%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWC089-1 : 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 : n006.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 08:52:10 AM UTC 2026
% Result : Unsatisfiable 95.47s 28.08s
% Output : Refutation 98.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 196
% Syntax : Number of formulae : 1195 ( 403 unt; 0 typ; 0 def)
% Number of atoms : 3793 ( 779 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 10082 (2014 ~;1824 |; 0 &;6244 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 75 ( 72 usr; 9 con; 0-2 aty)
% Number of variables : 1576 ( 0 ^;1576 !; 0 ?;1576 :)
% 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(neq_decl,type,
neq: $i > $i > $o ).
thf(nil_decl,type,
nil: $i ).
thf(segmentP_decl,type,
segmentP: $i > $i > $o ).
thf(tl_decl,type,
tl: $i > $i ).
thf(app_decl,type,
app: $i > $i > $i ).
thf(ssItem_decl,type,
ssItem: $i > $o ).
thf(cons_decl,type,
cons: $i > $i > $i ).
thf(hd_decl,type,
hd: $i > $i ).
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(totalorderedP_decl,type,
totalorderedP: $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(memberP_decl,type,
memberP: $i > $i > $o ).
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(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(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(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(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(310,plain,
! [B: $i,A: $i] :
( ( B @ ssItem )
| ( A @ duplicatefreeP )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[309]) ).
thf(25864,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( B @ ssItem )
| ( A @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[199,310]) ).
thf(25865,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( B @ ssItem )
| ( A @ duplicatefreeP ) ),
inference(simp,[status(thm)],[25864]) ).
thf(25866,plain,
! [A: $i] :
( ( A @ ssItem )
| ( sk1 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[25865:[bind(A,$thf( sk1 ))]]) ).
thf(25953,plain,
! [A: $i] :
( ( A @ ssItem )
| ( sk1 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[25866]) ).
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(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(3693,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ssList )
!= ( B @ ssList ) )
| ( A @ ( B @ app ) @ ssList )
| ~ $true
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[202,254]) ).
thf(3694,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ssList )
!= ( B @ ssList ) )
| ( A @ ( B @ app ) @ ssList )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[3693]) ).
thf(3695,plain,
! [A: $i] :
( ( A @ ( sk2 @ app ) @ ssList )
| ~ ( A @ ssList ) ),
inference(pattern_uni,[status(thm)],[3694:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(5407,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf62 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[233,3695]) ).
thf(5408,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf62 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[5407]) ).
thf(5409,plain,
! [A: $i] : ( A @ skaf62 @ ( sk2 @ app ) @ ssList ),
inference(pattern_uni,[status(thm)],[5408:[bind(A,$thf( C )),bind(B,$thf( C @ skaf62 ))]]) ).
thf(5561,plain,
! [A: $i] : ( A @ skaf62 @ ( sk2 @ app ) @ ssList ),
inference(simp,[status(thm)],[5409]) ).
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(5501,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf66 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[539,3695]) ).
thf(5502,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf66 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[5501]) ).
thf(5503,plain,
! [A: $i] : ( A @ skaf66 @ ( sk2 @ app ) @ ssList ),
inference(pattern_uni,[status(thm)],[5502:[bind(A,$thf( C )),bind(B,$thf( C @ skaf66 ))]]) ).
thf(5593,plain,
! [A: $i] : ( A @ skaf66 @ ( sk2 @ app ) @ ssList ),
inference(simp,[status(thm)],[5503]) ).
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(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(5473,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf76 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[599,3695]) ).
thf(5474,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf76 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[5473]) ).
thf(5475,plain,
! [A: $i] : ( A @ skaf76 @ ( sk2 @ app ) @ ssList ),
inference(pattern_uni,[status(thm)],[5474:[bind(A,$thf( C )),bind(B,$thf( C @ skaf76 ))]]) ).
thf(5587,plain,
! [A: $i] : ( A @ skaf76 @ ( sk2 @ app ) @ ssList ),
inference(simp,[status(thm)],[5475]) ).
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(288,plain,
! [A: $i] :
( ( nil @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[287]) ).
thf(17155,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf76 @ ( sk2 @ app ) @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5587,288]) ).
thf(17156,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf76 @ ( sk2 @ app ) @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[17155]) ).
thf(17157,plain,
! [A: $i] : ( nil @ ( A @ skaf76 @ ( sk2 @ app ) @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[17156:[bind(A,$thf( E )),bind(B,$thf( E @ skaf76 @ ( sk2 @ app ) ))]]) ).
thf(17226,plain,
! [A: $i] : ( nil @ ( A @ skaf76 @ ( sk2 @ app ) @ rearsegP ) ),
inference(simp,[status(thm)],[17157]) ).
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(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(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(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(2218,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[578,434]) ).
thf(2219,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[2218]) ).
thf(2220,plain,
! [A: $i] :
~ ( A @ skaf54 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[2219:[bind(A,$thf( C )),bind(B,$thf( C @ skaf54 ))]]) ).
thf(2250,plain,
! [A: $i] :
~ ( A @ skaf54 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[2220]) ).
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(7,negated_conjecture,
nil @ ( sk2 @ neq ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
thf(203,plain,
nil @ ( sk2 @ neq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
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(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(280,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(cnf,[status(esa)],[279]) ).
thf(281,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[280]) ).
thf(282,plain,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[281]) ).
thf(15016,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[521,282]) ).
thf(15017,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[15016]) ).
thf(15018,plain,
~ ( skac2 @ ( skac2 @ neq ) ),
inference(pattern_uni,[status(thm)],[15017:[bind(A,$thf( skac2 ))]]) ).
thf(15086,plain,
( ( ( skac2 @ ( skac2 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[203,15018]) ).
thf(15087,plain,
( ( skac2 @ ( skac2 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[15086]) ).
thf(15098,plain,
( ( skac2 != nil )
| ( skac2 != sk2 ) ),
inference(simp,[status(thm)],[15087]) ).
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(17021,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf63 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[538,288]) ).
thf(17022,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf63 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[17021]) ).
thf(17023,plain,
! [A: $i] : ( nil @ ( A @ skaf63 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[17022:[bind(A,$thf( C )),bind(B,$thf( C @ skaf63 ))]]) ).
thf(17278,plain,
! [A: $i] : ( nil @ ( A @ skaf63 @ rearsegP ) ),
inference(simp,[status(thm)],[17023]) ).
thf(17012,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[202,288]) ).
thf(17013,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[17012]) ).
thf(17014,plain,
nil @ ( sk2 @ rearsegP ),
inference(pattern_uni,[status(thm)],[17013:[bind(A,$thf( sk2 ))]]) ).
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(2242,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[395,434]) ).
thf(2243,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[2242]) ).
thf(2244,plain,
! [A: $i] :
~ ( A @ skaf70 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[2243:[bind(A,$thf( C )),bind(B,$thf( C @ skaf70 ))]]) ).
thf(2248,plain,
! [A: $i] :
~ ( A @ skaf70 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[2244]) ).
thf(8,negated_conjecture,
! [A: $i] :
( ~ ( A @ ( sk1 @ segmentP ) )
| ~ ( A @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( A @ neq ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
thf(206,plain,
! [A: $i] :
( ~ ( A @ ( sk1 @ segmentP ) )
| ~ ( A @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( A @ neq ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(208,plain,
! [A: $i] :
( ~ ( A @ ( sk1 @ segmentP ) )
| ~ ( A @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( A @ neq ) )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[206]) ).
thf(644,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( sk1 @ segmentP ) )
| ~ ( A @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[199,208]) ).
thf(645,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( sk1 @ segmentP ) )
| ~ ( A @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[644]) ).
thf(646,plain,
( ~ ( sk1 @ ( sk1 @ segmentP ) )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[645:[bind(A,$thf( sk1 ))]]) ).
thf(10,negated_conjecture,
( ( nil @ ( sk3 @ neq ) )
| ~ ( nil @ ( sk4 @ neq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
thf(198,plain,
( ( nil @ ( sk3 @ neq ) )
| ~ ( nil @ ( sk4 @ neq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(215,plain,
( ( nil @ ( sk3 @ neq ) )
| ~ ( nil @ ( sk4 @ neq ) ) ),
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(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(664,plain,
( ( nil @ ( sk1 @ neq ) )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(rewrite,[status(thm)],[215,211,216]) ).
thf(665,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ( nil @ ( sk1 @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[203,664]) ).
thf(666,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ( nil @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[665]) ).
thf(667,plain,
nil @ ( sk1 @ neq ),
inference(pattern_uni,[status(thm)],[666:[]]) ).
thf(727,plain,
( ~ ( sk1 @ ( sk1 @ segmentP ) )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ $true ),
inference(rewrite,[status(thm)],[646,667]) ).
thf(728,plain,
( ~ ( sk1 @ ( sk1 @ segmentP ) )
| ~ ( sk1 @ ( sk2 @ segmentP ) ) ),
inference(simp,[status(thm)],[727]) ).
thf(740,plain,
( ~ $true
| ( ( sk1 @ ( sk2 @ segmentP ) )
!= ( sk1 @ ( sk1 @ segmentP ) ) )
| ~ ( sk1 @ ( sk1 @ segmentP ) ) ),
inference(eqfactor_ordered,[status(thm)],[728]) ).
thf(741,plain,
( ( ( sk1 @ ( sk2 @ segmentP ) )
!= ( sk1 @ ( sk1 @ segmentP ) ) )
| ~ ( sk1 @ ( sk1 @ segmentP ) ) ),
inference(simp,[status(thm)],[740]) ).
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(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(239,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ~ ( A @ ssList )
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
inference(cnf,[status(esa)],[238]) ).
thf(1969,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ~ $true
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[202,239]) ).
thf(1970,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
inference(simp,[status(thm)],[1969]) ).
thf(1971,plain,
( ( sk2 @ strictorderedP )
| ~ ( sk2 @ skaf70 @ ( sk2 @ skaf69 @ lt ) ) ),
inference(pattern_uni,[status(thm)],[1970:[bind(A,$thf( sk2 ))]]) ).
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(269,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ lt ) )
| ~ ( B @ ( A @ lt ) ) ),
inference(cnf,[status(esa)],[268]) ).
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(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(5513,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf80 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[432,3695]) ).
thf(5514,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf80 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[5513]) ).
thf(5515,plain,
! [A: $i] : ( A @ skaf80 @ ( sk2 @ app ) @ ssList ),
inference(pattern_uni,[status(thm)],[5514:[bind(A,$thf( C )),bind(B,$thf( C @ skaf80 ))]]) ).
thf(5550,plain,
! [A: $i] : ( A @ skaf80 @ ( sk2 @ app ) @ ssList ),
inference(simp,[status(thm)],[5515]) ).
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(17077,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf71 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[593,288]) ).
thf(17078,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf71 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[17077]) ).
thf(17079,plain,
! [A: $i] : ( nil @ ( A @ skaf71 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[17078:[bind(A,$thf( C )),bind(B,$thf( C @ skaf71 ))]]) ).
thf(17253,plain,
! [A: $i] : ( nil @ ( A @ skaf71 @ rearsegP ) ),
inference(simp,[status(thm)],[17079]) ).
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(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(274,plain,
! [A: $i] :
( ( nil = A )
| ( A @ tl @ ssList )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[273]) ).
thf(275,plain,
! [A: $i] :
( ( A @ tl @ ssList )
| ~ ( A @ ssList )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[274]) ).
thf(11550,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ tl @ ssList )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[202,275]) ).
thf(11551,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ tl @ ssList )
| ( nil = A ) ),
inference(simp,[status(thm)],[11550]) ).
thf(11552,plain,
( ( sk2 @ tl @ ssList )
| ( nil = sk2 ) ),
inference(pattern_uni,[status(thm)],[11551:[bind(A,$thf( sk2 ))]]) ).
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(1184,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[202,232]) ).
thf(1185,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[1184]) ).
thf(1186,plain,
~ ( sk2 @ ( sk2 @ neq ) ),
inference(pattern_uni,[status(thm)],[1185:[bind(A,$thf( sk2 ))]]) ).
thf(1243,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[203,1186]) ).
thf(1244,plain,
( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[1243]) ).
thf(1247,plain,
( ( nil != sk2 )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[1244]) ).
thf(1249,plain,
nil != sk2,
inference(simp,[status(thm)],[1247]) ).
thf(13658,plain,
sk2 @ tl @ ssList,
inference(simplifyReflect,[status(thm)],[11552,1249]) ).
thf(13706,plain,
! [A: $i] :
( ( ( sk2 @ tl @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13658,3695]) ).
thf(13707,plain,
! [A: $i] :
( ( ( sk2 @ tl @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[13706]) ).
thf(13708,plain,
sk2 @ tl @ ( sk2 @ app ) @ ssList,
inference(pattern_uni,[status(thm)],[13707:[bind(A,$thf( sk2 @ tl ))]]) ).
thf(14380,plain,
! [A: $i] :
( ( ( sk2 @ tl @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13708,3695]) ).
thf(14381,plain,
! [A: $i] :
( ( ( sk2 @ tl @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[14380]) ).
thf(14382,plain,
sk2 @ tl @ ( sk2 @ app ) @ ( sk2 @ app ) @ ssList,
inference(pattern_uni,[status(thm)],[14381:[bind(A,$thf( sk2 @ tl @ ( sk2 @ app ) ))]]) ).
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(1190,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf62 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[233,232]) ).
thf(1191,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf62 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1190]) ).
thf(1192,plain,
! [A: $i] :
~ ( A @ skaf62 @ ( A @ skaf62 @ neq ) ),
inference(pattern_uni,[status(thm)],[1191:[bind(A,$thf( C )),bind(B,$thf( C @ skaf62 ))]]) ).
thf(1233,plain,
! [A: $i] :
~ ( A @ skaf62 @ ( A @ skaf62 @ neq ) ),
inference(simp,[status(thm)],[1192]) ).
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(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(917,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem )
| ~ $true ),
inference(rewrite,[status(thm)],[226,283]) ).
thf(918,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem ) ),
inference(simp,[status(thm)],[917]) ).
thf(928,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[521,918]) ).
thf(929,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[928]) ).
thf(930,plain,
nil @ ( skac2 @ cons ) @ totalorderedP,
inference(pattern_uni,[status(thm)],[929:[bind(A,$thf( skac2 ))]]) ).
thf(5391,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[202,3695]) ).
thf(5392,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[5391]) ).
thf(5393,plain,
sk2 @ ( sk2 @ app ) @ ssList,
inference(pattern_uni,[status(thm)],[5392:[bind(A,$thf( sk2 ))]]) ).
thf(6378,plain,
! [A: $i] :
( ( ( sk2 @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5393,3695]) ).
thf(6379,plain,
! [A: $i] :
( ( ( sk2 @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[6378]) ).
thf(6380,plain,
sk2 @ ( sk2 @ app ) @ ( sk2 @ app ) @ ssList,
inference(pattern_uni,[status(thm)],[6379:[bind(A,$thf( sk2 @ ( sk2 @ app ) ))]]) ).
thf(6653,plain,
! [A: $i] :
( ( ( sk2 @ ( sk2 @ app ) @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6380,3695]) ).
thf(6654,plain,
! [A: $i] :
( ( ( sk2 @ ( sk2 @ app ) @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[6653]) ).
thf(6655,plain,
sk2 @ ( sk2 @ app ) @ ( sk2 @ app ) @ ( sk2 @ app ) @ ssList,
inference(pattern_uni,[status(thm)],[6654:[bind(A,$thf( sk2 @ ( sk2 @ app ) @ ( sk2 @ app ) ))]]) ).
thf(12356,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ tl @ ssList )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[199,275]) ).
thf(12357,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ tl @ ssList )
| ( nil = A ) ),
inference(simp,[status(thm)],[12356]) ).
thf(12358,plain,
( ( sk1 @ tl @ ssList )
| ( nil = sk1 ) ),
inference(pattern_uni,[status(thm)],[12357:[bind(A,$thf( sk1 ))]]) ).
thf(1208,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[199,232]) ).
thf(1209,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[1208]) ).
thf(1210,plain,
~ ( sk1 @ ( sk1 @ neq ) ),
inference(pattern_uni,[status(thm)],[1209:[bind(A,$thf( sk1 ))]]) ).
thf(1252,plain,
( ( ( nil @ ( sk1 @ neq ) )
!= ( sk1 @ ( sk1 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[667,1210]) ).
thf(1253,plain,
( ( nil @ ( sk1 @ neq ) )
!= ( sk1 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[1252]) ).
thf(1255,plain,
( ( nil != sk1 )
| ( sk1 != sk1 ) ),
inference(simp,[status(thm)],[1253]) ).
thf(1256,plain,
nil != sk1,
inference(simp,[status(thm)],[1255]) ).
thf(13757,plain,
sk1 @ tl @ ssList,
inference(simplifyReflect,[status(thm)],[12358,1256]) ).
thf(13777,plain,
! [A: $i] :
( ( ( sk1 @ tl @ ssList )
!= ( A @ ssList ) )
| ( A @ tl @ ssList )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[13757,275]) ).
thf(13778,plain,
! [A: $i] :
( ( ( sk1 @ tl @ ssList )
!= ( A @ ssList ) )
| ( A @ tl @ ssList )
| ( nil = A ) ),
inference(simp,[status(thm)],[13777]) ).
thf(13779,plain,
( ( sk1 @ tl @ tl @ ssList )
| ( ( sk1 @ tl )
= nil ) ),
inference(pattern_uni,[status(thm)],[13778:[bind(A,$thf( sk1 @ tl ))]]) ).
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(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(17189,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf73 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[383,288]) ).
thf(17190,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf73 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[17189]) ).
thf(17191,plain,
! [A: $i] : ( nil @ ( A @ skaf73 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[17190:[bind(A,$thf( C )),bind(B,$thf( C @ skaf73 ))]]) ).
thf(17243,plain,
! [A: $i] : ( nil @ ( A @ skaf73 @ rearsegP ) ),
inference(simp,[status(thm)],[17191]) ).
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(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(324,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderedP )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[323]) ).
thf(29706,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[534,324]) ).
thf(29707,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[29706]) ).
thf(29708,plain,
nil @ ( skac3 @ cons ) @ strictorderedP,
inference(pattern_uni,[status(thm)],[29707:[bind(A,$thf( skac3 ))]]) ).
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(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(5495,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[199,3695]) ).
thf(5496,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[5495]) ).
thf(5497,plain,
sk1 @ ( sk2 @ app ) @ ssList,
inference(pattern_uni,[status(thm)],[5496:[bind(A,$thf( sk1 ))]]) ).
thf(6496,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[5497,232]) ).
thf(6497,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[6496]) ).
thf(6498,plain,
~ ( sk1 @ ( sk2 @ app ) @ ( sk1 @ ( sk2 @ app ) @ neq ) ),
inference(pattern_uni,[status(thm)],[6497:[bind(A,$thf( sk1 @ ( sk2 @ app ) ))]]) ).
thf(6748,plain,
( ( ( sk1 @ ( sk2 @ app ) @ ( sk1 @ ( sk2 @ app ) @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[203,6498]) ).
thf(6749,plain,
( ( sk1 @ ( sk2 @ app ) @ ( sk1 @ ( sk2 @ app ) @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[6748]) ).
thf(6754,plain,
( ( ( sk1 @ ( sk2 @ app ) )
!= nil )
| ( ( sk1 @ ( sk2 @ app ) )
!= sk2 ) ),
inference(simp,[status(thm)],[6749]) ).
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(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(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(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(5431,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf81 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[499,3695]) ).
thf(5432,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf81 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[5431]) ).
thf(5433,plain,
! [A: $i] : ( A @ skaf81 @ ( sk2 @ app ) @ ssList ),
inference(pattern_uni,[status(thm)],[5432:[bind(A,$thf( C )),bind(B,$thf( C @ skaf81 ))]]) ).
thf(5573,plain,
! [A: $i] : ( A @ skaf81 @ ( sk2 @ app ) @ ssList ),
inference(simp,[status(thm)],[5433]) ).
thf(17176,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf81 @ ( sk2 @ app ) @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5573,288]) ).
thf(17177,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf81 @ ( sk2 @ app ) @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[17176]) ).
thf(17178,plain,
! [A: $i] : ( nil @ ( A @ skaf81 @ ( sk2 @ app ) @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[17177:[bind(A,$thf( E )),bind(B,$thf( E @ skaf81 @ ( sk2 @ app ) ))]]) ).
thf(17234,plain,
! [A: $i] : ( nil @ ( A @ skaf81 @ ( sk2 @ app ) @ rearsegP ) ),
inference(simp,[status(thm)],[17178]) ).
thf(2215,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[534,434]) ).
thf(2216,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[2215]) ).
thf(2217,plain,
~ ( skac3 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[2216:[bind(A,$thf( skac3 ))]]) ).
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(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(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(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(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(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(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(5523,plain,
! [A: $i] :
( ( ( nil @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[283,3695]) ).
thf(5524,plain,
! [A: $i] :
( ( ( nil @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[5523]) ).
thf(5525,plain,
nil @ ( sk2 @ app ) @ ssList,
inference(pattern_uni,[status(thm)],[5524:[bind(A,$thf( nil ))]]) ).
thf(6588,plain,
! [A: $i] :
( ( ( nil @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[5525,232]) ).
thf(6589,plain,
! [A: $i] :
( ( ( nil @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[6588]) ).
thf(6590,plain,
~ ( nil @ ( sk2 @ app ) @ ( nil @ ( sk2 @ app ) @ neq ) ),
inference(pattern_uni,[status(thm)],[6589:[bind(A,$thf( nil @ ( sk2 @ app ) ))]]) ).
thf(7456,plain,
( ( ( nil @ ( sk2 @ app ) @ ( nil @ ( sk2 @ app ) @ neq ) )
!= ( nil @ ( sk1 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[667,6590]) ).
thf(7457,plain,
( ( nil @ ( sk2 @ app ) @ ( nil @ ( sk2 @ app ) @ neq ) )
!= ( nil @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[7456]) ).
thf(7464,plain,
( ( ( nil @ ( sk2 @ app ) )
!= nil )
| ( ( nil @ ( sk2 @ app ) )
!= sk1 ) ),
inference(simp,[status(thm)],[7457]) ).
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(1832,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[570,918]) ).
thf(1833,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[1832]) ).
thf(1834,plain,
! [A: $i] : ( nil @ ( A @ skaf83 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[1833:[bind(A,$thf( C )),bind(B,$thf( C @ skaf83 ))]]) ).
thf(1847,plain,
! [A: $i] : ( nil @ ( A @ skaf83 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[1834]) ).
thf(964,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[395,918]) ).
thf(965,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[964]) ).
thf(966,plain,
! [A: $i] : ( nil @ ( A @ skaf70 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[965:[bind(A,$thf( C )),bind(B,$thf( C @ skaf70 ))]]) ).
thf(969,plain,
! [A: $i] : ( nil @ ( A @ skaf70 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[966]) ).
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(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(29695,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[570,324]) ).
thf(29696,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[29695]) ).
thf(29697,plain,
! [A: $i] : ( nil @ ( A @ skaf83 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[29696:[bind(A,$thf( C )),bind(B,$thf( C @ skaf83 ))]]) ).
thf(29788,plain,
! [A: $i] : ( nil @ ( A @ skaf83 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[29697]) ).
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(1219,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf53 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[447,232]) ).
thf(1220,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf53 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1219]) ).
thf(1221,plain,
! [A: $i] :
~ ( A @ skaf53 @ ( A @ skaf53 @ neq ) ),
inference(pattern_uni,[status(thm)],[1220:[bind(A,$thf( C )),bind(B,$thf( C @ skaf53 ))]]) ).
thf(1232,plain,
! [A: $i] :
~ ( A @ skaf53 @ ( A @ skaf53 @ neq ) ),
inference(simp,[status(thm)],[1221]) ).
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(305,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ rearsegP ) ) ),
inference(cnf,[status(esa)],[304]) ).
thf(306,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ~ ( A @ ( nil @ rearsegP ) )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[305]) ).
thf(23719,plain,
! [A: $i] :
( ( nil != nil )
| ( A != sk1 )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ rearsegP ) ) ),
inference(paramod_ordered,[status(thm)],[306,1256]) ).
thf(23720,plain,
! [A: $i] :
( ( A != sk1 )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ rearsegP ) ) ),
inference(pattern_uni,[status(thm)],[23719:[]]) ).
thf(24724,plain,
( ~ ( sk1 @ ssList )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(simp,[status(thm)],[23720]) ).
thf(25216,plain,
( ~ $true
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(rewrite,[status(thm)],[24724,199]) ).
thf(25217,plain,
~ ( sk1 @ ( nil @ rearsegP ) ),
inference(simp,[status(thm)],[25216]) ).
thf(2005,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ~ $true
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[199,239]) ).
thf(2006,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
inference(simp,[status(thm)],[2005]) ).
thf(2007,plain,
( ( sk1 @ strictorderedP )
| ~ ( sk1 @ skaf70 @ ( sk1 @ skaf69 @ lt ) ) ),
inference(pattern_uni,[status(thm)],[2006:[bind(A,$thf( sk1 ))]]) ).
thf(13807,plain,
! [A: $i] :
( ( ( sk1 @ tl @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13757,3695]) ).
thf(13808,plain,
! [A: $i] :
( ( ( sk1 @ tl @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[13807]) ).
thf(13809,plain,
sk1 @ tl @ ( sk2 @ app ) @ ssList,
inference(pattern_uni,[status(thm)],[13808:[bind(A,$thf( sk1 @ tl ))]]) ).
thf(14531,plain,
! [A: $i] :
( ( ( sk1 @ tl @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13809,3695]) ).
thf(14532,plain,
! [A: $i] :
( ( ( sk1 @ tl @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[14531]) ).
thf(14533,plain,
sk1 @ tl @ ( sk2 @ app ) @ ( sk2 @ app ) @ ssList,
inference(pattern_uni,[status(thm)],[14532:[bind(A,$thf( sk1 @ tl @ ( sk2 @ app ) ))]]) ).
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(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(1276,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf68 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[470,232]) ).
thf(1277,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf68 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1276]) ).
thf(1278,plain,
! [A: $i] :
~ ( A @ skaf68 @ ( A @ skaf68 @ neq ) ),
inference(pattern_uni,[status(thm)],[1277:[bind(A,$thf( C )),bind(B,$thf( C @ skaf68 ))]]) ).
thf(1283,plain,
! [A: $i] :
~ ( A @ skaf68 @ ( A @ skaf68 @ neq ) ),
inference(simp,[status(thm)],[1278]) ).
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(1101,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[423,918]) ).
thf(1102,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[1101]) ).
thf(1103,plain,
! [A: $i] : ( nil @ ( A @ skaf49 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[1102:[bind(A,$thf( C )),bind(B,$thf( C @ skaf49 ))]]) ).
thf(1109,plain,
! [A: $i] : ( nil @ ( A @ skaf49 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[1103]) ).
thf(5384,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf52 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[481,3695]) ).
thf(5385,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf52 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[5384]) ).
thf(5386,plain,
! [A: $i] : ( A @ skaf52 @ ( sk2 @ app ) @ ssList ),
inference(pattern_uni,[status(thm)],[5385:[bind(A,$thf( C )),bind(B,$thf( C @ skaf52 ))]]) ).
thf(5549,plain,
! [A: $i] : ( A @ skaf52 @ ( sk2 @ app ) @ ssList ),
inference(simp,[status(thm)],[5386]) ).
thf(17182,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf52 @ ( sk2 @ app ) @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5549,288]) ).
thf(17183,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf52 @ ( sk2 @ app ) @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[17182]) ).
thf(17184,plain,
! [A: $i] : ( nil @ ( A @ skaf52 @ ( sk2 @ app ) @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[17183:[bind(A,$thf( E )),bind(B,$thf( E @ skaf52 @ ( sk2 @ app ) ))]]) ).
thf(17238,plain,
! [A: $i] : ( nil @ ( A @ skaf52 @ ( sk2 @ app ) @ rearsegP ) ),
inference(simp,[status(thm)],[17184]) ).
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(17122,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf57 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[313,288]) ).
thf(17123,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf57 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[17122]) ).
thf(17124,plain,
! [A: $i] : ( nil @ ( A @ skaf57 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[17123:[bind(A,$thf( C )),bind(B,$thf( C @ skaf57 ))]]) ).
thf(17266,plain,
! [A: $i] : ( nil @ ( A @ skaf57 @ rearsegP ) ),
inference(simp,[status(thm)],[17124]) ).
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(931,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[267,918]) ).
thf(932,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[931]) ).
thf(933,plain,
! [A: $i] : ( nil @ ( A @ skaf64 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[932:[bind(A,$thf( C )),bind(B,$thf( C @ skaf64 ))]]) ).
thf(937,plain,
! [A: $i] : ( nil @ ( A @ skaf64 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[933]) ).
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(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(2230,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[391,434]) ).
thf(2231,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[2230]) ).
thf(2232,plain,
! [A: $i] :
~ ( A @ skaf55 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[2231:[bind(A,$thf( C )),bind(B,$thf( C @ skaf55 ))]]) ).
thf(2254,plain,
! [A: $i] :
~ ( A @ skaf55 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[2232]) ).
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(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(13836,plain,
! [A: $i] :
( ( ( sk1 @ tl @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[13757,232]) ).
thf(13837,plain,
! [A: $i] :
( ( ( sk1 @ tl @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[13836]) ).
thf(13838,plain,
~ ( sk1 @ tl @ ( sk1 @ tl @ neq ) ),
inference(pattern_uni,[status(thm)],[13837:[bind(A,$thf( sk1 @ tl ))]]) ).
thf(14603,plain,
( ( ( sk1 @ tl @ ( sk1 @ tl @ neq ) )
!= ( nil @ ( sk1 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[667,13838]) ).
thf(14604,plain,
( ( sk1 @ tl @ ( sk1 @ tl @ neq ) )
!= ( nil @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[14603]) ).
thf(14622,plain,
( ( ( sk1 @ tl )
!= nil )
| ( ( sk1 @ tl )
!= sk1 ) ),
inference(simp,[status(thm)],[14604]) ).
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(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(312,plain,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf59 @ ( A @ skaf60 @ lt ) ) ),
inference(cnf,[status(esa)],[311]) ).
thf(647,plain,
! [A: $i] :
( ( ( nil @ ( sk2 @ neq ) )
!= ( nil @ ( A @ neq ) ) )
| ~ ( A @ ( sk1 @ segmentP ) )
| ~ ( A @ ( sk2 @ segmentP ) )
| ~ $true
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[203,208]) ).
thf(648,plain,
! [A: $i] :
( ( ( nil @ ( sk2 @ neq ) )
!= ( nil @ ( A @ neq ) ) )
| ~ ( A @ ( sk1 @ segmentP ) )
| ~ ( A @ ( sk2 @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[647]) ).
thf(649,plain,
( ~ ( sk2 @ ( sk1 @ segmentP ) )
| ~ ( sk2 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ssList ) ),
inference(pattern_uni,[status(thm)],[648:[bind(A,$thf( sk2 ))]]) ).
thf(657,plain,
( ~ ( sk2 @ ( sk1 @ segmentP ) )
| ~ ( sk2 @ ( sk2 @ segmentP ) )
| ~ $true ),
inference(rewrite,[status(thm)],[649,202]) ).
thf(658,plain,
( ~ ( sk2 @ ( sk1 @ segmentP ) )
| ~ ( sk2 @ ( sk2 @ segmentP ) ) ),
inference(simp,[status(thm)],[657]) ).
thf(659,plain,
( ~ $true
| ( ( sk2 @ ( sk2 @ segmentP ) )
!= ( sk2 @ ( sk1 @ segmentP ) ) )
| ~ ( sk2 @ ( sk1 @ segmentP ) ) ),
inference(eqfactor_ordered,[status(thm)],[658]) ).
thf(660,plain,
( ( ( sk2 @ ( sk2 @ segmentP ) )
!= ( sk2 @ ( sk1 @ segmentP ) ) )
| ~ ( sk2 @ ( sk1 @ segmentP ) ) ),
inference(simp,[status(thm)],[659]) ).
thf(1213,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf73 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[383,232]) ).
thf(1214,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf73 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1213]) ).
thf(1215,plain,
! [A: $i] :
~ ( A @ skaf73 @ ( A @ skaf73 @ neq ) ),
inference(pattern_uni,[status(thm)],[1214:[bind(A,$thf( C )),bind(B,$thf( C @ skaf73 ))]]) ).
thf(1242,plain,
! [A: $i] :
~ ( A @ skaf73 @ ( A @ skaf73 @ neq ) ),
inference(simp,[status(thm)],[1215]) ).
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(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(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(6750,plain,
( ( ( sk1 @ ( sk2 @ app ) @ ( sk1 @ ( sk2 @ app ) @ neq ) )
!= ( nil @ ( sk1 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[667,6498]) ).
thf(6751,plain,
( ( sk1 @ ( sk2 @ app ) @ ( sk1 @ ( sk2 @ app ) @ neq ) )
!= ( nil @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[6750]) ).
thf(6760,plain,
( ( ( sk1 @ ( sk2 @ app ) )
!= nil )
| ( ( sk1 @ ( sk2 @ app ) )
!= sk1 ) ),
inference(simp,[status(thm)],[6751]) ).
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(5507,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf73 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[383,3695]) ).
thf(5508,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf73 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[5507]) ).
thf(5509,plain,
! [A: $i] : ( A @ skaf73 @ ( sk2 @ app ) @ ssList ),
inference(pattern_uni,[status(thm)],[5508:[bind(A,$thf( C )),bind(B,$thf( C @ skaf73 ))]]) ).
thf(5547,plain,
! [A: $i] : ( A @ skaf73 @ ( sk2 @ app ) @ ssList ),
inference(simp,[status(thm)],[5509]) ).
thf(17089,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf73 @ ( sk2 @ app ) @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5547,288]) ).
thf(17090,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf73 @ ( sk2 @ app ) @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[17089]) ).
thf(17091,plain,
! [A: $i] : ( nil @ ( A @ skaf73 @ ( sk2 @ app ) @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[17090:[bind(A,$thf( E )),bind(B,$thf( E @ skaf73 @ ( sk2 @ app ) ))]]) ).
thf(17257,plain,
! [A: $i] : ( nil @ ( A @ skaf73 @ ( sk2 @ app ) @ rearsegP ) ),
inference(simp,[status(thm)],[17091]) ).
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(9,negated_conjecture,
( ( nil != sk4 )
| ( nil = sk3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
thf(201,plain,
( ( nil != sk4 )
| ( nil = sk3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
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(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(5449,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf56 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[586,3695]) ).
thf(5450,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf56 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[5449]) ).
thf(5451,plain,
! [A: $i] : ( A @ skaf56 @ ( sk2 @ app ) @ ssList ),
inference(pattern_uni,[status(thm)],[5450:[bind(A,$thf( C )),bind(B,$thf( C @ skaf56 ))]]) ).
thf(5579,plain,
! [A: $i] : ( A @ skaf56 @ ( sk2 @ app ) @ ssList ),
inference(simp,[status(thm)],[5451]) ).
thf(17060,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf56 @ ( sk2 @ app ) @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5579,288]) ).
thf(17061,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf56 @ ( sk2 @ app ) @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[17060]) ).
thf(17062,plain,
! [A: $i] : ( nil @ ( A @ skaf56 @ ( sk2 @ app ) @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[17061:[bind(A,$thf( E )),bind(B,$thf( E @ skaf56 @ ( sk2 @ app ) ))]]) ).
thf(17242,plain,
! [A: $i] : ( nil @ ( A @ skaf56 @ ( sk2 @ app ) @ rearsegP ) ),
inference(simp,[status(thm)],[17062]) ).
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(2212,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[574,434]) ).
thf(2213,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[2212]) ).
thf(2214,plain,
! [A: $i] :
~ ( A @ skaf74 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[2213:[bind(A,$thf( C )),bind(B,$thf( C @ skaf74 ))]]) ).
thf(2249,plain,
! [A: $i] :
~ ( A @ skaf74 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[2214]) ).
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(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(271,plain,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) ) ),
inference(cnf,[status(esa)],[270]) ).
thf(272,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) )
| ( B = A ) ),
inference(lifteq,[status(thm)],[271]) ).
thf(8939,plain,
! [B: $i,A: $i] :
( ( B != nil )
| ( A != sk1 )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) ) ),
inference(paramod_ordered,[status(thm)],[272,1256]) ).
thf(8940,plain,
! [A: $i] :
( ( A != sk1 )
| ~ ( nil @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( nil @ geq ) )
| ~ ( nil @ ( A @ geq ) ) ),
inference(pattern_uni,[status(thm)],[8939:[bind(A,$thf( A )),bind(B,$thf( nil ))]]) ).
thf(10102,plain,
( ~ ( nil @ ssItem )
| ~ ( sk1 @ ssItem )
| ~ ( sk1 @ ( nil @ geq ) )
| ~ ( nil @ ( sk1 @ geq ) ) ),
inference(simp,[status(thm)],[8940]) ).
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(25673,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( B @ ssItem )
| ( A @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[202,310]) ).
thf(25674,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( B @ ssItem )
| ( A @ duplicatefreeP ) ),
inference(simp,[status(thm)],[25673]) ).
thf(25675,plain,
! [A: $i] :
( ( A @ ssItem )
| ( sk2 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[25674:[bind(A,$thf( sk2 ))]]) ).
thf(25976,plain,
! [A: $i] :
( ( A @ ssItem )
| ( sk2 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[25675]) ).
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(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(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(17030,plain,
! [A: $i] :
( ( ( sk2 @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5393,288]) ).
thf(17031,plain,
! [A: $i] :
( ( ( sk2 @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[17030]) ).
thf(17032,plain,
nil @ ( sk2 @ ( sk2 @ app ) @ rearsegP ),
inference(pattern_uni,[status(thm)],[17031:[bind(A,$thf( sk2 @ ( sk2 @ app ) ))]]) ).
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(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(5489,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf51 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[531,3695]) ).
thf(5490,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf51 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[5489]) ).
thf(5491,plain,
! [A: $i] : ( A @ skaf51 @ ( sk2 @ app ) @ ssList ),
inference(pattern_uni,[status(thm)],[5490:[bind(A,$thf( C )),bind(B,$thf( C @ skaf51 ))]]) ).
thf(5590,plain,
! [A: $i] : ( A @ skaf51 @ ( sk2 @ app ) @ ssList ),
inference(simp,[status(thm)],[5491]) ).
thf(17192,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf51 @ ( sk2 @ app ) @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5590,288]) ).
thf(17193,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf51 @ ( sk2 @ app ) @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[17192]) ).
thf(17194,plain,
! [A: $i] : ( nil @ ( A @ skaf51 @ ( sk2 @ app ) @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[17193:[bind(A,$thf( E )),bind(B,$thf( E @ skaf51 @ ( sk2 @ app ) ))]]) ).
thf(17245,plain,
! [A: $i] : ( nil @ ( A @ skaf51 @ ( sk2 @ app ) @ rearsegP ) ),
inference(simp,[status(thm)],[17194]) ).
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(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(2427,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[609,918]) ).
thf(2428,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[2427]) ).
thf(2429,plain,
! [A: $i] : ( nil @ ( A @ skaf78 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[2428:[bind(A,$thf( C )),bind(B,$thf( C @ skaf78 ))]]) ).
thf(2445,plain,
! [A: $i] : ( nil @ ( A @ skaf78 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[2429]) ).
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(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(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(29761,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[267,324]) ).
thf(29762,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[29761]) ).
thf(29763,plain,
! [A: $i] : ( nil @ ( A @ skaf64 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[29762:[bind(A,$thf( C )),bind(B,$thf( C @ skaf64 ))]]) ).
thf(29789,plain,
! [A: $i] : ( nil @ ( A @ skaf64 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[29763]) ).
thf(2206,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[570,434]) ).
thf(2207,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[2206]) ).
thf(2208,plain,
! [A: $i] :
~ ( A @ skaf83 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[2207:[bind(A,$thf( C )),bind(B,$thf( C @ skaf83 ))]]) ).
thf(2245,plain,
! [A: $i] :
~ ( A @ skaf83 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[2208]) ).
thf(1222,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf80 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[432,232]) ).
thf(1223,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf80 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1222]) ).
thf(1224,plain,
! [A: $i] :
~ ( A @ skaf80 @ ( A @ skaf80 @ neq ) ),
inference(pattern_uni,[status(thm)],[1223:[bind(A,$thf( C )),bind(B,$thf( C @ skaf80 ))]]) ).
thf(1234,plain,
! [A: $i] :
~ ( A @ skaf80 @ ( A @ skaf80 @ neq ) ),
inference(simp,[status(thm)],[1224]) ).
thf(17140,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf76 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[599,288]) ).
thf(17141,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf76 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[17140]) ).
thf(17142,plain,
! [A: $i] : ( nil @ ( A @ skaf76 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[17141:[bind(A,$thf( C )),bind(B,$thf( C @ skaf76 ))]]) ).
thf(17274,plain,
! [A: $i] : ( nil @ ( A @ skaf76 @ rearsegP ) ),
inference(simp,[status(thm)],[17142]) ).
thf(1225,plain,
! [A: $i] :
( ( ( nil @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[283,232]) ).
thf(1226,plain,
! [A: $i] :
( ( ( nil @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[1225]) ).
thf(1227,plain,
~ ( nil @ ( nil @ neq ) ),
inference(pattern_uni,[status(thm)],[1226:[bind(A,$thf( nil ))]]) ).
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(17104,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf58 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[343,288]) ).
thf(17105,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf58 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[17104]) ).
thf(17106,plain,
! [A: $i] : ( nil @ ( A @ skaf58 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[17105:[bind(A,$thf( C )),bind(B,$thf( C @ skaf58 ))]]) ).
thf(17264,plain,
! [A: $i] : ( nil @ ( A @ skaf58 @ rearsegP ) ),
inference(simp,[status(thm)],[17106]) ).
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(8689,plain,
! [B: $i,A: $i] :
( ( B != nil )
| ( A != sk2 )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) ) ),
inference(paramod_ordered,[status(thm)],[272,1249]) ).
thf(8690,plain,
! [A: $i] :
( ( A != sk2 )
| ~ ( nil @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( nil @ geq ) )
| ~ ( nil @ ( A @ geq ) ) ),
inference(pattern_uni,[status(thm)],[8689:[bind(A,$thf( A )),bind(B,$thf( nil ))]]) ).
thf(10021,plain,
( ~ ( nil @ ssItem )
| ~ ( sk2 @ ssItem )
| ~ ( sk2 @ ( nil @ geq ) )
| ~ ( nil @ ( sk2 @ geq ) ) ),
inference(simp,[status(thm)],[8690]) ).
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(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(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(5510,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf77 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[300,3695]) ).
thf(5511,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf77 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[5510]) ).
thf(5512,plain,
! [A: $i] : ( A @ skaf77 @ ( sk2 @ app ) @ ssList ),
inference(pattern_uni,[status(thm)],[5511:[bind(A,$thf( C )),bind(B,$thf( C @ skaf77 ))]]) ).
thf(5548,plain,
! [A: $i] : ( A @ skaf77 @ ( sk2 @ app ) @ ssList ),
inference(simp,[status(thm)],[5512]) ).
thf(17152,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf77 @ ( sk2 @ app ) @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5548,288]) ).
thf(17153,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf77 @ ( sk2 @ app ) @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[17152]) ).
thf(17154,plain,
! [A: $i] : ( nil @ ( A @ skaf77 @ ( sk2 @ app ) @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[17153:[bind(A,$thf( E )),bind(B,$thf( E @ skaf77 @ ( sk2 @ app ) ))]]) ).
thf(17225,plain,
! [A: $i] : ( nil @ ( A @ skaf77 @ ( sk2 @ app ) @ rearsegP ) ),
inference(simp,[status(thm)],[17154]) ).
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(1455,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf81 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[499,232]) ).
thf(1456,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf81 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1455]) ).
thf(1457,plain,
! [A: $i] :
~ ( A @ skaf81 @ ( A @ skaf81 @ neq ) ),
inference(pattern_uni,[status(thm)],[1456:[bind(A,$thf( C )),bind(B,$thf( C @ skaf81 ))]]) ).
thf(1461,plain,
! [A: $i] :
~ ( A @ skaf81 @ ( A @ skaf81 @ neq ) ),
inference(simp,[status(thm)],[1457]) ).
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(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(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(1216,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf77 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[300,232]) ).
thf(1217,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf77 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1216]) ).
thf(1218,plain,
! [A: $i] :
~ ( A @ skaf77 @ ( A @ skaf77 @ neq ) ),
inference(pattern_uni,[status(thm)],[1217:[bind(A,$thf( C )),bind(B,$thf( C @ skaf77 ))]]) ).
thf(1230,plain,
! [A: $i] :
~ ( A @ skaf77 @ ( A @ skaf77 @ neq ) ),
inference(simp,[status(thm)],[1218]) ).
thf(3640,plain,
! [A: $i] :
( ( ( A @ skaf77 @ ( A @ skaf77 @ neq ) )
!= ( nil @ ( sk1 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[667,1230]) ).
thf(3641,plain,
! [A: $i] :
( ( A @ skaf77 @ ( A @ skaf77 @ neq ) )
!= ( nil @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[3640]) ).
thf(3643,plain,
! [A: $i] :
( ( ( A @ skaf77 )
!= nil )
| ( ( A @ skaf77 )
!= sk1 ) ),
inference(simp,[status(thm)],[3641]) ).
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(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(13676,plain,
! [A: $i] :
( ( ( sk2 @ tl @ ssList )
!= ( A @ ssList ) )
| ( A @ tl @ ssList )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[13658,275]) ).
thf(13677,plain,
! [A: $i] :
( ( ( sk2 @ tl @ ssList )
!= ( A @ ssList ) )
| ( A @ tl @ ssList )
| ( nil = A ) ),
inference(simp,[status(thm)],[13676]) ).
thf(13678,plain,
( ( sk2 @ tl @ tl @ ssList )
| ( ( sk2 @ tl )
= nil ) ),
inference(pattern_uni,[status(thm)],[13677:[bind(A,$thf( sk2 @ tl ))]]) ).
thf(17216,plain,
! [A: $i] :
( ( ( sk2 @ tl @ tl @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( ( sk2 @ tl )
= nil ) ),
inference(paramod_ordered,[status(thm)],[13678,288]) ).
thf(17217,plain,
! [A: $i] :
( ( ( sk2 @ tl @ tl @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( ( sk2 @ tl )
= nil ) ),
inference(simp,[status(thm)],[17216]) ).
thf(17218,plain,
( ( nil @ ( sk2 @ tl @ tl @ rearsegP ) )
| ( ( sk2 @ tl )
= nil ) ),
inference(pattern_uni,[status(thm)],[17217:[bind(A,$thf( sk2 @ tl @ tl ))]]) ).
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(17116,plain,
! [A: $i] :
( ( ( nil @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5525,288]) ).
thf(17117,plain,
! [A: $i] :
( ( ( nil @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[17116]) ).
thf(17118,plain,
nil @ ( nil @ ( sk2 @ app ) @ rearsegP ),
inference(pattern_uni,[status(thm)],[17117:[bind(A,$thf( nil @ ( sk2 @ app ) ))]]) ).
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(2347,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[199,241]) ).
thf(2348,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP ) ),
inference(simp,[status(thm)],[2347]) ).
thf(2349,plain,
( ( sk1 @ skaf50 @ ( sk1 @ skaf49 @ leq ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[2348:[bind(A,$thf( sk1 ))]]) ).
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(1187,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf75 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[448,232]) ).
thf(1188,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf75 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1187]) ).
thf(1189,plain,
! [A: $i] :
~ ( A @ skaf75 @ ( A @ skaf75 @ neq ) ),
inference(pattern_uni,[status(thm)],[1188:[bind(A,$thf( C )),bind(B,$thf( C @ skaf75 ))]]) ).
thf(1231,plain,
! [A: $i] :
~ ( A @ skaf75 @ ( A @ skaf75 @ neq ) ),
inference(simp,[status(thm)],[1189]) ).
thf(3650,plain,
! [A: $i] :
( ( ( A @ skaf75 @ ( A @ skaf75 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[203,1231]) ).
thf(3651,plain,
! [A: $i] :
( ( A @ skaf75 @ ( A @ skaf75 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[3650]) ).
thf(3654,plain,
! [A: $i] :
( ( ( A @ skaf75 )
!= nil )
| ( ( A @ skaf75 )
!= sk2 ) ),
inference(simp,[status(thm)],[3651]) ).
thf(2302,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[202,241]) ).
thf(2303,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP ) ),
inference(simp,[status(thm)],[2302]) ).
thf(2304,plain,
( ( sk2 @ skaf50 @ ( sk2 @ skaf49 @ leq ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[2303:[bind(A,$thf( sk2 ))]]) ).
thf(7454,plain,
( ( ( nil @ ( sk2 @ app ) @ ( nil @ ( sk2 @ app ) @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[203,6590]) ).
thf(7455,plain,
( ( nil @ ( sk2 @ app ) @ ( nil @ ( sk2 @ app ) @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[7454]) ).
thf(7463,plain,
( ( ( nil @ ( sk2 @ app ) )
!= nil )
| ( ( nil @ ( sk2 @ app ) )
!= sk2 ) ),
inference(simp,[status(thm)],[7455]) ).
thf(14992,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[534,282]) ).
thf(14993,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[14992]) ).
thf(14994,plain,
~ ( skac3 @ ( skac3 @ neq ) ),
inference(pattern_uni,[status(thm)],[14993:[bind(A,$thf( skac3 ))]]) ).
thf(15062,plain,
( ( ( skac3 @ ( skac3 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[203,14994]) ).
thf(15063,plain,
( ( skac3 @ ( skac3 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[15062]) ).
thf(15074,plain,
( ( skac3 != nil )
| ( skac3 != sk2 ) ),
inference(simp,[status(thm)],[15063]) ).
thf(22935,plain,
! [A: $i] :
( ( A != skac2 )
| ( nil != nil )
| ( skac2 != sk2 )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ rearsegP ) ) ),
inference(paramod_ordered,[status(thm)],[306,15098]) ).
thf(22936,plain,
! [A: $i] :
( ( A != skac2 )
| ( skac2 != sk2 )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ rearsegP ) ) ),
inference(simp,[status(thm)],[22935]) ).
thf(22937,plain,
( ( skac2 != sk2 )
| ~ ( skac2 @ ssList )
| ~ ( skac2 @ ( nil @ rearsegP ) ) ),
inference(pattern_uni,[status(thm)],[22936:[bind(A,$thf( skac2 ))]]) ).
thf(6559,plain,
! [A: $i] :
( ( ( nil @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5525,3695]) ).
thf(6560,plain,
! [A: $i] :
( ( ( nil @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[6559]) ).
thf(6561,plain,
nil @ ( sk2 @ app ) @ ( sk2 @ app ) @ ssList,
inference(pattern_uni,[status(thm)],[6560:[bind(A,$thf( nil @ ( sk2 @ app ) ))]]) ).
thf(7383,plain,
! [A: $i] :
( ( ( nil @ ( sk2 @ app ) @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6561,3695]) ).
thf(7384,plain,
! [A: $i] :
( ( ( nil @ ( sk2 @ app ) @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[7383]) ).
thf(7385,plain,
nil @ ( sk2 @ app ) @ ( sk2 @ app ) @ ( sk2 @ app ) @ ssList,
inference(pattern_uni,[status(thm)],[7384:[bind(A,$thf( nil @ ( sk2 @ app ) @ ( sk2 @ app ) ))]]) ).
thf(5422,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf67 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[493,3695]) ).
thf(5423,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf67 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[5422]) ).
thf(5424,plain,
! [A: $i] : ( A @ skaf67 @ ( sk2 @ app ) @ ssList ),
inference(pattern_uni,[status(thm)],[5423:[bind(A,$thf( C )),bind(B,$thf( C @ skaf67 ))]]) ).
thf(5570,plain,
! [A: $i] : ( A @ skaf67 @ ( sk2 @ app ) @ ssList ),
inference(simp,[status(thm)],[5424]) ).
thf(17161,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf67 @ ( sk2 @ app ) @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5570,288]) ).
thf(17162,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf67 @ ( sk2 @ app ) @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[17161]) ).
thf(17163,plain,
! [A: $i] : ( nil @ ( A @ skaf67 @ ( sk2 @ app ) @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[17162:[bind(A,$thf( E )),bind(B,$thf( E @ skaf67 @ ( sk2 @ app ) ))]]) ).
thf(17228,plain,
! [A: $i] : ( nil @ ( A @ skaf67 @ ( sk2 @ app ) @ rearsegP ) ),
inference(simp,[status(thm)],[17163]) ).
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(2566,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ singletonP )
| ( ( nil @ ( A @ skaf44 @ cons ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[199,244]) ).
thf(2567,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ singletonP )
| ( ( nil @ ( A @ skaf44 @ cons ) )
= A ) ),
inference(simp,[status(thm)],[2566]) ).
thf(2568,plain,
( ~ ( sk1 @ singletonP )
| ( ( nil @ ( sk1 @ skaf44 @ cons ) )
= sk1 ) ),
inference(pattern_uni,[status(thm)],[2567:[bind(A,$thf( sk1 ))]]) ).
thf(922,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[357,918]) ).
thf(923,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[922]) ).
thf(924,plain,
! [A: $i] : ( nil @ ( A @ skaf44 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[923:[bind(A,$thf( C )),bind(B,$thf( C @ skaf44 ))]]) ).
thf(940,plain,
! [A: $i] : ( nil @ ( A @ skaf44 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[924]) ).
thf(3627,plain,
! [A: $i] :
( ( ( nil @ ( sk1 @ skaf44 @ cons ) )
!= ( nil @ ( A @ skaf44 @ cons ) ) )
| ( sk1 @ totalorderedP )
| ~ ( sk1 @ singletonP ) ),
inference(paramod_ordered,[status(thm)],[2568,940]) ).
thf(3628,plain,
( ( sk1 @ totalorderedP )
| ~ ( sk1 @ singletonP ) ),
inference(pattern_uni,[status(thm)],[3627:[bind(A,$thf( sk1 ))]]) ).
thf(14422,plain,
! [A: $i] :
( ( ( sk2 @ tl @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[13708,232]) ).
thf(14423,plain,
! [A: $i] :
( ( ( sk2 @ tl @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[14422]) ).
thf(14424,plain,
~ ( sk2 @ tl @ ( sk2 @ app ) @ ( sk2 @ tl @ ( sk2 @ app ) @ neq ) ),
inference(pattern_uni,[status(thm)],[14423:[bind(A,$thf( sk2 @ tl @ ( sk2 @ app ) ))]]) ).
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(934,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[390,918]) ).
thf(935,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[934]) ).
thf(936,plain,
! [A: $i] : ( nil @ ( A @ skaf69 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[935:[bind(A,$thf( C )),bind(B,$thf( C @ skaf69 ))]]) ).
thf(938,plain,
! [A: $i] : ( nil @ ( A @ skaf69 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[936]) ).
thf(11,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( sk3 @ ( nil @ neq ) )
| ~ ( sk3 @ ( nil @ neq ) )
| ( ( sk3 @ hd )
!= D )
| ( ( nil @ ( D @ cons ) )
!= C )
| ~ ( D @ ssItem )
| ( ( C @ ( B @ app ) )
!= A )
| ( ( sk3 @ tl )
!= B )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ( sk4 = A )
| ~ ( A @ ssList )
| ~ ( nil @ ( sk4 @ neq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
thf(205,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( sk3 @ ( nil @ neq ) )
| ~ ( sk3 @ ( nil @ neq ) )
| ( ( sk3 @ hd )
!= D )
| ( ( nil @ ( D @ cons ) )
!= C )
| ~ ( D @ ssItem )
| ( ( C @ ( B @ app ) )
!= A )
| ( ( sk3 @ tl )
!= B )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ( sk4 = A )
| ~ ( A @ ssList )
| ~ ( nil @ ( sk4 @ neq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
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(17095,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf61 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[398,288]) ).
thf(17096,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf61 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[17095]) ).
thf(17097,plain,
! [A: $i] : ( nil @ ( A @ skaf61 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[17096:[bind(A,$thf( C )),bind(B,$thf( C @ skaf61 ))]]) ).
thf(17261,plain,
! [A: $i] : ( nil @ ( A @ skaf61 @ rearsegP ) ),
inference(simp,[status(thm)],[17097]) ).
thf(5425,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf71 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[593,3695]) ).
thf(5426,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf71 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[5425]) ).
thf(5427,plain,
! [A: $i] : ( A @ skaf71 @ ( sk2 @ app ) @ ssList ),
inference(pattern_uni,[status(thm)],[5426:[bind(A,$thf( C )),bind(B,$thf( C @ skaf71 ))]]) ).
thf(5571,plain,
! [A: $i] : ( A @ skaf71 @ ( sk2 @ app ) @ ssList ),
inference(simp,[status(thm)],[5427]) ).
thf(17027,plain,
! [A: $i] :
( ( ( sk1 @ tl @ tl @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( ( sk1 @ tl )
= nil ) ),
inference(paramod_ordered,[status(thm)],[13779,288]) ).
thf(17028,plain,
! [A: $i] :
( ( ( sk1 @ tl @ tl @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( ( sk1 @ tl )
= nil ) ),
inference(simp,[status(thm)],[17027]) ).
thf(17029,plain,
( ( nil @ ( sk1 @ tl @ tl @ rearsegP ) )
| ( ( sk1 @ tl )
= nil ) ),
inference(pattern_uni,[status(thm)],[17028:[bind(A,$thf( sk1 @ tl @ tl ))]]) ).
thf(661,plain,
( ( sk2 != sk2 )
| ( sk2 != sk1 )
| ~ ( sk2 @ ( sk1 @ segmentP ) ) ),
inference(simp,[status(thm)],[659]) ).
thf(662,plain,
( ( sk2 != sk1 )
| ~ ( sk2 @ ( sk1 @ segmentP ) ) ),
inference(simp,[status(thm)],[661]) ).
thf(17051,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf62 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[233,288]) ).
thf(17052,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf62 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[17051]) ).
thf(17053,plain,
! [A: $i] : ( nil @ ( A @ skaf62 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[17052:[bind(A,$thf( C )),bind(B,$thf( C @ skaf62 ))]]) ).
thf(17235,plain,
! [A: $i] : ( nil @ ( A @ skaf62 @ rearsegP ) ),
inference(simp,[status(thm)],[17053]) ).
thf(6407,plain,
! [A: $i] :
( ( ( sk2 @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[5393,232]) ).
thf(6408,plain,
! [A: $i] :
( ( ( sk2 @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[6407]) ).
thf(6409,plain,
~ ( sk2 @ ( sk2 @ app ) @ ( sk2 @ ( sk2 @ app ) @ neq ) ),
inference(pattern_uni,[status(thm)],[6408:[bind(A,$thf( sk2 @ ( sk2 @ app ) ))]]) ).
thf(5400,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf75 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[448,3695]) ).
thf(5401,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf75 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[5400]) ).
thf(5402,plain,
! [A: $i] : ( A @ skaf75 @ ( sk2 @ app ) @ ssList ),
inference(pattern_uni,[status(thm)],[5401:[bind(A,$thf( C )),bind(B,$thf( C @ skaf75 ))]]) ).
thf(5557,plain,
! [A: $i] : ( A @ skaf75 @ ( sk2 @ app ) @ ssList ),
inference(simp,[status(thm)],[5402]) ).
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(1205,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf57 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[313,232]) ).
thf(1206,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf57 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1205]) ).
thf(1207,plain,
! [A: $i] :
~ ( A @ skaf57 @ ( A @ skaf57 @ neq ) ),
inference(pattern_uni,[status(thm)],[1206:[bind(A,$thf( C )),bind(B,$thf( C @ skaf57 ))]]) ).
thf(1241,plain,
! [A: $i] :
~ ( A @ skaf57 @ ( A @ skaf57 @ neq ) ),
inference(simp,[status(thm)],[1207]) ).
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(5394,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf63 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[538,3695]) ).
thf(5395,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf63 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[5394]) ).
thf(5396,plain,
! [A: $i] : ( A @ skaf63 @ ( sk2 @ app ) @ ssList ),
inference(pattern_uni,[status(thm)],[5395:[bind(A,$thf( C )),bind(B,$thf( C @ skaf63 ))]]) ).
thf(5554,plain,
! [A: $i] : ( A @ skaf63 @ ( sk2 @ app ) @ ssList ),
inference(simp,[status(thm)],[5396]) ).
thf(17201,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf63 @ ( sk2 @ app ) @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5554,288]) ).
thf(17202,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf63 @ ( sk2 @ app ) @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[17201]) ).
thf(17203,plain,
! [A: $i] : ( nil @ ( A @ skaf63 @ ( sk2 @ app ) @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[17202:[bind(A,$thf( E )),bind(B,$thf( E @ skaf63 @ ( sk2 @ app ) ))]]) ).
thf(17250,plain,
! [A: $i] : ( nil @ ( A @ skaf63 @ ( sk2 @ app ) @ rearsegP ) ),
inference(simp,[status(thm)],[17203]) ).
thf(2233,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[521,434]) ).
thf(2234,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[2233]) ).
thf(2235,plain,
~ ( skac2 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[2234:[bind(A,$thf( skac2 ))]]) ).
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(17048,plain,
! [A: $i] :
( ( ( sk1 @ tl @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13757,288]) ).
thf(17049,plain,
! [A: $i] :
( ( ( sk1 @ tl @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[17048]) ).
thf(17050,plain,
nil @ ( sk1 @ tl @ rearsegP ),
inference(pattern_uni,[status(thm)],[17049:[bind(A,$thf( sk1 @ tl ))]]) ).
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(2227,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[579,434]) ).
thf(2228,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[2227]) ).
thf(2229,plain,
! [A: $i] :
~ ( A @ skaf65 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[2228:[bind(A,$thf( C )),bind(B,$thf( C @ skaf65 ))]]) ).
thf(2253,plain,
! [A: $i] :
~ ( A @ skaf65 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[2229]) ).
thf(15383,plain,
! [A: $i] :
( ( A != skac3 )
| ( nil != nil )
| ( skac3 != sk2 )
| ( A @ tl @ ssList )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[275,15074]) ).
thf(15384,plain,
! [A: $i] :
( ( A != skac3 )
| ( skac3 != sk2 )
| ( A @ tl @ ssList )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[15383]) ).
thf(15385,plain,
( ( skac3 != sk2 )
| ( skac3 @ tl @ ssList )
| ~ ( skac3 @ ssList ) ),
inference(pattern_uni,[status(thm)],[15384:[bind(A,$thf( skac3 ))]]) ).
thf(22386,plain,
( ( ( skac3 @ ssList )
!= ( sk2 @ ssList ) )
| ( skac3 != sk2 )
| ( skac3 @ tl @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[202,15385]) ).
thf(22387,plain,
( ( ( skac3 @ ssList )
!= ( sk2 @ ssList ) )
| ( skac3 != sk2 )
| ( skac3 @ tl @ ssList ) ),
inference(simp,[status(thm)],[22386]) ).
thf(22706,plain,
( ( skac3 != sk2 )
| ( skac3 != sk2 )
| ( skac3 @ tl @ ssList ) ),
inference(simp,[status(thm)],[22387]) ).
thf(22748,plain,
( ( skac3 != sk2 )
| ( skac3 @ tl @ ssList ) ),
inference(simp,[status(thm)],[22706]) ).
thf(22761,plain,
! [A: $i] :
( ( ( skac3 @ tl @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( skac3 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[22748,288]) ).
thf(22762,plain,
! [A: $i] :
( ( ( skac3 @ tl @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( skac3 != sk2 ) ),
inference(simp,[status(thm)],[22761]) ).
thf(22763,plain,
( ( nil @ ( skac3 @ tl @ rearsegP ) )
| ( skac3 != sk2 ) ),
inference(pattern_uni,[status(thm)],[22762:[bind(A,$thf( skac3 @ tl ))]]) ).
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(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(6467,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5497,3695]) ).
thf(6468,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[6467]) ).
thf(6469,plain,
sk1 @ ( sk2 @ app ) @ ( sk2 @ app ) @ ssList,
inference(pattern_uni,[status(thm)],[6468:[bind(A,$thf( sk1 @ ( sk2 @ app ) ))]]) ).
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(218,plain,
skac3 != skac2,
inference(polarity_switch,[status(thm)],[217]) ).
thf(219,plain,
skac2 != skac3,
inference(lifteq,[status(thm)],[218]) ).
thf(8981,plain,
! [B: $i,A: $i] :
( ( B != skac2 )
| ( A != skac3 )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) ) ),
inference(paramod_ordered,[status(thm)],[272,219]) ).
thf(8982,plain,
! [A: $i] :
( ( A != skac3 )
| ~ ( skac2 @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( skac2 @ geq ) )
| ~ ( skac2 @ ( A @ geq ) ) ),
inference(pattern_uni,[status(thm)],[8981:[bind(A,$thf( A )),bind(B,$thf( skac2 ))]]) ).
thf(10120,plain,
( ~ ( skac2 @ ssItem )
| ~ ( skac3 @ ssItem )
| ~ ( skac3 @ ( skac2 @ geq ) )
| ~ ( skac2 @ ( skac3 @ geq ) ) ),
inference(simp,[status(thm)],[8982]) ).
thf(22247,plain,
( ~ $true
| ~ $true
| ~ ( skac3 @ ( skac2 @ geq ) )
| ~ ( skac2 @ ( skac3 @ geq ) ) ),
inference(rewrite,[status(thm)],[10120,534,521]) ).
thf(22248,plain,
( ~ ( skac3 @ ( skac2 @ geq ) )
| ~ ( skac2 @ ( skac3 @ geq ) ) ),
inference(simp,[status(thm)],[22247]) ).
thf(285,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ skaf45 ) @ ( B @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ frontsegP ) ) ),
inference(cnf,[status(esa)],[284]) ).
thf(286,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ frontsegP ) )
| ( ( B @ ( A @ skaf45 ) @ ( B @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[285]) ).
thf(17009,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf52 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[481,288]) ).
thf(17010,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf52 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[17009]) ).
thf(17011,plain,
! [A: $i] : ( nil @ ( A @ skaf52 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[17010:[bind(A,$thf( C )),bind(B,$thf( C @ skaf52 ))]]) ).
thf(17273,plain,
! [A: $i] : ( nil @ ( A @ skaf52 @ rearsegP ) ),
inference(simp,[status(thm)],[17011]) ).
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(17039,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf75 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[448,288]) ).
thf(17040,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf75 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[17039]) ).
thf(17041,plain,
! [A: $i] : ( nil @ ( A @ skaf75 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[17040:[bind(A,$thf( C )),bind(B,$thf( C @ skaf75 ))]]) ).
thf(17231,plain,
! [A: $i] : ( nil @ ( A @ skaf75 @ rearsegP ) ),
inference(simp,[status(thm)],[17041]) ).
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(742,plain,
( ( sk1 != sk1 )
| ( sk2 != sk1 )
| ~ ( sk1 @ ( sk1 @ segmentP ) ) ),
inference(simp,[status(thm)],[740]) ).
thf(743,plain,
( ( sk2 != sk1 )
| ~ ( sk1 @ ( sk1 @ segmentP ) ) ),
inference(simp,[status(thm)],[742]) ).
thf(13741,plain,
! [A: $i] :
( ( ( sk2 @ tl @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[13658,232]) ).
thf(13742,plain,
! [A: $i] :
( ( ( sk2 @ tl @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[13741]) ).
thf(13743,plain,
~ ( sk2 @ tl @ ( sk2 @ tl @ neq ) ),
inference(pattern_uni,[status(thm)],[13742:[bind(A,$thf( sk2 @ tl ))]]) ).
thf(14450,plain,
( ( ( sk2 @ tl @ ( sk2 @ tl @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[203,13743]) ).
thf(14451,plain,
( ( sk2 @ tl @ ( sk2 @ tl @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[14450]) ).
thf(14470,plain,
( ( ( sk2 @ tl )
!= nil )
| ( ( sk2 @ tl )
!= sk2 ) ),
inference(simp,[status(thm)],[14451]) ).
thf(14790,plain,
( ( ( sk2 @ tl )
!= ( sk2 @ tl ) )
| ( nil != nil )
| ( ( sk2 @ tl )
!= sk2 )
| ( sk2 @ tl @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[13678,14470]) ).
thf(14791,plain,
( ( ( sk2 @ tl )
!= ( sk2 @ tl ) )
| ( ( sk2 @ tl )
!= sk2 )
| ( sk2 @ tl @ tl @ ssList ) ),
inference(simp,[status(thm)],[14790]) ).
thf(14792,plain,
( ( ( sk2 @ tl )
!= sk2 )
| ( sk2 @ tl @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[14791:[]]) ).
thf(290,plain,
! [B: $i,A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= nil ) ),
inference(cnf,[status(esa)],[289]) ).
thf(291,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( nil = A )
| ( ( B @ ( A @ app ) )
!= nil ) ),
inference(lifteq,[status(thm)],[290]) ).
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(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(1421,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf52 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[481,232]) ).
thf(1422,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf52 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1421]) ).
thf(1423,plain,
! [A: $i] :
~ ( A @ skaf52 @ ( A @ skaf52 @ neq ) ),
inference(pattern_uni,[status(thm)],[1422:[bind(A,$thf( C )),bind(B,$thf( C @ skaf52 ))]]) ).
thf(1428,plain,
! [A: $i] :
~ ( A @ skaf52 @ ( A @ skaf52 @ neq ) ),
inference(simp,[status(thm)],[1423]) ).
thf(17113,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ app ) @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6469,288]) ).
thf(17114,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ app ) @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[17113]) ).
thf(17115,plain,
nil @ ( sk1 @ ( sk2 @ app ) @ ( sk2 @ app ) @ rearsegP ),
inference(pattern_uni,[status(thm)],[17114:[bind(A,$thf( sk1 @ ( sk2 @ app ) @ ( sk2 @ app ) ))]]) ).
thf(17207,plain,
! [A: $i] :
( ( ( sk2 @ ( sk2 @ app ) @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6380,288]) ).
thf(17208,plain,
! [A: $i] :
( ( ( sk2 @ ( sk2 @ app ) @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[17207]) ).
thf(17209,plain,
nil @ ( sk2 @ ( sk2 @ app ) @ ( sk2 @ app ) @ rearsegP ),
inference(pattern_uni,[status(thm)],[17208:[bind(A,$thf( sk2 @ ( sk2 @ app ) @ ( sk2 @ app ) ))]]) ).
thf(1199,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf58 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[343,232]) ).
thf(1200,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf58 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1199]) ).
thf(1201,plain,
! [A: $i] :
~ ( A @ skaf58 @ ( A @ skaf58 @ neq ) ),
inference(pattern_uni,[status(thm)],[1200:[bind(A,$thf( C )),bind(B,$thf( C @ skaf58 ))]]) ).
thf(1239,plain,
! [A: $i] :
~ ( A @ skaf58 @ ( A @ skaf58 @ neq ) ),
inference(simp,[status(thm)],[1201]) ).
thf(5492,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf68 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[470,3695]) ).
thf(5493,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf68 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[5492]) ).
thf(5494,plain,
! [A: $i] : ( A @ skaf68 @ ( sk2 @ app ) @ ssList ),
inference(pattern_uni,[status(thm)],[5493:[bind(A,$thf( C )),bind(B,$thf( C @ skaf68 ))]]) ).
thf(5591,plain,
! [A: $i] : ( A @ skaf68 @ ( sk2 @ app ) @ ssList ),
inference(simp,[status(thm)],[5494]) ).
thf(17222,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf68 @ ( sk2 @ app ) @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5591,288]) ).
thf(17223,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf68 @ ( sk2 @ app ) @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[17222]) ).
thf(17224,plain,
! [A: $i] : ( nil @ ( A @ skaf68 @ ( sk2 @ app ) @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[17223:[bind(A,$thf( E )),bind(B,$thf( E @ skaf68 @ ( sk2 @ app ) ))]]) ).
thf(17260,plain,
! [A: $i] : ( nil @ ( A @ skaf68 @ ( sk2 @ app ) @ rearsegP ) ),
inference(simp,[status(thm)],[17224]) ).
thf(5446,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf61 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[398,3695]) ).
thf(5447,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf61 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[5446]) ).
thf(5448,plain,
! [A: $i] : ( A @ skaf61 @ ( sk2 @ app ) @ ssList ),
inference(pattern_uni,[status(thm)],[5447:[bind(A,$thf( C )),bind(B,$thf( C @ skaf61 ))]]) ).
thf(5578,plain,
! [A: $i] : ( A @ skaf61 @ ( sk2 @ app ) @ ssList ),
inference(simp,[status(thm)],[5448]) ).
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(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(5526,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf82 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[575,3695]) ).
thf(5527,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf82 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[5526]) ).
thf(5528,plain,
! [A: $i] : ( A @ skaf82 @ ( sk2 @ app ) @ ssList ),
inference(pattern_uni,[status(thm)],[5527:[bind(A,$thf( C )),bind(B,$thf( C @ skaf82 ))]]) ).
thf(5556,plain,
! [A: $i] : ( A @ skaf82 @ ( sk2 @ app ) @ ssList ),
inference(simp,[status(thm)],[5528]) ).
thf(5452,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf58 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[343,3695]) ).
thf(5453,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf58 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[5452]) ).
thf(5454,plain,
! [A: $i] : ( A @ skaf58 @ ( sk2 @ app ) @ ssList ),
inference(pattern_uni,[status(thm)],[5453:[bind(A,$thf( C )),bind(B,$thf( C @ skaf58 ))]]) ).
thf(5580,plain,
! [A: $i] : ( A @ skaf58 @ ( sk2 @ app ) @ ssList ),
inference(simp,[status(thm)],[5454]) ).
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(6813,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ app ) @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6469,3695]) ).
thf(6814,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ app ) @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[6813]) ).
thf(6815,plain,
sk1 @ ( sk2 @ app ) @ ( sk2 @ app ) @ ( sk2 @ app ) @ ssList,
inference(pattern_uni,[status(thm)],[6814:[bind(A,$thf( sk1 @ ( sk2 @ app ) @ ( sk2 @ app ) ))]]) ).
thf(2236,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[267,434]) ).
thf(2237,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[2236]) ).
thf(2238,plain,
! [A: $i] :
~ ( A @ skaf64 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[2237:[bind(A,$thf( C )),bind(B,$thf( C @ skaf64 ))]]) ).
thf(2257,plain,
! [A: $i] :
~ ( A @ skaf64 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[2238]) ).
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(2239,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[589,434]) ).
thf(2240,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[2239]) ).
thf(2241,plain,
! [A: $i] :
~ ( A @ skaf50 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[2240:[bind(A,$thf( C )),bind(B,$thf( C @ skaf50 ))]]) ).
thf(2246,plain,
! [A: $i] :
~ ( A @ skaf50 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[2241]) ).
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(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(316,plain,
! [B: $i,A: $i] :
( ( B @ singletonP )
| ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( nil @ ( A @ cons ) )
!= B ) ),
inference(cnf,[status(esa)],[315]) ).
thf(317,plain,
! [B: $i,A: $i] :
( ( B @ singletonP )
| ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( nil @ ( A @ cons ) )
!= B ) ),
inference(lifteq,[status(thm)],[316]) ).
thf(318,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ singletonP )
| ~ ( nil @ ( A @ cons ) @ ssList )
| ~ ( A @ ssItem ) ),
inference(simp,[status(thm)],[317]) ).
thf(302,plain,
! [A: $i] :
( ( ( A @ skaf53 @ ( A @ skaf50 @ cons ) @ ( A @ skaf52 @ ( A @ skaf49 @ cons ) @ ( A @ skaf51 @ app ) @ app ) )
= A )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[301]) ).
thf(303,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ~ ( A @ ssList )
| ( ( A @ skaf53 @ ( A @ skaf50 @ cons ) @ ( A @ skaf52 @ ( A @ skaf49 @ cons ) @ ( A @ skaf51 @ app ) @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[302]) ).
thf(14452,plain,
( ( ( sk2 @ tl @ ( sk2 @ tl @ neq ) )
!= ( nil @ ( sk1 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[667,13743]) ).
thf(14453,plain,
( ( sk2 @ tl @ ( sk2 @ tl @ neq ) )
!= ( nil @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[14452]) ).
thf(14471,plain,
( ( ( sk2 @ tl )
!= nil )
| ( ( sk2 @ tl )
!= sk1 ) ),
inference(simp,[status(thm)],[14453]) ).
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(5464,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf57 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[313,3695]) ).
thf(5465,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf57 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[5464]) ).
thf(5466,plain,
! [A: $i] : ( A @ skaf57 @ ( sk2 @ app ) @ ssList ),
inference(pattern_uni,[status(thm)],[5465:[bind(A,$thf( C )),bind(B,$thf( C @ skaf57 ))]]) ).
thf(5584,plain,
! [A: $i] : ( A @ skaf57 @ ( sk2 @ app ) @ ssList ),
inference(simp,[status(thm)],[5466]) ).
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(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(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(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(2413,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[609,434]) ).
thf(2414,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[2413]) ).
thf(2415,plain,
! [A: $i] :
~ ( A @ skaf78 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[2414:[bind(A,$thf( C )),bind(B,$thf( C @ skaf78 ))]]) ).
thf(2446,plain,
! [A: $i] :
~ ( A @ skaf78 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[2415]) ).
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(17198,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf80 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[432,288]) ).
thf(17199,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf80 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[17198]) ).
thf(17200,plain,
! [A: $i] : ( nil @ ( A @ skaf80 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[17199:[bind(A,$thf( C )),bind(B,$thf( C @ skaf80 ))]]) ).
thf(17248,plain,
! [A: $i] : ( nil @ ( A @ skaf80 @ rearsegP ) ),
inference(simp,[status(thm)],[17200]) ).
thf(2224,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[402,434]) ).
thf(2225,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[2224]) ).
thf(2226,plain,
! [A: $i] :
~ ( A @ skaf60 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[2225:[bind(A,$thf( C )),bind(B,$thf( C @ skaf60 ))]]) ).
thf(2252,plain,
! [A: $i] :
~ ( A @ skaf60 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[2226]) ).
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(5517,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf53 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[447,3695]) ).
thf(5518,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf53 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[5517]) ).
thf(5519,plain,
! [A: $i] : ( A @ skaf53 @ ( sk2 @ app ) @ ssList ),
inference(pattern_uni,[status(thm)],[5518:[bind(A,$thf( C )),bind(B,$thf( C @ skaf53 ))]]) ).
thf(5552,plain,
! [A: $i] : ( A @ skaf53 @ ( sk2 @ app ) @ ssList ),
inference(simp,[status(thm)],[5519]) ).
thf(5410,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf72 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[248,3695]) ).
thf(5411,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf72 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[5410]) ).
thf(5412,plain,
! [A: $i] : ( A @ skaf72 @ ( sk2 @ app ) @ ssList ),
inference(pattern_uni,[status(thm)],[5411:[bind(A,$thf( C )),bind(B,$thf( C @ skaf72 ))]]) ).
thf(5563,plain,
! [A: $i] : ( A @ skaf72 @ ( sk2 @ app ) @ ssList ),
inference(simp,[status(thm)],[5412]) ).
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(17101,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf75 @ ( sk2 @ app ) @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5557,288]) ).
thf(17102,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf75 @ ( sk2 @ app ) @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[17101]) ).
thf(17103,plain,
! [A: $i] : ( nil @ ( A @ skaf75 @ ( sk2 @ app ) @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[17102:[bind(A,$thf( E )),bind(B,$thf( E @ skaf75 @ ( sk2 @ app ) ))]]) ).
thf(17263,plain,
! [A: $i] : ( nil @ ( A @ skaf75 @ ( sk2 @ app ) @ rearsegP ) ),
inference(simp,[status(thm)],[17103]) ).
thf(17167,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[199,288]) ).
thf(17168,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[17167]) ).
thf(17169,plain,
nil @ ( sk1 @ rearsegP ),
inference(pattern_uni,[status(thm)],[17168:[bind(A,$thf( sk1 ))]]) ).
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(277,plain,
! [A: $i] :
( ( ( A @ skaf68 @ ( A @ skaf65 @ cons ) @ ( A @ skaf67 @ ( A @ skaf64 @ cons ) @ ( A @ skaf66 @ app ) @ app ) )
= A )
| ( A @ totalorderedP )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[276]) ).
thf(278,plain,
! [A: $i] :
( ( A @ totalorderedP )
| ~ ( A @ ssList )
| ( ( A @ skaf68 @ ( A @ skaf65 @ cons ) @ ( A @ skaf67 @ ( A @ skaf64 @ cons ) @ ( A @ skaf66 @ app ) @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[277]) ).
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(297,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(cnf,[status(esa)],[296]) ).
thf(298,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 )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) )
| ( ( E @ ( B @ cons ) @ ( D @ ( A @ cons ) @ ( C @ app ) @ app ) )
!= F ) ),
inference(lifteq,[status(thm)],[297]) ).
thf(299,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ cons ) @ ( D @ ( A @ cons ) @ ( C @ app ) @ app ) @ ssList )
| ~ ( E @ ( B @ cons ) @ ( D @ ( A @ cons ) @ ( C @ app ) @ app ) @ cyclefreeP )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssList )
| ~ ( D @ ssList )
| ~ ( E @ ssList )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[298]) ).
thf(650,plain,
! [A: $i] :
( ~ $true
| ( ( A @ ( sk2 @ segmentP ) )
!= ( A @ ( sk1 @ segmentP ) ) )
| ~ ( A @ ( sk1 @ segmentP ) )
| ~ ( nil @ ( A @ neq ) )
| ~ ( A @ ssList ) ),
inference(eqfactor_ordered,[status(thm)],[208]) ).
thf(652,plain,
! [A: $i] :
( ( A != A )
| ( sk2 != sk1 )
| ~ ( A @ ( sk1 @ segmentP ) )
| ~ ( nil @ ( A @ neq ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[650]) ).
thf(653,plain,
! [A: $i] :
( ( sk2 != sk1 )
| ~ ( A @ ( sk1 @ segmentP ) )
| ~ ( nil @ ( A @ neq ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[652]) ).
thf(6718,plain,
( ( ( sk2 @ ( sk2 @ app ) @ ( sk2 @ ( sk2 @ app ) @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[203,6409]) ).
thf(6719,plain,
( ( sk2 @ ( sk2 @ app ) @ ( sk2 @ ( sk2 @ app ) @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[6718]) ).
thf(6730,plain,
( ( ( sk2 @ ( sk2 @ app ) )
!= nil )
| ( ( sk2 @ ( sk2 @ app ) )
!= sk2 ) ),
inference(simp,[status(thm)],[6719]) ).
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(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(925,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[534,918]) ).
thf(926,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[925]) ).
thf(927,plain,
nil @ ( skac3 @ cons ) @ totalorderedP,
inference(pattern_uni,[status(thm)],[926:[bind(A,$thf( skac3 ))]]) ).
thf(919,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[249,918]) ).
thf(920,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[919]) ).
thf(921,plain,
! [A: $i] : ( nil @ ( A @ skaf79 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[920:[bind(A,$thf( C )),bind(B,$thf( C @ skaf79 ))]]) ).
thf(939,plain,
! [A: $i] : ( nil @ ( A @ skaf79 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[921]) ).
thf(17210,plain,
! [A: $i] :
( ( ( nil @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[283,288]) ).
thf(17211,plain,
! [A: $i] :
( ( ( nil @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[17210]) ).
thf(17212,plain,
nil @ ( nil @ rearsegP ),
inference(pattern_uni,[status(thm)],[17211:[bind(A,$thf( nil ))]]) ).
thf(17074,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf67 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[493,288]) ).
thf(17075,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf67 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[17074]) ).
thf(17076,plain,
! [A: $i] : ( nil @ ( A @ skaf67 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[17075:[bind(A,$thf( C )),bind(B,$thf( C @ skaf67 ))]]) ).
thf(17251,plain,
! [A: $i] : ( nil @ ( A @ skaf67 @ rearsegP ) ),
inference(simp,[status(thm)],[17076]) ).
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(17128,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf61 @ ( sk2 @ app ) @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5578,288]) ).
thf(17129,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf61 @ ( sk2 @ app ) @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[17128]) ).
thf(17130,plain,
! [A: $i] : ( nil @ ( A @ skaf61 @ ( sk2 @ app ) @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[17129:[bind(A,$thf( E )),bind(B,$thf( E @ skaf61 @ ( sk2 @ app ) ))]]) ).
thf(17268,plain,
! [A: $i] : ( nil @ ( A @ skaf61 @ ( sk2 @ app ) @ rearsegP ) ),
inference(simp,[status(thm)],[17130]) ).
thf(17110,plain,
! [A: $i] :
( ( ( nil @ ( sk2 @ app ) @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6561,288]) ).
thf(17111,plain,
! [A: $i] :
( ( ( nil @ ( sk2 @ app ) @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[17110]) ).
thf(17112,plain,
nil @ ( nil @ ( sk2 @ app ) @ ( sk2 @ app ) @ rearsegP ),
inference(pattern_uni,[status(thm)],[17111:[bind(A,$thf( nil @ ( sk2 @ app ) @ ( sk2 @ app ) ))]]) ).
thf(2203,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[249,434]) ).
thf(2204,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[2203]) ).
thf(2205,plain,
! [A: $i] :
~ ( A @ skaf79 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[2204:[bind(A,$thf( C )),bind(B,$thf( C @ skaf79 ))]]) ).
thf(2256,plain,
! [A: $i] :
~ ( A @ skaf79 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[2205]) ).
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(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(14773,plain,
( ( ( sk2 @ tl )
!= ( sk2 @ tl ) )
| ( nil != nil )
| ( ( sk2 @ tl )
!= sk1 )
| ( sk2 @ tl @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[13678,14471]) ).
thf(14774,plain,
( ( ( sk2 @ tl )
!= ( sk2 @ tl ) )
| ( ( sk2 @ tl )
!= sk1 )
| ( sk2 @ tl @ tl @ ssList ) ),
inference(simp,[status(thm)],[14773]) ).
thf(14775,plain,
( ( ( sk2 @ tl )
!= sk1 )
| ( sk2 @ tl @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[14774:[]]) ).
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(949,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[391,918]) ).
thf(950,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[949]) ).
thf(951,plain,
! [A: $i] : ( nil @ ( A @ skaf55 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[950:[bind(A,$thf( C )),bind(B,$thf( C @ skaf55 ))]]) ).
thf(954,plain,
! [A: $i] : ( nil @ ( A @ skaf55 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[951]) ).
thf(15064,plain,
( ( ( skac3 @ ( skac3 @ neq ) )
!= ( nil @ ( sk1 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[667,14994]) ).
thf(15065,plain,
( ( skac3 @ ( skac3 @ neq ) )
!= ( nil @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[15064]) ).
thf(15075,plain,
( ( skac3 != nil )
| ( skac3 != sk1 ) ),
inference(simp,[status(thm)],[15065]) ).
thf(17083,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf81 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[499,288]) ).
thf(17084,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf81 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[17083]) ).
thf(17085,plain,
! [A: $i] : ( nil @ ( A @ skaf81 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[17084:[bind(A,$thf( C )),bind(B,$thf( C @ skaf81 ))]]) ).
thf(17255,plain,
! [A: $i] : ( nil @ ( A @ skaf81 @ rearsegP ) ),
inference(simp,[status(thm)],[17085]) ).
thf(3638,plain,
! [A: $i] :
( ( ( A @ skaf77 @ ( A @ skaf77 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[203,1230]) ).
thf(3639,plain,
! [A: $i] :
( ( A @ skaf77 @ ( A @ skaf77 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[3638]) ).
thf(3642,plain,
! [A: $i] :
( ( ( A @ skaf77 )
!= nil )
| ( ( A @ skaf77 )
!= sk2 ) ),
inference(simp,[status(thm)],[3639]) ).
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(2456,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[631,434]) ).
thf(2457,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[2456]) ).
thf(2458,plain,
! [A: $i] :
~ ( A @ skaf59 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[2457:[bind(A,$thf( C )),bind(B,$thf( C @ skaf59 ))]]) ).
thf(2486,plain,
! [A: $i] :
~ ( A @ skaf59 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[2458]) ).
thf(2075,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[579,918]) ).
thf(2076,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[2075]) ).
thf(2077,plain,
! [A: $i] : ( nil @ ( A @ skaf65 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[2076:[bind(A,$thf( C )),bind(B,$thf( C @ skaf65 ))]]) ).
thf(2092,plain,
! [A: $i] : ( nil @ ( A @ skaf65 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[2077]) ).
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(3652,plain,
! [A: $i] :
( ( ( A @ skaf75 @ ( A @ skaf75 @ neq ) )
!= ( nil @ ( sk1 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[667,1231]) ).
thf(3653,plain,
! [A: $i] :
( ( A @ skaf75 @ ( A @ skaf75 @ neq ) )
!= ( nil @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[3652]) ).
thf(3655,plain,
! [A: $i] :
( ( ( A @ skaf75 )
!= nil )
| ( ( A @ skaf75 )
!= sk1 ) ),
inference(simp,[status(thm)],[3653]) ).
thf(1193,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf72 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[248,232]) ).
thf(1194,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf72 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1193]) ).
thf(1195,plain,
! [A: $i] :
~ ( A @ skaf72 @ ( A @ skaf72 @ neq ) ),
inference(pattern_uni,[status(thm)],[1194:[bind(A,$thf( C )),bind(B,$thf( C @ skaf72 ))]]) ).
thf(1235,plain,
! [A: $i] :
~ ( A @ skaf72 @ ( A @ skaf72 @ neq ) ),
inference(simp,[status(thm)],[1195]) ).
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(2209,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[357,434]) ).
thf(2210,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[2209]) ).
thf(2211,plain,
! [A: $i] :
~ ( A @ skaf44 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[2210:[bind(A,$thf( C )),bind(B,$thf( C @ skaf44 ))]]) ).
thf(2247,plain,
! [A: $i] :
~ ( A @ skaf44 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[2211]) ).
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(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(17098,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf56 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[586,288]) ).
thf(17099,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf56 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[17098]) ).
thf(17100,plain,
! [A: $i] : ( nil @ ( A @ skaf56 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[17099:[bind(A,$thf( C )),bind(B,$thf( C @ skaf56 ))]]) ).
thf(17262,plain,
! [A: $i] : ( nil @ ( A @ skaf56 @ rearsegP ) ),
inference(simp,[status(thm)],[17100]) ).
thf(17042,plain,
! [A: $i] :
( ( ( sk1 @ tl @ ( sk2 @ app ) @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14533,288]) ).
thf(17043,plain,
! [A: $i] :
( ( ( sk1 @ tl @ ( sk2 @ app ) @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[17042]) ).
thf(17044,plain,
nil @ ( sk1 @ tl @ ( sk2 @ app ) @ ( sk2 @ app ) @ rearsegP ),
inference(pattern_uni,[status(thm)],[17043:[bind(A,$thf( sk1 @ tl @ ( sk2 @ app ) @ ( 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(1871,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[574,918]) ).
thf(1872,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[1871]) ).
thf(1873,plain,
! [A: $i] : ( nil @ ( A @ skaf74 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[1872:[bind(A,$thf( C )),bind(B,$thf( C @ skaf74 ))]]) ).
thf(1881,plain,
! [A: $i] : ( nil @ ( A @ skaf74 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[1873]) ).
thf(1202,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf61 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[398,232]) ).
thf(1203,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf61 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1202]) ).
thf(1204,plain,
! [A: $i] :
~ ( A @ skaf61 @ ( A @ skaf61 @ neq ) ),
inference(pattern_uni,[status(thm)],[1203:[bind(A,$thf( C )),bind(B,$thf( C @ skaf61 ))]]) ).
thf(1240,plain,
! [A: $i] :
~ ( A @ skaf61 @ ( A @ skaf61 @ neq ) ),
inference(simp,[status(thm)],[1204]) ).
thf(17195,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf77 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[300,288]) ).
thf(17196,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf77 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[17195]) ).
thf(17197,plain,
! [A: $i] : ( nil @ ( A @ skaf77 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[17196:[bind(A,$thf( C )),bind(B,$thf( C @ skaf77 ))]]) ).
thf(17247,plain,
! [A: $i] : ( nil @ ( A @ skaf77 @ rearsegP ) ),
inference(simp,[status(thm)],[17197]) ).
thf(1078,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[402,918]) ).
thf(1079,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[1078]) ).
thf(1080,plain,
! [A: $i] : ( nil @ ( A @ skaf60 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[1079:[bind(A,$thf( C )),bind(B,$thf( C @ skaf60 ))]]) ).
thf(1084,plain,
! [A: $i] : ( nil @ ( A @ skaf60 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[1080]) ).
thf(15088,plain,
( ( ( skac2 @ ( skac2 @ neq ) )
!= ( nil @ ( sk1 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[667,15018]) ).
thf(15089,plain,
( ( skac2 @ ( skac2 @ neq ) )
!= ( nil @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[15088]) ).
thf(15099,plain,
( ( skac2 != nil )
| ( skac2 != sk1 ) ),
inference(simp,[status(thm)],[15089]) ).
thf(17119,plain,
! [A: $i] :
( ( ( sk1 @ tl @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13809,288]) ).
thf(17120,plain,
! [A: $i] :
( ( ( sk1 @ tl @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[17119]) ).
thf(17121,plain,
nil @ ( sk1 @ tl @ ( sk2 @ app ) @ rearsegP ),
inference(pattern_uni,[status(thm)],[17120:[bind(A,$thf( sk1 @ tl @ ( sk2 @ app ) ))]]) ).
thf(29752,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[521,324]) ).
thf(29753,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[29752]) ).
thf(29754,plain,
nil @ ( skac2 @ cons ) @ strictorderedP,
inference(pattern_uni,[status(thm)],[29753:[bind(A,$thf( skac2 ))]]) ).
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(17086,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5497,288]) ).
thf(17087,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[17086]) ).
thf(17088,plain,
nil @ ( sk1 @ ( sk2 @ app ) @ rearsegP ),
inference(pattern_uni,[status(thm)],[17087:[bind(A,$thf( sk1 @ ( sk2 @ app ) ))]]) ).
thf(17054,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf72 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[248,288]) ).
thf(17055,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf72 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[17054]) ).
thf(17056,plain,
! [A: $i] : ( nil @ ( A @ skaf72 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[17055:[bind(A,$thf( C )),bind(B,$thf( C @ skaf72 ))]]) ).
thf(17237,plain,
! [A: $i] : ( nil @ ( A @ skaf72 @ rearsegP ) ),
inference(simp,[status(thm)],[17056]) ).
thf(17092,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf71 @ ( sk2 @ app ) @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5571,288]) ).
thf(17093,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf71 @ ( sk2 @ app ) @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[17092]) ).
thf(17094,plain,
! [A: $i] : ( nil @ ( A @ skaf71 @ ( sk2 @ app ) @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[17093:[bind(A,$thf( E )),bind(B,$thf( E @ skaf71 @ ( sk2 @ app ) ))]]) ).
thf(17259,plain,
! [A: $i] : ( nil @ ( A @ skaf71 @ ( sk2 @ app ) @ rearsegP ) ),
inference(simp,[status(thm)],[17094]) ).
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(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(17045,plain,
! [A: $i] :
( ( ( sk2 @ tl @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13708,288]) ).
thf(17046,plain,
! [A: $i] :
( ( ( sk2 @ tl @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[17045]) ).
thf(17047,plain,
nil @ ( sk2 @ tl @ ( sk2 @ app ) @ rearsegP ),
inference(pattern_uni,[status(thm)],[17046:[bind(A,$thf( sk2 @ tl @ ( sk2 @ app ) ))]]) ).
thf(2221,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[423,434]) ).
thf(2222,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[2221]) ).
thf(2223,plain,
! [A: $i] :
~ ( A @ skaf49 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[2222:[bind(A,$thf( C )),bind(B,$thf( C @ skaf49 ))]]) ).
thf(2251,plain,
! [A: $i] :
~ ( A @ skaf49 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[2223]) ).
thf(17164,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf68 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[470,288]) ).
thf(17165,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf68 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[17164]) ).
thf(17166,plain,
! [A: $i] : ( nil @ ( A @ skaf68 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[17165:[bind(A,$thf( C )),bind(B,$thf( C @ skaf68 ))]]) ).
thf(17230,plain,
! [A: $i] : ( nil @ ( A @ skaf68 @ rearsegP ) ),
inference(simp,[status(thm)],[17166]) ).
thf(258,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ geq ) ) ),
inference(cnf,[status(esa)],[257]) ).
thf(17018,plain,
! [A: $i] :
( ( ( sk2 @ tl @ ( sk2 @ app ) @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14382,288]) ).
thf(17019,plain,
! [A: $i] :
( ( ( sk2 @ tl @ ( sk2 @ app ) @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[17018]) ).
thf(17020,plain,
nil @ ( sk2 @ tl @ ( sk2 @ app ) @ ( sk2 @ app ) @ rearsegP ),
inference(pattern_uni,[status(thm)],[17019:[bind(A,$thf( sk2 @ tl @ ( sk2 @ app ) @ ( sk2 @ app ) ))]]) ).
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(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(22980,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( nil @ rearsegP ) )
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[202,306]) ).
thf(22981,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ rearsegP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[22980]) ).
thf(22982,plain,
( ~ ( sk2 @ ( nil @ rearsegP ) )
| ( nil = sk2 ) ),
inference(pattern_uni,[status(thm)],[22981:[bind(A,$thf( sk2 ))]]) ).
thf(25342,plain,
~ ( sk2 @ ( nil @ rearsegP ) ),
inference(simplifyReflect,[status(thm)],[22982,1249]) ).
thf(17158,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf51 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[531,288]) ).
thf(17159,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf51 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[17158]) ).
thf(17160,plain,
! [A: $i] : ( nil @ ( A @ skaf51 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[17159:[bind(A,$thf( C )),bind(B,$thf( C @ skaf51 ))]]) ).
thf(17227,plain,
! [A: $i] : ( nil @ ( A @ skaf51 @ rearsegP ) ),
inference(simp,[status(thm)],[17160]) ).
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(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(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(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(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(1438,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf67 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[493,232]) ).
thf(1439,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf67 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1438]) ).
thf(1440,plain,
! [A: $i] :
~ ( A @ skaf67 @ ( A @ skaf67 @ neq ) ),
inference(pattern_uni,[status(thm)],[1439:[bind(A,$thf( C )),bind(B,$thf( C @ skaf67 ))]]) ).
thf(1444,plain,
! [A: $i] :
~ ( A @ skaf67 @ ( A @ skaf67 @ neq ) ),
inference(simp,[status(thm)],[1440]) ).
thf(14573,plain,
! [A: $i] :
( ( ( sk1 @ tl @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[13809,232]) ).
thf(14574,plain,
! [A: $i] :
( ( ( sk1 @ tl @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[14573]) ).
thf(14575,plain,
~ ( sk1 @ tl @ ( sk2 @ app ) @ ( sk1 @ tl @ ( sk2 @ app ) @ neq ) ),
inference(pattern_uni,[status(thm)],[14574:[bind(A,$thf( sk1 @ tl @ ( sk2 @ app ) ))]]) ).
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(17173,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf66 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[539,288]) ).
thf(17174,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf66 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[17173]) ).
thf(17175,plain,
! [A: $i] : ( nil @ ( A @ skaf66 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[17174:[bind(A,$thf( C )),bind(B,$thf( C @ skaf66 ))]]) ).
thf(17233,plain,
! [A: $i] : ( nil @ ( A @ skaf66 @ rearsegP ) ),
inference(simp,[status(thm)],[17175]) ).
thf(1943,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[578,918]) ).
thf(1944,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[1943]) ).
thf(1945,plain,
! [A: $i] : ( nil @ ( A @ skaf54 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[1944:[bind(A,$thf( C )),bind(B,$thf( C @ skaf54 ))]]) ).
thf(1957,plain,
! [A: $i] : ( nil @ ( A @ skaf54 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[1945]) ).
thf(2200,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[390,434]) ).
thf(2201,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[2200]) ).
thf(2202,plain,
! [A: $i] :
~ ( A @ skaf69 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[2201:[bind(A,$thf( C )),bind(B,$thf( C @ skaf69 ))]]) ).
thf(2255,plain,
! [A: $i] :
~ ( A @ skaf69 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[2202]) ).
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(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(2515,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ singletonP )
| ( ( nil @ ( A @ skaf44 @ cons ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[202,244]) ).
thf(2516,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ singletonP )
| ( ( nil @ ( A @ skaf44 @ cons ) )
= A ) ),
inference(simp,[status(thm)],[2515]) ).
thf(2517,plain,
( ~ ( sk2 @ singletonP )
| ( ( nil @ ( sk2 @ skaf44 @ cons ) )
= sk2 ) ),
inference(pattern_uni,[status(thm)],[2516:[bind(A,$thf( sk2 ))]]) ).
thf(2681,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(2682,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ duplicatefreeP )
| ( ( A @ skaf77 @ ( A @ skaf74 @ cons ) @ ( A @ skaf76 @ ( A @ skaf74 @ cons ) @ ( A @ skaf75 @ app ) @ app ) )
= A ) ),
inference(simp,[status(thm)],[2681]) ).
thf(2683,plain,
( ( sk2 @ duplicatefreeP )
| ( ( sk2 @ skaf77 @ ( sk2 @ skaf74 @ cons ) @ ( sk2 @ skaf76 @ ( sk2 @ skaf74 @ cons ) @ ( sk2 @ skaf75 @ app ) @ app ) )
= sk2 ) ),
inference(pattern_uni,[status(thm)],[2682:[bind(A,$thf( sk2 ))]]) ).
thf(22880,plain,
! [A: $i] :
( ( ( skac3 @ tl @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) )
| ( skac3 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[22748,232]) ).
thf(22881,plain,
! [A: $i] :
( ( ( skac3 @ tl @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ( skac3 != sk2 ) ),
inference(simp,[status(thm)],[22880]) ).
thf(22882,plain,
( ~ ( skac3 @ tl @ ( skac3 @ tl @ neq ) )
| ( skac3 != sk2 ) ),
inference(pattern_uni,[status(thm)],[22881:[bind(A,$thf( skac3 @ tl ))]]) ).
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(17204,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf53 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[447,288]) ).
thf(17205,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf53 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[17204]) ).
thf(17206,plain,
! [A: $i] : ( nil @ ( A @ skaf53 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[17205:[bind(A,$thf( C )),bind(B,$thf( C @ skaf53 ))]]) ).
thf(17252,plain,
! [A: $i] : ( nil @ ( A @ skaf53 @ rearsegP ) ),
inference(simp,[status(thm)],[17206]) ).
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(293,plain,
! [A: $i] :
( ( ( A @ skaf63 @ ( A @ skaf60 @ cons ) @ ( A @ skaf62 @ ( A @ skaf59 @ cons ) @ ( A @ skaf61 @ app ) @ app ) )
= A )
| ( A @ strictorderP )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[292]) ).
thf(294,plain,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ ssList )
| ( ( A @ skaf63 @ ( A @ skaf60 @ cons ) @ ( A @ skaf62 @ ( A @ skaf59 @ cons ) @ ( A @ skaf61 @ app ) @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[293]) ).
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(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(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(2470,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[631,918]) ).
thf(2471,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[2470]) ).
thf(2472,plain,
! [A: $i] : ( nil @ ( A @ skaf59 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[2471:[bind(A,$thf( C )),bind(B,$thf( C @ skaf59 ))]]) ).
thf(2485,plain,
! [A: $i] : ( nil @ ( A @ skaf59 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[2472]) ).
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(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(2147,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[589,918]) ).
thf(2148,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[2147]) ).
thf(2149,plain,
! [A: $i] : ( nil @ ( A @ skaf50 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[2148:[bind(A,$thf( C )),bind(B,$thf( C @ skaf50 ))]]) ).
thf(2159,plain,
! [A: $i] : ( nil @ ( A @ skaf50 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[2149]) ).
thf(2638,plain,
! [A: $i] :
( ( ( nil @ ( sk2 @ skaf44 @ cons ) )
!= ( nil @ ( A @ cons ) ) )
| ( sk2 @ totalorderedP )
| ~ ( A @ ssItem )
| ~ ( sk2 @ singletonP ) ),
inference(paramod_ordered,[status(thm)],[2517,918]) ).
thf(2639,plain,
( ( sk2 @ totalorderedP )
| ~ ( sk2 @ skaf44 @ ssItem )
| ~ ( sk2 @ singletonP ) ),
inference(pattern_uni,[status(thm)],[2638:[bind(A,$thf( sk2 @ skaf44 ))]]) ).
thf(2809,plain,
( ( sk2 @ totalorderedP )
| ~ $true
| ~ ( sk2 @ singletonP ) ),
inference(rewrite,[status(thm)],[2639,357]) ).
thf(2810,plain,
( ( sk2 @ totalorderedP )
| ~ ( sk2 @ singletonP ) ),
inference(simp,[status(thm)],[2809]) ).
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(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(6720,plain,
( ( ( sk2 @ ( sk2 @ app ) @ ( sk2 @ ( sk2 @ app ) @ neq ) )
!= ( nil @ ( sk1 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[667,6409]) ).
thf(6721,plain,
( ( sk2 @ ( sk2 @ app ) @ ( sk2 @ ( sk2 @ app ) @ neq ) )
!= ( nil @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[6720]) ).
thf(6733,plain,
( ( ( sk2 @ ( sk2 @ app ) )
!= nil )
| ( ( sk2 @ ( sk2 @ app ) )
!= sk1 ) ),
inference(simp,[status(thm)],[6721]) ).
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(17213,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf82 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[575,288]) ).
thf(17214,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf82 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[17213]) ).
thf(17215,plain,
! [A: $i] : ( nil @ ( A @ skaf82 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[17214:[bind(A,$thf( C )),bind(B,$thf( C @ skaf82 ))]]) ).
thf(17256,plain,
! [A: $i] : ( nil @ ( A @ skaf82 @ rearsegP ) ),
inference(simp,[status(thm)],[17215]) ).
thf(17033,plain,
! [A: $i] :
( ( ( sk2 @ tl @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13658,288]) ).
thf(17034,plain,
! [A: $i] :
( ( ( sk2 @ tl @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[17033]) ).
thf(17035,plain,
nil @ ( sk2 @ tl @ rearsegP ),
inference(pattern_uni,[status(thm)],[17034:[bind(A,$thf( sk2 @ tl ))]]) ).
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(14601,plain,
( ( ( sk1 @ tl @ ( sk1 @ tl @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[203,13838]) ).
thf(14602,plain,
( ( sk1 @ tl @ ( sk1 @ tl @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[14601]) ).
thf(14621,plain,
( ( ( sk1 @ tl )
!= nil )
| ( ( sk1 @ tl )
!= sk2 ) ),
inference(simp,[status(thm)],[14602]) ).
thf(320,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ rearsegP ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( B @ ( A @ app ) )
!= C ) ),
inference(cnf,[status(esa)],[319]) ).
thf(321,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ rearsegP ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( B @ ( A @ app ) )
!= C ) ),
inference(lifteq,[status(thm)],[320]) ).
thf(322,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ app ) @ rearsegP ) )
| ~ ( B @ ( A @ app ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[321]) ).
thf(1502,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf52 @ ssList )
!= ( B @ ssList ) )
| ( sk2 != sk1 )
| ~ ( B @ ( sk1 @ segmentP ) )
| ~ ( nil @ ( B @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[481,653]) ).
thf(1503,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf52 @ ssList )
!= ( B @ ssList ) )
| ( sk2 != sk1 )
| ~ ( B @ ( sk1 @ segmentP ) )
| ~ ( nil @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1502]) ).
thf(1504,plain,
! [A: $i] :
( ( sk2 != sk1 )
| ~ ( A @ skaf52 @ ( sk1 @ segmentP ) )
| ~ ( nil @ ( A @ skaf52 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[1503:[bind(A,$thf( C )),bind(B,$thf( C @ skaf52 ))]]) ).
thf(1565,plain,
! [A: $i] :
( ( sk2 != sk1 )
| ~ ( A @ skaf52 @ ( sk1 @ segmentP ) )
| ~ ( nil @ ( A @ skaf52 @ neq ) ) ),
inference(simp,[status(thm)],[1504]) ).
thf(222,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ geq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnf,[status(esa)],[221]) ).
thf(39801,plain,
$false,
inference(e,[status(thm)],[25953,5561,5593,234,17226,628,249,481,2250,408,15098,17278,17014,2248,741,449,247,1971,269,217,276,202,597,5550,17253,384,14382,500,1233,340,538,930,6655,13779,472,17243,5393,288,29708,301,257,6754,565,13658,570,504,17234,2217,587,344,357,460,421,284,416,325,289,448,7464,261,1847,969,606,228,29788,1232,25217,2007,216,14533,238,514,353,1283,1109,17238,211,253,17266,937,574,2254,13708,221,453,6498,396,14622,411,312,660,13757,1242,265,206,13838,307,292,233,248,6760,439,270,17257,546,201,381,17242,534,220,366,2249,392,424,630,275,349,5579,10102,429,25976,229,252,197,625,435,329,551,17032,456,324,17245,467,2445,522,15018,583,493,1210,29789,2245,1234,17274,1227,17264,403,10021,593,610,420,499,5497,17225,578,488,554,1461,476,526,590,3643,471,256,637,17218,5547,489,17118,2349,622,3654,1249,2304,7463,1231,15074,22937,7385,17228,3628,14424,244,938,205,311,17261,5571,17029,586,662,17235,6409,5557,343,237,1241,266,398,17250,2235,618,17050,2253,22763,6561,375,601,279,6469,5525,296,22248,423,14994,286,2568,13809,17273,204,1256,259,17231,402,743,14792,579,291,391,445,313,3695,335,236,1428,17115,17209,1239,17260,5578,540,5556,5580,604,219,6815,2257,2246,362,318,434,303,208,599,245,14471,387,5584,494,631,535,609,594,2446,483,240,17248,2252,198,462,5552,5563,477,17263,323,17169,521,399,278,223,306,563,299,267,241,653,6730,658,5587,426,589,531,548,927,255,487,939,17212,5548,17251,617,17268,17112,2256,14470,5570,557,580,295,14775,282,414,954,1230,310,15075,17255,3642,370,2486,199,2092,331,1186,3655,1235,470,576,2247,613,600,17262,17044,314,571,1881,1240,250,17247,1084,15099,17121,5573,29754,368,17088,17237,539,17259,482,203,319,17047,2251,17230,304,258,17020,390,632,418,25342,17227,517,568,378,235,207,667,5549,272,383,5590,346,1444,14575,287,433,510,17233,300,1957,2255,432,262,5554,405,273,373,2517,2683,447,315,22882,326,358,437,17252,6380,635,532,283,239,242,294,918,506,268,474,6590,395,728,332,575,2485,528,200,13678,442,2159,2810,464,5591,337,940,6733,543,560,17256,17035,496,254,227,14621,322,309,1565,222,22748,13743,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC089-1 : 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
% 0.13/5.41 % Computer : n006.cluster.edu
% 0.13/5.41 % Model : x86_64 x86_64
% 0.13/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.41 % Memory : 8046.5625MB
% 0.13/5.41 % OS : Linux 6.8.0-71-generic
% 0.13/5.41 % CPULimit : 300
% 0.13/5.41 % WCLimit : 300
% 0.13/5.41 % DateTime : Sat Sep 26 12:13:52 UTC 2026
% 0.13/5.41 % CPUTime :
% 0.13/5.41 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
% 0.17/5.97 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.46/6.26 % [INFO] Parsing done (281ms).
% 1.46/6.27 % [INFO] Running in sequential loop mode.
% 2.47/6.67 % [INFO] eprover registered as external prover.
% 2.47/6.68 % [INFO] Scanning for conjecture ...
% 2.94/6.83 % [INFO] Found a conjecture (or negated_conjecture) and 185 axioms. Running axiom selection ...
% 3.13/6.97 % [INFO] Axiom selection finished. Selected 185 axioms (removed 0 axioms).
% 3.53/7.11 % [INFO] Problem is propositional (TPTP CNF).
% 3.53/7.12 % [INFO] Type checking passed.
% 3.79/7.13 % [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 ...
% 94.75/28.07 % External prover 'e' found a proof!
% 94.75/28.07 % [INFO] Killing All external provers ...
% 94.75/28.08 % Time passed: 22535ms (effective reasoning time: 21798ms)
% 95.47/28.08 % 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
% 95.47/28.08 % No. of inferences in proof: 1195
% 95.47/28.08 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 22535 ms resp. 21798 ms w/o parsing
% 98.06/28.51 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 98.06/28.52 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------