%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : COL100-1 : 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 : n008.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 10:11:11 AM UTC 2026
% Result : Unsatisfiable 5.87s 1.21s
% Output : CNFRefutation 5.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 19
% Syntax : Number of formulae : 141 ( 96 unt; 0 typ; 0 def)
% Number of atoms : 681 ( 271 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 1495 ( 174 ~; 188 |; 0 &;1133 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 9 con; 0-4 aty)
% Number of variables : 359 ( 0 ^; 359 !; 0 ?; 359 :)
% 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,
( ( member @ ( pair @ y @ yp ) @ ( trancl @ r ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(42,plain,
( ( ! [ZA: $i] :
( ~ ( member @ ( pair @ z @ ZA ) @ ( trancl @ r ) )
| ~ ( member @ ( pair @ yp @ ZA ) @ ( trancl @ r ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(43,plain,
( ( diamond @ r )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(44,plain,
( ( member @ ( pair @ y @ ya ) @ ( trancl @ r ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(45,plain,
( ( member @ ( pair @ ya @ z ) @ r )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(46,plain,
( ( ! [YP: $i] :
( ~ ( member @ ( pair @ y @ YP ) @ ( trancl @ r ) )
| ( member @ ( pair @ ya @ ( sk1 @ YP ) ) @ ( trancl @ r ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(47,plain,
( ( ! [YP: $i] :
( ~ ( member @ ( pair @ y @ YP ) @ ( trancl @ r ) )
| ( member @ ( pair @ YP @ ( sk1 @ YP ) ) @ ( trancl @ r ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(48,plain,
( ( combK != combS )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(49,plain,
( ( ! [P: $i,Q: $i] :
( combK
!= ( comb_app @ P @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(50,plain,
( ( ! [P: $i,Q: $i] :
( combS
!= ( comb_app @ P @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(51,plain,
( ( ! [P1: $i,Q1: $i,P2: $i,Q2: $i] :
( ( ( comb_app @ P1 @ Q1 )
!= ( comb_app @ P2 @ Q2 ) )
| ( P1 = P2 ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(52,plain,
( ( ! [P1: $i,Q1: $i,P2: $i,Q2: $i] :
( ( ( comb_app @ P1 @ Q1 )
!= ( comb_app @ P2 @ Q2 ) )
| ( Q1 = Q2 ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(53,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)],[27]) ).
thf(54,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(55,plain,
( ( ! [R: $i] : ( trans @ ( trancl @ R ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(56,plain,
( ( ! [R: $i,A: $i,B: $i,C: $i] :
( ~ ( trans @ R )
| ~ ( member @ ( pair @ A @ B ) @ R )
| ~ ( member @ ( pair @ B @ C ) @ R )
| ( member @ ( pair @ A @ C ) @ R ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(57,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(copy,[status(thm)],[23]) ).
thf(58,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(copy,[status(thm)],[22]) ).
thf(59,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[40]) ).
thf(60,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)],[51]) ).
thf(61,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)],[53]) ).
thf(62,plain,
( ( combK != combS )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(63,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)],[52]) ).
thf(64,plain,
( ( ! [SX0: $i,SX1: $i] :
( combK
!= ( comb_app @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(65,plain,
( ( ! [SX0: $i,SX1: $i] :
( combS
!= ( comb_app @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(66,plain,
! [SV1: $i] :
( ( ~ ( member @ ( pair @ z @ SV1 ) @ ( trancl @ r ) )
| ~ ( member @ ( pair @ yp @ SV1 ) @ ( trancl @ r ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(67,plain,
! [SV2: $i] :
( ( ~ ( member @ ( pair @ y @ SV2 ) @ ( trancl @ r ) )
| ( member @ ( pair @ ya @ ( sk1 @ SV2 ) ) @ ( trancl @ r ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(68,plain,
! [SV3: $i] :
( ( ~ ( member @ ( pair @ y @ SV3 ) @ ( trancl @ r ) )
| ( member @ ( pair @ SV3 @ ( sk1 @ SV3 ) ) @ ( trancl @ r ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(69,plain,
! [SV4: $i] :
( ( ! [SY35: $i,SY36: $i] :
( ~ ( member @ ( pair @ SV4 @ SY35 ) @ SY36 )
| ( member @ ( pair @ SV4 @ SY35 ) @ ( trancl @ SY36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(70,plain,
! [SV5: $i] :
( ( trans @ ( trancl @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(71,plain,
! [SV6: $i] :
( ( ! [SY37: $i,SY38: $i,SY39: $i] :
( ~ ( trans @ SV6 )
| ~ ( member @ ( pair @ SY37 @ SY38 ) @ SV6 )
| ~ ( member @ ( pair @ SY38 @ SY39 ) @ SV6 )
| ( member @ ( pair @ SY37 @ SY39 ) @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(72,plain,
! [SV7: $i] :
( ( ! [SY40: $i,SY41: $i,SY42: $i] :
( ~ ( diamond @ SV7 )
| ~ ( member @ ( pair @ SY40 @ SY41 ) @ ( trancl @ SV7 ) )
| ~ ( member @ ( pair @ SY40 @ SY42 ) @ SV7 )
| ( member @ ( pair @ SY42 @ ( diamond_strip_lemmaD_sk1 @ SY40 @ SY41 @ SY42 @ SV7 ) ) @ ( trancl @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(73,plain,
! [SV8: $i] :
( ( ! [SY43: $i,SY44: $i,SY45: $i] :
( ~ ( diamond @ SV8 )
| ~ ( member @ ( pair @ SY43 @ SY44 ) @ ( trancl @ SV8 ) )
| ~ ( member @ ( pair @ SY43 @ SY45 ) @ SV8 )
| ( member @ ( pair @ SY44 @ ( diamond_strip_lemmaD_sk1 @ SY43 @ SY44 @ SY45 @ SV8 ) ) @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(74,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(75,plain,
! [SV9: $i] :
( ( ! [SY46: $i,SY47: $i,SY48: $i] :
( ( ( comb_app @ SV9 @ SY46 )
!= ( comb_app @ SY47 @ SY48 ) )
| ( SV9 = SY47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(76,plain,
! [SV10: $i] :
( ( ! [SY49: $i,SY50: $i,SY51: $i] :
( ( SV10 != SY49 )
| ( SY50 != SY51 )
| ( ( comb_app @ SV10 @ SY50 )
= ( comb_app @ SY49 @ SY51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(77,plain,
( ( combK = combS )
= $false ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(78,plain,
! [SV11: $i] :
( ( ! [SY52: $i,SY53: $i,SY54: $i] :
( ( ( comb_app @ SV11 @ SY52 )
!= ( comb_app @ SY53 @ SY54 ) )
| ( SY52 = SY54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(79,plain,
! [SV12: $i] :
( ( ! [SY55: $i] :
( combK
!= ( comb_app @ SV12 @ SY55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(80,plain,
! [SV13: $i] :
( ( ! [SY56: $i] :
( combS
!= ( comb_app @ SV13 @ SY56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(81,plain,
! [SV1: $i] :
( ( ( ~ ( member @ ( pair @ z @ SV1 ) @ ( trancl @ r ) ) )
= $true )
| ( ( ~ ( member @ ( pair @ yp @ SV1 ) @ ( trancl @ r ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[66]) ).
thf(82,plain,
! [SV2: $i] :
( ( ( ~ ( member @ ( pair @ y @ SV2 ) @ ( trancl @ r ) ) )
= $true )
| ( ( member @ ( pair @ ya @ ( sk1 @ SV2 ) ) @ ( trancl @ r ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[67]) ).
thf(83,plain,
! [SV3: $i] :
( ( ( ~ ( member @ ( pair @ y @ SV3 ) @ ( trancl @ r ) ) )
= $true )
| ( ( member @ ( pair @ SV3 @ ( sk1 @ SV3 ) ) @ ( trancl @ r ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(84,plain,
! [SV14: $i,SV4: $i] :
( ( ! [SY57: $i] :
( ~ ( member @ ( pair @ SV4 @ SV14 ) @ SY57 )
| ( member @ ( pair @ SV4 @ SV14 ) @ ( trancl @ SY57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(85,plain,
! [SV15: $i,SV6: $i] :
( ( ! [SY58: $i,SY59: $i] :
( ~ ( trans @ SV6 )
| ~ ( member @ ( pair @ SV15 @ SY58 ) @ SV6 )
| ~ ( member @ ( pair @ SY58 @ SY59 ) @ SV6 )
| ( member @ ( pair @ SV15 @ SY59 ) @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(86,plain,
! [SV16: $i,SV7: $i] :
( ( ! [SY60: $i,SY61: $i] :
( ~ ( diamond @ SV7 )
| ~ ( member @ ( pair @ SV16 @ SY60 ) @ ( trancl @ SV7 ) )
| ~ ( member @ ( pair @ SV16 @ SY61 ) @ SV7 )
| ( member @ ( pair @ SY61 @ ( diamond_strip_lemmaD_sk1 @ SV16 @ SY60 @ SY61 @ SV7 ) ) @ ( trancl @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(87,plain,
! [SV17: $i,SV8: $i] :
( ( ! [SY62: $i,SY63: $i] :
( ~ ( diamond @ SV8 )
| ~ ( member @ ( pair @ SV17 @ SY62 ) @ ( trancl @ SV8 ) )
| ~ ( member @ ( pair @ SV17 @ SY63 ) @ SV8 )
| ( member @ ( pair @ SY62 @ ( diamond_strip_lemmaD_sk1 @ SV17 @ SY62 @ SY63 @ SV8 ) ) @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(88,plain,
! [SV18: $i,SV9: $i] :
( ( ! [SY64: $i,SY65: $i] :
( ( ( comb_app @ SV9 @ SV18 )
!= ( comb_app @ SY64 @ SY65 ) )
| ( SV9 = SY64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(89,plain,
! [SV19: $i,SV10: $i] :
( ( ! [SY66: $i,SY67: $i] :
( ( SV10 != SV19 )
| ( SY66 != SY67 )
| ( ( comb_app @ SV10 @ SY66 )
= ( comb_app @ SV19 @ SY67 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(90,plain,
! [SV20: $i,SV11: $i] :
( ( ! [SY68: $i,SY69: $i] :
( ( ( comb_app @ SV11 @ SV20 )
!= ( comb_app @ SY68 @ SY69 ) )
| ( SV20 = SY69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(91,plain,
! [SV21: $i,SV12: $i] :
( ( combK
!= ( comb_app @ SV12 @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(92,plain,
! [SV22: $i,SV13: $i] :
( ( combS
!= ( comb_app @ SV13 @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(93,plain,
! [SV1: $i] :
( ( ( member @ ( pair @ z @ SV1 ) @ ( trancl @ r ) )
= $false )
| ( ( ~ ( member @ ( pair @ yp @ SV1 ) @ ( trancl @ r ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(94,plain,
! [SV2: $i] :
( ( ( member @ ( pair @ y @ SV2 ) @ ( trancl @ r ) )
= $false )
| ( ( member @ ( pair @ ya @ ( sk1 @ SV2 ) ) @ ( trancl @ r ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(95,plain,
! [SV3: $i] :
( ( ( member @ ( pair @ y @ SV3 ) @ ( trancl @ r ) )
= $false )
| ( ( member @ ( pair @ SV3 @ ( sk1 @ SV3 ) ) @ ( trancl @ r ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(96,plain,
! [SV23: $i,SV14: $i,SV4: $i] :
( ( ~ ( member @ ( pair @ SV4 @ SV14 ) @ SV23 )
| ( member @ ( pair @ SV4 @ SV14 ) @ ( trancl @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(97,plain,
! [SV24: $i,SV15: $i,SV6: $i] :
( ( ! [SY70: $i] :
( ~ ( trans @ SV6 )
| ~ ( member @ ( pair @ SV15 @ SV24 ) @ SV6 )
| ~ ( member @ ( pair @ SV24 @ SY70 ) @ SV6 )
| ( member @ ( pair @ SV15 @ SY70 ) @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(98,plain,
! [SV25: $i,SV16: $i,SV7: $i] :
( ( ! [SY71: $i] :
( ~ ( diamond @ SV7 )
| ~ ( member @ ( pair @ SV16 @ SV25 ) @ ( trancl @ SV7 ) )
| ~ ( member @ ( pair @ SV16 @ SY71 ) @ SV7 )
| ( member @ ( pair @ SY71 @ ( diamond_strip_lemmaD_sk1 @ SV16 @ SV25 @ SY71 @ SV7 ) ) @ ( trancl @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(99,plain,
! [SV26: $i,SV17: $i,SV8: $i] :
( ( ! [SY72: $i] :
( ~ ( diamond @ SV8 )
| ~ ( member @ ( pair @ SV17 @ SV26 ) @ ( trancl @ SV8 ) )
| ~ ( member @ ( pair @ SV17 @ SY72 ) @ SV8 )
| ( member @ ( pair @ SV26 @ ( diamond_strip_lemmaD_sk1 @ SV17 @ SV26 @ SY72 @ SV8 ) ) @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(100,plain,
! [SV27: $i,SV18: $i,SV9: $i] :
( ( ! [SY73: $i] :
( ( ( comb_app @ SV9 @ SV18 )
!= ( comb_app @ SV27 @ SY73 ) )
| ( SV9 = SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(101,plain,
! [SV28: $i,SV19: $i,SV10: $i] :
( ( ! [SY74: $i] :
( ( SV10 != SV19 )
| ( SV28 != SY74 )
| ( ( comb_app @ SV10 @ SV28 )
= ( comb_app @ SV19 @ SY74 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(102,plain,
! [SV29: $i,SV20: $i,SV11: $i] :
( ( ! [SY75: $i] :
( ( ( comb_app @ SV11 @ SV20 )
!= ( comb_app @ SV29 @ SY75 ) )
| ( SV20 = SY75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(103,plain,
! [SV21: $i,SV12: $i] :
( ( combK
= ( comb_app @ SV12 @ SV21 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(104,plain,
! [SV22: $i,SV13: $i] :
( ( combS
= ( comb_app @ SV13 @ SV22 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(105,plain,
! [SV1: $i] :
( ( ( member @ ( pair @ yp @ SV1 ) @ ( trancl @ r ) )
= $false )
| ( ( member @ ( pair @ z @ SV1 ) @ ( trancl @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(106,plain,
! [SV23: $i,SV14: $i,SV4: $i] :
( ( ( ~ ( member @ ( pair @ SV4 @ SV14 ) @ SV23 ) )
= $true )
| ( ( member @ ( pair @ SV4 @ SV14 ) @ ( trancl @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(107,plain,
! [SV30: $i,SV24: $i,SV15: $i,SV6: $i] :
( ( ~ ( trans @ SV6 )
| ~ ( member @ ( pair @ SV15 @ SV24 ) @ SV6 )
| ~ ( member @ ( pair @ SV24 @ SV30 ) @ SV6 )
| ( member @ ( pair @ SV15 @ SV30 ) @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(108,plain,
! [SV31: $i,SV25: $i,SV16: $i,SV7: $i] :
( ( ~ ( diamond @ SV7 )
| ~ ( member @ ( pair @ SV16 @ SV25 ) @ ( trancl @ SV7 ) )
| ~ ( member @ ( pair @ SV16 @ SV31 ) @ SV7 )
| ( member @ ( pair @ SV31 @ ( diamond_strip_lemmaD_sk1 @ SV16 @ SV25 @ SV31 @ SV7 ) ) @ ( trancl @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(109,plain,
! [SV32: $i,SV26: $i,SV17: $i,SV8: $i] :
( ( ~ ( diamond @ SV8 )
| ~ ( member @ ( pair @ SV17 @ SV26 ) @ ( trancl @ SV8 ) )
| ~ ( member @ ( pair @ SV17 @ SV32 ) @ SV8 )
| ( member @ ( pair @ SV26 @ ( diamond_strip_lemmaD_sk1 @ SV17 @ SV26 @ SV32 @ SV8 ) ) @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(110,plain,
! [SV33: $i,SV27: $i,SV18: $i,SV9: $i] :
( ( ( ( comb_app @ SV9 @ SV18 )
!= ( comb_app @ SV27 @ SV33 ) )
| ( SV9 = SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(111,plain,
! [SV34: $i,SV28: $i,SV19: $i,SV10: $i] :
( ( ( SV10 != SV19 )
| ( SV28 != SV34 )
| ( ( comb_app @ SV10 @ SV28 )
= ( comb_app @ SV19 @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(112,plain,
! [SV35: $i,SV29: $i,SV20: $i,SV11: $i] :
( ( ( ( comb_app @ SV11 @ SV20 )
!= ( comb_app @ SV29 @ SV35 ) )
| ( SV20 = SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(113,plain,
! [SV23: $i,SV14: $i,SV4: $i] :
( ( ( member @ ( pair @ SV4 @ SV14 ) @ SV23 )
= $false )
| ( ( member @ ( pair @ SV4 @ SV14 ) @ ( trancl @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(114,plain,
! [SV30: $i,SV24: $i,SV15: $i,SV6: $i] :
( ( ( ~ ( trans @ SV6 ) )
= $true )
| ( ( ~ ( member @ ( pair @ SV15 @ SV24 ) @ SV6 )
| ~ ( member @ ( pair @ SV24 @ SV30 ) @ SV6 )
| ( member @ ( pair @ SV15 @ SV30 ) @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(115,plain,
! [SV31: $i,SV25: $i,SV16: $i,SV7: $i] :
( ( ( ~ ( diamond @ SV7 ) )
= $true )
| ( ( ~ ( member @ ( pair @ SV16 @ SV25 ) @ ( trancl @ SV7 ) )
| ~ ( member @ ( pair @ SV16 @ SV31 ) @ SV7 )
| ( member @ ( pair @ SV31 @ ( diamond_strip_lemmaD_sk1 @ SV16 @ SV25 @ SV31 @ SV7 ) ) @ ( trancl @ SV7 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(116,plain,
! [SV32: $i,SV26: $i,SV17: $i,SV8: $i] :
( ( ( ~ ( diamond @ SV8 ) )
= $true )
| ( ( ~ ( member @ ( pair @ SV17 @ SV26 ) @ ( trancl @ SV8 ) )
| ~ ( member @ ( pair @ SV17 @ SV32 ) @ SV8 )
| ( member @ ( pair @ SV26 @ ( diamond_strip_lemmaD_sk1 @ SV17 @ SV26 @ SV32 @ SV8 ) ) @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(117,plain,
! [SV33: $i,SV27: $i,SV18: $i,SV9: $i] :
( ( ( ( comb_app @ SV9 @ SV18 )
!= ( comb_app @ SV27 @ SV33 ) )
= $true )
| ( ( SV9 = SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(118,plain,
! [SV34: $i,SV28: $i,SV19: $i,SV10: $i] :
( ( ( SV10 != SV19 )
= $true )
| ( ( ( SV28 != SV34 )
| ( ( comb_app @ SV10 @ SV28 )
= ( comb_app @ SV19 @ SV34 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(119,plain,
! [SV35: $i,SV29: $i,SV20: $i,SV11: $i] :
( ( ( ( comb_app @ SV11 @ SV20 )
!= ( comb_app @ SV29 @ SV35 ) )
= $true )
| ( ( SV20 = SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(120,plain,
! [SV30: $i,SV24: $i,SV15: $i,SV6: $i] :
( ( ( trans @ SV6 )
= $false )
| ( ( ~ ( member @ ( pair @ SV15 @ SV24 ) @ SV6 )
| ~ ( member @ ( pair @ SV24 @ SV30 ) @ SV6 )
| ( member @ ( pair @ SV15 @ SV30 ) @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(121,plain,
! [SV31: $i,SV25: $i,SV16: $i,SV7: $i] :
( ( ( diamond @ SV7 )
= $false )
| ( ( ~ ( member @ ( pair @ SV16 @ SV25 ) @ ( trancl @ SV7 ) )
| ~ ( member @ ( pair @ SV16 @ SV31 ) @ SV7 )
| ( member @ ( pair @ SV31 @ ( diamond_strip_lemmaD_sk1 @ SV16 @ SV25 @ SV31 @ SV7 ) ) @ ( trancl @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(122,plain,
! [SV32: $i,SV26: $i,SV17: $i,SV8: $i] :
( ( ( diamond @ SV8 )
= $false )
| ( ( ~ ( member @ ( pair @ SV17 @ SV26 ) @ ( trancl @ SV8 ) )
| ~ ( member @ ( pair @ SV17 @ SV32 ) @ SV8 )
| ( member @ ( pair @ SV26 @ ( diamond_strip_lemmaD_sk1 @ SV17 @ SV26 @ SV32 @ SV8 ) ) @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(123,plain,
! [SV33: $i,SV27: $i,SV18: $i,SV9: $i] :
( ( ( ( comb_app @ SV9 @ SV18 )
= ( comb_app @ SV27 @ SV33 ) )
= $false )
| ( ( SV9 = SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(124,plain,
! [SV34: $i,SV28: $i,SV19: $i,SV10: $i] :
( ( ( SV10 = SV19 )
= $false )
| ( ( ( SV28 != SV34 )
| ( ( comb_app @ SV10 @ SV28 )
= ( comb_app @ SV19 @ SV34 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(125,plain,
! [SV35: $i,SV29: $i,SV20: $i,SV11: $i] :
( ( ( ( comb_app @ SV11 @ SV20 )
= ( comb_app @ SV29 @ SV35 ) )
= $false )
| ( ( SV20 = SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(126,plain,
! [SV30: $i,SV6: $i,SV24: $i,SV15: $i] :
( ( ( ~ ( member @ ( pair @ SV15 @ SV24 ) @ SV6 ) )
= $true )
| ( ( ~ ( member @ ( pair @ SV24 @ SV30 ) @ SV6 )
| ( member @ ( pair @ SV15 @ SV30 ) @ SV6 ) )
= $true )
| ( ( trans @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(127,plain,
! [SV31: $i,SV7: $i,SV25: $i,SV16: $i] :
( ( ( ~ ( member @ ( pair @ SV16 @ SV25 ) @ ( trancl @ SV7 ) ) )
= $true )
| ( ( ~ ( member @ ( pair @ SV16 @ SV31 ) @ SV7 )
| ( member @ ( pair @ SV31 @ ( diamond_strip_lemmaD_sk1 @ SV16 @ SV25 @ SV31 @ SV7 ) ) @ ( trancl @ SV7 ) ) )
= $true )
| ( ( diamond @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(128,plain,
! [SV32: $i,SV8: $i,SV26: $i,SV17: $i] :
( ( ( ~ ( member @ ( pair @ SV17 @ SV26 ) @ ( trancl @ SV8 ) ) )
= $true )
| ( ( ~ ( member @ ( pair @ SV17 @ SV32 ) @ SV8 )
| ( member @ ( pair @ SV26 @ ( diamond_strip_lemmaD_sk1 @ SV17 @ SV26 @ SV32 @ SV8 ) ) @ SV8 ) )
= $true )
| ( ( diamond @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[122]) ).
thf(129,plain,
! [SV19: $i,SV10: $i,SV34: $i,SV28: $i] :
( ( ( SV28 != SV34 )
= $true )
| ( ( ( comb_app @ SV10 @ SV28 )
= ( comb_app @ SV19 @ SV34 ) )
= $true )
| ( ( SV10 = SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(130,plain,
! [SV30: $i,SV6: $i,SV24: $i,SV15: $i] :
( ( ( member @ ( pair @ SV15 @ SV24 ) @ SV6 )
= $false )
| ( ( ~ ( member @ ( pair @ SV24 @ SV30 ) @ SV6 )
| ( member @ ( pair @ SV15 @ SV30 ) @ SV6 ) )
= $true )
| ( ( trans @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(131,plain,
! [SV31: $i,SV7: $i,SV25: $i,SV16: $i] :
( ( ( member @ ( pair @ SV16 @ SV25 ) @ ( trancl @ SV7 ) )
= $false )
| ( ( ~ ( member @ ( pair @ SV16 @ SV31 ) @ SV7 )
| ( member @ ( pair @ SV31 @ ( diamond_strip_lemmaD_sk1 @ SV16 @ SV25 @ SV31 @ SV7 ) ) @ ( trancl @ SV7 ) ) )
= $true )
| ( ( diamond @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(132,plain,
! [SV32: $i,SV8: $i,SV26: $i,SV17: $i] :
( ( ( member @ ( pair @ SV17 @ SV26 ) @ ( trancl @ SV8 ) )
= $false )
| ( ( ~ ( member @ ( pair @ SV17 @ SV32 ) @ SV8 )
| ( member @ ( pair @ SV26 @ ( diamond_strip_lemmaD_sk1 @ SV17 @ SV26 @ SV32 @ SV8 ) ) @ SV8 ) )
= $true )
| ( ( diamond @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(133,plain,
! [SV19: $i,SV10: $i,SV34: $i,SV28: $i] :
( ( ( SV28 = SV34 )
= $false )
| ( ( ( comb_app @ SV10 @ SV28 )
= ( comb_app @ SV19 @ SV34 ) )
= $true )
| ( ( SV10 = SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(134,plain,
! [SV15: $i,SV6: $i,SV30: $i,SV24: $i] :
( ( ( ~ ( member @ ( pair @ SV24 @ SV30 ) @ SV6 ) )
= $true )
| ( ( member @ ( pair @ SV15 @ SV30 ) @ SV6 )
= $true )
| ( ( member @ ( pair @ SV15 @ SV24 ) @ SV6 )
= $false )
| ( ( trans @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(135,plain,
! [SV25: $i,SV7: $i,SV31: $i,SV16: $i] :
( ( ( ~ ( member @ ( pair @ SV16 @ SV31 ) @ SV7 ) )
= $true )
| ( ( member @ ( pair @ SV31 @ ( diamond_strip_lemmaD_sk1 @ SV16 @ SV25 @ SV31 @ SV7 ) ) @ ( trancl @ SV7 ) )
= $true )
| ( ( member @ ( pair @ SV16 @ SV25 ) @ ( trancl @ SV7 ) )
= $false )
| ( ( diamond @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(136,plain,
! [SV26: $i,SV8: $i,SV32: $i,SV17: $i] :
( ( ( ~ ( member @ ( pair @ SV17 @ SV32 ) @ SV8 ) )
= $true )
| ( ( member @ ( pair @ SV26 @ ( diamond_strip_lemmaD_sk1 @ SV17 @ SV26 @ SV32 @ SV8 ) ) @ SV8 )
= $true )
| ( ( member @ ( pair @ SV17 @ SV26 ) @ ( trancl @ SV8 ) )
= $false )
| ( ( diamond @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(137,plain,
! [SV15: $i,SV6: $i,SV30: $i,SV24: $i] :
( ( ( member @ ( pair @ SV24 @ SV30 ) @ SV6 )
= $false )
| ( ( member @ ( pair @ SV15 @ SV30 ) @ SV6 )
= $true )
| ( ( member @ ( pair @ SV15 @ SV24 ) @ SV6 )
= $false )
| ( ( trans @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(138,plain,
! [SV25: $i,SV7: $i,SV31: $i,SV16: $i] :
( ( ( member @ ( pair @ SV16 @ SV31 ) @ SV7 )
= $false )
| ( ( member @ ( pair @ SV31 @ ( diamond_strip_lemmaD_sk1 @ SV16 @ SV25 @ SV31 @ SV7 ) ) @ ( trancl @ SV7 ) )
= $true )
| ( ( member @ ( pair @ SV16 @ SV25 ) @ ( trancl @ SV7 ) )
= $false )
| ( ( diamond @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(139,plain,
! [SV26: $i,SV8: $i,SV32: $i,SV17: $i] :
( ( ( member @ ( pair @ SV17 @ SV32 ) @ SV8 )
= $false )
| ( ( member @ ( pair @ SV26 @ ( diamond_strip_lemmaD_sk1 @ SV17 @ SV26 @ SV32 @ SV8 ) ) @ SV8 )
= $true )
| ( ( member @ ( pair @ SV17 @ SV26 ) @ ( trancl @ SV8 ) )
= $false )
| ( ( diamond @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(140,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[41,139,138,137,133,125,123,113,105,104,103,95,94,77,74,70,45,44,43]) ).
thf(141,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL100-1 : 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 : n008.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
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 18:35:24 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
% 5.87/1.21
% 5.87/1.21 No.of.Axioms: 18
% 5.87/1.21
% 5.87/1.21 Length.of.Defs: 0
% 5.87/1.21
% 5.87/1.21 Contains.Choice.Funs: false
% 5.87/1.21 ...
% 5.87/1.21
% 5.87/1.21 ********************************
% 5.87/1.21 * All subproblems solved! *
% 5.87/1.21 ********************************
% 5.87/1.21 % 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:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:140,loop_count:0,foatp_calls:1,translation:fof_full)
% 5.87/1.21
% 5.87/1.21 %**** Beginning of derivation protocol ****
% 5.87/1.21 % SZS output start CNFRefutation
% See solution above
% 5.87/1.21
% 5.87/1.21 %**** End of derivation protocol ****
% 5.87/1.21 %**** no. of clauses in derivation: 141 ****
% 5.87/1.21 %**** clause counter: 140 ****
% 5.87/1.21
% 5.87/1.21 % 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:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:140,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------