TSTP Solution File: SET968+1 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET968+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 03:06:37 EDT 2022
% Result : Theorem 0.19s 0.48s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 18
% Syntax : Number of formulae : 77 ( 59 unt; 9 typ; 0 def)
% Number of atoms : 219 ( 112 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 628 ( 34 ~; 15 |; 4 &; 571 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 144 ( 0 ^ 140 !; 4 ?; 144 :)
% 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_SY20,type,
sK2_SY20: $i ).
thf(tp_sK3_SY23,type,
sK3_SY23: $i ).
thf(tp_sK4_SY25,type,
sK4_SY25: $i ).
thf(tp_sK5_A,type,
sK5_A: $i ).
thf(tp_sK6_A,type,
sK6_A: $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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',t120_zfmisc_1) ).
thf(3,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(4,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(8,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(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/sandbox2/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] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(15,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(16,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(17,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(18,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(19,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(20,plain,
( ( ! [SY20: $i,SY21: $i,SY22: $i] :
( ( cartesian_product2 @ ( set_union2 @ sK1_A @ SY20 ) @ ( set_union2 @ SY21 @ SY22 ) )
= ( set_union2 @ ( set_union2 @ ( set_union2 @ ( cartesian_product2 @ sK1_A @ SY21 ) @ ( cartesian_product2 @ sK1_A @ SY22 ) ) @ ( cartesian_product2 @ SY20 @ SY21 ) ) @ ( cartesian_product2 @ SY20 @ SY22 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[11]) ).
thf(21,plain,
( ( ! [SY23: $i,SY24: $i] :
( ( cartesian_product2 @ ( set_union2 @ sK1_A @ sK2_SY20 ) @ ( set_union2 @ SY23 @ SY24 ) )
= ( set_union2 @ ( set_union2 @ ( set_union2 @ ( cartesian_product2 @ sK1_A @ SY23 ) @ ( cartesian_product2 @ sK1_A @ SY24 ) ) @ ( cartesian_product2 @ sK2_SY20 @ SY23 ) ) @ ( cartesian_product2 @ sK2_SY20 @ SY24 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[20]) ).
thf(22,plain,
( ( ! [SY25: $i] :
( ( cartesian_product2 @ ( set_union2 @ sK1_A @ sK2_SY20 ) @ ( set_union2 @ sK3_SY23 @ SY25 ) )
= ( set_union2 @ ( set_union2 @ ( set_union2 @ ( cartesian_product2 @ sK1_A @ sK3_SY23 ) @ ( cartesian_product2 @ sK1_A @ SY25 ) ) @ ( cartesian_product2 @ sK2_SY20 @ sK3_SY23 ) ) @ ( cartesian_product2 @ sK2_SY20 @ SY25 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[21]) ).
thf(23,plain,
( ( ( cartesian_product2 @ ( set_union2 @ sK1_A @ sK2_SY20 ) @ ( set_union2 @ sK3_SY23 @ sK4_SY25 ) )
= ( set_union2 @ ( set_union2 @ ( set_union2 @ ( cartesian_product2 @ sK1_A @ sK3_SY23 ) @ ( cartesian_product2 @ sK1_A @ sK4_SY25 ) ) @ ( cartesian_product2 @ sK2_SY20 @ sK3_SY23 ) ) @ ( cartesian_product2 @ sK2_SY20 @ sK4_SY25 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[22]) ).
thf(24,plain,
( ( ( ( cartesian_product2 @ ( set_union2 @ sK1_A @ sK2_SY20 ) @ ( set_union2 @ sK3_SY23 @ sK4_SY25 ) )
!= ( set_union2 @ ( set_union2 @ ( set_union2 @ ( cartesian_product2 @ sK1_A @ sK3_SY23 ) @ ( cartesian_product2 @ sK1_A @ sK4_SY25 ) ) @ ( cartesian_product2 @ sK2_SY20 @ sK3_SY23 ) ) @ ( cartesian_product2 @ sK2_SY20 @ sK4_SY25 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[23]) ).
thf(25,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( cartesian_product2 @ ( set_union2 @ A @ B ) @ C )
= ( set_union2 @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) ) )
& ! [B: $i,C: $i] :
( ( cartesian_product2 @ C @ ( set_union2 @ A @ B ) )
= ( set_union2 @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(26,plain,
( ( ~ ( empty @ sK5_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(27,plain,
( ( empty @ sK6_A )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(28,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[16]) ).
thf(29,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(30,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(31,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(32,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(33,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(34,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(35,plain,
( ( empty @ sK6_A )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(36,plain,
( ( ~ ( empty @ sK5_A ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(37,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( cartesian_product2 @ ( set_union2 @ A @ B ) @ C )
= ( set_union2 @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) ) )
& ! [B: $i,C: $i] :
( ( cartesian_product2 @ C @ ( set_union2 @ A @ B ) )
= ( set_union2 @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(38,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(39,plain,
( ( ( ( cartesian_product2 @ ( set_union2 @ sK1_A @ sK2_SY20 ) @ ( set_union2 @ sK3_SY23 @ sK4_SY25 ) )
!= ( set_union2 @ ( set_union2 @ ( set_union2 @ ( cartesian_product2 @ sK1_A @ sK3_SY23 ) @ ( cartesian_product2 @ sK1_A @ sK4_SY25 ) ) @ ( cartesian_product2 @ sK2_SY20 @ sK3_SY23 ) ) @ ( cartesian_product2 @ sK2_SY20 @ sK4_SY25 ) ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(40,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ( cartesian_product2 @ ( set_union2 @ SX0 @ SX1 ) @ SX2 )
= ( set_union2 @ ( cartesian_product2 @ SX0 @ SX2 ) @ ( cartesian_product2 @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( cartesian_product2 @ SX2 @ ( set_union2 @ SX0 @ SX1 ) )
= ( set_union2 @ ( cartesian_product2 @ SX2 @ SX0 ) @ ( cartesian_product2 @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(41,plain,
! [SV1: $i] :
( ( ! [SY26: $i] :
( ( set_union2 @ SV1 @ SY26 )
= ( set_union2 @ SY26 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(42,plain,
! [SV2: $i] :
( ( ( empty @ SV2 )
| ! [SY27: $i] :
~ ( empty @ ( set_union2 @ SV2 @ SY27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(43,plain,
! [SV3: $i] :
( ( ( empty @ SV3 )
| ! [SY28: $i] :
~ ( empty @ ( set_union2 @ SY28 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(44,plain,
! [SV4: $i] :
( ( ( set_union2 @ SV4 @ SV4 )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(45,plain,
( ( empty @ sK5_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(46,plain,
! [SV5: $i] :
( ( ! [SY29: $i,SY30: $i] :
( ( set_union2 @ ( set_union2 @ SV5 @ SY29 ) @ SY30 )
= ( set_union2 @ SV5 @ ( set_union2 @ SY29 @ SY30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(47,plain,
( ( ( cartesian_product2 @ ( set_union2 @ sK1_A @ sK2_SY20 ) @ ( set_union2 @ sK3_SY23 @ sK4_SY25 ) )
= ( set_union2 @ ( set_union2 @ ( set_union2 @ ( cartesian_product2 @ sK1_A @ sK3_SY23 ) @ ( cartesian_product2 @ sK1_A @ sK4_SY25 ) ) @ ( cartesian_product2 @ sK2_SY20 @ sK3_SY23 ) ) @ ( cartesian_product2 @ sK2_SY20 @ sK4_SY25 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(48,plain,
! [SV6: $i] :
( ( ~ ( ~ ! [SY31: $i,SY32: $i] :
( ( cartesian_product2 @ ( set_union2 @ SV6 @ SY31 ) @ SY32 )
= ( set_union2 @ ( cartesian_product2 @ SV6 @ SY32 ) @ ( cartesian_product2 @ SY31 @ SY32 ) ) )
| ~ ! [SY33: $i,SY34: $i] :
( ( cartesian_product2 @ SY34 @ ( set_union2 @ SV6 @ SY33 ) )
= ( set_union2 @ ( cartesian_product2 @ SY34 @ SV6 ) @ ( cartesian_product2 @ SY34 @ SY33 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(49,plain,
! [SV7: $i,SV1: $i] :
( ( ( set_union2 @ SV1 @ SV7 )
= ( set_union2 @ SV7 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(50,plain,
! [SV2: $i] :
( ( ( empty @ SV2 )
= $true )
| ( ( ! [SY27: $i] :
~ ( empty @ ( set_union2 @ SV2 @ SY27 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(51,plain,
! [SV3: $i] :
( ( ( empty @ SV3 )
= $true )
| ( ( ! [SY28: $i] :
~ ( empty @ ( set_union2 @ SY28 @ SV3 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(52,plain,
! [SV8: $i,SV5: $i] :
( ( ! [SY35: $i] :
( ( set_union2 @ ( set_union2 @ SV5 @ SV8 ) @ SY35 )
= ( set_union2 @ SV5 @ ( set_union2 @ SV8 @ SY35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(53,plain,
! [SV6: $i] :
( ( ~ ! [SY31: $i,SY32: $i] :
( ( cartesian_product2 @ ( set_union2 @ SV6 @ SY31 ) @ SY32 )
= ( set_union2 @ ( cartesian_product2 @ SV6 @ SY32 ) @ ( cartesian_product2 @ SY31 @ SY32 ) ) )
| ~ ! [SY33: $i,SY34: $i] :
( ( cartesian_product2 @ SY34 @ ( set_union2 @ SV6 @ SY33 ) )
= ( set_union2 @ ( cartesian_product2 @ SY34 @ SV6 ) @ ( cartesian_product2 @ SY34 @ SY33 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(54,plain,
! [SV9: $i,SV2: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV2 @ SV9 ) ) )
= $true )
| ( ( empty @ SV2 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(55,plain,
! [SV3: $i,SV10: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV10 @ SV3 ) ) )
= $true )
| ( ( empty @ SV3 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(56,plain,
! [SV11: $i,SV8: $i,SV5: $i] :
( ( ( set_union2 @ ( set_union2 @ SV5 @ SV8 ) @ SV11 )
= ( set_union2 @ SV5 @ ( set_union2 @ SV8 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(57,plain,
! [SV6: $i] :
( ( ~ ! [SY31: $i,SY32: $i] :
( ( cartesian_product2 @ ( set_union2 @ SV6 @ SY31 ) @ SY32 )
= ( set_union2 @ ( cartesian_product2 @ SV6 @ SY32 ) @ ( cartesian_product2 @ SY31 @ SY32 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[53]) ).
thf(58,plain,
! [SV6: $i] :
( ( ~ ! [SY33: $i,SY34: $i] :
( ( cartesian_product2 @ SY34 @ ( set_union2 @ SV6 @ SY33 ) )
= ( set_union2 @ ( cartesian_product2 @ SY34 @ SV6 ) @ ( cartesian_product2 @ SY34 @ SY33 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[53]) ).
thf(59,plain,
! [SV9: $i,SV2: $i] :
( ( ( empty @ ( set_union2 @ SV2 @ SV9 ) )
= $false )
| ( ( empty @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(60,plain,
! [SV3: $i,SV10: $i] :
( ( ( empty @ ( set_union2 @ SV10 @ SV3 ) )
= $false )
| ( ( empty @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(61,plain,
! [SV6: $i] :
( ( ! [SY31: $i,SY32: $i] :
( ( cartesian_product2 @ ( set_union2 @ SV6 @ SY31 ) @ SY32 )
= ( set_union2 @ ( cartesian_product2 @ SV6 @ SY32 ) @ ( cartesian_product2 @ SY31 @ SY32 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[57]) ).
thf(62,plain,
! [SV6: $i] :
( ( ! [SY33: $i,SY34: $i] :
( ( cartesian_product2 @ SY34 @ ( set_union2 @ SV6 @ SY33 ) )
= ( set_union2 @ ( cartesian_product2 @ SY34 @ SV6 ) @ ( cartesian_product2 @ SY34 @ SY33 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[58]) ).
thf(63,plain,
! [SV12: $i,SV6: $i] :
( ( ! [SY36: $i] :
( ( cartesian_product2 @ ( set_union2 @ SV6 @ SV12 ) @ SY36 )
= ( set_union2 @ ( cartesian_product2 @ SV6 @ SY36 ) @ ( cartesian_product2 @ SV12 @ SY36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(64,plain,
! [SV13: $i,SV6: $i] :
( ( ! [SY37: $i] :
( ( cartesian_product2 @ SY37 @ ( set_union2 @ SV6 @ SV13 ) )
= ( set_union2 @ ( cartesian_product2 @ SY37 @ SV6 ) @ ( cartesian_product2 @ SY37 @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(65,plain,
! [SV14: $i,SV12: $i,SV6: $i] :
( ( ( cartesian_product2 @ ( set_union2 @ SV6 @ SV12 ) @ SV14 )
= ( set_union2 @ ( cartesian_product2 @ SV6 @ SV14 ) @ ( cartesian_product2 @ SV12 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(66,plain,
! [SV13: $i,SV6: $i,SV15: $i] :
( ( ( cartesian_product2 @ SV15 @ ( set_union2 @ SV6 @ SV13 ) )
= ( set_union2 @ ( cartesian_product2 @ SV15 @ SV6 ) @ ( cartesian_product2 @ SV15 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(67,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[35,66,65,60,59,56,49,47,45,44]) ).
thf(68,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET968+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34 % Computer : n005.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jul 11 02:47:07 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35
% 0.12/0.35 No.of.Axioms: 8
% 0.12/0.35
% 0.12/0.35 Length.of.Defs: 0
% 0.12/0.35
% 0.12/0.35 Contains.Choice.Funs: false
% 0.12/0.35 (rf:0,axioms:8,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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:10,loop_count:0,foatp_calls:0,translation:fof_full)....
% 0.19/0.48
% 0.19/0.48 ********************************
% 0.19/0.48 * All subproblems solved! *
% 0.19/0.48 ********************************
% 0.19/0.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:8,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:10,ordering:none,proof_output:1,protocol_output:false,clause_count:67,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.48
% 0.19/0.48 %**** Beginning of derivation protocol ****
% 0.19/0.48 % SZS output start CNFRefutation
% See solution above
% 0.19/0.48
% 0.19/0.48 %**** End of derivation protocol ****
% 0.19/0.48 %**** no. of clauses in derivation: 68 ****
% 0.19/0.48 %**** clause counter: 67 ****
% 0.19/0.48
% 0.19/0.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:8,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:10,ordering:none,proof_output:1,protocol_output:false,clause_count:67,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------