%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU649^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:45:54 AM UTC 2026
% Result : Theorem 0.60s 0.28s
% Output : CNFRefutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of formulae : 70 ( 44 unt; 0 typ; 5 def)
% Number of atoms : 426 ( 194 equ; 0 cnn)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 644 ( 60 ~; 95 |; 0 &; 440 @)
% ( 0 <=>; 49 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 174 ( 0 ^; 174 !; 0 ?; 174 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_emptyset,type,
emptyset: $i ).
thf(tp_eqinunit,type,
eqinunit: $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK2_SY25,type,
sK2_SY25: $i ).
thf(tp_sK3_SY27,type,
sK3_SY27: $i > $i > $i ).
thf(tp_sK4_SY28,type,
sK4_SY28: $i > $i > $i ).
thf(tp_sK5_SY28,type,
sK5_SY28: $i > $i > $i ).
thf(tp_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(tp_setadjoinIL,type,
setadjoinIL: $o ).
thf(tp_setext,type,
setext: $o ).
thf(tp_uniqinunit,type,
uniqinunit: $o ).
thf(tp_upairset2E,type,
upairset2E: $o ).
thf(eqinunit,definition,
( eqinunit
= ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqinunit) ).
thf(setadjoinIL,definition,
( setadjoinIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL) ).
thf(setext,definition,
( setext
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setext) ).
thf(uniqinunit,definition,
( uniqinunit
= ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).
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,
( setext
=> ( setadjoinIL
=> ( uniqinunit
=> ( eqinunit
=> ( upairset2E
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR11) ).
thf(2,negated_conjecture,
( ( setext
=> ( setadjoinIL
=> ( uniqinunit
=> ( eqinunit
=> ( upairset2E
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( A = B ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,eqinunit,setadjoinIL,setext,uniqinunit,upairset2E]) ).
thf(4,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( A = B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,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(9,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xx @ emptyset ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(10,plain,
( ( ~ ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(11,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(12,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(13,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(14,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(15,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( A = B ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(16,plain,
( ( ~ ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(17,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
= ( setadjoin @ SX0 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16,eqinunit,setadjoinIL,setext,uniqinunit,upairset2E]) ).
thf(18,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13,eqinunit,setadjoinIL,setext,uniqinunit,upairset2E]) ).
thf(19,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12,eqinunit,setadjoinIL,setext,uniqinunit,upairset2E]) ).
thf(20,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) )
| ( SX2 = SX0 )
| ( SX2 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11,eqinunit,setadjoinIL,setext,uniqinunit,upairset2E]) ).
thf(21,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15,eqinunit,setadjoinIL,setext,uniqinunit,upairset2E]) ).
thf(22,plain,
! [SV1: $i] :
( ( ! [SY17: $i] : ( in @ SV1 @ ( setadjoin @ SV1 @ SY17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(23,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
= ( setadjoin @ SX0 @ emptyset ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(24,plain,
! [SV2: $i] :
( ( ! [SY18: $i] :
( ~ ( in @ SV2 @ ( setadjoin @ SY18 @ emptyset ) )
| ( SV2 = SY18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(25,plain,
! [SV3: $i] :
( ( ! [SY19: $i] :
( ( SV3 != SY19 )
| ( in @ SV3 @ ( setadjoin @ SY19 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(26,plain,
! [SV4: $i] :
( ( ! [SY20: $i,SY21: $i] :
( ~ ( in @ SY21 @ ( setadjoin @ SV4 @ ( setadjoin @ SY20 @ emptyset ) ) )
| ( SY21 = SV4 )
| ( SY21 = SY20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(27,plain,
! [SV5: $i] :
( ( ! [SY22: $i] :
( ~ ! [SY23: $i] :
( ~ ( in @ SY23 @ SV5 )
| ( in @ SY23 @ SY22 ) )
| ~ ! [SY24: $i] :
( ~ ( in @ SY24 @ SY22 )
| ( in @ SY24 @ SV5 ) )
| ( SV5 = SY22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(28,plain,
! [SV6: $i,SV1: $i] :
( ( in @ SV1 @ ( setadjoin @ SV1 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(29,plain,
( ( ! [SY25: $i] :
( ( sK1_SX0 != SY25 )
| ( ( setadjoin @ sK1_SX0 @ ( setadjoin @ SY25 @ emptyset ) )
= ( setadjoin @ sK1_SX0 @ emptyset ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[23]) ).
thf(30,plain,
! [SV7: $i,SV2: $i] :
( ( ~ ( in @ SV2 @ ( setadjoin @ SV7 @ emptyset ) )
| ( SV2 = SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(31,plain,
! [SV8: $i,SV3: $i] :
( ( ( SV3 != SV8 )
| ( in @ SV3 @ ( setadjoin @ SV8 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(32,plain,
! [SV9: $i,SV4: $i] :
( ( ! [SY26: $i] :
( ~ ( in @ SY26 @ ( setadjoin @ SV4 @ ( setadjoin @ SV9 @ emptyset ) ) )
| ( SY26 = SV4 )
| ( SY26 = SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(33,plain,
! [SV10: $i,SV5: $i] :
( ( ~ ! [SY27: $i] :
( ~ ( in @ SY27 @ SV5 )
| ( in @ SY27 @ SV10 ) )
| ~ ! [SY28: $i] :
( ~ ( in @ SY28 @ SV10 )
| ( in @ SY28 @ SV5 ) )
| ( SV5 = SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(34,plain,
( ( ( sK1_SX0 != sK2_SY25 )
| ( ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK2_SY25 @ emptyset ) )
= ( setadjoin @ sK1_SX0 @ emptyset ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[29]) ).
thf(35,plain,
! [SV7: $i,SV2: $i] :
( ( ( ~ ( in @ SV2 @ ( setadjoin @ SV7 @ emptyset ) ) )
= $true )
| ( ( SV2 = SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[30]) ).
thf(36,plain,
! [SV8: $i,SV3: $i] :
( ( ( SV3 != SV8 )
= $true )
| ( ( in @ SV3 @ ( setadjoin @ SV8 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(37,plain,
! [SV9: $i,SV4: $i,SV11: $i] :
( ( ~ ( in @ SV11 @ ( setadjoin @ SV4 @ ( setadjoin @ SV9 @ emptyset ) ) )
| ( SV11 = SV4 )
| ( SV11 = SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(38,plain,
! [SV10: $i,SV5: $i] :
( ( ( ~ ! [SY27: $i] :
( ~ ( in @ SY27 @ SV5 )
| ( in @ SY27 @ SV10 ) ) )
= $true )
| ( ( ~ ! [SY28: $i] :
( ~ ( in @ SY28 @ SV10 )
| ( in @ SY28 @ SV5 ) )
| ( SV5 = SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(39,plain,
( ( sK1_SX0 != sK2_SY25 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(40,plain,
( ( ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK2_SY25 @ emptyset ) )
= ( setadjoin @ sK1_SX0 @ emptyset ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(41,plain,
! [SV7: $i,SV2: $i] :
( ( ( in @ SV2 @ ( setadjoin @ SV7 @ emptyset ) )
= $false )
| ( ( SV2 = SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(42,plain,
! [SV8: $i,SV3: $i] :
( ( ( SV3 = SV8 )
= $false )
| ( ( in @ SV3 @ ( setadjoin @ SV8 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(43,plain,
! [SV9: $i,SV4: $i,SV11: $i] :
( ( ( ~ ( in @ SV11 @ ( setadjoin @ SV4 @ ( setadjoin @ SV9 @ emptyset ) ) ) )
= $true )
| ( ( ( SV11 = SV4 )
| ( SV11 = SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(44,plain,
! [SV10: $i,SV5: $i] :
( ( ( ! [SY27: $i] :
( ~ ( in @ SY27 @ SV5 )
| ( in @ SY27 @ SV10 ) ) )
= $false )
| ( ( ~ ! [SY28: $i] :
( ~ ( in @ SY28 @ SV10 )
| ( in @ SY28 @ SV5 ) )
| ( SV5 = SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(45,plain,
( ( sK1_SX0 = sK2_SY25 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[39]) ).
thf(46,plain,
! [SV9: $i,SV4: $i,SV11: $i] :
( ( ( in @ SV11 @ ( setadjoin @ SV4 @ ( setadjoin @ SV9 @ emptyset ) ) )
= $false )
| ( ( ( SV11 = SV4 )
| ( SV11 = SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(47,plain,
! [SV5: $i,SV10: $i] :
( ( ( ~ ( in @ ( sK3_SY27 @ SV10 @ SV5 ) @ SV5 )
| ( in @ ( sK3_SY27 @ SV10 @ SV5 ) @ SV10 ) )
= $false )
| ( ( ~ ! [SY28: $i] :
( ~ ( in @ SY28 @ SV10 )
| ( in @ SY28 @ SV5 ) )
| ( SV5 = SV10 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[44]) ).
thf(48,plain,
! [SV9: $i,SV4: $i,SV11: $i] :
( ( ( SV11 = SV4 )
= $true )
| ( ( SV11 = SV9 )
= $true )
| ( ( in @ SV11 @ ( setadjoin @ SV4 @ ( setadjoin @ SV9 @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(49,plain,
! [SV5: $i,SV10: $i] :
( ( ( ~ ( in @ ( sK3_SY27 @ SV10 @ SV5 ) @ SV5 ) )
= $false )
| ( ( ~ ! [SY28: $i] :
( ~ ( in @ SY28 @ SV10 )
| ( in @ SY28 @ SV5 ) )
| ( SV5 = SV10 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(50,plain,
! [SV5: $i,SV10: $i] :
( ( ( in @ ( sK3_SY27 @ SV10 @ SV5 ) @ SV10 )
= $false )
| ( ( ~ ! [SY28: $i] :
( ~ ( in @ SY28 @ SV10 )
| ( in @ SY28 @ SV5 ) )
| ( SV5 = SV10 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(51,plain,
! [SV5: $i,SV10: $i] :
( ( ( in @ ( sK3_SY27 @ SV10 @ SV5 ) @ SV5 )
= $true )
| ( ( ~ ! [SY28: $i] :
( ~ ( in @ SY28 @ SV10 )
| ( in @ SY28 @ SV5 ) )
| ( SV5 = SV10 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(52,plain,
! [SV5: $i,SV10: $i] :
( ( ( ~ ! [SY28: $i] :
( ~ ( in @ SY28 @ SV10 )
| ( in @ SY28 @ SV5 ) ) )
= $true )
| ( ( SV5 = SV10 )
= $true )
| ( ( in @ ( sK3_SY27 @ SV10 @ SV5 ) @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(53,plain,
! [SV5: $i,SV10: $i] :
( ( ( ~ ! [SY28: $i] :
( ~ ( in @ SY28 @ SV10 )
| ( in @ SY28 @ SV5 ) ) )
= $true )
| ( ( SV5 = SV10 )
= $true )
| ( ( in @ ( sK3_SY27 @ SV10 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(54,plain,
! [SV5: $i,SV10: $i] :
( ( ( ! [SY28: $i] :
( ~ ( in @ SY28 @ SV10 )
| ( in @ SY28 @ SV5 ) ) )
= $false )
| ( ( SV5 = SV10 )
= $true )
| ( ( in @ ( sK3_SY27 @ SV10 @ SV5 ) @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(55,plain,
! [SV5: $i,SV10: $i] :
( ( ( ! [SY28: $i] :
( ~ ( in @ SY28 @ SV10 )
| ( in @ SY28 @ SV5 ) ) )
= $false )
| ( ( SV5 = SV10 )
= $true )
| ( ( in @ ( sK3_SY27 @ SV10 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(56,plain,
! [SV10: $i,SV5: $i] :
( ( ( ~ ( in @ ( sK4_SY28 @ SV5 @ SV10 ) @ SV10 )
| ( in @ ( sK4_SY28 @ SV5 @ SV10 ) @ SV5 ) )
= $false )
| ( ( SV5 = SV10 )
= $true )
| ( ( in @ ( sK3_SY27 @ SV10 @ SV5 ) @ SV10 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[54]) ).
thf(57,plain,
! [SV10: $i,SV5: $i] :
( ( ( ~ ( in @ ( sK5_SY28 @ SV5 @ SV10 ) @ SV10 )
| ( in @ ( sK5_SY28 @ SV5 @ SV10 ) @ SV5 ) )
= $false )
| ( ( SV5 = SV10 )
= $true )
| ( ( in @ ( sK3_SY27 @ SV10 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[55]) ).
thf(58,plain,
! [SV10: $i,SV5: $i] :
( ( ( ~ ( in @ ( sK4_SY28 @ SV5 @ SV10 ) @ SV10 ) )
= $false )
| ( ( SV5 = SV10 )
= $true )
| ( ( in @ ( sK3_SY27 @ SV10 @ SV5 ) @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(59,plain,
! [SV10: $i,SV5: $i] :
( ( ( in @ ( sK4_SY28 @ SV5 @ SV10 ) @ SV5 )
= $false )
| ( ( SV5 = SV10 )
= $true )
| ( ( in @ ( sK3_SY27 @ SV10 @ SV5 ) @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(60,plain,
! [SV10: $i,SV5: $i] :
( ( ( ~ ( in @ ( sK5_SY28 @ SV5 @ SV10 ) @ SV10 ) )
= $false )
| ( ( SV5 = SV10 )
= $true )
| ( ( in @ ( sK3_SY27 @ SV10 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(61,plain,
! [SV10: $i,SV5: $i] :
( ( ( in @ ( sK5_SY28 @ SV5 @ SV10 ) @ SV5 )
= $false )
| ( ( SV5 = SV10 )
= $true )
| ( ( in @ ( sK3_SY27 @ SV10 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(62,plain,
! [SV10: $i,SV5: $i] :
( ( ( in @ ( sK4_SY28 @ SV5 @ SV10 ) @ SV10 )
= $true )
| ( ( SV5 = SV10 )
= $true )
| ( ( in @ ( sK3_SY27 @ SV10 @ SV5 ) @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[58]) ).
thf(63,plain,
! [SV10: $i,SV5: $i] :
( ( ( in @ ( sK5_SY28 @ SV5 @ SV10 ) @ SV10 )
= $true )
| ( ( SV5 = SV10 )
= $true )
| ( ( in @ ( sK3_SY27 @ SV10 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[60]) ).
thf(64,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[28,63,62,61,59,48,45,42,41,40]) ).
thf(65,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU649^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.02 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Oct 6 15:29:31 UTC 2026
% 0.10/0.11 % CPUTime :
% 0.10/0.12 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.60/0.28
% 0.60/0.28 No.of.Axioms: 0
% 0.60/0.28
% 0.60/0.28 Length.of.Defs: 963
% 0.60/0.28
% 0.60/0.28 Contains.Choice.Funs: false
% 0.60/0.28 ..
% 0.60/0.28
% 0.60/0.28 ********************************
% 0.60/0.28 * All subproblems solved! *
% 0.60/0.28 ********************************
% 0.60/0.28 % SZS status Theorem for /export/starexec/sandbox2/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:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:64,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.60/0.28
% 0.60/0.28 %**** Beginning of derivation protocol ****
% 0.60/0.28 % SZS output start CNFRefutation
% See solution above
% 0.60/0.28
% 0.60/0.28 %**** End of derivation protocol ****
% 0.60/0.28 %**** no. of clauses in derivation: 65 ****
% 0.60/0.28 %**** clause counter: 64 ****
% 0.60/0.28
% 0.60/0.28 % SZS status Theorem for /export/starexec/sandbox2/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:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:64,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------