TSTP Solution File: SET865-2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET865-2 : 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 : n028.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 03:05:50 EDT 2022
% Result : Unsatisfiable 0.21s 0.43s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 19
% Syntax : Number of formulae : 80 ( 43 unt; 10 typ; 0 def)
% Number of atoms : 340 ( 111 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 880 ( 81 ~; 92 |; 0 &; 707 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 150 ( 0 ^ 150 !; 0 ?; 150 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_Union,type,
c_Union: $i > $i > $i ).
thf(tp_c_Zorn_OHausdorff__1,type,
c_Zorn_OHausdorff__1: $i > $i > $i ).
thf(tp_c_Zorn_Ochain,type,
c_Zorn_Ochain: $i > $i > $i ).
thf(tp_c_Zorn_Omaxchain,type,
c_Zorn_Omaxchain: $i > $i > $i ).
thf(tp_c_in,type,
c_in: $i > $i > $i > $o ).
thf(tp_c_lessequals,type,
c_lessequals: $i > $i > $i > $o ).
thf(tp_t_a,type,
t_a: $i ).
thf(tp_tc_set,type,
tc_set: $i > $i ).
thf(tp_v_S,type,
v_S: $i ).
thf(tp_v_x,type,
v_x: $i > $i ).
thf(1,axiom,
! [V_S: $i,T_a: $i] : ( c_lessequals @ ( c_Zorn_Omaxchain @ V_S @ T_a ) @ ( c_Zorn_Ochain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ ( tc_set @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Omaxchain__subset__chain_0) ).
thf(2,axiom,
! [V_u: $i,V_S: $i,T_a: $i,V_c: $i] :
( ~ ( c_in @ V_u @ V_S @ ( tc_set @ T_a ) )
| ~ ( c_in @ V_c @ ( c_Zorn_Omaxchain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ~ ( c_lessequals @ ( c_Union @ V_c @ T_a ) @ V_u @ ( tc_set @ T_a ) )
| ( ( c_Union @ V_c @ T_a )
= V_u ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Omaxchain__Zorn_0) ).
thf(3,axiom,
! [V_S: $i,T_a: $i] : ( c_in @ ( c_Zorn_OHausdorff__1 @ V_S @ T_a ) @ ( c_Zorn_Omaxchain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OHausdorff_0) ).
thf(4,axiom,
! [V_c: $i,V_A: $i,T_a: $i,V_B: $i] :
( ~ ( c_in @ V_c @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
| ( c_in @ V_c @ V_B @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
thf(5,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(6,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[5]) ).
thf(7,negated_conjecture,
! [V_U: $i] :
( ( V_U
!= ( v_x @ V_U ) )
| ~ ( c_in @ V_U @ v_S @ ( tc_set @ t_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(8,negated_conjecture,
! [V_U: $i] :
( ( c_lessequals @ V_U @ ( v_x @ V_U ) @ ( tc_set @ t_a ) )
| ~ ( c_in @ V_U @ v_S @ ( tc_set @ t_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(9,negated_conjecture,
! [V_U: $i] :
( ( c_in @ ( v_x @ V_U ) @ v_S @ ( tc_set @ t_a ) )
| ~ ( c_in @ V_U @ v_S @ ( tc_set @ t_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(10,negated_conjecture,
! [V_U: $i] :
( ( c_in @ ( c_Union @ V_U @ t_a ) @ v_S @ ( tc_set @ t_a ) )
| ~ ( c_in @ V_U @ ( c_Zorn_Ochain @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(11,plain,
$false = $false,
inference(unfold_def,[status(thm)],[6]) ).
thf(12,plain,
( ( ! [V_S: $i,T_a: $i] : ( c_lessequals @ ( c_Zorn_Omaxchain @ V_S @ T_a ) @ ( c_Zorn_Ochain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ ( tc_set @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(13,plain,
( ( ! [V_u: $i,V_S: $i,T_a: $i,V_c: $i] :
( ~ ( c_in @ V_u @ V_S @ ( tc_set @ T_a ) )
| ~ ( c_in @ V_c @ ( c_Zorn_Omaxchain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ~ ( c_lessequals @ ( c_Union @ V_c @ T_a ) @ V_u @ ( tc_set @ T_a ) )
| ( ( c_Union @ V_c @ T_a )
= V_u ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(14,plain,
( ( ! [V_S: $i,T_a: $i] : ( c_in @ ( c_Zorn_OHausdorff__1 @ V_S @ T_a ) @ ( c_Zorn_Omaxchain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(15,plain,
( ( ! [V_c: $i,V_A: $i,T_a: $i,V_B: $i] :
( ~ ( c_in @ V_c @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
| ( c_in @ V_c @ V_B @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(16,plain,
( ( ! [V_U: $i] :
( ( V_U
!= ( v_x @ V_U ) )
| ~ ( c_in @ V_U @ v_S @ ( tc_set @ t_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(17,plain,
( ( ! [V_U: $i] :
( ( c_lessequals @ V_U @ ( v_x @ V_U ) @ ( tc_set @ t_a ) )
| ~ ( c_in @ V_U @ v_S @ ( tc_set @ t_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(18,plain,
( ( ! [V_U: $i] :
( ( c_in @ ( v_x @ V_U ) @ v_S @ ( tc_set @ t_a ) )
| ~ ( c_in @ V_U @ v_S @ ( tc_set @ t_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(19,plain,
( ( ! [V_U: $i] :
( ( c_in @ ( c_Union @ V_U @ t_a ) @ v_S @ ( tc_set @ t_a ) )
| ~ ( c_in @ V_U @ ( c_Zorn_Ochain @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(20,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(21,plain,
( ( ! [V_u: $i,V_S: $i,T_a: $i] :
( ~ ( c_in @ V_u @ V_S @ ( tc_set @ T_a ) )
| ! [V_c: $i] :
( ~ ( c_in @ V_c @ ( c_Zorn_Omaxchain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ~ ( c_lessequals @ ( c_Union @ V_c @ T_a ) @ V_u @ ( tc_set @ T_a ) )
| ( ( c_Union @ V_c @ T_a )
= V_u ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(22,plain,
( ( ! [V_c: $i,V_A: $i,T_a: $i] :
( ~ ( c_in @ V_c @ V_A @ T_a )
| ! [V_B: $i] :
( ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
| ( c_in @ V_c @ V_B @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(23,plain,
( ( ! [V_U: $i] :
( ( V_U
!= ( v_x @ V_U ) )
| ~ ( c_in @ V_U @ v_S @ ( tc_set @ t_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[16]) ).
thf(24,plain,
( ( ! [V_U: $i] :
( ( c_in @ ( c_Union @ V_U @ t_a ) @ v_S @ ( tc_set @ t_a ) )
| ~ ( c_in @ V_U @ ( c_Zorn_Ochain @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(25,plain,
( ( ! [V_U: $i] :
( ( c_in @ ( v_x @ V_U ) @ v_S @ ( tc_set @ t_a ) )
| ~ ( c_in @ V_U @ v_S @ ( tc_set @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(26,plain,
( ( ! [V_U: $i] :
( ( c_lessequals @ V_U @ ( v_x @ V_U ) @ ( tc_set @ t_a ) )
| ~ ( c_in @ V_U @ v_S @ ( tc_set @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(27,plain,
( ( ! [V_U: $i] :
( ( V_U
!= ( v_x @ V_U ) )
| ~ ( c_in @ V_U @ v_S @ ( tc_set @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(28,plain,
( ( ! [V_c: $i,V_A: $i,T_a: $i] :
( ~ ( c_in @ V_c @ V_A @ T_a )
| ! [V_B: $i] :
( ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
| ( c_in @ V_c @ V_B @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(29,plain,
( ( ! [V_S: $i,T_a: $i] : ( c_in @ ( c_Zorn_OHausdorff__1 @ V_S @ T_a ) @ ( c_Zorn_Omaxchain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(30,plain,
( ( ! [V_u: $i,V_S: $i,T_a: $i] :
( ~ ( c_in @ V_u @ V_S @ ( tc_set @ T_a ) )
| ! [V_c: $i] :
( ~ ( c_in @ V_c @ ( c_Zorn_Omaxchain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ~ ( c_lessequals @ ( c_Union @ V_c @ T_a ) @ V_u @ ( tc_set @ T_a ) )
| ( ( c_Union @ V_c @ T_a )
= V_u ) ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(31,plain,
( ( ! [V_S: $i,T_a: $i] : ( c_lessequals @ ( c_Zorn_Omaxchain @ V_S @ T_a ) @ ( c_Zorn_Ochain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ ( tc_set @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(32,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(33,plain,
! [SV1: $i] :
( ( ( c_in @ ( c_Union @ SV1 @ t_a ) @ v_S @ ( tc_set @ t_a ) )
| ~ ( c_in @ SV1 @ ( c_Zorn_Ochain @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(34,plain,
! [SV2: $i] :
( ( ( c_in @ ( v_x @ SV2 ) @ v_S @ ( tc_set @ t_a ) )
| ~ ( c_in @ SV2 @ v_S @ ( tc_set @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(35,plain,
! [SV3: $i] :
( ( ( c_lessequals @ SV3 @ ( v_x @ SV3 ) @ ( tc_set @ t_a ) )
| ~ ( c_in @ SV3 @ v_S @ ( tc_set @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(36,plain,
! [SV4: $i] :
( ( ( SV4
!= ( v_x @ SV4 ) )
| ~ ( c_in @ SV4 @ v_S @ ( tc_set @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(37,plain,
! [SV5: $i] :
( ( ! [SY16: $i,SY17: $i] :
( ~ ( c_in @ SV5 @ SY16 @ SY17 )
| ! [SY18: $i] :
( ~ ( c_lessequals @ SY16 @ SY18 @ ( tc_set @ SY17 ) )
| ( c_in @ SV5 @ SY18 @ SY17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(38,plain,
! [SV6: $i] :
( ( ! [SY19: $i] : ( c_in @ ( c_Zorn_OHausdorff__1 @ SV6 @ SY19 ) @ ( c_Zorn_Omaxchain @ SV6 @ SY19 ) @ ( tc_set @ ( tc_set @ SY19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(39,plain,
! [SV7: $i] :
( ( ! [SY20: $i,SY21: $i] :
( ~ ( c_in @ SV7 @ SY20 @ ( tc_set @ SY21 ) )
| ! [SY22: $i] :
( ~ ( c_in @ SY22 @ ( c_Zorn_Omaxchain @ SY20 @ SY21 ) @ ( tc_set @ ( tc_set @ SY21 ) ) )
| ~ ( c_lessequals @ ( c_Union @ SY22 @ SY21 ) @ SV7 @ ( tc_set @ SY21 ) )
| ( ( c_Union @ SY22 @ SY21 )
= SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(40,plain,
! [SV8: $i] :
( ( ! [SY23: $i] : ( c_lessequals @ ( c_Zorn_Omaxchain @ SV8 @ SY23 ) @ ( c_Zorn_Ochain @ SV8 @ SY23 ) @ ( tc_set @ ( tc_set @ ( tc_set @ SY23 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(41,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(42,plain,
! [SV1: $i] :
( ( ( c_in @ ( c_Union @ SV1 @ t_a ) @ v_S @ ( tc_set @ t_a ) )
= $true )
| ( ( ~ ( c_in @ SV1 @ ( c_Zorn_Ochain @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(43,plain,
! [SV2: $i] :
( ( ( c_in @ ( v_x @ SV2 ) @ v_S @ ( tc_set @ t_a ) )
= $true )
| ( ( ~ ( c_in @ SV2 @ v_S @ ( tc_set @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).
thf(44,plain,
! [SV3: $i] :
( ( ( c_lessequals @ SV3 @ ( v_x @ SV3 ) @ ( tc_set @ t_a ) )
= $true )
| ( ( ~ ( c_in @ SV3 @ v_S @ ( tc_set @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(45,plain,
! [SV4: $i] :
( ( ( ( SV4
!= ( v_x @ SV4 ) ) )
= $true )
| ( ( ~ ( c_in @ SV4 @ v_S @ ( tc_set @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(46,plain,
! [SV9: $i,SV5: $i] :
( ( ! [SY24: $i] :
( ~ ( c_in @ SV5 @ SV9 @ SY24 )
| ! [SY25: $i] :
( ~ ( c_lessequals @ SV9 @ SY25 @ ( tc_set @ SY24 ) )
| ( c_in @ SV5 @ SY25 @ SY24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(47,plain,
! [SV10: $i,SV6: $i] :
( ( c_in @ ( c_Zorn_OHausdorff__1 @ SV6 @ SV10 ) @ ( c_Zorn_Omaxchain @ SV6 @ SV10 ) @ ( tc_set @ ( tc_set @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(48,plain,
! [SV11: $i,SV7: $i] :
( ( ! [SY26: $i] :
( ~ ( c_in @ SV7 @ SV11 @ ( tc_set @ SY26 ) )
| ! [SY27: $i] :
( ~ ( c_in @ SY27 @ ( c_Zorn_Omaxchain @ SV11 @ SY26 ) @ ( tc_set @ ( tc_set @ SY26 ) ) )
| ~ ( c_lessequals @ ( c_Union @ SY27 @ SY26 ) @ SV7 @ ( tc_set @ SY26 ) )
| ( ( c_Union @ SY27 @ SY26 )
= SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(49,plain,
! [SV12: $i,SV8: $i] :
( ( c_lessequals @ ( c_Zorn_Omaxchain @ SV8 @ SV12 ) @ ( c_Zorn_Ochain @ SV8 @ SV12 ) @ ( tc_set @ ( tc_set @ ( tc_set @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(50,plain,
! [SV1: $i] :
( ( ( c_in @ SV1 @ ( c_Zorn_Ochain @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) )
= $false )
| ( ( c_in @ ( c_Union @ SV1 @ t_a ) @ v_S @ ( tc_set @ t_a ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(51,plain,
! [SV2: $i] :
( ( ( c_in @ SV2 @ v_S @ ( tc_set @ t_a ) )
= $false )
| ( ( c_in @ ( v_x @ SV2 ) @ v_S @ ( tc_set @ t_a ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(52,plain,
! [SV3: $i] :
( ( ( c_in @ SV3 @ v_S @ ( tc_set @ t_a ) )
= $false )
| ( ( c_lessequals @ SV3 @ ( v_x @ SV3 ) @ ( tc_set @ t_a ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(53,plain,
! [SV4: $i] :
( ( ( SV4
= ( v_x @ SV4 ) )
= $false )
| ( ( ~ ( c_in @ SV4 @ v_S @ ( tc_set @ t_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(54,plain,
! [SV13: $i,SV9: $i,SV5: $i] :
( ( ~ ( c_in @ SV5 @ SV9 @ SV13 )
| ! [SY28: $i] :
( ~ ( c_lessequals @ SV9 @ SY28 @ ( tc_set @ SV13 ) )
| ( c_in @ SV5 @ SY28 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(55,plain,
! [SV14: $i,SV11: $i,SV7: $i] :
( ( ~ ( c_in @ SV7 @ SV11 @ ( tc_set @ SV14 ) )
| ! [SY29: $i] :
( ~ ( c_in @ SY29 @ ( c_Zorn_Omaxchain @ SV11 @ SV14 ) @ ( tc_set @ ( tc_set @ SV14 ) ) )
| ~ ( c_lessequals @ ( c_Union @ SY29 @ SV14 ) @ SV7 @ ( tc_set @ SV14 ) )
| ( ( c_Union @ SY29 @ SV14 )
= SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(56,plain,
! [SV4: $i] :
( ( ( c_in @ SV4 @ v_S @ ( tc_set @ t_a ) )
= $false )
| ( ( SV4
= ( v_x @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(57,plain,
! [SV13: $i,SV9: $i,SV5: $i] :
( ( ( ~ ( c_in @ SV5 @ SV9 @ SV13 ) )
= $true )
| ( ( ! [SY28: $i] :
( ~ ( c_lessequals @ SV9 @ SY28 @ ( tc_set @ SV13 ) )
| ( c_in @ SV5 @ SY28 @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[54]) ).
thf(58,plain,
! [SV14: $i,SV11: $i,SV7: $i] :
( ( ( ~ ( c_in @ SV7 @ SV11 @ ( tc_set @ SV14 ) ) )
= $true )
| ( ( ! [SY29: $i] :
( ~ ( c_in @ SY29 @ ( c_Zorn_Omaxchain @ SV11 @ SV14 ) @ ( tc_set @ ( tc_set @ SV14 ) ) )
| ~ ( c_lessequals @ ( c_Union @ SY29 @ SV14 ) @ SV7 @ ( tc_set @ SV14 ) )
| ( ( c_Union @ SY29 @ SV14 )
= SV7 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(59,plain,
! [SV13: $i,SV9: $i,SV5: $i] :
( ( ( c_in @ SV5 @ SV9 @ SV13 )
= $false )
| ( ( ! [SY28: $i] :
( ~ ( c_lessequals @ SV9 @ SY28 @ ( tc_set @ SV13 ) )
| ( c_in @ SV5 @ SY28 @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(60,plain,
! [SV14: $i,SV11: $i,SV7: $i] :
( ( ( c_in @ SV7 @ SV11 @ ( tc_set @ SV14 ) )
= $false )
| ( ( ! [SY29: $i] :
( ~ ( c_in @ SY29 @ ( c_Zorn_Omaxchain @ SV11 @ SV14 ) @ ( tc_set @ ( tc_set @ SV14 ) ) )
| ~ ( c_lessequals @ ( c_Union @ SY29 @ SV14 ) @ SV7 @ ( tc_set @ SV14 ) )
| ( ( c_Union @ SY29 @ SV14 )
= SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(61,plain,
! [SV5: $i,SV13: $i,SV15: $i,SV9: $i] :
( ( ( ~ ( c_lessequals @ SV9 @ SV15 @ ( tc_set @ SV13 ) )
| ( c_in @ SV5 @ SV15 @ SV13 ) )
= $true )
| ( ( c_in @ SV5 @ SV9 @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(62,plain,
! [SV7: $i,SV14: $i,SV11: $i,SV16: $i] :
( ( ( ~ ( c_in @ SV16 @ ( c_Zorn_Omaxchain @ SV11 @ SV14 ) @ ( tc_set @ ( tc_set @ SV14 ) ) )
| ~ ( c_lessequals @ ( c_Union @ SV16 @ SV14 ) @ SV7 @ ( tc_set @ SV14 ) )
| ( ( c_Union @ SV16 @ SV14 )
= SV7 ) )
= $true )
| ( ( c_in @ SV7 @ SV11 @ ( tc_set @ SV14 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(63,plain,
! [SV5: $i,SV13: $i,SV15: $i,SV9: $i] :
( ( ( ~ ( c_lessequals @ SV9 @ SV15 @ ( tc_set @ SV13 ) ) )
= $true )
| ( ( c_in @ SV5 @ SV15 @ SV13 )
= $true )
| ( ( c_in @ SV5 @ SV9 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(64,plain,
! [SV7: $i,SV14: $i,SV11: $i,SV16: $i] :
( ( ( ~ ( c_in @ SV16 @ ( c_Zorn_Omaxchain @ SV11 @ SV14 ) @ ( tc_set @ ( tc_set @ SV14 ) ) ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Union @ SV16 @ SV14 ) @ SV7 @ ( tc_set @ SV14 ) )
| ( ( c_Union @ SV16 @ SV14 )
= SV7 ) )
= $true )
| ( ( c_in @ SV7 @ SV11 @ ( tc_set @ SV14 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(65,plain,
! [SV5: $i,SV13: $i,SV15: $i,SV9: $i] :
( ( ( c_lessequals @ SV9 @ SV15 @ ( tc_set @ SV13 ) )
= $false )
| ( ( c_in @ SV5 @ SV15 @ SV13 )
= $true )
| ( ( c_in @ SV5 @ SV9 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(66,plain,
! [SV7: $i,SV14: $i,SV11: $i,SV16: $i] :
( ( ( c_in @ SV16 @ ( c_Zorn_Omaxchain @ SV11 @ SV14 ) @ ( tc_set @ ( tc_set @ SV14 ) ) )
= $false )
| ( ( ~ ( c_lessequals @ ( c_Union @ SV16 @ SV14 ) @ SV7 @ ( tc_set @ SV14 ) )
| ( ( c_Union @ SV16 @ SV14 )
= SV7 ) )
= $true )
| ( ( c_in @ SV7 @ SV11 @ ( tc_set @ SV14 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(67,plain,
! [SV11: $i,SV7: $i,SV14: $i,SV16: $i] :
( ( ( ~ ( c_lessequals @ ( c_Union @ SV16 @ SV14 ) @ SV7 @ ( tc_set @ SV14 ) ) )
= $true )
| ( ( ( c_Union @ SV16 @ SV14 )
= SV7 )
= $true )
| ( ( c_in @ SV16 @ ( c_Zorn_Omaxchain @ SV11 @ SV14 ) @ ( tc_set @ ( tc_set @ SV14 ) ) )
= $false )
| ( ( c_in @ SV7 @ SV11 @ ( tc_set @ SV14 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[66]) ).
thf(68,plain,
! [SV11: $i,SV7: $i,SV14: $i,SV16: $i] :
( ( ( c_lessequals @ ( c_Union @ SV16 @ SV14 ) @ SV7 @ ( tc_set @ SV14 ) )
= $false )
| ( ( ( c_Union @ SV16 @ SV14 )
= SV7 )
= $true )
| ( ( c_in @ SV16 @ ( c_Zorn_Omaxchain @ SV11 @ SV14 ) @ ( tc_set @ ( tc_set @ SV14 ) ) )
= $false )
| ( ( c_in @ SV7 @ SV11 @ ( tc_set @ SV14 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(69,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[41,68,65,56,52,51,50,49,47]) ).
thf(70,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET865-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.14 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.35 % Computer : n028.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sat Jul 9 17:45:41 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36
% 0.14/0.36 No.of.Axioms: 8
% 0.14/0.36
% 0.14/0.36 Length.of.Defs: 0
% 0.14/0.36
% 0.14/0.36 Contains.Choice.Funs: false
% 0.14/0.37 (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)...
% 0.21/0.43
% 0.21/0.43 ********************************
% 0.21/0.43 * All subproblems solved! *
% 0.21/0.43 ********************************
% 0.21/0.43 % SZS status Unsatisfiable 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:69,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.21/0.43
% 0.21/0.43 %**** Beginning of derivation protocol ****
% 0.21/0.43 % SZS output start CNFRefutation
% See solution above
% 0.21/0.43
% 0.21/0.43 %**** End of derivation protocol ****
% 0.21/0.43 %**** no. of clauses in derivation: 70 ****
% 0.21/0.43 %**** clause counter: 69 ****
% 0.21/0.43
% 0.21/0.43 % SZS status Unsatisfiable 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:69,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------