%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU553^2 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 0.11s 0.20s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 13 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 40 ( 27 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 25 ( 2 ~; 0 |; 0 &; 18 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 4 con; 0-2 aty)
% Number of variables : 7 ( 0 ^; 7 !; 0 ?; 7 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY2,type,
sK2_SY2: $i ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( A = B )
=> ( ( powerset @ A )
= ( powerset @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powerset__Cong) ).
thf(2,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( powerset @ A )
= ( powerset @ B ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( powerset @ A )
= ( powerset @ B ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [SY2: $i] :
( ( sK1_A = SY2 )
=> ( ( powerset @ sK1_A )
= ( powerset @ SY2 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ( sK1_A = sK2_SY2 )
=> ( ( powerset @ sK1_A )
= ( powerset @ sK2_SY2 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( sK1_A = sK2_SY2 )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(7,plain,
( ( ( powerset @ sK1_A )
= ( powerset @ sK2_SY2 ) )
= $false ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(8,plain,
( ( ( powerset @ sK1_A )
!= ( powerset @ sK2_SY2 ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( sK1_A = sK2_SY2 )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(10,plain,
( ( ( powerset @ sK1_A )
!= ( powerset @ sK2_SY2 ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(11,plain,
( ( ( powerset @ sK1_A )
= ( powerset @ sK2_SY2 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[10]) ).
thf(12,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[9,11]) ).
thf(13,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU553^2 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.17 % Computer : n020.cluster.edu
% 0.11/0.17 % Model : x86_64 x86_64
% 0.11/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.17 % Memory : 8046.5625MB
% 0.11/0.17 % OS : Linux 6.8.0-71-generic
% 0.11/0.17 % CPULimit : 300
% 0.11/0.17 % WCLimit : 300
% 0.11/0.17 % DateTime : Tue Oct 6 15:28:51 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.20
% 0.11/0.20 No.of.Axioms: 0
% 0.11/0.20
% 0.11/0.20 Length.of.Defs: 0
% 0.11/0.20
% 0.11/0.20 Contains.Choice.Funs: false
% 0.11/0.20
% 0.11/0.20 ********************************
% 0.11/0.20 * All subproblems solved! *
% 0.11/0.20 ********************************
% 0.11/0.20 % SZS status Theorem for /export/starexec/sandbox/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:12,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.11/0.20
% 0.11/0.20 %**** Beginning of derivation protocol ****
% 0.11/0.20 % SZS output start CNFRefutation
% See solution above
% 0.11/0.20
% 0.11/0.20 %**** End of derivation protocol ****
% 0.11/0.20 %**** no. of clauses in derivation: 13 ****
% 0.11/0.20 %**** clause counter: 12 ****
% 0.11/0.20
% 0.11/0.20 % SZS status Theorem for /export/starexec/sandbox/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:12,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------