%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU152+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 : n009.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 10:43:06 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 66 ( 53 unt; 0 typ; 0 def)
% Number of atoms : 241 ( 92 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 334 ( 45 ~; 31 |; 0 &; 244 @)
% ( 3 <=>; 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 : 9 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 99 ( 0 ^; 99 !; 0 ?; 99 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY14,type,
sK2_SY14: $i ).
thf(tp_set_union2,type,
set_union2: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(1,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(2,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(5,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_xboole_0) ).
thf(6,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(9,conjecture,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l23_zfmisc_1) ).
thf(10,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[9]) ).
thf(11,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $false ),
inference(unfold_def,[status(thm)],[10]) ).
thf(12,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(13,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(14,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(15,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(16,plain,
$true = $true,
inference(unfold_def,[status(thm)],[5]) ).
thf(17,plain,
$true = $true,
inference(unfold_def,[status(thm)],[6]) ).
thf(18,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(19,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(20,plain,
( ( ! [SY14: $i] :
( ( in @ sK1_A @ SY14 )
=> ( ( set_union2 @ ( singleton @ sK1_A ) @ SY14 )
= SY14 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[11]) ).
thf(21,plain,
( ( ( in @ sK1_A @ sK2_SY14 )
=> ( ( set_union2 @ ( singleton @ sK1_A ) @ sK2_SY14 )
= sK2_SY14 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[20]) ).
thf(22,plain,
( ( in @ sK1_A @ sK2_SY14 )
= $true ),
inference(standard_cnf,[status(thm)],[21]) ).
thf(23,plain,
( ( ( set_union2 @ ( singleton @ sK1_A ) @ sK2_SY14 )
= sK2_SY14 )
= $false ),
inference(standard_cnf,[status(thm)],[21]) ).
thf(24,plain,
( ( ( set_union2 @ ( singleton @ sK1_A ) @ sK2_SY14 )
!= sK2_SY14 )
= $true ),
inference(polarity_switch,[status(thm)],[23]) ).
thf(25,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(26,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(27,plain,
$true = $true,
inference(copy,[status(thm)],[17]) ).
thf(28,plain,
$true = $true,
inference(copy,[status(thm)],[16]) ).
thf(29,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(30,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(31,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(32,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(33,plain,
( ( in @ sK1_A @ sK2_SY14 )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(34,plain,
( ( ( set_union2 @ ( singleton @ sK1_A ) @ sK2_SY14 )
!= sK2_SY14 )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(35,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) )
| ~ ( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(36,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(37,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_union2 @ SX0 @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(38,plain,
! [SV1: $i] :
( ( ! [SY15: $i] :
( ( set_union2 @ SV1 @ SY15 )
= ( set_union2 @ SY15 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(39,plain,
! [SV2: $i] :
( ( ! [SY16: $i] :
( ( set_union2 @ SV2 @ SV2 )
= SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(40,plain,
! [SV3: $i] :
( ( ! [SY17: $i] : ( subset @ SV3 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(41,plain,
( ( ( set_union2 @ ( singleton @ sK1_A ) @ sK2_SY14 )
= sK2_SY14 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(42,plain,
! [SV4: $i] :
( ( ! [SY18: $i] :
~ ( ~ ( ~ ( subset @ ( singleton @ SV4 ) @ SY18 )
| ( in @ SV4 @ SY18 ) )
| ~ ( ~ ( in @ SV4 @ SY18 )
| ( subset @ ( singleton @ SV4 ) @ SY18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(43,plain,
! [SV5: $i] :
( ( ! [SY19: $i] :
( ~ ( in @ SV5 @ SY19 )
| ~ ( in @ SY19 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(44,plain,
! [SV6: $i] :
( ( ! [SY20: $i] :
( ~ ( subset @ SV6 @ SY20 )
| ( ( set_union2 @ SV6 @ SY20 )
= SY20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(45,plain,
! [SV7: $i,SV1: $i] :
( ( ( set_union2 @ SV1 @ SV7 )
= ( set_union2 @ SV7 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(46,plain,
! [SV2: $i] :
( ( ( set_union2 @ SV2 @ SV2 )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(47,plain,
! [SV3: $i] :
( ( subset @ SV3 @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(48,plain,
! [SV10: $i,SV4: $i] :
( ( ~ ( ~ ( ~ ( subset @ ( singleton @ SV4 ) @ SV10 )
| ( in @ SV4 @ SV10 ) )
| ~ ( ~ ( in @ SV4 @ SV10 )
| ( subset @ ( singleton @ SV4 ) @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(49,plain,
! [SV11: $i,SV5: $i] :
( ( ~ ( in @ SV5 @ SV11 )
| ~ ( in @ SV11 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(50,plain,
! [SV12: $i,SV6: $i] :
( ( ~ ( subset @ SV6 @ SV12 )
| ( ( set_union2 @ SV6 @ SV12 )
= SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(51,plain,
! [SV10: $i,SV4: $i] :
( ( ~ ( ~ ( subset @ ( singleton @ SV4 ) @ SV10 )
| ( in @ SV4 @ SV10 ) )
| ~ ( ~ ( in @ SV4 @ SV10 )
| ( subset @ ( singleton @ SV4 ) @ SV10 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(52,plain,
! [SV11: $i,SV5: $i] :
( ( ( ~ ( in @ SV5 @ SV11 ) )
= $true )
| ( ( ~ ( in @ SV11 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(53,plain,
! [SV12: $i,SV6: $i] :
( ( ( ~ ( subset @ SV6 @ SV12 ) )
= $true )
| ( ( ( set_union2 @ SV6 @ SV12 )
= SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(54,plain,
! [SV10: $i,SV4: $i] :
( ( ~ ( ~ ( subset @ ( singleton @ SV4 ) @ SV10 )
| ( in @ SV4 @ SV10 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[51]) ).
thf(55,plain,
! [SV10: $i,SV4: $i] :
( ( ~ ( ~ ( in @ SV4 @ SV10 )
| ( subset @ ( singleton @ SV4 ) @ SV10 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[51]) ).
thf(56,plain,
! [SV11: $i,SV5: $i] :
( ( ( in @ SV5 @ SV11 )
= $false )
| ( ( ~ ( in @ SV11 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(57,plain,
! [SV12: $i,SV6: $i] :
( ( ( subset @ SV6 @ SV12 )
= $false )
| ( ( ( set_union2 @ SV6 @ SV12 )
= SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(58,plain,
! [SV10: $i,SV4: $i] :
( ( ~ ( subset @ ( singleton @ SV4 ) @ SV10 )
| ( in @ SV4 @ SV10 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(59,plain,
! [SV10: $i,SV4: $i] :
( ( ~ ( in @ SV4 @ SV10 )
| ( subset @ ( singleton @ SV4 ) @ SV10 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(60,plain,
! [SV5: $i,SV11: $i] :
( ( ( in @ SV11 @ SV5 )
= $false )
| ( ( in @ SV5 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(61,plain,
! [SV10: $i,SV4: $i] :
( ( ( ~ ( subset @ ( singleton @ SV4 ) @ SV10 ) )
= $true )
| ( ( in @ SV4 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(62,plain,
! [SV10: $i,SV4: $i] :
( ( ( ~ ( in @ SV4 @ SV10 ) )
= $true )
| ( ( subset @ ( singleton @ SV4 ) @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(63,plain,
! [SV10: $i,SV4: $i] :
( ( ( subset @ ( singleton @ SV4 ) @ SV10 )
= $false )
| ( ( in @ SV4 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(64,plain,
! [SV10: $i,SV4: $i] :
( ( ( in @ SV4 @ SV10 )
= $false )
| ( ( subset @ ( singleton @ SV4 ) @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(65,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[27,64,63,60,57,47,46,45,41,33,28]) ).
thf(66,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU152+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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.20 % Computer : n009.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.21 % DateTime : Tue Oct 6 15:01:47 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.25
% 0.08/0.25 No.of.Axioms: 8
% 0.08/0.25
% 0.08/0.25 Length.of.Defs: 0
% 0.08/0.25
% 0.08/0.25 Contains.Choice.Funs: false
% 0.08/0.25 .
% 0.08/0.25
% 0.08/0.25 ********************************
% 0.08/0.25 * All subproblems solved! *
% 0.08/0.25 ********************************
% 0.08/0.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:9,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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:65,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.25
% 0.08/0.25 %**** Beginning of derivation protocol ****
% 0.08/0.25 % SZS output start CNFRefutation
% See solution above
% 0.08/0.25
% 0.08/0.25 %**** End of derivation protocol ****
% 0.08/0.25 %**** no. of clauses in derivation: 66 ****
% 0.08/0.25 %**** clause counter: 65 ****
% 0.08/0.25
% 0.08/0.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:9,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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:65,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------