TSTP Solution File: SEU620^2 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU620^2 : 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 : n014.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 12:13:25 EDT 2022
% Result : Theorem 0.19s 0.43s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 15
% Syntax : Number of formulae : 46 ( 28 unt; 11 typ; 3 def)
% Number of atoms : 167 ( 69 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 1363 ( 57 ~; 29 |; 16 &;1258 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 79 ( 3 ^ 64 !; 12 ?; 79 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_emptyset,type,
emptyset: $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_iskpair,type,
iskpair: $i > $o ).
thf(tp_kpair,type,
kpair: $i > $i > $i ).
thf(tp_kpairiskpair,type,
kpairiskpair: $o ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i ).
thf(tp_sK2_SY21,type,
sK2_SY21: $i ).
thf(tp_sK3_SY7,type,
sK3_SY7: $i > $i > $i ).
thf(tp_sK4_SY26,type,
sK4_SY26: $i > $i > $i ).
thf(tp_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(tp_setunion,type,
setunion: $i > $i ).
thf(iskpair,definition,
( iskpair
= ( ^ [A: $i] :
? [Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
& ? [Xy: $i] :
( ( in @ Xy @ ( setunion @ A ) )
& ( A
= ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iskpair) ).
thf(kpair,definition,
( kpair
= ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpair) ).
thf(kpairiskpair,definition,
( kpairiskpair
= ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairiskpair) ).
thf(1,conjecture,
( kpairiskpair
=> ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairp) ).
thf(2,negated_conjecture,
( ( kpairiskpair
=> ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [SY5: $i,SY6: $i] :
? [SY7: $i] :
( ( in @ SY7 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY5 @ ( setadjoin @ SY6 @ emptyset ) ) @ emptyset ) ) ) )
& ? [SY8: $i] :
( ( in @ SY8 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY5 @ ( setadjoin @ SY6 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ SY5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY5 @ ( setadjoin @ SY6 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SY7 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY7 @ ( setadjoin @ SY8 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ! [SY0: $i,SY1: $i] :
? [SY3: $i] :
( ( in @ SY3 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) @ emptyset ) ) ) )
& ? [SY4: $i] :
( ( in @ SY4 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SY3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY3 @ ( setadjoin @ SY4 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,iskpair,kpair,kpairiskpair]) ).
thf(4,plain,
( ( ! [SY5: $i,SY6: $i] :
? [SY7: $i] :
( ( in @ SY7 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY5 @ ( setadjoin @ SY6 @ emptyset ) ) @ emptyset ) ) ) )
& ? [SY8: $i] :
( ( in @ SY8 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY5 @ ( setadjoin @ SY6 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ SY5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY5 @ ( setadjoin @ SY6 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SY7 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY7 @ ( setadjoin @ SY8 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [SY0: $i,SY1: $i] :
? [SY3: $i] :
( ( in @ SY3 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) @ emptyset ) ) ) )
& ? [SY4: $i] :
( ( in @ SY4 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SY3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY3 @ ( setadjoin @ SY4 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ~ ! [SY0: $i,SY1: $i] :
? [SY3: $i] :
( ( in @ SY3 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) @ emptyset ) ) ) )
& ? [SY4: $i] :
( ( in @ SY4 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SY3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY3 @ ( setadjoin @ SY4 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [SY24: $i] :
( ! [SY25: $i] :
( ( ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY24 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY24 @ ( setadjoin @ SY25 @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ SY25 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) ) ) ) )
| ~ ( in @ SY24 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(8,plain,
( ( ! [SY5: $i,SY6: $i] :
( ( ( setadjoin @ ( setadjoin @ SY5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY5 @ ( setadjoin @ SY6 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ ( sK3_SY7 @ SY6 @ SY5 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK3_SY7 @ SY6 @ SY5 ) @ ( setadjoin @ ( sK4_SY26 @ SY6 @ SY5 ) @ emptyset ) ) @ emptyset ) ) )
& ( in @ ( sK4_SY26 @ SY6 @ SY5 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SY5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY5 @ ( setadjoin @ SY6 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ ( sK3_SY7 @ SY6 @ SY5 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SY5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY5 @ ( setadjoin @ SY6 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(9,plain,
( ( ! [SY5: $i,SY6: $i] :
( ( ( setadjoin @ ( setadjoin @ SY5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY5 @ ( setadjoin @ SY6 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ ( sK3_SY7 @ SY6 @ SY5 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK3_SY7 @ SY6 @ SY5 ) @ ( setadjoin @ ( sK4_SY26 @ SY6 @ SY5 ) @ emptyset ) ) @ emptyset ) ) )
& ( in @ ( sK4_SY26 @ SY6 @ SY5 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SY5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY5 @ ( setadjoin @ SY6 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ ( sK3_SY7 @ SY6 @ SY5 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SY5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY5 @ ( setadjoin @ SY6 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(10,plain,
( ( ! [SY24: $i] :
( ! [SY25: $i] :
( ( ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY24 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY24 @ ( setadjoin @ SY25 @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ SY25 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) ) ) ) )
| ~ ( in @ SY24 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(11,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ~ ( ( ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK3_SY7 @ SX1 @ SX0 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK3_SY7 @ SX1 @ SX0 ) @ ( setadjoin @ ( sK4_SY26 @ SX1 @ SX0 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK4_SY26 @ SX1 @ SX0 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) ) ) ) )
| ~ ( in @ ( sK3_SY7 @ SX1 @ SX0 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9,iskpair,kpair,kpairiskpair]) ).
thf(12,plain,
! [SV1: $i] :
( ( ! [SY27: $i] :
( ( ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SY27 @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ SY27 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) ) ) ) )
| ~ ( in @ SV1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(13,plain,
! [SV2: $i] :
( ( ! [SY28: $i] :
~ ( ~ ~ ( ( ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SY28 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK3_SY7 @ SY28 @ SV2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK3_SY7 @ SY28 @ SV2 ) @ ( setadjoin @ ( sK4_SY26 @ SY28 @ SV2 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK4_SY26 @ SY28 @ SV2 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SY28 @ emptyset ) ) @ emptyset ) ) ) ) )
| ~ ( in @ ( sK3_SY7 @ SY28 @ SV2 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SY28 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(14,plain,
! [SV1: $i] :
( ( ( ! [SY27: $i] :
( ( ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SY27 @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ SY27 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true )
| ( ( ~ ( in @ SV1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[12]) ).
thf(15,plain,
! [SV3: $i,SV2: $i] :
( ( ~ ( ~ ~ ( ( ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK3_SY7 @ SV3 @ SV2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK3_SY7 @ SV3 @ SV2 ) @ ( setadjoin @ ( sK4_SY26 @ SV3 @ SV2 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK4_SY26 @ SV3 @ SV2 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) ) ) ) )
| ~ ( in @ ( sK3_SY7 @ SV3 @ SV2 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(16,plain,
! [SV4: $i,SV1: $i] :
( ( ( ( ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV4 @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ SV4 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true )
| ( ( ~ ( in @ SV1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(17,plain,
! [SV3: $i,SV2: $i] :
( ( ~ ~ ( ( ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK3_SY7 @ SV3 @ SV2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK3_SY7 @ SV3 @ SV2 ) @ ( setadjoin @ ( sK4_SY26 @ SV3 @ SV2 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK4_SY26 @ SV3 @ SV2 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) ) ) ) )
| ~ ( in @ ( sK3_SY7 @ SV3 @ SV2 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(18,plain,
! [SV4: $i,SV1: $i] :
( ( ( ( ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV4 @ emptyset ) ) @ emptyset ) ) ) )
= $true )
| ( ( ~ ( in @ SV4 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true )
| ( ( ~ ( in @ SV1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[16]) ).
thf(19,plain,
! [SV3: $i,SV2: $i] :
( ( ~ ~ ( ( ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK3_SY7 @ SV3 @ SV2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK3_SY7 @ SV3 @ SV2 ) @ ( setadjoin @ ( sK4_SY26 @ SV3 @ SV2 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK4_SY26 @ SV3 @ SV2 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(20,plain,
! [SV2: $i,SV3: $i] :
( ( ~ ( in @ ( sK3_SY7 @ SV3 @ SV2 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(21,plain,
! [SV4: $i,SV1: $i] :
( ( ( ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV4 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( ~ ( in @ SV4 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true )
| ( ( ~ ( in @ SV1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(22,plain,
! [SV3: $i,SV2: $i] :
( ( ~ ( ( ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK3_SY7 @ SV3 @ SV2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK3_SY7 @ SV3 @ SV2 ) @ ( setadjoin @ ( sK4_SY26 @ SV3 @ SV2 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK4_SY26 @ SV3 @ SV2 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(23,plain,
! [SV2: $i,SV3: $i] :
( ( in @ ( sK3_SY7 @ SV3 @ SV2 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(24,plain,
! [SV1: $i,SV4: $i] :
( ( ( in @ SV4 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV4 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( ~ ( in @ SV1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(25,plain,
! [SV3: $i,SV2: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK3_SY7 @ SV3 @ SV2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK3_SY7 @ SV3 @ SV2 ) @ ( setadjoin @ ( sK4_SY26 @ SV3 @ SV2 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK4_SY26 @ SV3 @ SV2 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(26,plain,
! [SV4: $i,SV1: $i] :
( ( ( in @ SV1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV4 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( in @ SV4 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(27,plain,
! [SV3: $i,SV2: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK3_SY7 @ SV3 @ SV2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK3_SY7 @ SV3 @ SV2 ) @ ( setadjoin @ ( sK4_SY26 @ SV3 @ SV2 ) @ emptyset ) ) @ emptyset ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(28,plain,
! [SV2: $i,SV3: $i] :
( ( ~ ( in @ ( sK4_SY26 @ SV3 @ SV2 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(29,plain,
! [SV3: $i,SV2: $i] :
( ( ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ ( sK3_SY7 @ SV3 @ SV2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK3_SY7 @ SV3 @ SV2 ) @ ( setadjoin @ ( sK4_SY26 @ SV3 @ SV2 ) @ emptyset ) ) @ emptyset ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(30,plain,
! [SV2: $i,SV3: $i] :
( ( in @ ( sK4_SY26 @ SV3 @ SV2 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(31,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[23,30,29,26]) ).
thf(32,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU620^2 : TPTP v8.1.0. Released v3.7.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 20 06:39:18 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 0
% 0.13/0.35
% 0.13/0.35 Length.of.Defs: 783
% 0.13/0.35
% 0.13/0.35 Contains.Choice.Funs: false
% 0.13/0.35 (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)...
% 0.19/0.43
% 0.19/0.43 ********************************
% 0.19/0.43 * All subproblems solved! *
% 0.19/0.43 ********************************
% 0.19/0.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,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:31,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.44
% 0.19/0.44 %**** Beginning of derivation protocol ****
% 0.19/0.44 % SZS output start CNFRefutation
% See solution above
% 0.19/0.44
% 0.19/0.44 %**** End of derivation protocol ****
% 0.19/0.44 %**** no. of clauses in derivation: 32 ****
% 0.19/0.44 %**** clause counter: 31 ****
% 0.19/0.44
% 0.19/0.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,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:31,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------