%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET883+1 : TPTP v9.3.1. Released v3.2.0.
% 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 : n004.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 10:42:28 AM UTC 2026
% Result : Theorem 0.07s 0.21s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 31 unt; 0 typ; 0 def)
% Number of atoms : 110 ( 48 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 103 ( 11 ~; 6 |; 0 &; 79 @)
% ( 0 <=>; 7 =>; 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 : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 34 ( 0 ^; 30 !; 4 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY8,type,
sK2_SY8: $i ).
thf(tp_sK3_A,type,
sK3_A: $i ).
thf(tp_sK4_A,type,
sK4_A: $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(1,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(2,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(3,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(4,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(5,conjecture,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_zfmisc_1) ).
thf(6,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[5]) ).
thf(7,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ) )
= $false ),
inference(unfold_def,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(9,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(10,plain,
( ( ? [A: $i] : ( empty @ 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] :
( ( subset @ ( singleton @ sK1_A ) @ ( singleton @ SY8 ) )
=> ( sK1_A = SY8 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[7]) ).
thf(13,plain,
( ( ( subset @ ( singleton @ sK1_A ) @ ( singleton @ sK2_SY8 ) )
=> ( sK1_A = sK2_SY8 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[12]) ).
thf(14,plain,
( ( subset @ ( singleton @ sK1_A ) @ ( singleton @ sK2_SY8 ) )
= $true ),
inference(standard_cnf,[status(thm)],[13]) ).
thf(15,plain,
( ( sK1_A = sK2_SY8 )
= $false ),
inference(standard_cnf,[status(thm)],[13]) ).
thf(16,plain,
( ( sK1_A != sK2_SY8 )
= $true ),
inference(polarity_switch,[status(thm)],[15]) ).
thf(17,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(18,plain,
( ( ~ ( empty @ sK3_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(19,plain,
( ( empty @ sK4_A )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(20,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(21,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(22,plain,
( ( empty @ sK4_A )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(23,plain,
( ( ~ ( empty @ sK3_A ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(24,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(25,plain,
( ( subset @ ( singleton @ sK1_A ) @ ( singleton @ sK2_SY8 ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(26,plain,
( ( sK1_A != sK2_SY8 )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(27,plain,
! [SV1: $i] :
( ( subset @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(28,plain,
( ( empty @ sK3_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(29,plain,
! [SV2: $i] :
( ( ! [SY9: $i] :
( ~ ( subset @ ( singleton @ SV2 ) @ ( singleton @ SY9 ) )
| ( SV2 = SY9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(30,plain,
( ( sK1_A = sK2_SY8 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(31,plain,
! [SV3: $i,SV2: $i] :
( ( ~ ( subset @ ( singleton @ SV2 ) @ ( singleton @ SV3 ) )
| ( SV2 = SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(32,plain,
! [SV3: $i,SV2: $i] :
( ( ( ~ ( subset @ ( singleton @ SV2 ) @ ( singleton @ SV3 ) ) )
= $true )
| ( ( SV2 = SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(33,plain,
! [SV3: $i,SV2: $i] :
( ( ( subset @ ( singleton @ SV2 ) @ ( singleton @ SV3 ) )
= $false )
| ( ( SV2 = SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(34,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[22,33,30,28,27,25]) ).
thf(35,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET883+1 : TPTP v9.3.1. Released v3.2.0.
% 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 : n004.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 14:55:39 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
% 0.07/0.21
% 0.07/0.21 No.of.Axioms: 4
% 0.07/0.21
% 0.07/0.21 Length.of.Defs: 0
% 0.07/0.21
% 0.07/0.21 Contains.Choice.Funs: false
% 0.07/0.21
% 0.07/0.21 ********************************
% 0.07/0.21 * All subproblems solved! *
% 0.07/0.21 ********************************
% 0.07/0.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:5,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:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:34,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 0.07/0.21
% 0.07/0.21 %**** Beginning of derivation protocol ****
% 0.07/0.21 % SZS output start CNFRefutation
% See solution above
% 0.07/0.21
% 0.07/0.21 %**** End of derivation protocol ****
% 0.07/0.21 %**** no. of clauses in derivation: 35 ****
% 0.07/0.21 %**** clause counter: 34 ****
% 0.07/0.21
% 0.07/0.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:5,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:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:34,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------