TSTP Solution File: SEU821^2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU821^2 : TPTP v8.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 12:15:12 EDT 2022
% Result : Theorem 0.18s 0.39s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 14
% Syntax : Number of formulae : 83 ( 37 unt; 10 typ; 3 def)
% Number of atoms : 653 ( 183 equ; 0 cnn)
% Maximal formula atoms : 6 ( 8 avg)
% Number of connectives : 1081 ( 133 ~; 206 |; 24 &; 668 @)
% ( 0 <=>; 50 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 151 ( 3 ^ 144 !; 4 ?; 151 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_nonempty,type,
nonempty: $i > $o ).
thf(tp_ordinal,type,
ordinal: $i > $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i ).
thf(tp_sK2_SY31,type,
sK2_SY31: $i ).
thf(tp_sK3_Xx,type,
sK3_Xx: $i > $i ).
thf(tp_stricttotalorderedByIn,type,
stricttotalorderedByIn: $i > $o ).
thf(tp_transitiveset,type,
transitiveset: $i > $o ).
thf(tp_wellorderedByIn,type,
wellorderedByIn: $i > $o ).
thf(ordinal,definition,
( ordinal
= ( ^ [Xx: $i] :
( ( transitiveset @ Xx )
& ( wellorderedByIn @ Xx ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinal) ).
thf(stricttotalorderedByIn,definition,
( stricttotalorderedByIn
= ( ^ [A: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [X: $i] :
( ( in @ X @ A )
=> ! [Y: $i] :
( ( in @ Y @ A )
=> ( ( ( in @ Xx @ X )
& ( in @ X @ Y ) )
=> ( in @ Xx @ Y ) ) ) ) )
& ! [X: $i] :
( ( in @ X @ A )
=> ! [Y: $i] :
( ( in @ Y @ A )
=> ( ( X = Y )
| ( in @ X @ Y )
| ( in @ Y @ X ) ) ) )
& ! [X: $i] :
( ( in @ X @ A )
=> ~ ( in @ X @ X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stricttotalorderedByIn) ).
thf(wellorderedByIn,definition,
( wellorderedByIn
= ( ^ [A: $i] :
( ( stricttotalorderedByIn @ A )
& ! [X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( ( nonempty @ X )
=> ? [Xx: $i] :
( ( in @ Xx @ X )
& ! [Y: $i] :
( ( in @ Y @ X )
=> ( ( Xx = Y )
| ( in @ Xx @ Y ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellorderedByIn) ).
thf(1,conjecture,
! [X: $i] :
( ( ordinal @ X )
=> ! [A: $i] :
( ( in @ A @ X )
=> ~ ( in @ A @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinalIrrefl) ).
thf(2,negated_conjecture,
( ( ! [X: $i] :
( ( ordinal @ X )
=> ! [A: $i] :
( ( in @ A @ X )
=> ~ ( in @ A @ A ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [SY0: $i] :
( ( ( transitiveset @ SY0 )
& ! [SY1: $i] :
( ( in @ SY1 @ SY0 )
=> ! [SY2: $i] :
( ( in @ SY2 @ SY0 )
=> ! [SY3: $i] :
( ( in @ SY3 @ SY0 )
=> ( ( ( in @ SY1 @ SY2 )
& ( in @ SY2 @ SY3 ) )
=> ( in @ SY1 @ SY3 ) ) ) ) )
& ! [SY4: $i] :
( ( in @ SY4 @ SY0 )
=> ! [SY5: $i] :
( ( in @ SY5 @ SY0 )
=> ( ( SY4 = SY5 )
| ( in @ SY4 @ SY5 )
| ( in @ SY5 @ SY4 ) ) ) )
& ! [SY6: $i] :
( ( in @ SY6 @ SY0 )
=> ~ ( in @ SY6 @ SY6 ) )
& ! [SY7: $i] :
( ( in @ SY7 @ ( powerset @ SY0 ) )
=> ( ( nonempty @ SY7 )
=> ? [Xx: $i] :
( ( in @ Xx @ SY7 )
& ! [Y: $i] :
( ( in @ Y @ SY7 )
=> ( ( Xx = Y )
| ( in @ Xx @ Y ) ) ) ) ) ) )
=> ! [A: $i] :
( ( in @ A @ SY0 )
=> ~ ( in @ A @ A ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,ordinal,stricttotalorderedByIn,wellorderedByIn]) ).
thf(4,plain,
( ( ( ( transitiveset @ sK1_SY0 )
& ! [SY22: $i] :
( ( in @ SY22 @ sK1_SY0 )
=> ! [SY23: $i] :
( ( in @ SY23 @ sK1_SY0 )
=> ! [SY24: $i] :
( ( in @ SY24 @ sK1_SY0 )
=> ( ( ( in @ SY22 @ SY23 )
& ( in @ SY23 @ SY24 ) )
=> ( in @ SY22 @ SY24 ) ) ) ) )
& ! [SY25: $i] :
( ( in @ SY25 @ sK1_SY0 )
=> ! [SY26: $i] :
( ( in @ SY26 @ sK1_SY0 )
=> ( ( SY25 = SY26 )
| ( in @ SY25 @ SY26 )
| ( in @ SY26 @ SY25 ) ) ) )
& ! [SY27: $i] :
( ( in @ SY27 @ sK1_SY0 )
=> ~ ( in @ SY27 @ SY27 ) )
& ! [SY28: $i] :
( ( in @ SY28 @ ( powerset @ sK1_SY0 ) )
=> ( ( nonempty @ SY28 )
=> ? [Xx: $i] :
( ( in @ Xx @ SY28 )
& ! [Y: $i] :
( ( in @ Y @ SY28 )
=> ( ( Xx = Y )
| ( in @ Xx @ Y ) ) ) ) ) ) )
=> ! [SY31: $i] :
( ( in @ SY31 @ sK1_SY0 )
=> ~ ( in @ SY31 @ SY31 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( transitiveset @ sK1_SY0 )
= $true ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(6,plain,
( ( ! [SY22: $i] :
( ( in @ SY22 @ sK1_SY0 )
=> ! [SY23: $i] :
( ( in @ SY23 @ sK1_SY0 )
=> ! [SY24: $i] :
( ( in @ SY24 @ sK1_SY0 )
=> ( ( ( in @ SY22 @ SY23 )
& ( in @ SY23 @ SY24 ) )
=> ( in @ SY22 @ SY24 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(7,plain,
( ( ! [SY25: $i] :
( ( in @ SY25 @ sK1_SY0 )
=> ! [SY26: $i] :
( ( in @ SY26 @ sK1_SY0 )
=> ( ( SY25 = SY26 )
| ( in @ SY25 @ SY26 )
| ( in @ SY26 @ SY25 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(8,plain,
( ( ! [SY27: $i] :
( ( in @ SY27 @ sK1_SY0 )
=> ~ ( in @ SY27 @ SY27 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(9,plain,
( ( ! [SY28: $i] :
( ( in @ SY28 @ ( powerset @ sK1_SY0 ) )
=> ( ( nonempty @ SY28 )
=> ? [Xx: $i] :
( ( in @ Xx @ SY28 )
& ! [Y: $i] :
( ( in @ Y @ SY28 )
=> ( ( Xx = Y )
| ( in @ Xx @ Y ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(10,plain,
( ( ! [SY31: $i] :
( ( in @ SY31 @ sK1_SY0 )
=> ~ ( in @ SY31 @ SY31 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(11,plain,
( ( ~ ! [SY31: $i] :
( ( in @ SY31 @ sK1_SY0 )
=> ~ ( in @ SY31 @ SY31 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(12,plain,
( ( ( in @ sK2_SY31 @ sK1_SY0 )
& ( in @ sK2_SY31 @ sK2_SY31 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(13,plain,
( ( ! [SY22: $i] :
( ~ ( in @ SY22 @ sK1_SY0 )
| ! [SY23: $i] :
( ~ ( in @ SY23 @ sK1_SY0 )
| ! [SY24: $i] :
( ~ ( in @ SY24 @ sK1_SY0 )
| ~ ( in @ SY22 @ SY23 )
| ~ ( in @ SY23 @ SY24 )
| ( in @ SY22 @ SY24 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(14,plain,
( ( ! [SY25: $i] :
( ~ ( in @ SY25 @ sK1_SY0 )
| ! [SY26: $i] :
( ~ ( in @ SY26 @ sK1_SY0 )
| ( in @ SY26 @ SY25 )
| ( SY25 = SY26 )
| ( in @ SY25 @ SY26 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(15,plain,
( ( ! [SY27: $i] :
( ~ ( in @ SY27 @ sK1_SY0 )
| ~ ( in @ SY27 @ SY27 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(16,plain,
( ( ! [SY28: $i] :
( ~ ( in @ SY28 @ ( powerset @ sK1_SY0 ) )
| ~ ( nonempty @ SY28 )
| ( ! [SY32: $i] :
( ~ ( in @ SY32 @ SY28 )
| ( ( sK3_Xx @ SY28 )
= SY32 )
| ( in @ ( sK3_Xx @ SY28 ) @ SY32 ) )
& ( in @ ( sK3_Xx @ SY28 ) @ SY28 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(17,plain,
( ( ! [SY28: $i] :
( ~ ( in @ SY28 @ ( powerset @ sK1_SY0 ) )
| ~ ( nonempty @ SY28 )
| ( ! [SY32: $i] :
( ~ ( in @ SY32 @ SY28 )
| ( ( sK3_Xx @ SY28 )
= SY32 )
| ( in @ ( sK3_Xx @ SY28 ) @ SY32 ) )
& ( in @ ( sK3_Xx @ SY28 ) @ SY28 ) ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(18,plain,
( ( ! [SY27: $i] :
( ~ ( in @ SY27 @ sK1_SY0 )
| ~ ( in @ SY27 @ SY27 ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(19,plain,
( ( ! [SY25: $i] :
( ~ ( in @ SY25 @ sK1_SY0 )
| ! [SY26: $i] :
( ~ ( in @ SY26 @ sK1_SY0 )
| ( in @ SY26 @ SY25 )
| ( SY25 = SY26 )
| ( in @ SY25 @ SY26 ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(20,plain,
( ( ! [SY22: $i] :
( ~ ( in @ SY22 @ sK1_SY0 )
| ! [SY23: $i] :
( ~ ( in @ SY23 @ sK1_SY0 )
| ! [SY24: $i] :
( ~ ( in @ SY24 @ sK1_SY0 )
| ~ ( in @ SY22 @ SY23 )
| ~ ( in @ SY23 @ SY24 )
| ( in @ SY22 @ SY24 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(21,plain,
( ( transitiveset @ sK1_SY0 )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(22,plain,
( ( ( in @ sK2_SY31 @ sK1_SY0 )
& ( in @ sK2_SY31 @ sK2_SY31 ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(23,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ ( powerset @ sK1_SY0 ) )
| ~ ( nonempty @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( ( sK3_Xx @ SX0 )
= SX1 )
| ( in @ ( sK3_Xx @ SX0 ) @ SX1 ) )
| ~ ( in @ ( sK3_Xx @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17,ordinal,stricttotalorderedByIn,wellorderedByIn]) ).
thf(24,plain,
( ( ~ ( ~ ( in @ sK2_SY31 @ sK1_SY0 )
| ~ ( in @ sK2_SY31 @ sK2_SY31 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22,ordinal,stricttotalorderedByIn,wellorderedByIn]) ).
thf(25,plain,
! [SV1: $i] :
( ( ~ ( in @ SV1 @ sK1_SY0 )
| ~ ( in @ SV1 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(26,plain,
! [SV2: $i] :
( ( ~ ( in @ SV2 @ sK1_SY0 )
| ! [SY33: $i] :
( ~ ( in @ SY33 @ sK1_SY0 )
| ( in @ SY33 @ SV2 )
| ( SV2 = SY33 )
| ( in @ SV2 @ SY33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(27,plain,
! [SV3: $i] :
( ( ~ ( in @ SV3 @ sK1_SY0 )
| ! [SY34: $i] :
( ~ ( in @ SY34 @ sK1_SY0 )
| ! [SY35: $i] :
( ~ ( in @ SY35 @ sK1_SY0 )
| ~ ( in @ SV3 @ SY34 )
| ~ ( in @ SY34 @ SY35 )
| ( in @ SV3 @ SY35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(28,plain,
! [SV4: $i] :
( ( ~ ( in @ SV4 @ ( powerset @ sK1_SY0 ) )
| ~ ( nonempty @ SV4 )
| ~ ( ~ ! [SY36: $i] :
( ~ ( in @ SY36 @ SV4 )
| ( ( sK3_Xx @ SV4 )
= SY36 )
| ( in @ ( sK3_Xx @ SV4 ) @ SY36 ) )
| ~ ( in @ ( sK3_Xx @ SV4 ) @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(29,plain,
( ( ~ ( in @ sK2_SY31 @ sK1_SY0 )
| ~ ( in @ sK2_SY31 @ sK2_SY31 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(30,plain,
! [SV1: $i] :
( ( ( ~ ( in @ SV1 @ sK1_SY0 ) )
= $true )
| ( ( ~ ( in @ SV1 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[25]) ).
thf(31,plain,
! [SV2: $i] :
( ( ( ~ ( in @ SV2 @ sK1_SY0 ) )
= $true )
| ( ( ! [SY33: $i] :
( ~ ( in @ SY33 @ sK1_SY0 )
| ( in @ SY33 @ SV2 )
| ( SV2 = SY33 )
| ( in @ SV2 @ SY33 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(32,plain,
! [SV3: $i] :
( ( ( ~ ( in @ SV3 @ sK1_SY0 ) )
= $true )
| ( ( ! [SY34: $i] :
( ~ ( in @ SY34 @ sK1_SY0 )
| ! [SY35: $i] :
( ~ ( in @ SY35 @ sK1_SY0 )
| ~ ( in @ SV3 @ SY34 )
| ~ ( in @ SY34 @ SY35 )
| ( in @ SV3 @ SY35 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(33,plain,
! [SV4: $i] :
( ( ( ~ ( in @ SV4 @ ( powerset @ sK1_SY0 ) ) )
= $true )
| ( ( ~ ( nonempty @ SV4 )
| ~ ( ~ ! [SY36: $i] :
( ~ ( in @ SY36 @ SV4 )
| ( ( sK3_Xx @ SV4 )
= SY36 )
| ( in @ ( sK3_Xx @ SV4 ) @ SY36 ) )
| ~ ( in @ ( sK3_Xx @ SV4 ) @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(34,plain,
( ( ~ ( in @ sK2_SY31 @ sK1_SY0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(35,plain,
( ( ~ ( in @ sK2_SY31 @ sK2_SY31 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(36,plain,
! [SV1: $i] :
( ( ( in @ SV1 @ sK1_SY0 )
= $false )
| ( ( ~ ( in @ SV1 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(37,plain,
! [SV2: $i] :
( ( ( in @ SV2 @ sK1_SY0 )
= $false )
| ( ( ! [SY33: $i] :
( ~ ( in @ SY33 @ sK1_SY0 )
| ( in @ SY33 @ SV2 )
| ( SV2 = SY33 )
| ( in @ SV2 @ SY33 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(38,plain,
! [SV3: $i] :
( ( ( in @ SV3 @ sK1_SY0 )
= $false )
| ( ( ! [SY34: $i] :
( ~ ( in @ SY34 @ sK1_SY0 )
| ! [SY35: $i] :
( ~ ( in @ SY35 @ sK1_SY0 )
| ~ ( in @ SV3 @ SY34 )
| ~ ( in @ SY34 @ SY35 )
| ( in @ SV3 @ SY35 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(39,plain,
! [SV4: $i] :
( ( ( in @ SV4 @ ( powerset @ sK1_SY0 ) )
= $false )
| ( ( ~ ( nonempty @ SV4 )
| ~ ( ~ ! [SY36: $i] :
( ~ ( in @ SY36 @ SV4 )
| ( ( sK3_Xx @ SV4 )
= SY36 )
| ( in @ ( sK3_Xx @ SV4 ) @ SY36 ) )
| ~ ( in @ ( sK3_Xx @ SV4 ) @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(40,plain,
( ( in @ sK2_SY31 @ sK1_SY0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(41,plain,
( ( in @ sK2_SY31 @ sK2_SY31 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(42,plain,
! [SV1: $i] :
( ( ( in @ SV1 @ SV1 )
= $false )
| ( ( in @ SV1 @ sK1_SY0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(43,plain,
! [SV2: $i,SV5: $i] :
( ( ( ~ ( in @ SV5 @ sK1_SY0 )
| ( in @ SV5 @ SV2 )
| ( SV2 = SV5 )
| ( in @ SV2 @ SV5 ) )
= $true )
| ( ( in @ SV2 @ sK1_SY0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(44,plain,
! [SV3: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ sK1_SY0 )
| ! [SY37: $i] :
( ~ ( in @ SY37 @ sK1_SY0 )
| ~ ( in @ SV3 @ SV6 )
| ~ ( in @ SV6 @ SY37 )
| ( in @ SV3 @ SY37 ) ) )
= $true )
| ( ( in @ SV3 @ sK1_SY0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(45,plain,
! [SV4: $i] :
( ( ( ~ ( nonempty @ SV4 ) )
= $true )
| ( ( ~ ( ~ ! [SY36: $i] :
( ~ ( in @ SY36 @ SV4 )
| ( ( sK3_Xx @ SV4 )
= SY36 )
| ( in @ ( sK3_Xx @ SV4 ) @ SY36 ) )
| ~ ( in @ ( sK3_Xx @ SV4 ) @ SV4 ) ) )
= $true )
| ( ( in @ SV4 @ ( powerset @ sK1_SY0 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(46,plain,
! [SV2: $i,SV5: $i] :
( ( ( ~ ( in @ SV5 @ sK1_SY0 ) )
= $true )
| ( ( ( in @ SV5 @ SV2 )
| ( SV2 = SV5 )
| ( in @ SV2 @ SV5 ) )
= $true )
| ( ( in @ SV2 @ sK1_SY0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(47,plain,
! [SV3: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ sK1_SY0 ) )
= $true )
| ( ( ! [SY37: $i] :
( ~ ( in @ SY37 @ sK1_SY0 )
| ~ ( in @ SV3 @ SV6 )
| ~ ( in @ SV6 @ SY37 )
| ( in @ SV3 @ SY37 ) ) )
= $true )
| ( ( in @ SV3 @ sK1_SY0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(48,plain,
! [SV4: $i] :
( ( ( nonempty @ SV4 )
= $false )
| ( ( ~ ( ~ ! [SY36: $i] :
( ~ ( in @ SY36 @ SV4 )
| ( ( sK3_Xx @ SV4 )
= SY36 )
| ( in @ ( sK3_Xx @ SV4 ) @ SY36 ) )
| ~ ( in @ ( sK3_Xx @ SV4 ) @ SV4 ) ) )
= $true )
| ( ( in @ SV4 @ ( powerset @ sK1_SY0 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(49,plain,
! [SV2: $i,SV5: $i] :
( ( ( in @ SV5 @ sK1_SY0 )
= $false )
| ( ( ( in @ SV5 @ SV2 )
| ( SV2 = SV5 )
| ( in @ SV2 @ SV5 ) )
= $true )
| ( ( in @ SV2 @ sK1_SY0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(50,plain,
! [SV3: $i,SV6: $i] :
( ( ( in @ SV6 @ sK1_SY0 )
= $false )
| ( ( ! [SY37: $i] :
( ~ ( in @ SY37 @ sK1_SY0 )
| ~ ( in @ SV3 @ SV6 )
| ~ ( in @ SV6 @ SY37 )
| ( in @ SV3 @ SY37 ) ) )
= $true )
| ( ( in @ SV3 @ sK1_SY0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(51,plain,
! [SV4: $i] :
( ( ( ~ ! [SY36: $i] :
( ~ ( in @ SY36 @ SV4 )
| ( ( sK3_Xx @ SV4 )
= SY36 )
| ( in @ ( sK3_Xx @ SV4 ) @ SY36 ) )
| ~ ( in @ ( sK3_Xx @ SV4 ) @ SV4 ) )
= $false )
| ( ( nonempty @ SV4 )
= $false )
| ( ( in @ SV4 @ ( powerset @ sK1_SY0 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(52,plain,
! [SV2: $i,SV5: $i] :
( ( ( in @ SV5 @ SV2 )
= $true )
| ( ( ( SV2 = SV5 )
| ( in @ SV2 @ SV5 ) )
= $true )
| ( ( in @ SV5 @ sK1_SY0 )
= $false )
| ( ( in @ SV2 @ sK1_SY0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(53,plain,
! [SV6: $i,SV3: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ sK1_SY0 )
| ~ ( in @ SV3 @ SV6 )
| ~ ( in @ SV6 @ SV7 )
| ( in @ SV3 @ SV7 ) )
= $true )
| ( ( in @ SV6 @ sK1_SY0 )
= $false )
| ( ( in @ SV3 @ sK1_SY0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(54,plain,
! [SV4: $i] :
( ( ( ~ ! [SY36: $i] :
( ~ ( in @ SY36 @ SV4 )
| ( ( sK3_Xx @ SV4 )
= SY36 )
| ( in @ ( sK3_Xx @ SV4 ) @ SY36 ) ) )
= $false )
| ( ( nonempty @ SV4 )
= $false )
| ( ( in @ SV4 @ ( powerset @ sK1_SY0 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[51]) ).
thf(55,plain,
! [SV4: $i] :
( ( ( ~ ( in @ ( sK3_Xx @ SV4 ) @ SV4 ) )
= $false )
| ( ( nonempty @ SV4 )
= $false )
| ( ( in @ SV4 @ ( powerset @ sK1_SY0 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[51]) ).
thf(56,plain,
! [SV5: $i,SV2: $i] :
( ( ( SV2 = SV5 )
= $true )
| ( ( in @ SV2 @ SV5 )
= $true )
| ( ( in @ SV5 @ SV2 )
= $true )
| ( ( in @ SV5 @ sK1_SY0 )
= $false )
| ( ( in @ SV2 @ sK1_SY0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(57,plain,
! [SV6: $i,SV3: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ sK1_SY0 ) )
= $true )
| ( ( ~ ( in @ SV3 @ SV6 )
| ~ ( in @ SV6 @ SV7 )
| ( in @ SV3 @ SV7 ) )
= $true )
| ( ( in @ SV6 @ sK1_SY0 )
= $false )
| ( ( in @ SV3 @ sK1_SY0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[53]) ).
thf(58,plain,
! [SV4: $i] :
( ( ( ! [SY36: $i] :
( ~ ( in @ SY36 @ SV4 )
| ( ( sK3_Xx @ SV4 )
= SY36 )
| ( in @ ( sK3_Xx @ SV4 ) @ SY36 ) ) )
= $true )
| ( ( nonempty @ SV4 )
= $false )
| ( ( in @ SV4 @ ( powerset @ sK1_SY0 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(59,plain,
! [SV4: $i] :
( ( ( in @ ( sK3_Xx @ SV4 ) @ SV4 )
= $true )
| ( ( nonempty @ SV4 )
= $false )
| ( ( in @ SV4 @ ( powerset @ sK1_SY0 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(60,plain,
! [SV6: $i,SV3: $i,SV7: $i] :
( ( ( in @ SV7 @ sK1_SY0 )
= $false )
| ( ( ~ ( in @ SV3 @ SV6 )
| ~ ( in @ SV6 @ SV7 )
| ( in @ SV3 @ SV7 ) )
= $true )
| ( ( in @ SV6 @ sK1_SY0 )
= $false )
| ( ( in @ SV3 @ sK1_SY0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(61,plain,
! [SV4: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ SV4 )
| ( ( sK3_Xx @ SV4 )
= SV8 )
| ( in @ ( sK3_Xx @ SV4 ) @ SV8 ) )
= $true )
| ( ( nonempty @ SV4 )
= $false )
| ( ( in @ SV4 @ ( powerset @ sK1_SY0 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(62,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV6 )
| ~ ( in @ SV6 @ SV7 ) )
= $true )
| ( ( in @ SV3 @ SV7 )
= $true )
| ( ( in @ SV7 @ sK1_SY0 )
= $false )
| ( ( in @ SV6 @ sK1_SY0 )
= $false )
| ( ( in @ SV3 @ sK1_SY0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(63,plain,
! [SV4: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ SV4 ) )
= $true )
| ( ( ( ( sK3_Xx @ SV4 )
= SV8 )
| ( in @ ( sK3_Xx @ SV4 ) @ SV8 ) )
= $true )
| ( ( nonempty @ SV4 )
= $false )
| ( ( in @ SV4 @ ( powerset @ sK1_SY0 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(64,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV6 ) )
= $true )
| ( ( ~ ( in @ SV6 @ SV7 ) )
= $true )
| ( ( in @ SV3 @ SV7 )
= $true )
| ( ( in @ SV7 @ sK1_SY0 )
= $false )
| ( ( in @ SV6 @ sK1_SY0 )
= $false )
| ( ( in @ SV3 @ sK1_SY0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(65,plain,
! [SV4: $i,SV8: $i] :
( ( ( in @ SV8 @ SV4 )
= $false )
| ( ( ( ( sK3_Xx @ SV4 )
= SV8 )
| ( in @ ( sK3_Xx @ SV4 ) @ SV8 ) )
= $true )
| ( ( nonempty @ SV4 )
= $false )
| ( ( in @ SV4 @ ( powerset @ sK1_SY0 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(66,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( in @ SV3 @ SV6 )
= $false )
| ( ( ~ ( in @ SV6 @ SV7 ) )
= $true )
| ( ( in @ SV3 @ SV7 )
= $true )
| ( ( in @ SV7 @ sK1_SY0 )
= $false )
| ( ( in @ SV6 @ sK1_SY0 )
= $false )
| ( ( in @ SV3 @ sK1_SY0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(67,plain,
! [SV8: $i,SV4: $i] :
( ( ( ( sK3_Xx @ SV4 )
= SV8 )
= $true )
| ( ( in @ ( sK3_Xx @ SV4 ) @ SV8 )
= $true )
| ( ( in @ SV8 @ SV4 )
= $false )
| ( ( nonempty @ SV4 )
= $false )
| ( ( in @ SV4 @ ( powerset @ sK1_SY0 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(68,plain,
! [SV3: $i,SV7: $i,SV6: $i] :
( ( ( in @ SV6 @ SV7 )
= $false )
| ( ( in @ SV3 @ SV6 )
= $false )
| ( ( in @ SV3 @ SV7 )
= $true )
| ( ( in @ SV7 @ sK1_SY0 )
= $false )
| ( ( in @ SV6 @ sK1_SY0 )
= $false )
| ( ( in @ SV3 @ sK1_SY0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(69,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[21,68,67,59,56,42,41,40]) ).
thf(70,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU821^2 : TPTP v8.1.0. Released v3.7.0.
% 0.03/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.32 % Computer : n032.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Sun Jun 19 04:28:32 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.12/0.32
% 0.12/0.32 No.of.Axioms: 0
% 0.12/0.32
% 0.12/0.32 Length.of.Defs: 895
% 0.12/0.32
% 0.12/0.32 Contains.Choice.Funs: false
% 0.12/0.33 (rf:0,axioms:0,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)....
% 0.18/0.38
% 0.18/0.38 ********************************
% 0.18/0.38 * All subproblems solved! *
% 0.18/0.38 ********************************
% 0.18/0.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:5,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:69,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.18/0.39
% 0.18/0.39 %**** Beginning of derivation protocol ****
% 0.18/0.39 % SZS output start CNFRefutation
% See solution above
% 0.18/0.39
% 0.18/0.39 %**** End of derivation protocol ****
% 0.18/0.39 %**** no. of clauses in derivation: 70 ****
% 0.18/0.39 %**** clause counter: 69 ****
% 0.18/0.39
% 0.18/0.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:5,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:69,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------