TSTP Solution File: COL100-1 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : COL100-1 : 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 : n023.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 00:34:50 EDT 2022
% Result : Unsatisfiable 1.52s 1.71s
% Output : CNFRefutation 1.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 34
% Syntax : Number of formulae : 159 ( 90 unt; 15 typ; 0 def)
% Number of atoms : 723 ( 286 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 1552 ( 172 ~; 197 |; 0 &;1183 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 9 con; 0-4 aty)
% Number of variables : 371 ( 0 ^ 371 !; 0 ?; 371 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_combK,type,
combK: $i ).
thf(tp_combS,type,
combS: $i ).
thf(tp_comb_app,type,
comb_app: $i > $i > $i ).
thf(tp_diamond,type,
diamond: $i > $o ).
thf(tp_diamond_strip_lemmaD_sk1,type,
diamond_strip_lemmaD_sk1: $i > $i > $i > $i > $i ).
thf(tp_member,type,
member: $i > $i > $o ).
thf(tp_pair,type,
pair: $i > $i > $i ).
thf(tp_r,type,
r: $i ).
thf(tp_sk1,type,
sk1: $i > $i ).
thf(tp_trancl,type,
trancl: $i > $i ).
thf(tp_trans,type,
trans: $i > $o ).
thf(tp_y,type,
y: $i ).
thf(tp_ya,type,
ya: $i ).
thf(tp_yp,type,
yp: $i ).
thf(tp_z,type,
z: $i ).
thf(1,axiom,
! [R: $i,X: $i,Y: $i,YP: $i] :
( ~ ( diamond @ R )
| ~ ( member @ ( pair @ X @ Y ) @ ( trancl @ R ) )
| ~ ( member @ ( pair @ X @ YP ) @ R )
| ( member @ ( pair @ Y @ ( diamond_strip_lemmaD_sk1 @ X @ Y @ YP @ R ) ) @ R ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diamond_strip_lemmaD2) ).
thf(2,axiom,
! [R: $i,X: $i,Y: $i,YP: $i] :
( ~ ( diamond @ R )
| ~ ( member @ ( pair @ X @ Y ) @ ( trancl @ R ) )
| ~ ( member @ ( pair @ X @ YP ) @ R )
| ( member @ ( pair @ YP @ ( diamond_strip_lemmaD_sk1 @ X @ Y @ YP @ R ) ) @ ( trancl @ R ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diamond_strip_lemmaD1) ).
thf(3,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(4,axiom,
! [R: $i] : ( trans @ ( trancl @ R ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',trans_trancl) ).
thf(5,axiom,
! [A: $i,B: $i,R: $i] :
( ~ ( member @ ( pair @ A @ B ) @ R )
| ( member @ ( pair @ A @ B ) @ ( trancl @ R ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r_into_trancl) ).
thf(6,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(7,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(8,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(9,axiom,
! [P: $i,Q: $i] :
( combS
!= ( comb_app @ P @ Q ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_app) ).
thf(10,axiom,
! [P: $i,Q: $i] :
( combK
!= ( comb_app @ P @ Q ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_app) ).
thf(11,axiom,
combK != combS,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_s) ).
thf(12,axiom,
! [YP: $i] :
( ~ ( member @ ( pair @ y @ YP ) @ ( trancl @ r ) )
| ( member @ ( pair @ YP @ ( sk1 @ YP ) ) @ ( trancl @ r ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diamond_trancl_2h5) ).
thf(13,axiom,
! [YP: $i] :
( ~ ( member @ ( pair @ y @ YP ) @ ( trancl @ r ) )
| ( member @ ( pair @ ya @ ( sk1 @ YP ) ) @ ( trancl @ r ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diamond_trancl_2h4) ).
thf(14,axiom,
member @ ( pair @ ya @ z ) @ r,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diamond_trancl_2h3) ).
thf(15,axiom,
member @ ( pair @ y @ ya ) @ ( trancl @ r ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diamond_trancl_2h2) ).
thf(16,axiom,
diamond @ r,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diamond_trancl_2h1) ).
thf(17,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(18,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[17]) ).
thf(19,negated_conjecture,
! [ZA: $i] :
( ~ ( member @ ( pair @ z @ ZA ) @ ( trancl @ r ) )
| ~ ( member @ ( pair @ yp @ ZA ) @ ( trancl @ r ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diamond_trancl_2c2) ).
thf(20,negated_conjecture,
member @ ( pair @ y @ yp ) @ ( trancl @ r ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diamond_trancl_2c1) ).
thf(21,plain,
$false = $false,
inference(unfold_def,[status(thm)],[18]) ).
thf(22,plain,
( ( ! [R: $i,X: $i,Y: $i,YP: $i] :
( ~ ( diamond @ R )
| ~ ( member @ ( pair @ X @ Y ) @ ( trancl @ R ) )
| ~ ( member @ ( pair @ X @ YP ) @ R )
| ( member @ ( pair @ Y @ ( diamond_strip_lemmaD_sk1 @ X @ Y @ YP @ R ) ) @ R ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(23,plain,
( ( ! [R: $i,X: $i,Y: $i,YP: $i] :
( ~ ( diamond @ R )
| ~ ( member @ ( pair @ X @ Y ) @ ( trancl @ R ) )
| ~ ( member @ ( pair @ X @ YP ) @ R )
| ( member @ ( pair @ YP @ ( diamond_strip_lemmaD_sk1 @ X @ Y @ YP @ R ) ) @ ( trancl @ R ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(24,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)],[3]) ).
thf(25,plain,
( ( ! [R: $i] : ( trans @ ( trancl @ R ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(26,plain,
( ( ! [A: $i,B: $i,R: $i] :
( ~ ( member @ ( pair @ A @ B ) @ R )
| ( member @ ( pair @ A @ B ) @ ( trancl @ R ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(27,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)],[6]) ).
thf(28,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)],[7]) ).
thf(29,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)],[8]) ).
thf(30,plain,
( ( ! [P: $i,Q: $i] :
( combS
!= ( comb_app @ P @ Q ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(31,plain,
( ( ! [P: $i,Q: $i] :
( combK
!= ( comb_app @ P @ Q ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(32,plain,
( ( ( combK != combS ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(33,plain,
( ( ! [YP: $i] :
( ~ ( member @ ( pair @ y @ YP ) @ ( trancl @ r ) )
| ( member @ ( pair @ YP @ ( sk1 @ YP ) ) @ ( trancl @ r ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(34,plain,
( ( ! [YP: $i] :
( ~ ( member @ ( pair @ y @ YP ) @ ( trancl @ r ) )
| ( member @ ( pair @ ya @ ( sk1 @ YP ) ) @ ( trancl @ r ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(35,plain,
( ( member @ ( pair @ ya @ z ) @ r )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(36,plain,
( ( member @ ( pair @ y @ ya ) @ ( trancl @ r ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(37,plain,
( ( diamond @ r )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(38,plain,
( ( ! [ZA: $i] :
( ~ ( member @ ( pair @ z @ ZA ) @ ( trancl @ r ) )
| ~ ( member @ ( pair @ yp @ ZA ) @ ( trancl @ r ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(39,plain,
( ( member @ ( pair @ y @ yp ) @ ( trancl @ r ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(40,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[21]) ).
thf(41,plain,
( ( ! [R: $i,X: $i] :
( ~ ( diamond @ R )
| ! [Y: $i] :
( ~ ( member @ ( pair @ X @ Y ) @ ( trancl @ R ) )
| ! [YP: $i] :
( ~ ( member @ ( pair @ X @ YP ) @ R )
| ( member @ ( pair @ Y @ ( diamond_strip_lemmaD_sk1 @ X @ Y @ YP @ R ) ) @ R ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(42,plain,
( ( ! [R: $i,X: $i] :
( ~ ( diamond @ R )
| ! [Y: $i] :
( ~ ( member @ ( pair @ X @ Y ) @ ( trancl @ R ) )
| ! [YP: $i] :
( ~ ( member @ ( pair @ X @ YP ) @ R )
| ( member @ ( pair @ YP @ ( diamond_strip_lemmaD_sk1 @ X @ Y @ YP @ R ) ) @ ( trancl @ R ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(43,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)],[24]) ).
thf(44,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)],[27]) ).
thf(45,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)],[28]) ).
thf(46,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)],[29]) ).
thf(47,plain,
( ( ! [P: $i,Q: $i] :
( combS
!= ( comb_app @ P @ Q ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[30]) ).
thf(48,plain,
( ( ! [P: $i,Q: $i] :
( combK
!= ( comb_app @ P @ Q ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[31]) ).
thf(49,plain,
( ( ( combK != combS ) )
= $true ),
inference(extcnf_combined,[status(esa)],[32]) ).
thf(50,plain,
( ( member @ ( pair @ y @ yp ) @ ( trancl @ r ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(51,plain,
( ( ! [ZA: $i] :
( ~ ( member @ ( pair @ z @ ZA ) @ ( trancl @ r ) )
| ~ ( member @ ( pair @ yp @ ZA ) @ ( trancl @ r ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(52,plain,
( ( diamond @ r )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(53,plain,
( ( member @ ( pair @ y @ ya ) @ ( trancl @ r ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(54,plain,
( ( member @ ( pair @ ya @ z ) @ r )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(55,plain,
( ( ! [YP: $i] :
( ~ ( member @ ( pair @ y @ YP ) @ ( trancl @ r ) )
| ( member @ ( pair @ ya @ ( sk1 @ YP ) ) @ ( trancl @ r ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(56,plain,
( ( ! [YP: $i] :
( ~ ( member @ ( pair @ y @ YP ) @ ( trancl @ r ) )
| ( member @ ( pair @ YP @ ( sk1 @ YP ) ) @ ( trancl @ r ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(57,plain,
( ( ( combK != combS ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(58,plain,
( ( ! [P: $i,Q: $i] :
( combK
!= ( comb_app @ P @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(59,plain,
( ( ! [P: $i,Q: $i] :
( combS
!= ( comb_app @ P @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(60,plain,
( ( ! [P1: $i,Q1: $i,P2: $i] :
( ! [Q2: $i] :
( ( comb_app @ P1 @ Q1 )
!= ( comb_app @ P2 @ Q2 ) )
| ( P1 = P2 ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(61,plain,
( ( ! [P1: $i,Q1: $i,P2: $i,Q2: $i] :
( ( ( comb_app @ P1 @ Q1 )
!= ( comb_app @ P2 @ Q2 ) )
| ( Q1 = Q2 ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(62,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)],[44]) ).
thf(63,plain,
( ( ! [A: $i,B: $i,R: $i] :
( ~ ( member @ ( pair @ A @ B ) @ R )
| ( member @ ( pair @ A @ B ) @ ( trancl @ R ) ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(64,plain,
( ( ! [R: $i] : ( trans @ ( trancl @ R ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(65,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)],[43]) ).
thf(66,plain,
( ( ! [R: $i,X: $i] :
( ~ ( diamond @ R )
| ! [Y: $i] :
( ~ ( member @ ( pair @ X @ Y ) @ ( trancl @ R ) )
| ! [YP: $i] :
( ~ ( member @ ( pair @ X @ YP ) @ R )
| ( member @ ( pair @ YP @ ( diamond_strip_lemmaD_sk1 @ X @ Y @ YP @ R ) ) @ ( trancl @ R ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(67,plain,
( ( ! [R: $i,X: $i] :
( ~ ( diamond @ R )
| ! [Y: $i] :
( ~ ( member @ ( pair @ X @ Y ) @ ( trancl @ R ) )
| ! [YP: $i] :
( ~ ( member @ ( pair @ X @ YP ) @ R )
| ( member @ ( pair @ Y @ ( diamond_strip_lemmaD_sk1 @ X @ Y @ YP @ R ) ) @ R ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(68,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(69,plain,
! [SV1: $i] :
( ( ~ ( member @ ( pair @ z @ SV1 ) @ ( trancl @ r ) )
| ~ ( member @ ( pair @ yp @ SV1 ) @ ( trancl @ r ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(70,plain,
! [SV2: $i] :
( ( ~ ( member @ ( pair @ y @ SV2 ) @ ( trancl @ r ) )
| ( member @ ( pair @ ya @ ( sk1 @ SV2 ) ) @ ( trancl @ r ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(71,plain,
! [SV3: $i] :
( ( ~ ( member @ ( pair @ y @ SV3 ) @ ( trancl @ r ) )
| ( member @ ( pair @ SV3 @ ( sk1 @ SV3 ) ) @ ( trancl @ r ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(72,plain,
( ( combK = combS )
= $false ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(73,plain,
! [SV4: $i] :
( ( ! [SY35: $i] :
( combK
!= ( comb_app @ SV4 @ SY35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(74,plain,
! [SV5: $i] :
( ( ! [SY36: $i] :
( combS
!= ( comb_app @ SV5 @ SY36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(75,plain,
! [SV6: $i] :
( ( ! [SY37: $i,SY38: $i] :
( ! [SY39: $i] :
( ( comb_app @ SV6 @ SY37 )
!= ( comb_app @ SY38 @ SY39 ) )
| ( SV6 = SY38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(76,plain,
! [SV7: $i] :
( ( ! [SY40: $i,SY41: $i,SY42: $i] :
( ( ( comb_app @ SV7 @ SY40 )
!= ( comb_app @ SY41 @ SY42 ) )
| ( SY40 = SY42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(77,plain,
! [SV8: $i] :
( ( ! [SY43: $i] :
( ( SV8 != SY43 )
| ! [SY44: $i,SY45: $i] :
( ( SY44 != SY45 )
| ( ( comb_app @ SV8 @ SY44 )
= ( comb_app @ SY43 @ SY45 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(78,plain,
! [SV9: $i] :
( ( ! [SY46: $i,SY47: $i] :
( ~ ( member @ ( pair @ SV9 @ SY46 ) @ SY47 )
| ( member @ ( pair @ SV9 @ SY46 ) @ ( trancl @ SY47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(79,plain,
! [SV10: $i] :
( ( trans @ ( trancl @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(80,plain,
! [SV11: $i] :
( ( ! [SY48: $i] :
( ~ ( trans @ SV11 )
| ! [SY49: $i] :
( ~ ( member @ ( pair @ SY48 @ SY49 ) @ SV11 )
| ! [SY50: $i] :
( ~ ( member @ ( pair @ SY49 @ SY50 ) @ SV11 )
| ( member @ ( pair @ SY48 @ SY50 ) @ SV11 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(81,plain,
! [SV12: $i] :
( ( ! [SY51: $i] :
( ~ ( diamond @ SV12 )
| ! [SY52: $i] :
( ~ ( member @ ( pair @ SY51 @ SY52 ) @ ( trancl @ SV12 ) )
| ! [SY53: $i] :
( ~ ( member @ ( pair @ SY51 @ SY53 ) @ SV12 )
| ( member @ ( pair @ SY53 @ ( diamond_strip_lemmaD_sk1 @ SY51 @ SY52 @ SY53 @ SV12 ) ) @ ( trancl @ SV12 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(82,plain,
! [SV13: $i] :
( ( ! [SY54: $i] :
( ~ ( diamond @ SV13 )
| ! [SY55: $i] :
( ~ ( member @ ( pair @ SY54 @ SY55 ) @ ( trancl @ SV13 ) )
| ! [SY56: $i] :
( ~ ( member @ ( pair @ SY54 @ SY56 ) @ SV13 )
| ( member @ ( pair @ SY55 @ ( diamond_strip_lemmaD_sk1 @ SY54 @ SY55 @ SY56 @ SV13 ) ) @ SV13 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(83,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(84,plain,
! [SV1: $i] :
( ( ( ~ ( member @ ( pair @ z @ SV1 ) @ ( trancl @ r ) ) )
= $true )
| ( ( ~ ( member @ ( pair @ yp @ SV1 ) @ ( trancl @ r ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[69]) ).
thf(85,plain,
! [SV2: $i] :
( ( ( ~ ( member @ ( pair @ y @ SV2 ) @ ( trancl @ r ) ) )
= $true )
| ( ( member @ ( pair @ ya @ ( sk1 @ SV2 ) ) @ ( trancl @ r ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(86,plain,
! [SV3: $i] :
( ( ( ~ ( member @ ( pair @ y @ SV3 ) @ ( trancl @ r ) ) )
= $true )
| ( ( member @ ( pair @ SV3 @ ( sk1 @ SV3 ) ) @ ( trancl @ r ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[71]) ).
thf(87,plain,
! [SV14: $i,SV4: $i] :
( ( ( combK
!= ( comb_app @ SV4 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(88,plain,
! [SV15: $i,SV5: $i] :
( ( ( combS
!= ( comb_app @ SV5 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(89,plain,
! [SV16: $i,SV6: $i] :
( ( ! [SY57: $i] :
( ! [SY58: $i] :
( ( comb_app @ SV6 @ SV16 )
!= ( comb_app @ SY57 @ SY58 ) )
| ( SV6 = SY57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(90,plain,
! [SV17: $i,SV7: $i] :
( ( ! [SY59: $i,SY60: $i] :
( ( ( comb_app @ SV7 @ SV17 )
!= ( comb_app @ SY59 @ SY60 ) )
| ( SV17 = SY60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(91,plain,
! [SV18: $i,SV8: $i] :
( ( ( SV8 != SV18 )
| ! [SY61: $i,SY62: $i] :
( ( SY61 != SY62 )
| ( ( comb_app @ SV8 @ SY61 )
= ( comb_app @ SV18 @ SY62 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(92,plain,
! [SV19: $i,SV9: $i] :
( ( ! [SY63: $i] :
( ~ ( member @ ( pair @ SV9 @ SV19 ) @ SY63 )
| ( member @ ( pair @ SV9 @ SV19 ) @ ( trancl @ SY63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(93,plain,
! [SV20: $i,SV11: $i] :
( ( ~ ( trans @ SV11 )
| ! [SY64: $i] :
( ~ ( member @ ( pair @ SV20 @ SY64 ) @ SV11 )
| ! [SY65: $i] :
( ~ ( member @ ( pair @ SY64 @ SY65 ) @ SV11 )
| ( member @ ( pair @ SV20 @ SY65 ) @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(94,plain,
! [SV21: $i,SV12: $i] :
( ( ~ ( diamond @ SV12 )
| ! [SY66: $i] :
( ~ ( member @ ( pair @ SV21 @ SY66 ) @ ( trancl @ SV12 ) )
| ! [SY67: $i] :
( ~ ( member @ ( pair @ SV21 @ SY67 ) @ SV12 )
| ( member @ ( pair @ SY67 @ ( diamond_strip_lemmaD_sk1 @ SV21 @ SY66 @ SY67 @ SV12 ) ) @ ( trancl @ SV12 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(95,plain,
! [SV22: $i,SV13: $i] :
( ( ~ ( diamond @ SV13 )
| ! [SY68: $i] :
( ~ ( member @ ( pair @ SV22 @ SY68 ) @ ( trancl @ SV13 ) )
| ! [SY69: $i] :
( ~ ( member @ ( pair @ SV22 @ SY69 ) @ SV13 )
| ( member @ ( pair @ SY68 @ ( diamond_strip_lemmaD_sk1 @ SV22 @ SY68 @ SY69 @ SV13 ) ) @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(96,plain,
! [SV1: $i] :
( ( ( member @ ( pair @ z @ SV1 ) @ ( trancl @ r ) )
= $false )
| ( ( ~ ( member @ ( pair @ yp @ SV1 ) @ ( trancl @ r ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(97,plain,
! [SV2: $i] :
( ( ( member @ ( pair @ y @ SV2 ) @ ( trancl @ r ) )
= $false )
| ( ( member @ ( pair @ ya @ ( sk1 @ SV2 ) ) @ ( trancl @ r ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(98,plain,
! [SV3: $i] :
( ( ( member @ ( pair @ y @ SV3 ) @ ( trancl @ r ) )
= $false )
| ( ( member @ ( pair @ SV3 @ ( sk1 @ SV3 ) ) @ ( trancl @ r ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(99,plain,
! [SV14: $i,SV4: $i] :
( ( combK
= ( comb_app @ SV4 @ SV14 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(100,plain,
! [SV15: $i,SV5: $i] :
( ( combS
= ( comb_app @ SV5 @ SV15 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(101,plain,
! [SV23: $i,SV16: $i,SV6: $i] :
( ( ! [SY70: $i] :
( ( comb_app @ SV6 @ SV16 )
!= ( comb_app @ SV23 @ SY70 ) )
| ( SV6 = SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(102,plain,
! [SV24: $i,SV17: $i,SV7: $i] :
( ( ! [SY71: $i] :
( ( ( comb_app @ SV7 @ SV17 )
!= ( comb_app @ SV24 @ SY71 ) )
| ( SV17 = SY71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(103,plain,
! [SV18: $i,SV8: $i] :
( ( ( ( SV8 != SV18 ) )
= $true )
| ( ( ! [SY61: $i,SY62: $i] :
( ( SY61 != SY62 )
| ( ( comb_app @ SV8 @ SY61 )
= ( comb_app @ SV18 @ SY62 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(104,plain,
! [SV25: $i,SV19: $i,SV9: $i] :
( ( ~ ( member @ ( pair @ SV9 @ SV19 ) @ SV25 )
| ( member @ ( pair @ SV9 @ SV19 ) @ ( trancl @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(105,plain,
! [SV20: $i,SV11: $i] :
( ( ( ~ ( trans @ SV11 ) )
= $true )
| ( ( ! [SY64: $i] :
( ~ ( member @ ( pair @ SV20 @ SY64 ) @ SV11 )
| ! [SY65: $i] :
( ~ ( member @ ( pair @ SY64 @ SY65 ) @ SV11 )
| ( member @ ( pair @ SV20 @ SY65 ) @ SV11 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(106,plain,
! [SV21: $i,SV12: $i] :
( ( ( ~ ( diamond @ SV12 ) )
= $true )
| ( ( ! [SY66: $i] :
( ~ ( member @ ( pair @ SV21 @ SY66 ) @ ( trancl @ SV12 ) )
| ! [SY67: $i] :
( ~ ( member @ ( pair @ SV21 @ SY67 ) @ SV12 )
| ( member @ ( pair @ SY67 @ ( diamond_strip_lemmaD_sk1 @ SV21 @ SY66 @ SY67 @ SV12 ) ) @ ( trancl @ SV12 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(107,plain,
! [SV22: $i,SV13: $i] :
( ( ( ~ ( diamond @ SV13 ) )
= $true )
| ( ( ! [SY68: $i] :
( ~ ( member @ ( pair @ SV22 @ SY68 ) @ ( trancl @ SV13 ) )
| ! [SY69: $i] :
( ~ ( member @ ( pair @ SV22 @ SY69 ) @ SV13 )
| ( member @ ( pair @ SY68 @ ( diamond_strip_lemmaD_sk1 @ SV22 @ SY68 @ SY69 @ SV13 ) ) @ SV13 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(108,plain,
! [SV1: $i] :
( ( ( member @ ( pair @ yp @ SV1 ) @ ( trancl @ r ) )
= $false )
| ( ( member @ ( pair @ z @ SV1 ) @ ( trancl @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(109,plain,
! [SV23: $i,SV16: $i,SV6: $i] :
( ( ( ! [SY70: $i] :
( ( comb_app @ SV6 @ SV16 )
!= ( comb_app @ SV23 @ SY70 ) ) )
= $true )
| ( ( SV6 = SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(110,plain,
! [SV26: $i,SV24: $i,SV17: $i,SV7: $i] :
( ( ( ( comb_app @ SV7 @ SV17 )
!= ( comb_app @ SV24 @ SV26 ) )
| ( SV17 = SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(111,plain,
! [SV18: $i,SV8: $i] :
( ( ( SV8 = SV18 )
= $false )
| ( ( ! [SY61: $i,SY62: $i] :
( ( SY61 != SY62 )
| ( ( comb_app @ SV8 @ SY61 )
= ( comb_app @ SV18 @ SY62 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(112,plain,
! [SV25: $i,SV19: $i,SV9: $i] :
( ( ( ~ ( member @ ( pair @ SV9 @ SV19 ) @ SV25 ) )
= $true )
| ( ( member @ ( pair @ SV9 @ SV19 ) @ ( trancl @ SV25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(113,plain,
! [SV20: $i,SV11: $i] :
( ( ( trans @ SV11 )
= $false )
| ( ( ! [SY64: $i] :
( ~ ( member @ ( pair @ SV20 @ SY64 ) @ SV11 )
| ! [SY65: $i] :
( ~ ( member @ ( pair @ SY64 @ SY65 ) @ SV11 )
| ( member @ ( pair @ SV20 @ SY65 ) @ SV11 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(114,plain,
! [SV21: $i,SV12: $i] :
( ( ( diamond @ SV12 )
= $false )
| ( ( ! [SY66: $i] :
( ~ ( member @ ( pair @ SV21 @ SY66 ) @ ( trancl @ SV12 ) )
| ! [SY67: $i] :
( ~ ( member @ ( pair @ SV21 @ SY67 ) @ SV12 )
| ( member @ ( pair @ SY67 @ ( diamond_strip_lemmaD_sk1 @ SV21 @ SY66 @ SY67 @ SV12 ) ) @ ( trancl @ SV12 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(115,plain,
! [SV22: $i,SV13: $i] :
( ( ( diamond @ SV13 )
= $false )
| ( ( ! [SY68: $i] :
( ~ ( member @ ( pair @ SV22 @ SY68 ) @ ( trancl @ SV13 ) )
| ! [SY69: $i] :
( ~ ( member @ ( pair @ SV22 @ SY69 ) @ SV13 )
| ( member @ ( pair @ SY68 @ ( diamond_strip_lemmaD_sk1 @ SV22 @ SY68 @ SY69 @ SV13 ) ) @ SV13 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(116,plain,
! [SV27: $i,SV23: $i,SV16: $i,SV6: $i] :
( ( ( ( ( comb_app @ SV6 @ SV16 )
!= ( comb_app @ SV23 @ SV27 ) ) )
= $true )
| ( ( SV6 = SV23 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(117,plain,
! [SV26: $i,SV24: $i,SV17: $i,SV7: $i] :
( ( ( ( ( comb_app @ SV7 @ SV17 )
!= ( comb_app @ SV24 @ SV26 ) ) )
= $true )
| ( ( SV17 = SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(118,plain,
! [SV18: $i,SV8: $i,SV28: $i] :
( ( ( ! [SY72: $i] :
( ( SV28 != SY72 )
| ( ( comb_app @ SV8 @ SV28 )
= ( comb_app @ SV18 @ SY72 ) ) ) )
= $true )
| ( ( SV8 = SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(119,plain,
! [SV25: $i,SV19: $i,SV9: $i] :
( ( ( member @ ( pair @ SV9 @ SV19 ) @ SV25 )
= $false )
| ( ( member @ ( pair @ SV9 @ SV19 ) @ ( trancl @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(120,plain,
! [SV11: $i,SV29: $i,SV20: $i] :
( ( ( ~ ( member @ ( pair @ SV20 @ SV29 ) @ SV11 )
| ! [SY73: $i] :
( ~ ( member @ ( pair @ SV29 @ SY73 ) @ SV11 )
| ( member @ ( pair @ SV20 @ SY73 ) @ SV11 ) ) )
= $true )
| ( ( trans @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(121,plain,
! [SV12: $i,SV30: $i,SV21: $i] :
( ( ( ~ ( member @ ( pair @ SV21 @ SV30 ) @ ( trancl @ SV12 ) )
| ! [SY74: $i] :
( ~ ( member @ ( pair @ SV21 @ SY74 ) @ SV12 )
| ( member @ ( pair @ SY74 @ ( diamond_strip_lemmaD_sk1 @ SV21 @ SV30 @ SY74 @ SV12 ) ) @ ( trancl @ SV12 ) ) ) )
= $true )
| ( ( diamond @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(122,plain,
! [SV13: $i,SV31: $i,SV22: $i] :
( ( ( ~ ( member @ ( pair @ SV22 @ SV31 ) @ ( trancl @ SV13 ) )
| ! [SY75: $i] :
( ~ ( member @ ( pair @ SV22 @ SY75 ) @ SV13 )
| ( member @ ( pair @ SV31 @ ( diamond_strip_lemmaD_sk1 @ SV22 @ SV31 @ SY75 @ SV13 ) ) @ SV13 ) ) )
= $true )
| ( ( diamond @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(123,plain,
! [SV27: $i,SV23: $i,SV16: $i,SV6: $i] :
( ( ( ( comb_app @ SV6 @ SV16 )
= ( comb_app @ SV23 @ SV27 ) )
= $false )
| ( ( SV6 = SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(124,plain,
! [SV26: $i,SV24: $i,SV17: $i,SV7: $i] :
( ( ( ( comb_app @ SV7 @ SV17 )
= ( comb_app @ SV24 @ SV26 ) )
= $false )
| ( ( SV17 = SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(125,plain,
! [SV18: $i,SV8: $i,SV32: $i,SV28: $i] :
( ( ( ( SV28 != SV32 )
| ( ( comb_app @ SV8 @ SV28 )
= ( comb_app @ SV18 @ SV32 ) ) )
= $true )
| ( ( SV8 = SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(126,plain,
! [SV11: $i,SV29: $i,SV20: $i] :
( ( ( ~ ( member @ ( pair @ SV20 @ SV29 ) @ SV11 ) )
= $true )
| ( ( ! [SY73: $i] :
( ~ ( member @ ( pair @ SV29 @ SY73 ) @ SV11 )
| ( member @ ( pair @ SV20 @ SY73 ) @ SV11 ) ) )
= $true )
| ( ( trans @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(127,plain,
! [SV12: $i,SV30: $i,SV21: $i] :
( ( ( ~ ( member @ ( pair @ SV21 @ SV30 ) @ ( trancl @ SV12 ) ) )
= $true )
| ( ( ! [SY74: $i] :
( ~ ( member @ ( pair @ SV21 @ SY74 ) @ SV12 )
| ( member @ ( pair @ SY74 @ ( diamond_strip_lemmaD_sk1 @ SV21 @ SV30 @ SY74 @ SV12 ) ) @ ( trancl @ SV12 ) ) ) )
= $true )
| ( ( diamond @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(128,plain,
! [SV13: $i,SV31: $i,SV22: $i] :
( ( ( ~ ( member @ ( pair @ SV22 @ SV31 ) @ ( trancl @ SV13 ) ) )
= $true )
| ( ( ! [SY75: $i] :
( ~ ( member @ ( pair @ SV22 @ SY75 ) @ SV13 )
| ( member @ ( pair @ SV31 @ ( diamond_strip_lemmaD_sk1 @ SV22 @ SV31 @ SY75 @ SV13 ) ) @ SV13 ) ) )
= $true )
| ( ( diamond @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[122]) ).
thf(129,plain,
! [SV18: $i,SV8: $i,SV32: $i,SV28: $i] :
( ( ( ( SV28 != SV32 ) )
= $true )
| ( ( ( comb_app @ SV8 @ SV28 )
= ( comb_app @ SV18 @ SV32 ) )
= $true )
| ( ( SV8 = SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(130,plain,
! [SV11: $i,SV29: $i,SV20: $i] :
( ( ( member @ ( pair @ SV20 @ SV29 ) @ SV11 )
= $false )
| ( ( ! [SY73: $i] :
( ~ ( member @ ( pair @ SV29 @ SY73 ) @ SV11 )
| ( member @ ( pair @ SV20 @ SY73 ) @ SV11 ) ) )
= $true )
| ( ( trans @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(131,plain,
! [SV12: $i,SV30: $i,SV21: $i] :
( ( ( member @ ( pair @ SV21 @ SV30 ) @ ( trancl @ SV12 ) )
= $false )
| ( ( ! [SY74: $i] :
( ~ ( member @ ( pair @ SV21 @ SY74 ) @ SV12 )
| ( member @ ( pair @ SY74 @ ( diamond_strip_lemmaD_sk1 @ SV21 @ SV30 @ SY74 @ SV12 ) ) @ ( trancl @ SV12 ) ) ) )
= $true )
| ( ( diamond @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(132,plain,
! [SV13: $i,SV31: $i,SV22: $i] :
( ( ( member @ ( pair @ SV22 @ SV31 ) @ ( trancl @ SV13 ) )
= $false )
| ( ( ! [SY75: $i] :
( ~ ( member @ ( pair @ SV22 @ SY75 ) @ SV13 )
| ( member @ ( pair @ SV31 @ ( diamond_strip_lemmaD_sk1 @ SV22 @ SV31 @ SY75 @ SV13 ) ) @ SV13 ) ) )
= $true )
| ( ( diamond @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(133,plain,
! [SV18: $i,SV8: $i,SV32: $i,SV28: $i] :
( ( ( SV28 = SV32 )
= $false )
| ( ( ( comb_app @ SV8 @ SV28 )
= ( comb_app @ SV18 @ SV32 ) )
= $true )
| ( ( SV8 = SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(134,plain,
! [SV20: $i,SV11: $i,SV33: $i,SV29: $i] :
( ( ( ~ ( member @ ( pair @ SV29 @ SV33 ) @ SV11 )
| ( member @ ( pair @ SV20 @ SV33 ) @ SV11 ) )
= $true )
| ( ( member @ ( pair @ SV20 @ SV29 ) @ SV11 )
= $false )
| ( ( trans @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(135,plain,
! [SV30: $i,SV12: $i,SV34: $i,SV21: $i] :
( ( ( ~ ( member @ ( pair @ SV21 @ SV34 ) @ SV12 )
| ( member @ ( pair @ SV34 @ ( diamond_strip_lemmaD_sk1 @ SV21 @ SV30 @ SV34 @ SV12 ) ) @ ( trancl @ SV12 ) ) )
= $true )
| ( ( member @ ( pair @ SV21 @ SV30 ) @ ( trancl @ SV12 ) )
= $false )
| ( ( diamond @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(136,plain,
! [SV31: $i,SV13: $i,SV35: $i,SV22: $i] :
( ( ( ~ ( member @ ( pair @ SV22 @ SV35 ) @ SV13 )
| ( member @ ( pair @ SV31 @ ( diamond_strip_lemmaD_sk1 @ SV22 @ SV31 @ SV35 @ SV13 ) ) @ SV13 ) )
= $true )
| ( ( member @ ( pair @ SV22 @ SV31 ) @ ( trancl @ SV13 ) )
= $false )
| ( ( diamond @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(137,plain,
! [SV20: $i,SV11: $i,SV33: $i,SV29: $i] :
( ( ( ~ ( member @ ( pair @ SV29 @ SV33 ) @ SV11 ) )
= $true )
| ( ( member @ ( pair @ SV20 @ SV33 ) @ SV11 )
= $true )
| ( ( member @ ( pair @ SV20 @ SV29 ) @ SV11 )
= $false )
| ( ( trans @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(138,plain,
! [SV30: $i,SV12: $i,SV34: $i,SV21: $i] :
( ( ( ~ ( member @ ( pair @ SV21 @ SV34 ) @ SV12 ) )
= $true )
| ( ( member @ ( pair @ SV34 @ ( diamond_strip_lemmaD_sk1 @ SV21 @ SV30 @ SV34 @ SV12 ) ) @ ( trancl @ SV12 ) )
= $true )
| ( ( member @ ( pair @ SV21 @ SV30 ) @ ( trancl @ SV12 ) )
= $false )
| ( ( diamond @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(139,plain,
! [SV31: $i,SV13: $i,SV35: $i,SV22: $i] :
( ( ( ~ ( member @ ( pair @ SV22 @ SV35 ) @ SV13 ) )
= $true )
| ( ( member @ ( pair @ SV31 @ ( diamond_strip_lemmaD_sk1 @ SV22 @ SV31 @ SV35 @ SV13 ) ) @ SV13 )
= $true )
| ( ( member @ ( pair @ SV22 @ SV31 ) @ ( trancl @ SV13 ) )
= $false )
| ( ( diamond @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(140,plain,
! [SV20: $i,SV11: $i,SV33: $i,SV29: $i] :
( ( ( member @ ( pair @ SV29 @ SV33 ) @ SV11 )
= $false )
| ( ( member @ ( pair @ SV20 @ SV33 ) @ SV11 )
= $true )
| ( ( member @ ( pair @ SV20 @ SV29 ) @ SV11 )
= $false )
| ( ( trans @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(141,plain,
! [SV30: $i,SV12: $i,SV34: $i,SV21: $i] :
( ( ( member @ ( pair @ SV21 @ SV34 ) @ SV12 )
= $false )
| ( ( member @ ( pair @ SV34 @ ( diamond_strip_lemmaD_sk1 @ SV21 @ SV30 @ SV34 @ SV12 ) ) @ ( trancl @ SV12 ) )
= $true )
| ( ( member @ ( pair @ SV21 @ SV30 ) @ ( trancl @ SV12 ) )
= $false )
| ( ( diamond @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(142,plain,
! [SV31: $i,SV13: $i,SV35: $i,SV22: $i] :
( ( ( member @ ( pair @ SV22 @ SV35 ) @ SV13 )
= $false )
| ( ( member @ ( pair @ SV31 @ ( diamond_strip_lemmaD_sk1 @ SV22 @ SV31 @ SV35 @ SV13 ) ) @ SV13 )
= $true )
| ( ( member @ ( pair @ SV22 @ SV31 ) @ ( trancl @ SV13 ) )
= $false )
| ( ( diamond @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(143,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[50,142,141,140,133,124,123,119,108,100,99,98,97,83,79,72,54,53,52]) ).
thf(144,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[143]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : COL100-1 : TPTP v8.1.0. Released v2.7.0.
% 0.03/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue May 31 06:51:41 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.35
% 0.12/0.35 No.of.Axioms: 18
% 0.12/0.35
% 0.12/0.35 Length.of.Defs: 0
% 0.12/0.35
% 0.12/0.35 Contains.Choice.Funs: false
% 0.12/0.36 (rf:0,axioms:18,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:20,loop_count:0,foatp_calls:0,translation:fof_full)........
% 1.52/1.71
% 1.52/1.71 ********************************
% 1.52/1.71 * All subproblems solved! *
% 1.52/1.71 ********************************
% 1.52/1.71 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:18,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:143,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.52/1.72
% 1.52/1.72 %**** Beginning of derivation protocol ****
% 1.52/1.72 % SZS output start CNFRefutation
% See solution above
% 1.52/1.73
% 1.52/1.73 %**** End of derivation protocol ****
% 1.52/1.73 %**** no. of clauses in derivation: 144 ****
% 1.52/1.73 %**** clause counter: 143 ****
% 1.52/1.73
% 1.52/1.73 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:18,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:143,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------