%------------------------------------------------------------------------------
% 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 0.09s 0.30s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of formulae : 169 ( 75 unt; 0 typ; 0 def)
% Number of atoms : 1072 ( 371 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 1981 ( 274 ~; 279 |; 6 &;1394 @)
% ( 4 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 5 con; 0-4 aty)
% Number of variables : 327 ( 8 ^; 319 !; 0 ?; 327 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_del,type,
del: $tType ).
thf(tp_ap,type,
ap: $i > $i > $i ).
thf(tp_arr,type,
arr: del > del > del ).
thf(tp_bool,type,
bool: del ).
thf(tp_c_2Ebool_2ET,type,
c_2Ebool_2ET: $i ).
thf(tp_c_2Emin_2E_3D,type,
c_2Emin_2E_3D: del > $i ).
thf(tp_ind,type,
ind: del ).
thf(tp_inj__o,type,
inj__o: $o > $i ).
thf(tp_lam,type,
lam: del > ( $i > $i ) > $i ).
thf(tp_mem,type,
mem: $i > del > $o ).
thf(tp_p,type,
p: $i > $o ).
thf(tp_sK1_X,type,
sK1_X: $i > $i > del > del > $i ).
thf(tp_sK2_X,type,
sK2_X: ( $i > $i ) > del > del > $i ).
thf(1,axiom,
( $true
<=> ( ( lam @ bool
@ ^ [V0x: $i] : V0x )
= ( lam @ bool
@ ^ [V1x: $i] : V1x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_thm_2Ebool_2ET__DEF) ).
thf(2,axiom,
! [A: del,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/sandbox/benchmark/theBenchmark.p',ax_eq_p) ).
thf(3,axiom,
! [A_27a: del] : ( mem @ ( c_2Emin_2E_3D @ A_27a ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Emin_2E_3D) ).
thf(4,axiom,
p @ c_2Ebool_2ET,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_true_p) ).
thf(5,axiom,
mem @ c_2Ebool_2ET @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2ET) ).
thf(6,axiom,
! [A: del,F: $i > $i,X: $i] :
( ( mem @ X @ A )
=> ( ( ap @ ( lam @ A @ F ) @ X )
= ( F @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta) ).
thf(7,axiom,
! [A: del,B: del,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/sandbox/benchmark/theBenchmark.p',funcext) ).
thf(8,axiom,
! [A: del,B: del,F: $i > $i] :
( ! [X: $i] :
( ( mem @ X @ A )
=> ( mem @ ( F @ X ) @ B ) )
=> ( mem @ ( lam @ A @ F ) @ ( arr @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam_tp) ).
thf(9,axiom,
! [A: del,B: del,F: $i] :
( ( mem @ F @ ( arr @ A @ B ) )
=> ! [X: $i] :
( ( mem @ X @ A )
=> ( mem @ ( ap @ F @ X ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_tp) ).
thf(10,axiom,
! [X: $i] :
( ( mem @ X @ bool )
=> ( X
= ( inj__o @ ( p @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_iso_mem_o) ).
thf(11,axiom,
! [X: $o] : ( mem @ ( inj__o @ X ) @ bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_mem_o) ).
thf(12,axiom,
! [X: $o] :
( ( p @ ( inj__o @ X ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_surj_o) ).
thf(13,conjecture,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2ETRUTH) ).
thf(14,negated_conjecture,
$true = $false,
inference(negate_conjecture,[status(cth)],[13]) ).
thf(15,plain,
$true = $false,
inference(unfold_def,[status(thm)],[14]) ).
thf(16,plain,
( ( $true
<=> ( ( lam @ bool
@ ^ [V0x: $i] : V0x )
= ( lam @ bool
@ ^ [V1x: $i] : V1x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(17,plain,
( ( ! [A: del,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(18,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Emin_2E_3D @ A_27a ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(19,plain,
( ( p @ c_2Ebool_2ET )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(20,plain,
( ( mem @ c_2Ebool_2ET @ bool )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(21,plain,
( ( ! [A: del,F: $i > $i,X: $i] :
( ( mem @ X @ A )
=> ( ( ap @ ( lam @ A @ F ) @ X )
= ( F @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(22,plain,
( ( ! [A: del,B: del,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)],[7]) ).
thf(23,plain,
( ( ! [A: del,B: del,F: $i > $i] :
( ! [X: $i] :
( ( mem @ X @ A )
=> ( mem @ ( F @ X ) @ B ) )
=> ( mem @ ( lam @ A @ F ) @ ( arr @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(24,plain,
( ( ! [A: del,B: del,F: $i] :
( ( mem @ F @ ( arr @ A @ B ) )
=> ! [X: $i] :
( ( mem @ X @ A )
=> ( mem @ ( ap @ F @ X ) @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(25,plain,
( ( ! [X: $i] :
( ( mem @ X @ bool )
=> ( X
= ( inj__o @ ( p @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(26,plain,
( ( ! [X: $o] : ( mem @ ( inj__o @ X ) @ bool ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(27,plain,
( ( ! [X: $o] :
( ( p @ ( inj__o @ X ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(28,plain,
( ( ~ $true ) = $true ),
inference(polarity_switch,[status(thm)],[15]) ).
thf(29,plain,
( ( ( lam @ bool
@ ^ [V0x: $i] : V0x )
= ( lam @ bool
@ ^ [V1x: $i] : V1x ) )
= $true ),
inference(extcnf_combined,[status(esa)],[16]) ).
thf(30,plain,
( ( ! [A: del,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)],[17]) ).
thf(31,plain,
( ( ! [A: del,F: $i > $i,X: $i] :
( ~ ( mem @ X @ A )
| ( ( ap @ ( lam @ A @ F ) @ X )
= ( F @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(32,plain,
( ( ! [A: del,B: del,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)],[22]) ).
thf(33,plain,
( ( ! [A: del,B: del,F: $i > $i] :
( ( ( mem @ ( sK2_X @ F @ B @ A ) @ A )
& ~ ( mem @ ( F @ ( sK2_X @ F @ B @ A ) ) @ B ) )
| ( mem @ ( lam @ A @ F ) @ ( arr @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(34,plain,
( ( ! [A: del,B: del,F: $i] :
( ~ ( mem @ F @ ( arr @ A @ B ) )
| ! [X: $i] :
( ~ ( mem @ X @ A )
| ( mem @ ( ap @ F @ X ) @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(35,plain,
( ( ! [X: $i] :
( ~ ( mem @ X @ bool )
| ( X
= ( inj__o @ ( p @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(36,plain,
( ( ! [X: $o] :
( ( p @ ( inj__o @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(37,plain,
( ( ! [X: $o] : ( mem @ ( inj__o @ X ) @ bool ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(38,plain,
( ( ! [X: $i] :
( ~ ( mem @ X @ bool )
| ( X
= ( inj__o @ ( p @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(39,plain,
( ( ! [A: del,B: del,F: $i] :
( ~ ( mem @ F @ ( arr @ A @ B ) )
| ! [X: $i] :
( ~ ( mem @ X @ A )
| ( mem @ ( ap @ F @ X ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(40,plain,
( ( ! [A: del,B: del,F: $i > $i] :
( ( ( mem @ ( sK2_X @ F @ B @ A ) @ A )
& ~ ( mem @ ( F @ ( sK2_X @ F @ B @ A ) ) @ B ) )
| ( mem @ ( lam @ A @ F ) @ ( arr @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(41,plain,
( ( ! [A: del,B: del,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)],[32]) ).
thf(42,plain,
( ( ! [A: del,F: $i > $i,X: $i] :
( ~ ( mem @ X @ A )
| ( ( ap @ ( lam @ A @ F ) @ X )
= ( F @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(43,plain,
( ( mem @ c_2Ebool_2ET @ bool )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(44,plain,
( ( p @ c_2Ebool_2ET )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(45,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Emin_2E_3D @ A_27a ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(46,plain,
( ( ! [A: del,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)],[30]) ).
thf(47,plain,
( ( ( lam @ bool
@ ^ [V0x: $i] : V0x )
= ( lam @ bool
@ ^ [V1x: $i] : V1x ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(48,plain,
( ( ~ $true ) = $true ),
inference(copy,[status(thm)],[28]) ).
thf(49,plain,
( ( ! [SX0: del,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)],[46]) ).
thf(50,plain,
( ( ! [SX0: del,SX1: del,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)],[41]) ).
thf(51,plain,
( ( ! [SX0: del,SX1: del,SX2: $i > $i] :
( ~ ( ~ ( mem @ ( sK2_X @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( mem @ ( SX2 @ ( sK2_X @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ( mem @ ( lam @ SX0 @ SX2 ) @ ( arr @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(52,plain,
! [SV1: $o] :
( ( ( p @ ( inj__o @ SV1 ) )
= SV1 )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[36]) ).
thf(53,plain,
( ( ( p @ ( inj__o @ $true ) )
= $true )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[36]) ).
thf(54,plain,
( ( ( p @ ( inj__o @ $false ) )
= $false )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[36]) ).
thf(55,plain,
! [SV2: $o] :
( ( mem @ ( inj__o @ SV2 ) @ bool )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[37]) ).
thf(56,plain,
( ( mem @ ( inj__o @ $true ) @ bool )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[37]) ).
thf(57,plain,
( ( mem @ ( inj__o @ $false ) @ bool )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[37]) ).
thf(58,plain,
! [SV3: $i] :
( ( ~ ( mem @ SV3 @ bool )
| ( SV3
= ( inj__o @ ( p @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(59,plain,
! [SV4: del] :
( ( ! [SY25: del,SY26: $i] :
( ~ ( mem @ SY26 @ ( arr @ SV4 @ SY25 ) )
| ! [SY27: $i] :
( ~ ( mem @ SY27 @ SV4 )
| ( mem @ ( ap @ SY26 @ SY27 ) @ SY25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(60,plain,
! [SV5: del] :
( ( ! [SY28: $i > $i,SY29: $i] :
( ~ ( mem @ SY29 @ SV5 )
| ( ( ap @ ( lam @ SV5 @ SY28 ) @ SY29 )
= ( SY28 @ SY29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(61,plain,
! [SV6: del] :
( ( mem @ ( c_2Emin_2E_3D @ SV6 ) @ ( arr @ SV6 @ ( arr @ SV6 @ bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(62,plain,
$true = $false,
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(63,plain,
! [SV7: del] :
( ( ! [SY30: $i] :
( ~ ( mem @ SY30 @ SV7 )
| ~ ( ~ ! [SY31: $i] :
( ~ ( mem @ SY31 @ SV7 )
| ( SY30 != SY31 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV7 ) @ SY30 ) @ SY31 ) ) )
| ~ ! [SY32: $i] :
( ~ ( mem @ SY32 @ SV7 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV7 ) @ SY30 ) @ SY32 ) )
| ( SY30 = SY32 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(64,plain,
! [SV8: del] :
( ( ! [SY33: del,SY34: $i] :
( ~ ( mem @ SY34 @ ( arr @ SV8 @ SY33 ) )
| ! [SY35: $i] :
( ~ ( mem @ SY35 @ ( arr @ SV8 @ SY33 ) )
| ~ ( ~ ( mem @ ( sK1_X @ SY35 @ SY34 @ SY33 @ SV8 ) @ SV8 )
| ~ ( ( ( ap @ SY34 @ ( sK1_X @ SY35 @ SY34 @ SY33 @ SV8 ) )
!= ( ap @ SY35 @ ( sK1_X @ SY35 @ SY34 @ SY33 @ SV8 ) ) ) ) )
| ( SY34 = SY35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(65,plain,
! [SV9: del] :
( ( ! [SY36: del,SY37: $i > $i] :
( ~ ( ~ ( mem @ ( sK2_X @ SY37 @ SY36 @ SV9 ) @ SV9 )
| ~ ~ ( mem @ ( SY37 @ ( sK2_X @ SY37 @ SY36 @ SV9 ) ) @ SY36 ) )
| ( mem @ ( lam @ SV9 @ SY37 ) @ ( arr @ SV9 @ SY36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(66,plain,
! [SV1: $o] :
( ( ~ ( ( p @ ( inj__o @ SV1 ) )
| SV1 )
| ~ ( ~ ( p @ ( inj__o @ SV1 ) )
| ~ SV1 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[52]) ).
thf(67,plain,
! [SV1: $o] :
( ( ( p @ ( inj__o @ SV1 ) )
= SV1 )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[52]) ).
thf(68,plain,
( ( ~ ( ( p @ ( inj__o @ $true ) )
| $true )
| ~ ( ~ ( p @ ( inj__o @ $true ) )
| ~ $true ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[53]) ).
thf(69,plain,
( ( ( p @ ( inj__o @ $true ) )
= $true )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[53]) ).
thf(70,plain,
( ( ~ ( ( p @ ( inj__o @ $false ) )
| $false )
| ~ ( ~ ( p @ ( inj__o @ $false ) )
| ~ $false ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[54]) ).
thf(71,plain,
( ( ( p @ ( inj__o @ $false ) )
= $false )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[54]) ).
thf(72,plain,
! [SV3: $i] :
( ( ( ~ ( mem @ SV3 @ bool ) )
= $true )
| ( ( SV3
= ( inj__o @ ( p @ SV3 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(73,plain,
! [SV10: del,SV4: del] :
( ( ! [SY38: $i] :
( ~ ( mem @ SY38 @ ( arr @ SV4 @ SV10 ) )
| ! [SY39: $i] :
( ~ ( mem @ SY39 @ SV4 )
| ( mem @ ( ap @ SY38 @ SY39 ) @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(74,plain,
! [SV11: $i > $i,SV5: del] :
( ( ! [SY40: $i] :
( ~ ( mem @ SY40 @ SV5 )
| ( ( ap @ ( lam @ SV5 @ SV11 ) @ SY40 )
= ( SV11 @ SY40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(75,plain,
! [SV7: del,SV12: $i] :
( ( ~ ( mem @ SV12 @ SV7 )
| ~ ( ~ ! [SY41: $i] :
( ~ ( mem @ SY41 @ SV7 )
| ( SV12 != SY41 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV7 ) @ SV12 ) @ SY41 ) ) )
| ~ ! [SY42: $i] :
( ~ ( mem @ SY42 @ SV7 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV7 ) @ SV12 ) @ SY42 ) )
| ( SV12 = SY42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(76,plain,
! [SV13: del,SV8: del] :
( ( ! [SY43: $i] :
( ~ ( mem @ SY43 @ ( arr @ SV8 @ SV13 ) )
| ! [SY44: $i] :
( ~ ( mem @ SY44 @ ( arr @ SV8 @ SV13 ) )
| ~ ( ~ ( mem @ ( sK1_X @ SY44 @ SY43 @ SV13 @ SV8 ) @ SV8 )
| ~ ( ( ( ap @ SY43 @ ( sK1_X @ SY44 @ SY43 @ SV13 @ SV8 ) )
!= ( ap @ SY44 @ ( sK1_X @ SY44 @ SY43 @ SV13 @ SV8 ) ) ) ) )
| ( SY43 = SY44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(77,plain,
! [SV9: del,SV14: del] :
( ( ! [SY45: $i > $i] :
( ~ ( ~ ( mem @ ( sK2_X @ SY45 @ SV14 @ SV9 ) @ SV9 )
| ~ ~ ( mem @ ( SY45 @ ( sK2_X @ SY45 @ SV14 @ SV9 ) ) @ SV14 ) )
| ( mem @ ( lam @ SV9 @ SY45 ) @ ( arr @ SV9 @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(78,plain,
! [SV1: $o] :
( ( ( ~ ( ( p @ ( inj__o @ SV1 ) )
| SV1 ) )
= $true )
| ( ( ~ ( ~ ( p @ ( inj__o @ SV1 ) )
| ~ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[66]) ).
thf(79,plain,
( ( ( ~ ( ( p @ ( inj__o @ $true ) )
| $true ) )
= $true )
| ( ( ~ ( ~ ( p @ ( inj__o @ $true ) )
| ~ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(80,plain,
( ( ( ~ ( ( p @ ( inj__o @ $false ) )
| $false ) )
= $true )
| ( ( ~ ( ~ ( p @ ( inj__o @ $false ) )
| ~ $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(81,plain,
! [SV3: $i] :
( ( ( mem @ SV3 @ bool )
= $false )
| ( ( SV3
= ( inj__o @ ( p @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(82,plain,
! [SV10: del,SV4: del,SV15: $i] :
( ( ~ ( mem @ SV15 @ ( arr @ SV4 @ SV10 ) )
| ! [SY46: $i] :
( ~ ( mem @ SY46 @ SV4 )
| ( mem @ ( ap @ SV15 @ SY46 ) @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(83,plain,
! [SV11: $i > $i,SV5: del,SV16: $i] :
( ( ~ ( mem @ SV16 @ SV5 )
| ( ( ap @ ( lam @ SV5 @ SV11 ) @ SV16 )
= ( SV11 @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(84,plain,
! [SV7: del,SV12: $i] :
( ( ( ~ ( mem @ SV12 @ SV7 ) )
= $true )
| ( ( ~ ( ~ ! [SY41: $i] :
( ~ ( mem @ SY41 @ SV7 )
| ( SV12 != SY41 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV7 ) @ SV12 ) @ SY41 ) ) )
| ~ ! [SY42: $i] :
( ~ ( mem @ SY42 @ SV7 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV7 ) @ SV12 ) @ SY42 ) )
| ( SV12 = SY42 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(85,plain,
! [SV13: del,SV8: del,SV17: $i] :
( ( ~ ( mem @ SV17 @ ( arr @ SV8 @ SV13 ) )
| ! [SY47: $i] :
( ~ ( mem @ SY47 @ ( arr @ SV8 @ SV13 ) )
| ~ ( ~ ( mem @ ( sK1_X @ SY47 @ SV17 @ SV13 @ SV8 ) @ SV8 )
| ~ ( ( ( ap @ SV17 @ ( sK1_X @ SY47 @ SV17 @ SV13 @ SV8 ) )
!= ( ap @ SY47 @ ( sK1_X @ SY47 @ SV17 @ SV13 @ SV8 ) ) ) ) )
| ( SV17 = SY47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(86,plain,
! [SV9: del,SV14: del,SV18: $i > $i] :
( ( ~ ( ~ ( mem @ ( sK2_X @ SV18 @ SV14 @ SV9 ) @ SV9 )
| ~ ~ ( mem @ ( SV18 @ ( sK2_X @ SV18 @ SV14 @ SV9 ) ) @ SV14 ) )
| ( mem @ ( lam @ SV9 @ SV18 ) @ ( arr @ SV9 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(87,plain,
! [SV1: $o] :
( ( ( ( p @ ( inj__o @ SV1 ) )
| SV1 )
= $false )
| ( ( ~ ( ~ ( p @ ( inj__o @ SV1 ) )
| ~ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(88,plain,
( ( ( ( p @ ( inj__o @ $true ) )
| $true )
= $false )
| ( ( ~ ( ~ ( p @ ( inj__o @ $true ) )
| ~ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(89,plain,
( ( ( ( p @ ( inj__o @ $false ) )
| $false )
= $false )
| ( ( ~ ( ~ ( p @ ( inj__o @ $false ) )
| ~ $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(90,plain,
! [SV10: del,SV4: del,SV15: $i] :
( ( ( ~ ( mem @ SV15 @ ( arr @ SV4 @ SV10 ) ) )
= $true )
| ( ( ! [SY46: $i] :
( ~ ( mem @ SY46 @ SV4 )
| ( mem @ ( ap @ SV15 @ SY46 ) @ SV10 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(91,plain,
! [SV11: $i > $i,SV5: del,SV16: $i] :
( ( ( ~ ( mem @ SV16 @ SV5 ) )
= $true )
| ( ( ( ap @ ( lam @ SV5 @ SV11 ) @ SV16 )
= ( SV11 @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(92,plain,
! [SV7: del,SV12: $i] :
( ( ( mem @ SV12 @ SV7 )
= $false )
| ( ( ~ ( ~ ! [SY41: $i] :
( ~ ( mem @ SY41 @ SV7 )
| ( SV12 != SY41 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV7 ) @ SV12 ) @ SY41 ) ) )
| ~ ! [SY42: $i] :
( ~ ( mem @ SY42 @ SV7 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV7 ) @ SV12 ) @ SY42 ) )
| ( SV12 = SY42 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(93,plain,
! [SV13: del,SV8: del,SV17: $i] :
( ( ( ~ ( mem @ SV17 @ ( arr @ SV8 @ SV13 ) ) )
= $true )
| ( ( ! [SY47: $i] :
( ~ ( mem @ SY47 @ ( arr @ SV8 @ SV13 ) )
| ~ ( ~ ( mem @ ( sK1_X @ SY47 @ SV17 @ SV13 @ SV8 ) @ SV8 )
| ~ ( ( ( ap @ SV17 @ ( sK1_X @ SY47 @ SV17 @ SV13 @ SV8 ) )
!= ( ap @ SY47 @ ( sK1_X @ SY47 @ SV17 @ SV13 @ SV8 ) ) ) ) )
| ( SV17 = SY47 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(94,plain,
! [SV9: del,SV14: del,SV18: $i > $i] :
( ( ( ~ ( ~ ( mem @ ( sK2_X @ SV18 @ SV14 @ SV9 ) @ SV9 )
| ~ ~ ( mem @ ( SV18 @ ( sK2_X @ SV18 @ SV14 @ SV9 ) ) @ SV14 ) ) )
= $true )
| ( ( mem @ ( lam @ SV9 @ SV18 ) @ ( arr @ SV9 @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(95,plain,
! [SV1: $o] :
( ( ( p @ ( inj__o @ SV1 ) )
= $false )
| ( ( ~ ( ~ ( p @ ( inj__o @ SV1 ) )
| ~ SV1 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[87]) ).
thf(96,plain,
! [SV1: $o] :
( ( SV1 = $false )
| ( ( ~ ( ~ ( p @ ( inj__o @ SV1 ) )
| ~ SV1 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[87]) ).
thf(97,plain,
( ( ( p @ ( inj__o @ $true ) )
= $false )
| ( ( ~ ( ~ ( p @ ( inj__o @ $true ) )
| ~ $true ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[88]) ).
thf(98,plain,
( ( $true = $false )
| ( ( ~ ( ~ ( p @ ( inj__o @ $true ) )
| ~ $true ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[88]) ).
thf(99,plain,
( ( ( p @ ( inj__o @ $false ) )
= $false )
| ( ( ~ ( ~ ( p @ ( inj__o @ $false ) )
| ~ $false ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[89]) ).
thf(100,plain,
( ( $false = $false )
| ( ( ~ ( ~ ( p @ ( inj__o @ $false ) )
| ~ $false ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[89]) ).
thf(101,plain,
! [SV10: del,SV4: del,SV15: $i] :
( ( ( mem @ SV15 @ ( arr @ SV4 @ SV10 ) )
= $false )
| ( ( ! [SY46: $i] :
( ~ ( mem @ SY46 @ SV4 )
| ( mem @ ( ap @ SV15 @ SY46 ) @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(102,plain,
! [SV11: $i > $i,SV5: del,SV16: $i] :
( ( ( mem @ SV16 @ SV5 )
= $false )
| ( ( ( ap @ ( lam @ SV5 @ SV11 ) @ SV16 )
= ( SV11 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(103,plain,
! [SV12: $i,SV7: del] :
( ( ( ~ ! [SY41: $i] :
( ~ ( mem @ SY41 @ SV7 )
| ( SV12 != SY41 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV7 ) @ SV12 ) @ SY41 ) ) )
| ~ ! [SY42: $i] :
( ~ ( mem @ SY42 @ SV7 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV7 ) @ SV12 ) @ SY42 ) )
| ( SV12 = SY42 ) ) )
= $false )
| ( ( mem @ SV12 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(104,plain,
! [SV13: del,SV8: del,SV17: $i] :
( ( ( mem @ SV17 @ ( arr @ SV8 @ SV13 ) )
= $false )
| ( ( ! [SY47: $i] :
( ~ ( mem @ SY47 @ ( arr @ SV8 @ SV13 ) )
| ~ ( ~ ( mem @ ( sK1_X @ SY47 @ SV17 @ SV13 @ SV8 ) @ SV8 )
| ~ ( ( ( ap @ SV17 @ ( sK1_X @ SY47 @ SV17 @ SV13 @ SV8 ) )
!= ( ap @ SY47 @ ( sK1_X @ SY47 @ SV17 @ SV13 @ SV8 ) ) ) ) )
| ( SV17 = SY47 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(105,plain,
! [SV9: del,SV14: del,SV18: $i > $i] :
( ( ( ~ ( mem @ ( sK2_X @ SV18 @ SV14 @ SV9 ) @ SV9 )
| ~ ~ ( mem @ ( SV18 @ ( sK2_X @ SV18 @ SV14 @ SV9 ) ) @ SV14 ) )
= $false )
| ( ( mem @ ( lam @ SV9 @ SV18 ) @ ( arr @ SV9 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(106,plain,
! [SV1: $o] :
( ( ( ~ ( p @ ( inj__o @ SV1 ) )
| ~ SV1 )
= $false )
| ( ( p @ ( inj__o @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(107,plain,
! [SV1: $o] :
( ( ( ~ ( p @ ( inj__o @ SV1 ) )
| ~ SV1 )
= $false )
| ( SV1 = $false ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(108,plain,
( ( ( ~ ( p @ ( inj__o @ $true ) )
| ~ $true )
= $false )
| ( ( p @ ( inj__o @ $true ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(109,plain,
( ( ( ~ ( p @ ( inj__o @ $true ) )
| ~ $true )
= $false )
| ( $true = $false ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(110,plain,
( ( ( ~ ( p @ ( inj__o @ $false ) )
| ~ $false )
= $false )
| ( ( p @ ( inj__o @ $false ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(111,plain,
( ( ( ~ ( p @ ( inj__o @ $false ) )
| ~ $false )
= $false )
| ( $false = $false ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(112,plain,
! [SV10: del,SV15: $i,SV4: del,SV19: $i] :
( ( ( ~ ( mem @ SV19 @ SV4 )
| ( mem @ ( ap @ SV15 @ SV19 ) @ SV10 ) )
= $true )
| ( ( mem @ SV15 @ ( arr @ SV4 @ SV10 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(113,plain,
! [SV12: $i,SV7: del] :
( ( ( ~ ! [SY41: $i] :
( ~ ( mem @ SY41 @ SV7 )
| ( SV12 != SY41 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV7 ) @ SV12 ) @ SY41 ) ) ) )
= $false )
| ( ( mem @ SV12 @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[103]) ).
thf(114,plain,
! [SV12: $i,SV7: del] :
( ( ( ~ ! [SY42: $i] :
( ~ ( mem @ SY42 @ SV7 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV7 ) @ SV12 ) @ SY42 ) )
| ( SV12 = SY42 ) ) )
= $false )
| ( ( mem @ SV12 @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[103]) ).
thf(115,plain,
! [SV17: $i,SV13: del,SV8: del,SV20: $i] :
( ( ( ~ ( mem @ SV20 @ ( arr @ SV8 @ SV13 ) )
| ~ ( ~ ( mem @ ( sK1_X @ SV20 @ SV17 @ SV13 @ SV8 ) @ SV8 )
| ~ ( ( ( ap @ SV17 @ ( sK1_X @ SV20 @ SV17 @ SV13 @ SV8 ) )
!= ( ap @ SV20 @ ( sK1_X @ SV20 @ SV17 @ SV13 @ SV8 ) ) ) ) )
| ( SV17 = SV20 ) )
= $true )
| ( ( mem @ SV17 @ ( arr @ SV8 @ SV13 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(116,plain,
! [SV9: del,SV14: del,SV18: $i > $i] :
( ( ( ~ ( mem @ ( sK2_X @ SV18 @ SV14 @ SV9 ) @ SV9 ) )
= $false )
| ( ( mem @ ( lam @ SV9 @ SV18 ) @ ( arr @ SV9 @ SV14 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[105]) ).
thf(117,plain,
! [SV9: del,SV14: del,SV18: $i > $i] :
( ( ( ~ ~ ( mem @ ( SV18 @ ( sK2_X @ SV18 @ SV14 @ SV9 ) ) @ SV14 ) )
= $false )
| ( ( mem @ ( lam @ SV9 @ SV18 ) @ ( arr @ SV9 @ SV14 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[105]) ).
thf(118,plain,
! [SV1: $o] :
( ( ( ~ ( p @ ( inj__o @ SV1 ) ) )
= $false )
| ( ( p @ ( inj__o @ SV1 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[106]) ).
thf(119,plain,
! [SV1: $o] :
( ( ( ~ SV1 ) = $false )
| ( ( p @ ( inj__o @ SV1 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[106]) ).
thf(120,plain,
! [SV1: $o] :
( ( ( ~ ( p @ ( inj__o @ SV1 ) ) )
= $false )
| ( SV1 = $false ) ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(121,plain,
! [SV1: $o] :
( ( ( ~ SV1 ) = $false )
| ( SV1 = $false ) ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(122,plain,
( ( ( ~ ( p @ ( inj__o @ $true ) ) )
= $false )
| ( ( p @ ( inj__o @ $true ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[108]) ).
thf(123,plain,
( ( ( ~ $true ) = $false )
| ( ( p @ ( inj__o @ $true ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[108]) ).
thf(124,plain,
( ( ( ~ ( p @ ( inj__o @ $true ) ) )
= $false )
| ( $true = $false ) ),
inference(extcnf_or_neg,[status(thm)],[109]) ).
thf(125,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false ) ),
inference(extcnf_or_neg,[status(thm)],[109]) ).
thf(126,plain,
( ( ( ~ ( p @ ( inj__o @ $false ) ) )
= $false )
| ( ( p @ ( inj__o @ $false ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[110]) ).
thf(127,plain,
( ( ( ~ $false ) = $false )
| ( ( p @ ( inj__o @ $false ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[110]) ).
thf(128,plain,
( ( ( ~ ( p @ ( inj__o @ $false ) ) )
= $false )
| ( $false = $false ) ),
inference(extcnf_or_neg,[status(thm)],[111]) ).
thf(129,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false ) ),
inference(extcnf_or_neg,[status(thm)],[111]) ).
thf(130,plain,
! [SV10: del,SV15: $i,SV4: del,SV19: $i] :
( ( ( ~ ( mem @ SV19 @ SV4 ) )
= $true )
| ( ( mem @ ( ap @ SV15 @ SV19 ) @ SV10 )
= $true )
| ( ( mem @ SV15 @ ( arr @ SV4 @ SV10 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(131,plain,
! [SV12: $i,SV7: del] :
( ( ( ! [SY41: $i] :
( ~ ( mem @ SY41 @ SV7 )
| ( SV12 != SY41 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV7 ) @ SV12 ) @ SY41 ) ) ) )
= $true )
| ( ( mem @ SV12 @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[113]) ).
thf(132,plain,
! [SV12: $i,SV7: del] :
( ( ( ! [SY42: $i] :
( ~ ( mem @ SY42 @ SV7 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV7 ) @ SV12 ) @ SY42 ) )
| ( SV12 = SY42 ) ) )
= $true )
| ( ( mem @ SV12 @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(133,plain,
! [SV17: $i,SV13: del,SV8: del,SV20: $i] :
( ( ( ~ ( mem @ SV20 @ ( arr @ SV8 @ SV13 ) ) )
= $true )
| ( ( ~ ( ~ ( mem @ ( sK1_X @ SV20 @ SV17 @ SV13 @ SV8 ) @ SV8 )
| ~ ( ( ( ap @ SV17 @ ( sK1_X @ SV20 @ SV17 @ SV13 @ SV8 ) )
!= ( ap @ SV20 @ ( sK1_X @ SV20 @ SV17 @ SV13 @ SV8 ) ) ) ) )
| ( SV17 = SV20 ) )
= $true )
| ( ( mem @ SV17 @ ( arr @ SV8 @ SV13 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(134,plain,
! [SV9: del,SV14: del,SV18: $i > $i] :
( ( ( mem @ ( sK2_X @ SV18 @ SV14 @ SV9 ) @ SV9 )
= $true )
| ( ( mem @ ( lam @ SV9 @ SV18 ) @ ( arr @ SV9 @ SV14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[116]) ).
thf(135,plain,
! [SV9: del,SV14: del,SV18: $i > $i] :
( ( ( ~ ( mem @ ( SV18 @ ( sK2_X @ SV18 @ SV14 @ SV9 ) ) @ SV14 ) )
= $true )
| ( ( mem @ ( lam @ SV9 @ SV18 ) @ ( arr @ SV9 @ SV14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(136,plain,
! [SV1: $o] :
( ( ( p @ ( inj__o @ SV1 ) )
= $true )
| ( ( p @ ( inj__o @ SV1 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[118]) ).
thf(137,plain,
! [SV1: $o] :
( ( SV1 = $true )
| ( ( p @ ( inj__o @ SV1 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[119]) ).
thf(138,plain,
! [SV1: $o] :
( ( ( p @ ( inj__o @ SV1 ) )
= $true )
| ( SV1 = $false ) ),
inference(extcnf_not_neg,[status(thm)],[120]) ).
thf(139,plain,
! [SV1: $o] :
( ( SV1 = $true )
| ( SV1 = $false ) ),
inference(extcnf_not_neg,[status(thm)],[121]) ).
thf(140,plain,
( ( ( p @ ( inj__o @ $true ) )
= $true )
| ( ( p @ ( inj__o @ $true ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(141,plain,
( ( $true = $true )
| ( ( p @ ( inj__o @ $true ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(142,plain,
( ( ( p @ ( inj__o @ $true ) )
= $true )
| ( $true = $false ) ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(143,plain,
( ( $true = $true )
| ( $true = $false ) ),
inference(extcnf_not_neg,[status(thm)],[125]) ).
thf(144,plain,
( ( ( p @ ( inj__o @ $false ) )
= $true )
| ( ( p @ ( inj__o @ $false ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[126]) ).
thf(145,plain,
( ( $false = $true )
| ( ( p @ ( inj__o @ $false ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(146,plain,
( ( ( p @ ( inj__o @ $false ) )
= $true )
| ( $false = $false ) ),
inference(extcnf_not_neg,[status(thm)],[128]) ).
thf(147,plain,
( ( $false = $true )
| ( $false = $false ) ),
inference(extcnf_not_neg,[status(thm)],[129]) ).
thf(148,plain,
! [SV10: del,SV15: $i,SV4: del,SV19: $i] :
( ( ( mem @ SV19 @ SV4 )
= $false )
| ( ( mem @ ( ap @ SV15 @ SV19 ) @ SV10 )
= $true )
| ( ( mem @ SV15 @ ( arr @ SV4 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(149,plain,
! [SV12: $i,SV7: del,SV21: $i] :
( ( ( ~ ( mem @ SV21 @ SV7 )
| ( SV12 != SV21 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV7 ) @ SV12 ) @ SV21 ) ) )
= $true )
| ( ( mem @ SV12 @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(150,plain,
! [SV12: $i,SV7: del,SV22: $i] :
( ( ( ~ ( mem @ SV22 @ SV7 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV7 ) @ SV12 ) @ SV22 ) )
| ( SV12 = SV22 ) )
= $true )
| ( ( mem @ SV12 @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(151,plain,
! [SV17: $i,SV13: del,SV8: del,SV20: $i] :
( ( ( mem @ SV20 @ ( arr @ SV8 @ SV13 ) )
= $false )
| ( ( ~ ( ~ ( mem @ ( sK1_X @ SV20 @ SV17 @ SV13 @ SV8 ) @ SV8 )
| ~ ( ( ( ap @ SV17 @ ( sK1_X @ SV20 @ SV17 @ SV13 @ SV8 ) )
!= ( ap @ SV20 @ ( sK1_X @ SV20 @ SV17 @ SV13 @ SV8 ) ) ) ) )
| ( SV17 = SV20 ) )
= $true )
| ( ( mem @ SV17 @ ( arr @ SV8 @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(152,plain,
! [SV9: del,SV14: del,SV18: $i > $i] :
( ( ( mem @ ( SV18 @ ( sK2_X @ SV18 @ SV14 @ SV9 ) ) @ SV14 )
= $false )
| ( ( mem @ ( lam @ SV9 @ SV18 ) @ ( arr @ SV9 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(153,plain,
! [SV12: $i,SV7: del,SV21: $i] :
( ( ( ~ ( mem @ SV21 @ SV7 ) )
= $true )
| ( ( ( SV12 != SV21 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV7 ) @ SV12 ) @ SV21 ) ) )
= $true )
| ( ( mem @ SV12 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(154,plain,
! [SV12: $i,SV7: del,SV22: $i] :
( ( ( ~ ( mem @ SV22 @ SV7 ) )
= $true )
| ( ( ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV7 ) @ SV12 ) @ SV22 ) )
| ( SV12 = SV22 ) )
= $true )
| ( ( mem @ SV12 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(155,plain,
! [SV8: del,SV13: del,SV17: $i,SV20: $i] :
( ( ( ~ ( ~ ( mem @ ( sK1_X @ SV20 @ SV17 @ SV13 @ SV8 ) @ SV8 )
| ~ ( ( ( ap @ SV17 @ ( sK1_X @ SV20 @ SV17 @ SV13 @ SV8 ) )
!= ( ap @ SV20 @ ( sK1_X @ SV20 @ SV17 @ SV13 @ SV8 ) ) ) ) ) )
= $true )
| ( ( SV17 = SV20 )
= $true )
| ( ( mem @ SV20 @ ( arr @ SV8 @ SV13 ) )
= $false )
| ( ( mem @ SV17 @ ( arr @ SV8 @ SV13 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(156,plain,
! [SV12: $i,SV7: del,SV21: $i] :
( ( ( mem @ SV21 @ SV7 )
= $false )
| ( ( ( SV12 != SV21 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV7 ) @ SV12 ) @ SV21 ) ) )
= $true )
| ( ( mem @ SV12 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(157,plain,
! [SV12: $i,SV7: del,SV22: $i] :
( ( ( mem @ SV22 @ SV7 )
= $false )
| ( ( ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV7 ) @ SV12 ) @ SV22 ) )
| ( SV12 = SV22 ) )
= $true )
| ( ( mem @ SV12 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(158,plain,
! [SV8: del,SV13: del,SV17: $i,SV20: $i] :
( ( ( ~ ( mem @ ( sK1_X @ SV20 @ SV17 @ SV13 @ SV8 ) @ SV8 )
| ~ ( ( ( ap @ SV17 @ ( sK1_X @ SV20 @ SV17 @ SV13 @ SV8 ) )
!= ( ap @ SV20 @ ( sK1_X @ SV20 @ SV17 @ SV13 @ SV8 ) ) ) ) )
= $false )
| ( ( SV17 = SV20 )
= $true )
| ( ( mem @ SV20 @ ( arr @ SV8 @ SV13 ) )
= $false )
| ( ( mem @ SV17 @ ( arr @ SV8 @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(159,plain,
! [SV7: del,SV21: $i,SV12: $i] :
( ( ( SV12 != SV21 )
= $true )
| ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV7 ) @ SV12 ) @ SV21 ) )
= $true )
| ( ( mem @ SV21 @ SV7 )
= $false )
| ( ( mem @ SV12 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(160,plain,
! [SV22: $i,SV12: $i,SV7: del] :
( ( ( ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV7 ) @ SV12 ) @ SV22 ) ) )
= $true )
| ( ( SV12 = SV22 )
= $true )
| ( ( mem @ SV22 @ SV7 )
= $false )
| ( ( mem @ SV12 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(161,plain,
! [SV8: del,SV13: del,SV17: $i,SV20: $i] :
( ( ( ~ ( mem @ ( sK1_X @ SV20 @ SV17 @ SV13 @ SV8 ) @ SV8 ) )
= $false )
| ( ( SV17 = SV20 )
= $true )
| ( ( mem @ SV20 @ ( arr @ SV8 @ SV13 ) )
= $false )
| ( ( mem @ SV17 @ ( arr @ SV8 @ SV13 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[158]) ).
thf(162,plain,
! [SV8: del,SV13: del,SV20: $i,SV17: $i] :
( ( ( ~ ( ( ( ap @ SV17 @ ( sK1_X @ SV20 @ SV17 @ SV13 @ SV8 ) )
!= ( ap @ SV20 @ ( sK1_X @ SV20 @ SV17 @ SV13 @ SV8 ) ) ) ) )
= $false )
| ( ( SV17 = SV20 )
= $true )
| ( ( mem @ SV20 @ ( arr @ SV8 @ SV13 ) )
= $false )
| ( ( mem @ SV17 @ ( arr @ SV8 @ SV13 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[158]) ).
thf(163,plain,
! [SV7: del,SV21: $i,SV12: $i] :
( ( ( SV12 = SV21 )
= $false )
| ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV7 ) @ SV12 ) @ SV21 ) )
= $true )
| ( ( mem @ SV21 @ SV7 )
= $false )
| ( ( mem @ SV12 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(164,plain,
! [SV22: $i,SV12: $i,SV7: del] :
( ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV7 ) @ SV12 ) @ SV22 ) )
= $false )
| ( ( SV12 = SV22 )
= $true )
| ( ( mem @ SV22 @ SV7 )
= $false )
| ( ( mem @ SV12 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(165,plain,
! [SV8: del,SV13: del,SV17: $i,SV20: $i] :
( ( ( mem @ ( sK1_X @ SV20 @ SV17 @ SV13 @ SV8 ) @ SV8 )
= $true )
| ( ( SV17 = SV20 )
= $true )
| ( ( mem @ SV20 @ ( arr @ SV8 @ SV13 ) )
= $false )
| ( ( mem @ SV17 @ ( arr @ SV8 @ SV13 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[161]) ).
thf(166,plain,
! [SV8: del,SV13: del,SV20: $i,SV17: $i] :
( ( ( ( ap @ SV17 @ ( sK1_X @ SV20 @ SV17 @ SV13 @ SV8 ) )
!= ( ap @ SV20 @ ( sK1_X @ SV20 @ SV17 @ SV13 @ SV8 ) ) )
= $true )
| ( ( SV17 = SV20 )
= $true )
| ( ( mem @ SV20 @ ( arr @ SV8 @ SV13 ) )
= $false )
| ( ( mem @ SV17 @ ( arr @ SV8 @ SV13 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[162]) ).
thf(167,plain,
! [SV8: del,SV13: del,SV20: $i,SV17: $i] :
( ( ( ( ap @ SV17 @ ( sK1_X @ SV20 @ SV17 @ SV13 @ SV8 ) )
= ( ap @ SV20 @ ( sK1_X @ SV20 @ SV17 @ SV13 @ SV8 ) ) )
= $false )
| ( ( SV17 = SV20 )
= $true )
| ( ( mem @ SV20 @ ( arr @ SV8 @ SV13 ) )
= $false )
| ( ( mem @ SV17 @ ( arr @ SV8 @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(168,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[43,167,165,164,163,152,148,147,146,145,144,143,142,141,140,139,138,137,136,134,102,81,71,69,67,62,61,57,56,55,47,44]) ).
thf(169,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[168]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP001^2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.21 % Computer : n019.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Oct 6 11:06:40 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.30
% 0.09/0.30 No.of.Axioms: 12
% 0.09/0.30
% 0.09/0.30 Length.of.Defs: 0
% 0.09/0.30
% 0.09/0.30 Contains.Choice.Funs: false
% 0.09/0.30 .....
% 0.09/0.30
% 0.09/0.30 ********************************
% 0.09/0.30 * All subproblems solved! *
% 0.09/0.30 ********************************
% 0.09/0.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:12,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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:168,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 0.09/0.30
% 0.09/0.30 %**** Beginning of derivation protocol ****
% 0.09/0.30 % SZS output start CNFRefutation
% See solution above
% 0.27/0.30
% 0.27/0.30 %**** End of derivation protocol ****
% 0.27/0.30 %**** no. of clauses in derivation: 169 ****
% 0.27/0.30 %**** clause counter: 168 ****
% 0.27/0.30
% 0.27/0.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:12,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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:168,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------