%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : COL088-1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:11:08 AM UTC 2026
% Result : Unsatisfiable 97.78s 20.18s
% Output : CNFRefutation 97.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 45
% Syntax : Number of formulae : 344 ( 219 unt; 0 typ; 0 def)
% Number of atoms : 1750 ( 582 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 4256 ( 411 ~; 512 |; 0 &;3333 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 10 con; 0-3 aty)
% Number of variables : 911 ( 0 ^; 911 !; 0 ?; 911 :)
% 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_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_r,type,
r: $i ).
thf(tp_rtrancl,type,
rtrancl: $i > $i ).
thf(tp_trans,type,
trans: $i > $o ).
thf(tp_y,type,
y: $i ).
thf(tp_z,type,
z: $i ).
thf(1,axiom,
! [P3: $i,Q3: $i,R3: $i,C: $i] :
( ~ ( member @ ( pair @ P3 @ Q3 ) @ contract )
| ~ ( member @ R3 @ comb )
| ~ ( member @ ( pair @ ( comb_app @ R3 @ Q3 ) @ C ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ R3 @ P3 ) @ C ) @ ( rtrancl @ contract ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reduction_rls_4) ).
thf(2,axiom,
! [P3: $i,Q3: $i,R3: $i,C: $i] :
( ~ ( member @ ( pair @ P3 @ Q3 ) @ contract )
| ~ ( member @ R3 @ comb )
| ~ ( member @ ( pair @ ( comb_app @ Q3 @ R3 ) @ C ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ P3 @ R3 ) @ C ) @ ( rtrancl @ contract ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reduction_rls_3) ).
thf(3,axiom,
! [P3: $i,Q3: $i,R3: $i,C: $i] :
( ~ ( member @ P3 @ comb )
| ~ ( member @ Q3 @ comb )
| ~ ( member @ R3 @ comb )
| ~ ( member @ ( pair @ ( comb_app @ ( comb_app @ P3 @ R3 ) @ ( comb_app @ Q3 @ R3 ) ) @ C ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ P3 ) @ Q3 ) @ R3 ) @ C ) @ ( rtrancl @ contract ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reduction_rls_2) ).
thf(4,axiom,
! [B: $i,Q3: $i,C: $i] :
( ~ ( member @ B @ comb )
| ~ ( member @ Q3 @ comb )
| ~ ( member @ ( pair @ B @ C ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ B ) @ Q3 ) @ C ) @ ( rtrancl @ contract ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reduction_rls_1) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ~ ( member @ ( pair @ A @ B ) @ contract )
| ( member @ B @ comb ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contract_combD2) ).
thf(6,axiom,
! [R: $i] : ( trans @ ( rtrancl @ R ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',trans_rtrancl) ).
thf(7,axiom,
! [R: $i,A: $i,B: $i,C: $i] :
( ~ ( trans @ R )
| ~ ( member @ ( pair @ A @ B ) @ R )
| ~ ( member @ ( pair @ B @ C ) @ R )
| ( member @ ( pair @ A @ C ) @ R ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transD) ).
thf(8,axiom,
! [R: $i] :
~ ( member @ ( pair @ combS @ R ) @ contract ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_contractE) ).
thf(9,axiom,
! [R: $i] :
~ ( member @ ( pair @ combK @ R ) @ contract ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_contractE) ).
thf(10,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(11,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(12,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(13,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(14,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(15,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(16,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(17,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(18,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(19,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(20,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(21,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(22,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(23,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(24,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(25,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(26,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(27,axiom,
! [A: $i] :
( ~ ( member @ A @ comb )
| ( member @ ( pair @ A @ A ) @ ( rtrancl @ contract ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reduction_refl) ).
thf(28,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(29,axiom,
member @ combS @ comb,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',comb_intros2) ).
thf(30,axiom,
member @ combK @ comb,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',comb_intros1) ).
thf(31,axiom,
! [P: $i,Q: $i] :
( ~ ( member @ ( comb_app @ P @ Q ) @ comb )
| ( member @ Q @ comb ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_E2) ).
thf(32,axiom,
! [P: $i,Q: $i] :
( ~ ( member @ ( comb_app @ P @ Q ) @ comb )
| ( member @ P @ comb ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_E1) ).
thf(33,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(34,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(35,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(36,axiom,
! [P: $i,Q: $i] :
( combS
!= ( comb_app @ P @ Q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_app) ).
thf(37,axiom,
! [P: $i,Q: $i] :
( combK
!= ( comb_app @ P @ Q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_app) ).
thf(38,axiom,
combK != combS,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_s) ).
thf(39,axiom,
member @ ( pair @ ( comb_app @ p @ r ) @ ( comb_app @ y @ r ) ) @ ( rtrancl @ contract ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_reduce1_2h5) ).
thf(40,axiom,
member @ ( pair @ y @ z ) @ contract,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_reduce1_2h4) ).
thf(41,axiom,
member @ ( pair @ p @ y ) @ ( rtrancl @ contract ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_reduce1_2h3) ).
thf(42,axiom,
member @ p @ comb,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_reduce1_2h2) ).
thf(43,axiom,
member @ r @ comb,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_reduce1_2h1) ).
thf(44,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(45,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[44]) ).
thf(46,negated_conjecture,
~ ( member @ ( pair @ ( comb_app @ p @ r ) @ ( comb_app @ z @ r ) ) @ ( rtrancl @ contract ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_reduce1_2c1) ).
thf(47,plain,
$false = $false,
inference(unfold_def,[status(thm)],[45]) ).
thf(48,plain,
( ( ! [P3: $i,Q3: $i,R3: $i,C: $i] :
( ~ ( member @ ( pair @ P3 @ Q3 ) @ contract )
| ~ ( member @ R3 @ comb )
| ~ ( member @ ( pair @ ( comb_app @ R3 @ Q3 ) @ C ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ R3 @ P3 ) @ C ) @ ( rtrancl @ contract ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(49,plain,
( ( ! [P3: $i,Q3: $i,R3: $i,C: $i] :
( ~ ( member @ ( pair @ P3 @ Q3 ) @ contract )
| ~ ( member @ R3 @ comb )
| ~ ( member @ ( pair @ ( comb_app @ Q3 @ R3 ) @ C ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ P3 @ R3 ) @ C ) @ ( rtrancl @ contract ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(50,plain,
( ( ! [P3: $i,Q3: $i,R3: $i,C: $i] :
( ~ ( member @ P3 @ comb )
| ~ ( member @ Q3 @ comb )
| ~ ( member @ R3 @ comb )
| ~ ( member @ ( pair @ ( comb_app @ ( comb_app @ P3 @ R3 ) @ ( comb_app @ Q3 @ R3 ) ) @ C ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ P3 ) @ Q3 ) @ R3 ) @ C ) @ ( rtrancl @ contract ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(51,plain,
( ( ! [B: $i,Q3: $i,C: $i] :
( ~ ( member @ B @ comb )
| ~ ( member @ Q3 @ comb )
| ~ ( member @ ( pair @ B @ C ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ B ) @ Q3 ) @ C ) @ ( rtrancl @ contract ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(52,plain,
( ( ! [A: $i,B: $i] :
( ~ ( member @ ( pair @ A @ B ) @ contract )
| ( member @ B @ comb ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(53,plain,
( ( ! [R: $i] : ( trans @ ( rtrancl @ R ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(54,plain,
( ( ! [R: $i,A: $i,B: $i,C: $i] :
( ~ ( trans @ R )
| ~ ( member @ ( pair @ A @ B ) @ R )
| ~ ( member @ ( pair @ B @ C ) @ R )
| ( member @ ( pair @ A @ C ) @ R ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(55,plain,
( ( ! [R: $i] :
~ ( member @ ( pair @ combS @ R ) @ contract ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(56,plain,
( ( ! [R: $i] :
~ ( member @ ( pair @ combK @ R ) @ contract ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(57,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)],[10]) ).
thf(58,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c4 @ P @ Q @ R )
| ( member @ P @ comb ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(59,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)],[12]) ).
thf(60,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)],[13]) ).
thf(61,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c3 @ P @ Q @ R )
| ( member @ Q @ comb ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(62,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)],[15]) ).
thf(63,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)],[16]) ).
thf(64,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)],[17]) ).
thf(65,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c2 @ P @ Q @ R )
| ( member @ Q @ comb ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(66,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)],[19]) ).
thf(67,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)],[20]) ).
thf(68,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c1 @ P @ Q @ R )
| ( P
= ( comb_app @ combK @ R ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(69,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c1 @ P @ Q @ R )
| ( member @ Q @ comb ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(70,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c1 @ P @ Q @ R )
| ( member @ R @ comb ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(71,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)],[24]) ).
thf(72,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)],[25]) ).
thf(73,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)],[26]) ).
thf(74,plain,
( ( ! [A: $i] :
( ~ ( member @ A @ comb )
| ( member @ ( pair @ A @ A ) @ ( rtrancl @ contract ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(75,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( member @ P @ comb )
| ~ ( member @ Q @ comb )
| ( member @ ( comb_app @ P @ Q ) @ comb ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(76,plain,
( ( member @ combS @ comb )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(77,plain,
( ( member @ combK @ comb )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(78,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( member @ ( comb_app @ P @ Q ) @ comb )
| ( member @ Q @ comb ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(79,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( member @ ( comb_app @ P @ Q ) @ comb )
| ( member @ P @ comb ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(80,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)],[33]) ).
thf(81,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)],[34]) ).
thf(82,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)],[35]) ).
thf(83,plain,
( ( ! [P: $i,Q: $i] :
( combS
!= ( comb_app @ P @ Q ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(84,plain,
( ( ! [P: $i,Q: $i] :
( combK
!= ( comb_app @ P @ Q ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(85,plain,
( ( combK != combS )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(86,plain,
( ( member @ ( pair @ ( comb_app @ p @ r ) @ ( comb_app @ y @ r ) ) @ ( rtrancl @ contract ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(87,plain,
( ( member @ ( pair @ y @ z ) @ contract )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(88,plain,
( ( member @ ( pair @ p @ y ) @ ( rtrancl @ contract ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(89,plain,
( ( member @ p @ comb )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(90,plain,
( ( member @ r @ comb )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(91,plain,
( ( ~ ( member @ ( pair @ ( comb_app @ p @ r ) @ ( comb_app @ z @ r ) ) @ ( rtrancl @ contract ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(92,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[47]) ).
thf(93,plain,
( ( ~ ( member @ ( pair @ ( comb_app @ p @ r ) @ ( comb_app @ z @ r ) ) @ ( rtrancl @ contract ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(94,plain,
( ( member @ r @ comb )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(95,plain,
( ( member @ p @ comb )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(96,plain,
( ( member @ ( pair @ p @ y ) @ ( rtrancl @ contract ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(97,plain,
( ( member @ ( pair @ y @ z ) @ contract )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(98,plain,
( ( member @ ( pair @ ( comb_app @ p @ r ) @ ( comb_app @ y @ r ) ) @ ( rtrancl @ contract ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(99,plain,
( ( combK != combS )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(100,plain,
( ( ! [P: $i,Q: $i] :
( combK
!= ( comb_app @ P @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(101,plain,
( ( ! [P: $i,Q: $i] :
( combS
!= ( comb_app @ P @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(102,plain,
( ( ! [P1: $i,Q1: $i,P2: $i,Q2: $i] :
( ( ( comb_app @ P1 @ Q1 )
!= ( comb_app @ P2 @ Q2 ) )
| ( P1 = P2 ) ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(103,plain,
( ( ! [P1: $i,Q1: $i,P2: $i,Q2: $i] :
( ( ( comb_app @ P1 @ Q1 )
!= ( comb_app @ P2 @ Q2 ) )
| ( Q1 = Q2 ) ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(104,plain,
( ( ! [P1: $i,P2: $i,Q1: $i,Q2: $i] :
( ( P1 != P2 )
| ( Q1 != Q2 )
| ( ( comb_app @ P1 @ Q1 )
= ( comb_app @ P2 @ Q2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(105,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( member @ ( comb_app @ P @ Q ) @ comb )
| ( member @ P @ comb ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(106,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( member @ ( comb_app @ P @ Q ) @ comb )
| ( member @ Q @ comb ) ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(107,plain,
( ( member @ combK @ comb )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(108,plain,
( ( member @ combS @ comb )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(109,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( member @ P @ comb )
| ~ ( member @ Q @ comb )
| ( member @ ( comb_app @ P @ Q ) @ comb ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(110,plain,
( ( ! [A: $i] :
( ~ ( member @ A @ comb )
| ( member @ ( pair @ A @ A ) @ ( rtrancl @ contract ) ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(111,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( member @ P @ comb )
| ~ ( member @ Q @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ P ) @ Q ) @ P ) @ contract ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(112,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(copy,[status(thm)],[72]) ).
thf(113,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)],[71]) ).
thf(114,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c1 @ P @ Q @ R )
| ( member @ R @ comb ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(115,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c1 @ P @ Q @ R )
| ( member @ Q @ comb ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(116,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c1 @ P @ Q @ R )
| ( P
= ( comb_app @ combK @ R ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(117,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)],[67]) ).
thf(118,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)],[66]) ).
thf(119,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c2 @ P @ Q @ R )
| ( member @ Q @ comb ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(120,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)],[64]) ).
thf(121,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)],[63]) ).
thf(122,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)],[62]) ).
thf(123,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c3 @ P @ Q @ R )
| ( member @ Q @ comb ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(124,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)],[60]) ).
thf(125,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)],[59]) ).
thf(126,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c4 @ P @ Q @ R )
| ( member @ P @ comb ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(127,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)],[57]) ).
thf(128,plain,
( ( ! [R: $i] :
~ ( member @ ( pair @ combK @ R ) @ contract ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(129,plain,
( ( ! [R: $i] :
~ ( member @ ( pair @ combS @ R ) @ contract ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(130,plain,
( ( ! [R: $i,A: $i,B: $i,C: $i] :
( ~ ( trans @ R )
| ~ ( member @ ( pair @ A @ B ) @ R )
| ~ ( member @ ( pair @ B @ C ) @ R )
| ( member @ ( pair @ A @ C ) @ R ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(131,plain,
( ( ! [R: $i] : ( trans @ ( rtrancl @ R ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(132,plain,
( ( ! [A: $i,B: $i] :
( ~ ( member @ ( pair @ A @ B ) @ contract )
| ( member @ B @ comb ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(133,plain,
( ( ! [B: $i,Q3: $i,C: $i] :
( ~ ( member @ B @ comb )
| ~ ( member @ Q3 @ comb )
| ~ ( member @ ( pair @ B @ C ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ B ) @ Q3 ) @ C ) @ ( rtrancl @ contract ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(134,plain,
( ( ! [P3: $i,Q3: $i,R3: $i,C: $i] :
( ~ ( member @ P3 @ comb )
| ~ ( member @ Q3 @ comb )
| ~ ( member @ R3 @ comb )
| ~ ( member @ ( pair @ ( comb_app @ ( comb_app @ P3 @ R3 ) @ ( comb_app @ Q3 @ R3 ) ) @ C ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ P3 ) @ Q3 ) @ R3 ) @ C ) @ ( rtrancl @ contract ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(135,plain,
( ( ! [P3: $i,Q3: $i,R3: $i,C: $i] :
( ~ ( member @ ( pair @ P3 @ Q3 ) @ contract )
| ~ ( member @ R3 @ comb )
| ~ ( member @ ( pair @ ( comb_app @ Q3 @ R3 ) @ C ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ P3 @ R3 ) @ C ) @ ( rtrancl @ contract ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(136,plain,
( ( ! [P3: $i,Q3: $i,R3: $i,C: $i] :
( ~ ( member @ ( pair @ P3 @ Q3 ) @ contract )
| ~ ( member @ R3 @ comb )
| ~ ( member @ ( pair @ ( comb_app @ R3 @ Q3 ) @ C ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ R3 @ P3 ) @ C ) @ ( rtrancl @ contract ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(137,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[92]) ).
thf(138,plain,
( ( combK != combS )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(139,plain,
( ( ! [SX0: $i,SX1: $i] :
( combS
!= ( comb_app @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(140,plain,
( ( ! [SX0: $i,SX1: $i] :
( combK
!= ( comb_app @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(141,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( comb_app @ SX0 @ SX1 )
!= ( comb_app @ SX2 @ SX3 ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(142,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( comb_app @ SX0 @ SX1 )
!= ( comb_app @ SX2 @ SX3 ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(143,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( SX0 != SX1 )
| ( SX2 != SX3 )
| ( ( comb_app @ SX0 @ SX2 )
= ( comb_app @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(144,plain,
( ( member @ ( pair @ ( comb_app @ p @ r ) @ ( comb_app @ z @ r ) ) @ ( rtrancl @ contract ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(145,plain,
! [SV1: $i] :
( ( ! [SY97: $i] :
( ~ ( member @ ( comb_app @ SV1 @ SY97 ) @ comb )
| ( member @ SV1 @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(146,plain,
! [SV2: $i] :
( ( ! [SY98: $i] :
( ~ ( member @ ( comb_app @ SV2 @ SY98 ) @ comb )
| ( member @ SY98 @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(147,plain,
! [SV3: $i] :
( ( ! [SY99: $i] :
( ~ ( member @ SV3 @ comb )
| ~ ( member @ SY99 @ comb )
| ( member @ ( comb_app @ SV3 @ SY99 ) @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(148,plain,
! [SV4: $i] :
( ( ~ ( member @ SV4 @ comb )
| ( member @ ( pair @ SV4 @ SV4 ) @ ( rtrancl @ contract ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(149,plain,
! [SV5: $i] :
( ( ! [SY100: $i] :
( ~ ( member @ SV5 @ comb )
| ~ ( member @ SY100 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV5 ) @ SY100 ) @ SV5 ) @ contract ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(150,plain,
! [SV6: $i] :
( ( ! [SY101: $i,SY102: $i] :
( ~ ( member @ SV6 @ comb )
| ~ ( member @ SY101 @ comb )
| ~ ( member @ SY102 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV6 ) @ SY101 ) @ SY102 ) @ ( comb_app @ ( comb_app @ SV6 @ SY102 ) @ ( comb_app @ SY101 @ SY102 ) ) ) @ contract ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(151,plain,
! [SV7: $i] :
( ( ! [SY103: $i,SY104: $i] :
( ~ ( member @ ( pair @ ( comb_app @ SV7 @ SY103 ) @ SY104 ) @ contract )
| ( ap_contractE_c1 @ SV7 @ SY103 @ SY104 )
| ( ap_contractE_c2 @ SV7 @ SY103 @ SY104 )
| ( ap_contractE_c3 @ SV7 @ SY103 @ SY104 )
| ( ap_contractE_c4 @ SV7 @ SY103 @ SY104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(152,plain,
! [SV8: $i] :
( ( ! [SY105: $i,SY106: $i] :
( ~ ( ap_contractE_c1 @ SV8 @ SY105 @ SY106 )
| ( member @ SY106 @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(153,plain,
! [SV9: $i] :
( ( ! [SY107: $i,SY108: $i] :
( ~ ( ap_contractE_c1 @ SV9 @ SY107 @ SY108 )
| ( member @ SY107 @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(154,plain,
! [SV10: $i] :
( ( ! [SY109: $i,SY110: $i] :
( ~ ( ap_contractE_c1 @ SV10 @ SY109 @ SY110 )
| ( SV10
= ( comb_app @ combK @ SY110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(155,plain,
! [SV11: $i] :
( ( ! [SY111: $i,SY112: $i] :
( ~ ( ap_contractE_c2 @ SV11 @ SY111 @ SY112 )
| ( member @ ( ap_contractE_sk1p @ SV11 @ SY111 @ SY112 ) @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(156,plain,
! [SV12: $i] :
( ( ! [SY113: $i,SY114: $i] :
( ~ ( ap_contractE_c2 @ SV12 @ SY113 @ SY114 )
| ( member @ ( ap_contractE_sk1q @ SV12 @ SY113 @ SY114 ) @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(157,plain,
! [SV13: $i] :
( ( ! [SY115: $i,SY116: $i] :
( ~ ( ap_contractE_c2 @ SV13 @ SY115 @ SY116 )
| ( member @ SY115 @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(158,plain,
! [SV14: $i] :
( ( ! [SY117: $i,SY118: $i] :
( ~ ( ap_contractE_c2 @ SV14 @ SY117 @ SY118 )
| ( SY118
= ( comb_app @ ( comb_app @ ( ap_contractE_sk1p @ SV14 @ SY117 @ SY118 ) @ SY117 ) @ ( comb_app @ ( ap_contractE_sk1q @ SV14 @ SY117 @ SY118 ) @ SY117 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(159,plain,
! [SV15: $i] :
( ( ! [SY119: $i,SY120: $i] :
( ~ ( ap_contractE_c2 @ SV15 @ SY119 @ SY120 )
| ( SV15
= ( comb_app @ ( comb_app @ combS @ ( ap_contractE_sk1p @ SV15 @ SY119 @ SY120 ) ) @ ( ap_contractE_sk1q @ SV15 @ SY119 @ SY120 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(160,plain,
! [SV16: $i] :
( ( ! [SY121: $i,SY122: $i] :
( ~ ( ap_contractE_c3 @ SV16 @ SY121 @ SY122 )
| ( member @ ( pair @ SV16 @ ( ap_contractE_sk2q @ SV16 @ SY121 @ SY122 ) ) @ contract ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(161,plain,
! [SV17: $i] :
( ( ! [SY123: $i,SY124: $i] :
( ~ ( ap_contractE_c3 @ SV17 @ SY123 @ SY124 )
| ( member @ SY123 @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(162,plain,
! [SV18: $i] :
( ( ! [SY125: $i,SY126: $i] :
( ~ ( ap_contractE_c3 @ SV18 @ SY125 @ SY126 )
| ( SY126
= ( comb_app @ ( ap_contractE_sk2q @ SV18 @ SY125 @ SY126 ) @ SY125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(163,plain,
! [SV19: $i] :
( ( ! [SY127: $i,SY128: $i] :
( ~ ( ap_contractE_c4 @ SV19 @ SY127 @ SY128 )
| ( member @ ( pair @ SY127 @ ( ap_contractE_sk3q @ SV19 @ SY127 @ SY128 ) ) @ contract ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(164,plain,
! [SV20: $i] :
( ( ! [SY129: $i,SY130: $i] :
( ~ ( ap_contractE_c4 @ SV20 @ SY129 @ SY130 )
| ( member @ SV20 @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(165,plain,
! [SV21: $i] :
( ( ! [SY131: $i,SY132: $i] :
( ~ ( ap_contractE_c4 @ SV21 @ SY131 @ SY132 )
| ( SY132
= ( comb_app @ SV21 @ ( ap_contractE_sk3q @ SV21 @ SY131 @ SY132 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(166,plain,
! [SV22: $i] :
( ( ~ ( member @ ( pair @ combK @ SV22 ) @ contract ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(167,plain,
! [SV23: $i] :
( ( ~ ( member @ ( pair @ combS @ SV23 ) @ contract ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(168,plain,
! [SV24: $i] :
( ( ! [SY133: $i,SY134: $i,SY135: $i] :
( ~ ( trans @ SV24 )
| ~ ( member @ ( pair @ SY133 @ SY134 ) @ SV24 )
| ~ ( member @ ( pair @ SY134 @ SY135 ) @ SV24 )
| ( member @ ( pair @ SY133 @ SY135 ) @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(169,plain,
! [SV25: $i] :
( ( trans @ ( rtrancl @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(170,plain,
! [SV26: $i] :
( ( ! [SY136: $i] :
( ~ ( member @ ( pair @ SV26 @ SY136 ) @ contract )
| ( member @ SY136 @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(171,plain,
! [SV27: $i] :
( ( ! [SY137: $i,SY138: $i] :
( ~ ( member @ SV27 @ comb )
| ~ ( member @ SY137 @ comb )
| ~ ( member @ ( pair @ SV27 @ SY138 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV27 ) @ SY137 ) @ SY138 ) @ ( rtrancl @ contract ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(172,plain,
! [SV28: $i] :
( ( ! [SY139: $i,SY140: $i,SY141: $i] :
( ~ ( member @ SV28 @ comb )
| ~ ( member @ SY139 @ comb )
| ~ ( member @ SY140 @ comb )
| ~ ( member @ ( pair @ ( comb_app @ ( comb_app @ SV28 @ SY140 ) @ ( comb_app @ SY139 @ SY140 ) ) @ SY141 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV28 ) @ SY139 ) @ SY140 ) @ SY141 ) @ ( rtrancl @ contract ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(173,plain,
! [SV29: $i] :
( ( ! [SY142: $i,SY143: $i,SY144: $i] :
( ~ ( member @ ( pair @ SV29 @ SY142 ) @ contract )
| ~ ( member @ SY143 @ comb )
| ~ ( member @ ( pair @ ( comb_app @ SY142 @ SY143 ) @ SY144 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ SV29 @ SY143 ) @ SY144 ) @ ( rtrancl @ contract ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(174,plain,
! [SV30: $i] :
( ( ! [SY145: $i,SY146: $i,SY147: $i] :
( ~ ( member @ ( pair @ SV30 @ SY145 ) @ contract )
| ~ ( member @ SY146 @ comb )
| ~ ( member @ ( pair @ ( comb_app @ SY146 @ SY145 ) @ SY147 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ SY146 @ SV30 ) @ SY147 ) @ ( rtrancl @ contract ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(175,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(176,plain,
( ( combK = combS )
= $false ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(177,plain,
! [SV31: $i] :
( ( ! [SY148: $i] :
( combS
!= ( comb_app @ SV31 @ SY148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(178,plain,
! [SV32: $i] :
( ( ! [SY149: $i] :
( combK
!= ( comb_app @ SV32 @ SY149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(179,plain,
! [SV33: $i] :
( ( ! [SY150: $i,SY151: $i,SY152: $i] :
( ( ( comb_app @ SV33 @ SY150 )
!= ( comb_app @ SY151 @ SY152 ) )
| ( SV33 = SY151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(180,plain,
! [SV34: $i] :
( ( ! [SY153: $i,SY154: $i,SY155: $i] :
( ( ( comb_app @ SV34 @ SY153 )
!= ( comb_app @ SY154 @ SY155 ) )
| ( SY153 = SY155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(181,plain,
! [SV35: $i] :
( ( ! [SY156: $i,SY157: $i,SY158: $i] :
( ( SV35 != SY156 )
| ( SY157 != SY158 )
| ( ( comb_app @ SV35 @ SY157 )
= ( comb_app @ SY156 @ SY158 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(182,plain,
! [SV36: $i,SV1: $i] :
( ( ~ ( member @ ( comb_app @ SV1 @ SV36 ) @ comb )
| ( member @ SV1 @ comb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(183,plain,
! [SV37: $i,SV2: $i] :
( ( ~ ( member @ ( comb_app @ SV2 @ SV37 ) @ comb )
| ( member @ SV37 @ comb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(184,plain,
! [SV38: $i,SV3: $i] :
( ( ~ ( member @ SV3 @ comb )
| ~ ( member @ SV38 @ comb )
| ( member @ ( comb_app @ SV3 @ SV38 ) @ comb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(185,plain,
! [SV4: $i] :
( ( ( ~ ( member @ SV4 @ comb ) )
= $true )
| ( ( member @ ( pair @ SV4 @ SV4 ) @ ( rtrancl @ contract ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(186,plain,
! [SV39: $i,SV5: $i] :
( ( ~ ( member @ SV5 @ comb )
| ~ ( member @ SV39 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV5 ) @ SV39 ) @ SV5 ) @ contract ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(187,plain,
! [SV40: $i,SV6: $i] :
( ( ! [SY159: $i] :
( ~ ( member @ SV6 @ comb )
| ~ ( member @ SV40 @ comb )
| ~ ( member @ SY159 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV6 ) @ SV40 ) @ SY159 ) @ ( comb_app @ ( comb_app @ SV6 @ SY159 ) @ ( comb_app @ SV40 @ SY159 ) ) ) @ contract ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(188,plain,
! [SV41: $i,SV7: $i] :
( ( ! [SY160: $i] :
( ~ ( member @ ( pair @ ( comb_app @ SV7 @ SV41 ) @ SY160 ) @ contract )
| ( ap_contractE_c1 @ SV7 @ SV41 @ SY160 )
| ( ap_contractE_c2 @ SV7 @ SV41 @ SY160 )
| ( ap_contractE_c3 @ SV7 @ SV41 @ SY160 )
| ( ap_contractE_c4 @ SV7 @ SV41 @ SY160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(189,plain,
! [SV42: $i,SV8: $i] :
( ( ! [SY161: $i] :
( ~ ( ap_contractE_c1 @ SV8 @ SV42 @ SY161 )
| ( member @ SY161 @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(190,plain,
! [SV43: $i,SV9: $i] :
( ( ! [SY162: $i] :
( ~ ( ap_contractE_c1 @ SV9 @ SV43 @ SY162 )
| ( member @ SV43 @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(191,plain,
! [SV44: $i,SV10: $i] :
( ( ! [SY163: $i] :
( ~ ( ap_contractE_c1 @ SV10 @ SV44 @ SY163 )
| ( SV10
= ( comb_app @ combK @ SY163 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(192,plain,
! [SV45: $i,SV11: $i] :
( ( ! [SY164: $i] :
( ~ ( ap_contractE_c2 @ SV11 @ SV45 @ SY164 )
| ( member @ ( ap_contractE_sk1p @ SV11 @ SV45 @ SY164 ) @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(193,plain,
! [SV46: $i,SV12: $i] :
( ( ! [SY165: $i] :
( ~ ( ap_contractE_c2 @ SV12 @ SV46 @ SY165 )
| ( member @ ( ap_contractE_sk1q @ SV12 @ SV46 @ SY165 ) @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(194,plain,
! [SV47: $i,SV13: $i] :
( ( ! [SY166: $i] :
( ~ ( ap_contractE_c2 @ SV13 @ SV47 @ SY166 )
| ( member @ SV47 @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(195,plain,
! [SV48: $i,SV14: $i] :
( ( ! [SY167: $i] :
( ~ ( ap_contractE_c2 @ SV14 @ SV48 @ SY167 )
| ( SY167
= ( comb_app @ ( comb_app @ ( ap_contractE_sk1p @ SV14 @ SV48 @ SY167 ) @ SV48 ) @ ( comb_app @ ( ap_contractE_sk1q @ SV14 @ SV48 @ SY167 ) @ SV48 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(196,plain,
! [SV49: $i,SV15: $i] :
( ( ! [SY168: $i] :
( ~ ( ap_contractE_c2 @ SV15 @ SV49 @ SY168 )
| ( SV15
= ( comb_app @ ( comb_app @ combS @ ( ap_contractE_sk1p @ SV15 @ SV49 @ SY168 ) ) @ ( ap_contractE_sk1q @ SV15 @ SV49 @ SY168 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(197,plain,
! [SV50: $i,SV16: $i] :
( ( ! [SY169: $i] :
( ~ ( ap_contractE_c3 @ SV16 @ SV50 @ SY169 )
| ( member @ ( pair @ SV16 @ ( ap_contractE_sk2q @ SV16 @ SV50 @ SY169 ) ) @ contract ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(198,plain,
! [SV51: $i,SV17: $i] :
( ( ! [SY170: $i] :
( ~ ( ap_contractE_c3 @ SV17 @ SV51 @ SY170 )
| ( member @ SV51 @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(199,plain,
! [SV52: $i,SV18: $i] :
( ( ! [SY171: $i] :
( ~ ( ap_contractE_c3 @ SV18 @ SV52 @ SY171 )
| ( SY171
= ( comb_app @ ( ap_contractE_sk2q @ SV18 @ SV52 @ SY171 ) @ SV52 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(200,plain,
! [SV53: $i,SV19: $i] :
( ( ! [SY172: $i] :
( ~ ( ap_contractE_c4 @ SV19 @ SV53 @ SY172 )
| ( member @ ( pair @ SV53 @ ( ap_contractE_sk3q @ SV19 @ SV53 @ SY172 ) ) @ contract ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(201,plain,
! [SV54: $i,SV20: $i] :
( ( ! [SY173: $i] :
( ~ ( ap_contractE_c4 @ SV20 @ SV54 @ SY173 )
| ( member @ SV20 @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(202,plain,
! [SV55: $i,SV21: $i] :
( ( ! [SY174: $i] :
( ~ ( ap_contractE_c4 @ SV21 @ SV55 @ SY174 )
| ( SY174
= ( comb_app @ SV21 @ ( ap_contractE_sk3q @ SV21 @ SV55 @ SY174 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(203,plain,
! [SV22: $i] :
( ( member @ ( pair @ combK @ SV22 ) @ contract )
= $false ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(204,plain,
! [SV23: $i] :
( ( member @ ( pair @ combS @ SV23 ) @ contract )
= $false ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(205,plain,
! [SV56: $i,SV24: $i] :
( ( ! [SY175: $i,SY176: $i] :
( ~ ( trans @ SV24 )
| ~ ( member @ ( pair @ SV56 @ SY175 ) @ SV24 )
| ~ ( member @ ( pair @ SY175 @ SY176 ) @ SV24 )
| ( member @ ( pair @ SV56 @ SY176 ) @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(206,plain,
! [SV57: $i,SV26: $i] :
( ( ~ ( member @ ( pair @ SV26 @ SV57 ) @ contract )
| ( member @ SV57 @ comb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(207,plain,
! [SV58: $i,SV27: $i] :
( ( ! [SY177: $i] :
( ~ ( member @ SV27 @ comb )
| ~ ( member @ SV58 @ comb )
| ~ ( member @ ( pair @ SV27 @ SY177 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV27 ) @ SV58 ) @ SY177 ) @ ( rtrancl @ contract ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(208,plain,
! [SV59: $i,SV28: $i] :
( ( ! [SY178: $i,SY179: $i] :
( ~ ( member @ SV28 @ comb )
| ~ ( member @ SV59 @ comb )
| ~ ( member @ SY178 @ comb )
| ~ ( member @ ( pair @ ( comb_app @ ( comb_app @ SV28 @ SY178 ) @ ( comb_app @ SV59 @ SY178 ) ) @ SY179 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV28 ) @ SV59 ) @ SY178 ) @ SY179 ) @ ( rtrancl @ contract ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(209,plain,
! [SV60: $i,SV29: $i] :
( ( ! [SY180: $i,SY181: $i] :
( ~ ( member @ ( pair @ SV29 @ SV60 ) @ contract )
| ~ ( member @ SY180 @ comb )
| ~ ( member @ ( pair @ ( comb_app @ SV60 @ SY180 ) @ SY181 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ SV29 @ SY180 ) @ SY181 ) @ ( rtrancl @ contract ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(210,plain,
! [SV61: $i,SV30: $i] :
( ( ! [SY182: $i,SY183: $i] :
( ~ ( member @ ( pair @ SV30 @ SV61 ) @ contract )
| ~ ( member @ SY182 @ comb )
| ~ ( member @ ( pair @ ( comb_app @ SY182 @ SV61 ) @ SY183 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ SY182 @ SV30 ) @ SY183 ) @ ( rtrancl @ contract ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(211,plain,
! [SV62: $i,SV31: $i] :
( ( combS
!= ( comb_app @ SV31 @ SV62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(212,plain,
! [SV63: $i,SV32: $i] :
( ( combK
!= ( comb_app @ SV32 @ SV63 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(213,plain,
! [SV64: $i,SV33: $i] :
( ( ! [SY184: $i,SY185: $i] :
( ( ( comb_app @ SV33 @ SV64 )
!= ( comb_app @ SY184 @ SY185 ) )
| ( SV33 = SY184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(214,plain,
! [SV65: $i,SV34: $i] :
( ( ! [SY186: $i,SY187: $i] :
( ( ( comb_app @ SV34 @ SV65 )
!= ( comb_app @ SY186 @ SY187 ) )
| ( SV65 = SY187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(215,plain,
! [SV66: $i,SV35: $i] :
( ( ! [SY188: $i,SY189: $i] :
( ( SV35 != SV66 )
| ( SY188 != SY189 )
| ( ( comb_app @ SV35 @ SY188 )
= ( comb_app @ SV66 @ SY189 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(216,plain,
! [SV36: $i,SV1: $i] :
( ( ( ~ ( member @ ( comb_app @ SV1 @ SV36 ) @ comb ) )
= $true )
| ( ( member @ SV1 @ comb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(217,plain,
! [SV37: $i,SV2: $i] :
( ( ( ~ ( member @ ( comb_app @ SV2 @ SV37 ) @ comb ) )
= $true )
| ( ( member @ SV37 @ comb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(218,plain,
! [SV38: $i,SV3: $i] :
( ( ( ~ ( member @ SV3 @ comb ) )
= $true )
| ( ( ~ ( member @ SV38 @ comb )
| ( member @ ( comb_app @ SV3 @ SV38 ) @ comb ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(219,plain,
! [SV4: $i] :
( ( ( member @ SV4 @ comb )
= $false )
| ( ( member @ ( pair @ SV4 @ SV4 ) @ ( rtrancl @ contract ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(220,plain,
! [SV39: $i,SV5: $i] :
( ( ( ~ ( member @ SV5 @ comb ) )
= $true )
| ( ( ~ ( member @ SV39 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV5 ) @ SV39 ) @ SV5 ) @ contract ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(221,plain,
! [SV67: $i,SV40: $i,SV6: $i] :
( ( ~ ( member @ SV6 @ comb )
| ~ ( member @ SV40 @ comb )
| ~ ( member @ SV67 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV6 ) @ SV40 ) @ SV67 ) @ ( comb_app @ ( comb_app @ SV6 @ SV67 ) @ ( comb_app @ SV40 @ SV67 ) ) ) @ contract ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(222,plain,
! [SV68: $i,SV41: $i,SV7: $i] :
( ( ~ ( member @ ( pair @ ( comb_app @ SV7 @ SV41 ) @ SV68 ) @ contract )
| ( ap_contractE_c1 @ SV7 @ SV41 @ SV68 )
| ( ap_contractE_c2 @ SV7 @ SV41 @ SV68 )
| ( ap_contractE_c3 @ SV7 @ SV41 @ SV68 )
| ( ap_contractE_c4 @ SV7 @ SV41 @ SV68 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(223,plain,
! [SV69: $i,SV42: $i,SV8: $i] :
( ( ~ ( ap_contractE_c1 @ SV8 @ SV42 @ SV69 )
| ( member @ SV69 @ comb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(224,plain,
! [SV70: $i,SV43: $i,SV9: $i] :
( ( ~ ( ap_contractE_c1 @ SV9 @ SV43 @ SV70 )
| ( member @ SV43 @ comb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(225,plain,
! [SV71: $i,SV44: $i,SV10: $i] :
( ( ~ ( ap_contractE_c1 @ SV10 @ SV44 @ SV71 )
| ( SV10
= ( comb_app @ combK @ SV71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(226,plain,
! [SV72: $i,SV45: $i,SV11: $i] :
( ( ~ ( ap_contractE_c2 @ SV11 @ SV45 @ SV72 )
| ( member @ ( ap_contractE_sk1p @ SV11 @ SV45 @ SV72 ) @ comb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(227,plain,
! [SV73: $i,SV46: $i,SV12: $i] :
( ( ~ ( ap_contractE_c2 @ SV12 @ SV46 @ SV73 )
| ( member @ ( ap_contractE_sk1q @ SV12 @ SV46 @ SV73 ) @ comb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(228,plain,
! [SV74: $i,SV47: $i,SV13: $i] :
( ( ~ ( ap_contractE_c2 @ SV13 @ SV47 @ SV74 )
| ( member @ SV47 @ comb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(229,plain,
! [SV75: $i,SV48: $i,SV14: $i] :
( ( ~ ( ap_contractE_c2 @ SV14 @ SV48 @ SV75 )
| ( SV75
= ( comb_app @ ( comb_app @ ( ap_contractE_sk1p @ SV14 @ SV48 @ SV75 ) @ SV48 ) @ ( comb_app @ ( ap_contractE_sk1q @ SV14 @ SV48 @ SV75 ) @ SV48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(230,plain,
! [SV76: $i,SV49: $i,SV15: $i] :
( ( ~ ( ap_contractE_c2 @ SV15 @ SV49 @ SV76 )
| ( SV15
= ( comb_app @ ( comb_app @ combS @ ( ap_contractE_sk1p @ SV15 @ SV49 @ SV76 ) ) @ ( ap_contractE_sk1q @ SV15 @ SV49 @ SV76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(231,plain,
! [SV77: $i,SV50: $i,SV16: $i] :
( ( ~ ( ap_contractE_c3 @ SV16 @ SV50 @ SV77 )
| ( member @ ( pair @ SV16 @ ( ap_contractE_sk2q @ SV16 @ SV50 @ SV77 ) ) @ contract ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(232,plain,
! [SV78: $i,SV51: $i,SV17: $i] :
( ( ~ ( ap_contractE_c3 @ SV17 @ SV51 @ SV78 )
| ( member @ SV51 @ comb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(233,plain,
! [SV79: $i,SV52: $i,SV18: $i] :
( ( ~ ( ap_contractE_c3 @ SV18 @ SV52 @ SV79 )
| ( SV79
= ( comb_app @ ( ap_contractE_sk2q @ SV18 @ SV52 @ SV79 ) @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(234,plain,
! [SV80: $i,SV53: $i,SV19: $i] :
( ( ~ ( ap_contractE_c4 @ SV19 @ SV53 @ SV80 )
| ( member @ ( pair @ SV53 @ ( ap_contractE_sk3q @ SV19 @ SV53 @ SV80 ) ) @ contract ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(235,plain,
! [SV81: $i,SV54: $i,SV20: $i] :
( ( ~ ( ap_contractE_c4 @ SV20 @ SV54 @ SV81 )
| ( member @ SV20 @ comb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(236,plain,
! [SV82: $i,SV55: $i,SV21: $i] :
( ( ~ ( ap_contractE_c4 @ SV21 @ SV55 @ SV82 )
| ( SV82
= ( comb_app @ SV21 @ ( ap_contractE_sk3q @ SV21 @ SV55 @ SV82 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(237,plain,
! [SV83: $i,SV56: $i,SV24: $i] :
( ( ! [SY190: $i] :
( ~ ( trans @ SV24 )
| ~ ( member @ ( pair @ SV56 @ SV83 ) @ SV24 )
| ~ ( member @ ( pair @ SV83 @ SY190 ) @ SV24 )
| ( member @ ( pair @ SV56 @ SY190 ) @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(238,plain,
! [SV57: $i,SV26: $i] :
( ( ( ~ ( member @ ( pair @ SV26 @ SV57 ) @ contract ) )
= $true )
| ( ( member @ SV57 @ comb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[206]) ).
thf(239,plain,
! [SV84: $i,SV58: $i,SV27: $i] :
( ( ~ ( member @ SV27 @ comb )
| ~ ( member @ SV58 @ comb )
| ~ ( member @ ( pair @ SV27 @ SV84 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV27 ) @ SV58 ) @ SV84 ) @ ( rtrancl @ contract ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(240,plain,
! [SV85: $i,SV59: $i,SV28: $i] :
( ( ! [SY191: $i] :
( ~ ( member @ SV28 @ comb )
| ~ ( member @ SV59 @ comb )
| ~ ( member @ SV85 @ comb )
| ~ ( member @ ( pair @ ( comb_app @ ( comb_app @ SV28 @ SV85 ) @ ( comb_app @ SV59 @ SV85 ) ) @ SY191 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV28 ) @ SV59 ) @ SV85 ) @ SY191 ) @ ( rtrancl @ contract ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(241,plain,
! [SV86: $i,SV60: $i,SV29: $i] :
( ( ! [SY192: $i] :
( ~ ( member @ ( pair @ SV29 @ SV60 ) @ contract )
| ~ ( member @ SV86 @ comb )
| ~ ( member @ ( pair @ ( comb_app @ SV60 @ SV86 ) @ SY192 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ SV29 @ SV86 ) @ SY192 ) @ ( rtrancl @ contract ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(242,plain,
! [SV87: $i,SV61: $i,SV30: $i] :
( ( ! [SY193: $i] :
( ~ ( member @ ( pair @ SV30 @ SV61 ) @ contract )
| ~ ( member @ SV87 @ comb )
| ~ ( member @ ( pair @ ( comb_app @ SV87 @ SV61 ) @ SY193 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ SV87 @ SV30 ) @ SY193 ) @ ( rtrancl @ contract ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(243,plain,
! [SV62: $i,SV31: $i] :
( ( combS
= ( comb_app @ SV31 @ SV62 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(244,plain,
! [SV63: $i,SV32: $i] :
( ( combK
= ( comb_app @ SV32 @ SV63 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(245,plain,
! [SV88: $i,SV64: $i,SV33: $i] :
( ( ! [SY194: $i] :
( ( ( comb_app @ SV33 @ SV64 )
!= ( comb_app @ SV88 @ SY194 ) )
| ( SV33 = SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(246,plain,
! [SV89: $i,SV65: $i,SV34: $i] :
( ( ! [SY195: $i] :
( ( ( comb_app @ SV34 @ SV65 )
!= ( comb_app @ SV89 @ SY195 ) )
| ( SV65 = SY195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(247,plain,
! [SV90: $i,SV66: $i,SV35: $i] :
( ( ! [SY196: $i] :
( ( SV35 != SV66 )
| ( SV90 != SY196 )
| ( ( comb_app @ SV35 @ SV90 )
= ( comb_app @ SV66 @ SY196 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(248,plain,
! [SV36: $i,SV1: $i] :
( ( ( member @ ( comb_app @ SV1 @ SV36 ) @ comb )
= $false )
| ( ( member @ SV1 @ comb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(249,plain,
! [SV37: $i,SV2: $i] :
( ( ( member @ ( comb_app @ SV2 @ SV37 ) @ comb )
= $false )
| ( ( member @ SV37 @ comb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(250,plain,
! [SV38: $i,SV3: $i] :
( ( ( member @ SV3 @ comb )
= $false )
| ( ( ~ ( member @ SV38 @ comb )
| ( member @ ( comb_app @ SV3 @ SV38 ) @ comb ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(251,plain,
! [SV39: $i,SV5: $i] :
( ( ( member @ SV5 @ comb )
= $false )
| ( ( ~ ( member @ SV39 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV5 ) @ SV39 ) @ SV5 ) @ contract ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(252,plain,
! [SV67: $i,SV40: $i,SV6: $i] :
( ( ( ~ ( member @ SV6 @ comb ) )
= $true )
| ( ( ~ ( member @ SV40 @ comb )
| ~ ( member @ SV67 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV6 ) @ SV40 ) @ SV67 ) @ ( comb_app @ ( comb_app @ SV6 @ SV67 ) @ ( comb_app @ SV40 @ SV67 ) ) ) @ contract ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(253,plain,
! [SV68: $i,SV41: $i,SV7: $i] :
( ( ( ~ ( member @ ( pair @ ( comb_app @ SV7 @ SV41 ) @ SV68 ) @ contract ) )
= $true )
| ( ( ( ap_contractE_c1 @ SV7 @ SV41 @ SV68 )
| ( ap_contractE_c2 @ SV7 @ SV41 @ SV68 )
| ( ap_contractE_c3 @ SV7 @ SV41 @ SV68 )
| ( ap_contractE_c4 @ SV7 @ SV41 @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[222]) ).
thf(254,plain,
! [SV69: $i,SV42: $i,SV8: $i] :
( ( ( ~ ( ap_contractE_c1 @ SV8 @ SV42 @ SV69 ) )
= $true )
| ( ( member @ SV69 @ comb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(255,plain,
! [SV70: $i,SV43: $i,SV9: $i] :
( ( ( ~ ( ap_contractE_c1 @ SV9 @ SV43 @ SV70 ) )
= $true )
| ( ( member @ SV43 @ comb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[224]) ).
thf(256,plain,
! [SV71: $i,SV44: $i,SV10: $i] :
( ( ( ~ ( ap_contractE_c1 @ SV10 @ SV44 @ SV71 ) )
= $true )
| ( ( SV10
= ( comb_app @ combK @ SV71 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(257,plain,
! [SV72: $i,SV45: $i,SV11: $i] :
( ( ( ~ ( ap_contractE_c2 @ SV11 @ SV45 @ SV72 ) )
= $true )
| ( ( member @ ( ap_contractE_sk1p @ SV11 @ SV45 @ SV72 ) @ comb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[226]) ).
thf(258,plain,
! [SV73: $i,SV46: $i,SV12: $i] :
( ( ( ~ ( ap_contractE_c2 @ SV12 @ SV46 @ SV73 ) )
= $true )
| ( ( member @ ( ap_contractE_sk1q @ SV12 @ SV46 @ SV73 ) @ comb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(259,plain,
! [SV74: $i,SV47: $i,SV13: $i] :
( ( ( ~ ( ap_contractE_c2 @ SV13 @ SV47 @ SV74 ) )
= $true )
| ( ( member @ SV47 @ comb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[228]) ).
thf(260,plain,
! [SV75: $i,SV48: $i,SV14: $i] :
( ( ( ~ ( ap_contractE_c2 @ SV14 @ SV48 @ SV75 ) )
= $true )
| ( ( SV75
= ( comb_app @ ( comb_app @ ( ap_contractE_sk1p @ SV14 @ SV48 @ SV75 ) @ SV48 ) @ ( comb_app @ ( ap_contractE_sk1q @ SV14 @ SV48 @ SV75 ) @ SV48 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[229]) ).
thf(261,plain,
! [SV76: $i,SV49: $i,SV15: $i] :
( ( ( ~ ( ap_contractE_c2 @ SV15 @ SV49 @ SV76 ) )
= $true )
| ( ( SV15
= ( comb_app @ ( comb_app @ combS @ ( ap_contractE_sk1p @ SV15 @ SV49 @ SV76 ) ) @ ( ap_contractE_sk1q @ SV15 @ SV49 @ SV76 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[230]) ).
thf(262,plain,
! [SV77: $i,SV50: $i,SV16: $i] :
( ( ( ~ ( ap_contractE_c3 @ SV16 @ SV50 @ SV77 ) )
= $true )
| ( ( member @ ( pair @ SV16 @ ( ap_contractE_sk2q @ SV16 @ SV50 @ SV77 ) ) @ contract )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[231]) ).
thf(263,plain,
! [SV78: $i,SV51: $i,SV17: $i] :
( ( ( ~ ( ap_contractE_c3 @ SV17 @ SV51 @ SV78 ) )
= $true )
| ( ( member @ SV51 @ comb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[232]) ).
thf(264,plain,
! [SV79: $i,SV52: $i,SV18: $i] :
( ( ( ~ ( ap_contractE_c3 @ SV18 @ SV52 @ SV79 ) )
= $true )
| ( ( SV79
= ( comb_app @ ( ap_contractE_sk2q @ SV18 @ SV52 @ SV79 ) @ SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[233]) ).
thf(265,plain,
! [SV80: $i,SV53: $i,SV19: $i] :
( ( ( ~ ( ap_contractE_c4 @ SV19 @ SV53 @ SV80 ) )
= $true )
| ( ( member @ ( pair @ SV53 @ ( ap_contractE_sk3q @ SV19 @ SV53 @ SV80 ) ) @ contract )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[234]) ).
thf(266,plain,
! [SV81: $i,SV54: $i,SV20: $i] :
( ( ( ~ ( ap_contractE_c4 @ SV20 @ SV54 @ SV81 ) )
= $true )
| ( ( member @ SV20 @ comb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[235]) ).
thf(267,plain,
! [SV82: $i,SV55: $i,SV21: $i] :
( ( ( ~ ( ap_contractE_c4 @ SV21 @ SV55 @ SV82 ) )
= $true )
| ( ( SV82
= ( comb_app @ SV21 @ ( ap_contractE_sk3q @ SV21 @ SV55 @ SV82 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[236]) ).
thf(268,plain,
! [SV91: $i,SV83: $i,SV56: $i,SV24: $i] :
( ( ~ ( trans @ SV24 )
| ~ ( member @ ( pair @ SV56 @ SV83 ) @ SV24 )
| ~ ( member @ ( pair @ SV83 @ SV91 ) @ SV24 )
| ( member @ ( pair @ SV56 @ SV91 ) @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(269,plain,
! [SV57: $i,SV26: $i] :
( ( ( member @ ( pair @ SV26 @ SV57 ) @ contract )
= $false )
| ( ( member @ SV57 @ comb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(270,plain,
! [SV84: $i,SV58: $i,SV27: $i] :
( ( ( ~ ( member @ SV27 @ comb ) )
= $true )
| ( ( ~ ( member @ SV58 @ comb )
| ~ ( member @ ( pair @ SV27 @ SV84 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV27 ) @ SV58 ) @ SV84 ) @ ( rtrancl @ contract ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[239]) ).
thf(271,plain,
! [SV92: $i,SV85: $i,SV59: $i,SV28: $i] :
( ( ~ ( member @ SV28 @ comb )
| ~ ( member @ SV59 @ comb )
| ~ ( member @ SV85 @ comb )
| ~ ( member @ ( pair @ ( comb_app @ ( comb_app @ SV28 @ SV85 ) @ ( comb_app @ SV59 @ SV85 ) ) @ SV92 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV28 ) @ SV59 ) @ SV85 ) @ SV92 ) @ ( rtrancl @ contract ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(272,plain,
! [SV93: $i,SV86: $i,SV60: $i,SV29: $i] :
( ( ~ ( member @ ( pair @ SV29 @ SV60 ) @ contract )
| ~ ( member @ SV86 @ comb )
| ~ ( member @ ( pair @ ( comb_app @ SV60 @ SV86 ) @ SV93 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ SV29 @ SV86 ) @ SV93 ) @ ( rtrancl @ contract ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(273,plain,
! [SV94: $i,SV87: $i,SV61: $i,SV30: $i] :
( ( ~ ( member @ ( pair @ SV30 @ SV61 ) @ contract )
| ~ ( member @ SV87 @ comb )
| ~ ( member @ ( pair @ ( comb_app @ SV87 @ SV61 ) @ SV94 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ SV87 @ SV30 ) @ SV94 ) @ ( rtrancl @ contract ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(274,plain,
! [SV95: $i,SV88: $i,SV64: $i,SV33: $i] :
( ( ( ( comb_app @ SV33 @ SV64 )
!= ( comb_app @ SV88 @ SV95 ) )
| ( SV33 = SV88 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[245]) ).
thf(275,plain,
! [SV96: $i,SV89: $i,SV65: $i,SV34: $i] :
( ( ( ( comb_app @ SV34 @ SV65 )
!= ( comb_app @ SV89 @ SV96 ) )
| ( SV65 = SV96 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[246]) ).
thf(276,plain,
! [SV97: $i,SV90: $i,SV66: $i,SV35: $i] :
( ( ( SV35 != SV66 )
| ( SV90 != SV97 )
| ( ( comb_app @ SV35 @ SV90 )
= ( comb_app @ SV66 @ SV97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(277,plain,
! [SV3: $i,SV38: $i] :
( ( ( ~ ( member @ SV38 @ comb ) )
= $true )
| ( ( member @ ( comb_app @ SV3 @ SV38 ) @ comb )
= $true )
| ( ( member @ SV3 @ comb )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[250]) ).
thf(278,plain,
! [SV5: $i,SV39: $i] :
( ( ( ~ ( member @ SV39 @ comb ) )
= $true )
| ( ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV5 ) @ SV39 ) @ SV5 ) @ contract )
= $true )
| ( ( member @ SV5 @ comb )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[251]) ).
thf(279,plain,
! [SV67: $i,SV40: $i,SV6: $i] :
( ( ( member @ SV6 @ comb )
= $false )
| ( ( ~ ( member @ SV40 @ comb )
| ~ ( member @ SV67 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV6 ) @ SV40 ) @ SV67 ) @ ( comb_app @ ( comb_app @ SV6 @ SV67 ) @ ( comb_app @ SV40 @ SV67 ) ) ) @ contract ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(280,plain,
! [SV68: $i,SV41: $i,SV7: $i] :
( ( ( member @ ( pair @ ( comb_app @ SV7 @ SV41 ) @ SV68 ) @ contract )
= $false )
| ( ( ( ap_contractE_c1 @ SV7 @ SV41 @ SV68 )
| ( ap_contractE_c2 @ SV7 @ SV41 @ SV68 )
| ( ap_contractE_c3 @ SV7 @ SV41 @ SV68 )
| ( ap_contractE_c4 @ SV7 @ SV41 @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(281,plain,
! [SV69: $i,SV42: $i,SV8: $i] :
( ( ( ap_contractE_c1 @ SV8 @ SV42 @ SV69 )
= $false )
| ( ( member @ SV69 @ comb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(282,plain,
! [SV70: $i,SV43: $i,SV9: $i] :
( ( ( ap_contractE_c1 @ SV9 @ SV43 @ SV70 )
= $false )
| ( ( member @ SV43 @ comb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(283,plain,
! [SV71: $i,SV44: $i,SV10: $i] :
( ( ( ap_contractE_c1 @ SV10 @ SV44 @ SV71 )
= $false )
| ( ( SV10
= ( comb_app @ combK @ SV71 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(284,plain,
! [SV72: $i,SV45: $i,SV11: $i] :
( ( ( ap_contractE_c2 @ SV11 @ SV45 @ SV72 )
= $false )
| ( ( member @ ( ap_contractE_sk1p @ SV11 @ SV45 @ SV72 ) @ comb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(285,plain,
! [SV73: $i,SV46: $i,SV12: $i] :
( ( ( ap_contractE_c2 @ SV12 @ SV46 @ SV73 )
= $false )
| ( ( member @ ( ap_contractE_sk1q @ SV12 @ SV46 @ SV73 ) @ comb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(286,plain,
! [SV74: $i,SV47: $i,SV13: $i] :
( ( ( ap_contractE_c2 @ SV13 @ SV47 @ SV74 )
= $false )
| ( ( member @ SV47 @ comb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(287,plain,
! [SV75: $i,SV48: $i,SV14: $i] :
( ( ( ap_contractE_c2 @ SV14 @ SV48 @ SV75 )
= $false )
| ( ( SV75
= ( comb_app @ ( comb_app @ ( ap_contractE_sk1p @ SV14 @ SV48 @ SV75 ) @ SV48 ) @ ( comb_app @ ( ap_contractE_sk1q @ SV14 @ SV48 @ SV75 ) @ SV48 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(288,plain,
! [SV76: $i,SV49: $i,SV15: $i] :
( ( ( ap_contractE_c2 @ SV15 @ SV49 @ SV76 )
= $false )
| ( ( SV15
= ( comb_app @ ( comb_app @ combS @ ( ap_contractE_sk1p @ SV15 @ SV49 @ SV76 ) ) @ ( ap_contractE_sk1q @ SV15 @ SV49 @ SV76 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(289,plain,
! [SV77: $i,SV50: $i,SV16: $i] :
( ( ( ap_contractE_c3 @ SV16 @ SV50 @ SV77 )
= $false )
| ( ( member @ ( pair @ SV16 @ ( ap_contractE_sk2q @ SV16 @ SV50 @ SV77 ) ) @ contract )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(290,plain,
! [SV78: $i,SV51: $i,SV17: $i] :
( ( ( ap_contractE_c3 @ SV17 @ SV51 @ SV78 )
= $false )
| ( ( member @ SV51 @ comb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(291,plain,
! [SV79: $i,SV52: $i,SV18: $i] :
( ( ( ap_contractE_c3 @ SV18 @ SV52 @ SV79 )
= $false )
| ( ( SV79
= ( comb_app @ ( ap_contractE_sk2q @ SV18 @ SV52 @ SV79 ) @ SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(292,plain,
! [SV80: $i,SV53: $i,SV19: $i] :
( ( ( ap_contractE_c4 @ SV19 @ SV53 @ SV80 )
= $false )
| ( ( member @ ( pair @ SV53 @ ( ap_contractE_sk3q @ SV19 @ SV53 @ SV80 ) ) @ contract )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[265]) ).
thf(293,plain,
! [SV81: $i,SV54: $i,SV20: $i] :
( ( ( ap_contractE_c4 @ SV20 @ SV54 @ SV81 )
= $false )
| ( ( member @ SV20 @ comb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[266]) ).
thf(294,plain,
! [SV82: $i,SV55: $i,SV21: $i] :
( ( ( ap_contractE_c4 @ SV21 @ SV55 @ SV82 )
= $false )
| ( ( SV82
= ( comb_app @ SV21 @ ( ap_contractE_sk3q @ SV21 @ SV55 @ SV82 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(295,plain,
! [SV91: $i,SV83: $i,SV56: $i,SV24: $i] :
( ( ( ~ ( trans @ SV24 ) )
= $true )
| ( ( ~ ( member @ ( pair @ SV56 @ SV83 ) @ SV24 )
| ~ ( member @ ( pair @ SV83 @ SV91 ) @ SV24 )
| ( member @ ( pair @ SV56 @ SV91 ) @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[268]) ).
thf(296,plain,
! [SV84: $i,SV58: $i,SV27: $i] :
( ( ( member @ SV27 @ comb )
= $false )
| ( ( ~ ( member @ SV58 @ comb )
| ~ ( member @ ( pair @ SV27 @ SV84 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV27 ) @ SV58 ) @ SV84 ) @ ( rtrancl @ contract ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(297,plain,
! [SV92: $i,SV85: $i,SV59: $i,SV28: $i] :
( ( ( ~ ( member @ SV28 @ comb ) )
= $true )
| ( ( ~ ( member @ SV59 @ comb )
| ~ ( member @ SV85 @ comb )
| ~ ( member @ ( pair @ ( comb_app @ ( comb_app @ SV28 @ SV85 ) @ ( comb_app @ SV59 @ SV85 ) ) @ SV92 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV28 ) @ SV59 ) @ SV85 ) @ SV92 ) @ ( rtrancl @ contract ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[271]) ).
thf(298,plain,
! [SV93: $i,SV86: $i,SV60: $i,SV29: $i] :
( ( ( ~ ( member @ ( pair @ SV29 @ SV60 ) @ contract ) )
= $true )
| ( ( ~ ( member @ SV86 @ comb )
| ~ ( member @ ( pair @ ( comb_app @ SV60 @ SV86 ) @ SV93 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ SV29 @ SV86 ) @ SV93 ) @ ( rtrancl @ contract ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[272]) ).
thf(299,plain,
! [SV94: $i,SV87: $i,SV61: $i,SV30: $i] :
( ( ( ~ ( member @ ( pair @ SV30 @ SV61 ) @ contract ) )
= $true )
| ( ( ~ ( member @ SV87 @ comb )
| ~ ( member @ ( pair @ ( comb_app @ SV87 @ SV61 ) @ SV94 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ SV87 @ SV30 ) @ SV94 ) @ ( rtrancl @ contract ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[273]) ).
thf(300,plain,
! [SV95: $i,SV88: $i,SV64: $i,SV33: $i] :
( ( ( ( comb_app @ SV33 @ SV64 )
!= ( comb_app @ SV88 @ SV95 ) )
= $true )
| ( ( SV33 = SV88 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[274]) ).
thf(301,plain,
! [SV96: $i,SV89: $i,SV65: $i,SV34: $i] :
( ( ( ( comb_app @ SV34 @ SV65 )
!= ( comb_app @ SV89 @ SV96 ) )
= $true )
| ( ( SV65 = SV96 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[275]) ).
thf(302,plain,
! [SV97: $i,SV90: $i,SV66: $i,SV35: $i] :
( ( ( SV35 != SV66 )
= $true )
| ( ( ( SV90 != SV97 )
| ( ( comb_app @ SV35 @ SV90 )
= ( comb_app @ SV66 @ SV97 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[276]) ).
thf(303,plain,
! [SV3: $i,SV38: $i] :
( ( ( member @ SV38 @ comb )
= $false )
| ( ( member @ ( comb_app @ SV3 @ SV38 ) @ comb )
= $true )
| ( ( member @ SV3 @ comb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(304,plain,
! [SV5: $i,SV39: $i] :
( ( ( member @ SV39 @ comb )
= $false )
| ( ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV5 ) @ SV39 ) @ SV5 ) @ contract )
= $true )
| ( ( member @ SV5 @ comb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(305,plain,
! [SV6: $i,SV67: $i,SV40: $i] :
( ( ( ~ ( member @ SV40 @ comb ) )
= $true )
| ( ( ~ ( member @ SV67 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV6 ) @ SV40 ) @ SV67 ) @ ( comb_app @ ( comb_app @ SV6 @ SV67 ) @ ( comb_app @ SV40 @ SV67 ) ) ) @ contract ) )
= $true )
| ( ( member @ SV6 @ comb )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[279]) ).
thf(306,plain,
! [SV68: $i,SV41: $i,SV7: $i] :
( ( ( ap_contractE_c1 @ SV7 @ SV41 @ SV68 )
= $true )
| ( ( ( ap_contractE_c2 @ SV7 @ SV41 @ SV68 )
| ( ap_contractE_c3 @ SV7 @ SV41 @ SV68 )
| ( ap_contractE_c4 @ SV7 @ SV41 @ SV68 ) )
= $true )
| ( ( member @ ( pair @ ( comb_app @ SV7 @ SV41 ) @ SV68 ) @ contract )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[280]) ).
thf(307,plain,
! [SV91: $i,SV83: $i,SV56: $i,SV24: $i] :
( ( ( trans @ SV24 )
= $false )
| ( ( ~ ( member @ ( pair @ SV56 @ SV83 ) @ SV24 )
| ~ ( member @ ( pair @ SV83 @ SV91 ) @ SV24 )
| ( member @ ( pair @ SV56 @ SV91 ) @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(308,plain,
! [SV84: $i,SV27: $i,SV58: $i] :
( ( ( ~ ( member @ SV58 @ comb ) )
= $true )
| ( ( ~ ( member @ ( pair @ SV27 @ SV84 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV27 ) @ SV58 ) @ SV84 ) @ ( rtrancl @ contract ) ) )
= $true )
| ( ( member @ SV27 @ comb )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[296]) ).
thf(309,plain,
! [SV92: $i,SV85: $i,SV59: $i,SV28: $i] :
( ( ( member @ SV28 @ comb )
= $false )
| ( ( ~ ( member @ SV59 @ comb )
| ~ ( member @ SV85 @ comb )
| ~ ( member @ ( pair @ ( comb_app @ ( comb_app @ SV28 @ SV85 ) @ ( comb_app @ SV59 @ SV85 ) ) @ SV92 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV28 ) @ SV59 ) @ SV85 ) @ SV92 ) @ ( rtrancl @ contract ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[297]) ).
thf(310,plain,
! [SV93: $i,SV86: $i,SV60: $i,SV29: $i] :
( ( ( member @ ( pair @ SV29 @ SV60 ) @ contract )
= $false )
| ( ( ~ ( member @ SV86 @ comb )
| ~ ( member @ ( pair @ ( comb_app @ SV60 @ SV86 ) @ SV93 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ SV29 @ SV86 ) @ SV93 ) @ ( rtrancl @ contract ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[298]) ).
thf(311,plain,
! [SV94: $i,SV87: $i,SV61: $i,SV30: $i] :
( ( ( member @ ( pair @ SV30 @ SV61 ) @ contract )
= $false )
| ( ( ~ ( member @ SV87 @ comb )
| ~ ( member @ ( pair @ ( comb_app @ SV87 @ SV61 ) @ SV94 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ SV87 @ SV30 ) @ SV94 ) @ ( rtrancl @ contract ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[299]) ).
thf(312,plain,
! [SV95: $i,SV88: $i,SV64: $i,SV33: $i] :
( ( ( ( comb_app @ SV33 @ SV64 )
= ( comb_app @ SV88 @ SV95 ) )
= $false )
| ( ( SV33 = SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[300]) ).
thf(313,plain,
! [SV96: $i,SV89: $i,SV65: $i,SV34: $i] :
( ( ( ( comb_app @ SV34 @ SV65 )
= ( comb_app @ SV89 @ SV96 ) )
= $false )
| ( ( SV65 = SV96 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(314,plain,
! [SV97: $i,SV90: $i,SV66: $i,SV35: $i] :
( ( ( SV35 = SV66 )
= $false )
| ( ( ( SV90 != SV97 )
| ( ( comb_app @ SV35 @ SV90 )
= ( comb_app @ SV66 @ SV97 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[302]) ).
thf(315,plain,
! [SV6: $i,SV67: $i,SV40: $i] :
( ( ( member @ SV40 @ comb )
= $false )
| ( ( ~ ( member @ SV67 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV6 ) @ SV40 ) @ SV67 ) @ ( comb_app @ ( comb_app @ SV6 @ SV67 ) @ ( comb_app @ SV40 @ SV67 ) ) ) @ contract ) )
= $true )
| ( ( member @ SV6 @ comb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[305]) ).
thf(316,plain,
! [SV68: $i,SV41: $i,SV7: $i] :
( ( ( ap_contractE_c2 @ SV7 @ SV41 @ SV68 )
= $true )
| ( ( ( ap_contractE_c3 @ SV7 @ SV41 @ SV68 )
| ( ap_contractE_c4 @ SV7 @ SV41 @ SV68 ) )
= $true )
| ( ( ap_contractE_c1 @ SV7 @ SV41 @ SV68 )
= $true )
| ( ( member @ ( pair @ ( comb_app @ SV7 @ SV41 ) @ SV68 ) @ contract )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[306]) ).
thf(317,plain,
! [SV91: $i,SV24: $i,SV83: $i,SV56: $i] :
( ( ( ~ ( member @ ( pair @ SV56 @ SV83 ) @ SV24 ) )
= $true )
| ( ( ~ ( member @ ( pair @ SV83 @ SV91 ) @ SV24 )
| ( member @ ( pair @ SV56 @ SV91 ) @ SV24 ) )
= $true )
| ( ( trans @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[307]) ).
thf(318,plain,
! [SV84: $i,SV27: $i,SV58: $i] :
( ( ( member @ SV58 @ comb )
= $false )
| ( ( ~ ( member @ ( pair @ SV27 @ SV84 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV27 ) @ SV58 ) @ SV84 ) @ ( rtrancl @ contract ) ) )
= $true )
| ( ( member @ SV27 @ comb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(319,plain,
! [SV92: $i,SV28: $i,SV85: $i,SV59: $i] :
( ( ( ~ ( member @ SV59 @ comb ) )
= $true )
| ( ( ~ ( member @ SV85 @ comb )
| ~ ( member @ ( pair @ ( comb_app @ ( comb_app @ SV28 @ SV85 ) @ ( comb_app @ SV59 @ SV85 ) ) @ SV92 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV28 ) @ SV59 ) @ SV85 ) @ SV92 ) @ ( rtrancl @ contract ) ) )
= $true )
| ( ( member @ SV28 @ comb )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[309]) ).
thf(320,plain,
! [SV29: $i,SV93: $i,SV60: $i,SV86: $i] :
( ( ( ~ ( member @ SV86 @ comb ) )
= $true )
| ( ( ~ ( member @ ( pair @ ( comb_app @ SV60 @ SV86 ) @ SV93 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ SV29 @ SV86 ) @ SV93 ) @ ( rtrancl @ contract ) ) )
= $true )
| ( ( member @ ( pair @ SV29 @ SV60 ) @ contract )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[310]) ).
thf(321,plain,
! [SV30: $i,SV94: $i,SV61: $i,SV87: $i] :
( ( ( ~ ( member @ SV87 @ comb ) )
= $true )
| ( ( ~ ( member @ ( pair @ ( comb_app @ SV87 @ SV61 ) @ SV94 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ SV87 @ SV30 ) @ SV94 ) @ ( rtrancl @ contract ) ) )
= $true )
| ( ( member @ ( pair @ SV30 @ SV61 ) @ contract )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[311]) ).
thf(322,plain,
! [SV66: $i,SV35: $i,SV97: $i,SV90: $i] :
( ( ( SV90 != SV97 )
= $true )
| ( ( ( comb_app @ SV35 @ SV90 )
= ( comb_app @ SV66 @ SV97 ) )
= $true )
| ( ( SV35 = SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[314]) ).
thf(323,plain,
! [SV40: $i,SV6: $i,SV67: $i] :
( ( ( ~ ( member @ SV67 @ comb ) )
= $true )
| ( ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV6 ) @ SV40 ) @ SV67 ) @ ( comb_app @ ( comb_app @ SV6 @ SV67 ) @ ( comb_app @ SV40 @ SV67 ) ) ) @ contract )
= $true )
| ( ( member @ SV40 @ comb )
= $false )
| ( ( member @ SV6 @ comb )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[315]) ).
thf(324,plain,
! [SV68: $i,SV41: $i,SV7: $i] :
( ( ( ap_contractE_c3 @ SV7 @ SV41 @ SV68 )
= $true )
| ( ( ap_contractE_c4 @ SV7 @ SV41 @ SV68 )
= $true )
| ( ( ap_contractE_c2 @ SV7 @ SV41 @ SV68 )
= $true )
| ( ( ap_contractE_c1 @ SV7 @ SV41 @ SV68 )
= $true )
| ( ( member @ ( pair @ ( comb_app @ SV7 @ SV41 ) @ SV68 ) @ contract )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[316]) ).
thf(325,plain,
! [SV91: $i,SV24: $i,SV83: $i,SV56: $i] :
( ( ( member @ ( pair @ SV56 @ SV83 ) @ SV24 )
= $false )
| ( ( ~ ( member @ ( pair @ SV83 @ SV91 ) @ SV24 )
| ( member @ ( pair @ SV56 @ SV91 ) @ SV24 ) )
= $true )
| ( ( trans @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(326,plain,
! [SV58: $i,SV84: $i,SV27: $i] :
( ( ( ~ ( member @ ( pair @ SV27 @ SV84 ) @ ( rtrancl @ contract ) ) )
= $true )
| ( ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV27 ) @ SV58 ) @ SV84 ) @ ( rtrancl @ contract ) )
= $true )
| ( ( member @ SV58 @ comb )
= $false )
| ( ( member @ SV27 @ comb )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[318]) ).
thf(327,plain,
! [SV92: $i,SV28: $i,SV85: $i,SV59: $i] :
( ( ( member @ SV59 @ comb )
= $false )
| ( ( ~ ( member @ SV85 @ comb )
| ~ ( member @ ( pair @ ( comb_app @ ( comb_app @ SV28 @ SV85 ) @ ( comb_app @ SV59 @ SV85 ) ) @ SV92 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV28 ) @ SV59 ) @ SV85 ) @ SV92 ) @ ( rtrancl @ contract ) ) )
= $true )
| ( ( member @ SV28 @ comb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[319]) ).
thf(328,plain,
! [SV29: $i,SV93: $i,SV60: $i,SV86: $i] :
( ( ( member @ SV86 @ comb )
= $false )
| ( ( ~ ( member @ ( pair @ ( comb_app @ SV60 @ SV86 ) @ SV93 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ SV29 @ SV86 ) @ SV93 ) @ ( rtrancl @ contract ) ) )
= $true )
| ( ( member @ ( pair @ SV29 @ SV60 ) @ contract )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[320]) ).
thf(329,plain,
! [SV30: $i,SV94: $i,SV61: $i,SV87: $i] :
( ( ( member @ SV87 @ comb )
= $false )
| ( ( ~ ( member @ ( pair @ ( comb_app @ SV87 @ SV61 ) @ SV94 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ SV87 @ SV30 ) @ SV94 ) @ ( rtrancl @ contract ) ) )
= $true )
| ( ( member @ ( pair @ SV30 @ SV61 ) @ contract )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(330,plain,
! [SV66: $i,SV35: $i,SV97: $i,SV90: $i] :
( ( ( SV90 = SV97 )
= $false )
| ( ( ( comb_app @ SV35 @ SV90 )
= ( comb_app @ SV66 @ SV97 ) )
= $true )
| ( ( SV35 = SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[322]) ).
thf(331,plain,
! [SV40: $i,SV6: $i,SV67: $i] :
( ( ( member @ SV67 @ comb )
= $false )
| ( ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV6 ) @ SV40 ) @ SV67 ) @ ( comb_app @ ( comb_app @ SV6 @ SV67 ) @ ( comb_app @ SV40 @ SV67 ) ) ) @ contract )
= $true )
| ( ( member @ SV40 @ comb )
= $false )
| ( ( member @ SV6 @ comb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[323]) ).
thf(332,plain,
! [SV56: $i,SV24: $i,SV91: $i,SV83: $i] :
( ( ( ~ ( member @ ( pair @ SV83 @ SV91 ) @ SV24 ) )
= $true )
| ( ( member @ ( pair @ SV56 @ SV91 ) @ SV24 )
= $true )
| ( ( member @ ( pair @ SV56 @ SV83 ) @ SV24 )
= $false )
| ( ( trans @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[325]) ).
thf(333,plain,
! [SV58: $i,SV84: $i,SV27: $i] :
( ( ( member @ ( pair @ SV27 @ SV84 ) @ ( rtrancl @ contract ) )
= $false )
| ( ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV27 ) @ SV58 ) @ SV84 ) @ ( rtrancl @ contract ) )
= $true )
| ( ( member @ SV58 @ comb )
= $false )
| ( ( member @ SV27 @ comb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(334,plain,
! [SV92: $i,SV59: $i,SV28: $i,SV85: $i] :
( ( ( ~ ( member @ SV85 @ comb ) )
= $true )
| ( ( ~ ( member @ ( pair @ ( comb_app @ ( comb_app @ SV28 @ SV85 ) @ ( comb_app @ SV59 @ SV85 ) ) @ SV92 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV28 ) @ SV59 ) @ SV85 ) @ SV92 ) @ ( rtrancl @ contract ) ) )
= $true )
| ( ( member @ SV59 @ comb )
= $false )
| ( ( member @ SV28 @ comb )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[327]) ).
thf(335,plain,
! [SV29: $i,SV93: $i,SV86: $i,SV60: $i] :
( ( ( ~ ( member @ ( pair @ ( comb_app @ SV60 @ SV86 ) @ SV93 ) @ ( rtrancl @ contract ) ) )
= $true )
| ( ( member @ ( pair @ ( comb_app @ SV29 @ SV86 ) @ SV93 ) @ ( rtrancl @ contract ) )
= $true )
| ( ( member @ SV86 @ comb )
= $false )
| ( ( member @ ( pair @ SV29 @ SV60 ) @ contract )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[328]) ).
thf(336,plain,
! [SV30: $i,SV94: $i,SV61: $i,SV87: $i] :
( ( ( ~ ( member @ ( pair @ ( comb_app @ SV87 @ SV61 ) @ SV94 ) @ ( rtrancl @ contract ) ) )
= $true )
| ( ( member @ ( pair @ ( comb_app @ SV87 @ SV30 ) @ SV94 ) @ ( rtrancl @ contract ) )
= $true )
| ( ( member @ SV87 @ comb )
= $false )
| ( ( member @ ( pair @ SV30 @ SV61 ) @ contract )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[329]) ).
thf(337,plain,
! [SV56: $i,SV24: $i,SV91: $i,SV83: $i] :
( ( ( member @ ( pair @ SV83 @ SV91 ) @ SV24 )
= $false )
| ( ( member @ ( pair @ SV56 @ SV91 ) @ SV24 )
= $true )
| ( ( member @ ( pair @ SV56 @ SV83 ) @ SV24 )
= $false )
| ( ( trans @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(338,plain,
! [SV92: $i,SV59: $i,SV28: $i,SV85: $i] :
( ( ( member @ SV85 @ comb )
= $false )
| ( ( ~ ( member @ ( pair @ ( comb_app @ ( comb_app @ SV28 @ SV85 ) @ ( comb_app @ SV59 @ SV85 ) ) @ SV92 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV28 ) @ SV59 ) @ SV85 ) @ SV92 ) @ ( rtrancl @ contract ) ) )
= $true )
| ( ( member @ SV59 @ comb )
= $false )
| ( ( member @ SV28 @ comb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(339,plain,
! [SV29: $i,SV93: $i,SV86: $i,SV60: $i] :
( ( ( member @ ( pair @ ( comb_app @ SV60 @ SV86 ) @ SV93 ) @ ( rtrancl @ contract ) )
= $false )
| ( ( member @ ( pair @ ( comb_app @ SV29 @ SV86 ) @ SV93 ) @ ( rtrancl @ contract ) )
= $true )
| ( ( member @ SV86 @ comb )
= $false )
| ( ( member @ ( pair @ SV29 @ SV60 ) @ contract )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(340,plain,
! [SV30: $i,SV94: $i,SV61: $i,SV87: $i] :
( ( ( member @ ( pair @ ( comb_app @ SV87 @ SV61 ) @ SV94 ) @ ( rtrancl @ contract ) )
= $false )
| ( ( member @ ( pair @ ( comb_app @ SV87 @ SV30 ) @ SV94 ) @ ( rtrancl @ contract ) )
= $true )
| ( ( member @ SV87 @ comb )
= $false )
| ( ( member @ ( pair @ SV30 @ SV61 ) @ contract )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[336]) ).
thf(341,plain,
! [SV92: $i,SV59: $i,SV85: $i,SV28: $i] :
( ( ( ~ ( member @ ( pair @ ( comb_app @ ( comb_app @ SV28 @ SV85 ) @ ( comb_app @ SV59 @ SV85 ) ) @ SV92 ) @ ( rtrancl @ contract ) ) )
= $true )
| ( ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV28 ) @ SV59 ) @ SV85 ) @ SV92 ) @ ( rtrancl @ contract ) )
= $true )
| ( ( member @ SV85 @ comb )
= $false )
| ( ( member @ SV59 @ comb )
= $false )
| ( ( member @ SV28 @ comb )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[338]) ).
thf(342,plain,
! [SV92: $i,SV59: $i,SV85: $i,SV28: $i] :
( ( ( member @ ( pair @ ( comb_app @ ( comb_app @ SV28 @ SV85 ) @ ( comb_app @ SV59 @ SV85 ) ) @ SV92 ) @ ( rtrancl @ contract ) )
= $false )
| ( ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV28 ) @ SV59 ) @ SV85 ) @ SV92 ) @ ( rtrancl @ contract ) )
= $true )
| ( ( member @ SV85 @ comb )
= $false )
| ( ( member @ SV59 @ comb )
= $false )
| ( ( member @ SV28 @ comb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[341]) ).
thf(343,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[94,342,340,339,337,333,331,330,324,313,312,304,303,294,293,292,291,290,289,288,287,286,285,284,283,282,281,269,249,248,244,243,219,204,203,176,175,169,144,108,107,98,97,96,95]) ).
thf(344,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[343]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL088-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.19 % Computer : n015.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 18:38:13 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 97.78/20.18
% 97.78/20.18 No.of.Axioms: 44
% 97.78/20.18
% 97.78/20.18 Length.of.Defs: 0
% 97.78/20.18
% 97.78/20.18 Contains.Choice.Funs: false
% 97.78/20.18 .........
% 97.78/20.18
% 97.78/20.18 ********************************
% 97.78/20.18 * All subproblems solved! *
% 97.78/20.18 ********************************
% 97.78/20.18 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:44,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:343,loop_count:0,foatp_calls:1,translation:fof_full)
% 97.78/20.18
% 97.78/20.18 %**** Beginning of derivation protocol ****
% 97.78/20.18 % SZS output start CNFRefutation
% See solution above
% 97.78/20.19
% 97.78/20.19 %**** End of derivation protocol ****
% 97.78/20.19 %**** no. of clauses in derivation: 344 ****
% 97.78/20.19 %**** clause counter: 343 ****
% 97.78/20.19
% 97.78/20.19 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:44,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:343,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------