TSTP Solution File: SEU627^2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU627^2 : 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 : n009.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 12:13:28 EDT 2022
% Result : Theorem 0.21s 0.44s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 20
% Syntax : Number of formulae : 81 ( 48 unt; 15 typ; 4 def)
% Number of atoms : 350 ( 106 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 919 ( 85 ~; 70 |; 6 &; 718 @)
% ( 0 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 11 con; 0-2 aty)
% Number of variables : 168 ( 0 ^ 168 !; 0 ?; 168 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_binunion,type,
binunion: $i > $i > $i ).
thf(tp_emptyset,type,
emptyset: $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY21,type,
sK2_SY21: $i ).
thf(tp_sK3_SY24,type,
sK3_SY24: $i ).
thf(tp_sK4_SY26,type,
sK4_SY26: $i ).
thf(tp_sK5_Xx,type,
sK5_Xx: $i > $i > $i ).
thf(tp_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(tp_singletoninpowunion,type,
singletoninpowunion: $o ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_subsetI2,type,
subsetI2: $o ).
thf(tp_upairinpowunion,type,
upairinpowunion: $o ).
thf(tp_upairset2E,type,
upairset2E: $o ).
thf(singletoninpowunion,definition,
( singletoninpowunion
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletoninpowunion) ).
thf(subsetI2,definition,
( subsetI2
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI2) ).
thf(upairinpowunion,definition,
( upairinpowunion
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairinpowunion) ).
thf(upairset2E,definition,
( upairset2E
= ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairset2E) ).
thf(1,conjecture,
( subsetI2
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairinpowunion
=> ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ubforcartprodlem1) ).
thf(2,negated_conjecture,
( ( subsetI2
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairinpowunion
=> ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) )
=> ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) )
=> ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,singletoninpowunion,subsetI2,upairinpowunion,upairset2E]) ).
thf(4,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(9,plain,
( ( ~ ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(10,plain,
( ( ( in @ sK3_SY24 @ sK1_A )
& ( in @ sK4_SY26 @ sK2_SY21 )
& ~ ( subset @ ( setadjoin @ ( setadjoin @ sK3_SY24 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3_SY24 @ ( setadjoin @ sK4_SY26 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ sK1_A @ sK2_SY21 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(11,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK5_Xx @ B @ A ) @ A )
& ~ ( in @ ( sK5_Xx @ B @ A ) @ B ) )
| ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(12,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(13,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ~ ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
| ( Xz = Xx )
| ( Xz = Xy ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(14,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ B )
| ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(15,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ B )
| ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(16,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ~ ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
| ( Xz = Xx )
| ( Xz = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(17,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(18,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK5_Xx @ B @ A ) @ A )
& ~ ( in @ ( sK5_Xx @ B @ A ) @ B ) )
| ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(19,plain,
( ( ( in @ sK3_SY24 @ sK1_A )
& ( in @ sK4_SY26 @ sK2_SY21 )
& ~ ( subset @ ( setadjoin @ ( setadjoin @ sK3_SY24 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3_SY24 @ ( setadjoin @ sK4_SY26 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ sK1_A @ sK2_SY21 ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(20,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK5_Xx @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK5_Xx @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18,singletoninpowunion,subsetI2,upairinpowunion,upairset2E]) ).
thf(21,plain,
( ( ~ ( ~ ( in @ sK3_SY24 @ sK1_A )
| ~ ~ ( ~ ( in @ sK4_SY26 @ sK2_SY21 )
| ~ ~ ( subset @ ( setadjoin @ ( setadjoin @ sK3_SY24 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3_SY24 @ ( setadjoin @ sK4_SY26 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ sK1_A @ sK2_SY21 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19,singletoninpowunion,subsetI2,upairinpowunion,upairset2E]) ).
thf(22,plain,
! [SV1: $i] :
( ( ! [SY27: $i,SY28: $i] :
( ~ ( in @ SY28 @ SV1 )
| ! [SY29: $i] :
( ~ ( in @ SY29 @ SY27 )
| ( in @ ( setadjoin @ SY28 @ ( setadjoin @ SY29 @ emptyset ) ) @ ( powerset @ ( binunion @ SV1 @ SY27 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(23,plain,
! [SV2: $i] :
( ( ! [SY30: $i,SY31: $i] :
( ~ ( in @ SY31 @ ( setadjoin @ SV2 @ ( setadjoin @ SY30 @ emptyset ) ) )
| ( SY31 = SV2 )
| ( SY31 = SY30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(24,plain,
! [SV3: $i] :
( ( ! [SY32: $i,SY33: $i] :
( ~ ( in @ SY33 @ SV3 )
| ( in @ ( setadjoin @ SY33 @ emptyset ) @ ( powerset @ ( binunion @ SV3 @ SY32 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(25,plain,
! [SV4: $i] :
( ( ! [SY34: $i] :
( ~ ( ~ ( in @ ( sK5_Xx @ SY34 @ SV4 ) @ SV4 )
| ~ ~ ( in @ ( sK5_Xx @ SY34 @ SV4 ) @ SY34 ) )
| ( subset @ SV4 @ SY34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(26,plain,
( ( ~ ( in @ sK3_SY24 @ sK1_A )
| ~ ~ ( ~ ( in @ sK4_SY26 @ sK2_SY21 )
| ~ ~ ( subset @ ( setadjoin @ ( setadjoin @ sK3_SY24 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3_SY24 @ ( setadjoin @ sK4_SY26 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ sK1_A @ sK2_SY21 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(27,plain,
! [SV5: $i,SV1: $i] :
( ( ! [SY35: $i] :
( ~ ( in @ SY35 @ SV1 )
| ! [SY36: $i] :
( ~ ( in @ SY36 @ SV5 )
| ( in @ ( setadjoin @ SY35 @ ( setadjoin @ SY36 @ emptyset ) ) @ ( powerset @ ( binunion @ SV1 @ SV5 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(28,plain,
! [SV6: $i,SV2: $i] :
( ( ! [SY37: $i] :
( ~ ( in @ SY37 @ ( setadjoin @ SV2 @ ( setadjoin @ SV6 @ emptyset ) ) )
| ( SY37 = SV2 )
| ( SY37 = SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(29,plain,
! [SV7: $i,SV3: $i] :
( ( ! [SY38: $i] :
( ~ ( in @ SY38 @ SV3 )
| ( in @ ( setadjoin @ SY38 @ emptyset ) @ ( powerset @ ( binunion @ SV3 @ SV7 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(30,plain,
! [SV4: $i,SV8: $i] :
( ( ~ ( ~ ( in @ ( sK5_Xx @ SV8 @ SV4 ) @ SV4 )
| ~ ~ ( in @ ( sK5_Xx @ SV8 @ SV4 ) @ SV8 ) )
| ( subset @ SV4 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(31,plain,
( ( ~ ( in @ sK3_SY24 @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(32,plain,
( ( ~ ~ ( ~ ( in @ sK4_SY26 @ sK2_SY21 )
| ~ ~ ( subset @ ( setadjoin @ ( setadjoin @ sK3_SY24 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3_SY24 @ ( setadjoin @ sK4_SY26 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ sK1_A @ sK2_SY21 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(33,plain,
! [SV5: $i,SV1: $i,SV9: $i] :
( ( ~ ( in @ SV9 @ SV1 )
| ! [SY39: $i] :
( ~ ( in @ SY39 @ SV5 )
| ( in @ ( setadjoin @ SV9 @ ( setadjoin @ SY39 @ emptyset ) ) @ ( powerset @ ( binunion @ SV1 @ SV5 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(34,plain,
! [SV6: $i,SV2: $i,SV10: $i] :
( ( ~ ( in @ SV10 @ ( setadjoin @ SV2 @ ( setadjoin @ SV6 @ emptyset ) ) )
| ( SV10 = SV2 )
| ( SV10 = SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(35,plain,
! [SV7: $i,SV3: $i,SV11: $i] :
( ( ~ ( in @ SV11 @ SV3 )
| ( in @ ( setadjoin @ SV11 @ emptyset ) @ ( powerset @ ( binunion @ SV3 @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(36,plain,
! [SV4: $i,SV8: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_Xx @ SV8 @ SV4 ) @ SV4 )
| ~ ~ ( in @ ( sK5_Xx @ SV8 @ SV4 ) @ SV8 ) ) )
= $true )
| ( ( subset @ SV4 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[30]) ).
thf(37,plain,
( ( in @ sK3_SY24 @ sK1_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[31]) ).
thf(38,plain,
( ( ~ ( ~ ( in @ sK4_SY26 @ sK2_SY21 )
| ~ ~ ( subset @ ( setadjoin @ ( setadjoin @ sK3_SY24 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3_SY24 @ ( setadjoin @ sK4_SY26 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ sK1_A @ sK2_SY21 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(39,plain,
! [SV5: $i,SV1: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ SV1 ) )
= $true )
| ( ( ! [SY39: $i] :
( ~ ( in @ SY39 @ SV5 )
| ( in @ ( setadjoin @ SV9 @ ( setadjoin @ SY39 @ emptyset ) ) @ ( powerset @ ( binunion @ SV1 @ SV5 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(40,plain,
! [SV6: $i,SV2: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ ( setadjoin @ SV2 @ ( setadjoin @ SV6 @ emptyset ) ) ) )
= $true )
| ( ( ( SV10 = SV2 )
| ( SV10 = SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).
thf(41,plain,
! [SV7: $i,SV3: $i,SV11: $i] :
( ( ( ~ ( in @ SV11 @ SV3 ) )
= $true )
| ( ( in @ ( setadjoin @ SV11 @ emptyset ) @ ( powerset @ ( binunion @ SV3 @ SV7 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(42,plain,
! [SV4: $i,SV8: $i] :
( ( ( ~ ( in @ ( sK5_Xx @ SV8 @ SV4 ) @ SV4 )
| ~ ~ ( in @ ( sK5_Xx @ SV8 @ SV4 ) @ SV8 ) )
= $false )
| ( ( subset @ SV4 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(43,plain,
( ( ~ ( in @ sK4_SY26 @ sK2_SY21 )
| ~ ~ ( subset @ ( setadjoin @ ( setadjoin @ sK3_SY24 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3_SY24 @ ( setadjoin @ sK4_SY26 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ sK1_A @ sK2_SY21 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(44,plain,
! [SV5: $i,SV1: $i,SV9: $i] :
( ( ( in @ SV9 @ SV1 )
= $false )
| ( ( ! [SY39: $i] :
( ~ ( in @ SY39 @ SV5 )
| ( in @ ( setadjoin @ SV9 @ ( setadjoin @ SY39 @ emptyset ) ) @ ( powerset @ ( binunion @ SV1 @ SV5 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(45,plain,
! [SV6: $i,SV2: $i,SV10: $i] :
( ( ( in @ SV10 @ ( setadjoin @ SV2 @ ( setadjoin @ SV6 @ emptyset ) ) )
= $false )
| ( ( ( SV10 = SV2 )
| ( SV10 = SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(46,plain,
! [SV7: $i,SV3: $i,SV11: $i] :
( ( ( in @ SV11 @ SV3 )
= $false )
| ( ( in @ ( setadjoin @ SV11 @ emptyset ) @ ( powerset @ ( binunion @ SV3 @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(47,plain,
! [SV4: $i,SV8: $i] :
( ( ( ~ ( in @ ( sK5_Xx @ SV8 @ SV4 ) @ SV4 ) )
= $false )
| ( ( subset @ SV4 @ SV8 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(48,plain,
! [SV4: $i,SV8: $i] :
( ( ( ~ ~ ( in @ ( sK5_Xx @ SV8 @ SV4 ) @ SV8 ) )
= $false )
| ( ( subset @ SV4 @ SV8 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(49,plain,
( ( ~ ( in @ sK4_SY26 @ sK2_SY21 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[43]) ).
thf(50,plain,
( ( ~ ~ ( subset @ ( setadjoin @ ( setadjoin @ sK3_SY24 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3_SY24 @ ( setadjoin @ sK4_SY26 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ sK1_A @ sK2_SY21 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[43]) ).
thf(51,plain,
! [SV1: $i,SV9: $i,SV5: $i,SV12: $i] :
( ( ( ~ ( in @ SV12 @ SV5 )
| ( in @ ( setadjoin @ SV9 @ ( setadjoin @ SV12 @ emptyset ) ) @ ( powerset @ ( binunion @ SV1 @ SV5 ) ) ) )
= $true )
| ( ( in @ SV9 @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(52,plain,
! [SV6: $i,SV2: $i,SV10: $i] :
( ( ( SV10 = SV2 )
= $true )
| ( ( SV10 = SV6 )
= $true )
| ( ( in @ SV10 @ ( setadjoin @ SV2 @ ( setadjoin @ SV6 @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(53,plain,
! [SV4: $i,SV8: $i] :
( ( ( in @ ( sK5_Xx @ SV8 @ SV4 ) @ SV4 )
= $true )
| ( ( subset @ SV4 @ SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[47]) ).
thf(54,plain,
! [SV4: $i,SV8: $i] :
( ( ( ~ ( in @ ( sK5_Xx @ SV8 @ SV4 ) @ SV8 ) )
= $true )
| ( ( subset @ SV4 @ SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(55,plain,
( ( in @ sK4_SY26 @ sK2_SY21 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(56,plain,
( ( ~ ( subset @ ( setadjoin @ ( setadjoin @ sK3_SY24 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3_SY24 @ ( setadjoin @ sK4_SY26 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ sK1_A @ sK2_SY21 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(57,plain,
! [SV1: $i,SV9: $i,SV5: $i,SV12: $i] :
( ( ( ~ ( in @ SV12 @ SV5 ) )
= $true )
| ( ( in @ ( setadjoin @ SV9 @ ( setadjoin @ SV12 @ emptyset ) ) @ ( powerset @ ( binunion @ SV1 @ SV5 ) ) )
= $true )
| ( ( in @ SV9 @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(58,plain,
! [SV4: $i,SV8: $i] :
( ( ( in @ ( sK5_Xx @ SV8 @ SV4 ) @ SV8 )
= $false )
| ( ( subset @ SV4 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(59,plain,
( ( subset @ ( setadjoin @ ( setadjoin @ sK3_SY24 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3_SY24 @ ( setadjoin @ sK4_SY26 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ sK1_A @ sK2_SY21 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(60,plain,
! [SV1: $i,SV9: $i,SV5: $i,SV12: $i] :
( ( ( in @ SV12 @ SV5 )
= $false )
| ( ( in @ ( setadjoin @ SV9 @ ( setadjoin @ SV12 @ emptyset ) ) @ ( powerset @ ( binunion @ SV1 @ SV5 ) ) )
= $true )
| ( ( in @ SV9 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(61,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[37,60,59,58,55,53,52,46]) ).
thf(62,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SEU627^2 : TPTP v8.1.0. Released v3.7.0.
% 0.13/0.14 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.36 % Computer : n009.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Sun Jun 19 14:12:52 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.37
% 0.14/0.37 No.of.Axioms: 0
% 0.14/0.37
% 0.14/0.37 Length.of.Defs: 921
% 0.14/0.37
% 0.14/0.37 Contains.Choice.Funs: false
% 0.14/0.37 (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)...
% 0.21/0.44
% 0.21/0.44 ********************************
% 0.21/0.44 * All subproblems solved! *
% 0.21/0.44 ********************************
% 0.21/0.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:4,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:61,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.21/0.45
% 0.21/0.45 %**** Beginning of derivation protocol ****
% 0.21/0.45 % SZS output start CNFRefutation
% See solution above
% 0.21/0.45
% 0.21/0.45 %**** End of derivation protocol ****
% 0.21/0.45 %**** no. of clauses in derivation: 62 ****
% 0.21/0.45 %**** clause counter: 61 ****
% 0.21/0.45
% 0.21/0.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:4,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:61,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------