%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU552^2 : 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 : n003.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 10:45:01 AM UTC 2026
% Result : Theorem 0.10s 0.20s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 1
% Syntax : Number of formulae : 20 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 72 ( 52 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 86 ( 14 ~; 2 |; 2 &; 56 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 6 con; 0-2 aty)
% Number of variables : 21 ( 0 ^; 21 !; 0 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_sK1_Xx,type,
sK1_Xx: $i ).
thf(tp_sK2_SY4,type,
sK2_SY4: $i ).
thf(tp_sK3_SY7,type,
sK3_SY7: $i ).
thf(tp_sK4_SY9,type,
sK4_SY9: $i ).
thf(tp_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(1,conjecture,
! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ! [Xz: $i,Xu: $i] :
( ( Xz = Xu )
=> ( ( setadjoin @ Xx @ Xz )
= ( setadjoin @ Xy @ Xu ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoin__Cong) ).
thf(2,negated_conjecture,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ! [Xz: $i,Xu: $i] :
( ( Xz = Xu )
=> ( ( setadjoin @ Xx @ Xz )
= ( setadjoin @ Xy @ Xu ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ! [Xz: $i,Xu: $i] :
( ( Xz = Xu )
=> ( ( setadjoin @ Xx @ Xz )
= ( setadjoin @ Xy @ Xu ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [SY4: $i] :
( ( sK1_Xx = SY4 )
=> ! [SY5: $i,SY6: $i] :
( ( SY5 = SY6 )
=> ( ( setadjoin @ sK1_Xx @ SY5 )
= ( setadjoin @ SY4 @ SY6 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ( sK1_Xx = sK2_SY4 )
=> ! [SY7: $i,SY8: $i] :
( ( SY7 = SY8 )
=> ( ( setadjoin @ sK1_Xx @ SY7 )
= ( setadjoin @ sK2_SY4 @ SY8 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( sK1_Xx = sK2_SY4 )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [SY7: $i,SY8: $i] :
( ( SY7 = SY8 )
=> ( ( setadjoin @ sK1_Xx @ SY7 )
= ( setadjoin @ sK2_SY4 @ SY8 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(8,plain,
( ( ~ ! [SY7: $i,SY8: $i] :
( ( SY7 = SY8 )
=> ( ( setadjoin @ sK1_Xx @ SY7 )
= ( setadjoin @ sK2_SY4 @ SY8 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( ( sK3_SY7 = sK4_SY9 )
& ( ( setadjoin @ sK1_Xx @ sK3_SY7 )
!= ( setadjoin @ sK2_SY4 @ sK4_SY9 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(10,plain,
( ( sK1_Xx = sK2_SY4 )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(11,plain,
( ( ( sK3_SY7 = sK4_SY9 )
& ( ( setadjoin @ sK1_Xx @ sK3_SY7 )
!= ( setadjoin @ sK2_SY4 @ sK4_SY9 ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(12,plain,
( ( ~ ( ( sK3_SY7 != sK4_SY9 )
| ~ ( ( ( setadjoin @ sK1_Xx @ sK3_SY7 )
!= ( setadjoin @ sK2_SY4 @ sK4_SY9 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(13,plain,
( ( ( sK3_SY7 != sK4_SY9 )
| ~ ( ( ( setadjoin @ sK1_Xx @ sK3_SY7 )
!= ( setadjoin @ sK2_SY4 @ sK4_SY9 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(14,plain,
( ( sK3_SY7 != sK4_SY9 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(15,plain,
( ( ~ ( ( ( setadjoin @ sK1_Xx @ sK3_SY7 )
!= ( setadjoin @ sK2_SY4 @ sK4_SY9 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( sK3_SY7 = sK4_SY9 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( ( setadjoin @ sK1_Xx @ sK3_SY7 )
!= ( setadjoin @ sK2_SY4 @ sK4_SY9 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(18,plain,
( ( ( setadjoin @ sK1_Xx @ sK3_SY7 )
= ( setadjoin @ sK2_SY4 @ sK4_SY9 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(19,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[10,18,16]) ).
thf(20,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU552^2 : 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
% 0.10/0.17 % Computer : n003.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Oct 6 15:29:54 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.20
% 0.10/0.20 No.of.Axioms: 0
% 0.10/0.20
% 0.10/0.20 Length.of.Defs: 0
% 0.10/0.20
% 0.10/0.20 Contains.Choice.Funs: false
% 0.10/0.20
% 0.10/0.20 ********************************
% 0.10/0.20 * All subproblems solved! *
% 0.10/0.20 ********************************
% 0.10/0.20 % 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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:19,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.10/0.20
% 0.10/0.20 %**** Beginning of derivation protocol ****
% 0.10/0.20 % SZS output start CNFRefutation
% See solution above
% 0.10/0.20
% 0.10/0.20 %**** End of derivation protocol ****
% 0.10/0.20 %**** no. of clauses in derivation: 20 ****
% 0.10/0.20 %**** clause counter: 19 ****
% 0.10/0.20
% 0.10/0.20 % 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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:19,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------