%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU306+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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 10:43:53 AM UTC 2026
% Result : Theorem 0.07s 0.23s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 41 ( 37 unt; 0 typ; 0 def)
% Number of atoms : 120 ( 49 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 70 ( 9 ~; 4 |; 0 &; 50 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 5 con; 0-2 aty)
% Number of variables : 15 ( 0 ^; 12 !; 3 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cast_as_carrier_subset,type,
cast_as_carrier_subset: $i > $i ).
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_natural,type,
natural: $i > $o ).
thf(tp_one_sorted_str,type,
one_sorted_str: $i > $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_the_carrier,type,
the_carrier: $i > $i ).
thf(tp_v1_int_1,type,
v1_int_1: $i > $o ).
thf(tp_v1_membered,type,
v1_membered: $i > $o ).
thf(tp_v1_rat_1,type,
v1_rat_1: $i > $o ).
thf(tp_v1_xcmplx_0,type,
v1_xcmplx_0: $i > $o ).
thf(tp_v1_xreal_0,type,
v1_xreal_0: $i > $o ).
thf(tp_v2_membered,type,
v2_membered: $i > $o ).
thf(tp_v3_membered,type,
v3_membered: $i > $o ).
thf(tp_v4_membered,type,
v4_membered: $i > $o ).
thf(tp_v5_membered,type,
v5_membered: $i > $o ).
thf(1,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_pre_topc) ).
thf(2,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_struct_0) ).
thf(3,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_struct_0) ).
thf(5,axiom,
? [A: $i] : ( one_sorted_str @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(8,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(9,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(38,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(40,conjecture,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_pre_topc) ).
thf(41,negated_conjecture,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[40]) ).
thf(42,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[41]) ).
thf(43,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(44,plain,
$true = $true,
inference(unfold_def,[status(thm)],[2]) ).
thf(45,plain,
$true = $true,
inference(unfold_def,[status(thm)],[3]) ).
thf(46,plain,
( ( ? [A: $i] : ( one_sorted_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(47,plain,
$true = $true,
inference(unfold_def,[status(thm)],[8]) ).
thf(48,plain,
$true = $true,
inference(unfold_def,[status(thm)],[9]) ).
thf(49,plain,
$true = $true,
inference(unfold_def,[status(thm)],[38]) ).
thf(50,plain,
( ( ( one_sorted_str @ sK1_A )
=> ( ( cast_as_carrier_subset @ sK1_A )
= ( the_carrier @ sK1_A ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[42]) ).
thf(51,plain,
( ( one_sorted_str @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[50]) ).
thf(52,plain,
( ( ( cast_as_carrier_subset @ sK1_A )
= ( the_carrier @ sK1_A ) )
= $false ),
inference(standard_cnf,[status(thm)],[50]) ).
thf(53,plain,
( ( ( cast_as_carrier_subset @ sK1_A )
!= ( the_carrier @ sK1_A ) )
= $true ),
inference(polarity_switch,[status(thm)],[52]) ).
thf(54,plain,
$true = $true,
inference(copy,[status(thm)],[49]) ).
thf(55,plain,
$true = $true,
inference(copy,[status(thm)],[48]) ).
thf(56,plain,
$true = $true,
inference(copy,[status(thm)],[47]) ).
thf(57,plain,
( ( ? [A: $i] : ( one_sorted_str @ A ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(58,plain,
$true = $true,
inference(copy,[status(thm)],[45]) ).
thf(59,plain,
$true = $true,
inference(copy,[status(thm)],[44]) ).
thf(60,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(61,plain,
( ( one_sorted_str @ sK1_A )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(62,plain,
( ( ( cast_as_carrier_subset @ sK1_A )
!= ( the_carrier @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(63,plain,
( ( ~ ! [SX0: $i] :
~ ( one_sorted_str @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(64,plain,
( ( ! [SX0: $i] :
( ~ ( one_sorted_str @ SX0 )
| ( ( cast_as_carrier_subset @ SX0 )
= ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(65,plain,
( ( ( cast_as_carrier_subset @ sK1_A )
= ( the_carrier @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(66,plain,
( ( ! [SX0: $i] :
~ ( one_sorted_str @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(67,plain,
! [SV1: $i] :
( ( ~ ( one_sorted_str @ SV1 )
| ( ( cast_as_carrier_subset @ SV1 )
= ( the_carrier @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(68,plain,
( ( ~ ( one_sorted_str @ sK2_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[66]) ).
thf(69,plain,
! [SV1: $i] :
( ( ( ~ ( one_sorted_str @ SV1 ) )
= $true )
| ( ( ( cast_as_carrier_subset @ SV1 )
= ( the_carrier @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[67]) ).
thf(70,plain,
( ( one_sorted_str @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(71,plain,
! [SV1: $i] :
( ( ( one_sorted_str @ SV1 )
= $false )
| ( ( ( cast_as_carrier_subset @ SV1 )
= ( the_carrier @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(72,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[54,71,70,65,61,59,58,56,55]) ).
thf(73,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU306+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n016.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 15:18:02 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.23
% 0.07/0.23 No.of.Axioms: 7
% 0.07/0.23
% 0.07/0.23 Length.of.Defs: 0
% 0.07/0.23
% 0.07/0.23 Contains.Choice.Funs: false
% 0.07/0.23
% 0.07/0.23 ********************************
% 0.07/0.23 * All subproblems solved! *
% 0.07/0.23 ********************************
% 0.07/0.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:8,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:72,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.23
% 0.07/0.23 %**** Beginning of derivation protocol ****
% 0.07/0.23 % SZS output start CNFRefutation
% See solution above
% 0.07/0.23
% 0.07/0.23 %**** End of derivation protocol ****
% 0.07/0.23 %**** no. of clauses in derivation: 41 ****
% 0.07/0.23 %**** clause counter: 72 ****
% 0.07/0.23
% 0.07/0.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:8,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:72,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------