%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU547^2 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 10:44:57 AM UTC 2026
% Result : Theorem 0.10s 0.18s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 1
% Syntax : Number of formulae : 22 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 92 ( 41 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 102 ( 14 ~; 9 |; 0 &; 58 @)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 1 avg)
% Number of types : 2 ( 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 : 28 ( 0 ^; 28 !; 0 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY4,type,
sK2_SY4: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK4_SY9,type,
sK4_SY9: $i ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
=> ( in @ Xy @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inCongP) ).
thf(2,negated_conjecture,
( ( ! [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 ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [SY4: $i] :
( ( sK1_A = SY4 )
=> ! [SY5: $i,SY6: $i] :
( ( SY5 = SY6 )
=> ( ( in @ SY5 @ sK1_A )
=> ( in @ SY6 @ SY4 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ( sK1_A = sK2_SY4 )
=> ! [SY7: $i,SY8: $i] :
( ( SY7 = SY8 )
=> ( ( in @ SY7 @ sK1_A )
=> ( in @ SY8 @ sK2_SY4 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( sK1_A = sK2_SY4 )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [SY7: $i,SY8: $i] :
( ( SY7 = SY8 )
=> ( ( in @ SY7 @ sK1_A )
=> ( in @ SY8 @ sK2_SY4 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(8,plain,
( ( ~ ! [SY7: $i,SY8: $i] :
( ( SY7 = SY8 )
=> ( ( in @ SY7 @ sK1_A )
=> ( in @ SY8 @ sK2_SY4 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( sK1_A = sK2_SY4 )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(10,plain,
( ( ~ ! [SY7: $i,SY8: $i] :
( ( SY7 = SY8 )
=> ( ( in @ SY7 @ sK1_A )
=> ( in @ SY8 @ sK2_SY4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(11,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( in @ SX0 @ sK1_A )
| ( in @ SX1 @ sK2_SY4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(12,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( in @ SX0 @ sK1_A )
| ( in @ SX1 @ sK2_SY4 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(13,plain,
( ( ! [SY9: $i] :
( ( sK3_SX0 != SY9 )
| ~ ( in @ sK3_SX0 @ sK1_A )
| ( in @ SY9 @ sK2_SY4 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[12]) ).
thf(14,plain,
( ( ( sK3_SX0 != sK4_SY9 )
| ~ ( in @ sK3_SX0 @ sK1_A )
| ( in @ sK4_SY9 @ sK2_SY4 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[13]) ).
thf(15,plain,
( ( sK3_SX0 != sK4_SY9 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(16,plain,
( ( ~ ( in @ sK3_SX0 @ sK1_A )
| ( in @ sK4_SY9 @ sK2_SY4 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( sK3_SX0 = sK4_SY9 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(18,plain,
( ( ~ ( in @ sK3_SX0 @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(19,plain,
( ( in @ sK4_SY9 @ sK2_SY4 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(20,plain,
( ( in @ sK3_SX0 @ sK1_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[18]) ).
thf(21,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[9,20,19,17]) ).
thf(22,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU547^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.15 % Computer : n006.cluster.edu
% 0.10/0.15 % Model : x86_64 x86_64
% 0.10/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.15 % Memory : 8046.5625MB
% 0.10/0.15 % OS : Linux 6.8.0-71-generic
% 0.10/0.15 % CPULimit : 300
% 0.10/0.15 % WCLimit : 300
% 0.10/0.15 % DateTime : Tue Oct 6 15:27:37 UTC 2026
% 0.10/0.16 % CPUTime :
% 0.10/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.18
% 0.10/0.18 No.of.Axioms: 0
% 0.10/0.18
% 0.10/0.18 Length.of.Defs: 0
% 0.10/0.18
% 0.10/0.18 Contains.Choice.Funs: false
% 0.10/0.18
% 0.10/0.18 ********************************
% 0.10/0.18 * All subproblems solved! *
% 0.10/0.18 ********************************
% 0.10/0.18 % 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:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:21,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.10/0.18
% 0.10/0.18 %**** Beginning of derivation protocol ****
% 0.10/0.18 % SZS output start CNFRefutation
% See solution above
% 0.10/0.18
% 0.10/0.18 %**** End of derivation protocol ****
% 0.10/0.18 %**** no. of clauses in derivation: 22 ****
% 0.10/0.18 %**** clause counter: 21 ****
% 0.10/0.18
% 0.10/0.18 % 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:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:21,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------