%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU112+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 : n014.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 10:42:54 AM UTC 2026
% Result : Theorem 0.06s 0.29s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 91 ( 64 unt; 0 typ; 0 def)
% Number of atoms : 381 ( 120 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 618 ( 100 ~; 57 |; 6 &; 440 @)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 22 usr; 5 con; 0-2 aty)
% Number of variables : 172 ( 0 ^; 172 !; 0 ?; 172 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cap_closed,type,
cap_closed: $i > $o ).
thf(tp_cup_closed,type,
cup_closed: $i > $o ).
thf(tp_diff_closed,type,
diff_closed: $i > $o ).
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_epsilon_connected,type,
epsilon_connected: $i > $o ).
thf(tp_epsilon_transitive,type,
epsilon_transitive: $i > $o ).
thf(tp_finite,type,
finite: $i > $o ).
thf(tp_finite_subsets,type,
finite_subsets: $i > $i ).
thf(tp_function,type,
function: $i > $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_natural,type,
natural: $i > $o ).
thf(tp_one_to_one,type,
one_to_one: $i > $o ).
thf(tp_ordinal,type,
ordinal: $i > $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_preboolean,type,
preboolean: $i > $o ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY23,type,
sK2_SY23: $i ).
thf(tp_set_union2,type,
set_union2: $i > $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(1,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_xboole_1) ).
thf(3,axiom,
! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( finite_subsets @ A ) @ ( finite_subsets @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_finsub_1) ).
thf(12,axiom,
! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
thf(13,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc9_finset_1) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(32,axiom,
! [A: $i] : ( preboolean @ ( finite_subsets @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_finsub_1) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(40,conjecture,
! [A: $i,B: $i] : ( subset @ ( set_union2 @ ( finite_subsets @ A ) @ ( finite_subsets @ B ) ) @ ( finite_subsets @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_finsub_1) ).
thf(41,negated_conjecture,
( ( ! [A: $i,B: $i] : ( subset @ ( set_union2 @ ( finite_subsets @ A ) @ ( finite_subsets @ B ) ) @ ( finite_subsets @ ( set_union2 @ A @ B ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[40]) ).
thf(42,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_union2 @ ( finite_subsets @ A ) @ ( finite_subsets @ B ) ) @ ( finite_subsets @ ( set_union2 @ A @ B ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[41]) ).
thf(43,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(44,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(45,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( finite_subsets @ A ) @ ( finite_subsets @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(46,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(47,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(48,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(49,plain,
( ( ! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(50,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(51,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(52,plain,
( ( ! [A: $i] : ( preboolean @ ( finite_subsets @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(53,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(54,plain,
( ( ! [SY23: $i] : ( subset @ ( set_union2 @ ( finite_subsets @ sK1_A ) @ ( finite_subsets @ SY23 ) ) @ ( finite_subsets @ ( set_union2 @ sK1_A @ SY23 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[42]) ).
thf(55,plain,
( ( subset @ ( set_union2 @ ( finite_subsets @ sK1_A ) @ ( finite_subsets @ sK2_SY23 ) ) @ ( finite_subsets @ ( set_union2 @ sK1_A @ sK2_SY23 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[54]) ).
thf(56,plain,
( ( ~ ( subset @ ( set_union2 @ ( finite_subsets @ sK1_A ) @ ( finite_subsets @ sK2_SY23 ) ) @ ( finite_subsets @ ( set_union2 @ sK1_A @ sK2_SY23 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[55]) ).
thf(57,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(58,plain,
( ( ! [A: $i] : ( preboolean @ ( finite_subsets @ A ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(59,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(60,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(61,plain,
( ( ! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(62,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(63,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(64,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(65,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( finite_subsets @ A ) @ ( finite_subsets @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(66,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(67,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(68,plain,
( ( ~ ( subset @ ( set_union2 @ ( finite_subsets @ sK1_A ) @ ( finite_subsets @ sK2_SY23 ) ) @ ( finite_subsets @ ( set_union2 @ sK1_A @ sK2_SY23 ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(69,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( finite_subsets @ SX0 ) @ ( finite_subsets @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(70,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( finite @ SX0 )
| ~ ( finite @ SX1 ) )
| ( finite @ ( set_union2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(71,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( empty @ SX0 )
| ~ ( empty @ ( set_union2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(72,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( empty @ SX0 )
| ~ ( empty @ ( set_union2 @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(73,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX2 @ SX1 ) )
| ( subset @ ( set_union2 @ SX0 @ SX2 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(74,plain,
! [SV1: $i] :
( ( ! [SY24: $i] :
( ( set_union2 @ SV1 @ SY24 )
= ( set_union2 @ SY24 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(75,plain,
! [SV2: $i] :
( ( preboolean @ ( finite_subsets @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(76,plain,
! [SV3: $i] :
( ( ! [SY25: $i] :
( ( set_union2 @ SV3 @ SV3 )
= SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(77,plain,
! [SV4: $i] :
( ( ! [SY26: $i] : ( subset @ SV4 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(78,plain,
! [SV5: $i] :
( ( ( set_union2 @ SV5 @ empty_set )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(79,plain,
! [SV6: $i] :
( ( ! [SY27: $i] : ( subset @ SV6 @ ( set_union2 @ SV6 @ SY27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(80,plain,
( ( subset @ ( set_union2 @ ( finite_subsets @ sK1_A ) @ ( finite_subsets @ sK2_SY23 ) ) @ ( finite_subsets @ ( set_union2 @ sK1_A @ sK2_SY23 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(81,plain,
! [SV7: $i] :
( ( ! [SY28: $i] :
( ~ ( subset @ SV7 @ SY28 )
| ( subset @ ( finite_subsets @ SV7 ) @ ( finite_subsets @ SY28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(82,plain,
! [SV8: $i] :
( ( ! [SY29: $i] :
( ~ ~ ( ~ ( finite @ SV8 )
| ~ ( finite @ SY29 ) )
| ( finite @ ( set_union2 @ SV8 @ SY29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(83,plain,
! [SV9: $i] :
( ( ! [SY30: $i] :
( ~ ~ ( empty @ SV9 )
| ~ ( empty @ ( set_union2 @ SV9 @ SY30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(84,plain,
! [SV10: $i] :
( ( ! [SY31: $i] :
( ~ ~ ( empty @ SV10 )
| ~ ( empty @ ( set_union2 @ SY31 @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(85,plain,
! [SV11: $i] :
( ( ! [SY32: $i,SY33: $i] :
( ~ ~ ( ~ ( subset @ SV11 @ SY32 )
| ~ ( subset @ SY33 @ SY32 ) )
| ( subset @ ( set_union2 @ SV11 @ SY33 ) @ SY32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(86,plain,
! [SV12: $i,SV1: $i] :
( ( ( set_union2 @ SV1 @ SV12 )
= ( set_union2 @ SV12 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(87,plain,
! [SV3: $i] :
( ( ( set_union2 @ SV3 @ SV3 )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(88,plain,
! [SV4: $i] :
( ( subset @ SV4 @ SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(89,plain,
! [SV15: $i,SV6: $i] :
( ( subset @ SV6 @ ( set_union2 @ SV6 @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(90,plain,
! [SV16: $i,SV7: $i] :
( ( ~ ( subset @ SV7 @ SV16 )
| ( subset @ ( finite_subsets @ SV7 ) @ ( finite_subsets @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(91,plain,
! [SV17: $i,SV8: $i] :
( ( ~ ~ ( ~ ( finite @ SV8 )
| ~ ( finite @ SV17 ) )
| ( finite @ ( set_union2 @ SV8 @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(92,plain,
! [SV18: $i,SV9: $i] :
( ( ~ ~ ( empty @ SV9 )
| ~ ( empty @ ( set_union2 @ SV9 @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(93,plain,
! [SV19: $i,SV10: $i] :
( ( ~ ~ ( empty @ SV10 )
| ~ ( empty @ ( set_union2 @ SV19 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(94,plain,
! [SV20: $i,SV11: $i] :
( ( ! [SY34: $i] :
( ~ ~ ( ~ ( subset @ SV11 @ SV20 )
| ~ ( subset @ SY34 @ SV20 ) )
| ( subset @ ( set_union2 @ SV11 @ SY34 ) @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(95,plain,
! [SV16: $i,SV7: $i] :
( ( ( ~ ( subset @ SV7 @ SV16 ) )
= $true )
| ( ( subset @ ( finite_subsets @ SV7 ) @ ( finite_subsets @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(96,plain,
! [SV17: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( finite @ SV8 )
| ~ ( finite @ SV17 ) ) )
= $true )
| ( ( finite @ ( set_union2 @ SV8 @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(97,plain,
! [SV18: $i,SV9: $i] :
( ( ( ~ ~ ( empty @ SV9 ) )
= $true )
| ( ( ~ ( empty @ ( set_union2 @ SV9 @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(98,plain,
! [SV19: $i,SV10: $i] :
( ( ( ~ ~ ( empty @ SV10 ) )
= $true )
| ( ( ~ ( empty @ ( set_union2 @ SV19 @ SV10 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(99,plain,
! [SV21: $i,SV20: $i,SV11: $i] :
( ( ~ ~ ( ~ ( subset @ SV11 @ SV20 )
| ~ ( subset @ SV21 @ SV20 ) )
| ( subset @ ( set_union2 @ SV11 @ SV21 ) @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(100,plain,
! [SV16: $i,SV7: $i] :
( ( ( subset @ SV7 @ SV16 )
= $false )
| ( ( subset @ ( finite_subsets @ SV7 ) @ ( finite_subsets @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(101,plain,
! [SV17: $i,SV8: $i] :
( ( ( ~ ( ~ ( finite @ SV8 )
| ~ ( finite @ SV17 ) ) )
= $false )
| ( ( finite @ ( set_union2 @ SV8 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(102,plain,
! [SV18: $i,SV9: $i] :
( ( ( ~ ( empty @ SV9 ) )
= $false )
| ( ( ~ ( empty @ ( set_union2 @ SV9 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(103,plain,
! [SV19: $i,SV10: $i] :
( ( ( ~ ( empty @ SV10 ) )
= $false )
| ( ( ~ ( empty @ ( set_union2 @ SV19 @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(104,plain,
! [SV21: $i,SV20: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV11 @ SV20 )
| ~ ( subset @ SV21 @ SV20 ) ) )
= $true )
| ( ( subset @ ( set_union2 @ SV11 @ SV21 ) @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(105,plain,
! [SV17: $i,SV8: $i] :
( ( ( ~ ( finite @ SV8 )
| ~ ( finite @ SV17 ) )
= $true )
| ( ( finite @ ( set_union2 @ SV8 @ SV17 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[101]) ).
thf(106,plain,
! [SV18: $i,SV9: $i] :
( ( ( empty @ SV9 )
= $true )
| ( ( ~ ( empty @ ( set_union2 @ SV9 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[102]) ).
thf(107,plain,
! [SV19: $i,SV10: $i] :
( ( ( empty @ SV10 )
= $true )
| ( ( ~ ( empty @ ( set_union2 @ SV19 @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[103]) ).
thf(108,plain,
! [SV21: $i,SV20: $i,SV11: $i] :
( ( ( ~ ( ~ ( subset @ SV11 @ SV20 )
| ~ ( subset @ SV21 @ SV20 ) ) )
= $false )
| ( ( subset @ ( set_union2 @ SV11 @ SV21 ) @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(109,plain,
! [SV17: $i,SV8: $i] :
( ( ( ~ ( finite @ SV8 ) )
= $true )
| ( ( ~ ( finite @ SV17 ) )
= $true )
| ( ( finite @ ( set_union2 @ SV8 @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(110,plain,
! [SV18: $i,SV9: $i] :
( ( ( empty @ ( set_union2 @ SV9 @ SV18 ) )
= $false )
| ( ( empty @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(111,plain,
! [SV10: $i,SV19: $i] :
( ( ( empty @ ( set_union2 @ SV19 @ SV10 ) )
= $false )
| ( ( empty @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(112,plain,
! [SV21: $i,SV20: $i,SV11: $i] :
( ( ( ~ ( subset @ SV11 @ SV20 )
| ~ ( subset @ SV21 @ SV20 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV11 @ SV21 ) @ SV20 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(113,plain,
! [SV17: $i,SV8: $i] :
( ( ( finite @ SV8 )
= $false )
| ( ( ~ ( finite @ SV17 ) )
= $true )
| ( ( finite @ ( set_union2 @ SV8 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(114,plain,
! [SV21: $i,SV20: $i,SV11: $i] :
( ( ( ~ ( subset @ SV11 @ SV20 ) )
= $true )
| ( ( ~ ( subset @ SV21 @ SV20 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV11 @ SV21 ) @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(115,plain,
! [SV8: $i,SV17: $i] :
( ( ( finite @ SV17 )
= $false )
| ( ( finite @ SV8 )
= $false )
| ( ( finite @ ( set_union2 @ SV8 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(116,plain,
! [SV21: $i,SV20: $i,SV11: $i] :
( ( ( subset @ SV11 @ SV20 )
= $false )
| ( ( ~ ( subset @ SV21 @ SV20 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV11 @ SV21 ) @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(117,plain,
! [SV11: $i,SV20: $i,SV21: $i] :
( ( ( subset @ SV21 @ SV20 )
= $false )
| ( ( subset @ SV11 @ SV20 )
= $false )
| ( ( subset @ ( set_union2 @ SV11 @ SV21 ) @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(118,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[75,117,115,111,110,100,89,88,87,86,80,78]) ).
thf(119,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[118]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU112+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
% 0.06/0.20 % Computer : n014.cluster.edu
% 0.06/0.20 % Model : x86_64 x86_64
% 0.06/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.20 % Memory : 8046.5625MB
% 0.06/0.20 % OS : Linux 6.8.0-71-generic
% 0.06/0.20 % CPULimit : 300
% 0.06/0.20 % WCLimit : 300
% 0.06/0.20 % DateTime : Tue Oct 6 15:00:11 UTC 2026
% 0.06/0.20 % CPUTime :
% 0.06/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.29
% 0.06/0.29 No.of.Axioms: 11
% 0.06/0.29
% 0.06/0.29 Length.of.Defs: 0
% 0.06/0.29
% 0.06/0.29 Contains.Choice.Funs: false
% 0.06/0.29 ..
% 0.06/0.29
% 0.06/0.29 ********************************
% 0.06/0.29 * All subproblems solved! *
% 0.06/0.29 ********************************
% 0.06/0.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:11,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:118,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.06/0.29
% 0.06/0.29 %**** Beginning of derivation protocol ****
% 0.06/0.29 % SZS output start CNFRefutation
% See solution above
% 0.06/0.29
% 0.06/0.29 %**** End of derivation protocol ****
% 0.06/0.29 %**** no. of clauses in derivation: 91 ****
% 0.06/0.29 %**** clause counter: 118 ****
% 0.06/0.29
% 0.06/0.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:11,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:118,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------