TSTP Solution File: COL089-1 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : COL089-1 : 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 : n022.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 00:34:47 EDT 2022
% Result : Unsatisfiable 9.22s 9.44s
% Output : CNFRefutation 9.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 66
% Syntax : Number of formulae : 378 ( 209 unt; 21 typ; 0 def)
% Number of atoms : 1879 ( 626 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 4455 ( 415 ~; 540 |; 0 &;3500 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 10 con; 0-3 aty)
% Number of variables : 951 ( 0 ^ 951 !; 0 ?; 951 :)
% 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,
! [A: $i,B: $i] :
( ~ ( member @ ( pair @ A @ B ) @ contract )
| ( member @ B @ comb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contract_combD2) ).
thf(2,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/sandbox2/benchmark/theBenchmark.p',transD) ).
thf(3,axiom,
! [R: $i] : ( trans @ ( rtrancl @ R ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',trans_rtrancl) ).
thf(4,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/sandbox2/benchmark/theBenchmark.p',reduction_rls_4) ).
thf(5,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/sandbox2/benchmark/theBenchmark.p',reduction_rls_3) ).
thf(6,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/sandbox2/benchmark/theBenchmark.p',reduction_rls_2) ).
thf(7,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/sandbox2/benchmark/theBenchmark.p',reduction_rls_1) ).
thf(8,axiom,
! [R: $i] :
~ ( member @ ( pair @ combS @ R ) @ contract ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_contractE) ).
thf(9,axiom,
! [R: $i] :
~ ( member @ ( pair @ combK @ R ) @ contract ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',contract_K) ).
thf(27,axiom,
! [A: $i] :
( ~ ( member @ A @ comb )
| ( member @ ( pair @ A @ A ) @ ( rtrancl @ contract ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',comb_intros3) ).
thf(29,axiom,
member @ combS @ comb,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',comb_intros2) ).
thf(30,axiom,
member @ combK @ comb,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',comb_intros1) ).
thf(31,axiom,
! [P: $i,Q: $i] :
( ~ ( member @ ( comb_app @ P @ Q ) @ comb )
| ( member @ Q @ comb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_E2) ).
thf(32,axiom,
! [P: $i,Q: $i] :
( ~ ( member @ ( comb_app @ P @ Q ) @ comb )
| ( member @ P @ comb ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',app_app1) ).
thf(36,axiom,
! [P: $i,Q: $i] :
( combS
!= ( comb_app @ P @ Q ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_app) ).
thf(37,axiom,
! [P: $i,Q: $i] :
( combK
!= ( comb_app @ P @ Q ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_app) ).
thf(38,axiom,
combK != combS,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_s) ).
thf(39,axiom,
member @ ( pair @ ( comb_app @ r @ p ) @ ( comb_app @ r @ y ) ) @ ( rtrancl @ contract ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_reduce2_2h5) ).
thf(40,axiom,
member @ ( pair @ y @ z ) @ contract,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_reduce2_2h4) ).
thf(41,axiom,
member @ ( pair @ p @ y ) @ ( rtrancl @ contract ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_reduce2_2h3) ).
thf(42,axiom,
member @ p @ comb,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_reduce2_2h2) ).
thf(43,axiom,
member @ r @ comb,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_reduce2_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 @ r @ p ) @ ( comb_app @ r @ z ) ) @ ( rtrancl @ contract ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_reduce2_2c1) ).
thf(47,plain,
$false = $false,
inference(unfold_def,[status(thm)],[45]) ).
thf(48,plain,
( ( ! [A: $i,B: $i] :
( ~ ( member @ ( pair @ A @ B ) @ contract )
| ( member @ B @ comb ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(49,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)],[2]) ).
thf(50,plain,
( ( ! [R: $i] : ( trans @ ( rtrancl @ R ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(51,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)],[4]) ).
thf(52,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)],[5]) ).
thf(53,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)],[6]) ).
thf(54,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)],[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 @ r @ p ) @ ( comb_app @ r @ y ) ) @ ( 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 @ r @ p ) @ ( comb_app @ r @ z ) ) @ ( rtrancl @ contract ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(92,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[47]) ).
thf(93,plain,
( ( ! [R: $i,A: $i] :
( ~ ( trans @ R )
| ! [B: $i] :
( ~ ( member @ ( pair @ A @ B ) @ R )
| ! [C: $i] :
( ~ ( member @ ( pair @ B @ C ) @ R )
| ( member @ ( pair @ A @ C ) @ R ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[49]) ).
thf(94,plain,
( ( ! [P3: $i,Q3: $i] :
( ~ ( member @ ( pair @ P3 @ Q3 ) @ contract )
| ! [R3: $i] :
( ~ ( member @ R3 @ comb )
| ! [C: $i] :
( ~ ( member @ ( pair @ ( comb_app @ R3 @ Q3 ) @ C ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ R3 @ P3 ) @ C ) @ ( rtrancl @ contract ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[51]) ).
thf(95,plain,
( ( ! [P3: $i,Q3: $i] :
( ~ ( member @ ( pair @ P3 @ Q3 ) @ contract )
| ! [R3: $i] :
( ~ ( member @ R3 @ comb )
| ! [C: $i] :
( ~ ( member @ ( pair @ ( comb_app @ Q3 @ R3 ) @ C ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ P3 @ R3 ) @ C ) @ ( rtrancl @ contract ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[52]) ).
thf(96,plain,
( ( ! [P3: $i,Q3: $i] :
( ~ ( member @ P3 @ comb )
| ~ ( member @ Q3 @ comb )
| ! [R3: $i] :
( ~ ( member @ R3 @ comb )
| ! [C: $i] :
( ~ ( 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(extcnf_combined,[status(esa)],[53]) ).
thf(97,plain,
( ( ! [B: $i] :
( ~ ( member @ B @ comb )
| ! [Q3: $i] :
( ~ ( member @ Q3 @ comb )
| ! [C: $i] :
( ~ ( member @ ( pair @ B @ C ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ B ) @ Q3 ) @ C ) @ ( rtrancl @ contract ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[54]) ).
thf(98,plain,
( ( ! [P: $i] :
( ! [Q: $i,R: $i] :
~ ( ap_contractE_c4 @ P @ Q @ R )
| ( member @ P @ comb ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[58]) ).
thf(99,plain,
( ( ! [P: $i,Q: $i] :
( ! [R: $i] :
~ ( ap_contractE_c3 @ P @ Q @ R )
| ( member @ Q @ comb ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[61]) ).
thf(100,plain,
( ( ! [P: $i,Q: $i] :
( ! [R: $i] :
~ ( ap_contractE_c2 @ P @ Q @ R )
| ( member @ Q @ comb ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[65]) ).
thf(101,plain,
( ( ! [P: $i,Q: $i] :
( ! [R: $i] :
~ ( ap_contractE_c1 @ P @ Q @ R )
| ( member @ Q @ comb ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[69]) ).
thf(102,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)],[72]) ).
thf(103,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)],[73]) ).
thf(104,plain,
( ( ! [P: $i] :
( ~ ( member @ P @ comb )
| ! [Q: $i] :
( ~ ( member @ Q @ comb )
| ( member @ ( comb_app @ P @ Q ) @ comb ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[75]) ).
thf(105,plain,
( ( ! [P: $i] :
( ! [Q: $i] :
~ ( member @ ( comb_app @ P @ Q ) @ comb )
| ( member @ P @ comb ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[79]) ).
thf(106,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)],[80]) ).
thf(107,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)],[81]) ).
thf(108,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)],[82]) ).
thf(109,plain,
( ( ! [P: $i,Q: $i] :
( combS
!= ( comb_app @ P @ Q ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[83]) ).
thf(110,plain,
( ( ! [P: $i,Q: $i] :
( combK
!= ( comb_app @ P @ Q ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[84]) ).
thf(111,plain,
( ( ( combK != combS ) )
= $true ),
inference(extcnf_combined,[status(esa)],[85]) ).
thf(112,plain,
( ( ~ ( member @ ( pair @ ( comb_app @ r @ p ) @ ( comb_app @ r @ z ) ) @ ( rtrancl @ contract ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(113,plain,
( ( member @ r @ comb )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(114,plain,
( ( member @ p @ comb )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(115,plain,
( ( member @ ( pair @ p @ y ) @ ( rtrancl @ contract ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(116,plain,
( ( member @ ( pair @ y @ z ) @ contract )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(117,plain,
( ( member @ ( pair @ ( comb_app @ r @ p ) @ ( comb_app @ r @ y ) ) @ ( rtrancl @ contract ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(118,plain,
( ( ( combK != combS ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(119,plain,
( ( ! [P: $i,Q: $i] :
( combK
!= ( comb_app @ P @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(120,plain,
( ( ! [P: $i,Q: $i] :
( combS
!= ( comb_app @ P @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(121,plain,
( ( ! [P1: $i,Q1: $i,P2: $i] :
( ! [Q2: $i] :
( ( comb_app @ P1 @ Q1 )
!= ( comb_app @ P2 @ Q2 ) )
| ( P1 = P2 ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(122,plain,
( ( ! [P1: $i,Q1: $i,P2: $i,Q2: $i] :
( ( ( comb_app @ P1 @ Q1 )
!= ( comb_app @ P2 @ Q2 ) )
| ( Q1 = Q2 ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(123,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)],[106]) ).
thf(124,plain,
( ( ! [P: $i] :
( ! [Q: $i] :
~ ( member @ ( comb_app @ P @ Q ) @ comb )
| ( member @ P @ comb ) ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(125,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( member @ ( comb_app @ P @ Q ) @ comb )
| ( member @ Q @ comb ) ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(126,plain,
( ( member @ combK @ comb )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(127,plain,
( ( member @ combS @ comb )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(128,plain,
( ( ! [P: $i] :
( ~ ( member @ P @ comb )
| ! [Q: $i] :
( ~ ( member @ Q @ comb )
| ( member @ ( comb_app @ P @ Q ) @ comb ) ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(129,plain,
( ( ! [A: $i] :
( ~ ( member @ A @ comb )
| ( member @ ( pair @ A @ A ) @ ( rtrancl @ contract ) ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(130,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)],[103]) ).
thf(131,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)],[102]) ).
thf(132,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(133,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c1 @ P @ Q @ R )
| ( member @ R @ comb ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(134,plain,
( ( ! [P: $i,Q: $i] :
( ! [R: $i] :
~ ( ap_contractE_c1 @ P @ Q @ R )
| ( member @ Q @ comb ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(135,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(136,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(137,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(138,plain,
( ( ! [P: $i,Q: $i] :
( ! [R: $i] :
~ ( ap_contractE_c2 @ P @ Q @ R )
| ( member @ Q @ comb ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(139,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(140,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(141,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(142,plain,
( ( ! [P: $i,Q: $i] :
( ! [R: $i] :
~ ( ap_contractE_c3 @ P @ Q @ R )
| ( member @ Q @ comb ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(143,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(144,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(145,plain,
( ( ! [P: $i] :
( ! [Q: $i,R: $i] :
~ ( ap_contractE_c4 @ P @ Q @ R )
| ( member @ P @ comb ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(146,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(147,plain,
( ( ! [R: $i] :
~ ( member @ ( pair @ combK @ R ) @ contract ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(148,plain,
( ( ! [R: $i] :
~ ( member @ ( pair @ combS @ R ) @ contract ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(149,plain,
( ( ! [B: $i] :
( ~ ( member @ B @ comb )
| ! [Q3: $i] :
( ~ ( member @ Q3 @ comb )
| ! [C: $i] :
( ~ ( member @ ( pair @ B @ C ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ B ) @ Q3 ) @ C ) @ ( rtrancl @ contract ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(150,plain,
( ( ! [P3: $i,Q3: $i] :
( ~ ( member @ P3 @ comb )
| ~ ( member @ Q3 @ comb )
| ! [R3: $i] :
( ~ ( member @ R3 @ comb )
| ! [C: $i] :
( ~ ( 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)],[96]) ).
thf(151,plain,
( ( ! [P3: $i,Q3: $i] :
( ~ ( member @ ( pair @ P3 @ Q3 ) @ contract )
| ! [R3: $i] :
( ~ ( member @ R3 @ comb )
| ! [C: $i] :
( ~ ( member @ ( pair @ ( comb_app @ Q3 @ R3 ) @ C ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ P3 @ R3 ) @ C ) @ ( rtrancl @ contract ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(152,plain,
( ( ! [P3: $i,Q3: $i] :
( ~ ( member @ ( pair @ P3 @ Q3 ) @ contract )
| ! [R3: $i] :
( ~ ( member @ R3 @ comb )
| ! [C: $i] :
( ~ ( member @ ( pair @ ( comb_app @ R3 @ Q3 ) @ C ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ R3 @ P3 ) @ C ) @ ( rtrancl @ contract ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(153,plain,
( ( ! [R: $i] : ( trans @ ( rtrancl @ R ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(154,plain,
( ( ! [R: $i,A: $i] :
( ~ ( trans @ R )
| ! [B: $i] :
( ~ ( member @ ( pair @ A @ B ) @ R )
| ! [C: $i] :
( ~ ( member @ ( pair @ B @ C ) @ R )
| ( member @ ( pair @ A @ C ) @ R ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(155,plain,
( ( ! [A: $i,B: $i] :
( ~ ( member @ ( pair @ A @ B ) @ contract )
| ( member @ B @ comb ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(156,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(157,plain,
( ( member @ ( pair @ ( comb_app @ r @ p ) @ ( comb_app @ r @ z ) ) @ ( rtrancl @ contract ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(158,plain,
( ( combK = combS )
= $false ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(159,plain,
! [SV1: $i] :
( ( ! [SY97: $i] :
( combK
!= ( comb_app @ SV1 @ SY97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(160,plain,
! [SV2: $i] :
( ( ! [SY98: $i] :
( combS
!= ( comb_app @ SV2 @ SY98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(161,plain,
! [SV3: $i] :
( ( ! [SY99: $i,SY100: $i] :
( ! [SY101: $i] :
( ( comb_app @ SV3 @ SY99 )
!= ( comb_app @ SY100 @ SY101 ) )
| ( SV3 = SY100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(162,plain,
! [SV4: $i] :
( ( ! [SY102: $i,SY103: $i,SY104: $i] :
( ( ( comb_app @ SV4 @ SY102 )
!= ( comb_app @ SY103 @ SY104 ) )
| ( SY102 = SY104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(163,plain,
! [SV5: $i] :
( ( ! [SY105: $i] :
( ( SV5 != SY105 )
| ! [SY106: $i,SY107: $i] :
( ( SY106 != SY107 )
| ( ( comb_app @ SV5 @ SY106 )
= ( comb_app @ SY105 @ SY107 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(164,plain,
! [SV6: $i] :
( ( ! [SY108: $i] :
~ ( member @ ( comb_app @ SV6 @ SY108 ) @ comb )
| ( member @ SV6 @ comb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(165,plain,
! [SV7: $i] :
( ( ! [SY109: $i] :
( ~ ( member @ ( comb_app @ SV7 @ SY109 ) @ comb )
| ( member @ SY109 @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(166,plain,
! [SV8: $i] :
( ( ~ ( member @ SV8 @ comb )
| ! [SY110: $i] :
( ~ ( member @ SY110 @ comb )
| ( member @ ( comb_app @ SV8 @ SY110 ) @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(167,plain,
! [SV9: $i] :
( ( ~ ( member @ SV9 @ comb )
| ( member @ ( pair @ SV9 @ SV9 ) @ ( rtrancl @ contract ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(168,plain,
! [SV10: $i] :
( ( ~ ( member @ SV10 @ comb )
| ! [SY111: $i] :
( ~ ( member @ SY111 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV10 ) @ SY111 ) @ SV10 ) @ contract ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(169,plain,
! [SV11: $i] :
( ( ~ ( member @ SV11 @ comb )
| ! [SY112: $i] :
( ~ ( member @ SY112 @ comb )
| ! [SY113: $i] :
( ~ ( member @ SY113 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV11 ) @ SY112 ) @ SY113 ) @ ( comb_app @ ( comb_app @ SV11 @ SY113 ) @ ( comb_app @ SY112 @ SY113 ) ) ) @ contract ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(170,plain,
! [SV12: $i] :
( ( ! [SY114: $i,SY115: $i] :
( ~ ( member @ ( pair @ ( comb_app @ SV12 @ SY114 ) @ SY115 ) @ contract )
| ( ap_contractE_c1 @ SV12 @ SY114 @ SY115 )
| ( ap_contractE_c2 @ SV12 @ SY114 @ SY115 )
| ( ap_contractE_c3 @ SV12 @ SY114 @ SY115 )
| ( ap_contractE_c4 @ SV12 @ SY114 @ SY115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(171,plain,
! [SV13: $i] :
( ( ! [SY116: $i,SY117: $i] :
( ~ ( ap_contractE_c1 @ SV13 @ SY116 @ SY117 )
| ( member @ SY117 @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(172,plain,
! [SV14: $i] :
( ( ! [SY118: $i] :
( ! [SY119: $i] :
~ ( ap_contractE_c1 @ SV14 @ SY118 @ SY119 )
| ( member @ SY118 @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(173,plain,
! [SV15: $i] :
( ( ! [SY120: $i,SY121: $i] :
( ~ ( ap_contractE_c1 @ SV15 @ SY120 @ SY121 )
| ( SV15
= ( comb_app @ combK @ SY121 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(174,plain,
! [SV16: $i] :
( ( ! [SY122: $i,SY123: $i] :
( ~ ( ap_contractE_c2 @ SV16 @ SY122 @ SY123 )
| ( member @ ( ap_contractE_sk1p @ SV16 @ SY122 @ SY123 ) @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(175,plain,
! [SV17: $i] :
( ( ! [SY124: $i,SY125: $i] :
( ~ ( ap_contractE_c2 @ SV17 @ SY124 @ SY125 )
| ( member @ ( ap_contractE_sk1q @ SV17 @ SY124 @ SY125 ) @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(176,plain,
! [SV18: $i] :
( ( ! [SY126: $i] :
( ! [SY127: $i] :
~ ( ap_contractE_c2 @ SV18 @ SY126 @ SY127 )
| ( member @ SY126 @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(177,plain,
! [SV19: $i] :
( ( ! [SY128: $i,SY129: $i] :
( ~ ( ap_contractE_c2 @ SV19 @ SY128 @ SY129 )
| ( SY129
= ( comb_app @ ( comb_app @ ( ap_contractE_sk1p @ SV19 @ SY128 @ SY129 ) @ SY128 ) @ ( comb_app @ ( ap_contractE_sk1q @ SV19 @ SY128 @ SY129 ) @ SY128 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(178,plain,
! [SV20: $i] :
( ( ! [SY130: $i,SY131: $i] :
( ~ ( ap_contractE_c2 @ SV20 @ SY130 @ SY131 )
| ( SV20
= ( comb_app @ ( comb_app @ combS @ ( ap_contractE_sk1p @ SV20 @ SY130 @ SY131 ) ) @ ( ap_contractE_sk1q @ SV20 @ SY130 @ SY131 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(179,plain,
! [SV21: $i] :
( ( ! [SY132: $i,SY133: $i] :
( ~ ( ap_contractE_c3 @ SV21 @ SY132 @ SY133 )
| ( member @ ( pair @ SV21 @ ( ap_contractE_sk2q @ SV21 @ SY132 @ SY133 ) ) @ contract ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(180,plain,
! [SV22: $i] :
( ( ! [SY134: $i] :
( ! [SY135: $i] :
~ ( ap_contractE_c3 @ SV22 @ SY134 @ SY135 )
| ( member @ SY134 @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(181,plain,
! [SV23: $i] :
( ( ! [SY136: $i,SY137: $i] :
( ~ ( ap_contractE_c3 @ SV23 @ SY136 @ SY137 )
| ( SY137
= ( comb_app @ ( ap_contractE_sk2q @ SV23 @ SY136 @ SY137 ) @ SY136 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(182,plain,
! [SV24: $i] :
( ( ! [SY138: $i,SY139: $i] :
( ~ ( ap_contractE_c4 @ SV24 @ SY138 @ SY139 )
| ( member @ ( pair @ SY138 @ ( ap_contractE_sk3q @ SV24 @ SY138 @ SY139 ) ) @ contract ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(183,plain,
! [SV25: $i] :
( ( ! [SY140: $i,SY141: $i] :
~ ( ap_contractE_c4 @ SV25 @ SY140 @ SY141 )
| ( member @ SV25 @ comb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(184,plain,
! [SV26: $i] :
( ( ! [SY142: $i,SY143: $i] :
( ~ ( ap_contractE_c4 @ SV26 @ SY142 @ SY143 )
| ( SY143
= ( comb_app @ SV26 @ ( ap_contractE_sk3q @ SV26 @ SY142 @ SY143 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(185,plain,
! [SV27: $i] :
( ( ~ ( member @ ( pair @ combK @ SV27 ) @ contract ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(186,plain,
! [SV28: $i] :
( ( ~ ( member @ ( pair @ combS @ SV28 ) @ contract ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(187,plain,
! [SV29: $i] :
( ( ~ ( member @ SV29 @ comb )
| ! [SY144: $i] :
( ~ ( member @ SY144 @ comb )
| ! [SY145: $i] :
( ~ ( member @ ( pair @ SV29 @ SY145 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV29 ) @ SY144 ) @ SY145 ) @ ( rtrancl @ contract ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(188,plain,
! [SV30: $i] :
( ( ! [SY146: $i] :
( ~ ( member @ SV30 @ comb )
| ~ ( member @ SY146 @ comb )
| ! [SY147: $i] :
( ~ ( member @ SY147 @ comb )
| ! [SY148: $i] :
( ~ ( member @ ( pair @ ( comb_app @ ( comb_app @ SV30 @ SY147 ) @ ( comb_app @ SY146 @ SY147 ) ) @ SY148 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV30 ) @ SY146 ) @ SY147 ) @ SY148 ) @ ( rtrancl @ contract ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(189,plain,
! [SV31: $i] :
( ( ! [SY149: $i] :
( ~ ( member @ ( pair @ SV31 @ SY149 ) @ contract )
| ! [SY150: $i] :
( ~ ( member @ SY150 @ comb )
| ! [SY151: $i] :
( ~ ( member @ ( pair @ ( comb_app @ SY149 @ SY150 ) @ SY151 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ SV31 @ SY150 ) @ SY151 ) @ ( rtrancl @ contract ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(190,plain,
! [SV32: $i] :
( ( ! [SY152: $i] :
( ~ ( member @ ( pair @ SV32 @ SY152 ) @ contract )
| ! [SY153: $i] :
( ~ ( member @ SY153 @ comb )
| ! [SY154: $i] :
( ~ ( member @ ( pair @ ( comb_app @ SY153 @ SY152 ) @ SY154 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ SY153 @ SV32 ) @ SY154 ) @ ( rtrancl @ contract ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(191,plain,
! [SV33: $i] :
( ( trans @ ( rtrancl @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(192,plain,
! [SV34: $i] :
( ( ! [SY155: $i] :
( ~ ( trans @ SV34 )
| ! [SY156: $i] :
( ~ ( member @ ( pair @ SY155 @ SY156 ) @ SV34 )
| ! [SY157: $i] :
( ~ ( member @ ( pair @ SY156 @ SY157 ) @ SV34 )
| ( member @ ( pair @ SY155 @ SY157 ) @ SV34 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(193,plain,
! [SV35: $i] :
( ( ! [SY158: $i] :
( ~ ( member @ ( pair @ SV35 @ SY158 ) @ contract )
| ( member @ SY158 @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(194,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(195,plain,
! [SV36: $i,SV1: $i] :
( ( ( combK
!= ( comb_app @ SV1 @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(196,plain,
! [SV37: $i,SV2: $i] :
( ( ( combS
!= ( comb_app @ SV2 @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(197,plain,
! [SV38: $i,SV3: $i] :
( ( ! [SY159: $i] :
( ! [SY160: $i] :
( ( comb_app @ SV3 @ SV38 )
!= ( comb_app @ SY159 @ SY160 ) )
| ( SV3 = SY159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(198,plain,
! [SV39: $i,SV4: $i] :
( ( ! [SY161: $i,SY162: $i] :
( ( ( comb_app @ SV4 @ SV39 )
!= ( comb_app @ SY161 @ SY162 ) )
| ( SV39 = SY162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(199,plain,
! [SV40: $i,SV5: $i] :
( ( ( SV5 != SV40 )
| ! [SY163: $i,SY164: $i] :
( ( SY163 != SY164 )
| ( ( comb_app @ SV5 @ SY163 )
= ( comb_app @ SV40 @ SY164 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(200,plain,
! [SV6: $i] :
( ( ( ! [SY108: $i] :
~ ( member @ ( comb_app @ SV6 @ SY108 ) @ comb ) )
= $true )
| ( ( member @ SV6 @ comb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(201,plain,
! [SV41: $i,SV7: $i] :
( ( ~ ( member @ ( comb_app @ SV7 @ SV41 ) @ comb )
| ( member @ SV41 @ comb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(202,plain,
! [SV8: $i] :
( ( ( ~ ( member @ SV8 @ comb ) )
= $true )
| ( ( ! [SY110: $i] :
( ~ ( member @ SY110 @ comb )
| ( member @ ( comb_app @ SV8 @ SY110 ) @ comb ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(203,plain,
! [SV9: $i] :
( ( ( ~ ( member @ SV9 @ comb ) )
= $true )
| ( ( member @ ( pair @ SV9 @ SV9 ) @ ( rtrancl @ contract ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(204,plain,
! [SV10: $i] :
( ( ( ~ ( member @ SV10 @ comb ) )
= $true )
| ( ( ! [SY111: $i] :
( ~ ( member @ SY111 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV10 ) @ SY111 ) @ SV10 ) @ contract ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(205,plain,
! [SV11: $i] :
( ( ( ~ ( member @ SV11 @ comb ) )
= $true )
| ( ( ! [SY112: $i] :
( ~ ( member @ SY112 @ comb )
| ! [SY113: $i] :
( ~ ( member @ SY113 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV11 ) @ SY112 ) @ SY113 ) @ ( comb_app @ ( comb_app @ SV11 @ SY113 ) @ ( comb_app @ SY112 @ SY113 ) ) ) @ contract ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(206,plain,
! [SV42: $i,SV12: $i] :
( ( ! [SY165: $i] :
( ~ ( member @ ( pair @ ( comb_app @ SV12 @ SV42 ) @ SY165 ) @ contract )
| ( ap_contractE_c1 @ SV12 @ SV42 @ SY165 )
| ( ap_contractE_c2 @ SV12 @ SV42 @ SY165 )
| ( ap_contractE_c3 @ SV12 @ SV42 @ SY165 )
| ( ap_contractE_c4 @ SV12 @ SV42 @ SY165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(207,plain,
! [SV43: $i,SV13: $i] :
( ( ! [SY166: $i] :
( ~ ( ap_contractE_c1 @ SV13 @ SV43 @ SY166 )
| ( member @ SY166 @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(208,plain,
! [SV44: $i,SV14: $i] :
( ( ! [SY167: $i] :
~ ( ap_contractE_c1 @ SV14 @ SV44 @ SY167 )
| ( member @ SV44 @ comb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(209,plain,
! [SV45: $i,SV15: $i] :
( ( ! [SY168: $i] :
( ~ ( ap_contractE_c1 @ SV15 @ SV45 @ SY168 )
| ( SV15
= ( comb_app @ combK @ SY168 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(210,plain,
! [SV46: $i,SV16: $i] :
( ( ! [SY169: $i] :
( ~ ( ap_contractE_c2 @ SV16 @ SV46 @ SY169 )
| ( member @ ( ap_contractE_sk1p @ SV16 @ SV46 @ SY169 ) @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(211,plain,
! [SV47: $i,SV17: $i] :
( ( ! [SY170: $i] :
( ~ ( ap_contractE_c2 @ SV17 @ SV47 @ SY170 )
| ( member @ ( ap_contractE_sk1q @ SV17 @ SV47 @ SY170 ) @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(212,plain,
! [SV48: $i,SV18: $i] :
( ( ! [SY171: $i] :
~ ( ap_contractE_c2 @ SV18 @ SV48 @ SY171 )
| ( member @ SV48 @ comb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(213,plain,
! [SV49: $i,SV19: $i] :
( ( ! [SY172: $i] :
( ~ ( ap_contractE_c2 @ SV19 @ SV49 @ SY172 )
| ( SY172
= ( comb_app @ ( comb_app @ ( ap_contractE_sk1p @ SV19 @ SV49 @ SY172 ) @ SV49 ) @ ( comb_app @ ( ap_contractE_sk1q @ SV19 @ SV49 @ SY172 ) @ SV49 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(214,plain,
! [SV50: $i,SV20: $i] :
( ( ! [SY173: $i] :
( ~ ( ap_contractE_c2 @ SV20 @ SV50 @ SY173 )
| ( SV20
= ( comb_app @ ( comb_app @ combS @ ( ap_contractE_sk1p @ SV20 @ SV50 @ SY173 ) ) @ ( ap_contractE_sk1q @ SV20 @ SV50 @ SY173 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(215,plain,
! [SV51: $i,SV21: $i] :
( ( ! [SY174: $i] :
( ~ ( ap_contractE_c3 @ SV21 @ SV51 @ SY174 )
| ( member @ ( pair @ SV21 @ ( ap_contractE_sk2q @ SV21 @ SV51 @ SY174 ) ) @ contract ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(216,plain,
! [SV52: $i,SV22: $i] :
( ( ! [SY175: $i] :
~ ( ap_contractE_c3 @ SV22 @ SV52 @ SY175 )
| ( member @ SV52 @ comb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(217,plain,
! [SV53: $i,SV23: $i] :
( ( ! [SY176: $i] :
( ~ ( ap_contractE_c3 @ SV23 @ SV53 @ SY176 )
| ( SY176
= ( comb_app @ ( ap_contractE_sk2q @ SV23 @ SV53 @ SY176 ) @ SV53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(218,plain,
! [SV54: $i,SV24: $i] :
( ( ! [SY177: $i] :
( ~ ( ap_contractE_c4 @ SV24 @ SV54 @ SY177 )
| ( member @ ( pair @ SV54 @ ( ap_contractE_sk3q @ SV24 @ SV54 @ SY177 ) ) @ contract ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(219,plain,
! [SV25: $i] :
( ( ( ! [SY140: $i,SY141: $i] :
~ ( ap_contractE_c4 @ SV25 @ SY140 @ SY141 ) )
= $true )
| ( ( member @ SV25 @ comb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(220,plain,
! [SV55: $i,SV26: $i] :
( ( ! [SY178: $i] :
( ~ ( ap_contractE_c4 @ SV26 @ SV55 @ SY178 )
| ( SY178
= ( comb_app @ SV26 @ ( ap_contractE_sk3q @ SV26 @ SV55 @ SY178 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(221,plain,
! [SV27: $i] :
( ( member @ ( pair @ combK @ SV27 ) @ contract )
= $false ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(222,plain,
! [SV28: $i] :
( ( member @ ( pair @ combS @ SV28 ) @ contract )
= $false ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(223,plain,
! [SV29: $i] :
( ( ( ~ ( member @ SV29 @ comb ) )
= $true )
| ( ( ! [SY144: $i] :
( ~ ( member @ SY144 @ comb )
| ! [SY145: $i] :
( ~ ( member @ ( pair @ SV29 @ SY145 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV29 ) @ SY144 ) @ SY145 ) @ ( rtrancl @ contract ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(224,plain,
! [SV56: $i,SV30: $i] :
( ( ~ ( member @ SV30 @ comb )
| ~ ( member @ SV56 @ comb )
| ! [SY179: $i] :
( ~ ( member @ SY179 @ comb )
| ! [SY180: $i] :
( ~ ( member @ ( pair @ ( comb_app @ ( comb_app @ SV30 @ SY179 ) @ ( comb_app @ SV56 @ SY179 ) ) @ SY180 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV30 ) @ SV56 ) @ SY179 ) @ SY180 ) @ ( rtrancl @ contract ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(225,plain,
! [SV57: $i,SV31: $i] :
( ( ~ ( member @ ( pair @ SV31 @ SV57 ) @ contract )
| ! [SY181: $i] :
( ~ ( member @ SY181 @ comb )
| ! [SY182: $i] :
( ~ ( member @ ( pair @ ( comb_app @ SV57 @ SY181 ) @ SY182 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ SV31 @ SY181 ) @ SY182 ) @ ( rtrancl @ contract ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(226,plain,
! [SV58: $i,SV32: $i] :
( ( ~ ( member @ ( pair @ SV32 @ SV58 ) @ contract )
| ! [SY183: $i] :
( ~ ( member @ SY183 @ comb )
| ! [SY184: $i] :
( ~ ( member @ ( pair @ ( comb_app @ SY183 @ SV58 ) @ SY184 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ SY183 @ SV32 ) @ SY184 ) @ ( rtrancl @ contract ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(227,plain,
! [SV59: $i,SV34: $i] :
( ( ~ ( trans @ SV34 )
| ! [SY185: $i] :
( ~ ( member @ ( pair @ SV59 @ SY185 ) @ SV34 )
| ! [SY186: $i] :
( ~ ( member @ ( pair @ SY185 @ SY186 ) @ SV34 )
| ( member @ ( pair @ SV59 @ SY186 ) @ SV34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(228,plain,
! [SV60: $i,SV35: $i] :
( ( ~ ( member @ ( pair @ SV35 @ SV60 ) @ contract )
| ( member @ SV60 @ comb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(229,plain,
! [SV36: $i,SV1: $i] :
( ( combK
= ( comb_app @ SV1 @ SV36 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(230,plain,
! [SV37: $i,SV2: $i] :
( ( combS
= ( comb_app @ SV2 @ SV37 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(231,plain,
! [SV61: $i,SV38: $i,SV3: $i] :
( ( ! [SY187: $i] :
( ( comb_app @ SV3 @ SV38 )
!= ( comb_app @ SV61 @ SY187 ) )
| ( SV3 = SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(232,plain,
! [SV62: $i,SV39: $i,SV4: $i] :
( ( ! [SY188: $i] :
( ( ( comb_app @ SV4 @ SV39 )
!= ( comb_app @ SV62 @ SY188 ) )
| ( SV39 = SY188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(233,plain,
! [SV40: $i,SV5: $i] :
( ( ( ( SV5 != SV40 ) )
= $true )
| ( ( ! [SY163: $i,SY164: $i] :
( ( SY163 != SY164 )
| ( ( comb_app @ SV5 @ SY163 )
= ( comb_app @ SV40 @ SY164 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[199]) ).
thf(234,plain,
! [SV63: $i,SV6: $i] :
( ( ( ~ ( member @ ( comb_app @ SV6 @ SV63 ) @ comb ) )
= $true )
| ( ( member @ SV6 @ comb )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(235,plain,
! [SV41: $i,SV7: $i] :
( ( ( ~ ( member @ ( comb_app @ SV7 @ SV41 ) @ comb ) )
= $true )
| ( ( member @ SV41 @ comb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(236,plain,
! [SV8: $i] :
( ( ( member @ SV8 @ comb )
= $false )
| ( ( ! [SY110: $i] :
( ~ ( member @ SY110 @ comb )
| ( member @ ( comb_app @ SV8 @ SY110 ) @ comb ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(237,plain,
! [SV9: $i] :
( ( ( member @ SV9 @ comb )
= $false )
| ( ( member @ ( pair @ SV9 @ SV9 ) @ ( rtrancl @ contract ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(238,plain,
! [SV10: $i] :
( ( ( member @ SV10 @ comb )
= $false )
| ( ( ! [SY111: $i] :
( ~ ( member @ SY111 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV10 ) @ SY111 ) @ SV10 ) @ contract ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(239,plain,
! [SV11: $i] :
( ( ( member @ SV11 @ comb )
= $false )
| ( ( ! [SY112: $i] :
( ~ ( member @ SY112 @ comb )
| ! [SY113: $i] :
( ~ ( member @ SY113 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV11 ) @ SY112 ) @ SY113 ) @ ( comb_app @ ( comb_app @ SV11 @ SY113 ) @ ( comb_app @ SY112 @ SY113 ) ) ) @ contract ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(240,plain,
! [SV64: $i,SV42: $i,SV12: $i] :
( ( ~ ( member @ ( pair @ ( comb_app @ SV12 @ SV42 ) @ SV64 ) @ contract )
| ( ap_contractE_c1 @ SV12 @ SV42 @ SV64 )
| ( ap_contractE_c2 @ SV12 @ SV42 @ SV64 )
| ( ap_contractE_c3 @ SV12 @ SV42 @ SV64 )
| ( ap_contractE_c4 @ SV12 @ SV42 @ SV64 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(241,plain,
! [SV65: $i,SV43: $i,SV13: $i] :
( ( ~ ( ap_contractE_c1 @ SV13 @ SV43 @ SV65 )
| ( member @ SV65 @ comb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(242,plain,
! [SV44: $i,SV14: $i] :
( ( ( ! [SY167: $i] :
~ ( ap_contractE_c1 @ SV14 @ SV44 @ SY167 ) )
= $true )
| ( ( member @ SV44 @ comb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[208]) ).
thf(243,plain,
! [SV66: $i,SV45: $i,SV15: $i] :
( ( ~ ( ap_contractE_c1 @ SV15 @ SV45 @ SV66 )
| ( SV15
= ( comb_app @ combK @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(244,plain,
! [SV67: $i,SV46: $i,SV16: $i] :
( ( ~ ( ap_contractE_c2 @ SV16 @ SV46 @ SV67 )
| ( member @ ( ap_contractE_sk1p @ SV16 @ SV46 @ SV67 ) @ comb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(245,plain,
! [SV68: $i,SV47: $i,SV17: $i] :
( ( ~ ( ap_contractE_c2 @ SV17 @ SV47 @ SV68 )
| ( member @ ( ap_contractE_sk1q @ SV17 @ SV47 @ SV68 ) @ comb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(246,plain,
! [SV48: $i,SV18: $i] :
( ( ( ! [SY171: $i] :
~ ( ap_contractE_c2 @ SV18 @ SV48 @ SY171 ) )
= $true )
| ( ( member @ SV48 @ comb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[212]) ).
thf(247,plain,
! [SV69: $i,SV49: $i,SV19: $i] :
( ( ~ ( ap_contractE_c2 @ SV19 @ SV49 @ SV69 )
| ( SV69
= ( comb_app @ ( comb_app @ ( ap_contractE_sk1p @ SV19 @ SV49 @ SV69 ) @ SV49 ) @ ( comb_app @ ( ap_contractE_sk1q @ SV19 @ SV49 @ SV69 ) @ SV49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(248,plain,
! [SV70: $i,SV50: $i,SV20: $i] :
( ( ~ ( ap_contractE_c2 @ SV20 @ SV50 @ SV70 )
| ( SV20
= ( comb_app @ ( comb_app @ combS @ ( ap_contractE_sk1p @ SV20 @ SV50 @ SV70 ) ) @ ( ap_contractE_sk1q @ SV20 @ SV50 @ SV70 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(249,plain,
! [SV71: $i,SV51: $i,SV21: $i] :
( ( ~ ( ap_contractE_c3 @ SV21 @ SV51 @ SV71 )
| ( member @ ( pair @ SV21 @ ( ap_contractE_sk2q @ SV21 @ SV51 @ SV71 ) ) @ contract ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(250,plain,
! [SV52: $i,SV22: $i] :
( ( ( ! [SY175: $i] :
~ ( ap_contractE_c3 @ SV22 @ SV52 @ SY175 ) )
= $true )
| ( ( member @ SV52 @ comb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(251,plain,
! [SV72: $i,SV53: $i,SV23: $i] :
( ( ~ ( ap_contractE_c3 @ SV23 @ SV53 @ SV72 )
| ( SV72
= ( comb_app @ ( ap_contractE_sk2q @ SV23 @ SV53 @ SV72 ) @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(252,plain,
! [SV73: $i,SV54: $i,SV24: $i] :
( ( ~ ( ap_contractE_c4 @ SV24 @ SV54 @ SV73 )
| ( member @ ( pair @ SV54 @ ( ap_contractE_sk3q @ SV24 @ SV54 @ SV73 ) ) @ contract ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(253,plain,
! [SV74: $i,SV25: $i] :
( ( ( ! [SY189: $i] :
~ ( ap_contractE_c4 @ SV25 @ SV74 @ SY189 ) )
= $true )
| ( ( member @ SV25 @ comb )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(254,plain,
! [SV75: $i,SV55: $i,SV26: $i] :
( ( ~ ( ap_contractE_c4 @ SV26 @ SV55 @ SV75 )
| ( SV75
= ( comb_app @ SV26 @ ( ap_contractE_sk3q @ SV26 @ SV55 @ SV75 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(255,plain,
! [SV29: $i] :
( ( ( member @ SV29 @ comb )
= $false )
| ( ( ! [SY144: $i] :
( ~ ( member @ SY144 @ comb )
| ! [SY145: $i] :
( ~ ( member @ ( pair @ SV29 @ SY145 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV29 ) @ SY144 ) @ SY145 ) @ ( rtrancl @ contract ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(256,plain,
! [SV56: $i,SV30: $i] :
( ( ( ~ ( member @ SV30 @ comb ) )
= $true )
| ( ( ~ ( member @ SV56 @ comb )
| ! [SY179: $i] :
( ~ ( member @ SY179 @ comb )
| ! [SY180: $i] :
( ~ ( member @ ( pair @ ( comb_app @ ( comb_app @ SV30 @ SY179 ) @ ( comb_app @ SV56 @ SY179 ) ) @ SY180 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV30 ) @ SV56 ) @ SY179 ) @ SY180 ) @ ( rtrancl @ contract ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[224]) ).
thf(257,plain,
! [SV57: $i,SV31: $i] :
( ( ( ~ ( member @ ( pair @ SV31 @ SV57 ) @ contract ) )
= $true )
| ( ( ! [SY181: $i] :
( ~ ( member @ SY181 @ comb )
| ! [SY182: $i] :
( ~ ( member @ ( pair @ ( comb_app @ SV57 @ SY181 ) @ SY182 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ SV31 @ SY181 ) @ SY182 ) @ ( rtrancl @ contract ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(258,plain,
! [SV58: $i,SV32: $i] :
( ( ( ~ ( member @ ( pair @ SV32 @ SV58 ) @ contract ) )
= $true )
| ( ( ! [SY183: $i] :
( ~ ( member @ SY183 @ comb )
| ! [SY184: $i] :
( ~ ( member @ ( pair @ ( comb_app @ SY183 @ SV58 ) @ SY184 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ SY183 @ SV32 ) @ SY184 ) @ ( rtrancl @ contract ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[226]) ).
thf(259,plain,
! [SV59: $i,SV34: $i] :
( ( ( ~ ( trans @ SV34 ) )
= $true )
| ( ( ! [SY185: $i] :
( ~ ( member @ ( pair @ SV59 @ SY185 ) @ SV34 )
| ! [SY186: $i] :
( ~ ( member @ ( pair @ SY185 @ SY186 ) @ SV34 )
| ( member @ ( pair @ SV59 @ SY186 ) @ SV34 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(260,plain,
! [SV60: $i,SV35: $i] :
( ( ( ~ ( member @ ( pair @ SV35 @ SV60 ) @ contract ) )
= $true )
| ( ( member @ SV60 @ comb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[228]) ).
thf(261,plain,
! [SV61: $i,SV38: $i,SV3: $i] :
( ( ( ! [SY187: $i] :
( ( comb_app @ SV3 @ SV38 )
!= ( comb_app @ SV61 @ SY187 ) ) )
= $true )
| ( ( SV3 = SV61 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[231]) ).
thf(262,plain,
! [SV76: $i,SV62: $i,SV39: $i,SV4: $i] :
( ( ( ( comb_app @ SV4 @ SV39 )
!= ( comb_app @ SV62 @ SV76 ) )
| ( SV39 = SV76 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(263,plain,
! [SV40: $i,SV5: $i] :
( ( ( SV5 = SV40 )
= $false )
| ( ( ! [SY163: $i,SY164: $i] :
( ( SY163 != SY164 )
| ( ( comb_app @ SV5 @ SY163 )
= ( comb_app @ SV40 @ SY164 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(264,plain,
! [SV63: $i,SV6: $i] :
( ( ( member @ ( comb_app @ SV6 @ SV63 ) @ comb )
= $false )
| ( ( member @ SV6 @ comb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(265,plain,
! [SV41: $i,SV7: $i] :
( ( ( member @ ( comb_app @ SV7 @ SV41 ) @ comb )
= $false )
| ( ( member @ SV41 @ comb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(266,plain,
! [SV8: $i,SV77: $i] :
( ( ( ~ ( member @ SV77 @ comb )
| ( member @ ( comb_app @ SV8 @ SV77 ) @ comb ) )
= $true )
| ( ( member @ SV8 @ comb )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[236]) ).
thf(267,plain,
! [SV10: $i,SV78: $i] :
( ( ( ~ ( member @ SV78 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV10 ) @ SV78 ) @ SV10 ) @ contract ) )
= $true )
| ( ( member @ SV10 @ comb )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(268,plain,
! [SV11: $i,SV79: $i] :
( ( ( ~ ( member @ SV79 @ comb )
| ! [SY190: $i] :
( ~ ( member @ SY190 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV11 ) @ SV79 ) @ SY190 ) @ ( comb_app @ ( comb_app @ SV11 @ SY190 ) @ ( comb_app @ SV79 @ SY190 ) ) ) @ contract ) ) )
= $true )
| ( ( member @ SV11 @ comb )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(269,plain,
! [SV64: $i,SV42: $i,SV12: $i] :
( ( ( ~ ( member @ ( pair @ ( comb_app @ SV12 @ SV42 ) @ SV64 ) @ contract ) )
= $true )
| ( ( ( ap_contractE_c1 @ SV12 @ SV42 @ SV64 )
| ( ap_contractE_c2 @ SV12 @ SV42 @ SV64 )
| ( ap_contractE_c3 @ SV12 @ SV42 @ SV64 )
| ( ap_contractE_c4 @ SV12 @ SV42 @ SV64 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[240]) ).
thf(270,plain,
! [SV65: $i,SV43: $i,SV13: $i] :
( ( ( ~ ( ap_contractE_c1 @ SV13 @ SV43 @ SV65 ) )
= $true )
| ( ( member @ SV65 @ comb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[241]) ).
thf(271,plain,
! [SV80: $i,SV44: $i,SV14: $i] :
( ( ( ~ ( ap_contractE_c1 @ SV14 @ SV44 @ SV80 ) )
= $true )
| ( ( member @ SV44 @ comb )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(272,plain,
! [SV66: $i,SV45: $i,SV15: $i] :
( ( ( ~ ( ap_contractE_c1 @ SV15 @ SV45 @ SV66 ) )
= $true )
| ( ( SV15
= ( comb_app @ combK @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[243]) ).
thf(273,plain,
! [SV67: $i,SV46: $i,SV16: $i] :
( ( ( ~ ( ap_contractE_c2 @ SV16 @ SV46 @ SV67 ) )
= $true )
| ( ( member @ ( ap_contractE_sk1p @ SV16 @ SV46 @ SV67 ) @ comb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[244]) ).
thf(274,plain,
! [SV68: $i,SV47: $i,SV17: $i] :
( ( ( ~ ( ap_contractE_c2 @ SV17 @ SV47 @ SV68 ) )
= $true )
| ( ( member @ ( ap_contractE_sk1q @ SV17 @ SV47 @ SV68 ) @ comb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[245]) ).
thf(275,plain,
! [SV81: $i,SV48: $i,SV18: $i] :
( ( ( ~ ( ap_contractE_c2 @ SV18 @ SV48 @ SV81 ) )
= $true )
| ( ( member @ SV48 @ comb )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[246]) ).
thf(276,plain,
! [SV69: $i,SV49: $i,SV19: $i] :
( ( ( ~ ( ap_contractE_c2 @ SV19 @ SV49 @ SV69 ) )
= $true )
| ( ( SV69
= ( comb_app @ ( comb_app @ ( ap_contractE_sk1p @ SV19 @ SV49 @ SV69 ) @ SV49 ) @ ( comb_app @ ( ap_contractE_sk1q @ SV19 @ SV49 @ SV69 ) @ SV49 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[247]) ).
thf(277,plain,
! [SV70: $i,SV50: $i,SV20: $i] :
( ( ( ~ ( ap_contractE_c2 @ SV20 @ SV50 @ SV70 ) )
= $true )
| ( ( SV20
= ( comb_app @ ( comb_app @ combS @ ( ap_contractE_sk1p @ SV20 @ SV50 @ SV70 ) ) @ ( ap_contractE_sk1q @ SV20 @ SV50 @ SV70 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[248]) ).
thf(278,plain,
! [SV71: $i,SV51: $i,SV21: $i] :
( ( ( ~ ( ap_contractE_c3 @ SV21 @ SV51 @ SV71 ) )
= $true )
| ( ( member @ ( pair @ SV21 @ ( ap_contractE_sk2q @ SV21 @ SV51 @ SV71 ) ) @ contract )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[249]) ).
thf(279,plain,
! [SV82: $i,SV52: $i,SV22: $i] :
( ( ( ~ ( ap_contractE_c3 @ SV22 @ SV52 @ SV82 ) )
= $true )
| ( ( member @ SV52 @ comb )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(280,plain,
! [SV72: $i,SV53: $i,SV23: $i] :
( ( ( ~ ( ap_contractE_c3 @ SV23 @ SV53 @ SV72 ) )
= $true )
| ( ( SV72
= ( comb_app @ ( ap_contractE_sk2q @ SV23 @ SV53 @ SV72 ) @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[251]) ).
thf(281,plain,
! [SV73: $i,SV54: $i,SV24: $i] :
( ( ( ~ ( ap_contractE_c4 @ SV24 @ SV54 @ SV73 ) )
= $true )
| ( ( member @ ( pair @ SV54 @ ( ap_contractE_sk3q @ SV24 @ SV54 @ SV73 ) ) @ contract )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[252]) ).
thf(282,plain,
! [SV83: $i,SV74: $i,SV25: $i] :
( ( ( ~ ( ap_contractE_c4 @ SV25 @ SV74 @ SV83 ) )
= $true )
| ( ( member @ SV25 @ comb )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[253]) ).
thf(283,plain,
! [SV75: $i,SV55: $i,SV26: $i] :
( ( ( ~ ( ap_contractE_c4 @ SV26 @ SV55 @ SV75 ) )
= $true )
| ( ( SV75
= ( comb_app @ SV26 @ ( ap_contractE_sk3q @ SV26 @ SV55 @ SV75 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[254]) ).
thf(284,plain,
! [SV29: $i,SV84: $i] :
( ( ( ~ ( member @ SV84 @ comb )
| ! [SY191: $i] :
( ~ ( member @ ( pair @ SV29 @ SY191 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV29 ) @ SV84 ) @ SY191 ) @ ( rtrancl @ contract ) ) ) )
= $true )
| ( ( member @ SV29 @ comb )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(285,plain,
! [SV56: $i,SV30: $i] :
( ( ( member @ SV30 @ comb )
= $false )
| ( ( ~ ( member @ SV56 @ comb )
| ! [SY179: $i] :
( ~ ( member @ SY179 @ comb )
| ! [SY180: $i] :
( ~ ( member @ ( pair @ ( comb_app @ ( comb_app @ SV30 @ SY179 ) @ ( comb_app @ SV56 @ SY179 ) ) @ SY180 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV30 ) @ SV56 ) @ SY179 ) @ SY180 ) @ ( rtrancl @ contract ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(286,plain,
! [SV57: $i,SV31: $i] :
( ( ( member @ ( pair @ SV31 @ SV57 ) @ contract )
= $false )
| ( ( ! [SY181: $i] :
( ~ ( member @ SY181 @ comb )
| ! [SY182: $i] :
( ~ ( member @ ( pair @ ( comb_app @ SV57 @ SY181 ) @ SY182 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ SV31 @ SY181 ) @ SY182 ) @ ( rtrancl @ contract ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(287,plain,
! [SV58: $i,SV32: $i] :
( ( ( member @ ( pair @ SV32 @ SV58 ) @ contract )
= $false )
| ( ( ! [SY183: $i] :
( ~ ( member @ SY183 @ comb )
| ! [SY184: $i] :
( ~ ( member @ ( pair @ ( comb_app @ SY183 @ SV58 ) @ SY184 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ SY183 @ SV32 ) @ SY184 ) @ ( rtrancl @ contract ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(288,plain,
! [SV59: $i,SV34: $i] :
( ( ( trans @ SV34 )
= $false )
| ( ( ! [SY185: $i] :
( ~ ( member @ ( pair @ SV59 @ SY185 ) @ SV34 )
| ! [SY186: $i] :
( ~ ( member @ ( pair @ SY185 @ SY186 ) @ SV34 )
| ( member @ ( pair @ SV59 @ SY186 ) @ SV34 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(289,plain,
! [SV60: $i,SV35: $i] :
( ( ( member @ ( pair @ SV35 @ SV60 ) @ contract )
= $false )
| ( ( member @ SV60 @ comb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(290,plain,
! [SV85: $i,SV61: $i,SV38: $i,SV3: $i] :
( ( ( ( ( comb_app @ SV3 @ SV38 )
!= ( comb_app @ SV61 @ SV85 ) ) )
= $true )
| ( ( SV3 = SV61 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(291,plain,
! [SV76: $i,SV62: $i,SV39: $i,SV4: $i] :
( ( ( ( ( comb_app @ SV4 @ SV39 )
!= ( comb_app @ SV62 @ SV76 ) ) )
= $true )
| ( ( SV39 = SV76 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[262]) ).
thf(292,plain,
! [SV40: $i,SV5: $i,SV86: $i] :
( ( ( ! [SY192: $i] :
( ( SV86 != SY192 )
| ( ( comb_app @ SV5 @ SV86 )
= ( comb_app @ SV40 @ SY192 ) ) ) )
= $true )
| ( ( SV5 = SV40 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(293,plain,
! [SV8: $i,SV77: $i] :
( ( ( ~ ( member @ SV77 @ comb ) )
= $true )
| ( ( member @ ( comb_app @ SV8 @ SV77 ) @ comb )
= $true )
| ( ( member @ SV8 @ comb )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[266]) ).
thf(294,plain,
! [SV10: $i,SV78: $i] :
( ( ( ~ ( member @ SV78 @ comb ) )
= $true )
| ( ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV10 ) @ SV78 ) @ SV10 ) @ contract )
= $true )
| ( ( member @ SV10 @ comb )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[267]) ).
thf(295,plain,
! [SV11: $i,SV79: $i] :
( ( ( ~ ( member @ SV79 @ comb ) )
= $true )
| ( ( ! [SY190: $i] :
( ~ ( member @ SY190 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV11 ) @ SV79 ) @ SY190 ) @ ( comb_app @ ( comb_app @ SV11 @ SY190 ) @ ( comb_app @ SV79 @ SY190 ) ) ) @ contract ) ) )
= $true )
| ( ( member @ SV11 @ comb )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[268]) ).
thf(296,plain,
! [SV64: $i,SV42: $i,SV12: $i] :
( ( ( member @ ( pair @ ( comb_app @ SV12 @ SV42 ) @ SV64 ) @ contract )
= $false )
| ( ( ( ap_contractE_c1 @ SV12 @ SV42 @ SV64 )
| ( ap_contractE_c2 @ SV12 @ SV42 @ SV64 )
| ( ap_contractE_c3 @ SV12 @ SV42 @ SV64 )
| ( ap_contractE_c4 @ SV12 @ SV42 @ SV64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(297,plain,
! [SV65: $i,SV43: $i,SV13: $i] :
( ( ( ap_contractE_c1 @ SV13 @ SV43 @ SV65 )
= $false )
| ( ( member @ SV65 @ comb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(298,plain,
! [SV80: $i,SV44: $i,SV14: $i] :
( ( ( ap_contractE_c1 @ SV14 @ SV44 @ SV80 )
= $false )
| ( ( member @ SV44 @ comb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[271]) ).
thf(299,plain,
! [SV66: $i,SV45: $i,SV15: $i] :
( ( ( ap_contractE_c1 @ SV15 @ SV45 @ SV66 )
= $false )
| ( ( SV15
= ( comb_app @ combK @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(300,plain,
! [SV67: $i,SV46: $i,SV16: $i] :
( ( ( ap_contractE_c2 @ SV16 @ SV46 @ SV67 )
= $false )
| ( ( member @ ( ap_contractE_sk1p @ SV16 @ SV46 @ SV67 ) @ comb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[273]) ).
thf(301,plain,
! [SV68: $i,SV47: $i,SV17: $i] :
( ( ( ap_contractE_c2 @ SV17 @ SV47 @ SV68 )
= $false )
| ( ( member @ ( ap_contractE_sk1q @ SV17 @ SV47 @ SV68 ) @ comb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(302,plain,
! [SV81: $i,SV48: $i,SV18: $i] :
( ( ( ap_contractE_c2 @ SV18 @ SV48 @ SV81 )
= $false )
| ( ( member @ SV48 @ comb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(303,plain,
! [SV69: $i,SV49: $i,SV19: $i] :
( ( ( ap_contractE_c2 @ SV19 @ SV49 @ SV69 )
= $false )
| ( ( SV69
= ( comb_app @ ( comb_app @ ( ap_contractE_sk1p @ SV19 @ SV49 @ SV69 ) @ SV49 ) @ ( comb_app @ ( ap_contractE_sk1q @ SV19 @ SV49 @ SV69 ) @ SV49 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(304,plain,
! [SV70: $i,SV50: $i,SV20: $i] :
( ( ( ap_contractE_c2 @ SV20 @ SV50 @ SV70 )
= $false )
| ( ( SV20
= ( comb_app @ ( comb_app @ combS @ ( ap_contractE_sk1p @ SV20 @ SV50 @ SV70 ) ) @ ( ap_contractE_sk1q @ SV20 @ SV50 @ SV70 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(305,plain,
! [SV71: $i,SV51: $i,SV21: $i] :
( ( ( ap_contractE_c3 @ SV21 @ SV51 @ SV71 )
= $false )
| ( ( member @ ( pair @ SV21 @ ( ap_contractE_sk2q @ SV21 @ SV51 @ SV71 ) ) @ contract )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(306,plain,
! [SV82: $i,SV52: $i,SV22: $i] :
( ( ( ap_contractE_c3 @ SV22 @ SV52 @ SV82 )
= $false )
| ( ( member @ SV52 @ comb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(307,plain,
! [SV72: $i,SV53: $i,SV23: $i] :
( ( ( ap_contractE_c3 @ SV23 @ SV53 @ SV72 )
= $false )
| ( ( SV72
= ( comb_app @ ( ap_contractE_sk2q @ SV23 @ SV53 @ SV72 ) @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(308,plain,
! [SV73: $i,SV54: $i,SV24: $i] :
( ( ( ap_contractE_c4 @ SV24 @ SV54 @ SV73 )
= $false )
| ( ( member @ ( pair @ SV54 @ ( ap_contractE_sk3q @ SV24 @ SV54 @ SV73 ) ) @ contract )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(309,plain,
! [SV83: $i,SV74: $i,SV25: $i] :
( ( ( ap_contractE_c4 @ SV25 @ SV74 @ SV83 )
= $false )
| ( ( member @ SV25 @ comb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[282]) ).
thf(310,plain,
! [SV75: $i,SV55: $i,SV26: $i] :
( ( ( ap_contractE_c4 @ SV26 @ SV55 @ SV75 )
= $false )
| ( ( SV75
= ( comb_app @ SV26 @ ( ap_contractE_sk3q @ SV26 @ SV55 @ SV75 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(311,plain,
! [SV29: $i,SV84: $i] :
( ( ( ~ ( member @ SV84 @ comb ) )
= $true )
| ( ( ! [SY191: $i] :
( ~ ( member @ ( pair @ SV29 @ SY191 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV29 ) @ SV84 ) @ SY191 ) @ ( rtrancl @ contract ) ) ) )
= $true )
| ( ( member @ SV29 @ comb )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[284]) ).
thf(312,plain,
! [SV30: $i,SV56: $i] :
( ( ( ~ ( member @ SV56 @ comb ) )
= $true )
| ( ( ! [SY179: $i] :
( ~ ( member @ SY179 @ comb )
| ! [SY180: $i] :
( ~ ( member @ ( pair @ ( comb_app @ ( comb_app @ SV30 @ SY179 ) @ ( comb_app @ SV56 @ SY179 ) ) @ SY180 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV30 ) @ SV56 ) @ SY179 ) @ SY180 ) @ ( rtrancl @ contract ) ) ) ) )
= $true )
| ( ( member @ SV30 @ comb )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[285]) ).
thf(313,plain,
! [SV31: $i,SV57: $i,SV87: $i] :
( ( ( ~ ( member @ SV87 @ comb )
| ! [SY193: $i] :
( ~ ( member @ ( pair @ ( comb_app @ SV57 @ SV87 ) @ SY193 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ SV31 @ SV87 ) @ SY193 ) @ ( rtrancl @ contract ) ) ) )
= $true )
| ( ( member @ ( pair @ SV31 @ SV57 ) @ contract )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(314,plain,
! [SV32: $i,SV58: $i,SV88: $i] :
( ( ( ~ ( member @ SV88 @ comb )
| ! [SY194: $i] :
( ~ ( member @ ( pair @ ( comb_app @ SV88 @ SV58 ) @ SY194 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ SV88 @ SV32 ) @ SY194 ) @ ( rtrancl @ contract ) ) ) )
= $true )
| ( ( member @ ( pair @ SV32 @ SV58 ) @ contract )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(315,plain,
! [SV34: $i,SV89: $i,SV59: $i] :
( ( ( ~ ( member @ ( pair @ SV59 @ SV89 ) @ SV34 )
| ! [SY195: $i] :
( ~ ( member @ ( pair @ SV89 @ SY195 ) @ SV34 )
| ( member @ ( pair @ SV59 @ SY195 ) @ SV34 ) ) )
= $true )
| ( ( trans @ SV34 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(316,plain,
! [SV85: $i,SV61: $i,SV38: $i,SV3: $i] :
( ( ( ( comb_app @ SV3 @ SV38 )
= ( comb_app @ SV61 @ SV85 ) )
= $false )
| ( ( SV3 = SV61 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(317,plain,
! [SV76: $i,SV62: $i,SV39: $i,SV4: $i] :
( ( ( ( comb_app @ SV4 @ SV39 )
= ( comb_app @ SV62 @ SV76 ) )
= $false )
| ( ( SV39 = SV76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(318,plain,
! [SV40: $i,SV5: $i,SV90: $i,SV86: $i] :
( ( ( ( SV86 != SV90 )
| ( ( comb_app @ SV5 @ SV86 )
= ( comb_app @ SV40 @ SV90 ) ) )
= $true )
| ( ( SV5 = SV40 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[292]) ).
thf(319,plain,
! [SV8: $i,SV77: $i] :
( ( ( member @ SV77 @ comb )
= $false )
| ( ( member @ ( comb_app @ SV8 @ SV77 ) @ comb )
= $true )
| ( ( member @ SV8 @ comb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[293]) ).
thf(320,plain,
! [SV10: $i,SV78: $i] :
( ( ( member @ SV78 @ comb )
= $false )
| ( ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV10 ) @ SV78 ) @ SV10 ) @ contract )
= $true )
| ( ( member @ SV10 @ comb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[294]) ).
thf(321,plain,
! [SV11: $i,SV79: $i] :
( ( ( member @ SV79 @ comb )
= $false )
| ( ( ! [SY190: $i] :
( ~ ( member @ SY190 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV11 ) @ SV79 ) @ SY190 ) @ ( comb_app @ ( comb_app @ SV11 @ SY190 ) @ ( comb_app @ SV79 @ SY190 ) ) ) @ contract ) ) )
= $true )
| ( ( member @ SV11 @ comb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(322,plain,
! [SV64: $i,SV42: $i,SV12: $i] :
( ( ( ap_contractE_c1 @ SV12 @ SV42 @ SV64 )
= $true )
| ( ( ( ap_contractE_c2 @ SV12 @ SV42 @ SV64 )
| ( ap_contractE_c3 @ SV12 @ SV42 @ SV64 )
| ( ap_contractE_c4 @ SV12 @ SV42 @ SV64 ) )
= $true )
| ( ( member @ ( pair @ ( comb_app @ SV12 @ SV42 ) @ SV64 ) @ contract )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[296]) ).
thf(323,plain,
! [SV29: $i,SV84: $i] :
( ( ( member @ SV84 @ comb )
= $false )
| ( ( ! [SY191: $i] :
( ~ ( member @ ( pair @ SV29 @ SY191 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV29 ) @ SV84 ) @ SY191 ) @ ( rtrancl @ contract ) ) ) )
= $true )
| ( ( member @ SV29 @ comb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[311]) ).
thf(324,plain,
! [SV30: $i,SV56: $i] :
( ( ( member @ SV56 @ comb )
= $false )
| ( ( ! [SY179: $i] :
( ~ ( member @ SY179 @ comb )
| ! [SY180: $i] :
( ~ ( member @ ( pair @ ( comb_app @ ( comb_app @ SV30 @ SY179 ) @ ( comb_app @ SV56 @ SY179 ) ) @ SY180 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV30 ) @ SV56 ) @ SY179 ) @ SY180 ) @ ( rtrancl @ contract ) ) ) ) )
= $true )
| ( ( member @ SV30 @ comb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(325,plain,
! [SV31: $i,SV57: $i,SV87: $i] :
( ( ( ~ ( member @ SV87 @ comb ) )
= $true )
| ( ( ! [SY193: $i] :
( ~ ( member @ ( pair @ ( comb_app @ SV57 @ SV87 ) @ SY193 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ SV31 @ SV87 ) @ SY193 ) @ ( rtrancl @ contract ) ) ) )
= $true )
| ( ( member @ ( pair @ SV31 @ SV57 ) @ contract )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[313]) ).
thf(326,plain,
! [SV32: $i,SV58: $i,SV88: $i] :
( ( ( ~ ( member @ SV88 @ comb ) )
= $true )
| ( ( ! [SY194: $i] :
( ~ ( member @ ( pair @ ( comb_app @ SV88 @ SV58 ) @ SY194 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ SV88 @ SV32 ) @ SY194 ) @ ( rtrancl @ contract ) ) ) )
= $true )
| ( ( member @ ( pair @ SV32 @ SV58 ) @ contract )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[314]) ).
thf(327,plain,
! [SV34: $i,SV89: $i,SV59: $i] :
( ( ( ~ ( member @ ( pair @ SV59 @ SV89 ) @ SV34 ) )
= $true )
| ( ( ! [SY195: $i] :
( ~ ( member @ ( pair @ SV89 @ SY195 ) @ SV34 )
| ( member @ ( pair @ SV59 @ SY195 ) @ SV34 ) ) )
= $true )
| ( ( trans @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[315]) ).
thf(328,plain,
! [SV40: $i,SV5: $i,SV90: $i,SV86: $i] :
( ( ( ( SV86 != SV90 ) )
= $true )
| ( ( ( comb_app @ SV5 @ SV86 )
= ( comb_app @ SV40 @ SV90 ) )
= $true )
| ( ( SV5 = SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[318]) ).
thf(329,plain,
! [SV79: $i,SV11: $i,SV91: $i] :
( ( ( ~ ( member @ SV91 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV11 ) @ SV79 ) @ SV91 ) @ ( comb_app @ ( comb_app @ SV11 @ SV91 ) @ ( comb_app @ SV79 @ SV91 ) ) ) @ contract ) )
= $true )
| ( ( member @ SV79 @ comb )
= $false )
| ( ( member @ SV11 @ comb )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[321]) ).
thf(330,plain,
! [SV64: $i,SV42: $i,SV12: $i] :
( ( ( ap_contractE_c2 @ SV12 @ SV42 @ SV64 )
= $true )
| ( ( ( ap_contractE_c3 @ SV12 @ SV42 @ SV64 )
| ( ap_contractE_c4 @ SV12 @ SV42 @ SV64 ) )
= $true )
| ( ( ap_contractE_c1 @ SV12 @ SV42 @ SV64 )
= $true )
| ( ( member @ ( pair @ ( comb_app @ SV12 @ SV42 ) @ SV64 ) @ contract )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[322]) ).
thf(331,plain,
! [SV84: $i,SV92: $i,SV29: $i] :
( ( ( ~ ( member @ ( pair @ SV29 @ SV92 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV29 ) @ SV84 ) @ SV92 ) @ ( rtrancl @ contract ) ) )
= $true )
| ( ( member @ SV84 @ comb )
= $false )
| ( ( member @ SV29 @ comb )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[323]) ).
thf(332,plain,
! [SV56: $i,SV30: $i,SV93: $i] :
( ( ( ~ ( member @ SV93 @ comb )
| ! [SY196: $i] :
( ~ ( member @ ( pair @ ( comb_app @ ( comb_app @ SV30 @ SV93 ) @ ( comb_app @ SV56 @ SV93 ) ) @ SY196 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV30 ) @ SV56 ) @ SV93 ) @ SY196 ) @ ( rtrancl @ contract ) ) ) )
= $true )
| ( ( member @ SV56 @ comb )
= $false )
| ( ( member @ SV30 @ comb )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(333,plain,
! [SV31: $i,SV57: $i,SV87: $i] :
( ( ( member @ SV87 @ comb )
= $false )
| ( ( ! [SY193: $i] :
( ~ ( member @ ( pair @ ( comb_app @ SV57 @ SV87 ) @ SY193 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ SV31 @ SV87 ) @ SY193 ) @ ( rtrancl @ contract ) ) ) )
= $true )
| ( ( member @ ( pair @ SV31 @ SV57 ) @ contract )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(334,plain,
! [SV32: $i,SV58: $i,SV88: $i] :
( ( ( member @ SV88 @ comb )
= $false )
| ( ( ! [SY194: $i] :
( ~ ( member @ ( pair @ ( comb_app @ SV88 @ SV58 ) @ SY194 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ SV88 @ SV32 ) @ SY194 ) @ ( rtrancl @ contract ) ) ) )
= $true )
| ( ( member @ ( pair @ SV32 @ SV58 ) @ contract )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(335,plain,
! [SV34: $i,SV89: $i,SV59: $i] :
( ( ( member @ ( pair @ SV59 @ SV89 ) @ SV34 )
= $false )
| ( ( ! [SY195: $i] :
( ~ ( member @ ( pair @ SV89 @ SY195 ) @ SV34 )
| ( member @ ( pair @ SV59 @ SY195 ) @ SV34 ) ) )
= $true )
| ( ( trans @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[327]) ).
thf(336,plain,
! [SV40: $i,SV5: $i,SV90: $i,SV86: $i] :
( ( ( SV86 = SV90 )
= $false )
| ( ( ( comb_app @ SV5 @ SV86 )
= ( comb_app @ SV40 @ SV90 ) )
= $true )
| ( ( SV5 = SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(337,plain,
! [SV79: $i,SV11: $i,SV91: $i] :
( ( ( ~ ( member @ SV91 @ comb ) )
= $true )
| ( ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV11 ) @ SV79 ) @ SV91 ) @ ( comb_app @ ( comb_app @ SV11 @ SV91 ) @ ( comb_app @ SV79 @ SV91 ) ) ) @ contract )
= $true )
| ( ( member @ SV79 @ comb )
= $false )
| ( ( member @ SV11 @ comb )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[329]) ).
thf(338,plain,
! [SV64: $i,SV42: $i,SV12: $i] :
( ( ( ap_contractE_c3 @ SV12 @ SV42 @ SV64 )
= $true )
| ( ( ap_contractE_c4 @ SV12 @ SV42 @ SV64 )
= $true )
| ( ( ap_contractE_c2 @ SV12 @ SV42 @ SV64 )
= $true )
| ( ( ap_contractE_c1 @ SV12 @ SV42 @ SV64 )
= $true )
| ( ( member @ ( pair @ ( comb_app @ SV12 @ SV42 ) @ SV64 ) @ contract )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[330]) ).
thf(339,plain,
! [SV84: $i,SV92: $i,SV29: $i] :
( ( ( ~ ( member @ ( pair @ SV29 @ SV92 ) @ ( rtrancl @ contract ) ) )
= $true )
| ( ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV29 ) @ SV84 ) @ SV92 ) @ ( rtrancl @ contract ) )
= $true )
| ( ( member @ SV84 @ comb )
= $false )
| ( ( member @ SV29 @ comb )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[331]) ).
thf(340,plain,
! [SV56: $i,SV30: $i,SV93: $i] :
( ( ( ~ ( member @ SV93 @ comb ) )
= $true )
| ( ( ! [SY196: $i] :
( ~ ( member @ ( pair @ ( comb_app @ ( comb_app @ SV30 @ SV93 ) @ ( comb_app @ SV56 @ SV93 ) ) @ SY196 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV30 ) @ SV56 ) @ SV93 ) @ SY196 ) @ ( rtrancl @ contract ) ) ) )
= $true )
| ( ( member @ SV56 @ comb )
= $false )
| ( ( member @ SV30 @ comb )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[332]) ).
thf(341,plain,
! [SV31: $i,SV94: $i,SV87: $i,SV57: $i] :
( ( ( ~ ( member @ ( pair @ ( comb_app @ SV57 @ SV87 ) @ SV94 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ SV31 @ SV87 ) @ SV94 ) @ ( rtrancl @ contract ) ) )
= $true )
| ( ( member @ SV87 @ comb )
= $false )
| ( ( member @ ( pair @ SV31 @ SV57 ) @ contract )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[333]) ).
thf(342,plain,
! [SV32: $i,SV95: $i,SV58: $i,SV88: $i] :
( ( ( ~ ( member @ ( pair @ ( comb_app @ SV88 @ SV58 ) @ SV95 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ SV88 @ SV32 ) @ SV95 ) @ ( rtrancl @ contract ) ) )
= $true )
| ( ( member @ SV88 @ comb )
= $false )
| ( ( member @ ( pair @ SV32 @ SV58 ) @ contract )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[334]) ).
thf(343,plain,
! [SV59: $i,SV34: $i,SV96: $i,SV89: $i] :
( ( ( ~ ( member @ ( pair @ SV89 @ SV96 ) @ SV34 )
| ( member @ ( pair @ SV59 @ SV96 ) @ SV34 ) )
= $true )
| ( ( member @ ( pair @ SV59 @ SV89 ) @ SV34 )
= $false )
| ( ( trans @ SV34 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[335]) ).
thf(344,plain,
! [SV79: $i,SV11: $i,SV91: $i] :
( ( ( member @ SV91 @ comb )
= $false )
| ( ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV11 ) @ SV79 ) @ SV91 ) @ ( comb_app @ ( comb_app @ SV11 @ SV91 ) @ ( comb_app @ SV79 @ SV91 ) ) ) @ contract )
= $true )
| ( ( member @ SV79 @ comb )
= $false )
| ( ( member @ SV11 @ comb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[337]) ).
thf(345,plain,
! [SV84: $i,SV92: $i,SV29: $i] :
( ( ( member @ ( pair @ SV29 @ SV92 ) @ ( rtrancl @ contract ) )
= $false )
| ( ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV29 ) @ SV84 ) @ SV92 ) @ ( rtrancl @ contract ) )
= $true )
| ( ( member @ SV84 @ comb )
= $false )
| ( ( member @ SV29 @ comb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(346,plain,
! [SV56: $i,SV30: $i,SV93: $i] :
( ( ( member @ SV93 @ comb )
= $false )
| ( ( ! [SY196: $i] :
( ~ ( member @ ( pair @ ( comb_app @ ( comb_app @ SV30 @ SV93 ) @ ( comb_app @ SV56 @ SV93 ) ) @ SY196 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV30 ) @ SV56 ) @ SV93 ) @ SY196 ) @ ( rtrancl @ contract ) ) ) )
= $true )
| ( ( member @ SV56 @ comb )
= $false )
| ( ( member @ SV30 @ comb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[340]) ).
thf(347,plain,
! [SV31: $i,SV94: $i,SV87: $i,SV57: $i] :
( ( ( ~ ( member @ ( pair @ ( comb_app @ SV57 @ SV87 ) @ SV94 ) @ ( rtrancl @ contract ) ) )
= $true )
| ( ( member @ ( pair @ ( comb_app @ SV31 @ SV87 ) @ SV94 ) @ ( rtrancl @ contract ) )
= $true )
| ( ( member @ SV87 @ comb )
= $false )
| ( ( member @ ( pair @ SV31 @ SV57 ) @ contract )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[341]) ).
thf(348,plain,
! [SV32: $i,SV95: $i,SV58: $i,SV88: $i] :
( ( ( ~ ( member @ ( pair @ ( comb_app @ SV88 @ SV58 ) @ SV95 ) @ ( rtrancl @ contract ) ) )
= $true )
| ( ( member @ ( pair @ ( comb_app @ SV88 @ SV32 ) @ SV95 ) @ ( rtrancl @ contract ) )
= $true )
| ( ( member @ SV88 @ comb )
= $false )
| ( ( member @ ( pair @ SV32 @ SV58 ) @ contract )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[342]) ).
thf(349,plain,
! [SV59: $i,SV34: $i,SV96: $i,SV89: $i] :
( ( ( ~ ( member @ ( pair @ SV89 @ SV96 ) @ SV34 ) )
= $true )
| ( ( member @ ( pair @ SV59 @ SV96 ) @ SV34 )
= $true )
| ( ( member @ ( pair @ SV59 @ SV89 ) @ SV34 )
= $false )
| ( ( trans @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[343]) ).
thf(350,plain,
! [SV97: $i,SV56: $i,SV93: $i,SV30: $i] :
( ( ( ~ ( member @ ( pair @ ( comb_app @ ( comb_app @ SV30 @ SV93 ) @ ( comb_app @ SV56 @ SV93 ) ) @ SV97 ) @ ( rtrancl @ contract ) )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV30 ) @ SV56 ) @ SV93 ) @ SV97 ) @ ( rtrancl @ contract ) ) )
= $true )
| ( ( member @ SV93 @ comb )
= $false )
| ( ( member @ SV56 @ comb )
= $false )
| ( ( member @ SV30 @ comb )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(351,plain,
! [SV31: $i,SV94: $i,SV87: $i,SV57: $i] :
( ( ( member @ ( pair @ ( comb_app @ SV57 @ SV87 ) @ SV94 ) @ ( rtrancl @ contract ) )
= $false )
| ( ( member @ ( pair @ ( comb_app @ SV31 @ SV87 ) @ SV94 ) @ ( rtrancl @ contract ) )
= $true )
| ( ( member @ SV87 @ comb )
= $false )
| ( ( member @ ( pair @ SV31 @ SV57 ) @ contract )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[347]) ).
thf(352,plain,
! [SV32: $i,SV95: $i,SV58: $i,SV88: $i] :
( ( ( member @ ( pair @ ( comb_app @ SV88 @ SV58 ) @ SV95 ) @ ( rtrancl @ contract ) )
= $false )
| ( ( member @ ( pair @ ( comb_app @ SV88 @ SV32 ) @ SV95 ) @ ( rtrancl @ contract ) )
= $true )
| ( ( member @ SV88 @ comb )
= $false )
| ( ( member @ ( pair @ SV32 @ SV58 ) @ contract )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[348]) ).
thf(353,plain,
! [SV59: $i,SV34: $i,SV96: $i,SV89: $i] :
( ( ( member @ ( pair @ SV89 @ SV96 ) @ SV34 )
= $false )
| ( ( member @ ( pair @ SV59 @ SV96 ) @ SV34 )
= $true )
| ( ( member @ ( pair @ SV59 @ SV89 ) @ SV34 )
= $false )
| ( ( trans @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[349]) ).
thf(354,plain,
! [SV97: $i,SV56: $i,SV93: $i,SV30: $i] :
( ( ( ~ ( member @ ( pair @ ( comb_app @ ( comb_app @ SV30 @ SV93 ) @ ( comb_app @ SV56 @ SV93 ) ) @ SV97 ) @ ( rtrancl @ contract ) ) )
= $true )
| ( ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV30 ) @ SV56 ) @ SV93 ) @ SV97 ) @ ( rtrancl @ contract ) )
= $true )
| ( ( member @ SV93 @ comb )
= $false )
| ( ( member @ SV56 @ comb )
= $false )
| ( ( member @ SV30 @ comb )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[350]) ).
thf(355,plain,
! [SV97: $i,SV56: $i,SV93: $i,SV30: $i] :
( ( ( member @ ( pair @ ( comb_app @ ( comb_app @ SV30 @ SV93 ) @ ( comb_app @ SV56 @ SV93 ) ) @ SV97 ) @ ( rtrancl @ contract ) )
= $false )
| ( ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV30 ) @ SV56 ) @ SV93 ) @ SV97 ) @ ( rtrancl @ contract ) )
= $true )
| ( ( member @ SV93 @ comb )
= $false )
| ( ( member @ SV56 @ comb )
= $false )
| ( ( member @ SV30 @ comb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[354]) ).
thf(356,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[113,355,353,352,351,345,344,338,336,320,319,317,316,310,309,308,307,306,305,304,303,302,301,300,299,298,297,289,265,264,237,230,229,222,221,194,191,158,157,127,126,117,116,115,114]) ).
thf(357,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[356]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COL089-1 : TPTP v8.1.0. Released v2.7.0.
% 0.03/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n022.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue May 31 08:18:22 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.18/0.37
% 0.18/0.37 No.of.Axioms: 44
% 0.18/0.37
% 0.18/0.37 Length.of.Defs: 0
% 0.18/0.37
% 0.18/0.37 Contains.Choice.Funs: false
% 0.18/0.39 .
% 0.18/0.42 (rf:0,axioms:44,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:46,loop_count:0,foatp_calls:0,translation:fof_full)....................
% 9.22/9.44
% 9.22/9.44 ********************************
% 9.22/9.44 * All subproblems solved! *
% 9.22/9.44 ********************************
% 9.22/9.44 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:44,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:356,loop_count:0,foatp_calls:1,translation:fof_full)
% 9.29/9.51
% 9.29/9.51 %**** Beginning of derivation protocol ****
% 9.29/9.51 % SZS output start CNFRefutation
% See solution above
% 9.29/9.51
% 9.29/9.51 %**** End of derivation protocol ****
% 9.29/9.51 %**** no. of clauses in derivation: 357 ****
% 9.29/9.51 %**** clause counter: 356 ****
% 9.29/9.51
% 9.29/9.51 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:44,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:356,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------