%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU548^2 : TPTP v9.3.1. Bugfixed v4.0.0.
% 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 : n018.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 10:44:58 AM UTC 2026
% Result : Theorem 0.11s 0.19s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 2
% Syntax : Number of formulae : 48 ( 26 unt; 0 typ; 1 def)
% Number of atoms : 320 ( 130 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 452 ( 100 ~; 93 |; 0 &; 226 @)
% ( 6 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 7 con; 0-2 aty)
% Number of variables : 100 ( 0 ^; 100 !; 0 ?; 100 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_inCongP,type,
inCongP: $o ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK2_SY15,type,
sK2_SY15: $i ).
thf(tp_sK3_SY20,type,
sK3_SY20: $i ).
thf(tp_sK4_SY22,type,
sK4_SY22: $i ).
thf(inCongP,definition,
( inCongP
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
=> ( in @ Xy @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inCongP) ).
thf(1,conjecture,
( inCongP
=> ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
<=> ( in @ Xy @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in__Cong) ).
thf(2,negated_conjecture,
( ( inCongP
=> ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
<=> ( in @ Xy @ B ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
=> ( in @ Xy @ B ) ) ) )
=> ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
<=> ( in @ Xy @ B ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,inCongP]) ).
thf(4,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
=> ( in @ Xy @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
<=> ( in @ Xy @ B ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ~ ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
<=> ( in @ Xy @ B ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
=> ( in @ Xy @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(8,plain,
( ( ~ ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
<=> ( in @ Xy @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ~ ( ~ ( ~ ( in @ SX2 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ~ ( ~ ( in @ SX3 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8,inCongP]) ).
thf(10,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX3 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7,inCongP]) ).
thf(11,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ~ ( ~ ( ~ ( in @ SX2 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ~ ( ~ ( in @ SX3 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9]) ).
thf(12,plain,
! [SV1: $i] :
( ( ! [SY12: $i] :
( ( SV1 != SY12 )
| ! [SY13: $i,SY14: $i] :
( ( SY13 != SY14 )
| ~ ( in @ SY13 @ SV1 )
| ( in @ SY14 @ SY12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(13,plain,
( ( ! [SY15: $i] :
( ( sK1_SX0 != SY15 )
| ! [SY16: $i,SY17: $i] :
( ( SY16 != SY17 )
| ~ ( ~ ( ~ ( in @ SY16 @ sK1_SX0 )
| ( in @ SY17 @ SY15 ) )
| ~ ( ~ ( in @ SY17 @ SY15 )
| ( in @ SY16 @ sK1_SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[11]) ).
thf(14,plain,
! [SV2: $i,SV1: $i] :
( ( ( SV1 != SV2 )
| ! [SY18: $i,SY19: $i] :
( ( SY18 != SY19 )
| ~ ( in @ SY18 @ SV1 )
| ( in @ SY19 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( ( sK1_SX0 != sK2_SY15 )
| ! [SY20: $i,SY21: $i] :
( ( SY20 != SY21 )
| ~ ( ~ ( ~ ( in @ SY20 @ sK1_SX0 )
| ( in @ SY21 @ sK2_SY15 ) )
| ~ ( ~ ( in @ SY21 @ sK2_SY15 )
| ( in @ SY20 @ sK1_SX0 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[13]) ).
thf(16,plain,
! [SV2: $i,SV1: $i] :
( ( ( SV1 != SV2 )
= $true )
| ( ( ! [SY18: $i,SY19: $i] :
( ( SY18 != SY19 )
| ~ ( in @ SY18 @ SV1 )
| ( in @ SY19 @ SV2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[14]) ).
thf(17,plain,
( ( sK1_SX0 != sK2_SY15 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[15]) ).
thf(18,plain,
( ( ! [SY20: $i,SY21: $i] :
( ( SY20 != SY21 )
| ~ ( ~ ( ~ ( in @ SY20 @ sK1_SX0 )
| ( in @ SY21 @ sK2_SY15 ) )
| ~ ( ~ ( in @ SY21 @ sK2_SY15 )
| ( in @ SY20 @ sK1_SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[15]) ).
thf(19,plain,
! [SV2: $i,SV1: $i] :
( ( ( SV1 = SV2 )
= $false )
| ( ( ! [SY18: $i,SY19: $i] :
( ( SY18 != SY19 )
| ~ ( in @ SY18 @ SV1 )
| ( in @ SY19 @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(20,plain,
( ( sK1_SX0 = sK2_SY15 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(21,plain,
( ( ! [SY22: $i] :
( ( sK3_SY20 != SY22 )
| ~ ( ~ ( ~ ( in @ sK3_SY20 @ sK1_SX0 )
| ( in @ SY22 @ sK2_SY15 ) )
| ~ ( ~ ( in @ SY22 @ sK2_SY15 )
| ( in @ sK3_SY20 @ sK1_SX0 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[18]) ).
thf(22,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ! [SY23: $i] :
( ( SV3 != SY23 )
| ~ ( in @ SV3 @ SV1 )
| ( in @ SY23 @ SV2 ) ) )
= $true )
| ( ( SV1 = SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(23,plain,
( ( ( sK3_SY20 != sK4_SY22 )
| ~ ( ~ ( ~ ( in @ sK3_SY20 @ sK1_SX0 )
| ( in @ sK4_SY22 @ sK2_SY15 ) )
| ~ ( ~ ( in @ sK4_SY22 @ sK2_SY15 )
| ( in @ sK3_SY20 @ sK1_SX0 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[21]) ).
thf(24,plain,
! [SV2: $i,SV1: $i,SV4: $i,SV3: $i] :
( ( ( ( SV3 != SV4 )
| ~ ( in @ SV3 @ SV1 )
| ( in @ SV4 @ SV2 ) )
= $true )
| ( ( SV1 = SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(25,plain,
( ( sK3_SY20 != sK4_SY22 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[23]) ).
thf(26,plain,
( ( ~ ( ~ ( ~ ( in @ sK3_SY20 @ sK1_SX0 )
| ( in @ sK4_SY22 @ sK2_SY15 ) )
| ~ ( ~ ( in @ sK4_SY22 @ sK2_SY15 )
| ( in @ sK3_SY20 @ sK1_SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[23]) ).
thf(27,plain,
! [SV2: $i,SV1: $i,SV4: $i,SV3: $i] :
( ( ( SV3 != SV4 )
= $true )
| ( ( ~ ( in @ SV3 @ SV1 )
| ( in @ SV4 @ SV2 ) )
= $true )
| ( ( SV1 = SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(28,plain,
( ( sK3_SY20 = sK4_SY22 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(29,plain,
( ( ~ ( ~ ( in @ sK3_SY20 @ sK1_SX0 )
| ( in @ sK4_SY22 @ sK2_SY15 ) )
| ~ ( ~ ( in @ sK4_SY22 @ sK2_SY15 )
| ( in @ sK3_SY20 @ sK1_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(30,plain,
! [SV2: $i,SV1: $i,SV4: $i,SV3: $i] :
( ( ( SV3 = SV4 )
= $false )
| ( ( ~ ( in @ SV3 @ SV1 )
| ( in @ SV4 @ SV2 ) )
= $true )
| ( ( SV1 = SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(31,plain,
( ( ( ~ ( ~ ( in @ sK3_SY20 @ sK1_SX0 )
| ( in @ sK4_SY22 @ sK2_SY15 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ sK4_SY22 @ sK2_SY15 )
| ( in @ sK3_SY20 @ sK1_SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(32,plain,
! [SV2: $i,SV4: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV1 ) )
= $true )
| ( ( in @ SV4 @ SV2 )
= $true )
| ( ( SV3 = SV4 )
= $false )
| ( ( SV1 = SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[30]) ).
thf(33,plain,
( ( ( ~ ( in @ sK3_SY20 @ sK1_SX0 )
| ( in @ sK4_SY22 @ sK2_SY15 ) )
= $false )
| ( ( ~ ( ~ ( in @ sK4_SY22 @ sK2_SY15 )
| ( in @ sK3_SY20 @ sK1_SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(34,plain,
! [SV2: $i,SV4: $i,SV1: $i,SV3: $i] :
( ( ( in @ SV3 @ SV1 )
= $false )
| ( ( in @ SV4 @ SV2 )
= $true )
| ( ( SV3 = SV4 )
= $false )
| ( ( SV1 = SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(35,plain,
( ( ( ~ ( in @ sK3_SY20 @ sK1_SX0 ) )
= $false )
| ( ( ~ ( ~ ( in @ sK4_SY22 @ sK2_SY15 )
| ( in @ sK3_SY20 @ sK1_SX0 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[33]) ).
thf(36,plain,
( ( ( in @ sK4_SY22 @ sK2_SY15 )
= $false )
| ( ( ~ ( ~ ( in @ sK4_SY22 @ sK2_SY15 )
| ( in @ sK3_SY20 @ sK1_SX0 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[33]) ).
thf(37,plain,
( ( ( in @ sK3_SY20 @ sK1_SX0 )
= $true )
| ( ( ~ ( ~ ( in @ sK4_SY22 @ sK2_SY15 )
| ( in @ sK3_SY20 @ sK1_SX0 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(38,plain,
( ( ( ~ ( in @ sK4_SY22 @ sK2_SY15 )
| ( in @ sK3_SY20 @ sK1_SX0 ) )
= $false )
| ( ( in @ sK4_SY22 @ sK2_SY15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(39,plain,
( ( ( ~ ( in @ sK4_SY22 @ sK2_SY15 )
| ( in @ sK3_SY20 @ sK1_SX0 ) )
= $false )
| ( ( in @ sK3_SY20 @ sK1_SX0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(40,plain,
( ( ( ~ ( in @ sK4_SY22 @ sK2_SY15 ) )
= $false )
| ( ( in @ sK4_SY22 @ sK2_SY15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(41,plain,
( ( ( in @ sK3_SY20 @ sK1_SX0 )
= $false )
| ( ( in @ sK4_SY22 @ sK2_SY15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(42,plain,
( ( ( ~ ( in @ sK4_SY22 @ sK2_SY15 ) )
= $false )
| ( ( in @ sK3_SY20 @ sK1_SX0 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(43,plain,
( ( ( in @ sK3_SY20 @ sK1_SX0 )
= $false )
| ( ( in @ sK3_SY20 @ sK1_SX0 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(44,plain,
( ( ( in @ sK4_SY22 @ sK2_SY15 )
= $true )
| ( ( in @ sK4_SY22 @ sK2_SY15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(45,plain,
( ( ( in @ sK4_SY22 @ sK2_SY15 )
= $true )
| ( ( in @ sK3_SY20 @ sK1_SX0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(46,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[20,45,44,43,41,34,28]) ).
thf(47,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU548^2 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.16 % Computer : n018.cluster.edu
% 0.11/0.16 % Model : x86_64 x86_64
% 0.11/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.16 % Memory : 8046.5625MB
% 0.11/0.16 % OS : Linux 6.8.0-71-generic
% 0.11/0.16 % CPULimit : 300
% 0.11/0.16 % WCLimit : 300
% 0.11/0.16 % DateTime : Tue Oct 6 15:30:22 UTC 2026
% 0.11/0.16 % CPUTime :
% 0.11/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.19
% 0.11/0.19 No.of.Axioms: 0
% 0.11/0.19
% 0.11/0.19 Length.of.Defs: 196
% 0.11/0.19
% 0.11/0.19 Contains.Choice.Funs: false
% 0.11/0.19 .
% 0.11/0.19
% 0.11/0.19 ********************************
% 0.11/0.19 * All subproblems solved! *
% 0.11/0.19 ********************************
% 0.11/0.19 % 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:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:46,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.11/0.19
% 0.11/0.19 %**** Beginning of derivation protocol ****
% 0.11/0.19 % SZS output start CNFRefutation
% See solution above
% 0.11/0.19
% 0.11/0.19 %**** End of derivation protocol ****
% 0.11/0.19 %**** no. of clauses in derivation: 47 ****
% 0.11/0.19 %**** clause counter: 46 ****
% 0.11/0.19
% 0.11/0.19 % 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:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:46,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------