TSTP Solution File: SEU360+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU360+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art07.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 2018MB
% OS : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sun Dec 26 07:44:41 EST 2010
% Result : Theorem 0.25s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 10
% Syntax : Number of formulae : 101 ( 10 unt; 0 def)
% Number of atoms : 596 ( 0 equ)
% Maximal formula atoms : 32 ( 5 avg)
% Number of connectives : 837 ( 342 ~; 357 |; 113 &)
% ( 4 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 192 ( 0 sgn 113 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(3,axiom,
! [X1] :
( ( antisymmetric_relstr(X1)
& rel_str(X1) )
=> ! [X2] :
( ex_sup_of_relstr_set(X1,X2)
<=> ? [X3] :
( element(X3,the_carrier(X1))
& relstr_set_smaller(X1,X2,X3)
& ! [X4] :
( element(X4,the_carrier(X1))
=> ( relstr_set_smaller(X1,X2,X4)
=> related(X1,X3,X4) ) ) ) ) ),
file('/tmp/tmpCOVOkr/sel_SEU360+1.p_1',t15_yellow_0) ).
fof(4,axiom,
! [X1] :
( ( antisymmetric_relstr(X1)
& rel_str(X1) )
=> ! [X2] :
( ex_inf_of_relstr_set(X1,X2)
<=> ? [X3] :
( element(X3,the_carrier(X1))
& relstr_element_smaller(X1,X2,X3)
& ! [X4] :
( element(X4,the_carrier(X1))
=> ( relstr_element_smaller(X1,X2,X4)
=> related(X1,X4,X3) ) ) ) ) ),
file('/tmp/tmpCOVOkr/sel_SEU360+1.p_1',t16_yellow_0) ).
fof(6,axiom,
! [X1] :
( rel_str(X1)
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ( relstr_set_smaller(X1,empty_set,X2)
& relstr_element_smaller(X1,empty_set,X2) ) ) ),
file('/tmp/tmpCOVOkr/sel_SEU360+1.p_1',t6_yellow_0) ).
fof(7,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
file('/tmp/tmpCOVOkr/sel_SEU360+1.p_1',t1_subset) ).
fof(9,conjecture,
! [X1] :
( ( ~ empty_carrier(X1)
& antisymmetric_relstr(X1)
& lower_bounded_relstr(X1)
& rel_str(X1) )
=> ( ex_sup_of_relstr_set(X1,empty_set)
& ex_inf_of_relstr_set(X1,the_carrier(X1)) ) ),
file('/tmp/tmpCOVOkr/sel_SEU360+1.p_1',t42_yellow_0) ).
fof(10,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(the_carrier(X1)) ),
file('/tmp/tmpCOVOkr/sel_SEU360+1.p_1',fc1_struct_0) ).
fof(16,axiom,
! [X1] :
( rel_str(X1)
=> one_sorted_str(X1) ),
file('/tmp/tmpCOVOkr/sel_SEU360+1.p_1',dt_l1_orders_2) ).
fof(17,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/tmp/tmpCOVOkr/sel_SEU360+1.p_1',t2_subset) ).
fof(19,axiom,
! [X1] :
( rel_str(X1)
=> ( lower_bounded_relstr(X1)
<=> ? [X2] :
( element(X2,the_carrier(X1))
& relstr_element_smaller(X1,the_carrier(X1),X2) ) ) ),
file('/tmp/tmpCOVOkr/sel_SEU360+1.p_1',d4_yellow_0) ).
fof(23,axiom,
! [X1] :
( rel_str(X1)
=> ! [X2,X3] :
( element(X3,the_carrier(X1))
=> ( relstr_element_smaller(X1,X2,X3)
<=> ! [X4] :
( element(X4,the_carrier(X1))
=> ( in(X4,X2)
=> related(X1,X3,X4) ) ) ) ) ),
file('/tmp/tmpCOVOkr/sel_SEU360+1.p_1',d8_lattice3) ).
fof(28,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& antisymmetric_relstr(X1)
& lower_bounded_relstr(X1)
& rel_str(X1) )
=> ( ex_sup_of_relstr_set(X1,empty_set)
& ex_inf_of_relstr_set(X1,the_carrier(X1)) ) ),
inference(assume_negation,[status(cth)],[9]) ).
fof(29,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& antisymmetric_relstr(X1)
& lower_bounded_relstr(X1)
& rel_str(X1) )
=> ( ex_sup_of_relstr_set(X1,empty_set)
& ex_inf_of_relstr_set(X1,the_carrier(X1)) ) ),
inference(fof_simplification,[status(thm)],[28,theory(equality)]) ).
fof(30,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[10,theory(equality)]) ).
fof(39,plain,
! [X1] :
( ~ antisymmetric_relstr(X1)
| ~ rel_str(X1)
| ! [X2] :
( ( ~ ex_sup_of_relstr_set(X1,X2)
| ? [X3] :
( element(X3,the_carrier(X1))
& relstr_set_smaller(X1,X2,X3)
& ! [X4] :
( ~ element(X4,the_carrier(X1))
| ~ relstr_set_smaller(X1,X2,X4)
| related(X1,X3,X4) ) ) )
& ( ! [X3] :
( ~ element(X3,the_carrier(X1))
| ~ relstr_set_smaller(X1,X2,X3)
| ? [X4] :
( element(X4,the_carrier(X1))
& relstr_set_smaller(X1,X2,X4)
& ~ related(X1,X3,X4) ) )
| ex_sup_of_relstr_set(X1,X2) ) ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(40,plain,
! [X5] :
( ~ antisymmetric_relstr(X5)
| ~ rel_str(X5)
| ! [X6] :
( ( ~ ex_sup_of_relstr_set(X5,X6)
| ? [X7] :
( element(X7,the_carrier(X5))
& relstr_set_smaller(X5,X6,X7)
& ! [X8] :
( ~ element(X8,the_carrier(X5))
| ~ relstr_set_smaller(X5,X6,X8)
| related(X5,X7,X8) ) ) )
& ( ! [X9] :
( ~ element(X9,the_carrier(X5))
| ~ relstr_set_smaller(X5,X6,X9)
| ? [X10] :
( element(X10,the_carrier(X5))
& relstr_set_smaller(X5,X6,X10)
& ~ related(X5,X9,X10) ) )
| ex_sup_of_relstr_set(X5,X6) ) ) ),
inference(variable_rename,[status(thm)],[39]) ).
fof(41,plain,
! [X5] :
( ~ antisymmetric_relstr(X5)
| ~ rel_str(X5)
| ! [X6] :
( ( ~ ex_sup_of_relstr_set(X5,X6)
| ( element(esk1_2(X5,X6),the_carrier(X5))
& relstr_set_smaller(X5,X6,esk1_2(X5,X6))
& ! [X8] :
( ~ element(X8,the_carrier(X5))
| ~ relstr_set_smaller(X5,X6,X8)
| related(X5,esk1_2(X5,X6),X8) ) ) )
& ( ! [X9] :
( ~ element(X9,the_carrier(X5))
| ~ relstr_set_smaller(X5,X6,X9)
| ( element(esk2_3(X5,X6,X9),the_carrier(X5))
& relstr_set_smaller(X5,X6,esk2_3(X5,X6,X9))
& ~ related(X5,X9,esk2_3(X5,X6,X9)) ) )
| ex_sup_of_relstr_set(X5,X6) ) ) ),
inference(skolemize,[status(esa)],[40]) ).
fof(42,plain,
! [X5,X6,X8,X9] :
( ( ( ~ element(X9,the_carrier(X5))
| ~ relstr_set_smaller(X5,X6,X9)
| ( element(esk2_3(X5,X6,X9),the_carrier(X5))
& relstr_set_smaller(X5,X6,esk2_3(X5,X6,X9))
& ~ related(X5,X9,esk2_3(X5,X6,X9)) )
| ex_sup_of_relstr_set(X5,X6) )
& ( ( ( ~ element(X8,the_carrier(X5))
| ~ relstr_set_smaller(X5,X6,X8)
| related(X5,esk1_2(X5,X6),X8) )
& element(esk1_2(X5,X6),the_carrier(X5))
& relstr_set_smaller(X5,X6,esk1_2(X5,X6)) )
| ~ ex_sup_of_relstr_set(X5,X6) ) )
| ~ antisymmetric_relstr(X5)
| ~ rel_str(X5) ),
inference(shift_quantors,[status(thm)],[41]) ).
fof(43,plain,
! [X5,X6,X8,X9] :
( ( element(esk2_3(X5,X6,X9),the_carrier(X5))
| ~ element(X9,the_carrier(X5))
| ~ relstr_set_smaller(X5,X6,X9)
| ex_sup_of_relstr_set(X5,X6)
| ~ antisymmetric_relstr(X5)
| ~ rel_str(X5) )
& ( relstr_set_smaller(X5,X6,esk2_3(X5,X6,X9))
| ~ element(X9,the_carrier(X5))
| ~ relstr_set_smaller(X5,X6,X9)
| ex_sup_of_relstr_set(X5,X6)
| ~ antisymmetric_relstr(X5)
| ~ rel_str(X5) )
& ( ~ related(X5,X9,esk2_3(X5,X6,X9))
| ~ element(X9,the_carrier(X5))
| ~ relstr_set_smaller(X5,X6,X9)
| ex_sup_of_relstr_set(X5,X6)
| ~ antisymmetric_relstr(X5)
| ~ rel_str(X5) )
& ( ~ element(X8,the_carrier(X5))
| ~ relstr_set_smaller(X5,X6,X8)
| related(X5,esk1_2(X5,X6),X8)
| ~ ex_sup_of_relstr_set(X5,X6)
| ~ antisymmetric_relstr(X5)
| ~ rel_str(X5) )
& ( element(esk1_2(X5,X6),the_carrier(X5))
| ~ ex_sup_of_relstr_set(X5,X6)
| ~ antisymmetric_relstr(X5)
| ~ rel_str(X5) )
& ( relstr_set_smaller(X5,X6,esk1_2(X5,X6))
| ~ ex_sup_of_relstr_set(X5,X6)
| ~ antisymmetric_relstr(X5)
| ~ rel_str(X5) ) ),
inference(distribute,[status(thm)],[42]) ).
cnf(47,plain,
( ex_sup_of_relstr_set(X1,X2)
| ~ rel_str(X1)
| ~ antisymmetric_relstr(X1)
| ~ relstr_set_smaller(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ related(X1,X3,esk2_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[43]) ).
cnf(49,plain,
( ex_sup_of_relstr_set(X1,X2)
| element(esk2_3(X1,X2,X3),the_carrier(X1))
| ~ rel_str(X1)
| ~ antisymmetric_relstr(X1)
| ~ relstr_set_smaller(X1,X2,X3)
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[43]) ).
fof(50,plain,
! [X1] :
( ~ antisymmetric_relstr(X1)
| ~ rel_str(X1)
| ! [X2] :
( ( ~ ex_inf_of_relstr_set(X1,X2)
| ? [X3] :
( element(X3,the_carrier(X1))
& relstr_element_smaller(X1,X2,X3)
& ! [X4] :
( ~ element(X4,the_carrier(X1))
| ~ relstr_element_smaller(X1,X2,X4)
| related(X1,X4,X3) ) ) )
& ( ! [X3] :
( ~ element(X3,the_carrier(X1))
| ~ relstr_element_smaller(X1,X2,X3)
| ? [X4] :
( element(X4,the_carrier(X1))
& relstr_element_smaller(X1,X2,X4)
& ~ related(X1,X4,X3) ) )
| ex_inf_of_relstr_set(X1,X2) ) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(51,plain,
! [X5] :
( ~ antisymmetric_relstr(X5)
| ~ rel_str(X5)
| ! [X6] :
( ( ~ ex_inf_of_relstr_set(X5,X6)
| ? [X7] :
( element(X7,the_carrier(X5))
& relstr_element_smaller(X5,X6,X7)
& ! [X8] :
( ~ element(X8,the_carrier(X5))
| ~ relstr_element_smaller(X5,X6,X8)
| related(X5,X8,X7) ) ) )
& ( ! [X9] :
( ~ element(X9,the_carrier(X5))
| ~ relstr_element_smaller(X5,X6,X9)
| ? [X10] :
( element(X10,the_carrier(X5))
& relstr_element_smaller(X5,X6,X10)
& ~ related(X5,X10,X9) ) )
| ex_inf_of_relstr_set(X5,X6) ) ) ),
inference(variable_rename,[status(thm)],[50]) ).
fof(52,plain,
! [X5] :
( ~ antisymmetric_relstr(X5)
| ~ rel_str(X5)
| ! [X6] :
( ( ~ ex_inf_of_relstr_set(X5,X6)
| ( element(esk3_2(X5,X6),the_carrier(X5))
& relstr_element_smaller(X5,X6,esk3_2(X5,X6))
& ! [X8] :
( ~ element(X8,the_carrier(X5))
| ~ relstr_element_smaller(X5,X6,X8)
| related(X5,X8,esk3_2(X5,X6)) ) ) )
& ( ! [X9] :
( ~ element(X9,the_carrier(X5))
| ~ relstr_element_smaller(X5,X6,X9)
| ( element(esk4_3(X5,X6,X9),the_carrier(X5))
& relstr_element_smaller(X5,X6,esk4_3(X5,X6,X9))
& ~ related(X5,esk4_3(X5,X6,X9),X9) ) )
| ex_inf_of_relstr_set(X5,X6) ) ) ),
inference(skolemize,[status(esa)],[51]) ).
fof(53,plain,
! [X5,X6,X8,X9] :
( ( ( ~ element(X9,the_carrier(X5))
| ~ relstr_element_smaller(X5,X6,X9)
| ( element(esk4_3(X5,X6,X9),the_carrier(X5))
& relstr_element_smaller(X5,X6,esk4_3(X5,X6,X9))
& ~ related(X5,esk4_3(X5,X6,X9),X9) )
| ex_inf_of_relstr_set(X5,X6) )
& ( ( ( ~ element(X8,the_carrier(X5))
| ~ relstr_element_smaller(X5,X6,X8)
| related(X5,X8,esk3_2(X5,X6)) )
& element(esk3_2(X5,X6),the_carrier(X5))
& relstr_element_smaller(X5,X6,esk3_2(X5,X6)) )
| ~ ex_inf_of_relstr_set(X5,X6) ) )
| ~ antisymmetric_relstr(X5)
| ~ rel_str(X5) ),
inference(shift_quantors,[status(thm)],[52]) ).
fof(54,plain,
! [X5,X6,X8,X9] :
( ( element(esk4_3(X5,X6,X9),the_carrier(X5))
| ~ element(X9,the_carrier(X5))
| ~ relstr_element_smaller(X5,X6,X9)
| ex_inf_of_relstr_set(X5,X6)
| ~ antisymmetric_relstr(X5)
| ~ rel_str(X5) )
& ( relstr_element_smaller(X5,X6,esk4_3(X5,X6,X9))
| ~ element(X9,the_carrier(X5))
| ~ relstr_element_smaller(X5,X6,X9)
| ex_inf_of_relstr_set(X5,X6)
| ~ antisymmetric_relstr(X5)
| ~ rel_str(X5) )
& ( ~ related(X5,esk4_3(X5,X6,X9),X9)
| ~ element(X9,the_carrier(X5))
| ~ relstr_element_smaller(X5,X6,X9)
| ex_inf_of_relstr_set(X5,X6)
| ~ antisymmetric_relstr(X5)
| ~ rel_str(X5) )
& ( ~ element(X8,the_carrier(X5))
| ~ relstr_element_smaller(X5,X6,X8)
| related(X5,X8,esk3_2(X5,X6))
| ~ ex_inf_of_relstr_set(X5,X6)
| ~ antisymmetric_relstr(X5)
| ~ rel_str(X5) )
& ( element(esk3_2(X5,X6),the_carrier(X5))
| ~ ex_inf_of_relstr_set(X5,X6)
| ~ antisymmetric_relstr(X5)
| ~ rel_str(X5) )
& ( relstr_element_smaller(X5,X6,esk3_2(X5,X6))
| ~ ex_inf_of_relstr_set(X5,X6)
| ~ antisymmetric_relstr(X5)
| ~ rel_str(X5) ) ),
inference(distribute,[status(thm)],[53]) ).
cnf(58,plain,
( ex_inf_of_relstr_set(X1,X2)
| ~ rel_str(X1)
| ~ antisymmetric_relstr(X1)
| ~ relstr_element_smaller(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ related(X1,esk4_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[54]) ).
cnf(59,plain,
( ex_inf_of_relstr_set(X1,X2)
| relstr_element_smaller(X1,X2,esk4_3(X1,X2,X3))
| ~ rel_str(X1)
| ~ antisymmetric_relstr(X1)
| ~ relstr_element_smaller(X1,X2,X3)
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[54]) ).
cnf(60,plain,
( ex_inf_of_relstr_set(X1,X2)
| element(esk4_3(X1,X2,X3),the_carrier(X1))
| ~ rel_str(X1)
| ~ antisymmetric_relstr(X1)
| ~ relstr_element_smaller(X1,X2,X3)
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[54]) ).
fof(62,plain,
! [X1] :
( ~ rel_str(X1)
| ! [X2] :
( ~ element(X2,the_carrier(X1))
| ( relstr_set_smaller(X1,empty_set,X2)
& relstr_element_smaller(X1,empty_set,X2) ) ) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(63,plain,
! [X3] :
( ~ rel_str(X3)
| ! [X4] :
( ~ element(X4,the_carrier(X3))
| ( relstr_set_smaller(X3,empty_set,X4)
& relstr_element_smaller(X3,empty_set,X4) ) ) ),
inference(variable_rename,[status(thm)],[62]) ).
fof(64,plain,
! [X3,X4] :
( ~ element(X4,the_carrier(X3))
| ( relstr_set_smaller(X3,empty_set,X4)
& relstr_element_smaller(X3,empty_set,X4) )
| ~ rel_str(X3) ),
inference(shift_quantors,[status(thm)],[63]) ).
fof(65,plain,
! [X3,X4] :
( ( relstr_set_smaller(X3,empty_set,X4)
| ~ element(X4,the_carrier(X3))
| ~ rel_str(X3) )
& ( relstr_element_smaller(X3,empty_set,X4)
| ~ element(X4,the_carrier(X3))
| ~ rel_str(X3) ) ),
inference(distribute,[status(thm)],[64]) ).
cnf(67,plain,
( relstr_set_smaller(X1,empty_set,X2)
| ~ rel_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[65]) ).
fof(68,plain,
! [X1,X2] :
( ~ in(X1,X2)
| element(X1,X2) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(69,plain,
! [X3,X4] :
( ~ in(X3,X4)
| element(X3,X4) ),
inference(variable_rename,[status(thm)],[68]) ).
cnf(70,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[69]) ).
fof(74,negated_conjecture,
? [X1] :
( ~ empty_carrier(X1)
& antisymmetric_relstr(X1)
& lower_bounded_relstr(X1)
& rel_str(X1)
& ( ~ ex_sup_of_relstr_set(X1,empty_set)
| ~ ex_inf_of_relstr_set(X1,the_carrier(X1)) ) ),
inference(fof_nnf,[status(thm)],[29]) ).
fof(75,negated_conjecture,
? [X2] :
( ~ empty_carrier(X2)
& antisymmetric_relstr(X2)
& lower_bounded_relstr(X2)
& rel_str(X2)
& ( ~ ex_sup_of_relstr_set(X2,empty_set)
| ~ ex_inf_of_relstr_set(X2,the_carrier(X2)) ) ),
inference(variable_rename,[status(thm)],[74]) ).
fof(76,negated_conjecture,
( ~ empty_carrier(esk5_0)
& antisymmetric_relstr(esk5_0)
& lower_bounded_relstr(esk5_0)
& rel_str(esk5_0)
& ( ~ ex_sup_of_relstr_set(esk5_0,empty_set)
| ~ ex_inf_of_relstr_set(esk5_0,the_carrier(esk5_0)) ) ),
inference(skolemize,[status(esa)],[75]) ).
cnf(77,negated_conjecture,
( ~ ex_inf_of_relstr_set(esk5_0,the_carrier(esk5_0))
| ~ ex_sup_of_relstr_set(esk5_0,empty_set) ),
inference(split_conjunct,[status(thm)],[76]) ).
cnf(78,negated_conjecture,
rel_str(esk5_0),
inference(split_conjunct,[status(thm)],[76]) ).
cnf(79,negated_conjecture,
lower_bounded_relstr(esk5_0),
inference(split_conjunct,[status(thm)],[76]) ).
cnf(80,negated_conjecture,
antisymmetric_relstr(esk5_0),
inference(split_conjunct,[status(thm)],[76]) ).
cnf(81,negated_conjecture,
~ empty_carrier(esk5_0),
inference(split_conjunct,[status(thm)],[76]) ).
fof(82,plain,
! [X1] :
( empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ empty(the_carrier(X1)) ),
inference(fof_nnf,[status(thm)],[30]) ).
fof(83,plain,
! [X2] :
( empty_carrier(X2)
| ~ one_sorted_str(X2)
| ~ empty(the_carrier(X2)) ),
inference(variable_rename,[status(thm)],[82]) ).
cnf(84,plain,
( empty_carrier(X1)
| ~ empty(the_carrier(X1))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[83]) ).
fof(99,plain,
! [X1] :
( ~ rel_str(X1)
| one_sorted_str(X1) ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(100,plain,
! [X2] :
( ~ rel_str(X2)
| one_sorted_str(X2) ),
inference(variable_rename,[status(thm)],[99]) ).
cnf(101,plain,
( one_sorted_str(X1)
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[100]) ).
fof(102,plain,
! [X1,X2] :
( ~ element(X1,X2)
| empty(X2)
| in(X1,X2) ),
inference(fof_nnf,[status(thm)],[17]) ).
fof(103,plain,
! [X3,X4] :
( ~ element(X3,X4)
| empty(X4)
| in(X3,X4) ),
inference(variable_rename,[status(thm)],[102]) ).
cnf(104,plain,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[103]) ).
fof(106,plain,
! [X1] :
( ~ rel_str(X1)
| ( ( ~ lower_bounded_relstr(X1)
| ? [X2] :
( element(X2,the_carrier(X1))
& relstr_element_smaller(X1,the_carrier(X1),X2) ) )
& ( ! [X2] :
( ~ element(X2,the_carrier(X1))
| ~ relstr_element_smaller(X1,the_carrier(X1),X2) )
| lower_bounded_relstr(X1) ) ) ),
inference(fof_nnf,[status(thm)],[19]) ).
fof(107,plain,
! [X3] :
( ~ rel_str(X3)
| ( ( ~ lower_bounded_relstr(X3)
| ? [X4] :
( element(X4,the_carrier(X3))
& relstr_element_smaller(X3,the_carrier(X3),X4) ) )
& ( ! [X5] :
( ~ element(X5,the_carrier(X3))
| ~ relstr_element_smaller(X3,the_carrier(X3),X5) )
| lower_bounded_relstr(X3) ) ) ),
inference(variable_rename,[status(thm)],[106]) ).
fof(108,plain,
! [X3] :
( ~ rel_str(X3)
| ( ( ~ lower_bounded_relstr(X3)
| ( element(esk9_1(X3),the_carrier(X3))
& relstr_element_smaller(X3,the_carrier(X3),esk9_1(X3)) ) )
& ( ! [X5] :
( ~ element(X5,the_carrier(X3))
| ~ relstr_element_smaller(X3,the_carrier(X3),X5) )
| lower_bounded_relstr(X3) ) ) ),
inference(skolemize,[status(esa)],[107]) ).
fof(109,plain,
! [X3,X5] :
( ( ( ~ element(X5,the_carrier(X3))
| ~ relstr_element_smaller(X3,the_carrier(X3),X5)
| lower_bounded_relstr(X3) )
& ( ~ lower_bounded_relstr(X3)
| ( element(esk9_1(X3),the_carrier(X3))
& relstr_element_smaller(X3,the_carrier(X3),esk9_1(X3)) ) ) )
| ~ rel_str(X3) ),
inference(shift_quantors,[status(thm)],[108]) ).
fof(110,plain,
! [X3,X5] :
( ( ~ element(X5,the_carrier(X3))
| ~ relstr_element_smaller(X3,the_carrier(X3),X5)
| lower_bounded_relstr(X3)
| ~ rel_str(X3) )
& ( element(esk9_1(X3),the_carrier(X3))
| ~ lower_bounded_relstr(X3)
| ~ rel_str(X3) )
& ( relstr_element_smaller(X3,the_carrier(X3),esk9_1(X3))
| ~ lower_bounded_relstr(X3)
| ~ rel_str(X3) ) ),
inference(distribute,[status(thm)],[109]) ).
cnf(111,plain,
( relstr_element_smaller(X1,the_carrier(X1),esk9_1(X1))
| ~ rel_str(X1)
| ~ lower_bounded_relstr(X1) ),
inference(split_conjunct,[status(thm)],[110]) ).
cnf(112,plain,
( element(esk9_1(X1),the_carrier(X1))
| ~ rel_str(X1)
| ~ lower_bounded_relstr(X1) ),
inference(split_conjunct,[status(thm)],[110]) ).
fof(121,plain,
! [X1] :
( ~ rel_str(X1)
| ! [X2,X3] :
( ~ element(X3,the_carrier(X1))
| ( ( ~ relstr_element_smaller(X1,X2,X3)
| ! [X4] :
( ~ element(X4,the_carrier(X1))
| ~ in(X4,X2)
| related(X1,X3,X4) ) )
& ( ? [X4] :
( element(X4,the_carrier(X1))
& in(X4,X2)
& ~ related(X1,X3,X4) )
| relstr_element_smaller(X1,X2,X3) ) ) ) ),
inference(fof_nnf,[status(thm)],[23]) ).
fof(122,plain,
! [X5] :
( ~ rel_str(X5)
| ! [X6,X7] :
( ~ element(X7,the_carrier(X5))
| ( ( ~ relstr_element_smaller(X5,X6,X7)
| ! [X8] :
( ~ element(X8,the_carrier(X5))
| ~ in(X8,X6)
| related(X5,X7,X8) ) )
& ( ? [X9] :
( element(X9,the_carrier(X5))
& in(X9,X6)
& ~ related(X5,X7,X9) )
| relstr_element_smaller(X5,X6,X7) ) ) ) ),
inference(variable_rename,[status(thm)],[121]) ).
fof(123,plain,
! [X5] :
( ~ rel_str(X5)
| ! [X6,X7] :
( ~ element(X7,the_carrier(X5))
| ( ( ~ relstr_element_smaller(X5,X6,X7)
| ! [X8] :
( ~ element(X8,the_carrier(X5))
| ~ in(X8,X6)
| related(X5,X7,X8) ) )
& ( ( element(esk12_3(X5,X6,X7),the_carrier(X5))
& in(esk12_3(X5,X6,X7),X6)
& ~ related(X5,X7,esk12_3(X5,X6,X7)) )
| relstr_element_smaller(X5,X6,X7) ) ) ) ),
inference(skolemize,[status(esa)],[122]) ).
fof(124,plain,
! [X5,X6,X7,X8] :
( ( ( ~ element(X8,the_carrier(X5))
| ~ in(X8,X6)
| related(X5,X7,X8)
| ~ relstr_element_smaller(X5,X6,X7) )
& ( ( element(esk12_3(X5,X6,X7),the_carrier(X5))
& in(esk12_3(X5,X6,X7),X6)
& ~ related(X5,X7,esk12_3(X5,X6,X7)) )
| relstr_element_smaller(X5,X6,X7) ) )
| ~ element(X7,the_carrier(X5))
| ~ rel_str(X5) ),
inference(shift_quantors,[status(thm)],[123]) ).
fof(125,plain,
! [X5,X6,X7,X8] :
( ( ~ element(X8,the_carrier(X5))
| ~ in(X8,X6)
| related(X5,X7,X8)
| ~ relstr_element_smaller(X5,X6,X7)
| ~ element(X7,the_carrier(X5))
| ~ rel_str(X5) )
& ( element(esk12_3(X5,X6,X7),the_carrier(X5))
| relstr_element_smaller(X5,X6,X7)
| ~ element(X7,the_carrier(X5))
| ~ rel_str(X5) )
& ( in(esk12_3(X5,X6,X7),X6)
| relstr_element_smaller(X5,X6,X7)
| ~ element(X7,the_carrier(X5))
| ~ rel_str(X5) )
& ( ~ related(X5,X7,esk12_3(X5,X6,X7))
| relstr_element_smaller(X5,X6,X7)
| ~ element(X7,the_carrier(X5))
| ~ rel_str(X5) ) ),
inference(distribute,[status(thm)],[124]) ).
cnf(129,plain,
( related(X1,X2,X4)
| ~ rel_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ relstr_element_smaller(X1,X3,X2)
| ~ in(X4,X3)
| ~ element(X4,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[125]) ).
cnf(146,negated_conjecture,
( ~ one_sorted_str(esk5_0)
| ~ empty(the_carrier(esk5_0)) ),
inference(spm,[status(thm)],[81,84,theory(equality)]) ).
cnf(158,plain,
( related(X1,esk9_1(X1),X2)
| ~ in(X2,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ element(esk9_1(X1),the_carrier(X1))
| ~ rel_str(X1)
| ~ lower_bounded_relstr(X1) ),
inference(spm,[status(thm)],[129,111,theory(equality)]) ).
cnf(163,plain,
( related(X1,esk4_3(X1,X2,X3),X4)
| ex_inf_of_relstr_set(X1,X2)
| ~ in(X4,X2)
| ~ element(X4,the_carrier(X1))
| ~ element(esk4_3(X1,X2,X3),the_carrier(X1))
| ~ rel_str(X1)
| ~ relstr_element_smaller(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ antisymmetric_relstr(X1) ),
inference(spm,[status(thm)],[129,59,theory(equality)]) ).
cnf(166,negated_conjecture,
( ~ empty(the_carrier(esk5_0))
| ~ rel_str(esk5_0) ),
inference(spm,[status(thm)],[146,101,theory(equality)]) ).
cnf(167,negated_conjecture,
( ~ empty(the_carrier(esk5_0))
| $false ),
inference(rw,[status(thm)],[166,78,theory(equality)]) ).
cnf(168,negated_conjecture,
~ empty(the_carrier(esk5_0)),
inference(cn,[status(thm)],[167,theory(equality)]) ).
cnf(199,plain,
( related(X1,esk9_1(X1),X2)
| ~ lower_bounded_relstr(X1)
| ~ in(X2,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ rel_str(X1) ),
inference(csr,[status(thm)],[158,112]) ).
cnf(200,plain,
( related(X1,esk9_1(X1),X2)
| ~ lower_bounded_relstr(X1)
| ~ in(X2,the_carrier(X1))
| ~ rel_str(X1) ),
inference(csr,[status(thm)],[199,70]) ).
cnf(202,plain,
( ex_sup_of_relstr_set(X1,X2)
| ~ relstr_set_smaller(X1,X2,esk9_1(X1))
| ~ element(esk9_1(X1),the_carrier(X1))
| ~ rel_str(X1)
| ~ antisymmetric_relstr(X1)
| ~ lower_bounded_relstr(X1)
| ~ in(esk2_3(X1,X2,esk9_1(X1)),the_carrier(X1)) ),
inference(spm,[status(thm)],[47,200,theory(equality)]) ).
cnf(254,plain,
( ex_inf_of_relstr_set(X1,X2)
| related(X1,esk4_3(X1,X2,X3),X4)
| ~ in(X4,X2)
| ~ relstr_element_smaller(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ element(X4,the_carrier(X1))
| ~ rel_str(X1)
| ~ antisymmetric_relstr(X1) ),
inference(csr,[status(thm)],[163,60]) ).
cnf(257,plain,
( ex_inf_of_relstr_set(X1,X2)
| ~ relstr_element_smaller(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ rel_str(X1)
| ~ antisymmetric_relstr(X1)
| ~ in(X3,X2) ),
inference(spm,[status(thm)],[58,254,theory(equality)]) ).
cnf(258,plain,
( ex_inf_of_relstr_set(X1,the_carrier(X1))
| ~ in(esk9_1(X1),the_carrier(X1))
| ~ element(esk9_1(X1),the_carrier(X1))
| ~ rel_str(X1)
| ~ antisymmetric_relstr(X1)
| ~ lower_bounded_relstr(X1) ),
inference(spm,[status(thm)],[257,111,theory(equality)]) ).
cnf(285,plain,
( ex_inf_of_relstr_set(X1,the_carrier(X1))
| ~ lower_bounded_relstr(X1)
| ~ in(esk9_1(X1),the_carrier(X1))
| ~ rel_str(X1)
| ~ antisymmetric_relstr(X1) ),
inference(csr,[status(thm)],[258,70]) ).
cnf(286,plain,
( ex_inf_of_relstr_set(X1,the_carrier(X1))
| empty(the_carrier(X1))
| ~ lower_bounded_relstr(X1)
| ~ rel_str(X1)
| ~ antisymmetric_relstr(X1)
| ~ element(esk9_1(X1),the_carrier(X1)) ),
inference(spm,[status(thm)],[285,104,theory(equality)]) ).
cnf(291,plain,
( ex_inf_of_relstr_set(X1,the_carrier(X1))
| empty(the_carrier(X1))
| ~ lower_bounded_relstr(X1)
| ~ rel_str(X1)
| ~ antisymmetric_relstr(X1) ),
inference(csr,[status(thm)],[286,112]) ).
cnf(292,negated_conjecture,
( ex_inf_of_relstr_set(esk5_0,the_carrier(esk5_0))
| empty(the_carrier(esk5_0))
| ~ rel_str(esk5_0)
| ~ antisymmetric_relstr(esk5_0) ),
inference(spm,[status(thm)],[291,79,theory(equality)]) ).
cnf(295,negated_conjecture,
( ex_inf_of_relstr_set(esk5_0,the_carrier(esk5_0))
| empty(the_carrier(esk5_0))
| $false
| ~ antisymmetric_relstr(esk5_0) ),
inference(rw,[status(thm)],[292,78,theory(equality)]) ).
cnf(296,negated_conjecture,
( ex_inf_of_relstr_set(esk5_0,the_carrier(esk5_0))
| empty(the_carrier(esk5_0))
| $false
| $false ),
inference(rw,[status(thm)],[295,80,theory(equality)]) ).
cnf(297,negated_conjecture,
( ex_inf_of_relstr_set(esk5_0,the_carrier(esk5_0))
| empty(the_carrier(esk5_0)) ),
inference(cn,[status(thm)],[296,theory(equality)]) ).
cnf(298,negated_conjecture,
ex_inf_of_relstr_set(esk5_0,the_carrier(esk5_0)),
inference(sr,[status(thm)],[297,168,theory(equality)]) ).
cnf(300,negated_conjecture,
( $false
| ~ ex_sup_of_relstr_set(esk5_0,empty_set) ),
inference(rw,[status(thm)],[77,298,theory(equality)]) ).
cnf(301,negated_conjecture,
~ ex_sup_of_relstr_set(esk5_0,empty_set),
inference(cn,[status(thm)],[300,theory(equality)]) ).
cnf(365,plain,
( ex_sup_of_relstr_set(X1,X2)
| ~ lower_bounded_relstr(X1)
| ~ in(esk2_3(X1,X2,esk9_1(X1)),the_carrier(X1))
| ~ relstr_set_smaller(X1,X2,esk9_1(X1))
| ~ rel_str(X1)
| ~ antisymmetric_relstr(X1) ),
inference(csr,[status(thm)],[202,112]) ).
cnf(366,plain,
( ex_sup_of_relstr_set(X1,X2)
| empty(the_carrier(X1))
| ~ lower_bounded_relstr(X1)
| ~ relstr_set_smaller(X1,X2,esk9_1(X1))
| ~ rel_str(X1)
| ~ antisymmetric_relstr(X1)
| ~ element(esk2_3(X1,X2,esk9_1(X1)),the_carrier(X1)) ),
inference(spm,[status(thm)],[365,104,theory(equality)]) ).
cnf(367,plain,
( ex_sup_of_relstr_set(X1,X2)
| empty(the_carrier(X1))
| ~ lower_bounded_relstr(X1)
| ~ relstr_set_smaller(X1,X2,esk9_1(X1))
| ~ rel_str(X1)
| ~ antisymmetric_relstr(X1)
| ~ element(esk9_1(X1),the_carrier(X1)) ),
inference(spm,[status(thm)],[366,49,theory(equality)]) ).
cnf(368,plain,
( ex_sup_of_relstr_set(X1,X2)
| empty(the_carrier(X1))
| ~ lower_bounded_relstr(X1)
| ~ relstr_set_smaller(X1,X2,esk9_1(X1))
| ~ rel_str(X1)
| ~ antisymmetric_relstr(X1) ),
inference(csr,[status(thm)],[367,112]) ).
cnf(369,plain,
( ex_sup_of_relstr_set(X1,empty_set)
| empty(the_carrier(X1))
| ~ lower_bounded_relstr(X1)
| ~ rel_str(X1)
| ~ antisymmetric_relstr(X1)
| ~ element(esk9_1(X1),the_carrier(X1)) ),
inference(spm,[status(thm)],[368,67,theory(equality)]) ).
cnf(375,plain,
( ex_sup_of_relstr_set(X1,empty_set)
| empty(the_carrier(X1))
| ~ lower_bounded_relstr(X1)
| ~ rel_str(X1)
| ~ antisymmetric_relstr(X1) ),
inference(csr,[status(thm)],[369,112]) ).
cnf(376,negated_conjecture,
( ex_sup_of_relstr_set(esk5_0,empty_set)
| empty(the_carrier(esk5_0))
| ~ rel_str(esk5_0)
| ~ antisymmetric_relstr(esk5_0) ),
inference(spm,[status(thm)],[375,79,theory(equality)]) ).
cnf(379,negated_conjecture,
( ex_sup_of_relstr_set(esk5_0,empty_set)
| empty(the_carrier(esk5_0))
| $false
| ~ antisymmetric_relstr(esk5_0) ),
inference(rw,[status(thm)],[376,78,theory(equality)]) ).
cnf(380,negated_conjecture,
( ex_sup_of_relstr_set(esk5_0,empty_set)
| empty(the_carrier(esk5_0))
| $false
| $false ),
inference(rw,[status(thm)],[379,80,theory(equality)]) ).
cnf(381,negated_conjecture,
( ex_sup_of_relstr_set(esk5_0,empty_set)
| empty(the_carrier(esk5_0)) ),
inference(cn,[status(thm)],[380,theory(equality)]) ).
cnf(382,negated_conjecture,
empty(the_carrier(esk5_0)),
inference(sr,[status(thm)],[381,301,theory(equality)]) ).
cnf(383,negated_conjecture,
$false,
inference(sr,[status(thm)],[382,168,theory(equality)]) ).
cnf(384,negated_conjecture,
$false,
383,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU360+1.p
% --creating new selector for []
% -running prover on /tmp/tmpCOVOkr/sel_SEU360+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU360+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU360+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU360+1.p
% Solved 1 out of 1.
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% See solution above
% # SZS output end CNFRefutation
%
%------------------------------------------------------------------------------