%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET902+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 : n011.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 10:42:30 AM UTC 2026
% Result : Theorem 0.08s 0.21s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 9
% Syntax : Number of formulae : 103 ( 75 unt; 0 typ; 0 def)
% Number of atoms : 504 ( 314 equ; 0 cnn)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 788 ( 260 ~; 108 |; 48 &; 363 @)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 123 ( 0 ^; 123 !; 0 ?; 123 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY16,type,
sK2_SY16: $i ).
thf(tp_sK3_SY18,type,
sK3_SY18: $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 @ ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_zfmisc_1) ).
thf(6,axiom,
! [A: $i] :
( ( singleton @ A )
!= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(10,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(11,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(12,conjecture,
! [A: $i,B: $i,C: $i] :
~ ( ( ( singleton @ A )
= ( set_union2 @ B @ C ) )
& ~ ( ( B
= ( singleton @ A ) )
& ( C
= ( singleton @ A ) ) )
& ~ ( ( B = empty_set )
& ( C
= ( singleton @ A ) ) )
& ~ ( ( B
= ( singleton @ A ) )
& ( C = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_zfmisc_1) ).
thf(13,negated_conjecture,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( ( singleton @ A )
= ( set_union2 @ B @ C ) )
& ~ ( ( B
= ( singleton @ A ) )
& ( C
= ( singleton @ A ) ) )
& ~ ( ( B = empty_set )
& ( C
= ( singleton @ A ) ) )
& ~ ( ( B
= ( singleton @ A ) )
& ( C = empty_set ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[12]) ).
thf(14,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( ( singleton @ A )
= ( set_union2 @ B @ C ) )
& ~ ( ( B
= ( singleton @ A ) )
& ( C
= ( singleton @ A ) ) )
& ~ ( ( B = empty_set )
& ( C
= ( singleton @ A ) ) )
& ~ ( ( B
= ( singleton @ A ) )
& ( C = empty_set ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[13]) ).
thf(15,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(16,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(17,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(18,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(19,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(20,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(21,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(22,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(23,plain,
( ( ! [SY16: $i,SY17: $i] :
~ ( ( ( singleton @ sK1_A )
= ( set_union2 @ SY16 @ SY17 ) )
& ~ ( ( SY16
= ( singleton @ sK1_A ) )
& ( SY17
= ( singleton @ sK1_A ) ) )
& ~ ( ( SY16 = empty_set )
& ( SY17
= ( singleton @ sK1_A ) ) )
& ~ ( ( SY16
= ( singleton @ sK1_A ) )
& ( SY17 = empty_set ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[14]) ).
thf(24,plain,
( ( ! [SY18: $i] :
~ ( ( ( singleton @ sK1_A )
= ( set_union2 @ sK2_SY16 @ SY18 ) )
& ~ ( ( sK2_SY16
= ( singleton @ sK1_A ) )
& ( SY18
= ( singleton @ sK1_A ) ) )
& ~ ( ( sK2_SY16 = empty_set )
& ( SY18
= ( singleton @ sK1_A ) ) )
& ~ ( ( sK2_SY16
= ( singleton @ sK1_A ) )
& ( SY18 = empty_set ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[23]) ).
thf(25,plain,
( ( ~ ( ( ( singleton @ sK1_A )
= ( set_union2 @ sK2_SY16 @ sK3_SY18 ) )
& ~ ( ( sK2_SY16
= ( singleton @ sK1_A ) )
& ( sK3_SY18
= ( singleton @ sK1_A ) ) )
& ~ ( ( sK2_SY16 = empty_set )
& ( sK3_SY18
= ( singleton @ sK1_A ) ) )
& ~ ( ( sK2_SY16
= ( singleton @ sK1_A ) )
& ( sK3_SY18 = empty_set ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[24]) ).
thf(26,plain,
( ( ( ( singleton @ sK1_A )
= ( set_union2 @ sK2_SY16 @ sK3_SY18 ) )
& ~ ( ( sK2_SY16
= ( singleton @ sK1_A ) )
& ( sK3_SY18
= ( singleton @ sK1_A ) ) )
& ~ ( ( sK2_SY16 = empty_set )
& ( sK3_SY18
= ( singleton @ sK1_A ) ) )
& ~ ( ( sK2_SY16
= ( singleton @ sK1_A ) )
& ( sK3_SY18 = empty_set ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[25]) ).
thf(27,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(28,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(29,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(30,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(31,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(32,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(33,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(34,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(35,plain,
( ( ( ( singleton @ sK1_A )
= ( set_union2 @ sK2_SY16 @ sK3_SY18 ) )
& ~ ( ( sK2_SY16
= ( singleton @ sK1_A ) )
& ( sK3_SY18
= ( singleton @ sK1_A ) ) )
& ~ ( ( sK2_SY16 = empty_set )
& ( sK3_SY18
= ( singleton @ sK1_A ) ) )
& ~ ( ( sK2_SY16
= ( singleton @ sK1_A ) )
& ( sK3_SY18 = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(36,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( empty @ SX0 )
| ~ ( empty @ ( set_union2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(37,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ( ( singleton @ sK1_A )
!= ( set_union2 @ sK2_SY16 @ sK3_SY18 ) )
| ~ ~ ~ ( ( sK2_SY16
!= ( singleton @ sK1_A ) )
| ( sK3_SY18
!= ( singleton @ sK1_A ) ) ) )
| ~ ~ ~ ( ( sK2_SY16 != empty_set )
| ( sK3_SY18
!= ( singleton @ sK1_A ) ) ) )
| ~ ~ ~ ( ( sK2_SY16
!= ( singleton @ sK1_A ) )
| ( sK3_SY18 != empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(38,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ( ~ ( ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(39,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( empty @ SX0 )
| ~ ( empty @ ( set_union2 @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(40,plain,
( ( ! [SX0: $i] :
( ( singleton @ SX0 )
!= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(41,plain,
! [SV1: $i] :
( ( ! [SY19: $i] :
( ( set_union2 @ SV1 @ SY19 )
= ( set_union2 @ SY19 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(42,plain,
! [SV2: $i] :
( ( ! [SY20: $i] :
( ( set_union2 @ SV2 @ SV2 )
= SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(43,plain,
! [SV3: $i] :
( ( ! [SY21: $i] : ( subset @ SV3 @ ( set_union2 @ SV3 @ SY21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(44,plain,
! [SV4: $i] :
( ( ! [SY22: $i] :
( ~ ~ ( empty @ SV4 )
| ~ ( empty @ ( set_union2 @ SV4 @ SY22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(45,plain,
( ( ~ ~ ( ~ ~ ( ( ( singleton @ sK1_A )
!= ( set_union2 @ sK2_SY16 @ sK3_SY18 ) )
| ~ ~ ~ ( ( sK2_SY16
!= ( singleton @ sK1_A ) )
| ( sK3_SY18
!= ( singleton @ sK1_A ) ) ) )
| ~ ~ ~ ( ( sK2_SY16 != empty_set )
| ( sK3_SY18
!= ( singleton @ sK1_A ) ) ) )
| ~ ~ ~ ( ( sK2_SY16
!= ( singleton @ sK1_A ) )
| ( sK3_SY18 != empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(46,plain,
! [SV5: $i] :
( ( ! [SY23: $i] :
~ ( ~ ( ~ ( subset @ SV5 @ ( singleton @ SY23 ) )
| ( SV5 = empty_set )
| ( SV5
= ( singleton @ SY23 ) ) )
| ~ ( ~ ( ( SV5 = empty_set )
| ( SV5
= ( singleton @ SY23 ) ) )
| ( subset @ SV5 @ ( singleton @ SY23 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(47,plain,
! [SV6: $i] :
( ( ! [SY24: $i] :
( ~ ~ ( empty @ SV6 )
| ~ ( empty @ ( set_union2 @ SY24 @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(48,plain,
! [SV7: $i] :
( ( ( singleton @ SV7 )
!= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(49,plain,
! [SV8: $i,SV1: $i] :
( ( ( set_union2 @ SV1 @ SV8 )
= ( set_union2 @ SV8 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(50,plain,
! [SV2: $i] :
( ( ( set_union2 @ SV2 @ SV2 )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(51,plain,
! [SV10: $i,SV3: $i] :
( ( subset @ SV3 @ ( set_union2 @ SV3 @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(52,plain,
! [SV11: $i,SV4: $i] :
( ( ~ ~ ( empty @ SV4 )
| ~ ( empty @ ( set_union2 @ SV4 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(53,plain,
( ( ~ ~ ( ~ ~ ( ( ( singleton @ sK1_A )
!= ( set_union2 @ sK2_SY16 @ sK3_SY18 ) )
| ~ ~ ~ ( ( sK2_SY16
!= ( singleton @ sK1_A ) )
| ( sK3_SY18
!= ( singleton @ sK1_A ) ) ) )
| ~ ~ ~ ( ( sK2_SY16 != empty_set )
| ( sK3_SY18
!= ( singleton @ sK1_A ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[45]) ).
thf(54,plain,
( ( ~ ~ ~ ( ( sK2_SY16
!= ( singleton @ sK1_A ) )
| ( sK3_SY18 != empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[45]) ).
thf(55,plain,
! [SV12: $i,SV5: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV5 @ ( singleton @ SV12 ) )
| ( SV5 = empty_set )
| ( SV5
= ( singleton @ SV12 ) ) )
| ~ ( ~ ( ( SV5 = empty_set )
| ( SV5
= ( singleton @ SV12 ) ) )
| ( subset @ SV5 @ ( singleton @ SV12 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(56,plain,
! [SV13: $i,SV6: $i] :
( ( ~ ~ ( empty @ SV6 )
| ~ ( empty @ ( set_union2 @ SV13 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(57,plain,
! [SV7: $i] :
( ( ( singleton @ SV7 )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(58,plain,
! [SV11: $i,SV4: $i] :
( ( ( ~ ~ ( empty @ SV4 ) )
= $true )
| ( ( ~ ( empty @ ( set_union2 @ SV4 @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(59,plain,
( ( ~ ( ~ ~ ( ( ( singleton @ sK1_A )
!= ( set_union2 @ sK2_SY16 @ sK3_SY18 ) )
| ~ ~ ~ ( ( sK2_SY16
!= ( singleton @ sK1_A ) )
| ( sK3_SY18
!= ( singleton @ sK1_A ) ) ) )
| ~ ~ ~ ( ( sK2_SY16 != empty_set )
| ( sK3_SY18
!= ( singleton @ sK1_A ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(60,plain,
( ( ~ ~ ( ( sK2_SY16
!= ( singleton @ sK1_A ) )
| ( sK3_SY18 != empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(61,plain,
! [SV12: $i,SV5: $i] :
( ( ~ ( ~ ( subset @ SV5 @ ( singleton @ SV12 ) )
| ( SV5 = empty_set )
| ( SV5
= ( singleton @ SV12 ) ) )
| ~ ( ~ ( ( SV5 = empty_set )
| ( SV5
= ( singleton @ SV12 ) ) )
| ( subset @ SV5 @ ( singleton @ SV12 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(62,plain,
! [SV13: $i,SV6: $i] :
( ( ( ~ ~ ( empty @ SV6 ) )
= $true )
| ( ( ~ ( empty @ ( set_union2 @ SV13 @ SV6 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(63,plain,
! [SV11: $i,SV4: $i] :
( ( ( ~ ( empty @ SV4 ) )
= $false )
| ( ( ~ ( empty @ ( set_union2 @ SV4 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(64,plain,
( ( ~ ~ ( ( ( singleton @ sK1_A )
!= ( set_union2 @ sK2_SY16 @ sK3_SY18 ) )
| ~ ~ ~ ( ( sK2_SY16
!= ( singleton @ sK1_A ) )
| ( sK3_SY18
!= ( singleton @ sK1_A ) ) ) )
| ~ ~ ~ ( ( sK2_SY16 != empty_set )
| ( sK3_SY18
!= ( singleton @ sK1_A ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(65,plain,
( ( ~ ( ( sK2_SY16
!= ( singleton @ sK1_A ) )
| ( sK3_SY18 != empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(66,plain,
! [SV12: $i,SV5: $i] :
( ( ~ ( ~ ( subset @ SV5 @ ( singleton @ SV12 ) )
| ( SV5 = empty_set )
| ( SV5
= ( singleton @ SV12 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(67,plain,
! [SV12: $i,SV5: $i] :
( ( ~ ( ~ ( ( SV5 = empty_set )
| ( SV5
= ( singleton @ SV12 ) ) )
| ( subset @ SV5 @ ( singleton @ SV12 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(68,plain,
! [SV13: $i,SV6: $i] :
( ( ( ~ ( empty @ SV6 ) )
= $false )
| ( ( ~ ( empty @ ( set_union2 @ SV13 @ SV6 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(69,plain,
! [SV11: $i,SV4: $i] :
( ( ( empty @ SV4 )
= $true )
| ( ( ~ ( empty @ ( set_union2 @ SV4 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(70,plain,
( ( ~ ~ ( ( ( singleton @ sK1_A )
!= ( set_union2 @ sK2_SY16 @ sK3_SY18 ) )
| ~ ~ ~ ( ( sK2_SY16
!= ( singleton @ sK1_A ) )
| ( sK3_SY18
!= ( singleton @ sK1_A ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(71,plain,
( ( ~ ~ ~ ( ( sK2_SY16 != empty_set )
| ( sK3_SY18
!= ( singleton @ sK1_A ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(72,plain,
( ( ( sK2_SY16
!= ( singleton @ sK1_A ) )
| ( sK3_SY18 != empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[65]) ).
thf(73,plain,
! [SV12: $i,SV5: $i] :
( ( ~ ( subset @ SV5 @ ( singleton @ SV12 ) )
| ( SV5 = empty_set )
| ( SV5
= ( singleton @ SV12 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(74,plain,
! [SV12: $i,SV5: $i] :
( ( ~ ( ( SV5 = empty_set )
| ( SV5
= ( singleton @ SV12 ) ) )
| ( subset @ SV5 @ ( singleton @ SV12 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(75,plain,
! [SV13: $i,SV6: $i] :
( ( ( empty @ SV6 )
= $true )
| ( ( ~ ( empty @ ( set_union2 @ SV13 @ SV6 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(76,plain,
! [SV11: $i,SV4: $i] :
( ( ( empty @ ( set_union2 @ SV4 @ SV11 ) )
= $false )
| ( ( empty @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(77,plain,
( ( ~ ( ( ( singleton @ sK1_A )
!= ( set_union2 @ sK2_SY16 @ sK3_SY18 ) )
| ~ ~ ~ ( ( sK2_SY16
!= ( singleton @ sK1_A ) )
| ( sK3_SY18
!= ( singleton @ sK1_A ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(78,plain,
( ( ~ ~ ( ( sK2_SY16 != empty_set )
| ( sK3_SY18
!= ( singleton @ sK1_A ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(79,plain,
( ( ( sK2_SY16
!= ( singleton @ sK1_A ) )
= $true )
| ( ( sK3_SY18 != empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(80,plain,
! [SV12: $i,SV5: $i] :
( ( ( ~ ( subset @ SV5 @ ( singleton @ SV12 ) ) )
= $true )
| ( ( ( SV5 = empty_set )
| ( SV5
= ( singleton @ SV12 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(81,plain,
! [SV12: $i,SV5: $i] :
( ( ( ~ ( ( SV5 = empty_set )
| ( SV5
= ( singleton @ SV12 ) ) ) )
= $true )
| ( ( subset @ SV5 @ ( singleton @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(82,plain,
! [SV6: $i,SV13: $i] :
( ( ( empty @ ( set_union2 @ SV13 @ SV6 ) )
= $false )
| ( ( empty @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(83,plain,
( ( ( ( singleton @ sK1_A )
!= ( set_union2 @ sK2_SY16 @ sK3_SY18 ) )
| ~ ~ ~ ( ( sK2_SY16
!= ( singleton @ sK1_A ) )
| ( sK3_SY18
!= ( singleton @ sK1_A ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(84,plain,
( ( ~ ( ( sK2_SY16 != empty_set )
| ( sK3_SY18
!= ( singleton @ sK1_A ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(85,plain,
( ( ( sK2_SY16
= ( singleton @ sK1_A ) )
= $false )
| ( ( sK3_SY18 != empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(86,plain,
! [SV12: $i,SV5: $i] :
( ( ( subset @ SV5 @ ( singleton @ SV12 ) )
= $false )
| ( ( ( SV5 = empty_set )
| ( SV5
= ( singleton @ SV12 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(87,plain,
! [SV12: $i,SV5: $i] :
( ( ( ( SV5 = empty_set )
| ( SV5
= ( singleton @ SV12 ) ) )
= $false )
| ( ( subset @ SV5 @ ( singleton @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(88,plain,
( ( ( singleton @ sK1_A )
!= ( set_union2 @ sK2_SY16 @ sK3_SY18 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(89,plain,
( ( ~ ~ ~ ( ( sK2_SY16
!= ( singleton @ sK1_A ) )
| ( sK3_SY18
!= ( singleton @ sK1_A ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(90,plain,
( ( ( sK2_SY16 != empty_set )
| ( sK3_SY18
!= ( singleton @ sK1_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[84]) ).
thf(91,plain,
( ( ( sK3_SY18 = empty_set )
= $false )
| ( ( sK2_SY16
= ( singleton @ sK1_A ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(92,plain,
! [SV12: $i,SV5: $i] :
( ( ( SV5 = empty_set )
= $true )
| ( ( SV5
= ( singleton @ SV12 ) )
= $true )
| ( ( subset @ SV5 @ ( singleton @ SV12 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(93,plain,
! [SV12: $i,SV5: $i] :
( ( ( SV5 = empty_set )
= $false )
| ( ( subset @ SV5 @ ( singleton @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[87]) ).
thf(94,plain,
! [SV12: $i,SV5: $i] :
( ( ( SV5
= ( singleton @ SV12 ) )
= $false )
| ( ( subset @ SV5 @ ( singleton @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[87]) ).
thf(95,plain,
( ( ( singleton @ sK1_A )
= ( set_union2 @ sK2_SY16 @ sK3_SY18 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[88]) ).
thf(96,plain,
( ( ~ ~ ( ( sK2_SY16
!= ( singleton @ sK1_A ) )
| ( sK3_SY18
!= ( singleton @ sK1_A ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[89]) ).
thf(97,plain,
( ( ( sK2_SY16 != empty_set )
= $true )
| ( ( sK3_SY18
!= ( singleton @ sK1_A ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(98,plain,
( ( ~ ( ( sK2_SY16
!= ( singleton @ sK1_A ) )
| ( sK3_SY18
!= ( singleton @ sK1_A ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(99,plain,
( ( ( sK2_SY16 = empty_set )
= $false )
| ( ( sK3_SY18
!= ( singleton @ sK1_A ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(100,plain,
( ( ( sK2_SY16
!= ( singleton @ sK1_A ) )
| ( sK3_SY18
!= ( singleton @ sK1_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[98]) ).
thf(101,plain,
( ( ( sK3_SY18
= ( singleton @ sK1_A ) )
= $false )
| ( ( sK2_SY16 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(102,plain,
( ( ( sK2_SY16
!= ( singleton @ sK1_A ) )
= $true )
| ( ( sK3_SY18
!= ( singleton @ sK1_A ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(103,plain,
( ( ( sK2_SY16
= ( singleton @ sK1_A ) )
= $false )
| ( ( sK3_SY18
!= ( singleton @ sK1_A ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(104,plain,
( ( ( sK3_SY18
= ( singleton @ sK1_A ) )
= $false )
| ( ( sK2_SY16
= ( singleton @ sK1_A ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(105,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[28,104,101,95,94,93,92,91,82,76,57,51,50,49]) ).
thf(106,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[105]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET902+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
% 0.08/0.17 % Computer : n011.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Oct 6 14:55:51 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.21
% 0.08/0.21 No.of.Axioms: 8
% 0.08/0.21
% 0.08/0.21 Length.of.Defs: 0
% 0.08/0.21
% 0.08/0.21 Contains.Choice.Funs: false
% 0.08/0.21 ..
% 0.08/0.21
% 0.08/0.21 ********************************
% 0.08/0.21 * All subproblems solved! *
% 0.08/0.21 ********************************
% 0.08/0.21 % 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:105,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.21
% 0.08/0.21 %**** Beginning of derivation protocol ****
% 0.08/0.21 % SZS output start CNFRefutation
% See solution above
% 0.08/0.21
% 0.08/0.21 %**** End of derivation protocol ****
% 0.08/0.21 %**** no. of clauses in derivation: 103 ****
% 0.08/0.21 %**** clause counter: 105 ****
% 0.08/0.21
% 0.08/0.21 % 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:105,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------