%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ITP019+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 : n004.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 10:23:27 AM UTC 2026
% Result : Theorem 0.63s 0.34s
% Output : CNFRefutation 0.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of formulae : 103 ( 60 unt; 0 typ; 0 def)
% Number of atoms : 581 ( 260 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 1138 ( 121 ~; 136 |; 0 &; 837 @)
% ( 3 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 24 usr; 15 con; 0-4 aty)
% Number of variables : 216 ( 0 ^; 216 !; 0 ?; 216 :)
% 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_2EF,type,
c_2Ebool_2EF: $i ).
thf(tp_c_2Ebool_2ET,type,
c_2Ebool_2ET: $i ).
thf(tp_c_2Ebool_2E_21,type,
c_2Ebool_2E_21: $i > $i ).
thf(tp_c_2Ebool_2E_2F_5C,type,
c_2Ebool_2E_2F_5C: $i ).
thf(tp_c_2Ebool_2E_7E,type,
c_2Ebool_2E_7E: $i ).
thf(tp_c_2Ecomplex_2Ecomplex__inv,type,
c_2Ecomplex_2Ecomplex__inv: $i ).
thf(tp_c_2Ecomplex_2Ecomplex__of__num,type,
c_2Ecomplex_2Ecomplex__of__num: $i ).
thf(tp_c_2Emin_2E_3D,type,
c_2Emin_2E_3D: $i > $i ).
thf(tp_c_2Emin_2E_3D_3D_3E,type,
c_2Emin_2E_3D_3D_3E: $i ).
thf(tp_c_2Enum_2E0,type,
c_2Enum_2E0: $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_V0z,type,
sK1_V0z: $i ).
thf(tp_sK2_SY38,type,
sK2_SY38: $i > $i > $i > $i > $i ).
thf(tp_ty_2Enum_2Enum,type,
ty_2Enum_2Enum: $i ).
thf(tp_ty_2Epair_2Eprod,type,
ty_2Epair_2Eprod: $i > $i > $i ).
thf(tp_ty_2Erealax_2Ereal,type,
ty_2Erealax_2Ereal: $i ).
thf(1,axiom,
! [V0z: $i] :
( ( mem @ V0z @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
=> ( ( ( ap @ c_2Ecomplex_2Ecomplex__inv @ V0z )
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
<=> ( V0z
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ecomplex_2ECOMPLEX__INV__EQ__0) ).
thf(4,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2ETRUTH) ).
thf(9,axiom,
mem @ c_2Ecomplex_2Ecomplex__inv @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ecomplex_2Ecomplex__inv) ).
thf(11,axiom,
! [A0: $i] :
( ( ne @ A0 )
=> ! [A1: $i] :
( ( ne @ A1 )
=> ( ne @ ( ty_2Epair_2Eprod @ A0 @ A1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ne_ty_2Epair_2Eprod) ).
thf(12,axiom,
ne @ ty_2Erealax_2Ereal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ne_ty_2Erealax_2Ereal) ).
thf(13,axiom,
mem @ c_2Enum_2E0 @ ty_2Enum_2Enum,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Enum_2E0) ).
thf(25,axiom,
! [A: $i,X: $i] :
( ( mem @ X @ A )
=> ( ( ap @ ( i @ A ) @ X )
= X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ibeta) ).
thf(26,axiom,
! [A: $i,Y: $i,X: $i] :
( ( mem @ X @ A )
=> ( ( ap @ ( k @ A @ Y ) @ X )
= Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kbeta) ).
thf(27,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/sandbox/benchmark/theBenchmark.p',funcext) ).
thf(29,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/sandbox/benchmark/theBenchmark.p',ap_tp) ).
thf(33,conjecture,
! [V0z: $i] :
( ( mem @ V0z @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
=> ( ( V0z
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
=> ( ( ap @ c_2Ecomplex_2Ecomplex__inv @ V0z )
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ecomplex_2ECOMPLEX__INV__NZ) ).
thf(34,negated_conjecture,
( ( ! [V0z: $i] :
( ( mem @ V0z @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
=> ( ( V0z
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
=> ( ( ap @ c_2Ecomplex_2Ecomplex__inv @ V0z )
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[33]) ).
thf(35,plain,
( ( ! [V0z: $i] :
( ( mem @ V0z @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
=> ( ( V0z
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
=> ( ( ap @ c_2Ecomplex_2Ecomplex__inv @ V0z )
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[34]) ).
thf(36,plain,
( ( ! [V0z: $i] :
( ( mem @ V0z @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
=> ( ( ( ap @ c_2Ecomplex_2Ecomplex__inv @ V0z )
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
<=> ( V0z
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(37,plain,
$true = $true,
inference(unfold_def,[status(thm)],[4]) ).
thf(38,plain,
( ( mem @ c_2Ecomplex_2Ecomplex__inv @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(39,plain,
( ( ! [A0: $i] :
( ( ne @ A0 )
=> ! [A1: $i] :
( ( ne @ A1 )
=> ( ne @ ( ty_2Epair_2Eprod @ A0 @ A1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(40,plain,
( ( ne @ ty_2Erealax_2Ereal )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(41,plain,
( ( mem @ c_2Enum_2E0 @ ty_2Enum_2Enum )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(42,plain,
( ( ! [A: $i,X: $i] :
( ( mem @ X @ A )
=> ( ( ap @ ( i @ A ) @ X )
= X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(43,plain,
( ( ! [A: $i,Y: $i,X: $i] :
( ( mem @ X @ A )
=> ( ( ap @ ( k @ A @ Y ) @ X )
= Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(44,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)],[27]) ).
thf(45,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)],[29]) ).
thf(46,plain,
( ( ( mem @ sK1_V0z @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
=> ( ( sK1_V0z
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
=> ( ( ap @ c_2Ecomplex_2Ecomplex__inv @ sK1_V0z )
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[35]) ).
thf(47,plain,
( ( mem @ sK1_V0z @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
= $true ),
inference(standard_cnf,[status(thm)],[46]) ).
thf(48,plain,
( ( sK1_V0z
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
= $true ),
inference(standard_cnf,[status(thm)],[46]) ).
thf(49,plain,
( ( ( ap @ c_2Ecomplex_2Ecomplex__inv @ sK1_V0z )
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
= $false ),
inference(standard_cnf,[status(thm)],[46]) ).
thf(50,plain,
( ( ~ ( ( ( ap @ c_2Ecomplex_2Ecomplex__inv @ sK1_V0z )
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[49]) ).
thf(51,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)],[45]) ).
thf(52,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(copy,[status(thm)],[44]) ).
thf(53,plain,
( ( ! [A: $i,Y: $i,X: $i] :
( ( mem @ X @ A )
=> ( ( ap @ ( k @ A @ Y ) @ X )
= Y ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(54,plain,
( ( ! [A: $i,X: $i] :
( ( mem @ X @ A )
=> ( ( ap @ ( i @ A ) @ X )
= X ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(55,plain,
( ( mem @ c_2Enum_2E0 @ ty_2Enum_2Enum )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(56,plain,
( ( ne @ ty_2Erealax_2Ereal )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(57,plain,
( ( ! [A0: $i] :
( ( ne @ A0 )
=> ! [A1: $i] :
( ( ne @ A1 )
=> ( ne @ ( ty_2Epair_2Eprod @ A0 @ A1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(58,plain,
( ( mem @ c_2Ecomplex_2Ecomplex__inv @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(59,plain,
$true = $true,
inference(copy,[status(thm)],[37]) ).
thf(60,plain,
( ( ! [V0z: $i] :
( ( mem @ V0z @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
=> ( ( ( ap @ c_2Ecomplex_2Ecomplex__inv @ V0z )
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
<=> ( V0z
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(61,plain,
( ( sK1_V0z
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(62,plain,
( ( mem @ sK1_V0z @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(63,plain,
( ( ~ ( ( ( ap @ c_2Ecomplex_2Ecomplex__inv @ sK1_V0z )
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(64,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( mem @ SX2 @ ( arr @ SX0 @ SX1 ) )
| ! [SX3: $i] :
( ~ ( mem @ SX3 @ SX0 )
| ( mem @ ( ap @ SX2 @ SX3 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(65,plain,
( ( ~ ( ( ( ap @ c_2Ecomplex_2Ecomplex__inv @ sK1_V0z )
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(66,plain,
( ( ! [SX0: $i] :
( ~ ( ne @ SX0 )
| ! [SX1: $i] :
( ~ ( ne @ SX1 )
| ( ne @ ( ty_2Epair_2Eprod @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(67,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( mem @ SX2 @ SX0 )
| ( ( ap @ ( k @ SX0 @ SX1 ) @ SX2 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(68,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( mem @ SX1 @ SX0 )
| ( ( ap @ ( i @ SX0 ) @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(69,plain,
( ( sK1_V0z
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(70,plain,
( ( ! [SX0: $i] :
( ~ ( mem @ SX0 @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
| ~ ( ~ ( ( ( ap @ c_2Ecomplex_2Ecomplex__inv @ SX0 )
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
| ( SX0
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) )
| ~ ( ( SX0
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
| ( ( ap @ c_2Ecomplex_2Ecomplex__inv @ SX0 )
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(71,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( mem @ SX2 @ ( arr @ SX0 @ SX1 ) )
| ! [SX3: $i] :
( ~ ( mem @ SX3 @ ( arr @ SX0 @ SX1 ) )
| ~ ! [SX4: $i] :
( ~ ( mem @ SX4 @ SX0 )
| ( ( ap @ SX2 @ SX4 )
= ( ap @ SX3 @ SX4 ) ) )
| ( SX2 = SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(72,plain,
! [SV1: $i] :
( ( ! [SY18: $i,SY19: $i] :
( ~ ( mem @ SY19 @ ( arr @ SV1 @ SY18 ) )
| ! [SY20: $i] :
( ~ ( mem @ SY20 @ SV1 )
| ( mem @ ( ap @ SY19 @ SY20 ) @ SY18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(73,plain,
( ( ( ap @ c_2Ecomplex_2Ecomplex__inv @ sK1_V0z )
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(74,plain,
! [SV2: $i] :
( ( ~ ( ne @ SV2 )
| ! [SY21: $i] :
( ~ ( ne @ SY21 )
| ( ne @ ( ty_2Epair_2Eprod @ SV2 @ SY21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(75,plain,
! [SV3: $i] :
( ( ! [SY22: $i,SY23: $i] :
( ~ ( mem @ SY23 @ SV3 )
| ( ( ap @ ( k @ SV3 @ SY22 ) @ SY23 )
= SY22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(76,plain,
! [SV4: $i] :
( ( ! [SY24: $i] :
( ~ ( mem @ SY24 @ SV4 )
| ( ( ap @ ( i @ SV4 ) @ SY24 )
= SY24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(77,plain,
( ( sK1_V0z
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(78,plain,
! [SV5: $i] :
( ( ~ ( mem @ SV5 @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
| ~ ( ~ ( ( ( ap @ c_2Ecomplex_2Ecomplex__inv @ SV5 )
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
| ( SV5
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) )
| ~ ( ( SV5
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
| ( ( ap @ c_2Ecomplex_2Ecomplex__inv @ SV5 )
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(79,plain,
! [SV6: $i] :
( ( ! [SY25: $i,SY26: $i] :
( ~ ( mem @ SY26 @ ( arr @ SV6 @ SY25 ) )
| ! [SY27: $i] :
( ~ ( mem @ SY27 @ ( arr @ SV6 @ SY25 ) )
| ~ ! [SY28: $i] :
( ~ ( mem @ SY28 @ SV6 )
| ( ( ap @ SY26 @ SY28 )
= ( ap @ SY27 @ SY28 ) ) )
| ( SY26 = SY27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(80,plain,
! [SV7: $i,SV1: $i] :
( ( ! [SY29: $i] :
( ~ ( mem @ SY29 @ ( arr @ SV1 @ SV7 ) )
| ! [SY30: $i] :
( ~ ( mem @ SY30 @ SV1 )
| ( mem @ ( ap @ SY29 @ SY30 ) @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(81,plain,
( ( ( ap @ c_2Ecomplex_2Ecomplex__inv @ sK1_V0z )
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[73]) ).
thf(82,plain,
! [SV2: $i] :
( ( ( ~ ( ne @ SV2 ) )
= $true )
| ( ( ! [SY21: $i] :
( ~ ( ne @ SY21 )
| ( ne @ ( ty_2Epair_2Eprod @ SV2 @ SY21 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(83,plain,
! [SV8: $i,SV3: $i] :
( ( ! [SY31: $i] :
( ~ ( mem @ SY31 @ SV3 )
| ( ( ap @ ( k @ SV3 @ SV8 ) @ SY31 )
= SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(84,plain,
! [SV4: $i,SV9: $i] :
( ( ~ ( mem @ SV9 @ SV4 )
| ( ( ap @ ( i @ SV4 ) @ SV9 )
= SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(85,plain,
! [SV5: $i] :
( ( ( ~ ( mem @ SV5 @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) ) )
= $true )
| ( ( ~ ( ~ ( ( ( ap @ c_2Ecomplex_2Ecomplex__inv @ SV5 )
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
| ( SV5
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) )
| ~ ( ( SV5
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
| ( ( ap @ c_2Ecomplex_2Ecomplex__inv @ SV5 )
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[78]) ).
thf(86,plain,
! [SV10: $i,SV6: $i] :
( ( ! [SY32: $i] :
( ~ ( mem @ SY32 @ ( arr @ SV6 @ SV10 ) )
| ! [SY33: $i] :
( ~ ( mem @ SY33 @ ( arr @ SV6 @ SV10 ) )
| ~ ! [SY28: $i] :
( ~ ( mem @ SY28 @ SV6 )
| ( ( ap @ SY32 @ SY28 )
= ( ap @ SY33 @ SY28 ) ) )
| ( SY32 = SY33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(87,plain,
! [SV7: $i,SV1: $i,SV11: $i] :
( ( ~ ( mem @ SV11 @ ( arr @ SV1 @ SV7 ) )
| ! [SY35: $i] :
( ~ ( mem @ SY35 @ SV1 )
| ( mem @ ( ap @ SV11 @ SY35 ) @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(88,plain,
! [SV2: $i] :
( ( ( ne @ SV2 )
= $false )
| ( ( ! [SY21: $i] :
( ~ ( ne @ SY21 )
| ( ne @ ( ty_2Epair_2Eprod @ SV2 @ SY21 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(89,plain,
! [SV8: $i,SV3: $i,SV12: $i] :
( ( ~ ( mem @ SV12 @ SV3 )
| ( ( ap @ ( k @ SV3 @ SV8 ) @ SV12 )
= SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(90,plain,
! [SV4: $i,SV9: $i] :
( ( ( ~ ( mem @ SV9 @ SV4 ) )
= $true )
| ( ( ( ap @ ( i @ SV4 ) @ SV9 )
= SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(91,plain,
! [SV5: $i] :
( ( ( mem @ SV5 @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
= $false )
| ( ( ~ ( ~ ( ( ( ap @ c_2Ecomplex_2Ecomplex__inv @ SV5 )
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
| ( SV5
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) )
| ~ ( ( SV5
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
| ( ( ap @ c_2Ecomplex_2Ecomplex__inv @ SV5 )
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(92,plain,
! [SV10: $i,SV6: $i,SV13: $i] :
( ( ~ ( mem @ SV13 @ ( arr @ SV6 @ SV10 ) )
| ! [SY36: $i] :
( ~ ( mem @ SY36 @ ( arr @ SV6 @ SV10 ) )
| ~ ! [SY37: $i] :
( ~ ( mem @ SY37 @ SV6 )
| ( ( ap @ SV13 @ SY37 )
= ( ap @ SY36 @ SY37 ) ) )
| ( SV13 = SY36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(93,plain,
! [SV7: $i,SV1: $i,SV11: $i] :
( ( ( ~ ( mem @ SV11 @ ( arr @ SV1 @ SV7 ) ) )
= $true )
| ( ( ! [SY35: $i] :
( ~ ( mem @ SY35 @ SV1 )
| ( mem @ ( ap @ SV11 @ SY35 ) @ SV7 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(94,plain,
! [SV2: $i,SV14: $i] :
( ( ( ~ ( ne @ SV14 )
| ( ne @ ( ty_2Epair_2Eprod @ SV2 @ SV14 ) ) )
= $true )
| ( ( ne @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(95,plain,
! [SV8: $i,SV3: $i,SV12: $i] :
( ( ( ~ ( mem @ SV12 @ SV3 ) )
= $true )
| ( ( ( ap @ ( k @ SV3 @ SV8 ) @ SV12 )
= SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(96,plain,
! [SV4: $i,SV9: $i] :
( ( ( mem @ SV9 @ SV4 )
= $false )
| ( ( ( ap @ ( i @ SV4 ) @ SV9 )
= SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(97,plain,
! [SV5: $i] :
( ( ( ~ ( ( ( ap @ c_2Ecomplex_2Ecomplex__inv @ SV5 )
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
| ( SV5
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) )
| ~ ( ( SV5
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
| ( ( ap @ c_2Ecomplex_2Ecomplex__inv @ SV5 )
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) ) )
= $false )
| ( ( mem @ SV5 @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(98,plain,
! [SV10: $i,SV6: $i,SV13: $i] :
( ( ( ~ ( mem @ SV13 @ ( arr @ SV6 @ SV10 ) ) )
= $true )
| ( ( ! [SY36: $i] :
( ~ ( mem @ SY36 @ ( arr @ SV6 @ SV10 ) )
| ~ ! [SY37: $i] :
( ~ ( mem @ SY37 @ SV6 )
| ( ( ap @ SV13 @ SY37 )
= ( ap @ SY36 @ SY37 ) ) )
| ( SV13 = SY36 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(99,plain,
! [SV7: $i,SV1: $i,SV11: $i] :
( ( ( mem @ SV11 @ ( arr @ SV1 @ SV7 ) )
= $false )
| ( ( ! [SY35: $i] :
( ~ ( mem @ SY35 @ SV1 )
| ( mem @ ( ap @ SV11 @ SY35 ) @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(100,plain,
! [SV2: $i,SV14: $i] :
( ( ( ~ ( ne @ SV14 ) )
= $true )
| ( ( ne @ ( ty_2Epair_2Eprod @ SV2 @ SV14 ) )
= $true )
| ( ( ne @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(101,plain,
! [SV8: $i,SV3: $i,SV12: $i] :
( ( ( mem @ SV12 @ SV3 )
= $false )
| ( ( ( ap @ ( k @ SV3 @ SV8 ) @ SV12 )
= SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(102,plain,
! [SV5: $i] :
( ( ( ~ ( ( ( ap @ c_2Ecomplex_2Ecomplex__inv @ SV5 )
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
| ( SV5
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) ) )
= $false )
| ( ( mem @ SV5 @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[97]) ).
thf(103,plain,
! [SV5: $i] :
( ( ( ~ ( ( SV5
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
| ( ( ap @ c_2Ecomplex_2Ecomplex__inv @ SV5 )
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) ) )
= $false )
| ( ( mem @ SV5 @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[97]) ).
thf(104,plain,
! [SV10: $i,SV6: $i,SV13: $i] :
( ( ( mem @ SV13 @ ( arr @ SV6 @ SV10 ) )
= $false )
| ( ( ! [SY36: $i] :
( ~ ( mem @ SY36 @ ( arr @ SV6 @ SV10 ) )
| ~ ! [SY37: $i] :
( ~ ( mem @ SY37 @ SV6 )
| ( ( ap @ SV13 @ SY37 )
= ( ap @ SY36 @ SY37 ) ) )
| ( SV13 = SY36 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(105,plain,
! [SV7: $i,SV11: $i,SV1: $i,SV15: $i] :
( ( ( ~ ( mem @ SV15 @ SV1 )
| ( mem @ ( ap @ SV11 @ SV15 ) @ SV7 ) )
= $true )
| ( ( mem @ SV11 @ ( arr @ SV1 @ SV7 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(106,plain,
! [SV2: $i,SV14: $i] :
( ( ( ne @ SV14 )
= $false )
| ( ( ne @ ( ty_2Epair_2Eprod @ SV2 @ SV14 ) )
= $true )
| ( ( ne @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(107,plain,
! [SV5: $i] :
( ( ( ( ( ap @ c_2Ecomplex_2Ecomplex__inv @ SV5 )
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
| ( SV5
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) )
= $true )
| ( ( mem @ SV5 @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[102]) ).
thf(108,plain,
! [SV5: $i] :
( ( ( ( SV5
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
| ( ( ap @ c_2Ecomplex_2Ecomplex__inv @ SV5 )
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) )
= $true )
| ( ( mem @ SV5 @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[103]) ).
thf(109,plain,
! [SV13: $i,SV10: $i,SV6: $i,SV16: $i] :
( ( ( ~ ( mem @ SV16 @ ( arr @ SV6 @ SV10 ) )
| ~ ! [SY38: $i] :
( ~ ( mem @ SY38 @ SV6 )
| ( ( ap @ SV13 @ SY38 )
= ( ap @ SV16 @ SY38 ) ) )
| ( SV13 = SV16 ) )
= $true )
| ( ( mem @ SV13 @ ( arr @ SV6 @ SV10 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(110,plain,
! [SV7: $i,SV11: $i,SV1: $i,SV15: $i] :
( ( ( ~ ( mem @ SV15 @ SV1 ) )
= $true )
| ( ( mem @ ( ap @ SV11 @ SV15 ) @ SV7 )
= $true )
| ( ( mem @ SV11 @ ( arr @ SV1 @ SV7 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(111,plain,
! [SV5: $i] :
( ( ( ( ap @ c_2Ecomplex_2Ecomplex__inv @ SV5 )
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
= $true )
| ( ( SV5
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
= $true )
| ( ( mem @ SV5 @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(112,plain,
! [SV5: $i] :
( ( ( SV5
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
= $true )
| ( ( ( ap @ c_2Ecomplex_2Ecomplex__inv @ SV5 )
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
= $true )
| ( ( mem @ SV5 @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(113,plain,
! [SV13: $i,SV10: $i,SV6: $i,SV16: $i] :
( ( ( ~ ( mem @ SV16 @ ( arr @ SV6 @ SV10 ) ) )
= $true )
| ( ( ~ ! [SY38: $i] :
( ~ ( mem @ SY38 @ SV6 )
| ( ( ap @ SV13 @ SY38 )
= ( ap @ SV16 @ SY38 ) ) )
| ( SV13 = SV16 ) )
= $true )
| ( ( mem @ SV13 @ ( arr @ SV6 @ SV10 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(114,plain,
! [SV7: $i,SV11: $i,SV1: $i,SV15: $i] :
( ( ( mem @ SV15 @ SV1 )
= $false )
| ( ( mem @ ( ap @ SV11 @ SV15 ) @ SV7 )
= $true )
| ( ( mem @ SV11 @ ( arr @ SV1 @ SV7 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(115,plain,
! [SV5: $i] :
( ( ( ( ap @ c_2Ecomplex_2Ecomplex__inv @ SV5 )
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
= $false )
| ( ( SV5
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
= $true )
| ( ( mem @ SV5 @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(116,plain,
! [SV5: $i] :
( ( ( SV5
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
= $false )
| ( ( ( ap @ c_2Ecomplex_2Ecomplex__inv @ SV5 )
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
= $true )
| ( ( mem @ SV5 @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(117,plain,
! [SV13: $i,SV10: $i,SV6: $i,SV16: $i] :
( ( ( mem @ SV16 @ ( arr @ SV6 @ SV10 ) )
= $false )
| ( ( ~ ! [SY38: $i] :
( ~ ( mem @ SY38 @ SV6 )
| ( ( ap @ SV13 @ SY38 )
= ( ap @ SV16 @ SY38 ) ) )
| ( SV13 = SV16 ) )
= $true )
| ( ( mem @ SV13 @ ( arr @ SV6 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(118,plain,
! [SV10: $i,SV16: $i,SV13: $i,SV6: $i] :
( ( ( ~ ! [SY38: $i] :
( ~ ( mem @ SY38 @ SV6 )
| ( ( ap @ SV13 @ SY38 )
= ( ap @ SV16 @ SY38 ) ) ) )
= $true )
| ( ( SV13 = SV16 )
= $true )
| ( ( mem @ SV16 @ ( arr @ SV6 @ SV10 ) )
= $false )
| ( ( mem @ SV13 @ ( arr @ SV6 @ SV10 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[117]) ).
thf(119,plain,
! [SV10: $i,SV16: $i,SV13: $i,SV6: $i] :
( ( ( ! [SY38: $i] :
( ~ ( mem @ SY38 @ SV6 )
| ( ( ap @ SV13 @ SY38 )
= ( ap @ SV16 @ SY38 ) ) ) )
= $false )
| ( ( SV13 = SV16 )
= $true )
| ( ( mem @ SV16 @ ( arr @ SV6 @ SV10 ) )
= $false )
| ( ( mem @ SV13 @ ( arr @ SV6 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(120,plain,
! [SV6: $i,SV13: $i,SV16: $i,SV10: $i] :
( ( ( ~ ( mem @ ( sK2_SY38 @ SV10 @ SV16 @ SV13 @ SV6 ) @ SV6 )
| ( ( ap @ SV13 @ ( sK2_SY38 @ SV10 @ SV16 @ SV13 @ SV6 ) )
= ( ap @ SV16 @ ( sK2_SY38 @ SV10 @ SV16 @ SV13 @ SV6 ) ) ) )
= $false )
| ( ( SV13 = SV16 )
= $true )
| ( ( mem @ SV16 @ ( arr @ SV6 @ SV10 ) )
= $false )
| ( ( mem @ SV13 @ ( arr @ SV6 @ SV10 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[119]) ).
thf(121,plain,
! [SV6: $i,SV13: $i,SV16: $i,SV10: $i] :
( ( ( ~ ( mem @ ( sK2_SY38 @ SV10 @ SV16 @ SV13 @ SV6 ) @ SV6 ) )
= $false )
| ( ( SV13 = SV16 )
= $true )
| ( ( mem @ SV16 @ ( arr @ SV6 @ SV10 ) )
= $false )
| ( ( mem @ SV13 @ ( arr @ SV6 @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[120]) ).
thf(122,plain,
! [SV6: $i,SV16: $i,SV10: $i,SV13: $i] :
( ( ( ( ap @ SV13 @ ( sK2_SY38 @ SV10 @ SV16 @ SV13 @ SV6 ) )
= ( ap @ SV16 @ ( sK2_SY38 @ SV10 @ SV16 @ SV13 @ SV6 ) ) )
= $false )
| ( ( SV13 = SV16 )
= $true )
| ( ( mem @ SV16 @ ( arr @ SV6 @ SV10 ) )
= $false )
| ( ( mem @ SV13 @ ( arr @ SV6 @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[120]) ).
thf(123,plain,
! [SV6: $i,SV13: $i,SV16: $i,SV10: $i] :
( ( ( mem @ ( sK2_SY38 @ SV10 @ SV16 @ SV13 @ SV6 ) @ SV6 )
= $true )
| ( ( SV13 = SV16 )
= $true )
| ( ( mem @ SV16 @ ( arr @ SV6 @ SV10 ) )
= $false )
| ( ( mem @ SV13 @ ( arr @ SV6 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[121]) ).
thf(124,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[55,123,122,116,115,114,106,101,96,81,77,62,59,58,56]) ).
thf(125,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[124]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP019+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
% 0.08/0.20 % Computer : n004.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Oct 6 11:10:09 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.63/0.34
% 0.63/0.34 No.of.Axioms: 10
% 0.63/0.34
% 0.63/0.34 Length.of.Defs: 0
% 0.63/0.34
% 0.63/0.34 Contains.Choice.Funs: false
% 0.63/0.34 ...
% 0.63/0.34
% 0.63/0.34 ********************************
% 0.63/0.34 * All subproblems solved! *
% 0.63/0.34 ********************************
% 0.63/0.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:12,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:124,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.63/0.34
% 0.63/0.34 %**** Beginning of derivation protocol ****
% 0.63/0.34 % SZS output start CNFRefutation
% See solution above
% 0.63/0.34
% 0.63/0.34 %**** End of derivation protocol ****
% 0.63/0.34 %**** no. of clauses in derivation: 103 ****
% 0.63/0.34 %**** clause counter: 124 ****
% 0.63/0.34
% 0.63/0.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:12,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:124,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------