%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWC341-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:53:22 AM UTC 2026
% Result : Unsatisfiable 231.86s 85.71s
% Output : Refutation 222.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 196
% Syntax : Number of formulae : 760 ( 227 unt; 0 typ; 0 def)
% Number of atoms : 2440 ( 491 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 6809 (1468 ~;1352 |; 0 &;3989 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 76 ( 73 usr; 10 con; 0-2 aty)
% Number of variables : 1044 ( 0 ^;1044 !; 0 ?;1044 :)
% Comments :
%------------------------------------------------------------------------------
thf(ssList_decl,type,
ssList: $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(nil_decl,type,
nil: $i ).
thf(ssItem_decl,type,
ssItem: $i > $o ).
thf(sk5_decl,type,
sk5: $i ).
thf(neq_decl,type,
neq: $i > $i > $o ).
thf(cons_decl,type,
cons: $i > $i > $i ).
thf(memberP_decl,type,
memberP: $i > $i > $o ).
thf(segmentP_decl,type,
segmentP: $i > $i > $o ).
thf(totalorderedP_decl,type,
totalorderedP: $i > $o ).
thf(skac3_decl,type,
skac3: $i ).
thf(skac2_decl,type,
skac2: $i ).
thf(skaf43_decl,type,
skaf43: $i > $i > $i ).
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(geq_decl,type,
geq: $i > $i > $o ).
thf(lt_decl,type,
lt: $i > $i > $o ).
thf(gt_decl,type,
gt: $i > $i > $o ).
thf(skaf62_decl,type,
skaf62: $i > $i ).
thf(app_decl,type,
app: $i > $i > $i ).
thf(skaf69_decl,type,
skaf69: $i > $i ).
thf(skaf70_decl,type,
skaf70: $i > $i ).
thf(strictorderedP_decl,type,
strictorderedP: $i > $o ).
thf(cyclefreeP_decl,type,
cyclefreeP: $i > $o ).
thf(skaf49_decl,type,
skaf49: $i > $i ).
thf(skaf50_decl,type,
skaf50: $i > $i ).
thf(singletonP_decl,type,
singletonP: $i > $o ).
thf(skaf44_decl,type,
skaf44: $i > $i ).
thf(duplicatefreeP_decl,type,
duplicatefreeP: $i > $o ).
thf(skaf75_decl,type,
skaf75: $i > $i ).
thf(skaf74_decl,type,
skaf74: $i > $i ).
thf(skaf76_decl,type,
skaf76: $i > $i ).
thf(skaf77_decl,type,
skaf77: $i > $i ).
thf(skaf72_decl,type,
skaf72: $i > $i ).
thf(skaf79_decl,type,
skaf79: $i > $i ).
thf(hd_decl,type,
hd: $i > $i ).
thf(frontsegP_decl,type,
frontsegP: $i > $i > $o ).
thf(skaf71_decl,type,
skaf71: $i > $i ).
thf(skaf73_decl,type,
skaf73: $i > $i ).
thf(skaf46_decl,type,
skaf46: $i > $i > $i ).
thf(skaf64_decl,type,
skaf64: $i > $i ).
thf(tl_decl,type,
tl: $i > $i ).
thf(skaf66_decl,type,
skaf66: $i > $i ).
thf(skaf67_decl,type,
skaf67: $i > $i ).
thf(skaf65_decl,type,
skaf65: $i > $i ).
thf(skaf68_decl,type,
skaf68: $i > $i ).
thf(skaf45_decl,type,
skaf45: $i > $i > $i ).
thf(rearsegP_decl,type,
rearsegP: $i > $i > $o ).
thf(strictorderP_decl,type,
strictorderP: $i > $o ).
thf(skaf61_decl,type,
skaf61: $i > $i ).
thf(skaf59_decl,type,
skaf59: $i > $i ).
thf(skaf60_decl,type,
skaf60: $i > $i ).
thf(skaf63_decl,type,
skaf63: $i > $i ).
thf(skaf51_decl,type,
skaf51: $i > $i ).
thf(skaf52_decl,type,
skaf52: $i > $i ).
thf(skaf53_decl,type,
skaf53: $i > $i ).
thf(skaf57_decl,type,
skaf57: $i > $i ).
thf(equalelemsP_decl,type,
equalelemsP: $i > $o ).
thf(totalorderP_decl,type,
totalorderP: $i > $o ).
thf(skaf56_decl,type,
skaf56: $i > $i ).
thf(skaf54_decl,type,
skaf54: $i > $i ).
thf(skaf55_decl,type,
skaf55: $i > $i ).
thf(skaf58_decl,type,
skaf58: $i > $i ).
thf(skaf48_decl,type,
skaf48: $i > $i > $i ).
thf(skaf80_decl,type,
skaf80: $i > $i ).
thf(skaf47_decl,type,
skaf47: $i > $i > $i ).
thf(skaf78_decl,type,
skaf78: $i > $i ).
thf(skaf81_decl,type,
skaf81: $i > $i ).
thf(skaf83_decl,type,
skaf83: $i > $i ).
thf(skaf82_decl,type,
skaf82: $i > $i ).
thf(skaf42_decl,type,
skaf42: $i > $i > $i ).
thf(165,axiom,
! [A: $i] : ( A @ skaf74 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause21) ).
thf(574,plain,
! [A: $i] : ( A @ skaf74 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(106,axiom,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( nil @ memberP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause71) ).
thf(433,plain,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(434,plain,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(cnf,[status(esa)],[433]) ).
thf(1557,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[574,434]) ).
thf(1558,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1557]) ).
thf(1559,plain,
! [A: $i] :
~ ( A @ skaf74 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1558:[bind(A,$thf( C )),bind(B,$thf( C @ skaf74 ))]]) ).
thf(1586,plain,
! [A: $i] :
~ ( A @ skaf74 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1559]) ).
thf(89,axiom,
! [A: $i] : ( A @ skaf61 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause34) ).
thf(398,plain,
! [A: $i] : ( A @ skaf61 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(2,negated_conjecture,
sk2 @ ssList,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_2) ).
thf(202,plain,
sk2 @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(28,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ app ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause85) ).
thf(253,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ app ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(254,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ app ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[253]) ).
thf(3449,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ssList )
!= ( B @ ssList ) )
| ( A @ ( B @ app ) @ ssList )
| ~ $true
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[202,254]) ).
thf(3450,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ssList )
!= ( B @ ssList ) )
| ( A @ ( B @ app ) @ ssList )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[3449]) ).
thf(3451,plain,
! [A: $i] :
( ( A @ ( sk2 @ app ) @ ssList )
| ~ ( A @ ssList ) ),
inference(pattern_uni,[status(thm)],[3450:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(4753,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf61 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[398,3451]) ).
thf(4754,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf61 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[4753]) ).
thf(4755,plain,
! [A: $i] : ( A @ skaf61 @ ( sk2 @ app ) @ ssList ),
inference(pattern_uni,[status(thm)],[4754:[bind(A,$thf( C )),bind(B,$thf( C @ skaf61 ))]]) ).
thf(4835,plain,
! [A: $i] : ( A @ skaf61 @ ( sk2 @ app ) @ ssList ),
inference(simp,[status(thm)],[4755]) ).
thf(172,axiom,
! [A: $i] : ( A @ skaf56 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause39) ).
thf(586,plain,
! [A: $i] : ( A @ skaf56 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(4741,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf56 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[586,3451]) ).
thf(4742,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf56 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[4741]) ).
thf(4743,plain,
! [A: $i] : ( A @ skaf56 @ ( sk2 @ app ) @ ssList ),
inference(pattern_uni,[status(thm)],[4742:[bind(A,$thf( C )),bind(B,$thf( C @ skaf56 ))]]) ).
thf(4824,plain,
! [A: $i] : ( A @ skaf56 @ ( sk2 @ app ) @ ssList ),
inference(simp,[status(thm)],[4743]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ lt ) )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause147) ).
thf(234,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ lt ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(127,axiom,
! [A: $i] : ( A @ skaf52 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause43) ).
thf(481,plain,
! [A: $i] : ( A @ skaf52 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(87,axiom,
! [A: $i] : ( A @ skaf70 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause25) ).
thf(395,plain,
! [A: $i] : ( A @ skaf70 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(10,negated_conjecture,
( ~ ( nil @ ( sk4 @ neq ) )
| ( sk5 @ ( sk4 @ memberP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
thf(198,plain,
( ~ ( nil @ ( sk4 @ neq ) )
| ( sk5 @ ( sk4 @ memberP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(213,plain,
( ~ ( nil @ ( sk4 @ neq ) )
| ( sk5 @ ( sk4 @ memberP ) ) ),
inference(cnf,[status(esa)],[198]) ).
thf(5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
thf(197,plain,
sk2 = sk4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(211,plain,
sk4 = sk2,
inference(lifteq,[status(thm)],[197]) ).
thf(643,plain,
( ~ ( nil @ ( sk2 @ neq ) )
| ( sk5 @ ( sk2 @ memberP ) ) ),
inference(rewrite,[status(thm)],[213,211]) ).
thf(644,plain,
! [A: $i] :
( ( ( A @ ( nil @ memberP ) )
!= ( sk5 @ ( sk2 @ memberP ) ) )
| ~ ( A @ ssItem )
| ~ $true
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[643,434]) ).
thf(645,plain,
! [A: $i] :
( ( ( A @ ( nil @ memberP ) )
!= ( sk5 @ ( sk2 @ memberP ) ) )
| ~ ( A @ ssItem )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[644]) ).
thf(646,plain,
! [A: $i] :
( ( A != sk5 )
| ( nil != sk2 )
| ~ ( A @ ssItem )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[645]) ).
thf(647,plain,
( ( nil != sk2 )
| ~ ( sk5 @ ssItem )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[646]) ).
thf(902,plain,
! [A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( sk5 @ ssItem ) )
| ( nil != sk2 )
| ~ $true
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[395,647]) ).
thf(903,plain,
! [A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( sk5 @ ssItem ) )
| ( nil != sk2 )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[902]) ).
thf(909,plain,
! [A: $i] :
( ( ( A @ skaf70 )
!= sk5 )
| ( nil != sk2 )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[903]) ).
thf(191,axiom,
! [A: $i] :
( ( A @ ( A @ segmentP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause57) ).
thf(628,plain,
! [A: $i] :
( ( A @ ( A @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(26,axiom,
! [A: $i] : ( A @ skaf79 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause16) ).
thf(249,plain,
! [A: $i] : ( A @ skaf79 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(94,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ~ ( A @ ( B @ frontsegP ) )
| ~ ( B @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause129) ).
thf(408,plain,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ~ ( A @ ( B @ frontsegP ) )
| ~ ( B @ ( A @ frontsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(114,axiom,
! [A: $i] :
( ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause79) ).
thf(449,plain,
! [A: $i] :
( ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(24,axiom,
! [A: $i] :
( ( ( A @ skaf77 @ ( A @ skaf74 @ cons ) @ ( A @ skaf76 @ ( A @ skaf74 @ cons ) @ ( A @ skaf75 @ app ) @ app ) )
= A )
| ( A @ duplicatefreeP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause162) ).
thf(245,plain,
! [A: $i] :
( ( ( A @ skaf77 @ ( A @ skaf74 @ cons ) @ ( A @ skaf76 @ ( A @ skaf74 @ cons ) @ ( A @ skaf75 @ app ) @ app ) )
= A )
| ( A @ duplicatefreeP )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(246,plain,
! [A: $i] :
( ( ( A @ skaf77 @ ( A @ skaf74 @ cons ) @ ( A @ skaf76 @ ( A @ skaf74 @ cons ) @ ( A @ skaf75 @ app ) @ app ) )
= A )
| ( A @ duplicatefreeP )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[245]) ).
thf(247,plain,
! [A: $i] :
( ( A @ duplicatefreeP )
| ~ ( A @ ssList )
| ( ( A @ skaf77 @ ( A @ skaf74 @ cons ) @ ( A @ skaf76 @ ( A @ skaf74 @ cons ) @ ( A @ skaf75 @ app ) @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[246]) ).
thf(12,axiom,
skac3 != skac2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause54) ).
thf(217,plain,
skac3 != skac2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(38,axiom,
! [A: $i] :
( ( ( A @ skaf68 @ ( A @ skaf65 @ cons ) @ ( A @ skaf67 @ ( A @ skaf64 @ cons ) @ ( A @ skaf66 @ app ) @ app ) )
= A )
| ( A @ totalorderedP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause164) ).
thf(276,plain,
! [A: $i] :
( ( ( A @ skaf68 @ ( A @ skaf65 @ cons ) @ ( A @ skaf67 @ ( A @ skaf64 @ cons ) @ ( A @ skaf66 @ app ) @ app ) )
= A )
| ( A @ totalorderedP )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(178,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ lt ) )
| ~ ( B @ ( A @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause114) ).
thf(597,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ lt ) )
| ~ ( B @ ( A @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(82,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ~ ( A @ ( B @ rearsegP ) )
| ~ ( B @ ( A @ rearsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause128) ).
thf(384,plain,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ~ ( A @ ( B @ rearsegP ) )
| ~ ( B @ ( A @ rearsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(136,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ segmentP ) )
| ~ ( D @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ( ( C @ ( B @ ( A @ app ) @ app ) )
!= D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause173) ).
thf(500,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ segmentP ) )
| ~ ( D @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ( ( C @ ( B @ ( A @ app ) @ app ) )
!= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ totalorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause113) ).
thf(223,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ totalorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(224,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ totalorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(cnf,[status(esa)],[223]) ).
thf(225,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ totalorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[224]) ).
thf(226,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[225]) ).
thf(40,axiom,
nil @ ssList,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause8) ).
thf(283,plain,
nil @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(714,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem )
| ~ $true ),
inference(rewrite,[status(thm)],[226,283]) ).
thf(715,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem ) ),
inference(simp,[status(thm)],[714]) ).
thf(123,axiom,
! [A: $i] :
( ( nil @ ( A @ frontsegP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause60) ).
thf(472,plain,
! [A: $i] :
( ( nil @ ( A @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(887,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[395,715]) ).
thf(888,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[887]) ).
thf(889,plain,
! [A: $i] : ( nil @ ( A @ skaf70 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[888:[bind(A,$thf( C )),bind(B,$thf( C @ skaf70 ))]]) ).
thf(913,plain,
! [A: $i] : ( nil @ ( A @ skaf70 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[889]) ).
thf(65,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ totalorderedP )
| ~ ( B @ hd @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause159) ).
thf(340,plain,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ totalorderedP )
| ~ ( B @ hd @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(150,axiom,
! [A: $i] : ( A @ skaf63 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause32) ).
thf(538,plain,
! [A: $i] : ( A @ skaf63 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(85,axiom,
! [A: $i] : ( A @ skaf55 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause40) ).
thf(391,plain,
! [A: $i] : ( A @ skaf55 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(874,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[391,434]) ).
thf(875,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[874]) ).
thf(876,plain,
! [A: $i] :
~ ( A @ skaf55 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[875:[bind(A,$thf( C )),bind(B,$thf( C @ skaf55 ))]]) ).
thf(885,plain,
! [A: $i] :
~ ( A @ skaf55 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[876]) ).
thf(4801,plain,
! [A: $i] :
( ( ( nil @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[283,3451]) ).
thf(4802,plain,
! [A: $i] :
( ( ( nil @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[4801]) ).
thf(4803,plain,
nil @ ( sk2 @ app ) @ ssList,
inference(pattern_uni,[status(thm)],[4802:[bind(A,$thf( nil ))]]) ).
thf(48,axiom,
! [A: $i] :
( ( ( A @ skaf53 @ ( A @ skaf50 @ cons ) @ ( A @ skaf52 @ ( A @ skaf49 @ cons ) @ ( A @ skaf51 @ app ) @ app ) )
= A )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause167) ).
thf(301,plain,
! [A: $i] :
( ( ( A @ skaf53 @ ( A @ skaf50 @ cons ) @ ( A @ skaf52 @ ( A @ skaf49 @ cons ) @ ( A @ skaf51 @ app ) @ app ) )
= A )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(161,axiom,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ segmentP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause80) ).
thf(565,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ segmentP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(142,axiom,
skac2 @ ssItem,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause10) ).
thf(521,plain,
skac2 @ ssItem,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(649,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[521,434]) ).
thf(650,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[649]) ).
thf(651,plain,
~ ( skac2 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[650:[bind(A,$thf( skac2 ))]]) ).
thf(30,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ geq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause107) ).
thf(257,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ geq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(163,axiom,
! [A: $i] : ( A @ skaf83 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause12) ).
thf(570,plain,
! [A: $i] : ( A @ skaf83 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(4686,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[202,3451]) ).
thf(4687,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[4686]) ).
thf(4688,plain,
sk2 @ ( sk2 @ app ) @ ssList,
inference(pattern_uni,[status(thm)],[4687:[bind(A,$thf( sk2 ))]]) ).
thf(4894,plain,
! [A: $i] :
( ( ( sk2 @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4688,3451]) ).
thf(4895,plain,
! [A: $i] :
( ( ( sk2 @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[4894]) ).
thf(4896,plain,
sk2 @ ( sk2 @ app ) @ ( sk2 @ app ) @ ssList,
inference(pattern_uni,[status(thm)],[4895:[bind(A,$thf( sk2 @ ( sk2 @ app ) ))]]) ).
thf(34,axiom,
! [A: $i] : ( A @ skaf64 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause31) ).
thf(267,plain,
! [A: $i] : ( A @ skaf64 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(9,negated_conjecture,
( ~ ( nil @ ( sk4 @ neq ) )
| ( ( nil @ ( sk5 @ cons ) )
= sk3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
thf(201,plain,
( ~ ( nil @ ( sk4 @ neq ) )
| ( ( nil @ ( sk5 @ cons ) )
= sk3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(209,plain,
( ~ ( nil @ ( sk4 @ neq ) )
| ( ( nil @ ( sk5 @ cons ) )
= sk3 ) ),
inference(cnf,[status(esa)],[201]) ).
thf(210,plain,
( ~ ( nil @ ( sk4 @ neq ) )
| ( ( nil @ ( sk5 @ cons ) )
= sk3 ) ),
inference(lifteq,[status(thm)],[209]) ).
thf(6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
thf(200,plain,
sk1 = sk3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(216,plain,
sk3 = sk1,
inference(lifteq,[status(thm)],[200]) ).
thf(648,plain,
( ~ ( nil @ ( sk2 @ neq ) )
| ( ( nil @ ( sk5 @ cons ) )
= sk1 ) ),
inference(rewrite,[status(thm)],[210,211,216]) ).
thf(730,plain,
! [A: $i] :
( ( ( nil @ ( sk5 @ cons ) )
!= ( nil @ ( A @ cons ) ) )
| ( sk1 @ totalorderedP )
| ~ ( A @ ssItem )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[648,715]) ).
thf(731,plain,
( ( sk1 @ totalorderedP )
| ~ ( sk5 @ ssItem )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[730:[bind(A,$thf( sk5 ))]]) ).
thf(782,plain,
! [A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( sk5 @ ssItem ) )
| ( sk1 @ totalorderedP )
| ~ $true
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[267,731]) ).
thf(783,plain,
! [A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( sk5 @ ssItem ) )
| ( sk1 @ totalorderedP )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[782]) ).
thf(785,plain,
! [A: $i] :
( ( ( A @ skaf64 )
!= sk5 )
| ~ ( nil @ ( sk2 @ neq ) )
| ( sk1 @ totalorderedP ) ),
inference(simp,[status(thm)],[783]) ).
thf(137,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause65) ).
thf(504,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(173,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ ( D @ app ) @ app ) @ segmentP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( D @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ( A @ segmentP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause172) ).
thf(587,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ ( D @ app ) @ app ) @ segmentP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( D @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ( A @ segmentP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(67,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ gt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ gt ) )
| ~ ( B @ ( A @ gt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause146) ).
thf(344,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ gt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ gt ) )
| ~ ( B @ ( A @ gt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(1,negated_conjecture,
sk1 @ ssList,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
thf(199,plain,
sk1 @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(4771,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[199,3451]) ).
thf(4772,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[4771]) ).
thf(4773,plain,
sk1 @ ( sk2 @ app ) @ ssList,
inference(pattern_uni,[status(thm)],[4772:[bind(A,$thf( sk1 ))]]) ).
thf(5148,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4773,3451]) ).
thf(5149,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[5148]) ).
thf(5150,plain,
sk1 @ ( sk2 @ app ) @ ( sk2 @ app ) @ ssList,
inference(pattern_uni,[status(thm)],[5149:[bind(A,$thf( sk1 @ ( sk2 @ app ) ))]]) ).
thf(117,axiom,
! [A: $i] :
( ( A @ ( A @ leq ) )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause62) ).
thf(460,plain,
! [A: $i] :
( ( A @ ( A @ leq ) )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause115) ).
thf(229,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(230,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(cnf,[status(esa)],[229]) ).
thf(231,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[230]) ).
thf(232,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[231]) ).
thf(932,plain,
! [A: $i] :
( ( ( nil @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[283,232]) ).
thf(933,plain,
! [A: $i] :
( ( ( nil @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[932]) ).
thf(934,plain,
~ ( nil @ ( nil @ neq ) ),
inference(pattern_uni,[status(thm)],[933:[bind(A,$thf( nil ))]]) ).
thf(71,axiom,
! [A: $i] : ( A @ skaf44 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause47) ).
thf(357,plain,
! [A: $i] : ( A @ skaf44 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(100,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ gt ) )
| ~ ( B @ ( A @ gt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause110) ).
thf(421,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ gt ) )
| ~ ( B @ ( A @ gt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(183,axiom,
! [A: $i] :
( ( A @ equalelemsP )
| ~ ( A @ ssList )
| ( ( A @ skaf79 )
!= ( A @ skaf78 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause89) ).
thf(606,plain,
! [A: $i] :
( ( A @ equalelemsP )
| ~ ( A @ ssList )
| ( ( A @ skaf79 )
!= ( A @ skaf78 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(97,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ cons ) @ memberP ) )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( A @ ssList )
| ~ ( B @ ( A @ memberP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause139) ).
thf(416,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ cons ) @ memberP ) )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( A @ ssList )
| ~ ( B @ ( A @ memberP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(58,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf45 ) @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause51) ).
thf(325,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf45 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause106) ).
thf(227,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(228,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ lt ) ) ),
inference(cnf,[status(esa)],[227]) ).
thf(43,axiom,
! [B: $i,A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause118) ).
thf(289,plain,
! [B: $i,A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(113,axiom,
! [A: $i] : ( A @ skaf75 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause20) ).
thf(448,plain,
! [A: $i] : ( A @ skaf75 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(31,axiom,
! [A: $i] :
( ( ( A @ skaf73 @ ( A @ skaf70 @ cons ) @ ( A @ skaf72 @ ( A @ skaf69 @ cons ) @ ( A @ skaf71 @ app ) @ app ) )
= A )
| ( A @ strictorderedP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause163) ).
thf(259,plain,
! [A: $i] :
( ( ( A @ skaf73 @ ( A @ skaf70 @ cons ) @ ( A @ skaf72 @ ( A @ skaf69 @ cons ) @ ( A @ skaf71 @ app ) @ app ) )
= A )
| ( A @ strictorderedP )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(260,plain,
! [A: $i] :
( ( ( A @ skaf73 @ ( A @ skaf70 @ cons ) @ ( A @ skaf72 @ ( A @ skaf69 @ cons ) @ ( A @ skaf71 @ app ) @ app ) )
= A )
| ( A @ strictorderedP )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[259]) ).
thf(261,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ~ ( A @ ssList )
| ( ( A @ skaf73 @ ( A @ skaf70 @ cons ) @ ( A @ skaf72 @ ( A @ skaf69 @ cons ) @ ( A @ skaf71 @ app ) @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[260]) ).
thf(41,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ skaf45 ) @ ( B @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause132) ).
thf(284,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ skaf45 ) @ ( B @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ frontsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(766,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[357,434]) ).
thf(767,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[766]) ).
thf(768,plain,
! [A: $i] :
~ ( A @ skaf44 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[767:[bind(A,$thf( C )),bind(B,$thf( C @ skaf44 ))]]) ).
thf(770,plain,
! [A: $i] :
~ ( A @ skaf44 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[768]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ strictorderedP )
| ~ ( A @ ssList )
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause90) ).
thf(238,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ~ ( A @ ssList )
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(23,axiom,
! [A: $i] :
( ( ( nil @ ( A @ skaf44 @ cons ) )
= A )
| ~ ( A @ ssList )
| ~ ( A @ singletonP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause101) ).
thf(242,plain,
! [A: $i] :
( ( ( nil @ ( A @ skaf44 @ cons ) )
= A )
| ~ ( A @ ssList )
| ~ ( A @ singletonP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(243,plain,
! [A: $i] :
( ( ( nil @ ( A @ skaf44 @ cons ) )
= A )
| ~ ( A @ ssList )
| ~ ( A @ singletonP ) ),
inference(cnf,[status(esa)],[242]) ).
thf(244,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ~ ( A @ singletonP )
| ( ( nil @ ( A @ skaf44 @ cons ) )
= A ) ),
inference(lifteq,[status(thm)],[243]) ).
thf(1976,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ singletonP )
| ( ( nil @ ( A @ skaf44 @ cons ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[202,244]) ).
thf(1977,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ singletonP )
| ( ( nil @ ( A @ skaf44 @ cons ) )
= A ) ),
inference(simp,[status(thm)],[1976]) ).
thf(1978,plain,
( ~ ( sk2 @ singletonP )
| ( ( nil @ ( sk2 @ skaf44 @ cons ) )
= sk2 ) ),
inference(pattern_uni,[status(thm)],[1977:[bind(A,$thf( sk2 ))]]) ).
thf(140,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ app ) @ ( A @ cons ) )
= ( C @ ( B @ ( A @ cons ) @ app ) ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause157) ).
thf(514,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ app ) @ ( A @ cons ) )
= ( C @ ( B @ ( A @ cons ) @ app ) ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(70,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ app ) )
= nil )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( nil != B )
| ( nil != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause145) ).
thf(353,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ app ) )
= nil )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( nil != B )
| ( nil != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(148,axiom,
skac3 @ ssItem,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause9) ).
thf(534,plain,
skac3 @ ssItem,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(719,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[534,715]) ).
thf(720,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[719]) ).
thf(721,plain,
nil @ ( skac3 @ cons ) @ totalorderedP,
inference(pattern_uni,[status(thm)],[720:[bind(A,$thf( skac3 ))]]) ).
thf(11,negated_conjecture,
( ~ ( sk1 @ totalorderedP )
| ~ ( sk1 @ ( sk2 @ segmentP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
thf(205,plain,
( ~ ( sk1 @ totalorderedP )
| ~ ( sk1 @ ( sk2 @ segmentP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(212,plain,
( ~ ( sk1 @ totalorderedP )
| ~ ( sk1 @ ( sk2 @ segmentP ) ) ),
inference(cnf,[status(esa)],[205]) ).
thf(735,plain,
( ( ( nil @ ( skac3 @ cons ) @ totalorderedP )
!= ( sk1 @ totalorderedP ) )
| ~ $true
| ~ ( sk1 @ ( sk2 @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[721,212]) ).
thf(736,plain,
( ( ( nil @ ( skac3 @ cons ) @ totalorderedP )
!= ( sk1 @ totalorderedP ) )
| ~ ( sk1 @ ( sk2 @ segmentP ) ) ),
inference(simp,[status(thm)],[735]) ).
thf(738,plain,
( ( ( nil @ ( skac3 @ cons ) )
!= sk1 )
| ~ ( sk1 @ ( sk2 @ segmentP ) ) ),
inference(simp,[status(thm)],[736]) ).
thf(2160,plain,
( ( ( nil @ ( sk2 @ skaf44 @ cons ) )
!= ( nil @ ( skac3 @ cons ) ) )
| ( sk2 != sk1 )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ singletonP ) ),
inference(paramod_ordered,[status(thm)],[1978,738]) ).
thf(2172,plain,
( ( nil != nil )
| ( ( sk2 @ skaf44 )
!= skac3 )
| ( sk2 != sk1 )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ singletonP ) ),
inference(simp,[status(thm)],[2160]) ).
thf(2178,plain,
( ( ( sk2 @ skaf44 )
!= skac3 )
| ( sk2 != sk1 )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ singletonP ) ),
inference(simp,[status(thm)],[2172]) ).
thf(81,axiom,
! [A: $i] : ( A @ skaf73 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause22) ).
thf(383,plain,
! [A: $i] : ( A @ skaf73 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(926,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf73 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[383,232]) ).
thf(927,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf73 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[926]) ).
thf(928,plain,
! [A: $i] :
~ ( A @ skaf73 @ ( A @ skaf73 @ neq ) ),
inference(pattern_uni,[status(thm)],[927:[bind(A,$thf( C )),bind(B,$thf( C @ skaf73 ))]]) ).
thf(956,plain,
! [A: $i] :
~ ( A @ skaf73 @ ( A @ skaf73 @ neq ) ),
inference(simp,[status(thm)],[928]) ).
thf(115,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = A )
| ( C @ ( B @ memberP ) )
| ~ ( C @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( C @ ( B @ ( A @ cons ) @ memberP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause161) ).
thf(453,plain,
! [C: $i,B: $i,A: $i] :
( ( C = A )
| ( C @ ( B @ memberP ) )
| ~ ( C @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( C @ ( B @ ( A @ cons ) @ memberP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(88,axiom,
! [A: $i] :
( ( A @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause59) ).
thf(396,plain,
! [A: $i] :
( ( A @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(8,negated_conjecture,
( ~ ( nil @ ( sk4 @ neq ) )
| ( sk5 @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
thf(206,plain,
( ~ ( nil @ ( sk4 @ neq ) )
| ( sk5 @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(716,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[249,715]) ).
thf(717,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[716]) ).
thf(718,plain,
! [A: $i] : ( nil @ ( A @ skaf79 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[717:[bind(A,$thf( C )),bind(B,$thf( C @ skaf79 ))]]) ).
thf(734,plain,
! [A: $i] : ( nil @ ( A @ skaf79 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[718]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ geq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause108) ).
thf(221,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ geq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(652,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[534,434]) ).
thf(653,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[652]) ).
thf(654,plain,
~ ( skac3 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[653:[bind(A,$thf( skac3 ))]]) ).
thf(658,plain,
( ( ( skac3 @ ( nil @ memberP ) )
!= ( sk5 @ ( sk2 @ memberP ) ) )
| ~ $true
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[643,654]) ).
thf(659,plain,
( ( ( skac3 @ ( nil @ memberP ) )
!= ( sk5 @ ( sk2 @ memberP ) ) )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[658]) ).
thf(660,plain,
( ( skac3 != sk5 )
| ( nil != sk2 )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[659]) ).
thf(4679,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf52 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[481,3451]) ).
thf(4680,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf52 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[4679]) ).
thf(4681,plain,
! [A: $i] : ( A @ skaf52 @ ( sk2 @ app ) @ ssList ),
inference(pattern_uni,[status(thm)],[4680:[bind(A,$thf( C )),bind(B,$thf( C @ skaf52 ))]]) ).
thf(4825,plain,
! [A: $i] : ( A @ skaf52 @ ( sk2 @ app ) @ ssList ),
inference(simp,[status(thm)],[4681]) ).
thf(95,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( nil @ ( A @ cons ) @ app ) )
= ( B @ ( A @ cons ) ) )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause120) ).
thf(411,plain,
! [B: $i,A: $i] :
( ( ( B @ ( nil @ ( A @ cons ) @ app ) )
= ( B @ ( A @ cons ) ) )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(91,axiom,
! [A: $i] : ( A @ skaf60 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause35) ).
thf(402,plain,
! [A: $i] : ( A @ skaf60 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(975,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[402,434]) ).
thf(976,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[975]) ).
thf(977,plain,
! [A: $i] :
~ ( A @ skaf60 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[976:[bind(A,$thf( C )),bind(B,$thf( C @ skaf60 ))]]) ).
thf(988,plain,
! [A: $i] :
~ ( A @ skaf60 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[977]) ).
thf(32,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ lt ) )
| ~ ( F @ ssList )
| ~ ( F @ strictorderedP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause181) ).
thf(262,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ lt ) )
| ~ ( F @ ssList )
| ~ ( F @ strictorderedP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(263,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ lt ) )
| ~ ( F @ ssList )
| ~ ( F @ strictorderedP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= F ) ),
inference(cnf,[status(esa)],[262]) ).
thf(264,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ lt ) )
| ~ ( F @ ssList )
| ~ ( F @ strictorderedP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= F ) ),
inference(lifteq,[status(thm)],[263]) ).
thf(265,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ lt ) )
| ~ ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) @ ssList )
| ~ ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) @ strictorderedP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList ) ),
inference(simp,[status(thm)],[264]) ).
thf(84,axiom,
! [A: $i] : ( A @ skaf69 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause26) ).
thf(390,plain,
! [A: $i] : ( A @ skaf69 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(842,plain,
! [A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( sk5 @ ssItem ) )
| ( nil != sk2 )
| ~ $true
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[390,647]) ).
thf(843,plain,
! [A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( sk5 @ ssItem ) )
| ( nil != sk2 )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[842]) ).
thf(849,plain,
! [A: $i] :
( ( ( A @ skaf69 )
!= sk5 )
| ( nil != sk2 )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[843]) ).
thf(50,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause67) ).
thf(307,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(44,axiom,
! [A: $i] :
( ( ( A @ skaf63 @ ( A @ skaf60 @ cons ) @ ( A @ skaf62 @ ( A @ skaf59 @ cons ) @ ( A @ skaf61 @ app ) @ app ) )
= A )
| ( A @ strictorderP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause165) ).
thf(292,plain,
! [A: $i] :
( ( ( A @ skaf63 @ ( A @ skaf60 @ cons ) @ ( A @ skaf62 @ ( A @ skaf59 @ cons ) @ ( A @ skaf61 @ app ) @ app ) )
= A )
| ( A @ strictorderP )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(18,axiom,
! [A: $i] : ( A @ skaf62 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause33) ).
thf(233,plain,
! [A: $i] : ( A @ skaf62 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(25,axiom,
! [A: $i] : ( A @ skaf72 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause23) ).
thf(248,plain,
! [A: $i] : ( A @ skaf72 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(109,axiom,
! [A: $i] :
( ( ( nil @ ( A @ app ) )
= A )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause73) ).
thf(439,plain,
! [A: $i] :
( ( ( nil @ ( A @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(36,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause126) ).
thf(270,plain,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(154,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ app ) @ memberP ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ( A @ memberP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause140) ).
thf(546,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ app ) @ memberP ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ( A @ memberP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(923,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[202,232]) ).
thf(924,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[923]) ).
thf(925,plain,
~ ( sk2 @ ( sk2 @ neq ) ),
inference(pattern_uni,[status(thm)],[924:[bind(A,$thf( sk2 ))]]) ).
thf(80,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ geq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause148) ).
thf(381,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ geq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(13,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf43 ) @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause52) ).
thf(220,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf43 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(74,axiom,
! [A: $i] :
( ( A @ totalorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf54 @ ( A @ skaf55 @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause94) ).
thf(366,plain,
! [A: $i] :
( ( A @ totalorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf54 @ ( A @ skaf55 @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(66,axiom,
! [A: $i] : ( A @ skaf58 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause37) ).
thf(343,plain,
! [A: $i] : ( A @ skaf58 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(944,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf58 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[343,232]) ).
thf(945,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf58 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[944]) ).
thf(946,plain,
! [A: $i] :
~ ( A @ skaf58 @ ( A @ skaf58 @ neq ) ),
inference(pattern_uni,[status(thm)],[945:[bind(A,$thf( C )),bind(B,$thf( C @ skaf58 ))]]) ).
thf(957,plain,
! [A: $i] :
~ ( A @ skaf58 @ ( A @ skaf58 @ neq ) ),
inference(simp,[status(thm)],[946]) ).
thf(724,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[521,715]) ).
thf(725,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[724]) ).
thf(726,plain,
nil @ ( skac2 @ cons ) @ totalorderedP,
inference(pattern_uni,[status(thm)],[725:[bind(A,$thf( skac2 ))]]) ).
thf(743,plain,
( ( ( nil @ ( skac2 @ cons ) )
!= ( nil @ ( sk5 @ cons ) ) )
| ( sk1 @ totalorderedP )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[648,726]) ).
thf(745,plain,
( ( nil != nil )
| ( skac2 != sk5 )
| ~ ( nil @ ( sk2 @ neq ) )
| ( sk1 @ totalorderedP ) ),
inference(simp,[status(thm)],[743]) ).
thf(746,plain,
( ( skac2 != sk5 )
| ~ ( nil @ ( sk2 @ neq ) )
| ( sk1 @ totalorderedP ) ),
inference(simp,[status(thm)],[745]) ).
thf(69,axiom,
! [A: $i] :
( ( A @ ( nil @ rearsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause81) ).
thf(349,plain,
! [A: $i] :
( ( A @ ( nil @ rearsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(86,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause130) ).
thf(392,plain,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(102,axiom,
! [A: $i] :
( ( nil @ ( A @ segmentP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause56) ).
thf(424,plain,
! [A: $i] :
( ( nil @ ( A @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(192,axiom,
nil @ totalorderedP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause4) ).
thf(630,plain,
nil @ totalorderedP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(104,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ hd @ ( A @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ totalorderedP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause135) ).
thf(429,plain,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ hd @ ( A @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ totalorderedP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(193,axiom,
! [A: $i] : ( A @ skaf59 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause36) ).
thf(631,plain,
! [A: $i] : ( A @ skaf59 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(2110,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[631,434]) ).
thf(2111,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[2110]) ).
thf(2112,plain,
! [A: $i] :
~ ( A @ skaf59 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[2111:[bind(A,$thf( C )),bind(B,$thf( C @ skaf59 ))]]) ).
thf(2132,plain,
! [A: $i] :
~ ( A @ skaf59 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[2112]) ).
thf(120,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( B @ ( A @ cons ) )
!= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause99) ).
thf(467,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( B @ ( A @ cons ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(27,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ hd @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ strictorderedP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause134) ).
thf(250,plain,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ hd @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ strictorderedP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(251,plain,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ hd @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ strictorderedP ) ),
inference(cnf,[status(esa)],[250]) ).
thf(252,plain,
! [B: $i,A: $i] :
( ( B @ hd @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ strictorderedP )
| ( nil = B ) ),
inference(lifteq,[status(thm)],[251]) ).
thf(190,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ~ ( A @ ( B @ segmentP ) )
| ~ ( B @ ( A @ segmentP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause127) ).
thf(625,plain,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ~ ( A @ ( B @ segmentP ) )
| ~ ( B @ ( A @ segmentP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(872,plain,
! [A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( sk5 @ ssItem ) )
| ( nil != sk2 )
| ~ $true
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[391,647]) ).
thf(873,plain,
! [A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( sk5 @ ssItem ) )
| ( nil != sk2 )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[872]) ).
thf(879,plain,
! [A: $i] :
( ( ( A @ skaf55 )
!= sk5 )
| ( nil != sk2 )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[873]) ).
thf(107,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ equalelemsP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause64) ).
thf(435,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ equalelemsP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(60,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ gt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause105) ).
thf(329,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ gt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(132,axiom,
! [A: $i] : ( A @ skaf67 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause28) ).
thf(493,plain,
! [A: $i] : ( A @ skaf67 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(2034,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ singletonP )
| ( ( nil @ ( A @ skaf44 @ cons ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[199,244]) ).
thf(2035,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ singletonP )
| ( ( nil @ ( A @ skaf44 @ cons ) )
= A ) ),
inference(simp,[status(thm)],[2034]) ).
thf(2036,plain,
( ~ ( sk1 @ singletonP )
| ( ( nil @ ( sk1 @ skaf44 @ cons ) )
= sk1 ) ),
inference(pattern_uni,[status(thm)],[2035:[bind(A,$thf( sk1 ))]]) ).
thf(2186,plain,
( ( ( nil @ ( sk1 @ skaf44 @ cons ) )
!= ( nil @ ( skac3 @ cons ) ) )
| ( sk1 != sk1 )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( sk1 @ singletonP ) ),
inference(paramod_ordered,[status(thm)],[2036,738]) ).
thf(2187,plain,
( ( ( nil @ ( sk1 @ skaf44 @ cons ) )
!= ( nil @ ( skac3 @ cons ) ) )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( sk1 @ singletonP ) ),
inference(simp,[status(thm)],[2186]) ).
thf(2205,plain,
( ( nil != nil )
| ( ( sk1 @ skaf44 )
!= skac3 )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( sk1 @ singletonP ) ),
inference(simp,[status(thm)],[2187]) ).
thf(2211,plain,
( ( ( sk1 @ skaf44 )
!= skac3 )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( sk1 @ singletonP ) ),
inference(simp,[status(thm)],[2205]) ).
thf(156,axiom,
! [A: $i] :
( ( nil = A )
| ( ( A @ skaf82 @ ( A @ skaf83 @ cons ) )
= A )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause109) ).
thf(551,plain,
! [A: $i] :
( ( nil = A )
| ( ( A @ skaf82 @ ( A @ skaf83 @ cons ) )
= A )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(705,plain,
! [A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( sk5 @ ssItem ) )
| ( nil != sk2 )
| ~ $true
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[267,647]) ).
thf(706,plain,
! [A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( sk5 @ ssItem ) )
| ( nil != sk2 )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[705]) ).
thf(710,plain,
! [A: $i] :
( ( ( A @ skaf64 )
!= sk5 )
| ( nil != sk2 )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[706]) ).
thf(116,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ssList )
| ~ ( E @ duplicatefreeP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( D @ ssList )
| ( ( D @ ( B @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause179) ).
thf(456,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ssList )
| ~ ( E @ duplicatefreeP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( D @ ssList )
| ( ( D @ ( B @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(171,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D = B )
| ~ ( B @ ssList )
| ~ ( D @ ssList )
| ~ ( A @ ssItem )
| ~ ( C @ ssItem )
| ( ( B @ ( A @ cons ) )
!= ( D @ ( C @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause171) ).
thf(583,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D = B )
| ~ ( B @ ssList )
| ~ ( D @ ssList )
| ~ ( A @ ssItem )
| ~ ( C @ ssItem )
| ( ( B @ ( A @ cons ) )
!= ( D @ ( C @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(143,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ leq ) )
| ~ ( F @ ssList )
| ~ ( F @ totalorderedP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause182) ).
thf(522,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ leq ) )
| ~ ( F @ ssList )
| ~ ( F @ totalorderedP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(168,axiom,
! [A: $i] : ( A @ skaf54 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause41) ).
thf(578,plain,
! [A: $i] : ( A @ skaf54 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(92,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ app ) @ frontsegP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause137) ).
thf(403,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ app ) @ frontsegP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ( A @ frontsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(176,axiom,
! [A: $i] : ( A @ skaf71 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause24) ).
thf(593,plain,
! [A: $i] : ( A @ skaf71 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(99,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf48 ) @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause48) ).
thf(420,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf48 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(135,axiom,
! [A: $i] : ( A @ skaf81 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause14) ).
thf(499,plain,
! [A: $i] : ( A @ skaf81 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(964,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[402,715]) ).
thf(965,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[964]) ).
thf(966,plain,
! [A: $i] : ( nil @ ( A @ skaf60 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[965:[bind(A,$thf( C )),bind(B,$thf( C @ skaf60 ))]]) ).
thf(989,plain,
! [A: $i] : ( nil @ ( A @ skaf60 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[966]) ).
thf(692,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[249,434]) ).
thf(693,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[692]) ).
thf(694,plain,
! [A: $i] :
~ ( A @ skaf79 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[693:[bind(A,$thf( C )),bind(B,$thf( C @ skaf79 ))]]) ).
thf(697,plain,
! [A: $i] :
~ ( A @ skaf79 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[694]) ).
thf(1497,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[570,715]) ).
thf(1498,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[1497]) ).
thf(1499,plain,
! [A: $i] : ( nil @ ( A @ skaf83 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[1498:[bind(A,$thf( C )),bind(B,$thf( C @ skaf83 ))]]) ).
thf(1541,plain,
! [A: $i] : ( nil @ ( A @ skaf83 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[1499]) ).
thf(185,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ skaf48 ) @ ( B @ ( B @ ( A @ skaf47 ) @ app ) @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ segmentP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause168) ).
thf(610,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ skaf48 ) @ ( B @ ( B @ ( A @ skaf47 ) @ app ) @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ segmentP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(22,axiom,
! [A: $i] :
( ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause88) ).
thf(240,plain,
! [A: $i] :
( ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(241,plain,
! [A: $i] :
( ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[240]) ).
thf(1753,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[199,241]) ).
thf(1754,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP ) ),
inference(simp,[status(thm)],[1753]) ).
thf(1755,plain,
( ( sk1 @ skaf50 @ ( sk1 @ skaf49 @ leq ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1754:[bind(A,$thf( sk1 ))]]) ).
thf(857,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[391,715]) ).
thf(858,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[857]) ).
thf(859,plain,
! [A: $i] : ( nil @ ( A @ skaf55 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[858:[bind(A,$thf( C )),bind(B,$thf( C @ skaf55 ))]]) ).
thf(884,plain,
! [A: $i] : ( nil @ ( A @ skaf55 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[859]) ).
thf(130,axiom,
~ ( nil @ singletonP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause11) ).
thf(487,plain,
~ ( nil @ singletonP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(488,plain,
~ ( nil @ singletonP ),
inference(polarity_switch,[status(thm)],[487]) ).
thf(157,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ tl )
= B )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause96) ).
thf(554,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ tl )
= B )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(125,axiom,
nil @ cyclefreeP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause7) ).
thf(476,plain,
nil @ cyclefreeP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(208,plain,
( ~ ( nil @ ( sk4 @ neq ) )
| ( sk5 @ ssItem ) ),
inference(cnf,[status(esa)],[206]) ).
thf(642,plain,
( ~ ( nil @ ( sk2 @ neq ) )
| ( sk5 @ ssItem ) ),
inference(rewrite,[status(thm)],[208,211]) ).
thf(196,axiom,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( A @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause63) ).
thf(637,plain,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( A @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(131,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ lt ) )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause111) ).
thf(489,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ lt ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(175,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( A @ ssItem )
| ~ ( C @ ssItem )
| ~ ( B @ ssList )
| ~ ( D @ ssList )
| ~ ( D @ ( C @ cons ) @ ( B @ ( A @ cons ) @ frontsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause176) ).
thf(590,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( A @ ssItem )
| ~ ( C @ ssItem )
| ~ ( B @ ssList )
| ~ ( D @ ssList )
| ~ ( D @ ( C @ cons ) @ ( B @ ( A @ cons ) @ frontsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(1605,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[578,715]) ).
thf(1606,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[1605]) ).
thf(1607,plain,
! [A: $i] : ( nil @ ( A @ skaf54 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[1606:[bind(A,$thf( C )),bind(B,$thf( C @ skaf54 ))]]) ).
thf(1644,plain,
! [A: $i] : ( nil @ ( A @ skaf54 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[1607]) ).
thf(122,axiom,
nil @ totalorderP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause6) ).
thf(471,plain,
nil @ totalorderP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ frontsegP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( C @ ( B @ frontsegP ) )
| ~ ( B @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause154) ).
thf(255,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ frontsegP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( C @ ( B @ frontsegP ) )
| ~ ( B @ ( A @ frontsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(256,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ frontsegP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( C @ ( B @ frontsegP ) )
| ~ ( B @ ( A @ frontsegP ) ) ),
inference(cnf,[status(esa)],[255]) ).
thf(239,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ~ ( A @ ssList )
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
inference(cnf,[status(esa)],[238]) ).
thf(1412,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ~ $true
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[202,239]) ).
thf(1413,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
inference(simp,[status(thm)],[1412]) ).
thf(1414,plain,
( ( sk2 @ strictorderedP )
| ~ ( sk2 @ skaf70 @ ( sk2 @ skaf69 @ lt ) ) ),
inference(pattern_uni,[status(thm)],[1413:[bind(A,$thf( sk2 ))]]) ).
thf(144,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ app ) @ memberP ) )
| ~ ( B @ ssItem )
| ~ ( C @ ssList )
| ~ ( A @ ssList )
| ~ ( B @ ( A @ memberP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause141) ).
thf(526,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ app ) @ memberP ) )
| ~ ( B @ ssItem )
| ~ ( C @ ssList )
| ~ ( A @ ssList )
| ~ ( B @ ( A @ memberP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(189,axiom,
! [B: $i,A: $i] :
( ( nil = A )
| ( A = B )
| ( nil = B )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( A @ hd )
!= ( B @ hd ) )
| ( ( A @ tl )
!= ( B @ tl ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause177) ).
thf(622,plain,
! [B: $i,A: $i] :
( ( nil = A )
| ( A = B )
| ( nil = B )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( A @ hd )
!= ( B @ hd ) )
| ( ( A @ tl )
!= ( B @ tl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(1454,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ~ $true
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[199,239]) ).
thf(1455,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
inference(simp,[status(thm)],[1454]) ).
thf(1456,plain,
( ( sk1 @ strictorderedP )
| ~ ( sk1 @ skaf70 @ ( sk1 @ skaf69 @ lt ) ) ),
inference(pattern_uni,[status(thm)],[1455:[bind(A,$thf( sk1 ))]]) ).
thf(33,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf46 ) @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause50) ).
thf(266,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf46 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(655,plain,
( ( ( skac2 @ ( nil @ memberP ) )
!= ( sk5 @ ( sk2 @ memberP ) ) )
| ~ $true
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[643,651]) ).
thf(656,plain,
( ( ( skac2 @ ( nil @ memberP ) )
!= ( sk5 @ ( sk2 @ memberP ) ) )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[655]) ).
thf(657,plain,
( ( skac2 != sk5 )
| ( nil != sk2 )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[656]) ).
thf(2219,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ duplicatefreeP )
| ~ $true
| ( ( A @ skaf77 @ ( A @ skaf74 @ cons ) @ ( A @ skaf76 @ ( A @ skaf74 @ cons ) @ ( A @ skaf75 @ app ) @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[202,247]) ).
thf(2220,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ duplicatefreeP )
| ( ( A @ skaf77 @ ( A @ skaf74 @ cons ) @ ( A @ skaf76 @ ( A @ skaf74 @ cons ) @ ( A @ skaf75 @ app ) @ app ) )
= A ) ),
inference(simp,[status(thm)],[2219]) ).
thf(2221,plain,
( ( sk2 @ duplicatefreeP )
| ( ( sk2 @ skaf77 @ ( sk2 @ skaf74 @ cons ) @ ( sk2 @ skaf76 @ ( sk2 @ skaf74 @ cons ) @ ( sk2 @ skaf75 @ app ) @ app ) )
= sk2 ) ),
inference(pattern_uni,[status(thm)],[2220:[bind(A,$thf( sk2 ))]]) ).
thf(20,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ memberP ) )
| ( C @ ( B @ memberP ) )
| ~ ( C @ ssItem )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ( B @ ( A @ app ) @ memberP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause158) ).
thf(236,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ memberP ) )
| ( C @ ( B @ memberP ) )
| ~ ( C @ ssItem )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ( B @ ( A @ app ) @ memberP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(237,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ memberP ) )
| ( C @ ( B @ memberP ) )
| ~ ( C @ ssItem )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ( B @ ( A @ app ) @ memberP ) ) ),
inference(cnf,[status(esa)],[236]) ).
thf(52,axiom,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf59 @ ( A @ skaf60 @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause92) ).
thf(311,plain,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf59 @ ( A @ skaf60 @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(169,axiom,
! [A: $i] : ( A @ skaf65 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause30) ).
thf(579,plain,
! [A: $i] : ( A @ skaf65 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(1671,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[579,434]) ).
thf(1672,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1671]) ).
thf(1673,plain,
! [A: $i] :
~ ( A @ skaf65 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1672:[bind(A,$thf( C )),bind(B,$thf( C @ skaf65 ))]]) ).
thf(1695,plain,
! [A: $i] :
~ ( A @ skaf65 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1673]) ).
thf(755,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[357,715]) ).
thf(756,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[755]) ).
thf(757,plain,
! [A: $i] : ( nil @ ( A @ skaf44 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[756:[bind(A,$thf( C )),bind(B,$thf( C @ skaf44 ))]]) ).
thf(771,plain,
! [A: $i] : ( nil @ ( A @ skaf44 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[757]) ).
thf(2367,plain,
! [A: $i] :
( ( ( nil @ ( sk1 @ skaf44 @ cons ) )
!= ( nil @ ( A @ skaf44 @ cons ) ) )
| ( sk1 @ totalorderedP )
| ~ ( sk1 @ singletonP ) ),
inference(paramod_ordered,[status(thm)],[2036,771]) ).
thf(2368,plain,
( ( sk1 @ totalorderedP )
| ~ ( sk1 @ singletonP ) ),
inference(pattern_uni,[status(thm)],[2367:[bind(A,$thf( sk1 ))]]) ).
thf(1619,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[578,434]) ).
thf(1620,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1619]) ).
thf(1621,plain,
! [A: $i] :
~ ( A @ skaf54 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1620:[bind(A,$thf( C )),bind(B,$thf( C @ skaf54 ))]]) ).
thf(1648,plain,
! [A: $i] :
~ ( A @ skaf54 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1621]) ).
thf(747,plain,
( ( ( nil @ ( skac3 @ cons ) )
!= ( nil @ ( sk5 @ cons ) ) )
| ( sk1 != sk1 )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[648,738]) ).
thf(748,plain,
( ( ( nil @ ( skac3 @ cons ) )
!= ( nil @ ( sk5 @ cons ) ) )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[747]) ).
thf(749,plain,
( ( nil != nil )
| ( skac3 != sk5 )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[748]) ).
thf(750,plain,
( ( skac3 != sk5 )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[749]) ).
thf(188,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ strictorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause112) ).
thf(618,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ strictorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(844,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[390,434]) ).
thf(845,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[844]) ).
thf(846,plain,
! [A: $i] :
~ ( A @ skaf69 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[845:[bind(A,$thf( C )),bind(B,$thf( C @ skaf69 ))]]) ).
thf(856,plain,
! [A: $i] :
~ ( A @ skaf69 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[846]) ).
thf(39,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause117) ).
thf(279,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(46,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ssList )
| ~ ( F @ cyclefreeP )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssList )
| ~ ( D @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( B @ cons ) @ ( D @ ( A @ cons ) @ ( C @ app ) @ app ) )
!= F )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause185) ).
thf(296,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ssList )
| ~ ( F @ cyclefreeP )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssList )
| ~ ( D @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( B @ cons ) @ ( D @ ( A @ cons ) @ ( C @ app ) @ app ) )
!= F )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(181,axiom,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ frontsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause84) ).
thf(601,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ frontsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(78,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ( A @ ( B @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause102) ).
thf(375,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( A @ ( B @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(727,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[267,715]) ).
thf(728,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[727]) ).
thf(729,plain,
! [A: $i] : ( nil @ ( A @ skaf64 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[728:[bind(A,$thf( C )),bind(B,$thf( C @ skaf64 ))]]) ).
thf(733,plain,
! [A: $i] : ( nil @ ( A @ skaf64 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[729]) ).
thf(101,axiom,
! [A: $i] : ( A @ skaf49 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause46) ).
thf(423,plain,
! [A: $i] : ( A @ skaf49 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(1511,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[570,434]) ).
thf(1512,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1511]) ).
thf(1513,plain,
! [A: $i] :
~ ( A @ skaf83 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1512:[bind(A,$thf( C )),bind(B,$thf( C @ skaf83 ))]]) ).
thf(1535,plain,
! [A: $i] :
~ ( A @ skaf83 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1513]) ).
thf(47,axiom,
! [A: $i] : ( A @ skaf77 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause18) ).
thf(300,plain,
! [A: $i] : ( A @ skaf77 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(929,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf77 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[300,232]) ).
thf(930,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf77 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[929]) ).
thf(931,plain,
! [A: $i] :
~ ( A @ skaf77 @ ( A @ skaf77 @ neq ) ),
inference(pattern_uni,[status(thm)],[930:[bind(A,$thf( C )),bind(B,$thf( C @ skaf77 ))]]) ).
thf(958,plain,
! [A: $i] :
~ ( A @ skaf77 @ ( A @ skaf77 @ neq ) ),
inference(simp,[status(thm)],[931]) ).
thf(1657,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[579,715]) ).
thf(1658,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[1657]) ).
thf(1659,plain,
! [A: $i] : ( nil @ ( A @ skaf65 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[1658:[bind(A,$thf( C )),bind(B,$thf( C @ skaf65 ))]]) ).
thf(1701,plain,
! [A: $i] : ( nil @ ( A @ skaf65 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[1659]) ).
thf(3,negated_conjecture,
sk3 @ ssList,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
thf(204,plain,
sk3 @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,negated_conjecture,
( ( nil != sk4 )
| ( nil = sk3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
thf(203,plain,
( ( nil != sk4 )
| ( nil = sk3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(214,plain,
( ( nil != sk4 )
| ( nil = sk3 ) ),
inference(cnf,[status(esa)],[203]) ).
thf(215,plain,
( ( nil != sk4 )
| ( nil = sk3 ) ),
inference(lifteq,[status(thm)],[214]) ).
thf(641,plain,
( ( nil != sk2 )
| ( nil = sk1 ) ),
inference(rewrite,[status(thm)],[215,211,216]) ).
thf(111,axiom,
! [A: $i] :
( ( A @ totalorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf55 @ ( A @ skaf54 @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause95) ).
thf(445,plain,
! [A: $i] :
( ( A @ totalorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf55 @ ( A @ skaf54 @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(53,axiom,
! [A: $i] : ( A @ skaf57 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause38) ).
thf(313,plain,
! [A: $i] : ( A @ skaf57 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(174,axiom,
! [A: $i] : ( A @ skaf50 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause45) ).
thf(589,plain,
! [A: $i] : ( A @ skaf50 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(1838,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[589,434]) ).
thf(1839,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1838]) ).
thf(1840,plain,
! [A: $i] :
~ ( A @ skaf50 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1839:[bind(A,$thf( C )),bind(B,$thf( C @ skaf50 ))]]) ).
thf(1865,plain,
! [A: $i] :
~ ( A @ skaf50 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1840]) ).
thf(63,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause103) ).
thf(335,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(152,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( C @ ssList )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= ( C @ ( A @ app ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause150) ).
thf(540,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( C @ ssList )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= ( C @ ( A @ app ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(182,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause86) ).
thf(604,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(2360,plain,
! [A: $i] :
( ( ( nil @ ( sk2 @ skaf44 @ cons ) )
!= ( nil @ ( A @ skaf44 @ cons ) ) )
| ( sk2 @ totalorderedP )
| ~ ( sk2 @ singletonP ) ),
inference(paramod_ordered,[status(thm)],[1978,771]) ).
thf(2361,plain,
( ( sk2 @ totalorderedP )
| ~ ( sk2 @ singletonP ) ),
inference(pattern_uni,[status(thm)],[2360:[bind(A,$thf( sk2 ))]]) ).
thf(218,plain,
skac3 != skac2,
inference(polarity_switch,[status(thm)],[217]) ).
thf(219,plain,
skac2 != skac3,
inference(lifteq,[status(thm)],[218]) ).
thf(776,plain,
! [A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( sk5 @ ssItem ) )
| ( sk1 @ totalorderedP )
| ~ $true
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[357,731]) ).
thf(777,plain,
! [A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( sk5 @ ssItem ) )
| ( sk1 @ totalorderedP )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[776]) ).
thf(784,plain,
! [A: $i] :
( ( ( A @ skaf44 )
!= sk5 )
| ~ ( nil @ ( sk2 @ neq ) )
| ( sk1 @ totalorderedP ) ),
inference(simp,[status(thm)],[777]) ).
thf(73,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ cons ) @ ( A @ ( C @ cons ) @ frontsegP ) )
| ~ ( C @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( C != D )
| ~ ( B @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause178) ).
thf(362,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ cons ) @ ( A @ ( C @ cons ) @ frontsegP ) )
| ~ ( C @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( C != D )
| ~ ( B @ ( A @ frontsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(179,axiom,
! [A: $i] : ( A @ skaf76 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause19) ).
thf(599,plain,
! [A: $i] : ( A @ skaf76 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(126,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ leq ) )
| ( D @ ( B @ leq ) )
| ~ ( F @ ssList )
| ~ ( F @ totalorderP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause184) ).
thf(477,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ leq ) )
| ( D @ ( B @ leq ) )
| ~ ( F @ ssList )
| ~ ( F @ totalorderP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(83,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( B @ ( A @ cons ) )
!= nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause98) ).
thf(387,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( B @ ( A @ cons ) )
!= nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(133,axiom,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf60 @ ( A @ skaf59 @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause93) ).
thf(494,plain,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf60 @ ( A @ skaf59 @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(149,axiom,
! [A: $i] :
( ( nil = A )
| ( A @ hd @ ssItem )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause78) ).
thf(535,plain,
! [A: $i] :
( ( nil = A )
| ( A @ hd @ ssItem )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(57,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderedP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause66) ).
thf(323,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderedP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(177,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ skaf43 ) @ ( B @ cons ) @ ( B @ ( A @ skaf42 ) @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ memberP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause169) ).
thf(594,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ skaf43 ) @ ( B @ cons ) @ ( B @ ( A @ skaf42 ) @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ memberP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(129,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ lt ) )
| ( D @ ( B @ lt ) )
| ~ ( F @ ssList )
| ~ ( F @ strictorderP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause183) ).
thf(483,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ lt ) )
| ( D @ ( B @ lt ) )
| ~ ( F @ ssList )
| ~ ( F @ strictorderP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(764,plain,
! [A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( sk5 @ ssItem ) )
| ( nil != sk2 )
| ~ $true
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[357,647]) ).
thf(765,plain,
! [A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( sk5 @ ssItem ) )
| ( nil != sk2 )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[764]) ).
thf(769,plain,
! [A: $i] :
( ( ( A @ skaf44 )
!= sk5 )
| ( nil != sk2 )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[765]) ).
thf(118,axiom,
! [A: $i] :
( ( A @ totalorderedP )
| ~ ( A @ ssList )
| ~ ( A @ skaf65 @ ( A @ skaf64 @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause91) ).
thf(462,plain,
! [A: $i] :
( ( A @ totalorderedP )
| ~ ( A @ ssList )
| ~ ( A @ skaf65 @ ( A @ skaf64 @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(4909,plain,
! [A: $i] :
( ( ( sk2 @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[4688,232]) ).
thf(4910,plain,
! [A: $i] :
( ( ( sk2 @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[4909]) ).
thf(4911,plain,
~ ( sk2 @ ( sk2 @ app ) @ ( sk2 @ ( sk2 @ app ) @ neq ) ),
inference(pattern_uni,[status(thm)],[4910:[bind(A,$thf( sk2 @ ( sk2 @ app ) ))]]) ).
thf(184,axiom,
! [A: $i] : ( A @ skaf78 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause17) ).
thf(609,plain,
! [A: $i] : ( A @ skaf78 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(90,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( B @ ( A @ app ) )
!= ( B @ ( C @ app ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause151) ).
thf(399,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( B @ ( A @ app ) )
!= ( B @ ( C @ app ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(947,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf61 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[398,232]) ).
thf(948,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf61 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[947]) ).
thf(949,plain,
! [A: $i] :
~ ( A @ skaf61 @ ( A @ skaf61 @ neq ) ),
inference(pattern_uni,[status(thm)],[948:[bind(A,$thf( C )),bind(B,$thf( C @ skaf61 ))]]) ).
thf(959,plain,
! [A: $i] :
~ ( A @ skaf61 @ ( A @ skaf61 @ neq ) ),
inference(simp,[status(thm)],[949]) ).
thf(690,plain,
! [A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( sk5 @ ssItem ) )
| ( nil != sk2 )
| ~ $true
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[249,647]) ).
thf(691,plain,
! [A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( sk5 @ ssItem ) )
| ( nil != sk2 )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[690]) ).
thf(695,plain,
! [A: $i] :
( ( ( A @ skaf79 )
!= sk5 )
| ( nil != sk2 )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[691]) ).
thf(4744,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf58 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[343,3451]) ).
thf(4745,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf58 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[4744]) ).
thf(4746,plain,
! [A: $i] : ( A @ skaf58 @ ( sk2 @ app ) @ ssList ),
inference(pattern_uni,[status(thm)],[4745:[bind(A,$thf( C )),bind(B,$thf( C @ skaf58 ))]]) ).
thf(4827,plain,
! [A: $i] : ( A @ skaf58 @ ( sk2 @ app ) @ ssList ),
inference(simp,[status(thm)],[4746]) ).
thf(160,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause69) ).
thf(563,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(103,axiom,
! [A: $i] :
( ( nil = A )
| ( A @ hd @ ssItem )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause76) ).
thf(426,plain,
! [A: $i] :
( ( nil = A )
| ( A @ hd @ ssItem )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(146,axiom,
! [A: $i] : ( A @ skaf51 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause44) ).
thf(531,plain,
! [A: $i] : ( A @ skaf51 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(741,plain,
( ( ( nil @ ( skac2 @ cons ) @ totalorderedP )
!= ( sk1 @ totalorderedP ) )
| ~ $true
| ~ ( sk1 @ ( sk2 @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[726,212]) ).
thf(742,plain,
( ( ( nil @ ( skac2 @ cons ) @ totalorderedP )
!= ( sk1 @ totalorderedP ) )
| ~ ( sk1 @ ( sk2 @ segmentP ) ) ),
inference(simp,[status(thm)],[741]) ).
thf(744,plain,
( ( ( nil @ ( skac2 @ cons ) )
!= sk1 )
| ~ ( sk1 @ ( sk2 @ segmentP ) ) ),
inference(simp,[status(thm)],[742]) ).
thf(751,plain,
( ( ( nil @ ( skac2 @ cons ) )
!= ( nil @ ( sk5 @ cons ) ) )
| ( sk1 != sk1 )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[648,744]) ).
thf(752,plain,
( ( ( nil @ ( skac2 @ cons ) )
!= ( nil @ ( sk5 @ cons ) ) )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[751]) ).
thf(753,plain,
( ( nil != nil )
| ( skac2 != sk5 )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[752]) ).
thf(754,plain,
( ( skac2 != sk5 )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[753]) ).
thf(661,plain,
( ( ( nil @ totalorderedP )
!= ( sk1 @ totalorderedP ) )
| ~ $true
| ~ ( sk1 @ ( sk2 @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[630,212]) ).
thf(662,plain,
( ( ( nil @ totalorderedP )
!= ( sk1 @ totalorderedP ) )
| ~ ( sk1 @ ( sk2 @ segmentP ) ) ),
inference(simp,[status(thm)],[661]) ).
thf(663,plain,
( ( nil != sk1 )
| ~ ( sk1 @ ( sk2 @ segmentP ) ) ),
inference(simp,[status(thm)],[662]) ).
thf(155,axiom,
! [A: $i] :
( ( nil = A )
| ( A @ tl @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause77) ).
thf(548,plain,
! [A: $i] :
( ( nil = A )
| ( A @ tl @ ssList )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(187,axiom,
nil @ strictorderedP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause3) ).
thf(617,plain,
nil @ strictorderedP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(5163,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[4773,232]) ).
thf(5164,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[5163]) ).
thf(5165,plain,
~ ( sk1 @ ( sk2 @ app ) @ ( sk1 @ ( sk2 @ app ) @ neq ) ),
inference(pattern_uni,[status(thm)],[5164:[bind(A,$thf( sk1 @ ( sk2 @ app ) ))]]) ).
thf(994,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[423,715]) ).
thf(995,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[994]) ).
thf(996,plain,
! [A: $i] : ( nil @ ( A @ skaf49 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[995:[bind(A,$thf( C )),bind(B,$thf( C @ skaf49 ))]]) ).
thf(1018,plain,
! [A: $i] : ( nil @ ( A @ skaf49 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[996]) ).
thf(1916,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[609,715]) ).
thf(1917,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[1916]) ).
thf(1918,plain,
! [A: $i] : ( nil @ ( A @ skaf78 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[1917:[bind(A,$thf( C )),bind(B,$thf( C @ skaf78 ))]]) ).
thf(1961,plain,
! [A: $i] : ( nil @ ( A @ skaf78 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[1918]) ).
thf(45,axiom,
nil @ strictorderP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause5) ).
thf(295,plain,
nil @ strictorderP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(96,axiom,
! [A: $i] :
( ( A @ skaf49 @ ( A @ skaf50 @ leq ) )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause87) ).
thf(414,plain,
! [A: $i] :
( ( A @ skaf49 @ ( A @ skaf50 @ leq ) )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(707,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[267,434]) ).
thf(708,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[707]) ).
thf(709,plain,
! [A: $i] :
~ ( A @ skaf64 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[708:[bind(A,$thf( C )),bind(B,$thf( C @ skaf64 ))]]) ).
thf(712,plain,
! [A: $i] :
~ ( A @ skaf64 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[709]) ).
thf(158,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause122) ).
thf(557,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(170,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ app ) @ hd )
= ( B @ hd ) )
| ( nil = B )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause123) ).
thf(580,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ app ) @ hd )
= ( B @ hd ) )
| ( nil = B )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(827,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[390,715]) ).
thf(828,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[827]) ).
thf(829,plain,
! [A: $i] : ( nil @ ( A @ skaf69 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[828:[bind(A,$thf( C )),bind(B,$thf( C @ skaf69 ))]]) ).
thf(855,plain,
! [A: $i] : ( nil @ ( A @ skaf69 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[829]) ).
thf(61,axiom,
nil @ duplicatefreeP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause2) ).
thf(331,plain,
nil @ duplicatefreeP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(76,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ app ) @ app ) )
= ( A @ ( B @ app ) @ ( C @ app ) ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause149) ).
thf(370,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ app ) @ app ) )
= ( A @ ( B @ app ) @ ( C @ app ) ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(121,axiom,
! [A: $i] : ( A @ skaf68 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause27) ).
thf(470,plain,
! [A: $i] : ( A @ skaf68 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(167,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause156) ).
thf(576,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(1005,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[423,434]) ).
thf(1006,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1005]) ).
thf(1007,plain,
! [A: $i] :
~ ( A @ skaf49 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1006:[bind(A,$thf( C )),bind(B,$thf( C @ skaf49 ))]]) ).
thf(1023,plain,
! [A: $i] :
~ ( A @ skaf49 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1007]) ).
thf(186,axiom,
! [A: $i] :
( ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause83) ).
thf(613,plain,
! [A: $i] :
( ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(5224,plain,
! [A: $i] :
( ( ( nil @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[4803,232]) ).
thf(5225,plain,
! [A: $i] :
( ( ( nil @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[5224]) ).
thf(5226,plain,
~ ( nil @ ( sk2 @ app ) @ ( nil @ ( sk2 @ app ) @ neq ) ),
inference(pattern_uni,[status(thm)],[5225:[bind(A,$thf( nil @ ( sk2 @ app ) ))]]) ).
thf(54,axiom,
nil @ equalelemsP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause1) ).
thf(314,plain,
nil @ equalelemsP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(164,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause121) ).
thf(571,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(4756,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf57 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[313,3451]) ).
thf(4757,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf57 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[4756]) ).
thf(4758,plain,
! [A: $i] : ( A @ skaf57 @ ( sk2 @ app ) @ ssList ),
inference(pattern_uni,[status(thm)],[4757:[bind(A,$thf( C )),bind(B,$thf( C @ skaf57 ))]]) ).
thf(4838,plain,
! [A: $i] : ( A @ skaf57 @ ( sk2 @ app ) @ ssList ),
inference(simp,[status(thm)],[4758]) ).
thf(180,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf42 ) @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause53) ).
thf(600,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf42 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(1930,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[609,434]) ).
thf(1931,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1930]) ).
thf(1932,plain,
! [A: $i] :
~ ( A @ skaf78 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1931:[bind(A,$thf( C )),bind(B,$thf( C @ skaf78 ))]]) ).
thf(1955,plain,
! [A: $i] :
~ ( A @ skaf78 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1932]) ).
thf(151,axiom,
! [A: $i] : ( A @ skaf66 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause29) ).
thf(539,plain,
! [A: $i] : ( A @ skaf66 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(75,axiom,
! [A: $i] :
( ( A @ ( A @ geq ) )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause55) ).
thf(368,plain,
! [A: $i] :
( ( A @ ( A @ geq ) )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(128,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf47 ) @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause49) ).
thf(482,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf47 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(141,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ frontsegP ) )
| ~ ( C @ ssList )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause144) ).
thf(517,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ frontsegP ) )
| ~ ( C @ ssList )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(56,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ rearsegP ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( B @ ( A @ app ) )
!= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause143) ).
thf(319,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ rearsegP ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( B @ ( A @ app ) )
!= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(49,axiom,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ rearsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause82) ).
thf(304,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ rearsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(258,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ geq ) ) ),
inference(cnf,[status(esa)],[257]) ).
thf(194,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ strictorderedP )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ strictorderedP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause124) ).
thf(632,plain,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ strictorderedP )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ strictorderedP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(4689,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf63 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[538,3451]) ).
thf(4690,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf63 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[4689]) ).
thf(4691,plain,
! [A: $i] : ( A @ skaf63 @ ( sk2 @ app ) @ ssList ),
inference(pattern_uni,[status(thm)],[4690:[bind(A,$thf( C )),bind(B,$thf( C @ skaf63 ))]]) ).
thf(4834,plain,
! [A: $i] : ( A @ skaf63 @ ( sk2 @ app ) @ ssList ),
inference(simp,[status(thm)],[4691]) ).
thf(166,axiom,
! [A: $i] : ( A @ skaf82 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause13) ).
thf(575,plain,
! [A: $i] : ( A @ skaf82 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(4804,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf82 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[575,3451]) ).
thf(4805,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf82 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[4804]) ).
thf(4806,plain,
! [A: $i] : ( A @ skaf82 @ ( sk2 @ app ) @ ssList ),
inference(pattern_uni,[status(thm)],[4805:[bind(A,$thf( C )),bind(B,$thf( C @ skaf82 ))]]) ).
thf(4823,plain,
! [A: $i] : ( A @ skaf82 @ ( sk2 @ app ) @ ssList ),
inference(simp,[status(thm)],[4806]) ).
thf(98,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ frontsegP ) )
| ~ ( A @ ssItem )
| ~ ( C @ ssItem )
| ~ ( B @ ssList )
| ~ ( D @ ssList )
| ~ ( D @ ( C @ cons ) @ ( B @ ( A @ cons ) @ frontsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause174) ).
thf(418,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ frontsegP ) )
| ~ ( A @ ssItem )
| ~ ( C @ ssItem )
| ~ ( B @ ssList )
| ~ ( D @ ssList )
| ~ ( D @ ( C @ cons ) @ ( B @ ( A @ cons ) @ frontsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(1824,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[589,715]) ).
thf(1825,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[1824]) ).
thf(1826,plain,
! [A: $i] : ( nil @ ( A @ skaf50 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[1825:[bind(A,$thf( C )),bind(B,$thf( C @ skaf50 ))]]) ).
thf(1861,plain,
! [A: $i] : ( nil @ ( A @ skaf50 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[1826]) ).
thf(162,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ rearsegP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( C @ ( B @ rearsegP ) )
| ~ ( B @ ( A @ rearsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause153) ).
thf(568,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ rearsegP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( C @ ( B @ rearsegP ) )
| ~ ( B @ ( A @ rearsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(235,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ lt ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnf,[status(esa)],[234]) ).
thf(4,negated_conjecture,
sk4 @ ssList,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_4) ).
thf(207,plain,
sk4 @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5209,plain,
! [A: $i] :
( ( ( nil @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4803,3451]) ).
thf(5210,plain,
! [A: $i] :
( ( ( nil @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[5209]) ).
thf(5211,plain,
nil @ ( sk2 @ app ) @ ( sk2 @ app ) @ ssList,
inference(pattern_uni,[status(thm)],[5210:[bind(A,$thf( nil @ ( sk2 @ app ) ))]]) ).
thf(42,axiom,
! [A: $i] :
( ( nil @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause58) ).
thf(287,plain,
! [A: $i] :
( ( nil @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(904,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[395,434]) ).
thf(905,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[904]) ).
thf(906,plain,
! [A: $i] :
~ ( A @ skaf70 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[905:[bind(A,$thf( C )),bind(B,$thf( C @ skaf70 ))]]) ).
thf(914,plain,
! [A: $i] :
~ ( A @ skaf70 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[906]) ).
thf(79,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause119) ).
thf(378,plain,
! [B: $i,A: $i] :
( ( nil = B )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(139,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ memberP ) )
| ~ ( D @ ssList )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ( ( C @ ( B @ cons ) @ ( A @ app ) )
!= D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause175) ).
thf(510,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ memberP ) )
| ~ ( D @ ssList )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ( ( C @ ( B @ cons ) @ ( A @ app ) )
!= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(68,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ skaf46 ) @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ rearsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause131) ).
thf(346,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ skaf46 ) @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ rearsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(5355,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ app ) @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[5150,232]) ).
thf(5356,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ app ) @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[5355]) ).
thf(5357,plain,
~ ( sk1 @ ( sk2 @ app ) @ ( sk2 @ app ) @ ( sk1 @ ( sk2 @ app ) @ ( sk2 @ app ) @ neq ) ),
inference(pattern_uni,[status(thm)],[5356:[bind(A,$thf( sk1 @ ( sk2 @ app ) @ ( sk2 @ app ) ))]]) ).
thf(112,axiom,
! [A: $i] : ( A @ skaf53 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause42) ).
thf(447,plain,
! [A: $i] : ( A @ skaf53 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(55,axiom,
! [B: $i,A: $i] :
( ( B @ singletonP )
| ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( nil @ ( A @ cons ) )
!= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause116) ).
thf(315,plain,
! [B: $i,A: $i] :
( ( B @ singletonP )
| ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( nil @ ( A @ cons ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(105,axiom,
! [A: $i] : ( A @ skaf80 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause15) ).
thf(432,plain,
! [A: $i] : ( A @ skaf80 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(93,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ ( A @ cons ) @ strictorderedP )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ strictorderedP )
| ~ ( B @ hd @ ( A @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause160) ).
thf(405,plain,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ ( A @ cons ) @ strictorderedP )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ strictorderedP )
| ~ ( B @ hd @ ( A @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(37,axiom,
! [A: $i] :
( ( nil = A )
| ( A @ tl @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause75) ).
thf(273,plain,
! [A: $i] :
( ( nil = A )
| ( A @ tl @ ssList )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(77,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ app ) @ rearsegP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ( A @ rearsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause136) ).
thf(373,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ app ) @ rearsegP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ( A @ rearsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(59,axiom,
! [A: $i] :
( ( ( A @ skaf58 @ ( A @ skaf55 @ cons ) @ ( A @ skaf57 @ ( A @ skaf54 @ cons ) @ ( A @ skaf56 @ app ) @ app ) )
= A )
| ( A @ totalorderP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause166) ).
thf(326,plain,
! [A: $i] :
( ( ( A @ skaf58 @ ( A @ skaf55 @ cons ) @ ( A @ skaf57 @ ( A @ skaf54 @ cons ) @ ( A @ skaf56 @ app ) @ app ) )
= A )
| ( A @ totalorderP )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(72,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( E @ ssList )
| ~ ( E @ equalelemsP )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( A @ ssList )
| ~ ( D @ ssList )
| ( ( D @ ( C @ cons ) @ ( B @ cons ) @ ( A @ app ) )
!= E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause180) ).
thf(358,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( E @ ssList )
| ~ ( E @ equalelemsP )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( A @ ssList )
| ~ ( D @ ssList )
| ( ( D @ ( C @ cons ) @ ( B @ cons ) @ ( A @ app ) )
!= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(108,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ segmentP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( C @ ( B @ segmentP ) )
| ~ ( B @ ( A @ segmentP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause152) ).
thf(437,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ segmentP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( C @ ( B @ segmentP ) )
| ~ ( B @ ( A @ segmentP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(124,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ cyclefreeP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause70) ).
thf(474,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ cyclefreeP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(195,axiom,
! [A: $i] :
( ( A @ ( A @ frontsegP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause61) ).
thf(635,plain,
! [A: $i] :
( ( A @ ( A @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(147,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause68) ).
thf(532,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(953,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[199,232]) ).
thf(954,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[953]) ).
thf(955,plain,
~ ( sk1 @ ( sk1 @ neq ) ),
inference(pattern_uni,[status(thm)],[954:[bind(A,$thf( sk1 ))]]) ).
thf(138,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ cons ) @ memberP ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssList )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause138) ).
thf(506,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ cons ) @ memberP ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssList )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(35,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ lt ) )
| ~ ( B @ ( A @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause155) ).
thf(268,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ lt ) )
| ~ ( B @ ( A @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(5288,plain,
! [A: $i] :
( ( ( sk2 @ ( sk2 @ app ) @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[4896,232]) ).
thf(5289,plain,
! [A: $i] :
( ( ( sk2 @ ( sk2 @ app ) @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[5288]) ).
thf(5290,plain,
~ ( sk2 @ ( sk2 @ app ) @ ( sk2 @ app ) @ ( sk2 @ ( sk2 @ app ) @ ( sk2 @ app ) @ neq ) ),
inference(pattern_uni,[status(thm)],[5289:[bind(A,$thf( sk2 @ ( sk2 @ app ) @ ( sk2 @ app ) ))]]) ).
thf(737,plain,
( ( ( nil @ ( skac3 @ cons ) )
!= ( nil @ ( sk5 @ cons ) ) )
| ( sk1 @ totalorderedP )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[648,721]) ).
thf(739,plain,
( ( nil != nil )
| ( skac3 != sk5 )
| ~ ( nil @ ( sk2 @ neq ) )
| ( sk1 @ totalorderedP ) ),
inference(simp,[status(thm)],[737]) ).
thf(740,plain,
( ( skac3 != sk5 )
| ~ ( nil @ ( sk2 @ neq ) )
| ( sk1 @ totalorderedP ) ),
inference(simp,[status(thm)],[739]) ).
thf(119,axiom,
! [A: $i] :
( ( nil = A )
| ( ( A @ tl @ ( A @ hd @ cons ) )
= A )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause104) ).
thf(464,plain,
! [A: $i] :
( ( nil = A )
| ( ( A @ tl @ ( A @ hd @ cons ) )
= A )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(62,axiom,
! [A: $i] :
( ( ( A @ ( nil @ app ) )
= A )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause74) ).
thf(332,plain,
! [A: $i] :
( ( ( A @ ( nil @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(1543,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[574,715]) ).
thf(1544,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[1543]) ).
thf(1545,plain,
! [A: $i] : ( nil @ ( A @ skaf74 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[1544:[bind(A,$thf( C )),bind(B,$thf( C @ skaf74 ))]]) ).
thf(1582,plain,
! [A: $i] : ( nil @ ( A @ skaf74 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[1545]) ).
thf(145,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ app ) @ tl )
= ( A @ ( B @ tl @ app ) ) )
| ( nil = B )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause133) ).
thf(528,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ app ) @ tl )
= ( A @ ( B @ tl @ app ) ) )
| ( nil = B )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(1711,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[202,241]) ).
thf(1712,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP ) ),
inference(simp,[status(thm)],[1711]) ).
thf(1713,plain,
( ( sk2 @ skaf50 @ ( sk2 @ skaf49 @ leq ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1712:[bind(A,$thf( sk2 ))]]) ).
thf(110,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ( A @ ( B @ neq ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause100) ).
thf(442,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( A @ ( B @ neq ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(2096,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[631,715]) ).
thf(2097,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[2096]) ).
thf(2098,plain,
! [A: $i] : ( nil @ ( A @ skaf59 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[2097:[bind(A,$thf( C )),bind(B,$thf( C @ skaf59 ))]]) ).
thf(2138,plain,
! [A: $i] : ( nil @ ( A @ skaf59 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[2098]) ).
thf(5273,plain,
! [A: $i] :
( ( ( sk2 @ ( sk2 @ app ) @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4896,3451]) ).
thf(5274,plain,
! [A: $i] :
( ( ( sk2 @ ( sk2 @ app ) @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[5273]) ).
thf(5275,plain,
sk2 @ ( sk2 @ app ) @ ( sk2 @ app ) @ ( sk2 @ app ) @ ssList,
inference(pattern_uni,[status(thm)],[5274:[bind(A,$thf( sk2 @ ( sk2 @ app ) @ ( sk2 @ app ) ))]]) ).
thf(64,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ hd )
= A )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause97) ).
thf(337,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ hd )
= A )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(2198,plain,
( ( ( nil @ ( sk1 @ skaf44 @ cons ) )
!= ( nil @ ( skac2 @ cons ) ) )
| ( sk1 != sk1 )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( sk1 @ singletonP ) ),
inference(paramod_ordered,[status(thm)],[2036,744]) ).
thf(2199,plain,
( ( ( nil @ ( sk1 @ skaf44 @ cons ) )
!= ( nil @ ( skac2 @ cons ) ) )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( sk1 @ singletonP ) ),
inference(simp,[status(thm)],[2198]) ).
thf(2200,plain,
( ( nil != nil )
| ( ( sk1 @ skaf44 )
!= skac2 )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( sk1 @ singletonP ) ),
inference(simp,[status(thm)],[2199]) ).
thf(2206,plain,
( ( ( sk1 @ skaf44 )
!= skac2 )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( sk1 @ singletonP ) ),
inference(simp,[status(thm)],[2200]) ).
thf(51,axiom,
! [B: $i,A: $i] :
( ( B @ ssItem )
| ( A @ duplicatefreeP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause72) ).
thf(309,plain,
! [B: $i,A: $i] :
( ( B @ ssItem )
| ( A @ duplicatefreeP )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(153,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( B @ ssList )
| ~ ( D @ ssList )
| ~ ( A @ ssItem )
| ~ ( C @ ssItem )
| ( ( B @ ( A @ cons ) )
!= ( D @ ( C @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause170) ).
thf(543,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( B @ ssList )
| ~ ( D @ ssList )
| ~ ( A @ ssItem )
| ~ ( C @ ssItem )
| ( ( B @ ( A @ cons ) )
!= ( D @ ( C @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(159,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ totalorderedP )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ totalorderedP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause125) ).
thf(560,plain,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ totalorderedP )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ totalorderedP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(222,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ geq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnf,[status(esa)],[221]) ).
thf(134,axiom,
! [A: $i] :
( ( ( A @ skaf81 @ ( A @ skaf79 @ cons ) @ ( A @ skaf78 @ cons ) @ ( A @ skaf80 @ app ) )
= A )
| ( A @ equalelemsP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause142) ).
thf(496,plain,
! [A: $i] :
( ( ( A @ skaf81 @ ( A @ skaf79 @ cons ) @ ( A @ skaf78 @ cons ) @ ( A @ skaf80 @ app ) )
= A )
| ( A @ equalelemsP )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(2169,plain,
( ( ( nil @ ( sk2 @ skaf44 @ cons ) )
!= ( nil @ ( skac2 @ cons ) ) )
| ( sk2 != sk1 )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ singletonP ) ),
inference(paramod_ordered,[status(thm)],[1978,744]) ).
thf(2171,plain,
( ( nil != nil )
| ( ( sk2 @ skaf44 )
!= skac2 )
| ( sk2 != sk1 )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ singletonP ) ),
inference(simp,[status(thm)],[2169]) ).
thf(2177,plain,
( ( ( sk2 @ skaf44 )
!= skac2 )
| ( sk2 != sk1 )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ singletonP ) ),
inference(simp,[status(thm)],[2171]) ).
thf(162037,plain,
$false,
inference(e,[status(thm)],[1586,4835,4824,234,481,909,628,249,408,449,247,217,276,202,597,384,500,715,472,913,340,538,885,4803,301,565,651,257,570,4896,785,504,587,344,5150,460,934,357,421,606,416,325,228,289,448,261,284,770,238,1978,514,574,353,2178,216,211,253,956,453,396,206,734,221,660,4825,411,988,265,849,307,292,233,248,439,270,546,925,201,381,534,220,366,957,746,349,392,424,630,429,2132,467,229,252,197,625,879,435,329,493,2211,551,710,456,583,522,578,403,593,420,499,989,697,1541,610,1755,884,488,554,476,642,637,489,590,1644,212,471,256,1414,526,622,647,738,1456,654,721,244,266,205,657,2221,586,343,237,311,1695,398,2368,1648,750,618,856,279,296,601,375,733,423,402,579,1535,958,1701,204,259,641,391,445,313,1865,335,236,540,604,2361,219,784,362,245,434,4773,599,477,387,494,631,535,323,594,726,483,240,3451,769,198,462,4911,609,521,399,959,695,223,4827,563,267,241,426,589,531,255,754,663,548,648,487,617,5165,4688,1018,1961,295,414,712,557,580,855,199,331,370,643,470,576,744,1023,613,5226,314,571,4838,600,1955,250,539,368,771,482,203,517,319,304,258,390,632,4834,4823,731,418,1861,568,235,207,383,5211,287,914,378,433,510,346,2036,300,5357,447,315,432,262,405,273,373,326,358,437,474,635,532,955,283,239,242,506,268,5290,740,464,332,575,1582,528,200,1713,442,2138,395,5275,337,2206,309,543,560,222,496,232,2177,254,227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC341-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.13/0.55 % Computer : n004.cluster.edu
% 0.13/0.55 % Model : x86_64 x86_64
% 0.13/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.55 % Memory : 8046.5625MB
% 0.13/0.55 % OS : Linux 6.8.0-71-generic
% 0.13/0.55 % CPULimit : 300
% 0.13/0.55 % WCLimit : 300
% 0.13/0.55 % DateTime : Sat Sep 26 12:50:21 UTC 2026
% 0.18/0.55 % CPUTime :
% 0.18/0.55 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.18/1.00 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.60/1.40 % [INFO] Parsing done (389ms).
% 1.60/1.41 % [INFO] Running in sequential loop mode.
% 2.42/1.96 % [INFO] eprover registered as external prover.
% 2.42/1.96 % [INFO] Scanning for conjecture ...
% 2.80/2.14 % [INFO] Found a conjecture (or negated_conjecture) and 185 axioms. Running axiom selection ...
% 3.08/2.31 % [INFO] Axiom selection finished. Selected 185 axioms (removed 0 axioms).
% 3.46/2.56 % [INFO] Problem is propositional (TPTP CNF).
% 3.46/2.58 % [INFO] Type checking passed.
% 3.46/2.59 % [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 ...
% 231.86/85.70 % External prover 'e' found a proof!
% 231.86/85.70 % [INFO] Killing All external provers ...
% 231.86/85.70 % Time passed: 85062ms (effective reasoning time: 84287ms)
% 231.86/85.70 % 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
% 231.86/85.70 % No. of inferences in proof: 760
% 231.86/85.71 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 85062 ms resp. 84287 ms w/o parsing
% 222.64/85.92 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 222.64/85.92 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------