%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWX222-1 : TPTP v9.3.1. Released v9.3.0.
% 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 : n001.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 11:02:36 AM UTC 2026
% Result : Unsatisfiable 3.48s 0.84s
% Output : CNFRefutation 3.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 57
% Syntax : Number of formulae : 315 ( 286 unt; 0 typ; 0 def)
% Number of atoms : 981 ( 684 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 2127 ( 70 ~; 88 |; 0 &;1969 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 26 usr; 10 con; 0-4 aty)
% Number of variables : 862 ( 0 ^; 862 !; 0 ?; 862 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_andb,type,
andb: $i > $i > $i ).
thf(tp_app,type,
app: $i > $i > $i > $i ).
thf(tp_arr,type,
arr: $i > $i > $i ).
thf(tp_aux,type,
aux: $i > $i > $i > $i > $i ).
thf(tp_b,type,
b: $i ).
thf(tp_bfalse,type,
bfalse: $i ).
thf(tp_btrue,type,
btrue: $i ).
thf(tp_c,type,
c: $i ).
thf(tp_cons,type,
cons: $i > $i > $i ).
thf(tp_eq,type,
eq: $i > $i > $i ).
thf(tp_eq2,type,
eq2: $i > $i > $i ).
thf(tp_eq3,type,
eq3: $i > $i > $i ).
thf(tp_eq4,type,
eq4: $i > $i > $i ).
thf(tp_index,type,
index: $i > $i > $i ).
thf(tp_just,type,
just: $i > $i ).
thf(tp_lam,type,
lam: $i > $i ).
thf(tp_nf,type,
nf: $i > $i ).
thf(tp_nil,type,
nil: $i ).
thf(tp_notb,type,
notb: $i > $i ).
thf(tp_nothing,type,
nothing: $i ).
thf(tp_sat_synth_nf_k,type,
sat_synth_nf_k: $i > $i ).
thf(tp_suc,type,
suc: $i > $i ).
thf(tp_tc,type,
tc: $i > $i > $i > $i ).
thf(tp_var,type,
var: $i > $i ).
thf(tp_zero,type,
zero: $i ).
thf(1,axiom,
! [X: $i] :
( ( eq4 @ X @ X )
= btrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_054) ).
thf(2,axiom,
! [X: $i] :
( ( eq3 @ X @ X )
= btrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_053) ).
thf(3,axiom,
! [X: $i] :
( ( eq2 @ X @ X )
= btrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_052) ).
thf(4,axiom,
! [X: $i] :
( ( eq @ X @ X )
= btrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_051) ).
thf(5,axiom,
! [X: $i,Y: $i] :
( ( eq3 @ ( var @ X ) @ ( lam @ Y ) )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_050) ).
thf(6,axiom,
! [X: $i,Y: $i,Z: $i,X2: $i] :
( ( eq3 @ ( var @ X ) @ ( app @ Y @ Z @ X2 ) )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_049) ).
thf(7,axiom,
! [X: $i,Y: $i] :
( ( eq3 @ ( lam @ X ) @ ( var @ Y ) )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_048) ).
thf(8,axiom,
! [X: $i,Y: $i,Z: $i,X2: $i] :
( ( eq3 @ ( lam @ X ) @ ( app @ Y @ Z @ X2 ) )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_047) ).
thf(9,axiom,
! [X: $i,Y: $i,Z: $i,X2: $i] :
( ( eq3 @ ( app @ X @ Y @ Z ) @ ( var @ X2 ) )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_046) ).
thf(10,axiom,
! [X: $i,Y: $i,Z: $i,X2: $i] :
( ( eq3 @ ( app @ X @ Y @ Z ) @ ( lam @ X2 ) )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_045) ).
thf(11,axiom,
! [X: $i,Y: $i] :
( ( eq3 @ ( var @ X ) @ ( var @ Y ) )
= ( eq2 @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_044) ).
thf(12,axiom,
! [X: $i,Y: $i] :
( ( eq3 @ ( lam @ X ) @ ( lam @ Y ) )
= ( eq3 @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_043) ).
thf(13,axiom,
! [X: $i,X2: $i,Y: $i,X3: $i,Z: $i,X4: $i] :
( ( ( eq3 @ X @ X2 )
!= btrue )
| ( ( eq3 @ Y @ X3 )
!= btrue )
| ( ( eq3 @ ( app @ X @ Y @ Z ) @ ( app @ X2 @ X3 @ X4 ) )
= ( eq @ Z @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_042) ).
thf(14,axiom,
! [Y: $i,X3: $i,X: $i,X2: $i,Z: $i,X4: $i] :
( ( ( eq3 @ Y @ X3 )
!= bfalse )
| ( ( eq3 @ X @ X2 )
!= btrue )
| ( ( eq3 @ ( app @ X @ Y @ Z ) @ ( app @ X2 @ X3 @ X4 ) )
= bfalse ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_041) ).
thf(15,axiom,
! [X: $i,X2: $i,Y: $i,Z: $i,X3: $i,X4: $i] :
( ( ( eq3 @ X @ X2 )
!= bfalse )
| ( ( eq3 @ ( app @ X @ Y @ Z ) @ ( app @ X2 @ X3 @ X4 ) )
= bfalse ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_040) ).
thf(16,axiom,
! [X: $i,Y: $i] :
( ( eq @ c @ ( arr @ X @ Y ) )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_039) ).
thf(17,axiom,
! [X: $i,Y: $i] :
( ( eq @ b @ ( arr @ X @ Y ) )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_038) ).
thf(18,axiom,
! [X: $i,Y: $i] :
( ( eq @ a @ ( arr @ X @ Y ) )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_037) ).
thf(19,axiom,
! [X: $i,Y: $i] :
( ( eq @ ( arr @ X @ Y ) @ c )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_036) ).
thf(20,axiom,
! [X: $i,Y: $i] :
( ( eq @ ( arr @ X @ Y ) @ b )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_035) ).
thf(21,axiom,
! [X: $i,Y: $i] :
( ( eq @ ( arr @ X @ Y ) @ a )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_034) ).
thf(22,axiom,
! [X: $i,Z: $i,Y: $i,X2: $i] :
( ( ( eq @ X @ Z )
!= btrue )
| ( ( eq @ ( arr @ X @ Y ) @ ( arr @ Z @ X2 ) )
= ( eq @ Y @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_033) ).
thf(23,axiom,
! [X: $i,Z: $i,Y: $i,X2: $i] :
( ( ( eq @ X @ Z )
!= bfalse )
| ( ( eq @ ( arr @ X @ Y ) @ ( arr @ Z @ X2 ) )
= bfalse ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_032) ).
thf(24,axiom,
! [X: $i] :
( ( eq2 @ ( suc @ X ) @ zero )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_031) ).
thf(25,axiom,
! [X: $i] :
( ( eq2 @ zero @ ( suc @ X ) )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_030) ).
thf(26,axiom,
! [X: $i,Y: $i] :
( ( eq2 @ ( suc @ X ) @ ( suc @ Y ) )
= ( eq2 @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_029) ).
thf(27,axiom,
( ( eq4 @ btrue @ bfalse )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_028) ).
thf(28,axiom,
( ( eq4 @ bfalse @ btrue )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_027) ).
thf(29,axiom,
( ( eq @ c @ b )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_026) ).
thf(30,axiom,
( ( eq @ c @ a )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_025) ).
thf(31,axiom,
( ( eq @ b @ c )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_024) ).
thf(32,axiom,
( ( eq @ b @ a )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_023) ).
thf(33,axiom,
( ( eq @ a @ c )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_022) ).
thf(34,axiom,
( ( eq @ a @ b )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_021) ).
thf(35,axiom,
! [X: $i] :
( ( sat_synth_nf_k @ X )
= ( notb @ ( andb @ ( nf @ X ) @ ( tc @ nil @ X @ ( arr @ a @ ( arr @ b @ b ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_020) ).
thf(36,axiom,
! [X: $i,X3: $i,Z: $i] :
( ( tc @ X @ ( var @ X3 ) @ Z )
= ( aux @ X @ Z @ X3 @ ( index @ X @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_019) ).
thf(37,axiom,
! [X: $i,E: $i] :
( ( tc @ X @ ( lam @ E ) @ c )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_018) ).
thf(38,axiom,
! [X: $i,E: $i] :
( ( tc @ X @ ( lam @ E ) @ b )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_017) ).
thf(39,axiom,
! [X: $i,E: $i] :
( ( tc @ X @ ( lam @ E ) @ a )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_016) ).
thf(40,axiom,
! [X: $i,E: $i,Tx2: $i,T1: $i] :
( ( tc @ X @ ( lam @ E ) @ ( arr @ Tx2 @ T1 ) )
= ( tc @ ( cons @ Tx2 @ X ) @ E @ T1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_015) ).
thf(41,axiom,
! [X: $i,F: $i,X2: $i,Tx: $i,Z: $i] :
( ( tc @ X @ ( app @ F @ X2 @ Tx ) @ Z )
= ( andb @ ( tc @ X @ F @ ( arr @ Tx @ Z ) ) @ ( tc @ X @ X2 @ Tx ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_014) ).
thf(42,axiom,
! [X4: $i] :
( ( nf @ ( var @ X4 ) )
= btrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_013) ).
thf(43,axiom,
! [E: $i] :
( ( nf @ ( lam @ E ) )
= ( nf @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_012) ).
thf(44,axiom,
! [X: $i,Z: $i,X2: $i] :
( ( nf @ ( app @ ( var @ X ) @ Z @ X2 ) )
= ( andb @ ( nf @ ( var @ X ) ) @ ( nf @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_011) ).
thf(45,axiom,
! [X: $i,X3: $i,X4: $i,Z: $i,X2: $i] :
( ( nf @ ( app @ ( app @ X @ X3 @ X4 ) @ Z @ X2 ) )
= ( andb @ ( nf @ ( app @ X @ X3 @ X4 ) ) @ ( nf @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_010) ).
thf(46,axiom,
! [X3: $i,Z: $i,X2: $i] :
( ( nf @ ( app @ ( lam @ X3 ) @ Z @ X2 ) )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_009) ).
thf(47,axiom,
! [Q: $i] :
( ( andb @ bfalse @ Q )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_008) ).
thf(48,axiom,
! [Q: $i] :
( ( andb @ btrue @ Q )
= Q ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_007) ).
thf(49,axiom,
! [Z: $i,Xs: $i,N: $i] :
( ( index @ ( cons @ Z @ Xs ) @ ( suc @ N ) )
= ( index @ Xs @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_006) ).
thf(50,axiom,
! [Z: $i,Xs: $i] :
( ( index @ ( cons @ Z @ Xs ) @ zero )
= ( just @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_005) ).
thf(51,axiom,
! [Y: $i] :
( ( index @ nil @ Y )
= nothing ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_004) ).
thf(52,axiom,
( ( notb @ bfalse )
= btrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_003) ).
thf(53,axiom,
( ( notb @ btrue )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_002) ).
thf(54,axiom,
! [X: $i,Z: $i,X3: $i,Tx3: $i] :
( ( aux @ X @ Z @ X3 @ ( just @ Tx3 ) )
= ( eq @ Tx3 @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_001) ).
thf(55,axiom,
! [X: $i,Z: $i,X3: $i] :
( ( aux @ X @ Z @ X3 @ nothing )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom) ).
thf(56,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(57,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[56]) ).
thf(58,negated_conjecture,
! [X: $i] :
( ( eq4 @ ( sat_synth_nf_k @ X ) @ bfalse )
!= btrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
thf(59,plain,
$false = $false,
inference(unfold_def,[status(thm)],[57]) ).
thf(60,plain,
( ( ! [X: $i] :
( ( eq4 @ X @ X )
= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(61,plain,
( ( ! [X: $i] :
( ( eq3 @ X @ X )
= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(62,plain,
( ( ! [X: $i] :
( ( eq2 @ X @ X )
= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(63,plain,
( ( ! [X: $i] :
( ( eq @ X @ X )
= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(64,plain,
( ( ! [X: $i,Y: $i] :
( ( eq3 @ ( var @ X ) @ ( lam @ Y ) )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(65,plain,
( ( ! [X: $i,Y: $i,Z: $i,X2: $i] :
( ( eq3 @ ( var @ X ) @ ( app @ Y @ Z @ X2 ) )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(66,plain,
( ( ! [X: $i,Y: $i] :
( ( eq3 @ ( lam @ X ) @ ( var @ Y ) )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(67,plain,
( ( ! [X: $i,Y: $i,Z: $i,X2: $i] :
( ( eq3 @ ( lam @ X ) @ ( app @ Y @ Z @ X2 ) )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(68,plain,
( ( ! [X: $i,Y: $i,Z: $i,X2: $i] :
( ( eq3 @ ( app @ X @ Y @ Z ) @ ( var @ X2 ) )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(69,plain,
( ( ! [X: $i,Y: $i,Z: $i,X2: $i] :
( ( eq3 @ ( app @ X @ Y @ Z ) @ ( lam @ X2 ) )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(70,plain,
( ( ! [X: $i,Y: $i] :
( ( eq3 @ ( var @ X ) @ ( var @ Y ) )
= ( eq2 @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(71,plain,
( ( ! [X: $i,Y: $i] :
( ( eq3 @ ( lam @ X ) @ ( lam @ Y ) )
= ( eq3 @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(72,plain,
( ( ! [X: $i,X2: $i,Y: $i,X3: $i,Z: $i,X4: $i] :
( ( ( eq3 @ X @ X2 )
!= btrue )
| ( ( eq3 @ Y @ X3 )
!= btrue )
| ( ( eq3 @ ( app @ X @ Y @ Z ) @ ( app @ X2 @ X3 @ X4 ) )
= ( eq @ Z @ X4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(73,plain,
( ( ! [Y: $i,X3: $i,X: $i,X2: $i,Z: $i,X4: $i] :
( ( ( eq3 @ Y @ X3 )
!= bfalse )
| ( ( eq3 @ X @ X2 )
!= btrue )
| ( ( eq3 @ ( app @ X @ Y @ Z ) @ ( app @ X2 @ X3 @ X4 ) )
= bfalse ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(74,plain,
( ( ! [X: $i,X2: $i,Y: $i,Z: $i,X3: $i,X4: $i] :
( ( ( eq3 @ X @ X2 )
!= bfalse )
| ( ( eq3 @ ( app @ X @ Y @ Z ) @ ( app @ X2 @ X3 @ X4 ) )
= bfalse ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(75,plain,
( ( ! [X: $i,Y: $i] :
( ( eq @ c @ ( arr @ X @ Y ) )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(76,plain,
( ( ! [X: $i,Y: $i] :
( ( eq @ b @ ( arr @ X @ Y ) )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(77,plain,
( ( ! [X: $i,Y: $i] :
( ( eq @ a @ ( arr @ X @ Y ) )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(78,plain,
( ( ! [X: $i,Y: $i] :
( ( eq @ ( arr @ X @ Y ) @ c )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(79,plain,
( ( ! [X: $i,Y: $i] :
( ( eq @ ( arr @ X @ Y ) @ b )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(80,plain,
( ( ! [X: $i,Y: $i] :
( ( eq @ ( arr @ X @ Y ) @ a )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(81,plain,
( ( ! [X: $i,Z: $i,Y: $i,X2: $i] :
( ( ( eq @ X @ Z )
!= btrue )
| ( ( eq @ ( arr @ X @ Y ) @ ( arr @ Z @ X2 ) )
= ( eq @ Y @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(82,plain,
( ( ! [X: $i,Z: $i,Y: $i,X2: $i] :
( ( ( eq @ X @ Z )
!= bfalse )
| ( ( eq @ ( arr @ X @ Y ) @ ( arr @ Z @ X2 ) )
= bfalse ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(83,plain,
( ( ! [X: $i] :
( ( eq2 @ ( suc @ X ) @ zero )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(84,plain,
( ( ! [X: $i] :
( ( eq2 @ zero @ ( suc @ X ) )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(85,plain,
( ( ! [X: $i,Y: $i] :
( ( eq2 @ ( suc @ X ) @ ( suc @ Y ) )
= ( eq2 @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(86,plain,
( ( ( eq4 @ btrue @ bfalse )
= bfalse )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(87,plain,
( ( ( eq4 @ bfalse @ btrue )
= bfalse )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(88,plain,
( ( ( eq @ c @ b )
= bfalse )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(89,plain,
( ( ( eq @ c @ a )
= bfalse )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(90,plain,
( ( ( eq @ b @ c )
= bfalse )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(91,plain,
( ( ( eq @ b @ a )
= bfalse )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(92,plain,
( ( ( eq @ a @ c )
= bfalse )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(93,plain,
( ( ( eq @ a @ b )
= bfalse )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(94,plain,
( ( ! [X: $i] :
( ( sat_synth_nf_k @ X )
= ( notb @ ( andb @ ( nf @ X ) @ ( tc @ nil @ X @ ( arr @ a @ ( arr @ b @ b ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(95,plain,
( ( ! [X: $i,X3: $i,Z: $i] :
( ( tc @ X @ ( var @ X3 ) @ Z )
= ( aux @ X @ Z @ X3 @ ( index @ X @ X3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(96,plain,
( ( ! [X: $i,E: $i] :
( ( tc @ X @ ( lam @ E ) @ c )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(97,plain,
( ( ! [X: $i,E: $i] :
( ( tc @ X @ ( lam @ E ) @ b )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(98,plain,
( ( ! [X: $i,E: $i] :
( ( tc @ X @ ( lam @ E ) @ a )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(99,plain,
( ( ! [X: $i,E: $i,Tx2: $i,T1: $i] :
( ( tc @ X @ ( lam @ E ) @ ( arr @ Tx2 @ T1 ) )
= ( tc @ ( cons @ Tx2 @ X ) @ E @ T1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(100,plain,
( ( ! [X: $i,F: $i,X2: $i,Tx: $i,Z: $i] :
( ( tc @ X @ ( app @ F @ X2 @ Tx ) @ Z )
= ( andb @ ( tc @ X @ F @ ( arr @ Tx @ Z ) ) @ ( tc @ X @ X2 @ Tx ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(101,plain,
( ( ! [X4: $i] :
( ( nf @ ( var @ X4 ) )
= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(102,plain,
( ( ! [E: $i] :
( ( nf @ ( lam @ E ) )
= ( nf @ E ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(103,plain,
( ( ! [X: $i,Z: $i,X2: $i] :
( ( nf @ ( app @ ( var @ X ) @ Z @ X2 ) )
= ( andb @ ( nf @ ( var @ X ) ) @ ( nf @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(104,plain,
( ( ! [X: $i,X3: $i,X4: $i,Z: $i,X2: $i] :
( ( nf @ ( app @ ( app @ X @ X3 @ X4 ) @ Z @ X2 ) )
= ( andb @ ( nf @ ( app @ X @ X3 @ X4 ) ) @ ( nf @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(105,plain,
( ( ! [X3: $i,Z: $i,X2: $i] :
( ( nf @ ( app @ ( lam @ X3 ) @ Z @ X2 ) )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(106,plain,
( ( ! [Q: $i] :
( ( andb @ bfalse @ Q )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(107,plain,
( ( ! [Q: $i] :
( ( andb @ btrue @ Q )
= Q ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(108,plain,
( ( ! [Z: $i,Xs: $i,N: $i] :
( ( index @ ( cons @ Z @ Xs ) @ ( suc @ N ) )
= ( index @ Xs @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(109,plain,
( ( ! [Z: $i,Xs: $i] :
( ( index @ ( cons @ Z @ Xs ) @ zero )
= ( just @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(110,plain,
( ( ! [Y: $i] :
( ( index @ nil @ Y )
= nothing ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(111,plain,
( ( ( notb @ bfalse )
= btrue )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(112,plain,
( ( ( notb @ btrue )
= bfalse )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(113,plain,
( ( ! [X: $i,Z: $i,X3: $i,Tx3: $i] :
( ( aux @ X @ Z @ X3 @ ( just @ Tx3 ) )
= ( eq @ Tx3 @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(114,plain,
( ( ! [X: $i,Z: $i,X3: $i] :
( ( aux @ X @ Z @ X3 @ nothing )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(115,plain,
( ( ! [X: $i] :
( ( eq4 @ ( sat_synth_nf_k @ X ) @ bfalse )
!= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(116,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[59]) ).
thf(117,plain,
( ( ! [X: $i,X2: $i,Y: $i,X3: $i] :
( ( ( eq3 @ X @ X2 )
!= btrue )
| ( ( eq3 @ Y @ X3 )
!= btrue )
| ! [Z: $i,X4: $i] :
( ( eq3 @ ( app @ X @ Y @ Z ) @ ( app @ X2 @ X3 @ X4 ) )
= ( eq @ Z @ X4 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[72]) ).
thf(118,plain,
( ( ! [Y: $i,X3: $i,X: $i,X2: $i] :
( ( ( eq3 @ Y @ X3 )
!= bfalse )
| ( ( eq3 @ X @ X2 )
!= btrue )
| ! [Z: $i,X4: $i] :
( ( eq3 @ ( app @ X @ Y @ Z ) @ ( app @ X2 @ X3 @ X4 ) )
= bfalse ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[73]) ).
thf(119,plain,
( ( ! [X: $i,X2: $i,Y: $i,Z: $i] :
( ( ( eq3 @ X @ X2 )
!= bfalse )
| ! [X3: $i,X4: $i] :
( ( eq3 @ ( app @ X @ Y @ Z ) @ ( app @ X2 @ X3 @ X4 ) )
= bfalse ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[74]) ).
thf(120,plain,
( ( ! [X: $i,Z: $i] :
( ( ( eq @ X @ Z )
!= btrue )
| ! [Y: $i,X2: $i] :
( ( eq @ ( arr @ X @ Y ) @ ( arr @ Z @ X2 ) )
= ( eq @ Y @ X2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[81]) ).
thf(121,plain,
( ( ! [X: $i,Z: $i] :
( ( ( eq @ X @ Z )
!= bfalse )
| ! [Y: $i,X2: $i] :
( ( eq @ ( arr @ X @ Y ) @ ( arr @ Z @ X2 ) )
= bfalse ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[82]) ).
thf(122,plain,
( ( ! [X: $i] :
( ( eq4 @ ( sat_synth_nf_k @ X ) @ bfalse )
!= btrue ) )
= $true ),
inference(extcnf_combined,[status(esa)],[115]) ).
thf(123,plain,
( ( ! [X: $i] :
( ( eq4 @ ( sat_synth_nf_k @ X ) @ bfalse )
!= btrue ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(124,plain,
( ( ! [X: $i,Z: $i,X3: $i] :
( ( aux @ X @ Z @ X3 @ nothing )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(125,plain,
( ( ! [X: $i,Z: $i,X3: $i,Tx3: $i] :
( ( aux @ X @ Z @ X3 @ ( just @ Tx3 ) )
= ( eq @ Tx3 @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(126,plain,
( ( ( notb @ btrue )
= bfalse )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(127,plain,
( ( ( notb @ bfalse )
= btrue )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(128,plain,
( ( ! [Y: $i] :
( ( index @ nil @ Y )
= nothing ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(129,plain,
( ( ! [Z: $i,Xs: $i] :
( ( index @ ( cons @ Z @ Xs ) @ zero )
= ( just @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(130,plain,
( ( ! [Z: $i,Xs: $i,N: $i] :
( ( index @ ( cons @ Z @ Xs ) @ ( suc @ N ) )
= ( index @ Xs @ N ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(131,plain,
( ( ! [Q: $i] :
( ( andb @ btrue @ Q )
= Q ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(132,plain,
( ( ! [Q: $i] :
( ( andb @ bfalse @ Q )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(133,plain,
( ( ! [X3: $i,Z: $i,X2: $i] :
( ( nf @ ( app @ ( lam @ X3 ) @ Z @ X2 ) )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(134,plain,
( ( ! [X: $i,X3: $i,X4: $i,Z: $i,X2: $i] :
( ( nf @ ( app @ ( app @ X @ X3 @ X4 ) @ Z @ X2 ) )
= ( andb @ ( nf @ ( app @ X @ X3 @ X4 ) ) @ ( nf @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(135,plain,
( ( ! [X: $i,Z: $i,X2: $i] :
( ( nf @ ( app @ ( var @ X ) @ Z @ X2 ) )
= ( andb @ ( nf @ ( var @ X ) ) @ ( nf @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(136,plain,
( ( ! [E: $i] :
( ( nf @ ( lam @ E ) )
= ( nf @ E ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(137,plain,
( ( ! [X4: $i] :
( ( nf @ ( var @ X4 ) )
= btrue ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(138,plain,
( ( ! [X: $i,F: $i,X2: $i,Tx: $i,Z: $i] :
( ( tc @ X @ ( app @ F @ X2 @ Tx ) @ Z )
= ( andb @ ( tc @ X @ F @ ( arr @ Tx @ Z ) ) @ ( tc @ X @ X2 @ Tx ) ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(139,plain,
( ( ! [X: $i,E: $i,Tx2: $i,T1: $i] :
( ( tc @ X @ ( lam @ E ) @ ( arr @ Tx2 @ T1 ) )
= ( tc @ ( cons @ Tx2 @ X ) @ E @ T1 ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(140,plain,
( ( ! [X: $i,E: $i] :
( ( tc @ X @ ( lam @ E ) @ a )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(141,plain,
( ( ! [X: $i,E: $i] :
( ( tc @ X @ ( lam @ E ) @ b )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(142,plain,
( ( ! [X: $i,E: $i] :
( ( tc @ X @ ( lam @ E ) @ c )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(143,plain,
( ( ! [X: $i,X3: $i,Z: $i] :
( ( tc @ X @ ( var @ X3 ) @ Z )
= ( aux @ X @ Z @ X3 @ ( index @ X @ X3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(144,plain,
( ( ! [X: $i] :
( ( sat_synth_nf_k @ X )
= ( notb @ ( andb @ ( nf @ X ) @ ( tc @ nil @ X @ ( arr @ a @ ( arr @ b @ b ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(145,plain,
( ( ( eq @ a @ b )
= bfalse )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(146,plain,
( ( ( eq @ a @ c )
= bfalse )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(147,plain,
( ( ( eq @ b @ a )
= bfalse )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(148,plain,
( ( ( eq @ b @ c )
= bfalse )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(149,plain,
( ( ( eq @ c @ a )
= bfalse )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(150,plain,
( ( ( eq @ c @ b )
= bfalse )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(151,plain,
( ( ( eq4 @ bfalse @ btrue )
= bfalse )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(152,plain,
( ( ( eq4 @ btrue @ bfalse )
= bfalse )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(153,plain,
( ( ! [X: $i,Y: $i] :
( ( eq2 @ ( suc @ X ) @ ( suc @ Y ) )
= ( eq2 @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(154,plain,
( ( ! [X: $i] :
( ( eq2 @ zero @ ( suc @ X ) )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(155,plain,
( ( ! [X: $i] :
( ( eq2 @ ( suc @ X ) @ zero )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(156,plain,
( ( ! [X: $i,Z: $i] :
( ( ( eq @ X @ Z )
!= bfalse )
| ! [Y: $i,X2: $i] :
( ( eq @ ( arr @ X @ Y ) @ ( arr @ Z @ X2 ) )
= bfalse ) ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(157,plain,
( ( ! [X: $i,Z: $i] :
( ( ( eq @ X @ Z )
!= btrue )
| ! [Y: $i,X2: $i] :
( ( eq @ ( arr @ X @ Y ) @ ( arr @ Z @ X2 ) )
= ( eq @ Y @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(158,plain,
( ( ! [X: $i,Y: $i] :
( ( eq @ ( arr @ X @ Y ) @ a )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(159,plain,
( ( ! [X: $i,Y: $i] :
( ( eq @ ( arr @ X @ Y ) @ b )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(160,plain,
( ( ! [X: $i,Y: $i] :
( ( eq @ ( arr @ X @ Y ) @ c )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(161,plain,
( ( ! [X: $i,Y: $i] :
( ( eq @ a @ ( arr @ X @ Y ) )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(162,plain,
( ( ! [X: $i,Y: $i] :
( ( eq @ b @ ( arr @ X @ Y ) )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(163,plain,
( ( ! [X: $i,Y: $i] :
( ( eq @ c @ ( arr @ X @ Y ) )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(164,plain,
( ( ! [X: $i,X2: $i,Y: $i,Z: $i] :
( ( ( eq3 @ X @ X2 )
!= bfalse )
| ! [X3: $i,X4: $i] :
( ( eq3 @ ( app @ X @ Y @ Z ) @ ( app @ X2 @ X3 @ X4 ) )
= bfalse ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(165,plain,
( ( ! [Y: $i,X3: $i,X: $i,X2: $i] :
( ( ( eq3 @ Y @ X3 )
!= bfalse )
| ( ( eq3 @ X @ X2 )
!= btrue )
| ! [Z: $i,X4: $i] :
( ( eq3 @ ( app @ X @ Y @ Z ) @ ( app @ X2 @ X3 @ X4 ) )
= bfalse ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(166,plain,
( ( ! [X: $i,X2: $i,Y: $i,X3: $i] :
( ( ( eq3 @ X @ X2 )
!= btrue )
| ( ( eq3 @ Y @ X3 )
!= btrue )
| ! [Z: $i,X4: $i] :
( ( eq3 @ ( app @ X @ Y @ Z ) @ ( app @ X2 @ X3 @ X4 ) )
= ( eq @ Z @ X4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(167,plain,
( ( ! [X: $i,Y: $i] :
( ( eq3 @ ( lam @ X ) @ ( lam @ Y ) )
= ( eq3 @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(168,plain,
( ( ! [X: $i,Y: $i] :
( ( eq3 @ ( var @ X ) @ ( var @ Y ) )
= ( eq2 @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(169,plain,
( ( ! [X: $i,Y: $i,Z: $i,X2: $i] :
( ( eq3 @ ( app @ X @ Y @ Z ) @ ( lam @ X2 ) )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(170,plain,
( ( ! [X: $i,Y: $i,Z: $i,X2: $i] :
( ( eq3 @ ( app @ X @ Y @ Z ) @ ( var @ X2 ) )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(171,plain,
( ( ! [X: $i,Y: $i,Z: $i,X2: $i] :
( ( eq3 @ ( lam @ X ) @ ( app @ Y @ Z @ X2 ) )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(172,plain,
( ( ! [X: $i,Y: $i] :
( ( eq3 @ ( lam @ X ) @ ( var @ Y ) )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(173,plain,
( ( ! [X: $i,Y: $i,Z: $i,X2: $i] :
( ( eq3 @ ( var @ X ) @ ( app @ Y @ Z @ X2 ) )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(174,plain,
( ( ! [X: $i,Y: $i] :
( ( eq3 @ ( var @ X ) @ ( lam @ Y ) )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(175,plain,
( ( ! [X: $i] :
( ( eq @ X @ X )
= btrue ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(176,plain,
( ( ! [X: $i] :
( ( eq2 @ X @ X )
= btrue ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(177,plain,
( ( ! [X: $i] :
( ( eq3 @ X @ X )
= btrue ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(178,plain,
( ( ! [X: $i] :
( ( eq4 @ X @ X )
= btrue ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(179,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[116]) ).
thf(180,plain,
! [SV1: $i] :
( ( ( eq4 @ ( sat_synth_nf_k @ SV1 ) @ bfalse )
!= btrue )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(181,plain,
! [SV2: $i] :
( ( ! [SY118: $i,SY119: $i] :
( ( aux @ SV2 @ SY118 @ SY119 @ nothing )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(182,plain,
! [SV3: $i] :
( ( ! [SY120: $i,SY121: $i,SY122: $i] :
( ( aux @ SV3 @ SY120 @ SY121 @ ( just @ SY122 ) )
= ( eq @ SY122 @ SY120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(183,plain,
! [SV4: $i] :
( ( ( index @ nil @ SV4 )
= nothing )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(184,plain,
! [SV5: $i] :
( ( ! [SY123: $i] :
( ( index @ ( cons @ SV5 @ SY123 ) @ zero )
= ( just @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(185,plain,
! [SV6: $i] :
( ( ! [SY124: $i,SY125: $i] :
( ( index @ ( cons @ SV6 @ SY124 ) @ ( suc @ SY125 ) )
= ( index @ SY124 @ SY125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(186,plain,
! [SV7: $i] :
( ( ( andb @ btrue @ SV7 )
= SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(187,plain,
! [SV8: $i] :
( ( ( andb @ bfalse @ SV8 )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(188,plain,
! [SV9: $i] :
( ( ! [SY126: $i,SY127: $i] :
( ( nf @ ( app @ ( lam @ SV9 ) @ SY126 @ SY127 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(189,plain,
! [SV10: $i] :
( ( ! [SY128: $i,SY129: $i,SY130: $i,SY131: $i] :
( ( nf @ ( app @ ( app @ SV10 @ SY128 @ SY129 ) @ SY130 @ SY131 ) )
= ( andb @ ( nf @ ( app @ SV10 @ SY128 @ SY129 ) ) @ ( nf @ SY130 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(190,plain,
! [SV11: $i] :
( ( ! [SY132: $i,SY133: $i] :
( ( nf @ ( app @ ( var @ SV11 ) @ SY132 @ SY133 ) )
= ( andb @ ( nf @ ( var @ SV11 ) ) @ ( nf @ SY132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(191,plain,
! [SV12: $i] :
( ( ( nf @ ( lam @ SV12 ) )
= ( nf @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(192,plain,
! [SV13: $i] :
( ( ( nf @ ( var @ SV13 ) )
= btrue )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(193,plain,
! [SV14: $i] :
( ( ! [SY134: $i,SY135: $i,SY136: $i,SY137: $i] :
( ( tc @ SV14 @ ( app @ SY134 @ SY135 @ SY136 ) @ SY137 )
= ( andb @ ( tc @ SV14 @ SY134 @ ( arr @ SY136 @ SY137 ) ) @ ( tc @ SV14 @ SY135 @ SY136 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(194,plain,
! [SV15: $i] :
( ( ! [SY138: $i,SY139: $i,SY140: $i] :
( ( tc @ SV15 @ ( lam @ SY138 ) @ ( arr @ SY139 @ SY140 ) )
= ( tc @ ( cons @ SY139 @ SV15 ) @ SY138 @ SY140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(195,plain,
! [SV16: $i] :
( ( ! [SY141: $i] :
( ( tc @ SV16 @ ( lam @ SY141 ) @ a )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(196,plain,
! [SV17: $i] :
( ( ! [SY142: $i] :
( ( tc @ SV17 @ ( lam @ SY142 ) @ b )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(197,plain,
! [SV18: $i] :
( ( ! [SY143: $i] :
( ( tc @ SV18 @ ( lam @ SY143 ) @ c )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(198,plain,
! [SV19: $i] :
( ( ! [SY144: $i,SY145: $i] :
( ( tc @ SV19 @ ( var @ SY144 ) @ SY145 )
= ( aux @ SV19 @ SY145 @ SY144 @ ( index @ SV19 @ SY144 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(199,plain,
! [SV20: $i] :
( ( ( sat_synth_nf_k @ SV20 )
= ( notb @ ( andb @ ( nf @ SV20 ) @ ( tc @ nil @ SV20 @ ( arr @ a @ ( arr @ b @ b ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(200,plain,
! [SV21: $i] :
( ( ! [SY146: $i] :
( ( eq2 @ ( suc @ SV21 ) @ ( suc @ SY146 ) )
= ( eq2 @ SV21 @ SY146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(201,plain,
! [SV22: $i] :
( ( ( eq2 @ zero @ ( suc @ SV22 ) )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(202,plain,
! [SV23: $i] :
( ( ( eq2 @ ( suc @ SV23 ) @ zero )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(203,plain,
! [SV24: $i] :
( ( ! [SY147: $i] :
( ( ( eq @ SV24 @ SY147 )
!= bfalse )
| ! [SY148: $i,SY149: $i] :
( ( eq @ ( arr @ SV24 @ SY148 ) @ ( arr @ SY147 @ SY149 ) )
= bfalse ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(204,plain,
! [SV25: $i] :
( ( ! [SY150: $i] :
( ( ( eq @ SV25 @ SY150 )
!= btrue )
| ! [SY151: $i,SY152: $i] :
( ( eq @ ( arr @ SV25 @ SY151 ) @ ( arr @ SY150 @ SY152 ) )
= ( eq @ SY151 @ SY152 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(205,plain,
! [SV26: $i] :
( ( ! [SY153: $i] :
( ( eq @ ( arr @ SV26 @ SY153 ) @ a )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(206,plain,
! [SV27: $i] :
( ( ! [SY154: $i] :
( ( eq @ ( arr @ SV27 @ SY154 ) @ b )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(207,plain,
! [SV28: $i] :
( ( ! [SY155: $i] :
( ( eq @ ( arr @ SV28 @ SY155 ) @ c )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(208,plain,
! [SV29: $i] :
( ( ! [SY156: $i] :
( ( eq @ a @ ( arr @ SV29 @ SY156 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(209,plain,
! [SV30: $i] :
( ( ! [SY157: $i] :
( ( eq @ b @ ( arr @ SV30 @ SY157 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(210,plain,
! [SV31: $i] :
( ( ! [SY158: $i] :
( ( eq @ c @ ( arr @ SV31 @ SY158 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(211,plain,
! [SV32: $i] :
( ( ! [SY159: $i,SY160: $i,SY161: $i] :
( ( ( eq3 @ SV32 @ SY159 )
!= bfalse )
| ! [SY162: $i,SY163: $i] :
( ( eq3 @ ( app @ SV32 @ SY160 @ SY161 ) @ ( app @ SY159 @ SY162 @ SY163 ) )
= bfalse ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(212,plain,
! [SV33: $i] :
( ( ! [SY164: $i,SY165: $i,SY166: $i] :
( ( ( eq3 @ SV33 @ SY164 )
!= bfalse )
| ( ( eq3 @ SY165 @ SY166 )
!= btrue )
| ! [SY167: $i,SY168: $i] :
( ( eq3 @ ( app @ SY165 @ SV33 @ SY167 ) @ ( app @ SY166 @ SY164 @ SY168 ) )
= bfalse ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(213,plain,
! [SV34: $i] :
( ( ! [SY169: $i,SY170: $i,SY171: $i] :
( ( ( eq3 @ SV34 @ SY169 )
!= btrue )
| ( ( eq3 @ SY170 @ SY171 )
!= btrue )
| ! [SY172: $i,SY173: $i] :
( ( eq3 @ ( app @ SV34 @ SY170 @ SY172 ) @ ( app @ SY169 @ SY171 @ SY173 ) )
= ( eq @ SY172 @ SY173 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(214,plain,
! [SV35: $i] :
( ( ! [SY174: $i] :
( ( eq3 @ ( lam @ SV35 ) @ ( lam @ SY174 ) )
= ( eq3 @ SV35 @ SY174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(215,plain,
! [SV36: $i] :
( ( ! [SY175: $i] :
( ( eq3 @ ( var @ SV36 ) @ ( var @ SY175 ) )
= ( eq2 @ SV36 @ SY175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(216,plain,
! [SV37: $i] :
( ( ! [SY176: $i,SY177: $i,SY178: $i] :
( ( eq3 @ ( app @ SV37 @ SY176 @ SY177 ) @ ( lam @ SY178 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(217,plain,
! [SV38: $i] :
( ( ! [SY179: $i,SY180: $i,SY181: $i] :
( ( eq3 @ ( app @ SV38 @ SY179 @ SY180 ) @ ( var @ SY181 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(218,plain,
! [SV39: $i] :
( ( ! [SY182: $i,SY183: $i,SY184: $i] :
( ( eq3 @ ( lam @ SV39 ) @ ( app @ SY182 @ SY183 @ SY184 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(219,plain,
! [SV40: $i] :
( ( ! [SY185: $i] :
( ( eq3 @ ( lam @ SV40 ) @ ( var @ SY185 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(220,plain,
! [SV41: $i] :
( ( ! [SY186: $i,SY187: $i,SY188: $i] :
( ( eq3 @ ( var @ SV41 ) @ ( app @ SY186 @ SY187 @ SY188 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(221,plain,
! [SV42: $i] :
( ( ! [SY189: $i] :
( ( eq3 @ ( var @ SV42 ) @ ( lam @ SY189 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(222,plain,
! [SV43: $i] :
( ( ( eq @ SV43 @ SV43 )
= btrue )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(223,plain,
! [SV44: $i] :
( ( ( eq2 @ SV44 @ SV44 )
= btrue )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(224,plain,
! [SV45: $i] :
( ( ( eq3 @ SV45 @ SV45 )
= btrue )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(225,plain,
! [SV46: $i] :
( ( ( eq4 @ SV46 @ SV46 )
= btrue )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(226,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(227,plain,
! [SV1: $i] :
( ( ( eq4 @ ( sat_synth_nf_k @ SV1 ) @ bfalse )
= btrue )
= $false ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(228,plain,
! [SV47: $i,SV2: $i] :
( ( ! [SY190: $i] :
( ( aux @ SV2 @ SV47 @ SY190 @ nothing )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(229,plain,
! [SV48: $i,SV3: $i] :
( ( ! [SY191: $i,SY192: $i] :
( ( aux @ SV3 @ SV48 @ SY191 @ ( just @ SY192 ) )
= ( eq @ SY192 @ SV48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(230,plain,
! [SV49: $i,SV5: $i] :
( ( ( index @ ( cons @ SV5 @ SV49 ) @ zero )
= ( just @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(231,plain,
! [SV50: $i,SV6: $i] :
( ( ! [SY193: $i] :
( ( index @ ( cons @ SV6 @ SV50 ) @ ( suc @ SY193 ) )
= ( index @ SV50 @ SY193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(232,plain,
! [SV51: $i,SV9: $i] :
( ( ! [SY194: $i] :
( ( nf @ ( app @ ( lam @ SV9 ) @ SV51 @ SY194 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(233,plain,
! [SV52: $i,SV10: $i] :
( ( ! [SY195: $i,SY196: $i,SY197: $i] :
( ( nf @ ( app @ ( app @ SV10 @ SV52 @ SY195 ) @ SY196 @ SY197 ) )
= ( andb @ ( nf @ ( app @ SV10 @ SV52 @ SY195 ) ) @ ( nf @ SY196 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(234,plain,
! [SV53: $i,SV11: $i] :
( ( ! [SY198: $i] :
( ( nf @ ( app @ ( var @ SV11 ) @ SV53 @ SY198 ) )
= ( andb @ ( nf @ ( var @ SV11 ) ) @ ( nf @ SV53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(235,plain,
! [SV54: $i,SV14: $i] :
( ( ! [SY199: $i,SY200: $i,SY201: $i] :
( ( tc @ SV14 @ ( app @ SV54 @ SY199 @ SY200 ) @ SY201 )
= ( andb @ ( tc @ SV14 @ SV54 @ ( arr @ SY200 @ SY201 ) ) @ ( tc @ SV14 @ SY199 @ SY200 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(236,plain,
! [SV55: $i,SV15: $i] :
( ( ! [SY202: $i,SY203: $i] :
( ( tc @ SV15 @ ( lam @ SV55 ) @ ( arr @ SY202 @ SY203 ) )
= ( tc @ ( cons @ SY202 @ SV15 ) @ SV55 @ SY203 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(237,plain,
! [SV56: $i,SV16: $i] :
( ( ( tc @ SV16 @ ( lam @ SV56 ) @ a )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(238,plain,
! [SV57: $i,SV17: $i] :
( ( ( tc @ SV17 @ ( lam @ SV57 ) @ b )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(239,plain,
! [SV58: $i,SV18: $i] :
( ( ( tc @ SV18 @ ( lam @ SV58 ) @ c )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(240,plain,
! [SV59: $i,SV19: $i] :
( ( ! [SY204: $i] :
( ( tc @ SV19 @ ( var @ SV59 ) @ SY204 )
= ( aux @ SV19 @ SY204 @ SV59 @ ( index @ SV19 @ SV59 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(241,plain,
! [SV60: $i,SV21: $i] :
( ( ( eq2 @ ( suc @ SV21 ) @ ( suc @ SV60 ) )
= ( eq2 @ SV21 @ SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(242,plain,
! [SV61: $i,SV24: $i] :
( ( ( ( eq @ SV24 @ SV61 )
!= bfalse )
| ! [SY205: $i,SY206: $i] :
( ( eq @ ( arr @ SV24 @ SY205 ) @ ( arr @ SV61 @ SY206 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(243,plain,
! [SV62: $i,SV25: $i] :
( ( ( ( eq @ SV25 @ SV62 )
!= btrue )
| ! [SY207: $i,SY208: $i] :
( ( eq @ ( arr @ SV25 @ SY207 ) @ ( arr @ SV62 @ SY208 ) )
= ( eq @ SY207 @ SY208 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(244,plain,
! [SV63: $i,SV26: $i] :
( ( ( eq @ ( arr @ SV26 @ SV63 ) @ a )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(245,plain,
! [SV64: $i,SV27: $i] :
( ( ( eq @ ( arr @ SV27 @ SV64 ) @ b )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(246,plain,
! [SV65: $i,SV28: $i] :
( ( ( eq @ ( arr @ SV28 @ SV65 ) @ c )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(247,plain,
! [SV66: $i,SV29: $i] :
( ( ( eq @ a @ ( arr @ SV29 @ SV66 ) )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(248,plain,
! [SV67: $i,SV30: $i] :
( ( ( eq @ b @ ( arr @ SV30 @ SV67 ) )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(249,plain,
! [SV68: $i,SV31: $i] :
( ( ( eq @ c @ ( arr @ SV31 @ SV68 ) )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(250,plain,
! [SV69: $i,SV32: $i] :
( ( ! [SY209: $i,SY210: $i] :
( ( ( eq3 @ SV32 @ SV69 )
!= bfalse )
| ! [SY211: $i,SY212: $i] :
( ( eq3 @ ( app @ SV32 @ SY209 @ SY210 ) @ ( app @ SV69 @ SY211 @ SY212 ) )
= bfalse ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(251,plain,
! [SV70: $i,SV33: $i] :
( ( ! [SY213: $i,SY214: $i] :
( ( ( eq3 @ SV33 @ SV70 )
!= bfalse )
| ( ( eq3 @ SY213 @ SY214 )
!= btrue )
| ! [SY215: $i,SY216: $i] :
( ( eq3 @ ( app @ SY213 @ SV33 @ SY215 ) @ ( app @ SY214 @ SV70 @ SY216 ) )
= bfalse ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(252,plain,
! [SV71: $i,SV34: $i] :
( ( ! [SY217: $i,SY218: $i] :
( ( ( eq3 @ SV34 @ SV71 )
!= btrue )
| ( ( eq3 @ SY217 @ SY218 )
!= btrue )
| ! [SY219: $i,SY220: $i] :
( ( eq3 @ ( app @ SV34 @ SY217 @ SY219 ) @ ( app @ SV71 @ SY218 @ SY220 ) )
= ( eq @ SY219 @ SY220 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(253,plain,
! [SV72: $i,SV35: $i] :
( ( ( eq3 @ ( lam @ SV35 ) @ ( lam @ SV72 ) )
= ( eq3 @ SV35 @ SV72 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(254,plain,
! [SV73: $i,SV36: $i] :
( ( ( eq3 @ ( var @ SV36 ) @ ( var @ SV73 ) )
= ( eq2 @ SV36 @ SV73 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(255,plain,
! [SV74: $i,SV37: $i] :
( ( ! [SY221: $i,SY222: $i] :
( ( eq3 @ ( app @ SV37 @ SV74 @ SY221 ) @ ( lam @ SY222 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(256,plain,
! [SV75: $i,SV38: $i] :
( ( ! [SY223: $i,SY224: $i] :
( ( eq3 @ ( app @ SV38 @ SV75 @ SY223 ) @ ( var @ SY224 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(257,plain,
! [SV76: $i,SV39: $i] :
( ( ! [SY225: $i,SY226: $i] :
( ( eq3 @ ( lam @ SV39 ) @ ( app @ SV76 @ SY225 @ SY226 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(258,plain,
! [SV77: $i,SV40: $i] :
( ( ( eq3 @ ( lam @ SV40 ) @ ( var @ SV77 ) )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(259,plain,
! [SV78: $i,SV41: $i] :
( ( ! [SY227: $i,SY228: $i] :
( ( eq3 @ ( var @ SV41 ) @ ( app @ SV78 @ SY227 @ SY228 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(260,plain,
! [SV79: $i,SV42: $i] :
( ( ( eq3 @ ( var @ SV42 ) @ ( lam @ SV79 ) )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(261,plain,
! [SV80: $i,SV47: $i,SV2: $i] :
( ( ( aux @ SV2 @ SV47 @ SV80 @ nothing )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(262,plain,
! [SV81: $i,SV48: $i,SV3: $i] :
( ( ! [SY229: $i] :
( ( aux @ SV3 @ SV48 @ SV81 @ ( just @ SY229 ) )
= ( eq @ SY229 @ SV48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(263,plain,
! [SV82: $i,SV50: $i,SV6: $i] :
( ( ( index @ ( cons @ SV6 @ SV50 ) @ ( suc @ SV82 ) )
= ( index @ SV50 @ SV82 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(264,plain,
! [SV83: $i,SV51: $i,SV9: $i] :
( ( ( nf @ ( app @ ( lam @ SV9 ) @ SV51 @ SV83 ) )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(265,plain,
! [SV84: $i,SV52: $i,SV10: $i] :
( ( ! [SY230: $i,SY231: $i] :
( ( nf @ ( app @ ( app @ SV10 @ SV52 @ SV84 ) @ SY230 @ SY231 ) )
= ( andb @ ( nf @ ( app @ SV10 @ SV52 @ SV84 ) ) @ ( nf @ SY230 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(266,plain,
! [SV85: $i,SV53: $i,SV11: $i] :
( ( ( nf @ ( app @ ( var @ SV11 ) @ SV53 @ SV85 ) )
= ( andb @ ( nf @ ( var @ SV11 ) ) @ ( nf @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(267,plain,
! [SV86: $i,SV54: $i,SV14: $i] :
( ( ! [SY232: $i,SY233: $i] :
( ( tc @ SV14 @ ( app @ SV54 @ SV86 @ SY232 ) @ SY233 )
= ( andb @ ( tc @ SV14 @ SV54 @ ( arr @ SY232 @ SY233 ) ) @ ( tc @ SV14 @ SV86 @ SY232 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[235]) ).
thf(268,plain,
! [SV87: $i,SV55: $i,SV15: $i] :
( ( ! [SY234: $i] :
( ( tc @ SV15 @ ( lam @ SV55 ) @ ( arr @ SV87 @ SY234 ) )
= ( tc @ ( cons @ SV87 @ SV15 ) @ SV55 @ SY234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[236]) ).
thf(269,plain,
! [SV88: $i,SV59: $i,SV19: $i] :
( ( ( tc @ SV19 @ ( var @ SV59 ) @ SV88 )
= ( aux @ SV19 @ SV88 @ SV59 @ ( index @ SV19 @ SV59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(270,plain,
! [SV61: $i,SV24: $i] :
( ( ( ( eq @ SV24 @ SV61 )
!= bfalse )
= $true )
| ( ( ! [SY205: $i,SY206: $i] :
( ( eq @ ( arr @ SV24 @ SY205 ) @ ( arr @ SV61 @ SY206 ) )
= bfalse ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[242]) ).
thf(271,plain,
! [SV62: $i,SV25: $i] :
( ( ( ( eq @ SV25 @ SV62 )
!= btrue )
= $true )
| ( ( ! [SY207: $i,SY208: $i] :
( ( eq @ ( arr @ SV25 @ SY207 ) @ ( arr @ SV62 @ SY208 ) )
= ( eq @ SY207 @ SY208 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[243]) ).
thf(272,plain,
! [SV89: $i,SV69: $i,SV32: $i] :
( ( ! [SY235: $i] :
( ( ( eq3 @ SV32 @ SV69 )
!= bfalse )
| ! [SY236: $i,SY237: $i] :
( ( eq3 @ ( app @ SV32 @ SV89 @ SY235 ) @ ( app @ SV69 @ SY236 @ SY237 ) )
= bfalse ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(273,plain,
! [SV90: $i,SV70: $i,SV33: $i] :
( ( ! [SY238: $i] :
( ( ( eq3 @ SV33 @ SV70 )
!= bfalse )
| ( ( eq3 @ SV90 @ SY238 )
!= btrue )
| ! [SY239: $i,SY240: $i] :
( ( eq3 @ ( app @ SV90 @ SV33 @ SY239 ) @ ( app @ SY238 @ SV70 @ SY240 ) )
= bfalse ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(274,plain,
! [SV91: $i,SV71: $i,SV34: $i] :
( ( ! [SY241: $i] :
( ( ( eq3 @ SV34 @ SV71 )
!= btrue )
| ( ( eq3 @ SV91 @ SY241 )
!= btrue )
| ! [SY242: $i,SY243: $i] :
( ( eq3 @ ( app @ SV34 @ SV91 @ SY242 ) @ ( app @ SV71 @ SY241 @ SY243 ) )
= ( eq @ SY242 @ SY243 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[252]) ).
thf(275,plain,
! [SV92: $i,SV74: $i,SV37: $i] :
( ( ! [SY244: $i] :
( ( eq3 @ ( app @ SV37 @ SV74 @ SV92 ) @ ( lam @ SY244 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(276,plain,
! [SV93: $i,SV75: $i,SV38: $i] :
( ( ! [SY245: $i] :
( ( eq3 @ ( app @ SV38 @ SV75 @ SV93 ) @ ( var @ SY245 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[256]) ).
thf(277,plain,
! [SV94: $i,SV76: $i,SV39: $i] :
( ( ! [SY246: $i] :
( ( eq3 @ ( lam @ SV39 ) @ ( app @ SV76 @ SV94 @ SY246 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(278,plain,
! [SV95: $i,SV78: $i,SV41: $i] :
( ( ! [SY247: $i] :
( ( eq3 @ ( var @ SV41 ) @ ( app @ SV78 @ SV95 @ SY247 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[259]) ).
thf(279,plain,
! [SV96: $i,SV81: $i,SV48: $i,SV3: $i] :
( ( ( aux @ SV3 @ SV48 @ SV81 @ ( just @ SV96 ) )
= ( eq @ SV96 @ SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(280,plain,
! [SV97: $i,SV84: $i,SV52: $i,SV10: $i] :
( ( ! [SY248: $i] :
( ( nf @ ( app @ ( app @ SV10 @ SV52 @ SV84 ) @ SV97 @ SY248 ) )
= ( andb @ ( nf @ ( app @ SV10 @ SV52 @ SV84 ) ) @ ( nf @ SV97 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(281,plain,
! [SV98: $i,SV86: $i,SV54: $i,SV14: $i] :
( ( ! [SY249: $i] :
( ( tc @ SV14 @ ( app @ SV54 @ SV86 @ SV98 ) @ SY249 )
= ( andb @ ( tc @ SV14 @ SV54 @ ( arr @ SV98 @ SY249 ) ) @ ( tc @ SV14 @ SV86 @ SV98 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(282,plain,
! [SV99: $i,SV87: $i,SV55: $i,SV15: $i] :
( ( ( tc @ SV15 @ ( lam @ SV55 ) @ ( arr @ SV87 @ SV99 ) )
= ( tc @ ( cons @ SV87 @ SV15 ) @ SV55 @ SV99 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(283,plain,
! [SV61: $i,SV24: $i] :
( ( ( ( eq @ SV24 @ SV61 )
= bfalse )
= $false )
| ( ( ! [SY205: $i,SY206: $i] :
( ( eq @ ( arr @ SV24 @ SY205 ) @ ( arr @ SV61 @ SY206 ) )
= bfalse ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(284,plain,
! [SV62: $i,SV25: $i] :
( ( ( ( eq @ SV25 @ SV62 )
= btrue )
= $false )
| ( ( ! [SY207: $i,SY208: $i] :
( ( eq @ ( arr @ SV25 @ SY207 ) @ ( arr @ SV62 @ SY208 ) )
= ( eq @ SY207 @ SY208 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[271]) ).
thf(285,plain,
! [SV100: $i,SV89: $i,SV69: $i,SV32: $i] :
( ( ( ( eq3 @ SV32 @ SV69 )
!= bfalse )
| ! [SY250: $i,SY251: $i] :
( ( eq3 @ ( app @ SV32 @ SV89 @ SV100 ) @ ( app @ SV69 @ SY250 @ SY251 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(286,plain,
! [SV101: $i,SV90: $i,SV70: $i,SV33: $i] :
( ( ( ( eq3 @ SV33 @ SV70 )
!= bfalse )
| ( ( eq3 @ SV90 @ SV101 )
!= btrue )
| ! [SY252: $i,SY253: $i] :
( ( eq3 @ ( app @ SV90 @ SV33 @ SY252 ) @ ( app @ SV101 @ SV70 @ SY253 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(287,plain,
! [SV102: $i,SV91: $i,SV71: $i,SV34: $i] :
( ( ( ( eq3 @ SV34 @ SV71 )
!= btrue )
| ( ( eq3 @ SV91 @ SV102 )
!= btrue )
| ! [SY254: $i,SY255: $i] :
( ( eq3 @ ( app @ SV34 @ SV91 @ SY254 ) @ ( app @ SV71 @ SV102 @ SY255 ) )
= ( eq @ SY254 @ SY255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[274]) ).
thf(288,plain,
! [SV103: $i,SV92: $i,SV74: $i,SV37: $i] :
( ( ( eq3 @ ( app @ SV37 @ SV74 @ SV92 ) @ ( lam @ SV103 ) )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(289,plain,
! [SV104: $i,SV93: $i,SV75: $i,SV38: $i] :
( ( ( eq3 @ ( app @ SV38 @ SV75 @ SV93 ) @ ( var @ SV104 ) )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(290,plain,
! [SV105: $i,SV94: $i,SV76: $i,SV39: $i] :
( ( ( eq3 @ ( lam @ SV39 ) @ ( app @ SV76 @ SV94 @ SV105 ) )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(291,plain,
! [SV106: $i,SV95: $i,SV78: $i,SV41: $i] :
( ( ( eq3 @ ( var @ SV41 ) @ ( app @ SV78 @ SV95 @ SV106 ) )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(292,plain,
! [SV107: $i,SV97: $i,SV84: $i,SV52: $i,SV10: $i] :
( ( ( nf @ ( app @ ( app @ SV10 @ SV52 @ SV84 ) @ SV97 @ SV107 ) )
= ( andb @ ( nf @ ( app @ SV10 @ SV52 @ SV84 ) ) @ ( nf @ SV97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(293,plain,
! [SV108: $i,SV98: $i,SV86: $i,SV54: $i,SV14: $i] :
( ( ( tc @ SV14 @ ( app @ SV54 @ SV86 @ SV98 ) @ SV108 )
= ( andb @ ( tc @ SV14 @ SV54 @ ( arr @ SV98 @ SV108 ) ) @ ( tc @ SV14 @ SV86 @ SV98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[281]) ).
thf(294,plain,
! [SV61: $i,SV109: $i,SV24: $i] :
( ( ( ! [SY256: $i] :
( ( eq @ ( arr @ SV24 @ SV109 ) @ ( arr @ SV61 @ SY256 ) )
= bfalse ) )
= $true )
| ( ( ( eq @ SV24 @ SV61 )
= bfalse )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(295,plain,
! [SV62: $i,SV110: $i,SV25: $i] :
( ( ( ! [SY257: $i] :
( ( eq @ ( arr @ SV25 @ SV110 ) @ ( arr @ SV62 @ SY257 ) )
= ( eq @ SV110 @ SY257 ) ) )
= $true )
| ( ( ( eq @ SV25 @ SV62 )
= btrue )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[284]) ).
thf(296,plain,
! [SV100: $i,SV89: $i,SV69: $i,SV32: $i] :
( ( ( ( eq3 @ SV32 @ SV69 )
!= bfalse )
= $true )
| ( ( ! [SY250: $i,SY251: $i] :
( ( eq3 @ ( app @ SV32 @ SV89 @ SV100 ) @ ( app @ SV69 @ SY250 @ SY251 ) )
= bfalse ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[285]) ).
thf(297,plain,
! [SV101: $i,SV90: $i,SV70: $i,SV33: $i] :
( ( ( ( eq3 @ SV33 @ SV70 )
!= bfalse )
= $true )
| ( ( ( ( eq3 @ SV90 @ SV101 )
!= btrue )
| ! [SY252: $i,SY253: $i] :
( ( eq3 @ ( app @ SV90 @ SV33 @ SY252 ) @ ( app @ SV101 @ SV70 @ SY253 ) )
= bfalse ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[286]) ).
thf(298,plain,
! [SV102: $i,SV91: $i,SV71: $i,SV34: $i] :
( ( ( ( eq3 @ SV34 @ SV71 )
!= btrue )
= $true )
| ( ( ( ( eq3 @ SV91 @ SV102 )
!= btrue )
| ! [SY254: $i,SY255: $i] :
( ( eq3 @ ( app @ SV34 @ SV91 @ SY254 ) @ ( app @ SV71 @ SV102 @ SY255 ) )
= ( eq @ SY254 @ SY255 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[287]) ).
thf(299,plain,
! [SV111: $i,SV61: $i,SV109: $i,SV24: $i] :
( ( ( ( eq @ ( arr @ SV24 @ SV109 ) @ ( arr @ SV61 @ SV111 ) )
= bfalse )
= $true )
| ( ( ( eq @ SV24 @ SV61 )
= bfalse )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(300,plain,
! [SV112: $i,SV62: $i,SV110: $i,SV25: $i] :
( ( ( ( eq @ ( arr @ SV25 @ SV110 ) @ ( arr @ SV62 @ SV112 ) )
= ( eq @ SV110 @ SV112 ) )
= $true )
| ( ( ( eq @ SV25 @ SV62 )
= btrue )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(301,plain,
! [SV100: $i,SV89: $i,SV69: $i,SV32: $i] :
( ( ( ( eq3 @ SV32 @ SV69 )
= bfalse )
= $false )
| ( ( ! [SY250: $i,SY251: $i] :
( ( eq3 @ ( app @ SV32 @ SV89 @ SV100 ) @ ( app @ SV69 @ SY250 @ SY251 ) )
= bfalse ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(302,plain,
! [SV101: $i,SV90: $i,SV70: $i,SV33: $i] :
( ( ( ( eq3 @ SV33 @ SV70 )
= bfalse )
= $false )
| ( ( ( ( eq3 @ SV90 @ SV101 )
!= btrue )
| ! [SY252: $i,SY253: $i] :
( ( eq3 @ ( app @ SV90 @ SV33 @ SY252 ) @ ( app @ SV101 @ SV70 @ SY253 ) )
= bfalse ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[297]) ).
thf(303,plain,
! [SV102: $i,SV91: $i,SV71: $i,SV34: $i] :
( ( ( ( eq3 @ SV34 @ SV71 )
= btrue )
= $false )
| ( ( ( ( eq3 @ SV91 @ SV102 )
!= btrue )
| ! [SY254: $i,SY255: $i] :
( ( eq3 @ ( app @ SV34 @ SV91 @ SY254 ) @ ( app @ SV71 @ SV102 @ SY255 ) )
= ( eq @ SY254 @ SY255 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[298]) ).
thf(304,plain,
! [SV113: $i,SV69: $i,SV100: $i,SV89: $i,SV32: $i] :
( ( ( ! [SY258: $i] :
( ( eq3 @ ( app @ SV32 @ SV89 @ SV100 ) @ ( app @ SV69 @ SV113 @ SY258 ) )
= bfalse ) )
= $true )
| ( ( ( eq3 @ SV32 @ SV69 )
= bfalse )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[301]) ).
thf(305,plain,
! [SV70: $i,SV33: $i,SV101: $i,SV90: $i] :
( ( ( ( eq3 @ SV90 @ SV101 )
!= btrue )
= $true )
| ( ( ! [SY252: $i,SY253: $i] :
( ( eq3 @ ( app @ SV90 @ SV33 @ SY252 ) @ ( app @ SV101 @ SV70 @ SY253 ) )
= bfalse ) )
= $true )
| ( ( ( eq3 @ SV33 @ SV70 )
= bfalse )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[302]) ).
thf(306,plain,
! [SV71: $i,SV34: $i,SV102: $i,SV91: $i] :
( ( ( ( eq3 @ SV91 @ SV102 )
!= btrue )
= $true )
| ( ( ! [SY254: $i,SY255: $i] :
( ( eq3 @ ( app @ SV34 @ SV91 @ SY254 ) @ ( app @ SV71 @ SV102 @ SY255 ) )
= ( eq @ SY254 @ SY255 ) ) )
= $true )
| ( ( ( eq3 @ SV34 @ SV71 )
= btrue )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[303]) ).
thf(307,plain,
! [SV114: $i,SV113: $i,SV69: $i,SV100: $i,SV89: $i,SV32: $i] :
( ( ( ( eq3 @ ( app @ SV32 @ SV89 @ SV100 ) @ ( app @ SV69 @ SV113 @ SV114 ) )
= bfalse )
= $true )
| ( ( ( eq3 @ SV32 @ SV69 )
= bfalse )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[304]) ).
thf(308,plain,
! [SV70: $i,SV33: $i,SV101: $i,SV90: $i] :
( ( ( ( eq3 @ SV90 @ SV101 )
= btrue )
= $false )
| ( ( ! [SY252: $i,SY253: $i] :
( ( eq3 @ ( app @ SV90 @ SV33 @ SY252 ) @ ( app @ SV101 @ SV70 @ SY253 ) )
= bfalse ) )
= $true )
| ( ( ( eq3 @ SV33 @ SV70 )
= bfalse )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[305]) ).
thf(309,plain,
! [SV71: $i,SV34: $i,SV102: $i,SV91: $i] :
( ( ( ( eq3 @ SV91 @ SV102 )
= btrue )
= $false )
| ( ( ! [SY254: $i,SY255: $i] :
( ( eq3 @ ( app @ SV34 @ SV91 @ SY254 ) @ ( app @ SV71 @ SV102 @ SY255 ) )
= ( eq @ SY254 @ SY255 ) ) )
= $true )
| ( ( ( eq3 @ SV34 @ SV71 )
= btrue )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[306]) ).
thf(310,plain,
! [SV70: $i,SV101: $i,SV115: $i,SV33: $i,SV90: $i] :
( ( ( ! [SY259: $i] :
( ( eq3 @ ( app @ SV90 @ SV33 @ SV115 ) @ ( app @ SV101 @ SV70 @ SY259 ) )
= bfalse ) )
= $true )
| ( ( ( eq3 @ SV90 @ SV101 )
= btrue )
= $false )
| ( ( ( eq3 @ SV33 @ SV70 )
= bfalse )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[308]) ).
thf(311,plain,
! [SV102: $i,SV71: $i,SV116: $i,SV91: $i,SV34: $i] :
( ( ( ! [SY260: $i] :
( ( eq3 @ ( app @ SV34 @ SV91 @ SV116 ) @ ( app @ SV71 @ SV102 @ SY260 ) )
= ( eq @ SV116 @ SY260 ) ) )
= $true )
| ( ( ( eq3 @ SV91 @ SV102 )
= btrue )
= $false )
| ( ( ( eq3 @ SV34 @ SV71 )
= btrue )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(312,plain,
! [SV117: $i,SV70: $i,SV101: $i,SV115: $i,SV33: $i,SV90: $i] :
( ( ( ( eq3 @ ( app @ SV90 @ SV33 @ SV115 ) @ ( app @ SV101 @ SV70 @ SV117 ) )
= bfalse )
= $true )
| ( ( ( eq3 @ SV90 @ SV101 )
= btrue )
= $false )
| ( ( ( eq3 @ SV33 @ SV70 )
= bfalse )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(313,plain,
! [SV118: $i,SV102: $i,SV71: $i,SV116: $i,SV91: $i,SV34: $i] :
( ( ( ( eq3 @ ( app @ SV34 @ SV91 @ SV116 ) @ ( app @ SV71 @ SV102 @ SV118 ) )
= ( eq @ SV116 @ SV118 ) )
= $true )
| ( ( ( eq3 @ SV91 @ SV102 )
= btrue )
= $false )
| ( ( ( eq3 @ SV34 @ SV71 )
= btrue )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[311]) ).
thf(314,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[126,313,312,307,300,299,293,292,291,290,289,288,282,279,269,266,264,263,261,260,258,254,253,249,248,247,246,245,244,241,239,238,237,230,227,226,225,224,223,222,202,201,199,192,191,187,186,183,152,151,150,149,148,147,146,145,127]) ).
thf(315,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[314]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX222-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.21 % Computer : n001.cluster.edu
% 0.07/0.21 % Model : x86_64 x86_64
% 0.07/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.21 % Memory : 8046.5625MB
% 0.07/0.21 % OS : Linux 6.8.0-71-generic
% 0.07/0.21 % CPULimit : 300
% 0.07/0.21 % WCLimit : 300
% 0.07/0.21 % DateTime : Tue Oct 6 17:19:51 UTC 2026
% 0.07/0.22 % CPUTime :
% 0.07/0.22 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.48/0.84
% 3.48/0.84 No.of.Axioms: 56
% 3.48/0.84
% 3.48/0.84 Length.of.Defs: 0
% 3.48/0.84
% 3.48/0.84 Contains.Choice.Funs: false
% 3.48/0.84 ...........
% 3.48/0.84
% 3.48/0.84 ********************************
% 3.48/0.84 * All subproblems solved! *
% 3.48/0.84 ********************************
% 3.48/0.84 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:56,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:314,loop_count:0,foatp_calls:1,translation:fof_full)
% 3.48/0.84
% 3.48/0.84 %**** Beginning of derivation protocol ****
% 3.48/0.84 % SZS output start CNFRefutation
% See solution above
% 3.48/0.84
% 3.48/0.84 %**** End of derivation protocol ****
% 3.48/0.84 %**** no. of clauses in derivation: 315 ****
% 3.48/0.84 %**** clause counter: 314 ****
% 3.48/0.84
% 3.48/0.84 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:56,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:314,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------