%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : COL091-1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:11:09 AM UTC 2026
% Result : Unsatisfiable 0.53s 0.34s
% Output : CNFRefutation 0.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 34
% Syntax : Number of formulae : 259 ( 170 unt; 0 typ; 0 def)
% Number of atoms : 1171 ( 449 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 2476 ( 254 ~; 300 |; 0 &;1922 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 8 con; 0-3 aty)
% Number of variables : 649 ( 0 ^; 649 !; 0 ?; 649 :)
% 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(1,axiom,
! [R: $i] :
~ ( member @ ( pair @ combS @ R ) @ contract ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_contractE) ).
thf(2,axiom,
! [R: $i] :
~ ( member @ ( pair @ combK @ R ) @ contract ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_contractE) ).
thf(3,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(4,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(5,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(6,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(7,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(8,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(9,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(10,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(11,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(12,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(13,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(14,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(15,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(16,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(17,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(18,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(19,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(20,axiom,
! [A: $i] :
( ~ ( member @ A @ comb )
| ( member @ ( pair @ A @ A ) @ ( rtrancl @ contract ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reduction_refl) ).
thf(21,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(22,axiom,
member @ combS @ comb,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',comb_intros2) ).
thf(23,axiom,
member @ combK @ comb,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',comb_intros1) ).
thf(24,axiom,
! [P: $i,Q: $i] :
( ~ ( member @ ( comb_app @ P @ Q ) @ comb )
| ( member @ Q @ comb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_E2) ).
thf(25,axiom,
! [P: $i,Q: $i] :
( ~ ( member @ ( comb_app @ P @ Q ) @ comb )
| ( member @ P @ comb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_E1) ).
thf(26,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(27,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(28,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(29,axiom,
! [P: $i,Q: $i] :
( combS
!= ( comb_app @ P @ Q ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_app) ).
thf(30,axiom,
! [P: $i,Q: $i] :
( combK
!= ( comb_app @ P @ Q ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_app) ).
thf(31,axiom,
combK != combS,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_s) ).
thf(32,axiom,
member @ ( pair @ ( comb_app @ combK @ p ) @ r ) @ contract,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k1_contractD_h1) ).
thf(33,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(34,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[33]) ).
thf(35,negated_conjecture,
! [Q: $i] :
( ( r
!= ( comb_app @ combK @ Q ) )
| ~ ( member @ ( pair @ p @ Q ) @ contract ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k1_contractD_c1) ).
thf(36,plain,
$false = $false,
inference(unfold_def,[status(thm)],[34]) ).
thf(37,plain,
( ( ! [R: $i] :
~ ( member @ ( pair @ combS @ R ) @ contract ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(38,plain,
( ( ! [R: $i] :
~ ( member @ ( pair @ combK @ R ) @ contract ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(39,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)],[3]) ).
thf(40,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c4 @ P @ Q @ R )
| ( member @ P @ comb ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(41,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)],[5]) ).
thf(42,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)],[6]) ).
thf(43,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c3 @ P @ Q @ R )
| ( member @ Q @ comb ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(44,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)],[8]) ).
thf(45,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)],[9]) ).
thf(46,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)],[10]) ).
thf(47,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c2 @ P @ Q @ R )
| ( member @ Q @ comb ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(48,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)],[12]) ).
thf(49,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)],[13]) ).
thf(50,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c1 @ P @ Q @ R )
| ( P
= ( comb_app @ combK @ R ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(51,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c1 @ P @ Q @ R )
| ( member @ Q @ comb ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(52,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c1 @ P @ Q @ R )
| ( member @ R @ comb ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(53,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)],[17]) ).
thf(54,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)],[18]) ).
thf(55,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)],[19]) ).
thf(56,plain,
( ( ! [A: $i] :
( ~ ( member @ A @ comb )
| ( member @ ( pair @ A @ A ) @ ( rtrancl @ contract ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(57,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( member @ P @ comb )
| ~ ( member @ Q @ comb )
| ( member @ ( comb_app @ P @ Q ) @ comb ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(58,plain,
( ( member @ combS @ comb )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(59,plain,
( ( member @ combK @ comb )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(60,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( member @ ( comb_app @ P @ Q ) @ comb )
| ( member @ Q @ comb ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(61,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( member @ ( comb_app @ P @ Q ) @ comb )
| ( member @ P @ comb ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(62,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)],[26]) ).
thf(63,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)],[27]) ).
thf(64,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)],[28]) ).
thf(65,plain,
( ( ! [P: $i,Q: $i] :
( combS
!= ( comb_app @ P @ Q ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(66,plain,
( ( ! [P: $i,Q: $i] :
( combK
!= ( comb_app @ P @ Q ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(67,plain,
( ( combK != combS )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(68,plain,
( ( member @ ( pair @ ( comb_app @ combK @ p ) @ r ) @ contract )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(69,plain,
( ( ! [Q: $i] :
( ( r
!= ( comb_app @ combK @ Q ) )
| ~ ( member @ ( pair @ p @ Q ) @ contract ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(70,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[36]) ).
thf(71,plain,
( ( ! [Q: $i] :
( ( r
!= ( comb_app @ combK @ Q ) )
| ~ ( member @ ( pair @ p @ Q ) @ contract ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(72,plain,
( ( member @ ( pair @ ( comb_app @ combK @ p ) @ r ) @ contract )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(73,plain,
( ( combK != combS )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(74,plain,
( ( ! [P: $i,Q: $i] :
( combK
!= ( comb_app @ P @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(75,plain,
( ( ! [P: $i,Q: $i] :
( combS
!= ( comb_app @ P @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(76,plain,
( ( ! [P1: $i,Q1: $i,P2: $i,Q2: $i] :
( ( ( comb_app @ P1 @ Q1 )
!= ( comb_app @ P2 @ Q2 ) )
| ( P1 = P2 ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(77,plain,
( ( ! [P1: $i,Q1: $i,P2: $i,Q2: $i] :
( ( ( comb_app @ P1 @ Q1 )
!= ( comb_app @ P2 @ Q2 ) )
| ( Q1 = Q2 ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(78,plain,
( ( ! [P1: $i,P2: $i,Q1: $i,Q2: $i] :
( ( P1 != P2 )
| ( Q1 != Q2 )
| ( ( comb_app @ P1 @ Q1 )
= ( comb_app @ P2 @ Q2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(79,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( member @ ( comb_app @ P @ Q ) @ comb )
| ( member @ P @ comb ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(80,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( member @ ( comb_app @ P @ Q ) @ comb )
| ( member @ Q @ comb ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(81,plain,
( ( member @ combK @ comb )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(82,plain,
( ( member @ combS @ comb )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(83,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( member @ P @ comb )
| ~ ( member @ Q @ comb )
| ( member @ ( comb_app @ P @ Q ) @ comb ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(84,plain,
( ( ! [A: $i] :
( ~ ( member @ A @ comb )
| ( member @ ( pair @ A @ A ) @ ( rtrancl @ contract ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(85,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( member @ P @ comb )
| ~ ( member @ Q @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ P ) @ Q ) @ P ) @ contract ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(86,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( member @ P @ comb )
| ~ ( member @ Q @ comb )
| ~ ( member @ R @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ P ) @ Q ) @ R ) @ ( comb_app @ ( comb_app @ P @ R ) @ ( comb_app @ Q @ R ) ) ) @ contract ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(87,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)],[53]) ).
thf(88,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c1 @ P @ Q @ R )
| ( member @ R @ comb ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(89,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c1 @ P @ Q @ R )
| ( member @ Q @ comb ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(90,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c1 @ P @ Q @ R )
| ( P
= ( comb_app @ combK @ R ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(91,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)],[49]) ).
thf(92,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c2 @ P @ Q @ R )
| ( member @ ( ap_contractE_sk1q @ P @ Q @ R ) @ comb ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(93,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c2 @ P @ Q @ R )
| ( member @ Q @ comb ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(94,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)],[46]) ).
thf(95,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)],[45]) ).
thf(96,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)],[44]) ).
thf(97,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c3 @ P @ Q @ R )
| ( member @ Q @ comb ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(98,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)],[42]) ).
thf(99,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)],[41]) ).
thf(100,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ~ ( ap_contractE_c4 @ P @ Q @ R )
| ( member @ P @ comb ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(101,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)],[39]) ).
thf(102,plain,
( ( ! [R: $i] :
~ ( member @ ( pair @ combK @ R ) @ contract ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(103,plain,
( ( ! [R: $i] :
~ ( member @ ( pair @ combS @ R ) @ contract ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(104,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[70]) ).
thf(105,plain,
( ( combK != combS )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(106,plain,
( ( ! [SX0: $i] :
( ( r
!= ( comb_app @ combK @ SX0 ) )
| ~ ( member @ ( pair @ p @ SX0 ) @ contract ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(107,plain,
( ( ! [SX0: $i,SX1: $i] :
( combS
!= ( comb_app @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(108,plain,
( ( ! [SX0: $i,SX1: $i] :
( combK
!= ( comb_app @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(109,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( comb_app @ SX0 @ SX1 )
!= ( comb_app @ SX2 @ SX3 ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(110,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( comb_app @ SX0 @ SX1 )
!= ( comb_app @ SX2 @ SX3 ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(111,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( SX0 != SX1 )
| ( SX2 != SX3 )
| ( ( comb_app @ SX0 @ SX2 )
= ( comb_app @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(112,plain,
! [SV1: $i] :
( ( ! [SY76: $i] :
( ~ ( member @ ( comb_app @ SV1 @ SY76 ) @ comb )
| ( member @ SV1 @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(113,plain,
! [SV2: $i] :
( ( ! [SY77: $i] :
( ~ ( member @ ( comb_app @ SV2 @ SY77 ) @ comb )
| ( member @ SY77 @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(114,plain,
! [SV3: $i] :
( ( ! [SY78: $i] :
( ~ ( member @ SV3 @ comb )
| ~ ( member @ SY78 @ comb )
| ( member @ ( comb_app @ SV3 @ SY78 ) @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(115,plain,
! [SV4: $i] :
( ( ~ ( member @ SV4 @ comb )
| ( member @ ( pair @ SV4 @ SV4 ) @ ( rtrancl @ contract ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(116,plain,
! [SV5: $i] :
( ( ! [SY79: $i] :
( ~ ( member @ SV5 @ comb )
| ~ ( member @ SY79 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV5 ) @ SY79 ) @ SV5 ) @ contract ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(117,plain,
! [SV6: $i] :
( ( ! [SY80: $i,SY81: $i] :
( ~ ( member @ SV6 @ comb )
| ~ ( member @ SY80 @ comb )
| ~ ( member @ SY81 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV6 ) @ SY80 ) @ SY81 ) @ ( comb_app @ ( comb_app @ SV6 @ SY81 ) @ ( comb_app @ SY80 @ SY81 ) ) ) @ contract ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(118,plain,
! [SV7: $i] :
( ( ! [SY82: $i,SY83: $i] :
( ~ ( member @ ( pair @ ( comb_app @ SV7 @ SY82 ) @ SY83 ) @ contract )
| ( ap_contractE_c1 @ SV7 @ SY82 @ SY83 )
| ( ap_contractE_c2 @ SV7 @ SY82 @ SY83 )
| ( ap_contractE_c3 @ SV7 @ SY82 @ SY83 )
| ( ap_contractE_c4 @ SV7 @ SY82 @ SY83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(119,plain,
! [SV8: $i] :
( ( ! [SY84: $i,SY85: $i] :
( ~ ( ap_contractE_c1 @ SV8 @ SY84 @ SY85 )
| ( member @ SY85 @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(120,plain,
! [SV9: $i] :
( ( ! [SY86: $i,SY87: $i] :
( ~ ( ap_contractE_c1 @ SV9 @ SY86 @ SY87 )
| ( member @ SY86 @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(121,plain,
! [SV10: $i] :
( ( ! [SY88: $i,SY89: $i] :
( ~ ( ap_contractE_c1 @ SV10 @ SY88 @ SY89 )
| ( SV10
= ( comb_app @ combK @ SY89 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(122,plain,
! [SV11: $i] :
( ( ! [SY90: $i,SY91: $i] :
( ~ ( ap_contractE_c2 @ SV11 @ SY90 @ SY91 )
| ( member @ ( ap_contractE_sk1p @ SV11 @ SY90 @ SY91 ) @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(123,plain,
! [SV12: $i] :
( ( ! [SY92: $i,SY93: $i] :
( ~ ( ap_contractE_c2 @ SV12 @ SY92 @ SY93 )
| ( member @ ( ap_contractE_sk1q @ SV12 @ SY92 @ SY93 ) @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(124,plain,
! [SV13: $i] :
( ( ! [SY94: $i,SY95: $i] :
( ~ ( ap_contractE_c2 @ SV13 @ SY94 @ SY95 )
| ( member @ SY94 @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(125,plain,
! [SV14: $i] :
( ( ! [SY96: $i,SY97: $i] :
( ~ ( ap_contractE_c2 @ SV14 @ SY96 @ SY97 )
| ( SY97
= ( comb_app @ ( comb_app @ ( ap_contractE_sk1p @ SV14 @ SY96 @ SY97 ) @ SY96 ) @ ( comb_app @ ( ap_contractE_sk1q @ SV14 @ SY96 @ SY97 ) @ SY96 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(126,plain,
! [SV15: $i] :
( ( ! [SY98: $i,SY99: $i] :
( ~ ( ap_contractE_c2 @ SV15 @ SY98 @ SY99 )
| ( SV15
= ( comb_app @ ( comb_app @ combS @ ( ap_contractE_sk1p @ SV15 @ SY98 @ SY99 ) ) @ ( ap_contractE_sk1q @ SV15 @ SY98 @ SY99 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(127,plain,
! [SV16: $i] :
( ( ! [SY100: $i,SY101: $i] :
( ~ ( ap_contractE_c3 @ SV16 @ SY100 @ SY101 )
| ( member @ ( pair @ SV16 @ ( ap_contractE_sk2q @ SV16 @ SY100 @ SY101 ) ) @ contract ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(128,plain,
! [SV17: $i] :
( ( ! [SY102: $i,SY103: $i] :
( ~ ( ap_contractE_c3 @ SV17 @ SY102 @ SY103 )
| ( member @ SY102 @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(129,plain,
! [SV18: $i] :
( ( ! [SY104: $i,SY105: $i] :
( ~ ( ap_contractE_c3 @ SV18 @ SY104 @ SY105 )
| ( SY105
= ( comb_app @ ( ap_contractE_sk2q @ SV18 @ SY104 @ SY105 ) @ SY104 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(130,plain,
! [SV19: $i] :
( ( ! [SY106: $i,SY107: $i] :
( ~ ( ap_contractE_c4 @ SV19 @ SY106 @ SY107 )
| ( member @ ( pair @ SY106 @ ( ap_contractE_sk3q @ SV19 @ SY106 @ SY107 ) ) @ contract ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(131,plain,
! [SV20: $i] :
( ( ! [SY108: $i,SY109: $i] :
( ~ ( ap_contractE_c4 @ SV20 @ SY108 @ SY109 )
| ( member @ SV20 @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(132,plain,
! [SV21: $i] :
( ( ! [SY110: $i,SY111: $i] :
( ~ ( ap_contractE_c4 @ SV21 @ SY110 @ SY111 )
| ( SY111
= ( comb_app @ SV21 @ ( ap_contractE_sk3q @ SV21 @ SY110 @ SY111 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(133,plain,
! [SV22: $i] :
( ( ~ ( member @ ( pair @ combK @ SV22 ) @ contract ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(134,plain,
! [SV23: $i] :
( ( ~ ( member @ ( pair @ combS @ SV23 ) @ contract ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(135,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(136,plain,
( ( combK = combS )
= $false ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(137,plain,
! [SV24: $i] :
( ( ( r
!= ( comb_app @ combK @ SV24 ) )
| ~ ( member @ ( pair @ p @ SV24 ) @ contract ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(138,plain,
! [SV25: $i] :
( ( ! [SY112: $i] :
( combS
!= ( comb_app @ SV25 @ SY112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(139,plain,
! [SV26: $i] :
( ( ! [SY113: $i] :
( combK
!= ( comb_app @ SV26 @ SY113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(140,plain,
! [SV27: $i] :
( ( ! [SY114: $i,SY115: $i,SY116: $i] :
( ( ( comb_app @ SV27 @ SY114 )
!= ( comb_app @ SY115 @ SY116 ) )
| ( SV27 = SY115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(141,plain,
! [SV28: $i] :
( ( ! [SY117: $i,SY118: $i,SY119: $i] :
( ( ( comb_app @ SV28 @ SY117 )
!= ( comb_app @ SY118 @ SY119 ) )
| ( SY117 = SY119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(142,plain,
! [SV29: $i] :
( ( ! [SY120: $i,SY121: $i,SY122: $i] :
( ( SV29 != SY120 )
| ( SY121 != SY122 )
| ( ( comb_app @ SV29 @ SY121 )
= ( comb_app @ SY120 @ SY122 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(143,plain,
! [SV30: $i,SV1: $i] :
( ( ~ ( member @ ( comb_app @ SV1 @ SV30 ) @ comb )
| ( member @ SV1 @ comb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(144,plain,
! [SV31: $i,SV2: $i] :
( ( ~ ( member @ ( comb_app @ SV2 @ SV31 ) @ comb )
| ( member @ SV31 @ comb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(145,plain,
! [SV32: $i,SV3: $i] :
( ( ~ ( member @ SV3 @ comb )
| ~ ( member @ SV32 @ comb )
| ( member @ ( comb_app @ SV3 @ SV32 ) @ comb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(146,plain,
! [SV4: $i] :
( ( ( ~ ( member @ SV4 @ comb ) )
= $true )
| ( ( member @ ( pair @ SV4 @ SV4 ) @ ( rtrancl @ contract ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(147,plain,
! [SV33: $i,SV5: $i] :
( ( ~ ( member @ SV5 @ comb )
| ~ ( member @ SV33 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV5 ) @ SV33 ) @ SV5 ) @ contract ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(148,plain,
! [SV34: $i,SV6: $i] :
( ( ! [SY123: $i] :
( ~ ( member @ SV6 @ comb )
| ~ ( member @ SV34 @ comb )
| ~ ( member @ SY123 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV6 ) @ SV34 ) @ SY123 ) @ ( comb_app @ ( comb_app @ SV6 @ SY123 ) @ ( comb_app @ SV34 @ SY123 ) ) ) @ contract ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(149,plain,
! [SV35: $i,SV7: $i] :
( ( ! [SY124: $i] :
( ~ ( member @ ( pair @ ( comb_app @ SV7 @ SV35 ) @ SY124 ) @ contract )
| ( ap_contractE_c1 @ SV7 @ SV35 @ SY124 )
| ( ap_contractE_c2 @ SV7 @ SV35 @ SY124 )
| ( ap_contractE_c3 @ SV7 @ SV35 @ SY124 )
| ( ap_contractE_c4 @ SV7 @ SV35 @ SY124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(150,plain,
! [SV36: $i,SV8: $i] :
( ( ! [SY125: $i] :
( ~ ( ap_contractE_c1 @ SV8 @ SV36 @ SY125 )
| ( member @ SY125 @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(151,plain,
! [SV37: $i,SV9: $i] :
( ( ! [SY126: $i] :
( ~ ( ap_contractE_c1 @ SV9 @ SV37 @ SY126 )
| ( member @ SV37 @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(152,plain,
! [SV38: $i,SV10: $i] :
( ( ! [SY127: $i] :
( ~ ( ap_contractE_c1 @ SV10 @ SV38 @ SY127 )
| ( SV10
= ( comb_app @ combK @ SY127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(153,plain,
! [SV39: $i,SV11: $i] :
( ( ! [SY128: $i] :
( ~ ( ap_contractE_c2 @ SV11 @ SV39 @ SY128 )
| ( member @ ( ap_contractE_sk1p @ SV11 @ SV39 @ SY128 ) @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(154,plain,
! [SV40: $i,SV12: $i] :
( ( ! [SY129: $i] :
( ~ ( ap_contractE_c2 @ SV12 @ SV40 @ SY129 )
| ( member @ ( ap_contractE_sk1q @ SV12 @ SV40 @ SY129 ) @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(155,plain,
! [SV41: $i,SV13: $i] :
( ( ! [SY130: $i] :
( ~ ( ap_contractE_c2 @ SV13 @ SV41 @ SY130 )
| ( member @ SV41 @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(156,plain,
! [SV42: $i,SV14: $i] :
( ( ! [SY131: $i] :
( ~ ( ap_contractE_c2 @ SV14 @ SV42 @ SY131 )
| ( SY131
= ( comb_app @ ( comb_app @ ( ap_contractE_sk1p @ SV14 @ SV42 @ SY131 ) @ SV42 ) @ ( comb_app @ ( ap_contractE_sk1q @ SV14 @ SV42 @ SY131 ) @ SV42 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(157,plain,
! [SV43: $i,SV15: $i] :
( ( ! [SY132: $i] :
( ~ ( ap_contractE_c2 @ SV15 @ SV43 @ SY132 )
| ( SV15
= ( comb_app @ ( comb_app @ combS @ ( ap_contractE_sk1p @ SV15 @ SV43 @ SY132 ) ) @ ( ap_contractE_sk1q @ SV15 @ SV43 @ SY132 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(158,plain,
! [SV44: $i,SV16: $i] :
( ( ! [SY133: $i] :
( ~ ( ap_contractE_c3 @ SV16 @ SV44 @ SY133 )
| ( member @ ( pair @ SV16 @ ( ap_contractE_sk2q @ SV16 @ SV44 @ SY133 ) ) @ contract ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(159,plain,
! [SV45: $i,SV17: $i] :
( ( ! [SY134: $i] :
( ~ ( ap_contractE_c3 @ SV17 @ SV45 @ SY134 )
| ( member @ SV45 @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(160,plain,
! [SV46: $i,SV18: $i] :
( ( ! [SY135: $i] :
( ~ ( ap_contractE_c3 @ SV18 @ SV46 @ SY135 )
| ( SY135
= ( comb_app @ ( ap_contractE_sk2q @ SV18 @ SV46 @ SY135 ) @ SV46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(161,plain,
! [SV47: $i,SV19: $i] :
( ( ! [SY136: $i] :
( ~ ( ap_contractE_c4 @ SV19 @ SV47 @ SY136 )
| ( member @ ( pair @ SV47 @ ( ap_contractE_sk3q @ SV19 @ SV47 @ SY136 ) ) @ contract ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(162,plain,
! [SV48: $i,SV20: $i] :
( ( ! [SY137: $i] :
( ~ ( ap_contractE_c4 @ SV20 @ SV48 @ SY137 )
| ( member @ SV20 @ comb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(163,plain,
! [SV49: $i,SV21: $i] :
( ( ! [SY138: $i] :
( ~ ( ap_contractE_c4 @ SV21 @ SV49 @ SY138 )
| ( SY138
= ( comb_app @ SV21 @ ( ap_contractE_sk3q @ SV21 @ SV49 @ SY138 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(164,plain,
! [SV22: $i] :
( ( member @ ( pair @ combK @ SV22 ) @ contract )
= $false ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(165,plain,
! [SV23: $i] :
( ( member @ ( pair @ combS @ SV23 ) @ contract )
= $false ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(166,plain,
! [SV24: $i] :
( ( ( r
!= ( comb_app @ combK @ SV24 ) )
= $true )
| ( ( ~ ( member @ ( pair @ p @ SV24 ) @ contract ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(167,plain,
! [SV50: $i,SV25: $i] :
( ( combS
!= ( comb_app @ SV25 @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(168,plain,
! [SV51: $i,SV26: $i] :
( ( combK
!= ( comb_app @ SV26 @ SV51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(169,plain,
! [SV52: $i,SV27: $i] :
( ( ! [SY139: $i,SY140: $i] :
( ( ( comb_app @ SV27 @ SV52 )
!= ( comb_app @ SY139 @ SY140 ) )
| ( SV27 = SY139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(170,plain,
! [SV53: $i,SV28: $i] :
( ( ! [SY141: $i,SY142: $i] :
( ( ( comb_app @ SV28 @ SV53 )
!= ( comb_app @ SY141 @ SY142 ) )
| ( SV53 = SY142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(171,plain,
! [SV54: $i,SV29: $i] :
( ( ! [SY143: $i,SY144: $i] :
( ( SV29 != SV54 )
| ( SY143 != SY144 )
| ( ( comb_app @ SV29 @ SY143 )
= ( comb_app @ SV54 @ SY144 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(172,plain,
! [SV30: $i,SV1: $i] :
( ( ( ~ ( member @ ( comb_app @ SV1 @ SV30 ) @ comb ) )
= $true )
| ( ( member @ SV1 @ comb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(173,plain,
! [SV31: $i,SV2: $i] :
( ( ( ~ ( member @ ( comb_app @ SV2 @ SV31 ) @ comb ) )
= $true )
| ( ( member @ SV31 @ comb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(174,plain,
! [SV32: $i,SV3: $i] :
( ( ( ~ ( member @ SV3 @ comb ) )
= $true )
| ( ( ~ ( member @ SV32 @ comb )
| ( member @ ( comb_app @ SV3 @ SV32 ) @ comb ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(175,plain,
! [SV4: $i] :
( ( ( member @ SV4 @ comb )
= $false )
| ( ( member @ ( pair @ SV4 @ SV4 ) @ ( rtrancl @ contract ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(176,plain,
! [SV33: $i,SV5: $i] :
( ( ( ~ ( member @ SV5 @ comb ) )
= $true )
| ( ( ~ ( member @ SV33 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV5 ) @ SV33 ) @ SV5 ) @ contract ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(177,plain,
! [SV55: $i,SV34: $i,SV6: $i] :
( ( ~ ( member @ SV6 @ comb )
| ~ ( member @ SV34 @ comb )
| ~ ( member @ SV55 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV6 ) @ SV34 ) @ SV55 ) @ ( comb_app @ ( comb_app @ SV6 @ SV55 ) @ ( comb_app @ SV34 @ SV55 ) ) ) @ contract ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(178,plain,
! [SV56: $i,SV35: $i,SV7: $i] :
( ( ~ ( member @ ( pair @ ( comb_app @ SV7 @ SV35 ) @ SV56 ) @ contract )
| ( ap_contractE_c1 @ SV7 @ SV35 @ SV56 )
| ( ap_contractE_c2 @ SV7 @ SV35 @ SV56 )
| ( ap_contractE_c3 @ SV7 @ SV35 @ SV56 )
| ( ap_contractE_c4 @ SV7 @ SV35 @ SV56 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(179,plain,
! [SV57: $i,SV36: $i,SV8: $i] :
( ( ~ ( ap_contractE_c1 @ SV8 @ SV36 @ SV57 )
| ( member @ SV57 @ comb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(180,plain,
! [SV58: $i,SV37: $i,SV9: $i] :
( ( ~ ( ap_contractE_c1 @ SV9 @ SV37 @ SV58 )
| ( member @ SV37 @ comb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(181,plain,
! [SV59: $i,SV38: $i,SV10: $i] :
( ( ~ ( ap_contractE_c1 @ SV10 @ SV38 @ SV59 )
| ( SV10
= ( comb_app @ combK @ SV59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(182,plain,
! [SV60: $i,SV39: $i,SV11: $i] :
( ( ~ ( ap_contractE_c2 @ SV11 @ SV39 @ SV60 )
| ( member @ ( ap_contractE_sk1p @ SV11 @ SV39 @ SV60 ) @ comb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(183,plain,
! [SV61: $i,SV40: $i,SV12: $i] :
( ( ~ ( ap_contractE_c2 @ SV12 @ SV40 @ SV61 )
| ( member @ ( ap_contractE_sk1q @ SV12 @ SV40 @ SV61 ) @ comb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(184,plain,
! [SV62: $i,SV41: $i,SV13: $i] :
( ( ~ ( ap_contractE_c2 @ SV13 @ SV41 @ SV62 )
| ( member @ SV41 @ comb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(185,plain,
! [SV63: $i,SV42: $i,SV14: $i] :
( ( ~ ( ap_contractE_c2 @ SV14 @ SV42 @ SV63 )
| ( SV63
= ( comb_app @ ( comb_app @ ( ap_contractE_sk1p @ SV14 @ SV42 @ SV63 ) @ SV42 ) @ ( comb_app @ ( ap_contractE_sk1q @ SV14 @ SV42 @ SV63 ) @ SV42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(186,plain,
! [SV64: $i,SV43: $i,SV15: $i] :
( ( ~ ( ap_contractE_c2 @ SV15 @ SV43 @ SV64 )
| ( SV15
= ( comb_app @ ( comb_app @ combS @ ( ap_contractE_sk1p @ SV15 @ SV43 @ SV64 ) ) @ ( ap_contractE_sk1q @ SV15 @ SV43 @ SV64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(187,plain,
! [SV65: $i,SV44: $i,SV16: $i] :
( ( ~ ( ap_contractE_c3 @ SV16 @ SV44 @ SV65 )
| ( member @ ( pair @ SV16 @ ( ap_contractE_sk2q @ SV16 @ SV44 @ SV65 ) ) @ contract ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(188,plain,
! [SV66: $i,SV45: $i,SV17: $i] :
( ( ~ ( ap_contractE_c3 @ SV17 @ SV45 @ SV66 )
| ( member @ SV45 @ comb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(189,plain,
! [SV67: $i,SV46: $i,SV18: $i] :
( ( ~ ( ap_contractE_c3 @ SV18 @ SV46 @ SV67 )
| ( SV67
= ( comb_app @ ( ap_contractE_sk2q @ SV18 @ SV46 @ SV67 ) @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(190,plain,
! [SV68: $i,SV47: $i,SV19: $i] :
( ( ~ ( ap_contractE_c4 @ SV19 @ SV47 @ SV68 )
| ( member @ ( pair @ SV47 @ ( ap_contractE_sk3q @ SV19 @ SV47 @ SV68 ) ) @ contract ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(191,plain,
! [SV69: $i,SV48: $i,SV20: $i] :
( ( ~ ( ap_contractE_c4 @ SV20 @ SV48 @ SV69 )
| ( member @ SV20 @ comb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(192,plain,
! [SV70: $i,SV49: $i,SV21: $i] :
( ( ~ ( ap_contractE_c4 @ SV21 @ SV49 @ SV70 )
| ( SV70
= ( comb_app @ SV21 @ ( ap_contractE_sk3q @ SV21 @ SV49 @ SV70 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(193,plain,
! [SV24: $i] :
( ( ( r
= ( comb_app @ combK @ SV24 ) )
= $false )
| ( ( ~ ( member @ ( pair @ p @ SV24 ) @ contract ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(194,plain,
! [SV50: $i,SV25: $i] :
( ( combS
= ( comb_app @ SV25 @ SV50 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(195,plain,
! [SV51: $i,SV26: $i] :
( ( combK
= ( comb_app @ SV26 @ SV51 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(196,plain,
! [SV71: $i,SV52: $i,SV27: $i] :
( ( ! [SY145: $i] :
( ( ( comb_app @ SV27 @ SV52 )
!= ( comb_app @ SV71 @ SY145 ) )
| ( SV27 = SV71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(197,plain,
! [SV72: $i,SV53: $i,SV28: $i] :
( ( ! [SY146: $i] :
( ( ( comb_app @ SV28 @ SV53 )
!= ( comb_app @ SV72 @ SY146 ) )
| ( SV53 = SY146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(198,plain,
! [SV73: $i,SV54: $i,SV29: $i] :
( ( ! [SY147: $i] :
( ( SV29 != SV54 )
| ( SV73 != SY147 )
| ( ( comb_app @ SV29 @ SV73 )
= ( comb_app @ SV54 @ SY147 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(199,plain,
! [SV30: $i,SV1: $i] :
( ( ( member @ ( comb_app @ SV1 @ SV30 ) @ comb )
= $false )
| ( ( member @ SV1 @ comb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(200,plain,
! [SV31: $i,SV2: $i] :
( ( ( member @ ( comb_app @ SV2 @ SV31 ) @ comb )
= $false )
| ( ( member @ SV31 @ comb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(201,plain,
! [SV32: $i,SV3: $i] :
( ( ( member @ SV3 @ comb )
= $false )
| ( ( ~ ( member @ SV32 @ comb )
| ( member @ ( comb_app @ SV3 @ SV32 ) @ comb ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(202,plain,
! [SV33: $i,SV5: $i] :
( ( ( member @ SV5 @ comb )
= $false )
| ( ( ~ ( member @ SV33 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV5 ) @ SV33 ) @ SV5 ) @ contract ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(203,plain,
! [SV55: $i,SV34: $i,SV6: $i] :
( ( ( ~ ( member @ SV6 @ comb ) )
= $true )
| ( ( ~ ( member @ SV34 @ comb )
| ~ ( member @ SV55 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV6 ) @ SV34 ) @ SV55 ) @ ( comb_app @ ( comb_app @ SV6 @ SV55 ) @ ( comb_app @ SV34 @ SV55 ) ) ) @ contract ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(204,plain,
! [SV56: $i,SV35: $i,SV7: $i] :
( ( ( ~ ( member @ ( pair @ ( comb_app @ SV7 @ SV35 ) @ SV56 ) @ contract ) )
= $true )
| ( ( ( ap_contractE_c1 @ SV7 @ SV35 @ SV56 )
| ( ap_contractE_c2 @ SV7 @ SV35 @ SV56 )
| ( ap_contractE_c3 @ SV7 @ SV35 @ SV56 )
| ( ap_contractE_c4 @ SV7 @ SV35 @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(205,plain,
! [SV57: $i,SV36: $i,SV8: $i] :
( ( ( ~ ( ap_contractE_c1 @ SV8 @ SV36 @ SV57 ) )
= $true )
| ( ( member @ SV57 @ comb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[179]) ).
thf(206,plain,
! [SV58: $i,SV37: $i,SV9: $i] :
( ( ( ~ ( ap_contractE_c1 @ SV9 @ SV37 @ SV58 ) )
= $true )
| ( ( member @ SV37 @ comb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[180]) ).
thf(207,plain,
! [SV59: $i,SV38: $i,SV10: $i] :
( ( ( ~ ( ap_contractE_c1 @ SV10 @ SV38 @ SV59 ) )
= $true )
| ( ( SV10
= ( comb_app @ combK @ SV59 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[181]) ).
thf(208,plain,
! [SV60: $i,SV39: $i,SV11: $i] :
( ( ( ~ ( ap_contractE_c2 @ SV11 @ SV39 @ SV60 ) )
= $true )
| ( ( member @ ( ap_contractE_sk1p @ SV11 @ SV39 @ SV60 ) @ comb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(209,plain,
! [SV61: $i,SV40: $i,SV12: $i] :
( ( ( ~ ( ap_contractE_c2 @ SV12 @ SV40 @ SV61 ) )
= $true )
| ( ( member @ ( ap_contractE_sk1q @ SV12 @ SV40 @ SV61 ) @ comb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(210,plain,
! [SV62: $i,SV41: $i,SV13: $i] :
( ( ( ~ ( ap_contractE_c2 @ SV13 @ SV41 @ SV62 ) )
= $true )
| ( ( member @ SV41 @ comb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(211,plain,
! [SV63: $i,SV42: $i,SV14: $i] :
( ( ( ~ ( ap_contractE_c2 @ SV14 @ SV42 @ SV63 ) )
= $true )
| ( ( SV63
= ( comb_app @ ( comb_app @ ( ap_contractE_sk1p @ SV14 @ SV42 @ SV63 ) @ SV42 ) @ ( comb_app @ ( ap_contractE_sk1q @ SV14 @ SV42 @ SV63 ) @ SV42 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(212,plain,
! [SV64: $i,SV43: $i,SV15: $i] :
( ( ( ~ ( ap_contractE_c2 @ SV15 @ SV43 @ SV64 ) )
= $true )
| ( ( SV15
= ( comb_app @ ( comb_app @ combS @ ( ap_contractE_sk1p @ SV15 @ SV43 @ SV64 ) ) @ ( ap_contractE_sk1q @ SV15 @ SV43 @ SV64 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(213,plain,
! [SV65: $i,SV44: $i,SV16: $i] :
( ( ( ~ ( ap_contractE_c3 @ SV16 @ SV44 @ SV65 ) )
= $true )
| ( ( member @ ( pair @ SV16 @ ( ap_contractE_sk2q @ SV16 @ SV44 @ SV65 ) ) @ contract )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(214,plain,
! [SV66: $i,SV45: $i,SV17: $i] :
( ( ( ~ ( ap_contractE_c3 @ SV17 @ SV45 @ SV66 ) )
= $true )
| ( ( member @ SV45 @ comb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(215,plain,
! [SV67: $i,SV46: $i,SV18: $i] :
( ( ( ~ ( ap_contractE_c3 @ SV18 @ SV46 @ SV67 ) )
= $true )
| ( ( SV67
= ( comb_app @ ( ap_contractE_sk2q @ SV18 @ SV46 @ SV67 ) @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(216,plain,
! [SV68: $i,SV47: $i,SV19: $i] :
( ( ( ~ ( ap_contractE_c4 @ SV19 @ SV47 @ SV68 ) )
= $true )
| ( ( member @ ( pair @ SV47 @ ( ap_contractE_sk3q @ SV19 @ SV47 @ SV68 ) ) @ contract )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(217,plain,
! [SV69: $i,SV48: $i,SV20: $i] :
( ( ( ~ ( ap_contractE_c4 @ SV20 @ SV48 @ SV69 ) )
= $true )
| ( ( member @ SV20 @ comb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(218,plain,
! [SV70: $i,SV49: $i,SV21: $i] :
( ( ( ~ ( ap_contractE_c4 @ SV21 @ SV49 @ SV70 ) )
= $true )
| ( ( SV70
= ( comb_app @ SV21 @ ( ap_contractE_sk3q @ SV21 @ SV49 @ SV70 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(219,plain,
! [SV24: $i] :
( ( ( member @ ( pair @ p @ SV24 ) @ contract )
= $false )
| ( ( r
= ( comb_app @ combK @ SV24 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(220,plain,
! [SV74: $i,SV71: $i,SV52: $i,SV27: $i] :
( ( ( ( comb_app @ SV27 @ SV52 )
!= ( comb_app @ SV71 @ SV74 ) )
| ( SV27 = SV71 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(221,plain,
! [SV75: $i,SV72: $i,SV53: $i,SV28: $i] :
( ( ( ( comb_app @ SV28 @ SV53 )
!= ( comb_app @ SV72 @ SV75 ) )
| ( SV53 = SV75 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(222,plain,
! [SV76: $i,SV73: $i,SV54: $i,SV29: $i] :
( ( ( SV29 != SV54 )
| ( SV73 != SV76 )
| ( ( comb_app @ SV29 @ SV73 )
= ( comb_app @ SV54 @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(223,plain,
! [SV3: $i,SV32: $i] :
( ( ( ~ ( member @ SV32 @ comb ) )
= $true )
| ( ( member @ ( comb_app @ SV3 @ SV32 ) @ comb )
= $true )
| ( ( member @ SV3 @ comb )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(224,plain,
! [SV5: $i,SV33: $i] :
( ( ( ~ ( member @ SV33 @ comb ) )
= $true )
| ( ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV5 ) @ SV33 ) @ SV5 ) @ contract )
= $true )
| ( ( member @ SV5 @ comb )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[202]) ).
thf(225,plain,
! [SV55: $i,SV34: $i,SV6: $i] :
( ( ( member @ SV6 @ comb )
= $false )
| ( ( ~ ( member @ SV34 @ comb )
| ~ ( member @ SV55 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV6 ) @ SV34 ) @ SV55 ) @ ( comb_app @ ( comb_app @ SV6 @ SV55 ) @ ( comb_app @ SV34 @ SV55 ) ) ) @ contract ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(226,plain,
! [SV56: $i,SV35: $i,SV7: $i] :
( ( ( member @ ( pair @ ( comb_app @ SV7 @ SV35 ) @ SV56 ) @ contract )
= $false )
| ( ( ( ap_contractE_c1 @ SV7 @ SV35 @ SV56 )
| ( ap_contractE_c2 @ SV7 @ SV35 @ SV56 )
| ( ap_contractE_c3 @ SV7 @ SV35 @ SV56 )
| ( ap_contractE_c4 @ SV7 @ SV35 @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(227,plain,
! [SV57: $i,SV36: $i,SV8: $i] :
( ( ( ap_contractE_c1 @ SV8 @ SV36 @ SV57 )
= $false )
| ( ( member @ SV57 @ comb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(228,plain,
! [SV58: $i,SV37: $i,SV9: $i] :
( ( ( ap_contractE_c1 @ SV9 @ SV37 @ SV58 )
= $false )
| ( ( member @ SV37 @ comb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(229,plain,
! [SV59: $i,SV38: $i,SV10: $i] :
( ( ( ap_contractE_c1 @ SV10 @ SV38 @ SV59 )
= $false )
| ( ( SV10
= ( comb_app @ combK @ SV59 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(230,plain,
! [SV60: $i,SV39: $i,SV11: $i] :
( ( ( ap_contractE_c2 @ SV11 @ SV39 @ SV60 )
= $false )
| ( ( member @ ( ap_contractE_sk1p @ SV11 @ SV39 @ SV60 ) @ comb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(231,plain,
! [SV61: $i,SV40: $i,SV12: $i] :
( ( ( ap_contractE_c2 @ SV12 @ SV40 @ SV61 )
= $false )
| ( ( member @ ( ap_contractE_sk1q @ SV12 @ SV40 @ SV61 ) @ comb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(232,plain,
! [SV62: $i,SV41: $i,SV13: $i] :
( ( ( ap_contractE_c2 @ SV13 @ SV41 @ SV62 )
= $false )
| ( ( member @ SV41 @ comb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(233,plain,
! [SV63: $i,SV42: $i,SV14: $i] :
( ( ( ap_contractE_c2 @ SV14 @ SV42 @ SV63 )
= $false )
| ( ( SV63
= ( comb_app @ ( comb_app @ ( ap_contractE_sk1p @ SV14 @ SV42 @ SV63 ) @ SV42 ) @ ( comb_app @ ( ap_contractE_sk1q @ SV14 @ SV42 @ SV63 ) @ SV42 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(234,plain,
! [SV64: $i,SV43: $i,SV15: $i] :
( ( ( ap_contractE_c2 @ SV15 @ SV43 @ SV64 )
= $false )
| ( ( SV15
= ( comb_app @ ( comb_app @ combS @ ( ap_contractE_sk1p @ SV15 @ SV43 @ SV64 ) ) @ ( ap_contractE_sk1q @ SV15 @ SV43 @ SV64 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(235,plain,
! [SV65: $i,SV44: $i,SV16: $i] :
( ( ( ap_contractE_c3 @ SV16 @ SV44 @ SV65 )
= $false )
| ( ( member @ ( pair @ SV16 @ ( ap_contractE_sk2q @ SV16 @ SV44 @ SV65 ) ) @ contract )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(236,plain,
! [SV66: $i,SV45: $i,SV17: $i] :
( ( ( ap_contractE_c3 @ SV17 @ SV45 @ SV66 )
= $false )
| ( ( member @ SV45 @ comb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(237,plain,
! [SV67: $i,SV46: $i,SV18: $i] :
( ( ( ap_contractE_c3 @ SV18 @ SV46 @ SV67 )
= $false )
| ( ( SV67
= ( comb_app @ ( ap_contractE_sk2q @ SV18 @ SV46 @ SV67 ) @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(238,plain,
! [SV68: $i,SV47: $i,SV19: $i] :
( ( ( ap_contractE_c4 @ SV19 @ SV47 @ SV68 )
= $false )
| ( ( member @ ( pair @ SV47 @ ( ap_contractE_sk3q @ SV19 @ SV47 @ SV68 ) ) @ contract )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(239,plain,
! [SV69: $i,SV48: $i,SV20: $i] :
( ( ( ap_contractE_c4 @ SV20 @ SV48 @ SV69 )
= $false )
| ( ( member @ SV20 @ comb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(240,plain,
! [SV70: $i,SV49: $i,SV21: $i] :
( ( ( ap_contractE_c4 @ SV21 @ SV49 @ SV70 )
= $false )
| ( ( SV70
= ( comb_app @ SV21 @ ( ap_contractE_sk3q @ SV21 @ SV49 @ SV70 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(241,plain,
! [SV74: $i,SV71: $i,SV52: $i,SV27: $i] :
( ( ( ( comb_app @ SV27 @ SV52 )
!= ( comb_app @ SV71 @ SV74 ) )
= $true )
| ( ( SV27 = SV71 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(242,plain,
! [SV75: $i,SV72: $i,SV53: $i,SV28: $i] :
( ( ( ( comb_app @ SV28 @ SV53 )
!= ( comb_app @ SV72 @ SV75 ) )
= $true )
| ( ( SV53 = SV75 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(243,plain,
! [SV76: $i,SV73: $i,SV54: $i,SV29: $i] :
( ( ( SV29 != SV54 )
= $true )
| ( ( ( SV73 != SV76 )
| ( ( comb_app @ SV29 @ SV73 )
= ( comb_app @ SV54 @ SV76 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[222]) ).
thf(244,plain,
! [SV3: $i,SV32: $i] :
( ( ( member @ SV32 @ comb )
= $false )
| ( ( member @ ( comb_app @ SV3 @ SV32 ) @ comb )
= $true )
| ( ( member @ SV3 @ comb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(245,plain,
! [SV5: $i,SV33: $i] :
( ( ( member @ SV33 @ comb )
= $false )
| ( ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ SV5 ) @ SV33 ) @ SV5 ) @ contract )
= $true )
| ( ( member @ SV5 @ comb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(246,plain,
! [SV6: $i,SV55: $i,SV34: $i] :
( ( ( ~ ( member @ SV34 @ comb ) )
= $true )
| ( ( ~ ( member @ SV55 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV6 ) @ SV34 ) @ SV55 ) @ ( comb_app @ ( comb_app @ SV6 @ SV55 ) @ ( comb_app @ SV34 @ SV55 ) ) ) @ contract ) )
= $true )
| ( ( member @ SV6 @ comb )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(247,plain,
! [SV56: $i,SV35: $i,SV7: $i] :
( ( ( ap_contractE_c1 @ SV7 @ SV35 @ SV56 )
= $true )
| ( ( ( ap_contractE_c2 @ SV7 @ SV35 @ SV56 )
| ( ap_contractE_c3 @ SV7 @ SV35 @ SV56 )
| ( ap_contractE_c4 @ SV7 @ SV35 @ SV56 ) )
= $true )
| ( ( member @ ( pair @ ( comb_app @ SV7 @ SV35 ) @ SV56 ) @ contract )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[226]) ).
thf(248,plain,
! [SV74: $i,SV71: $i,SV52: $i,SV27: $i] :
( ( ( ( comb_app @ SV27 @ SV52 )
= ( comb_app @ SV71 @ SV74 ) )
= $false )
| ( ( SV27 = SV71 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(249,plain,
! [SV75: $i,SV72: $i,SV53: $i,SV28: $i] :
( ( ( ( comb_app @ SV28 @ SV53 )
= ( comb_app @ SV72 @ SV75 ) )
= $false )
| ( ( SV53 = SV75 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(250,plain,
! [SV76: $i,SV73: $i,SV54: $i,SV29: $i] :
( ( ( SV29 = SV54 )
= $false )
| ( ( ( SV73 != SV76 )
| ( ( comb_app @ SV29 @ SV73 )
= ( comb_app @ SV54 @ SV76 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(251,plain,
! [SV6: $i,SV55: $i,SV34: $i] :
( ( ( member @ SV34 @ comb )
= $false )
| ( ( ~ ( member @ SV55 @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV6 ) @ SV34 ) @ SV55 ) @ ( comb_app @ ( comb_app @ SV6 @ SV55 ) @ ( comb_app @ SV34 @ SV55 ) ) ) @ contract ) )
= $true )
| ( ( member @ SV6 @ comb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(252,plain,
! [SV56: $i,SV35: $i,SV7: $i] :
( ( ( ap_contractE_c2 @ SV7 @ SV35 @ SV56 )
= $true )
| ( ( ( ap_contractE_c3 @ SV7 @ SV35 @ SV56 )
| ( ap_contractE_c4 @ SV7 @ SV35 @ SV56 ) )
= $true )
| ( ( ap_contractE_c1 @ SV7 @ SV35 @ SV56 )
= $true )
| ( ( member @ ( pair @ ( comb_app @ SV7 @ SV35 ) @ SV56 ) @ contract )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[247]) ).
thf(253,plain,
! [SV54: $i,SV29: $i,SV76: $i,SV73: $i] :
( ( ( SV73 != SV76 )
= $true )
| ( ( ( comb_app @ SV29 @ SV73 )
= ( comb_app @ SV54 @ SV76 ) )
= $true )
| ( ( SV29 = SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[250]) ).
thf(254,plain,
! [SV34: $i,SV6: $i,SV55: $i] :
( ( ( ~ ( member @ SV55 @ comb ) )
= $true )
| ( ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV6 ) @ SV34 ) @ SV55 ) @ ( comb_app @ ( comb_app @ SV6 @ SV55 ) @ ( comb_app @ SV34 @ SV55 ) ) ) @ contract )
= $true )
| ( ( member @ SV34 @ comb )
= $false )
| ( ( member @ SV6 @ comb )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[251]) ).
thf(255,plain,
! [SV56: $i,SV35: $i,SV7: $i] :
( ( ( ap_contractE_c3 @ SV7 @ SV35 @ SV56 )
= $true )
| ( ( ap_contractE_c4 @ SV7 @ SV35 @ SV56 )
= $true )
| ( ( ap_contractE_c2 @ SV7 @ SV35 @ SV56 )
= $true )
| ( ( ap_contractE_c1 @ SV7 @ SV35 @ SV56 )
= $true )
| ( ( member @ ( pair @ ( comb_app @ SV7 @ SV35 ) @ SV56 ) @ contract )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[252]) ).
thf(256,plain,
! [SV54: $i,SV29: $i,SV76: $i,SV73: $i] :
( ( ( SV73 = SV76 )
= $false )
| ( ( ( comb_app @ SV29 @ SV73 )
= ( comb_app @ SV54 @ SV76 ) )
= $true )
| ( ( SV29 = SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(257,plain,
! [SV34: $i,SV6: $i,SV55: $i] :
( ( ( member @ SV55 @ comb )
= $false )
| ( ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ SV6 ) @ SV34 ) @ SV55 ) @ ( comb_app @ ( comb_app @ SV6 @ SV55 ) @ ( comb_app @ SV34 @ SV55 ) ) ) @ contract )
= $true )
| ( ( member @ SV34 @ comb )
= $false )
| ( ( member @ SV6 @ comb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(258,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[72,257,256,255,249,248,245,244,240,239,238,237,236,235,234,233,232,231,230,229,228,227,219,200,199,195,194,175,165,164,136,135,82,81]) ).
thf(259,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[258]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL091-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n020.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Oct 6 18:35:36 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.53/0.34
% 0.53/0.34 No.of.Axioms: 33
% 0.53/0.34
% 0.53/0.34 Length.of.Defs: 0
% 0.53/0.34
% 0.53/0.34 Contains.Choice.Funs: false
% 0.53/0.34 ......
% 0.53/0.34
% 0.53/0.34 ********************************
% 0.53/0.34 * All subproblems solved! *
% 0.53/0.34 ********************************
% 0.53/0.34 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:33,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:258,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.53/0.34
% 0.53/0.34 %**** Beginning of derivation protocol ****
% 0.53/0.34 % SZS output start CNFRefutation
% See solution above
% 0.53/0.34
% 0.53/0.34 %**** End of derivation protocol ****
% 0.53/0.34 %**** no. of clauses in derivation: 259 ****
% 0.53/0.34 %**** clause counter: 258 ****
% 0.53/0.34
% 0.53/0.34 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:33,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:258,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------