) @ ( skaf70 @ sk1 ) )
| ( strictorderedP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[1236:[bind(A,$thf( sk1 ))]]) ).
thf(133,axiom,
! [A: $i] : ( ssList @ ( skaf67 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause28) ).
thf(497,plain,
! [A: $i] : ( ssList @ ( skaf67 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(15456,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( skaf67 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[497,292]) ).
thf(15457,plain,
! [A: $i] : ( rearsegP @ ( skaf67 @ A ) @ nil ),
inference(pattern_uni,[status(thm)],[15456:[bind(A,$thf( C )),bind(B,$thf( skaf67 @ C ))]]) ).
thf(15537,plain,
! [A: $i] : ( rearsegP @ ( skaf67 @ A ) @ nil ),
inference(simp,[status(thm)],[15457]) ).
thf(141,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ~ ( ssList @ C )
| ( ( cons @ A @ ( app @ B @ C ) )
= ( app @ ( cons @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause157) ).
thf(518,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ~ ( ssList @ C )
| ( ( cons @ A @ ( app @ B @ C ) )
= ( app @ ( cons @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(82,axiom,
! [A: $i] : ( ssList @ ( skaf73 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause22) ).
thf(387,plain,
! [A: $i] : ( ssList @ ( skaf73 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(2,negated_conjecture,
ssList @ sk2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_2) ).
thf(203,plain,
ssList @ sk2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(29,axiom,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( ssList @ ( app @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause85) ).
thf(257,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( ssList @ ( app @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(258,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( ssList @ ( app @ B @ A ) ) ),
inference(cnf,[status(esa)],[257]) ).
thf(2921,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( app @ B @ A ) )
| ( ( ssList @ sk2 )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[203,258]) ).
thf(2922,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( app @ sk2 @ A ) ) ),
inference(pattern_uni,[status(thm)],[2921:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(3951,plain,
! [B: $i,A: $i] :
( ( ssList @ ( app @ sk2 @ B ) )
| ( ( ssList @ ( skaf73 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[387,2922]) ).
thf(3952,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( skaf73 @ A ) ) ),
inference(pattern_uni,[status(thm)],[3951:[bind(A,$thf( C )),bind(B,$thf( skaf73 @ C ))]]) ).
thf(4015,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( skaf73 @ A ) ) ),
inference(simp,[status(thm)],[3952]) ).
thf(38,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( tl @ A ) )
| ( nil = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause75) ).
thf(277,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( tl @ A ) )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(278,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( tl @ A ) )
| ( nil = A ) ),
inference(cnf,[status(esa)],[277]) ).
thf(279,plain,
! [A: $i] :
( ( nil = A )
| ~ ( ssList @ A )
| ( ssList @ ( tl @ A ) ) ),
inference(lifteq,[status(thm)],[278]) ).
thf(10974,plain,
! [A: $i] :
( ( nil = A )
| ( ssList @ ( tl @ A ) )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[200,279]) ).
thf(10975,plain,
( ( nil = sk1 )
| ( ssList @ ( tl @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[10974:[bind(A,$thf( sk1 ))]]) ).
thf(193,axiom,
totalorderedP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause4) ).
thf(634,plain,
totalorderedP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(12163,plain,
( ( ssList @ ( tl @ sk1 ) )
| ( totalorderedP @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[10975,634]) ).
thf(12164,plain,
( ( ssList @ ( tl @ sk1 ) )
| ( totalorderedP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[12163:[]]) ).
thf(17501,plain,
! [A: $i] :
( ( totalorderedP @ sk1 )
| ( ssList @ ( app @ sk2 @ A ) )
| ( ( ssList @ ( tl @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12164,2922]) ).
thf(17502,plain,
( ( totalorderedP @ sk1 )
| ( ssList @ ( app @ sk2 @ ( tl @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[17501:[bind(A,$thf( tl @ sk1 ))]]) ).
thf(157,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( cons @ ( skaf83 @ A ) @ ( skaf82 @ A ) )
= A )
| ( nil = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause109) ).
thf(555,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( cons @ ( skaf83 @ A ) @ ( skaf82 @ A ) )
= A )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(191,axiom,
! [B: $i,A: $i] :
( ~ ( segmentP @ A @ B )
| ~ ( segmentP @ B @ A )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause127) ).
thf(629,plain,
! [B: $i,A: $i] :
( ~ ( segmentP @ A @ B )
| ~ ( segmentP @ B @ A )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(10806,plain,
! [A: $i] :
( ( nil = A )
| ( ssList @ ( tl @ A ) )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[203,279]) ).
thf(10807,plain,
( ( nil = sk2 )
| ( ssList @ ( tl @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[10806:[bind(A,$thf( sk2 ))]]) ).
thf(7,negated_conjecture,
( ( nil = sk3 )
| ( nil != sk4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
thf(205,plain,
( ( nil = sk3 )
| ( nil != sk4 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(212,plain,
( ( nil = sk3 )
| ( nil != sk4 ) ),
inference(cnf,[status(esa)],[205]) ).
thf(213,plain,
( ( nil = sk3 )
| ( nil != sk4 ) ),
inference(lifteq,[status(thm)],[212]) ).
thf(6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
thf(201,plain,
sk1 = sk3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(211,plain,
sk3 = sk1,
inference(lifteq,[status(thm)],[201]) ).
thf(5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
thf(198,plain,
sk2 = sk4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(217,plain,
sk4 = sk2,
inference(lifteq,[status(thm)],[198]) ).
thf(645,plain,
( ( nil = sk1 )
| ( nil != sk2 ) ),
inference(rewrite,[status(thm)],[213,211,217]) ).
thf(11818,plain,
( ( ssList @ ( tl @ sk2 ) )
| ( nil = sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[10807,645]) ).
thf(11819,plain,
( ( ssList @ ( tl @ sk2 ) )
| ( nil = sk1 ) ),
inference(pattern_uni,[status(thm)],[11818:[]]) ).
thf(8,negated_conjecture,
( ( nil != sk2 )
| ( nil != sk1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
thf(208,plain,
( ( nil != sk2 )
| ( nil != sk1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(215,plain,
( ( nil != sk2 )
| ( nil != sk1 ) ),
inference(cnf,[status(esa)],[208]) ).
thf(216,plain,
( ( nil != sk2 )
| ( nil != sk1 ) ),
inference(lifteq,[status(thm)],[215]) ).
thf(11863,plain,
( ( ssList @ ( tl @ sk2 ) )
| ( nil != sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[10807,216]) ).
thf(11864,plain,
( ( ssList @ ( tl @ sk2 ) )
| ( nil != sk1 ) ),
inference(pattern_uni,[status(thm)],[11863:[]]) ).
thf(13717,plain,
( ( ssList @ ( tl @ sk2 ) )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[11819,11864]) ).
thf(13718,plain,
ssList @ ( tl @ sk2 ),
inference(pattern_uni,[status(thm)],[13717:[]]) ).
thf(13768,plain,
! [A: $i] :
( ( ssList @ ( app @ sk2 @ A ) )
| ( ( ssList @ ( tl @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13718,2922]) ).
thf(13769,plain,
ssList @ ( app @ sk2 @ ( tl @ sk2 ) ),
inference(pattern_uni,[status(thm)],[13768:[bind(A,$thf( tl @ sk2 ))]]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( neq @ A @ B )
| ~ ( ssList @ B )
| ~ ( ssList @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause115) ).
thf(233,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( neq @ A @ B )
| ~ ( ssList @ B )
| ~ ( ssList @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(234,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( neq @ A @ B )
| ~ ( ssList @ B )
| ~ ( ssList @ A ) ),
inference(cnf,[status(esa)],[233]) ).
thf(235,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( neq @ A @ B )
| ~ ( ssList @ B )
| ~ ( ssList @ A ) ),
inference(lifteq,[status(thm)],[234]) ).
thf(236,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ~ ( ssList @ A ) ),
inference(simp,[status(thm)],[235]) ).
thf(13954,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ( ( ssList @ ( app @ sk2 @ ( tl @ sk2 ) ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13769,236]) ).
thf(13955,plain,
~ ( neq @ ( app @ sk2 @ ( tl @ sk2 ) ) @ ( app @ sk2 @ ( tl @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[13954:[bind(A,$thf( app @ sk2 @ ( tl @ sk2 ) ))]]) ).
thf(177,axiom,
! [A: $i] : ( ssList @ ( skaf71 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause24) ).
thf(597,plain,
! [A: $i] : ( ssList @ ( skaf71 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(3895,plain,
! [B: $i,A: $i] :
( ( ssList @ ( app @ sk2 @ B ) )
| ( ( ssList @ ( skaf71 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[597,2922]) ).
thf(3896,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( skaf71 @ A ) ) ),
inference(pattern_uni,[status(thm)],[3895:[bind(A,$thf( C )),bind(B,$thf( skaf71 @ C ))]]) ).
thf(4021,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( skaf71 @ A ) ) ),
inference(simp,[status(thm)],[3896]) ).
thf(9418,plain,
! [B: $i,A: $i] :
( ( ssList @ ( app @ sk2 @ B ) )
| ( ( ssList @ ( app @ sk2 @ ( skaf71 @ A ) ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4021,2922]) ).
thf(9419,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( skaf71 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[9418:[bind(A,$thf( E )),bind(B,$thf( app @ sk2 @ ( skaf71 @ E ) ))]]) ).
thf(9458,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( skaf71 @ A ) ) ) ),
inference(simp,[status(thm)],[9419]) ).
thf(73,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( app @ A @ ( cons @ B @ ( cons @ C @ D ) ) )
!= E )
| ~ ( ssList @ D )
| ~ ( ssList @ A )
| ~ ( ssItem @ C )
| ~ ( ssItem @ B )
| ~ ( equalelemsP @ E )
| ~ ( ssList @ E )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause180) ).
thf(362,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( app @ A @ ( cons @ B @ ( cons @ C @ D ) ) )
!= E )
| ~ ( ssList @ D )
| ~ ( ssList @ A )
| ~ ( ssItem @ C )
| ~ ( ssItem @ B )
| ~ ( equalelemsP @ E )
| ~ ( ssList @ E )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(363,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( app @ A @ ( cons @ B @ ( cons @ C @ D ) ) )
!= E )
| ~ ( ssList @ D )
| ~ ( ssList @ A )
| ~ ( ssItem @ C )
| ~ ( ssItem @ B )
| ~ ( equalelemsP @ E )
| ~ ( ssList @ E )
| ( B = C ) ),
inference(cnf,[status(esa)],[362]) ).
thf(364,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( app @ A @ ( cons @ B @ ( cons @ C @ D ) ) )
!= E )
| ( B = C )
| ~ ( ssList @ D )
| ~ ( ssList @ A )
| ~ ( ssItem @ C )
| ~ ( ssItem @ B )
| ~ ( equalelemsP @ E )
| ~ ( ssList @ E ) ),
inference(lifteq,[status(thm)],[363]) ).
thf(365,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( ssList @ D )
| ~ ( ssList @ A )
| ~ ( ssItem @ C )
| ~ ( ssItem @ B )
| ~ ( equalelemsP @ ( app @ A @ ( cons @ B @ ( cons @ C @ D ) ) ) )
| ~ ( ssList @ ( app @ A @ ( cons @ B @ ( cons @ C @ D ) ) ) ) ),
inference(simp,[status(thm)],[364]) ).
thf(86,axiom,
! [A: $i] : ( ssItem @ ( skaf55 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause40) ).
thf(395,plain,
! [A: $i] : ( ssItem @ ( skaf55 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(13846,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssItem @ ( skaf55 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[395,286]) ).
thf(13847,plain,
! [A: $i] :
~ ( neq @ ( skaf55 @ A ) @ ( skaf55 @ A ) ),
inference(pattern_uni,[status(thm)],[13846:[bind(A,$thf( C )),bind(B,$thf( skaf55 @ C ))]]) ).
thf(13859,plain,
! [A: $i] :
~ ( neq @ ( skaf55 @ A ) @ ( skaf55 @ A ) ),
inference(simp,[status(thm)],[13847]) ).
thf(67,axiom,
! [A: $i] : ( ssList @ ( skaf58 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause37) ).
thf(347,plain,
! [A: $i] : ( ssList @ ( skaf58 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(48,axiom,
! [A: $i] : ( ssList @ ( skaf77 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause18) ).
thf(304,plain,
! [A: $i] : ( ssList @ ( skaf77 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(3964,plain,
! [B: $i,A: $i] :
( ( ssList @ ( app @ sk2 @ B ) )
| ( ( ssList @ ( skaf77 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[304,2922]) ).
thf(3965,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( skaf77 @ A ) ) ),
inference(pattern_uni,[status(thm)],[3964:[bind(A,$thf( C )),bind(B,$thf( skaf77 @ C ))]]) ).
thf(4026,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( skaf77 @ A ) ) ),
inference(simp,[status(thm)],[3965]) ).
thf(11460,plain,
! [B: $i,A: $i] :
( ( ssList @ ( app @ sk2 @ B ) )
| ( ( ssList @ ( app @ sk2 @ ( skaf77 @ A ) ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4026,2922]) ).
thf(11461,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( skaf77 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[11460:[bind(A,$thf( E )),bind(B,$thf( app @ sk2 @ ( skaf77 @ E ) ))]]) ).
thf(11504,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( skaf77 @ A ) ) ) ),
inference(simp,[status(thm)],[11461]) ).
thf(19,axiom,
! [A: $i] : ( ssList @ ( skaf62 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause33) ).
thf(237,plain,
! [A: $i] : ( ssList @ ( skaf62 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(3936,plain,
! [B: $i,A: $i] :
( ( ssList @ ( app @ sk2 @ B ) )
| ( ( ssList @ ( skaf62 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[237,2922]) ).
thf(3937,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( skaf62 @ A ) ) ),
inference(pattern_uni,[status(thm)],[3936:[bind(A,$thf( C )),bind(B,$thf( skaf62 @ C ))]]) ).
thf(4008,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( skaf62 @ A ) ) ),
inference(simp,[status(thm)],[3937]) ).
thf(15356,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( app @ sk2 @ ( skaf62 @ A ) ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4008,292]) ).
thf(15357,plain,
! [A: $i] : ( rearsegP @ ( app @ sk2 @ ( skaf62 @ A ) ) @ nil ),
inference(pattern_uni,[status(thm)],[15356:[bind(A,$thf( E )),bind(B,$thf( app @ sk2 @ ( skaf62 @ E ) ))]]) ).
thf(15558,plain,
! [A: $i] : ( rearsegP @ ( app @ sk2 @ ( skaf62 @ A ) ) @ nil ),
inference(simp,[status(thm)],[15357]) ).
thf(61,axiom,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( lt @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause105) ).
thf(333,plain,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( lt @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(3978,plain,
! [A: $i] :
( ( ssList @ ( app @ sk2 @ A ) )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[200,2922]) ).
thf(3979,plain,
ssList @ ( app @ sk2 @ sk1 ),
inference(pattern_uni,[status(thm)],[3978:[bind(A,$thf( sk1 ))]]) ).
thf(25,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( duplicatefreeP @ A )
| ( ( app @ ( app @ ( skaf75 @ A ) @ ( cons @ ( skaf74 @ A ) @ ( skaf76 @ A ) ) ) @ ( cons @ ( skaf74 @ A ) @ ( skaf77 @ A ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause162) ).
thf(249,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( duplicatefreeP @ A )
| ( ( app @ ( app @ ( skaf75 @ A ) @ ( cons @ ( skaf74 @ A ) @ ( skaf76 @ A ) ) ) @ ( cons @ ( skaf74 @ A ) @ ( skaf77 @ A ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(131,axiom,
~ ( singletonP @ nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause11) ).
thf(491,plain,
~ ( singletonP @ nil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(492,plain,
~ ( singletonP @ nil ),
inference(polarity_switch,[status(thm)],[491]) ).
thf(12147,plain,
( ( ssList @ ( tl @ sk1 ) )
| ~ ( singletonP @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[10975,492]) ).
thf(12148,plain,
( ( ssList @ ( tl @ sk1 ) )
| ~ ( singletonP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[12147:[]]) ).
thf(120,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( cons @ ( hd @ A ) @ ( tl @ A ) )
= A )
| ( nil = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause104) ).
thf(468,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( cons @ ( hd @ A ) @ ( tl @ A ) )
= A )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(89,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( rearsegP @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause59) ).
thf(400,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( rearsegP @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(401,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( rearsegP @ A @ A ) ),
inference(cnf,[status(esa)],[400]) ).
thf(84818,plain,
! [A: $i] :
( ( rearsegP @ A @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[200,401]) ).
thf(84819,plain,
rearsegP @ sk1 @ sk1,
inference(pattern_uni,[status(thm)],[84818:[bind(A,$thf( sk1 ))]]) ).
thf(127,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( app @ ( app @ A @ ( cons @ B @ C ) ) @ ( cons @ D @ E ) )
!= F )
| ~ ( ssList @ E )
| ~ ( ssList @ C )
| ~ ( ssList @ A )
| ~ ( ssItem @ D )
| ~ ( ssItem @ B )
| ~ ( totalorderP @ F )
| ~ ( ssList @ F )
| ( leq @ B @ D )
| ( leq @ D @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause184) ).
thf(481,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( app @ ( app @ A @ ( cons @ B @ C ) ) @ ( cons @ D @ E ) )
!= F )
| ~ ( ssList @ E )
| ~ ( ssList @ C )
| ~ ( ssList @ A )
| ~ ( ssItem @ D )
| ~ ( ssItem @ B )
| ~ ( totalorderP @ F )
| ~ ( ssList @ F )
| ( leq @ B @ D )
| ( leq @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(69,axiom,
! [B: $i,A: $i] :
( ~ ( rearsegP @ A @ B )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( ( app @ ( skaf46 @ A @ B ) @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause131) ).
thf(350,plain,
! [B: $i,A: $i] :
( ~ ( rearsegP @ A @ B )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( ( app @ ( skaf46 @ A @ B ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(351,plain,
! [B: $i,A: $i] :
( ~ ( rearsegP @ A @ B )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( ( app @ ( skaf46 @ A @ B ) @ B )
= A ) ),
inference(cnf,[status(esa)],[350]) ).
thf(352,plain,
! [B: $i,A: $i] :
( ( ( app @ ( skaf46 @ A @ B ) @ B )
= A )
| ~ ( rearsegP @ A @ B )
| ~ ( ssList @ B )
| ~ ( ssList @ A ) ),
inference(lifteq,[status(thm)],[351]) ).
thf(90,axiom,
! [A: $i] : ( ssList @ ( skaf61 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause34) ).
thf(402,plain,
! [A: $i] : ( ssList @ ( skaf61 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(3938,plain,
! [B: $i,A: $i] :
( ( ssList @ ( app @ sk2 @ B ) )
| ( ( ssList @ ( skaf61 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[402,2922]) ).
thf(3939,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( skaf61 @ A ) ) ),
inference(pattern_uni,[status(thm)],[3938:[bind(A,$thf( C )),bind(B,$thf( skaf61 @ C ))]]) ).
thf(4009,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( skaf61 @ A ) ) ),
inference(simp,[status(thm)],[3939]) ).
thf(15442,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( app @ sk2 @ ( skaf61 @ A ) ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4009,292]) ).
thf(15443,plain,
! [A: $i] : ( rearsegP @ ( app @ sk2 @ ( skaf61 @ A ) ) @ nil ),
inference(pattern_uni,[status(thm)],[15442:[bind(A,$thf( E )),bind(B,$thf( app @ sk2 @ ( skaf61 @ E ) ))]]) ).
thf(15532,plain,
! [A: $i] : ( rearsegP @ ( app @ sk2 @ ( skaf61 @ A ) ) @ nil ),
inference(simp,[status(thm)],[15443]) ).
thf(169,axiom,
! [A: $i] : ( ssItem @ ( skaf54 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause41) ).
thf(582,plain,
! [A: $i] : ( ssItem @ ( skaf54 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(76,axiom,
! [A: $i] :
( ~ ( ssItem @ A )
| ( geq @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause55) ).
thf(372,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( geq @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(373,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( geq @ A @ A ) ),
inference(cnf,[status(esa)],[372]) ).
thf(55264,plain,
! [B: $i,A: $i] :
( ( geq @ B @ B )
| ( ( ssItem @ ( skaf60 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[406,373]) ).
thf(55265,plain,
! [A: $i] : ( geq @ ( skaf60 @ A ) @ ( skaf60 @ A ) ),
inference(pattern_uni,[status(thm)],[55264:[bind(A,$thf( C )),bind(B,$thf( skaf60 @ C ))]]) ).
thf(55309,plain,
! [A: $i] : ( geq @ ( skaf60 @ A ) @ ( skaf60 @ A ) ),
inference(simp,[status(thm)],[55265]) ).
thf(3962,plain,
! [B: $i,A: $i] :
( ( ssList @ ( app @ sk2 @ B ) )
| ( ( ssList @ ( skaf67 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[497,2922]) ).
thf(3963,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( skaf67 @ A ) ) ),
inference(pattern_uni,[status(thm)],[3962:[bind(A,$thf( C )),bind(B,$thf( skaf67 @ C ))]]) ).
thf(4024,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( skaf67 @ A ) ) ),
inference(simp,[status(thm)],[3963]) ).
thf(9732,plain,
! [B: $i,A: $i] :
( ( ssList @ ( app @ sk2 @ B ) )
| ( ( ssList @ ( app @ sk2 @ ( skaf67 @ A ) ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4024,2922]) ).
thf(9733,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( skaf67 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[9732:[bind(A,$thf( E )),bind(B,$thf( app @ sk2 @ ( skaf67 @ E ) ))]]) ).
thf(9769,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( skaf67 @ A ) ) ) ),
inference(simp,[status(thm)],[9733]) ).
thf(106,axiom,
! [A: $i] : ( ssList @ ( skaf80 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause15) ).
thf(436,plain,
! [A: $i] : ( ssList @ ( skaf80 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(84632,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ B )
| ( ( ssList @ ( skaf80 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[436,401]) ).
thf(84633,plain,
! [A: $i] : ( rearsegP @ ( skaf80 @ A ) @ ( skaf80 @ A ) ),
inference(pattern_uni,[status(thm)],[84632:[bind(A,$thf( C )),bind(B,$thf( skaf80 @ C ))]]) ).
thf(84901,plain,
! [A: $i] : ( rearsegP @ ( skaf80 @ A ) @ ( skaf80 @ A ) ),
inference(simp,[status(thm)],[84633]) ).
thf(79,axiom,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( neq @ B @ A )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause102) ).
thf(379,plain,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( neq @ B @ A )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(860,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[200,236]) ).
thf(861,plain,
~ ( neq @ sk1 @ sk1 ),
inference(pattern_uni,[status(thm)],[860:[bind(A,$thf( sk1 ))]]) ).
thf(3972,plain,
! [A: $i] :
( ( ssList @ ( app @ sk2 @ A ) )
| ( ( ssList @ nil )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[287,2922]) ).
thf(3973,plain,
ssList @ ( app @ sk2 @ nil ),
inference(pattern_uni,[status(thm)],[3972:[bind(A,$thf( nil ))]]) ).
thf(15360,plain,
! [A: $i] :
( ( rearsegP @ A @ nil )
| ( ( ssList @ ( app @ sk2 @ nil ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3973,292]) ).
thf(15361,plain,
rearsegP @ ( app @ sk2 @ nil ) @ nil,
inference(pattern_uni,[status(thm)],[15360:[bind(A,$thf( app @ sk2 @ nil ))]]) ).
thf(93,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( frontsegP @ A @ B )
| ~ ( ssList @ C )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( frontsegP @ ( app @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause137) ).
thf(407,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( frontsegP @ A @ B )
| ~ ( ssList @ C )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( frontsegP @ ( app @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(408,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( frontsegP @ A @ B )
| ~ ( ssList @ C )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( frontsegP @ ( app @ A @ C ) @ B ) ),
inference(cnf,[status(esa)],[407]) ).
thf(15378,plain,
! [A: $i] :
( ( nil = sk1 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( tl @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10975,292]) ).
thf(15379,plain,
( ( nil = sk1 )
| ( rearsegP @ ( tl @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[15378:[bind(A,$thf( tl @ sk1 ))]]) ).
thf(123,axiom,
totalorderP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause6) ).
thf(475,plain,
totalorderP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(25259,plain,
( ( rearsegP @ ( tl @ sk1 ) @ nil )
| ( totalorderP @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[15379,475]) ).
thf(25260,plain,
( ( rearsegP @ ( tl @ sk1 ) @ nil )
| ( totalorderP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[25259:[]]) ).
thf(15474,plain,
! [A: $i] :
( ( rearsegP @ A @ nil )
| ( ( ssList @ nil )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[287,292]) ).
thf(15475,plain,
rearsegP @ nil @ nil,
inference(pattern_uni,[status(thm)],[15474:[bind(A,$thf( nil ))]]) ).
thf(55,axiom,
equalelemsP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause1) ).
thf(318,plain,
equalelemsP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(26295,plain,
( ~ ( rearsegP @ nil @ sk1 )
| ( equalelemsP @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[21492,318]) ).
thf(26296,plain,
( ~ ( rearsegP @ nil @ sk1 )
| ( equalelemsP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[26295:[]]) ).
thf(59025,plain,
( ( equalelemsP @ sk1 )
| ( ( rearsegP @ nil @ nil )
!= ( rearsegP @ nil @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[15475,26296]) ).
thf(59099,plain,
( ( equalelemsP @ sk1 )
| ( nil != nil )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[59025]) ).
thf(59140,plain,
( ( equalelemsP @ sk1 )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[59099]) ).
thf(37,axiom,
! [B: $i,A: $i] :
( ~ ( geq @ A @ B )
| ~ ( geq @ B @ A )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause126) ).
thf(274,plain,
! [B: $i,A: $i] :
( ~ ( geq @ A @ B )
| ~ ( geq @ B @ A )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(275,plain,
! [B: $i,A: $i] :
( ~ ( geq @ A @ B )
| ~ ( geq @ B @ A )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( B = A ) ),
inference(cnf,[status(esa)],[274]) ).
thf(276,plain,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( geq @ A @ B )
| ~ ( geq @ B @ A )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B ) ),
inference(lifteq,[status(thm)],[275]) ).
thf(25424,plain,
( ( rearsegP @ ( tl @ sk1 ) @ nil )
| ( equalelemsP @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[15379,318]) ).
thf(25425,plain,
( ( rearsegP @ ( tl @ sk1 ) @ nil )
| ( equalelemsP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[25424:[]]) ).
thf(112,axiom,
! [A: $i] :
( ~ ( leq @ ( skaf54 @ A ) @ ( skaf55 @ A ) )
| ~ ( ssList @ A )
| ( totalorderP @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause95) ).
thf(449,plain,
! [A: $i] :
( ~ ( leq @ ( skaf54 @ A ) @ ( skaf55 @ A ) )
| ~ ( ssList @ A )
| ( totalorderP @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(186,axiom,
! [B: $i,A: $i] :
( ~ ( segmentP @ A @ B )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( ( app @ ( app @ ( skaf47 @ A @ B ) @ B ) @ ( skaf48 @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause168) ).
thf(614,plain,
! [B: $i,A: $i] :
( ~ ( segmentP @ A @ B )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( ( app @ ( app @ ( skaf47 @ A @ B ) @ B ) @ ( skaf48 @ B @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(33,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( app @ ( app @ A @ ( cons @ B @ C ) ) @ ( cons @ D @ E ) )
!= F )
| ~ ( ssList @ E )
| ~ ( ssList @ C )
| ~ ( ssList @ A )
| ~ ( ssItem @ D )
| ~ ( ssItem @ B )
| ~ ( strictorderedP @ F )
| ~ ( ssList @ F )
| ( lt @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause181) ).
thf(266,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( app @ ( app @ A @ ( cons @ B @ C ) ) @ ( cons @ D @ E ) )
!= F )
| ~ ( ssList @ E )
| ~ ( ssList @ C )
| ~ ( ssList @ A )
| ~ ( ssItem @ D )
| ~ ( ssItem @ B )
| ~ ( strictorderedP @ F )
| ~ ( ssList @ F )
| ( lt @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(267,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( app @ ( app @ A @ ( cons @ B @ C ) ) @ ( cons @ D @ E ) )
!= F )
| ~ ( ssList @ E )
| ~ ( ssList @ C )
| ~ ( ssList @ A )
| ~ ( ssItem @ D )
| ~ ( ssItem @ B )
| ~ ( strictorderedP @ F )
| ~ ( ssList @ F )
| ( lt @ B @ D ) ),
inference(cnf,[status(esa)],[266]) ).
thf(268,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( app @ ( app @ A @ ( cons @ B @ C ) ) @ ( cons @ D @ E ) )
!= F )
| ~ ( ssList @ E )
| ~ ( ssList @ C )
| ~ ( ssList @ A )
| ~ ( ssItem @ D )
| ~ ( ssItem @ B )
| ~ ( strictorderedP @ F )
| ~ ( ssList @ F )
| ( lt @ B @ D ) ),
inference(lifteq,[status(thm)],[267]) ).
thf(269,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( ssList @ E )
| ~ ( ssList @ C )
| ~ ( ssList @ A )
| ~ ( ssItem @ D )
| ~ ( ssItem @ B )
| ~ ( strictorderedP @ ( app @ ( app @ A @ ( cons @ B @ C ) ) @ ( cons @ D @ E ) ) )
| ~ ( ssList @ ( app @ ( app @ A @ ( cons @ B @ C ) ) @ ( cons @ D @ E ) ) )
| ( lt @ B @ D ) ),
inference(simp,[status(thm)],[268]) ).
thf(9,negated_conjecture,
( ( ssItem @ sk5 )
| ~ ( neq @ sk4 @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
thf(202,plain,
( ( ssItem @ sk5 )
| ~ ( neq @ sk4 @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(23,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( cyclefreeP @ A )
| ( leq @ ( skaf49 @ A ) @ ( skaf50 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause88) ).
thf(244,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( cyclefreeP @ A )
| ( leq @ ( skaf49 @ A ) @ ( skaf50 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(245,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( cyclefreeP @ A )
| ( leq @ ( skaf49 @ A ) @ ( skaf50 @ A ) ) ),
inference(cnf,[status(esa)],[244]) ).
thf(1436,plain,
! [A: $i] :
( ( cyclefreeP @ A )
| ( leq @ ( skaf49 @ A ) @ ( skaf50 @ A ) )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[200,245]) ).
thf(1437,plain,
( ( cyclefreeP @ sk1 )
| ( leq @ ( skaf49 @ sk1 ) @ ( skaf50 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[1436:[bind(A,$thf( sk1 ))]]) ).
thf(46,axiom,
strictorderP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause5) ).
thf(299,plain,
strictorderP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(25458,plain,
( ( rearsegP @ ( tl @ sk1 ) @ nil )
| ( strictorderP @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[15379,299]) ).
thf(25459,plain,
( ( rearsegP @ ( tl @ sk1 ) @ nil )
| ( strictorderP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[25458:[]]) ).
thf(103,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( segmentP @ A @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause56) ).
thf(428,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( segmentP @ A @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(429,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( segmentP @ A @ nil ) ),
inference(cnf,[status(esa)],[428]) ).
thf(110262,plain,
! [A: $i] :
( ( segmentP @ A @ nil )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[203,429]) ).
thf(110263,plain,
segmentP @ sk2 @ nil,
inference(pattern_uni,[status(thm)],[110262:[bind(A,$thf( sk2 ))]]) ).
thf(81,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( geq @ A @ B )
| ~ ( geq @ B @ C )
| ~ ( ssItem @ C )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( geq @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause148) ).
thf(385,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( geq @ A @ B )
| ~ ( geq @ B @ C )
| ~ ( ssItem @ C )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( geq @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(80,axiom,
! [B: $i,A: $i] :
( ( ( app @ A @ B )
!= nil )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( nil = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause119) ).
thf(382,plain,
! [B: $i,A: $i] :
( ( ( app @ A @ B )
!= nil )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( nil = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(383,plain,
! [B: $i,A: $i] :
( ( ( app @ A @ B )
!= nil )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( nil = B ) ),
inference(cnf,[status(esa)],[382]) ).
thf(384,plain,
! [B: $i,A: $i] :
( ( ( app @ A @ B )
!= nil )
| ( nil = B )
| ~ ( ssList @ B )
| ~ ( ssList @ A ) ),
inference(lifteq,[status(thm)],[383]) ).
thf(155,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( memberP @ A @ B )
| ~ ( ssList @ C )
| ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ( memberP @ ( app @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause140) ).
thf(550,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( memberP @ A @ B )
| ~ ( ssList @ C )
| ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ( memberP @ ( app @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(135,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( equalelemsP @ A )
| ( ( app @ ( skaf80 @ A ) @ ( cons @ ( skaf78 @ A ) @ ( cons @ ( skaf79 @ A ) @ ( skaf81 @ A ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause142) ).
thf(500,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( equalelemsP @ A )
| ( ( app @ ( skaf80 @ A ) @ ( cons @ ( skaf78 @ A ) @ ( cons @ ( skaf79 @ A ) @ ( skaf81 @ A ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( geq @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause108) ).
thf(225,plain,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( geq @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(226,plain,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( geq @ B @ A ) ),
inference(cnf,[status(esa)],[225]) ).
thf(13,axiom,
skac3 != skac2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause54) ).
thf(221,plain,
skac3 != skac2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(222,plain,
skac3 != skac2,
inference(polarity_switch,[status(thm)],[221]) ).
thf(223,plain,
skac2 != skac3,
inference(lifteq,[status(thm)],[222]) ).
thf(7900,plain,
! [B: $i,A: $i] :
( ~ ( geq @ A @ B )
| ~ ( geq @ B @ A )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( A != skac3 )
| ( B != skac2 ) ),
inference(paramod_ordered,[status(thm)],[276,223]) ).
thf(7901,plain,
! [A: $i] :
( ~ ( geq @ A @ skac2 )
| ~ ( geq @ skac2 @ A )
| ~ ( ssItem @ A )
| ~ ( ssItem @ skac2 )
| ( A != skac3 ) ),
inference(pattern_uni,[status(thm)],[7900:[bind(A,$thf( A )),bind(B,$thf( skac2 ))]]) ).
thf(9021,plain,
( ~ ( geq @ skac3 @ skac2 )
| ~ ( geq @ skac2 @ skac3 )
| ~ ( ssItem @ skac3 )
| ~ ( ssItem @ skac2 ) ),
inference(simp,[status(thm)],[7901]) ).
thf(149,axiom,
ssItem @ skac3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause9) ).
thf(538,plain,
ssItem @ skac3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(143,axiom,
ssItem @ skac2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause10) ).
thf(525,plain,
ssItem @ skac2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(9479,plain,
( ~ ( geq @ skac3 @ skac2 )
| ~ ( geq @ skac2 @ skac3 )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[9021,538,525]) ).
thf(9480,plain,
( ~ ( geq @ skac3 @ skac2 )
| ~ ( geq @ skac2 @ skac3 ) ),
inference(simp,[status(thm)],[9479]) ).
thf(9507,plain,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ~ ( geq @ skac3 @ skac2 )
| ( ( geq @ B @ A )
!= ( geq @ skac2 @ skac3 ) ) ),
inference(paramod_ordered,[status(thm)],[226,9480]) ).
thf(9508,plain,
( ~ ( leq @ skac3 @ skac2 )
| ~ ( ssItem @ skac3 )
| ~ ( ssItem @ skac2 )
| ~ ( geq @ skac3 @ skac2 ) ),
inference(pattern_uni,[status(thm)],[9507:[bind(A,$thf( skac3 )),bind(B,$thf( skac2 ))]]) ).
thf(15281,plain,
( ~ ( leq @ skac3 @ skac2 )
| ~ $true
| ~ $true
| ~ ( geq @ skac3 @ skac2 ) ),
inference(rewrite,[status(thm)],[9508,538,525]) ).
thf(15282,plain,
( ~ ( leq @ skac3 @ skac2 )
| ~ ( geq @ skac3 @ skac2 ) ),
inference(simp,[status(thm)],[15281]) ).
thf(10,negated_conjecture,
( ( ( cons @ sk5 @ nil )
= sk3 )
| ~ ( neq @ sk4 @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
thf(199,plain,
( ( ( cons @ sk5 @ nil )
= sk3 )
| ~ ( neq @ sk4 @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(218,plain,
( ( ( cons @ sk5 @ nil )
= sk3 )
| ~ ( neq @ sk4 @ nil ) ),
inference(cnf,[status(esa)],[199]) ).
thf(219,plain,
( ( ( cons @ sk5 @ nil )
= sk3 )
| ~ ( neq @ sk4 @ nil ) ),
inference(lifteq,[status(thm)],[218]) ).
thf(648,plain,
( ( ( cons @ sk5 @ nil )
= sk1 )
| ~ ( neq @ sk2 @ nil ) ),
inference(rewrite,[status(thm)],[219,211,217]) ).
thf(702,plain,
! [A: $i] :
( ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ skac2 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[525,697]) ).
thf(703,plain,
totalorderedP @ ( cons @ skac2 @ nil ),
inference(pattern_uni,[status(thm)],[702:[bind(A,$thf( skac2 ))]]) ).
thf(713,plain,
( ~ ( neq @ sk2 @ nil )
| ( totalorderedP @ sk1 )
| ( ( cons @ skac2 @ nil )
!= ( cons @ sk5 @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[648,703]) ).
thf(714,plain,
( ( totalorderedP @ sk1 )
| ~ ( neq @ sk2 @ nil )
| ( skac2 != sk5 )
| ( nil != nil ) ),
inference(simp,[status(thm)],[713]) ).
thf(715,plain,
( ( totalorderedP @ sk1 )
| ~ ( neq @ sk2 @ nil )
| ( skac2 != sk5 ) ),
inference(simp,[status(thm)],[714]) ).
thf(35,axiom,
! [A: $i] : ( ssItem @ ( skaf64 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause31) ).
thf(271,plain,
! [A: $i] : ( ssItem @ ( skaf64 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(58,axiom,
! [A: $i] :
( ~ ( ssItem @ A )
| ( strictorderedP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause66) ).
thf(327,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( strictorderedP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(328,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( strictorderedP @ ( cons @ A @ nil ) ) ),
inference(cnf,[status(esa)],[327]) ).
thf(27986,plain,
! [B: $i,A: $i] :
( ( strictorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf64 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[271,328]) ).
thf(27987,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf64 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[27986:[bind(A,$thf( C )),bind(B,$thf( skaf64 @ C ))]]) ).
thf(28018,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf64 @ A ) @ nil ) ),
inference(simp,[status(thm)],[27987]) ).
thf(64,axiom,
! [B: $i,A: $i] :
( ~ ( lt @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( leq @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause103) ).
thf(339,plain,
! [B: $i,A: $i] :
( ~ ( lt @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( leq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(340,plain,
! [B: $i,A: $i] :
( ~ ( lt @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( leq @ A @ B ) ),
inference(cnf,[status(esa)],[339]) ).
thf(173,axiom,
! [A: $i] : ( ssList @ ( skaf56 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause39) ).
thf(590,plain,
! [A: $i] : ( ssList @ ( skaf56 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(1497,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf56 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[590,236]) ).
thf(1498,plain,
! [A: $i] :
~ ( neq @ ( skaf56 @ A ) @ ( skaf56 @ A ) ),
inference(pattern_uni,[status(thm)],[1497:[bind(A,$thf( C )),bind(B,$thf( skaf56 @ C ))]]) ).
thf(1507,plain,
! [A: $i] :
~ ( neq @ ( skaf56 @ A ) @ ( skaf56 @ A ) ),
inference(simp,[status(thm)],[1498]) ).
thf(14,axiom,
! [B: $i,A: $i] : ( ssList @ ( skaf43 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause52) ).
thf(224,plain,
! [B: $i,A: $i] : ( ssList @ ( skaf43 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(15392,plain,
! [C: $i,B: $i,A: $i] :
( ( rearsegP @ C @ nil )
| ( ( ssList @ ( skaf43 @ A @ B ) )
!= ( ssList @ C ) ) ),
inference(paramod_ordered,[status(thm)],[224,292]) ).
thf(15393,plain,
! [B: $i,A: $i] : ( rearsegP @ ( skaf43 @ A @ B ) @ nil ),
inference(pattern_uni,[status(thm)],[15392:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( skaf43 @ D @ E ))]]) ).
thf(15514,plain,
! [B: $i,A: $i] : ( rearsegP @ ( skaf43 @ A @ B ) @ nil ),
inference(simp,[status(thm)],[15393]) ).
thf(194,axiom,
! [A: $i] : ( ssItem @ ( skaf59 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause36) ).
thf(635,plain,
! [A: $i] : ( ssItem @ ( skaf59 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(1710,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf59 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[635,697]) ).
thf(1711,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf59 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[1710:[bind(A,$thf( C )),bind(B,$thf( skaf59 @ C ))]]) ).
thf(1735,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf59 @ A ) @ nil ) ),
inference(simp,[status(thm)],[1711]) ).
thf(15336,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( app @ sk2 @ ( skaf73 @ A ) ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4015,292]) ).
thf(15337,plain,
! [A: $i] : ( rearsegP @ ( app @ sk2 @ ( skaf73 @ A ) ) @ nil ),
inference(pattern_uni,[status(thm)],[15336:[bind(A,$thf( E )),bind(B,$thf( app @ sk2 @ ( skaf73 @ E ) ))]]) ).
thf(15541,plain,
! [A: $i] : ( rearsegP @ ( app @ sk2 @ ( skaf73 @ A ) ) @ nil ),
inference(simp,[status(thm)],[15337]) ).
thf(166,axiom,
! [A: $i] : ( ssItem @ ( skaf74 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause21) ).
thf(578,plain,
! [A: $i] : ( ssItem @ ( skaf74 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(55260,plain,
! [B: $i,A: $i] :
( ( geq @ B @ B )
| ( ( ssItem @ ( skaf74 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[578,373]) ).
thf(55261,plain,
! [A: $i] : ( geq @ ( skaf74 @ A ) @ ( skaf74 @ A ) ),
inference(pattern_uni,[status(thm)],[55260:[bind(A,$thf( C )),bind(B,$thf( skaf74 @ C ))]]) ).
thf(55307,plain,
! [A: $i] : ( geq @ ( skaf74 @ A ) @ ( skaf74 @ A ) ),
inference(simp,[status(thm)],[55261]) ).
thf(15334,plain,
! [A: $i] :
( ( rearsegP @ A @ nil )
| ( ( ssList @ ( app @ sk2 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3979,292]) ).
thf(15335,plain,
rearsegP @ ( app @ sk2 @ sk1 ) @ nil,
inference(pattern_uni,[status(thm)],[15334:[bind(A,$thf( app @ sk2 @ sk1 ))]]) ).
thf(706,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf64 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[271,697]) ).
thf(707,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf64 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[706:[bind(A,$thf( C )),bind(B,$thf( skaf64 @ C ))]]) ).
thf(709,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf64 @ A ) @ nil ) ),
inference(simp,[status(thm)],[707]) ).
thf(96,axiom,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( ( app @ ( cons @ A @ nil ) @ B )
= ( cons @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause120) ).
thf(415,plain,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( ( app @ ( cons @ A @ nil ) @ B )
= ( cons @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(416,plain,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( ( app @ ( cons @ A @ nil ) @ B )
= ( cons @ A @ B ) ) ),
inference(cnf,[status(esa)],[415]) ).
thf(417,plain,
! [B: $i,A: $i] :
( ( ( app @ ( cons @ A @ nil ) @ B )
= ( cons @ A @ B ) )
| ~ ( ssItem @ A )
| ~ ( ssList @ B ) ),
inference(lifteq,[status(thm)],[416]) ).
thf(42,axiom,
! [B: $i,A: $i] :
( ~ ( frontsegP @ A @ B )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( ( app @ B @ ( skaf45 @ A @ B ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause132) ).
thf(288,plain,
! [B: $i,A: $i] :
( ~ ( frontsegP @ A @ B )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( ( app @ B @ ( skaf45 @ A @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(858,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ( ( ssList @ nil )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[287,236]) ).
thf(859,plain,
~ ( neq @ nil @ nil ),
inference(pattern_uni,[status(thm)],[858:[bind(A,$thf( nil ))]]) ).
thf(26383,plain,
( ~ ( rearsegP @ nil @ sk1 )
| ~ ( neq @ sk1 @ nil )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[21492,859]) ).
thf(26384,plain,
( ~ ( rearsegP @ nil @ sk1 )
| ~ ( neq @ sk1 @ nil ) ),
inference(pattern_uni,[status(thm)],[26383:[]]) ).
thf(53759,plain,
( ~ ( neq @ sk1 @ nil )
| ( ( rearsegP @ nil @ sk1 )
!= ( rearsegP @ sk1 @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[15489,26384]) ).
thf(53780,plain,
( ~ ( neq @ sk1 @ nil )
| ( nil != sk1 )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[53759]) ).
thf(53831,plain,
( ~ ( neq @ sk1 @ nil )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[53780]) ).
thf(185,axiom,
! [A: $i] : ( ssItem @ ( skaf78 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause17) ).
thf(613,plain,
! [A: $i] : ( ssItem @ ( skaf78 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(55274,plain,
! [B: $i,A: $i] :
( ( geq @ B @ B )
| ( ( ssItem @ ( skaf78 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[613,373]) ).
thf(55275,plain,
! [A: $i] : ( geq @ ( skaf78 @ A ) @ ( skaf78 @ A ) ),
inference(pattern_uni,[status(thm)],[55274:[bind(A,$thf( C )),bind(B,$thf( skaf78 @ C ))]]) ).
thf(55313,plain,
! [A: $i] : ( geq @ ( skaf78 @ A ) @ ( skaf78 @ A ) ),
inference(simp,[status(thm)],[55275]) ).
thf(152,axiom,
! [A: $i] : ( ssList @ ( skaf66 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause29) ).
thf(543,plain,
! [A: $i] : ( ssList @ ( skaf66 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(1258,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf66 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[543,236]) ).
thf(1259,plain,
! [A: $i] :
~ ( neq @ ( skaf66 @ A ) @ ( skaf66 @ A ) ),
inference(pattern_uni,[status(thm)],[1258:[bind(A,$thf( C )),bind(B,$thf( skaf66 @ C ))]]) ).
thf(1265,plain,
! [A: $i] :
~ ( neq @ ( skaf66 @ A ) @ ( skaf66 @ A ) ),
inference(simp,[status(thm)],[1259]) ).
thf(107,axiom,
! [A: $i] :
( ~ ( memberP @ nil @ A )
| ~ ( ssItem @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause71) ).
thf(437,plain,
! [A: $i] :
( ~ ( memberP @ nil @ A )
| ~ ( ssItem @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(438,plain,
! [A: $i] :
( ~ ( memberP @ nil @ A )
| ~ ( ssItem @ A ) ),
inference(cnf,[status(esa)],[437]) ).
thf(1683,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf78 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[613,438]) ).
thf(1684,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf78 @ A ) ),
inference(pattern_uni,[status(thm)],[1683:[bind(A,$thf( C )),bind(B,$thf( skaf78 @ C ))]]) ).
thf(1703,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf78 @ A ) ),
inference(simp,[status(thm)],[1684]) ).
thf(3891,plain,
! [A: $i] :
( ( ssList @ ( app @ sk2 @ A ) )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[203,2922]) ).
thf(3892,plain,
ssList @ ( app @ sk2 @ sk2 ),
inference(pattern_uni,[status(thm)],[3891:[bind(A,$thf( sk2 ))]]) ).
thf(4031,plain,
! [A: $i] :
( ( ssList @ ( app @ sk2 @ A ) )
| ( ( ssList @ ( app @ sk2 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3892,2922]) ).
thf(4032,plain,
ssList @ ( app @ sk2 @ ( app @ sk2 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[4031:[bind(A,$thf( app @ sk2 @ sk2 ))]]) ).
thf(4327,plain,
! [A: $i] :
( ( ssList @ ( app @ sk2 @ A ) )
| ( ( ssList @ ( app @ sk2 @ ( app @ sk2 @ sk2 ) ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4032,2922]) ).
thf(4328,plain,
ssList @ ( app @ sk2 @ ( app @ sk2 @ ( app @ sk2 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[4327:[bind(A,$thf( app @ sk2 @ ( app @ sk2 @ sk2 ) ))]]) ).
thf(15434,plain,
! [A: $i] :
( ( rearsegP @ A @ nil )
| ( ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( app @ sk2 @ sk2 ) ) ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4328,292]) ).
thf(15435,plain,
rearsegP @ ( app @ sk2 @ ( app @ sk2 @ ( app @ sk2 @ sk2 ) ) ) @ nil,
inference(pattern_uni,[status(thm)],[15434:[bind(A,$thf( app @ sk2 @ ( app @ sk2 @ ( app @ sk2 @ sk2 ) ) ))]]) ).
thf(4237,plain,
! [A: $i] :
( ( ssList @ ( app @ sk2 @ A ) )
| ( ( ssList @ ( app @ sk2 @ nil ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3973,2922]) ).
thf(4238,plain,
ssList @ ( app @ sk2 @ ( app @ sk2 @ nil ) ),
inference(pattern_uni,[status(thm)],[4237:[bind(A,$thf( app @ sk2 @ nil ))]]) ).
thf(114,axiom,
! [A: $i] : ( ssList @ ( skaf75 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause20) ).
thf(452,plain,
! [A: $i] : ( ssList @ ( skaf75 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(84657,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ B )
| ( ( ssList @ ( skaf75 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[452,401]) ).
thf(84658,plain,
! [A: $i] : ( rearsegP @ ( skaf75 @ A ) @ ( skaf75 @ A ) ),
inference(pattern_uni,[status(thm)],[84657:[bind(A,$thf( C )),bind(B,$thf( skaf75 @ C ))]]) ).
thf(84910,plain,
! [A: $i] : ( rearsegP @ ( skaf75 @ A ) @ ( skaf75 @ A ) ),
inference(simp,[status(thm)],[84658]) ).
thf(4283,plain,
! [A: $i] :
( ( ssList @ ( app @ sk2 @ A ) )
| ( ( ssList @ ( app @ sk2 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3979,2922]) ).
thf(4284,plain,
ssList @ ( app @ sk2 @ ( app @ sk2 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[4283:[bind(A,$thf( app @ sk2 @ sk1 ))]]) ).
thf(15386,plain,
! [A: $i] :
( ( rearsegP @ A @ nil )
| ( ( ssList @ ( app @ sk2 @ ( app @ sk2 @ sk1 ) ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4284,292]) ).
thf(15387,plain,
rearsegP @ ( app @ sk2 @ ( app @ sk2 @ sk1 ) ) @ nil,
inference(pattern_uni,[status(thm)],[15386:[bind(A,$thf( app @ sk2 @ ( app @ sk2 @ sk1 ) ))]]) ).
thf(137,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( app @ ( app @ A @ B ) @ C )
!= D )
| ~ ( ssList @ C )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( ssList @ D )
| ( segmentP @ D @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause173) ).
thf(504,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( app @ ( app @ A @ B ) @ C )
!= D )
| ~ ( ssList @ C )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( ssList @ D )
| ( segmentP @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(15406,plain,
! [A: $i] :
( ( rearsegP @ A @ nil )
| ( ( ssList @ ( tl @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13718,292]) ).
thf(15407,plain,
rearsegP @ ( tl @ sk2 ) @ nil,
inference(pattern_uni,[status(thm)],[15406:[bind(A,$thf( tl @ sk2 ))]]) ).
thf(15647,plain,
( ( ssList @ ( tl @ sk1 ) )
| ( rearsegP @ ( tl @ sk2 ) @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[10975,15407]) ).
thf(15648,plain,
( ( ssList @ ( tl @ sk1 ) )
| ( rearsegP @ ( tl @ sk2 ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[15647:[]]) ).
thf(172,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( cons @ A @ B )
!= ( cons @ C @ D ) )
| ~ ( ssItem @ C )
| ~ ( ssItem @ A )
| ~ ( ssList @ D )
| ~ ( ssList @ B )
| ( D = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause171) ).
thf(587,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( cons @ A @ B )
!= ( cons @ C @ D ) )
| ~ ( ssItem @ C )
| ~ ( ssItem @ A )
| ~ ( ssList @ D )
| ~ ( ssList @ B )
| ( D = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(66,axiom,
! [B: $i,A: $i] :
( ~ ( leq @ A @ ( hd @ B ) )
| ~ ( totalorderedP @ B )
| ~ ( ssList @ B )
| ~ ( ssItem @ A )
| ( totalorderedP @ ( cons @ A @ B ) )
| ( nil = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause159) ).
thf(344,plain,
! [B: $i,A: $i] :
( ~ ( leq @ A @ ( hd @ B ) )
| ~ ( totalorderedP @ B )
| ~ ( ssList @ B )
| ~ ( ssItem @ A )
| ( totalorderedP @ ( cons @ A @ B ) )
| ( nil = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(4348,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ( ( ssList @ ( app @ sk2 @ ( app @ sk2 @ sk2 ) ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4032,236]) ).
thf(4349,plain,
~ ( neq @ ( app @ sk2 @ ( app @ sk2 @ sk2 ) ) @ ( app @ sk2 @ ( app @ sk2 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[4348:[bind(A,$thf( app @ sk2 @ ( app @ sk2 @ sk2 ) ))]]) ).
thf(3897,plain,
! [B: $i,A: $i] :
( ( ssList @ ( app @ sk2 @ B ) )
| ( ( ssList @ ( skaf80 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[436,2922]) ).
thf(3898,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( skaf80 @ A ) ) ),
inference(pattern_uni,[status(thm)],[3897:[bind(A,$thf( C )),bind(B,$thf( skaf80 @ C ))]]) ).
thf(4023,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( skaf80 @ A ) ) ),
inference(simp,[status(thm)],[3898]) ).
thf(71,axiom,
! [B: $i,A: $i] :
( ( nil != A )
| ( nil != B )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( ( app @ A @ B )
= nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause145) ).
thf(357,plain,
! [B: $i,A: $i] :
( ( nil != A )
| ( nil != B )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( ( app @ A @ B )
= nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(55239,plain,
! [B: $i,A: $i] :
( ( geq @ B @ B )
| ( ( ssItem @ ( skaf54 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[582,373]) ).
thf(55240,plain,
! [A: $i] : ( geq @ ( skaf54 @ A ) @ ( skaf54 @ A ) ),
inference(pattern_uni,[status(thm)],[55239:[bind(A,$thf( C )),bind(B,$thf( skaf54 @ C ))]]) ).
thf(55302,plain,
! [A: $i] : ( geq @ ( skaf54 @ A ) @ ( skaf54 @ A ) ),
inference(simp,[status(thm)],[55240]) ).
thf(188,axiom,
strictorderedP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause3) ).
thf(621,plain,
strictorderedP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(26310,plain,
( ~ ( rearsegP @ nil @ sk1 )
| ( strictorderedP @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[21492,621]) ).
thf(26311,plain,
( ~ ( rearsegP @ nil @ sk1 )
| ( strictorderedP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[26310:[]]) ).
thf(180,axiom,
! [A: $i] : ( ssList @ ( skaf76 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause19) ).
thf(603,plain,
! [A: $i] : ( ssList @ ( skaf76 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(1565,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf76 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[603,236]) ).
thf(1566,plain,
! [A: $i] :
~ ( neq @ ( skaf76 @ A ) @ ( skaf76 @ A ) ),
inference(pattern_uni,[status(thm)],[1565:[bind(A,$thf( C )),bind(B,$thf( skaf76 @ C ))]]) ).
thf(1577,plain,
! [A: $i] :
~ ( neq @ ( skaf76 @ A ) @ ( skaf76 @ A ) ),
inference(simp,[status(thm)],[1566]) ).
thf(28002,plain,
! [B: $i,A: $i] :
( ( strictorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf78 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[613,328]) ).
thf(28003,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf78 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[28002:[bind(A,$thf( C )),bind(B,$thf( skaf78 @ C ))]]) ).
thf(28028,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf78 @ A ) @ nil ) ),
inference(simp,[status(thm)],[28003]) ).
thf(151,axiom,
! [A: $i] : ( ssList @ ( skaf63 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause32) ).
thf(542,plain,
! [A: $i] : ( ssList @ ( skaf63 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(117,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( app @ ( app @ A @ ( cons @ B @ C ) ) @ ( cons @ B @ D ) )
!= E )
| ~ ( ssList @ D )
| ~ ( ssList @ C )
| ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ~ ( duplicatefreeP @ E )
| ~ ( ssList @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause179) ).
thf(460,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( app @ ( app @ A @ ( cons @ B @ C ) ) @ ( cons @ B @ D ) )
!= E )
| ~ ( ssList @ D )
| ~ ( ssList @ C )
| ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ~ ( duplicatefreeP @ E )
| ~ ( ssList @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(27962,plain,
! [B: $i,A: $i] :
( ( strictorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf74 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[578,328]) ).
thf(27963,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf74 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[27962:[bind(A,$thf( C )),bind(B,$thf( skaf74 @ C ))]]) ).
thf(28037,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf74 @ A ) @ nil ) ),
inference(simp,[status(thm)],[27963]) ).
thf(3982,plain,
! [B: $i,A: $i] :
( ( ssList @ ( app @ sk2 @ B ) )
| ( ( ssList @ ( skaf66 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[543,2922]) ).
thf(3983,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( skaf66 @ A ) ) ),
inference(pattern_uni,[status(thm)],[3982:[bind(A,$thf( C )),bind(B,$thf( skaf66 @ C ))]]) ).
thf(3998,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( skaf66 @ A ) ) ),
inference(simp,[status(thm)],[3983]) ).
thf(1360,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf54 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[582,438]) ).
thf(1361,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf54 @ A ) ),
inference(pattern_uni,[status(thm)],[1360:[bind(A,$thf( C )),bind(B,$thf( skaf54 @ C ))]]) ).
thf(1379,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf54 @ A ) ),
inference(simp,[status(thm)],[1361]) ).
thf(15476,plain,
! [A: $i] :
( ( rearsegP @ A @ nil )
| ( ( ssList @ ( app @ sk2 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3892,292]) ).
thf(15477,plain,
rearsegP @ ( app @ sk2 @ sk2 ) @ nil,
inference(pattern_uni,[status(thm)],[15476:[bind(A,$thf( app @ sk2 @ sk2 ))]]) ).
thf(98,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( memberP @ A @ B )
| ~ ( ssList @ A )
| ~ ( ssItem @ C )
| ~ ( ssItem @ B )
| ( memberP @ ( cons @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause139) ).
thf(420,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( memberP @ A @ B )
| ~ ( ssList @ A )
| ~ ( ssItem @ C )
| ~ ( ssItem @ B )
| ( memberP @ ( cons @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(421,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( memberP @ A @ B )
| ~ ( ssList @ A )
| ~ ( ssItem @ C )
| ~ ( ssItem @ B )
| ( memberP @ ( cons @ C @ A ) @ B ) ),
inference(cnf,[status(esa)],[420]) ).
thf(72,axiom,
! [A: $i] : ( ssItem @ ( skaf44 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause47) ).
thf(361,plain,
! [A: $i] : ( ssItem @ ( skaf44 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(762,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf44 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[361,438]) ).
thf(763,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf44 @ A ) ),
inference(pattern_uni,[status(thm)],[762:[bind(A,$thf( C )),bind(B,$thf( skaf44 @ C ))]]) ).
thf(770,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf44 @ A ) ),
inference(simp,[status(thm)],[763]) ).
thf(15380,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( app @ sk2 @ ( skaf71 @ A ) ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4021,292]) ).
thf(15381,plain,
! [A: $i] : ( rearsegP @ ( app @ sk2 @ ( skaf71 @ A ) ) @ nil ),
inference(pattern_uni,[status(thm)],[15380:[bind(A,$thf( E )),bind(B,$thf( app @ sk2 @ ( skaf71 @ E ) ))]]) ).
thf(15509,plain,
! [A: $i] : ( rearsegP @ ( app @ sk2 @ ( skaf71 @ A ) ) @ nil ),
inference(simp,[status(thm)],[15381]) ).
thf(170,axiom,
! [A: $i] : ( ssItem @ ( skaf65 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause30) ).
thf(583,plain,
! [A: $i] : ( ssItem @ ( skaf65 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(1469,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf65 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[583,438]) ).
thf(1470,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf65 @ A ) ),
inference(pattern_uni,[status(thm)],[1469:[bind(A,$thf( C )),bind(B,$thf( skaf65 @ C ))]]) ).
thf(1494,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf65 @ A ) ),
inference(simp,[status(thm)],[1470]) ).
thf(53,axiom,
! [A: $i] :
( ~ ( lt @ ( skaf60 @ A ) @ ( skaf59 @ A ) )
| ~ ( ssList @ A )
| ( strictorderP @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause92) ).
thf(315,plain,
! [A: $i] :
( ~ ( lt @ ( skaf60 @ A ) @ ( skaf59 @ A ) )
| ~ ( ssList @ A )
| ( strictorderP @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(316,plain,
! [A: $i] :
( ~ ( lt @ ( skaf60 @ A ) @ ( skaf59 @ A ) )
| ~ ( ssList @ A )
| ( strictorderP @ A ) ),
inference(cnf,[status(esa)],[315]) ).
thf(31,axiom,
! [B: $i,A: $i] :
( ~ ( geq @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( leq @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause107) ).
thf(261,plain,
! [B: $i,A: $i] :
( ~ ( geq @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( leq @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(55287,plain,
! [B: $i,A: $i] :
( ( geq @ B @ B )
| ( ( ssItem @ ( skaf55 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[395,373]) ).
thf(55288,plain,
! [A: $i] : ( geq @ ( skaf55 @ A ) @ ( skaf55 @ A ) ),
inference(pattern_uni,[status(thm)],[55287:[bind(A,$thf( C )),bind(B,$thf( skaf55 @ C ))]]) ).
thf(55317,plain,
! [A: $i] : ( geq @ ( skaf55 @ A ) @ ( skaf55 @ A ) ),
inference(simp,[status(thm)],[55288]) ).
thf(24,axiom,
! [A: $i] :
( ~ ( singletonP @ A )
| ~ ( ssList @ A )
| ( ( cons @ ( skaf44 @ A ) @ nil )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause101) ).
thf(246,plain,
! [A: $i] :
( ~ ( singletonP @ A )
| ~ ( ssList @ A )
| ( ( cons @ ( skaf44 @ A ) @ nil )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(247,plain,
! [A: $i] :
( ~ ( singletonP @ A )
| ~ ( ssList @ A )
| ( ( cons @ ( skaf44 @ A ) @ nil )
= A ) ),
inference(cnf,[status(esa)],[246]) ).
thf(248,plain,
! [A: $i] :
( ( ( cons @ ( skaf44 @ A ) @ nil )
= A )
| ~ ( singletonP @ A )
| ~ ( ssList @ A ) ),
inference(lifteq,[status(thm)],[247]) ).
thf(1640,plain,
! [A: $i] :
( ( ( cons @ ( skaf44 @ A ) @ nil )
= A )
| ~ ( singletonP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[200,248]) ).
thf(1641,plain,
( ( ( cons @ ( skaf44 @ sk1 ) @ nil )
= sk1 )
| ~ ( singletonP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[1640:[bind(A,$thf( sk1 ))]]) ).
thf(13927,plain,
! [A: $i] :
( ( ssList @ ( app @ sk2 @ A ) )
| ( ( ssList @ ( app @ sk2 @ ( tl @ sk2 ) ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13769,2922]) ).
thf(13928,plain,
ssList @ ( app @ sk2 @ ( app @ sk2 @ ( tl @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[13927:[bind(A,$thf( app @ sk2 @ ( tl @ sk2 ) ))]]) ).
thf(14779,plain,
! [A: $i] :
( ( ssList @ ( app @ sk2 @ A ) )
| ( ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( tl @ sk2 ) ) ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13928,2922]) ).
thf(14780,plain,
ssList @ ( app @ sk2 @ ( app @ sk2 @ ( app @ sk2 @ ( tl @ sk2 ) ) ) ),
inference(pattern_uni,[status(thm)],[14779:[bind(A,$thf( app @ sk2 @ ( app @ sk2 @ ( tl @ sk2 ) ) ))]]) ).
thf(174,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( segmentP @ A @ B )
| ~ ( ssList @ C )
| ~ ( ssList @ D )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( segmentP @ ( app @ ( app @ D @ A ) @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause172) ).
thf(591,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( segmentP @ A @ B )
| ~ ( ssList @ C )
| ~ ( ssList @ D )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( segmentP @ ( app @ ( app @ D @ A ) @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(110102,plain,
! [A: $i] :
( ( segmentP @ A @ nil )
| ( ( ssList @ ( app @ sk2 @ nil ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3973,429]) ).
thf(110103,plain,
segmentP @ ( app @ sk2 @ nil ) @ nil,
inference(pattern_uni,[status(thm)],[110102:[bind(A,$thf( app @ sk2 @ nil ))]]) ).
thf(128,axiom,
! [A: $i] : ( ssList @ ( skaf52 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause43) ).
thf(485,plain,
! [A: $i] : ( ssList @ ( skaf52 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(15352,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( skaf63 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[542,292]) ).
thf(15353,plain,
! [A: $i] : ( rearsegP @ ( skaf63 @ A ) @ nil ),
inference(pattern_uni,[status(thm)],[15352:[bind(A,$thf( C )),bind(B,$thf( skaf63 @ C ))]]) ).
thf(15554,plain,
! [A: $i] : ( rearsegP @ ( skaf63 @ A ) @ nil ),
inference(simp,[status(thm)],[15353]) ).
thf(84647,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ B )
| ( ( ssList @ ( skaf52 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[485,401]) ).
thf(84648,plain,
! [A: $i] : ( rearsegP @ ( skaf52 @ A ) @ ( skaf52 @ A ) ),
inference(pattern_uni,[status(thm)],[84647:[bind(A,$thf( C )),bind(B,$thf( skaf52 @ C ))]]) ).
thf(84906,plain,
! [A: $i] : ( rearsegP @ ( skaf52 @ A ) @ ( skaf52 @ A ) ),
inference(simp,[status(thm)],[84648]) ).
thf(652,plain,
! [A: $i] :
( ~ ( memberP @ nil @ A )
| ( ( ssItem @ skac2 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[525,438]) ).
thf(653,plain,
~ ( memberP @ nil @ skac2 ),
inference(pattern_uni,[status(thm)],[652:[bind(A,$thf( skac2 ))]]) ).
thf(26336,plain,
( ~ ( rearsegP @ nil @ sk1 )
| ~ ( memberP @ sk1 @ skac2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[21492,653]) ).
thf(26337,plain,
( ~ ( rearsegP @ nil @ sk1 )
| ~ ( memberP @ sk1 @ skac2 ) ),
inference(pattern_uni,[status(thm)],[26336:[]]) ).
thf(51369,plain,
( ~ ( memberP @ sk1 @ skac2 )
| ( ( rearsegP @ nil @ sk1 )
!= ( rearsegP @ sk1 @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[15489,26337]) ).
thf(51381,plain,
( ~ ( memberP @ sk1 @ skac2 )
| ( nil != sk1 )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[51369]) ).
thf(51451,plain,
( ~ ( memberP @ sk1 @ skac2 )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[51381]) ).
thf(21273,plain,
! [A: $i] :
( ( nil = A )
| ~ ( rearsegP @ nil @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[203,310]) ).
thf(21274,plain,
( ( nil = sk2 )
| ~ ( rearsegP @ nil @ sk2 ) ),
inference(pattern_uni,[status(thm)],[21273:[bind(A,$thf( sk2 ))]]) ).
thf(25581,plain,
( ~ ( rearsegP @ nil @ sk2 )
| ( nil = sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[21274,645]) ).
thf(25582,plain,
( ~ ( rearsegP @ nil @ sk2 )
| ( nil = sk1 ) ),
inference(pattern_uni,[status(thm)],[25581:[]]) ).
thf(20110,plain,
! [A: $i] :
( ~ ( rearsegP @ nil @ A )
| ~ ( ssList @ A )
| ( A != sk2 )
| ( nil != sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[310,216]) ).
thf(20111,plain,
! [A: $i] :
( ~ ( rearsegP @ nil @ A )
| ~ ( ssList @ A )
| ( A != sk2 )
| ( nil != sk1 ) ),
inference(pattern_uni,[status(thm)],[20110:[]]) ).
thf(21824,plain,
( ~ ( rearsegP @ nil @ sk2 )
| ~ ( ssList @ sk2 )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[20111]) ).
thf(24148,plain,
( ~ ( rearsegP @ nil @ sk2 )
| ~ $true
| ( nil != sk1 ) ),
inference(rewrite,[status(thm)],[21824,203]) ).
thf(24149,plain,
( ~ ( rearsegP @ nil @ sk2 )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[24148]) ).
thf(29978,plain,
( ~ ( rearsegP @ nil @ sk2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[25582,24149]) ).
thf(29979,plain,
~ ( rearsegP @ nil @ sk2 ),
inference(pattern_uni,[status(thm)],[29978:[]]) ).
thf(30435,plain,
( ~ ( rearsegP @ nil @ sk1 )
| ~ ( rearsegP @ sk1 @ sk2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[21492,29979]) ).
thf(30436,plain,
( ~ ( rearsegP @ nil @ sk1 )
| ~ ( rearsegP @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[30435:[]]) ).
thf(4257,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ( ( ssList @ ( app @ sk2 @ nil ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3973,236]) ).
thf(4258,plain,
~ ( neq @ ( app @ sk2 @ nil ) @ ( app @ sk2 @ nil ) ),
inference(pattern_uni,[status(thm)],[4257:[bind(A,$thf( app @ sk2 @ nil ))]]) ).
thf(110,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( app @ A @ nil )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause73) ).
thf(443,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( app @ A @ nil )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(77,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( ssList @ C )
| ( ( app @ ( app @ C @ B ) @ A )
= ( app @ C @ ( app @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause149) ).
thf(374,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( ssList @ C )
| ( ( app @ ( app @ C @ B ) @ A )
= ( app @ C @ ( app @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(375,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( ssList @ C )
| ( ( app @ ( app @ C @ B ) @ A )
= ( app @ C @ ( app @ B @ A ) ) ) ),
inference(cnf,[status(esa)],[374]) ).
thf(376,plain,
! [C: $i,B: $i,A: $i] :
( ( ( app @ ( app @ C @ B ) @ A )
= ( app @ C @ ( app @ B @ A ) ) )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( ssList @ C ) ),
inference(lifteq,[status(thm)],[375]) ).
thf(54,axiom,
! [A: $i] : ( ssList @ ( skaf57 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause38) ).
thf(317,plain,
! [A: $i] : ( ssList @ ( skaf57 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(15394,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( skaf57 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[317,292]) ).
thf(15395,plain,
! [A: $i] : ( rearsegP @ ( skaf57 @ A ) @ nil ),
inference(pattern_uni,[status(thm)],[15394:[bind(A,$thf( C )),bind(B,$thf( skaf57 @ C ))]]) ).
thf(15515,plain,
! [A: $i] : ( rearsegP @ ( skaf57 @ A ) @ nil ),
inference(simp,[status(thm)],[15395]) ).
thf(210,plain,
( ( ssItem @ sk5 )
| ~ ( neq @ sk4 @ nil ) ),
inference(cnf,[status(esa)],[202]) ).
thf(646,plain,
( ( ssItem @ sk5 )
| ~ ( neq @ sk2 @ nil ) ),
inference(rewrite,[status(thm)],[210,217]) ).
thf(6137,plain,
! [B: $i,A: $i] :
( ( ssList @ ( app @ sk2 @ B ) )
| ( ( ssList @ ( app @ sk2 @ ( skaf61 @ A ) ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4009,2922]) ).
thf(6138,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( skaf61 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[6137:[bind(A,$thf( E )),bind(B,$thf( app @ sk2 @ ( skaf61 @ E ) ))]]) ).
thf(6189,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( skaf61 @ A ) ) ) ),
inference(simp,[status(thm)],[6138]) ).
thf(27,axiom,
! [A: $i] : ( ssItem @ ( skaf79 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause16) ).
thf(253,plain,
! [A: $i] : ( ssItem @ ( skaf79 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(63,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( app @ nil @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause74) ).
thf(336,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( app @ nil @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(337,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( app @ nil @ A )
= A ) ),
inference(cnf,[status(esa)],[336]) ).
thf(338,plain,
! [A: $i] :
( ( ( app @ nil @ A )
= A )
| ~ ( ssList @ A ) ),
inference(lifteq,[status(thm)],[337]) ).
thf(31155,plain,
! [A: $i] :
( ( ( app @ nil @ A )
= A )
| ( ( ssList @ ( app @ sk2 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3892,338]) ).
thf(31156,plain,
( ( app @ nil @ ( app @ sk2 @ sk2 ) )
= ( app @ sk2 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[31155:[bind(A,$thf( app @ sk2 @ sk2 ))]]) ).
thf(101992,plain,
( ~ ( rearsegP @ sk1 @ sk2 )
| ( ( rearsegP @ nil @ sk1 )
!= ( rearsegP @ sk1 @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[15489,30436]) ).
thf(102071,plain,
( ~ ( rearsegP @ sk1 @ sk2 )
| ( nil != sk1 )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[101992]) ).
thf(102179,plain,
( ~ ( rearsegP @ sk1 @ sk2 )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[102071]) ).
thf(20,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( lt @ B @ C )
| ~ ( ssItem @ C )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( lt @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause147) ).
thf(238,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( lt @ B @ C )
| ~ ( ssItem @ C )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( lt @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(84776,plain,
! [A: $i] :
( ( rearsegP @ A @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[203,401]) ).
thf(84777,plain,
rearsegP @ sk2 @ sk2,
inference(pattern_uni,[status(thm)],[84776:[bind(A,$thf( sk2 ))]]) ).
thf(140,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( app @ A @ ( cons @ B @ C ) )
!= D )
| ~ ( ssList @ C )
| ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ~ ( ssList @ D )
| ( memberP @ D @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause175) ).
thf(514,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( app @ A @ ( cons @ B @ C ) )
!= D )
| ~ ( ssList @ C )
| ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ~ ( ssList @ D )
| ( memberP @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(68,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ~ ( gt @ B @ C )
| ~ ( ssItem @ C )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( gt @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause146) ).
thf(348,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ~ ( gt @ B @ C )
| ~ ( ssItem @ C )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( gt @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(164,axiom,
! [A: $i] : ( ssItem @ ( skaf83 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause12) ).
thf(574,plain,
! [A: $i] : ( ssItem @ ( skaf83 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(70,axiom,
! [A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ( rearsegP @ nil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause81) ).
thf(353,plain,
! [A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ( rearsegP @ nil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(28010,plain,
! [B: $i,A: $i] :
( ( strictorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf55 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[395,328]) ).
thf(28011,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf55 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[28010:[bind(A,$thf( C )),bind(B,$thf( skaf55 @ C ))]]) ).
thf(28032,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf55 @ A ) @ nil ) ),
inference(simp,[status(thm)],[28011]) ).
thf(698,plain,
! [A: $i] :
( ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ skac3 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[538,697]) ).
thf(699,plain,
totalorderedP @ ( cons @ skac3 @ nil ),
inference(pattern_uni,[status(thm)],[698:[bind(A,$thf( skac3 ))]]) ).
thf(12329,plain,
( ( ssList @ ( tl @ sk1 ) )
| ( totalorderedP @ ( cons @ skac3 @ sk1 ) )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[10975,699]) ).
thf(12330,plain,
( ( ssList @ ( tl @ sk1 ) )
| ( totalorderedP @ ( cons @ skac3 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[12329:[]]) ).
thf(27948,plain,
! [B: $i,A: $i] :
( ( strictorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf79 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[253,328]) ).
thf(27949,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf79 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[27948:[bind(A,$thf( C )),bind(B,$thf( skaf79 @ C ))]]) ).
thf(28033,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf79 @ A ) @ nil ) ),
inference(simp,[status(thm)],[27949]) ).
thf(39,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( totalorderedP @ A )
| ( ( app @ ( app @ ( skaf66 @ A ) @ ( cons @ ( skaf64 @ A ) @ ( skaf67 @ A ) ) ) @ ( cons @ ( skaf65 @ A ) @ ( skaf68 @ A ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause164) ).
thf(280,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( totalorderedP @ A )
| ( ( app @ ( app @ ( skaf66 @ A ) @ ( cons @ ( skaf64 @ A ) @ ( skaf67 @ A ) ) ) @ ( cons @ ( skaf65 @ A ) @ ( skaf68 @ A ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(44,axiom,
! [B: $i,A: $i] :
( ( ( app @ A @ B )
!= nil )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( nil = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause118) ).
thf(293,plain,
! [B: $i,A: $i] :
( ( ( app @ A @ B )
!= nil )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(856,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf77 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[304,236]) ).
thf(857,plain,
! [A: $i] :
~ ( neq @ ( skaf77 @ A ) @ ( skaf77 @ A ) ),
inference(pattern_uni,[status(thm)],[856:[bind(A,$thf( C )),bind(B,$thf( skaf77 @ C ))]]) ).
thf(866,plain,
! [A: $i] :
~ ( neq @ ( skaf77 @ A ) @ ( skaf77 @ A ) ),
inference(simp,[status(thm)],[857]) ).
thf(87,axiom,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( leq @ B @ A )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause130) ).
thf(396,plain,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( leq @ B @ A )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(9647,plain,
! [B: $i,A: $i] :
( ( ssList @ ( app @ sk2 @ B ) )
| ( ( ssList @ ( app @ sk2 @ ( skaf80 @ A ) ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4023,2922]) ).
thf(9648,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( skaf80 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[9647:[bind(A,$thf( E )),bind(B,$thf( app @ sk2 @ ( skaf80 @ E ) ))]]) ).
thf(9700,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( skaf80 @ A ) ) ) ),
inference(simp,[status(thm)],[9648]) ).
thf(3,negated_conjecture,
ssList @ sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
thf(206,plain,
ssList @ sk3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12155,plain,
( ( ssList @ ( tl @ sk1 ) )
| ( cyclefreeP @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[10975,480]) ).
thf(12156,plain,
( ( ssList @ ( tl @ sk1 ) )
| ( cyclefreeP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[12155:[]]) ).
thf(16724,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( ssList @ ( app @ sk2 @ A ) )
| ( ( ssList @ ( tl @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12156,2922]) ).
thf(16725,plain,
( ( cyclefreeP @ sk1 )
| ( ssList @ ( app @ sk2 @ ( tl @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[16724:[bind(A,$thf( tl @ sk1 ))]]) ).
thf(115,axiom,
! [A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ( segmentP @ nil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause79) ).
thf(453,plain,
! [A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ( segmentP @ nil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(94,axiom,
! [B: $i,A: $i] :
( ~ ( lt @ A @ ( hd @ B ) )
| ~ ( strictorderedP @ B )
| ~ ( ssList @ B )
| ~ ( ssItem @ A )
| ( strictorderedP @ ( cons @ A @ B ) )
| ( nil = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause160) ).
thf(409,plain,
! [B: $i,A: $i] :
( ~ ( lt @ A @ ( hd @ B ) )
| ~ ( strictorderedP @ B )
| ~ ( ssList @ B )
| ~ ( ssItem @ A )
| ( strictorderedP @ ( cons @ A @ B ) )
| ( nil = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(410,plain,
! [B: $i,A: $i] :
( ~ ( lt @ A @ ( hd @ B ) )
| ~ ( strictorderedP @ B )
| ~ ( ssList @ B )
| ~ ( ssItem @ A )
| ( strictorderedP @ ( cons @ A @ B ) )
| ( nil = B ) ),
inference(cnf,[status(esa)],[409]) ).
thf(411,plain,
! [B: $i,A: $i] :
( ( nil = B )
| ~ ( lt @ A @ ( hd @ B ) )
| ~ ( strictorderedP @ B )
| ~ ( ssList @ B )
| ~ ( ssItem @ A )
| ( strictorderedP @ ( cons @ A @ B ) ) ),
inference(lifteq,[status(thm)],[410]) ).
thf(167,axiom,
! [A: $i] : ( ssList @ ( skaf82 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause13) ).
thf(579,plain,
! [A: $i] : ( ssList @ ( skaf82 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(1338,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf82 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[579,236]) ).
thf(1339,plain,
! [A: $i] :
~ ( neq @ ( skaf82 @ A ) @ ( skaf82 @ A ) ),
inference(pattern_uni,[status(thm)],[1338:[bind(A,$thf( C )),bind(B,$thf( skaf82 @ C ))]]) ).
thf(1345,plain,
! [A: $i] :
~ ( neq @ ( skaf82 @ A ) @ ( skaf82 @ A ) ),
inference(simp,[status(thm)],[1339]) ).
thf(1200,plain,
! [A: $i] :
( ~ ( lt @ ( skaf69 @ A ) @ ( skaf70 @ A ) )
| ( strictorderedP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[203,243]) ).
thf(1201,plain,
( ~ ( lt @ ( skaf69 @ sk2 ) @ ( skaf70 @ sk2 ) )
| ( strictorderedP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[1200:[bind(A,$thf( sk2 ))]]) ).
thf(32,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( strictorderedP @ A )
| ( ( app @ ( app @ ( skaf71 @ A ) @ ( cons @ ( skaf69 @ A ) @ ( skaf72 @ A ) ) ) @ ( cons @ ( skaf70 @ A ) @ ( skaf73 @ A ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause163) ).
thf(263,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( strictorderedP @ A )
| ( ( app @ ( app @ ( skaf71 @ A ) @ ( cons @ ( skaf69 @ A ) @ ( skaf72 @ A ) ) ) @ ( cons @ ( skaf70 @ A ) @ ( skaf73 @ A ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(264,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( strictorderedP @ A )
| ( ( app @ ( app @ ( skaf71 @ A ) @ ( cons @ ( skaf69 @ A ) @ ( skaf72 @ A ) ) ) @ ( cons @ ( skaf70 @ A ) @ ( skaf73 @ A ) ) )
= A ) ),
inference(cnf,[status(esa)],[263]) ).
thf(265,plain,
! [A: $i] :
( ( ( app @ ( app @ ( skaf71 @ A ) @ ( cons @ ( skaf69 @ A ) @ ( skaf72 @ A ) ) ) @ ( cons @ ( skaf70 @ A ) @ ( skaf73 @ A ) ) )
= A )
| ~ ( ssList @ A )
| ( strictorderedP @ A ) ),
inference(lifteq,[status(thm)],[264]) ).
thf(26334,plain,
( ~ ( rearsegP @ nil @ sk1 )
| ( strictorderP @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[21492,299]) ).
thf(26335,plain,
( ~ ( rearsegP @ nil @ sk1 )
| ( strictorderP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[26334:[]]) ).
thf(67794,plain,
( ( strictorderP @ sk1 )
| ( ( rearsegP @ nil @ sk1 )
!= ( rearsegP @ sk1 @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[15489,26335]) ).
thf(67862,plain,
( ( strictorderP @ sk1 )
| ( nil != sk1 )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[67794]) ).
thf(67869,plain,
( ( strictorderP @ sk1 )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[67862]) ).
thf(49,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( cyclefreeP @ A )
| ( ( app @ ( app @ ( skaf51 @ A ) @ ( cons @ ( skaf49 @ A ) @ ( skaf52 @ A ) ) ) @ ( cons @ ( skaf50 @ A ) @ ( skaf53 @ A ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause167) ).
thf(305,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( cyclefreeP @ A )
| ( ( app @ ( app @ ( skaf51 @ A ) @ ( cons @ ( skaf49 @ A ) @ ( skaf52 @ A ) ) ) @ ( cons @ ( skaf50 @ A ) @ ( skaf53 @ A ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(306,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( cyclefreeP @ A )
| ( ( app @ ( app @ ( skaf51 @ A ) @ ( cons @ ( skaf49 @ A ) @ ( skaf52 @ A ) ) ) @ ( cons @ ( skaf50 @ A ) @ ( skaf53 @ A ) ) )
= A ) ),
inference(cnf,[status(esa)],[305]) ).
thf(307,plain,
! [A: $i] :
( ( ( app @ ( app @ ( skaf51 @ A ) @ ( cons @ ( skaf49 @ A ) @ ( skaf52 @ A ) ) ) @ ( cons @ ( skaf50 @ A ) @ ( skaf53 @ A ) ) )
= A )
| ~ ( ssList @ A )
| ( cyclefreeP @ A ) ),
inference(lifteq,[status(thm)],[306]) ).
thf(110303,plain,
! [A: $i] :
( ( segmentP @ A @ nil )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[200,429]) ).
thf(110304,plain,
segmentP @ sk1 @ nil,
inference(pattern_uni,[status(thm)],[110303:[bind(A,$thf( sk1 ))]]) ).
thf(3974,plain,
! [B: $i,A: $i] :
( ( ssList @ ( app @ sk2 @ B ) )
| ( ( ssList @ ( skaf76 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[603,2922]) ).
thf(3975,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( skaf76 @ A ) ) ),
inference(pattern_uni,[status(thm)],[3974:[bind(A,$thf( C )),bind(B,$thf( skaf76 @ C ))]]) ).
thf(3991,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( skaf76 @ A ) ) ),
inference(simp,[status(thm)],[3975]) ).
thf(4587,plain,
! [B: $i,A: $i] :
( ( ssList @ ( app @ sk2 @ B ) )
| ( ( ssList @ ( app @ sk2 @ ( skaf76 @ A ) ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3991,2922]) ).
thf(4588,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( skaf76 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[4587:[bind(A,$thf( E )),bind(B,$thf( app @ sk2 @ ( skaf76 @ E ) ))]]) ).
thf(4629,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( skaf76 @ A ) ) ) ),
inference(simp,[status(thm)],[4588]) ).
thf(649,plain,
! [A: $i] :
( ~ ( memberP @ nil @ A )
| ( ( ssItem @ skac3 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[538,438]) ).
thf(650,plain,
~ ( memberP @ nil @ skac3 ),
inference(pattern_uni,[status(thm)],[649:[bind(A,$thf( skac3 ))]]) ).
thf(12199,plain,
( ( ssList @ ( tl @ sk1 ) )
| ~ ( memberP @ sk1 @ skac3 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[10975,650]) ).
thf(12200,plain,
( ( ssList @ ( tl @ sk1 ) )
| ~ ( memberP @ sk1 @ skac3 ) ),
inference(pattern_uni,[status(thm)],[12199:[]]) ).
thf(799,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf55 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[395,697]) ).
thf(800,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf55 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[799:[bind(A,$thf( C )),bind(B,$thf( skaf55 @ C ))]]) ).
thf(810,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf55 @ A ) @ nil ) ),
inference(simp,[status(thm)],[800]) ).
thf(380,plain,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( neq @ B @ A )
| ( B = A ) ),
inference(cnf,[status(esa)],[379]) ).
thf(381,plain,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( neq @ B @ A ) ),
inference(lifteq,[status(thm)],[380]) ).
thf(84778,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ B )
| ( ( ssList @ ( skaf77 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[304,401]) ).
thf(84779,plain,
! [A: $i] : ( rearsegP @ ( skaf77 @ A ) @ ( skaf77 @ A ) ),
inference(pattern_uni,[status(thm)],[84778:[bind(A,$thf( C )),bind(B,$thf( skaf77 @ C ))]]) ).
thf(84859,plain,
! [A: $i] : ( rearsegP @ ( skaf77 @ A ) @ ( skaf77 @ A ) ),
inference(simp,[status(thm)],[84779]) ).
thf(74,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( frontsegP @ A @ B )
| ( C != D )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ~ ( ssItem @ D )
| ~ ( ssItem @ C )
| ( frontsegP @ ( cons @ C @ A ) @ ( cons @ D @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause178) ).
thf(366,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( frontsegP @ A @ B )
| ( C != D )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ~ ( ssItem @ D )
| ~ ( ssItem @ C )
| ( frontsegP @ ( cons @ C @ A ) @ ( cons @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(3905,plain,
! [B: $i,A: $i] :
( ( ssList @ ( app @ sk2 @ B ) )
| ( ( ssList @ ( skaf75 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[452,2922]) ).
thf(3906,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( skaf75 @ A ) ) ),
inference(pattern_uni,[status(thm)],[3905:[bind(A,$thf( C )),bind(B,$thf( skaf75 @ C ))]]) ).
thf(3987,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( skaf75 @ A ) ) ),
inference(simp,[status(thm)],[3906]) ).
thf(4531,plain,
! [B: $i,A: $i] :
( ( ssList @ ( app @ sk2 @ B ) )
| ( ( ssList @ ( app @ sk2 @ ( skaf75 @ A ) ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3987,2922]) ).
thf(4532,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( skaf75 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[4531:[bind(A,$thf( E )),bind(B,$thf( app @ sk2 @ ( skaf75 @ E ) ))]]) ).
thf(4576,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( skaf75 @ A ) ) ) ),
inference(simp,[status(thm)],[4532]) ).
thf(15494,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( skaf66 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[543,292]) ).
thf(15495,plain,
! [A: $i] : ( rearsegP @ ( skaf66 @ A ) @ nil ),
inference(pattern_uni,[status(thm)],[15494:[bind(A,$thf( C )),bind(B,$thf( skaf66 @ C ))]]) ).
thf(15503,plain,
! [A: $i] : ( rearsegP @ ( skaf66 @ A ) @ nil ),
inference(simp,[status(thm)],[15495]) ).
thf(108,axiom,
! [A: $i] :
( ~ ( ssItem @ A )
| ( equalelemsP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause64) ).
thf(439,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( equalelemsP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(13824,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssItem @ ( skaf65 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[583,286]) ).
thf(13825,plain,
! [A: $i] :
~ ( neq @ ( skaf65 @ A ) @ ( skaf65 @ A ) ),
inference(pattern_uni,[status(thm)],[13824:[bind(A,$thf( C )),bind(B,$thf( skaf65 @ C ))]]) ).
thf(13848,plain,
! [A: $i] :
~ ( neq @ ( skaf65 @ A ) @ ( skaf65 @ A ) ),
inference(simp,[status(thm)],[13825]) ).
thf(34,axiom,
! [B: $i,A: $i] : ( ssList @ ( skaf46 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause50) ).
thf(270,plain,
! [B: $i,A: $i] : ( ssList @ ( skaf46 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(15402,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( skaf56 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[590,292]) ).
thf(15403,plain,
! [A: $i] : ( rearsegP @ ( skaf56 @ A ) @ nil ),
inference(pattern_uni,[status(thm)],[15402:[bind(A,$thf( C )),bind(B,$thf( skaf56 @ C ))]]) ).
thf(15518,plain,
! [A: $i] : ( rearsegP @ ( skaf56 @ A ) @ nil ),
inference(simp,[status(thm)],[15403]) ).
thf(16664,plain,
! [A: $i] :
( ~ ( singletonP @ sk1 )
| ~ ( neq @ A @ A )
| ( ( ssList @ ( tl @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12148,236]) ).
thf(16665,plain,
( ~ ( singletonP @ sk1 )
| ~ ( neq @ ( tl @ sk1 ) @ ( tl @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[16664:[bind(A,$thf( tl @ sk1 ))]]) ).
thf(55270,plain,
! [B: $i,A: $i] :
( ( geq @ B @ B )
| ( ( ssItem @ ( skaf69 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[394,373]) ).
thf(55271,plain,
! [A: $i] : ( geq @ ( skaf69 @ A ) @ ( skaf69 @ A ) ),
inference(pattern_uni,[status(thm)],[55270:[bind(A,$thf( C )),bind(B,$thf( skaf69 @ C ))]]) ).
thf(55312,plain,
! [A: $i] : ( geq @ ( skaf69 @ A ) @ ( skaf69 @ A ) ),
inference(simp,[status(thm)],[55271]) ).
thf(3899,plain,
! [B: $i,A: $i] :
( ( ssList @ ( app @ sk2 @ B ) )
| ( ( ssList @ ( skaf52 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[485,2922]) ).
thf(3900,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( skaf52 @ A ) ) ),
inference(pattern_uni,[status(thm)],[3899:[bind(A,$thf( C )),bind(B,$thf( skaf52 @ C ))]]) ).
thf(4025,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( skaf52 @ A ) ) ),
inference(simp,[status(thm)],[3900]) ).
thf(11365,plain,
! [B: $i,A: $i] :
( ( ssList @ ( app @ sk2 @ B ) )
| ( ( ssList @ ( app @ sk2 @ ( skaf52 @ A ) ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4025,2922]) ).
thf(11366,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( skaf52 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[11365:[bind(A,$thf( E )),bind(B,$thf( app @ sk2 @ ( skaf52 @ E ) ))]]) ).
thf(11424,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( skaf52 @ A ) ) ) ),
inference(simp,[status(thm)],[11366]) ).
thf(334,plain,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( lt @ B @ A ) ),
inference(cnf,[status(esa)],[333]) ).
thf(3889,plain,
! [B: $i,A: $i] :
( ( ssList @ ( app @ sk2 @ B ) )
| ( ( ssList @ ( skaf63 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[542,2922]) ).
thf(3890,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( skaf63 @ A ) ) ),
inference(pattern_uni,[status(thm)],[3889:[bind(A,$thf( C )),bind(B,$thf( skaf63 @ C ))]]) ).
thf(4016,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( skaf63 @ A ) ) ),
inference(simp,[status(thm)],[3890]) ).
thf(175,axiom,
! [A: $i] : ( ssItem @ ( skaf50 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause45) ).
thf(593,plain,
! [A: $i] : ( ssItem @ ( skaf50 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(13828,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssItem @ ( skaf50 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[593,286]) ).
thf(13829,plain,
! [A: $i] :
~ ( neq @ ( skaf50 @ A ) @ ( skaf50 @ A ) ),
inference(pattern_uni,[status(thm)],[13828:[bind(A,$thf( C )),bind(B,$thf( skaf50 @ C ))]]) ).
thf(13850,plain,
! [A: $i] :
~ ( neq @ ( skaf50 @ A ) @ ( skaf50 @ A ) ),
inference(simp,[status(thm)],[13829]) ).
thf(178,axiom,
! [B: $i,A: $i] :
( ~ ( memberP @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssList @ A )
| ( ( app @ ( skaf42 @ A @ B ) @ ( cons @ B @ ( skaf43 @ B @ A ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause169) ).
thf(598,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssList @ A )
| ( ( app @ ( skaf42 @ A @ B ) @ ( cons @ B @ ( skaf43 @ B @ A ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(159,axiom,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( lt @ A @ B )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause122) ).
thf(561,plain,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( lt @ A @ B )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(15440,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( skaf73 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[387,292]) ).
thf(15441,plain,
! [A: $i] : ( rearsegP @ ( skaf73 @ A ) @ nil ),
inference(pattern_uni,[status(thm)],[15440:[bind(A,$thf( C )),bind(B,$thf( skaf73 @ C ))]]) ).
thf(15531,plain,
! [A: $i] : ( rearsegP @ ( skaf73 @ A ) @ nil ),
inference(simp,[status(thm)],[15441]) ).
thf(13818,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssItem @ ( skaf83 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[574,286]) ).
thf(13819,plain,
! [A: $i] :
~ ( neq @ ( skaf83 @ A ) @ ( skaf83 @ A ) ),
inference(pattern_uni,[status(thm)],[13818:[bind(A,$thf( C )),bind(B,$thf( skaf83 @ C ))]]) ).
thf(13860,plain,
! [A: $i] :
~ ( neq @ ( skaf83 @ A ) @ ( skaf83 @ A ) ),
inference(simp,[status(thm)],[13819]) ).
thf(52,axiom,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ( duplicatefreeP @ A )
| ( ssItem @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause72) ).
thf(313,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ( duplicatefreeP @ A )
| ( ssItem @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(314,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ( duplicatefreeP @ A )
| ( ssItem @ B ) ),
inference(cnf,[status(esa)],[313]) ).
thf(23057,plain,
! [B: $i,A: $i] :
( ( duplicatefreeP @ A )
| ( ssItem @ B )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[200,314]) ).
thf(23058,plain,
! [A: $i] :
( ( duplicatefreeP @ sk1 )
| ( ssItem @ A ) ),
inference(pattern_uni,[status(thm)],[23057:[bind(A,$thf( sk1 ))]]) ).
thf(23081,plain,
! [A: $i] :
( ( duplicatefreeP @ sk1 )
| ( ssItem @ A ) ),
inference(simp,[status(thm)],[23058]) ).
thf(26110,plain,
( ~ ( rearsegP @ nil @ sk1 )
| ~ ( singletonP @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[21492,492]) ).
thf(26111,plain,
( ~ ( rearsegP @ nil @ sk1 )
| ~ ( singletonP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[26110:[]]) ).
thf(29598,plain,
( ~ ( singletonP @ sk1 )
| ( ( rearsegP @ nil @ sk1 )
!= ( rearsegP @ sk1 @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[15489,26111]) ).
thf(29620,plain,
( ~ ( singletonP @ sk1 )
| ( nil != sk1 )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[29598]) ).
thf(29650,plain,
( ~ ( singletonP @ sk1 )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[29620]) ).
thf(30,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( frontsegP @ A @ B )
| ~ ( frontsegP @ B @ C )
| ~ ( ssList @ C )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( frontsegP @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause154) ).
thf(259,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( frontsegP @ A @ B )
| ~ ( frontsegP @ B @ C )
| ~ ( ssList @ C )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( frontsegP @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(260,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( frontsegP @ A @ B )
| ~ ( frontsegP @ B @ C )
| ~ ( ssList @ C )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( frontsegP @ A @ C ) ),
inference(cnf,[status(esa)],[259]) ).
thf(349,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ~ ( gt @ B @ C )
| ~ ( ssItem @ C )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( gt @ A @ C ) ),
inference(cnf,[status(esa)],[348]) ).
thf(122,axiom,
! [A: $i] : ( ssList @ ( skaf68 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause27) ).
thf(474,plain,
! [A: $i] : ( ssList @ ( skaf68 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(3976,plain,
! [B: $i,A: $i] :
( ( ssList @ ( app @ sk2 @ B ) )
| ( ( ssList @ ( skaf68 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[474,2922]) ).
thf(3977,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( skaf68 @ A ) ) ),
inference(pattern_uni,[status(thm)],[3976:[bind(A,$thf( C )),bind(B,$thf( skaf68 @ C ))]]) ).
thf(3993,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( skaf68 @ A ) ) ),
inference(simp,[status(thm)],[3977]) ).
thf(5322,plain,
! [B: $i,A: $i] :
( ( ssList @ ( app @ sk2 @ B ) )
| ( ( ssList @ ( app @ sk2 @ ( skaf68 @ A ) ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3993,2922]) ).
thf(5323,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( skaf68 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[5322:[bind(A,$thf( E )),bind(B,$thf( app @ sk2 @ ( skaf68 @ E ) ))]]) ).
thf(5366,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( skaf68 @ A ) ) ) ),
inference(simp,[status(thm)],[5323]) ).
thf(100,axiom,
! [B: $i,A: $i] : ( ssList @ ( skaf48 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause48) ).
thf(424,plain,
! [B: $i,A: $i] : ( ssList @ ( skaf48 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(784,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf69 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[394,438]) ).
thf(785,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf69 @ A ) ),
inference(pattern_uni,[status(thm)],[784:[bind(A,$thf( C )),bind(B,$thf( skaf69 @ C ))]]) ).
thf(788,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf69 @ A ) ),
inference(simp,[status(thm)],[785]) ).
thf(26,axiom,
! [A: $i] : ( ssList @ ( skaf72 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause23) ).
thf(252,plain,
! [A: $i] : ( ssList @ ( skaf72 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(15428,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( skaf61 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[402,292]) ).
thf(15429,plain,
! [A: $i] : ( rearsegP @ ( skaf61 @ A ) @ nil ),
inference(pattern_uni,[status(thm)],[15428:[bind(A,$thf( C )),bind(B,$thf( skaf61 @ C ))]]) ).
thf(15527,plain,
! [A: $i] : ( rearsegP @ ( skaf61 @ A ) @ nil ),
inference(simp,[status(thm)],[15429]) ).
thf(110246,plain,
! [A: $i] :
( ( segmentP @ A @ nil )
| ( ( ssList @ ( app @ sk2 @ ( tl @ sk2 ) ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13769,429]) ).
thf(110247,plain,
segmentP @ ( app @ sk2 @ ( tl @ sk2 ) ) @ nil,
inference(pattern_uni,[status(thm)],[110246:[bind(A,$thf( app @ sk2 @ ( tl @ sk2 ) ))]]) ).
thf(132,axiom,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( lt @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause111) ).
thf(493,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( lt @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(3940,plain,
! [B: $i,A: $i] :
( ( ssList @ ( app @ sk2 @ B ) )
| ( ( ssList @ ( skaf82 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[579,2922]) ).
thf(3941,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( skaf82 @ A ) ) ),
inference(pattern_uni,[status(thm)],[3940:[bind(A,$thf( C )),bind(B,$thf( skaf82 @ C ))]]) ).
thf(4010,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( skaf82 @ A ) ) ),
inference(simp,[status(thm)],[3941]) ).
thf(15468,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( app @ sk2 @ ( skaf82 @ A ) ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4010,292]) ).
thf(15469,plain,
! [A: $i] : ( rearsegP @ ( app @ sk2 @ ( skaf82 @ A ) ) @ nil ),
inference(pattern_uni,[status(thm)],[15468:[bind(A,$thf( E )),bind(B,$thf( app @ sk2 @ ( skaf82 @ E ) ))]]) ).
thf(15546,plain,
! [A: $i] : ( rearsegP @ ( app @ sk2 @ ( skaf82 @ A ) ) @ nil ),
inference(simp,[status(thm)],[15469]) ).
thf(84698,plain,
! [A: $i] :
( ( rearsegP @ A @ A )
| ( ( ssList @ ( tl @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13718,401]) ).
thf(84699,plain,
rearsegP @ ( tl @ sk2 ) @ ( tl @ sk2 ),
inference(pattern_uni,[status(thm)],[84698:[bind(A,$thf( tl @ sk2 ))]]) ).
thf(4379,plain,
! [A: $i] :
( ( ssList @ ( app @ sk2 @ A ) )
| ( ( ssList @ ( app @ sk2 @ ( app @ sk2 @ nil ) ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4238,2922]) ).
thf(4380,plain,
ssList @ ( app @ sk2 @ ( app @ sk2 @ ( app @ sk2 @ nil ) ) ),
inference(pattern_uni,[status(thm)],[4379:[bind(A,$thf( app @ sk2 @ ( app @ sk2 @ nil ) ))]]) ).
thf(15416,plain,
! [A: $i] :
( ( rearsegP @ A @ nil )
| ( ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( app @ sk2 @ nil ) ) ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4380,292]) ).
thf(15417,plain,
rearsegP @ ( app @ sk2 @ ( app @ sk2 @ ( app @ sk2 @ nil ) ) ) @ nil,
inference(pattern_uni,[status(thm)],[15416:[bind(A,$thf( app @ sk2 @ ( app @ sk2 @ ( app @ sk2 @ nil ) ) ))]]) ).
thf(15362,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( skaf52 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[485,292]) ).
thf(15363,plain,
! [A: $i] : ( rearsegP @ ( skaf52 @ A ) @ nil ),
inference(pattern_uni,[status(thm)],[15362:[bind(A,$thf( C )),bind(B,$thf( skaf52 @ C ))]]) ).
thf(15498,plain,
! [A: $i] : ( rearsegP @ ( skaf52 @ A ) @ nil ),
inference(simp,[status(thm)],[15363]) ).
thf(84649,plain,
! [A: $i] :
( ( rearsegP @ A @ A )
| ( ( ssList @ ( app @ sk2 @ nil ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3973,401]) ).
thf(84650,plain,
rearsegP @ ( app @ sk2 @ nil ) @ ( app @ sk2 @ nil ),
inference(pattern_uni,[status(thm)],[84649:[bind(A,$thf( app @ sk2 @ nil ))]]) ).
thf(59,axiom,
! [B: $i,A: $i] : ( ssList @ ( skaf45 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause51) ).
thf(329,plain,
! [B: $i,A: $i] : ( ssList @ ( skaf45 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(13788,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ( ( ssList @ ( tl @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13718,236]) ).
thf(13789,plain,
~ ( neq @ ( tl @ sk2 ) @ ( tl @ sk2 ) ),
inference(pattern_uni,[status(thm)],[13788:[bind(A,$thf( tl @ sk2 ))]]) ).
thf(88,axiom,
! [A: $i] : ( ssItem @ ( skaf70 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause25) ).
thf(399,plain,
! [A: $i] : ( ssItem @ ( skaf70 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(27988,plain,
! [B: $i,A: $i] :
( ( strictorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf70 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[399,328]) ).
thf(27989,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf70 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[27988:[bind(A,$thf( C )),bind(B,$thf( skaf70 @ C ))]]) ).
thf(28019,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf70 @ A ) @ nil ) ),
inference(simp,[status(thm)],[27989]) ).
thf(13834,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssItem @ ( skaf70 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[399,286]) ).
thf(13835,plain,
! [A: $i] :
~ ( neq @ ( skaf70 @ A ) @ ( skaf70 @ A ) ),
inference(pattern_uni,[status(thm)],[13834:[bind(A,$thf( C )),bind(B,$thf( skaf70 @ C ))]]) ).
thf(13853,plain,
! [A: $i] :
~ ( neq @ ( skaf70 @ A ) @ ( skaf70 @ A ) ),
inference(simp,[status(thm)],[13835]) ).
thf(27940,plain,
! [A: $i] :
( ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ skac3 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[538,328]) ).
thf(27941,plain,
strictorderedP @ ( cons @ skac3 @ nil ),
inference(pattern_uni,[status(thm)],[27940:[bind(A,$thf( skac3 ))]]) ).
thf(15484,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( app @ sk2 @ ( skaf67 @ A ) ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4024,292]) ).
thf(15485,plain,
! [A: $i] : ( rearsegP @ ( app @ sk2 @ ( skaf67 @ A ) ) @ nil ),
inference(pattern_uni,[status(thm)],[15484:[bind(A,$thf( E )),bind(B,$thf( app @ sk2 @ ( skaf67 @ E ) ))]]) ).
thf(15559,plain,
! [A: $i] : ( rearsegP @ ( app @ sk2 @ ( skaf67 @ A ) ) @ nil ),
inference(simp,[status(thm)],[15485]) ).
thf(1511,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf50 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[593,697]) ).
thf(1512,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf50 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[1511:[bind(A,$thf( C )),bind(B,$thf( skaf50 @ C ))]]) ).
thf(1534,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf50 @ A ) @ nil ) ),
inference(simp,[status(thm)],[1512]) ).
thf(15390,plain,
! [C: $i,B: $i,A: $i] :
( ( rearsegP @ C @ nil )
| ( ( ssList @ ( skaf45 @ A @ B ) )
!= ( ssList @ C ) ) ),
inference(paramod_ordered,[status(thm)],[329,292]) ).
thf(15391,plain,
! [B: $i,A: $i] : ( rearsegP @ ( skaf45 @ A @ B ) @ nil ),
inference(pattern_uni,[status(thm)],[15390:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( skaf45 @ D @ E ))]]) ).
thf(15513,plain,
! [B: $i,A: $i] : ( rearsegP @ ( skaf45 @ A @ B ) @ nil ),
inference(simp,[status(thm)],[15391]) ).
thf(91,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( app @ A @ B )
!= ( app @ C @ B ) )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( ssList @ C )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause151) ).
thf(403,plain,
! [C: $i,B: $i,A: $i] :
( ( ( app @ A @ B )
!= ( app @ C @ B ) )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( ssList @ C )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(83,axiom,
! [B: $i,A: $i] :
( ~ ( rearsegP @ A @ B )
| ~ ( rearsegP @ B @ A )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause128) ).
thf(388,plain,
! [B: $i,A: $i] :
( ~ ( rearsegP @ A @ B )
| ~ ( rearsegP @ B @ A )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(113,axiom,
! [A: $i] : ( ssList @ ( skaf53 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause42) ).
thf(451,plain,
! [A: $i] : ( ssList @ ( skaf53 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(3945,plain,
! [B: $i,A: $i] :
( ( ssList @ ( app @ sk2 @ B ) )
| ( ( ssList @ ( skaf53 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[451,2922]) ).
thf(3946,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( skaf53 @ A ) ) ),
inference(pattern_uni,[status(thm)],[3945:[bind(A,$thf( C )),bind(B,$thf( skaf53 @ C ))]]) ).
thf(4012,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( skaf53 @ A ) ) ),
inference(simp,[status(thm)],[3946]) ).
thf(184,axiom,
! [A: $i] :
( ( ( skaf79 @ A )
!= ( skaf78 @ A ) )
| ~ ( ssList @ A )
| ( equalelemsP @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause89) ).
thf(610,plain,
! [A: $i] :
( ( ( skaf79 @ A )
!= ( skaf78 @ A ) )
| ~ ( ssList @ A )
| ( equalelemsP @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(1396,plain,
! [A: $i] :
( ( cyclefreeP @ A )
| ( leq @ ( skaf49 @ A ) @ ( skaf50 @ A ) )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[203,245]) ).
thf(1397,plain,
( ( cyclefreeP @ sk2 )
| ( leq @ ( skaf49 @ sk2 ) @ ( skaf50 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[1396:[bind(A,$thf( sk2 ))]]) ).
thf(27964,plain,
! [B: $i,A: $i] :
( ( strictorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf50 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[593,328]) ).
thf(27965,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf50 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[27964:[bind(A,$thf( C )),bind(B,$thf( skaf50 @ C ))]]) ).
thf(28038,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf50 @ A ) @ nil ) ),
inference(simp,[status(thm)],[27965]) ).
thf(84679,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ B )
| ( ( ssList @ ( skaf72 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[252,401]) ).
thf(84680,plain,
! [A: $i] : ( rearsegP @ ( skaf72 @ A ) @ ( skaf72 @ A ) ),
inference(pattern_uni,[status(thm)],[84679:[bind(A,$thf( C )),bind(B,$thf( skaf72 @ C ))]]) ).
thf(84919,plain,
! [A: $i] : ( rearsegP @ ( skaf72 @ A ) @ ( skaf72 @ A ) ),
inference(simp,[status(thm)],[84680]) ).
thf(102,axiom,
! [A: $i] : ( ssItem @ ( skaf49 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause46) ).
thf(427,plain,
! [A: $i] : ( ssItem @ ( skaf49 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(994,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf49 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[427,697]) ).
thf(995,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf49 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[994:[bind(A,$thf( C )),bind(B,$thf( skaf49 @ C ))]]) ).
thf(1006,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf49 @ A ) @ nil ) ),
inference(simp,[status(thm)],[995]) ).
thf(110074,plain,
! [A: $i] :
( ( segmentP @ A @ nil )
| ( ( ssList @ ( app @ sk2 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3979,429]) ).
thf(110075,plain,
segmentP @ ( app @ sk2 @ sk1 ) @ nil,
inference(pattern_uni,[status(thm)],[110074:[bind(A,$thf( app @ sk2 @ sk1 ))]]) ).
thf(15458,plain,
! [A: $i] :
( ( rearsegP @ A @ nil )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[203,292]) ).
thf(15459,plain,
rearsegP @ sk2 @ nil,
inference(pattern_uni,[status(thm)],[15458:[bind(A,$thf( sk2 ))]]) ).
thf(4300,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ( ( ssList @ ( app @ sk2 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3979,236]) ).
thf(4301,plain,
~ ( neq @ ( app @ sk2 @ sk1 ) @ ( app @ sk2 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[4300:[bind(A,$thf( app @ sk2 @ sk1 ))]]) ).
thf(31152,plain,
! [A: $i] :
( ( ( app @ nil @ A )
= A )
| ( ( ssList @ nil )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[287,338]) ).
thf(31153,plain,
( ( app @ nil @ nil )
= nil ),
inference(pattern_uni,[status(thm)],[31152:[bind(A,$thf( nil ))]]) ).
thf(84807,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ B )
| ( ( ssList @ ( skaf76 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[603,401]) ).
thf(84808,plain,
! [A: $i] : ( rearsegP @ ( skaf76 @ A ) @ ( skaf76 @ A ) ),
inference(pattern_uni,[status(thm)],[84807:[bind(A,$thf( C )),bind(B,$thf( skaf76 @ C ))]]) ).
thf(84868,plain,
! [A: $i] : ( rearsegP @ ( skaf76 @ A ) @ ( skaf76 @ A ) ),
inference(simp,[status(thm)],[84808]) ).
thf(147,axiom,
! [A: $i] : ( ssList @ ( skaf51 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause44) ).
thf(535,plain,
! [A: $i] : ( ssList @ ( skaf51 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(84743,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ B )
| ( ( ssList @ ( skaf51 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[535,401]) ).
thf(84744,plain,
! [A: $i] : ( rearsegP @ ( skaf51 @ A ) @ ( skaf51 @ A ) ),
inference(pattern_uni,[status(thm)],[84743:[bind(A,$thf( C )),bind(B,$thf( skaf51 @ C ))]]) ).
thf(84851,plain,
! [A: $i] : ( rearsegP @ ( skaf51 @ A ) @ ( skaf51 @ A ) ),
inference(simp,[status(thm)],[84744]) ).
thf(144,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( app @ ( app @ A @ ( cons @ B @ C ) ) @ ( cons @ D @ E ) )
!= F )
| ~ ( ssList @ E )
| ~ ( ssList @ C )
| ~ ( ssList @ A )
| ~ ( ssItem @ D )
| ~ ( ssItem @ B )
| ~ ( totalorderedP @ F )
| ~ ( ssList @ F )
| ( leq @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause182) ).
thf(526,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( app @ ( app @ A @ ( cons @ B @ C ) ) @ ( cons @ D @ E ) )
!= F )
| ~ ( ssList @ E )
| ~ ( ssList @ C )
| ~ ( ssList @ A )
| ~ ( ssItem @ D )
| ~ ( ssItem @ B )
| ~ ( totalorderedP @ F )
| ~ ( ssList @ F )
| ( leq @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(1676,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf78 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[613,697]) ).
thf(1677,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf78 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[1676:[bind(A,$thf( C )),bind(B,$thf( skaf78 @ C ))]]) ).
thf(1700,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf78 @ A ) @ nil ) ),
inference(simp,[status(thm)],[1677]) ).
thf(15472,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( app @ sk2 @ ( skaf52 @ A ) ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4025,292]) ).
thf(15473,plain,
! [A: $i] : ( rearsegP @ ( app @ sk2 @ ( skaf52 @ A ) ) @ nil ),
inference(pattern_uni,[status(thm)],[15472:[bind(A,$thf( E )),bind(B,$thf( app @ sk2 @ ( skaf52 @ E ) ))]]) ).
thf(15550,plain,
! [A: $i] : ( rearsegP @ ( app @ sk2 @ ( skaf52 @ A ) ) @ nil ),
inference(simp,[status(thm)],[15473]) ).
thf(121,axiom,
! [B: $i,A: $i] :
( ( ( cons @ A @ B )
!= B )
| ~ ( ssItem @ A )
| ~ ( ssList @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause99) ).
thf(471,plain,
! [B: $i,A: $i] :
( ( ( cons @ A @ B )
!= B )
| ~ ( ssItem @ A )
| ~ ( ssList @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(28,axiom,
! [B: $i,A: $i] :
( ~ ( strictorderedP @ ( cons @ A @ B ) )
| ~ ( ssList @ B )
| ~ ( ssItem @ A )
| ( lt @ A @ ( hd @ B ) )
| ( nil = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause134) ).
thf(254,plain,
! [B: $i,A: $i] :
( ~ ( strictorderedP @ ( cons @ A @ B ) )
| ~ ( ssList @ B )
| ~ ( ssItem @ A )
| ( lt @ A @ ( hd @ B ) )
| ( nil = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(255,plain,
! [B: $i,A: $i] :
( ~ ( strictorderedP @ ( cons @ A @ B ) )
| ~ ( ssList @ B )
| ~ ( ssItem @ A )
| ( lt @ A @ ( hd @ B ) )
| ( nil = B ) ),
inference(cnf,[status(esa)],[254]) ).
thf(256,plain,
! [B: $i,A: $i] :
( ( nil = B )
| ~ ( strictorderedP @ ( cons @ A @ B ) )
| ~ ( ssList @ B )
| ~ ( ssItem @ A )
| ( lt @ A @ ( hd @ B ) ) ),
inference(lifteq,[status(thm)],[255]) ).
thf(4048,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ( ( ssList @ ( app @ sk2 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3892,236]) ).
thf(4049,plain,
~ ( neq @ ( app @ sk2 @ sk2 ) @ ( app @ sk2 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[4048:[bind(A,$thf( app @ sk2 @ sk2 ))]]) ).
thf(26108,plain,
( ~ ( rearsegP @ nil @ sk1 )
| ( totalorderP @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[21492,475]) ).
thf(26109,plain,
( ~ ( rearsegP @ nil @ sk1 )
| ( totalorderP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[26108:[]]) ).
thf(42901,plain,
( ( totalorderP @ sk1 )
| ( ( rearsegP @ nil @ nil )
!= ( rearsegP @ nil @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[15475,26109]) ).
thf(42939,plain,
( ( totalorderP @ sk1 )
| ( nil != nil )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[42901]) ).
thf(43005,plain,
( ( totalorderP @ sk1 )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[42939]) ).
thf(55250,plain,
! [B: $i,A: $i] :
( ( geq @ B @ B )
| ( ( ssItem @ ( skaf83 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[574,373]) ).
thf(55251,plain,
! [A: $i] : ( geq @ ( skaf83 @ A ) @ ( skaf83 @ A ) ),
inference(pattern_uni,[status(thm)],[55250:[bind(A,$thf( C )),bind(B,$thf( skaf83 @ C ))]]) ).
thf(55303,plain,
! [A: $i] : ( geq @ ( skaf83 @ A ) @ ( skaf83 @ A ) ),
inference(simp,[status(thm)],[55251]) ).
thf(124,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( frontsegP @ A @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause60) ).
thf(476,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( frontsegP @ A @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(6465,plain,
! [B: $i,A: $i] :
( ( ssList @ ( app @ sk2 @ B ) )
| ( ( ssList @ ( app @ sk2 @ ( skaf73 @ A ) ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4015,2922]) ).
thf(6466,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( skaf73 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[6465:[bind(A,$thf( E )),bind(B,$thf( app @ sk2 @ ( skaf73 @ E ) ))]]) ).
thf(6501,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( skaf73 @ A ) ) ) ),
inference(simp,[status(thm)],[6466]) ).
thf(27958,plain,
! [B: $i,A: $i] :
( ( strictorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf44 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[361,328]) ).
thf(27959,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf44 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[27958:[bind(A,$thf( C )),bind(B,$thf( skaf44 @ C ))]]) ).
thf(28035,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf44 @ A ) @ nil ) ),
inference(simp,[status(thm)],[27959]) ).
thf(33776,plain,
! [A: $i] :
( ~ ( singletonP @ sk1 )
| ( strictorderedP @ sk1 )
| ( ( cons @ ( skaf44 @ sk1 ) @ nil )
!= ( cons @ ( skaf44 @ A ) @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[1641,28035]) ).
thf(33777,plain,
( ~ ( singletonP @ sk1 )
| ( strictorderedP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[33776:[bind(A,$thf( sk1 ))]]) ).
thf(1014,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf80 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[436,236]) ).
thf(1015,plain,
! [A: $i] :
~ ( neq @ ( skaf80 @ A ) @ ( skaf80 @ A ) ),
inference(pattern_uni,[status(thm)],[1014:[bind(A,$thf( C )),bind(B,$thf( skaf80 @ C ))]]) ).
thf(1016,plain,
! [A: $i] :
~ ( neq @ ( skaf80 @ A ) @ ( skaf80 @ A ) ),
inference(simp,[status(thm)],[1015]) ).
thf(31120,plain,
! [A: $i] :
( ( ( app @ nil @ A )
= A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[203,338]) ).
thf(31121,plain,
( ( app @ nil @ sk2 )
= sk2 ),
inference(pattern_uni,[status(thm)],[31120:[bind(A,$thf( sk2 ))]]) ).
thf(154,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( cons @ A @ B )
!= ( cons @ C @ D ) )
| ~ ( ssItem @ C )
| ~ ( ssItem @ A )
| ~ ( ssList @ D )
| ~ ( ssList @ B )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause170) ).
thf(547,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( cons @ A @ B )
!= ( cons @ C @ D ) )
| ~ ( ssItem @ C )
| ~ ( ssItem @ A )
| ~ ( ssList @ D )
| ~ ( ssList @ B )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(189,axiom,
! [B: $i,A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ( strictorderedP @ ( cons @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause112) ).
thf(622,plain,
! [B: $i,A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ( strictorderedP @ ( cons @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(11,negated_conjecture,
( ( memberP @ sk4 @ sk5 )
| ~ ( neq @ sk4 @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
thf(207,plain,
( ( memberP @ sk4 @ sk5 )
| ~ ( neq @ sk4 @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(220,plain,
( ( memberP @ sk4 @ sk5 )
| ~ ( neq @ sk4 @ nil ) ),
inference(cnf,[status(esa)],[207]) ).
thf(647,plain,
( ( memberP @ sk2 @ sk5 )
| ~ ( neq @ sk2 @ nil ) ),
inference(rewrite,[status(thm)],[220,217]) ).
thf(700,plain,
! [A: $i] :
( ~ ( neq @ sk2 @ nil )
| ~ ( ssItem @ A )
| ( totalorderedP @ sk1 )
| ( ( cons @ sk5 @ nil )
!= ( cons @ A @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[648,697]) ).
thf(701,plain,
( ~ ( neq @ sk2 @ nil )
| ~ ( ssItem @ sk5 )
| ( totalorderedP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[700:[bind(A,$thf( sk5 ))]]) ).
thf(1269,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf83 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[574,697]) ).
thf(1270,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf83 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[1269:[bind(A,$thf( C )),bind(B,$thf( skaf83 @ C ))]]) ).
thf(1297,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf83 @ A ) @ nil ) ),
inference(simp,[status(thm)],[1270]) ).
thf(13838,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ( ( ssItem @ skac2 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[525,286]) ).
thf(13839,plain,
~ ( neq @ skac2 @ skac2 ),
inference(pattern_uni,[status(thm)],[13838:[bind(A,$thf( skac2 ))]]) ).
thf(116,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( memberP @ ( cons @ A @ B ) @ C )
| ~ ( ssList @ B )
| ~ ( ssItem @ A )
| ~ ( ssItem @ C )
| ( memberP @ B @ C )
| ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause161) ).
thf(457,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( memberP @ ( cons @ A @ B ) @ C )
| ~ ( ssList @ B )
| ~ ( ssItem @ A )
| ~ ( ssItem @ C )
| ( memberP @ B @ C )
| ( C = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(15486,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( skaf68 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[474,292]) ).
thf(15487,plain,
! [A: $i] : ( rearsegP @ ( skaf68 @ A ) @ nil ),
inference(pattern_uni,[status(thm)],[15486:[bind(A,$thf( C )),bind(B,$thf( skaf68 @ C ))]]) ).
thf(15560,plain,
! [A: $i] : ( rearsegP @ ( skaf68 @ A ) @ nil ),
inference(simp,[status(thm)],[15487]) ).
thf(162,axiom,
! [A: $i] :
( ~ ( segmentP @ nil @ A )
| ~ ( ssList @ A )
| ( nil = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause80) ).
thf(569,plain,
! [A: $i] :
( ~ ( segmentP @ nil @ A )
| ~ ( ssList @ A )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(15430,plain,
! [A: $i] :
( ( rearsegP @ A @ nil )
| ( ( ssList @ ( app @ sk2 @ ( app @ sk2 @ sk2 ) ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4032,292]) ).
thf(15431,plain,
rearsegP @ ( app @ sk2 @ ( app @ sk2 @ sk2 ) ) @ nil,
inference(pattern_uni,[status(thm)],[15430:[bind(A,$thf( app @ sk2 @ ( app @ sk2 @ sk2 ) ))]]) ).
thf(75,axiom,
! [A: $i] :
( ~ ( leq @ ( skaf55 @ A ) @ ( skaf54 @ A ) )
| ~ ( ssList @ A )
| ( totalorderP @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause94) ).
thf(370,plain,
! [A: $i] :
( ~ ( leq @ ( skaf55 @ A ) @ ( skaf54 @ A ) )
| ~ ( ssList @ A )
| ( totalorderP @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(371,plain,
! [A: $i] :
( ~ ( leq @ ( skaf55 @ A ) @ ( skaf54 @ A ) )
| ~ ( ssList @ A )
| ( totalorderP @ A ) ),
inference(cnf,[status(esa)],[370]) ).
thf(15480,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( skaf76 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[603,292]) ).
thf(15481,plain,
! [A: $i] : ( rearsegP @ ( skaf76 @ A ) @ nil ),
inference(pattern_uni,[status(thm)],[15480:[bind(A,$thf( C )),bind(B,$thf( skaf76 @ C ))]]) ).
thf(15555,plain,
! [A: $i] : ( rearsegP @ ( skaf76 @ A ) @ nil ),
inference(simp,[status(thm)],[15481]) ).
thf(84,axiom,
! [B: $i,A: $i] :
( ( ( cons @ A @ B )
!= nil )
| ~ ( ssItem @ A )
| ~ ( ssList @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause98) ).
thf(391,plain,
! [B: $i,A: $i] :
( ( ( cons @ A @ B )
!= nil )
| ~ ( ssItem @ A )
| ~ ( ssList @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(392,plain,
! [B: $i,A: $i] :
( ( ( cons @ A @ B )
!= nil )
| ~ ( ssItem @ A )
| ~ ( ssList @ B ) ),
inference(cnf,[status(esa)],[391]) ).
thf(393,plain,
! [B: $i,A: $i] :
( ( ( cons @ A @ B )
!= nil )
| ~ ( ssItem @ A )
| ~ ( ssList @ B ) ),
inference(lifteq,[status(thm)],[392]) ).
thf(136,axiom,
! [A: $i] : ( ssList @ ( skaf81 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause14) ).
thf(503,plain,
! [A: $i] : ( ssList @ ( skaf81 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(182,axiom,
! [A: $i] :
( ~ ( frontsegP @ nil @ A )
| ~ ( ssList @ A )
| ( nil = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause84) ).
thf(605,plain,
! [A: $i] :
( ~ ( frontsegP @ nil @ A )
| ~ ( ssList @ A )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(55258,plain,
! [B: $i,A: $i] :
( ( geq @ B @ B )
| ( ( ssItem @ ( skaf65 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[583,373]) ).
thf(55259,plain,
! [A: $i] : ( geq @ ( skaf65 @ A ) @ ( skaf65 @ A ) ),
inference(pattern_uni,[status(thm)],[55258:[bind(A,$thf( C )),bind(B,$thf( skaf65 @ C ))]]) ).
thf(55306,plain,
! [A: $i] : ( geq @ ( skaf65 @ A ) @ ( skaf65 @ A ) ),
inference(simp,[status(thm)],[55259]) ).
thf(84685,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ B )
| ( ( ssList @ ( skaf57 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[317,401]) ).
thf(84686,plain,
! [A: $i] : ( rearsegP @ ( skaf57 @ A ) @ ( skaf57 @ A ) ),
inference(pattern_uni,[status(thm)],[84685:[bind(A,$thf( C )),bind(B,$thf( skaf57 @ C ))]]) ).
thf(84922,plain,
! [A: $i] : ( rearsegP @ ( skaf57 @ A ) @ ( skaf57 @ A ) ),
inference(simp,[status(thm)],[84686]) ).
thf(3925,plain,
! [B: $i,A: $i] :
( ( ssList @ ( app @ sk2 @ B ) )
| ( ( ssList @ ( skaf57 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[317,2922]) ).
thf(3926,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( skaf57 @ A ) ) ),
inference(pattern_uni,[status(thm)],[3925:[bind(A,$thf( C )),bind(B,$thf( skaf57 @ C ))]]) ).
thf(4003,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( skaf57 @ A ) ) ),
inference(simp,[status(thm)],[3926]) ).
thf(15452,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( app @ sk2 @ ( skaf57 @ A ) ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4003,292]) ).
thf(15453,plain,
! [A: $i] : ( rearsegP @ ( app @ sk2 @ ( skaf57 @ A ) ) @ nil ),
inference(pattern_uni,[status(thm)],[15452:[bind(A,$thf( E )),bind(B,$thf( app @ sk2 @ ( skaf57 @ E ) ))]]) ).
thf(15535,plain,
! [A: $i] : ( rearsegP @ ( app @ sk2 @ ( skaf57 @ A ) ) @ nil ),
inference(simp,[status(thm)],[15453]) ).
thf(27994,plain,
! [A: $i] :
( ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ skac2 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[525,328]) ).
thf(27995,plain,
strictorderedP @ ( cons @ skac2 @ nil ),
inference(pattern_uni,[status(thm)],[27994:[bind(A,$thf( skac2 ))]]) ).
thf(158,axiom,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( ( tl @ ( cons @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause96) ).
thf(558,plain,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( ( tl @ ( cons @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(15350,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( app @ sk2 @ ( skaf80 @ A ) ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4023,292]) ).
thf(15351,plain,
! [A: $i] : ( rearsegP @ ( app @ sk2 @ ( skaf80 @ A ) ) @ nil ),
inference(pattern_uni,[status(thm)],[15350:[bind(A,$thf( E )),bind(B,$thf( app @ sk2 @ ( skaf80 @ E ) ))]]) ).
thf(15552,plain,
! [A: $i] : ( rearsegP @ ( app @ sk2 @ ( skaf80 @ A ) ) @ nil ),
inference(simp,[status(thm)],[15351]) ).
thf(145,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( memberP @ A @ B )
| ~ ( ssList @ A )
| ~ ( ssList @ C )
| ~ ( ssItem @ B )
| ( memberP @ ( app @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause141) ).
thf(530,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( memberP @ A @ B )
| ~ ( ssList @ A )
| ~ ( ssList @ C )
| ~ ( ssItem @ B )
| ( memberP @ ( app @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(26132,plain,
( ~ ( rearsegP @ nil @ sk1 )
| ( totalorderedP @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[21492,634]) ).
thf(26133,plain,
( ~ ( rearsegP @ nil @ sk1 )
| ( totalorderedP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[26132:[]]) ).
thf(55157,plain,
( ( totalorderedP @ sk1 )
| ( ( rearsegP @ nil @ sk1 )
!= ( rearsegP @ sk1 @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[15489,26133]) ).
thf(55209,plain,
( ( totalorderedP @ sk1 )
| ( nil != sk1 )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[55157]) ).
thf(55237,plain,
( ( totalorderedP @ sk1 )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[55209]) ).
thf(65,axiom,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( ( hd @ ( cons @ A @ B ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause97) ).
thf(341,plain,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( ( hd @ ( cons @ A @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(342,plain,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( ( hd @ ( cons @ A @ B ) )
= A ) ),
inference(cnf,[status(esa)],[341]) ).
thf(343,plain,
! [B: $i,A: $i] :
( ( ( hd @ ( cons @ A @ B ) )
= A )
| ~ ( ssItem @ A )
| ~ ( ssList @ B ) ),
inference(lifteq,[status(thm)],[342]) ).
thf(15348,plain,
! [A: $i] :
( ( rearsegP @ A @ nil )
| ( ( ssList @ ( app @ sk2 @ ( app @ sk2 @ nil ) ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4238,292]) ).
thf(15349,plain,
rearsegP @ ( app @ sk2 @ ( app @ sk2 @ nil ) ) @ nil,
inference(pattern_uni,[status(thm)],[15348:[bind(A,$thf( app @ sk2 @ ( app @ sk2 @ nil ) ))]]) ).
thf(15332,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( skaf58 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[347,292]) ).
thf(15333,plain,
! [A: $i] : ( rearsegP @ ( skaf58 @ A ) @ nil ),
inference(pattern_uni,[status(thm)],[15332:[bind(A,$thf( C )),bind(B,$thf( skaf58 @ C ))]]) ).
thf(15538,plain,
! [A: $i] : ( rearsegP @ ( skaf58 @ A ) @ nil ),
inference(simp,[status(thm)],[15333]) ).
thf(3893,plain,
! [B: $i,A: $i] :
( ( ssList @ ( app @ sk2 @ B ) )
| ( ( ssList @ ( skaf58 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[347,2922]) ).
thf(3894,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( skaf58 @ A ) ) ),
inference(pattern_uni,[status(thm)],[3893:[bind(A,$thf( C )),bind(B,$thf( skaf58 @ C ))]]) ).
thf(4019,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( skaf58 @ A ) ) ),
inference(simp,[status(thm)],[3894]) ).
thf(15490,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( app @ sk2 @ ( skaf58 @ A ) ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4019,292]) ).
thf(15491,plain,
! [A: $i] : ( rearsegP @ ( app @ sk2 @ ( skaf58 @ A ) ) @ nil ),
inference(pattern_uni,[status(thm)],[15490:[bind(A,$thf( E )),bind(B,$thf( app @ sk2 @ ( skaf58 @ E ) ))]]) ).
thf(15499,plain,
! [A: $i] : ( rearsegP @ ( app @ sk2 @ ( skaf58 @ A ) ) @ nil ),
inference(simp,[status(thm)],[15491]) ).
thf(138,axiom,
! [A: $i] :
( ~ ( ssItem @ A )
| ( duplicatefreeP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause65) ).
thf(508,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( duplicatefreeP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(110289,plain,
! [A: $i] :
( ( segmentP @ A @ nil )
| ( ( ssList @ ( app @ sk2 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3892,429]) ).
thf(110290,plain,
segmentP @ ( app @ sk2 @ sk2 ) @ nil,
inference(pattern_uni,[status(thm)],[110289:[bind(A,$thf( app @ sk2 @ sk2 ))]]) ).
thf(51,axiom,
! [A: $i] :
( ~ ( ssItem @ A )
| ( totalorderedP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause67) ).
thf(311,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( totalorderedP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(3919,plain,
! [B: $i,A: $i] :
( ( ssList @ ( app @ sk2 @ B ) )
| ( ( ssList @ ( skaf72 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[252,2922]) ).
thf(3920,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( skaf72 @ A ) ) ),
inference(pattern_uni,[status(thm)],[3919:[bind(A,$thf( C )),bind(B,$thf( skaf72 @ C ))]]) ).
thf(3999,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( skaf72 @ A ) ) ),
inference(simp,[status(thm)],[3920]) ).
thf(397,plain,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( leq @ B @ A )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( B = A ) ),
inference(cnf,[status(esa)],[396]) ).
thf(398,plain,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( leq @ A @ B )
| ~ ( leq @ B @ A )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B ) ),
inference(lifteq,[status(thm)],[397]) ).
thf(15370,plain,
! [C: $i,B: $i,A: $i] :
( ( rearsegP @ C @ nil )
| ( ( ssList @ ( skaf46 @ A @ B ) )
!= ( ssList @ C ) ) ),
inference(paramod_ordered,[status(thm)],[270,292]) ).
thf(15371,plain,
! [B: $i,A: $i] : ( rearsegP @ ( skaf46 @ A @ B ) @ nil ),
inference(pattern_uni,[status(thm)],[15370:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( skaf46 @ D @ E ))]]) ).
thf(15506,plain,
! [B: $i,A: $i] : ( rearsegP @ ( skaf46 @ A @ B ) @ nil ),
inference(simp,[status(thm)],[15371]) ).
thf(15410,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( skaf62 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[237,292]) ).
thf(15411,plain,
! [A: $i] : ( rearsegP @ ( skaf62 @ A ) @ nil ),
inference(pattern_uni,[status(thm)],[15410:[bind(A,$thf( C )),bind(B,$thf( skaf62 @ C ))]]) ).
thf(15520,plain,
! [A: $i] : ( rearsegP @ ( skaf62 @ A ) @ nil ),
inference(simp,[status(thm)],[15411]) ).
thf(95,axiom,
! [B: $i,A: $i] :
( ~ ( frontsegP @ A @ B )
| ~ ( frontsegP @ B @ A )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause129) ).
thf(412,plain,
! [B: $i,A: $i] :
( ~ ( frontsegP @ A @ B )
| ~ ( frontsegP @ B @ A )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(5676,plain,
! [B: $i,A: $i] :
( ( ssList @ ( app @ sk2 @ B ) )
| ( ( ssList @ ( app @ sk2 @ ( skaf57 @ A ) ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4003,2922]) ).
thf(5677,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( skaf57 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[5676:[bind(A,$thf( E )),bind(B,$thf( app @ sk2 @ ( skaf57 @ E ) ))]]) ).
thf(5722,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( skaf57 @ A ) ) ) ),
inference(simp,[status(thm)],[5677]) ).
thf(101,axiom,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ~ ( gt @ B @ A )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause110) ).
thf(425,plain,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ~ ( gt @ B @ A )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(27946,plain,
! [B: $i,A: $i] :
( ( strictorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf83 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[574,328]) ).
thf(27947,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf83 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[27946:[bind(A,$thf( C )),bind(B,$thf( skaf83 @ C ))]]) ).
thf(28031,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf83 @ A ) @ nil ) ),
inference(simp,[status(thm)],[27947]) ).
thf(9163,plain,
! [B: $i,A: $i] :
( ( ssList @ ( app @ sk2 @ B ) )
| ( ( ssList @ ( app @ sk2 @ ( skaf63 @ A ) ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4016,2922]) ).
thf(9164,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( skaf63 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[9163:[bind(A,$thf( E )),bind(B,$thf( app @ sk2 @ ( skaf63 @ E ) ))]]) ).
thf(9203,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( skaf63 @ A ) ) ) ),
inference(simp,[status(thm)],[9164]) ).
thf(12289,plain,
( ( ssList @ ( tl @ sk1 ) )
| ( strictorderP @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[10975,299]) ).
thf(12290,plain,
( ( ssList @ ( tl @ sk1 ) )
| ( strictorderP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[12289:[]]) ).
thf(1594,plain,
! [A: $i] :
( ( ( cons @ ( skaf44 @ A ) @ nil )
= A )
| ~ ( singletonP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[203,248]) ).
thf(1595,plain,
( ( ( cons @ ( skaf44 @ sk2 ) @ nil )
= sk2 )
| ~ ( singletonP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[1594:[bind(A,$thf( sk2 ))]]) ).
thf(3953,plain,
! [B: $i,A: $i] :
( ( ssList @ ( app @ sk2 @ B ) )
| ( ( ssList @ ( skaf51 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[535,2922]) ).
thf(3954,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( skaf51 @ A ) ) ),
inference(pattern_uni,[status(thm)],[3953:[bind(A,$thf( C )),bind(B,$thf( skaf51 @ C ))]]) ).
thf(4017,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( skaf51 @ A ) ) ),
inference(simp,[status(thm)],[3954]) ).
thf(3934,plain,
! [B: $i,A: $i] :
( ( ssList @ ( app @ sk2 @ B ) )
| ( ( ssList @ ( skaf81 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[503,2922]) ).
thf(3935,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( skaf81 @ A ) ) ),
inference(pattern_uni,[status(thm)],[3934:[bind(A,$thf( C )),bind(B,$thf( skaf81 @ C ))]]) ).
thf(4007,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( skaf81 @ A ) ) ),
inference(simp,[status(thm)],[3935]) ).
thf(6003,plain,
! [B: $i,A: $i] :
( ( ssList @ ( app @ sk2 @ B ) )
| ( ( ssList @ ( app @ sk2 @ ( skaf81 @ A ) ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4007,2922]) ).
thf(6004,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( skaf81 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[6003:[bind(A,$thf( E )),bind(B,$thf( app @ sk2 @ ( skaf81 @ E ) ))]]) ).
thf(6052,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( skaf81 @ A ) ) ) ),
inference(simp,[status(thm)],[6004]) ).
thf(62,axiom,
duplicatefreeP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause2) ).
thf(335,plain,
duplicatefreeP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(26287,plain,
( ~ ( rearsegP @ nil @ sk1 )
| ( duplicatefreeP @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[21492,335]) ).
thf(26288,plain,
( ~ ( rearsegP @ nil @ sk1 )
| ( duplicatefreeP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[26287:[]]) ).
thf(57427,plain,
( ( duplicatefreeP @ sk1 )
| ( ( rearsegP @ nil @ nil )
!= ( rearsegP @ nil @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[15475,26288]) ).
thf(57489,plain,
( ( duplicatefreeP @ sk1 )
| ( nil != nil )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[57427]) ).
thf(57537,plain,
( ( duplicatefreeP @ sk1 )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[57489]) ).
thf(179,axiom,
! [B: $i,A: $i] :
( ~ ( lt @ A @ B )
| ~ ( lt @ B @ A )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause114) ).
thf(601,plain,
! [B: $i,A: $i] :
( ~ ( lt @ A @ B )
| ~ ( lt @ B @ A )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(755,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf44 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[361,697]) ).
thf(756,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf44 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[755:[bind(A,$thf( C )),bind(B,$thf( skaf44 @ C ))]]) ).
thf(767,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf44 @ A ) @ nil ) ),
inference(simp,[status(thm)],[756]) ).
thf(1905,plain,
! [A: $i] :
( ~ ( singletonP @ sk2 )
| ( totalorderedP @ sk2 )
| ( ( cons @ ( skaf44 @ sk2 ) @ nil )
!= ( cons @ ( skaf44 @ A ) @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[1595,767]) ).
thf(1906,plain,
( ~ ( singletonP @ sk2 )
| ( totalorderedP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[1905:[bind(A,$thf( sk2 ))]]) ).
thf(45,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( strictorderP @ A )
| ( ( app @ ( app @ ( skaf61 @ A ) @ ( cons @ ( skaf59 @ A ) @ ( skaf62 @ A ) ) ) @ ( cons @ ( skaf60 @ A ) @ ( skaf63 @ A ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause165) ).
thf(296,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( strictorderP @ A )
| ( ( app @ ( app @ ( skaf61 @ A ) @ ( cons @ ( skaf59 @ A ) @ ( skaf62 @ A ) ) ) @ ( cons @ ( skaf60 @ A ) @ ( skaf63 @ A ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(297,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( strictorderP @ A )
| ( ( app @ ( app @ ( skaf61 @ A ) @ ( cons @ ( skaf59 @ A ) @ ( skaf62 @ A ) ) ) @ ( cons @ ( skaf60 @ A ) @ ( skaf63 @ A ) ) )
= A ) ),
inference(cnf,[status(esa)],[296]) ).
thf(298,plain,
! [A: $i] :
( ( ( app @ ( app @ ( skaf61 @ A ) @ ( cons @ ( skaf59 @ A ) @ ( skaf62 @ A ) ) ) @ ( cons @ ( skaf60 @ A ) @ ( skaf63 @ A ) ) )
= A )
| ~ ( ssList @ A )
| ( strictorderP @ A ) ),
inference(lifteq,[status(thm)],[297]) ).
thf(104,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssItem @ ( hd @ A ) )
| ( nil = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause76) ).
thf(430,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssItem @ ( hd @ A ) )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(15569,plain,
( ( ssList @ ( tl @ sk1 ) )
| ( rearsegP @ sk2 @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[10975,15459]) ).
thf(15570,plain,
( ( ssList @ ( tl @ sk1 ) )
| ( rearsegP @ sk2 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[15569:[]]) ).
thf(9505,plain,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ~ ( geq @ skac2 @ skac3 )
| ( ( geq @ B @ A )
!= ( geq @ skac3 @ skac2 ) ) ),
inference(paramod_ordered,[status(thm)],[226,9480]) ).
thf(9506,plain,
( ~ ( leq @ skac2 @ skac3 )
| ~ ( ssItem @ skac2 )
| ~ ( ssItem @ skac3 )
| ~ ( geq @ skac2 @ skac3 ) ),
inference(pattern_uni,[status(thm)],[9505:[bind(A,$thf( skac2 )),bind(B,$thf( skac3 ))]]) ).
thf(13609,plain,
( ~ ( leq @ skac2 @ skac3 )
| ~ $true
| ~ $true
| ~ ( geq @ skac2 @ skac3 ) ),
inference(rewrite,[status(thm)],[9506,538,525]) ).
thf(13610,plain,
( ~ ( leq @ skac2 @ skac3 )
| ~ ( geq @ skac2 @ skac3 ) ),
inference(simp,[status(thm)],[13609]) ).
thf(13646,plain,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ~ ( leq @ skac2 @ skac3 )
| ( ( geq @ B @ A )
!= ( geq @ skac2 @ skac3 ) ) ),
inference(paramod_ordered,[status(thm)],[226,13610]) ).
thf(13647,plain,
( ~ ( leq @ skac3 @ skac2 )
| ~ ( ssItem @ skac3 )
| ~ ( ssItem @ skac2 )
| ~ ( leq @ skac2 @ skac3 ) ),
inference(pattern_uni,[status(thm)],[13646:[bind(A,$thf( skac3 )),bind(B,$thf( skac2 ))]]) ).
thf(15666,plain,
( ~ ( leq @ skac3 @ skac2 )
| ~ $true
| ~ $true
| ~ ( leq @ skac2 @ skac3 ) ),
inference(rewrite,[status(thm)],[13647,538,525]) ).
thf(15667,plain,
( ~ ( leq @ skac3 @ skac2 )
| ~ ( leq @ skac2 @ skac3 ) ),
inference(simp,[status(thm)],[15666]) ).
thf(15706,plain,
( ~ ( leq @ skac3 @ skac2 )
| ( ( leq @ skac2 @ skac3 )
!= ( leq @ skac3 @ skac2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[15667]) ).
thf(15707,plain,
( ~ ( leq @ skac3 @ skac2 )
| ( ( leq @ skac2 @ skac3 )
!= ( leq @ skac3 @ skac2 ) ) ),
inference(simp,[status(thm)],[15706]) ).
thf(13826,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssItem @ ( skaf74 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[578,286]) ).
thf(13827,plain,
! [A: $i] :
~ ( neq @ ( skaf74 @ A ) @ ( skaf74 @ A ) ),
inference(pattern_uni,[status(thm)],[13826:[bind(A,$thf( C )),bind(B,$thf( skaf74 @ C ))]]) ).
thf(13849,plain,
! [A: $i] :
~ ( neq @ ( skaf74 @ A ) @ ( skaf74 @ A ) ),
inference(simp,[status(thm)],[13827]) ).
thf(171,axiom,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( nil = B )
| ( ( hd @ ( app @ B @ A ) )
= ( hd @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause123) ).
thf(584,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( nil = B )
| ( ( hd @ ( app @ B @ A ) )
= ( hd @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(110086,plain,
! [B: $i,A: $i] :
( ( segmentP @ B @ nil )
| ( ( ssList @ ( skaf80 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[436,429]) ).
thf(110087,plain,
! [A: $i] : ( segmentP @ ( skaf80 @ A ) @ nil ),
inference(pattern_uni,[status(thm)],[110086:[bind(A,$thf( C )),bind(B,$thf( skaf80 @ C ))]]) ).
thf(110317,plain,
! [A: $i] : ( segmentP @ ( skaf80 @ A ) @ nil ),
inference(simp,[status(thm)],[110087]) ).
thf(99,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( frontsegP @ ( cons @ A @ B ) @ ( cons @ C @ D ) )
| ~ ( ssList @ D )
| ~ ( ssList @ B )
| ~ ( ssItem @ C )
| ~ ( ssItem @ A )
| ( frontsegP @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause174) ).
thf(422,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( frontsegP @ ( cons @ A @ B ) @ ( cons @ C @ D ) )
| ~ ( ssList @ D )
| ~ ( ssList @ B )
| ~ ( ssItem @ C )
| ~ ( ssItem @ A )
| ( frontsegP @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(423,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( frontsegP @ ( cons @ A @ B ) @ ( cons @ C @ D ) )
| ~ ( ssList @ D )
| ~ ( ssList @ B )
| ~ ( ssItem @ C )
| ~ ( ssItem @ A )
| ( frontsegP @ B @ D ) ),
inference(cnf,[status(esa)],[422]) ).
thf(690,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf64 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[271,438]) ).
thf(691,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf64 @ A ) ),
inference(pattern_uni,[status(thm)],[690:[bind(A,$thf( C )),bind(B,$thf( skaf64 @ C ))]]) ).
thf(694,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf64 @ A ) ),
inference(simp,[status(thm)],[691]) ).
thf(842,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[203,236]) ).
thf(843,plain,
~ ( neq @ sk2 @ sk2 ),
inference(pattern_uni,[status(thm)],[842:[bind(A,$thf( sk2 ))]]) ).
thf(12,negated_conjecture,
( ~ ( neq @ sk1 @ nil )
| ~ ( segmentP @ sk2 @ sk1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
thf(204,plain,
( ~ ( neq @ sk1 @ nil )
| ~ ( segmentP @ sk2 @ sk1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(55283,plain,
! [B: $i,A: $i] :
( ( geq @ B @ B )
| ( ( ssItem @ ( skaf59 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[635,373]) ).
thf(55284,plain,
! [A: $i] : ( geq @ ( skaf59 @ A ) @ ( skaf59 @ A ) ),
inference(pattern_uni,[status(thm)],[55283:[bind(A,$thf( C )),bind(B,$thf( skaf59 @ C ))]]) ).
thf(55315,plain,
! [A: $i] : ( geq @ ( skaf59 @ A ) @ ( skaf59 @ A ) ),
inference(simp,[status(thm)],[55284]) ).
thf(9248,plain,
! [B: $i,A: $i] :
( ( ssList @ ( app @ sk2 @ B ) )
| ( ( ssList @ ( app @ sk2 @ ( skaf51 @ A ) ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4017,2922]) ).
thf(9249,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( skaf51 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[9248:[bind(A,$thf( E )),bind(B,$thf( app @ sk2 @ ( skaf51 @ E ) ))]]) ).
thf(9295,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( skaf51 @ A ) ) ) ),
inference(simp,[status(thm)],[9249]) ).
thf(250,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( duplicatefreeP @ A )
| ( ( app @ ( app @ ( skaf75 @ A ) @ ( cons @ ( skaf74 @ A ) @ ( skaf76 @ A ) ) ) @ ( cons @ ( skaf74 @ A ) @ ( skaf77 @ A ) ) )
= A ) ),
inference(cnf,[status(esa)],[249]) ).
thf(251,plain,
! [A: $i] :
( ( ( app @ ( app @ ( skaf75 @ A ) @ ( cons @ ( skaf74 @ A ) @ ( skaf76 @ A ) ) ) @ ( cons @ ( skaf74 @ A ) @ ( skaf77 @ A ) ) )
= A )
| ~ ( ssList @ A )
| ( duplicatefreeP @ A ) ),
inference(lifteq,[status(thm)],[250]) ).
thf(1794,plain,
! [A: $i] :
( ( ( app @ ( app @ ( skaf75 @ A ) @ ( cons @ ( skaf74 @ A ) @ ( skaf76 @ A ) ) ) @ ( cons @ ( skaf74 @ A ) @ ( skaf77 @ A ) ) )
= A )
| ( duplicatefreeP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[203,251]) ).
thf(1795,plain,
( ( ( app @ ( app @ ( skaf75 @ sk2 ) @ ( cons @ ( skaf74 @ sk2 ) @ ( skaf76 @ sk2 ) ) ) @ ( cons @ ( skaf74 @ sk2 ) @ ( skaf77 @ sk2 ) ) )
= sk2 )
| ( duplicatefreeP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[1794:[bind(A,$thf( sk2 ))]]) ).
thf(15366,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( skaf75 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[452,292]) ).
thf(15367,plain,
! [A: $i] : ( rearsegP @ ( skaf75 @ A ) @ nil ),
inference(pattern_uni,[status(thm)],[15366:[bind(A,$thf( C )),bind(B,$thf( skaf75 @ C ))]]) ).
thf(15502,plain,
! [A: $i] : ( rearsegP @ ( skaf75 @ A ) @ nil ),
inference(simp,[status(thm)],[15367]) ).
thf(30988,plain,
! [A: $i] :
( ( ( app @ nil @ A )
= A )
| ( ( ssList @ ( tl @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13718,338]) ).
thf(30989,plain,
( ( app @ nil @ ( tl @ sk2 ) )
= ( tl @ sk2 ) ),
inference(pattern_uni,[status(thm)],[30988:[bind(A,$thf( tl @ sk2 ))]]) ).
thf(12321,plain,
( ( ssList @ ( tl @ sk1 ) )
| ( totalorderedP @ ( cons @ skac2 @ sk1 ) )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[10975,703]) ).
thf(12322,plain,
( ( ssList @ ( tl @ sk1 ) )
| ( totalorderedP @ ( cons @ skac2 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[12321:[]]) ).
thf(197,axiom,
! [A: $i] :
( ~ ( lt @ A @ A )
| ~ ( ssItem @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause63) ).
thf(641,plain,
! [A: $i] :
( ~ ( lt @ A @ A )
| ~ ( ssItem @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(163,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( rearsegP @ A @ B )
| ~ ( rearsegP @ B @ C )
| ~ ( ssList @ C )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( rearsegP @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause153) ).
thf(572,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( rearsegP @ A @ B )
| ~ ( rearsegP @ B @ C )
| ~ ( ssList @ C )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( rearsegP @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(1303,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf74 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[578,697]) ).
thf(1304,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf74 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[1303:[bind(A,$thf( C )),bind(B,$thf( skaf74 @ C ))]]) ).
thf(1332,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf74 @ A ) @ nil ) ),
inference(simp,[status(thm)],[1304]) ).
thf(15593,plain,
( ( ssList @ ( tl @ sk1 ) )
| ( rearsegP @ nil @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[10975,15475]) ).
thf(15594,plain,
( ( ssList @ ( tl @ sk1 ) )
| ( rearsegP @ nil @ sk1 ) ),
inference(pattern_uni,[status(thm)],[15593:[]]) ).
thf(119,axiom,
! [A: $i] :
( ~ ( leq @ ( skaf64 @ A ) @ ( skaf65 @ A ) )
| ~ ( ssList @ A )
| ( totalorderedP @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause91) ).
thf(466,plain,
! [A: $i] :
( ~ ( leq @ ( skaf64 @ A ) @ ( skaf65 @ A ) )
| ~ ( ssList @ A )
| ( totalorderedP @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(12145,plain,
( ( ssList @ ( tl @ sk1 ) )
| ( totalorderP @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[10975,475]) ).
thf(12146,plain,
( ( ssList @ ( tl @ sk1 ) )
| ( totalorderP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[12145:[]]) ).
thf(12279,plain,
( ( ssList @ ( tl @ sk1 ) )
| ( strictorderedP @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[10975,621]) ).
thf(12280,plain,
( ( ssList @ ( tl @ sk1 ) )
| ( strictorderedP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[12279:[]]) ).
thf(33804,plain,
! [A: $i] :
( ~ ( singletonP @ sk2 )
| ( strictorderedP @ sk2 )
| ( ( cons @ ( skaf44 @ sk2 ) @ nil )
!= ( cons @ ( skaf44 @ A ) @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[1595,28035]) ).
thf(33805,plain,
( ~ ( singletonP @ sk2 )
| ( strictorderedP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[33804:[bind(A,$thf( sk2 ))]]) ).
thf(12255,plain,
( ( ssList @ ( tl @ sk1 ) )
| ( duplicatefreeP @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[10975,335]) ).
thf(12256,plain,
( ( ssList @ ( tl @ sk1 ) )
| ( duplicatefreeP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[12255:[]]) ).
thf(17589,plain,
! [A: $i] :
( ( duplicatefreeP @ sk1 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( tl @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12256,292]) ).
thf(17590,plain,
( ( duplicatefreeP @ sk1 )
| ( rearsegP @ ( tl @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[17589:[bind(A,$thf( tl @ sk1 ))]]) ).
thf(134,axiom,
! [A: $i] :
( ~ ( lt @ ( skaf59 @ A ) @ ( skaf60 @ A ) )
| ~ ( ssList @ A )
| ( strictorderP @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause93) ).
thf(498,plain,
! [A: $i] :
( ~ ( lt @ ( skaf59 @ A ) @ ( skaf60 @ A ) )
| ~ ( ssList @ A )
| ( strictorderP @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(181,axiom,
! [B: $i,A: $i] : ( ssList @ ( skaf42 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause53) ).
thf(604,plain,
! [B: $i,A: $i] : ( ssList @ ( skaf42 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(15438,plain,
! [C: $i,B: $i,A: $i] :
( ( rearsegP @ C @ nil )
| ( ( ssList @ ( skaf42 @ A @ B ) )
!= ( ssList @ C ) ) ),
inference(paramod_ordered,[status(thm)],[604,292]) ).
thf(15439,plain,
! [B: $i,A: $i] : ( rearsegP @ ( skaf42 @ A @ B ) @ nil ),
inference(pattern_uni,[status(thm)],[15438:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( skaf42 @ D @ E ))]]) ).
thf(15530,plain,
! [B: $i,A: $i] : ( rearsegP @ ( skaf42 @ A @ B ) @ nil ),
inference(simp,[status(thm)],[15439]) ).
thf(55268,plain,
! [B: $i,A: $i] :
( ( geq @ B @ B )
| ( ( ssItem @ ( skaf70 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[399,373]) ).
thf(55269,plain,
! [A: $i] : ( geq @ ( skaf70 @ A ) @ ( skaf70 @ A ) ),
inference(pattern_uni,[status(thm)],[55268:[bind(A,$thf( C )),bind(B,$thf( skaf70 @ C ))]]) ).
thf(55311,plain,
! [A: $i] : ( geq @ ( skaf70 @ A ) @ ( skaf70 @ A ) ),
inference(simp,[status(thm)],[55269]) ).
thf(78,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( rearsegP @ A @ B )
| ~ ( ssList @ C )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( rearsegP @ ( app @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause136) ).
thf(377,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( rearsegP @ A @ B )
| ~ ( ssList @ C )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( rearsegP @ ( app @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(13830,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssItem @ ( skaf60 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[406,286]) ).
thf(13831,plain,
! [A: $i] :
~ ( neq @ ( skaf60 @ A ) @ ( skaf60 @ A ) ),
inference(pattern_uni,[status(thm)],[13830:[bind(A,$thf( C )),bind(B,$thf( skaf60 @ C ))]]) ).
thf(13851,plain,
! [A: $i] :
~ ( neq @ ( skaf60 @ A ) @ ( skaf60 @ A ) ),
inference(simp,[status(thm)],[13831]) ).
thf(84824,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ B )
| ( ( ssList @ ( skaf66 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[543,401]) ).
thf(84825,plain,
! [A: $i] : ( rearsegP @ ( skaf66 @ A ) @ ( skaf66 @ A ) ),
inference(pattern_uni,[status(thm)],[84824:[bind(A,$thf( C )),bind(B,$thf( skaf66 @ C ))]]) ).
thf(84875,plain,
! [A: $i] : ( rearsegP @ ( skaf66 @ A ) @ ( skaf66 @ A ) ),
inference(simp,[status(thm)],[84825]) ).
thf(47,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( leq @ B @ A )
| ( ( app @ ( app @ C @ ( cons @ A @ D ) ) @ ( cons @ B @ E ) )
!= F )
| ~ ( ssList @ E )
| ~ ( ssList @ D )
| ~ ( ssList @ C )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ~ ( cyclefreeP @ F )
| ~ ( ssList @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause185) ).
thf(300,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( leq @ B @ A )
| ( ( app @ ( app @ C @ ( cons @ A @ D ) ) @ ( cons @ B @ E ) )
!= F )
| ~ ( ssList @ E )
| ~ ( ssList @ D )
| ~ ( ssList @ C )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ~ ( cyclefreeP @ F )
| ~ ( ssList @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(301,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( leq @ B @ A )
| ( ( app @ ( app @ C @ ( cons @ A @ D ) ) @ ( cons @ B @ E ) )
!= F )
| ~ ( ssList @ E )
| ~ ( ssList @ D )
| ~ ( ssList @ C )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ~ ( cyclefreeP @ F )
| ~ ( ssList @ F ) ),
inference(cnf,[status(esa)],[300]) ).
thf(302,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( app @ ( app @ C @ ( cons @ A @ D ) ) @ ( cons @ B @ E ) )
!= F )
| ~ ( leq @ A @ B )
| ~ ( leq @ B @ A )
| ~ ( ssList @ E )
| ~ ( ssList @ D )
| ~ ( ssList @ C )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ~ ( cyclefreeP @ F )
| ~ ( ssList @ F ) ),
inference(lifteq,[status(thm)],[301]) ).
thf(303,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( leq @ B @ A )
| ~ ( ssList @ E )
| ~ ( ssList @ D )
| ~ ( ssList @ C )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ~ ( cyclefreeP @ ( app @ ( app @ C @ ( cons @ A @ D ) ) @ ( cons @ B @ E ) ) )
| ~ ( ssList @ ( app @ ( app @ C @ ( cons @ A @ D ) ) @ ( cons @ B @ E ) ) ) ),
inference(simp,[status(thm)],[302]) ).
thf(757,plain,
! [A: $i] :
( ~ ( neq @ sk2 @ nil )
| ( totalorderedP @ sk1 )
| ( ( ssItem @ ( skaf44 @ A ) )
!= ( ssItem @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[361,701]) ).
thf(764,plain,
! [A: $i] :
( ( totalorderedP @ sk1 )
| ~ ( neq @ sk2 @ nil )
| ( ( skaf44 @ A )
!= sk5 ) ),
inference(simp,[status(thm)],[757]) ).
thf(1001,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf49 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[427,438]) ).
thf(1002,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf49 @ A ) ),
inference(pattern_uni,[status(thm)],[1001:[bind(A,$thf( C )),bind(B,$thf( skaf49 @ C ))]]) ).
thf(1011,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf49 @ A ) ),
inference(simp,[status(thm)],[1002]) ).
thf(97,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( cyclefreeP @ A )
| ( leq @ ( skaf50 @ A ) @ ( skaf49 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause87) ).
thf(418,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( cyclefreeP @ A )
| ( leq @ ( skaf50 @ A ) @ ( skaf49 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(419,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( cyclefreeP @ A )
| ( leq @ ( skaf50 @ A ) @ ( skaf49 @ A ) ) ),
inference(cnf,[status(esa)],[418]) ).
thf(84801,plain,
! [A: $i] :
( ( rearsegP @ A @ A )
| ( ( ssList @ ( app @ sk2 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3892,401]) ).
thf(84802,plain,
rearsegP @ ( app @ sk2 @ sk2 ) @ ( app @ sk2 @ sk2 ),
inference(pattern_uni,[status(thm)],[84801:[bind(A,$thf( app @ sk2 @ sk2 ))]]) ).
thf(161,axiom,
! [A: $i] :
( ~ ( ssItem @ A )
| ( totalorderP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause69) ).
thf(567,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( totalorderP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(84694,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ B )
| ( ( ssList @ ( skaf56 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[590,401]) ).
thf(84695,plain,
! [A: $i] : ( rearsegP @ ( skaf56 @ A ) @ ( skaf56 @ A ) ),
inference(pattern_uni,[status(thm)],[84694:[bind(A,$thf( C )),bind(B,$thf( skaf56 @ C ))]]) ).
thf(84925,plain,
! [A: $i] : ( rearsegP @ ( skaf56 @ A ) @ ( skaf56 @ A ) ),
inference(simp,[status(thm)],[84695]) ).
thf(30427,plain,
( ( rearsegP @ nil @ sk2 )
!= ( rearsegP @ sk2 @ nil ) ),
inference(paramod_ordered,[status(thm)],[15459,29979]) ).
thf(30475,plain,
( ( nil != sk2 )
| ( nil != sk2 ) ),
inference(simp,[status(thm)],[30427]) ).
thf(30524,plain,
nil != sk2,
inference(simp,[status(thm)],[30475]) ).
thf(1353,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf54 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[582,697]) ).
thf(1354,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf54 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[1353:[bind(A,$thf( C )),bind(B,$thf( skaf54 @ C ))]]) ).
thf(1376,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf54 @ A ) @ nil ) ),
inference(simp,[status(thm)],[1354]) ).
thf(850,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf57 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[317,236]) ).
thf(851,plain,
! [A: $i] :
~ ( neq @ ( skaf57 @ A ) @ ( skaf57 @ A ) ),
inference(pattern_uni,[status(thm)],[850:[bind(A,$thf( C )),bind(B,$thf( skaf57 @ C ))]]) ).
thf(863,plain,
! [A: $i] :
~ ( neq @ ( skaf57 @ A ) @ ( skaf57 @ A ) ),
inference(simp,[status(thm)],[851]) ).
thf(1169,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf81 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[503,236]) ).
thf(1170,plain,
! [A: $i] :
~ ( neq @ ( skaf81 @ A ) @ ( skaf81 @ A ) ),
inference(pattern_uni,[status(thm)],[1169:[bind(A,$thf( C )),bind(B,$thf( skaf81 @ C ))]]) ).
thf(1175,plain,
! [A: $i] :
~ ( neq @ ( skaf81 @ A ) @ ( skaf81 @ A ) ),
inference(simp,[status(thm)],[1170]) ).
thf(57,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( app @ A @ B )
!= C )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( ssList @ C )
| ( rearsegP @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause143) ).
thf(323,plain,
! [C: $i,B: $i,A: $i] :
( ( ( app @ A @ B )
!= C )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( ssList @ C )
| ( rearsegP @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(176,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( frontsegP @ ( cons @ A @ B ) @ ( cons @ C @ D ) )
| ~ ( ssList @ D )
| ~ ( ssList @ B )
| ~ ( ssItem @ C )
| ~ ( ssItem @ A )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause176) ).
thf(594,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( frontsegP @ ( cons @ A @ B ) @ ( cons @ C @ D ) )
| ~ ( ssList @ D )
| ~ ( ssList @ B )
| ~ ( ssItem @ C )
| ~ ( ssItem @ A )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(722,plain,
! [A: $i] :
( ~ ( neq @ sk2 @ nil )
| ( totalorderedP @ sk1 )
| ( ( ssItem @ ( skaf79 @ A ) )
!= ( ssItem @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[253,701]) ).
thf(726,plain,
! [A: $i] :
( ( totalorderedP @ sk1 )
| ~ ( neq @ sk2 @ nil )
| ( ( skaf79 @ A )
!= sk5 ) ),
inference(simp,[status(thm)],[722]) ).
thf(190,axiom,
! [B: $i,A: $i] :
( ( ( tl @ A )
!= ( tl @ B ) )
| ( ( hd @ A )
!= ( hd @ B ) )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( nil = B )
| ( A = B )
| ( nil = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause177) ).
thf(626,plain,
! [B: $i,A: $i] :
( ( ( tl @ A )
!= ( tl @ B ) )
| ( ( hd @ A )
!= ( hd @ B ) )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( nil = B )
| ( A = B )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(1546,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf71 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[597,236]) ).
thf(1547,plain,
! [A: $i] :
~ ( neq @ ( skaf71 @ A ) @ ( skaf71 @ A ) ),
inference(pattern_uni,[status(thm)],[1546:[bind(A,$thf( C )),bind(B,$thf( skaf71 @ C ))]]) ).
thf(1556,plain,
! [A: $i] :
~ ( neq @ ( skaf71 @ A ) @ ( skaf71 @ A ) ),
inference(simp,[status(thm)],[1547]) ).
thf(15432,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( skaf82 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[579,292]) ).
thf(15433,plain,
! [A: $i] : ( rearsegP @ ( skaf82 @ A ) @ nil ),
inference(pattern_uni,[status(thm)],[15432:[bind(A,$thf( C )),bind(B,$thf( skaf82 @ C ))]]) ).
thf(15528,plain,
! [A: $i] : ( rearsegP @ ( skaf82 @ A ) @ nil ),
inference(simp,[status(thm)],[15433]) ).
thf(156,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( tl @ A ) )
| ( nil = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause77) ).
thf(552,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( tl @ A ) )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(13844,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssItem @ ( skaf49 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[427,286]) ).
thf(13845,plain,
! [A: $i] :
~ ( neq @ ( skaf49 @ A ) @ ( skaf49 @ A ) ),
inference(pattern_uni,[status(thm)],[13844:[bind(A,$thf( C )),bind(B,$thf( skaf49 @ C ))]]) ).
thf(13857,plain,
! [A: $i] :
~ ( neq @ ( skaf49 @ A ) @ ( skaf49 @ A ) ),
inference(simp,[status(thm)],[13845]) ).
thf(13842,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssItem @ ( skaf59 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[635,286]) ).
thf(13843,plain,
! [A: $i] :
~ ( neq @ ( skaf59 @ A ) @ ( skaf59 @ A ) ),
inference(pattern_uni,[status(thm)],[13842:[bind(A,$thf( C )),bind(B,$thf( skaf59 @ C ))]]) ).
thf(13856,plain,
! [A: $i] :
~ ( neq @ ( skaf59 @ A ) @ ( skaf59 @ A ) ),
inference(simp,[status(thm)],[13843]) ).
thf(15338,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( skaf71 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[597,292]) ).
thf(15339,plain,
! [A: $i] : ( rearsegP @ ( skaf71 @ A ) @ nil ),
inference(pattern_uni,[status(thm)],[15338:[bind(A,$thf( C )),bind(B,$thf( skaf71 @ C ))]]) ).
thf(15543,plain,
! [A: $i] : ( rearsegP @ ( skaf71 @ A ) @ nil ),
inference(simp,[status(thm)],[15339]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( memberP @ ( app @ A @ B ) @ C )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ~ ( ssItem @ C )
| ( memberP @ B @ C )
| ( memberP @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause158) ).
thf(240,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( memberP @ ( app @ A @ B ) @ C )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ~ ( ssItem @ C )
| ( memberP @ B @ C )
| ( memberP @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(1027,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf68 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[474,236]) ).
thf(1028,plain,
! [A: $i] :
~ ( neq @ ( skaf68 @ A ) @ ( skaf68 @ A ) ),
inference(pattern_uni,[status(thm)],[1027:[bind(A,$thf( C )),bind(B,$thf( skaf68 @ C ))]]) ).
thf(1029,plain,
! [A: $i] :
~ ( neq @ ( skaf68 @ A ) @ ( skaf68 @ A ) ),
inference(simp,[status(thm)],[1028]) ).
thf(888,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf60 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[406,438]) ).
thf(889,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf60 @ A ) ),
inference(pattern_uni,[status(thm)],[888:[bind(A,$thf( C )),bind(B,$thf( skaf60 @ C ))]]) ).
thf(895,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf60 @ A ) ),
inference(simp,[status(thm)],[889]) ).
thf(84639,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ B )
| ( ( ssList @ ( skaf63 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[542,401]) ).
thf(84640,plain,
! [A: $i] : ( rearsegP @ ( skaf63 @ A ) @ ( skaf63 @ A ) ),
inference(pattern_uni,[status(thm)],[84639:[bind(A,$thf( C )),bind(B,$thf( skaf63 @ C ))]]) ).
thf(84903,plain,
! [A: $i] : ( rearsegP @ ( skaf63 @ A ) @ ( skaf63 @ A ) ),
inference(simp,[status(thm)],[84640]) ).
thf(84739,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ B )
| ( ( ssList @ ( skaf73 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[387,401]) ).
thf(84740,plain,
! [A: $i] : ( rearsegP @ ( skaf73 @ A ) @ ( skaf73 @ A ) ),
inference(pattern_uni,[status(thm)],[84739:[bind(A,$thf( C )),bind(B,$thf( skaf73 @ C ))]]) ).
thf(84849,plain,
! [A: $i] : ( rearsegP @ ( skaf73 @ A ) @ ( skaf73 @ A ) ),
inference(simp,[status(thm)],[84740]) ).
thf(26385,plain,
( ~ ( rearsegP @ nil @ sk1 )
| ~ ( neq @ nil @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[21492,859]) ).
thf(26386,plain,
( ~ ( rearsegP @ nil @ sk1 )
| ~ ( neq @ nil @ sk1 ) ),
inference(pattern_uni,[status(thm)],[26385:[]]) ).
thf(67531,plain,
( ~ ( neq @ nil @ sk1 )
| ( ( rearsegP @ nil @ nil )
!= ( rearsegP @ nil @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[15475,26386]) ).
thf(67592,plain,
( ~ ( neq @ nil @ sk1 )
| ( nil != nil )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[67531]) ).
thf(67651,plain,
( ~ ( neq @ nil @ sk1 )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[67592]) ).
thf(1020,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf75 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[452,236]) ).
thf(1021,plain,
! [A: $i] :
~ ( neq @ ( skaf75 @ A ) @ ( skaf75 @ A ) ),
inference(pattern_uni,[status(thm)],[1020:[bind(A,$thf( C )),bind(B,$thf( skaf75 @ C ))]]) ).
thf(1022,plain,
! [A: $i] :
~ ( neq @ ( skaf75 @ A ) @ ( skaf75 @ A ) ),
inference(simp,[status(thm)],[1021]) ).
thf(60,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( totalorderP @ A )
| ( ( app @ ( app @ ( skaf56 @ A ) @ ( cons @ ( skaf54 @ A ) @ ( skaf57 @ A ) ) ) @ ( cons @ ( skaf55 @ A ) @ ( skaf58 @ A ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause166) ).
thf(330,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( totalorderP @ A )
| ( ( app @ ( app @ ( skaf56 @ A ) @ ( cons @ ( skaf54 @ A ) @ ( skaf57 @ A ) ) ) @ ( cons @ ( skaf55 @ A ) @ ( skaf58 @ A ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(26192,plain,
( ~ ( rearsegP @ nil @ sk1 )
| ~ ( memberP @ sk1 @ skac3 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[21492,650]) ).
thf(26193,plain,
( ~ ( rearsegP @ nil @ sk1 )
| ~ ( memberP @ sk1 @ skac3 ) ),
inference(pattern_uni,[status(thm)],[26192:[]]) ).
thf(41614,plain,
( ~ ( memberP @ sk1 @ skac3 )
| ( ( rearsegP @ nil @ sk1 )
!= ( rearsegP @ sk1 @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[15489,26193]) ).
thf(41625,plain,
( ~ ( memberP @ sk1 @ skac3 )
| ( nil != sk1 )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[41614]) ).
thf(41683,plain,
( ~ ( memberP @ sk1 @ skac3 )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[41625]) ).
thf(28008,plain,
! [B: $i,A: $i] :
( ( strictorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf49 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[427,328]) ).
thf(28009,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf49 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[28008:[bind(A,$thf( C )),bind(B,$thf( skaf49 @ C ))]]) ).
thf(28030,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf49 @ A ) @ nil ) ),
inference(simp,[status(thm)],[28009]) ).
thf(27990,plain,
! [B: $i,A: $i] :
( ( strictorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf69 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[394,328]) ).
thf(27991,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf69 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[27990:[bind(A,$thf( C )),bind(B,$thf( skaf69 @ C ))]]) ).
thf(28020,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf69 @ A ) @ nil ) ),
inference(simp,[status(thm)],[27991]) ).
thf(142,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( app @ A @ B )
!= C )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ~ ( ssList @ C )
| ( frontsegP @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause144) ).
thf(521,plain,
! [C: $i,B: $i,A: $i] :
( ( ( app @ A @ B )
!= C )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ~ ( ssList @ C )
| ( frontsegP @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(66745,plain,
( ( strictorderedP @ sk1 )
| ( ( rearsegP @ nil @ nil )
!= ( rearsegP @ nil @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[15475,26311]) ).
thf(66803,plain,
( ( strictorderedP @ sk1 )
| ( nil != nil )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[66745]) ).
thf(66862,plain,
( ( strictorderedP @ sk1 )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[66803]) ).
thf(195,axiom,
! [B: $i,A: $i] :
( ~ ( strictorderedP @ ( cons @ A @ B ) )
| ~ ( ssList @ B )
| ~ ( ssItem @ A )
| ( strictorderedP @ B )
| ( nil = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause124) ).
thf(636,plain,
! [B: $i,A: $i] :
( ~ ( strictorderedP @ ( cons @ A @ B ) )
| ~ ( ssList @ B )
| ~ ( ssItem @ A )
| ( strictorderedP @ B )
| ( nil = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(846,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf72 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[252,236]) ).
thf(847,plain,
! [A: $i] :
~ ( neq @ ( skaf72 @ A ) @ ( skaf72 @ A ) ),
inference(pattern_uni,[status(thm)],[846:[bind(A,$thf( C )),bind(B,$thf( skaf72 @ C ))]]) ).
thf(868,plain,
! [A: $i] :
~ ( neq @ ( skaf72 @ A ) @ ( skaf72 @ A ) ),
inference(simp,[status(thm)],[847]) ).
thf(4501,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ( ( ssList @ ( app @ sk2 @ ( app @ sk2 @ sk1 ) ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4284,236]) ).
thf(4502,plain,
~ ( neq @ ( app @ sk2 @ ( app @ sk2 @ sk1 ) ) @ ( app @ sk2 @ ( app @ sk2 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[4501:[bind(A,$thf( app @ sk2 @ ( app @ sk2 @ sk1 ) ))]]) ).
thf(31177,plain,
! [A: $i] :
( ( ( app @ nil @ A )
= A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[200,338]) ).
thf(31178,plain,
( ( app @ nil @ sk1 )
= sk1 ),
inference(pattern_uni,[status(thm)],[31177:[bind(A,$thf( sk1 ))]]) ).
thf(15384,plain,
! [C: $i,B: $i,A: $i] :
( ( rearsegP @ C @ nil )
| ( ( ssList @ ( skaf48 @ A @ B ) )
!= ( ssList @ C ) ) ),
inference(paramod_ordered,[status(thm)],[424,292]) ).
thf(15385,plain,
! [B: $i,A: $i] : ( rearsegP @ ( skaf48 @ A @ B ) @ nil ),
inference(pattern_uni,[status(thm)],[15384:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( skaf48 @ D @ E ))]]) ).
thf(15511,plain,
! [B: $i,A: $i] : ( rearsegP @ ( skaf48 @ A @ B ) @ nil ),
inference(simp,[status(thm)],[15385]) ).
thf(110170,plain,
! [A: $i] :
( ( segmentP @ A @ nil )
| ( ( ssList @ ( tl @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13718,429]) ).
thf(110171,plain,
segmentP @ ( tl @ sk2 ) @ nil,
inference(pattern_uni,[status(thm)],[110170:[bind(A,$thf( tl @ sk2 ))]]) ).
thf(4480,plain,
! [A: $i] :
( ( ssList @ ( app @ sk2 @ A ) )
| ( ( ssList @ ( app @ sk2 @ ( app @ sk2 @ sk1 ) ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4284,2922]) ).
thf(4481,plain,
ssList @ ( app @ sk2 @ ( app @ sk2 @ ( app @ sk2 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[4480:[bind(A,$thf( app @ sk2 @ ( app @ sk2 @ sk1 ) ))]]) ).
thf(183,axiom,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( ssList @ ( cons @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause86) ).
thf(608,plain,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( ssList @ ( cons @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(15404,plain,
! [A: $i] :
( ( rearsegP @ A @ nil )
| ( ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( tl @ sk2 ) ) ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13928,292]) ).
thf(15405,plain,
rearsegP @ ( app @ sk2 @ ( app @ sk2 @ ( tl @ sk2 ) ) ) @ nil,
inference(pattern_uni,[status(thm)],[15404:[bind(A,$thf( app @ sk2 @ ( app @ sk2 @ ( tl @ sk2 ) ) ))]]) ).
thf(15436,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( skaf53 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[451,292]) ).
thf(15437,plain,
! [A: $i] : ( rearsegP @ ( skaf53 @ A ) @ nil ),
inference(pattern_uni,[status(thm)],[15436:[bind(A,$thf( C )),bind(B,$thf( skaf53 @ C ))]]) ).
thf(15529,plain,
! [A: $i] : ( rearsegP @ ( skaf53 @ A ) @ nil ),
inference(simp,[status(thm)],[15437]) ).
thf(241,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( memberP @ ( app @ A @ B ) @ C )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ~ ( ssItem @ C )
| ( memberP @ B @ C )
| ( memberP @ A @ C ) ),
inference(cnf,[status(esa)],[240]) ).
thf(55252,plain,
! [B: $i,A: $i] :
( ( geq @ B @ B )
| ( ( ssItem @ ( skaf79 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[253,373]) ).
thf(55253,plain,
! [A: $i] : ( geq @ ( skaf79 @ A ) @ ( skaf79 @ A ) ),
inference(pattern_uni,[status(thm)],[55252:[bind(A,$thf( C )),bind(B,$thf( skaf79 @ C ))]]) ).
thf(55304,plain,
! [A: $i] : ( geq @ ( skaf79 @ A ) @ ( skaf79 @ A ) ),
inference(simp,[status(thm)],[55253]) ).
thf(13820,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssItem @ ( skaf79 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[253,286]) ).
thf(13821,plain,
! [A: $i] :
~ ( neq @ ( skaf79 @ A ) @ ( skaf79 @ A ) ),
inference(pattern_uni,[status(thm)],[13820:[bind(A,$thf( C )),bind(B,$thf( skaf79 @ C ))]]) ).
thf(13861,plain,
! [A: $i] :
~ ( neq @ ( skaf79 @ A ) @ ( skaf79 @ A ) ),
inference(simp,[status(thm)],[13821]) ).
thf(13832,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssItem @ ( skaf64 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[271,286]) ).
thf(13833,plain,
! [A: $i] :
~ ( neq @ ( skaf64 @ A ) @ ( skaf64 @ A ) ),
inference(pattern_uni,[status(thm)],[13832:[bind(A,$thf( C )),bind(B,$thf( skaf64 @ C ))]]) ).
thf(13852,plain,
! [A: $i] :
~ ( neq @ ( skaf64 @ A ) @ ( skaf64 @ A ) ),
inference(simp,[status(thm)],[13833]) ).
thf(15446,plain,
! [A: $i] :
( ( rearsegP @ A @ nil )
| ( ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( app @ sk2 @ sk1 ) ) ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4481,292]) ).
thf(15447,plain,
rearsegP @ ( app @ sk2 @ ( app @ sk2 @ ( app @ sk2 @ sk1 ) ) ) @ nil,
inference(pattern_uni,[status(thm)],[15446:[bind(A,$thf( app @ sk2 @ ( app @ sk2 @ ( app @ sk2 @ sk1 ) ) ))]]) ).
thf(17503,plain,
! [A: $i] :
( ( totalorderedP @ sk1 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( tl @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12164,292]) ).
thf(17504,plain,
( ( totalorderedP @ sk1 )
| ( rearsegP @ ( tl @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[17503:[bind(A,$thf( tl @ sk1 ))]]) ).
thf(187,axiom,
! [A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ( frontsegP @ nil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause83) ).
thf(617,plain,
! [A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ( frontsegP @ nil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(3932,plain,
! [B: $i,A: $i] :
( ( ssList @ ( app @ sk2 @ B ) )
| ( ( ssList @ ( skaf56 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[590,2922]) ).
thf(3933,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( skaf56 @ A ) ) ),
inference(pattern_uni,[status(thm)],[3932:[bind(A,$thf( C )),bind(B,$thf( skaf56 @ C ))]]) ).
thf(4006,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( skaf56 @ A ) ) ),
inference(simp,[status(thm)],[3933]) ).
thf(15460,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( app @ sk2 @ ( skaf56 @ A ) ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4006,292]) ).
thf(15461,plain,
! [A: $i] : ( rearsegP @ ( app @ sk2 @ ( skaf56 @ A ) ) @ nil ),
inference(pattern_uni,[status(thm)],[15460:[bind(A,$thf( E )),bind(B,$thf( app @ sk2 @ ( skaf56 @ E ) ))]]) ).
thf(15539,plain,
! [A: $i] : ( rearsegP @ ( app @ sk2 @ ( skaf56 @ A ) ) @ nil ),
inference(simp,[status(thm)],[15461]) ).
thf(832,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf70 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[399,438]) ).
thf(833,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf70 @ A ) ),
inference(pattern_uni,[status(thm)],[832:[bind(A,$thf( C )),bind(B,$thf( skaf70 @ C ))]]) ).
thf(836,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf70 @ A ) ),
inference(simp,[status(thm)],[833]) ).
thf(426,plain,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ~ ( gt @ B @ A )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B ) ),
inference(cnf,[status(esa)],[425]) ).
thf(1160,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf67 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[497,236]) ).
thf(1161,plain,
! [A: $i] :
~ ( neq @ ( skaf67 @ A ) @ ( skaf67 @ A ) ),
inference(pattern_uni,[status(thm)],[1160:[bind(A,$thf( C )),bind(B,$thf( skaf67 @ C ))]]) ).
thf(1166,plain,
! [A: $i] :
~ ( neq @ ( skaf67 @ A ) @ ( skaf67 @ A ) ),
inference(simp,[status(thm)],[1161]) ).
thf(4,negated_conjecture,
ssList @ sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_4) ).
thf(209,plain,
ssList @ sk4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(130,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( app @ ( app @ A @ ( cons @ B @ C ) ) @ ( cons @ D @ E ) )
!= F )
| ~ ( ssList @ E )
| ~ ( ssList @ C )
| ~ ( ssList @ A )
| ~ ( ssItem @ D )
| ~ ( ssItem @ B )
| ~ ( strictorderP @ F )
| ~ ( ssList @ F )
| ( lt @ B @ D )
| ( lt @ D @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause183) ).
thf(487,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( app @ ( app @ A @ ( cons @ B @ C ) ) @ ( cons @ D @ E ) )
!= F )
| ~ ( ssList @ E )
| ~ ( ssList @ C )
| ~ ( ssList @ A )
| ~ ( ssItem @ D )
| ~ ( ssItem @ B )
| ~ ( strictorderP @ F )
| ~ ( ssList @ F )
| ( lt @ B @ D )
| ( lt @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(710,plain,
( ~ ( neq @ sk2 @ nil )
| ( totalorderedP @ sk1 )
| ( ( cons @ skac3 @ nil )
!= ( cons @ sk5 @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[648,699]) ).
thf(711,plain,
( ( totalorderedP @ sk1 )
| ~ ( neq @ sk2 @ nil )
| ( skac3 != sk5 )
| ( nil != nil ) ),
inference(simp,[status(thm)],[710]) ).
thf(712,plain,
( ( totalorderedP @ sk1 )
| ~ ( neq @ sk2 @ nil )
| ( skac3 != sk5 ) ),
inference(simp,[status(thm)],[711]) ).
thf(6070,plain,
! [B: $i,A: $i] :
( ( ssList @ ( app @ sk2 @ B ) )
| ( ( ssList @ ( app @ sk2 @ ( skaf62 @ A ) ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4008,2922]) ).
thf(6071,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( skaf62 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[6070:[bind(A,$thf( E )),bind(B,$thf( app @ sk2 @ ( skaf62 @ E ) ))]]) ).
thf(6120,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( skaf62 @ A ) ) ) ),
inference(simp,[status(thm)],[6071]) ).
thf(294,plain,
! [B: $i,A: $i] :
( ( ( app @ A @ B )
!= nil )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( nil = A ) ),
inference(cnf,[status(esa)],[293]) ).
thf(295,plain,
! [B: $i,A: $i] :
( ( ( app @ A @ B )
!= nil )
| ( nil = A )
| ~ ( ssList @ B )
| ~ ( ssList @ A ) ),
inference(lifteq,[status(thm)],[294]) ).
thf(15344,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( app @ sk2 @ ( skaf77 @ A ) ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4026,292]) ).
thf(15345,plain,
! [A: $i] : ( rearsegP @ ( app @ sk2 @ ( skaf77 @ A ) ) @ nil ),
inference(pattern_uni,[status(thm)],[15344:[bind(A,$thf( E )),bind(B,$thf( app @ sk2 @ ( skaf77 @ E ) ))]]) ).
thf(15549,plain,
! [A: $i] : ( rearsegP @ ( app @ sk2 @ ( skaf77 @ A ) ) @ nil ),
inference(simp,[status(thm)],[15345]) ).
thf(281,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( totalorderedP @ A )
| ( ( app @ ( app @ ( skaf66 @ A ) @ ( cons @ ( skaf64 @ A ) @ ( skaf67 @ A ) ) ) @ ( cons @ ( skaf65 @ A ) @ ( skaf68 @ A ) ) )
= A ) ),
inference(cnf,[status(esa)],[280]) ).
thf(282,plain,
! [A: $i] :
( ( ( app @ ( app @ ( skaf66 @ A ) @ ( cons @ ( skaf64 @ A ) @ ( skaf67 @ A ) ) ) @ ( cons @ ( skaf65 @ A ) @ ( skaf68 @ A ) ) )
= A )
| ~ ( ssList @ A )
| ( totalorderedP @ A ) ),
inference(lifteq,[status(thm)],[281]) ).
thf(84627,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ B )
| ( ( ssList @ ( skaf71 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[597,401]) ).
thf(84628,plain,
! [A: $i] : ( rearsegP @ ( skaf71 @ A ) @ ( skaf71 @ A ) ),
inference(pattern_uni,[status(thm)],[84627:[bind(A,$thf( C )),bind(B,$thf( skaf71 @ C ))]]) ).
thf(84899,plain,
! [A: $i] : ( rearsegP @ ( skaf71 @ A ) @ ( skaf71 @ A ) ),
inference(simp,[status(thm)],[84628]) ).
thf(5743,plain,
! [B: $i,A: $i] :
( ( ssList @ ( app @ sk2 @ B ) )
| ( ( ssList @ ( app @ sk2 @ ( skaf56 @ A ) ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4006,2922]) ).
thf(5744,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( skaf56 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[5743:[bind(A,$thf( E )),bind(B,$thf( app @ sk2 @ ( skaf56 @ E ) ))]]) ).
thf(5790,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( skaf56 @ A ) ) ) ),
inference(simp,[status(thm)],[5744]) ).
thf(168,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( leq @ B @ C )
| ~ ( ssItem @ C )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( leq @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause156) ).
thf(580,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( leq @ B @ C )
| ~ ( ssItem @ C )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( leq @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(15346,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( skaf80 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[436,292]) ).
thf(15347,plain,
! [A: $i] : ( rearsegP @ ( skaf80 @ A ) @ nil ),
inference(pattern_uni,[status(thm)],[15346:[bind(A,$thf( C )),bind(B,$thf( skaf80 @ C ))]]) ).
thf(15551,plain,
! [A: $i] : ( rearsegP @ ( skaf80 @ A ) @ nil ),
inference(simp,[status(thm)],[15347]) ).
thf(16726,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( tl @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12156,292]) ).
thf(16727,plain,
( ( cyclefreeP @ sk1 )
| ( rearsegP @ ( tl @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[16726:[bind(A,$thf( tl @ sk1 ))]]) ).
thf(30914,plain,
! [A: $i] :
( ( ( app @ nil @ A )
= A )
| ( ( ssList @ ( app @ sk2 @ nil ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3973,338]) ).
thf(30915,plain,
( ( app @ nil @ ( app @ sk2 @ nil ) )
= ( app @ sk2 @ nil ) ),
inference(pattern_uni,[status(thm)],[30914:[bind(A,$thf( app @ sk2 @ nil ))]]) ).
thf(413,plain,
! [B: $i,A: $i] :
( ~ ( frontsegP @ A @ B )
| ~ ( frontsegP @ B @ A )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( B = A ) ),
inference(cnf,[status(esa)],[412]) ).
thf(414,plain,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( frontsegP @ A @ B )
| ~ ( frontsegP @ B @ A )
| ~ ( ssList @ A )
| ~ ( ssList @ B ) ),
inference(lifteq,[status(thm)],[413]) ).
thf(12173,plain,
! [A: $i] :
( ( nil = sk1 )
| ( ssList @ ( app @ sk2 @ A ) )
| ( ( ssList @ ( tl @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10975,2922]) ).
thf(12174,plain,
( ( nil = sk1 )
| ( ssList @ ( app @ sk2 @ ( tl @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[12173:[bind(A,$thf( tl @ sk1 ))]]) ).
thf(55285,plain,
! [B: $i,A: $i] :
( ( geq @ B @ B )
| ( ( ssItem @ ( skaf49 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[427,373]) ).
thf(55286,plain,
! [A: $i] : ( geq @ ( skaf49 @ A ) @ ( skaf49 @ A ) ),
inference(pattern_uni,[status(thm)],[55285:[bind(A,$thf( C )),bind(B,$thf( skaf49 @ C ))]]) ).
thf(55316,plain,
! [A: $i] : ( geq @ ( skaf49 @ A ) @ ( skaf49 @ A ) ),
inference(simp,[status(thm)],[55286]) ).
thf(1276,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf83 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[574,438]) ).
thf(1277,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf83 @ A ) ),
inference(pattern_uni,[status(thm)],[1276:[bind(A,$thf( C )),bind(B,$thf( skaf83 @ C ))]]) ).
thf(1300,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf83 @ A ) ),
inference(simp,[status(thm)],[1277]) ).
thf(777,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf69 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[394,697]) ).
thf(778,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf69 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[777:[bind(A,$thf( C )),bind(B,$thf( skaf69 @ C ))]]) ).
thf(791,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf69 @ A ) @ nil ) ),
inference(simp,[status(thm)],[778]) ).
thf(109,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( segmentP @ A @ B )
| ~ ( segmentP @ B @ C )
| ~ ( ssList @ C )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( segmentP @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause152) ).
thf(441,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( segmentP @ A @ B )
| ~ ( segmentP @ B @ C )
| ~ ( ssList @ C )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( segmentP @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(15354,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( app @ sk2 @ ( skaf66 @ A ) ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3998,292]) ).
thf(15355,plain,
! [A: $i] : ( rearsegP @ ( app @ sk2 @ ( skaf66 @ A ) ) @ nil ),
inference(pattern_uni,[status(thm)],[15354:[bind(A,$thf( E )),bind(B,$thf( app @ sk2 @ ( skaf66 @ E ) ))]]) ).
thf(15556,plain,
! [A: $i] : ( rearsegP @ ( app @ sk2 @ ( skaf66 @ A ) ) @ nil ),
inference(simp,[status(thm)],[15355]) ).
thf(12143,plain,
( ( ssList @ ( tl @ sk1 ) )
| ( nil != sk2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[10975,216]) ).
thf(12144,plain,
( ( ssList @ ( tl @ sk1 ) )
| ( nil != sk2 ) ),
inference(pattern_uni,[status(thm)],[12143:[]]) ).
thf(15752,plain,
( ( ssList @ ( tl @ sk1 ) )
| ( sk2 != sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[10975,12144]) ).
thf(15753,plain,
( ( ssList @ ( tl @ sk1 ) )
| ( sk2 != sk1 ) ),
inference(pattern_uni,[status(thm)],[15752:[]]) ).
thf(1717,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf59 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[635,438]) ).
thf(1718,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf59 @ A ) ),
inference(pattern_uni,[status(thm)],[1717:[bind(A,$thf( C )),bind(B,$thf( skaf59 @ C ))]]) ).
thf(1738,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf59 @ A ) ),
inference(simp,[status(thm)],[1718]) ).
thf(153,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( app @ A @ B )
!= ( app @ A @ C ) )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ~ ( ssList @ C )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause150) ).
thf(544,plain,
! [C: $i,B: $i,A: $i] :
( ( ( app @ A @ B )
!= ( app @ A @ C ) )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ~ ( ssList @ C )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(15408,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( skaf81 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[503,292]) ).
thf(15409,plain,
! [A: $i] : ( rearsegP @ ( skaf81 @ A ) @ nil ),
inference(pattern_uni,[status(thm)],[15408:[bind(A,$thf( C )),bind(B,$thf( skaf81 @ C ))]]) ).
thf(15519,plain,
! [A: $i] : ( rearsegP @ ( skaf81 @ A ) @ nil ),
inference(simp,[status(thm)],[15409]) ).
thf(55256,plain,
! [B: $i,A: $i] :
( ( geq @ B @ B )
| ( ( ssItem @ ( skaf44 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[361,373]) ).
thf(55257,plain,
! [A: $i] : ( geq @ ( skaf44 @ A ) @ ( skaf44 @ A ) ),
inference(pattern_uni,[status(thm)],[55256:[bind(A,$thf( C )),bind(B,$thf( skaf44 @ C ))]]) ).
thf(55305,plain,
! [A: $i] : ( geq @ ( skaf44 @ A ) @ ( skaf44 @ A ) ),
inference(simp,[status(thm)],[55257]) ).
thf(15482,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( app @ sk2 @ ( skaf81 @ A ) ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4007,292]) ).
thf(15483,plain,
! [A: $i] : ( rearsegP @ ( app @ sk2 @ ( skaf81 @ A ) ) @ nil ),
inference(pattern_uni,[status(thm)],[15482:[bind(A,$thf( E )),bind(B,$thf( app @ sk2 @ ( skaf81 @ E ) ))]]) ).
thf(15557,plain,
! [A: $i] : ( rearsegP @ ( app @ sk2 @ ( skaf81 @ A ) ) @ nil ),
inference(simp,[status(thm)],[15483]) ).
thf(5456,plain,
! [B: $i,A: $i] :
( ( ssList @ ( app @ sk2 @ B ) )
| ( ( ssList @ ( app @ sk2 @ ( skaf72 @ A ) ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3999,2922]) ).
thf(5457,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( skaf72 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[5456:[bind(A,$thf( E )),bind(B,$thf( app @ sk2 @ ( skaf72 @ E ) ))]]) ).
thf(5504,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( skaf72 @ A ) ) ) ),
inference(simp,[status(thm)],[5457]) ).
thf(852,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf62 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[237,236]) ).
thf(853,plain,
! [A: $i] :
~ ( neq @ ( skaf62 @ A ) @ ( skaf62 @ A ) ),
inference(pattern_uni,[status(thm)],[852:[bind(A,$thf( C )),bind(B,$thf( skaf62 @ C ))]]) ).
thf(864,plain,
! [A: $i] :
~ ( neq @ ( skaf62 @ A ) @ ( skaf62 @ A ) ),
inference(simp,[status(thm)],[853]) ).
thf(723,plain,
! [A: $i] :
( ~ ( neq @ sk2 @ nil )
| ( totalorderedP @ sk1 )
| ( ( ssItem @ ( skaf64 @ A ) )
!= ( ssItem @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[271,701]) ).
thf(727,plain,
! [A: $i] :
( ( totalorderedP @ sk1 )
| ~ ( neq @ sk2 @ nil )
| ( ( skaf64 @ A )
!= sk5 ) ),
inference(simp,[status(thm)],[723]) ).
thf(386,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( geq @ A @ B )
| ~ ( geq @ B @ C )
| ~ ( ssItem @ C )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( geq @ A @ C ) ),
inference(cnf,[status(esa)],[385]) ).
thf(55246,plain,
! [A: $i] :
( ( geq @ A @ A )
| ( ( ssItem @ skac3 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[538,373]) ).
thf(55247,plain,
geq @ skac3 @ skac3,
inference(pattern_uni,[status(thm)],[55246:[bind(A,$thf( skac3 ))]]) ).
thf(111,axiom,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( neq @ B @ A )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause100) ).
thf(446,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( neq @ B @ A )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(13783,plain,
! [A: $i] :
( ( nil = A )
| ( ssList @ ( tl @ A ) )
| ( ( ssList @ ( tl @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13718,279]) ).
thf(13784,plain,
( ( ( tl @ sk2 )
= nil )
| ( ssList @ ( tl @ ( tl @ sk2 ) ) ) ),
inference(pattern_uni,[status(thm)],[13783:[bind(A,$thf( tl @ sk2 ))]]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ~ ( lt @ A @ B )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( gt @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause106) ).
thf(231,plain,
! [B: $i,A: $i] :
( ~ ( lt @ A @ B )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( gt @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(9333,plain,
! [B: $i,A: $i] :
( ( ssList @ ( app @ sk2 @ B ) )
| ( ( ssList @ ( app @ sk2 @ ( skaf58 @ A ) ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4019,2922]) ).
thf(9334,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( skaf58 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[9333:[bind(A,$thf( E )),bind(B,$thf( app @ sk2 @ ( skaf58 @ E ) ))]]) ).
thf(9389,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( skaf58 @ A ) ) ) ),
inference(simp,[status(thm)],[9334]) ).
thf(1151,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf52 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[485,236]) ).
thf(1152,plain,
! [A: $i] :
~ ( neq @ ( skaf52 @ A ) @ ( skaf52 @ A ) ),
inference(pattern_uni,[status(thm)],[1151:[bind(A,$thf( C )),bind(B,$thf( skaf52 @ C ))]]) ).
thf(1157,plain,
! [A: $i] :
~ ( neq @ ( skaf52 @ A ) @ ( skaf52 @ A ) ),
inference(simp,[status(thm)],[1152]) ).
thf(15470,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( app @ sk2 @ ( skaf68 @ A ) ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3993,292]) ).
thf(15471,plain,
! [A: $i] : ( rearsegP @ ( app @ sk2 @ ( skaf68 @ A ) ) @ nil ),
inference(pattern_uni,[status(thm)],[15470:[bind(A,$thf( E )),bind(B,$thf( app @ sk2 @ ( skaf68 @ E ) ))]]) ).
thf(15548,plain,
! [A: $i] : ( rearsegP @ ( app @ sk2 @ ( skaf68 @ A ) ) @ nil ),
inference(simp,[status(thm)],[15471]) ).
thf(55266,plain,
! [B: $i,A: $i] :
( ( geq @ B @ B )
| ( ( ssItem @ ( skaf64 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[271,373]) ).
thf(55267,plain,
! [A: $i] : ( geq @ ( skaf64 @ A ) @ ( skaf64 @ A ) ),
inference(pattern_uni,[status(thm)],[55266:[bind(A,$thf( C )),bind(B,$thf( skaf64 @ C ))]]) ).
thf(55310,plain,
! [A: $i] : ( geq @ ( skaf64 @ A ) @ ( skaf64 @ A ) ),
inference(simp,[status(thm)],[55267]) ).
thf(129,axiom,
! [B: $i,A: $i] : ( ssList @ ( skaf47 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause49) ).
thf(486,plain,
! [B: $i,A: $i] : ( ssList @ ( skaf47 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(15492,plain,
! [C: $i,B: $i,A: $i] :
( ( rearsegP @ C @ nil )
| ( ( ssList @ ( skaf47 @ A @ B ) )
!= ( ssList @ C ) ) ),
inference(paramod_ordered,[status(thm)],[486,292]) ).
thf(15493,plain,
! [B: $i,A: $i] : ( rearsegP @ ( skaf47 @ A @ B ) @ nil ),
inference(pattern_uni,[status(thm)],[15492:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( skaf47 @ D @ E ))]]) ).
thf(15501,plain,
! [B: $i,A: $i] : ( rearsegP @ ( skaf47 @ A @ B ) @ nil ),
inference(simp,[status(thm)],[15493]) ).
thf(30849,plain,
! [A: $i] :
( ( ( app @ nil @ A )
= A )
| ( ( ssList @ ( app @ sk2 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3979,338]) ).
thf(30850,plain,
( ( app @ nil @ ( app @ sk2 @ sk1 ) )
= ( app @ sk2 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[30849:[bind(A,$thf( app @ sk2 @ sk1 ))]]) ).
thf(84769,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ B )
| ( ( ssList @ ( skaf67 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[497,401]) ).
thf(84770,plain,
! [A: $i] : ( rearsegP @ ( skaf67 @ A ) @ ( skaf67 @ A ) ),
inference(pattern_uni,[status(thm)],[84769:[bind(A,$thf( C )),bind(B,$thf( skaf67 @ C ))]]) ).
thf(84856,plain,
! [A: $i] : ( rearsegP @ ( skaf67 @ A ) @ ( skaf67 @ A ) ),
inference(simp,[status(thm)],[84770]) ).
thf(150,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssItem @ ( hd @ A ) )
| ( nil = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause78) ).
thf(539,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssItem @ ( hd @ A ) )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(15424,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( app @ sk2 @ ( skaf51 @ A ) ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4017,292]) ).
thf(15425,plain,
! [A: $i] : ( rearsegP @ ( app @ sk2 @ ( skaf51 @ A ) ) @ nil ),
inference(pattern_uni,[status(thm)],[15424:[bind(A,$thf( E )),bind(B,$thf( app @ sk2 @ ( skaf51 @ E ) ))]]) ).
thf(15525,plain,
! [A: $i] : ( rearsegP @ ( app @ sk2 @ ( skaf51 @ A ) ) @ nil ),
inference(simp,[status(thm)],[15425]) ).
thf(806,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf55 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[395,438]) ).
thf(807,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf55 @ A ) ),
inference(pattern_uni,[status(thm)],[806:[bind(A,$thf( C )),bind(B,$thf( skaf55 @ C ))]]) ).
thf(813,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf55 @ A ) ),
inference(simp,[status(thm)],[807]) ).
thf(56,axiom,
! [B: $i,A: $i] :
( ( ( cons @ A @ nil )
!= B )
| ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( singletonP @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause116) ).
thf(319,plain,
! [B: $i,A: $i] :
( ( ( cons @ A @ nil )
!= B )
| ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( singletonP @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(28006,plain,
! [B: $i,A: $i] :
( ( strictorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf59 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[635,328]) ).
thf(28007,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf59 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[28006:[bind(A,$thf( C )),bind(B,$thf( skaf59 @ C ))]]) ).
thf(28029,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf59 @ A ) @ nil ) ),
inference(simp,[status(thm)],[28007]) ).
thf(389,plain,
! [B: $i,A: $i] :
( ~ ( rearsegP @ A @ B )
| ~ ( rearsegP @ B @ A )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( B = A ) ),
inference(cnf,[status(esa)],[388]) ).
thf(390,plain,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( rearsegP @ A @ B )
| ~ ( rearsegP @ B @ A )
| ~ ( ssList @ A )
| ~ ( ssList @ B ) ),
inference(lifteq,[status(thm)],[389]) ).
thf(192,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( segmentP @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause57) ).
thf(632,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( segmentP @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(13814,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssItem @ ( skaf54 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[582,286]) ).
thf(13815,plain,
! [A: $i] :
~ ( neq @ ( skaf54 @ A ) @ ( skaf54 @ A ) ),
inference(pattern_uni,[status(thm)],[13814:[bind(A,$thf( C )),bind(B,$thf( skaf54 @ C ))]]) ).
thf(13858,plain,
! [A: $i] :
~ ( neq @ ( skaf54 @ A ) @ ( skaf54 @ A ) ),
inference(simp,[status(thm)],[13815]) ).
thf(12267,plain,
( ( ssList @ ( tl @ sk1 ) )
| ( equalelemsP @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[10975,318]) ).
thf(12268,plain,
( ( ssList @ ( tl @ sk1 ) )
| ( equalelemsP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[12267:[]]) ).
thf(55262,plain,
! [B: $i,A: $i] :
( ( geq @ B @ B )
| ( ( ssItem @ ( skaf50 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[593,373]) ).
thf(55263,plain,
! [A: $i] : ( geq @ ( skaf50 @ A ) @ ( skaf50 @ A ) ),
inference(pattern_uni,[status(thm)],[55262:[bind(A,$thf( C )),bind(B,$thf( skaf50 @ C ))]]) ).
thf(55308,plain,
! [A: $i] : ( geq @ ( skaf50 @ A ) @ ( skaf50 @ A ) ),
inference(simp,[status(thm)],[55263]) ).
thf(1187,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf63 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[542,236]) ).
thf(1188,plain,
! [A: $i] :
~ ( neq @ ( skaf63 @ A ) @ ( skaf63 @ A ) ),
inference(pattern_uni,[status(thm)],[1187:[bind(A,$thf( C )),bind(B,$thf( skaf63 @ C ))]]) ).
thf(1193,plain,
! [A: $i] :
~ ( neq @ ( skaf63 @ A ) @ ( skaf63 @ A ) ),
inference(simp,[status(thm)],[1188]) ).
thf(125,axiom,
! [A: $i] :
( ~ ( ssItem @ A )
| ( cyclefreeP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause70) ).
thf(478,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( cyclefreeP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(679,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf79 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[253,438]) ).
thf(680,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf79 @ A ) ),
inference(pattern_uni,[status(thm)],[679:[bind(A,$thf( C )),bind(B,$thf( skaf79 @ C ))]]) ).
thf(684,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf79 @ A ) ),
inference(simp,[status(thm)],[680]) ).
thf(345,plain,
! [B: $i,A: $i] :
( ~ ( leq @ A @ ( hd @ B ) )
| ~ ( totalorderedP @ B )
| ~ ( ssList @ B )
| ~ ( ssItem @ A )
| ( totalorderedP @ ( cons @ A @ B ) )
| ( nil = B ) ),
inference(cnf,[status(esa)],[344]) ).
thf(346,plain,
! [B: $i,A: $i] :
( ( nil = B )
| ~ ( leq @ A @ ( hd @ B ) )
| ~ ( totalorderedP @ B )
| ~ ( ssList @ B )
| ~ ( ssItem @ A )
| ( totalorderedP @ ( cons @ A @ B ) ) ),
inference(lifteq,[status(thm)],[345]) ).
thf(15374,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( app @ sk2 @ ( skaf63 @ A ) ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4016,292]) ).
thf(15375,plain,
! [A: $i] : ( rearsegP @ ( app @ sk2 @ ( skaf63 @ A ) ) @ nil ),
inference(pattern_uni,[status(thm)],[15374:[bind(A,$thf( E )),bind(B,$thf( app @ sk2 @ ( skaf63 @ E ) ))]]) ).
thf(15508,plain,
! [A: $i] : ( rearsegP @ ( app @ sk2 @ ( skaf63 @ A ) ) @ nil ),
inference(simp,[status(thm)],[15375]) ).
thf(84623,plain,
! [A: $i] :
( ( rearsegP @ A @ A )
| ( ( ssList @ ( app @ sk2 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3979,401]) ).
thf(84624,plain,
rearsegP @ ( app @ sk2 @ sk1 ) @ ( app @ sk2 @ sk1 ),
inference(pattern_uni,[status(thm)],[84623:[bind(A,$thf( app @ sk2 @ sk1 ))]]) ).
thf(6204,plain,
! [B: $i,A: $i] :
( ( ssList @ ( app @ sk2 @ B ) )
| ( ( ssList @ ( app @ sk2 @ ( skaf82 @ A ) ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4010,2922]) ).
thf(6205,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( skaf82 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[6204:[bind(A,$thf( E )),bind(B,$thf( app @ sk2 @ ( skaf82 @ E ) ))]]) ).
thf(6257,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( skaf82 @ A ) ) ) ),
inference(simp,[status(thm)],[6205]) ).
thf(1462,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf65 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[583,697]) ).
thf(1463,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf65 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[1462:[bind(A,$thf( C )),bind(B,$thf( skaf65 @ C ))]]) ).
thf(1491,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf65 @ A ) @ nil ) ),
inference(simp,[status(thm)],[1463]) ).
thf(289,plain,
! [B: $i,A: $i] :
( ~ ( frontsegP @ A @ B )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( ( app @ B @ ( skaf45 @ A @ B ) )
= A ) ),
inference(cnf,[status(esa)],[288]) ).
thf(290,plain,
! [B: $i,A: $i] :
( ( ( app @ B @ ( skaf45 @ A @ B ) )
= A )
| ~ ( frontsegP @ A @ B )
| ~ ( ssList @ B )
| ~ ( ssList @ A ) ),
inference(lifteq,[status(thm)],[289]) ).
thf(378,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( rearsegP @ A @ B )
| ~ ( ssList @ C )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( rearsegP @ ( app @ C @ A ) @ B ) ),
inference(cnf,[status(esa)],[377]) ).
thf(27984,plain,
! [B: $i,A: $i] :
( ( strictorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf60 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[406,328]) ).
thf(27985,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf60 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[27984:[bind(A,$thf( C )),bind(B,$thf( skaf60 @ C ))]]) ).
thf(28017,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf60 @ A ) @ nil ) ),
inference(simp,[status(thm)],[27985]) ).
thf(105,axiom,
! [B: $i,A: $i] :
( ~ ( totalorderedP @ ( cons @ A @ B ) )
| ~ ( ssList @ B )
| ~ ( ssItem @ A )
| ( leq @ A @ ( hd @ B ) )
| ( nil = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause135) ).
thf(433,plain,
! [B: $i,A: $i] :
( ~ ( totalorderedP @ ( cons @ A @ B ) )
| ~ ( ssList @ B )
| ~ ( ssItem @ A )
| ( leq @ A @ ( hd @ B ) )
| ( nil = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(9509,plain,
( ~ ( geq @ skac3 @ skac2 )
| ( ( geq @ skac2 @ skac3 )
!= ( geq @ skac3 @ skac2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[9480]) ).
thf(9510,plain,
( ~ ( geq @ skac3 @ skac2 )
| ( ( geq @ skac2 @ skac3 )
!= ( geq @ skac3 @ skac2 ) ) ),
inference(simp,[status(thm)],[9509]) ).
thf(139,axiom,
! [C: $i,B: $i,A: $i] :
( ( A != B )
| ~ ( ssList @ C )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( memberP @ ( cons @ B @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause138) ).
thf(510,plain,
! [C: $i,B: $i,A: $i] :
( ( A != B )
| ~ ( ssList @ C )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( memberP @ ( cons @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(15450,plain,
! [A: $i] :
( ( rearsegP @ A @ nil )
| ( ( ssList @ ( app @ sk2 @ ( tl @ sk2 ) ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13769,292]) ).
thf(15451,plain,
rearsegP @ ( app @ sk2 @ ( tl @ sk2 ) ) @ nil,
inference(pattern_uni,[status(thm)],[15450:[bind(A,$thf( app @ sk2 @ ( tl @ sk2 ) ))]]) ).
thf(4403,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ( ( ssList @ ( app @ sk2 @ ( app @ sk2 @ nil ) ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4238,236]) ).
thf(4404,plain,
~ ( neq @ ( app @ sk2 @ ( app @ sk2 @ nil ) ) @ ( app @ sk2 @ ( app @ sk2 @ nil ) ) ),
inference(pattern_uni,[status(thm)],[4403:[bind(A,$thf( app @ sk2 @ ( app @ sk2 @ nil ) ))]]) ).
thf(36,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( lt @ A @ B )
| ~ ( lt @ B @ C )
| ~ ( ssItem @ C )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( lt @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause155) ).
thf(272,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( lt @ A @ B )
| ~ ( lt @ B @ C )
| ~ ( ssItem @ C )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( lt @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(15466,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( app @ sk2 @ ( skaf76 @ A ) ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3991,292]) ).
thf(15467,plain,
! [A: $i] : ( rearsegP @ ( app @ sk2 @ ( skaf76 @ A ) ) @ nil ),
inference(pattern_uni,[status(thm)],[15466:[bind(A,$thf( E )),bind(B,$thf( app @ sk2 @ ( skaf76 @ E ) ))]]) ).
thf(15544,plain,
! [A: $i] : ( rearsegP @ ( app @ sk2 @ ( skaf76 @ A ) ) @ nil ),
inference(simp,[status(thm)],[15467]) ).
thf(13840,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssItem @ ( skaf78 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[613,286]) ).
thf(13841,plain,
! [A: $i] :
~ ( neq @ ( skaf78 @ A ) @ ( skaf78 @ A ) ),
inference(pattern_uni,[status(thm)],[13840:[bind(A,$thf( C )),bind(B,$thf( skaf78 @ C ))]]) ).
thf(13855,plain,
! [A: $i] :
~ ( neq @ ( skaf78 @ A ) @ ( skaf78 @ A ) ),
inference(simp,[status(thm)],[13841]) ).
thf(148,axiom,
! [A: $i] :
( ~ ( ssItem @ A )
| ( strictorderP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause68) ).
thf(536,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( strictorderP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(214,plain,
( ~ ( neq @ sk1 @ nil )
| ~ ( segmentP @ sk2 @ sk1 ) ),
inference(cnf,[status(esa)],[204]) ).
thf(1907,plain,
! [A: $i] :
( ~ ( singletonP @ sk1 )
| ( totalorderedP @ sk1 )
| ( ( cons @ ( skaf44 @ sk1 ) @ nil )
!= ( cons @ ( skaf44 @ A ) @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[1641,767]) ).
thf(1908,plain,
( ~ ( singletonP @ sk1 )
| ( totalorderedP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[1907:[bind(A,$thf( sk1 ))]]) ).
thf(431,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssItem @ ( hd @ A ) )
| ( nil = A ) ),
inference(cnf,[status(esa)],[430]) ).
thf(432,plain,
! [A: $i] :
( ( nil = A )
| ~ ( ssList @ A )
| ( ssItem @ ( hd @ A ) ) ),
inference(lifteq,[status(thm)],[431]) ).
thf(262,plain,
! [B: $i,A: $i] :
( ~ ( geq @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( leq @ B @ A ) ),
inference(cnf,[status(esa)],[261]) ).
thf(27960,plain,
! [B: $i,A: $i] :
( ( strictorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf65 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[583,328]) ).
thf(27961,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf65 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[27960:[bind(A,$thf( C )),bind(B,$thf( skaf65 @ C ))]]) ).
thf(28036,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf65 @ A ) @ nil ) ),
inference(simp,[status(thm)],[27961]) ).
thf(84814,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ B )
| ( ( ssList @ ( skaf68 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[474,401]) ).
thf(84815,plain,
! [A: $i] : ( rearsegP @ ( skaf68 @ A ) @ ( skaf68 @ A ) ),
inference(pattern_uni,[status(thm)],[84814:[bind(A,$thf( C )),bind(B,$thf( skaf68 @ C ))]]) ).
thf(84871,plain,
! [A: $i] : ( rearsegP @ ( skaf68 @ A ) @ ( skaf68 @ A ) ),
inference(simp,[status(thm)],[84815]) ).
thf(404,plain,
! [C: $i,B: $i,A: $i] :
( ( ( app @ A @ B )
!= ( app @ C @ B ) )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( ssList @ C )
| ( A = C ) ),
inference(cnf,[status(esa)],[403]) ).
thf(405,plain,
! [C: $i,B: $i,A: $i] :
( ( ( app @ A @ B )
!= ( app @ C @ B ) )
| ( A = C )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( ssList @ C ) ),
inference(lifteq,[status(thm)],[404]) ).
thf(20112,plain,
! [A: $i] :
( ~ ( rearsegP @ nil @ A )
| ~ ( ssList @ A )
| ( nil != sk2 )
| ( A != sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[310,216]) ).
thf(20113,plain,
! [A: $i] :
( ~ ( rearsegP @ nil @ A )
| ~ ( ssList @ A )
| ( nil != sk2 )
| ( A != sk1 ) ),
inference(pattern_uni,[status(thm)],[20112:[]]) ).
thf(21826,plain,
( ~ ( rearsegP @ nil @ sk1 )
| ~ ( ssList @ sk1 )
| ( nil != sk2 ) ),
inference(simp,[status(thm)],[20113]) ).
thf(25057,plain,
( ~ ( rearsegP @ nil @ sk1 )
| ~ $true
| ( nil != sk2 ) ),
inference(rewrite,[status(thm)],[21826,200]) ).
thf(25058,plain,
( ~ ( rearsegP @ nil @ sk1 )
| ( nil != sk2 ) ),
inference(simp,[status(thm)],[25057]) ).
thf(26442,plain,
( ~ ( rearsegP @ nil @ sk1 )
| ( sk2 != sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[21492,25058]) ).
thf(26443,plain,
( ~ ( rearsegP @ nil @ sk1 )
| ( sk2 != sk1 ) ),
inference(pattern_uni,[status(thm)],[26442:[]]) ).
thf(844,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf58 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[347,236]) ).
thf(845,plain,
! [A: $i] :
~ ( neq @ ( skaf58 @ A ) @ ( skaf58 @ A ) ),
inference(pattern_uni,[status(thm)],[844:[bind(A,$thf( C )),bind(B,$thf( skaf58 @ C ))]]) ).
thf(867,plain,
! [A: $i] :
~ ( neq @ ( skaf58 @ A ) @ ( skaf58 @ A ) ),
inference(simp,[status(thm)],[845]) ).
thf(273,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( lt @ A @ B )
| ~ ( lt @ B @ C )
| ~ ( ssItem @ C )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( lt @ A @ C ) ),
inference(cnf,[status(esa)],[272]) ).
thf(13822,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssItem @ ( skaf44 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[361,286]) ).
thf(13823,plain,
! [A: $i] :
~ ( neq @ ( skaf44 @ A ) @ ( skaf44 @ A ) ),
inference(pattern_uni,[status(thm)],[13822:[bind(A,$thf( C )),bind(B,$thf( skaf44 @ C ))]]) ).
thf(13862,plain,
! [A: $i] :
~ ( neq @ ( skaf44 @ A ) @ ( skaf44 @ A ) ),
inference(simp,[status(thm)],[13823]) ).
thf(854,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf73 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[387,236]) ).
thf(855,plain,
! [A: $i] :
~ ( neq @ ( skaf73 @ A ) @ ( skaf73 @ A ) ),
inference(pattern_uni,[status(thm)],[854:[bind(A,$thf( C )),bind(B,$thf( skaf73 @ C ))]]) ).
thf(865,plain,
! [A: $i] :
~ ( neq @ ( skaf73 @ A ) @ ( skaf73 @ A ) ),
inference(simp,[status(thm)],[855]) ).
thf(324,plain,
! [C: $i,B: $i,A: $i] :
( ( ( app @ A @ B )
!= C )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( ssList @ C )
| ( rearsegP @ C @ B ) ),
inference(cnf,[status(esa)],[323]) ).
thf(325,plain,
! [C: $i,B: $i,A: $i] :
( ( ( app @ A @ B )
!= C )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( ssList @ C )
| ( rearsegP @ C @ B ) ),
inference(lifteq,[status(thm)],[324]) ).
thf(326,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( ssList @ ( app @ A @ B ) )
| ( rearsegP @ ( app @ A @ B ) @ B ) ),
inference(simp,[status(thm)],[325]) ).
thf(15462,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( skaf77 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[304,292]) ).
thf(15463,plain,
! [A: $i] : ( rearsegP @ ( skaf77 @ A ) @ nil ),
inference(pattern_uni,[status(thm)],[15462:[bind(A,$thf( C )),bind(B,$thf( skaf77 @ C ))]]) ).
thf(15540,plain,
! [A: $i] : ( rearsegP @ ( skaf77 @ A ) @ nil ),
inference(simp,[status(thm)],[15463]) ).
thf(15388,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( skaf72 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[252,292]) ).
thf(15389,plain,
! [A: $i] : ( rearsegP @ ( skaf72 @ A ) @ nil ),
inference(pattern_uni,[status(thm)],[15388:[bind(A,$thf( C )),bind(B,$thf( skaf72 @ C ))]]) ).
thf(15512,plain,
! [A: $i] : ( rearsegP @ ( skaf72 @ A ) @ nil ),
inference(simp,[status(thm)],[15389]) ).
thf(146,axiom,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( nil = B )
| ( ( tl @ ( app @ B @ A ) )
= ( app @ ( tl @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause133) ).
thf(532,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( nil = B )
| ( ( tl @ ( app @ B @ A ) )
= ( app @ ( tl @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(84759,plain,
! [A: $i] :
( ( rearsegP @ A @ A )
| ( ( ssList @ ( app @ sk2 @ ( tl @ sk2 ) ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13769,401]) ).
thf(84760,plain,
rearsegP @ ( app @ sk2 @ ( tl @ sk2 ) ) @ ( app @ sk2 @ ( tl @ sk2 ) ),
inference(pattern_uni,[status(thm)],[84759:[bind(A,$thf( app @ sk2 @ ( tl @ sk2 ) ))]]) ).
thf(160,axiom,
! [B: $i,A: $i] :
( ~ ( totalorderedP @ ( cons @ A @ B ) )
| ~ ( ssList @ B )
| ~ ( ssItem @ A )
| ( totalorderedP @ B )
| ( nil = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause125) ).
thf(564,plain,
! [B: $i,A: $i] :
( ~ ( totalorderedP @ ( cons @ A @ B ) )
| ~ ( ssList @ B )
| ~ ( ssItem @ A )
| ( totalorderedP @ B )
| ( nil = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(21052,plain,
! [A: $i] :
( ~ ( rearsegP @ nil @ A )
| ~ ( ssList @ A )
| ( skac3 != nil )
| ( A != skac2 ) ),
inference(paramod_ordered,[status(thm)],[310,223]) ).
thf(21053,plain,
( ~ ( rearsegP @ nil @ skac2 )
| ~ ( ssList @ skac2 )
| ( skac3 != nil ) ),
inference(pattern_uni,[status(thm)],[21052:[bind(A,$thf( skac2 ))]]) ).
thf(239,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( lt @ B @ C )
| ~ ( ssItem @ C )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( lt @ A @ C ) ),
inference(cnf,[status(esa)],[238]) ).
thf(27929,plain,
! [B: $i,A: $i] :
( ( strictorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf54 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[582,328]) ).
thf(27930,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf54 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[27929:[bind(A,$thf( C )),bind(B,$thf( skaf54 @ C ))]]) ).
thf(28021,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf54 @ A ) @ nil ) ),
inference(simp,[status(thm)],[27930]) ).
thf(15444,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( skaf51 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[535,292]) ).
thf(15445,plain,
! [A: $i] : ( rearsegP @ ( skaf51 @ A ) @ nil ),
inference(pattern_uni,[status(thm)],[15444:[bind(A,$thf( C )),bind(B,$thf( skaf51 @ C ))]]) ).
thf(15533,plain,
! [A: $i] : ( rearsegP @ ( skaf51 @ A ) @ nil ),
inference(simp,[status(thm)],[15445]) ).
thf(30718,plain,
( ( sk2 != sk1 )
| ( ( rearsegP @ nil @ sk1 )
!= ( rearsegP @ sk1 @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[15489,26443]) ).
thf(30722,plain,
( ( sk2 != sk1 )
| ( nil != sk1 )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[30718]) ).
thf(30767,plain,
( ( sk2 != sk1 )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[30722]) ).
thf(1310,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf74 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[578,438]) ).
thf(1311,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf74 @ A ) ),
inference(pattern_uni,[status(thm)],[1310:[bind(A,$thf( C )),bind(B,$thf( skaf74 @ C ))]]) ).
thf(1335,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf74 @ A ) ),
inference(simp,[status(thm)],[1311]) ).
thf(22291,plain,
( ~ ( ssList @ skac2 )
| ( skac3 != nil )
| ( ( rearsegP @ nil @ skac2 )
!= ( rearsegP @ nil @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[15475,21053]) ).
thf(22434,plain,
( ~ ( ssList @ skac2 )
| ( skac3 != nil )
| ( nil != nil )
| ( skac2 != nil ) ),
inference(simp,[status(thm)],[22291]) ).
thf(22448,plain,
( ~ ( ssList @ skac2 )
| ( skac3 != nil )
| ( skac2 != nil ) ),
inference(simp,[status(thm)],[22434]) ).
thf(22730,plain,
( ( skac3 != nil )
| ( skac2 != nil )
| ( ( ssList @ skac2 )
!= ( ssList @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[287,22448]) ).
thf(22758,plain,
( ( skac3 != nil )
| ( skac2 != nil )
| ( skac2 != nil ) ),
inference(simp,[status(thm)],[22730]) ).
thf(22833,plain,
( ( skac3 != nil )
| ( skac2 != nil ) ),
inference(simp,[status(thm)],[22758]) ).
thf(55272,plain,
! [A: $i] :
( ( geq @ A @ A )
| ( ( ssItem @ skac2 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[525,373]) ).
thf(55273,plain,
geq @ skac2 @ skac2,
inference(pattern_uni,[status(thm)],[55272:[bind(A,$thf( skac2 ))]]) ).
thf(118,axiom,
! [A: $i] :
( ~ ( ssItem @ A )
| ( leq @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause62) ).
thf(464,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( leq @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(331,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( totalorderP @ A )
| ( ( app @ ( app @ ( skaf56 @ A ) @ ( cons @ ( skaf54 @ A ) @ ( skaf57 @ A ) ) ) @ ( cons @ ( skaf55 @ A ) @ ( skaf58 @ A ) ) )
= A ) ),
inference(cnf,[status(esa)],[330]) ).
thf(332,plain,
! [A: $i] :
( ( ( app @ ( app @ ( skaf56 @ A ) @ ( cons @ ( skaf54 @ A ) @ ( skaf57 @ A ) ) ) @ ( cons @ ( skaf55 @ A ) @ ( skaf58 @ A ) ) )
= A )
| ~ ( ssList @ A )
| ( totalorderP @ A ) ),
inference(lifteq,[status(thm)],[331]) ).
thf(165,axiom,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( lt @ A @ B )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause121) ).
thf(575,plain,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( lt @ A @ B )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(1518,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf50 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[593,438]) ).
thf(1519,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf50 @ A ) ),
inference(pattern_uni,[status(thm)],[1518:[bind(A,$thf( C )),bind(B,$thf( skaf50 @ C ))]]) ).
thf(1537,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf50 @ A ) ),
inference(simp,[status(thm)],[1519]) ).
thf(1017,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf53 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[451,236]) ).
thf(1018,plain,
! [A: $i] :
~ ( neq @ ( skaf53 @ A ) @ ( skaf53 @ A ) ),
inference(pattern_uni,[status(thm)],[1017:[bind(A,$thf( C )),bind(B,$thf( skaf53 @ C ))]]) ).
thf(1019,plain,
! [A: $i] :
~ ( neq @ ( skaf53 @ A ) @ ( skaf53 @ A ) ),
inference(simp,[status(thm)],[1018]) ).
thf(84735,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ B )
| ( ( ssList @ ( skaf53 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[451,401]) ).
thf(84736,plain,
! [A: $i] : ( rearsegP @ ( skaf53 @ A ) @ ( skaf53 @ A ) ),
inference(pattern_uni,[status(thm)],[84735:[bind(A,$thf( C )),bind(B,$thf( skaf53 @ C ))]]) ).
thf(84847,plain,
! [A: $i] : ( rearsegP @ ( skaf53 @ A ) @ ( skaf53 @ A ) ),
inference(simp,[status(thm)],[84736]) ).
thf(6398,plain,
! [B: $i,A: $i] :
( ( ssList @ ( app @ sk2 @ B ) )
| ( ( ssList @ ( app @ sk2 @ ( skaf53 @ A ) ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4012,2922]) ).
thf(6399,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( skaf53 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[6398:[bind(A,$thf( E )),bind(B,$thf( app @ sk2 @ ( skaf53 @ E ) ))]]) ).
thf(6452,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( skaf53 @ A ) ) ) ),
inference(simp,[status(thm)],[6399]) ).
thf(869,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf61 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[402,236]) ).
thf(870,plain,
! [A: $i] :
~ ( neq @ ( skaf61 @ A ) @ ( skaf61 @ A ) ),
inference(pattern_uni,[status(thm)],[869:[bind(A,$thf( C )),bind(B,$thf( skaf61 @ C ))]]) ).
thf(871,plain,
! [A: $i] :
~ ( neq @ ( skaf61 @ A ) @ ( skaf61 @ A ) ),
inference(simp,[status(thm)],[870]) ).
thf(367,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( frontsegP @ A @ B )
| ( C != D )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ~ ( ssItem @ D )
| ~ ( ssItem @ C )
| ( frontsegP @ ( cons @ C @ A ) @ ( cons @ D @ B ) ) ),
inference(cnf,[status(esa)],[366]) ).
thf(368,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C != D )
| ~ ( frontsegP @ A @ B )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ~ ( ssItem @ D )
| ~ ( ssItem @ C )
| ( frontsegP @ ( cons @ C @ A ) @ ( cons @ D @ B ) ) ),
inference(lifteq,[status(thm)],[367]) ).
thf(369,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( frontsegP @ A @ B )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ~ ( ssItem @ C )
| ( frontsegP @ ( cons @ C @ A ) @ ( cons @ C @ B ) ) ),
inference(simp,[status(thm)],[368]) ).
thf(825,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf70 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[399,697]) ).
thf(826,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf70 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[825:[bind(A,$thf( C )),bind(B,$thf( skaf70 @ C ))]]) ).
thf(839,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf70 @ A ) @ nil ) ),
inference(simp,[status(thm)],[826]) ).
thf(15478,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( app @ sk2 @ ( skaf75 @ A ) ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3987,292]) ).
thf(15479,plain,
! [A: $i] : ( rearsegP @ ( app @ sk2 @ ( skaf75 @ A ) ) @ nil ),
inference(pattern_uni,[status(thm)],[15478:[bind(A,$thf( E )),bind(B,$thf( app @ sk2 @ ( skaf75 @ E ) ))]]) ).
thf(15553,plain,
! [A: $i] : ( rearsegP @ ( app @ sk2 @ ( skaf75 @ A ) ) @ nil ),
inference(simp,[status(thm)],[15479]) ).
thf(19018,plain,
! [A: $i] :
( ( strictorderedP @ sk1 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( tl @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12280,292]) ).
thf(19019,plain,
( ( strictorderedP @ sk1 )
| ( rearsegP @ ( tl @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[19018:[bind(A,$thf( tl @ sk1 ))]]) ).
thf(320,plain,
! [B: $i,A: $i] :
( ( ( cons @ A @ nil )
!= B )
| ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( singletonP @ B ) ),
inference(cnf,[status(esa)],[319]) ).
thf(321,plain,
! [B: $i,A: $i] :
( ( ( cons @ A @ nil )
!= B )
| ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( singletonP @ B ) ),
inference(lifteq,[status(thm)],[320]) ).
thf(322,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssList @ ( cons @ A @ nil ) )
| ( singletonP @ ( cons @ A @ nil ) ) ),
inference(simp,[status(thm)],[321]) ).
thf(13816,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ( ( ssItem @ skac3 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[538,286]) ).
thf(13817,plain,
~ ( neq @ skac3 @ skac3 ),
inference(pattern_uni,[status(thm)],[13816:[bind(A,$thf( skac3 ))]]) ).
thf(15412,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( app @ sk2 @ ( skaf72 @ A ) ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3999,292]) ).
thf(15413,plain,
! [A: $i] : ( rearsegP @ ( app @ sk2 @ ( skaf72 @ A ) ) @ nil ),
inference(pattern_uni,[status(thm)],[15412:[bind(A,$thf( E )),bind(B,$thf( app @ sk2 @ ( skaf72 @ E ) ))]]) ).
thf(15521,plain,
! [A: $i] : ( rearsegP @ ( app @ sk2 @ ( skaf72 @ A ) ) @ nil ),
inference(simp,[status(thm)],[15413]) ).
thf(23011,plain,
! [B: $i,A: $i] :
( ( duplicatefreeP @ A )
| ( ssItem @ B )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[203,314]) ).
thf(23012,plain,
! [A: $i] :
( ( duplicatefreeP @ sk2 )
| ( ssItem @ A ) ),
inference(pattern_uni,[status(thm)],[23011:[bind(A,$thf( sk2 ))]]) ).
thf(23156,plain,
! [A: $i] :
( ( duplicatefreeP @ sk2 )
| ( ssItem @ A ) ),
inference(simp,[status(thm)],[23012]) ).
thf(196,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( frontsegP @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause61) ).
thf(639,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( frontsegP @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(1178,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf51 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[535,236]) ).
thf(1179,plain,
! [A: $i] :
~ ( neq @ ( skaf51 @ A ) @ ( skaf51 @ A ) ),
inference(pattern_uni,[status(thm)],[1178:[bind(A,$thf( C )),bind(B,$thf( skaf51 @ C ))]]) ).
thf(1184,plain,
! [A: $i] :
~ ( neq @ ( skaf51 @ A ) @ ( skaf51 @ A ) ),
inference(simp,[status(thm)],[1179]) ).
thf(5389,plain,
! [B: $i,A: $i] :
( ( ssList @ ( app @ sk2 @ B ) )
| ( ( ssList @ ( app @ sk2 @ ( skaf66 @ A ) ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3998,2922]) ).
thf(5390,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( skaf66 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[5389:[bind(A,$thf( E )),bind(B,$thf( app @ sk2 @ ( skaf66 @ E ) ))]]) ).
thf(5436,plain,
! [A: $i] : ( ssList @ ( app @ sk2 @ ( app @ sk2 @ ( skaf66 @ A ) ) ) ),
inference(simp,[status(thm)],[5390]) ).
thf(110287,plain,
! [A: $i] :
( ( segmentP @ A @ nil )
| ( ( ssList @ nil )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[287,429]) ).
thf(110288,plain,
segmentP @ nil @ nil,
inference(pattern_uni,[status(thm)],[110287:[bind(A,$thf( nil ))]]) ).
thf(704,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf79 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[253,697]) ).
thf(705,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf79 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[704:[bind(A,$thf( C )),bind(B,$thf( skaf79 @ C ))]]) ).
thf(708,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf79 @ A ) @ nil ) ),
inference(simp,[status(thm)],[705]) ).
thf(232,plain,
! [B: $i,A: $i] :
( ~ ( lt @ A @ B )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( gt @ B @ A ) ),
inference(cnf,[status(esa)],[231]) ).
thf(15396,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( app @ sk2 @ ( skaf53 @ A ) ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4012,292]) ).
thf(15397,plain,
! [A: $i] : ( rearsegP @ ( app @ sk2 @ ( skaf53 @ A ) ) @ nil ),
inference(pattern_uni,[status(thm)],[15396:[bind(A,$thf( E )),bind(B,$thf( app @ sk2 @ ( skaf53 @ E ) ))]]) ).
thf(15516,plain,
! [A: $i] : ( rearsegP @ ( app @ sk2 @ ( skaf53 @ A ) ) @ nil ),
inference(simp,[status(thm)],[15397]) ).
thf(84619,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ B )
| ( ( ssList @ ( skaf58 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[347,401]) ).
thf(84620,plain,
! [A: $i] : ( rearsegP @ ( skaf58 @ A ) @ ( skaf58 @ A ) ),
inference(pattern_uni,[status(thm)],[84619:[bind(A,$thf( C )),bind(B,$thf( skaf58 @ C ))]]) ).
thf(84896,plain,
! [A: $i] : ( rearsegP @ ( skaf58 @ A ) @ ( skaf58 @ A ) ),
inference(simp,[status(thm)],[84620]) ).
thf(150745,plain,
$false,
inference(e,[status(thm)],[892,54031,13854,1237,15537,518,4015,17502,555,629,13955,9458,365,13859,347,11504,15558,333,3979,249,12148,468,84819,481,352,15532,582,55309,9769,308,84901,379,861,15361,408,25260,59140,217,276,25425,449,614,269,202,597,1437,25459,110263,385,384,550,500,15282,715,26125,28018,340,538,1507,15514,4026,1735,15541,55307,15335,709,417,288,53831,55313,436,1265,1703,15435,257,4238,84910,15387,372,504,15648,587,344,4349,4023,357,55302,26311,1577,28028,542,460,28037,3998,1379,9480,15477,421,770,15509,1494,316,261,4008,55317,1641,492,14780,591,110103,485,3973,15554,480,475,84906,51451,30436,4258,443,376,15515,211,646,6189,253,31156,102179,238,84777,514,348,574,353,28032,12330,28033,280,634,221,293,866,396,9700,243,206,16725,453,411,1345,428,1201,265,67869,307,2922,292,248,110304,4629,15379,201,12200,810,381,84859,366,4576,233,452,15503,439,13848,270,15518,16665,55312,11424,334,4016,13850,598,561,15531,429,13860,4021,10975,23081,29650,260,349,5366,424,407,15407,4284,788,252,361,15527,110247,583,493,15546,84699,15417,15498,224,84650,329,13789,28019,13853,27941,15559,578,697,317,650,1534,15513,403,388,4012,610,420,1397,28038,84919,1006,110075,15459,593,4301,31153,225,84868,84851,26111,526,1700,15550,328,471,256,4049,13928,339,43005,55303,476,6501,33777,1016,590,31121,547,622,647,701,1297,12164,13839,457,15560,13718,21492,569,15431,371,15555,393,503,605,55306,84922,266,205,15535,27995,558,15552,530,55237,343,237,15349,244,15538,15499,508,110290,311,3999,398,15506,15520,412,5722,425,28031,9203,12290,279,1595,4017,6052,57537,601,1906,298,430,4380,15570,15707,296,13849,584,110317,423,694,402,843,286,204,259,26296,55315,9295,4032,579,291,1795,15502,4328,30989,12322,641,391,382,572,1332,15594,466,335,236,12146,12280,350,26335,313,33805,17590,498,15530,406,274,55311,377,318,13851,84875,303,764,604,1011,419,362,84802,451,567,245,84925,271,208,30524,1376,863,1175,387,535,323,594,726,621,626,1556,198,15528,4009,552,13857,13856,15543,240,251,1029,895,84903,84849,67651,1022,330,41683,28030,28020,521,399,66862,636,868,4502,31178,15511,110171,226,438,4481,28035,15475,223,608,15405,394,15529,299,241,653,55304,13861,13852,374,15447,12156,17504,617,15539,836,426,1166,648,209,487,525,712,6120,295,15549,282,327,84899,5790,580,15551,16727,30915,414,12174,55316,409,263,310,12256,13769,199,1300,791,441,26133,15556,15753,338,1738,544,4003,370,15519,26386,55305,15557,336,703,613,5504,864,727,386,55247,314,446,859,497,26384,13784,231,9389,1157,15548,4006,55310,15501,30850,84856,539,203,15525,699,813,319,304,28029,258,390,3991,632,401,4010,418,13858,12268,55308,26288,246,207,1193,478,3993,684,346,15508,84624,6257,1491,290,378,28017,433,9510,510,13610,15667,15451,4404,272,15544,13855,4025,536,214,287,1908,300,315,432,262,3892,3987,28036,84871,405,26443,422,867,273,13862,26337,865,373,603,305,326,15540,341,4007,15512,400,635,532,84760,415,564,21053,239,242,28021,15533,437,30767,4024,1335,22833,474,767,55273,283,464,332,575,427,1537,1019,84847,6452,200,277,871,369,395,839,15553,19019,4019,322,486,13817,15521,23156,543,26193,639,491,29979,254,227,26109,1184,5436,15489,110288,708,232,15516,84896]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC119-1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n026.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 19 01:38:22 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.98/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.44/1.04 % [INFO] Parsing done (185ms).
% 1.44/1.05 % [INFO] Running in sequential loop mode.
% 2.01/1.25 % [INFO] eprover registered as external prover.
% 2.01/1.26 % [INFO] cvc4 registered as external prover.
% 2.01/1.26 % [INFO] Scanning for conjecture ...
% 2.24/1.34 % [INFO] Found a conjecture and 185 axioms. Running axiom selection ...
% 2.41/1.43 % [INFO] Axiom selection finished. Selected 185 axioms (removed 0 axioms).
% 2.90/1.52 % [INFO] Problem is propositional (TPTP CNF).
% 2.90/1.53 % [INFO] Type checking passed.
% 2.90/1.54 % [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 ...
% 244.24/45.64 % External prover 'e' found a proof!
% 244.24/45.64 % [INFO] Killing All external provers ...
% 244.24/45.64 % Time passed: 45115ms (effective reasoning time: 44587ms)
% 244.24/45.64 % 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)>
% 244.24/45.64 % Axioms used in derivation (185): clause144, clause82, clause60, clause65, clause128, clause171, clause71, clause113, clause139, clause3, clause29, clause160, clause43, clause32, clause18, clause54, clause117, clause88, clause59, clause99, clause48, clause146, clause37, clause165, clause108, clause93, clause105, clause185, clause77, clause135, clause95, clause101, clause168, clause129, clause81, clause55, clause164, clause154, clause66, clause17, clause70, clause118, clause181, clause22, clause124, clause92, clause157, clause87, clause84, clause7, clause25, clause11, clause14, clause112, clause76, clause130, clause49, clause169, clause13, clause31, clause24, clause132, clause121, clause42, clause109, clause104, clause2, clause158, clause141, clause143, clause64, clause166, clause38, clause16, clause28, clause98, clause53, clause176, clause152, clause170, clause155, clause136, clause12, clause179, clause111, clause79, clause97, clause147, clause180, clause163, clause75, clause125, clause100, clause23, clause114, clause6, clause174, clause86, clause184, clause133, clause122, clause103, clause1, clause151, clause167, clause34, clause159, clause140, clause177, clause5, clause69, clause68, clause148, clause134, clause27, clause110, clause41, clause39, clause173, clause57, clause162, clause137, clause35, clause8, clause183, clause30, clause145, clause20, clause52, clause46, clause156, clause90, clause126, clause115, clause63, clause89, clause44, clause50, clause150, clause102, clause182, clause72, clause33, clause94, clause73, clause83, clause175, clause107, clause19, clause123, clause178, clause78, clause116, clause4, clause26, clause149, clause58, clause96, clause172, clause142, clause9, clause131, clause120, clause80, clause56, clause10, clause161, clause67, clause138, clause21, clause127, clause119, clause15, clause153, clause45, clause40, clause85, clause91, clause51, clause106, clause61, clause62, clause74, clause47, clause36
% 244.24/45.64 % No. of inferences in proof: 1511
% 244.24/45.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 45115 ms resp. 44587 ms w/o parsing
% 244.83/45.86 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 244.83/45.86 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------