%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET968+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 : n015.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 10:42:40 AM UTC 2026
% Result : Theorem 0.07s 0.26s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 60 ( 49 unt; 0 typ; 0 def)
% Number of atoms : 208 ( 106 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 646 ( 60 ~; 19 |; 3 &; 558 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 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 : 131 ( 0 ^; 131 !; 0 ?; 131 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cartesian_product2,type,
cartesian_product2: $i > $i > $i ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY18,type,
sK2_SY18: $i ).
thf(tp_sK3_SY21,type,
sK3_SY21: $i ).
thf(tp_sK4_SY23,type,
sK4_SY23: $i ).
thf(tp_set_union2,type,
set_union2: $i > $i > $i ).
thf(1,axiom,
! [A: $i,B: $i,C: $i] :
( ( set_union2 @ ( set_union2 @ A @ B ) @ C )
= ( set_union2 @ A @ ( set_union2 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_1) ).
thf(2,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( cartesian_product2 @ ( set_union2 @ A @ B ) @ C )
= ( set_union2 @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) ) )
& ( ( cartesian_product2 @ C @ ( set_union2 @ A @ B ) )
= ( set_union2 @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t120_zfmisc_1) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(8,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(9,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( cartesian_product2 @ ( set_union2 @ A @ B ) @ ( set_union2 @ C @ D ) )
= ( set_union2 @ ( set_union2 @ ( set_union2 @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ A @ D ) ) @ ( cartesian_product2 @ B @ C ) ) @ ( cartesian_product2 @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t121_zfmisc_1) ).
thf(10,negated_conjecture,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( cartesian_product2 @ ( set_union2 @ A @ B ) @ ( set_union2 @ C @ D ) )
= ( set_union2 @ ( set_union2 @ ( set_union2 @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ A @ D ) ) @ ( cartesian_product2 @ B @ C ) ) @ ( cartesian_product2 @ B @ D ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[9]) ).
thf(11,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( cartesian_product2 @ ( set_union2 @ A @ B ) @ ( set_union2 @ C @ D ) )
= ( set_union2 @ ( set_union2 @ ( set_union2 @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ A @ D ) ) @ ( cartesian_product2 @ B @ C ) ) @ ( cartesian_product2 @ B @ D ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[10]) ).
thf(12,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( set_union2 @ ( set_union2 @ A @ B ) @ C )
= ( set_union2 @ A @ ( set_union2 @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(13,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( cartesian_product2 @ ( set_union2 @ A @ B ) @ C )
= ( set_union2 @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) ) )
& ( ( cartesian_product2 @ C @ ( set_union2 @ A @ B ) )
= ( set_union2 @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(14,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(15,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(16,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(17,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(18,plain,
( ( ! [SY18: $i,SY19: $i,SY20: $i] :
( ( cartesian_product2 @ ( set_union2 @ sK1_A @ SY18 ) @ ( set_union2 @ SY19 @ SY20 ) )
= ( set_union2 @ ( set_union2 @ ( set_union2 @ ( cartesian_product2 @ sK1_A @ SY19 ) @ ( cartesian_product2 @ sK1_A @ SY20 ) ) @ ( cartesian_product2 @ SY18 @ SY19 ) ) @ ( cartesian_product2 @ SY18 @ SY20 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[11]) ).
thf(19,plain,
( ( ! [SY21: $i,SY22: $i] :
( ( cartesian_product2 @ ( set_union2 @ sK1_A @ sK2_SY18 ) @ ( set_union2 @ SY21 @ SY22 ) )
= ( set_union2 @ ( set_union2 @ ( set_union2 @ ( cartesian_product2 @ sK1_A @ SY21 ) @ ( cartesian_product2 @ sK1_A @ SY22 ) ) @ ( cartesian_product2 @ sK2_SY18 @ SY21 ) ) @ ( cartesian_product2 @ sK2_SY18 @ SY22 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[18]) ).
thf(20,plain,
( ( ! [SY23: $i] :
( ( cartesian_product2 @ ( set_union2 @ sK1_A @ sK2_SY18 ) @ ( set_union2 @ sK3_SY21 @ SY23 ) )
= ( set_union2 @ ( set_union2 @ ( set_union2 @ ( cartesian_product2 @ sK1_A @ sK3_SY21 ) @ ( cartesian_product2 @ sK1_A @ SY23 ) ) @ ( cartesian_product2 @ sK2_SY18 @ sK3_SY21 ) ) @ ( cartesian_product2 @ sK2_SY18 @ SY23 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[19]) ).
thf(21,plain,
( ( ( cartesian_product2 @ ( set_union2 @ sK1_A @ sK2_SY18 ) @ ( set_union2 @ sK3_SY21 @ sK4_SY23 ) )
= ( set_union2 @ ( set_union2 @ ( set_union2 @ ( cartesian_product2 @ sK1_A @ sK3_SY21 ) @ ( cartesian_product2 @ sK1_A @ sK4_SY23 ) ) @ ( cartesian_product2 @ sK2_SY18 @ sK3_SY21 ) ) @ ( cartesian_product2 @ sK2_SY18 @ sK4_SY23 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[20]) ).
thf(22,plain,
( ( ( cartesian_product2 @ ( set_union2 @ sK1_A @ sK2_SY18 ) @ ( set_union2 @ sK3_SY21 @ sK4_SY23 ) )
!= ( set_union2 @ ( set_union2 @ ( set_union2 @ ( cartesian_product2 @ sK1_A @ sK3_SY21 ) @ ( cartesian_product2 @ sK1_A @ sK4_SY23 ) ) @ ( cartesian_product2 @ sK2_SY18 @ sK3_SY21 ) ) @ ( cartesian_product2 @ sK2_SY18 @ sK4_SY23 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[21]) ).
thf(23,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(24,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(25,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(26,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(27,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( cartesian_product2 @ ( set_union2 @ A @ B ) @ C )
= ( set_union2 @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) ) )
& ( ( cartesian_product2 @ C @ ( set_union2 @ A @ B ) )
= ( set_union2 @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(28,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( set_union2 @ ( set_union2 @ A @ B ) @ C )
= ( set_union2 @ A @ ( set_union2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(29,plain,
( ( ( cartesian_product2 @ ( set_union2 @ sK1_A @ sK2_SY18 ) @ ( set_union2 @ sK3_SY21 @ sK4_SY23 ) )
!= ( set_union2 @ ( set_union2 @ ( set_union2 @ ( cartesian_product2 @ sK1_A @ sK3_SY21 ) @ ( cartesian_product2 @ sK1_A @ sK4_SY23 ) ) @ ( cartesian_product2 @ sK2_SY18 @ sK3_SY21 ) ) @ ( cartesian_product2 @ sK2_SY18 @ sK4_SY23 ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(30,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ( ( cartesian_product2 @ ( set_union2 @ SX0 @ SX1 ) @ SX2 )
!= ( set_union2 @ ( cartesian_product2 @ SX0 @ SX2 ) @ ( cartesian_product2 @ SX1 @ SX2 ) ) )
| ( ( cartesian_product2 @ SX2 @ ( set_union2 @ SX0 @ SX1 ) )
!= ( set_union2 @ ( cartesian_product2 @ SX2 @ SX0 ) @ ( cartesian_product2 @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(31,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( empty @ SX0 )
| ~ ( empty @ ( set_union2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(32,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( empty @ SX0 )
| ~ ( empty @ ( set_union2 @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(33,plain,
! [SV1: $i] :
( ( ! [SY24: $i] :
( ( set_union2 @ SV1 @ SY24 )
= ( set_union2 @ SY24 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(34,plain,
! [SV2: $i] :
( ( ! [SY25: $i] :
( ( set_union2 @ SV2 @ SV2 )
= SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(35,plain,
! [SV3: $i] :
( ( ! [SY26: $i,SY27: $i] :
( ( set_union2 @ ( set_union2 @ SV3 @ SY26 ) @ SY27 )
= ( set_union2 @ SV3 @ ( set_union2 @ SY26 @ SY27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(36,plain,
( ( ( cartesian_product2 @ ( set_union2 @ sK1_A @ sK2_SY18 ) @ ( set_union2 @ sK3_SY21 @ sK4_SY23 ) )
= ( set_union2 @ ( set_union2 @ ( set_union2 @ ( cartesian_product2 @ sK1_A @ sK3_SY21 ) @ ( cartesian_product2 @ sK1_A @ sK4_SY23 ) ) @ ( cartesian_product2 @ sK2_SY18 @ sK3_SY21 ) ) @ ( cartesian_product2 @ sK2_SY18 @ sK4_SY23 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(37,plain,
! [SV4: $i] :
( ( ! [SY28: $i,SY29: $i] :
~ ( ( ( cartesian_product2 @ ( set_union2 @ SV4 @ SY28 ) @ SY29 )
!= ( set_union2 @ ( cartesian_product2 @ SV4 @ SY29 ) @ ( cartesian_product2 @ SY28 @ SY29 ) ) )
| ( ( cartesian_product2 @ SY29 @ ( set_union2 @ SV4 @ SY28 ) )
!= ( set_union2 @ ( cartesian_product2 @ SY29 @ SV4 ) @ ( cartesian_product2 @ SY29 @ SY28 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(38,plain,
! [SV5: $i] :
( ( ! [SY30: $i] :
( ~ ~ ( empty @ SV5 )
| ~ ( empty @ ( set_union2 @ SV5 @ SY30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(39,plain,
! [SV6: $i] :
( ( ! [SY31: $i] :
( ~ ~ ( empty @ SV6 )
| ~ ( empty @ ( set_union2 @ SY31 @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(40,plain,
! [SV7: $i,SV1: $i] :
( ( ( set_union2 @ SV1 @ SV7 )
= ( set_union2 @ SV7 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(41,plain,
! [SV2: $i] :
( ( ( set_union2 @ SV2 @ SV2 )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(42,plain,
! [SV9: $i,SV3: $i] :
( ( ! [SY32: $i] :
( ( set_union2 @ ( set_union2 @ SV3 @ SV9 ) @ SY32 )
= ( set_union2 @ SV3 @ ( set_union2 @ SV9 @ SY32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(43,plain,
! [SV10: $i,SV4: $i] :
( ( ! [SY33: $i] :
~ ( ( ( cartesian_product2 @ ( set_union2 @ SV4 @ SV10 ) @ SY33 )
!= ( set_union2 @ ( cartesian_product2 @ SV4 @ SY33 ) @ ( cartesian_product2 @ SV10 @ SY33 ) ) )
| ( ( cartesian_product2 @ SY33 @ ( set_union2 @ SV4 @ SV10 ) )
!= ( set_union2 @ ( cartesian_product2 @ SY33 @ SV4 ) @ ( cartesian_product2 @ SY33 @ SV10 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(44,plain,
! [SV11: $i,SV5: $i] :
( ( ~ ~ ( empty @ SV5 )
| ~ ( empty @ ( set_union2 @ SV5 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(45,plain,
! [SV12: $i,SV6: $i] :
( ( ~ ~ ( empty @ SV6 )
| ~ ( empty @ ( set_union2 @ SV12 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(46,plain,
! [SV13: $i,SV9: $i,SV3: $i] :
( ( ( set_union2 @ ( set_union2 @ SV3 @ SV9 ) @ SV13 )
= ( set_union2 @ SV3 @ ( set_union2 @ SV9 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(47,plain,
! [SV14: $i,SV10: $i,SV4: $i] :
( ( ~ ( ( ( cartesian_product2 @ ( set_union2 @ SV4 @ SV10 ) @ SV14 )
!= ( set_union2 @ ( cartesian_product2 @ SV4 @ SV14 ) @ ( cartesian_product2 @ SV10 @ SV14 ) ) )
| ( ( cartesian_product2 @ SV14 @ ( set_union2 @ SV4 @ SV10 ) )
!= ( set_union2 @ ( cartesian_product2 @ SV14 @ SV4 ) @ ( cartesian_product2 @ SV14 @ SV10 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(48,plain,
! [SV11: $i,SV5: $i] :
( ( ( ~ ~ ( empty @ SV5 ) )
= $true )
| ( ( ~ ( empty @ ( set_union2 @ SV5 @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(49,plain,
! [SV12: $i,SV6: $i] :
( ( ( ~ ~ ( empty @ SV6 ) )
= $true )
| ( ( ~ ( empty @ ( set_union2 @ SV12 @ SV6 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(50,plain,
! [SV14: $i,SV10: $i,SV4: $i] :
( ( ( ( cartesian_product2 @ ( set_union2 @ SV4 @ SV10 ) @ SV14 )
!= ( set_union2 @ ( cartesian_product2 @ SV4 @ SV14 ) @ ( cartesian_product2 @ SV10 @ SV14 ) ) )
| ( ( cartesian_product2 @ SV14 @ ( set_union2 @ SV4 @ SV10 ) )
!= ( set_union2 @ ( cartesian_product2 @ SV14 @ SV4 ) @ ( cartesian_product2 @ SV14 @ SV10 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(51,plain,
! [SV11: $i,SV5: $i] :
( ( ( ~ ( empty @ SV5 ) )
= $false )
| ( ( ~ ( empty @ ( set_union2 @ SV5 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(52,plain,
! [SV12: $i,SV6: $i] :
( ( ( ~ ( empty @ SV6 ) )
= $false )
| ( ( ~ ( empty @ ( set_union2 @ SV12 @ SV6 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(53,plain,
! [SV14: $i,SV10: $i,SV4: $i] :
( ( ( cartesian_product2 @ ( set_union2 @ SV4 @ SV10 ) @ SV14 )
!= ( set_union2 @ ( cartesian_product2 @ SV4 @ SV14 ) @ ( cartesian_product2 @ SV10 @ SV14 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[50]) ).
thf(54,plain,
! [SV10: $i,SV4: $i,SV14: $i] :
( ( ( cartesian_product2 @ SV14 @ ( set_union2 @ SV4 @ SV10 ) )
!= ( set_union2 @ ( cartesian_product2 @ SV14 @ SV4 ) @ ( cartesian_product2 @ SV14 @ SV10 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[50]) ).
thf(55,plain,
! [SV11: $i,SV5: $i] :
( ( ( empty @ SV5 )
= $true )
| ( ( ~ ( empty @ ( set_union2 @ SV5 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(56,plain,
! [SV12: $i,SV6: $i] :
( ( ( empty @ SV6 )
= $true )
| ( ( ~ ( empty @ ( set_union2 @ SV12 @ SV6 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(57,plain,
! [SV14: $i,SV10: $i,SV4: $i] :
( ( ( cartesian_product2 @ ( set_union2 @ SV4 @ SV10 ) @ SV14 )
= ( set_union2 @ ( cartesian_product2 @ SV4 @ SV14 ) @ ( cartesian_product2 @ SV10 @ SV14 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(58,plain,
! [SV10: $i,SV4: $i,SV14: $i] :
( ( ( cartesian_product2 @ SV14 @ ( set_union2 @ SV4 @ SV10 ) )
= ( set_union2 @ ( cartesian_product2 @ SV14 @ SV4 ) @ ( cartesian_product2 @ SV14 @ SV10 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(59,plain,
! [SV11: $i,SV5: $i] :
( ( ( empty @ ( set_union2 @ SV5 @ SV11 ) )
= $false )
| ( ( empty @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(60,plain,
! [SV6: $i,SV12: $i] :
( ( ( empty @ ( set_union2 @ SV12 @ SV6 ) )
= $false )
| ( ( empty @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(61,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[36,60,59,58,57,46,41,40]) ).
thf(62,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET968+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.17 % Computer : n015.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Oct 6 15:01:13 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
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% 0.07/0.26 No.of.Axioms: 6
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% 0.07/0.26 Length.of.Defs: 0
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% 0.07/0.26 Contains.Choice.Funs: false
% 0.07/0.26 .
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% 0.07/0.26 ********************************
% 0.07/0.26 * All subproblems solved! *
% 0.07/0.26 ********************************
% 0.07/0.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:6,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:61,loop_count:0,foatp_calls:1,translation:fof_full)
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% 0.07/0.26 %**** Beginning of derivation protocol ****
% 0.07/0.26 % SZS output start CNFRefutation
% See solution above
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% 0.07/0.26 %**** End of derivation protocol ****
% 0.07/0.26 %**** no. of clauses in derivation: 60 ****
% 0.07/0.26 %**** clause counter: 61 ****
% 0.07/0.26
% 0.07/0.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:6,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:61,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------