%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ITP001+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 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 : n003.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 10:22:58 AM UTC 2026
% Result : Theorem 0.08s 0.24s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 14
% Syntax : Number of formulae : 141 ( 65 unt; 0 typ; 0 def)
% Number of atoms : 1072 ( 387 equ; 0 cnn)
% Maximal formula atoms : 5 ( 7 avg)
% Number of connectives : 2023 ( 279 ~; 361 |; 6 &;1337 @)
% ( 6 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 5 con; 0-4 aty)
% Number of variables : 345 ( 0 ^; 345 !; 0 ?; 345 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_ap,type,
ap: $i > $i > $i ).
thf(tp_arr,type,
arr: $i > $i > $i ).
thf(tp_bool,type,
bool: $i ).
thf(tp_c_2Ebool_2ET,type,
c_2Ebool_2ET: $i ).
thf(tp_c_2Emin_2E_3D,type,
c_2Emin_2E_3D: $i > $i ).
thf(tp_i,type,
i: $i > $i ).
thf(tp_ind,type,
ind: $i ).
thf(tp_k,type,
k: $i > $i > $i ).
thf(tp_mem,type,
mem: $i > $i > $o ).
thf(tp_ne,type,
ne: $i > $o ).
thf(tp_p,type,
p: $i > $o ).
thf(tp_sK1_X,type,
sK1_X: $i > $i > $i > $i > $i ).
thf(1,axiom,
( $true
<=> ( ( i @ bool )
= ( i @ bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_thm_2Ebool_2ET__DEF) ).
thf(2,axiom,
! [A: $i] :
( ( ne @ A )
=> ! [X: $i] :
( ( mem @ X @ A )
=> ! [Y: $i] :
( ( mem @ Y @ A )
=> ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ X ) @ Y ) )
<=> ( X = Y ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_eq_p) ).
thf(3,axiom,
! [A_27a: $i] :
( ( ne @ A_27a )
=> ( mem @ ( c_2Emin_2E_3D @ A_27a ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Emin_2E_3D) ).
thf(4,axiom,
p @ c_2Ebool_2ET,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_true_p) ).
thf(5,axiom,
mem @ c_2Ebool_2ET @ bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2ET) ).
thf(6,axiom,
! [A: $i,X: $i] :
( ( mem @ X @ A )
=> ( ( ap @ ( i @ A ) @ X )
= X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ibeta) ).
thf(7,axiom,
! [A: $i,Y: $i,X: $i] :
( ( mem @ X @ A )
=> ( ( ap @ ( k @ A @ Y ) @ X )
= Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kbeta) ).
thf(8,axiom,
! [A: $i,B: $i,F: $i] :
( ( mem @ F @ ( arr @ A @ B ) )
=> ! [G: $i] :
( ( mem @ G @ ( arr @ A @ B ) )
=> ( ! [X: $i] :
( ( mem @ X @ A )
=> ( ( ap @ F @ X )
= ( ap @ G @ X ) ) )
=> ( F = G ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcext) ).
thf(9,axiom,
! [Q: $i] :
( ( mem @ Q @ bool )
=> ! [R: $i] :
( ( mem @ R @ bool )
=> ( ( ( p @ Q )
<=> ( p @ R ) )
=> ( Q = R ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',boolext) ).
thf(10,axiom,
! [A: $i,B: $i,F: $i] :
( ( mem @ F @ ( arr @ A @ B ) )
=> ! [X: $i] :
( ( mem @ X @ A )
=> ( mem @ ( ap @ F @ X ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_tp) ).
thf(11,axiom,
! [A: $i] :
( ( ne @ A )
=> ! [B: $i] :
( ( ne @ B )
=> ( ne @ ( arr @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arr_ne) ).
thf(12,axiom,
ne @ ind,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ind_ne) ).
thf(13,axiom,
ne @ bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bool_ne) ).
thf(14,conjecture,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ebool_2ETRUTH) ).
thf(15,negated_conjecture,
$true = $false,
inference(negate_conjecture,[status(cth)],[14]) ).
thf(16,plain,
$true = $false,
inference(unfold_def,[status(thm)],[15]) ).
thf(17,plain,
( ( $true
<=> ( ( i @ bool )
= ( i @ bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(18,plain,
( ( ! [A: $i] :
( ( ne @ A )
=> ! [X: $i] :
( ( mem @ X @ A )
=> ! [Y: $i] :
( ( mem @ Y @ A )
=> ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ X ) @ Y ) )
<=> ( X = Y ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(19,plain,
( ( ! [A_27a: $i] :
( ( ne @ A_27a )
=> ( mem @ ( c_2Emin_2E_3D @ A_27a ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(20,plain,
( ( p @ c_2Ebool_2ET )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(21,plain,
( ( mem @ c_2Ebool_2ET @ bool )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(22,plain,
( ( ! [A: $i,X: $i] :
( ( mem @ X @ A )
=> ( ( ap @ ( i @ A ) @ X )
= X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(23,plain,
( ( ! [A: $i,Y: $i,X: $i] :
( ( mem @ X @ A )
=> ( ( ap @ ( k @ A @ Y ) @ X )
= Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(24,plain,
( ( ! [A: $i,B: $i,F: $i] :
( ( mem @ F @ ( arr @ A @ B ) )
=> ! [G: $i] :
( ( mem @ G @ ( arr @ A @ B ) )
=> ( ! [X: $i] :
( ( mem @ X @ A )
=> ( ( ap @ F @ X )
= ( ap @ G @ X ) ) )
=> ( F = G ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(25,plain,
( ( ! [Q: $i] :
( ( mem @ Q @ bool )
=> ! [R: $i] :
( ( mem @ R @ bool )
=> ( ( ( p @ Q )
<=> ( p @ R ) )
=> ( Q = R ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(26,plain,
( ( ! [A: $i,B: $i,F: $i] :
( ( mem @ F @ ( arr @ A @ B ) )
=> ! [X: $i] :
( ( mem @ X @ A )
=> ( mem @ ( ap @ F @ X ) @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(27,plain,
( ( ! [A: $i] :
( ( ne @ A )
=> ! [B: $i] :
( ( ne @ B )
=> ( ne @ ( arr @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(28,plain,
( ( ne @ ind )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(29,plain,
( ( ne @ bool )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(30,plain,
( ( ~ $true ) = $true ),
inference(polarity_switch,[status(thm)],[16]) ).
thf(31,plain,
$true = $true,
inference(extcnf_combined,[status(esa)],[17]) ).
thf(32,plain,
( ( ! [A: $i] :
( ~ ( ne @ A )
| ! [X: $i] :
( ~ ( mem @ X @ A )
| ( ! [Y: $i] :
( ~ ( mem @ Y @ A )
| ( X != Y )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ X ) @ Y ) ) )
& ! [Y: $i] :
( ~ ( mem @ Y @ A )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ X ) @ Y ) )
| ( X = Y ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(33,plain,
( ( ! [A_27a: $i] :
( ~ ( ne @ A_27a )
| ( mem @ ( c_2Emin_2E_3D @ A_27a ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(34,plain,
( ( ! [A: $i,X: $i] :
( ~ ( mem @ X @ A )
| ( ( ap @ ( i @ A ) @ X )
= X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(35,plain,
( ( ! [A: $i,Y: $i,X: $i] :
( ~ ( mem @ X @ A )
| ( ( ap @ ( k @ A @ Y ) @ X )
= Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(36,plain,
( ( ! [A: $i,B: $i,F: $i] :
( ~ ( mem @ F @ ( arr @ A @ B ) )
| ! [G: $i] :
( ~ ( mem @ G @ ( arr @ A @ B ) )
| ( ( mem @ ( sK1_X @ G @ F @ B @ A ) @ A )
& ( ( ap @ F @ ( sK1_X @ G @ F @ B @ A ) )
!= ( ap @ G @ ( sK1_X @ G @ F @ B @ A ) ) ) )
| ( F = G ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(37,plain,
( ( ! [Q: $i] :
( ~ ( mem @ Q @ bool )
| ( ! [R: $i] :
( ~ ( mem @ R @ bool )
| ~ ( p @ Q )
| ~ ( p @ R )
| ( Q = R ) )
& ! [R: $i] :
( ~ ( mem @ R @ bool )
| ( p @ Q )
| ( p @ R )
| ( Q = R ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(38,plain,
( ( ! [A: $i,B: $i,F: $i] :
( ~ ( mem @ F @ ( arr @ A @ B ) )
| ! [X: $i] :
( ~ ( mem @ X @ A )
| ( mem @ ( ap @ F @ X ) @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[26]) ).
thf(39,plain,
( ( ! [A: $i] :
( ~ ( ne @ A )
| ! [B: $i] :
( ~ ( ne @ B )
| ( ne @ ( arr @ A @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[27]) ).
thf(40,plain,
( ( ne @ bool )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(41,plain,
( ( ne @ ind )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(42,plain,
( ( ! [A: $i] :
( ~ ( ne @ A )
| ! [B: $i] :
( ~ ( ne @ B )
| ( ne @ ( arr @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(43,plain,
( ( ! [A: $i,B: $i,F: $i] :
( ~ ( mem @ F @ ( arr @ A @ B ) )
| ! [X: $i] :
( ~ ( mem @ X @ A )
| ( mem @ ( ap @ F @ X ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(44,plain,
( ( ! [Q: $i] :
( ~ ( mem @ Q @ bool )
| ( ! [R: $i] :
( ~ ( mem @ R @ bool )
| ~ ( p @ Q )
| ~ ( p @ R )
| ( Q = R ) )
& ! [R: $i] :
( ~ ( mem @ R @ bool )
| ( p @ Q )
| ( p @ R )
| ( Q = R ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(45,plain,
( ( ! [A: $i,B: $i,F: $i] :
( ~ ( mem @ F @ ( arr @ A @ B ) )
| ! [G: $i] :
( ~ ( mem @ G @ ( arr @ A @ B ) )
| ( ( mem @ ( sK1_X @ G @ F @ B @ A ) @ A )
& ( ( ap @ F @ ( sK1_X @ G @ F @ B @ A ) )
!= ( ap @ G @ ( sK1_X @ G @ F @ B @ A ) ) ) )
| ( F = G ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(46,plain,
( ( ! [A: $i,Y: $i,X: $i] :
( ~ ( mem @ X @ A )
| ( ( ap @ ( k @ A @ Y ) @ X )
= Y ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(47,plain,
( ( ! [A: $i,X: $i] :
( ~ ( mem @ X @ A )
| ( ( ap @ ( i @ A ) @ X )
= X ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(48,plain,
( ( mem @ c_2Ebool_2ET @ bool )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(49,plain,
( ( p @ c_2Ebool_2ET )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(50,plain,
( ( ! [A_27a: $i] :
( ~ ( ne @ A_27a )
| ( mem @ ( c_2Emin_2E_3D @ A_27a ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(51,plain,
( ( ! [A: $i] :
( ~ ( ne @ A )
| ! [X: $i] :
( ~ ( mem @ X @ A )
| ( ! [Y: $i] :
( ~ ( mem @ Y @ A )
| ( X != Y )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ X ) @ Y ) ) )
& ! [Y: $i] :
( ~ ( mem @ Y @ A )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ X ) @ Y ) )
| ( X = Y ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(52,plain,
$true = $true,
inference(copy,[status(thm)],[31]) ).
thf(53,plain,
( ( ~ $true ) = $true ),
inference(copy,[status(thm)],[30]) ).
thf(54,plain,
( ( ! [SX0: $i] :
( ~ ( ne @ SX0 )
| ! [SX1: $i] :
( ~ ( mem @ SX1 @ SX0 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( mem @ SX2 @ SX0 )
| ( SX1 != SX2 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SX0 ) @ SX1 ) @ SX2 ) ) )
| ~ ! [SX2: $i] :
( ~ ( mem @ SX2 @ SX0 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SX0 ) @ SX1 ) @ SX2 ) )
| ( SX1 = SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(55,plain,
( ( ! [SX0: $i] :
( ~ ( mem @ SX0 @ bool )
| ~ ( ~ ! [SX1: $i] :
( ~ ( mem @ SX1 @ bool )
| ~ ( p @ SX0 )
| ~ ( p @ SX1 )
| ( SX0 = SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( mem @ SX1 @ bool )
| ( p @ SX0 )
| ( p @ SX1 )
| ( SX0 = SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(56,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( mem @ SX2 @ ( arr @ SX0 @ SX1 ) )
| ! [SX3: $i] :
( ~ ( mem @ SX3 @ ( arr @ SX0 @ SX1 ) )
| ~ ( ~ ( mem @ ( sK1_X @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( ( ( ap @ SX2 @ ( sK1_X @ SX3 @ SX2 @ SX1 @ SX0 ) )
!= ( ap @ SX3 @ ( sK1_X @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ( SX2 = SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(57,plain,
! [SV1: $i] :
( ( ~ ( ne @ SV1 )
| ! [SY22: $i] :
( ~ ( ne @ SY22 )
| ( ne @ ( arr @ SV1 @ SY22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(58,plain,
! [SV2: $i] :
( ( ! [SY23: $i,SY24: $i] :
( ~ ( mem @ SY24 @ ( arr @ SV2 @ SY23 ) )
| ! [SY25: $i] :
( ~ ( mem @ SY25 @ SV2 )
| ( mem @ ( ap @ SY24 @ SY25 ) @ SY23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(59,plain,
! [SV3: $i] :
( ( ! [SY26: $i,SY27: $i] :
( ~ ( mem @ SY27 @ SV3 )
| ( ( ap @ ( k @ SV3 @ SY26 ) @ SY27 )
= SY26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(60,plain,
! [SV4: $i] :
( ( ! [SY28: $i] :
( ~ ( mem @ SY28 @ SV4 )
| ( ( ap @ ( i @ SV4 ) @ SY28 )
= SY28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(61,plain,
! [SV5: $i] :
( ( ~ ( ne @ SV5 )
| ( mem @ ( c_2Emin_2E_3D @ SV5 ) @ ( arr @ SV5 @ ( arr @ SV5 @ bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(62,plain,
$true = $false,
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(63,plain,
! [SV6: $i] :
( ( ~ ( ne @ SV6 )
| ! [SY29: $i] :
( ~ ( mem @ SY29 @ SV6 )
| ~ ( ~ ! [SY30: $i] :
( ~ ( mem @ SY30 @ SV6 )
| ( SY29 != SY30 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV6 ) @ SY29 ) @ SY30 ) ) )
| ~ ! [SY31: $i] :
( ~ ( mem @ SY31 @ SV6 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV6 ) @ SY29 ) @ SY31 ) )
| ( SY29 = SY31 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(64,plain,
! [SV7: $i] :
( ( ~ ( mem @ SV7 @ bool )
| ~ ( ~ ! [SY32: $i] :
( ~ ( mem @ SY32 @ bool )
| ~ ( p @ SV7 )
| ~ ( p @ SY32 )
| ( SV7 = SY32 ) )
| ~ ! [SY33: $i] :
( ~ ( mem @ SY33 @ bool )
| ( p @ SV7 )
| ( p @ SY33 )
| ( SV7 = SY33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(65,plain,
! [SV8: $i] :
( ( ! [SY34: $i,SY35: $i] :
( ~ ( mem @ SY35 @ ( arr @ SV8 @ SY34 ) )
| ! [SY36: $i] :
( ~ ( mem @ SY36 @ ( arr @ SV8 @ SY34 ) )
| ~ ( ~ ( mem @ ( sK1_X @ SY36 @ SY35 @ SY34 @ SV8 ) @ SV8 )
| ~ ( ( ( ap @ SY35 @ ( sK1_X @ SY36 @ SY35 @ SY34 @ SV8 ) )
!= ( ap @ SY36 @ ( sK1_X @ SY36 @ SY35 @ SY34 @ SV8 ) ) ) ) )
| ( SY35 = SY36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(66,plain,
! [SV1: $i] :
( ( ( ~ ( ne @ SV1 ) )
= $true )
| ( ( ! [SY22: $i] :
( ~ ( ne @ SY22 )
| ( ne @ ( arr @ SV1 @ SY22 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(67,plain,
! [SV9: $i,SV2: $i] :
( ( ! [SY37: $i] :
( ~ ( mem @ SY37 @ ( arr @ SV2 @ SV9 ) )
| ! [SY38: $i] :
( ~ ( mem @ SY38 @ SV2 )
| ( mem @ ( ap @ SY37 @ SY38 ) @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(68,plain,
! [SV10: $i,SV3: $i] :
( ( ! [SY39: $i] :
( ~ ( mem @ SY39 @ SV3 )
| ( ( ap @ ( k @ SV3 @ SV10 ) @ SY39 )
= SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(69,plain,
! [SV4: $i,SV11: $i] :
( ( ~ ( mem @ SV11 @ SV4 )
| ( ( ap @ ( i @ SV4 ) @ SV11 )
= SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(70,plain,
! [SV5: $i] :
( ( ( ~ ( ne @ SV5 ) )
= $true )
| ( ( mem @ ( c_2Emin_2E_3D @ SV5 ) @ ( arr @ SV5 @ ( arr @ SV5 @ bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(71,plain,
! [SV6: $i] :
( ( ( ~ ( ne @ SV6 ) )
= $true )
| ( ( ! [SY29: $i] :
( ~ ( mem @ SY29 @ SV6 )
| ~ ( ~ ! [SY30: $i] :
( ~ ( mem @ SY30 @ SV6 )
| ( SY29 != SY30 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV6 ) @ SY29 ) @ SY30 ) ) )
| ~ ! [SY31: $i] :
( ~ ( mem @ SY31 @ SV6 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV6 ) @ SY29 ) @ SY31 ) )
| ( SY29 = SY31 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(72,plain,
! [SV7: $i] :
( ( ( ~ ( mem @ SV7 @ bool ) )
= $true )
| ( ( ~ ( ~ ! [SY32: $i] :
( ~ ( mem @ SY32 @ bool )
| ~ ( p @ SV7 )
| ~ ( p @ SY32 )
| ( SV7 = SY32 ) )
| ~ ! [SY33: $i] :
( ~ ( mem @ SY33 @ bool )
| ( p @ SV7 )
| ( p @ SY33 )
| ( SV7 = SY33 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(73,plain,
! [SV12: $i,SV8: $i] :
( ( ! [SY40: $i] :
( ~ ( mem @ SY40 @ ( arr @ SV8 @ SV12 ) )
| ! [SY41: $i] :
( ~ ( mem @ SY41 @ ( arr @ SV8 @ SV12 ) )
| ~ ( ~ ( mem @ ( sK1_X @ SY41 @ SY40 @ SV12 @ SV8 ) @ SV8 )
| ~ ( ( ( ap @ SY40 @ ( sK1_X @ SY41 @ SY40 @ SV12 @ SV8 ) )
!= ( ap @ SY41 @ ( sK1_X @ SY41 @ SY40 @ SV12 @ SV8 ) ) ) ) )
| ( SY40 = SY41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(74,plain,
! [SV1: $i] :
( ( ( ne @ SV1 )
= $false )
| ( ( ! [SY22: $i] :
( ~ ( ne @ SY22 )
| ( ne @ ( arr @ SV1 @ SY22 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(75,plain,
! [SV9: $i,SV2: $i,SV13: $i] :
( ( ~ ( mem @ SV13 @ ( arr @ SV2 @ SV9 ) )
| ! [SY42: $i] :
( ~ ( mem @ SY42 @ SV2 )
| ( mem @ ( ap @ SV13 @ SY42 ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(76,plain,
! [SV10: $i,SV3: $i,SV14: $i] :
( ( ~ ( mem @ SV14 @ SV3 )
| ( ( ap @ ( k @ SV3 @ SV10 ) @ SV14 )
= SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(77,plain,
! [SV4: $i,SV11: $i] :
( ( ( ~ ( mem @ SV11 @ SV4 ) )
= $true )
| ( ( ( ap @ ( i @ SV4 ) @ SV11 )
= SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[69]) ).
thf(78,plain,
! [SV5: $i] :
( ( ( ne @ SV5 )
= $false )
| ( ( mem @ ( c_2Emin_2E_3D @ SV5 ) @ ( arr @ SV5 @ ( arr @ SV5 @ bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(79,plain,
! [SV6: $i] :
( ( ( ne @ SV6 )
= $false )
| ( ( ! [SY29: $i] :
( ~ ( mem @ SY29 @ SV6 )
| ~ ( ~ ! [SY30: $i] :
( ~ ( mem @ SY30 @ SV6 )
| ( SY29 != SY30 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV6 ) @ SY29 ) @ SY30 ) ) )
| ~ ! [SY31: $i] :
( ~ ( mem @ SY31 @ SV6 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV6 ) @ SY29 ) @ SY31 ) )
| ( SY29 = SY31 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(80,plain,
! [SV7: $i] :
( ( ( mem @ SV7 @ bool )
= $false )
| ( ( ~ ( ~ ! [SY32: $i] :
( ~ ( mem @ SY32 @ bool )
| ~ ( p @ SV7 )
| ~ ( p @ SY32 )
| ( SV7 = SY32 ) )
| ~ ! [SY33: $i] :
( ~ ( mem @ SY33 @ bool )
| ( p @ SV7 )
| ( p @ SY33 )
| ( SV7 = SY33 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(81,plain,
! [SV12: $i,SV8: $i,SV15: $i] :
( ( ~ ( mem @ SV15 @ ( arr @ SV8 @ SV12 ) )
| ! [SY43: $i] :
( ~ ( mem @ SY43 @ ( arr @ SV8 @ SV12 ) )
| ~ ( ~ ( mem @ ( sK1_X @ SY43 @ SV15 @ SV12 @ SV8 ) @ SV8 )
| ~ ( ( ( ap @ SV15 @ ( sK1_X @ SY43 @ SV15 @ SV12 @ SV8 ) )
!= ( ap @ SY43 @ ( sK1_X @ SY43 @ SV15 @ SV12 @ SV8 ) ) ) ) )
| ( SV15 = SY43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(82,plain,
! [SV1: $i,SV16: $i] :
( ( ( ~ ( ne @ SV16 )
| ( ne @ ( arr @ SV1 @ SV16 ) ) )
= $true )
| ( ( ne @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(83,plain,
! [SV9: $i,SV2: $i,SV13: $i] :
( ( ( ~ ( mem @ SV13 @ ( arr @ SV2 @ SV9 ) ) )
= $true )
| ( ( ! [SY42: $i] :
( ~ ( mem @ SY42 @ SV2 )
| ( mem @ ( ap @ SV13 @ SY42 ) @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(84,plain,
! [SV10: $i,SV3: $i,SV14: $i] :
( ( ( ~ ( mem @ SV14 @ SV3 ) )
= $true )
| ( ( ( ap @ ( k @ SV3 @ SV10 ) @ SV14 )
= SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(85,plain,
! [SV4: $i,SV11: $i] :
( ( ( mem @ SV11 @ SV4 )
= $false )
| ( ( ( ap @ ( i @ SV4 ) @ SV11 )
= SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(86,plain,
! [SV6: $i,SV17: $i] :
( ( ( ~ ( mem @ SV17 @ SV6 )
| ~ ( ~ ! [SY44: $i] :
( ~ ( mem @ SY44 @ SV6 )
| ( SV17 != SY44 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV6 ) @ SV17 ) @ SY44 ) ) )
| ~ ! [SY45: $i] :
( ~ ( mem @ SY45 @ SV6 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV6 ) @ SV17 ) @ SY45 ) )
| ( SV17 = SY45 ) ) ) )
= $true )
| ( ( ne @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(87,plain,
! [SV7: $i] :
( ( ( ~ ! [SY32: $i] :
( ~ ( mem @ SY32 @ bool )
| ~ ( p @ SV7 )
| ~ ( p @ SY32 )
| ( SV7 = SY32 ) )
| ~ ! [SY33: $i] :
( ~ ( mem @ SY33 @ bool )
| ( p @ SV7 )
| ( p @ SY33 )
| ( SV7 = SY33 ) ) )
= $false )
| ( ( mem @ SV7 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(88,plain,
! [SV12: $i,SV8: $i,SV15: $i] :
( ( ( ~ ( mem @ SV15 @ ( arr @ SV8 @ SV12 ) ) )
= $true )
| ( ( ! [SY43: $i] :
( ~ ( mem @ SY43 @ ( arr @ SV8 @ SV12 ) )
| ~ ( ~ ( mem @ ( sK1_X @ SY43 @ SV15 @ SV12 @ SV8 ) @ SV8 )
| ~ ( ( ( ap @ SV15 @ ( sK1_X @ SY43 @ SV15 @ SV12 @ SV8 ) )
!= ( ap @ SY43 @ ( sK1_X @ SY43 @ SV15 @ SV12 @ SV8 ) ) ) ) )
| ( SV15 = SY43 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(89,plain,
! [SV1: $i,SV16: $i] :
( ( ( ~ ( ne @ SV16 ) )
= $true )
| ( ( ne @ ( arr @ SV1 @ SV16 ) )
= $true )
| ( ( ne @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(90,plain,
! [SV9: $i,SV2: $i,SV13: $i] :
( ( ( mem @ SV13 @ ( arr @ SV2 @ SV9 ) )
= $false )
| ( ( ! [SY42: $i] :
( ~ ( mem @ SY42 @ SV2 )
| ( mem @ ( ap @ SV13 @ SY42 ) @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(91,plain,
! [SV10: $i,SV3: $i,SV14: $i] :
( ( ( mem @ SV14 @ SV3 )
= $false )
| ( ( ( ap @ ( k @ SV3 @ SV10 ) @ SV14 )
= SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(92,plain,
! [SV6: $i,SV17: $i] :
( ( ( ~ ( mem @ SV17 @ SV6 ) )
= $true )
| ( ( ~ ( ~ ! [SY44: $i] :
( ~ ( mem @ SY44 @ SV6 )
| ( SV17 != SY44 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV6 ) @ SV17 ) @ SY44 ) ) )
| ~ ! [SY45: $i] :
( ~ ( mem @ SY45 @ SV6 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV6 ) @ SV17 ) @ SY45 ) )
| ( SV17 = SY45 ) ) ) )
= $true )
| ( ( ne @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(93,plain,
! [SV7: $i] :
( ( ( ~ ! [SY32: $i] :
( ~ ( mem @ SY32 @ bool )
| ~ ( p @ SV7 )
| ~ ( p @ SY32 )
| ( SV7 = SY32 ) ) )
= $false )
| ( ( mem @ SV7 @ bool )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[87]) ).
thf(94,plain,
! [SV7: $i] :
( ( ( ~ ! [SY33: $i] :
( ~ ( mem @ SY33 @ bool )
| ( p @ SV7 )
| ( p @ SY33 )
| ( SV7 = SY33 ) ) )
= $false )
| ( ( mem @ SV7 @ bool )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[87]) ).
thf(95,plain,
! [SV12: $i,SV8: $i,SV15: $i] :
( ( ( mem @ SV15 @ ( arr @ SV8 @ SV12 ) )
= $false )
| ( ( ! [SY43: $i] :
( ~ ( mem @ SY43 @ ( arr @ SV8 @ SV12 ) )
| ~ ( ~ ( mem @ ( sK1_X @ SY43 @ SV15 @ SV12 @ SV8 ) @ SV8 )
| ~ ( ( ( ap @ SV15 @ ( sK1_X @ SY43 @ SV15 @ SV12 @ SV8 ) )
!= ( ap @ SY43 @ ( sK1_X @ SY43 @ SV15 @ SV12 @ SV8 ) ) ) ) )
| ( SV15 = SY43 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(96,plain,
! [SV1: $i,SV16: $i] :
( ( ( ne @ SV16 )
= $false )
| ( ( ne @ ( arr @ SV1 @ SV16 ) )
= $true )
| ( ( ne @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(97,plain,
! [SV9: $i,SV13: $i,SV2: $i,SV18: $i] :
( ( ( ~ ( mem @ SV18 @ SV2 )
| ( mem @ ( ap @ SV13 @ SV18 ) @ SV9 ) )
= $true )
| ( ( mem @ SV13 @ ( arr @ SV2 @ SV9 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(98,plain,
! [SV6: $i,SV17: $i] :
( ( ( mem @ SV17 @ SV6 )
= $false )
| ( ( ~ ( ~ ! [SY44: $i] :
( ~ ( mem @ SY44 @ SV6 )
| ( SV17 != SY44 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV6 ) @ SV17 ) @ SY44 ) ) )
| ~ ! [SY45: $i] :
( ~ ( mem @ SY45 @ SV6 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV6 ) @ SV17 ) @ SY45 ) )
| ( SV17 = SY45 ) ) ) )
= $true )
| ( ( ne @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(99,plain,
! [SV7: $i] :
( ( ( ! [SY32: $i] :
( ~ ( mem @ SY32 @ bool )
| ~ ( p @ SV7 )
| ~ ( p @ SY32 )
| ( SV7 = SY32 ) ) )
= $true )
| ( ( mem @ SV7 @ bool )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[93]) ).
thf(100,plain,
! [SV7: $i] :
( ( ( ! [SY33: $i] :
( ~ ( mem @ SY33 @ bool )
| ( p @ SV7 )
| ( p @ SY33 )
| ( SV7 = SY33 ) ) )
= $true )
| ( ( mem @ SV7 @ bool )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[94]) ).
thf(101,plain,
! [SV15: $i,SV12: $i,SV8: $i,SV19: $i] :
( ( ( ~ ( mem @ SV19 @ ( arr @ SV8 @ SV12 ) )
| ~ ( ~ ( mem @ ( sK1_X @ SV19 @ SV15 @ SV12 @ SV8 ) @ SV8 )
| ~ ( ( ( ap @ SV15 @ ( sK1_X @ SV19 @ SV15 @ SV12 @ SV8 ) )
!= ( ap @ SV19 @ ( sK1_X @ SV19 @ SV15 @ SV12 @ SV8 ) ) ) ) )
| ( SV15 = SV19 ) )
= $true )
| ( ( mem @ SV15 @ ( arr @ SV8 @ SV12 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(102,plain,
! [SV9: $i,SV13: $i,SV2: $i,SV18: $i] :
( ( ( ~ ( mem @ SV18 @ SV2 ) )
= $true )
| ( ( mem @ ( ap @ SV13 @ SV18 ) @ SV9 )
= $true )
| ( ( mem @ SV13 @ ( arr @ SV2 @ SV9 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(103,plain,
! [SV17: $i,SV6: $i] :
( ( ( ~ ! [SY44: $i] :
( ~ ( mem @ SY44 @ SV6 )
| ( SV17 != SY44 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV6 ) @ SV17 ) @ SY44 ) ) )
| ~ ! [SY45: $i] :
( ~ ( mem @ SY45 @ SV6 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV6 ) @ SV17 ) @ SY45 ) )
| ( SV17 = SY45 ) ) )
= $false )
| ( ( mem @ SV17 @ SV6 )
= $false )
| ( ( ne @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(104,plain,
! [SV7: $i,SV20: $i] :
( ( ( ~ ( mem @ SV20 @ bool )
| ~ ( p @ SV7 )
| ~ ( p @ SV20 )
| ( SV7 = SV20 ) )
= $true )
| ( ( mem @ SV7 @ bool )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(105,plain,
! [SV7: $i,SV21: $i] :
( ( ( ~ ( mem @ SV21 @ bool )
| ( p @ SV7 )
| ( p @ SV21 )
| ( SV7 = SV21 ) )
= $true )
| ( ( mem @ SV7 @ bool )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(106,plain,
! [SV15: $i,SV12: $i,SV8: $i,SV19: $i] :
( ( ( ~ ( mem @ SV19 @ ( arr @ SV8 @ SV12 ) ) )
= $true )
| ( ( ~ ( ~ ( mem @ ( sK1_X @ SV19 @ SV15 @ SV12 @ SV8 ) @ SV8 )
| ~ ( ( ( ap @ SV15 @ ( sK1_X @ SV19 @ SV15 @ SV12 @ SV8 ) )
!= ( ap @ SV19 @ ( sK1_X @ SV19 @ SV15 @ SV12 @ SV8 ) ) ) ) )
| ( SV15 = SV19 ) )
= $true )
| ( ( mem @ SV15 @ ( arr @ SV8 @ SV12 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(107,plain,
! [SV9: $i,SV13: $i,SV2: $i,SV18: $i] :
( ( ( mem @ SV18 @ SV2 )
= $false )
| ( ( mem @ ( ap @ SV13 @ SV18 ) @ SV9 )
= $true )
| ( ( mem @ SV13 @ ( arr @ SV2 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(108,plain,
! [SV17: $i,SV6: $i] :
( ( ( ~ ! [SY44: $i] :
( ~ ( mem @ SY44 @ SV6 )
| ( SV17 != SY44 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV6 ) @ SV17 ) @ SY44 ) ) ) )
= $false )
| ( ( mem @ SV17 @ SV6 )
= $false )
| ( ( ne @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[103]) ).
thf(109,plain,
! [SV17: $i,SV6: $i] :
( ( ( ~ ! [SY45: $i] :
( ~ ( mem @ SY45 @ SV6 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV6 ) @ SV17 ) @ SY45 ) )
| ( SV17 = SY45 ) ) )
= $false )
| ( ( mem @ SV17 @ SV6 )
= $false )
| ( ( ne @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[103]) ).
thf(110,plain,
! [SV7: $i,SV20: $i] :
( ( ( ~ ( mem @ SV20 @ bool ) )
= $true )
| ( ( ~ ( p @ SV7 )
| ~ ( p @ SV20 )
| ( SV7 = SV20 ) )
= $true )
| ( ( mem @ SV7 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(111,plain,
! [SV7: $i,SV21: $i] :
( ( ( ~ ( mem @ SV21 @ bool ) )
= $true )
| ( ( ( p @ SV7 )
| ( p @ SV21 )
| ( SV7 = SV21 ) )
= $true )
| ( ( mem @ SV7 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(112,plain,
! [SV15: $i,SV12: $i,SV8: $i,SV19: $i] :
( ( ( mem @ SV19 @ ( arr @ SV8 @ SV12 ) )
= $false )
| ( ( ~ ( ~ ( mem @ ( sK1_X @ SV19 @ SV15 @ SV12 @ SV8 ) @ SV8 )
| ~ ( ( ( ap @ SV15 @ ( sK1_X @ SV19 @ SV15 @ SV12 @ SV8 ) )
!= ( ap @ SV19 @ ( sK1_X @ SV19 @ SV15 @ SV12 @ SV8 ) ) ) ) )
| ( SV15 = SV19 ) )
= $true )
| ( ( mem @ SV15 @ ( arr @ SV8 @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(113,plain,
! [SV17: $i,SV6: $i] :
( ( ( ! [SY44: $i] :
( ~ ( mem @ SY44 @ SV6 )
| ( SV17 != SY44 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV6 ) @ SV17 ) @ SY44 ) ) ) )
= $true )
| ( ( mem @ SV17 @ SV6 )
= $false )
| ( ( ne @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(114,plain,
! [SV17: $i,SV6: $i] :
( ( ( ! [SY45: $i] :
( ~ ( mem @ SY45 @ SV6 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV6 ) @ SV17 ) @ SY45 ) )
| ( SV17 = SY45 ) ) )
= $true )
| ( ( mem @ SV17 @ SV6 )
= $false )
| ( ( ne @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(115,plain,
! [SV7: $i,SV20: $i] :
( ( ( mem @ SV20 @ bool )
= $false )
| ( ( ~ ( p @ SV7 )
| ~ ( p @ SV20 )
| ( SV7 = SV20 ) )
= $true )
| ( ( mem @ SV7 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(116,plain,
! [SV7: $i,SV21: $i] :
( ( ( mem @ SV21 @ bool )
= $false )
| ( ( ( p @ SV7 )
| ( p @ SV21 )
| ( SV7 = SV21 ) )
= $true )
| ( ( mem @ SV7 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(117,plain,
! [SV8: $i,SV12: $i,SV15: $i,SV19: $i] :
( ( ( ~ ( ~ ( mem @ ( sK1_X @ SV19 @ SV15 @ SV12 @ SV8 ) @ SV8 )
| ~ ( ( ( ap @ SV15 @ ( sK1_X @ SV19 @ SV15 @ SV12 @ SV8 ) )
!= ( ap @ SV19 @ ( sK1_X @ SV19 @ SV15 @ SV12 @ SV8 ) ) ) ) ) )
= $true )
| ( ( SV15 = SV19 )
= $true )
| ( ( mem @ SV19 @ ( arr @ SV8 @ SV12 ) )
= $false )
| ( ( mem @ SV15 @ ( arr @ SV8 @ SV12 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(118,plain,
! [SV17: $i,SV6: $i,SV22: $i] :
( ( ( ~ ( mem @ SV22 @ SV6 )
| ( SV17 != SV22 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV6 ) @ SV17 ) @ SV22 ) ) )
= $true )
| ( ( mem @ SV17 @ SV6 )
= $false )
| ( ( ne @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(119,plain,
! [SV17: $i,SV6: $i,SV23: $i] :
( ( ( ~ ( mem @ SV23 @ SV6 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV6 ) @ SV17 ) @ SV23 ) )
| ( SV17 = SV23 ) )
= $true )
| ( ( mem @ SV17 @ SV6 )
= $false )
| ( ( ne @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(120,plain,
! [SV20: $i,SV7: $i] :
( ( ( ~ ( p @ SV7 )
| ~ ( p @ SV20 ) )
= $true )
| ( ( SV7 = SV20 )
= $true )
| ( ( mem @ SV20 @ bool )
= $false )
| ( ( mem @ SV7 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(121,plain,
! [SV21: $i,SV7: $i] :
( ( ( ( p @ SV7 )
| ( p @ SV21 ) )
= $true )
| ( ( SV7 = SV21 )
= $true )
| ( ( mem @ SV21 @ bool )
= $false )
| ( ( mem @ SV7 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(122,plain,
! [SV8: $i,SV12: $i,SV15: $i,SV19: $i] :
( ( ( ~ ( mem @ ( sK1_X @ SV19 @ SV15 @ SV12 @ SV8 ) @ SV8 )
| ~ ( ( ( ap @ SV15 @ ( sK1_X @ SV19 @ SV15 @ SV12 @ SV8 ) )
!= ( ap @ SV19 @ ( sK1_X @ SV19 @ SV15 @ SV12 @ SV8 ) ) ) ) )
= $false )
| ( ( SV15 = SV19 )
= $true )
| ( ( mem @ SV19 @ ( arr @ SV8 @ SV12 ) )
= $false )
| ( ( mem @ SV15 @ ( arr @ SV8 @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(123,plain,
! [SV17: $i,SV6: $i,SV22: $i] :
( ( ( ~ ( mem @ SV22 @ SV6 ) )
= $true )
| ( ( ( SV17 != SV22 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV6 ) @ SV17 ) @ SV22 ) ) )
= $true )
| ( ( mem @ SV17 @ SV6 )
= $false )
| ( ( ne @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(124,plain,
! [SV17: $i,SV6: $i,SV23: $i] :
( ( ( ~ ( mem @ SV23 @ SV6 ) )
= $true )
| ( ( ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV6 ) @ SV17 ) @ SV23 ) )
| ( SV17 = SV23 ) )
= $true )
| ( ( mem @ SV17 @ SV6 )
= $false )
| ( ( ne @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(125,plain,
! [SV20: $i,SV7: $i] :
( ( ( ~ ( p @ SV7 ) )
= $true )
| ( ( ~ ( p @ SV20 ) )
= $true )
| ( ( SV7 = SV20 )
= $true )
| ( ( mem @ SV20 @ bool )
= $false )
| ( ( mem @ SV7 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(126,plain,
! [SV21: $i,SV7: $i] :
( ( ( p @ SV7 )
= $true )
| ( ( p @ SV21 )
= $true )
| ( ( SV7 = SV21 )
= $true )
| ( ( mem @ SV21 @ bool )
= $false )
| ( ( mem @ SV7 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(127,plain,
! [SV8: $i,SV12: $i,SV15: $i,SV19: $i] :
( ( ( ~ ( mem @ ( sK1_X @ SV19 @ SV15 @ SV12 @ SV8 ) @ SV8 ) )
= $false )
| ( ( SV15 = SV19 )
= $true )
| ( ( mem @ SV19 @ ( arr @ SV8 @ SV12 ) )
= $false )
| ( ( mem @ SV15 @ ( arr @ SV8 @ SV12 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[122]) ).
thf(128,plain,
! [SV8: $i,SV12: $i,SV19: $i,SV15: $i] :
( ( ( ~ ( ( ( ap @ SV15 @ ( sK1_X @ SV19 @ SV15 @ SV12 @ SV8 ) )
!= ( ap @ SV19 @ ( sK1_X @ SV19 @ SV15 @ SV12 @ SV8 ) ) ) ) )
= $false )
| ( ( SV15 = SV19 )
= $true )
| ( ( mem @ SV19 @ ( arr @ SV8 @ SV12 ) )
= $false )
| ( ( mem @ SV15 @ ( arr @ SV8 @ SV12 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[122]) ).
thf(129,plain,
! [SV17: $i,SV6: $i,SV22: $i] :
( ( ( mem @ SV22 @ SV6 )
= $false )
| ( ( ( SV17 != SV22 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV6 ) @ SV17 ) @ SV22 ) ) )
= $true )
| ( ( mem @ SV17 @ SV6 )
= $false )
| ( ( ne @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(130,plain,
! [SV17: $i,SV6: $i,SV23: $i] :
( ( ( mem @ SV23 @ SV6 )
= $false )
| ( ( ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV6 ) @ SV17 ) @ SV23 ) )
| ( SV17 = SV23 ) )
= $true )
| ( ( mem @ SV17 @ SV6 )
= $false )
| ( ( ne @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(131,plain,
! [SV20: $i,SV7: $i] :
( ( ( p @ SV7 )
= $false )
| ( ( ~ ( p @ SV20 ) )
= $true )
| ( ( SV7 = SV20 )
= $true )
| ( ( mem @ SV20 @ bool )
= $false )
| ( ( mem @ SV7 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(132,plain,
! [SV8: $i,SV12: $i,SV15: $i,SV19: $i] :
( ( ( mem @ ( sK1_X @ SV19 @ SV15 @ SV12 @ SV8 ) @ SV8 )
= $true )
| ( ( SV15 = SV19 )
= $true )
| ( ( mem @ SV19 @ ( arr @ SV8 @ SV12 ) )
= $false )
| ( ( mem @ SV15 @ ( arr @ SV8 @ SV12 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(133,plain,
! [SV8: $i,SV12: $i,SV19: $i,SV15: $i] :
( ( ( ( ap @ SV15 @ ( sK1_X @ SV19 @ SV15 @ SV12 @ SV8 ) )
!= ( ap @ SV19 @ ( sK1_X @ SV19 @ SV15 @ SV12 @ SV8 ) ) )
= $true )
| ( ( SV15 = SV19 )
= $true )
| ( ( mem @ SV19 @ ( arr @ SV8 @ SV12 ) )
= $false )
| ( ( mem @ SV15 @ ( arr @ SV8 @ SV12 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[128]) ).
thf(134,plain,
! [SV6: $i,SV22: $i,SV17: $i] :
( ( ( SV17 != SV22 )
= $true )
| ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV6 ) @ SV17 ) @ SV22 ) )
= $true )
| ( ( mem @ SV22 @ SV6 )
= $false )
| ( ( mem @ SV17 @ SV6 )
= $false )
| ( ( ne @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(135,plain,
! [SV23: $i,SV17: $i,SV6: $i] :
( ( ( ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV6 ) @ SV17 ) @ SV23 ) ) )
= $true )
| ( ( SV17 = SV23 )
= $true )
| ( ( mem @ SV23 @ SV6 )
= $false )
| ( ( mem @ SV17 @ SV6 )
= $false )
| ( ( ne @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(136,plain,
! [SV7: $i,SV20: $i] :
( ( ( p @ SV20 )
= $false )
| ( ( p @ SV7 )
= $false )
| ( ( SV7 = SV20 )
= $true )
| ( ( mem @ SV20 @ bool )
= $false )
| ( ( mem @ SV7 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(137,plain,
! [SV8: $i,SV12: $i,SV19: $i,SV15: $i] :
( ( ( ( ap @ SV15 @ ( sK1_X @ SV19 @ SV15 @ SV12 @ SV8 ) )
= ( ap @ SV19 @ ( sK1_X @ SV19 @ SV15 @ SV12 @ SV8 ) ) )
= $false )
| ( ( SV15 = SV19 )
= $true )
| ( ( mem @ SV19 @ ( arr @ SV8 @ SV12 ) )
= $false )
| ( ( mem @ SV15 @ ( arr @ SV8 @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(138,plain,
! [SV6: $i,SV22: $i,SV17: $i] :
( ( ( SV17 = SV22 )
= $false )
| ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV6 ) @ SV17 ) @ SV22 ) )
= $true )
| ( ( mem @ SV22 @ SV6 )
= $false )
| ( ( mem @ SV17 @ SV6 )
= $false )
| ( ( ne @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(139,plain,
! [SV23: $i,SV17: $i,SV6: $i] :
( ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV6 ) @ SV17 ) @ SV23 ) )
= $false )
| ( ( SV17 = SV23 )
= $true )
| ( ( mem @ SV23 @ SV6 )
= $false )
| ( ( mem @ SV17 @ SV6 )
= $false )
| ( ( ne @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(140,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[40,139,138,137,136,132,126,107,96,91,85,78,62,52,49,48,41]) ).
thf(141,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP001+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 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 : n003.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 11:08:34 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
% 0.08/0.24
% 0.08/0.24 No.of.Axioms: 13
% 0.08/0.24
% 0.08/0.24 Length.of.Defs: 0
% 0.08/0.24
% 0.08/0.24 Contains.Choice.Funs: false
% 0.08/0.24 .....
% 0.08/0.24
% 0.08/0.24 ********************************
% 0.08/0.24 * All subproblems solved! *
% 0.08/0.24 ********************************
% 0.08/0.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:13,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: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)
% 0.08/0.24
% 0.08/0.24 %**** Beginning of derivation protocol ****
% 0.08/0.24 % SZS output start CNFRefutation
% See solution above
% 0.08/0.24
% 0.08/0.24 %**** End of derivation protocol ****
% 0.08/0.24 %**** no. of clauses in derivation: 141 ****
% 0.08/0.24 %**** clause counter: 140 ****
% 0.08/0.24
% 0.08/0.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:13,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: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)
%------------------------------------------------------------------------------