%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWC382-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:53:34 AM UTC 2026
% Result : Unsatisfiable 104.16s 21.33s
% Output : Refutation 105.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 197
% Syntax : Number of formulae : 883 ( 298 unt; 0 typ; 0 def)
% Number of atoms : 2813 ( 546 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 7843 (1633 ~;1458 |; 0 &;4752 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 75 ( 72 usr; 9 con; 0-2 aty)
% Number of variables : 1250 ( 0 ^;1250 !; 0 ?;1250 :)
% 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(ssItem_decl,type,
ssItem: $i > $o ).
thf(cons_decl,type,
cons: $i > $i > $i ).
thf(hd_decl,type,
hd: $i > $i ).
thf(singletonP_decl,type,
singletonP: $i > $o ).
thf(segmentP_decl,type,
segmentP: $i > $i > $o ).
thf(skac3_decl,type,
skac3: $i ).
thf(skac2_decl,type,
skac2: $i ).
thf(skaf43_decl,type,
skaf43: $i > $i > $i ).
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(geq_decl,type,
geq: $i > $i > $o ).
thf(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(app_decl,type,
app: $i > $i > $i ).
thf(skaf69_decl,type,
skaf69: $i > $i ).
thf(skaf70_decl,type,
skaf70: $i > $i ).
thf(strictorderedP_decl,type,
strictorderedP: $i > $o ).
thf(cyclefreeP_decl,type,
cyclefreeP: $i > $o ).
thf(skaf49_decl,type,
skaf49: $i > $i ).
thf(skaf50_decl,type,
skaf50: $i > $i ).
thf(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(tl_decl,type,
tl: $i > $i ).
thf(skaf66_decl,type,
skaf66: $i > $i ).
thf(skaf67_decl,type,
skaf67: $i > $i ).
thf(skaf65_decl,type,
skaf65: $i > $i ).
thf(skaf68_decl,type,
skaf68: $i > $i ).
thf(skaf45_decl,type,
skaf45: $i > $i > $i ).
thf(rearsegP_decl,type,
rearsegP: $i > $i > $o ).
thf(strictorderP_decl,type,
strictorderP: $i > $o ).
thf(skaf61_decl,type,
skaf61: $i > $i ).
thf(skaf59_decl,type,
skaf59: $i > $i ).
thf(skaf60_decl,type,
skaf60: $i > $i ).
thf(skaf63_decl,type,
skaf63: $i > $i ).
thf(skaf51_decl,type,
skaf51: $i > $i ).
thf(skaf52_decl,type,
skaf52: $i > $i ).
thf(skaf53_decl,type,
skaf53: $i > $i ).
thf(skaf57_decl,type,
skaf57: $i > $i ).
thf(equalelemsP_decl,type,
equalelemsP: $i > $o ).
thf(totalorderP_decl,type,
totalorderP: $i > $o ).
thf(skaf56_decl,type,
skaf56: $i > $i ).
thf(skaf54_decl,type,
skaf54: $i > $i ).
thf(skaf55_decl,type,
skaf55: $i > $i ).
thf(skaf58_decl,type,
skaf58: $i > $i ).
thf(skaf48_decl,type,
skaf48: $i > $i > $i ).
thf(skaf80_decl,type,
skaf80: $i > $i ).
thf(skaf47_decl,type,
skaf47: $i > $i > $i ).
thf(skaf78_decl,type,
skaf78: $i > $i ).
thf(skaf81_decl,type,
skaf81: $i > $i ).
thf(skaf83_decl,type,
skaf83: $i > $i ).
thf(skaf82_decl,type,
skaf82: $i > $i ).
thf(skaf42_decl,type,
skaf42: $i > $i > $i ).
thf(191,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(629,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)],[191]) ).
thf(2,negated_conjecture,
sk2 @ ssList,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_2) ).
thf(203,plain,
sk2 @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(22,axiom,
! [A: $i] :
( ( A @ strictorderedP )
| ~ ( A @ ssList )
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause90) ).
thf(242,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ~ ( A @ ssList )
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(243,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ~ ( A @ ssList )
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
inference(cnf,[status(esa)],[242]) ).
thf(1821,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ~ $true
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[203,243]) ).
thf(1822,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
inference(simp,[status(thm)],[1821]) ).
thf(1823,plain,
( ( sk2 @ strictorderedP )
| ~ ( sk2 @ skaf70 @ ( sk2 @ skaf69 @ lt ) ) ),
inference(pattern_uni,[status(thm)],[1822:[bind(A,$thf( sk2 ))]]) ).
thf(169,axiom,
! [A: $i] : ( A @ skaf54 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause41) ).
thf(582,plain,
! [A: $i] : ( A @ skaf54 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(107,axiom,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( nil @ memberP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause71) ).
thf(437,plain,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(438,plain,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(cnf,[status(esa)],[437]) ).
thf(1997,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[582,438]) ).
thf(1998,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1997]) ).
thf(1999,plain,
! [A: $i] :
~ ( A @ skaf54 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1998:[bind(A,$thf( C )),bind(B,$thf( C @ skaf54 ))]]) ).
thf(2031,plain,
! [A: $i] :
~ ( A @ skaf54 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1999]) ).
thf(67,axiom,
! [A: $i] : ( A @ skaf58 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause37) ).
thf(347,plain,
! [A: $i] : ( A @ skaf58 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(48,axiom,
! [A: $i] : ( A @ skaf77 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause18) ).
thf(304,plain,
! [A: $i] : ( A @ skaf77 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause115) ).
thf(233,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(234,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(cnf,[status(esa)],[233]) ).
thf(235,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[234]) ).
thf(236,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[235]) ).
thf(842,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf77 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[304,236]) ).
thf(843,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf77 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[842]) ).
thf(844,plain,
! [A: $i] :
~ ( A @ skaf77 @ ( A @ skaf77 @ neq ) ),
inference(pattern_uni,[status(thm)],[843:[bind(A,$thf( C )),bind(B,$thf( C @ skaf77 ))]]) ).
thf(846,plain,
! [A: $i] :
~ ( A @ skaf77 @ ( A @ skaf77 @ neq ) ),
inference(simp,[status(thm)],[844]) ).
thf(141,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(518,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)],[141]) ).
thf(157,axiom,
! [A: $i] :
( ( nil = A )
| ( ( A @ skaf82 @ ( A @ skaf83 @ cons ) )
= A )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause109) ).
thf(555,plain,
! [A: $i] :
( ( nil = A )
| ( ( A @ skaf82 @ ( A @ skaf83 @ cons ) )
= A )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(127,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(481,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)],[127]) ).
thf(61,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ gt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause105) ).
thf(333,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ gt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(25,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(249,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)],[25]) ).
thf(1,negated_conjecture,
sk1 @ ssList,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
thf(200,plain,
sk1 @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(24,axiom,
! [A: $i] :
( ( ( nil @ ( A @ skaf44 @ cons ) )
= A )
| ~ ( A @ ssList )
| ~ ( A @ singletonP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause101) ).
thf(246,plain,
! [A: $i] :
( ( ( nil @ ( A @ skaf44 @ cons ) )
= A )
| ~ ( A @ ssList )
| ~ ( A @ singletonP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(247,plain,
! [A: $i] :
( ( ( nil @ ( A @ skaf44 @ cons ) )
= A )
| ~ ( A @ ssList )
| ~ ( A @ singletonP ) ),
inference(cnf,[status(esa)],[246]) ).
thf(248,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ~ ( A @ singletonP )
| ( ( nil @ ( A @ skaf44 @ cons ) )
= A ) ),
inference(lifteq,[status(thm)],[247]) ).
thf(2478,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ singletonP )
| ( ( nil @ ( A @ skaf44 @ cons ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[200,248]) ).
thf(2479,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ singletonP )
| ( ( nil @ ( A @ skaf44 @ cons ) )
= A ) ),
inference(simp,[status(thm)],[2478]) ).
thf(2480,plain,
( ~ ( sk1 @ singletonP )
| ( ( nil @ ( sk1 @ skaf44 @ cons ) )
= sk1 ) ),
inference(pattern_uni,[status(thm)],[2479:[bind(A,$thf( sk1 ))]]) ).
thf(120,axiom,
! [A: $i] :
( ( nil = A )
| ( ( A @ tl @ ( A @ hd @ cons ) )
= A )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause104) ).
thf(468,plain,
! [A: $i] :
( ( nil = A )
| ( ( A @ tl @ ( A @ hd @ cons ) )
= A )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(170,axiom,
! [A: $i] : ( A @ skaf65 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause30) ).
thf(583,plain,
! [A: $i] : ( A @ skaf65 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ totalorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause113) ).
thf(227,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ totalorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(228,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ totalorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(cnf,[status(esa)],[227]) ).
thf(229,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ totalorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[228]) ).
thf(230,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[229]) ).
thf(41,axiom,
nil @ ssList,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause8) ).
thf(287,plain,
nil @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(863,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem )
| ~ $true ),
inference(rewrite,[status(thm)],[230,287]) ).
thf(864,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem ) ),
inference(simp,[status(thm)],[863]) ).
thf(2054,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[583,864]) ).
thf(2055,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[2054]) ).
thf(2056,plain,
! [A: $i] : ( nil @ ( A @ skaf65 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[2055:[bind(A,$thf( C )),bind(B,$thf( C @ skaf65 ))]]) ).
thf(2077,plain,
! [A: $i] : ( nil @ ( A @ skaf65 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[2056]) ).
thf(143,axiom,
skac2 @ ssItem,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause10) ).
thf(525,plain,
skac2 @ ssItem,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(681,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[525,438]) ).
thf(682,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[681]) ).
thf(683,plain,
~ ( skac2 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[682:[bind(A,$thf( skac2 ))]]) ).
thf(37,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(274,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)],[37]) ).
thf(275,plain,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) ) ),
inference(cnf,[status(esa)],[274]) ).
thf(276,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) )
| ( B = A ) ),
inference(lifteq,[status(thm)],[275]) ).
thf(29,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ app ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause85) ).
thf(257,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ app ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(258,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ app ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[257]) ).
thf(3956,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ssList )
!= ( B @ ssList ) )
| ( A @ ( B @ app ) @ ssList )
| ~ $true
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[203,258]) ).
thf(3957,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ssList )
!= ( B @ ssList ) )
| ( A @ ( B @ app ) @ ssList )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[3956]) ).
thf(3958,plain,
! [A: $i] :
( ( A @ ( sk2 @ app ) @ ssList )
| ~ ( A @ ssList ) ),
inference(pattern_uni,[status(thm)],[3957:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(6373,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[203,3958]) ).
thf(6374,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[6373]) ).
thf(6375,plain,
sk2 @ ( sk2 @ app ) @ ssList,
inference(pattern_uni,[status(thm)],[6374:[bind(A,$thf( sk2 ))]]) ).
thf(6493,plain,
! [A: $i] :
( ( ( sk2 @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6375,3958]) ).
thf(6494,plain,
! [A: $i] :
( ( ( sk2 @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[6493]) ).
thf(6495,plain,
sk2 @ ( sk2 @ app ) @ ( sk2 @ app ) @ ssList,
inference(pattern_uni,[status(thm)],[6494:[bind(A,$thf( sk2 @ ( sk2 @ app ) ))]]) ).
thf(50,axiom,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ rearsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause82) ).
thf(308,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ rearsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(112,axiom,
! [A: $i] :
( ( A @ totalorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf55 @ ( A @ skaf54 @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause95) ).
thf(449,plain,
! [A: $i] :
( ( A @ totalorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf55 @ ( A @ skaf54 @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(79,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ( A @ ( B @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause102) ).
thf(379,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( A @ ( B @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(102,axiom,
! [A: $i] : ( A @ skaf49 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause46) ).
thf(427,plain,
! [A: $i] : ( A @ skaf49 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(1134,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[427,864]) ).
thf(1135,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[1134]) ).
thf(1136,plain,
! [A: $i] : ( nil @ ( A @ skaf49 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[1135:[bind(A,$thf( C )),bind(B,$thf( C @ skaf49 ))]]) ).
thf(1158,plain,
! [A: $i] : ( nil @ ( A @ skaf49 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[1136]) ).
thf(186,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(614,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)],[186]) ).
thf(33,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(266,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)],[33]) ).
thf(267,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)],[266]) ).
thf(268,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)],[267]) ).
thf(269,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)],[268]) ).
thf(9,negated_conjecture,
! [B: $i,A: $i] :
( ( nil @ ( sk2 @ neq ) )
| ~ ( sk4 @ ( nil @ neq ) )
| ( ( sk4 @ hd )
!= B )
| ( ( nil @ ( B @ cons ) )
!= A )
| ~ ( B @ ssItem )
| ( sk3 = A )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
thf(202,plain,
! [B: $i,A: $i] :
( ( nil @ ( sk2 @ neq ) )
| ~ ( sk4 @ ( nil @ neq ) )
| ( ( sk4 @ hd )
!= B )
| ( ( nil @ ( B @ cons ) )
!= A )
| ~ ( B @ ssItem )
| ( sk3 = A )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(177,axiom,
! [A: $i] : ( A @ skaf71 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause24) ).
thf(597,plain,
! [A: $i] : ( A @ skaf71 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(81,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(385,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)],[81]) ).
thf(155,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(550,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)],[155]) ).
thf(135,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(500,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)],[135]) ).
thf(7,negated_conjecture,
( ( nil @ ( sk2 @ neq ) )
| ( nil @ ( sk2 @ neq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
thf(205,plain,
nil @ ( sk2 @ neq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(90,axiom,
! [A: $i] : ( A @ skaf61 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause34) ).
thf(402,plain,
! [A: $i] : ( A @ skaf61 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(1096,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf61 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[402,236]) ).
thf(1097,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf61 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1096]) ).
thf(1098,plain,
! [A: $i] :
~ ( A @ skaf61 @ ( A @ skaf61 @ neq ) ),
inference(pattern_uni,[status(thm)],[1097:[bind(A,$thf( C )),bind(B,$thf( C @ skaf61 ))]]) ).
thf(1103,plain,
! [A: $i] :
~ ( A @ skaf61 @ ( A @ skaf61 @ neq ) ),
inference(simp,[status(thm)],[1098]) ).
thf(3779,plain,
! [A: $i] :
( ( ( A @ skaf61 @ ( A @ skaf61 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[205,1103]) ).
thf(3780,plain,
! [A: $i] :
( ( A @ skaf61 @ ( A @ skaf61 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[3779]) ).
thf(3781,plain,
! [A: $i] :
( ( ( A @ skaf61 )
!= nil )
| ( ( A @ skaf61 )
!= sk2 ) ),
inference(simp,[status(thm)],[3780]) ).
thf(82,axiom,
! [A: $i] : ( A @ skaf73 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause22) ).
thf(387,plain,
! [A: $i] : ( A @ skaf73 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(909,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf73 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[387,236]) ).
thf(910,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf73 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[909]) ).
thf(911,plain,
! [A: $i] :
~ ( A @ skaf73 @ ( A @ skaf73 @ neq ) ),
inference(pattern_uni,[status(thm)],[910:[bind(A,$thf( C )),bind(B,$thf( C @ skaf73 ))]]) ).
thf(913,plain,
! [A: $i] :
~ ( A @ skaf73 @ ( A @ skaf73 @ neq ) ),
inference(simp,[status(thm)],[911]) ).
thf(2578,plain,
! [A: $i] :
( ( ( A @ skaf77 @ ( A @ skaf77 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[205,846]) ).
thf(2579,plain,
! [A: $i] :
( ( A @ skaf77 @ ( A @ skaf77 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[2578]) ).
thf(2580,plain,
! [A: $i] :
( ( ( A @ skaf77 )
!= nil )
| ( ( A @ skaf77 )
!= sk2 ) ),
inference(simp,[status(thm)],[2579]) ).
thf(86,axiom,
! [A: $i] : ( A @ skaf55 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause40) ).
thf(395,plain,
! [A: $i] : ( A @ skaf55 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(1053,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[395,438]) ).
thf(1054,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1053]) ).
thf(1055,plain,
! [A: $i] :
~ ( A @ skaf55 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1054:[bind(A,$thf( C )),bind(B,$thf( C @ skaf55 ))]]) ).
thf(1063,plain,
! [A: $i] :
~ ( A @ skaf55 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1055]) ).
thf(59,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf45 ) @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause51) ).
thf(329,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf45 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(4607,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf45 ) @ ssList )
!= ( C @ ssList ) )
| ~ $true
| ~ ( C @ ( C @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[329,236]) ).
thf(4608,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf45 ) @ ssList )
!= ( C @ ssList ) )
| ~ ( C @ ( C @ neq ) ) ),
inference(simp,[status(thm)],[4607]) ).
thf(4609,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ skaf45 ) @ ( B @ ( A @ skaf45 ) @ neq ) ),
inference(pattern_uni,[status(thm)],[4608:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf45 ) ))]]) ).
thf(4638,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ skaf45 ) @ ( B @ ( A @ skaf45 ) @ neq ) ),
inference(simp,[status(thm)],[4609]) ).
thf(114,axiom,
! [A: $i] : ( A @ skaf75 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause20) ).
thf(452,plain,
! [A: $i] : ( A @ skaf75 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(6276,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf75 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[452,3958]) ).
thf(6277,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf75 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[6276]) ).
thf(6278,plain,
! [A: $i] : ( A @ skaf75 @ ( sk2 @ app ) @ ssList ),
inference(pattern_uni,[status(thm)],[6277:[bind(A,$thf( C )),bind(B,$thf( C @ skaf75 ))]]) ).
thf(6416,plain,
! [A: $i] : ( A @ skaf75 @ ( sk2 @ app ) @ ssList ),
inference(simp,[status(thm)],[6278]) ).
thf(149,axiom,
skac3 @ ssItem,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause9) ).
thf(538,plain,
skac3 @ ssItem,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(23,axiom,
! [A: $i] :
( ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause88) ).
thf(244,plain,
! [A: $i] :
( ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(245,plain,
! [A: $i] :
( ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[244]) ).
thf(2144,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[203,245]) ).
thf(2145,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP ) ),
inference(simp,[status(thm)],[2144]) ).
thf(2146,plain,
( ( sk2 @ skaf50 @ ( sk2 @ skaf49 @ leq ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[2145:[bind(A,$thf( sk2 ))]]) ).
thf(38,axiom,
! [A: $i] :
( ( nil = A )
| ( A @ tl @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause75) ).
thf(277,plain,
! [A: $i] :
( ( nil = A )
| ( A @ tl @ ssList )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(278,plain,
! [A: $i] :
( ( nil = A )
| ( A @ tl @ ssList )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[277]) ).
thf(279,plain,
! [A: $i] :
( ( A @ tl @ ssList )
| ~ ( A @ ssList )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[278]) ).
thf(12027,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ tl @ ssList )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[200,279]) ).
thf(12028,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ tl @ ssList )
| ( nil = A ) ),
inference(simp,[status(thm)],[12027]) ).
thf(12029,plain,
( ( sk1 @ tl @ ssList )
| ( nil = sk1 ) ),
inference(pattern_uni,[status(thm)],[12028:[bind(A,$thf( sk1 ))]]) ).
thf(764,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[203,236]) ).
thf(765,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[764]) ).
thf(766,plain,
~ ( sk2 @ ( sk2 @ neq ) ),
inference(pattern_uni,[status(thm)],[765:[bind(A,$thf( sk2 ))]]) ).
thf(799,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[205,766]) ).
thf(800,plain,
( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[799]) ).
thf(801,plain,
( ( nil != sk2 )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[800]) ).
thf(802,plain,
nil != sk2,
inference(simp,[status(thm)],[801]) ).
thf(13146,plain,
( ( nil != nil )
| ( sk2 != sk1 )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[12029,802]) ).
thf(13147,plain,
( ( sk2 != sk1 )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[13146:[]]) ).
thf(6388,plain,
! [A: $i] :
( ( ( nil @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[287,3958]) ).
thf(6389,plain,
! [A: $i] :
( ( ( nil @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[6388]) ).
thf(6390,plain,
nil @ ( sk2 @ app ) @ ssList,
inference(pattern_uni,[status(thm)],[6389:[bind(A,$thf( nil ))]]) ).
thf(6852,plain,
! [A: $i] :
( ( ( nil @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[6390,236]) ).
thf(6853,plain,
! [A: $i] :
( ( ( nil @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[6852]) ).
thf(6854,plain,
~ ( nil @ ( sk2 @ app ) @ ( nil @ ( sk2 @ app ) @ neq ) ),
inference(pattern_uni,[status(thm)],[6853:[bind(A,$thf( nil @ ( sk2 @ app ) ))]]) ).
thf(7221,plain,
( ( ( nil @ ( sk2 @ app ) @ ( nil @ ( sk2 @ app ) @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[205,6854]) ).
thf(7222,plain,
( ( nil @ ( sk2 @ app ) @ ( nil @ ( sk2 @ app ) @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[7221]) ).
thf(7235,plain,
( ( ( nil @ ( sk2 @ app ) )
!= nil )
| ( ( nil @ ( sk2 @ app ) )
!= sk2 ) ),
inference(simp,[status(thm)],[7222]) ).
thf(42,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(288,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)],[42]) ).
thf(122,axiom,
! [A: $i] : ( A @ skaf68 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause27) ).
thf(474,plain,
! [A: $i] : ( A @ skaf68 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(1359,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf68 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[474,236]) ).
thf(1360,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf68 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1359]) ).
thf(1361,plain,
! [A: $i] :
~ ( A @ skaf68 @ ( A @ skaf68 @ neq ) ),
inference(pattern_uni,[status(thm)],[1360:[bind(A,$thf( C )),bind(B,$thf( C @ skaf68 ))]]) ).
thf(1366,plain,
! [A: $i] :
~ ( A @ skaf68 @ ( A @ skaf68 @ neq ) ),
inference(simp,[status(thm)],[1361]) ).
thf(106,axiom,
! [A: $i] : ( A @ skaf80 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause15) ).
thf(436,plain,
! [A: $i] : ( A @ skaf80 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(147,axiom,
! [A: $i] : ( A @ skaf51 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause44) ).
thf(535,plain,
! [A: $i] : ( A @ skaf51 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(1642,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf51 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[535,236]) ).
thf(1643,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf51 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1642]) ).
thf(1644,plain,
! [A: $i] :
~ ( A @ skaf51 @ ( A @ skaf51 @ neq ) ),
inference(pattern_uni,[status(thm)],[1643:[bind(A,$thf( C )),bind(B,$thf( C @ skaf51 ))]]) ).
thf(1660,plain,
! [A: $i] :
~ ( A @ skaf51 @ ( A @ skaf51 @ neq ) ),
inference(simp,[status(thm)],[1644]) ).
thf(76,axiom,
! [A: $i] :
( ( A @ ( A @ geq ) )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause55) ).
thf(372,plain,
! [A: $i] :
( ( A @ ( A @ geq ) )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(137,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(504,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)],[137]) ).
thf(164,axiom,
! [A: $i] : ( A @ skaf83 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause12) ).
thf(574,plain,
! [A: $i] : ( A @ skaf83 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(1879,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[574,864]) ).
thf(1880,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[1879]) ).
thf(1881,plain,
! [A: $i] : ( nil @ ( A @ skaf83 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[1880:[bind(A,$thf( C )),bind(B,$thf( C @ skaf83 ))]]) ).
thf(1907,plain,
! [A: $i] : ( nil @ ( A @ skaf83 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[1881]) ).
thf(172,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(587,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)],[172]) ).
thf(66,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(344,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)],[66]) ).
thf(71,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(357,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)],[71]) ).
thf(136,axiom,
! [A: $i] : ( A @ skaf81 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause14) ).
thf(503,plain,
! [A: $i] : ( A @ skaf81 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(6321,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf81 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[503,3958]) ).
thf(6322,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf81 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[6321]) ).
thf(6323,plain,
! [A: $i] : ( A @ skaf81 @ ( sk2 @ app ) @ ssList ),
inference(pattern_uni,[status(thm)],[6322:[bind(A,$thf( C )),bind(B,$thf( C @ skaf81 ))]]) ).
thf(6434,plain,
! [A: $i] : ( A @ skaf81 @ ( sk2 @ app ) @ ssList ),
inference(simp,[status(thm)],[6323]) ).
thf(151,axiom,
! [A: $i] : ( A @ skaf63 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause32) ).
thf(542,plain,
! [A: $i] : ( A @ skaf63 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(117,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(460,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)],[117]) ).
thf(54,axiom,
! [A: $i] : ( A @ skaf57 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause38) ).
thf(317,plain,
! [A: $i] : ( A @ skaf57 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(849,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf57 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[317,236]) ).
thf(850,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf57 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[849]) ).
thf(851,plain,
! [A: $i] :
~ ( A @ skaf57 @ ( A @ skaf57 @ neq ) ),
inference(pattern_uni,[status(thm)],[850:[bind(A,$thf( C )),bind(B,$thf( C @ skaf57 ))]]) ).
thf(853,plain,
! [A: $i] :
~ ( A @ skaf57 @ ( A @ skaf57 @ neq ) ),
inference(simp,[status(thm)],[851]) ).
thf(35,axiom,
! [A: $i] : ( A @ skaf64 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause31) ).
thf(271,plain,
! [A: $i] : ( A @ skaf64 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(876,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[271,864]) ).
thf(877,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[876]) ).
thf(878,plain,
! [A: $i] : ( nil @ ( A @ skaf64 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[877:[bind(A,$thf( C )),bind(B,$thf( C @ skaf64 ))]]) ).
thf(881,plain,
! [A: $i] : ( nil @ ( A @ skaf64 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[878]) ).
thf(31,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ geq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause107) ).
thf(261,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ geq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(152,axiom,
! [A: $i] : ( A @ skaf66 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause29) ).
thf(543,plain,
! [A: $i] : ( A @ skaf66 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(1687,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf66 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[543,236]) ).
thf(1688,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf66 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1687]) ).
thf(1689,plain,
! [A: $i] :
~ ( A @ skaf66 @ ( A @ skaf66 @ neq ) ),
inference(pattern_uni,[status(thm)],[1688:[bind(A,$thf( C )),bind(B,$thf( C @ skaf66 ))]]) ).
thf(1704,plain,
! [A: $i] :
~ ( A @ skaf66 @ ( A @ skaf66 @ neq ) ),
inference(simp,[status(thm)],[1689]) ).
thf(868,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[525,864]) ).
thf(869,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[868]) ).
thf(870,plain,
nil @ ( skac2 @ cons ) @ totalorderedP,
inference(pattern_uni,[status(thm)],[869:[bind(A,$thf( skac2 ))]]) ).
thf(5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
thf(198,plain,
sk2 = sk4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(216,plain,
sk4 = sk2,
inference(lifteq,[status(thm)],[198]) ).
thf(123,axiom,
nil @ totalorderP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause6) ).
thf(475,plain,
nil @ totalorderP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(131,axiom,
~ ( nil @ singletonP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause11) ).
thf(491,plain,
~ ( nil @ singletonP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(492,plain,
~ ( nil @ singletonP ),
inference(polarity_switch,[status(thm)],[491]) ).
thf(174,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(591,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)],[174]) ).
thf(110,axiom,
! [A: $i] :
( ( ( nil @ ( A @ app ) )
= A )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause73) ).
thf(443,plain,
! [A: $i] :
( ( ( nil @ ( A @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(27,axiom,
! [A: $i] : ( A @ skaf79 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause16) ).
thf(253,plain,
! [A: $i] : ( A @ skaf79 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(128,axiom,
! [A: $i] : ( A @ skaf52 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause43) ).
thf(485,plain,
! [A: $i] : ( A @ skaf52 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(20,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(238,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)],[20]) ).
thf(140,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(514,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)],[140]) ).
thf(70,axiom,
! [A: $i] :
( ( A @ ( nil @ rearsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause81) ).
thf(353,plain,
! [A: $i] :
( ( A @ ( nil @ rearsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(68,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(348,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)],[68]) ).
thf(72,axiom,
! [A: $i] : ( A @ skaf44 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause47) ).
thf(361,plain,
! [A: $i] : ( A @ skaf44 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(888,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[361,864]) ).
thf(889,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[888]) ).
thf(890,plain,
! [A: $i] : ( nil @ ( A @ skaf44 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[889:[bind(A,$thf( C )),bind(B,$thf( C @ skaf44 ))]]) ).
thf(905,plain,
! [A: $i] : ( nil @ ( A @ skaf44 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[890]) ).
thf(126,axiom,
nil @ cyclefreeP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause7) ).
thf(480,plain,
nil @ cyclefreeP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(39,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(280,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)],[39]) ).
thf(193,axiom,
nil @ totalorderedP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause4) ).
thf(634,plain,
nil @ totalorderedP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(13,axiom,
skac3 != skac2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause54) ).
thf(221,plain,
skac3 != skac2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(44,axiom,
! [B: $i,A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause118) ).
thf(293,plain,
! [B: $i,A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(115,axiom,
! [A: $i] :
( ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause79) ).
thf(453,plain,
! [A: $i] :
( ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(87,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(396,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)],[87]) ).
thf(2462,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ singletonP )
| ( ( nil @ ( A @ skaf44 @ cons ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[203,248]) ).
thf(2463,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ singletonP )
| ( ( nil @ ( A @ skaf44 @ cons ) )
= A ) ),
inference(simp,[status(thm)],[2462]) ).
thf(2464,plain,
( ~ ( sk2 @ singletonP )
| ( ( nil @ ( sk2 @ skaf44 @ cons ) )
= sk2 ) ),
inference(pattern_uni,[status(thm)],[2463:[bind(A,$thf( sk2 ))]]) ).
thf(2798,plain,
! [A: $i] :
( ( ( nil @ ( sk2 @ skaf44 @ cons ) )
!= ( nil @ ( A @ skaf44 @ cons ) ) )
| ( sk2 @ totalorderedP )
| ~ ( sk2 @ singletonP ) ),
inference(paramod_ordered,[status(thm)],[2464,905]) ).
thf(2799,plain,
( ( sk2 @ totalorderedP )
| ~ ( sk2 @ singletonP ) ),
inference(pattern_uni,[status(thm)],[2798:[bind(A,$thf( sk2 ))]]) ).
thf(103,axiom,
! [A: $i] :
( ( nil @ ( A @ segmentP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause56) ).
thf(428,plain,
! [A: $i] :
( ( nil @ ( A @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(32,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(263,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)],[32]) ).
thf(264,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)],[263]) ).
thf(265,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)],[264]) ).
thf(13154,plain,
( ( nil != nil )
| ~ ( sk1 @ singletonP )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[12029,492]) ).
thf(13155,plain,
( ~ ( sk1 @ singletonP )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[13154:[]]) ).
thf(3,negated_conjecture,
sk3 @ ssList,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
thf(206,plain,
sk3 @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(108,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ equalelemsP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause64) ).
thf(439,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ equalelemsP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(34,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf46 ) @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause50) ).
thf(270,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf46 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
thf(201,plain,
sk1 = sk3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11826,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ tl @ ssList )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[203,279]) ).
thf(11827,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ tl @ ssList )
| ( nil = A ) ),
inference(simp,[status(thm)],[11826]) ).
thf(11828,plain,
( ( sk2 @ tl @ ssList )
| ( nil = sk2 ) ),
inference(pattern_uni,[status(thm)],[11827:[bind(A,$thf( sk2 ))]]) ).
thf(13009,plain,
sk2 @ tl @ ssList,
inference(simplifyReflect,[status(thm)],[11828,802]) ).
thf(13047,plain,
! [A: $i] :
( ( ( sk2 @ tl @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13009,3958]) ).
thf(13048,plain,
! [A: $i] :
( ( ( sk2 @ tl @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[13047]) ).
thf(13049,plain,
sk2 @ tl @ ( sk2 @ app ) @ ssList,
inference(pattern_uni,[status(thm)],[13048:[bind(A,$thf( sk2 @ tl ))]]) ).
thf(74,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(366,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)],[74]) ).
thf(6352,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf73 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[387,3958]) ).
thf(6353,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf73 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[6352]) ).
thf(6354,plain,
! [A: $i] : ( A @ skaf73 @ ( sk2 @ app ) @ ssList ),
inference(pattern_uni,[status(thm)],[6353:[bind(A,$thf( C )),bind(B,$thf( C @ skaf73 ))]]) ).
thf(6442,plain,
! [A: $i] : ( A @ skaf73 @ ( sk2 @ app ) @ ssList ),
inference(simp,[status(thm)],[6354]) ).
thf(791,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[271,438]) ).
thf(792,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[791]) ).
thf(793,plain,
! [A: $i] :
~ ( A @ skaf64 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[792:[bind(A,$thf( C )),bind(B,$thf( C @ skaf64 ))]]) ).
thf(798,plain,
! [A: $i] :
~ ( A @ skaf64 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[793]) ).
thf(175,axiom,
! [A: $i] : ( A @ skaf50 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause45) ).
thf(593,plain,
! [A: $i] : ( A @ skaf50 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(2228,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[593,438]) ).
thf(2229,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[2228]) ).
thf(2230,plain,
! [A: $i] :
~ ( A @ skaf50 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[2229:[bind(A,$thf( C )),bind(B,$thf( C @ skaf50 ))]]) ).
thf(2264,plain,
! [A: $i] :
~ ( A @ skaf50 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[2230]) ).
thf(178,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(598,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)],[178]) ).
thf(159,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(561,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)],[159]) ).
thf(100,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf48 ) @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause48) ).
thf(424,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf48 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(93,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(407,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)],[93]) ).
thf(19,axiom,
! [A: $i] : ( A @ skaf62 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause33) ).
thf(237,plain,
! [A: $i] : ( A @ skaf62 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(776,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf62 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[237,236]) ).
thf(777,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf62 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[776]) ).
thf(778,plain,
! [A: $i] :
~ ( A @ skaf62 @ ( A @ skaf62 @ neq ) ),
inference(pattern_uni,[status(thm)],[777:[bind(A,$thf( C )),bind(B,$thf( C @ skaf62 ))]]) ).
thf(788,plain,
! [A: $i] :
~ ( A @ skaf62 @ ( A @ skaf62 @ neq ) ),
inference(simp,[status(thm)],[778]) ).
thf(30,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(259,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)],[30]) ).
thf(260,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)],[259]) ).
thf(858,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf58 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[347,236]) ).
thf(859,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf58 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[858]) ).
thf(860,plain,
! [A: $i] :
~ ( A @ skaf58 @ ( A @ skaf58 @ neq ) ),
inference(pattern_uni,[status(thm)],[859:[bind(A,$thf( C )),bind(B,$thf( C @ skaf58 ))]]) ).
thf(862,plain,
! [A: $i] :
~ ( A @ skaf58 @ ( A @ skaf58 @ neq ) ),
inference(simp,[status(thm)],[860]) ).
thf(26,axiom,
! [A: $i] : ( A @ skaf72 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause23) ).
thf(252,plain,
! [A: $i] : ( A @ skaf72 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(2818,plain,
! [A: $i] :
( ( ( A @ skaf58 @ ( A @ skaf58 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[205,862]) ).
thf(2819,plain,
! [A: $i] :
( ( A @ skaf58 @ ( A @ skaf58 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[2818]) ).
thf(2820,plain,
! [A: $i] :
( ( ( A @ skaf58 )
!= nil )
| ( ( A @ skaf58 )
!= sk2 ) ),
inference(simp,[status(thm)],[2819]) ).
thf(166,axiom,
! [A: $i] : ( A @ skaf74 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause21) ).
thf(578,plain,
! [A: $i] : ( A @ skaf74 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(1928,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[578,864]) ).
thf(1929,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[1928]) ).
thf(1930,plain,
! [A: $i] : ( nil @ ( A @ skaf74 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[1929:[bind(A,$thf( C )),bind(B,$thf( C @ skaf74 ))]]) ).
thf(1951,plain,
! [A: $i] : ( nil @ ( A @ skaf74 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[1930]) ).
thf(132,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ lt ) )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause111) ).
thf(493,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ lt ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(173,axiom,
! [A: $i] : ( A @ skaf56 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause39) ).
thf(590,plain,
! [A: $i] : ( A @ skaf56 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(2191,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf56 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[590,236]) ).
thf(2192,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf56 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[2191]) ).
thf(2193,plain,
! [A: $i] :
~ ( A @ skaf56 @ ( A @ skaf56 @ neq ) ),
inference(pattern_uni,[status(thm)],[2192:[bind(A,$thf( C )),bind(B,$thf( C @ skaf56 ))]]) ).
thf(2213,plain,
! [A: $i] :
~ ( A @ skaf56 @ ( A @ skaf56 @ neq ) ),
inference(simp,[status(thm)],[2193]) ).
thf(92,axiom,
! [A: $i] : ( A @ skaf60 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause35) ).
thf(406,plain,
! [A: $i] : ( A @ skaf60 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(1104,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[406,864]) ).
thf(1105,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[1104]) ).
thf(1106,plain,
! [A: $i] : ( nil @ ( A @ skaf60 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[1105:[bind(A,$thf( C )),bind(B,$thf( C @ skaf60 ))]]) ).
thf(1128,plain,
! [A: $i] : ( nil @ ( A @ skaf60 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[1106]) ).
thf(13152,plain,
( ( nil != nil )
| ( sk1 @ totalorderP )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[12029,475]) ).
thf(13153,plain,
( ( sk1 @ totalorderP )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[13152:[]]) ).
thf(14,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf43 ) @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause52) ).
thf(224,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf43 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(871,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[253,864]) ).
thf(872,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[871]) ).
thf(873,plain,
! [A: $i] : ( nil @ ( A @ skaf79 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[872:[bind(A,$thf( C )),bind(B,$thf( C @ skaf79 ))]]) ).
thf(879,plain,
! [A: $i] : ( nil @ ( A @ skaf79 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[873]) ).
thf(6300,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf72 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[252,3958]) ).
thf(6301,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf72 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[6300]) ).
thf(6302,plain,
! [A: $i] : ( A @ skaf72 @ ( sk2 @ app ) @ ssList ),
inference(pattern_uni,[status(thm)],[6301:[bind(A,$thf( C )),bind(B,$thf( C @ skaf72 ))]]) ).
thf(6427,plain,
! [A: $i] : ( A @ skaf72 @ ( sk2 @ app ) @ ssList ),
inference(simp,[status(thm)],[6302]) ).
thf(13064,plain,
! [A: $i] :
( ( ( sk2 @ tl @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[13009,236]) ).
thf(13065,plain,
! [A: $i] :
( ( ( sk2 @ tl @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[13064]) ).
thf(13066,plain,
~ ( sk2 @ tl @ ( sk2 @ tl @ neq ) ),
inference(pattern_uni,[status(thm)],[13065:[bind(A,$thf( sk2 @ tl ))]]) ).
thf(13938,plain,
( ( ( sk2 @ tl @ ( sk2 @ tl @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[205,13066]) ).
thf(13939,plain,
( ( sk2 @ tl @ ( sk2 @ tl @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[13938]) ).
thf(13946,plain,
( ( ( sk2 @ tl )
!= nil )
| ( ( sk2 @ tl )
!= sk2 ) ),
inference(simp,[status(thm)],[13939]) ).
thf(6398,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[200,3958]) ).
thf(6399,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[6398]) ).
thf(6400,plain,
sk1 @ ( sk2 @ app ) @ ssList,
inference(pattern_uni,[status(thm)],[6399:[bind(A,$thf( sk1 ))]]) ).
thf(6938,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[6400,236]) ).
thf(6939,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[6938]) ).
thf(6940,plain,
~ ( sk1 @ ( sk2 @ app ) @ ( sk1 @ ( sk2 @ app ) @ neq ) ),
inference(pattern_uni,[status(thm)],[6939:[bind(A,$thf( sk1 @ ( sk2 @ app ) ))]]) ).
thf(2575,plain,
! [A: $i] :
( ( ( A @ skaf62 @ ( A @ skaf62 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[205,788]) ).
thf(2576,plain,
! [A: $i] :
( ( A @ skaf62 @ ( A @ skaf62 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[2575]) ).
thf(2577,plain,
! [A: $i] :
( ( ( A @ skaf62 )
!= nil )
| ( ( A @ skaf62 )
!= sk2 ) ),
inference(simp,[status(thm)],[2576]) ).
thf(91,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(403,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)],[91]) ).
thf(83,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(388,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)],[83]) ).
thf(184,axiom,
! [A: $i] :
( ( A @ equalelemsP )
| ~ ( A @ ssList )
| ( ( A @ skaf79 )
!= ( A @ skaf78 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause89) ).
thf(610,plain,
! [A: $i] :
( ( A @ equalelemsP )
| ~ ( A @ ssList )
| ( ( A @ skaf79 )
!= ( A @ skaf78 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(781,plain,
! [A: $i] :
( ( ( nil @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[287,236]) ).
thf(782,plain,
! [A: $i] :
( ( ( nil @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[781]) ).
thf(783,plain,
~ ( nil @ ( nil @ neq ) ),
inference(pattern_uni,[status(thm)],[782:[bind(A,$thf( nil ))]]) ).
thf(98,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(420,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)],[98]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ geq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause108) ).
thf(225,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ geq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(64,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause103) ).
thf(339,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(124,axiom,
! [A: $i] :
( ( nil @ ( A @ frontsegP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause60) ).
thf(476,plain,
! [A: $i] :
( ( nil @ ( A @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(144,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(526,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)],[144]) ).
thf(154,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(547,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)],[154]) ).
thf(121,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( B @ ( A @ cons ) )
!= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause99) ).
thf(471,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( B @ ( A @ cons ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(28,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(254,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)],[28]) ).
thf(255,plain,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ hd @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ strictorderedP ) ),
inference(cnf,[status(esa)],[254]) ).
thf(256,plain,
! [B: $i,A: $i] :
( ( B @ hd @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ strictorderedP )
| ( nil = B ) ),
inference(lifteq,[status(thm)],[255]) ).
thf(189,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ strictorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause112) ).
thf(622,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ strictorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(7012,plain,
! [A: $i] :
( ( ( sk2 @ ( sk2 @ app ) @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6495,3958]) ).
thf(7013,plain,
! [A: $i] :
( ( ( sk2 @ ( sk2 @ app ) @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[7012]) ).
thf(7014,plain,
sk2 @ ( sk2 @ app ) @ ( sk2 @ app ) @ ( sk2 @ app ) @ ssList,
inference(pattern_uni,[status(thm)],[7013:[bind(A,$thf( sk2 @ ( sk2 @ app ) @ ( sk2 @ app ) ))]]) ).
thf(1123,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[406,438]) ).
thf(1124,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1123]) ).
thf(1125,plain,
! [A: $i] :
~ ( A @ skaf60 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1124:[bind(A,$thf( C )),bind(B,$thf( C @ skaf60 ))]]) ).
thf(1131,plain,
! [A: $i] :
~ ( A @ skaf60 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1125]) ).
thf(6318,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf56 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[590,3958]) ).
thf(6319,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf56 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[6318]) ).
thf(6320,plain,
! [A: $i] : ( A @ skaf56 @ ( sk2 @ app ) @ ssList ),
inference(pattern_uni,[status(thm)],[6319:[bind(A,$thf( C )),bind(B,$thf( C @ skaf56 ))]]) ).
thf(6433,plain,
! [A: $i] : ( A @ skaf56 @ ( sk2 @ app ) @ ssList ),
inference(simp,[status(thm)],[6320]) ).
thf(162,axiom,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ segmentP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause80) ).
thf(569,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ segmentP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(222,plain,
skac3 != skac2,
inference(polarity_switch,[status(thm)],[221]) ).
thf(223,plain,
skac2 != skac3,
inference(lifteq,[status(thm)],[222]) ).
thf(8729,plain,
! [B: $i,A: $i] :
( ( B != skac2 )
| ( A != skac3 )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) ) ),
inference(paramod_ordered,[status(thm)],[276,223]) ).
thf(8730,plain,
! [A: $i] :
( ( A != skac3 )
| ~ ( skac2 @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( skac2 @ geq ) )
| ~ ( skac2 @ ( A @ geq ) ) ),
inference(pattern_uni,[status(thm)],[8729:[bind(A,$thf( A )),bind(B,$thf( skac2 ))]]) ).
thf(9492,plain,
( ~ ( skac2 @ ssItem )
| ~ ( skac3 @ ssItem )
| ~ ( skac3 @ ( skac2 @ geq ) )
| ~ ( skac2 @ ( skac3 @ geq ) ) ),
inference(simp,[status(thm)],[8730]) ).
thf(12961,plain,
( ~ $true
| ~ $true
| ~ ( skac3 @ ( skac2 @ geq ) )
| ~ ( skac2 @ ( skac3 @ geq ) ) ),
inference(rewrite,[status(thm)],[9492,538,525]) ).
thf(12962,plain,
( ~ ( skac3 @ ( skac2 @ geq ) )
| ~ ( skac2 @ ( skac3 @ geq ) ) ),
inference(simp,[status(thm)],[12961]) ).
thf(1034,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[395,864]) ).
thf(1035,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[1034]) ).
thf(1036,plain,
! [A: $i] : ( nil @ ( A @ skaf55 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[1035:[bind(A,$thf( C )),bind(B,$thf( C @ skaf55 ))]]) ).
thf(1060,plain,
! [A: $i] : ( nil @ ( A @ skaf55 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[1036]) ).
thf(116,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(457,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)],[116]) ).
thf(182,axiom,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ frontsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause84) ).
thf(605,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ frontsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(138,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause65) ).
thf(508,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(51,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause67) ).
thf(311,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(11,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( nil @ ( sk4 @ neq ) )
| ~ ( sk4 @ ( nil @ neq ) )
| ( ( sk4 @ hd )
!= B )
| ( ( nil @ ( B @ cons ) )
!= A )
| ~ ( B @ ssItem )
| ( sk3 = A )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
thf(207,plain,
! [B: $i,A: $i] :
( ~ ( nil @ ( sk4 @ neq ) )
| ~ ( sk4 @ ( nil @ neq ) )
| ( ( sk4 @ hd )
!= B )
| ( ( nil @ ( B @ cons ) )
!= A )
| ~ ( B @ ssItem )
| ( sk3 = A )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(218,plain,
! [B: $i,A: $i] :
( ~ ( nil @ ( sk4 @ neq ) )
| ~ ( sk4 @ ( nil @ neq ) )
| ( ( sk4 @ hd )
!= B )
| ( ( nil @ ( B @ cons ) )
!= A )
| ~ ( B @ ssItem )
| ( sk3 = A )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[207]) ).
thf(219,plain,
! [B: $i,A: $i] :
( ~ ( nil @ ( sk4 @ neq ) )
| ~ ( sk4 @ ( nil @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( ( sk4 @ hd )
!= B )
| ( ( nil @ ( B @ cons ) )
!= A )
| ( sk3 = A ) ),
inference(lifteq,[status(thm)],[218]) ).
thf(220,plain,
( ~ ( nil @ ( sk4 @ neq ) )
| ~ ( sk4 @ ( nil @ neq ) )
| ~ ( sk4 @ hd @ ssItem )
| ~ ( nil @ ( sk4 @ hd @ cons ) @ ssList )
| ( ( nil @ ( sk4 @ hd @ cons ) )
= sk3 ) ),
inference(simp,[status(thm)],[219]) ).
thf(213,plain,
sk3 = sk1,
inference(lifteq,[status(thm)],[201]) ).
thf(652,plain,
( ~ ( nil @ ( sk2 @ neq ) )
| ~ ( sk2 @ ( nil @ neq ) )
| ~ ( sk2 @ hd @ ssItem )
| ~ ( nil @ ( sk2 @ hd @ cons ) @ ssList )
| ( ( nil @ ( sk2 @ hd @ cons ) )
= sk1 ) ),
inference(rewrite,[status(thm)],[220,213,216]) ).
thf(655,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true
| ~ ( sk2 @ ( nil @ neq ) )
| ~ ( sk2 @ hd @ ssItem )
| ~ ( nil @ ( sk2 @ hd @ cons ) @ ssList )
| ( ( nil @ ( sk2 @ hd @ cons ) )
= sk1 ) ),
inference(paramod_ordered,[status(thm)],[205,652]) ).
thf(656,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ ( sk2 @ ( nil @ neq ) )
| ~ ( sk2 @ hd @ ssItem )
| ~ ( nil @ ( sk2 @ hd @ cons ) @ ssList )
| ( ( nil @ ( sk2 @ hd @ cons ) )
= sk1 ) ),
inference(simp,[status(thm)],[655]) ).
thf(657,plain,
( ~ ( sk2 @ ( nil @ neq ) )
| ~ ( sk2 @ hd @ ssItem )
| ~ ( nil @ ( sk2 @ hd @ cons ) @ ssList )
| ( ( nil @ ( sk2 @ hd @ cons ) )
= sk1 ) ),
inference(pattern_uni,[status(thm)],[656:[]]) ).
thf(158,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ tl )
= B )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause96) ).
thf(558,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ tl )
= B )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(145,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(530,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)],[145]) ).
thf(133,axiom,
! [A: $i] : ( A @ skaf67 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause28) ).
thf(497,plain,
! [A: $i] : ( A @ skaf67 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(1600,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf67 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[497,236]) ).
thf(1601,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf67 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1600]) ).
thf(1602,plain,
! [A: $i] :
~ ( A @ skaf67 @ ( A @ skaf67 @ neq ) ),
inference(pattern_uni,[status(thm)],[1601:[bind(A,$thf( C )),bind(B,$thf( C @ skaf67 ))]]) ).
thf(1616,plain,
! [A: $i] :
~ ( A @ skaf67 @ ( A @ skaf67 @ neq ) ),
inference(simp,[status(thm)],[1602]) ).
thf(95,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(412,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)],[95]) ).
thf(101,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ gt ) )
| ~ ( B @ ( A @ gt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause110) ).
thf(425,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ gt ) )
| ~ ( B @ ( A @ gt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(2005,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[582,864]) ).
thf(2006,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[2005]) ).
thf(2007,plain,
! [A: $i] : ( nil @ ( A @ skaf54 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[2006:[bind(A,$thf( C )),bind(B,$thf( C @ skaf54 ))]]) ).
thf(2033,plain,
! [A: $i] : ( nil @ ( A @ skaf54 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[2007]) ).
thf(194,axiom,
! [A: $i] : ( A @ skaf59 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause36) ).
thf(635,plain,
! [A: $i] : ( A @ skaf59 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(2544,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[635,864]) ).
thf(2545,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[2544]) ).
thf(2546,plain,
! [A: $i] : ( nil @ ( A @ skaf59 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[2545:[bind(A,$thf( C )),bind(B,$thf( C @ skaf59 ))]]) ).
thf(2570,plain,
! [A: $i] : ( nil @ ( A @ skaf59 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[2546]) ).
thf(250,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)],[249]) ).
thf(251,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)],[250]) ).
thf(2732,plain,
! [A: $i] :
( ( ( sk1 @ 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)],[200,251]) ).
thf(2733,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ duplicatefreeP )
| ( ( A @ skaf77 @ ( A @ skaf74 @ cons ) @ ( A @ skaf76 @ ( A @ skaf74 @ cons ) @ ( A @ skaf75 @ app ) @ app ) )
= A ) ),
inference(simp,[status(thm)],[2732]) ).
thf(2734,plain,
( ( sk1 @ duplicatefreeP )
| ( ( sk1 @ skaf77 @ ( sk1 @ skaf74 @ cons ) @ ( sk1 @ skaf76 @ ( sk1 @ skaf74 @ cons ) @ ( sk1 @ skaf75 @ app ) @ app ) )
= sk1 ) ),
inference(pattern_uni,[status(thm)],[2733:[bind(A,$thf( sk1 ))]]) ).
thf(45,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(296,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)],[45]) ).
thf(179,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ lt ) )
| ~ ( B @ ( A @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause114) ).
thf(601,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ lt ) )
| ~ ( B @ ( A @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(167,axiom,
! [A: $i] : ( A @ skaf82 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause13) ).
thf(579,plain,
! [A: $i] : ( A @ skaf82 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(6333,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf82 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[579,3958]) ).
thf(6334,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf82 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[6333]) ).
thf(6335,plain,
! [A: $i] : ( A @ skaf82 @ ( sk2 @ app ) @ ssList ),
inference(pattern_uni,[status(thm)],[6334:[bind(A,$thf( C )),bind(B,$thf( C @ skaf82 ))]]) ).
thf(6437,plain,
! [A: $i] : ( A @ skaf82 @ ( sk2 @ app ) @ ssList ),
inference(simp,[status(thm)],[6335]) ).
thf(104,axiom,
! [A: $i] :
( ( nil = A )
| ( A @ hd @ ssItem )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause76) ).
thf(430,plain,
! [A: $i] :
( ( nil = A )
| ( A @ hd @ ssItem )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(171,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(584,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)],[171]) ).
thf(899,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[361,438]) ).
thf(900,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[899]) ).
thf(901,plain,
! [A: $i] :
~ ( A @ skaf44 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[900:[bind(A,$thf( C )),bind(B,$thf( C @ skaf44 ))]]) ).
thf(904,plain,
! [A: $i] :
~ ( A @ skaf44 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[901]) ).
thf(2815,plain,
! [A: $i] :
( ( ( A @ skaf57 @ ( A @ skaf57 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[205,853]) ).
thf(2816,plain,
! [A: $i] :
( ( A @ skaf57 @ ( A @ skaf57 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[2815]) ).
thf(2817,plain,
! [A: $i] :
( ( ( A @ skaf57 )
!= nil )
| ( ( A @ skaf57 )
!= sk2 ) ),
inference(simp,[status(thm)],[2816]) ).
thf(12,negated_conjecture,
( ~ ( nil @ ( sk4 @ neq ) )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( sk1 @ singletonP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
thf(204,plain,
( ~ ( nil @ ( sk4 @ neq ) )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( sk1 @ singletonP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(6925,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6400,3958]) ).
thf(6926,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[6925]) ).
thf(6927,plain,
sk1 @ ( sk2 @ app ) @ ( sk2 @ app ) @ ssList,
inference(pattern_uni,[status(thm)],[6926:[bind(A,$thf( sk1 @ ( sk2 @ app ) ))]]) ).
thf(2536,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[635,438]) ).
thf(2537,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[2536]) ).
thf(2538,plain,
! [A: $i] :
~ ( A @ skaf59 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[2537:[bind(A,$thf( C )),bind(B,$thf( C @ skaf59 ))]]) ).
thf(2568,plain,
! [A: $i] :
~ ( A @ skaf59 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[2538]) ).
thf(43,axiom,
! [A: $i] :
( ( nil @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause58) ).
thf(291,plain,
! [A: $i] :
( ( nil @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(84,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( B @ ( A @ cons ) )
!= nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause98) ).
thf(391,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( B @ ( A @ cons ) )
!= nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(80,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause119) ).
thf(382,plain,
! [B: $i,A: $i] :
( ( nil = B )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(52,axiom,
! [B: $i,A: $i] :
( ( B @ ssItem )
| ( A @ duplicatefreeP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause72) ).
thf(313,plain,
! [B: $i,A: $i] :
( ( B @ ssItem )
| ( A @ duplicatefreeP )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(773,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf43 ) @ ssList )
!= ( C @ ssList ) )
| ~ $true
| ~ ( C @ ( C @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[224,236]) ).
thf(774,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf43 ) @ ssList )
!= ( C @ ssList ) )
| ~ ( C @ ( C @ neq ) ) ),
inference(simp,[status(thm)],[773]) ).
thf(775,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ skaf43 ) @ ( B @ ( A @ skaf43 ) @ neq ) ),
inference(pattern_uni,[status(thm)],[774:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf43 ) ))]]) ).
thf(787,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ skaf43 ) @ ( B @ ( A @ skaf43 ) @ neq ) ),
inference(simp,[status(thm)],[775]) ).
thf(134,axiom,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf60 @ ( A @ skaf59 @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause93) ).
thf(498,plain,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf60 @ ( A @ skaf59 @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(119,axiom,
! [A: $i] :
( ( A @ totalorderedP )
| ~ ( A @ ssList )
| ~ ( A @ skaf65 @ ( A @ skaf64 @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause91) ).
thf(466,plain,
! [A: $i] :
( ( A @ totalorderedP )
| ~ ( A @ ssList )
| ~ ( A @ skaf65 @ ( A @ skaf64 @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(62,axiom,
nil @ duplicatefreeP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause2) ).
thf(335,plain,
nil @ duplicatefreeP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(1349,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf75 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[452,236]) ).
thf(1350,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf75 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1349]) ).
thf(1351,plain,
! [A: $i] :
~ ( A @ skaf75 @ ( A @ skaf75 @ neq ) ),
inference(pattern_uni,[status(thm)],[1350:[bind(A,$thf( C )),bind(B,$thf( C @ skaf75 ))]]) ).
thf(1356,plain,
! [A: $i] :
~ ( A @ skaf75 @ ( A @ skaf75 @ neq ) ),
inference(simp,[status(thm)],[1351]) ).
thf(69,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(350,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)],[69]) ).
thf(197,axiom,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( A @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause63) ).
thf(641,plain,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( A @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(2159,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[200,245]) ).
thf(2160,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP ) ),
inference(simp,[status(thm)],[2159]) ).
thf(2161,plain,
( ( sk1 @ skaf50 @ ( sk1 @ skaf49 @ leq ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[2160:[bind(A,$thf( sk1 ))]]) ).
thf(163,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(572,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)],[163]) ).
thf(180,axiom,
! [A: $i] : ( A @ skaf76 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause19) ).
thf(603,plain,
! [A: $i] : ( A @ skaf76 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(2304,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf76 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[603,236]) ).
thf(2305,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf76 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[2304]) ).
thf(2306,plain,
! [A: $i] :
~ ( A @ skaf76 @ ( A @ skaf76 @ neq ) ),
inference(pattern_uni,[status(thm)],[2305:[bind(A,$thf( C )),bind(B,$thf( C @ skaf76 ))]]) ).
thf(2326,plain,
! [A: $i] :
~ ( A @ skaf76 @ ( A @ skaf76 @ neq ) ),
inference(simp,[status(thm)],[2306]) ).
thf(88,axiom,
! [A: $i] : ( A @ skaf70 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause25) ).
thf(399,plain,
! [A: $i] : ( A @ skaf70 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(1064,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[399,864]) ).
thf(1065,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[1064]) ).
thf(1066,plain,
! [A: $i] : ( nil @ ( A @ skaf70 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[1065:[bind(A,$thf( C )),bind(B,$thf( C @ skaf70 ))]]) ).
thf(1090,plain,
! [A: $i] : ( nil @ ( A @ skaf70 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[1066]) ).
thf(6355,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf51 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[535,3958]) ).
thf(6356,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf51 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[6355]) ).
thf(6357,plain,
! [A: $i] : ( A @ skaf51 @ ( sk2 @ app ) @ ssList ),
inference(pattern_uni,[status(thm)],[6356:[bind(A,$thf( C )),bind(B,$thf( C @ skaf51 ))]]) ).
thf(6443,plain,
! [A: $i] : ( A @ skaf51 @ ( sk2 @ app ) @ ssList ),
inference(simp,[status(thm)],[6357]) ).
thf(78,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(377,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)],[78]) ).
thf(55,axiom,
nil @ equalelemsP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause1) ).
thf(318,plain,
nil @ equalelemsP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(1369,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf52 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[485,236]) ).
thf(1370,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf52 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1369]) ).
thf(1371,plain,
! [A: $i] :
~ ( A @ skaf52 @ ( A @ skaf52 @ neq ) ),
inference(pattern_uni,[status(thm)],[1370:[bind(A,$thf( C )),bind(B,$thf( C @ skaf52 ))]]) ).
thf(1376,plain,
! [A: $i] :
~ ( A @ skaf52 @ ( A @ skaf52 @ neq ) ),
inference(simp,[status(thm)],[1371]) ).
thf(874,plain,
! [A: $i] :
( ( ( nil @ ( sk2 @ hd @ cons ) )
!= ( nil @ ( A @ cons ) ) )
| ( sk1 @ totalorderedP )
| ~ ( A @ ssItem )
| ~ ( sk2 @ ( nil @ neq ) )
| ~ ( sk2 @ hd @ ssItem )
| ~ ( nil @ ( sk2 @ hd @ cons ) @ ssList ) ),
inference(paramod_ordered,[status(thm)],[657,864]) ).
thf(875,plain,
( ( sk1 @ totalorderedP )
| ~ ( sk2 @ hd @ ssItem )
| ~ ( sk2 @ ( nil @ neq ) )
| ~ ( sk2 @ hd @ ssItem )
| ~ ( nil @ ( sk2 @ hd @ cons ) @ ssList ) ),
inference(pattern_uni,[status(thm)],[874:[bind(A,$thf( sk2 @ hd ))]]) ).
thf(880,plain,
( ( sk1 @ totalorderedP )
| ~ ( sk2 @ ( nil @ neq ) )
| ~ ( sk2 @ hd @ ssItem )
| ~ ( nil @ ( sk2 @ hd @ cons ) @ ssList ) ),
inference(simp,[status(thm)],[875]) ).
thf(935,plain,
( ( ( sk2 @ hd @ ssItem )
!= ( skac3 @ ssItem ) )
| ( sk1 @ totalorderedP )
| ~ ( sk2 @ ( nil @ neq ) )
| ~ $true
| ~ ( nil @ ( sk2 @ hd @ cons ) @ ssList ) ),
inference(paramod_ordered,[status(thm)],[538,880]) ).
thf(936,plain,
( ( ( sk2 @ hd @ ssItem )
!= ( skac3 @ ssItem ) )
| ( sk1 @ totalorderedP )
| ~ ( sk2 @ ( nil @ neq ) )
| ~ ( nil @ ( sk2 @ hd @ cons ) @ ssList ) ),
inference(simp,[status(thm)],[935]) ).
thf(979,plain,
( ( ( sk2 @ hd )
!= skac3 )
| ~ ( sk2 @ ( nil @ neq ) )
| ~ ( nil @ ( sk2 @ hd @ cons ) @ ssList )
| ( sk1 @ totalorderedP ) ),
inference(simp,[status(thm)],[936]) ).
thf(181,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf42 ) @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause53) ).
thf(604,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf42 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(73,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(362,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)],[73]) ).
thf(113,axiom,
! [A: $i] : ( A @ skaf53 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause42) ).
thf(451,plain,
! [A: $i] : ( A @ skaf53 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(161,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause69) ).
thf(567,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(214,plain,
( ~ ( nil @ ( sk4 @ neq ) )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( sk1 @ singletonP ) ),
inference(cnf,[status(esa)],[204]) ).
thf(646,plain,
( ~ ( nil @ ( sk2 @ neq ) )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( sk1 @ singletonP ) ),
inference(rewrite,[status(thm)],[214,216]) ).
thf(647,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( sk1 @ singletonP ) ),
inference(paramod_ordered,[status(thm)],[205,646]) ).
thf(648,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( sk1 @ singletonP ) ),
inference(simp,[status(thm)],[647]) ).
thf(649,plain,
( ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( sk1 @ singletonP ) ),
inference(pattern_uni,[status(thm)],[648:[]]) ).
thf(8,negated_conjecture,
( ~ ( nil @ ( sk4 @ neq ) )
| ( nil @ ( sk2 @ neq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
thf(208,plain,
( ~ ( nil @ ( sk4 @ neq ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(156,axiom,
! [A: $i] :
( ( nil = A )
| ( A @ tl @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause77) ).
thf(552,plain,
! [A: $i] :
( ( nil = A )
| ( A @ tl @ ssList )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(57,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(323,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)],[57]) ).
thf(176,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(594,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)],[176]) ).
thf(188,axiom,
nil @ strictorderedP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause3) ).
thf(621,plain,
nil @ strictorderedP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(190,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(626,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)],[190]) ).
thf(767,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[200,236]) ).
thf(768,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[767]) ).
thf(769,plain,
~ ( sk1 @ ( sk1 @ neq ) ),
inference(pattern_uni,[status(thm)],[768:[bind(A,$thf( sk1 ))]]) ).
thf(60,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(330,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)],[60]) ).
thf(85,axiom,
! [A: $i] : ( A @ skaf69 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause26) ).
thf(394,plain,
! [A: $i] : ( A @ skaf69 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(925,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[394,438]) ).
thf(926,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[925]) ).
thf(927,plain,
! [A: $i] :
~ ( A @ skaf69 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[926:[bind(A,$thf( C )),bind(B,$thf( C @ skaf69 ))]]) ).
thf(932,plain,
! [A: $i] :
~ ( A @ skaf69 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[927]) ).
thf(21,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(240,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)],[21]) ).
thf(1836,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ~ $true
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[200,243]) ).
thf(1837,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
inference(simp,[status(thm)],[1836]) ).
thf(1838,plain,
( ( sk1 @ strictorderedP )
| ~ ( sk1 @ skaf70 @ ( sk1 @ skaf69 @ lt ) ) ),
inference(pattern_uni,[status(thm)],[1837:[bind(A,$thf( sk1 ))]]) ).
thf(142,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(521,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)],[142]) ).
thf(2046,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[583,438]) ).
thf(2047,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[2046]) ).
thf(2048,plain,
! [A: $i] :
~ ( A @ skaf65 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[2047:[bind(A,$thf( C )),bind(B,$thf( C @ skaf65 ))]]) ).
thf(2075,plain,
! [A: $i] :
~ ( A @ skaf65 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[2048]) ).
thf(195,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(636,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)],[195]) ).
thf(46,axiom,
nil @ strictorderP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause5) ).
thf(299,plain,
nil @ strictorderP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(226,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ geq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnf,[status(esa)],[225]) ).
thf(241,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)],[240]) ).
thf(183,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause86) ).
thf(608,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(6836,plain,
! [A: $i] :
( ( ( nil @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6390,3958]) ).
thf(6837,plain,
! [A: $i] :
( ( ( nil @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[6836]) ).
thf(6838,plain,
nil @ ( sk2 @ app ) @ ( sk2 @ app ) @ ssList,
inference(pattern_uni,[status(thm)],[6837:[bind(A,$thf( nil @ ( sk2 @ app ) ))]]) ).
thf(6404,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf66 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[543,3958]) ).
thf(6405,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf66 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[6404]) ).
thf(6406,plain,
! [A: $i] : ( A @ skaf66 @ ( sk2 @ app ) @ ssList ),
inference(pattern_uni,[status(thm)],[6405:[bind(A,$thf( C )),bind(B,$thf( C @ skaf66 ))]]) ).
thf(6417,plain,
! [A: $i] : ( A @ skaf66 @ ( sk2 @ app ) @ ssList ),
inference(simp,[status(thm)],[6406]) ).
thf(678,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[538,438]) ).
thf(679,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[678]) ).
thf(680,plain,
~ ( skac3 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[679:[bind(A,$thf( skac3 ))]]) ).
thf(1871,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[574,438]) ).
thf(1872,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1871]) ).
thf(1873,plain,
! [A: $i] :
~ ( A @ skaf83 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1872:[bind(A,$thf( C )),bind(B,$thf( C @ skaf83 ))]]) ).
thf(1905,plain,
! [A: $i] :
~ ( A @ skaf83 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1873]) ).
thf(77,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(374,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)],[77]) ).
thf(770,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf72 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[252,236]) ).
thf(771,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf72 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[770]) ).
thf(772,plain,
! [A: $i] :
~ ( A @ skaf72 @ ( A @ skaf72 @ neq ) ),
inference(pattern_uni,[status(thm)],[771:[bind(A,$thf( C )),bind(B,$thf( C @ skaf72 ))]]) ).
thf(786,plain,
! [A: $i] :
~ ( A @ skaf72 @ ( A @ skaf72 @ neq ) ),
inference(simp,[status(thm)],[772]) ).
thf(1682,plain,
! [A: $i] :
( ( ( A @ skaf72 @ ( A @ skaf72 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[205,786]) ).
thf(1683,plain,
! [A: $i] :
( ( A @ skaf72 @ ( A @ skaf72 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[1682]) ).
thf(1684,plain,
! [A: $i] :
( ( ( A @ skaf72 )
!= nil )
| ( ( A @ skaf72 )
!= sk2 ) ),
inference(simp,[status(thm)],[1683]) ).
thf(187,axiom,
! [A: $i] :
( ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause83) ).
thf(617,plain,
! [A: $i] :
( ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(4,negated_conjecture,
sk4 @ ssList,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_4) ).
thf(209,plain,
sk4 @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(130,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(487,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)],[130]) ).
thf(168,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(580,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)],[168]) ).
thf(281,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)],[280]) ).
thf(282,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)],[281]) ).
thf(968,plain,
( ( ( nil @ ( sk2 @ hd @ cons ) @ ssList )
!= ( nil @ ssList ) )
| ( sk1 @ totalorderedP )
| ~ ( sk2 @ ( nil @ neq ) )
| ~ ( sk2 @ hd @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[287,880]) ).
thf(969,plain,
( ( ( nil @ ( sk2 @ hd @ cons ) @ ssList )
!= ( nil @ ssList ) )
| ( sk1 @ totalorderedP )
| ~ ( sk2 @ ( nil @ neq ) )
| ~ ( sk2 @ hd @ ssItem ) ),
inference(simp,[status(thm)],[968]) ).
thf(971,plain,
( ( ( nil @ ( sk2 @ hd @ cons ) )
!= nil )
| ~ ( sk2 @ ( nil @ neq ) )
| ~ ( sk2 @ hd @ ssItem )
| ( sk1 @ totalorderedP ) ),
inference(simp,[status(thm)],[969]) ).
thf(58,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderedP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause66) ).
thf(327,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderedP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(94,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(409,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)],[94]) ).
thf(13841,plain,
! [A: $i] :
( ( ( sk2 @ tl @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13049,3958]) ).
thf(13842,plain,
! [A: $i] :
( ( ( sk2 @ tl @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ( A @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[13841]) ).
thf(13843,plain,
sk2 @ tl @ ( sk2 @ app ) @ ( sk2 @ app ) @ ssList,
inference(pattern_uni,[status(thm)],[13842:[bind(A,$thf( sk2 @ tl @ ( sk2 @ app ) ))]]) ).
thf(10,negated_conjecture,
( ( nil @ ( sk2 @ neq ) )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( sk1 @ singletonP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
thf(199,plain,
( ( nil @ ( sk2 @ neq ) )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( sk1 @ singletonP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1621,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf81 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[503,236]) ).
thf(1622,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf81 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1621]) ).
thf(1623,plain,
! [A: $i] :
~ ( A @ skaf81 @ ( A @ skaf81 @ neq ) ),
inference(pattern_uni,[status(thm)],[1622:[bind(A,$thf( C )),bind(B,$thf( C @ skaf81 ))]]) ).
thf(1637,plain,
! [A: $i] :
~ ( A @ skaf81 @ ( A @ skaf81 @ neq ) ),
inference(simp,[status(thm)],[1623]) ).
thf(109,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(441,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)],[109]) ).
thf(75,axiom,
! [A: $i] :
( ( A @ totalorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf54 @ ( A @ skaf55 @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause94) ).
thf(370,plain,
! [A: $i] :
( ( A @ totalorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf54 @ ( A @ skaf55 @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(6506,plain,
! [A: $i] :
( ( ( sk2 @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[6375,236]) ).
thf(6507,plain,
! [A: $i] :
( ( ( sk2 @ ( sk2 @ app ) @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[6506]) ).
thf(6508,plain,
~ ( sk2 @ ( sk2 @ app ) @ ( sk2 @ ( sk2 @ app ) @ neq ) ),
inference(pattern_uni,[status(thm)],[6507:[bind(A,$thf( sk2 @ ( sk2 @ app ) ))]]) ).
thf(6330,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf61 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[402,3958]) ).
thf(6331,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf61 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[6330]) ).
thf(6332,plain,
! [A: $i] : ( A @ skaf61 @ ( sk2 @ app ) @ ssList ),
inference(pattern_uni,[status(thm)],[6331:[bind(A,$thf( C )),bind(B,$thf( C @ skaf61 ))]]) ).
thf(6436,plain,
! [A: $i] : ( A @ skaf61 @ ( sk2 @ app ) @ ssList ),
inference(simp,[status(thm)],[6332]) ).
thf(1663,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf63 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[542,236]) ).
thf(1664,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf63 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1663]) ).
thf(1665,plain,
! [A: $i] :
~ ( A @ skaf63 @ ( A @ skaf63 @ neq ) ),
inference(pattern_uni,[status(thm)],[1664:[bind(A,$thf( C )),bind(B,$thf( C @ skaf63 ))]]) ).
thf(1679,plain,
! [A: $i] :
~ ( A @ skaf63 @ ( A @ skaf63 @ neq ) ),
inference(simp,[status(thm)],[1665]) ).
thf(1329,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf80 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[436,236]) ).
thf(1330,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf80 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1329]) ).
thf(1331,plain,
! [A: $i] :
~ ( A @ skaf80 @ ( A @ skaf80 @ neq ) ),
inference(pattern_uni,[status(thm)],[1330:[bind(A,$thf( C )),bind(B,$thf( C @ skaf80 ))]]) ).
thf(1336,plain,
! [A: $i] :
~ ( A @ skaf80 @ ( A @ skaf80 @ neq ) ),
inference(simp,[status(thm)],[1331]) ).
thf(153,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(544,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)],[153]) ).
thf(63,axiom,
! [A: $i] :
( ( ( A @ ( nil @ app ) )
= A )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause74) ).
thf(336,plain,
! [A: $i] :
( ( ( A @ ( nil @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(185,axiom,
! [A: $i] : ( A @ skaf78 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause17) ).
thf(613,plain,
! [A: $i] : ( A @ skaf78 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(111,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ( A @ ( B @ neq ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause100) ).
thf(446,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( A @ ( B @ neq ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(2236,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[593,864]) ).
thf(2237,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[2236]) ).
thf(2238,plain,
! [A: $i] : ( nil @ ( A @ skaf50 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[2237:[bind(A,$thf( C )),bind(B,$thf( C @ skaf50 ))]]) ).
thf(2266,plain,
! [A: $i] : ( nil @ ( A @ skaf50 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[2238]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause106) ).
thf(231,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(150,axiom,
! [A: $i] :
( ( nil = A )
| ( A @ hd @ ssItem )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause78) ).
thf(539,plain,
! [A: $i] :
( ( nil = A )
| ( A @ hd @ ssItem )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(1339,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf53 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[451,236]) ).
thf(1340,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf53 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1339]) ).
thf(1341,plain,
! [A: $i] :
~ ( A @ skaf53 @ ( A @ skaf53 @ neq ) ),
inference(pattern_uni,[status(thm)],[1340:[bind(A,$thf( C )),bind(B,$thf( C @ skaf53 ))]]) ).
thf(1346,plain,
! [A: $i] :
~ ( A @ skaf53 @ ( A @ skaf53 @ neq ) ),
inference(simp,[status(thm)],[1341]) ).
thf(4168,plain,
! [A: $i] :
( ( ( A @ skaf53 @ ( A @ skaf53 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[205,1346]) ).
thf(4169,plain,
! [A: $i] :
( ( A @ skaf53 @ ( A @ skaf53 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[4168]) ).
thf(4170,plain,
! [A: $i] :
( ( ( A @ skaf53 )
!= nil )
| ( ( A @ skaf53 )
!= sk2 ) ),
inference(simp,[status(thm)],[4169]) ).
thf(1920,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[578,438]) ).
thf(1921,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1920]) ).
thf(1922,plain,
! [A: $i] :
~ ( A @ skaf74 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1921:[bind(A,$thf( C )),bind(B,$thf( C @ skaf74 ))]]) ).
thf(1949,plain,
! [A: $i] :
~ ( A @ skaf74 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1922]) ).
thf(937,plain,
( ( ( sk2 @ hd @ ssItem )
!= ( skac2 @ ssItem ) )
| ( sk1 @ totalorderedP )
| ~ ( sk2 @ ( nil @ neq ) )
| ~ $true
| ~ ( nil @ ( sk2 @ hd @ cons ) @ ssList ) ),
inference(paramod_ordered,[status(thm)],[525,880]) ).
thf(938,plain,
( ( ( sk2 @ hd @ ssItem )
!= ( skac2 @ ssItem ) )
| ( sk1 @ totalorderedP )
| ~ ( sk2 @ ( nil @ neq ) )
| ~ ( nil @ ( sk2 @ hd @ cons ) @ ssList ) ),
inference(simp,[status(thm)],[937]) ).
thf(976,plain,
( ( ( sk2 @ hd )
!= skac2 )
| ~ ( sk2 @ ( nil @ neq ) )
| ~ ( nil @ ( sk2 @ hd @ cons ) @ ssList )
| ( sk1 @ totalorderedP ) ),
inference(simp,[status(thm)],[938]) ).
thf(56,axiom,
! [B: $i,A: $i] :
( ( B @ singletonP )
| ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( nil @ ( A @ cons ) )
!= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause116) ).
thf(319,plain,
! [B: $i,A: $i] :
( ( B @ singletonP )
| ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( nil @ ( A @ cons ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(192,axiom,
! [A: $i] :
( ( A @ ( A @ segmentP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause57) ).
thf(632,plain,
! [A: $i] :
( ( A @ ( A @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(4674,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf48 ) @ ssList )
!= ( C @ ssList ) )
| ~ $true
| ~ ( C @ ( C @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[424,236]) ).
thf(4675,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf48 ) @ ssList )
!= ( C @ ssList ) )
| ~ ( C @ ( C @ neq ) ) ),
inference(simp,[status(thm)],[4674]) ).
thf(4676,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ skaf48 ) @ ( B @ ( A @ skaf48 ) @ neq ) ),
inference(pattern_uni,[status(thm)],[4675:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf48 ) ))]]) ).
thf(4705,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ skaf48 ) @ ( B @ ( A @ skaf48 ) @ neq ) ),
inference(simp,[status(thm)],[4676]) ).
thf(97,axiom,
! [A: $i] :
( ( A @ skaf49 @ ( A @ skaf50 @ leq ) )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause87) ).
thf(418,plain,
! [A: $i] :
( ( A @ skaf49 @ ( A @ skaf50 @ leq ) )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(6309,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf57 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[317,3958]) ).
thf(6310,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf57 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[6309]) ).
thf(6311,plain,
! [A: $i] : ( A @ skaf57 @ ( sk2 @ app ) @ ssList ),
inference(pattern_uni,[status(thm)],[6310:[bind(A,$thf( C )),bind(B,$thf( C @ skaf57 ))]]) ).
thf(6430,plain,
! [A: $i] : ( A @ skaf57 @ ( sk2 @ app ) @ ssList ),
inference(simp,[status(thm)],[6311]) ).
thf(914,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[394,864]) ).
thf(915,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[914]) ).
thf(916,plain,
! [A: $i] : ( nil @ ( A @ skaf69 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[915:[bind(A,$thf( C )),bind(B,$thf( C @ skaf69 ))]]) ).
thf(929,plain,
! [A: $i] : ( nil @ ( A @ skaf69 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[916]) ).
thf(125,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ cyclefreeP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause70) ).
thf(478,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ cyclefreeP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(2272,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf71 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[597,236]) ).
thf(2273,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf71 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[2272]) ).
thf(2274,plain,
! [A: $i] :
~ ( A @ skaf71 @ ( A @ skaf71 @ neq ) ),
inference(pattern_uni,[status(thm)],[2273:[bind(A,$thf( C )),bind(B,$thf( C @ skaf71 ))]]) ).
thf(2294,plain,
! [A: $i] :
~ ( A @ skaf71 @ ( A @ skaf71 @ neq ) ),
inference(simp,[status(thm)],[2274]) ).
thf(148,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause68) ).
thf(536,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(105,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(433,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)],[105]) ).
thf(139,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(510,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)],[139]) ).
thf(756,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[253,438]) ).
thf(757,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[756]) ).
thf(758,plain,
! [A: $i] :
~ ( A @ skaf79 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[757:[bind(A,$thf( C )),bind(B,$thf( C @ skaf79 ))]]) ).
thf(763,plain,
! [A: $i] :
~ ( A @ skaf79 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[758]) ).
thf(36,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(272,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)],[36]) ).
thf(1153,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[427,438]) ).
thf(1154,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1153]) ).
thf(1155,plain,
! [A: $i] :
~ ( A @ skaf49 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1154:[bind(A,$thf( C )),bind(B,$thf( C @ skaf49 ))]]) ).
thf(1161,plain,
! [A: $i] :
~ ( A @ skaf49 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1155]) ).
thf(53,axiom,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf59 @ ( A @ skaf60 @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause92) ).
thf(315,plain,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf59 @ ( A @ skaf60 @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(6339,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf53 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[451,3958]) ).
thf(6340,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf53 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[6339]) ).
thf(6341,plain,
! [A: $i] : ( A @ skaf53 @ ( sk2 @ app ) @ ssList ),
inference(pattern_uni,[status(thm)],[6340:[bind(A,$thf( C )),bind(B,$thf( C @ skaf53 ))]]) ).
thf(6439,plain,
! [A: $i] : ( A @ skaf53 @ ( sk2 @ app ) @ ssList ),
inference(simp,[status(thm)],[6341]) ).
thf(2717,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)],[203,251]) ).
thf(2718,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ duplicatefreeP )
| ( ( A @ skaf77 @ ( A @ skaf74 @ cons ) @ ( A @ skaf76 @ ( A @ skaf74 @ cons ) @ ( A @ skaf75 @ app ) @ app ) )
= A ) ),
inference(simp,[status(thm)],[2717]) ).
thf(2719,plain,
( ( sk2 @ duplicatefreeP )
| ( ( sk2 @ skaf77 @ ( sk2 @ skaf74 @ cons ) @ ( sk2 @ skaf76 @ ( sk2 @ skaf74 @ cons ) @ ( sk2 @ skaf75 @ app ) @ app ) )
= sk2 ) ),
inference(pattern_uni,[status(thm)],[2718:[bind(A,$thf( sk2 ))]]) ).
thf(1964,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf82 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[579,236]) ).
thf(1965,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf82 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1964]) ).
thf(1966,plain,
! [A: $i] :
~ ( A @ skaf82 @ ( A @ skaf82 @ neq ) ),
inference(pattern_uni,[status(thm)],[1965:[bind(A,$thf( C )),bind(B,$thf( C @ skaf82 ))]]) ).
thf(1986,plain,
! [A: $i] :
~ ( A @ skaf82 @ ( A @ skaf82 @ neq ) ),
inference(simp,[status(thm)],[1966]) ).
thf(99,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(422,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)],[99]) ).
thf(2349,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[613,864]) ).
thf(2350,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[2349]) ).
thf(2351,plain,
! [A: $i] : ( nil @ ( A @ skaf78 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[2350:[bind(A,$thf( C )),bind(B,$thf( C @ skaf78 ))]]) ).
thf(2374,plain,
! [A: $i] : ( nil @ ( A @ skaf78 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[2351]) ).
thf(47,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(300,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)],[47]) ).
thf(833,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk1 @ ( sk1 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[205,769]) ).
thf(834,plain,
( ( nil @ ( sk2 @ neq ) )
!= ( sk1 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[833]) ).
thf(835,plain,
( ( nil != sk1 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[834]) ).
thf(262,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ geq ) ) ),
inference(cnf,[status(esa)],[261]) ).
thf(865,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[538,864]) ).
thf(866,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[865]) ).
thf(867,plain,
nil @ ( skac3 @ cons ) @ totalorderedP,
inference(pattern_uni,[status(thm)],[866:[bind(A,$thf( skac3 ))]]) ).
thf(273,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)],[272]) ).
thf(160,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(564,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)],[160]) ).
thf(49,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(305,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)],[49]) ).
thf(65,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ hd )
= A )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause97) ).
thf(341,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ hd )
= A )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(89,axiom,
! [A: $i] :
( ( A @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause59) ).
thf(400,plain,
! [A: $i] :
( ( A @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(146,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(532,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)],[146]) ).
thf(40,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause117) ).
thf(283,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(96,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(415,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)],[96]) ).
thf(7188,plain,
( ( ( sk2 @ ( sk2 @ app ) @ ( sk2 @ ( sk2 @ app ) @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[205,6508]) ).
thf(7189,plain,
( ( sk2 @ ( sk2 @ app ) @ ( sk2 @ ( sk2 @ app ) @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[7188]) ).
thf(7199,plain,
( ( ( sk2 @ ( sk2 @ app ) )
!= nil )
| ( ( sk2 @ ( sk2 @ app ) )
!= sk2 ) ),
inference(simp,[status(thm)],[7189]) ).
thf(239,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)],[238]) ).
thf(2794,plain,
! [A: $i] :
( ( ( nil @ ( sk1 @ skaf44 @ cons ) )
!= ( nil @ ( A @ skaf44 @ cons ) ) )
| ( sk1 @ totalorderedP )
| ~ ( sk1 @ singletonP ) ),
inference(paramod_ordered,[status(thm)],[2480,905]) ).
thf(2795,plain,
( ( sk1 @ totalorderedP )
| ~ ( sk1 @ singletonP ) ),
inference(pattern_uni,[status(thm)],[2794:[bind(A,$thf( sk1 ))]]) ).
thf(118,axiom,
! [A: $i] :
( ( A @ ( A @ leq ) )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause62) ).
thf(464,plain,
! [A: $i] :
( ( A @ ( A @ leq ) )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(165,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(575,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)],[165]) ).
thf(6324,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf62 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[237,3958]) ).
thf(6325,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf62 @ ssList )
!= ( B @ ssList ) )
| ( B @ ( sk2 @ app ) @ ssList ) ),
inference(simp,[status(thm)],[6324]) ).
thf(6326,plain,
! [A: $i] : ( A @ skaf62 @ ( sk2 @ app ) @ ssList ),
inference(pattern_uni,[status(thm)],[6325:[bind(A,$thf( C )),bind(B,$thf( C @ skaf62 ))]]) ).
thf(6435,plain,
! [A: $i] : ( A @ skaf62 @ ( sk2 @ app ) @ ssList ),
inference(simp,[status(thm)],[6326]) ).
thf(3770,plain,
! [A: $i] :
( ( ( A @ skaf73 @ ( A @ skaf73 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[205,913]) ).
thf(3771,plain,
! [A: $i] :
( ( A @ skaf73 @ ( A @ skaf73 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[3770]) ).
thf(3772,plain,
! [A: $i] :
( ( ( A @ skaf73 )
!= nil )
| ( ( A @ skaf73 )
!= sk2 ) ),
inference(simp,[status(thm)],[3771]) ).
thf(2341,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[613,438]) ).
thf(2342,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[2341]) ).
thf(2343,plain,
! [A: $i] :
~ ( A @ skaf78 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[2342:[bind(A,$thf( C )),bind(B,$thf( C @ skaf78 ))]]) ).
thf(2372,plain,
! [A: $i] :
~ ( A @ skaf78 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[2343]) ).
thf(1083,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[399,438]) ).
thf(1084,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1083]) ).
thf(1085,plain,
! [A: $i] :
~ ( A @ skaf70 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1084:[bind(A,$thf( C )),bind(B,$thf( C @ skaf70 ))]]) ).
thf(1093,plain,
! [A: $i] :
~ ( A @ skaf70 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1085]) ).
thf(129,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf47 ) @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause49) ).
thf(486,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf47 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(4540,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf46 ) @ ssList )
!= ( C @ ssList ) )
| ~ $true
| ~ ( C @ ( C @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[270,236]) ).
thf(4541,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf46 ) @ ssList )
!= ( C @ ssList ) )
| ~ ( C @ ( C @ neq ) ) ),
inference(simp,[status(thm)],[4540]) ).
thf(4542,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ skaf46 ) @ ( B @ ( A @ skaf46 ) @ neq ) ),
inference(pattern_uni,[status(thm)],[4541:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf46 ) ))]]) ).
thf(4584,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ skaf46 ) @ ( B @ ( A @ skaf46 ) @ neq ) ),
inference(simp,[status(thm)],[4542]) ).
thf(196,axiom,
! [A: $i] :
( ( A @ ( A @ frontsegP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause61) ).
thf(639,plain,
! [A: $i] :
( ( A @ ( A @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(9993,plain,
( ( ( sk1 @ ( sk2 @ app ) @ ( sk1 @ ( sk2 @ app ) @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[205,6940]) ).
thf(9994,plain,
( ( sk1 @ ( sk2 @ app ) @ ( sk1 @ ( sk2 @ app ) @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[9993]) ).
thf(10002,plain,
( ( ( sk1 @ ( sk2 @ app ) )
!= nil )
| ( ( sk1 @ ( sk2 @ app ) )
!= sk2 ) ),
inference(simp,[status(thm)],[9994]) ).
thf(232,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ lt ) ) ),
inference(cnf,[status(esa)],[231]) ).
thf(4159,plain,
! [A: $i] :
( ( ( A @ skaf80 @ ( A @ skaf80 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[205,1336]) ).
thf(4160,plain,
! [A: $i] :
( ( A @ skaf80 @ ( A @ skaf80 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[4159]) ).
thf(4161,plain,
! [A: $i] :
( ( ( A @ skaf80 )
!= nil )
| ( ( A @ skaf80 )
!= sk2 ) ),
inference(simp,[status(thm)],[4160]) ).
thf(19371,plain,
$false,
inference(e,[status(thm)],[629,1823,2031,347,846,518,555,481,333,249,2480,468,2077,683,276,6495,308,449,379,1158,582,614,269,202,597,385,550,500,3781,913,2580,1063,4638,6416,538,2146,13147,7235,288,1366,436,257,1660,372,504,1907,587,802,344,357,6434,542,460,853,881,261,1704,870,216,475,492,591,443,253,485,238,514,353,348,574,905,480,766,280,634,221,293,453,396,2799,243,428,265,13155,206,248,439,270,201,12029,13049,366,6442,798,233,452,2264,598,561,424,407,788,260,862,3958,2464,252,361,2820,329,1951,583,493,2213,1128,13153,224,879,6427,578,13946,317,6940,6375,2577,403,388,593,610,783,420,225,339,476,13009,526,13066,590,547,471,256,622,7014,1131,6433,569,12962,1060,457,503,605,237,244,266,205,508,311,657,558,530,1616,6400,412,425,1103,2033,2570,279,2734,296,601,6437,430,584,904,402,2817,204,259,6927,2568,579,291,391,382,313,787,498,466,335,1356,350,641,2161,572,2326,1090,236,406,274,6443,377,245,318,1376,979,604,362,451,567,880,649,271,208,387,552,535,323,594,213,621,626,769,198,330,932,240,251,1838,521,2075,399,636,394,299,226,438,241,223,608,6838,6417,680,1905,374,1684,617,209,487,525,580,282,971,327,409,263,13843,199,1637,441,370,6508,6436,1679,1336,544,336,613,864,446,497,2266,231,539,4170,1949,203,976,6390,319,304,258,632,4705,418,786,6430,207,929,478,2294,536,6854,246,433,510,763,272,1161,287,315,6439,2719,1986,422,603,2374,300,835,262,867,273,564,305,341,437,474,400,532,1346,283,415,7199,239,242,635,2795,464,575,427,6435,3772,200,277,2372,1093,395,486,4584,639,491,10002,232,254,227,543,4161]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC382-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.22/0.48 % Computer : n004.cluster.edu
% 0.22/0.48 % Model : x86_64 x86_64
% 0.22/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.48 % Memory : 8046.5625MB
% 0.22/0.48 % OS : Linux 6.8.0-71-generic
% 0.22/0.49 % CPULimit : 300
% 0.22/0.49 % WCLimit : 300
% 0.22/0.49 % DateTime : Sat Sep 26 12:55:52 UTC 2026
% 0.22/0.49 % CPUTime :
% 0.22/0.49 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
% 1.06/1.19 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.40/1.63 % [INFO] Parsing done (438ms).
% 2.40/1.65 % [INFO] Running in sequential loop mode.
% 3.94/2.18 % [INFO] eprover registered as external prover.
% 3.94/2.18 % [INFO] Scanning for conjecture ...
% 4.34/2.30 % [INFO] Found a conjecture (or negated_conjecture) and 185 axioms. Running axiom selection ...
% 4.66/2.44 % [INFO] Axiom selection finished. Selected 185 axioms (removed 0 axioms).
% 5.12/2.57 % [INFO] Problem is propositional (TPTP CNF).
% 5.12/2.58 % [INFO] Type checking passed.
% 5.12/2.59 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 104.16/21.32 % External prover 'e' found a proof!
% 104.16/21.32 % [INFO] Killing All external provers ...
% 104.16/21.32 % Time passed: 20623ms (effective reasoning time: 19658ms)
% 104.16/21.32 % 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
% 104.16/21.32 % No. of inferences in proof: 883
% 104.16/21.33 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 20623 ms resp. 19658 ms w/o parsing
% 105.70/21.66 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 105.70/21.67 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------