TSTP Solution File: COL092-1 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : COL092-1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Fri Jul 15 00:34:48 EDT 2022
% Result : Unsatisfiable 0.40s 0.94s
% Output : CNFRefutation 0.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 83
% Syntax : Number of formulae : 479 ( 263 unt; 27 typ; 0 def)
% Number of atoms : 2176 ( 768 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 4852 ( 447 ~; 578 |; 0 &;3827 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 55 ( 55 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 27 usr; 9 con; 0-3 aty)
% Number of variables : 1163 ( 0 ^1163 !; 0 ?;1163 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_ap_contractE_c1,type,
ap_contractE_c1: $i > $i > $i > $o ).
thf(tp_ap_contractE_c2,type,
ap_contractE_c2: $i > $i > $i > $o ).
thf(tp_ap_contractE_c3,type,
ap_contractE_c3: $i > $i > $i > $o ).
thf(tp_ap_contractE_c4,type,
ap_contractE_c4: $i > $i > $i > $o ).
thf(tp_ap_contractE_sk1p,type,
ap_contractE_sk1p: $i > $i > $i > $i ).
thf(tp_ap_contractE_sk1q,type,
ap_contractE_sk1q: $i > $i > $i > $i ).
thf(tp_ap_contractE_sk2q,type,
ap_contractE_sk2q: $i > $i > $i > $i ).
thf(tp_ap_contractE_sk3q,type,
ap_contractE_sk3q: $i > $i > $i > $i ).
thf(tp_ap_parcontractE_c1,type,
ap_parcontractE_c1: $i > $i > $i > $o ).
thf(tp_ap_parcontractE_c2,type,
ap_parcontractE_c2: $i > $i > $i > $o ).
thf(tp_ap_parcontractE_c3,type,
ap_parcontractE_c3: $i > $i > $i > $o ).
thf(tp_ap_parcontractE_c4,type,
ap_parcontractE_c4: $i > $i > $i > $o ).
thf(tp_ap_parcontractE_sk1p,type,
ap_parcontractE_sk1p: $i > $i > $i > $i ).
thf(tp_ap_parcontractE_sk1q,type,
ap_parcontractE_sk1q: $i > $i > $i > $i ).
thf(tp_ap_parcontractE_sk2q,type,
ap_parcontractE_sk2q: $i > $i > $i > $i ).
thf(tp_ap_parcontractE_sk2s,type,
ap_parcontractE_sk2s: $i > $i > $i > $i ).
thf(tp_comb,type,
comb: $i ).
thf(tp_combK,type,
combK: $i ).
thf(tp_combS,type,
combS: $i ).
thf(tp_comb_app,type,
comb_app: $i > $i > $i ).
thf(tp_contract,type,
contract: $i ).
thf(tp_member,type,
member: $i > $i > $o ).
thf(tp_p,type,
p: $i ).
thf(tp_pair,type,
pair: $i > $i > $i ).
thf(tp_parcontract,type,
parcontract: $i ).
thf(tp_r,type,
r: $i ).
thf(tp_rtrancl,type,
rtrancl: $i > $i ).
thf(1,axiom,
! [P: $i,Q: $i,R: $i] :
( ~ ( ap_parcontractE_c4 @ P @ Q @ R )
| ( R
= ( comb_app @ ( ap_parcontractE_sk2q @ P @ Q @ R ) @ ( ap_parcontractE_sk2s @ P @ Q @ R ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE14) ).
thf(2,axiom,
! [P: $i,Q: $i,R: $i] :
( ~ ( ap_parcontractE_c4 @ P @ Q @ R )
| ( member @ ( pair @ Q @ ( ap_parcontractE_sk2s @ P @ Q @ R ) ) @ parcontract ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE13) ).
thf(3,axiom,
! [P: $i,Q: $i,R: $i] :
( ~ ( ap_parcontractE_c4 @ P @ Q @ R )
| ( member @ ( pair @ P @ ( ap_parcontractE_sk2q @ P @ Q @ R ) ) @ parcontract ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE12) ).
thf(4,axiom,
! [P: $i,Q: $i,R: $i] :
( ~ ( ap_parcontractE_c3 @ P @ Q @ R )
| ( P
= ( comb_app @ ( comb_app @ combS @ ( ap_parcontractE_sk1p @ P @ Q @ R ) ) @ ( ap_parcontractE_sk1q @ P @ Q @ R ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE11) ).
thf(5,axiom,
! [P: $i,Q: $i,R: $i] :
( ~ ( ap_parcontractE_c3 @ P @ Q @ R )
| ( R
= ( comb_app @ ( comb_app @ ( ap_parcontractE_sk1p @ P @ Q @ R ) @ Q ) @ ( comb_app @ ( ap_parcontractE_sk1q @ P @ Q @ R ) @ Q ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE10) ).
thf(6,axiom,
! [P: $i,Q: $i,R: $i] :
( ~ ( ap_parcontractE_c3 @ P @ Q @ R )
| ( member @ Q @ comb ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE9) ).
thf(7,axiom,
! [P: $i,Q: $i,R: $i] :
( ~ ( ap_parcontractE_c3 @ P @ Q @ R )
| ( member @ ( ap_parcontractE_sk1q @ P @ Q @ R ) @ comb ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE8) ).
thf(8,axiom,
! [P: $i,Q: $i,R: $i] :
( ~ ( ap_parcontractE_c3 @ P @ Q @ R )
| ( member @ ( ap_parcontractE_sk1p @ P @ Q @ R ) @ comb ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE7) ).
thf(9,axiom,
! [P: $i,Q: $i,R: $i] :
( ~ ( ap_parcontractE_c2 @ P @ Q @ R )
| ( P
= ( comb_app @ combK @ R ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE6) ).
thf(10,axiom,
! [P: $i,Q: $i,R: $i] :
( ~ ( ap_parcontractE_c2 @ P @ Q @ R )
| ( member @ Q @ comb ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE5) ).
thf(11,axiom,
! [P: $i,Q: $i,R: $i] :
( ~ ( ap_parcontractE_c2 @ P @ Q @ R )
| ( member @ R @ comb ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE4) ).
thf(12,axiom,
! [P: $i,Q: $i,R: $i] :
( ~ ( ap_parcontractE_c1 @ P @ Q @ R )
| ( R
= ( comb_app @ P @ Q ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE3) ).
thf(13,axiom,
! [P: $i,Q: $i,R: $i] :
( ~ ( ap_parcontractE_c1 @ P @ Q @ R )
| ( member @ ( comb_app @ P @ Q ) @ comb ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE2) ).
thf(14,axiom,
! [P: $i,Q: $i,R: $i] :
( ~ ( member @ ( pair @ ( comb_app @ P @ Q ) @ R ) @ parcontract )
| ( ap_parcontractE_c1 @ P @ Q @ R )
| ( ap_parcontractE_c2 @ P @ Q @ R )
| ( ap_parcontractE_c3 @ P @ Q @ R )
| ( ap_parcontractE_c4 @ P @ Q @ R ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE1) ).
thf(15,axiom,
! [R: $i] :
( ~ ( member @ ( pair @ combS @ R ) @ parcontract )
| ( R = combS ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_parcontractE2) ).
thf(16,axiom,
! [R: $i] :
( ~ ( member @ ( pair @ combS @ R ) @ parcontract )
| ( member @ combS @ comb ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_parcontractE1) ).
thf(17,axiom,
! [R: $i] :
( ~ ( member @ ( pair @ combK @ R ) @ parcontract )
| ( R = combK ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_parcontractE2) ).
thf(18,axiom,
! [R: $i] :
( ~ ( member @ ( pair @ combK @ R ) @ parcontract )
| ( member @ combK @ comb ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_parcontractE1) ).
thf(19,axiom,
! [P: $i,Q: $i,R: $i,S: $i] :
( ~ ( member @ ( pair @ P @ Q ) @ parcontract )
| ~ ( member @ ( pair @ R @ S ) @ parcontract )
| ( member @ ( pair @ ( comb_app @ P @ R ) @ ( comb_app @ Q @ S ) ) @ parcontract ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',parcontract_intros4) ).
thf(20,axiom,
! [P: $i,Q: $i,R: $i] :
( ~ ( member @ P @ comb )
| ~ ( member @ Q @ comb )
| ~ ( member @ R @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ P ) @ Q ) @ R ) @ ( comb_app @ ( comb_app @ P @ R ) @ ( comb_app @ Q @ R ) ) ) @ parcontract ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',parcontract_intros3) ).
thf(21,axiom,
! [P: $i,Q: $i] :
( ~ ( member @ P @ comb )
| ~ ( member @ Q @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ P ) @ Q ) @ P ) @ parcontract ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',parcontract_intros2) ).
thf(22,axiom,
! [P: $i] :
( ~ ( member @ P @ comb )
| ( member @ ( pair @ P @ P ) @ parcontract ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',parcontract_intros1) ).
thf(23,axiom,
! [R: $i] :
~ ( member @ ( pair @ combS @ R ) @ contract ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_contractE) ).
thf(24,axiom,
! [R: $i] :
~ ( member @ ( pair @ combK @ R ) @ contract ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_contractE) ).
thf(25,axiom,
! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c4 @ P @ Q @ R )
| ( R
= ( comb_app @ P @ ( ap_contractE_sk3q @ P @ Q @ R ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE15) ).
thf(26,axiom,
! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c4 @ P @ Q @ R )
| ( member @ P @ comb ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE14) ).
thf(27,axiom,
! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c4 @ P @ Q @ R )
| ( member @ ( pair @ Q @ ( ap_contractE_sk3q @ P @ Q @ R ) ) @ contract ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE13) ).
thf(28,axiom,
! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c3 @ P @ Q @ R )
| ( R
= ( comb_app @ ( ap_contractE_sk2q @ P @ Q @ R ) @ Q ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE12) ).
thf(29,axiom,
! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c3 @ P @ Q @ R )
| ( member @ Q @ comb ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE11) ).
thf(30,axiom,
! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c3 @ P @ Q @ R )
| ( member @ ( pair @ P @ ( ap_contractE_sk2q @ P @ Q @ R ) ) @ contract ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE10) ).
thf(31,axiom,
! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c2 @ P @ Q @ R )
| ( P
= ( comb_app @ ( comb_app @ combS @ ( ap_contractE_sk1p @ P @ Q @ R ) ) @ ( ap_contractE_sk1q @ P @ Q @ R ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE9) ).
thf(32,axiom,
! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c2 @ P @ Q @ R )
| ( R
= ( comb_app @ ( comb_app @ ( ap_contractE_sk1p @ P @ Q @ R ) @ Q ) @ ( comb_app @ ( ap_contractE_sk1q @ P @ Q @ R ) @ Q ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE8) ).
thf(33,axiom,
! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c2 @ P @ Q @ R )
| ( member @ Q @ comb ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE7) ).
thf(34,axiom,
! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c2 @ P @ Q @ R )
| ( member @ ( ap_contractE_sk1q @ P @ Q @ R ) @ comb ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE6) ).
thf(35,axiom,
! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c2 @ P @ Q @ R )
| ( member @ ( ap_contractE_sk1p @ P @ Q @ R ) @ comb ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE5) ).
thf(36,axiom,
! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c1 @ P @ Q @ R )
| ( P
= ( comb_app @ combK @ R ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE4) ).
thf(37,axiom,
! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c1 @ P @ Q @ R )
| ( member @ Q @ comb ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE3) ).
thf(38,axiom,
! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c1 @ P @ Q @ R )
| ( member @ R @ comb ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE2) ).
thf(39,axiom,
! [P: $i,Q: $i,R: $i] :
( ~ ( member @ ( pair @ ( comb_app @ P @ Q ) @ R ) @ contract )
| ( ap_contractE_c1 @ P @ Q @ R )
| ( ap_contractE_c2 @ P @ Q @ R )
| ( ap_contractE_c3 @ P @ Q @ R )
| ( ap_contractE_c4 @ P @ Q @ R ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE1) ).
thf(40,axiom,
! [P: $i,Q: $i,R: $i] :
( ~ ( member @ P @ comb )
| ~ ( member @ Q @ comb )
| ~ ( member @ R @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ P ) @ Q ) @ R ) @ ( comb_app @ ( comb_app @ P @ R ) @ ( comb_app @ Q @ R ) ) ) @ contract ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contract_S) ).
thf(41,axiom,
! [P: $i,Q: $i] :
( ~ ( member @ P @ comb )
| ~ ( member @ Q @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ P ) @ Q ) @ P ) @ contract ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contract_K) ).
thf(42,axiom,
! [A: $i] :
( ~ ( member @ A @ comb )
| ( member @ ( pair @ A @ A ) @ ( rtrancl @ contract ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reduction_refl) ).
thf(43,axiom,
! [P: $i,Q: $i] :
( ~ ( member @ P @ comb )
| ~ ( member @ Q @ comb )
| ( member @ ( comb_app @ P @ Q ) @ comb ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',comb_intros3) ).
thf(44,axiom,
member @ combS @ comb,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',comb_intros2) ).
thf(45,axiom,
member @ combK @ comb,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',comb_intros1) ).
thf(46,axiom,
! [P: $i,Q: $i] :
( ~ ( member @ ( comb_app @ P @ Q ) @ comb )
| ( member @ Q @ comb ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_E2) ).
thf(47,axiom,
! [P: $i,Q: $i] :
( ~ ( member @ ( comb_app @ P @ Q ) @ comb )
| ( member @ P @ comb ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_E1) ).
thf(48,axiom,
! [P1: $i,P2: $i,Q1: $i,Q2: $i] :
( ( P1 != P2 )
| ( Q1 != Q2 )
| ( ( comb_app @ P1 @ Q1 )
= ( comb_app @ P2 @ Q2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',app_app3) ).
thf(49,axiom,
! [P1: $i,Q1: $i,P2: $i,Q2: $i] :
( ( ( comb_app @ P1 @ Q1 )
!= ( comb_app @ P2 @ Q2 ) )
| ( Q1 = Q2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',app_app2) ).
thf(50,axiom,
! [P1: $i,Q1: $i,P2: $i,Q2: $i] :
( ( ( comb_app @ P1 @ Q1 )
!= ( comb_app @ P2 @ Q2 ) )
| ( P1 = P2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',app_app1) ).
thf(51,axiom,
! [P: $i,Q: $i] :
( combS
!= ( comb_app @ P @ Q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_app) ).
thf(52,axiom,
! [P: $i,Q: $i] :
( combK
!= ( comb_app @ P @ Q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_app) ).
thf(53,axiom,
combK != combS,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_s) ).
thf(54,axiom,
member @ ( pair @ ( comb_app @ combK @ p ) @ r ) @ parcontract,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k1_parcontractD_h1) ).
thf(55,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(56,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[55]) ).
thf(57,negated_conjecture,
! [PP: $i] :
( ( r
!= ( comb_app @ combK @ PP ) )
| ~ ( member @ ( pair @ p @ PP ) @ parcontract ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k1_parcontractD_c1) ).
thf(58,plain,
$false = $false,
inference(unfold_def,[status(thm)],[56]) ).
thf(59,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_parcontractE_c4 @ P @ Q @ R )
| ( R
= ( comb_app @ ( ap_parcontractE_sk2q @ P @ Q @ R ) @ ( ap_parcontractE_sk2s @ P @ Q @ R ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(60,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_parcontractE_c4 @ P @ Q @ R )
| ( member @ ( pair @ Q @ ( ap_parcontractE_sk2s @ P @ Q @ R ) ) @ parcontract ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(61,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_parcontractE_c4 @ P @ Q @ R )
| ( member @ ( pair @ P @ ( ap_parcontractE_sk2q @ P @ Q @ R ) ) @ parcontract ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(62,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_parcontractE_c3 @ P @ Q @ R )
| ( P
= ( comb_app @ ( comb_app @ combS @ ( ap_parcontractE_sk1p @ P @ Q @ R ) ) @ ( ap_parcontractE_sk1q @ P @ Q @ R ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(63,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_parcontractE_c3 @ P @ Q @ R )
| ( R
= ( comb_app @ ( comb_app @ ( ap_parcontractE_sk1p @ P @ Q @ R ) @ Q ) @ ( comb_app @ ( ap_parcontractE_sk1q @ P @ Q @ R ) @ Q ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(64,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_parcontractE_c3 @ P @ Q @ R )
| ( member @ Q @ comb ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(65,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_parcontractE_c3 @ P @ Q @ R )
| ( member @ ( ap_parcontractE_sk1q @ P @ Q @ R ) @ comb ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(66,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_parcontractE_c3 @ P @ Q @ R )
| ( member @ ( ap_parcontractE_sk1p @ P @ Q @ R ) @ comb ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(67,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_parcontractE_c2 @ P @ Q @ R )
| ( P
= ( comb_app @ combK @ R ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(68,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_parcontractE_c2 @ P @ Q @ R )
| ( member @ Q @ comb ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(69,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_parcontractE_c2 @ P @ Q @ R )
| ( member @ R @ comb ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(70,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_parcontractE_c1 @ P @ Q @ R )
| ( R
= ( comb_app @ P @ Q ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(71,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_parcontractE_c1 @ P @ Q @ R )
| ( member @ ( comb_app @ P @ Q ) @ comb ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(72,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( member @ ( pair @ ( comb_app @ P @ Q ) @ R ) @ parcontract )
| ( ap_parcontractE_c1 @ P @ Q @ R )
| ( ap_parcontractE_c2 @ P @ Q @ R )
| ( ap_parcontractE_c3 @ P @ Q @ R )
| ( ap_parcontractE_c4 @ P @ Q @ R ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(73,plain,
( ( ! [R: $i] :
( ~ ( member @ ( pair @ combS @ R ) @ parcontract )
| ( R = combS ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(74,plain,
( ( ! [R: $i] :
( ~ ( member @ ( pair @ combS @ R ) @ parcontract )
| ( member @ combS @ comb ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(75,plain,
( ( ! [R: $i] :
( ~ ( member @ ( pair @ combK @ R ) @ parcontract )
| ( R = combK ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(76,plain,
( ( ! [R: $i] :
( ~ ( member @ ( pair @ combK @ R ) @ parcontract )
| ( member @ combK @ comb ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(77,plain,
( ( ! [P: $i,Q: $i,R: $i,S: $i] :
( ~ ( member @ ( pair @ P @ Q ) @ parcontract )
| ~ ( member @ ( pair @ R @ S ) @ parcontract )
| ( member @ ( pair @ ( comb_app @ P @ R ) @ ( comb_app @ Q @ S ) ) @ parcontract ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(78,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( member @ P @ comb )
| ~ ( member @ Q @ comb )
| ~ ( member @ R @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ P ) @ Q ) @ R ) @ ( comb_app @ ( comb_app @ P @ R ) @ ( comb_app @ Q @ R ) ) ) @ parcontract ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(79,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( member @ P @ comb )
| ~ ( member @ Q @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ P ) @ Q ) @ P ) @ parcontract ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(80,plain,
( ( ! [P: $i] :
( ~ ( member @ P @ comb )
| ( member @ ( pair @ P @ P ) @ parcontract ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(81,plain,
( ( ! [R: $i] :
~ ( member @ ( pair @ combS @ R ) @ contract ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(82,plain,
( ( ! [R: $i] :
~ ( member @ ( pair @ combK @ R ) @ contract ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(83,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c4 @ P @ Q @ R )
| ( R
= ( comb_app @ P @ ( ap_contractE_sk3q @ P @ Q @ R ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(84,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c4 @ P @ Q @ R )
| ( member @ P @ comb ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(85,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c4 @ P @ Q @ R )
| ( member @ ( pair @ Q @ ( ap_contractE_sk3q @ P @ Q @ R ) ) @ contract ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(86,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c3 @ P @ Q @ R )
| ( R
= ( comb_app @ ( ap_contractE_sk2q @ P @ Q @ R ) @ Q ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(87,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c3 @ P @ Q @ R )
| ( member @ Q @ comb ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(88,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c3 @ P @ Q @ R )
| ( member @ ( pair @ P @ ( ap_contractE_sk2q @ P @ Q @ R ) ) @ contract ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(89,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c2 @ P @ Q @ R )
| ( P
= ( comb_app @ ( comb_app @ combS @ ( ap_contractE_sk1p @ P @ Q @ R ) ) @ ( ap_contractE_sk1q @ P @ Q @ R ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(90,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c2 @ P @ Q @ R )
| ( R
= ( comb_app @ ( comb_app @ ( ap_contractE_sk1p @ P @ Q @ R ) @ Q ) @ ( comb_app @ ( ap_contractE_sk1q @ P @ Q @ R ) @ Q ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(91,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c2 @ P @ Q @ R )
| ( member @ Q @ comb ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(92,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c2 @ P @ Q @ R )
| ( member @ ( ap_contractE_sk1q @ P @ Q @ R ) @ comb ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(93,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c2 @ P @ Q @ R )
| ( member @ ( ap_contractE_sk1p @ P @ Q @ R ) @ comb ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(94,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c1 @ P @ Q @ R )
| ( P
= ( comb_app @ combK @ R ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(95,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c1 @ P @ Q @ R )
| ( member @ Q @ comb ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(96,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c1 @ P @ Q @ R )
| ( member @ R @ comb ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(97,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( member @ ( pair @ ( comb_app @ P @ Q ) @ R ) @ contract )
| ( ap_contractE_c1 @ P @ Q @ R )
| ( ap_contractE_c2 @ P @ Q @ R )
| ( ap_contractE_c3 @ P @ Q @ R )
| ( ap_contractE_c4 @ P @ Q @ R ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(98,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( member @ P @ comb )
| ~ ( member @ Q @ comb )
| ~ ( member @ R @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ P ) @ Q ) @ R ) @ ( comb_app @ ( comb_app @ P @ R ) @ ( comb_app @ Q @ R ) ) ) @ contract ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(99,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( member @ P @ comb )
| ~ ( member @ Q @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ P ) @ Q ) @ P ) @ contract ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(100,plain,
( ( ! [A: $i] :
( ~ ( member @ A @ comb )
| ( member @ ( pair @ A @ A ) @ ( rtrancl @ contract ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(101,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( member @ P @ comb )
| ~ ( member @ Q @ comb )
| ( member @ ( comb_app @ P @ Q ) @ comb ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(102,plain,
( ( member @ combS @ comb )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(103,plain,
( ( member @ combK @ comb )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(104,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( member @ ( comb_app @ P @ Q ) @ comb )
| ( member @ Q @ comb ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(105,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( member @ ( comb_app @ P @ Q ) @ comb )
| ( member @ P @ comb ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(106,plain,
( ( ! [P1: $i,P2: $i,Q1: $i,Q2: $i] :
( ( P1 != P2 )
| ( Q1 != Q2 )
| ( ( comb_app @ P1 @ Q1 )
= ( comb_app @ P2 @ Q2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(107,plain,
( ( ! [P1: $i,Q1: $i,P2: $i,Q2: $i] :
( ( ( comb_app @ P1 @ Q1 )
!= ( comb_app @ P2 @ Q2 ) )
| ( Q1 = Q2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(108,plain,
( ( ! [P1: $i,Q1: $i,P2: $i,Q2: $i] :
( ( ( comb_app @ P1 @ Q1 )
!= ( comb_app @ P2 @ Q2 ) )
| ( P1 = P2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(109,plain,
( ( ! [P: $i,Q: $i] :
( combS
!= ( comb_app @ P @ Q ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(110,plain,
( ( ! [P: $i,Q: $i] :
( combK
!= ( comb_app @ P @ Q ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(111,plain,
( ( ( combK != combS ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(112,plain,
( ( member @ ( pair @ ( comb_app @ combK @ p ) @ r ) @ parcontract )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(113,plain,
( ( ! [PP: $i] :
( ( r
!= ( comb_app @ combK @ PP ) )
| ~ ( member @ ( pair @ p @ PP ) @ parcontract ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(114,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[58]) ).
thf(115,plain,
( ( ! [P: $i,Q: $i] :
( ! [R: $i] :
~ ( ap_parcontractE_c3 @ P @ Q @ R )
| ( member @ Q @ comb ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[64]) ).
thf(116,plain,
( ( ! [P: $i,Q: $i] :
( ! [R: $i] :
~ ( ap_parcontractE_c2 @ P @ Q @ R )
| ( member @ Q @ comb ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[68]) ).
thf(117,plain,
( ( ! [P: $i,Q: $i] :
( ! [R: $i] :
~ ( ap_parcontractE_c1 @ P @ Q @ R )
| ( member @ ( comb_app @ P @ Q ) @ comb ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[71]) ).
thf(118,plain,
( ( ! [R: $i] :
~ ( member @ ( pair @ combS @ R ) @ parcontract )
| ( member @ combS @ comb ) )
= $true ),
inference(extcnf_combined,[status(esa)],[74]) ).
thf(119,plain,
( ( ! [R: $i] :
~ ( member @ ( pair @ combK @ R ) @ parcontract )
| ( member @ combK @ comb ) )
= $true ),
inference(extcnf_combined,[status(esa)],[76]) ).
thf(120,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( member @ ( pair @ P @ Q ) @ parcontract )
| ! [R: $i,S: $i] :
( ~ ( member @ ( pair @ R @ S ) @ parcontract )
| ( member @ ( pair @ ( comb_app @ P @ R ) @ ( comb_app @ Q @ S ) ) @ parcontract ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[77]) ).
thf(121,plain,
( ( ! [P: $i] :
( ~ ( member @ P @ comb )
| ! [Q: $i] :
( ~ ( member @ Q @ comb )
| ! [R: $i] :
( ~ ( member @ R @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ P ) @ Q ) @ R ) @ ( comb_app @ ( comb_app @ P @ R ) @ ( comb_app @ Q @ R ) ) ) @ parcontract ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[78]) ).
thf(122,plain,
( ( ! [P: $i] :
( ~ ( member @ P @ comb )
| ! [Q: $i] :
( ~ ( member @ Q @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ P ) @ Q ) @ P ) @ parcontract ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[79]) ).
thf(123,plain,
( ( ! [P: $i] :
( ! [Q: $i,R: $i] :
~ ( ap_contractE_c4 @ P @ Q @ R )
| ( member @ P @ comb ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[84]) ).
thf(124,plain,
( ( ! [P: $i,Q: $i] :
( ! [R: $i] :
~ ( ap_contractE_c3 @ P @ Q @ R )
| ( member @ Q @ comb ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[87]) ).
thf(125,plain,
( ( ! [P: $i,Q: $i] :
( ! [R: $i] :
~ ( ap_contractE_c2 @ P @ Q @ R )
| ( member @ Q @ comb ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[91]) ).
thf(126,plain,
( ( ! [P: $i,Q: $i] :
( ! [R: $i] :
~ ( ap_contractE_c1 @ P @ Q @ R )
| ( member @ Q @ comb ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[95]) ).
thf(127,plain,
( ( ! [P: $i] :
( ~ ( member @ P @ comb )
| ! [Q: $i] :
( ~ ( member @ Q @ comb )
| ! [R: $i] :
( ~ ( member @ R @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ P ) @ Q ) @ R ) @ ( comb_app @ ( comb_app @ P @ R ) @ ( comb_app @ Q @ R ) ) ) @ contract ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[98]) ).
thf(128,plain,
( ( ! [P: $i] :
( ~ ( member @ P @ comb )
| ! [Q: $i] :
( ~ ( member @ Q @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ P ) @ Q ) @ P ) @ contract ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[99]) ).
thf(129,plain,
( ( ! [P: $i] :
( ~ ( member @ P @ comb )
| ! [Q: $i] :
( ~ ( member @ Q @ comb )
| ( member @ ( comb_app @ P @ Q ) @ comb ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[101]) ).
thf(130,plain,
( ( ! [P: $i] :
( ! [Q: $i] :
~ ( member @ ( comb_app @ P @ Q ) @ comb )
| ( member @ P @ comb ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[105]) ).
thf(131,plain,
( ( ! [P1: $i,P2: $i] :
( ( P1 != P2 )
| ! [Q1: $i,Q2: $i] :
( ( Q1 != Q2 )
| ( ( comb_app @ P1 @ Q1 )
= ( comb_app @ P2 @ Q2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[106]) ).
thf(132,plain,
( ( ! [P1: $i,Q1: $i,P2: $i,Q2: $i] :
( ( ( comb_app @ P1 @ Q1 )
!= ( comb_app @ P2 @ Q2 ) )
| ( Q1 = Q2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[107]) ).
thf(133,plain,
( ( ! [P1: $i,Q1: $i,P2: $i] :
( ! [Q2: $i] :
( ( comb_app @ P1 @ Q1 )
!= ( comb_app @ P2 @ Q2 ) )
| ( P1 = P2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[108]) ).
thf(134,plain,
( ( ! [P: $i,Q: $i] :
( combS
!= ( comb_app @ P @ Q ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[109]) ).
thf(135,plain,
( ( ! [P: $i,Q: $i] :
( combK
!= ( comb_app @ P @ Q ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[110]) ).
thf(136,plain,
( ( ( combK != combS ) )
= $true ),
inference(extcnf_combined,[status(esa)],[111]) ).
thf(137,plain,
( ( ! [PP: $i] :
( ( r
!= ( comb_app @ combK @ PP ) )
| ~ ( member @ ( pair @ p @ PP ) @ parcontract ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[113]) ).
thf(138,plain,
( ( ! [PP: $i] :
( ( r
!= ( comb_app @ combK @ PP ) )
| ~ ( member @ ( pair @ p @ PP ) @ parcontract ) ) )
= $true ),
inference(copy,[status(thm)],[137]) ).
thf(139,plain,
( ( member @ ( pair @ ( comb_app @ combK @ p ) @ r ) @ parcontract )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(140,plain,
( ( ( combK != combS ) )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(141,plain,
( ( ! [P: $i,Q: $i] :
( combK
!= ( comb_app @ P @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[135]) ).
thf(142,plain,
( ( ! [P: $i,Q: $i] :
( combS
!= ( comb_app @ P @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[134]) ).
thf(143,plain,
( ( ! [P1: $i,Q1: $i,P2: $i] :
( ! [Q2: $i] :
( ( comb_app @ P1 @ Q1 )
!= ( comb_app @ P2 @ Q2 ) )
| ( P1 = P2 ) ) )
= $true ),
inference(copy,[status(thm)],[133]) ).
thf(144,plain,
( ( ! [P1: $i,Q1: $i,P2: $i,Q2: $i] :
( ( ( comb_app @ P1 @ Q1 )
!= ( comb_app @ P2 @ Q2 ) )
| ( Q1 = Q2 ) ) )
= $true ),
inference(copy,[status(thm)],[132]) ).
thf(145,plain,
( ( ! [P1: $i,P2: $i] :
( ( P1 != P2 )
| ! [Q1: $i,Q2: $i] :
( ( Q1 != Q2 )
| ( ( comb_app @ P1 @ Q1 )
= ( comb_app @ P2 @ Q2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[131]) ).
thf(146,plain,
( ( ! [P: $i] :
( ! [Q: $i] :
~ ( member @ ( comb_app @ P @ Q ) @ comb )
| ( member @ P @ comb ) ) )
= $true ),
inference(copy,[status(thm)],[130]) ).
thf(147,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( member @ ( comb_app @ P @ Q ) @ comb )
| ( member @ Q @ comb ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(148,plain,
( ( member @ combK @ comb )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(149,plain,
( ( member @ combS @ comb )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(150,plain,
( ( ! [P: $i] :
( ~ ( member @ P @ comb )
| ! [Q: $i] :
( ~ ( member @ Q @ comb )
| ( member @ ( comb_app @ P @ Q ) @ comb ) ) ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(151,plain,
( ( ! [A: $i] :
( ~ ( member @ A @ comb )
| ( member @ ( pair @ A @ A ) @ ( rtrancl @ contract ) ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(152,plain,
( ( ! [P: $i] :
( ~ ( member @ P @ comb )
| ! [Q: $i] :
( ~ ( member @ Q @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ P ) @ Q ) @ P ) @ contract ) ) ) )
= $true ),
inference(copy,[status(thm)],[128]) ).
thf(153,plain,
( ( ! [P: $i] :
( ~ ( member @ P @ comb )
| ! [Q: $i] :
( ~ ( member @ Q @ comb )
| ! [R: $i] :
( ~ ( member @ R @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ P ) @ Q ) @ R ) @ ( comb_app @ ( comb_app @ P @ R ) @ ( comb_app @ Q @ R ) ) ) @ contract ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(154,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( member @ ( pair @ ( comb_app @ P @ Q ) @ R ) @ contract )
| ( ap_contractE_c1 @ P @ Q @ R )
| ( ap_contractE_c2 @ P @ Q @ R )
| ( ap_contractE_c3 @ P @ Q @ R )
| ( ap_contractE_c4 @ P @ Q @ R ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(155,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c1 @ P @ Q @ R )
| ( member @ R @ comb ) ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(156,plain,
( ( ! [P: $i,Q: $i] :
( ! [R: $i] :
~ ( ap_contractE_c1 @ P @ Q @ R )
| ( member @ Q @ comb ) ) )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(157,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c1 @ P @ Q @ R )
| ( P
= ( comb_app @ combK @ R ) ) ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(158,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c2 @ P @ Q @ R )
| ( member @ ( ap_contractE_sk1p @ P @ Q @ R ) @ comb ) ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(159,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c2 @ P @ Q @ R )
| ( member @ ( ap_contractE_sk1q @ P @ Q @ R ) @ comb ) ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(160,plain,
( ( ! [P: $i,Q: $i] :
( ! [R: $i] :
~ ( ap_contractE_c2 @ P @ Q @ R )
| ( member @ Q @ comb ) ) )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(161,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c2 @ P @ Q @ R )
| ( R
= ( comb_app @ ( comb_app @ ( ap_contractE_sk1p @ P @ Q @ R ) @ Q ) @ ( comb_app @ ( ap_contractE_sk1q @ P @ Q @ R ) @ Q ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(162,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c2 @ P @ Q @ R )
| ( P
= ( comb_app @ ( comb_app @ combS @ ( ap_contractE_sk1p @ P @ Q @ R ) ) @ ( ap_contractE_sk1q @ P @ Q @ R ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(163,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c3 @ P @ Q @ R )
| ( member @ ( pair @ P @ ( ap_contractE_sk2q @ P @ Q @ R ) ) @ contract ) ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(164,plain,
( ( ! [P: $i,Q: $i] :
( ! [R: $i] :
~ ( ap_contractE_c3 @ P @ Q @ R )
| ( member @ Q @ comb ) ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(165,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c3 @ P @ Q @ R )
| ( R
= ( comb_app @ ( ap_contractE_sk2q @ P @ Q @ R ) @ Q ) ) ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(166,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c4 @ P @ Q @ R )
| ( member @ ( pair @ Q @ ( ap_contractE_sk3q @ P @ Q @ R ) ) @ contract ) ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(167,plain,
( ( ! [P: $i] :
( ! [Q: $i,R: $i] :
~ ( ap_contractE_c4 @ P @ Q @ R )
| ( member @ P @ comb ) ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(168,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c4 @ P @ Q @ R )
| ( R
= ( comb_app @ P @ ( ap_contractE_sk3q @ P @ Q @ R ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(169,plain,
( ( ! [R: $i] :
~ ( member @ ( pair @ combK @ R ) @ contract ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(170,plain,
( ( ! [R: $i] :
~ ( member @ ( pair @ combS @ R ) @ contract ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(171,plain,
( ( ! [P: $i] :
( ~ ( member @ P @ comb )
| ( member @ ( pair @ P @ P ) @ parcontract ) ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(172,plain,
( ( ! [P: $i] :
( ~ ( member @ P @ comb )
| ! [Q: $i] :
( ~ ( member @ Q @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ P ) @ Q ) @ P ) @ parcontract ) ) ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(173,plain,
( ( ! [P: $i] :
( ~ ( member @ P @ comb )
| ! [Q: $i] :
( ~ ( member @ Q @ comb )
| ! [R: $i] :
( ~ ( member @ R @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ P ) @ Q ) @ R ) @ ( comb_app @ ( comb_app @ P @ R ) @ ( comb_app @ Q @ R ) ) ) @ parcontract ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(174,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( member @ ( pair @ P @ Q ) @ parcontract )
| ! [R: $i,S: $i] :
( ~ ( member @ ( pair @ R @ S ) @ parcontract )
| ( member @ ( pair @ ( comb_app @ P @ R ) @ ( comb_app @ Q @ S ) ) @ parcontract ) ) ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(175,plain,
( ( ! [R: $i] :
~ ( member @ ( pair @ combK @ R ) @ parcontract )
| ( member @ combK @ comb ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(176,plain,
( ( ! [R: $i] :
( ~ ( member @ ( pair @ combK @ R ) @ parcontract )
| ( R = combK ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(177,plain,
( ( ! [R: $i] :
~ ( member @ ( pair @ combS @ R ) @ parcontract )
| ( member @ combS @ comb ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(178,plain,
( ( ! [R: $i] :
( ~ ( member @ ( pair @ combS @ R ) @ parcontract )
| ( R = combS ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(179,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( member @ ( pair @ ( comb_app @ P @ Q ) @ R ) @ parcontract )
| ( ap_parcontractE_c1 @ P @ Q @ R )
| ( ap_parcontractE_c2 @ P @ Q @ R )
| ( ap_parcontractE_c3 @ P @ Q @ R )
| ( ap_parcontractE_c4 @ P @ Q @ R ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(180,plain,
( ( ! [P: $i,Q: $i] :
( ! [R: $i] :
~ ( ap_parcontractE_c1 @ P @ Q @ R )
| ( member @ ( comb_app @ P @ Q ) @ comb ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(181,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_parcontractE_c1 @ P @ Q @ R )
| ( R
= ( comb_app @ P @ Q ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(182,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_parcontractE_c2 @ P @ Q @ R )
| ( member @ R @ comb ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(183,plain,
( ( ! [P: $i,Q: $i] :
( ! [R: $i] :
~ ( ap_parcontractE_c2 @ P @ Q @ R )
| ( member @ Q @ comb ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(184,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_parcontractE_c2 @ P @ Q @ R )
| ( P
= ( comb_app @ combK @ R ) ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(185,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_parcontractE_c3 @ P @ Q @ R )
| ( member @ ( ap_parcontractE_sk1p @ P @ Q @ R ) @ comb ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(186,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_parcontractE_c3 @ P @ Q @ R )
| ( member @ ( ap_parcontractE_sk1q @ P @ Q @ R ) @ comb ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(187,plain,
( ( ! [P: $i,Q: $i] :
( ! [R: $i] :
~ ( ap_parcontractE_c3 @ P @ Q @ R )
| ( member @ Q @ comb ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(188,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_parcontractE_c3 @ P @ Q @ R )
| ( R
= ( comb_app @ ( comb_app @ ( ap_parcontractE_sk1p @ P @ Q @ R ) @ Q ) @ ( comb_app @ ( ap_parcontractE_sk1q @ P @ Q @ R ) @ Q ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(189,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_parcontractE_c3 @ P @ Q @ R )
| ( P
= ( comb_app @ ( comb_app @ combS @ ( ap_parcontractE_sk1p @ P @ Q @ R ) ) @ ( ap_parcontractE_sk1q @ P @ Q @ R ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(190,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_parcontractE_c4 @ P @ Q @ R )
| ( member @ ( pair @ P @ ( ap_parcontractE_sk2q @ P @ Q @ R ) ) @ parcontract ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(191,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_parcontractE_c4 @ P @ Q @ R )
| ( member @ ( pair @ Q @ ( ap_parcontractE_sk2s @ P @ Q @ R ) ) @ parcontract ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(192,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_parcontractE_c4 @ P @ Q @ R )
| ( R
= ( comb_app @ ( ap_parcontractE_sk2q @ P @ Q @ R ) @ ( ap_parcontractE_sk2s @ P @ Q @ R ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(193,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(194,plain,
! [SV1: $i] :
( ( ( r
!= ( comb_app @ combK @ SV1 ) )
| ~ ( member @ ( pair @ p @ SV1 ) @ parcontract ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(195,plain,
( ( combK = combS )
= $false ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(196,plain,
! [SV2: $i] :
( ( ! [SY132: $i] :
( combK
!= ( comb_app @ SV2 @ SY132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(197,plain,
! [SV3: $i] :
( ( ! [SY133: $i] :
( combS
!= ( comb_app @ SV3 @ SY133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(198,plain,
! [SV4: $i] :
( ( ! [SY134: $i,SY135: $i] :
( ! [SY136: $i] :
( ( comb_app @ SV4 @ SY134 )
!= ( comb_app @ SY135 @ SY136 ) )
| ( SV4 = SY135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(199,plain,
! [SV5: $i] :
( ( ! [SY137: $i,SY138: $i,SY139: $i] :
( ( ( comb_app @ SV5 @ SY137 )
!= ( comb_app @ SY138 @ SY139 ) )
| ( SY137 = SY139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(200,plain,
! [SV6: $i] :
( ( ! [SY140: $i] :
( ( SV6 != SY140 )
| ! [SY141: $i,SY142: $i] :
( ( SY141 != SY142 )
| ( ( comb_app @ SV6 @ SY141 )
= ( comb_app @ SY140 @ SY142 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(201,plain,
! [SV7: $i] :
( ( ! [SY143: $i] :
~ ( member @ ( comb_app @ SV7 @ SY143 ) @ comb )
| ( member @ SV7 @ comb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(202,plain,
! [SV8: $i] :
( ( ! [SY144: $i] :
( ~ ( member @ ( comb_app @ SV8 @ SY144 ) @ comb )
| ( member @ SY144 @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(203,plain,
! [SV9: $i] :
( ( ~ ( member @ SV9 @ comb )
| ! [SY145: $i] :
( ~ ( member @ SY145 @ comb )
| ( member @ ( comb_app @ SV9 @ SY145 ) @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(204,plain,
! [SV10: $i] :
( ( ~ ( member @ SV10 @ comb )
| ( member @ ( pair @ SV10 @ SV10 ) @ ( rtrancl @ contract ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(205,plain,
! [SV11: $i] :
( ( ~ ( member @ SV11 @ comb )
| ! [SY146: $i] :
( ~ ( member @ SY146 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV11 ) @ SY146 ) @ SV11 ) @ contract ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(206,plain,
! [SV12: $i] :
( ( ~ ( member @ SV12 @ comb )
| ! [SY147: $i] :
( ~ ( member @ SY147 @ comb )
| ! [SY148: $i] :
( ~ ( member @ SY148 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV12 ) @ SY147 ) @ SY148 ) @ ( comb_app @ ( comb_app @ SV12 @ SY148 ) @ ( comb_app @ SY147 @ SY148 ) ) ) @ contract ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(207,plain,
! [SV13: $i] :
( ( ! [SY149: $i,SY150: $i] :
( ~ ( member @ ( pair @ ( comb_app @ SV13 @ SY149 ) @ SY150 ) @ contract )
| ( ap_contractE_c1 @ SV13 @ SY149 @ SY150 )
| ( ap_contractE_c2 @ SV13 @ SY149 @ SY150 )
| ( ap_contractE_c3 @ SV13 @ SY149 @ SY150 )
| ( ap_contractE_c4 @ SV13 @ SY149 @ SY150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(208,plain,
! [SV14: $i] :
( ( ! [SY151: $i,SY152: $i] :
( ~ ( ap_contractE_c1 @ SV14 @ SY151 @ SY152 )
| ( member @ SY152 @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(209,plain,
! [SV15: $i] :
( ( ! [SY153: $i] :
( ! [SY154: $i] :
~ ( ap_contractE_c1 @ SV15 @ SY153 @ SY154 )
| ( member @ SY153 @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(210,plain,
! [SV16: $i] :
( ( ! [SY155: $i,SY156: $i] :
( ~ ( ap_contractE_c1 @ SV16 @ SY155 @ SY156 )
| ( SV16
= ( comb_app @ combK @ SY156 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(211,plain,
! [SV17: $i] :
( ( ! [SY157: $i,SY158: $i] :
( ~ ( ap_contractE_c2 @ SV17 @ SY157 @ SY158 )
| ( member @ ( ap_contractE_sk1p @ SV17 @ SY157 @ SY158 ) @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(212,plain,
! [SV18: $i] :
( ( ! [SY159: $i,SY160: $i] :
( ~ ( ap_contractE_c2 @ SV18 @ SY159 @ SY160 )
| ( member @ ( ap_contractE_sk1q @ SV18 @ SY159 @ SY160 ) @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(213,plain,
! [SV19: $i] :
( ( ! [SY161: $i] :
( ! [SY162: $i] :
~ ( ap_contractE_c2 @ SV19 @ SY161 @ SY162 )
| ( member @ SY161 @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(214,plain,
! [SV20: $i] :
( ( ! [SY163: $i,SY164: $i] :
( ~ ( ap_contractE_c2 @ SV20 @ SY163 @ SY164 )
| ( SY164
= ( comb_app @ ( comb_app @ ( ap_contractE_sk1p @ SV20 @ SY163 @ SY164 ) @ SY163 ) @ ( comb_app @ ( ap_contractE_sk1q @ SV20 @ SY163 @ SY164 ) @ SY163 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(215,plain,
! [SV21: $i] :
( ( ! [SY165: $i,SY166: $i] :
( ~ ( ap_contractE_c2 @ SV21 @ SY165 @ SY166 )
| ( SV21
= ( comb_app @ ( comb_app @ combS @ ( ap_contractE_sk1p @ SV21 @ SY165 @ SY166 ) ) @ ( ap_contractE_sk1q @ SV21 @ SY165 @ SY166 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(216,plain,
! [SV22: $i] :
( ( ! [SY167: $i,SY168: $i] :
( ~ ( ap_contractE_c3 @ SV22 @ SY167 @ SY168 )
| ( member @ ( pair @ SV22 @ ( ap_contractE_sk2q @ SV22 @ SY167 @ SY168 ) ) @ contract ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(217,plain,
! [SV23: $i] :
( ( ! [SY169: $i] :
( ! [SY170: $i] :
~ ( ap_contractE_c3 @ SV23 @ SY169 @ SY170 )
| ( member @ SY169 @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(218,plain,
! [SV24: $i] :
( ( ! [SY171: $i,SY172: $i] :
( ~ ( ap_contractE_c3 @ SV24 @ SY171 @ SY172 )
| ( SY172
= ( comb_app @ ( ap_contractE_sk2q @ SV24 @ SY171 @ SY172 ) @ SY171 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(219,plain,
! [SV25: $i] :
( ( ! [SY173: $i,SY174: $i] :
( ~ ( ap_contractE_c4 @ SV25 @ SY173 @ SY174 )
| ( member @ ( pair @ SY173 @ ( ap_contractE_sk3q @ SV25 @ SY173 @ SY174 ) ) @ contract ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(220,plain,
! [SV26: $i] :
( ( ! [SY175: $i,SY176: $i] :
~ ( ap_contractE_c4 @ SV26 @ SY175 @ SY176 )
| ( member @ SV26 @ comb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(221,plain,
! [SV27: $i] :
( ( ! [SY177: $i,SY178: $i] :
( ~ ( ap_contractE_c4 @ SV27 @ SY177 @ SY178 )
| ( SY178
= ( comb_app @ SV27 @ ( ap_contractE_sk3q @ SV27 @ SY177 @ SY178 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(222,plain,
! [SV28: $i] :
( ( ~ ( member @ ( pair @ combK @ SV28 ) @ contract ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(223,plain,
! [SV29: $i] :
( ( ~ ( member @ ( pair @ combS @ SV29 ) @ contract ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(224,plain,
! [SV30: $i] :
( ( ~ ( member @ SV30 @ comb )
| ( member @ ( pair @ SV30 @ SV30 ) @ parcontract ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(225,plain,
! [SV31: $i] :
( ( ~ ( member @ SV31 @ comb )
| ! [SY179: $i] :
( ~ ( member @ SY179 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV31 ) @ SY179 ) @ SV31 ) @ parcontract ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(226,plain,
! [SV32: $i] :
( ( ~ ( member @ SV32 @ comb )
| ! [SY180: $i] :
( ~ ( member @ SY180 @ comb )
| ! [SY181: $i] :
( ~ ( member @ SY181 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV32 ) @ SY180 ) @ SY181 ) @ ( comb_app @ ( comb_app @ SV32 @ SY181 ) @ ( comb_app @ SY180 @ SY181 ) ) ) @ parcontract ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(227,plain,
! [SV33: $i] :
( ( ! [SY182: $i] :
( ~ ( member @ ( pair @ SV33 @ SY182 ) @ parcontract )
| ! [SY183: $i,SY184: $i] :
( ~ ( member @ ( pair @ SY183 @ SY184 ) @ parcontract )
| ( member @ ( pair @ ( comb_app @ SV33 @ SY183 ) @ ( comb_app @ SY182 @ SY184 ) ) @ parcontract ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(228,plain,
( ( ( ! [R: $i] :
~ ( member @ ( pair @ combK @ R ) @ parcontract ) )
= $true )
| ( ( member @ combK @ comb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(229,plain,
! [SV34: $i] :
( ( ~ ( member @ ( pair @ combK @ SV34 ) @ parcontract )
| ( SV34 = combK ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(230,plain,
( ( ( ! [R: $i] :
~ ( member @ ( pair @ combS @ R ) @ parcontract ) )
= $true )
| ( ( member @ combS @ comb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(231,plain,
! [SV35: $i] :
( ( ~ ( member @ ( pair @ combS @ SV35 ) @ parcontract )
| ( SV35 = combS ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(232,plain,
! [SV36: $i] :
( ( ! [SY185: $i,SY186: $i] :
( ~ ( member @ ( pair @ ( comb_app @ SV36 @ SY185 ) @ SY186 ) @ parcontract )
| ( ap_parcontractE_c1 @ SV36 @ SY185 @ SY186 )
| ( ap_parcontractE_c2 @ SV36 @ SY185 @ SY186 )
| ( ap_parcontractE_c3 @ SV36 @ SY185 @ SY186 )
| ( ap_parcontractE_c4 @ SV36 @ SY185 @ SY186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(233,plain,
! [SV37: $i] :
( ( ! [SY187: $i] :
( ! [SY188: $i] :
~ ( ap_parcontractE_c1 @ SV37 @ SY187 @ SY188 )
| ( member @ ( comb_app @ SV37 @ SY187 ) @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(234,plain,
! [SV38: $i] :
( ( ! [SY189: $i,SY190: $i] :
( ~ ( ap_parcontractE_c1 @ SV38 @ SY189 @ SY190 )
| ( SY190
= ( comb_app @ SV38 @ SY189 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(235,plain,
! [SV39: $i] :
( ( ! [SY191: $i,SY192: $i] :
( ~ ( ap_parcontractE_c2 @ SV39 @ SY191 @ SY192 )
| ( member @ SY192 @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(236,plain,
! [SV40: $i] :
( ( ! [SY193: $i] :
( ! [SY194: $i] :
~ ( ap_parcontractE_c2 @ SV40 @ SY193 @ SY194 )
| ( member @ SY193 @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(237,plain,
! [SV41: $i] :
( ( ! [SY195: $i,SY196: $i] :
( ~ ( ap_parcontractE_c2 @ SV41 @ SY195 @ SY196 )
| ( SV41
= ( comb_app @ combK @ SY196 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(238,plain,
! [SV42: $i] :
( ( ! [SY197: $i,SY198: $i] :
( ~ ( ap_parcontractE_c3 @ SV42 @ SY197 @ SY198 )
| ( member @ ( ap_parcontractE_sk1p @ SV42 @ SY197 @ SY198 ) @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(239,plain,
! [SV43: $i] :
( ( ! [SY199: $i,SY200: $i] :
( ~ ( ap_parcontractE_c3 @ SV43 @ SY199 @ SY200 )
| ( member @ ( ap_parcontractE_sk1q @ SV43 @ SY199 @ SY200 ) @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(240,plain,
! [SV44: $i] :
( ( ! [SY201: $i] :
( ! [SY202: $i] :
~ ( ap_parcontractE_c3 @ SV44 @ SY201 @ SY202 )
| ( member @ SY201 @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(241,plain,
! [SV45: $i] :
( ( ! [SY203: $i,SY204: $i] :
( ~ ( ap_parcontractE_c3 @ SV45 @ SY203 @ SY204 )
| ( SY204
= ( comb_app @ ( comb_app @ ( ap_parcontractE_sk1p @ SV45 @ SY203 @ SY204 ) @ SY203 ) @ ( comb_app @ ( ap_parcontractE_sk1q @ SV45 @ SY203 @ SY204 ) @ SY203 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(242,plain,
! [SV46: $i] :
( ( ! [SY205: $i,SY206: $i] :
( ~ ( ap_parcontractE_c3 @ SV46 @ SY205 @ SY206 )
| ( SV46
= ( comb_app @ ( comb_app @ combS @ ( ap_parcontractE_sk1p @ SV46 @ SY205 @ SY206 ) ) @ ( ap_parcontractE_sk1q @ SV46 @ SY205 @ SY206 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(243,plain,
! [SV47: $i] :
( ( ! [SY207: $i,SY208: $i] :
( ~ ( ap_parcontractE_c4 @ SV47 @ SY207 @ SY208 )
| ( member @ ( pair @ SV47 @ ( ap_parcontractE_sk2q @ SV47 @ SY207 @ SY208 ) ) @ parcontract ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(244,plain,
! [SV48: $i] :
( ( ! [SY209: $i,SY210: $i] :
( ~ ( ap_parcontractE_c4 @ SV48 @ SY209 @ SY210 )
| ( member @ ( pair @ SY209 @ ( ap_parcontractE_sk2s @ SV48 @ SY209 @ SY210 ) ) @ parcontract ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(245,plain,
! [SV49: $i] :
( ( ! [SY211: $i,SY212: $i] :
( ~ ( ap_parcontractE_c4 @ SV49 @ SY211 @ SY212 )
| ( SY212
= ( comb_app @ ( ap_parcontractE_sk2q @ SV49 @ SY211 @ SY212 ) @ ( ap_parcontractE_sk2s @ SV49 @ SY211 @ SY212 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(246,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(247,plain,
! [SV1: $i] :
( ( ( ( r
!= ( comb_app @ combK @ SV1 ) ) )
= $true )
| ( ( ~ ( member @ ( pair @ p @ SV1 ) @ parcontract ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[194]) ).
thf(248,plain,
! [SV50: $i,SV2: $i] :
( ( ( combK
!= ( comb_app @ SV2 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(249,plain,
! [SV51: $i,SV3: $i] :
( ( ( combS
!= ( comb_app @ SV3 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(250,plain,
! [SV52: $i,SV4: $i] :
( ( ! [SY213: $i] :
( ! [SY214: $i] :
( ( comb_app @ SV4 @ SV52 )
!= ( comb_app @ SY213 @ SY214 ) )
| ( SV4 = SY213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(251,plain,
! [SV53: $i,SV5: $i] :
( ( ! [SY215: $i,SY216: $i] :
( ( ( comb_app @ SV5 @ SV53 )
!= ( comb_app @ SY215 @ SY216 ) )
| ( SV53 = SY216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(252,plain,
! [SV54: $i,SV6: $i] :
( ( ( SV6 != SV54 )
| ! [SY217: $i,SY218: $i] :
( ( SY217 != SY218 )
| ( ( comb_app @ SV6 @ SY217 )
= ( comb_app @ SV54 @ SY218 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(253,plain,
! [SV7: $i] :
( ( ( ! [SY143: $i] :
~ ( member @ ( comb_app @ SV7 @ SY143 ) @ comb ) )
= $true )
| ( ( member @ SV7 @ comb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(254,plain,
! [SV55: $i,SV8: $i] :
( ( ~ ( member @ ( comb_app @ SV8 @ SV55 ) @ comb )
| ( member @ SV55 @ comb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(255,plain,
! [SV9: $i] :
( ( ( ~ ( member @ SV9 @ comb ) )
= $true )
| ( ( ! [SY145: $i] :
( ~ ( member @ SY145 @ comb )
| ( member @ ( comb_app @ SV9 @ SY145 ) @ comb ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[203]) ).
thf(256,plain,
! [SV10: $i] :
( ( ( ~ ( member @ SV10 @ comb ) )
= $true )
| ( ( member @ ( pair @ SV10 @ SV10 ) @ ( rtrancl @ contract ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[204]) ).
thf(257,plain,
! [SV11: $i] :
( ( ( ~ ( member @ SV11 @ comb ) )
= $true )
| ( ( ! [SY146: $i] :
( ~ ( member @ SY146 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV11 ) @ SY146 ) @ SV11 ) @ contract ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[205]) ).
thf(258,plain,
! [SV12: $i] :
( ( ( ~ ( member @ SV12 @ comb ) )
= $true )
| ( ( ! [SY147: $i] :
( ~ ( member @ SY147 @ comb )
| ! [SY148: $i] :
( ~ ( member @ SY148 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV12 ) @ SY147 ) @ SY148 ) @ ( comb_app @ ( comb_app @ SV12 @ SY148 ) @ ( comb_app @ SY147 @ SY148 ) ) ) @ contract ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[206]) ).
thf(259,plain,
! [SV56: $i,SV13: $i] :
( ( ! [SY219: $i] :
( ~ ( member @ ( pair @ ( comb_app @ SV13 @ SV56 ) @ SY219 ) @ contract )
| ( ap_contractE_c1 @ SV13 @ SV56 @ SY219 )
| ( ap_contractE_c2 @ SV13 @ SV56 @ SY219 )
| ( ap_contractE_c3 @ SV13 @ SV56 @ SY219 )
| ( ap_contractE_c4 @ SV13 @ SV56 @ SY219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(260,plain,
! [SV57: $i,SV14: $i] :
( ( ! [SY220: $i] :
( ~ ( ap_contractE_c1 @ SV14 @ SV57 @ SY220 )
| ( member @ SY220 @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(261,plain,
! [SV58: $i,SV15: $i] :
( ( ! [SY221: $i] :
~ ( ap_contractE_c1 @ SV15 @ SV58 @ SY221 )
| ( member @ SV58 @ comb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(262,plain,
! [SV59: $i,SV16: $i] :
( ( ! [SY222: $i] :
( ~ ( ap_contractE_c1 @ SV16 @ SV59 @ SY222 )
| ( SV16
= ( comb_app @ combK @ SY222 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(263,plain,
! [SV60: $i,SV17: $i] :
( ( ! [SY223: $i] :
( ~ ( ap_contractE_c2 @ SV17 @ SV60 @ SY223 )
| ( member @ ( ap_contractE_sk1p @ SV17 @ SV60 @ SY223 ) @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(264,plain,
! [SV61: $i,SV18: $i] :
( ( ! [SY224: $i] :
( ~ ( ap_contractE_c2 @ SV18 @ SV61 @ SY224 )
| ( member @ ( ap_contractE_sk1q @ SV18 @ SV61 @ SY224 ) @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(265,plain,
! [SV62: $i,SV19: $i] :
( ( ! [SY225: $i] :
~ ( ap_contractE_c2 @ SV19 @ SV62 @ SY225 )
| ( member @ SV62 @ comb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(266,plain,
! [SV63: $i,SV20: $i] :
( ( ! [SY226: $i] :
( ~ ( ap_contractE_c2 @ SV20 @ SV63 @ SY226 )
| ( SY226
= ( comb_app @ ( comb_app @ ( ap_contractE_sk1p @ SV20 @ SV63 @ SY226 ) @ SV63 ) @ ( comb_app @ ( ap_contractE_sk1q @ SV20 @ SV63 @ SY226 ) @ SV63 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(267,plain,
! [SV64: $i,SV21: $i] :
( ( ! [SY227: $i] :
( ~ ( ap_contractE_c2 @ SV21 @ SV64 @ SY227 )
| ( SV21
= ( comb_app @ ( comb_app @ combS @ ( ap_contractE_sk1p @ SV21 @ SV64 @ SY227 ) ) @ ( ap_contractE_sk1q @ SV21 @ SV64 @ SY227 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(268,plain,
! [SV65: $i,SV22: $i] :
( ( ! [SY228: $i] :
( ~ ( ap_contractE_c3 @ SV22 @ SV65 @ SY228 )
| ( member @ ( pair @ SV22 @ ( ap_contractE_sk2q @ SV22 @ SV65 @ SY228 ) ) @ contract ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(269,plain,
! [SV66: $i,SV23: $i] :
( ( ! [SY229: $i] :
~ ( ap_contractE_c3 @ SV23 @ SV66 @ SY229 )
| ( member @ SV66 @ comb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(270,plain,
! [SV67: $i,SV24: $i] :
( ( ! [SY230: $i] :
( ~ ( ap_contractE_c3 @ SV24 @ SV67 @ SY230 )
| ( SY230
= ( comb_app @ ( ap_contractE_sk2q @ SV24 @ SV67 @ SY230 ) @ SV67 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(271,plain,
! [SV68: $i,SV25: $i] :
( ( ! [SY231: $i] :
( ~ ( ap_contractE_c4 @ SV25 @ SV68 @ SY231 )
| ( member @ ( pair @ SV68 @ ( ap_contractE_sk3q @ SV25 @ SV68 @ SY231 ) ) @ contract ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(272,plain,
! [SV26: $i] :
( ( ( ! [SY175: $i,SY176: $i] :
~ ( ap_contractE_c4 @ SV26 @ SY175 @ SY176 ) )
= $true )
| ( ( member @ SV26 @ comb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(273,plain,
! [SV69: $i,SV27: $i] :
( ( ! [SY232: $i] :
( ~ ( ap_contractE_c4 @ SV27 @ SV69 @ SY232 )
| ( SY232
= ( comb_app @ SV27 @ ( ap_contractE_sk3q @ SV27 @ SV69 @ SY232 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(274,plain,
! [SV28: $i] :
( ( member @ ( pair @ combK @ SV28 ) @ contract )
= $false ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(275,plain,
! [SV29: $i] :
( ( member @ ( pair @ combS @ SV29 ) @ contract )
= $false ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(276,plain,
! [SV30: $i] :
( ( ( ~ ( member @ SV30 @ comb ) )
= $true )
| ( ( member @ ( pair @ SV30 @ SV30 ) @ parcontract )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[224]) ).
thf(277,plain,
! [SV31: $i] :
( ( ( ~ ( member @ SV31 @ comb ) )
= $true )
| ( ( ! [SY179: $i] :
( ~ ( member @ SY179 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV31 ) @ SY179 ) @ SV31 ) @ parcontract ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(278,plain,
! [SV32: $i] :
( ( ( ~ ( member @ SV32 @ comb ) )
= $true )
| ( ( ! [SY180: $i] :
( ~ ( member @ SY180 @ comb )
| ! [SY181: $i] :
( ~ ( member @ SY181 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV32 ) @ SY180 ) @ SY181 ) @ ( comb_app @ ( comb_app @ SV32 @ SY181 ) @ ( comb_app @ SY180 @ SY181 ) ) ) @ parcontract ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[226]) ).
thf(279,plain,
! [SV70: $i,SV33: $i] :
( ( ~ ( member @ ( pair @ SV33 @ SV70 ) @ parcontract )
| ! [SY233: $i,SY234: $i] :
( ~ ( member @ ( pair @ SY233 @ SY234 ) @ parcontract )
| ( member @ ( pair @ ( comb_app @ SV33 @ SY233 ) @ ( comb_app @ SV70 @ SY234 ) ) @ parcontract ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(280,plain,
! [SV71: $i] :
( ( ( ~ ( member @ ( pair @ combK @ SV71 ) @ parcontract ) )
= $true )
| ( ( member @ combK @ comb )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(281,plain,
! [SV34: $i] :
( ( ( ~ ( member @ ( pair @ combK @ SV34 ) @ parcontract ) )
= $true )
| ( ( SV34 = combK )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[229]) ).
thf(282,plain,
! [SV72: $i] :
( ( ( ~ ( member @ ( pair @ combS @ SV72 ) @ parcontract ) )
= $true )
| ( ( member @ combS @ comb )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(283,plain,
! [SV35: $i] :
( ( ( ~ ( member @ ( pair @ combS @ SV35 ) @ parcontract ) )
= $true )
| ( ( SV35 = combS )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[231]) ).
thf(284,plain,
! [SV73: $i,SV36: $i] :
( ( ! [SY235: $i] :
( ~ ( member @ ( pair @ ( comb_app @ SV36 @ SV73 ) @ SY235 ) @ parcontract )
| ( ap_parcontractE_c1 @ SV36 @ SV73 @ SY235 )
| ( ap_parcontractE_c2 @ SV36 @ SV73 @ SY235 )
| ( ap_parcontractE_c3 @ SV36 @ SV73 @ SY235 )
| ( ap_parcontractE_c4 @ SV36 @ SV73 @ SY235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(285,plain,
! [SV74: $i,SV37: $i] :
( ( ! [SY236: $i] :
~ ( ap_parcontractE_c1 @ SV37 @ SV74 @ SY236 )
| ( member @ ( comb_app @ SV37 @ SV74 ) @ comb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(286,plain,
! [SV75: $i,SV38: $i] :
( ( ! [SY237: $i] :
( ~ ( ap_parcontractE_c1 @ SV38 @ SV75 @ SY237 )
| ( SY237
= ( comb_app @ SV38 @ SV75 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(287,plain,
! [SV76: $i,SV39: $i] :
( ( ! [SY238: $i] :
( ~ ( ap_parcontractE_c2 @ SV39 @ SV76 @ SY238 )
| ( member @ SY238 @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[235]) ).
thf(288,plain,
! [SV77: $i,SV40: $i] :
( ( ! [SY239: $i] :
~ ( ap_parcontractE_c2 @ SV40 @ SV77 @ SY239 )
| ( member @ SV77 @ comb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[236]) ).
thf(289,plain,
! [SV78: $i,SV41: $i] :
( ( ! [SY240: $i] :
( ~ ( ap_parcontractE_c2 @ SV41 @ SV78 @ SY240 )
| ( SV41
= ( comb_app @ combK @ SY240 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(290,plain,
! [SV79: $i,SV42: $i] :
( ( ! [SY241: $i] :
( ~ ( ap_parcontractE_c3 @ SV42 @ SV79 @ SY241 )
| ( member @ ( ap_parcontractE_sk1p @ SV42 @ SV79 @ SY241 ) @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(291,plain,
! [SV80: $i,SV43: $i] :
( ( ! [SY242: $i] :
( ~ ( ap_parcontractE_c3 @ SV43 @ SV80 @ SY242 )
| ( member @ ( ap_parcontractE_sk1q @ SV43 @ SV80 @ SY242 ) @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(292,plain,
! [SV81: $i,SV44: $i] :
( ( ! [SY243: $i] :
~ ( ap_parcontractE_c3 @ SV44 @ SV81 @ SY243 )
| ( member @ SV81 @ comb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(293,plain,
! [SV82: $i,SV45: $i] :
( ( ! [SY244: $i] :
( ~ ( ap_parcontractE_c3 @ SV45 @ SV82 @ SY244 )
| ( SY244
= ( comb_app @ ( comb_app @ ( ap_parcontractE_sk1p @ SV45 @ SV82 @ SY244 ) @ SV82 ) @ ( comb_app @ ( ap_parcontractE_sk1q @ SV45 @ SV82 @ SY244 ) @ SV82 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(294,plain,
! [SV83: $i,SV46: $i] :
( ( ! [SY245: $i] :
( ~ ( ap_parcontractE_c3 @ SV46 @ SV83 @ SY245 )
| ( SV46
= ( comb_app @ ( comb_app @ combS @ ( ap_parcontractE_sk1p @ SV46 @ SV83 @ SY245 ) ) @ ( ap_parcontractE_sk1q @ SV46 @ SV83 @ SY245 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(295,plain,
! [SV84: $i,SV47: $i] :
( ( ! [SY246: $i] :
( ~ ( ap_parcontractE_c4 @ SV47 @ SV84 @ SY246 )
| ( member @ ( pair @ SV47 @ ( ap_parcontractE_sk2q @ SV47 @ SV84 @ SY246 ) ) @ parcontract ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[243]) ).
thf(296,plain,
! [SV85: $i,SV48: $i] :
( ( ! [SY247: $i] :
( ~ ( ap_parcontractE_c4 @ SV48 @ SV85 @ SY247 )
| ( member @ ( pair @ SV85 @ ( ap_parcontractE_sk2s @ SV48 @ SV85 @ SY247 ) ) @ parcontract ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[244]) ).
thf(297,plain,
! [SV86: $i,SV49: $i] :
( ( ! [SY248: $i] :
( ~ ( ap_parcontractE_c4 @ SV49 @ SV86 @ SY248 )
| ( SY248
= ( comb_app @ ( ap_parcontractE_sk2q @ SV49 @ SV86 @ SY248 ) @ ( ap_parcontractE_sk2s @ SV49 @ SV86 @ SY248 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[245]) ).
thf(298,plain,
! [SV1: $i] :
( ( ( r
= ( comb_app @ combK @ SV1 ) )
= $false )
| ( ( ~ ( member @ ( pair @ p @ SV1 ) @ parcontract ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(299,plain,
! [SV50: $i,SV2: $i] :
( ( combK
= ( comb_app @ SV2 @ SV50 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(300,plain,
! [SV51: $i,SV3: $i] :
( ( combS
= ( comb_app @ SV3 @ SV51 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(301,plain,
! [SV87: $i,SV52: $i,SV4: $i] :
( ( ! [SY249: $i] :
( ( comb_app @ SV4 @ SV52 )
!= ( comb_app @ SV87 @ SY249 ) )
| ( SV4 = SV87 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(302,plain,
! [SV88: $i,SV53: $i,SV5: $i] :
( ( ! [SY250: $i] :
( ( ( comb_app @ SV5 @ SV53 )
!= ( comb_app @ SV88 @ SY250 ) )
| ( SV53 = SY250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(303,plain,
! [SV54: $i,SV6: $i] :
( ( ( ( SV6 != SV54 ) )
= $true )
| ( ( ! [SY217: $i,SY218: $i] :
( ( SY217 != SY218 )
| ( ( comb_app @ SV6 @ SY217 )
= ( comb_app @ SV54 @ SY218 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[252]) ).
thf(304,plain,
! [SV89: $i,SV7: $i] :
( ( ( ~ ( member @ ( comb_app @ SV7 @ SV89 ) @ comb ) )
= $true )
| ( ( member @ SV7 @ comb )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[253]) ).
thf(305,plain,
! [SV55: $i,SV8: $i] :
( ( ( ~ ( member @ ( comb_app @ SV8 @ SV55 ) @ comb ) )
= $true )
| ( ( member @ SV55 @ comb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[254]) ).
thf(306,plain,
! [SV9: $i] :
( ( ( member @ SV9 @ comb )
= $false )
| ( ( ! [SY145: $i] :
( ~ ( member @ SY145 @ comb )
| ( member @ ( comb_app @ SV9 @ SY145 ) @ comb ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(307,plain,
! [SV10: $i] :
( ( ( member @ SV10 @ comb )
= $false )
| ( ( member @ ( pair @ SV10 @ SV10 ) @ ( rtrancl @ contract ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(308,plain,
! [SV11: $i] :
( ( ( member @ SV11 @ comb )
= $false )
| ( ( ! [SY146: $i] :
( ~ ( member @ SY146 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV11 ) @ SY146 ) @ SV11 ) @ contract ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(309,plain,
! [SV12: $i] :
( ( ( member @ SV12 @ comb )
= $false )
| ( ( ! [SY147: $i] :
( ~ ( member @ SY147 @ comb )
| ! [SY148: $i] :
( ~ ( member @ SY148 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV12 ) @ SY147 ) @ SY148 ) @ ( comb_app @ ( comb_app @ SV12 @ SY148 ) @ ( comb_app @ SY147 @ SY148 ) ) ) @ contract ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(310,plain,
! [SV90: $i,SV56: $i,SV13: $i] :
( ( ~ ( member @ ( pair @ ( comb_app @ SV13 @ SV56 ) @ SV90 ) @ contract )
| ( ap_contractE_c1 @ SV13 @ SV56 @ SV90 )
| ( ap_contractE_c2 @ SV13 @ SV56 @ SV90 )
| ( ap_contractE_c3 @ SV13 @ SV56 @ SV90 )
| ( ap_contractE_c4 @ SV13 @ SV56 @ SV90 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[259]) ).
thf(311,plain,
! [SV91: $i,SV57: $i,SV14: $i] :
( ( ~ ( ap_contractE_c1 @ SV14 @ SV57 @ SV91 )
| ( member @ SV91 @ comb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[260]) ).
thf(312,plain,
! [SV58: $i,SV15: $i] :
( ( ( ! [SY221: $i] :
~ ( ap_contractE_c1 @ SV15 @ SV58 @ SY221 ) )
= $true )
| ( ( member @ SV58 @ comb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[261]) ).
thf(313,plain,
! [SV92: $i,SV59: $i,SV16: $i] :
( ( ~ ( ap_contractE_c1 @ SV16 @ SV59 @ SV92 )
| ( SV16
= ( comb_app @ combK @ SV92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(314,plain,
! [SV93: $i,SV60: $i,SV17: $i] :
( ( ~ ( ap_contractE_c2 @ SV17 @ SV60 @ SV93 )
| ( member @ ( ap_contractE_sk1p @ SV17 @ SV60 @ SV93 ) @ comb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(315,plain,
! [SV94: $i,SV61: $i,SV18: $i] :
( ( ~ ( ap_contractE_c2 @ SV18 @ SV61 @ SV94 )
| ( member @ ( ap_contractE_sk1q @ SV18 @ SV61 @ SV94 ) @ comb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(316,plain,
! [SV62: $i,SV19: $i] :
( ( ( ! [SY225: $i] :
~ ( ap_contractE_c2 @ SV19 @ SV62 @ SY225 ) )
= $true )
| ( ( member @ SV62 @ comb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(317,plain,
! [SV95: $i,SV63: $i,SV20: $i] :
( ( ~ ( ap_contractE_c2 @ SV20 @ SV63 @ SV95 )
| ( SV95
= ( comb_app @ ( comb_app @ ( ap_contractE_sk1p @ SV20 @ SV63 @ SV95 ) @ SV63 ) @ ( comb_app @ ( ap_contractE_sk1q @ SV20 @ SV63 @ SV95 ) @ SV63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(318,plain,
! [SV96: $i,SV64: $i,SV21: $i] :
( ( ~ ( ap_contractE_c2 @ SV21 @ SV64 @ SV96 )
| ( SV21
= ( comb_app @ ( comb_app @ combS @ ( ap_contractE_sk1p @ SV21 @ SV64 @ SV96 ) ) @ ( ap_contractE_sk1q @ SV21 @ SV64 @ SV96 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(319,plain,
! [SV97: $i,SV65: $i,SV22: $i] :
( ( ~ ( ap_contractE_c3 @ SV22 @ SV65 @ SV97 )
| ( member @ ( pair @ SV22 @ ( ap_contractE_sk2q @ SV22 @ SV65 @ SV97 ) ) @ contract ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(320,plain,
! [SV66: $i,SV23: $i] :
( ( ( ! [SY229: $i] :
~ ( ap_contractE_c3 @ SV23 @ SV66 @ SY229 ) )
= $true )
| ( ( member @ SV66 @ comb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[269]) ).
thf(321,plain,
! [SV98: $i,SV67: $i,SV24: $i] :
( ( ~ ( ap_contractE_c3 @ SV24 @ SV67 @ SV98 )
| ( SV98
= ( comb_app @ ( ap_contractE_sk2q @ SV24 @ SV67 @ SV98 ) @ SV67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(322,plain,
! [SV99: $i,SV68: $i,SV25: $i] :
( ( ~ ( ap_contractE_c4 @ SV25 @ SV68 @ SV99 )
| ( member @ ( pair @ SV68 @ ( ap_contractE_sk3q @ SV25 @ SV68 @ SV99 ) ) @ contract ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(323,plain,
! [SV100: $i,SV26: $i] :
( ( ( ! [SY251: $i] :
~ ( ap_contractE_c4 @ SV26 @ SV100 @ SY251 ) )
= $true )
| ( ( member @ SV26 @ comb )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(324,plain,
! [SV101: $i,SV69: $i,SV27: $i] :
( ( ~ ( ap_contractE_c4 @ SV27 @ SV69 @ SV101 )
| ( SV101
= ( comb_app @ SV27 @ ( ap_contractE_sk3q @ SV27 @ SV69 @ SV101 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(325,plain,
! [SV30: $i] :
( ( ( member @ SV30 @ comb )
= $false )
| ( ( member @ ( pair @ SV30 @ SV30 ) @ parcontract )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(326,plain,
! [SV31: $i] :
( ( ( member @ SV31 @ comb )
= $false )
| ( ( ! [SY179: $i] :
( ~ ( member @ SY179 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV31 ) @ SY179 ) @ SV31 ) @ parcontract ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(327,plain,
! [SV32: $i] :
( ( ( member @ SV32 @ comb )
= $false )
| ( ( ! [SY180: $i] :
( ~ ( member @ SY180 @ comb )
| ! [SY181: $i] :
( ~ ( member @ SY181 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV32 ) @ SY180 ) @ SY181 ) @ ( comb_app @ ( comb_app @ SV32 @ SY181 ) @ ( comb_app @ SY180 @ SY181 ) ) ) @ parcontract ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(328,plain,
! [SV70: $i,SV33: $i] :
( ( ( ~ ( member @ ( pair @ SV33 @ SV70 ) @ parcontract ) )
= $true )
| ( ( ! [SY233: $i,SY234: $i] :
( ~ ( member @ ( pair @ SY233 @ SY234 ) @ parcontract )
| ( member @ ( pair @ ( comb_app @ SV33 @ SY233 ) @ ( comb_app @ SV70 @ SY234 ) ) @ parcontract ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[279]) ).
thf(329,plain,
! [SV71: $i] :
( ( ( member @ ( pair @ combK @ SV71 ) @ parcontract )
= $false )
| ( ( member @ combK @ comb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(330,plain,
! [SV34: $i] :
( ( ( member @ ( pair @ combK @ SV34 ) @ parcontract )
= $false )
| ( ( SV34 = combK )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(331,plain,
! [SV72: $i] :
( ( ( member @ ( pair @ combS @ SV72 ) @ parcontract )
= $false )
| ( ( member @ combS @ comb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[282]) ).
thf(332,plain,
! [SV35: $i] :
( ( ( member @ ( pair @ combS @ SV35 ) @ parcontract )
= $false )
| ( ( SV35 = combS )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(333,plain,
! [SV102: $i,SV73: $i,SV36: $i] :
( ( ~ ( member @ ( pair @ ( comb_app @ SV36 @ SV73 ) @ SV102 ) @ parcontract )
| ( ap_parcontractE_c1 @ SV36 @ SV73 @ SV102 )
| ( ap_parcontractE_c2 @ SV36 @ SV73 @ SV102 )
| ( ap_parcontractE_c3 @ SV36 @ SV73 @ SV102 )
| ( ap_parcontractE_c4 @ SV36 @ SV73 @ SV102 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[284]) ).
thf(334,plain,
! [SV74: $i,SV37: $i] :
( ( ( ! [SY236: $i] :
~ ( ap_parcontractE_c1 @ SV37 @ SV74 @ SY236 ) )
= $true )
| ( ( member @ ( comb_app @ SV37 @ SV74 ) @ comb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[285]) ).
thf(335,plain,
! [SV103: $i,SV75: $i,SV38: $i] :
( ( ~ ( ap_parcontractE_c1 @ SV38 @ SV75 @ SV103 )
| ( SV103
= ( comb_app @ SV38 @ SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(336,plain,
! [SV104: $i,SV76: $i,SV39: $i] :
( ( ~ ( ap_parcontractE_c2 @ SV39 @ SV76 @ SV104 )
| ( member @ SV104 @ comb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(337,plain,
! [SV77: $i,SV40: $i] :
( ( ( ! [SY239: $i] :
~ ( ap_parcontractE_c2 @ SV40 @ SV77 @ SY239 ) )
= $true )
| ( ( member @ SV77 @ comb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[288]) ).
thf(338,plain,
! [SV105: $i,SV78: $i,SV41: $i] :
( ( ~ ( ap_parcontractE_c2 @ SV41 @ SV78 @ SV105 )
| ( SV41
= ( comb_app @ combK @ SV105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[289]) ).
thf(339,plain,
! [SV106: $i,SV79: $i,SV42: $i] :
( ( ~ ( ap_parcontractE_c3 @ SV42 @ SV79 @ SV106 )
| ( member @ ( ap_parcontractE_sk1p @ SV42 @ SV79 @ SV106 ) @ comb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[290]) ).
thf(340,plain,
! [SV107: $i,SV80: $i,SV43: $i] :
( ( ~ ( ap_parcontractE_c3 @ SV43 @ SV80 @ SV107 )
| ( member @ ( ap_parcontractE_sk1q @ SV43 @ SV80 @ SV107 ) @ comb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(341,plain,
! [SV81: $i,SV44: $i] :
( ( ( ! [SY243: $i] :
~ ( ap_parcontractE_c3 @ SV44 @ SV81 @ SY243 ) )
= $true )
| ( ( member @ SV81 @ comb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[292]) ).
thf(342,plain,
! [SV108: $i,SV82: $i,SV45: $i] :
( ( ~ ( ap_parcontractE_c3 @ SV45 @ SV82 @ SV108 )
| ( SV108
= ( comb_app @ ( comb_app @ ( ap_parcontractE_sk1p @ SV45 @ SV82 @ SV108 ) @ SV82 ) @ ( comb_app @ ( ap_parcontractE_sk1q @ SV45 @ SV82 @ SV108 ) @ SV82 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(343,plain,
! [SV109: $i,SV83: $i,SV46: $i] :
( ( ~ ( ap_parcontractE_c3 @ SV46 @ SV83 @ SV109 )
| ( SV46
= ( comb_app @ ( comb_app @ combS @ ( ap_parcontractE_sk1p @ SV46 @ SV83 @ SV109 ) ) @ ( ap_parcontractE_sk1q @ SV46 @ SV83 @ SV109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(344,plain,
! [SV110: $i,SV84: $i,SV47: $i] :
( ( ~ ( ap_parcontractE_c4 @ SV47 @ SV84 @ SV110 )
| ( member @ ( pair @ SV47 @ ( ap_parcontractE_sk2q @ SV47 @ SV84 @ SV110 ) ) @ parcontract ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(345,plain,
! [SV111: $i,SV85: $i,SV48: $i] :
( ( ~ ( ap_parcontractE_c4 @ SV48 @ SV85 @ SV111 )
| ( member @ ( pair @ SV85 @ ( ap_parcontractE_sk2s @ SV48 @ SV85 @ SV111 ) ) @ parcontract ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[296]) ).
thf(346,plain,
! [SV112: $i,SV86: $i,SV49: $i] :
( ( ~ ( ap_parcontractE_c4 @ SV49 @ SV86 @ SV112 )
| ( SV112
= ( comb_app @ ( ap_parcontractE_sk2q @ SV49 @ SV86 @ SV112 ) @ ( ap_parcontractE_sk2s @ SV49 @ SV86 @ SV112 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(347,plain,
! [SV1: $i] :
( ( ( member @ ( pair @ p @ SV1 ) @ parcontract )
= $false )
| ( ( r
= ( comb_app @ combK @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[298]) ).
thf(348,plain,
! [SV87: $i,SV52: $i,SV4: $i] :
( ( ( ! [SY249: $i] :
( ( comb_app @ SV4 @ SV52 )
!= ( comb_app @ SV87 @ SY249 ) ) )
= $true )
| ( ( SV4 = SV87 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[301]) ).
thf(349,plain,
! [SV113: $i,SV88: $i,SV53: $i,SV5: $i] :
( ( ( ( comb_app @ SV5 @ SV53 )
!= ( comb_app @ SV88 @ SV113 ) )
| ( SV53 = SV113 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[302]) ).
thf(350,plain,
! [SV54: $i,SV6: $i] :
( ( ( SV6 = SV54 )
= $false )
| ( ( ! [SY217: $i,SY218: $i] :
( ( SY217 != SY218 )
| ( ( comb_app @ SV6 @ SY217 )
= ( comb_app @ SV54 @ SY218 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(351,plain,
! [SV89: $i,SV7: $i] :
( ( ( member @ ( comb_app @ SV7 @ SV89 ) @ comb )
= $false )
| ( ( member @ SV7 @ comb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(352,plain,
! [SV55: $i,SV8: $i] :
( ( ( member @ ( comb_app @ SV8 @ SV55 ) @ comb )
= $false )
| ( ( member @ SV55 @ comb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[305]) ).
thf(353,plain,
! [SV9: $i,SV114: $i] :
( ( ( ~ ( member @ SV114 @ comb )
| ( member @ ( comb_app @ SV9 @ SV114 ) @ comb ) )
= $true )
| ( ( member @ SV9 @ comb )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(354,plain,
! [SV11: $i,SV115: $i] :
( ( ( ~ ( member @ SV115 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV11 ) @ SV115 ) @ SV11 ) @ contract ) )
= $true )
| ( ( member @ SV11 @ comb )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[308]) ).
thf(355,plain,
! [SV12: $i,SV116: $i] :
( ( ( ~ ( member @ SV116 @ comb )
| ! [SY252: $i] :
( ~ ( member @ SY252 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV12 ) @ SV116 ) @ SY252 ) @ ( comb_app @ ( comb_app @ SV12 @ SY252 ) @ ( comb_app @ SV116 @ SY252 ) ) ) @ contract ) ) )
= $true )
| ( ( member @ SV12 @ comb )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(356,plain,
! [SV90: $i,SV56: $i,SV13: $i] :
( ( ( ~ ( member @ ( pair @ ( comb_app @ SV13 @ SV56 ) @ SV90 ) @ contract ) )
= $true )
| ( ( ( ap_contractE_c1 @ SV13 @ SV56 @ SV90 )
| ( ap_contractE_c2 @ SV13 @ SV56 @ SV90 )
| ( ap_contractE_c3 @ SV13 @ SV56 @ SV90 )
| ( ap_contractE_c4 @ SV13 @ SV56 @ SV90 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[310]) ).
thf(357,plain,
! [SV91: $i,SV57: $i,SV14: $i] :
( ( ( ~ ( ap_contractE_c1 @ SV14 @ SV57 @ SV91 ) )
= $true )
| ( ( member @ SV91 @ comb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[311]) ).
thf(358,plain,
! [SV117: $i,SV58: $i,SV15: $i] :
( ( ( ~ ( ap_contractE_c1 @ SV15 @ SV58 @ SV117 ) )
= $true )
| ( ( member @ SV58 @ comb )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(359,plain,
! [SV92: $i,SV59: $i,SV16: $i] :
( ( ( ~ ( ap_contractE_c1 @ SV16 @ SV59 @ SV92 ) )
= $true )
| ( ( SV16
= ( comb_app @ combK @ SV92 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[313]) ).
thf(360,plain,
! [SV93: $i,SV60: $i,SV17: $i] :
( ( ( ~ ( ap_contractE_c2 @ SV17 @ SV60 @ SV93 ) )
= $true )
| ( ( member @ ( ap_contractE_sk1p @ SV17 @ SV60 @ SV93 ) @ comb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[314]) ).
thf(361,plain,
! [SV94: $i,SV61: $i,SV18: $i] :
( ( ( ~ ( ap_contractE_c2 @ SV18 @ SV61 @ SV94 ) )
= $true )
| ( ( member @ ( ap_contractE_sk1q @ SV18 @ SV61 @ SV94 ) @ comb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[315]) ).
thf(362,plain,
! [SV118: $i,SV62: $i,SV19: $i] :
( ( ( ~ ( ap_contractE_c2 @ SV19 @ SV62 @ SV118 ) )
= $true )
| ( ( member @ SV62 @ comb )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(363,plain,
! [SV95: $i,SV63: $i,SV20: $i] :
( ( ( ~ ( ap_contractE_c2 @ SV20 @ SV63 @ SV95 ) )
= $true )
| ( ( SV95
= ( comb_app @ ( comb_app @ ( ap_contractE_sk1p @ SV20 @ SV63 @ SV95 ) @ SV63 ) @ ( comb_app @ ( ap_contractE_sk1q @ SV20 @ SV63 @ SV95 ) @ SV63 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[317]) ).
thf(364,plain,
! [SV96: $i,SV64: $i,SV21: $i] :
( ( ( ~ ( ap_contractE_c2 @ SV21 @ SV64 @ SV96 ) )
= $true )
| ( ( SV21
= ( comb_app @ ( comb_app @ combS @ ( ap_contractE_sk1p @ SV21 @ SV64 @ SV96 ) ) @ ( ap_contractE_sk1q @ SV21 @ SV64 @ SV96 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[318]) ).
thf(365,plain,
! [SV97: $i,SV65: $i,SV22: $i] :
( ( ( ~ ( ap_contractE_c3 @ SV22 @ SV65 @ SV97 ) )
= $true )
| ( ( member @ ( pair @ SV22 @ ( ap_contractE_sk2q @ SV22 @ SV65 @ SV97 ) ) @ contract )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[319]) ).
thf(366,plain,
! [SV119: $i,SV66: $i,SV23: $i] :
( ( ( ~ ( ap_contractE_c3 @ SV23 @ SV66 @ SV119 ) )
= $true )
| ( ( member @ SV66 @ comb )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(367,plain,
! [SV98: $i,SV67: $i,SV24: $i] :
( ( ( ~ ( ap_contractE_c3 @ SV24 @ SV67 @ SV98 ) )
= $true )
| ( ( SV98
= ( comb_app @ ( ap_contractE_sk2q @ SV24 @ SV67 @ SV98 ) @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[321]) ).
thf(368,plain,
! [SV99: $i,SV68: $i,SV25: $i] :
( ( ( ~ ( ap_contractE_c4 @ SV25 @ SV68 @ SV99 ) )
= $true )
| ( ( member @ ( pair @ SV68 @ ( ap_contractE_sk3q @ SV25 @ SV68 @ SV99 ) ) @ contract )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[322]) ).
thf(369,plain,
! [SV120: $i,SV100: $i,SV26: $i] :
( ( ( ~ ( ap_contractE_c4 @ SV26 @ SV100 @ SV120 ) )
= $true )
| ( ( member @ SV26 @ comb )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[323]) ).
thf(370,plain,
! [SV101: $i,SV69: $i,SV27: $i] :
( ( ( ~ ( ap_contractE_c4 @ SV27 @ SV69 @ SV101 ) )
= $true )
| ( ( SV101
= ( comb_app @ SV27 @ ( ap_contractE_sk3q @ SV27 @ SV69 @ SV101 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[324]) ).
thf(371,plain,
! [SV31: $i,SV121: $i] :
( ( ( ~ ( member @ SV121 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV31 ) @ SV121 ) @ SV31 ) @ parcontract ) )
= $true )
| ( ( member @ SV31 @ comb )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[326]) ).
thf(372,plain,
! [SV32: $i,SV122: $i] :
( ( ( ~ ( member @ SV122 @ comb )
| ! [SY253: $i] :
( ~ ( member @ SY253 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV32 ) @ SV122 ) @ SY253 ) @ ( comb_app @ ( comb_app @ SV32 @ SY253 ) @ ( comb_app @ SV122 @ SY253 ) ) ) @ parcontract ) ) )
= $true )
| ( ( member @ SV32 @ comb )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(373,plain,
! [SV70: $i,SV33: $i] :
( ( ( member @ ( pair @ SV33 @ SV70 ) @ parcontract )
= $false )
| ( ( ! [SY233: $i,SY234: $i] :
( ~ ( member @ ( pair @ SY233 @ SY234 ) @ parcontract )
| ( member @ ( pair @ ( comb_app @ SV33 @ SY233 ) @ ( comb_app @ SV70 @ SY234 ) ) @ parcontract ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(374,plain,
! [SV102: $i,SV73: $i,SV36: $i] :
( ( ( ~ ( member @ ( pair @ ( comb_app @ SV36 @ SV73 ) @ SV102 ) @ parcontract ) )
= $true )
| ( ( ( ap_parcontractE_c1 @ SV36 @ SV73 @ SV102 )
| ( ap_parcontractE_c2 @ SV36 @ SV73 @ SV102 )
| ( ap_parcontractE_c3 @ SV36 @ SV73 @ SV102 )
| ( ap_parcontractE_c4 @ SV36 @ SV73 @ SV102 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[333]) ).
thf(375,plain,
! [SV123: $i,SV74: $i,SV37: $i] :
( ( ( ~ ( ap_parcontractE_c1 @ SV37 @ SV74 @ SV123 ) )
= $true )
| ( ( member @ ( comb_app @ SV37 @ SV74 ) @ comb )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[334]) ).
thf(376,plain,
! [SV103: $i,SV75: $i,SV38: $i] :
( ( ( ~ ( ap_parcontractE_c1 @ SV38 @ SV75 @ SV103 ) )
= $true )
| ( ( SV103
= ( comb_app @ SV38 @ SV75 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[335]) ).
thf(377,plain,
! [SV104: $i,SV76: $i,SV39: $i] :
( ( ( ~ ( ap_parcontractE_c2 @ SV39 @ SV76 @ SV104 ) )
= $true )
| ( ( member @ SV104 @ comb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[336]) ).
thf(378,plain,
! [SV124: $i,SV77: $i,SV40: $i] :
( ( ( ~ ( ap_parcontractE_c2 @ SV40 @ SV77 @ SV124 ) )
= $true )
| ( ( member @ SV77 @ comb )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(379,plain,
! [SV105: $i,SV78: $i,SV41: $i] :
( ( ( ~ ( ap_parcontractE_c2 @ SV41 @ SV78 @ SV105 ) )
= $true )
| ( ( SV41
= ( comb_app @ combK @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[338]) ).
thf(380,plain,
! [SV106: $i,SV79: $i,SV42: $i] :
( ( ( ~ ( ap_parcontractE_c3 @ SV42 @ SV79 @ SV106 ) )
= $true )
| ( ( member @ ( ap_parcontractE_sk1p @ SV42 @ SV79 @ SV106 ) @ comb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[339]) ).
thf(381,plain,
! [SV107: $i,SV80: $i,SV43: $i] :
( ( ( ~ ( ap_parcontractE_c3 @ SV43 @ SV80 @ SV107 ) )
= $true )
| ( ( member @ ( ap_parcontractE_sk1q @ SV43 @ SV80 @ SV107 ) @ comb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[340]) ).
thf(382,plain,
! [SV125: $i,SV81: $i,SV44: $i] :
( ( ( ~ ( ap_parcontractE_c3 @ SV44 @ SV81 @ SV125 ) )
= $true )
| ( ( member @ SV81 @ comb )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(383,plain,
! [SV108: $i,SV82: $i,SV45: $i] :
( ( ( ~ ( ap_parcontractE_c3 @ SV45 @ SV82 @ SV108 ) )
= $true )
| ( ( SV108
= ( comb_app @ ( comb_app @ ( ap_parcontractE_sk1p @ SV45 @ SV82 @ SV108 ) @ SV82 ) @ ( comb_app @ ( ap_parcontractE_sk1q @ SV45 @ SV82 @ SV108 ) @ SV82 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[342]) ).
thf(384,plain,
! [SV109: $i,SV83: $i,SV46: $i] :
( ( ( ~ ( ap_parcontractE_c3 @ SV46 @ SV83 @ SV109 ) )
= $true )
| ( ( SV46
= ( comb_app @ ( comb_app @ combS @ ( ap_parcontractE_sk1p @ SV46 @ SV83 @ SV109 ) ) @ ( ap_parcontractE_sk1q @ SV46 @ SV83 @ SV109 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[343]) ).
thf(385,plain,
! [SV110: $i,SV84: $i,SV47: $i] :
( ( ( ~ ( ap_parcontractE_c4 @ SV47 @ SV84 @ SV110 ) )
= $true )
| ( ( member @ ( pair @ SV47 @ ( ap_parcontractE_sk2q @ SV47 @ SV84 @ SV110 ) ) @ parcontract )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[344]) ).
thf(386,plain,
! [SV111: $i,SV85: $i,SV48: $i] :
( ( ( ~ ( ap_parcontractE_c4 @ SV48 @ SV85 @ SV111 ) )
= $true )
| ( ( member @ ( pair @ SV85 @ ( ap_parcontractE_sk2s @ SV48 @ SV85 @ SV111 ) ) @ parcontract )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[345]) ).
thf(387,plain,
! [SV112: $i,SV86: $i,SV49: $i] :
( ( ( ~ ( ap_parcontractE_c4 @ SV49 @ SV86 @ SV112 ) )
= $true )
| ( ( SV112
= ( comb_app @ ( ap_parcontractE_sk2q @ SV49 @ SV86 @ SV112 ) @ ( ap_parcontractE_sk2s @ SV49 @ SV86 @ SV112 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[346]) ).
thf(388,plain,
! [SV126: $i,SV87: $i,SV52: $i,SV4: $i] :
( ( ( ( ( comb_app @ SV4 @ SV52 )
!= ( comb_app @ SV87 @ SV126 ) ) )
= $true )
| ( ( SV4 = SV87 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(389,plain,
! [SV113: $i,SV88: $i,SV53: $i,SV5: $i] :
( ( ( ( ( comb_app @ SV5 @ SV53 )
!= ( comb_app @ SV88 @ SV113 ) ) )
= $true )
| ( ( SV53 = SV113 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[349]) ).
thf(390,plain,
! [SV54: $i,SV6: $i,SV127: $i] :
( ( ( ! [SY254: $i] :
( ( SV127 != SY254 )
| ( ( comb_app @ SV6 @ SV127 )
= ( comb_app @ SV54 @ SY254 ) ) ) )
= $true )
| ( ( SV6 = SV54 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(391,plain,
! [SV9: $i,SV114: $i] :
( ( ( ~ ( member @ SV114 @ comb ) )
= $true )
| ( ( member @ ( comb_app @ SV9 @ SV114 ) @ comb )
= $true )
| ( ( member @ SV9 @ comb )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[353]) ).
thf(392,plain,
! [SV11: $i,SV115: $i] :
( ( ( ~ ( member @ SV115 @ comb ) )
= $true )
| ( ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV11 ) @ SV115 ) @ SV11 ) @ contract )
= $true )
| ( ( member @ SV11 @ comb )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[354]) ).
thf(393,plain,
! [SV12: $i,SV116: $i] :
( ( ( ~ ( member @ SV116 @ comb ) )
= $true )
| ( ( ! [SY252: $i] :
( ~ ( member @ SY252 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV12 ) @ SV116 ) @ SY252 ) @ ( comb_app @ ( comb_app @ SV12 @ SY252 ) @ ( comb_app @ SV116 @ SY252 ) ) ) @ contract ) ) )
= $true )
| ( ( member @ SV12 @ comb )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[355]) ).
thf(394,plain,
! [SV90: $i,SV56: $i,SV13: $i] :
( ( ( member @ ( pair @ ( comb_app @ SV13 @ SV56 ) @ SV90 ) @ contract )
= $false )
| ( ( ( ap_contractE_c1 @ SV13 @ SV56 @ SV90 )
| ( ap_contractE_c2 @ SV13 @ SV56 @ SV90 )
| ( ap_contractE_c3 @ SV13 @ SV56 @ SV90 )
| ( ap_contractE_c4 @ SV13 @ SV56 @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[356]) ).
thf(395,plain,
! [SV91: $i,SV57: $i,SV14: $i] :
( ( ( ap_contractE_c1 @ SV14 @ SV57 @ SV91 )
= $false )
| ( ( member @ SV91 @ comb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(396,plain,
! [SV117: $i,SV58: $i,SV15: $i] :
( ( ( ap_contractE_c1 @ SV15 @ SV58 @ SV117 )
= $false )
| ( ( member @ SV58 @ comb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[358]) ).
thf(397,plain,
! [SV92: $i,SV59: $i,SV16: $i] :
( ( ( ap_contractE_c1 @ SV16 @ SV59 @ SV92 )
= $false )
| ( ( SV16
= ( comb_app @ combK @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[359]) ).
thf(398,plain,
! [SV93: $i,SV60: $i,SV17: $i] :
( ( ( ap_contractE_c2 @ SV17 @ SV60 @ SV93 )
= $false )
| ( ( member @ ( ap_contractE_sk1p @ SV17 @ SV60 @ SV93 ) @ comb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[360]) ).
thf(399,plain,
! [SV94: $i,SV61: $i,SV18: $i] :
( ( ( ap_contractE_c2 @ SV18 @ SV61 @ SV94 )
= $false )
| ( ( member @ ( ap_contractE_sk1q @ SV18 @ SV61 @ SV94 ) @ comb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(400,plain,
! [SV118: $i,SV62: $i,SV19: $i] :
( ( ( ap_contractE_c2 @ SV19 @ SV62 @ SV118 )
= $false )
| ( ( member @ SV62 @ comb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[362]) ).
thf(401,plain,
! [SV95: $i,SV63: $i,SV20: $i] :
( ( ( ap_contractE_c2 @ SV20 @ SV63 @ SV95 )
= $false )
| ( ( SV95
= ( comb_app @ ( comb_app @ ( ap_contractE_sk1p @ SV20 @ SV63 @ SV95 ) @ SV63 ) @ ( comb_app @ ( ap_contractE_sk1q @ SV20 @ SV63 @ SV95 ) @ SV63 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(402,plain,
! [SV96: $i,SV64: $i,SV21: $i] :
( ( ( ap_contractE_c2 @ SV21 @ SV64 @ SV96 )
= $false )
| ( ( SV21
= ( comb_app @ ( comb_app @ combS @ ( ap_contractE_sk1p @ SV21 @ SV64 @ SV96 ) ) @ ( ap_contractE_sk1q @ SV21 @ SV64 @ SV96 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[364]) ).
thf(403,plain,
! [SV97: $i,SV65: $i,SV22: $i] :
( ( ( ap_contractE_c3 @ SV22 @ SV65 @ SV97 )
= $false )
| ( ( member @ ( pair @ SV22 @ ( ap_contractE_sk2q @ SV22 @ SV65 @ SV97 ) ) @ contract )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[365]) ).
thf(404,plain,
! [SV119: $i,SV66: $i,SV23: $i] :
( ( ( ap_contractE_c3 @ SV23 @ SV66 @ SV119 )
= $false )
| ( ( member @ SV66 @ comb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[366]) ).
thf(405,plain,
! [SV98: $i,SV67: $i,SV24: $i] :
( ( ( ap_contractE_c3 @ SV24 @ SV67 @ SV98 )
= $false )
| ( ( SV98
= ( comb_app @ ( ap_contractE_sk2q @ SV24 @ SV67 @ SV98 ) @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[367]) ).
thf(406,plain,
! [SV99: $i,SV68: $i,SV25: $i] :
( ( ( ap_contractE_c4 @ SV25 @ SV68 @ SV99 )
= $false )
| ( ( member @ ( pair @ SV68 @ ( ap_contractE_sk3q @ SV25 @ SV68 @ SV99 ) ) @ contract )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[368]) ).
thf(407,plain,
! [SV120: $i,SV100: $i,SV26: $i] :
( ( ( ap_contractE_c4 @ SV26 @ SV100 @ SV120 )
= $false )
| ( ( member @ SV26 @ comb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[369]) ).
thf(408,plain,
! [SV101: $i,SV69: $i,SV27: $i] :
( ( ( ap_contractE_c4 @ SV27 @ SV69 @ SV101 )
= $false )
| ( ( SV101
= ( comb_app @ SV27 @ ( ap_contractE_sk3q @ SV27 @ SV69 @ SV101 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[370]) ).
thf(409,plain,
! [SV31: $i,SV121: $i] :
( ( ( ~ ( member @ SV121 @ comb ) )
= $true )
| ( ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV31 ) @ SV121 ) @ SV31 ) @ parcontract )
= $true )
| ( ( member @ SV31 @ comb )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[371]) ).
thf(410,plain,
! [SV32: $i,SV122: $i] :
( ( ( ~ ( member @ SV122 @ comb ) )
= $true )
| ( ( ! [SY253: $i] :
( ~ ( member @ SY253 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV32 ) @ SV122 ) @ SY253 ) @ ( comb_app @ ( comb_app @ SV32 @ SY253 ) @ ( comb_app @ SV122 @ SY253 ) ) ) @ parcontract ) ) )
= $true )
| ( ( member @ SV32 @ comb )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[372]) ).
thf(411,plain,
! [SV70: $i,SV33: $i,SV128: $i] :
( ( ( ! [SY255: $i] :
( ~ ( member @ ( pair @ SV128 @ SY255 ) @ parcontract )
| ( member @ ( pair @ ( comb_app @ SV33 @ SV128 ) @ ( comb_app @ SV70 @ SY255 ) ) @ parcontract ) ) )
= $true )
| ( ( member @ ( pair @ SV33 @ SV70 ) @ parcontract )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[373]) ).
thf(412,plain,
! [SV102: $i,SV73: $i,SV36: $i] :
( ( ( member @ ( pair @ ( comb_app @ SV36 @ SV73 ) @ SV102 ) @ parcontract )
= $false )
| ( ( ( ap_parcontractE_c1 @ SV36 @ SV73 @ SV102 )
| ( ap_parcontractE_c2 @ SV36 @ SV73 @ SV102 )
| ( ap_parcontractE_c3 @ SV36 @ SV73 @ SV102 )
| ( ap_parcontractE_c4 @ SV36 @ SV73 @ SV102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(413,plain,
! [SV123: $i,SV74: $i,SV37: $i] :
( ( ( ap_parcontractE_c1 @ SV37 @ SV74 @ SV123 )
= $false )
| ( ( member @ ( comb_app @ SV37 @ SV74 ) @ comb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[375]) ).
thf(414,plain,
! [SV103: $i,SV75: $i,SV38: $i] :
( ( ( ap_parcontractE_c1 @ SV38 @ SV75 @ SV103 )
= $false )
| ( ( SV103
= ( comb_app @ SV38 @ SV75 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(415,plain,
! [SV104: $i,SV76: $i,SV39: $i] :
( ( ( ap_parcontractE_c2 @ SV39 @ SV76 @ SV104 )
= $false )
| ( ( member @ SV104 @ comb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(416,plain,
! [SV124: $i,SV77: $i,SV40: $i] :
( ( ( ap_parcontractE_c2 @ SV40 @ SV77 @ SV124 )
= $false )
| ( ( member @ SV77 @ comb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(417,plain,
! [SV105: $i,SV78: $i,SV41: $i] :
( ( ( ap_parcontractE_c2 @ SV41 @ SV78 @ SV105 )
= $false )
| ( ( SV41
= ( comb_app @ combK @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(418,plain,
! [SV106: $i,SV79: $i,SV42: $i] :
( ( ( ap_parcontractE_c3 @ SV42 @ SV79 @ SV106 )
= $false )
| ( ( member @ ( ap_parcontractE_sk1p @ SV42 @ SV79 @ SV106 ) @ comb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(419,plain,
! [SV107: $i,SV80: $i,SV43: $i] :
( ( ( ap_parcontractE_c3 @ SV43 @ SV80 @ SV107 )
= $false )
| ( ( member @ ( ap_parcontractE_sk1q @ SV43 @ SV80 @ SV107 ) @ comb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[381]) ).
thf(420,plain,
! [SV125: $i,SV81: $i,SV44: $i] :
( ( ( ap_parcontractE_c3 @ SV44 @ SV81 @ SV125 )
= $false )
| ( ( member @ SV81 @ comb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[382]) ).
thf(421,plain,
! [SV108: $i,SV82: $i,SV45: $i] :
( ( ( ap_parcontractE_c3 @ SV45 @ SV82 @ SV108 )
= $false )
| ( ( SV108
= ( comb_app @ ( comb_app @ ( ap_parcontractE_sk1p @ SV45 @ SV82 @ SV108 ) @ SV82 ) @ ( comb_app @ ( ap_parcontractE_sk1q @ SV45 @ SV82 @ SV108 ) @ SV82 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[383]) ).
thf(422,plain,
! [SV109: $i,SV83: $i,SV46: $i] :
( ( ( ap_parcontractE_c3 @ SV46 @ SV83 @ SV109 )
= $false )
| ( ( SV46
= ( comb_app @ ( comb_app @ combS @ ( ap_parcontractE_sk1p @ SV46 @ SV83 @ SV109 ) ) @ ( ap_parcontractE_sk1q @ SV46 @ SV83 @ SV109 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[384]) ).
thf(423,plain,
! [SV110: $i,SV84: $i,SV47: $i] :
( ( ( ap_parcontractE_c4 @ SV47 @ SV84 @ SV110 )
= $false )
| ( ( member @ ( pair @ SV47 @ ( ap_parcontractE_sk2q @ SV47 @ SV84 @ SV110 ) ) @ parcontract )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(424,plain,
! [SV111: $i,SV85: $i,SV48: $i] :
( ( ( ap_parcontractE_c4 @ SV48 @ SV85 @ SV111 )
= $false )
| ( ( member @ ( pair @ SV85 @ ( ap_parcontractE_sk2s @ SV48 @ SV85 @ SV111 ) ) @ parcontract )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[386]) ).
thf(425,plain,
! [SV112: $i,SV86: $i,SV49: $i] :
( ( ( ap_parcontractE_c4 @ SV49 @ SV86 @ SV112 )
= $false )
| ( ( SV112
= ( comb_app @ ( ap_parcontractE_sk2q @ SV49 @ SV86 @ SV112 ) @ ( ap_parcontractE_sk2s @ SV49 @ SV86 @ SV112 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[387]) ).
thf(426,plain,
! [SV126: $i,SV87: $i,SV52: $i,SV4: $i] :
( ( ( ( comb_app @ SV4 @ SV52 )
= ( comb_app @ SV87 @ SV126 ) )
= $false )
| ( ( SV4 = SV87 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[388]) ).
thf(427,plain,
! [SV113: $i,SV88: $i,SV53: $i,SV5: $i] :
( ( ( ( comb_app @ SV5 @ SV53 )
= ( comb_app @ SV88 @ SV113 ) )
= $false )
| ( ( SV53 = SV113 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[389]) ).
thf(428,plain,
! [SV54: $i,SV6: $i,SV129: $i,SV127: $i] :
( ( ( ( SV127 != SV129 )
| ( ( comb_app @ SV6 @ SV127 )
= ( comb_app @ SV54 @ SV129 ) ) )
= $true )
| ( ( SV6 = SV54 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(429,plain,
! [SV9: $i,SV114: $i] :
( ( ( member @ SV114 @ comb )
= $false )
| ( ( member @ ( comb_app @ SV9 @ SV114 ) @ comb )
= $true )
| ( ( member @ SV9 @ comb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[391]) ).
thf(430,plain,
! [SV11: $i,SV115: $i] :
( ( ( member @ SV115 @ comb )
= $false )
| ( ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV11 ) @ SV115 ) @ SV11 ) @ contract )
= $true )
| ( ( member @ SV11 @ comb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(431,plain,
! [SV12: $i,SV116: $i] :
( ( ( member @ SV116 @ comb )
= $false )
| ( ( ! [SY252: $i] :
( ~ ( member @ SY252 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV12 ) @ SV116 ) @ SY252 ) @ ( comb_app @ ( comb_app @ SV12 @ SY252 ) @ ( comb_app @ SV116 @ SY252 ) ) ) @ contract ) ) )
= $true )
| ( ( member @ SV12 @ comb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[393]) ).
thf(432,plain,
! [SV90: $i,SV56: $i,SV13: $i] :
( ( ( ap_contractE_c1 @ SV13 @ SV56 @ SV90 )
= $true )
| ( ( ( ap_contractE_c2 @ SV13 @ SV56 @ SV90 )
| ( ap_contractE_c3 @ SV13 @ SV56 @ SV90 )
| ( ap_contractE_c4 @ SV13 @ SV56 @ SV90 ) )
= $true )
| ( ( member @ ( pair @ ( comb_app @ SV13 @ SV56 ) @ SV90 ) @ contract )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[394]) ).
thf(433,plain,
! [SV31: $i,SV121: $i] :
( ( ( member @ SV121 @ comb )
= $false )
| ( ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV31 ) @ SV121 ) @ SV31 ) @ parcontract )
= $true )
| ( ( member @ SV31 @ comb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[409]) ).
thf(434,plain,
! [SV32: $i,SV122: $i] :
( ( ( member @ SV122 @ comb )
= $false )
| ( ( ! [SY253: $i] :
( ~ ( member @ SY253 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV32 ) @ SV122 ) @ SY253 ) @ ( comb_app @ ( comb_app @ SV32 @ SY253 ) @ ( comb_app @ SV122 @ SY253 ) ) ) @ parcontract ) ) )
= $true )
| ( ( member @ SV32 @ comb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[410]) ).
thf(435,plain,
! [SV70: $i,SV33: $i,SV130: $i,SV128: $i] :
( ( ( ~ ( member @ ( pair @ SV128 @ SV130 ) @ parcontract )
| ( member @ ( pair @ ( comb_app @ SV33 @ SV128 ) @ ( comb_app @ SV70 @ SV130 ) ) @ parcontract ) )
= $true )
| ( ( member @ ( pair @ SV33 @ SV70 ) @ parcontract )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(436,plain,
! [SV102: $i,SV73: $i,SV36: $i] :
( ( ( ap_parcontractE_c1 @ SV36 @ SV73 @ SV102 )
= $true )
| ( ( ( ap_parcontractE_c2 @ SV36 @ SV73 @ SV102 )
| ( ap_parcontractE_c3 @ SV36 @ SV73 @ SV102 )
| ( ap_parcontractE_c4 @ SV36 @ SV73 @ SV102 ) )
= $true )
| ( ( member @ ( pair @ ( comb_app @ SV36 @ SV73 ) @ SV102 ) @ parcontract )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[412]) ).
thf(437,plain,
! [SV54: $i,SV6: $i,SV129: $i,SV127: $i] :
( ( ( ( SV127 != SV129 ) )
= $true )
| ( ( ( comb_app @ SV6 @ SV127 )
= ( comb_app @ SV54 @ SV129 ) )
= $true )
| ( ( SV6 = SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[428]) ).
thf(438,plain,
! [SV116: $i,SV12: $i,SV131: $i] :
( ( ( ~ ( member @ SV131 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV12 ) @ SV116 ) @ SV131 ) @ ( comb_app @ ( comb_app @ SV12 @ SV131 ) @ ( comb_app @ SV116 @ SV131 ) ) ) @ contract ) )
= $true )
| ( ( member @ SV116 @ comb )
= $false )
| ( ( member @ SV12 @ comb )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(439,plain,
! [SV90: $i,SV56: $i,SV13: $i] :
( ( ( ap_contractE_c2 @ SV13 @ SV56 @ SV90 )
= $true )
| ( ( ( ap_contractE_c3 @ SV13 @ SV56 @ SV90 )
| ( ap_contractE_c4 @ SV13 @ SV56 @ SV90 ) )
= $true )
| ( ( ap_contractE_c1 @ SV13 @ SV56 @ SV90 )
= $true )
| ( ( member @ ( pair @ ( comb_app @ SV13 @ SV56 ) @ SV90 ) @ contract )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[432]) ).
thf(440,plain,
! [SV122: $i,SV32: $i,SV132: $i] :
( ( ( ~ ( member @ SV132 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV32 ) @ SV122 ) @ SV132 ) @ ( comb_app @ ( comb_app @ SV32 @ SV132 ) @ ( comb_app @ SV122 @ SV132 ) ) ) @ parcontract ) )
= $true )
| ( ( member @ SV122 @ comb )
= $false )
| ( ( member @ SV32 @ comb )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[434]) ).
thf(441,plain,
! [SV70: $i,SV33: $i,SV130: $i,SV128: $i] :
( ( ( ~ ( member @ ( pair @ SV128 @ SV130 ) @ parcontract ) )
= $true )
| ( ( member @ ( pair @ ( comb_app @ SV33 @ SV128 ) @ ( comb_app @ SV70 @ SV130 ) ) @ parcontract )
= $true )
| ( ( member @ ( pair @ SV33 @ SV70 ) @ parcontract )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[435]) ).
thf(442,plain,
! [SV102: $i,SV73: $i,SV36: $i] :
( ( ( ap_parcontractE_c2 @ SV36 @ SV73 @ SV102 )
= $true )
| ( ( ( ap_parcontractE_c3 @ SV36 @ SV73 @ SV102 )
| ( ap_parcontractE_c4 @ SV36 @ SV73 @ SV102 ) )
= $true )
| ( ( ap_parcontractE_c1 @ SV36 @ SV73 @ SV102 )
= $true )
| ( ( member @ ( pair @ ( comb_app @ SV36 @ SV73 ) @ SV102 ) @ parcontract )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[436]) ).
thf(443,plain,
! [SV54: $i,SV6: $i,SV129: $i,SV127: $i] :
( ( ( SV127 = SV129 )
= $false )
| ( ( ( comb_app @ SV6 @ SV127 )
= ( comb_app @ SV54 @ SV129 ) )
= $true )
| ( ( SV6 = SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[437]) ).
thf(444,plain,
! [SV116: $i,SV12: $i,SV131: $i] :
( ( ( ~ ( member @ SV131 @ comb ) )
= $true )
| ( ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV12 ) @ SV116 ) @ SV131 ) @ ( comb_app @ ( comb_app @ SV12 @ SV131 ) @ ( comb_app @ SV116 @ SV131 ) ) ) @ contract )
= $true )
| ( ( member @ SV116 @ comb )
= $false )
| ( ( member @ SV12 @ comb )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[438]) ).
thf(445,plain,
! [SV90: $i,SV56: $i,SV13: $i] :
( ( ( ap_contractE_c3 @ SV13 @ SV56 @ SV90 )
= $true )
| ( ( ap_contractE_c4 @ SV13 @ SV56 @ SV90 )
= $true )
| ( ( ap_contractE_c2 @ SV13 @ SV56 @ SV90 )
= $true )
| ( ( ap_contractE_c1 @ SV13 @ SV56 @ SV90 )
= $true )
| ( ( member @ ( pair @ ( comb_app @ SV13 @ SV56 ) @ SV90 ) @ contract )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[439]) ).
thf(446,plain,
! [SV122: $i,SV32: $i,SV132: $i] :
( ( ( ~ ( member @ SV132 @ comb ) )
= $true )
| ( ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV32 ) @ SV122 ) @ SV132 ) @ ( comb_app @ ( comb_app @ SV32 @ SV132 ) @ ( comb_app @ SV122 @ SV132 ) ) ) @ parcontract )
= $true )
| ( ( member @ SV122 @ comb )
= $false )
| ( ( member @ SV32 @ comb )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[440]) ).
thf(447,plain,
! [SV70: $i,SV33: $i,SV130: $i,SV128: $i] :
( ( ( member @ ( pair @ SV128 @ SV130 ) @ parcontract )
= $false )
| ( ( member @ ( pair @ ( comb_app @ SV33 @ SV128 ) @ ( comb_app @ SV70 @ SV130 ) ) @ parcontract )
= $true )
| ( ( member @ ( pair @ SV33 @ SV70 ) @ parcontract )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[441]) ).
thf(448,plain,
! [SV102: $i,SV73: $i,SV36: $i] :
( ( ( ap_parcontractE_c3 @ SV36 @ SV73 @ SV102 )
= $true )
| ( ( ap_parcontractE_c4 @ SV36 @ SV73 @ SV102 )
= $true )
| ( ( ap_parcontractE_c2 @ SV36 @ SV73 @ SV102 )
= $true )
| ( ( ap_parcontractE_c1 @ SV36 @ SV73 @ SV102 )
= $true )
| ( ( member @ ( pair @ ( comb_app @ SV36 @ SV73 ) @ SV102 ) @ parcontract )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[442]) ).
thf(449,plain,
! [SV116: $i,SV12: $i,SV131: $i] :
( ( ( member @ SV131 @ comb )
= $false )
| ( ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV12 ) @ SV116 ) @ SV131 ) @ ( comb_app @ ( comb_app @ SV12 @ SV131 ) @ ( comb_app @ SV116 @ SV131 ) ) ) @ contract )
= $true )
| ( ( member @ SV116 @ comb )
= $false )
| ( ( member @ SV12 @ comb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[444]) ).
thf(450,plain,
! [SV122: $i,SV32: $i,SV132: $i] :
( ( ( member @ SV132 @ comb )
= $false )
| ( ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV32 ) @ SV122 ) @ SV132 ) @ ( comb_app @ ( comb_app @ SV32 @ SV132 ) @ ( comb_app @ SV122 @ SV132 ) ) ) @ parcontract )
= $true )
| ( ( member @ SV122 @ comb )
= $false )
| ( ( member @ SV32 @ comb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[446]) ).
thf(451,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[139,450,449,448,447,445,443,433,430,429,427,426,425,424,423,422,421,420,419,418,417,416,415,414,413,408,407,406,405,404,403,402,401,400,399,398,397,396,395,352,351,347,332,331,330,329,325,307,300,299,275,274,246,195,149,148]) ).
thf(452,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[451]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : COL092-1 : TPTP v8.1.0. Released v2.7.0.
% 0.13/0.14 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.36 % Computer : n024.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Tue May 31 16:09:21 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.40 .
% 0.14/0.41
% 0.14/0.41 No.of.Axioms: 55
% 0.14/0.41
% 0.14/0.41 Length.of.Defs: 0
% 0.14/0.41
% 0.14/0.41 Contains.Choice.Funs: false
% 0.21/0.44 .
% 0.21/0.46 (rf:0,axioms:55,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:57,loop_count:0,foatp_calls:0,translation:fof_full).......................
% 0.40/0.94
% 0.40/0.94 ********************************
% 0.40/0.94 * All subproblems solved! *
% 0.40/0.94 ********************************
% 0.40/0.94 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:55,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:451,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.84/1.04
% 0.84/1.04 %**** Beginning of derivation protocol ****
% 0.84/1.04 % SZS output start CNFRefutation
% See solution above
% 0.84/1.04
% 0.84/1.04 %**** End of derivation protocol ****
% 0.84/1.04 %**** no. of clauses in derivation: 452 ****
% 0.84/1.04 %**** clause counter: 451 ****
% 0.84/1.04
% 0.84/1.04 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:55,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:451,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------