TSTP Solution File: SWC166-1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWC166-1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n005.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 12:10:06 EDT 2023
% Result : Unsatisfiable 141.28s 25.62s
% Output : Refutation 141.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 274
% Syntax : Number of formulae : 1355 ( 491 unt; 76 typ; 0 def)
% Number of atoms : 3473 ( 768 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 9644 (1884 ~;1694 |; 0 &;6066 @)
% ( 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 : 79 ( 76 usr; 13 con; 0-2 aty)
% Number of variables : 1579 ( 0 ^;1579 !; 0 ?;1579 :)
% 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(singletonP_type,type,
singletonP: $i > $o ).
thf(ssItem_type,type,
ssItem: $i > $o ).
thf(sk5_type,type,
sk5: $i ).
thf(sk6_type,type,
sk6: $i ).
thf(sk7_type,type,
sk7: $i ).
thf(sk8_type,type,
sk8: $i ).
thf(app_type,type,
app: $i > $i > $i ).
thf(cons_type,type,
cons: $i > $i > $i ).
thf(nil_type,type,
nil: $i ).
thf(neq_type,type,
neq: $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(memberP_type,type,
memberP: $i > $i > $o ).
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(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(segmentP_type,type,
segmentP: $i > $i > $o ).
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(38,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(269,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)],[38]) ).
thf(270,plain,
! [B: $i,A: $i] :
( ~ ( geq @ A @ B )
| ~ ( geq @ B @ A )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( B = A ) ),
inference(cnf,[status(esa)],[269]) ).
thf(271,plain,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( geq @ A @ B )
| ~ ( geq @ B @ A )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B ) ),
inference(lifteq,[status(thm)],[270]) ).
thf(14,axiom,
skac3 != skac2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause54) ).
thf(216,plain,
skac3 != skac2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(217,plain,
skac3 != skac2,
inference(polarity_switch,[status(thm)],[216]) ).
thf(218,plain,
skac2 != skac3,
inference(lifteq,[status(thm)],[217]) ).
thf(7017,plain,
! [B: $i,A: $i] :
( ~ ( geq @ A @ B )
| ~ ( geq @ B @ A )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( A != skac3 )
| ( B != skac2 ) ),
inference(paramod_ordered,[status(thm)],[271,218]) ).
thf(7018,plain,
! [A: $i] :
( ~ ( geq @ A @ skac2 )
| ~ ( geq @ skac2 @ A )
| ~ ( ssItem @ A )
| ~ ( ssItem @ skac2 )
| ( A != skac3 ) ),
inference(pattern_uni,[status(thm)],[7017:[bind(A,$thf( A )),bind(B,$thf( skac2 ))]]) ).
thf(7591,plain,
( ~ ( geq @ skac3 @ skac2 )
| ~ ( geq @ skac2 @ skac3 )
| ~ ( ssItem @ skac3 )
| ~ ( ssItem @ skac2 ) ),
inference(simp,[status(thm)],[7018]) ).
thf(150,axiom,
ssItem @ skac3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause9) ).
thf(533,plain,
ssItem @ skac3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(144,axiom,
ssItem @ skac2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause10) ).
thf(520,plain,
ssItem @ skac2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(9875,plain,
( ~ ( geq @ skac3 @ skac2 )
| ~ ( geq @ skac2 @ skac3 )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[7591,533,520]) ).
thf(9876,plain,
( ~ ( geq @ skac3 @ skac2 )
| ~ ( geq @ skac2 @ skac3 ) ),
inference(simp,[status(thm)],[9875]) ).
thf(9923,plain,
( ~ ( geq @ skac3 @ skac2 )
| ( ( geq @ skac2 @ skac3 )
!= ( geq @ skac3 @ skac2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[9876]) ).
thf(9929,plain,
( ~ ( geq @ skac3 @ skac2 )
| ( ( geq @ skac2 @ skac3 )
!= ( geq @ skac3 @ skac2 ) ) ),
inference(simp,[status(thm)],[9923]) ).
thf(152,axiom,
! [A: $i] : ( ssList @ ( skaf63 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause32) ).
thf(537,plain,
! [A: $i] : ( ssList @ ( skaf63 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(64,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( app @ nil @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause74) ).
thf(331,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( app @ nil @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(332,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( app @ nil @ A )
= A ) ),
inference(cnf,[status(esa)],[331]) ).
thf(333,plain,
! [A: $i] :
( ( ( app @ nil @ A )
= A )
| ~ ( ssList @ A ) ),
inference(lifteq,[status(thm)],[332]) ).
thf(24656,plain,
! [B: $i,A: $i] :
( ( ( app @ nil @ B )
= B )
| ( ( ssList @ ( skaf63 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[537,333]) ).
thf(24657,plain,
! [A: $i] :
( ( app @ nil @ ( skaf63 @ A ) )
= ( skaf63 @ A ) ),
inference(pattern_uni,[status(thm)],[24656:[bind(A,$thf( C )),bind(B,$thf( skaf63 @ C ))]]) ).
thf(24878,plain,
! [A: $i] :
( ( app @ nil @ ( skaf63 @ A ) )
= ( skaf63 @ A ) ),
inference(simp,[status(thm)],[24657]) ).
thf(194,axiom,
totalorderedP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause4) ).
thf(629,plain,
totalorderedP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(8,negated_conjecture,
ssItem @ sk5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
thf(210,plain,
ssItem @ sk5,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(133,axiom,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( lt @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause111) ).
thf(488,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( lt @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(489,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( lt @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A ) ),
inference(cnf,[status(esa)],[488]) ).
thf(490,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( lt @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A ) ),
inference(lifteq,[status(thm)],[489]) ).
thf(491,plain,
! [A: $i] :
( ~ ( lt @ A @ A )
| ~ ( ssItem @ A ) ),
inference(simp,[status(thm)],[490]) ).
thf(759,plain,
! [A: $i] :
( ~ ( lt @ A @ A )
| ( ( ssItem @ sk5 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[210,491]) ).
thf(760,plain,
~ ( lt @ sk5 @ sk5 ),
inference(pattern_uni,[status(thm)],[759:[bind(A,$thf( sk5 ))]]) ).
thf(186,axiom,
! [A: $i] : ( ssItem @ ( skaf78 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause17) ).
thf(608,plain,
! [A: $i] : ( ssItem @ ( skaf78 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(2768,plain,
! [B: $i,A: $i] :
( ~ ( lt @ B @ B )
| ( ( ssItem @ ( skaf78 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[608,491]) ).
thf(2769,plain,
! [A: $i] :
~ ( lt @ ( skaf78 @ A ) @ ( skaf78 @ A ) ),
inference(pattern_uni,[status(thm)],[2768:[bind(A,$thf( C )),bind(B,$thf( skaf78 @ C ))]]) ).
thf(2778,plain,
! [A: $i] :
~ ( lt @ ( skaf78 @ A ) @ ( skaf78 @ A ) ),
inference(simp,[status(thm)],[2769]) ).
thf(70,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(345,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)],[70]) ).
thf(346,plain,
! [B: $i,A: $i] :
( ~ ( rearsegP @ A @ B )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( ( app @ ( skaf46 @ A @ B ) @ B )
= A ) ),
inference(cnf,[status(esa)],[345]) ).
thf(347,plain,
! [B: $i,A: $i] :
( ( ( app @ ( skaf46 @ A @ B ) @ B )
= A )
| ~ ( rearsegP @ A @ B )
| ~ ( ssList @ B )
| ~ ( ssList @ A ) ),
inference(lifteq,[status(thm)],[346]) ).
thf(21,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(233,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)],[21]) ).
thf(234,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)],[233]) ).
thf(76,axiom,
! [A: $i] :
( ~ ( leq @ ( skaf55 @ A ) @ ( skaf54 @ A ) )
| ~ ( ssList @ A )
| ( totalorderP @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause94) ).
thf(365,plain,
! [A: $i] :
( ~ ( leq @ ( skaf55 @ A ) @ ( skaf54 @ A ) )
| ~ ( ssList @ A )
| ( totalorderP @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(89,axiom,
! [A: $i] : ( ssItem @ ( skaf70 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause25) ).
thf(394,plain,
! [A: $i] : ( ssItem @ ( skaf70 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(1176,plain,
! [B: $i,A: $i] :
( ~ ( lt @ B @ B )
| ( ( ssItem @ ( skaf70 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[394,491]) ).
thf(1177,plain,
! [A: $i] :
~ ( lt @ ( skaf70 @ A ) @ ( skaf70 @ A ) ),
inference(pattern_uni,[status(thm)],[1176:[bind(A,$thf( C )),bind(B,$thf( skaf70 @ C ))]]) ).
thf(1190,plain,
! [A: $i] :
~ ( lt @ ( skaf70 @ A ) @ ( skaf70 @ A ) ),
inference(simp,[status(thm)],[1177]) ).
thf(29,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(249,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)],[29]) ).
thf(148,axiom,
! [A: $i] : ( ssList @ ( skaf51 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause44) ).
thf(530,plain,
! [A: $i] : ( ssList @ ( skaf51 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( neq @ A @ B )
| ~ ( ssList @ B )
| ~ ( ssList @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause115) ).
thf(228,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( neq @ A @ B )
| ~ ( ssList @ B )
| ~ ( ssList @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(229,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( neq @ A @ B )
| ~ ( ssList @ B )
| ~ ( ssList @ A ) ),
inference(cnf,[status(esa)],[228]) ).
thf(230,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( neq @ A @ B )
| ~ ( ssList @ B )
| ~ ( ssList @ A ) ),
inference(lifteq,[status(thm)],[229]) ).
thf(231,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ~ ( ssList @ A ) ),
inference(simp,[status(thm)],[230]) ).
thf(1547,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf51 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[530,231]) ).
thf(1548,plain,
! [A: $i] :
~ ( neq @ ( skaf51 @ A ) @ ( skaf51 @ A ) ),
inference(pattern_uni,[status(thm)],[1547:[bind(A,$thf( C )),bind(B,$thf( skaf51 @ C ))]]) ).
thf(1554,plain,
! [A: $i] :
~ ( neq @ ( skaf51 @ A ) @ ( skaf51 @ A ) ),
inference(simp,[status(thm)],[1548]) ).
thf(87,axiom,
! [A: $i] : ( ssItem @ ( skaf55 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause40) ).
thf(390,plain,
! [A: $i] : ( ssItem @ ( skaf55 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ( totalorderedP @ ( cons @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause113) ).
thf(222,plain,
! [B: $i,A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ( totalorderedP @ ( cons @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(223,plain,
! [B: $i,A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ( totalorderedP @ ( cons @ B @ A ) ) ),
inference(cnf,[status(esa)],[222]) ).
thf(224,plain,
! [B: $i,A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ( totalorderedP @ ( cons @ B @ A ) ) ),
inference(lifteq,[status(thm)],[223]) ).
thf(225,plain,
! [A: $i] :
( ~ ( ssList @ nil )
| ~ ( ssItem @ A )
| ( totalorderedP @ ( cons @ A @ nil ) ) ),
inference(simp,[status(thm)],[224]) ).
thf(42,axiom,
ssList @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause8) ).
thf(282,plain,
ssList @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(715,plain,
! [A: $i] :
( ~ $true
| ~ ( ssItem @ A )
| ( totalorderedP @ ( cons @ A @ nil ) ) ),
inference(rewrite,[status(thm)],[225,282]) ).
thf(716,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( totalorderedP @ ( cons @ A @ nil ) ) ),
inference(simp,[status(thm)],[715]) ).
thf(1097,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf55 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[390,716]) ).
thf(1098,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf55 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[1097:[bind(A,$thf( C )),bind(B,$thf( skaf55 @ C ))]]) ).
thf(1110,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf55 @ A ) @ nil ) ),
inference(simp,[status(thm)],[1098]) ).
thf(130,axiom,
! [B: $i,A: $i] : ( ssList @ ( skaf47 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause49) ).
thf(481,plain,
! [B: $i,A: $i] : ( ssList @ ( skaf47 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(72,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(352,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)],[72]) ).
thf(173,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(582,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)],[173]) ).
thf(9,negated_conjecture,
ssItem @ sk6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
thf(203,plain,
ssItem @ sk6,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(41,axiom,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( neq @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause117) ).
thf(278,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( neq @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(279,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( neq @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A ) ),
inference(cnf,[status(esa)],[278]) ).
thf(280,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( neq @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A ) ),
inference(lifteq,[status(thm)],[279]) ).
thf(281,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ~ ( ssItem @ A ) ),
inference(simp,[status(thm)],[280]) ).
thf(729,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ( ( ssItem @ sk6 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[203,281]) ).
thf(730,plain,
~ ( neq @ sk6 @ sk6 ),
inference(pattern_uni,[status(thm)],[729:[bind(A,$thf( sk6 ))]]) ).
thf(178,axiom,
! [A: $i] : ( ssList @ ( skaf71 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause24) ).
thf(592,plain,
! [A: $i] : ( ssList @ ( skaf71 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(44,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( rearsegP @ A @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause58) ).
thf(286,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( rearsegP @ A @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(287,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( rearsegP @ A @ nil ) ),
inference(cnf,[status(esa)],[286]) ).
thf(12005,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( skaf71 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[592,287]) ).
thf(12006,plain,
! [A: $i] : ( rearsegP @ ( skaf71 @ A ) @ nil ),
inference(pattern_uni,[status(thm)],[12005:[bind(A,$thf( C )),bind(B,$thf( skaf71 @ C ))]]) ).
thf(12040,plain,
! [A: $i] : ( rearsegP @ ( skaf71 @ A ) @ nil ),
inference(simp,[status(thm)],[12006]) ).
thf(11,negated_conjecture,
ssList @ sk8,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
thf(209,plain,
ssList @ sk8,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(39,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( tl @ A ) )
| ( nil = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause75) ).
thf(272,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( tl @ A ) )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(273,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( tl @ A ) )
| ( nil = A ) ),
inference(cnf,[status(esa)],[272]) ).
thf(274,plain,
! [A: $i] :
( ( nil = A )
| ~ ( ssList @ A )
| ( ssList @ ( tl @ A ) ) ),
inference(lifteq,[status(thm)],[273]) ).
thf(9286,plain,
! [A: $i] :
( ( nil = A )
| ( ssList @ ( tl @ A ) )
| ( ( ssList @ sk8 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[209,274]) ).
thf(9287,plain,
( ( nil = sk8 )
| ( ssList @ ( tl @ sk8 ) ) ),
inference(pattern_uni,[status(thm)],[9286:[bind(A,$thf( sk8 ))]]) ).
thf(47,axiom,
strictorderP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause5) ).
thf(294,plain,
strictorderP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(10911,plain,
( ( ssList @ ( tl @ sk8 ) )
| ( strictorderP @ sk8 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[9287,294]) ).
thf(10912,plain,
( ( ssList @ ( tl @ sk8 ) )
| ( strictorderP @ sk8 ) ),
inference(pattern_uni,[status(thm)],[10911:[]]) ).
thf(53,axiom,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ( duplicatefreeP @ A )
| ( ssItem @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause72) ).
thf(308,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ( duplicatefreeP @ A )
| ( ssItem @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(27,axiom,
! [A: $i] : ( ssList @ ( skaf72 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause23) ).
thf(247,plain,
! [A: $i] : ( ssList @ ( skaf72 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(1,negated_conjecture,
ssList @ sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
thf(201,plain,
ssList @ sk1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(309,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ( duplicatefreeP @ A )
| ( ssItem @ B ) ),
inference(cnf,[status(esa)],[308]) ).
thf(17972,plain,
! [B: $i,A: $i] :
( ( duplicatefreeP @ A )
| ( ssItem @ B )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[201,309]) ).
thf(17973,plain,
! [A: $i] :
( ( duplicatefreeP @ sk1 )
| ( ssItem @ A ) ),
inference(pattern_uni,[status(thm)],[17972:[bind(A,$thf( sk1 ))]]) ).
thf(18114,plain,
! [A: $i] :
( ( duplicatefreeP @ sk1 )
| ( ssItem @ A ) ),
inference(simp,[status(thm)],[17973]) ).
thf(6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
thf(202,plain,
sk1 = sk3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(24802,plain,
! [B: $i,A: $i] :
( ( ( app @ nil @ B )
= B )
| ( ( ssList @ ( skaf71 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[592,333]) ).
thf(24803,plain,
! [A: $i] :
( ( app @ nil @ ( skaf71 @ A ) )
= ( skaf71 @ A ) ),
inference(pattern_uni,[status(thm)],[24802:[bind(A,$thf( C )),bind(B,$thf( skaf71 @ C ))]]) ).
thf(24907,plain,
! [A: $i] :
( ( app @ nil @ ( skaf71 @ A ) )
= ( skaf71 @ A ) ),
inference(simp,[status(thm)],[24803]) ).
thf(36,axiom,
! [A: $i] : ( ssItem @ ( skaf64 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause31) ).
thf(266,plain,
! [A: $i] : ( ssItem @ ( skaf64 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(870,plain,
! [B: $i,A: $i] :
( ~ ( lt @ B @ B )
| ( ( ssItem @ ( skaf64 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[266,491]) ).
thf(871,plain,
! [A: $i] :
~ ( lt @ ( skaf64 @ A ) @ ( skaf64 @ A ) ),
inference(pattern_uni,[status(thm)],[870:[bind(A,$thf( C )),bind(B,$thf( skaf64 @ C ))]]) ).
thf(878,plain,
! [A: $i] :
~ ( lt @ ( skaf64 @ A ) @ ( skaf64 @ A ) ),
inference(simp,[status(thm)],[871]) ).
thf(108,axiom,
! [A: $i] :
( ~ ( memberP @ nil @ A )
| ~ ( ssItem @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause71) ).
thf(432,plain,
! [A: $i] :
( ~ ( memberP @ nil @ A )
| ~ ( ssItem @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(433,plain,
! [A: $i] :
( ~ ( memberP @ nil @ A )
| ~ ( ssItem @ A ) ),
inference(cnf,[status(esa)],[432]) ).
thf(654,plain,
! [A: $i] :
( ~ ( memberP @ nil @ A )
| ( ( ssItem @ skac2 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[520,433]) ).
thf(655,plain,
~ ( memberP @ nil @ skac2 ),
inference(pattern_uni,[status(thm)],[654:[bind(A,$thf( skac2 ))]]) ).
thf(86,axiom,
! [A: $i] : ( ssItem @ ( skaf69 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause26) ).
thf(389,plain,
! [A: $i] : ( ssItem @ ( skaf69 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(1054,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf69 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[389,433]) ).
thf(1055,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf69 @ A ) ),
inference(pattern_uni,[status(thm)],[1054:[bind(A,$thf( C )),bind(B,$thf( skaf69 @ C ))]]) ).
thf(1078,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf69 @ A ) ),
inference(simp,[status(thm)],[1055]) ).
thf(23,axiom,
! [A: $i] :
( ~ ( lt @ ( skaf69 @ A ) @ ( skaf70 @ A ) )
| ~ ( ssList @ A )
| ( strictorderedP @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause90) ).
thf(237,plain,
! [A: $i] :
( ~ ( lt @ ( skaf69 @ A ) @ ( skaf70 @ A ) )
| ~ ( ssList @ A )
| ( strictorderedP @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(238,plain,
! [A: $i] :
( ~ ( lt @ ( skaf69 @ A ) @ ( skaf70 @ A ) )
| ~ ( ssList @ A )
| ( strictorderedP @ A ) ),
inference(cnf,[status(esa)],[237]) ).
thf(1136,plain,
! [A: $i] :
( ~ ( lt @ ( skaf69 @ A ) @ ( skaf70 @ A ) )
| ( strictorderedP @ A )
| ( ( ssList @ sk8 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[209,238]) ).
thf(1137,plain,
( ~ ( lt @ ( skaf69 @ sk8 ) @ ( skaf70 @ sk8 ) )
| ( strictorderedP @ sk8 ) ),
inference(pattern_uni,[status(thm)],[1136:[bind(A,$thf( sk8 ))]]) ).
thf(158,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( cons @ ( skaf83 @ A ) @ ( skaf82 @ A ) )
= A )
| ( nil = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause109) ).
thf(550,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( cons @ ( skaf83 @ A ) @ ( skaf82 @ A ) )
= A )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(181,axiom,
! [A: $i] : ( ssList @ ( skaf76 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause19) ).
thf(598,plain,
! [A: $i] : ( ssList @ ( skaf76 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(24636,plain,
! [B: $i,A: $i] :
( ( ( app @ nil @ B )
= B )
| ( ( ssList @ ( skaf76 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[598,333]) ).
thf(24637,plain,
! [A: $i] :
( ( app @ nil @ ( skaf76 @ A ) )
= ( skaf76 @ A ) ),
inference(pattern_uni,[status(thm)],[24636:[bind(A,$thf( C )),bind(B,$thf( skaf76 @ C ))]]) ).
thf(24874,plain,
! [A: $i] :
( ( app @ nil @ ( skaf76 @ A ) )
= ( skaf76 @ A ) ),
inference(simp,[status(thm)],[24637]) ).
thf(195,axiom,
! [A: $i] : ( ssItem @ ( skaf59 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause36) ).
thf(630,plain,
! [A: $i] : ( ssItem @ ( skaf59 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(2811,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssItem @ ( skaf59 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[630,281]) ).
thf(2812,plain,
! [A: $i] :
~ ( neq @ ( skaf59 @ A ) @ ( skaf59 @ A ) ),
inference(pattern_uni,[status(thm)],[2811:[bind(A,$thf( C )),bind(B,$thf( skaf59 @ C ))]]) ).
thf(2844,plain,
! [A: $i] :
~ ( neq @ ( skaf59 @ A ) @ ( skaf59 @ A ) ),
inference(simp,[status(thm)],[2812]) ).
thf(153,axiom,
! [A: $i] : ( ssList @ ( skaf66 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause29) ).
thf(538,plain,
! [A: $i] : ( ssList @ ( skaf66 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(137,axiom,
! [A: $i] : ( ssList @ ( skaf81 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause14) ).
thf(498,plain,
! [A: $i] : ( ssList @ ( skaf81 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(24697,plain,
! [B: $i,A: $i] :
( ( ( app @ nil @ B )
= B )
| ( ( ssList @ ( skaf81 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[498,333]) ).
thf(24698,plain,
! [A: $i] :
( ( app @ nil @ ( skaf81 @ A ) )
= ( skaf81 @ A ) ),
inference(pattern_uni,[status(thm)],[24697:[bind(A,$thf( C )),bind(B,$thf( skaf81 @ C ))]]) ).
thf(24885,plain,
! [A: $i] :
( ( app @ nil @ ( skaf81 @ A ) )
= ( skaf81 @ A ) ),
inference(simp,[status(thm)],[24698]) ).
thf(2,negated_conjecture,
ssList @ sk2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_2) ).
thf(205,plain,
ssList @ sk2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(26,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(244,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)],[26]) ).
thf(245,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)],[244]) ).
thf(246,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)],[245]) ).
thf(1670,plain,
! [A: $i] :
( ( ( app @ ( app @ ( skaf75 @ A ) @ ( cons @ ( skaf74 @ A ) @ ( skaf76 @ A ) ) ) @ ( cons @ ( skaf74 @ A ) @ ( skaf77 @ A ) ) )
= A )
| ( duplicatefreeP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[205,246]) ).
thf(1671,plain,
( ( ( app @ ( app @ ( skaf75 @ sk2 ) @ ( cons @ ( skaf74 @ sk2 ) @ ( skaf76 @ sk2 ) ) ) @ ( cons @ ( skaf74 @ sk2 ) @ ( skaf77 @ sk2 ) ) )
= sk2 )
| ( duplicatefreeP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[1670:[bind(A,$thf( sk2 ))]]) ).
thf(24,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( cyclefreeP @ A )
| ( leq @ ( skaf49 @ A ) @ ( skaf50 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause88) ).
thf(239,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( cyclefreeP @ A )
| ( leq @ ( skaf49 @ A ) @ ( skaf50 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(240,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( cyclefreeP @ A )
| ( leq @ ( skaf49 @ A ) @ ( skaf50 @ A ) ) ),
inference(cnf,[status(esa)],[239]) ).
thf(1309,plain,
! [A: $i] :
( ( cyclefreeP @ A )
| ( leq @ ( skaf49 @ A ) @ ( skaf50 @ A ) )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[205,240]) ).
thf(1310,plain,
( ( cyclefreeP @ sk2 )
| ( leq @ ( skaf49 @ sk2 ) @ ( skaf50 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[1309:[bind(A,$thf( sk2 ))]]) ).
thf(95,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(404,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)],[95]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( geq @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause108) ).
thf(220,plain,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( geq @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(221,plain,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( geq @ B @ A ) ),
inference(cnf,[status(esa)],[220]) ).
thf(683,plain,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( ssItem @ A )
| ( geq @ B @ A )
| ( ( ssItem @ sk6 )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[203,221]) ).
thf(684,plain,
! [A: $i] :
( ~ ( leq @ A @ sk6 )
| ~ ( ssItem @ A )
| ( geq @ sk6 @ A ) ),
inference(pattern_uni,[status(thm)],[683:[bind(A,$thf( A )),bind(B,$thf( sk6 ))]]) ).
thf(897,plain,
! [A: $i] :
( ~ ( leq @ A @ sk6 )
| ( geq @ sk6 @ A )
| ( ( ssItem @ sk6 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[203,684]) ).
thf(898,plain,
( ~ ( leq @ sk6 @ sk6 )
| ( geq @ sk6 @ sk6 ) ),
inference(pattern_uni,[status(thm)],[897:[bind(A,$thf( sk6 ))]]) ).
thf(170,axiom,
! [A: $i] : ( ssItem @ ( skaf54 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause41) ).
thf(577,plain,
! [A: $i] : ( ssItem @ ( skaf54 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(1826,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf54 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[577,716]) ).
thf(1827,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf54 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[1826:[bind(A,$thf( C )),bind(B,$thf( skaf54 @ C ))]]) ).
thf(1835,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf54 @ A ) @ nil ) ),
inference(simp,[status(thm)],[1827]) ).
thf(114,axiom,
! [A: $i] : ( ssList @ ( skaf53 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause42) ).
thf(446,plain,
! [A: $i] : ( ssList @ ( skaf53 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(24772,plain,
! [B: $i,A: $i] :
( ( ( app @ nil @ B )
= B )
| ( ( ssList @ ( skaf53 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[446,333]) ).
thf(24773,plain,
! [A: $i] :
( ( app @ nil @ ( skaf53 @ A ) )
= ( skaf53 @ A ) ),
inference(pattern_uni,[status(thm)],[24772:[bind(A,$thf( C )),bind(B,$thf( skaf53 @ C ))]]) ).
thf(24902,plain,
! [A: $i] :
( ( app @ nil @ ( skaf53 @ A ) )
= ( skaf53 @ A ) ),
inference(simp,[status(thm)],[24773]) ).
thf(1126,plain,
! [A: $i] :
( ~ ( lt @ ( skaf69 @ A ) @ ( skaf70 @ A ) )
| ( strictorderedP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[205,238]) ).
thf(1127,plain,
( ~ ( lt @ ( skaf69 @ sk2 ) @ ( skaf70 @ sk2 ) )
| ( strictorderedP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[1126:[bind(A,$thf( sk2 ))]]) ).
thf(100,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(417,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)],[100]) ).
thf(49,axiom,
! [A: $i] : ( ssList @ ( skaf77 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause18) ).
thf(299,plain,
! [A: $i] : ( ssList @ ( skaf77 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(883,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf77 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[299,231]) ).
thf(884,plain,
! [A: $i] :
~ ( neq @ ( skaf77 @ A ) @ ( skaf77 @ A ) ),
inference(pattern_uni,[status(thm)],[883:[bind(A,$thf( C )),bind(B,$thf( skaf77 @ C ))]]) ).
thf(885,plain,
! [A: $i] :
~ ( neq @ ( skaf77 @ A ) @ ( skaf77 @ A ) ),
inference(simp,[status(thm)],[884]) ).
thf(11911,plain,
! [C: $i,B: $i,A: $i] :
( ( rearsegP @ C @ nil )
| ( ( ssList @ ( skaf47 @ A @ B ) )
!= ( ssList @ C ) ) ),
inference(paramod_ordered,[status(thm)],[481,287]) ).
thf(11912,plain,
! [B: $i,A: $i] : ( rearsegP @ ( skaf47 @ A @ B ) @ nil ),
inference(pattern_uni,[status(thm)],[11911:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( skaf47 @ D @ E ))]]) ).
thf(12009,plain,
! [B: $i,A: $i] : ( rearsegP @ ( skaf47 @ A @ B ) @ nil ),
inference(simp,[status(thm)],[11912]) ).
thf(110,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(436,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)],[110]) ).
thf(174,axiom,
! [A: $i] : ( ssList @ ( skaf56 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause39) ).
thf(585,plain,
! [A: $i] : ( ssList @ ( skaf56 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(1896,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf56 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[585,231]) ).
thf(1897,plain,
! [A: $i] :
~ ( neq @ ( skaf56 @ A ) @ ( skaf56 @ A ) ),
inference(pattern_uni,[status(thm)],[1896:[bind(A,$thf( C )),bind(B,$thf( skaf56 @ C ))]]) ).
thf(1904,plain,
! [A: $i] :
~ ( neq @ ( skaf56 @ A ) @ ( skaf56 @ A ) ),
inference(simp,[status(thm)],[1897]) ).
thf(25,axiom,
! [A: $i] :
( ~ ( singletonP @ A )
| ~ ( ssList @ A )
| ( ( cons @ ( skaf44 @ A ) @ nil )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause101) ).
thf(241,plain,
! [A: $i] :
( ~ ( singletonP @ A )
| ~ ( ssList @ A )
| ( ( cons @ ( skaf44 @ A ) @ nil )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(242,plain,
! [A: $i] :
( ~ ( singletonP @ A )
| ~ ( ssList @ A )
| ( ( cons @ ( skaf44 @ A ) @ nil )
= A ) ),
inference(cnf,[status(esa)],[241]) ).
thf(243,plain,
! [A: $i] :
( ( ( cons @ ( skaf44 @ A ) @ nil )
= A )
| ~ ( singletonP @ A )
| ~ ( ssList @ A ) ),
inference(lifteq,[status(thm)],[242]) ).
thf(1442,plain,
! [A: $i] :
( ( ( cons @ ( skaf44 @ A ) @ nil )
= A )
| ~ ( singletonP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[201,243]) ).
thf(1443,plain,
( ( ( cons @ ( skaf44 @ sk1 ) @ nil )
= sk1 )
| ~ ( singletonP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[1442:[bind(A,$thf( sk1 ))]]) ).
thf(7,negated_conjecture,
singletonP @ sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
thf(207,plain,
singletonP @ sk3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(212,plain,
sk3 = sk1,
inference(lifteq,[status(thm)],[202]) ).
thf(641,plain,
singletonP @ sk1,
inference(rewrite,[status(thm)],[207,212]) ).
thf(2868,plain,
( ( ( cons @ ( skaf44 @ sk1 ) @ nil )
= sk1 )
| ~ $true ),
inference(rewrite,[status(thm)],[1443,641]) ).
thf(2869,plain,
( ( cons @ ( skaf44 @ sk1 ) @ nil )
= sk1 ),
inference(simp,[status(thm)],[2868]) ).
thf(45,axiom,
! [B: $i,A: $i] :
( ( ( app @ A @ B )
!= nil )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( nil = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause118) ).
thf(288,plain,
! [B: $i,A: $i] :
( ( ( app @ A @ B )
!= nil )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(8755,plain,
! [A: $i] :
( ( nil = A )
| ( ssList @ ( tl @ A ) )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[201,274]) ).
thf(8756,plain,
( ( nil = sk1 )
| ( ssList @ ( tl @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[8755:[bind(A,$thf( sk1 ))]]) ).
thf(132,axiom,
~ ( singletonP @ nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause11) ).
thf(486,plain,
~ ( singletonP @ nil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(487,plain,
~ ( singletonP @ nil ),
inference(polarity_switch,[status(thm)],[486]) ).
thf(638,plain,
( ( singletonP @ nil )
!= ( singletonP @ sk3 ) ),
inference(paramod_ordered,[status(thm)],[207,487]) ).
thf(639,plain,
nil != sk3,
inference(simp,[status(thm)],[638]) ).
thf(643,plain,
nil != sk1,
inference(rewrite,[status(thm)],[639,212]) ).
thf(9945,plain,
ssList @ ( tl @ sk1 ),
inference(simplifyReflect,[status(thm)],[8756,643]) ).
thf(9993,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ( ( ssList @ ( tl @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9945,231]) ).
thf(9994,plain,
~ ( neq @ ( tl @ sk1 ) @ ( tl @ sk1 ) ),
inference(pattern_uni,[status(thm)],[9993:[bind(A,$thf( tl @ sk1 ))]]) ).
thf(650,plain,
! [A: $i] :
( ~ ( memberP @ nil @ A )
| ( ( ssItem @ sk6 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[203,433]) ).
thf(651,plain,
~ ( memberP @ nil @ sk6 ),
inference(pattern_uni,[status(thm)],[650:[bind(A,$thf( sk6 ))]]) ).
thf(32,axiom,
! [B: $i,A: $i] :
( ~ ( geq @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( leq @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause107) ).
thf(256,plain,
! [B: $i,A: $i] :
( ~ ( geq @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( leq @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(257,plain,
! [B: $i,A: $i] :
( ~ ( geq @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( leq @ B @ A ) ),
inference(cnf,[status(esa)],[256]) ).
thf(2727,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf76 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[598,231]) ).
thf(2728,plain,
! [A: $i] :
~ ( neq @ ( skaf76 @ A ) @ ( skaf76 @ A ) ),
inference(pattern_uni,[status(thm)],[2727:[bind(A,$thf( C )),bind(B,$thf( skaf76 @ C ))]]) ).
thf(2735,plain,
! [A: $i] :
~ ( neq @ ( skaf76 @ A ) @ ( skaf76 @ A ) ),
inference(simp,[status(thm)],[2728]) ).
thf(79,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(372,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)],[79]) ).
thf(10,negated_conjecture,
ssList @ sk7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
thf(200,plain,
ssList @ sk7,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1329,plain,
! [A: $i] :
( ( cyclefreeP @ A )
| ( leq @ ( skaf49 @ A ) @ ( skaf50 @ A ) )
| ( ( ssList @ sk7 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[200,240]) ).
thf(1330,plain,
( ( cyclefreeP @ sk7 )
| ( leq @ ( skaf49 @ sk7 ) @ ( skaf50 @ sk7 ) ) ),
inference(pattern_uni,[status(thm)],[1329:[bind(A,$thf( sk7 ))]]) ).
thf(701,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[205,231]) ).
thf(702,plain,
~ ( neq @ sk2 @ sk2 ),
inference(pattern_uni,[status(thm)],[701:[bind(A,$thf( sk2 ))]]) ).
thf(69,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(343,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)],[69]) ).
thf(344,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)],[343]) ).
thf(9499,plain,
! [A: $i] :
( ( nil = A )
| ( ssList @ ( tl @ A ) )
| ( ( ssList @ sk7 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[200,274]) ).
thf(9500,plain,
( ( nil = sk7 )
| ( ssList @ ( tl @ sk7 ) ) ),
inference(pattern_uni,[status(thm)],[9499:[bind(A,$thf( sk7 ))]]) ).
thf(11935,plain,
! [A: $i] :
( ( rearsegP @ A @ nil )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[201,287]) ).
thf(11936,plain,
rearsegP @ sk1 @ nil,
inference(pattern_uni,[status(thm)],[11935:[bind(A,$thf( sk1 ))]]) ).
thf(12064,plain,
( ( ssList @ ( tl @ sk7 ) )
| ( rearsegP @ sk1 @ sk7 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[9500,11936]) ).
thf(12065,plain,
( ( ssList @ ( tl @ sk7 ) )
| ( rearsegP @ sk1 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[12064:[]]) ).
thf(74,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(357,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)],[74]) ).
thf(63,axiom,
duplicatefreeP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause2) ).
thf(330,plain,
duplicatefreeP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(11050,plain,
( ( ssList @ ( tl @ sk7 ) )
| ( duplicatefreeP @ sk7 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[9500,330]) ).
thf(11051,plain,
( ( ssList @ ( tl @ sk7 ) )
| ( duplicatefreeP @ sk7 ) ),
inference(pattern_uni,[status(thm)],[11050:[]]) ).
thf(889,plain,
! [A: $i] :
( ~ ( leq @ A @ sk6 )
| ( geq @ sk6 @ A )
| ( ( ssItem @ skac3 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[533,684]) ).
thf(890,plain,
( ~ ( leq @ skac3 @ sk6 )
| ( geq @ sk6 @ skac3 ) ),
inference(pattern_uni,[status(thm)],[889:[bind(A,$thf( skac3 ))]]) ).
thf(9910,plain,
( ~ ( leq @ skac3 @ sk6 )
| ~ ( geq @ skac3 @ skac2 )
| ( ( geq @ skac2 @ skac3 )
!= ( geq @ sk6 @ skac3 ) ) ),
inference(paramod_ordered,[status(thm)],[890,9876]) ).
thf(9931,plain,
( ~ ( leq @ skac3 @ sk6 )
| ~ ( geq @ skac3 @ skac2 )
| ( skac2 != sk6 )
| ( skac3 != skac3 ) ),
inference(simp,[status(thm)],[9910]) ).
thf(9938,plain,
( ~ ( leq @ skac3 @ sk6 )
| ~ ( geq @ skac3 @ skac2 )
| ( skac2 != sk6 ) ),
inference(simp,[status(thm)],[9931]) ).
thf(155,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(542,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)],[155]) ).
thf(129,axiom,
! [A: $i] : ( ssList @ ( skaf52 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause43) ).
thf(480,plain,
! [A: $i] : ( ssList @ ( skaf52 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(1403,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf52 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[480,231]) ).
thf(1404,plain,
! [A: $i] :
~ ( neq @ ( skaf52 @ A ) @ ( skaf52 @ A ) ),
inference(pattern_uni,[status(thm)],[1403:[bind(A,$thf( C )),bind(B,$thf( skaf52 @ C ))]]) ).
thf(1409,plain,
! [A: $i] :
~ ( neq @ ( skaf52 @ A ) @ ( skaf52 @ A ) ),
inference(simp,[status(thm)],[1404]) ).
thf(723,plain,
! [A: $i] :
( ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ sk5 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[210,716]) ).
thf(724,plain,
totalorderedP @ ( cons @ sk5 @ nil ),
inference(pattern_uni,[status(thm)],[723:[bind(A,$thf( sk5 ))]]) ).
thf(166,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(570,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)],[166]) ).
thf(11985,plain,
! [A: $i] :
( ( rearsegP @ A @ nil )
| ( ( ssList @ sk8 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[209,287]) ).
thf(11986,plain,
rearsegP @ sk8 @ nil,
inference(pattern_uni,[status(thm)],[11985:[bind(A,$thf( sk8 ))]]) ).
thf(161,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(559,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)],[161]) ).
thf(115,axiom,
! [A: $i] : ( ssList @ ( skaf75 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause20) ).
thf(447,plain,
! [A: $i] : ( ssList @ ( skaf75 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(1373,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf75 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[447,231]) ).
thf(1374,plain,
! [A: $i] :
~ ( neq @ ( skaf75 @ A ) @ ( skaf75 @ A ) ),
inference(pattern_uni,[status(thm)],[1373:[bind(A,$thf( C )),bind(B,$thf( skaf75 @ C ))]]) ).
thf(1379,plain,
! [A: $i] :
~ ( neq @ ( skaf75 @ A ) @ ( skaf75 @ A ) ),
inference(simp,[status(thm)],[1374]) ).
thf(51,axiom,
! [A: $i] :
( ~ ( rearsegP @ nil @ A )
| ~ ( ssList @ A )
| ( nil = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause82) ).
thf(303,plain,
! [A: $i] :
( ~ ( rearsegP @ nil @ A )
| ~ ( ssList @ A )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(304,plain,
! [A: $i] :
( ~ ( rearsegP @ nil @ A )
| ~ ( ssList @ A )
| ( nil = A ) ),
inference(cnf,[status(esa)],[303]) ).
thf(305,plain,
! [A: $i] :
( ( nil = A )
| ~ ( rearsegP @ nil @ A )
| ~ ( ssList @ A ) ),
inference(lifteq,[status(thm)],[304]) ).
thf(16668,plain,
! [A: $i] :
( ~ ( rearsegP @ nil @ A )
| ~ ( ssList @ A )
| ( A != sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[305,643]) ).
thf(16669,plain,
! [A: $i] :
( ~ ( rearsegP @ nil @ A )
| ~ ( ssList @ A )
| ( A != sk1 ) ),
inference(pattern_uni,[status(thm)],[16668:[]]) ).
thf(17086,plain,
( ~ ( rearsegP @ nil @ sk1 )
| ~ ( ssList @ sk1 ) ),
inference(simp,[status(thm)],[16669]) ).
thf(17561,plain,
( ~ ( rearsegP @ nil @ sk1 )
| ~ $true ),
inference(rewrite,[status(thm)],[17086,201]) ).
thf(17562,plain,
~ ( rearsegP @ nil @ sk1 ),
inference(simp,[status(thm)],[17561]) ).
thf(1565,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf63 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[537,231]) ).
thf(1566,plain,
! [A: $i] :
~ ( neq @ ( skaf63 @ A ) @ ( skaf63 @ A ) ),
inference(pattern_uni,[status(thm)],[1565:[bind(A,$thf( C )),bind(B,$thf( skaf63 @ C ))]]) ).
thf(1572,plain,
! [A: $i] :
~ ( neq @ ( skaf63 @ A ) @ ( skaf63 @ A ) ),
inference(simp,[status(thm)],[1566]) ).
thf(61,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(325,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)],[61]) ).
thf(11131,plain,
( ( ssList @ ( tl @ sk7 ) )
| ( strictorderP @ sk7 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[9500,294]) ).
thf(11132,plain,
( ( ssList @ ( tl @ sk7 ) )
| ( strictorderP @ sk7 ) ),
inference(pattern_uni,[status(thm)],[11131:[]]) ).
thf(91,axiom,
! [A: $i] : ( ssList @ ( skaf61 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause34) ).
thf(397,plain,
! [A: $i] : ( ssList @ ( skaf61 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(24619,plain,
! [B: $i,A: $i] :
( ( ( app @ nil @ B )
= B )
| ( ( ssList @ ( skaf61 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[397,333]) ).
thf(24620,plain,
! [A: $i] :
( ( app @ nil @ ( skaf61 @ A ) )
= ( skaf61 @ A ) ),
inference(pattern_uni,[status(thm)],[24619:[bind(A,$thf( C )),bind(B,$thf( skaf61 @ C ))]]) ).
thf(24871,plain,
! [A: $i] :
( ( app @ nil @ ( skaf61 @ A ) )
= ( skaf61 @ A ) ),
inference(simp,[status(thm)],[24620]) ).
thf(116,axiom,
! [A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ( segmentP @ nil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause79) ).
thf(448,plain,
! [A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ( segmentP @ nil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(1466,plain,
! [A: $i] :
( ( ( cons @ ( skaf44 @ A ) @ nil )
= A )
| ~ ( singletonP @ A )
| ( ( ssList @ sk8 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[209,243]) ).
thf(1467,plain,
( ( ( cons @ ( skaf44 @ sk8 ) @ nil )
= sk8 )
| ~ ( singletonP @ sk8 ) ),
inference(pattern_uni,[status(thm)],[1466:[bind(A,$thf( sk8 ))]]) ).
thf(73,axiom,
! [A: $i] : ( ssItem @ ( skaf44 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause47) ).
thf(356,plain,
! [A: $i] : ( ssItem @ ( skaf44 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(1010,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf44 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[356,716]) ).
thf(1011,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf44 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[1010:[bind(A,$thf( C )),bind(B,$thf( skaf44 @ C ))]]) ).
thf(1027,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf44 @ A ) @ nil ) ),
inference(simp,[status(thm)],[1011]) ).
thf(5075,plain,
! [A: $i] :
( ~ ( singletonP @ sk8 )
| ( totalorderedP @ sk8 )
| ( ( cons @ ( skaf44 @ sk8 ) @ nil )
!= ( cons @ ( skaf44 @ A ) @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[1467,1027]) ).
thf(5076,plain,
( ~ ( singletonP @ sk8 )
| ( totalorderedP @ sk8 ) ),
inference(pattern_uni,[status(thm)],[5075:[bind(A,$thf( sk8 ))]]) ).
thf(34,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(261,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)],[34]) ).
thf(93,axiom,
! [A: $i] : ( ssItem @ ( skaf60 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause35) ).
thf(401,plain,
! [A: $i] : ( ssItem @ ( skaf60 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(1221,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf60 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[401,716]) ).
thf(1222,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf60 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[1221:[bind(A,$thf( C )),bind(B,$thf( skaf60 @ C ))]]) ).
thf(1232,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf60 @ A ) @ nil ) ),
inference(simp,[status(thm)],[1222]) ).
thf(176,axiom,
! [A: $i] : ( ssItem @ ( skaf50 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause45) ).
thf(588,plain,
! [A: $i] : ( ssItem @ ( skaf50 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(59,axiom,
! [A: $i] :
( ~ ( ssItem @ A )
| ( strictorderedP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause66) ).
thf(322,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( strictorderedP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(323,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( strictorderedP @ ( cons @ A @ nil ) ) ),
inference(cnf,[status(esa)],[322]) ).
thf(20913,plain,
! [B: $i,A: $i] :
( ( strictorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf50 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[588,323]) ).
thf(20914,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf50 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[20913:[bind(A,$thf( C )),bind(B,$thf( skaf50 @ C ))]]) ).
thf(20946,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf50 @ A ) @ nil ) ),
inference(simp,[status(thm)],[20914]) ).
thf(860,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssItem @ ( skaf64 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[266,281]) ).
thf(861,plain,
! [A: $i] :
~ ( neq @ ( skaf64 @ A ) @ ( skaf64 @ A ) ),
inference(pattern_uni,[status(thm)],[860:[bind(A,$thf( C )),bind(B,$thf( skaf64 @ C ))]]) ).
thf(881,plain,
! [A: $i] :
~ ( neq @ ( skaf64 @ A ) @ ( skaf64 @ A ) ),
inference(simp,[status(thm)],[861]) ).
thf(1477,plain,
! [A: $i] :
( ( ( cons @ ( skaf44 @ A ) @ nil )
= A )
| ~ ( singletonP @ A )
| ( ( ssList @ sk7 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[200,243]) ).
thf(1478,plain,
( ( ( cons @ ( skaf44 @ sk7 ) @ nil )
= sk7 )
| ~ ( singletonP @ sk7 ) ),
inference(pattern_uni,[status(thm)],[1477:[bind(A,$thf( sk7 ))]]) ).
thf(20862,plain,
! [B: $i,A: $i] :
( ( strictorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf44 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[356,323]) ).
thf(20863,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf44 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[20862:[bind(A,$thf( C )),bind(B,$thf( skaf44 @ C ))]]) ).
thf(20957,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf44 @ A ) @ nil ) ),
inference(simp,[status(thm)],[20863]) ).
thf(27540,plain,
! [A: $i] :
( ~ ( singletonP @ sk7 )
| ( strictorderedP @ sk7 )
| ( ( cons @ ( skaf44 @ sk7 ) @ nil )
!= ( cons @ ( skaf44 @ A ) @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[1478,20957]) ).
thf(27541,plain,
( ~ ( singletonP @ sk7 )
| ( strictorderedP @ sk7 ) ),
inference(pattern_uni,[status(thm)],[27540:[bind(A,$thf( sk7 ))]]) ).
thf(6941,plain,
! [B: $i,A: $i] :
( ~ ( geq @ A @ B )
| ~ ( geq @ B @ A )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( A != sk1 )
| ( B != nil ) ),
inference(paramod_ordered,[status(thm)],[271,643]) ).
thf(6942,plain,
! [A: $i] :
( ~ ( geq @ A @ nil )
| ~ ( geq @ nil @ A )
| ~ ( ssItem @ A )
| ~ ( ssItem @ nil )
| ( A != sk1 ) ),
inference(pattern_uni,[status(thm)],[6941:[bind(A,$thf( A )),bind(B,$thf( nil ))]]) ).
thf(7560,plain,
( ~ ( geq @ sk1 @ nil )
| ~ ( geq @ nil @ sk1 )
| ~ ( ssItem @ sk1 )
| ~ ( ssItem @ nil ) ),
inference(simp,[status(thm)],[6942]) ).
thf(127,axiom,
cyclefreeP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause7) ).
thf(475,plain,
cyclefreeP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(134,axiom,
! [A: $i] : ( ssList @ ( skaf67 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause28) ).
thf(492,plain,
! [A: $i] : ( ssList @ ( skaf67 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(83,axiom,
! [A: $i] : ( ssList @ ( skaf73 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause22) ).
thf(382,plain,
! [A: $i] : ( ssList @ ( skaf73 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(11955,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( skaf73 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[382,287]) ).
thf(11956,plain,
! [A: $i] : ( rearsegP @ ( skaf73 @ A ) @ nil ),
inference(pattern_uni,[status(thm)],[11955:[bind(A,$thf( C )),bind(B,$thf( skaf73 @ C ))]]) ).
thf(12023,plain,
! [A: $i] : ( rearsegP @ ( skaf73 @ A ) @ nil ),
inference(simp,[status(thm)],[11956]) ).
thf(11947,plain,
! [A: $i] :
( ( rearsegP @ A @ nil )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[205,287]) ).
thf(11948,plain,
rearsegP @ sk2 @ nil,
inference(pattern_uni,[status(thm)],[11947:[bind(A,$thf( sk2 ))]]) ).
thf(12068,plain,
( ( ssList @ ( tl @ sk8 ) )
| ( rearsegP @ sk2 @ sk8 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[9287,11948]) ).
thf(12069,plain,
( ( ssList @ ( tl @ sk8 ) )
| ( rearsegP @ sk2 @ sk8 ) ),
inference(pattern_uni,[status(thm)],[12068:[]]) ).
thf(20,axiom,
! [A: $i] : ( ssList @ ( skaf62 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause33) ).
thf(232,plain,
! [A: $i] : ( ssList @ ( skaf62 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(12007,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( skaf62 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[232,287]) ).
thf(12008,plain,
! [A: $i] : ( rearsegP @ ( skaf62 @ A ) @ nil ),
inference(pattern_uni,[status(thm)],[12007:[bind(A,$thf( C )),bind(B,$thf( skaf62 @ C ))]]) ).
thf(12041,plain,
! [A: $i] : ( rearsegP @ ( skaf62 @ A ) @ nil ),
inference(simp,[status(thm)],[12008]) ).
thf(1162,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssItem @ ( skaf70 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[394,281]) ).
thf(1163,plain,
! [A: $i] :
~ ( neq @ ( skaf70 @ A ) @ ( skaf70 @ A ) ),
inference(pattern_uni,[status(thm)],[1162:[bind(A,$thf( C )),bind(B,$thf( skaf70 @ C ))]]) ).
thf(1183,plain,
! [A: $i] :
~ ( neq @ ( skaf70 @ A ) @ ( skaf70 @ A ) ),
inference(simp,[status(thm)],[1163]) ).
thf(35,axiom,
! [B: $i,A: $i] : ( ssList @ ( skaf46 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause50) ).
thf(265,plain,
! [B: $i,A: $i] : ( ssList @ ( skaf46 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(11933,plain,
! [C: $i,B: $i,A: $i] :
( ( rearsegP @ C @ nil )
| ( ( ssList @ ( skaf46 @ A @ B ) )
!= ( ssList @ C ) ) ),
inference(paramod_ordered,[status(thm)],[265,287]) ).
thf(11934,plain,
! [B: $i,A: $i] : ( rearsegP @ ( skaf46 @ A @ B ) @ nil ),
inference(pattern_uni,[status(thm)],[11933:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( skaf46 @ D @ E ))]]) ).
thf(12018,plain,
! [B: $i,A: $i] : ( rearsegP @ ( skaf46 @ A @ B ) @ nil ),
inference(simp,[status(thm)],[11934]) ).
thf(755,plain,
! [A: $i] :
( ~ ( lt @ A @ A )
| ( ( ssItem @ skac2 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[520,491]) ).
thf(756,plain,
~ ( lt @ skac2 @ skac2 ),
inference(pattern_uni,[status(thm)],[755:[bind(A,$thf( skac2 ))]]) ).
thf(27801,plain,
( ( strictorderedP @ sk7 )
| ( ( singletonP @ sk7 )
!= ( singletonP @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[641,27541]) ).
thf(27817,plain,
( ( strictorderedP @ sk7 )
| ( sk7 != sk1 ) ),
inference(simp,[status(thm)],[27801]) ).
thf(58,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(318,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)],[58]) ).
thf(319,plain,
! [C: $i,B: $i,A: $i] :
( ( ( app @ A @ B )
!= C )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( ssList @ C )
| ( rearsegP @ C @ B ) ),
inference(cnf,[status(esa)],[318]) ).
thf(320,plain,
! [C: $i,B: $i,A: $i] :
( ( ( app @ A @ B )
!= C )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( ssList @ C )
| ( rearsegP @ C @ B ) ),
inference(lifteq,[status(thm)],[319]) ).
thf(321,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( ssList @ ( app @ A @ B ) )
| ( rearsegP @ ( app @ A @ B ) @ B ) ),
inference(simp,[status(thm)],[320]) ).
thf(4,negated_conjecture,
ssList @ sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_4) ).
thf(211,plain,
ssList @ sk4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(30,axiom,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( ssList @ ( app @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause85) ).
thf(252,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( ssList @ ( app @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(253,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( ssList @ ( app @ B @ A ) ) ),
inference(cnf,[status(esa)],[252]) ).
thf(71,axiom,
! [A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ( rearsegP @ nil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause81) ).
thf(348,plain,
! [A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ( rearsegP @ nil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(168,axiom,
! [A: $i] : ( ssList @ ( skaf82 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause13) ).
thf(574,plain,
! [A: $i] : ( ssList @ ( skaf82 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(24630,plain,
! [A: $i] :
( ( ( app @ nil @ A )
= A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[201,333]) ).
thf(24631,plain,
( ( app @ nil @ sk1 )
= sk1 ),
inference(pattern_uni,[status(thm)],[24630:[bind(A,$thf( sk1 ))]]) ).
thf(17990,plain,
! [B: $i,A: $i] :
( ( duplicatefreeP @ A )
| ( ssItem @ B )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[205,309]) ).
thf(17991,plain,
! [A: $i] :
( ( duplicatefreeP @ sk2 )
| ( ssItem @ A ) ),
inference(pattern_uni,[status(thm)],[17990:[bind(A,$thf( sk2 ))]]) ).
thf(18123,plain,
! [A: $i] :
( ( duplicatefreeP @ sk2 )
| ( ssItem @ A ) ),
inference(simp,[status(thm)],[17991]) ).
thf(167,axiom,
! [A: $i] : ( ssItem @ ( skaf74 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause21) ).
thf(573,plain,
! [A: $i] : ( ssItem @ ( skaf74 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(20873,plain,
! [B: $i,A: $i] :
( ( strictorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf74 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[573,323]) ).
thf(20874,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf74 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[20873:[bind(A,$thf( C )),bind(B,$thf( skaf74 @ C ))]]) ).
thf(20934,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf74 @ A ) @ nil ) ),
inference(simp,[status(thm)],[20874]) ).
thf(2819,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf59 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[630,433]) ).
thf(2820,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf59 @ A ) ),
inference(pattern_uni,[status(thm)],[2819:[bind(A,$thf( C )),bind(B,$thf( skaf59 @ C ))]]) ).
thf(2833,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf59 @ A ) ),
inference(simp,[status(thm)],[2820]) ).
thf(197,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( frontsegP @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause61) ).
thf(634,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( frontsegP @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(46,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(291,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)],[46]) ).
thf(292,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)],[291]) ).
thf(293,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)],[292]) ).
thf(165,axiom,
! [A: $i] : ( ssItem @ ( skaf83 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause12) ).
thf(569,plain,
! [A: $i] : ( ssItem @ ( skaf83 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(1604,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssItem @ ( skaf83 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[569,281]) ).
thf(1605,plain,
! [A: $i] :
~ ( neq @ ( skaf83 @ A ) @ ( skaf83 @ A ) ),
inference(pattern_uni,[status(thm)],[1604:[bind(A,$thf( C )),bind(B,$thf( skaf83 @ C ))]]) ).
thf(1622,plain,
! [A: $i] :
~ ( neq @ ( skaf83 @ A ) @ ( skaf83 @ A ) ),
inference(simp,[status(thm)],[1605]) ).
thf(123,axiom,
! [A: $i] : ( ssList @ ( skaf68 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause27) ).
thf(469,plain,
! [A: $i] : ( ssList @ ( skaf68 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(1388,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf68 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[469,231]) ).
thf(1389,plain,
! [A: $i] :
~ ( neq @ ( skaf68 @ A ) @ ( skaf68 @ A ) ),
inference(pattern_uni,[status(thm)],[1388:[bind(A,$thf( C )),bind(B,$thf( skaf68 @ C ))]]) ).
thf(1394,plain,
! [A: $i] :
~ ( neq @ ( skaf68 @ A ) @ ( skaf68 @ A ) ),
inference(simp,[status(thm)],[1389]) ).
thf(106,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(428,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)],[106]) ).
thf(12,negated_conjecture,
( ( app @ ( app @ ( app @ sk7 @ ( cons @ sk5 @ nil ) ) @ ( cons @ sk6 @ nil ) ) @ sk8 )
= sk1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
thf(206,plain,
( ( app @ ( app @ ( app @ sk7 @ ( cons @ sk5 @ nil ) ) @ ( cons @ sk6 @ nil ) ) @ sk8 )
= sk1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(20917,plain,
! [B: $i,A: $i] :
( ( strictorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf60 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[401,323]) ).
thf(20918,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf60 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[20917:[bind(A,$thf( C )),bind(B,$thf( skaf60 @ C ))]]) ).
thf(20949,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf60 @ A ) @ nil ) ),
inference(simp,[status(thm)],[20918]) ).
thf(11989,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( skaf56 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[585,287]) ).
thf(11990,plain,
! [A: $i] : ( rearsegP @ ( skaf56 @ A ) @ nil ),
inference(pattern_uni,[status(thm)],[11989:[bind(A,$thf( C )),bind(B,$thf( skaf56 @ C ))]]) ).
thf(12036,plain,
! [A: $i] : ( rearsegP @ ( skaf56 @ A ) @ nil ),
inference(simp,[status(thm)],[11990]) ).
thf(8346,plain,
! [A: $i] :
( ~ ( singletonP @ sk7 )
| ( totalorderedP @ sk7 )
| ( ( cons @ ( skaf44 @ sk7 ) @ nil )
!= ( cons @ ( skaf44 @ A ) @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[1478,1027]) ).
thf(8347,plain,
( ~ ( singletonP @ sk7 )
| ( totalorderedP @ sk7 ) ),
inference(pattern_uni,[status(thm)],[8346:[bind(A,$thf( sk7 ))]]) ).
thf(28,axiom,
! [A: $i] : ( ssItem @ ( skaf79 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause16) ).
thf(248,plain,
! [A: $i] : ( ssItem @ ( skaf79 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(829,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf79 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[248,433]) ).
thf(830,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf79 @ A ) ),
inference(pattern_uni,[status(thm)],[829:[bind(A,$thf( C )),bind(B,$thf( skaf79 @ C ))]]) ).
thf(849,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf79 @ A ) ),
inference(simp,[status(thm)],[830]) ).
thf(16160,plain,
! [A: $i] :
( ( nil = A )
| ~ ( rearsegP @ nil @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[205,305]) ).
thf(16161,plain,
( ( nil = sk2 )
| ~ ( rearsegP @ nil @ sk2 ) ),
inference(pattern_uni,[status(thm)],[16160:[bind(A,$thf( sk2 ))]]) ).
thf(21541,plain,
( ~ ( rearsegP @ nil @ sk2 )
| ~ ( rearsegP @ sk2 @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[16161,17562]) ).
thf(21542,plain,
( ~ ( rearsegP @ nil @ sk2 )
| ~ ( rearsegP @ sk2 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[21541:[]]) ).
thf(10932,plain,
( ( ssList @ ( tl @ sk7 ) )
| ( totalorderedP @ sk7 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[9500,629]) ).
thf(10933,plain,
( ( ssList @ ( tl @ sk7 ) )
| ( totalorderedP @ sk7 ) ),
inference(pattern_uni,[status(thm)],[10932:[]]) ).
thf(147,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(527,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)],[147]) ).
thf(55,axiom,
! [A: $i] : ( ssList @ ( skaf57 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause38) ).
thf(312,plain,
! [A: $i] : ( ssList @ ( skaf57 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(8497,plain,
( ( totalorderedP @ sk7 )
| ( ( singletonP @ sk7 )
!= ( singletonP @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[641,8347]) ).
thf(8508,plain,
( ( totalorderedP @ sk7 )
| ( sk7 != sk1 ) ),
inference(simp,[status(thm)],[8497]) ).
thf(82,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(380,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)],[82]) ).
thf(8922,plain,
! [A: $i] :
( ( nil = A )
| ( ssList @ ( tl @ A ) )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[205,274]) ).
thf(8923,plain,
( ( nil = sk2 )
| ( ssList @ ( tl @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[8922:[bind(A,$thf( sk2 ))]]) ).
thf(10179,plain,
( ( ssList @ ( tl @ sk2 ) )
| ~ ( singletonP @ sk2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[8923,487]) ).
thf(10180,plain,
( ( ssList @ ( tl @ sk2 ) )
| ~ ( singletonP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[10179:[]]) ).
thf(12843,plain,
! [A: $i] :
( ~ ( singletonP @ sk2 )
| ~ ( neq @ A @ A )
| ( ( ssList @ ( tl @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10180,231]) ).
thf(12844,plain,
( ~ ( singletonP @ sk2 )
| ~ ( neq @ ( tl @ sk2 ) @ ( tl @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[12843:[bind(A,$thf( tl @ sk2 ))]]) ).
thf(13351,plain,
( ~ ( neq @ ( tl @ sk2 ) @ ( tl @ sk2 ) )
| ( ( singletonP @ sk2 )
!= ( singletonP @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[641,12844]) ).
thf(13386,plain,
( ~ ( neq @ ( tl @ sk2 ) @ ( tl @ sk2 ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[13351]) ).
thf(21735,plain,
( ~ ( rearsegP @ nil @ sk2 )
| ~ ( singletonP @ sk2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[16161,487]) ).
thf(21736,plain,
( ~ ( rearsegP @ nil @ sk2 )
| ~ ( singletonP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[21735:[]]) ).
thf(712,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf62 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[232,231]) ).
thf(713,plain,
! [A: $i] :
~ ( neq @ ( skaf62 @ A ) @ ( skaf62 @ A ) ),
inference(pattern_uni,[status(thm)],[712:[bind(A,$thf( C )),bind(B,$thf( skaf62 @ C ))]]) ).
thf(714,plain,
! [A: $i] :
~ ( neq @ ( skaf62 @ A ) @ ( skaf62 @ A ) ),
inference(simp,[status(thm)],[713]) ).
thf(2758,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf78 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[608,433]) ).
thf(2759,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf78 @ A ) ),
inference(pattern_uni,[status(thm)],[2758:[bind(A,$thf( C )),bind(B,$thf( skaf78 @ C ))]]) ).
thf(2773,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf78 @ A ) ),
inference(simp,[status(thm)],[2759]) ).
thf(117,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(452,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)],[117]) ).
thf(10830,plain,
( ( ssList @ ( tl @ sk8 ) )
| ( duplicatefreeP @ sk8 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[9287,330]) ).
thf(10831,plain,
( ( ssList @ ( tl @ sk8 ) )
| ( duplicatefreeP @ sk8 ) ),
inference(pattern_uni,[status(thm)],[10830:[]]) ).
thf(366,plain,
! [A: $i] :
( ~ ( leq @ ( skaf55 @ A ) @ ( skaf54 @ A ) )
| ~ ( ssList @ A )
| ( totalorderP @ A ) ),
inference(cnf,[status(esa)],[365]) ).
thf(151,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssItem @ ( hd @ A ) )
| ( nil = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause78) ).
thf(534,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssItem @ ( hd @ A ) )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(1444,plain,
! [A: $i] :
( ( ( cons @ ( skaf44 @ A ) @ nil )
= A )
| ~ ( singletonP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[205,243]) ).
thf(1445,plain,
( ( ( cons @ ( skaf44 @ sk2 ) @ nil )
= sk2 )
| ~ ( singletonP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[1444:[bind(A,$thf( sk2 ))]]) ).
thf(3766,plain,
! [A: $i] :
( ~ ( singletonP @ sk2 )
| ( totalorderedP @ sk2 )
| ( ( cons @ ( skaf44 @ sk2 ) @ nil )
!= ( cons @ ( skaf44 @ A ) @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[1445,1027]) ).
thf(3767,plain,
( ~ ( singletonP @ sk2 )
| ( totalorderedP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[3766:[bind(A,$thf( sk2 ))]]) ).
thf(1058,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf69 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[389,716]) ).
thf(1059,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf69 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[1058:[bind(A,$thf( C )),bind(B,$thf( skaf69 @ C ))]]) ).
thf(1067,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf69 @ A ) @ nil ) ),
inference(simp,[status(thm)],[1059]) ).
thf(11951,plain,
! [A: $i] :
( ( nil = sk2 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( tl @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8923,287]) ).
thf(11952,plain,
( ( nil = sk2 )
| ( rearsegP @ ( tl @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[11951:[bind(A,$thf( tl @ sk2 ))]]) ).
thf(24675,plain,
! [B: $i,A: $i] :
( ( ( app @ nil @ B )
= B )
| ( ( ssList @ ( skaf51 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[530,333]) ).
thf(24676,plain,
! [A: $i] :
( ( app @ nil @ ( skaf51 @ A ) )
= ( skaf51 @ A ) ),
inference(pattern_uni,[status(thm)],[24675:[bind(A,$thf( C )),bind(B,$thf( skaf51 @ C ))]]) ).
thf(24879,plain,
! [A: $i] :
( ( app @ nil @ ( skaf51 @ A ) )
= ( skaf51 @ A ) ),
inference(simp,[status(thm)],[24676]) ).
thf(10877,plain,
( ( ssList @ ( tl @ sk8 ) )
| ~ ( singletonP @ sk8 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[9287,487]) ).
thf(10878,plain,
( ( ssList @ ( tl @ sk8 ) )
| ~ ( singletonP @ sk8 ) ),
inference(pattern_uni,[status(thm)],[10877:[]]) ).
thf(15530,plain,
! [A: $i] :
( ~ ( singletonP @ sk8 )
| ~ ( neq @ A @ A )
| ( ( ssList @ ( tl @ sk8 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10878,231]) ).
thf(15531,plain,
( ~ ( singletonP @ sk8 )
| ~ ( neq @ ( tl @ sk8 ) @ ( tl @ sk8 ) ) ),
inference(pattern_uni,[status(thm)],[15530:[bind(A,$thf( tl @ sk8 ))]]) ).
thf(40,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(275,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)],[40]) ).
thf(11997,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( skaf53 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[446,287]) ).
thf(11998,plain,
! [A: $i] : ( rearsegP @ ( skaf53 @ A ) @ nil ),
inference(pattern_uni,[status(thm)],[11997:[bind(A,$thf( C )),bind(B,$thf( skaf53 @ C ))]]) ).
thf(12037,plain,
! [A: $i] : ( rearsegP @ ( skaf53 @ A ) @ nil ),
inference(simp,[status(thm)],[11998]) ).
thf(10132,plain,
( ( ssList @ ( tl @ sk2 ) )
| ( duplicatefreeP @ sk2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[8923,330]) ).
thf(10133,plain,
( ( ssList @ ( tl @ sk2 ) )
| ( duplicatefreeP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[10132:[]]) ).
thf(103,axiom,
! [A: $i] : ( ssItem @ ( skaf49 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause46) ).
thf(422,plain,
! [A: $i] : ( ssItem @ ( skaf49 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(1260,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf49 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[422,716]) ).
thf(1261,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf49 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[1260:[bind(A,$thf( C )),bind(B,$thf( skaf49 @ C ))]]) ).
thf(1274,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf49 @ A ) @ nil ) ),
inference(simp,[status(thm)],[1261]) ).
thf(2659,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf50 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[588,433]) ).
thf(2660,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf50 @ A ) ),
inference(pattern_uni,[status(thm)],[2659:[bind(A,$thf( C )),bind(B,$thf( skaf50 @ C ))]]) ).
thf(2673,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf50 @ A ) ),
inference(simp,[status(thm)],[2660]) ).
thf(16598,plain,
! [A: $i] :
( ( nil = A )
| ~ ( rearsegP @ nil @ A )
| ( ( ssList @ sk8 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[209,305]) ).
thf(16599,plain,
( ( nil = sk8 )
| ~ ( rearsegP @ nil @ sk8 ) ),
inference(pattern_uni,[status(thm)],[16598:[bind(A,$thf( sk8 ))]]) ).
thf(24026,plain,
( ~ ( rearsegP @ nil @ sk8 )
| ~ ( singletonP @ sk8 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[16599,487]) ).
thf(24027,plain,
( ~ ( rearsegP @ nil @ sk8 )
| ~ ( singletonP @ sk8 ) ),
inference(pattern_uni,[status(thm)],[24026:[]]) ).
thf(65,axiom,
! [B: $i,A: $i] :
( ~ ( lt @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( leq @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause103) ).
thf(334,plain,
! [B: $i,A: $i] :
( ~ ( lt @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( leq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(20858,plain,
! [B: $i,A: $i] :
( ( strictorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf59 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[630,323]) ).
thf(20859,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf59 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[20858:[bind(A,$thf( C )),bind(B,$thf( skaf59 @ C ))]]) ).
thf(20953,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf59 @ A ) @ nil ) ),
inference(simp,[status(thm)],[20859]) ).
thf(11921,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( skaf67 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[492,287]) ).
thf(11922,plain,
! [A: $i] : ( rearsegP @ ( skaf67 @ A ) @ nil ),
inference(pattern_uni,[status(thm)],[11921:[bind(A,$thf( C )),bind(B,$thf( skaf67 @ C ))]]) ).
thf(12012,plain,
! [A: $i] : ( rearsegP @ ( skaf67 @ A ) @ nil ),
inference(simp,[status(thm)],[11922]) ).
thf(50,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(300,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)],[50]) ).
thf(301,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)],[300]) ).
thf(302,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)],[301]) ).
thf(33,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(258,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)],[33]) ).
thf(259,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)],[258]) ).
thf(260,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)],[259]) ).
thf(189,axiom,
strictorderedP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause3) ).
thf(616,plain,
strictorderedP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(11036,plain,
( ( ssList @ ( tl @ sk7 ) )
| ( strictorderedP @ sk7 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[9500,616]) ).
thf(11037,plain,
( ( ssList @ ( tl @ sk7 ) )
| ( strictorderedP @ sk7 ) ),
inference(pattern_uni,[status(thm)],[11036:[]]) ).
thf(96,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(407,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)],[96]) ).
thf(75,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(361,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)],[75]) ).
thf(21528,plain,
( ~ ( rearsegP @ nil @ sk2 )
| ~ ( memberP @ sk2 @ sk6 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[16161,651]) ).
thf(21529,plain,
( ~ ( rearsegP @ nil @ sk2 )
| ~ ( memberP @ sk2 @ sk6 ) ),
inference(pattern_uni,[status(thm)],[21528:[]]) ).
thf(45671,plain,
( ~ ( memberP @ sk2 @ sk6 )
| ( ( rearsegP @ nil @ sk2 )
!= ( rearsegP @ sk2 @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[11948,21529]) ).
thf(45784,plain,
( ~ ( memberP @ sk2 @ sk6 )
| ( nil != sk2 )
| ( nil != sk2 ) ),
inference(simp,[status(thm)],[45671]) ).
thf(45825,plain,
( ~ ( memberP @ sk2 @ sk6 )
| ( nil != sk2 ) ),
inference(simp,[status(thm)],[45784]) ).
thf(60,axiom,
! [B: $i,A: $i] : ( ssList @ ( skaf45 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause51) ).
thf(324,plain,
! [B: $i,A: $i] : ( ssList @ ( skaf45 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(4759,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( neq @ C @ C )
| ( ( ssList @ ( skaf45 @ A @ B ) )
!= ( ssList @ C ) ) ),
inference(paramod_ordered,[status(thm)],[324,231]) ).
thf(4760,plain,
! [B: $i,A: $i] :
~ ( neq @ ( skaf45 @ A @ B ) @ ( skaf45 @ A @ B ) ),
inference(pattern_uni,[status(thm)],[4759:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( skaf45 @ D @ E ))]]) ).
thf(4776,plain,
! [B: $i,A: $i] :
~ ( neq @ ( skaf45 @ A @ B ) @ ( skaf45 @ A @ B ) ),
inference(simp,[status(thm)],[4760]) ).
thf(1608,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf83 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[569,433]) ).
thf(1609,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf83 @ A ) ),
inference(pattern_uni,[status(thm)],[1608:[bind(A,$thf( C )),bind(B,$thf( skaf83 @ C ))]]) ).
thf(1624,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf83 @ A ) ),
inference(simp,[status(thm)],[1609]) ).
thf(15,axiom,
! [B: $i,A: $i] : ( ssList @ ( skaf43 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause52) ).
thf(219,plain,
! [B: $i,A: $i] : ( ssList @ ( skaf43 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(11959,plain,
! [C: $i,B: $i,A: $i] :
( ( rearsegP @ C @ nil )
| ( ( ssList @ ( skaf43 @ A @ B ) )
!= ( ssList @ C ) ) ),
inference(paramod_ordered,[status(thm)],[219,287]) ).
thf(11960,plain,
! [B: $i,A: $i] : ( rearsegP @ ( skaf43 @ A @ B ) @ nil ),
inference(pattern_uni,[status(thm)],[11959:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( skaf43 @ D @ E ))]]) ).
thf(12025,plain,
! [B: $i,A: $i] : ( rearsegP @ ( skaf43 @ A @ B ) @ nil ),
inference(simp,[status(thm)],[11960]) ).
thf(120,axiom,
! [A: $i] :
( ~ ( leq @ ( skaf64 @ A ) @ ( skaf65 @ A ) )
| ~ ( ssList @ A )
| ( totalorderedP @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause91) ).
thf(461,plain,
! [A: $i] :
( ~ ( leq @ ( skaf64 @ A ) @ ( skaf65 @ A ) )
| ~ ( ssList @ A )
| ( totalorderedP @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(135,axiom,
! [A: $i] :
( ~ ( lt @ ( skaf59 @ A ) @ ( skaf60 @ A ) )
| ~ ( ssList @ A )
| ( strictorderP @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause93) ).
thf(493,plain,
! [A: $i] :
( ~ ( lt @ ( skaf59 @ A ) @ ( skaf60 @ A ) )
| ~ ( ssList @ A )
| ( strictorderP @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(11939,plain,
! [C: $i,B: $i,A: $i] :
( ( rearsegP @ C @ nil )
| ( ( ssList @ ( skaf45 @ A @ B ) )
!= ( ssList @ C ) ) ),
inference(paramod_ordered,[status(thm)],[324,287]) ).
thf(11940,plain,
! [B: $i,A: $i] : ( rearsegP @ ( skaf45 @ A @ B ) @ nil ),
inference(pattern_uni,[status(thm)],[11939:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( skaf45 @ D @ E ))]]) ).
thf(12020,plain,
! [B: $i,A: $i] : ( rearsegP @ ( skaf45 @ A @ B ) @ nil ),
inference(simp,[status(thm)],[11940]) ).
thf(709,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ( ( ssList @ sk8 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[209,231]) ).
thf(710,plain,
~ ( neq @ sk8 @ sk8 ),
inference(pattern_uni,[status(thm)],[709:[bind(A,$thf( sk8 ))]]) ).
thf(20911,plain,
! [A: $i] :
( ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ sk6 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[203,323]) ).
thf(20912,plain,
strictorderedP @ ( cons @ sk6 @ nil ),
inference(pattern_uni,[status(thm)],[20911:[bind(A,$thf( sk6 ))]]) ).
thf(62,axiom,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( lt @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause105) ).
thf(328,plain,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( lt @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(329,plain,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( lt @ B @ A ) ),
inference(cnf,[status(esa)],[328]) ).
thf(43,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(283,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)],[43]) ).
thf(284,plain,
! [B: $i,A: $i] :
( ~ ( frontsegP @ A @ B )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( ( app @ B @ ( skaf45 @ A @ B ) )
= A ) ),
inference(cnf,[status(esa)],[283]) ).
thf(285,plain,
! [B: $i,A: $i] :
( ( ( app @ B @ ( skaf45 @ A @ B ) )
= A )
| ~ ( frontsegP @ A @ B )
| ~ ( ssList @ B )
| ~ ( ssList @ A ) ),
inference(lifteq,[status(thm)],[284]) ).
thf(1089,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssItem @ ( skaf55 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[390,281]) ).
thf(1090,plain,
! [A: $i] :
~ ( neq @ ( skaf55 @ A ) @ ( skaf55 @ A ) ),
inference(pattern_uni,[status(thm)],[1089:[bind(A,$thf( C )),bind(B,$thf( skaf55 @ C ))]]) ).
thf(1106,plain,
! [A: $i] :
~ ( neq @ ( skaf55 @ A ) @ ( skaf55 @ A ) ),
inference(simp,[status(thm)],[1090]) ).
thf(171,axiom,
! [A: $i] : ( ssItem @ ( skaf65 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause30) ).
thf(578,plain,
! [A: $i] : ( ssItem @ ( skaf65 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(696,plain,
! [A: $i] :
( ~ ( memberP @ nil @ A )
| ( ( ssItem @ skac3 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[533,433]) ).
thf(697,plain,
~ ( memberP @ nil @ skac3 ),
inference(pattern_uni,[status(thm)],[696:[bind(A,$thf( skac3 ))]]) ).
thf(1797,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf82 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[574,231]) ).
thf(1798,plain,
! [A: $i] :
~ ( neq @ ( skaf82 @ A ) @ ( skaf82 @ A ) ),
inference(pattern_uni,[status(thm)],[1797:[bind(A,$thf( C )),bind(B,$thf( skaf82 @ C ))]]) ).
thf(1804,plain,
! [A: $i] :
~ ( neq @ ( skaf82 @ A ) @ ( skaf82 @ A ) ),
inference(simp,[status(thm)],[1798]) ).
thf(20903,plain,
! [B: $i,A: $i] :
( ( strictorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf78 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[608,323]) ).
thf(20904,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf78 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[20903:[bind(A,$thf( C )),bind(B,$thf( skaf78 @ C ))]]) ).
thf(20944,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf78 @ A ) @ nil ) ),
inference(simp,[status(thm)],[20904]) ).
thf(24654,plain,
! [A: $i] :
( ( ( app @ nil @ A )
= A )
| ( ( ssList @ ( tl @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9945,333]) ).
thf(24655,plain,
( ( app @ nil @ ( tl @ sk1 ) )
= ( tl @ sk1 ) ),
inference(pattern_uni,[status(thm)],[24654:[bind(A,$thf( tl @ sk1 ))]]) ).
thf(11929,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( skaf61 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[397,287]) ).
thf(11930,plain,
! [A: $i] : ( rearsegP @ ( skaf61 @ A ) @ nil ),
inference(pattern_uni,[status(thm)],[11929:[bind(A,$thf( C )),bind(B,$thf( skaf61 @ C ))]]) ).
thf(12016,plain,
! [A: $i] : ( rearsegP @ ( skaf61 @ A ) @ nil ),
inference(simp,[status(thm)],[11930]) ).
thf(24783,plain,
! [B: $i,A: $i] :
( ( ( app @ nil @ B )
= B )
| ( ( ssList @ ( skaf75 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[447,333]) ).
thf(24784,plain,
! [A: $i] :
( ( app @ nil @ ( skaf75 @ A ) )
= ( skaf75 @ A ) ),
inference(pattern_uni,[status(thm)],[24783:[bind(A,$thf( C )),bind(B,$thf( skaf75 @ C ))]]) ).
thf(24903,plain,
! [A: $i] :
( ( app @ nil @ ( skaf75 @ A ) )
= ( skaf75 @ A ) ),
inference(simp,[status(thm)],[24784]) ).
thf(24590,plain,
! [C: $i,B: $i,A: $i] :
( ( ( app @ nil @ C )
= C )
| ( ( ssList @ ( skaf47 @ A @ B ) )
!= ( ssList @ C ) ) ),
inference(paramod_ordered,[status(thm)],[481,333]) ).
thf(24591,plain,
! [B: $i,A: $i] :
( ( app @ nil @ ( skaf47 @ A @ B ) )
= ( skaf47 @ A @ B ) ),
inference(pattern_uni,[status(thm)],[24590:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( skaf47 @ D @ E ))]]) ).
thf(24862,plain,
! [B: $i,A: $i] :
( ( app @ nil @ ( skaf47 @ A @ B ) )
= ( skaf47 @ A @ B ) ),
inference(simp,[status(thm)],[24591]) ).
thf(179,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(593,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)],[179]) ).
thf(24043,plain,
( ~ ( rearsegP @ nil @ sk8 )
| ( sk8 != sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[16599,643]) ).
thf(24044,plain,
( ~ ( rearsegP @ nil @ sk8 )
| ( sk8 != sk1 ) ),
inference(pattern_uni,[status(thm)],[24043:[]]) ).
thf(102,axiom,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ~ ( gt @ B @ A )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause110) ).
thf(420,plain,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ~ ( gt @ B @ A )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(11979,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( skaf77 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[299,287]) ).
thf(11980,plain,
! [A: $i] : ( rearsegP @ ( skaf77 @ A ) @ nil ),
inference(pattern_uni,[status(thm)],[11979:[bind(A,$thf( C )),bind(B,$thf( skaf77 @ C ))]]) ).
thf(12033,plain,
! [A: $i] : ( rearsegP @ ( skaf77 @ A ) @ nil ),
inference(simp,[status(thm)],[11980]) ).
thf(21510,plain,
( ~ ( rearsegP @ nil @ sk2 )
| ( totalorderedP @ sk2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[16161,629]) ).
thf(21511,plain,
( ~ ( rearsegP @ nil @ sk2 )
| ( totalorderedP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[21510:[]]) ).
thf(1252,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssItem @ ( skaf49 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[422,281]) ).
thf(1253,plain,
! [A: $i] :
~ ( neq @ ( skaf49 @ A ) @ ( skaf49 @ A ) ),
inference(pattern_uni,[status(thm)],[1252:[bind(A,$thf( C )),bind(B,$thf( skaf49 @ C ))]]) ).
thf(1270,plain,
! [A: $i] :
~ ( neq @ ( skaf49 @ A ) @ ( skaf49 @ A ) ),
inference(simp,[status(thm)],[1253]) ).
thf(57,axiom,
! [B: $i,A: $i] :
( ( ( cons @ A @ nil )
!= B )
| ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( singletonP @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause116) ).
thf(314,plain,
! [B: $i,A: $i] :
( ( ( cons @ A @ nil )
!= B )
| ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( singletonP @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(315,plain,
! [B: $i,A: $i] :
( ( ( cons @ A @ nil )
!= B )
| ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( singletonP @ B ) ),
inference(cnf,[status(esa)],[314]) ).
thf(316,plain,
! [B: $i,A: $i] :
( ( ( cons @ A @ nil )
!= B )
| ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( singletonP @ B ) ),
inference(lifteq,[status(thm)],[315]) ).
thf(317,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssList @ ( cons @ A @ nil ) )
| ( singletonP @ ( cons @ A @ nil ) ) ),
inference(simp,[status(thm)],[316]) ).
thf(24669,plain,
! [A: $i] :
( ( ( app @ nil @ A )
= A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[205,333]) ).
thf(24670,plain,
( ( app @ nil @ sk2 )
= sk2 ),
inference(pattern_uni,[status(thm)],[24669:[bind(A,$thf( sk2 ))]]) ).
thf(1865,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf65 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[578,716]) ).
thf(1866,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf65 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[1865:[bind(A,$thf( C )),bind(B,$thf( skaf65 @ C ))]]) ).
thf(1878,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf65 @ A ) @ nil ) ),
inference(simp,[status(thm)],[1866]) ).
thf(24753,plain,
! [A: $i] :
( ( ( app @ nil @ A )
= A )
| ( ( ssList @ sk8 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[209,333]) ).
thf(24754,plain,
( ( app @ nil @ sk8 )
= sk8 ),
inference(pattern_uni,[status(thm)],[24753:[bind(A,$thf( sk8 ))]]) ).
thf(138,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(499,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)],[138]) ).
thf(24617,plain,
! [B: $i,A: $i] :
( ( ( app @ nil @ B )
= B )
| ( ( ssList @ ( skaf52 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[480,333]) ).
thf(24618,plain,
! [A: $i] :
( ( app @ nil @ ( skaf52 @ A ) )
= ( skaf52 @ A ) ),
inference(pattern_uni,[status(thm)],[24617:[bind(A,$thf( C )),bind(B,$thf( skaf52 @ C ))]]) ).
thf(24870,plain,
! [A: $i] :
( ( app @ nil @ ( skaf52 @ A ) )
= ( skaf52 @ A ) ),
inference(simp,[status(thm)],[24618]) ).
thf(67,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(339,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)],[67]) ).
thf(107,axiom,
! [A: $i] : ( ssList @ ( skaf80 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause15) ).
thf(431,plain,
! [A: $i] : ( ssList @ ( skaf80 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(1287,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf80 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[431,231]) ).
thf(1288,plain,
! [A: $i] :
~ ( neq @ ( skaf80 @ A ) @ ( skaf80 @ A ) ),
inference(pattern_uni,[status(thm)],[1287:[bind(A,$thf( C )),bind(B,$thf( skaf80 @ C ))]]) ).
thf(1292,plain,
! [A: $i] :
~ ( neq @ ( skaf80 @ A ) @ ( skaf80 @ A ) ),
inference(simp,[status(thm)],[1288]) ).
thf(11937,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( skaf76 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[598,287]) ).
thf(11938,plain,
! [A: $i] : ( rearsegP @ ( skaf76 @ A ) @ nil ),
inference(pattern_uni,[status(thm)],[11937:[bind(A,$thf( C )),bind(B,$thf( skaf76 @ C ))]]) ).
thf(12019,plain,
! [A: $i] : ( rearsegP @ ( skaf76 @ A ) @ nil ),
inference(simp,[status(thm)],[11938]) ).
thf(128,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(476,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)],[128]) ).
thf(1418,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf67 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[492,231]) ).
thf(1419,plain,
! [A: $i] :
~ ( neq @ ( skaf67 @ A ) @ ( skaf67 @ A ) ),
inference(pattern_uni,[status(thm)],[1418:[bind(A,$thf( C )),bind(B,$thf( skaf67 @ C ))]]) ).
thf(1424,plain,
! [A: $i] :
~ ( neq @ ( skaf67 @ A ) @ ( skaf67 @ A ) ),
inference(simp,[status(thm)],[1419]) ).
thf(1699,plain,
! [A: $i] :
( ( ( app @ ( app @ ( skaf75 @ A ) @ ( cons @ ( skaf74 @ A ) @ ( skaf76 @ A ) ) ) @ ( cons @ ( skaf74 @ A ) @ ( skaf77 @ A ) ) )
= A )
| ( duplicatefreeP @ A )
| ( ( ssList @ sk8 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[209,246]) ).
thf(1700,plain,
( ( ( app @ ( app @ ( skaf75 @ sk8 ) @ ( cons @ ( skaf74 @ sk8 ) @ ( skaf76 @ sk8 ) ) ) @ ( cons @ ( skaf74 @ sk8 ) @ ( skaf77 @ sk8 ) ) )
= sk8 )
| ( duplicatefreeP @ sk8 ) ),
inference(pattern_uni,[status(thm)],[1699:[bind(A,$thf( sk8 ))]]) ).
thf(12090,plain,
( ( ssList @ ( tl @ sk7 ) )
| ( rearsegP @ sk2 @ sk7 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[9500,11948]) ).
thf(12091,plain,
( ( ssList @ ( tl @ sk7 ) )
| ( rearsegP @ sk2 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[12090:[]]) ).
thf(1035,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf73 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[382,231]) ).
thf(1036,plain,
! [A: $i] :
~ ( neq @ ( skaf73 @ A ) @ ( skaf73 @ A ) ),
inference(pattern_uni,[status(thm)],[1035:[bind(A,$thf( C )),bind(B,$thf( skaf73 @ C ))]]) ).
thf(1039,plain,
! [A: $i] :
~ ( neq @ ( skaf73 @ A ) @ ( skaf73 @ A ) ),
inference(simp,[status(thm)],[1036]) ).
thf(157,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( tl @ A ) )
| ( nil = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause77) ).
thf(547,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( tl @ A ) )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(125,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( frontsegP @ A @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause60) ).
thf(471,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( frontsegP @ A @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(705,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ( ( ssList @ sk7 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[200,231]) ).
thf(706,plain,
~ ( neq @ sk7 @ sk7 ),
inference(pattern_uni,[status(thm)],[705:[bind(A,$thf( sk7 ))]]) ).
thf(12044,plain,
( ( ssList @ ( tl @ sk2 ) )
| ( rearsegP @ sk1 @ sk2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[8923,11936]) ).
thf(12045,plain,
( ( ssList @ ( tl @ sk2 ) )
| ( rearsegP @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[12044:[]]) ).
thf(11987,plain,
! [A: $i] :
( ( rearsegP @ A @ nil )
| ( ( ssList @ nil )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[282,287]) ).
thf(11988,plain,
rearsegP @ nil @ nil,
inference(pattern_uni,[status(thm)],[11987:[bind(A,$thf( nil ))]]) ).
thf(16753,plain,
! [A: $i] :
( ~ ( rearsegP @ nil @ A )
| ~ ( ssList @ A )
| ( skac3 != nil )
| ( A != skac2 ) ),
inference(paramod_ordered,[status(thm)],[305,218]) ).
thf(16754,plain,
( ~ ( rearsegP @ nil @ skac2 )
| ~ ( ssList @ skac2 )
| ( skac3 != nil ) ),
inference(pattern_uni,[status(thm)],[16753:[bind(A,$thf( skac2 ))]]) ).
thf(18969,plain,
( ~ ( ssList @ skac2 )
| ( skac3 != nil )
| ( ( rearsegP @ nil @ skac2 )
!= ( rearsegP @ nil @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[11988,16754]) ).
thf(19064,plain,
( ~ ( ssList @ skac2 )
| ( skac3 != nil )
| ( nil != nil )
| ( skac2 != nil ) ),
inference(simp,[status(thm)],[18969]) ).
thf(19091,plain,
( ~ ( ssList @ skac2 )
| ( skac3 != nil )
| ( skac2 != nil ) ),
inference(simp,[status(thm)],[19064]) ).
thf(19923,plain,
( ( skac3 != nil )
| ( skac2 != nil )
| ( ( ssList @ skac2 )
!= ( ssList @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[282,19091]) ).
thf(19995,plain,
( ( skac3 != nil )
| ( skac2 != nil )
| ( skac2 != nil ) ),
inference(simp,[status(thm)],[19923]) ).
thf(19997,plain,
( ( skac3 != nil )
| ( skac2 != nil ) ),
inference(simp,[status(thm)],[19995]) ).
thf(1323,plain,
! [A: $i] :
( ( cyclefreeP @ A )
| ( leq @ ( skaf49 @ A ) @ ( skaf50 @ A ) )
| ( ( ssList @ sk8 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[209,240]) ).
thf(1324,plain,
( ( cyclefreeP @ sk8 )
| ( leq @ ( skaf49 @ sk8 ) @ ( skaf50 @ sk8 ) ) ),
inference(pattern_uni,[status(thm)],[1323:[bind(A,$thf( sk8 ))]]) ).
thf(24796,plain,
! [B: $i,A: $i] :
( ( ( app @ nil @ B )
= B )
| ( ( ssList @ ( skaf68 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[469,333]) ).
thf(24797,plain,
! [A: $i] :
( ( app @ nil @ ( skaf68 @ A ) )
= ( skaf68 @ A ) ),
inference(pattern_uni,[status(thm)],[24796:[bind(A,$thf( C )),bind(B,$thf( skaf68 @ C ))]]) ).
thf(24906,plain,
! [A: $i] :
( ( app @ nil @ ( skaf68 @ A ) )
= ( skaf68 @ A ) ),
inference(simp,[status(thm)],[24797]) ).
thf(101,axiom,
! [B: $i,A: $i] : ( ssList @ ( skaf48 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause48) ).
thf(419,plain,
! [B: $i,A: $i] : ( ssList @ ( skaf48 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(4815,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( neq @ C @ C )
| ( ( ssList @ ( skaf48 @ A @ B ) )
!= ( ssList @ C ) ) ),
inference(paramod_ordered,[status(thm)],[419,231]) ).
thf(4816,plain,
! [B: $i,A: $i] :
~ ( neq @ ( skaf48 @ A @ B ) @ ( skaf48 @ A @ B ) ),
inference(pattern_uni,[status(thm)],[4815:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( skaf48 @ D @ E ))]]) ).
thf(4829,plain,
! [B: $i,A: $i] :
~ ( neq @ ( skaf48 @ A @ B ) @ ( skaf48 @ A @ B ) ),
inference(simp,[status(thm)],[4816]) ).
thf(10960,plain,
( ( ssList @ ( tl @ sk7 ) )
| ( cyclefreeP @ sk7 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[9500,475]) ).
thf(10961,plain,
( ( ssList @ ( tl @ sk7 ) )
| ( cyclefreeP @ sk7 ) ),
inference(pattern_uni,[status(thm)],[10960:[]]) ).
thf(10046,plain,
( ( ssList @ ( tl @ sk2 ) )
| ( cyclefreeP @ sk2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[8923,475]) ).
thf(10047,plain,
( ( ssList @ ( tl @ sk2 ) )
| ( cyclefreeP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[10046:[]]) ).
thf(1857,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssItem @ ( skaf65 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[578,281]) ).
thf(1858,plain,
! [A: $i] :
~ ( neq @ ( skaf65 @ A ) @ ( skaf65 @ A ) ),
inference(pattern_uni,[status(thm)],[1857:[bind(A,$thf( C )),bind(B,$thf( skaf65 @ C ))]]) ).
thf(1874,plain,
! [A: $i] :
~ ( neq @ ( skaf65 @ A ) @ ( skaf65 @ A ) ),
inference(simp,[status(thm)],[1858]) ).
thf(24742,plain,
! [B: $i,A: $i] :
( ( ( app @ nil @ B )
= B )
| ( ( ssList @ ( skaf80 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[431,333]) ).
thf(24743,plain,
! [A: $i] :
( ( app @ nil @ ( skaf80 @ A ) )
= ( skaf80 @ A ) ),
inference(pattern_uni,[status(thm)],[24742:[bind(A,$thf( C )),bind(B,$thf( skaf80 @ C ))]]) ).
thf(24899,plain,
! [A: $i] :
( ( app @ nil @ ( skaf80 @ A ) )
= ( skaf80 @ A ) ),
inference(simp,[status(thm)],[24743]) ).
thf(47029,plain,
( ~ ( rearsegP @ sk2 @ sk1 )
| ( ( rearsegP @ nil @ sk2 )
!= ( rearsegP @ sk2 @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[11948,21542]) ).
thf(47166,plain,
( ~ ( rearsegP @ sk2 @ sk1 )
| ( nil != sk2 )
| ( nil != sk2 ) ),
inference(simp,[status(thm)],[47029]) ).
thf(47258,plain,
( ~ ( rearsegP @ sk2 @ sk1 )
| ( nil != sk2 ) ),
inference(simp,[status(thm)],[47166]) ).
thf(16936,plain,
! [A: $i] :
( ( nil = A )
| ~ ( rearsegP @ nil @ A )
| ( ( ssList @ sk7 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[200,305]) ).
thf(16937,plain,
( ( nil = sk7 )
| ~ ( rearsegP @ nil @ sk7 ) ),
inference(pattern_uni,[status(thm)],[16936:[bind(A,$thf( sk7 ))]]) ).
thf(139,axiom,
! [A: $i] :
( ~ ( ssItem @ A )
| ( duplicatefreeP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause65) ).
thf(503,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( duplicatefreeP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(185,axiom,
! [A: $i] :
( ( ( skaf79 @ A )
!= ( skaf78 @ A ) )
| ~ ( ssList @ A )
| ( equalelemsP @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause89) ).
thf(605,plain,
! [A: $i] :
( ( ( skaf79 @ A )
!= ( skaf78 @ A ) )
| ~ ( ssList @ A )
| ( equalelemsP @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(4145,plain,
( ( totalorderedP @ sk2 )
| ( ( singletonP @ sk2 )
!= ( singletonP @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[641,3767]) ).
thf(4148,plain,
( ( totalorderedP @ sk2 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[4145]) ).
thf(1197,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf61 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[397,231]) ).
thf(1198,plain,
! [A: $i] :
~ ( neq @ ( skaf61 @ A ) @ ( skaf61 @ A ) ),
inference(pattern_uni,[status(thm)],[1197:[bind(A,$thf( C )),bind(B,$thf( skaf61 @ C ))]]) ).
thf(1202,plain,
! [A: $i] :
~ ( neq @ ( skaf61 @ A ) @ ( skaf61 @ A ) ),
inference(simp,[status(thm)],[1198]) ).
thf(358,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)],[357]) ).
thf(359,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)],[358]) ).
thf(360,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)],[359]) ).
thf(54,axiom,
! [A: $i] :
( ~ ( lt @ ( skaf60 @ A ) @ ( skaf59 @ A ) )
| ~ ( ssList @ A )
| ( strictorderP @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause92) ).
thf(310,plain,
! [A: $i] :
( ~ ( lt @ ( skaf60 @ A ) @ ( skaf59 @ A ) )
| ~ ( ssList @ A )
| ( strictorderP @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(311,plain,
! [A: $i] :
( ~ ( lt @ ( skaf60 @ A ) @ ( skaf59 @ A ) )
| ~ ( ssList @ A )
| ( strictorderP @ A ) ),
inference(cnf,[status(esa)],[310]) ).
thf(1822,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf54 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[577,433]) ).
thf(1823,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf54 @ A ) ),
inference(pattern_uni,[status(thm)],[1822:[bind(A,$thf( C )),bind(B,$thf( skaf54 @ C ))]]) ).
thf(1846,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf54 @ A ) ),
inference(simp,[status(thm)],[1823]) ).
thf(18038,plain,
! [B: $i,A: $i] :
( ( duplicatefreeP @ A )
| ( ssItem @ B )
| ( ( ssList @ sk8 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[209,309]) ).
thf(18039,plain,
! [A: $i] :
( ( duplicatefreeP @ sk8 )
| ( ssItem @ A ) ),
inference(pattern_uni,[status(thm)],[18038:[bind(A,$thf( sk8 ))]]) ).
thf(18144,plain,
! [A: $i] :
( ( duplicatefreeP @ sk8 )
| ( ssItem @ A ) ),
inference(simp,[status(thm)],[18039]) ).
thf(92,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(398,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)],[92]) ).
thf(1170,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf70 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[394,716]) ).
thf(1171,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf70 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[1170:[bind(A,$thf( C )),bind(B,$thf( skaf70 @ C ))]]) ).
thf(1187,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf70 @ A ) @ nil ) ),
inference(simp,[status(thm)],[1171]) ).
thf(1166,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf70 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[394,433]) ).
thf(1167,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf70 @ A ) ),
inference(pattern_uni,[status(thm)],[1166:[bind(A,$thf( C )),bind(B,$thf( skaf70 @ C ))]]) ).
thf(1185,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf70 @ A ) ),
inference(simp,[status(thm)],[1167]) ).
thf(175,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(586,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)],[175]) ).
thf(1213,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssItem @ ( skaf60 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[401,281]) ).
thf(1214,plain,
! [A: $i] :
~ ( neq @ ( skaf60 @ A ) @ ( skaf60 @ A ) ),
inference(pattern_uni,[status(thm)],[1213:[bind(A,$thf( C )),bind(B,$thf( skaf60 @ C ))]]) ).
thf(1241,plain,
! [A: $i] :
~ ( neq @ ( skaf60 @ A ) @ ( skaf60 @ A ) ),
inference(simp,[status(thm)],[1214]) ).
thf(22632,plain,
( ~ ( singletonP @ sk2 )
| ( ( rearsegP @ nil @ sk2 )
!= ( rearsegP @ sk2 @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[11948,21736]) ).
thf(22702,plain,
( ~ ( singletonP @ sk2 )
| ( nil != sk2 )
| ( nil != sk2 ) ),
inference(simp,[status(thm)],[22632]) ).
thf(22731,plain,
( ~ ( singletonP @ sk2 )
| ( nil != sk2 ) ),
inference(simp,[status(thm)],[22702]) ).
thf(124,axiom,
totalorderP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause6) ).
thf(470,plain,
totalorderP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(10189,plain,
( ( ssList @ ( tl @ sk2 ) )
| ( totalorderP @ sk2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[8923,470]) ).
thf(10190,plain,
( ( ssList @ ( tl @ sk2 ) )
| ( totalorderP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[10189:[]]) ).
thf(717,plain,
! [A: $i] :
( ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ skac3 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[533,716]) ).
thf(718,plain,
totalorderedP @ ( cons @ skac3 @ nil ),
inference(pattern_uni,[status(thm)],[717:[bind(A,$thf( skac3 ))]]) ).
thf(886,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf57 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[312,231]) ).
thf(887,plain,
! [A: $i] :
~ ( neq @ ( skaf57 @ A ) @ ( skaf57 @ A ) ),
inference(pattern_uni,[status(thm)],[886:[bind(A,$thf( C )),bind(B,$thf( skaf57 @ C ))]]) ).
thf(888,plain,
! [A: $i] :
~ ( neq @ ( skaf57 @ A ) @ ( skaf57 @ A ) ),
inference(simp,[status(thm)],[887]) ).
thf(48,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(295,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)],[48]) ).
thf(296,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)],[295]) ).
thf(297,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)],[296]) ).
thf(298,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)],[297]) ).
thf(142,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(513,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)],[142]) ).
thf(262,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)],[261]) ).
thf(263,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)],[262]) ).
thf(264,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)],[263]) ).
thf(56,axiom,
equalelemsP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause1) ).
thf(313,plain,
equalelemsP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(11015,plain,
( ( ssList @ ( tl @ sk7 ) )
| ( equalelemsP @ sk7 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[9500,313]) ).
thf(11016,plain,
( ( ssList @ ( tl @ sk7 ) )
| ( equalelemsP @ sk7 ) ),
inference(pattern_uni,[status(thm)],[11015:[]]) ).
thf(20875,plain,
! [B: $i,A: $i] :
( ( strictorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf54 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[577,323]) ).
thf(20876,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf54 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[20875:[bind(A,$thf( C )),bind(B,$thf( skaf54 @ C ))]]) ).
thf(20935,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf54 @ A ) @ nil ) ),
inference(simp,[status(thm)],[20876]) ).
thf(113,axiom,
! [A: $i] :
( ~ ( leq @ ( skaf54 @ A ) @ ( skaf55 @ A ) )
| ~ ( ssList @ A )
| ( totalorderP @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause95) ).
thf(444,plain,
! [A: $i] :
( ~ ( leq @ ( skaf54 @ A ) @ ( skaf55 @ A ) )
| ~ ( ssList @ A )
| ( totalorderP @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(10889,plain,
( ( ssList @ ( tl @ sk8 ) )
| ( sk8 != sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[9287,643]) ).
thf(10890,plain,
( ( ssList @ ( tl @ sk8 ) )
| ( sk8 != sk1 ) ),
inference(pattern_uni,[status(thm)],[10889:[]]) ).
thf(27581,plain,
! [A: $i] :
( ~ ( singletonP @ sk8 )
| ( strictorderedP @ sk8 )
| ( ( cons @ ( skaf44 @ sk8 ) @ nil )
!= ( cons @ ( skaf44 @ A ) @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[1467,20957]) ).
thf(27582,plain,
( ~ ( singletonP @ sk8 )
| ( strictorderedP @ sk8 ) ),
inference(pattern_uni,[status(thm)],[27581:[bind(A,$thf( sk8 ))]]) ).
thf(11109,plain,
( ( ssList @ ( tl @ sk7 ) )
| ( sk7 != sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[9500,643]) ).
thf(11110,plain,
( ( ssList @ ( tl @ sk7 ) )
| ( sk7 != sk1 ) ),
inference(pattern_uni,[status(thm)],[11109:[]]) ).
thf(105,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssItem @ ( hd @ A ) )
| ( nil = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause76) ).
thf(425,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssItem @ ( hd @ A ) )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(20866,plain,
! [B: $i,A: $i] :
( ( strictorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf83 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[569,323]) ).
thf(20867,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf83 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[20866:[bind(A,$thf( C )),bind(B,$thf( skaf83 @ C ))]]) ).
thf(20932,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf83 @ A ) @ nil ) ),
inference(simp,[status(thm)],[20867]) ).
thf(18068,plain,
! [B: $i,A: $i] :
( ( duplicatefreeP @ A )
| ( ssItem @ B )
| ( ( ssList @ sk7 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[200,309]) ).
thf(18069,plain,
! [A: $i] :
( ( duplicatefreeP @ sk7 )
| ( ssItem @ A ) ),
inference(pattern_uni,[status(thm)],[18068:[bind(A,$thf( sk7 ))]]) ).
thf(18095,plain,
! [A: $i] :
( ( duplicatefreeP @ sk7 )
| ( ssItem @ A ) ),
inference(simp,[status(thm)],[18069]) ).
thf(11919,plain,
! [A: $i] :
( ( nil = sk8 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( tl @ sk8 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9287,287]) ).
thf(11920,plain,
( ( nil = sk8 )
| ( rearsegP @ ( tl @ sk8 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[11919:[bind(A,$thf( tl @ sk8 ))]]) ).
thf(5595,plain,
( ( totalorderedP @ sk8 )
| ( ( singletonP @ sk8 )
!= ( singletonP @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[641,5076]) ).
thf(5598,plain,
( ( totalorderedP @ sk8 )
| ( sk8 != sk1 ) ),
inference(simp,[status(thm)],[5595]) ).
thf(162,axiom,
! [A: $i] :
( ~ ( ssItem @ A )
| ( totalorderP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause69) ).
thf(562,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( totalorderP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(94,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(402,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)],[94]) ).
thf(731,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ( ( ssItem @ sk5 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[210,281]) ).
thf(732,plain,
~ ( neq @ sk5 @ sk5 ),
inference(pattern_uni,[status(thm)],[731:[bind(A,$thf( sk5 ))]]) ).
thf(27530,plain,
! [A: $i] :
( ( strictorderedP @ sk1 )
| ( ( cons @ ( skaf44 @ sk1 ) @ nil )
!= ( cons @ ( skaf44 @ A ) @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[2869,20957]) ).
thf(27531,plain,
strictorderedP @ sk1,
inference(pattern_uni,[status(thm)],[27530:[bind(A,$thf( sk1 ))]]) ).
thf(20850,plain,
! [B: $i,A: $i] :
( ( strictorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf69 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[389,323]) ).
thf(20851,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf69 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[20850:[bind(A,$thf( C )),bind(B,$thf( skaf69 @ C ))]]) ).
thf(20947,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf69 @ A ) @ nil ) ),
inference(simp,[status(thm)],[20851]) ).
thf(11999,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( skaf75 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[447,287]) ).
thf(12000,plain,
! [A: $i] : ( rearsegP @ ( skaf75 @ A ) @ nil ),
inference(pattern_uni,[status(thm)],[11999:[bind(A,$thf( C )),bind(B,$thf( skaf75 @ C ))]]) ).
thf(12038,plain,
! [A: $i] : ( rearsegP @ ( skaf75 @ A ) @ nil ),
inference(simp,[status(thm)],[12000]) ).
thf(24605,plain,
! [B: $i,A: $i] :
( ( ( app @ nil @ B )
= B )
| ( ( ssList @ ( skaf67 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[492,333]) ).
thf(24606,plain,
! [A: $i] :
( ( app @ nil @ ( skaf67 @ A ) )
= ( skaf67 @ A ) ),
inference(pattern_uni,[status(thm)],[24605:[bind(A,$thf( C )),bind(B,$thf( skaf67 @ C ))]]) ).
thf(24865,plain,
! [A: $i] :
( ( app @ nil @ ( skaf67 @ A ) )
= ( skaf67 @ A ) ),
inference(simp,[status(thm)],[24606]) ).
thf(156,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(545,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)],[156]) ).
thf(98,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( cyclefreeP @ A )
| ( leq @ ( skaf50 @ A ) @ ( skaf49 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause87) ).
thf(413,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( cyclefreeP @ A )
| ( leq @ ( skaf50 @ A ) @ ( skaf49 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(11967,plain,
! [C: $i,B: $i,A: $i] :
( ( rearsegP @ C @ nil )
| ( ( ssList @ ( skaf48 @ A @ B ) )
!= ( ssList @ C ) ) ),
inference(paramod_ordered,[status(thm)],[419,287]) ).
thf(11968,plain,
! [B: $i,A: $i] : ( rearsegP @ ( skaf48 @ A @ B ) @ nil ),
inference(pattern_uni,[status(thm)],[11967:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( skaf48 @ D @ E ))]]) ).
thf(12028,plain,
! [B: $i,A: $i] : ( rearsegP @ ( skaf48 @ A @ B ) @ nil ),
inference(simp,[status(thm)],[11968]) ).
thf(4126,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( neq @ C @ C )
| ( ( ssList @ ( skaf46 @ A @ B ) )
!= ( ssList @ C ) ) ),
inference(paramod_ordered,[status(thm)],[265,231]) ).
thf(4127,plain,
! [B: $i,A: $i] :
~ ( neq @ ( skaf46 @ A @ B ) @ ( skaf46 @ A @ B ) ),
inference(pattern_uni,[status(thm)],[4126:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( skaf46 @ D @ E ))]]) ).
thf(4144,plain,
! [B: $i,A: $i] :
~ ( neq @ ( skaf46 @ A @ B ) @ ( skaf46 @ A @ B ) ),
inference(simp,[status(thm)],[4127]) ).
thf(47369,plain,
( ( totalorderedP @ sk2 )
| ( ( rearsegP @ nil @ sk2 )
!= ( rearsegP @ sk2 @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[11948,21511]) ).
thf(47495,plain,
( ( totalorderedP @ sk2 )
| ( nil != sk2 )
| ( nil != sk2 ) ),
inference(simp,[status(thm)],[47369]) ).
thf(47497,plain,
( ( totalorderedP @ sk2 )
| ( nil != sk2 ) ),
inference(simp,[status(thm)],[47495]) ).
thf(104,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( segmentP @ A @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause56) ).
thf(423,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( segmentP @ A @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(31290,plain,
( ( strictorderedP @ sk8 )
| ( ( singletonP @ sk8 )
!= ( singletonP @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[641,27582]) ).
thf(31310,plain,
( ( strictorderedP @ sk8 )
| ( sk8 != sk1 ) ),
inference(simp,[status(thm)],[31290]) ).
thf(20846,plain,
! [A: $i] :
( ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ skac3 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[533,323]) ).
thf(20847,plain,
strictorderedP @ ( cons @ skac3 @ nil ),
inference(pattern_uni,[status(thm)],[20846:[bind(A,$thf( skac3 ))]]) ).
thf(707,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( neq @ C @ C )
| ( ( ssList @ ( skaf43 @ A @ B ) )
!= ( ssList @ C ) ) ),
inference(paramod_ordered,[status(thm)],[219,231]) ).
thf(708,plain,
! [B: $i,A: $i] :
~ ( neq @ ( skaf43 @ A @ B ) @ ( skaf43 @ A @ B ) ),
inference(pattern_uni,[status(thm)],[707:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( skaf43 @ D @ E ))]]) ).
thf(711,plain,
! [B: $i,A: $i] :
~ ( neq @ ( skaf43 @ A @ B ) @ ( skaf43 @ A @ B ) ),
inference(simp,[status(thm)],[708]) ).
thf(172,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(579,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)],[172]) ).
thf(11915,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( skaf66 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[538,287]) ).
thf(11916,plain,
! [A: $i] : ( rearsegP @ ( skaf66 @ A ) @ nil ),
inference(pattern_uni,[status(thm)],[11915:[bind(A,$thf( C )),bind(B,$thf( skaf66 @ C ))]]) ).
thf(12011,plain,
! [A: $i] : ( rearsegP @ ( skaf66 @ A ) @ nil ),
inference(simp,[status(thm)],[11916]) ).
thf(13,negated_conjecture,
~ ( neq @ sk5 @ sk6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
thf(204,plain,
~ ( neq @ sk5 @ sk6 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(88,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(391,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)],[88]) ).
thf(1758,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssItem @ ( skaf74 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[573,281]) ).
thf(1759,plain,
! [A: $i] :
~ ( neq @ ( skaf74 @ A ) @ ( skaf74 @ A ) ),
inference(pattern_uni,[status(thm)],[1758:[bind(A,$thf( C )),bind(B,$thf( skaf74 @ C ))]]) ).
thf(1786,plain,
! [A: $i] :
~ ( neq @ ( skaf74 @ A ) @ ( skaf74 @ A ) ),
inference(simp,[status(thm)],[1759]) ).
thf(122,axiom,
! [B: $i,A: $i] :
( ( ( cons @ A @ B )
!= B )
| ~ ( ssItem @ A )
| ~ ( ssList @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause99) ).
thf(466,plain,
! [B: $i,A: $i] :
( ( ( cons @ A @ B )
!= B )
| ~ ( ssItem @ A )
| ~ ( ssList @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(335,plain,
! [B: $i,A: $i] :
( ~ ( lt @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( leq @ A @ B ) ),
inference(cnf,[status(esa)],[334]) ).
thf(22,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(235,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)],[22]) ).
thf(236,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)],[235]) ).
thf(703,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ( ( ssList @ nil )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[282,231]) ).
thf(704,plain,
~ ( neq @ nil @ nil ),
inference(pattern_uni,[status(thm)],[703:[bind(A,$thf( nil ))]]) ).
thf(10740,plain,
( ( ssList @ ( tl @ sk8 ) )
| ( cyclefreeP @ sk8 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[9287,475]) ).
thf(10741,plain,
( ( ssList @ ( tl @ sk8 ) )
| ( cyclefreeP @ sk8 ) ),
inference(pattern_uni,[status(thm)],[10740:[]]) ).
thf(11995,plain,
! [A: $i] :
( ( nil = sk7 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( tl @ sk7 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9500,287]) ).
thf(11996,plain,
( ( nil = sk7 )
| ( rearsegP @ ( tl @ sk7 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[11995:[bind(A,$thf( tl @ sk7 ))]]) ).
thf(24592,plain,
! [B: $i,A: $i] :
( ( ( app @ nil @ B )
= B )
| ( ( ssList @ ( skaf72 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[247,333]) ).
thf(24593,plain,
! [A: $i] :
( ( app @ nil @ ( skaf72 @ A ) )
= ( skaf72 @ A ) ),
inference(pattern_uni,[status(thm)],[24592:[bind(A,$thf( C )),bind(B,$thf( skaf72 @ C ))]]) ).
thf(24863,plain,
! [A: $i] :
( ( app @ nil @ ( skaf72 @ A ) )
= ( skaf72 @ A ) ),
inference(simp,[status(thm)],[24593]) ).
thf(899,plain,
! [A: $i] :
( ~ ( leq @ A @ sk6 )
| ( geq @ sk6 @ A )
| ( ( ssItem @ sk5 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[210,684]) ).
thf(900,plain,
( ~ ( leq @ sk5 @ sk6 )
| ( geq @ sk6 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[899:[bind(A,$thf( sk5 ))]]) ).
thf(11981,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( skaf80 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[431,287]) ).
thf(11982,plain,
! [A: $i] : ( rearsegP @ ( skaf80 @ A ) @ nil ),
inference(pattern_uni,[status(thm)],[11981:[bind(A,$thf( C )),bind(B,$thf( skaf80 @ C ))]]) ).
thf(12034,plain,
! [A: $i] : ( rearsegP @ ( skaf80 @ A ) @ nil ),
inference(simp,[status(thm)],[11982]) ).
thf(20927,plain,
! [A: $i] :
( ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ sk5 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[210,323]) ).
thf(20928,plain,
strictorderedP @ ( cons @ sk5 @ nil ),
inference(pattern_uni,[status(thm)],[20927:[bind(A,$thf( sk5 ))]]) ).
thf(81,axiom,
! [B: $i,A: $i] :
( ( ( app @ A @ B )
!= nil )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( nil = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause119) ).
thf(377,plain,
! [B: $i,A: $i] :
( ( ( app @ A @ B )
!= nil )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( nil = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(164,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(567,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)],[164]) ).
thf(182,axiom,
! [B: $i,A: $i] : ( ssList @ ( skaf42 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause53) ).
thf(599,plain,
! [B: $i,A: $i] : ( ssList @ ( skaf42 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(11927,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( skaf52 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[480,287]) ).
thf(11928,plain,
! [A: $i] : ( rearsegP @ ( skaf52 @ A ) @ nil ),
inference(pattern_uni,[status(thm)],[11927:[bind(A,$thf( C )),bind(B,$thf( skaf52 @ C ))]]) ).
thf(12015,plain,
! [A: $i] : ( rearsegP @ ( skaf52 @ A ) @ nil ),
inference(simp,[status(thm)],[11928]) ).
thf(141,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(509,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)],[141]) ).
thf(10887,plain,
( ( ssList @ ( tl @ sk8 ) )
| ( totalorderP @ sk8 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[9287,470]) ).
thf(10888,plain,
( ( ssList @ ( tl @ sk8 ) )
| ( totalorderP @ sk8 ) ),
inference(pattern_uni,[status(thm)],[10887:[]]) ).
thf(109,axiom,
! [A: $i] :
( ~ ( ssItem @ A )
| ( equalelemsP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause64) ).
thf(434,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( equalelemsP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(10097,plain,
( ( ssList @ ( tl @ sk2 ) )
| ( equalelemsP @ sk2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[8923,313]) ).
thf(10098,plain,
( ( ssList @ ( tl @ sk2 ) )
| ( equalelemsP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[10097:[]]) ).
thf(3,negated_conjecture,
ssList @ sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
thf(208,plain,
ssList @ sk3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(20891,plain,
! [A: $i] :
( ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ skac2 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[520,323]) ).
thf(20892,plain,
strictorderedP @ ( cons @ skac2 @ nil ),
inference(pattern_uni,[status(thm)],[20891:[bind(A,$thf( skac2 ))]]) ).
thf(196,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(631,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)],[196]) ).
thf(757,plain,
! [A: $i] :
( ~ ( lt @ A @ A )
| ( ( ssItem @ sk6 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[203,491]) ).
thf(758,plain,
~ ( lt @ sk6 @ sk6 ),
inference(pattern_uni,[status(thm)],[757:[bind(A,$thf( sk6 ))]]) ).
thf(24438,plain,
( ~ ( rearsegP @ nil @ sk7 )
| ~ ( singletonP @ sk7 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[16937,487]) ).
thf(24439,plain,
( ~ ( rearsegP @ nil @ sk7 )
| ~ ( singletonP @ sk7 ) ),
inference(pattern_uni,[status(thm)],[24438:[]]) ).
thf(27671,plain,
( ~ ( singletonP @ sk7 )
| ( ( rearsegP @ nil @ nil )
!= ( rearsegP @ nil @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[11988,24439]) ).
thf(27712,plain,
( ~ ( singletonP @ sk7 )
| ( nil != nil )
| ( nil != sk7 ) ),
inference(simp,[status(thm)],[27671]) ).
thf(27735,plain,
( ~ ( singletonP @ sk7 )
| ( nil != sk7 ) ),
inference(simp,[status(thm)],[27712]) ).
thf(187,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(609,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)],[187]) ).
thf(191,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(621,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)],[191]) ).
thf(2700,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf71 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[592,231]) ).
thf(2701,plain,
! [A: $i] :
~ ( neq @ ( skaf71 @ A ) @ ( skaf71 @ A ) ),
inference(pattern_uni,[status(thm)],[2700:[bind(A,$thf( C )),bind(B,$thf( skaf71 @ C ))]]) ).
thf(2710,plain,
! [A: $i] :
~ ( neq @ ( skaf71 @ A ) @ ( skaf71 @ A ) ),
inference(simp,[status(thm)],[2701]) ).
thf(1666,plain,
! [A: $i] :
( ( ( app @ ( app @ ( skaf75 @ A ) @ ( cons @ ( skaf74 @ A ) @ ( skaf76 @ A ) ) ) @ ( cons @ ( skaf74 @ A ) @ ( skaf77 @ A ) ) )
= A )
| ( duplicatefreeP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[201,246]) ).
thf(1667,plain,
( ( ( app @ ( app @ ( skaf75 @ sk1 ) @ ( cons @ ( skaf74 @ sk1 ) @ ( skaf76 @ sk1 ) ) ) @ ( cons @ ( skaf74 @ sk1 ) @ ( skaf77 @ sk1 ) ) )
= sk1 )
| ( duplicatefreeP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[1666:[bind(A,$thf( sk1 ))]]) ).
thf(77,axiom,
! [A: $i] :
( ~ ( ssItem @ A )
| ( geq @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause55) ).
thf(367,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( geq @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(213,plain,
( ( app @ ( app @ ( app @ sk7 @ ( cons @ sk5 @ nil ) ) @ ( cons @ sk6 @ nil ) ) @ sk8 )
= sk1 ),
inference(lifteq,[status(thm)],[206]) ).
thf(725,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ( ( ssItem @ skac3 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[533,281]) ).
thf(726,plain,
~ ( neq @ skac3 @ skac3 ),
inference(pattern_uni,[status(thm)],[725:[bind(A,$thf( skac3 ))]]) ).
thf(827,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssItem @ ( skaf79 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[248,281]) ).
thf(828,plain,
! [A: $i] :
~ ( neq @ ( skaf79 @ A ) @ ( skaf79 @ A ) ),
inference(pattern_uni,[status(thm)],[827:[bind(A,$thf( C )),bind(B,$thf( skaf79 @ C ))]]) ).
thf(848,plain,
! [A: $i] :
~ ( neq @ ( skaf79 @ A ) @ ( skaf79 @ A ) ),
inference(simp,[status(thm)],[828]) ).
thf(699,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[201,231]) ).
thf(700,plain,
~ ( neq @ sk1 @ sk1 ),
inference(pattern_uni,[status(thm)],[699:[bind(A,$thf( sk1 ))]]) ).
thf(250,plain,
! [B: $i,A: $i] :
( ~ ( strictorderedP @ ( cons @ A @ B ) )
| ~ ( ssList @ B )
| ~ ( ssItem @ A )
| ( lt @ A @ ( hd @ B ) )
| ( nil = B ) ),
inference(cnf,[status(esa)],[249]) ).
thf(251,plain,
! [B: $i,A: $i] :
( ( nil = B )
| ~ ( strictorderedP @ ( cons @ A @ B ) )
| ~ ( ssList @ B )
| ~ ( ssItem @ A )
| ( lt @ A @ ( hd @ B ) ) ),
inference(lifteq,[status(thm)],[250]) ).
thf(1832,plain,
! [B: $i,A: $i] :
( ~ ( lt @ B @ B )
| ( ( ssItem @ ( skaf54 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[577,491]) ).
thf(1833,plain,
! [A: $i] :
~ ( lt @ ( skaf54 @ A ) @ ( skaf54 @ A ) ),
inference(pattern_uni,[status(thm)],[1832:[bind(A,$thf( C )),bind(B,$thf( skaf54 @ C ))]]) ).
thf(1838,plain,
! [A: $i] :
~ ( lt @ ( skaf54 @ A ) @ ( skaf54 @ A ) ),
inference(simp,[status(thm)],[1833]) ).
thf(145,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(521,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)],[145]) ).
thf(68,axiom,
! [A: $i] : ( ssList @ ( skaf58 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause37) ).
thf(342,plain,
! [A: $i] : ( ssList @ ( skaf58 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(24746,plain,
! [B: $i,A: $i] :
( ( ( app @ nil @ B )
= B )
| ( ( ssList @ ( skaf58 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[342,333]) ).
thf(24747,plain,
! [A: $i] :
( ( app @ nil @ ( skaf58 @ A ) )
= ( skaf58 @ A ) ),
inference(pattern_uni,[status(thm)],[24746:[bind(A,$thf( C )),bind(B,$thf( skaf58 @ C ))]]) ).
thf(24900,plain,
! [A: $i] :
( ( app @ nil @ ( skaf58 @ A ) )
= ( skaf58 @ A ) ),
inference(simp,[status(thm)],[24747]) ).
thf(198,axiom,
! [A: $i] :
( ~ ( lt @ A @ A )
| ~ ( ssItem @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause63) ).
thf(636,plain,
! [A: $i] :
( ~ ( lt @ A @ A )
| ~ ( ssItem @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(118,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(455,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)],[118]) ).
thf(24455,plain,
( ~ ( rearsegP @ nil @ sk7 )
| ( sk7 != sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[16937,643]) ).
thf(24456,plain,
( ~ ( rearsegP @ nil @ sk7 )
| ( sk7 != sk1 ) ),
inference(pattern_uni,[status(thm)],[24455:[]]) ).
thf(1103,plain,
! [B: $i,A: $i] :
( ~ ( lt @ B @ B )
| ( ( ssItem @ ( skaf55 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[390,491]) ).
thf(1104,plain,
! [A: $i] :
~ ( lt @ ( skaf55 @ A ) @ ( skaf55 @ A ) ),
inference(pattern_uni,[status(thm)],[1103:[bind(A,$thf( C )),bind(B,$thf( skaf55 @ C ))]]) ).
thf(1113,plain,
! [A: $i] :
~ ( lt @ ( skaf55 @ A ) @ ( skaf55 @ A ) ),
inference(simp,[status(thm)],[1104]) ).
thf(1762,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf74 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[573,433]) ).
thf(1763,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf74 @ A ) ),
inference(pattern_uni,[status(thm)],[1762:[bind(A,$thf( C )),bind(B,$thf( skaf74 @ C ))]]) ).
thf(1775,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf74 @ A ) ),
inference(simp,[status(thm)],[1763]) ).
thf(2823,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf59 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[630,716]) ).
thf(2824,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf59 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[2823:[bind(A,$thf( C )),bind(B,$thf( skaf59 @ C ))]]) ).
thf(2835,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf59 @ A ) @ nil ) ),
inference(simp,[status(thm)],[2824]) ).
thf(52,axiom,
! [A: $i] :
( ~ ( ssItem @ A )
| ( totalorderedP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause67) ).
thf(306,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( totalorderedP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ~ ( lt @ A @ B )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( gt @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause106) ).
thf(226,plain,
! [B: $i,A: $i] :
( ~ ( lt @ A @ B )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( gt @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(1358,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf53 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[446,231]) ).
thf(1359,plain,
! [A: $i] :
~ ( neq @ ( skaf53 @ A ) @ ( skaf53 @ A ) ),
inference(pattern_uni,[status(thm)],[1358:[bind(A,$thf( C )),bind(B,$thf( skaf53 @ C ))]]) ).
thf(1364,plain,
! [A: $i] :
~ ( neq @ ( skaf53 @ A ) @ ( skaf53 @ A ) ),
inference(simp,[status(thm)],[1359]) ).
thf(37,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(267,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)],[37]) ).
thf(2896,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( totalorderedP @ sk1 )
| ( ( cons @ ( skaf44 @ sk1 ) @ nil )
!= ( cons @ A @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[2869,716]) ).
thf(2897,plain,
( ~ ( ssItem @ ( skaf44 @ sk1 ) )
| ( totalorderedP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[2896:[bind(A,$thf( skaf44 @ sk1 ))]]) ).
thf(3177,plain,
( ~ $true
| ( totalorderedP @ sk1 ) ),
inference(rewrite,[status(thm)],[2897,356]) ).
thf(3178,plain,
totalorderedP @ sk1,
inference(simp,[status(thm)],[3177]) ).
thf(140,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(505,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)],[140]) ).
thf(10118,plain,
( ( ssList @ ( tl @ sk2 ) )
| ( strictorderedP @ sk2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[8923,616]) ).
thf(10119,plain,
( ( ssList @ ( tl @ sk2 ) )
| ( strictorderedP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[10118:[]]) ).
thf(111,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( app @ A @ nil )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause73) ).
thf(438,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( app @ A @ nil )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(652,plain,
! [A: $i] :
( ~ ( memberP @ nil @ A )
| ( ( ssItem @ sk5 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[210,433]) ).
thf(653,plain,
~ ( memberP @ nil @ sk5 ),
inference(pattern_uni,[status(thm)],[652:[bind(A,$thf( sk5 ))]]) ).
thf(1612,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf83 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[569,716]) ).
thf(1613,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf83 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[1612:[bind(A,$thf( C )),bind(B,$thf( skaf83 @ C ))]]) ).
thf(1626,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf83 @ A ) @ nil ) ),
inference(simp,[status(thm)],[1613]) ).
thf(721,plain,
! [A: $i] :
( ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ sk6 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[203,716]) ).
thf(722,plain,
totalorderedP @ ( cons @ sk6 @ nil ),
inference(pattern_uni,[status(thm)],[721:[bind(A,$thf( sk6 ))]]) ).
thf(11943,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( skaf63 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[537,287]) ).
thf(11944,plain,
! [A: $i] : ( rearsegP @ ( skaf63 @ A ) @ nil ),
inference(pattern_uni,[status(thm)],[11943:[bind(A,$thf( C )),bind(B,$thf( skaf63 @ C ))]]) ).
thf(12021,plain,
! [A: $i] : ( rearsegP @ ( skaf63 @ A ) @ nil ),
inference(simp,[status(thm)],[11944]) ).
thf(177,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(589,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)],[177]) ).
thf(149,axiom,
! [A: $i] :
( ~ ( ssItem @ A )
| ( strictorderP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause68) ).
thf(531,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( strictorderP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(2750,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssItem @ ( skaf78 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[608,281]) ).
thf(2751,plain,
! [A: $i] :
~ ( neq @ ( skaf78 @ A ) @ ( skaf78 @ A ) ),
inference(pattern_uni,[status(thm)],[2750:[bind(A,$thf( C )),bind(B,$thf( skaf78 @ C ))]]) ).
thf(2784,plain,
! [A: $i] :
~ ( neq @ ( skaf78 @ A ) @ ( skaf78 @ A ) ),
inference(simp,[status(thm)],[2751]) ).
thf(80,axiom,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( neq @ B @ A )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause102) ).
thf(374,plain,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( neq @ B @ A )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(31,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(254,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)],[31]) ).
thf(255,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)],[254]) ).
thf(1266,plain,
! [B: $i,A: $i] :
( ~ ( lt @ B @ B )
| ( ( ssItem @ ( skaf49 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[422,491]) ).
thf(1267,plain,
! [A: $i] :
~ ( lt @ ( skaf49 @ A ) @ ( skaf49 @ A ) ),
inference(pattern_uni,[status(thm)],[1266:[bind(A,$thf( C )),bind(B,$thf( skaf49 @ C ))]]) ).
thf(1277,plain,
! [A: $i] :
~ ( lt @ ( skaf49 @ A ) @ ( skaf49 @ A ) ),
inference(simp,[status(thm)],[1267]) ).
thf(753,plain,
! [A: $i] :
( ~ ( lt @ A @ A )
| ( ( ssItem @ skac3 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[533,491]) ).
thf(754,plain,
~ ( lt @ skac3 @ skac3 ),
inference(pattern_uni,[status(thm)],[753:[bind(A,$thf( skac3 ))]]) ).
thf(159,axiom,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( ( tl @ ( cons @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause96) ).
thf(553,plain,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( ( tl @ ( cons @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(12042,plain,
( ( ssList @ ( tl @ sk8 ) )
| ( rearsegP @ sk1 @ sk8 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[9287,11936]) ).
thf(12043,plain,
( ( ssList @ ( tl @ sk8 ) )
| ( rearsegP @ sk1 @ sk8 ) ),
inference(pattern_uni,[status(thm)],[12042:[]]) ).
thf(126,axiom,
! [A: $i] :
( ~ ( ssItem @ A )
| ( cyclefreeP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause70) ).
thf(473,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( cyclefreeP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(1050,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssItem @ ( skaf69 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[389,281]) ).
thf(1051,plain,
! [A: $i] :
~ ( neq @ ( skaf69 @ A ) @ ( skaf69 @ A ) ),
inference(pattern_uni,[status(thm)],[1050:[bind(A,$thf( C )),bind(B,$thf( skaf69 @ C ))]]) ).
thf(1076,plain,
! [A: $i] :
~ ( neq @ ( skaf69 @ A ) @ ( skaf69 @ A ) ),
inference(simp,[status(thm)],[1051]) ).
thf(646,plain,
( ( ( app @ ( app @ sk1 @ ( cons @ sk6 @ nil ) ) @ sk8 )
= sk1 )
| ( ( app @ ( app @ ( app @ sk7 @ ( cons @ sk5 @ nil ) ) @ ( cons @ sk6 @ nil ) ) @ sk8 )
!= ( app @ sk7 @ ( cons @ sk5 @ nil ) ) ) ),
inference(paramod_ordered,[status(thm)],[213,213]) ).
thf(648,plain,
( ( ( app @ ( app @ sk1 @ ( cons @ sk6 @ nil ) ) @ sk8 )
= sk1 )
| ( ( app @ ( app @ sk7 @ ( cons @ sk5 @ nil ) ) @ ( cons @ sk6 @ nil ) )
!= sk7 )
| ( ( cons @ sk5 @ nil )
!= sk8 ) ),
inference(simp,[status(thm)],[646]) ).
thf(27577,plain,
! [A: $i] :
( ~ ( singletonP @ sk2 )
| ( strictorderedP @ sk2 )
| ( ( cons @ ( skaf44 @ sk2 ) @ nil )
!= ( cons @ ( skaf44 @ A ) @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[1445,20957]) ).
thf(27578,plain,
( ~ ( singletonP @ sk2 )
| ( strictorderedP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[27577:[bind(A,$thf( sk2 ))]]) ).
thf(190,axiom,
! [B: $i,A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ( strictorderedP @ ( cons @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause112) ).
thf(617,plain,
! [B: $i,A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ( strictorderedP @ ( cons @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(143,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(516,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)],[143]) ).
thf(2651,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssItem @ ( skaf50 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[588,281]) ).
thf(2652,plain,
! [A: $i] :
~ ( neq @ ( skaf50 @ A ) @ ( skaf50 @ A ) ),
inference(pattern_uni,[status(thm)],[2651:[bind(A,$thf( C )),bind(B,$thf( skaf50 @ C ))]]) ).
thf(2684,plain,
! [A: $i] :
~ ( neq @ ( skaf50 @ A ) @ ( skaf50 @ A ) ),
inference(simp,[status(thm)],[2652]) ).
thf(146,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(525,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)],[146]) ).
thf(11097,plain,
( ( ssList @ ( tl @ sk7 ) )
| ~ ( singletonP @ sk7 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[9500,487]) ).
thf(11098,plain,
( ( ssList @ ( tl @ sk7 ) )
| ~ ( singletonP @ sk7 ) ),
inference(pattern_uni,[status(thm)],[11097:[]]) ).
thf(20919,plain,
! [B: $i,A: $i] :
( ( strictorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf49 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[422,323]) ).
thf(20920,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf49 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[20919:[bind(A,$thf( C )),bind(B,$thf( skaf49 @ C ))]]) ).
thf(20951,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf49 @ A ) @ nil ) ),
inference(simp,[status(thm)],[20920]) ).
thf(326,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)],[325]) ).
thf(327,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)],[326]) ).
thf(24615,plain,
! [B: $i,A: $i] :
( ( ( app @ nil @ B )
= B )
| ( ( ssList @ ( skaf82 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[574,333]) ).
thf(24616,plain,
! [A: $i] :
( ( app @ nil @ ( skaf82 @ A ) )
= ( skaf82 @ A ) ),
inference(pattern_uni,[status(thm)],[24615:[bind(A,$thf( C )),bind(B,$thf( skaf82 @ C ))]]) ).
thf(24869,plain,
! [A: $i] :
( ( app @ nil @ ( skaf82 @ A ) )
= ( skaf82 @ A ) ),
inference(simp,[status(thm)],[24616]) ).
thf(2669,plain,
! [B: $i,A: $i] :
( ~ ( lt @ B @ B )
| ( ( ssItem @ ( skaf50 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[588,491]) ).
thf(2670,plain,
! [A: $i] :
~ ( lt @ ( skaf50 @ A ) @ ( skaf50 @ A ) ),
inference(pattern_uni,[status(thm)],[2669:[bind(A,$thf( C )),bind(B,$thf( skaf50 @ C ))]]) ).
thf(2678,plain,
! [A: $i] :
~ ( lt @ ( skaf50 @ A ) @ ( skaf50 @ A ) ),
inference(simp,[status(thm)],[2670]) ).
thf(1772,plain,
! [B: $i,A: $i] :
( ~ ( lt @ B @ B )
| ( ( ssItem @ ( skaf74 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[573,491]) ).
thf(1773,plain,
! [A: $i] :
~ ( lt @ ( skaf74 @ A ) @ ( skaf74 @ A ) ),
inference(pattern_uni,[status(thm)],[1772:[bind(A,$thf( C )),bind(B,$thf( skaf74 @ C ))]]) ).
thf(1780,plain,
! [A: $i] :
~ ( lt @ ( skaf74 @ A ) @ ( skaf74 @ A ) ),
inference(simp,[status(thm)],[1773]) ).
thf(1006,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf44 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[356,433]) ).
thf(1007,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf44 @ A ) ),
inference(pattern_uni,[status(thm)],[1006:[bind(A,$thf( C )),bind(B,$thf( skaf44 @ C ))]]) ).
thf(1025,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf44 @ A ) ),
inference(simp,[status(thm)],[1007]) ).
thf(1064,plain,
! [B: $i,A: $i] :
( ~ ( lt @ B @ B )
| ( ( ssItem @ ( skaf69 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[389,491]) ).
thf(1065,plain,
! [A: $i] :
~ ( lt @ ( skaf69 @ A ) @ ( skaf69 @ A ) ),
inference(pattern_uni,[status(thm)],[1064:[bind(A,$thf( C )),bind(B,$thf( skaf69 @ C ))]]) ).
thf(1070,plain,
! [A: $i] :
~ ( lt @ ( skaf69 @ A ) @ ( skaf69 @ A ) ),
inference(simp,[status(thm)],[1065]) ).
thf(864,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf64 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[266,716]) ).
thf(865,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf64 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[864:[bind(A,$thf( C )),bind(B,$thf( skaf64 @ C ))]]) ).
thf(872,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf64 @ A ) @ nil ) ),
inference(simp,[status(thm)],[865]) ).
thf(20915,plain,
! [B: $i,A: $i] :
( ( strictorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf55 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[390,323]) ).
thf(20916,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf55 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[20915:[bind(A,$thf( C )),bind(B,$thf( skaf55 @ C ))]]) ).
thf(20948,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf55 @ A ) @ nil ) ),
inference(simp,[status(thm)],[20916]) ).
thf(1217,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf60 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[401,433]) ).
thf(1218,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf60 @ A ) ),
inference(pattern_uni,[status(thm)],[1217:[bind(A,$thf( C )),bind(B,$thf( skaf60 @ C ))]]) ).
thf(1230,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf60 @ A ) ),
inference(simp,[status(thm)],[1218]) ).
thf(25710,plain,
( ~ ( singletonP @ sk8 )
| ( ( rearsegP @ nil @ nil )
!= ( rearsegP @ nil @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[11988,24027]) ).
thf(25748,plain,
( ~ ( singletonP @ sk8 )
| ( nil != nil )
| ( nil != sk8 ) ),
inference(simp,[status(thm)],[25710]) ).
thf(25768,plain,
( ~ ( singletonP @ sk8 )
| ( nil != sk8 ) ),
inference(simp,[status(thm)],[25748]) ).
thf(10716,plain,
( ( ssList @ ( tl @ sk8 ) )
| ( totalorderedP @ sk8 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[9287,629]) ).
thf(10717,plain,
( ( ssList @ ( tl @ sk8 ) )
| ( totalorderedP @ sk8 ) ),
inference(pattern_uni,[status(thm)],[10716:[]]) ).
thf(121,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( cons @ ( hd @ A ) @ ( tl @ A ) )
= A )
| ( nil = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause104) ).
thf(463,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( cons @ ( hd @ A ) @ ( tl @ A ) )
= A )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(66,axiom,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( ( hd @ ( cons @ A @ B ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause97) ).
thf(336,plain,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( ( hd @ ( cons @ A @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(337,plain,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( ( hd @ ( cons @ A @ B ) )
= A ) ),
inference(cnf,[status(esa)],[336]) ).
thf(338,plain,
! [B: $i,A: $i] :
( ( ( hd @ ( cons @ A @ B ) )
= A )
| ~ ( ssItem @ A )
| ~ ( ssList @ B ) ),
inference(lifteq,[status(thm)],[337]) ).
thf(5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
thf(199,plain,
sk2 = sk4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12070,plain,
( ( ssList @ ( tl @ sk2 ) )
| ( rearsegP @ sk2 @ sk2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[8923,11948]) ).
thf(12071,plain,
( ( ssList @ ( tl @ sk2 ) )
| ( rearsegP @ sk2 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[12070:[]]) ).
thf(112,axiom,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( neq @ B @ A )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause100) ).
thf(441,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( neq @ B @ A )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(25975,plain,
( ( nil != sk8 )
| ( ( singletonP @ sk8 )
!= ( singletonP @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[641,25768]) ).
thf(26006,plain,
( ( nil != sk8 )
| ( sk8 != sk1 ) ),
inference(simp,[status(thm)],[25975]) ).
thf(21752,plain,
( ~ ( rearsegP @ nil @ sk2 )
| ( sk2 != sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[16161,643]) ).
thf(21753,plain,
( ~ ( rearsegP @ nil @ sk2 )
| ( sk2 != sk1 ) ),
inference(pattern_uni,[status(thm)],[21752:[]]) ).
thf(1227,plain,
! [B: $i,A: $i] :
( ~ ( lt @ B @ B )
| ( ( ssItem @ ( skaf60 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[401,491]) ).
thf(1228,plain,
! [A: $i] :
~ ( lt @ ( skaf60 @ A ) @ ( skaf60 @ A ) ),
inference(pattern_uni,[status(thm)],[1227:[bind(A,$thf( C )),bind(B,$thf( skaf60 @ C ))]]) ).
thf(1235,plain,
! [A: $i] :
~ ( lt @ ( skaf60 @ A ) @ ( skaf60 @ A ) ),
inference(simp,[status(thm)],[1228]) ).
thf(2663,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf50 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[588,716]) ).
thf(2664,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf50 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[2663:[bind(A,$thf( C )),bind(B,$thf( skaf50 @ C ))]]) ).
thf(2675,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf50 @ A ) @ nil ) ),
inference(simp,[status(thm)],[2664]) ).
thf(22742,plain,
( ( nil != sk2 )
| ( ( singletonP @ sk2 )
!= ( singletonP @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[641,22731]) ).
thf(22771,plain,
( ( nil != sk2 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[22742]) ).
thf(4927,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( neq @ C @ C )
| ( ( ssList @ ( skaf42 @ A @ B ) )
!= ( ssList @ C ) ) ),
inference(paramod_ordered,[status(thm)],[599,231]) ).
thf(4928,plain,
! [B: $i,A: $i] :
~ ( neq @ ( skaf42 @ A @ B ) @ ( skaf42 @ A @ B ) ),
inference(pattern_uni,[status(thm)],[4927:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( skaf42 @ D @ E ))]]) ).
thf(4932,plain,
! [B: $i,A: $i] :
~ ( neq @ ( skaf42 @ A @ B ) @ ( skaf42 @ A @ B ) ),
inference(simp,[status(thm)],[4928]) ).
thf(24597,plain,
! [B: $i,A: $i] :
( ( ( app @ nil @ B )
= B )
| ( ( ssList @ ( skaf66 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[538,333]) ).
thf(24598,plain,
! [A: $i] :
( ( app @ nil @ ( skaf66 @ A ) )
= ( skaf66 @ A ) ),
inference(pattern_uni,[status(thm)],[24597:[bind(A,$thf( C )),bind(B,$thf( skaf66 @ C ))]]) ).
thf(24864,plain,
! [A: $i] :
( ( app @ nil @ ( skaf66 @ A ) )
= ( skaf66 @ A ) ),
inference(simp,[status(thm)],[24598]) ).
thf(12003,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( skaf68 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[469,287]) ).
thf(12004,plain,
! [A: $i] : ( rearsegP @ ( skaf68 @ A ) @ nil ),
inference(pattern_uni,[status(thm)],[12003:[bind(A,$thf( C )),bind(B,$thf( skaf68 @ C ))]]) ).
thf(12039,plain,
! [A: $i] : ( rearsegP @ ( skaf68 @ A ) @ nil ),
inference(simp,[status(thm)],[12004]) ).
thf(987,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf58 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[342,231]) ).
thf(988,plain,
! [A: $i] :
~ ( neq @ ( skaf58 @ A ) @ ( skaf58 @ A ) ),
inference(pattern_uni,[status(thm)],[987:[bind(A,$thf( C )),bind(B,$thf( skaf58 @ C ))]]) ).
thf(991,plain,
! [A: $i] :
~ ( neq @ ( skaf58 @ A ) @ ( skaf58 @ A ) ),
inference(simp,[status(thm)],[988]) ).
thf(2829,plain,
! [B: $i,A: $i] :
( ~ ( lt @ B @ B )
| ( ( ssItem @ ( skaf59 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[630,491]) ).
thf(2830,plain,
! [A: $i] :
~ ( lt @ ( skaf59 @ A ) @ ( skaf59 @ A ) ),
inference(pattern_uni,[status(thm)],[2829:[bind(A,$thf( C )),bind(B,$thf( skaf59 @ C ))]]) ).
thf(2838,plain,
! [A: $i] :
~ ( lt @ ( skaf59 @ A ) @ ( skaf59 @ A ) ),
inference(simp,[status(thm)],[2830]) ).
thf(10022,plain,
( ( ssList @ ( tl @ sk2 ) )
| ( totalorderedP @ sk2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[8923,629]) ).
thf(10023,plain,
( ( ssList @ ( tl @ sk2 ) )
| ( totalorderedP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[10022:[]]) ).
thf(1140,plain,
! [A: $i] :
( ~ ( lt @ ( skaf69 @ A ) @ ( skaf70 @ A ) )
| ( strictorderedP @ A )
| ( ( ssList @ sk7 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[200,238]) ).
thf(1141,plain,
( ~ ( lt @ ( skaf69 @ sk7 ) @ ( skaf70 @ sk7 ) )
| ( strictorderedP @ sk7 ) ),
inference(pattern_uni,[status(thm)],[1140:[bind(A,$thf( sk7 ))]]) ).
thf(1529,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf81 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[498,231]) ).
thf(1530,plain,
! [A: $i] :
~ ( neq @ ( skaf81 @ A ) @ ( skaf81 @ A ) ),
inference(pattern_uni,[status(thm)],[1529:[bind(A,$thf( C )),bind(B,$thf( skaf81 @ C ))]]) ).
thf(1536,plain,
! [A: $i] :
~ ( neq @ ( skaf81 @ A ) @ ( skaf81 @ A ) ),
inference(simp,[status(thm)],[1530]) ).
thf(24804,plain,
! [B: $i,A: $i] :
( ( ( app @ nil @ B )
= B )
| ( ( ssList @ ( skaf62 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[232,333]) ).
thf(24805,plain,
! [A: $i] :
( ( app @ nil @ ( skaf62 @ A ) )
= ( skaf62 @ A ) ),
inference(pattern_uni,[status(thm)],[24804:[bind(A,$thf( C )),bind(B,$thf( skaf62 @ C ))]]) ).
thf(24908,plain,
! [A: $i] :
( ( app @ nil @ ( skaf62 @ A ) )
= ( skaf62 @ A ) ),
inference(simp,[status(thm)],[24805]) ).
thf(1002,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssItem @ ( skaf44 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[356,281]) ).
thf(1003,plain,
! [A: $i] :
~ ( neq @ ( skaf44 @ A ) @ ( skaf44 @ A ) ),
inference(pattern_uni,[status(thm)],[1002:[bind(A,$thf( C )),bind(B,$thf( skaf44 @ C ))]]) ).
thf(1023,plain,
! [A: $i] :
~ ( neq @ ( skaf44 @ A ) @ ( skaf44 @ A ) ),
inference(simp,[status(thm)],[1003]) ).
thf(11925,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( skaf82 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[574,287]) ).
thf(11926,plain,
! [A: $i] : ( rearsegP @ ( skaf82 @ A ) @ nil ),
inference(pattern_uni,[status(thm)],[11925:[bind(A,$thf( C )),bind(B,$thf( skaf82 @ C ))]]) ).
thf(12014,plain,
! [A: $i] : ( rearsegP @ ( skaf82 @ A ) @ nil ),
inference(simp,[status(thm)],[11926]) ).
thf(183,axiom,
! [A: $i] :
( ~ ( frontsegP @ nil @ A )
| ~ ( ssList @ A )
| ( nil = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause84) ).
thf(600,plain,
! [A: $i] :
( ~ ( frontsegP @ nil @ A )
| ~ ( ssList @ A )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(1583,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf66 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[538,231]) ).
thf(1584,plain,
! [A: $i] :
~ ( neq @ ( skaf66 @ A ) @ ( skaf66 @ A ) ),
inference(pattern_uni,[status(thm)],[1583:[bind(A,$thf( C )),bind(B,$thf( skaf66 @ C ))]]) ).
thf(1585,plain,
! [A: $i] :
~ ( neq @ ( skaf66 @ A ) @ ( skaf66 @ A ) ),
inference(simp,[status(thm)],[1584]) ).
thf(85,axiom,
! [B: $i,A: $i] :
( ( ( cons @ A @ B )
!= nil )
| ~ ( ssItem @ A )
| ~ ( ssList @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause98) ).
thf(386,plain,
! [B: $i,A: $i] :
( ( ( cons @ A @ B )
!= nil )
| ~ ( ssItem @ A )
| ~ ( ssList @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(24759,plain,
! [A: $i] :
( ( ( app @ nil @ A )
= A )
| ( ( ssList @ nil )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[282,333]) ).
thf(24760,plain,
( ( app @ nil @ nil )
= nil ),
inference(pattern_uni,[status(thm)],[24759:[bind(A,$thf( nil ))]]) ).
thf(27749,plain,
( ( nil != sk7 )
| ( ( singletonP @ sk7 )
!= ( singletonP @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[641,27735]) ).
thf(27780,plain,
( ( nil != sk7 )
| ( sk7 != sk1 ) ),
inference(simp,[status(thm)],[27749]) ).
thf(1871,plain,
! [B: $i,A: $i] :
( ~ ( lt @ B @ B )
| ( ( ssItem @ ( skaf65 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[578,491]) ).
thf(1872,plain,
! [A: $i] :
~ ( lt @ ( skaf65 @ A ) @ ( skaf65 @ A ) ),
inference(pattern_uni,[status(thm)],[1871:[bind(A,$thf( C )),bind(B,$thf( skaf65 @ C ))]]) ).
thf(1881,plain,
! [A: $i] :
~ ( lt @ ( skaf65 @ A ) @ ( skaf65 @ A ) ),
inference(simp,[status(thm)],[1872]) ).
thf(1256,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf49 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[422,433]) ).
thf(1257,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf49 @ A ) ),
inference(pattern_uni,[status(thm)],[1256:[bind(A,$thf( C )),bind(B,$thf( skaf49 @ C ))]]) ).
thf(1272,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf49 @ A ) ),
inference(simp,[status(thm)],[1257]) ).
thf(11107,plain,
( ( ssList @ ( tl @ sk7 ) )
| ( totalorderP @ sk7 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[9500,470]) ).
thf(11108,plain,
( ( ssList @ ( tl @ sk7 ) )
| ( totalorderP @ sk7 ) ),
inference(pattern_uni,[status(thm)],[11107:[]]) ).
thf(188,axiom,
! [A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ( frontsegP @ nil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause83) ).
thf(612,plain,
! [A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ( frontsegP @ nil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(10213,plain,
( ( ssList @ ( tl @ sk2 ) )
| ( strictorderP @ sk2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[8923,294]) ).
thf(10214,plain,
( ( ssList @ ( tl @ sk2 ) )
| ( strictorderP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[10213:[]]) ).
thf(837,plain,
! [B: $i,A: $i] :
( ~ ( lt @ B @ B )
| ( ( ssItem @ ( skaf79 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[248,491]) ).
thf(838,plain,
! [A: $i] :
~ ( lt @ ( skaf79 @ A ) @ ( skaf79 @ A ) ),
inference(pattern_uni,[status(thm)],[837:[bind(A,$thf( C )),bind(B,$thf( skaf79 @ C ))]]) ).
thf(845,plain,
! [A: $i] :
~ ( lt @ ( skaf79 @ A ) @ ( skaf79 @ A ) ),
inference(simp,[status(thm)],[838]) ).
thf(193,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( segmentP @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause57) ).
thf(627,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( segmentP @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(24738,plain,
! [B: $i,A: $i] :
( ( ( app @ nil @ B )
= B )
| ( ( ssList @ ( skaf77 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[299,333]) ).
thf(24739,plain,
! [A: $i] :
( ( app @ nil @ ( skaf77 @ A ) )
= ( skaf77 @ A ) ),
inference(pattern_uni,[status(thm)],[24738:[bind(A,$thf( C )),bind(B,$thf( skaf77 @ C ))]]) ).
thf(24898,plain,
! [A: $i] :
( ( app @ nil @ ( skaf77 @ A ) )
= ( skaf77 @ A ) ),
inference(simp,[status(thm)],[24739]) ).
thf(160,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(556,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)],[160]) ).
thf(1818,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssItem @ ( skaf54 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[577,281]) ).
thf(1819,plain,
! [A: $i] :
~ ( neq @ ( skaf54 @ A ) @ ( skaf54 @ A ) ),
inference(pattern_uni,[status(thm)],[1818:[bind(A,$thf( C )),bind(B,$thf( skaf54 @ C ))]]) ).
thf(1844,plain,
! [A: $i] :
~ ( neq @ ( skaf54 @ A ) @ ( skaf54 @ A ) ),
inference(simp,[status(thm)],[1819]) ).
thf(10795,plain,
( ( ssList @ ( tl @ sk8 ) )
| ( equalelemsP @ sk8 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[9287,313]) ).
thf(10796,plain,
( ( ssList @ ( tl @ sk8 ) )
| ( equalelemsP @ sk8 ) ),
inference(pattern_uni,[status(thm)],[10795:[]]) ).
thf(136,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(495,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)],[136]) ).
thf(2762,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf78 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[608,716]) ).
thf(2763,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf78 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[2762:[bind(A,$thf( C )),bind(B,$thf( skaf78 @ C ))]]) ).
thf(2775,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf78 @ A ) @ nil ) ),
inference(simp,[status(thm)],[2763]) ).
thf(11941,plain,
! [A: $i] :
( ( rearsegP @ A @ nil )
| ( ( ssList @ ( tl @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9945,287]) ).
thf(11942,plain,
rearsegP @ ( tl @ sk1 ) @ nil,
inference(pattern_uni,[status(thm)],[11941:[bind(A,$thf( tl @ sk1 ))]]) ).
thf(1093,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf55 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[390,433]) ).
thf(1094,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf55 @ A ) ),
inference(pattern_uni,[status(thm)],[1093:[bind(A,$thf( C )),bind(B,$thf( skaf55 @ C ))]]) ).
thf(1108,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf55 @ A ) ),
inference(simp,[status(thm)],[1094]) ).
thf(154,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(539,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)],[154]) ).
thf(131,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(482,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)],[131]) ).
thf(11913,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( skaf72 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[247,287]) ).
thf(11914,plain,
! [A: $i] : ( rearsegP @ ( skaf72 @ A ) @ nil ),
inference(pattern_uni,[status(thm)],[11913:[bind(A,$thf( C )),bind(B,$thf( skaf72 @ C ))]]) ).
thf(12010,plain,
! [A: $i] : ( rearsegP @ ( skaf72 @ A ) @ nil ),
inference(simp,[status(thm)],[11914]) ).
thf(895,plain,
! [A: $i] :
( ~ ( leq @ A @ sk6 )
| ( geq @ sk6 @ A )
| ( ( ssItem @ skac2 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[520,684]) ).
thf(896,plain,
( ~ ( leq @ skac2 @ sk6 )
| ( geq @ sk6 @ skac2 ) ),
inference(pattern_uni,[status(thm)],[895:[bind(A,$thf( skac2 ))]]) ).
thf(1618,plain,
! [B: $i,A: $i] :
( ~ ( lt @ B @ B )
| ( ( ssItem @ ( skaf83 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[569,491]) ).
thf(1619,plain,
! [A: $i] :
~ ( lt @ ( skaf83 @ A ) @ ( skaf83 @ A ) ),
inference(pattern_uni,[status(thm)],[1618:[bind(A,$thf( C )),bind(B,$thf( skaf83 @ C ))]]) ).
thf(1629,plain,
! [A: $i] :
~ ( lt @ ( skaf83 @ A ) @ ( skaf83 @ A ) ),
inference(simp,[status(thm)],[1619]) ).
thf(4871,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( neq @ C @ C )
| ( ( ssList @ ( skaf47 @ A @ B ) )
!= ( ssList @ C ) ) ),
inference(paramod_ordered,[status(thm)],[481,231]) ).
thf(4872,plain,
! [B: $i,A: $i] :
~ ( neq @ ( skaf47 @ A @ B ) @ ( skaf47 @ A @ B ) ),
inference(pattern_uni,[status(thm)],[4871:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( skaf47 @ D @ E ))]]) ).
thf(4881,plain,
! [B: $i,A: $i] :
~ ( neq @ ( skaf47 @ A @ B ) @ ( skaf47 @ A @ B ) ),
inference(simp,[status(thm)],[4872]) ).
thf(9919,plain,
( ~ ( leq @ skac2 @ sk6 )
| ~ ( geq @ skac2 @ skac3 )
| ( ( geq @ skac3 @ skac2 )
!= ( geq @ sk6 @ skac2 ) ) ),
inference(paramod_ordered,[status(thm)],[896,9876]) ).
thf(9935,plain,
( ~ ( leq @ skac2 @ sk6 )
| ~ ( geq @ skac2 @ skac3 )
| ( skac3 != sk6 )
| ( skac2 != skac2 ) ),
inference(simp,[status(thm)],[9919]) ).
thf(9940,plain,
( ~ ( leq @ skac2 @ sk6 )
| ~ ( geq @ skac2 @ skac3 )
| ( skac3 != sk6 ) ),
inference(simp,[status(thm)],[9935]) ).
thf(21517,plain,
( ~ ( rearsegP @ nil @ sk2 )
| ~ ( memberP @ sk2 @ skac2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[16161,655]) ).
thf(21518,plain,
( ~ ( rearsegP @ nil @ sk2 )
| ~ ( memberP @ sk2 @ skac2 ) ),
inference(pattern_uni,[status(thm)],[21517:[]]) ).
thf(24764,plain,
! [B: $i,A: $i] :
( ( ( app @ nil @ B )
= B )
| ( ( ssList @ ( skaf56 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[585,333]) ).
thf(24765,plain,
! [A: $i] :
( ( app @ nil @ ( skaf56 @ A ) )
= ( skaf56 @ A ) ),
inference(pattern_uni,[status(thm)],[24764:[bind(A,$thf( C )),bind(B,$thf( skaf56 @ C ))]]) ).
thf(24901,plain,
! [A: $i] :
( ( app @ nil @ ( skaf56 @ A ) )
= ( skaf56 @ A ) ),
inference(simp,[status(thm)],[24765]) ).
thf(1016,plain,
! [B: $i,A: $i] :
( ~ ( lt @ B @ B )
| ( ( ssItem @ ( skaf44 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[356,491]) ).
thf(1017,plain,
! [A: $i] :
~ ( lt @ ( skaf44 @ A ) @ ( skaf44 @ A ) ),
inference(pattern_uni,[status(thm)],[1016:[bind(A,$thf( C )),bind(B,$thf( skaf44 @ C ))]]) ).
thf(1030,plain,
! [A: $i] :
~ ( lt @ ( skaf44 @ A ) @ ( skaf44 @ A ) ),
inference(simp,[status(thm)],[1017]) ).
thf(289,plain,
! [B: $i,A: $i] :
( ( ( app @ A @ B )
!= nil )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( nil = A ) ),
inference(cnf,[status(esa)],[288]) ).
thf(290,plain,
! [B: $i,A: $i] :
( ( ( app @ A @ B )
!= nil )
| ( nil = A )
| ~ ( ssList @ B )
| ~ ( ssList @ A ) ),
inference(lifteq,[status(thm)],[289]) ).
thf(1766,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf74 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[573,716]) ).
thf(1767,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf74 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[1766:[bind(A,$thf( C )),bind(B,$thf( skaf74 @ C ))]]) ).
thf(1777,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf74 @ A ) @ nil ) ),
inference(simp,[status(thm)],[1767]) ).
thf(1307,plain,
! [A: $i] :
( ( cyclefreeP @ A )
| ( leq @ ( skaf49 @ A ) @ ( skaf50 @ A ) )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[201,240]) ).
thf(1308,plain,
( ( cyclefreeP @ sk1 )
| ( leq @ ( skaf49 @ sk1 ) @ ( skaf50 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[1307:[bind(A,$thf( sk1 ))]]) ).
thf(35932,plain,
( ~ ( memberP @ sk2 @ skac2 )
| ( ( rearsegP @ nil @ sk2 )
!= ( rearsegP @ sk2 @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[11948,21518]) ).
thf(36043,plain,
( ~ ( memberP @ sk2 @ skac2 )
| ( nil != sk2 )
| ( nil != sk2 ) ),
inference(simp,[status(thm)],[35932]) ).
thf(36071,plain,
( ~ ( memberP @ sk2 @ skac2 )
| ( nil != sk2 ) ),
inference(simp,[status(thm)],[36043]) ).
thf(761,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf72 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[247,231]) ).
thf(762,plain,
! [A: $i] :
~ ( neq @ ( skaf72 @ A ) @ ( skaf72 @ A ) ),
inference(pattern_uni,[status(thm)],[761:[bind(A,$thf( C )),bind(B,$thf( skaf72 @ C ))]]) ).
thf(763,plain,
! [A: $i] :
~ ( neq @ ( skaf72 @ A ) @ ( skaf72 @ A ) ),
inference(simp,[status(thm)],[762]) ).
thf(11973,plain,
! [C: $i,B: $i,A: $i] :
( ( rearsegP @ C @ nil )
| ( ( ssList @ ( skaf42 @ A @ B ) )
!= ( ssList @ C ) ) ),
inference(paramod_ordered,[status(thm)],[599,287]) ).
thf(11974,plain,
! [B: $i,A: $i] : ( rearsegP @ ( skaf42 @ A @ B ) @ nil ),
inference(pattern_uni,[status(thm)],[11973:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( skaf42 @ D @ E ))]]) ).
thf(12031,plain,
! [B: $i,A: $i] : ( rearsegP @ ( skaf42 @ A @ B ) @ nil ),
inference(simp,[status(thm)],[11974]) ).
thf(11945,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( tl @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10047,287]) ).
thf(11946,plain,
( ( cyclefreeP @ sk2 )
| ( rearsegP @ ( tl @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[11945:[bind(A,$thf( tl @ sk2 ))]]) ).
thf(84,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(383,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)],[84]) ).
thf(214,plain,
~ ( neq @ sk5 @ sk6 ),
inference(polarity_switch,[status(thm)],[204]) ).
thf(1861,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf65 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[578,433]) ).
thf(1862,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf65 @ A ) ),
inference(pattern_uni,[status(thm)],[1861:[bind(A,$thf( C )),bind(B,$thf( skaf65 @ C ))]]) ).
thf(1876,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf65 @ A ) ),
inference(simp,[status(thm)],[1862]) ).
thf(20856,plain,
! [B: $i,A: $i] :
( ( strictorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf79 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[248,323]) ).
thf(20857,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf79 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[20856:[bind(A,$thf( C )),bind(B,$thf( skaf79 @ C ))]]) ).
thf(20952,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf79 @ A ) @ nil ) ),
inference(simp,[status(thm)],[20857]) ).
thf(184,axiom,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( ssList @ ( cons @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause86) ).
thf(603,plain,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( ssList @ ( cons @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(20860,plain,
! [B: $i,A: $i] :
( ( strictorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf65 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[578,323]) ).
thf(20861,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf65 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[20860:[bind(A,$thf( C )),bind(B,$thf( skaf65 @ C ))]]) ).
thf(20955,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf65 @ A ) @ nil ) ),
inference(simp,[status(thm)],[20861]) ).
thf(24695,plain,
! [B: $i,A: $i] :
( ( ( app @ nil @ B )
= B )
| ( ( ssList @ ( skaf73 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[382,333]) ).
thf(24696,plain,
! [A: $i] :
( ( app @ nil @ ( skaf73 @ A ) )
= ( skaf73 @ A ) ),
inference(pattern_uni,[status(thm)],[24695:[bind(A,$thf( C )),bind(B,$thf( skaf73 @ C ))]]) ).
thf(24884,plain,
! [A: $i] :
( ( app @ nil @ ( skaf73 @ A ) )
= ( skaf73 @ A ) ),
inference(simp,[status(thm)],[24696]) ).
thf(97,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(410,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)],[97]) ).
thf(163,axiom,
! [A: $i] :
( ~ ( segmentP @ nil @ A )
| ~ ( ssList @ A )
| ( nil = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause80) ).
thf(564,plain,
! [A: $i] :
( ~ ( segmentP @ nil @ A )
| ~ ( ssList @ A )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(268,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)],[267]) ).
thf(20905,plain,
! [B: $i,A: $i] :
( ( strictorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf70 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[394,323]) ).
thf(20906,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf70 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[20905:[bind(A,$thf( C )),bind(B,$thf( skaf70 @ C ))]]) ).
thf(20945,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf70 @ A ) @ nil ) ),
inference(simp,[status(thm)],[20906]) ).
thf(11957,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( skaf81 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[498,287]) ).
thf(11958,plain,
! [A: $i] : ( rearsegP @ ( skaf81 @ A ) @ nil ),
inference(pattern_uni,[status(thm)],[11957:[bind(A,$thf( C )),bind(B,$thf( skaf81 @ C ))]]) ).
thf(12024,plain,
! [A: $i] : ( rearsegP @ ( skaf81 @ A ) @ nil ),
inference(simp,[status(thm)],[11958]) ).
thf(99,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(415,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)],[99]) ).
thf(24626,plain,
! [B: $i,A: $i] :
( ( ( app @ nil @ B )
= B )
| ( ( ssList @ ( skaf57 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[312,333]) ).
thf(24627,plain,
! [A: $i] :
( ( app @ nil @ ( skaf57 @ A ) )
= ( skaf57 @ A ) ),
inference(pattern_uni,[status(thm)],[24626:[bind(A,$thf( C )),bind(B,$thf( skaf57 @ C ))]]) ).
thf(24872,plain,
! [A: $i] :
( ( app @ nil @ ( skaf57 @ A ) )
= ( skaf57 @ A ) ),
inference(simp,[status(thm)],[24627]) ).
thf(340,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)],[339]) ).
thf(341,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)],[340]) ).
thf(719,plain,
! [A: $i] :
( ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ skac2 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[520,716]) ).
thf(720,plain,
totalorderedP @ ( cons @ skac2 @ nil ),
inference(pattern_uni,[status(thm)],[719:[bind(A,$thf( skac2 ))]]) ).
thf(11953,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( skaf51 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[530,287]) ).
thf(11954,plain,
! [A: $i] : ( rearsegP @ ( skaf51 @ A ) @ nil ),
inference(pattern_uni,[status(thm)],[11953:[bind(A,$thf( C )),bind(B,$thf( skaf51 @ C ))]]) ).
thf(12022,plain,
! [A: $i] : ( rearsegP @ ( skaf51 @ A ) @ nil ),
inference(simp,[status(thm)],[11954]) ).
thf(727,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ( ( ssItem @ skac2 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[520,281]) ).
thf(728,plain,
~ ( neq @ skac2 @ skac2 ),
inference(pattern_uni,[status(thm)],[727:[bind(A,$thf( skac2 ))]]) ).
thf(12001,plain,
! [A: $i] :
( ( rearsegP @ A @ nil )
| ( ( ssList @ sk7 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[200,287]) ).
thf(12002,plain,
rearsegP @ sk7 @ nil,
inference(pattern_uni,[status(thm)],[12001:[bind(A,$thf( sk7 ))]]) ).
thf(169,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(575,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)],[169]) ).
thf(180,axiom,
! [B: $i,A: $i] :
( ~ ( lt @ A @ B )
| ~ ( lt @ B @ A )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause114) ).
thf(596,plain,
! [B: $i,A: $i] :
( ~ ( lt @ A @ B )
| ~ ( lt @ B @ A )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(119,axiom,
! [A: $i] :
( ~ ( ssItem @ A )
| ( leq @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause62) ).
thf(459,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( leq @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(24791,plain,
! [A: $i] :
( ( ( app @ nil @ A )
= A )
| ( ( ssList @ sk7 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[200,333]) ).
thf(24792,plain,
( ( app @ nil @ sk7 )
= sk7 ),
inference(pattern_uni,[status(thm)],[24791:[bind(A,$thf( sk7 ))]]) ).
thf(20870,plain,
! [B: $i,A: $i] :
( ( strictorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf64 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[266,323]) ).
thf(20871,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf64 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[20870:[bind(A,$thf( C )),bind(B,$thf( skaf64 @ C ))]]) ).
thf(20933,plain,
! [A: $i] : ( strictorderedP @ ( cons @ ( skaf64 @ A ) @ nil ) ),
inference(simp,[status(thm)],[20871]) ).
thf(276,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)],[275]) ).
thf(277,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)],[276]) ).
thf(90,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( rearsegP @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause59) ).
thf(395,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( rearsegP @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(192,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(624,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)],[192]) ).
thf(831,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf79 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[248,716]) ).
thf(832,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf79 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[831:[bind(A,$thf( C )),bind(B,$thf( skaf79 @ C ))]]) ).
thf(839,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf79 @ A ) @ nil ) ),
inference(simp,[status(thm)],[832]) ).
thf(78,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(369,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)],[78]) ).
thf(11983,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( skaf58 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[342,287]) ).
thf(11984,plain,
! [A: $i] : ( rearsegP @ ( skaf58 @ A ) @ nil ),
inference(pattern_uni,[status(thm)],[11983:[bind(A,$thf( C )),bind(B,$thf( skaf58 @ C ))]]) ).
thf(12035,plain,
! [A: $i] : ( rearsegP @ ( skaf58 @ A ) @ nil ),
inference(simp,[status(thm)],[11984]) ).
thf(11931,plain,
! [B: $i,A: $i] :
( ( rearsegP @ B @ nil )
| ( ( ssList @ ( skaf57 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[312,287]) ).
thf(11932,plain,
! [A: $i] : ( rearsegP @ ( skaf57 @ A ) @ nil ),
inference(pattern_uni,[status(thm)],[11931:[bind(A,$thf( C )),bind(B,$thf( skaf57 @ C ))]]) ).
thf(12017,plain,
! [A: $i] : ( rearsegP @ ( skaf57 @ A ) @ nil ),
inference(simp,[status(thm)],[11932]) ).
thf(215,plain,
sk4 = sk2,
inference(lifteq,[status(thm)],[199]) ).
thf(10816,plain,
( ( ssList @ ( tl @ sk8 ) )
| ( strictorderedP @ sk8 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[9287,616]) ).
thf(10817,plain,
( ( ssList @ ( tl @ sk8 ) )
| ( strictorderedP @ sk8 ) ),
inference(pattern_uni,[status(thm)],[10816:[]]) ).
thf(10191,plain,
( ( ssList @ ( tl @ sk2 ) )
| ( sk2 != sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[8923,643]) ).
thf(10192,plain,
( ( ssList @ ( tl @ sk2 ) )
| ( sk2 != sk1 ) ),
inference(pattern_uni,[status(thm)],[10191:[]]) ).
thf(362,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)],[361]) ).
thf(363,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)],[362]) ).
thf(364,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)],[363]) ).
thf(862,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf64 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[266,433]) ).
thf(863,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf64 @ A ) ),
inference(pattern_uni,[status(thm)],[862:[bind(A,$thf( C )),bind(B,$thf( skaf64 @ C ))]]) ).
thf(882,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf64 @ A ) ),
inference(simp,[status(thm)],[863]) ).
thf(227,plain,
! [B: $i,A: $i] :
( ~ ( lt @ A @ B )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( gt @ B @ A ) ),
inference(cnf,[status(esa)],[226]) ).
thf(11991,plain,
! [A: $i] :
( ( totalorderedP @ sk2 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( tl @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10023,287]) ).
thf(11992,plain,
( ( totalorderedP @ sk2 )
| ( rearsegP @ ( tl @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[11991:[bind(A,$thf( tl @ sk2 ))]]) ).
thf(27825,plain,
( ( strictorderedP @ sk2 )
| ( ( singletonP @ sk2 )
!= ( singletonP @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[641,27578]) ).
thf(27844,plain,
( ( strictorderedP @ sk2 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[27825]) ).
thf(81345,plain,
$false,
inference(e,[status(thm)],[9929,24878,629,760,2778,347,234,365,1190,333,249,1554,1110,481,352,582,730,12040,10912,308,247,18114,269,202,24907,878,655,1078,1137,550,24874,2844,538,24885,1671,1310,533,404,898,1835,24902,1127,417,885,12009,436,1904,2869,288,9994,651,257,389,2735,372,1330,702,344,12065,357,11051,9938,542,1409,724,9287,570,11986,559,1379,17562,1572,325,11132,24871,448,5076,261,1232,20946,881,27541,7560,228,216,475,492,12023,12069,238,12041,1183,480,12018,756,27817,321,211,253,348,574,24631,18123,20934,2833,634,221,293,1622,1394,243,428,206,20949,397,12036,8347,265,849,21542,10933,527,312,8508,248,380,13386,201,21736,714,2773,233,452,10831,220,366,534,3767,1067,11952,598,24879,15531,275,12037,10133,1274,2673,24027,334,20953,12012,302,260,11037,407,630,252,361,45825,4776,1624,12025,461,493,1027,11948,12020,710,324,20912,329,285,1106,578,697,1804,20944,9945,24655,12016,24903,356,24862,593,24044,420,12033,21511,20957,1270,317,24670,1878,24754,499,24870,488,339,1292,12019,537,476,1424,1700,12091,1039,547,328,471,256,212,706,12045,19997,1324,21529,1478,24906,4829,10961,10047,1874,569,24899,10180,47258,16937,503,605,4148,244,1202,360,205,311,8923,1846,18144,398,1187,16754,1185,586,343,237,1241,266,530,22731,10190,718,888,298,513,264,11016,20935,573,444,10890,27582,11110,425,20932,18095,11920,5598,562,402,732,27531,20947,12038,11936,286,24865,545,413,12028,4144,47497,423,31310,20847,577,711,579,291,281,12011,204,641,391,1786,313,498,466,335,236,704,10741,11996,24863,382,900,219,274,419,12034,20928,377,567,318,599,12015,509,10888,434,10098,616,303,271,208,20892,631,758,27735,609,323,621,330,2710,890,1667,345,367,213,726,848,700,520,240,251,1838,521,24900,636,455,24456,608,1113,1775,299,431,16599,2835,278,1445,394,306,226,1364,267,3178,505,10119,438,241,653,1626,722,12021,589,531,1467,2784,374,255,1277,342,754,553,12043,473,1076,648,209,27578,487,617,516,2684,525,10878,11098,282,20951,327,24869,2678,1780,310,11988,1025,295,1070,872,20948,1230,25768,331,10717,463,338,470,643,199,12071,24439,441,26006,585,21753,1235,2675,336,9500,22771,4932,24864,314,446,12039,991,2838,10023,1141,1536,24908,1023,12014,600,1585,386,24760,27780,1881,1272,11108,612,10214,845,231,627,24898,556,1844,10796,495,218,2775,11942,1108,539,9876,482,203,588,12010,896,16161,258,1629,4881,9940,390,21518,24901,401,1030,290,433,1777,207,1308,684,36071,235,246,763,12031,272,11946,383,716,214,287,447,432,1876,422,20952,603,20955,300,24884,410,564,305,210,239,294,268,20945,12024,283,415,24872,341,720,12022,728,12002,575,596,459,12844,24792,20933,200,277,395,624,839,369,12035,469,12017,309,215,10817,491,10192,222,592,364,232,882,254,227,322,11992,486,27844]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SWC166-1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.16/0.35 % Computer : n005.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Fri May 19 01:18:09 EDT 2023
% 0.16/0.35 % CPUTime :
% 0.87/0.83 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.57/1.01 % [INFO] Parsing done (174ms).
% 1.57/1.02 % [INFO] Running in sequential loop mode.
% 1.93/1.22 % [INFO] eprover registered as external prover.
% 1.93/1.22 % [INFO] cvc4 registered as external prover.
% 1.93/1.22 % [INFO] Scanning for conjecture ...
% 2.01/1.30 % [INFO] Found a conjecture and 185 axioms. Running axiom selection ...
% 2.26/1.38 % [INFO] Axiom selection finished. Selected 185 axioms (removed 0 axioms).
% 2.77/1.47 % [INFO] Problem is propositional (TPTP CNF).
% 2.77/1.49 % [INFO] Type checking passed.
% 2.77/1.49 % [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 ...
% 141.28/25.61 % External prover 'e' found a proof!
% 141.28/25.61 % [INFO] Killing All external provers ...
% 141.28/25.62 % Time passed: 25102ms (effective reasoning time: 24593ms)
% 141.28/25.62 % 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)>
% 141.28/25.62 % 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
% 141.28/25.62 % No. of inferences in proof: 1279
% 141.28/25.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 25102 ms resp. 24593 ms w/o parsing
% 141.52/25.81 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 141.52/25.81 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------