%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU163+1 : TPTP v9.3.1. Released v3.3.0.
% 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 : n007.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 10:43:11 AM UTC 2026
% Result : Theorem 0.08s 0.18s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 30 unt; 0 typ; 0 def)
% Number of atoms : 134 ( 37 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 167 ( 18 ~; 11 |; 0 &; 127 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 50 ( 0 ^; 50 !; 0 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY8,type,
sK2_SY8: $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_union,type,
union: $i > $i ).
thf(1,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l50_zfmisc_1) ).
thf(2,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_tarski) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(4,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(5,conjecture,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_zfmisc_1) ).
thf(6,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[5]) ).
thf(7,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(9,plain,
$true = $true,
inference(unfold_def,[status(thm)],[2]) ).
thf(10,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(11,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(12,plain,
( ( ! [SY8: $i] :
( ( in @ sK1_A @ SY8 )
=> ( subset @ sK1_A @ ( union @ SY8 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[7]) ).
thf(13,plain,
( ( ( in @ sK1_A @ sK2_SY8 )
=> ( subset @ sK1_A @ ( union @ sK2_SY8 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[12]) ).
thf(14,plain,
( ( in @ sK1_A @ sK2_SY8 )
= $true ),
inference(standard_cnf,[status(thm)],[13]) ).
thf(15,plain,
( ( subset @ sK1_A @ ( union @ sK2_SY8 ) )
= $false ),
inference(standard_cnf,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ( subset @ sK1_A @ ( union @ sK2_SY8 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[15]) ).
thf(17,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(18,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(19,plain,
$true = $true,
inference(copy,[status(thm)],[9]) ).
thf(20,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(21,plain,
( ( in @ sK1_A @ sK2_SY8 )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(22,plain,
( ( ~ ( subset @ sK1_A @ ( union @ sK2_SY8 ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(23,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ SX0 @ ( union @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(24,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(25,plain,
! [SV1: $i] :
( ( ! [SY9: $i] : ( subset @ SV1 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(26,plain,
( ( subset @ sK1_A @ ( union @ sK2_SY8 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(27,plain,
! [SV2: $i] :
( ( ! [SY10: $i] :
( ~ ( in @ SV2 @ SY10 )
| ( subset @ SV2 @ ( union @ SY10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(28,plain,
! [SV3: $i] :
( ( ! [SY11: $i] :
( ~ ( in @ SV3 @ SY11 )
| ~ ( in @ SY11 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(29,plain,
! [SV1: $i] :
( ( subset @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(30,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ( in @ SV2 @ SV5 )
| ( subset @ SV2 @ ( union @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(31,plain,
! [SV6: $i,SV3: $i] :
( ( ~ ( in @ SV3 @ SV6 )
| ~ ( in @ SV6 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(32,plain,
! [SV5: $i,SV2: $i] :
( ( ( ~ ( in @ SV2 @ SV5 ) )
= $true )
| ( ( subset @ SV2 @ ( union @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[30]) ).
thf(33,plain,
! [SV6: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV6 ) )
= $true )
| ( ( ~ ( in @ SV6 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(34,plain,
! [SV5: $i,SV2: $i] :
( ( ( in @ SV2 @ SV5 )
= $false )
| ( ( subset @ SV2 @ ( union @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(35,plain,
! [SV6: $i,SV3: $i] :
( ( ( in @ SV3 @ SV6 )
= $false )
| ( ( ~ ( in @ SV6 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(36,plain,
! [SV3: $i,SV6: $i] :
( ( ( in @ SV6 @ SV3 )
= $false )
| ( ( in @ SV3 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(37,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[19,36,34,29,26,21]) ).
thf(38,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU163+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.14 % Computer : n007.cluster.edu
% 0.08/0.14 % Model : x86_64 x86_64
% 0.08/0.14 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.14 % Memory : 8046.5625MB
% 0.08/0.14 % OS : Linux 6.8.0-71-generic
% 0.08/0.15 % CPULimit : 300
% 0.08/0.15 % WCLimit : 300
% 0.08/0.15 % DateTime : Tue Oct 6 15:00:30 UTC 2026
% 0.08/0.15 % CPUTime :
% 0.08/0.15 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.18
% 0.08/0.18 No.of.Axioms: 4
% 0.08/0.18
% 0.08/0.18 Length.of.Defs: 0
% 0.08/0.18
% 0.08/0.18 Contains.Choice.Funs: false
% 0.08/0.18
% 0.08/0.18 ********************************
% 0.08/0.18 * All subproblems solved! *
% 0.08/0.18 ********************************
% 0.08/0.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:5,ps:0,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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:37,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.18
% 0.08/0.18 %**** Beginning of derivation protocol ****
% 0.08/0.18 % SZS output start CNFRefutation
% See solution above
% 0.08/0.18
% 0.08/0.18 %**** End of derivation protocol ****
% 0.08/0.18 %**** no. of clauses in derivation: 38 ****
% 0.08/0.18 %**** clause counter: 37 ****
% 0.08/0.18
% 0.08/0.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:5,ps:0,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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:37,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------