TSTP Solution File: SEU138+2 by E---3.1
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1
% Problem : SEU138+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n014.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 : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 19:24:53 EDT 2023
% Result : Theorem 630.77s 80.32s
% Output : CNFRefutation 630.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 21
% Syntax : Number of formulae : 149 ( 82 unt; 0 def)
% Number of atoms : 312 ( 110 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 263 ( 100 ~; 120 |; 26 &)
% ( 13 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 379 ( 45 sgn; 116 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d4_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jO4ySwF23p/E---3.1_9672.p',d4_xboole_0) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox/tmp/tmp.jO4ySwF23p/E---3.1_9672.p',d3_tarski) ).
fof(d2_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jO4ySwF23p/E---3.1_9672.p',d2_xboole_0) ).
fof(t1_xboole_1,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
file('/export/starexec/sandbox/tmp/tmp.jO4ySwF23p/E---3.1_9672.p',t1_xboole_1) ).
fof(t17_xboole_1,lemma,
! [X1,X2] : subset(set_intersection2(X1,X2),X1),
file('/export/starexec/sandbox/tmp/tmp.jO4ySwF23p/E---3.1_9672.p',t17_xboole_1) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox/tmp/tmp.jO4ySwF23p/E---3.1_9672.p',commutativity_k3_xboole_0) ).
fof(l32_xboole_1,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/tmp/tmp.jO4ySwF23p/E---3.1_9672.p',l32_xboole_1) ).
fof(t36_xboole_1,lemma,
! [X1,X2] : subset(set_difference(X1,X2),X1),
file('/export/starexec/sandbox/tmp/tmp.jO4ySwF23p/E---3.1_9672.p',t36_xboole_1) ).
fof(d3_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jO4ySwF23p/E---3.1_9672.p',d3_xboole_0) ).
fof(t28_xboole_1,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_intersection2(X1,X2) = X1 ),
file('/export/starexec/sandbox/tmp/tmp.jO4ySwF23p/E---3.1_9672.p',t28_xboole_1) ).
fof(t39_xboole_1,lemma,
! [X1,X2] : set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
file('/export/starexec/sandbox/tmp/tmp.jO4ySwF23p/E---3.1_9672.p',t39_xboole_1) ).
fof(t1_boole,axiom,
! [X1] : set_union2(X1,empty_set) = X1,
file('/export/starexec/sandbox/tmp/tmp.jO4ySwF23p/E---3.1_9672.p',t1_boole) ).
fof(t40_xboole_1,lemma,
! [X1,X2] : set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
file('/export/starexec/sandbox/tmp/tmp.jO4ySwF23p/E---3.1_9672.p',t40_xboole_1) ).
fof(t7_xboole_1,lemma,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('/export/starexec/sandbox/tmp/tmp.jO4ySwF23p/E---3.1_9672.p',t7_xboole_1) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox/tmp/tmp.jO4ySwF23p/E---3.1_9672.p',commutativity_k2_xboole_0) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox/tmp/tmp.jO4ySwF23p/E---3.1_9672.p',d1_xboole_0) ).
fof(t12_xboole_1,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
file('/export/starexec/sandbox/tmp/tmp.jO4ySwF23p/E---3.1_9672.p',t12_xboole_1) ).
fof(d10_xboole_0,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.jO4ySwF23p/E---3.1_9672.p',d10_xboole_0) ).
fof(t3_boole,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
file('/export/starexec/sandbox/tmp/tmp.jO4ySwF23p/E---3.1_9672.p',t3_boole) ).
fof(idempotence_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X1) = X1,
file('/export/starexec/sandbox/tmp/tmp.jO4ySwF23p/E---3.1_9672.p',idempotence_k2_xboole_0) ).
fof(t48_xboole_1,conjecture,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
file('/export/starexec/sandbox/tmp/tmp.jO4ySwF23p/E---3.1_9672.p',t48_xboole_1) ).
fof(c_0_21,plain,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
inference(fof_simplification,[status(thm)],[d4_xboole_0]) ).
fof(c_0_22,plain,
! [X30,X31,X32,X33,X34,X35,X36,X37] :
( ( in(X33,X30)
| ~ in(X33,X32)
| X32 != set_difference(X30,X31) )
& ( ~ in(X33,X31)
| ~ in(X33,X32)
| X32 != set_difference(X30,X31) )
& ( ~ in(X34,X30)
| in(X34,X31)
| in(X34,X32)
| X32 != set_difference(X30,X31) )
& ( ~ in(esk4_3(X35,X36,X37),X37)
| ~ in(esk4_3(X35,X36,X37),X35)
| in(esk4_3(X35,X36,X37),X36)
| X37 = set_difference(X35,X36) )
& ( in(esk4_3(X35,X36,X37),X35)
| in(esk4_3(X35,X36,X37),X37)
| X37 = set_difference(X35,X36) )
& ( ~ in(esk4_3(X35,X36,X37),X36)
| in(esk4_3(X35,X36,X37),X37)
| X37 = set_difference(X35,X36) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])])])]) ).
cnf(c_0_23,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_24,plain,
! [X71,X72,X73,X74,X75] :
( ( ~ subset(X71,X72)
| ~ in(X73,X71)
| in(X73,X72) )
& ( in(esk7_2(X74,X75),X74)
| subset(X74,X75) )
& ( ~ in(esk7_2(X74,X75),X75)
| subset(X74,X75) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_tarski])])])])])]) ).
fof(c_0_25,plain,
! [X62,X63,X64,X65,X66,X67,X68,X69] :
( ( ~ in(X65,X64)
| in(X65,X62)
| in(X65,X63)
| X64 != set_union2(X62,X63) )
& ( ~ in(X66,X62)
| in(X66,X64)
| X64 != set_union2(X62,X63) )
& ( ~ in(X66,X63)
| in(X66,X64)
| X64 != set_union2(X62,X63) )
& ( ~ in(esk6_3(X67,X68,X69),X67)
| ~ in(esk6_3(X67,X68,X69),X69)
| X69 = set_union2(X67,X68) )
& ( ~ in(esk6_3(X67,X68,X69),X68)
| ~ in(esk6_3(X67,X68,X69),X69)
| X69 = set_union2(X67,X68) )
& ( in(esk6_3(X67,X68,X69),X69)
| in(esk6_3(X67,X68,X69),X67)
| in(esk6_3(X67,X68,X69),X68)
| X69 = set_union2(X67,X68) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_xboole_0])])])])])]) ).
cnf(c_0_26,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X4 != set_difference(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_28,lemma,
! [X87,X88,X89] :
( ~ subset(X87,X88)
| ~ subset(X88,X89)
| subset(X87,X89) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])]) ).
fof(c_0_29,lemma,
! [X19,X20] : subset(set_intersection2(X19,X20),X19),
inference(variable_rename,[status(thm)],[t17_xboole_1]) ).
fof(c_0_30,plain,
! [X7,X8] : set_intersection2(X7,X8) = set_intersection2(X8,X7),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
cnf(c_0_31,plain,
( ~ in(X1,set_difference(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[c_0_23]) ).
cnf(c_0_32,plain,
( in(esk7_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_33,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_34,plain,
( subset(X1,X2)
| ~ in(esk7_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_35,plain,
( in(X1,set_difference(X2,X3))
| in(X1,X3)
| ~ in(X1,X2) ),
inference(er,[status(thm)],[c_0_26]) ).
cnf(c_0_36,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X2,X3)) ),
inference(er,[status(thm)],[c_0_27]) ).
fof(c_0_37,lemma,
! [X39,X40] :
( ( set_difference(X39,X40) != empty_set
| subset(X39,X40) )
& ( ~ subset(X39,X40)
| set_difference(X39,X40) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_xboole_1])]) ).
fof(c_0_38,lemma,
! [X44,X45] : subset(set_difference(X44,X45),X44),
inference(variable_rename,[status(thm)],[t36_xboole_1]) ).
fof(c_0_39,plain,
! [X9,X10,X11,X12,X13,X14,X15,X16] :
( ( in(X12,X9)
| ~ in(X12,X11)
| X11 != set_intersection2(X9,X10) )
& ( in(X12,X10)
| ~ in(X12,X11)
| X11 != set_intersection2(X9,X10) )
& ( ~ in(X13,X9)
| ~ in(X13,X10)
| in(X13,X11)
| X11 != set_intersection2(X9,X10) )
& ( ~ in(esk3_3(X14,X15,X16),X16)
| ~ in(esk3_3(X14,X15,X16),X14)
| ~ in(esk3_3(X14,X15,X16),X15)
| X16 = set_intersection2(X14,X15) )
& ( in(esk3_3(X14,X15,X16),X14)
| in(esk3_3(X14,X15,X16),X16)
| X16 = set_intersection2(X14,X15) )
& ( in(esk3_3(X14,X15,X16),X15)
| in(esk3_3(X14,X15,X16),X16)
| X16 = set_intersection2(X14,X15) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_xboole_0])])])])])]) ).
cnf(c_0_40,lemma,
( subset(X1,X3)
| ~ subset(X1,X2)
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_41,lemma,
subset(set_intersection2(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_42,lemma,
! [X27,X28] :
( ~ subset(X27,X28)
| set_intersection2(X27,X28) = X27 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t28_xboole_1])]) ).
cnf(c_0_43,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_44,plain,
( subset(set_difference(X1,X2),X3)
| ~ in(esk7_2(set_difference(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_45,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[c_0_33]) ).
cnf(c_0_46,plain,
( subset(X1,set_difference(X2,X3))
| in(esk7_2(X1,set_difference(X2,X3)),X3)
| ~ in(esk7_2(X1,set_difference(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_47,plain,
( subset(set_difference(X1,X2),X3)
| in(esk7_2(set_difference(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_32]) ).
fof(c_0_48,lemma,
! [X48,X49] : set_union2(X48,set_difference(X49,X48)) = set_union2(X48,X49),
inference(variable_rename,[status(thm)],[t39_xboole_1]) ).
cnf(c_0_49,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_50,lemma,
subset(set_difference(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
fof(c_0_51,plain,
! [X97] : set_union2(X97,empty_set) = X97,
inference(variable_rename,[status(thm)],[t1_boole]) ).
fof(c_0_52,lemma,
! [X51,X52] : set_difference(set_union2(X51,X52),X52) = set_difference(X51,X52),
inference(variable_rename,[status(thm)],[t40_xboole_1]) ).
cnf(c_0_53,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_54,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_55,lemma,
( subset(X1,X2)
| ~ subset(X1,set_intersection2(X2,X3)) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_56,lemma,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_57,lemma,
subset(set_intersection2(X1,X2),X2),
inference(spm,[status(thm)],[c_0_41,c_0_43]) ).
fof(c_0_58,lemma,
! [X92,X93] : subset(X92,set_union2(X92,X93)),
inference(variable_rename,[status(thm)],[t7_xboole_1]) ).
fof(c_0_59,plain,
! [X99,X100] : set_union2(X99,X100) = set_union2(X100,X99),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
cnf(c_0_60,plain,
( subset(set_difference(X1,set_union2(X2,X3)),X4)
| ~ in(esk7_2(set_difference(X1,set_union2(X2,X3)),X4),X3) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_61,plain,
( subset(set_difference(X1,X2),set_difference(X1,X3))
| in(esk7_2(set_difference(X1,X2),set_difference(X1,X3)),X3) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_62,lemma,
set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_63,lemma,
set_difference(set_difference(X1,X2),X1) = empty_set,
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_64,plain,
set_union2(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_65,lemma,
set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_66,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X2,X3)) ),
inference(er,[status(thm)],[c_0_53]) ).
cnf(c_0_67,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X3,X2)) ),
inference(er,[status(thm)],[c_0_54]) ).
cnf(c_0_68,lemma,
subset(set_difference(set_intersection2(X1,X2),X3),X1),
inference(spm,[status(thm)],[c_0_55,c_0_50]) ).
cnf(c_0_69,lemma,
set_intersection2(X1,set_intersection2(X2,X1)) = set_intersection2(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_43]) ).
cnf(c_0_70,lemma,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_71,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_72,plain,
subset(set_difference(X1,set_union2(X2,X3)),set_difference(X1,X3)),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_73,lemma,
set_union2(X1,set_difference(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]) ).
fof(c_0_74,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
cnf(c_0_75,lemma,
subset(set_difference(X1,X2),set_union2(X1,X2)),
inference(spm,[status(thm)],[c_0_50,c_0_65]) ).
cnf(c_0_76,plain,
( subset(set_intersection2(X1,X2),X3)
| in(esk7_2(set_intersection2(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_66,c_0_32]) ).
cnf(c_0_77,plain,
( subset(set_intersection2(X1,X2),X3)
| in(esk7_2(set_intersection2(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_67,c_0_32]) ).
cnf(c_0_78,lemma,
subset(set_difference(set_intersection2(X1,X2),X3),X2),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_79,lemma,
set_intersection2(X1,set_union2(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_56,c_0_70]) ).
cnf(c_0_80,lemma,
set_difference(set_union2(X1,X2),X1) = set_difference(X2,X1),
inference(spm,[status(thm)],[c_0_65,c_0_71]) ).
cnf(c_0_81,lemma,
subset(set_difference(X1,X2),set_difference(X1,set_difference(X2,X3))),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
fof(c_0_82,plain,
! [X58,X59,X60] :
( ( X58 != empty_set
| ~ in(X59,X58) )
& ( in(esk5_1(X60),X60)
| X60 = empty_set ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_74])])])])]) ).
cnf(c_0_83,lemma,
subset(set_difference(X1,set_difference(X2,X1)),set_union2(X1,X2)),
inference(spm,[status(thm)],[c_0_75,c_0_62]) ).
fof(c_0_84,lemma,
! [X85,X86] :
( ~ subset(X85,X86)
| set_union2(X85,X86) = X86 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_xboole_1])]) ).
cnf(c_0_85,lemma,
subset(X1,set_union2(X2,X1)),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_86,lemma,
set_union2(X1,set_union2(X2,X1)) = set_union2(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_65]),c_0_62]) ).
cnf(c_0_87,plain,
( subset(set_intersection2(set_difference(X1,X2),X3),X4)
| ~ in(esk7_2(set_intersection2(set_difference(X1,X2),X3),X4),X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_76]) ).
cnf(c_0_88,plain,
( subset(set_intersection2(X1,X2),set_difference(X2,X3))
| in(esk7_2(set_intersection2(X1,X2),set_difference(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_46,c_0_77]) ).
cnf(c_0_89,lemma,
subset(set_difference(X1,X2),set_union2(X1,X3)),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_90,lemma,
set_difference(set_union2(X1,X2),set_difference(X2,X1)) = set_difference(X1,set_difference(X2,X1)),
inference(spm,[status(thm)],[c_0_65,c_0_62]) ).
cnf(c_0_91,lemma,
set_union2(set_union2(X1,X2),set_difference(X2,X1)) = set_union2(X1,X2),
inference(spm,[status(thm)],[c_0_73,c_0_80]) ).
cnf(c_0_92,lemma,
set_intersection2(set_difference(X1,X2),set_difference(X1,set_difference(X2,X3))) = set_difference(X1,X2),
inference(spm,[status(thm)],[c_0_56,c_0_81]) ).
cnf(c_0_93,lemma,
set_difference(set_difference(X1,X2),X2) = set_difference(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_62]),c_0_80]) ).
cnf(c_0_94,lemma,
set_intersection2(X1,set_difference(X1,X2)) = set_difference(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_50]),c_0_43]) ).
cnf(c_0_95,plain,
( in(esk5_1(X1),X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
fof(c_0_96,plain,
! [X82,X83] :
( ( subset(X82,X83)
| X82 != X83 )
& ( subset(X83,X82)
| X82 != X83 )
& ( ~ subset(X82,X83)
| ~ subset(X83,X82)
| X82 = X83 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])]) ).
cnf(c_0_97,lemma,
( subset(X1,set_union2(X2,X3))
| ~ subset(X1,set_difference(X2,set_difference(X3,X2))) ),
inference(spm,[status(thm)],[c_0_40,c_0_83]) ).
cnf(c_0_98,lemma,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_99,lemma,
subset(set_union2(X1,X2),set_union2(X2,X1)),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_100,lemma,
set_difference(X1,set_union2(X2,X1)) = empty_set,
inference(spm,[status(thm)],[c_0_49,c_0_85]) ).
fof(c_0_101,plain,
! [X50] : set_difference(X50,empty_set) = X50,
inference(variable_rename,[status(thm)],[t3_boole]) ).
cnf(c_0_102,plain,
subset(set_intersection2(set_difference(X1,X2),X3),set_difference(X3,X2)),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_103,lemma,
set_intersection2(set_difference(X1,X2),set_union2(X1,X3)) = set_difference(X1,X2),
inference(spm,[status(thm)],[c_0_56,c_0_89]) ).
cnf(c_0_104,lemma,
set_difference(set_difference(X1,X2),set_difference(X2,set_difference(X1,X2))) = set_difference(set_union2(X2,X1),set_difference(X2,set_difference(X1,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_90]),c_0_71]),c_0_91]) ).
cnf(c_0_105,lemma,
set_difference(set_difference(X1,X2),set_difference(X2,X3)) = set_difference(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_94]) ).
cnf(c_0_106,plain,
( set_intersection2(X1,X2) = empty_set
| in(esk5_1(set_intersection2(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_67,c_0_95]) ).
cnf(c_0_107,plain,
( set_intersection2(X1,X2) = empty_set
| in(esk5_1(set_intersection2(X1,X2)),X1) ),
inference(spm,[status(thm)],[c_0_66,c_0_95]) ).
cnf(c_0_108,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_109,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_110,lemma,
subset(set_difference(set_difference(X1,set_difference(X2,X1)),X3),set_union2(X1,X2)),
inference(spm,[status(thm)],[c_0_97,c_0_50]) ).
cnf(c_0_111,lemma,
set_union2(set_union2(X1,X2),set_union2(X2,X1)) = set_union2(X2,X1),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_112,lemma,
set_difference(set_union2(X1,X2),set_union2(X2,X1)) = empty_set,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_86]),c_0_100]) ).
cnf(c_0_113,plain,
set_difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_114,lemma,
subset(set_difference(X1,X2),set_difference(set_union2(X1,X3),X2)),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_115,lemma,
set_difference(set_union2(X1,X2),set_difference(X1,set_difference(X2,X1))) = set_difference(X2,X1),
inference(rw,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_116,plain,
( set_intersection2(X1,set_difference(X2,X3)) = empty_set
| ~ in(esk5_1(set_intersection2(X1,set_difference(X2,X3))),X3) ),
inference(spm,[status(thm)],[c_0_31,c_0_106]) ).
cnf(c_0_117,plain,
( set_intersection2(set_difference(X1,X2),X3) = empty_set
| in(esk5_1(set_intersection2(set_difference(X1,X2),X3)),X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_107]) ).
cnf(c_0_118,plain,
( in(X1,X4)
| ~ in(X1,X2)
| ~ in(X1,X3)
| X4 != set_intersection2(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_119,lemma,
( X1 = X2
| set_difference(X2,X1) != empty_set
| ~ subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_120,lemma,
subset(set_difference(set_union2(X1,X2),X3),set_union2(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_112]),c_0_113]) ).
cnf(c_0_121,lemma,
subset(set_difference(X1,set_difference(X1,set_difference(X2,X1))),set_difference(X2,X1)),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_122,plain,
set_intersection2(set_difference(X1,X2),set_difference(X3,X1)) = empty_set,
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
fof(c_0_123,plain,
! [X105] : set_union2(X105,X105) = X105,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k2_xboole_0])]) ).
cnf(c_0_124,plain,
( in(X1,set_intersection2(X2,X3))
| ~ in(X1,X3)
| ~ in(X1,X2) ),
inference(er,[status(thm)],[c_0_118]) ).
cnf(c_0_125,lemma,
( set_difference(set_union2(X1,X2),X3) = set_union2(X2,X1)
| set_difference(set_union2(X2,X1),set_difference(set_union2(X1,X2),X3)) != empty_set ),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_126,lemma,
set_difference(X1,set_difference(X1,set_difference(X2,X1))) = empty_set,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_121]),c_0_122]) ).
cnf(c_0_127,plain,
set_union2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_123]) ).
cnf(c_0_128,plain,
( subset(X1,set_intersection2(X2,X3))
| ~ in(esk7_2(X1,set_intersection2(X2,X3)),X3)
| ~ in(esk7_2(X1,set_intersection2(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_34,c_0_124]) ).
cnf(c_0_129,lemma,
set_difference(set_union2(X1,X2),set_difference(X1,X2)) = set_difference(X2,set_difference(X1,X2)),
inference(spm,[status(thm)],[c_0_90,c_0_71]) ).
cnf(c_0_130,lemma,
set_difference(X1,set_difference(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_127]),c_0_127]),c_0_127]) ).
cnf(c_0_131,plain,
( subset(set_intersection2(X1,X2),set_intersection2(X3,X2))
| ~ in(esk7_2(set_intersection2(X1,X2),set_intersection2(X3,X2)),X3) ),
inference(spm,[status(thm)],[c_0_128,c_0_77]) ).
cnf(c_0_132,plain,
( subset(set_intersection2(set_difference(X1,X2),X3),X4)
| in(esk7_2(set_intersection2(set_difference(X1,X2),X3),X4),X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_76]) ).
cnf(c_0_133,lemma,
set_difference(set_union2(X1,X2),set_difference(X1,X2)) = X2,
inference(rw,[status(thm)],[c_0_129,c_0_130]) ).
cnf(c_0_134,plain,
( subset(set_intersection2(X1,set_difference(X2,X3)),X4)
| ~ in(esk7_2(set_intersection2(X1,set_difference(X2,X3)),X4),X3) ),
inference(spm,[status(thm)],[c_0_31,c_0_77]) ).
cnf(c_0_135,plain,
( subset(set_intersection2(X1,X2),set_difference(X1,X3))
| in(esk7_2(set_intersection2(X1,X2),set_difference(X1,X3)),X3) ),
inference(spm,[status(thm)],[c_0_46,c_0_76]) ).
cnf(c_0_136,plain,
subset(set_intersection2(set_difference(X1,X2),X3),set_intersection2(X1,X3)),
inference(spm,[status(thm)],[c_0_131,c_0_132]) ).
cnf(c_0_137,lemma,
subset(set_difference(X1,set_difference(X1,X2)),X2),
inference(spm,[status(thm)],[c_0_114,c_0_133]) ).
cnf(c_0_138,plain,
subset(set_intersection2(X1,set_difference(X2,X3)),set_difference(X1,X3)),
inference(spm,[status(thm)],[c_0_134,c_0_135]) ).
fof(c_0_139,negated_conjecture,
~ ! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(assume_negation,[status(cth)],[t48_xboole_1]) ).
cnf(c_0_140,plain,
subset(set_intersection2(X1,set_difference(X2,X3)),set_intersection2(X2,X1)),
inference(spm,[status(thm)],[c_0_136,c_0_43]) ).
cnf(c_0_141,lemma,
set_intersection2(X1,set_difference(X2,set_difference(X2,X1))) = set_difference(X2,set_difference(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_137]),c_0_43]) ).
cnf(c_0_142,lemma,
set_difference(set_intersection2(X1,set_difference(X2,X3)),set_difference(X1,X3)) = empty_set,
inference(spm,[status(thm)],[c_0_49,c_0_138]) ).
fof(c_0_143,negated_conjecture,
set_difference(esk1_0,set_difference(esk1_0,esk2_0)) != set_intersection2(esk1_0,esk2_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_139])])]) ).
cnf(c_0_144,lemma,
subset(set_difference(X1,set_difference(X1,X2)),set_intersection2(X1,X2)),
inference(spm,[status(thm)],[c_0_140,c_0_141]) ).
cnf(c_0_145,lemma,
set_difference(set_intersection2(X1,X2),set_difference(X1,set_difference(X3,X2))) = empty_set,
inference(spm,[status(thm)],[c_0_142,c_0_130]) ).
cnf(c_0_146,negated_conjecture,
set_difference(esk1_0,set_difference(esk1_0,esk2_0)) != set_intersection2(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_143]) ).
cnf(c_0_147,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_144]),c_0_145])]) ).
cnf(c_0_148,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_146,c_0_147])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SEU138+2 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n014.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 2400
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon Oct 2 08:59:50 EDT 2023
% 0.12/0.32 % CPUTime :
% 0.17/0.44 Running first-order theorem proving
% 0.17/0.44 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.jO4ySwF23p/E---3.1_9672.p
% 630.77/80.32 # Version: 3.1pre001
% 630.77/80.32 # Preprocessing class: FSMSSMSSSSSNFFN.
% 630.77/80.32 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 630.77/80.32 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 630.77/80.32 # Starting new_bool_3 with 300s (1) cores
% 630.77/80.32 # Starting new_bool_1 with 300s (1) cores
% 630.77/80.32 # Starting sh5l with 300s (1) cores
% 630.77/80.32 # new_bool_1 with pid 9752 completed with status 0
% 630.77/80.32 # Result found by new_bool_1
% 630.77/80.32 # Preprocessing class: FSMSSMSSSSSNFFN.
% 630.77/80.32 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 630.77/80.32 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 630.77/80.32 # Starting new_bool_3 with 300s (1) cores
% 630.77/80.32 # Starting new_bool_1 with 300s (1) cores
% 630.77/80.32 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 630.77/80.32 # Search class: FGHSM-FFMF32-SFFFFFNN
% 630.77/80.32 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 630.77/80.32 # Starting G-E--_300_C01_F1_SE_CS_SP_S0Y with 163s (1) cores
% 630.77/80.32 # G-E--_300_C01_F1_SE_CS_SP_S0Y with pid 9755 completed with status 0
% 630.77/80.32 # Result found by G-E--_300_C01_F1_SE_CS_SP_S0Y
% 630.77/80.32 # Preprocessing class: FSMSSMSSSSSNFFN.
% 630.77/80.32 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 630.77/80.32 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 630.77/80.32 # Starting new_bool_3 with 300s (1) cores
% 630.77/80.32 # Starting new_bool_1 with 300s (1) cores
% 630.77/80.32 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 630.77/80.32 # Search class: FGHSM-FFMF32-SFFFFFNN
% 630.77/80.32 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 630.77/80.32 # Starting G-E--_300_C01_F1_SE_CS_SP_S0Y with 163s (1) cores
% 630.77/80.32 # Preprocessing time : 0.001 s
% 630.77/80.32
% 630.77/80.32 # Proof found!
% 630.77/80.32 # SZS status Theorem
% 630.77/80.32 # SZS output start CNFRefutation
% See solution above
% 630.77/80.32 # Parsed axioms : 51
% 630.77/80.32 # Removed by relevancy pruning/SinE : 8
% 630.77/80.32 # Initial clauses : 66
% 630.77/80.32 # Removed in clause preprocessing : 0
% 630.77/80.32 # Initial clauses in saturation : 66
% 630.77/80.32 # Processed clauses : 181589
% 630.77/80.32 # ...of these trivial : 7204
% 630.77/80.32 # ...subsumed : 168077
% 630.77/80.32 # ...remaining for further processing : 6308
% 630.77/80.32 # Other redundant clauses eliminated : 40497
% 630.77/80.32 # Clauses deleted for lack of memory : 388191
% 630.77/80.32 # Backward-subsumed : 202
% 630.77/80.32 # Backward-rewritten : 445
% 630.77/80.32 # Generated clauses : 5907855
% 630.77/80.32 # ...of the previous two non-redundant : 4289319
% 630.77/80.32 # ...aggressively subsumed : 0
% 630.77/80.32 # Contextual simplify-reflections : 34
% 630.77/80.32 # Paramodulations : 5866456
% 630.77/80.32 # Factorizations : 902
% 630.77/80.32 # NegExts : 0
% 630.77/80.32 # Equation resolutions : 40497
% 630.77/80.32 # Total rewrite steps : 3862564
% 630.77/80.32 # Propositional unsat checks : 0
% 630.77/80.32 # Propositional check models : 0
% 630.77/80.32 # Propositional check unsatisfiable : 0
% 630.77/80.32 # Propositional clauses : 0
% 630.77/80.32 # Propositional clauses after purity: 0
% 630.77/80.32 # Propositional unsat core size : 0
% 630.77/80.32 # Propositional preprocessing time : 0.000
% 630.77/80.32 # Propositional encoding time : 0.000
% 630.77/80.32 # Propositional solver time : 0.000
% 630.77/80.32 # Success case prop preproc time : 0.000
% 630.77/80.32 # Success case prop encoding time : 0.000
% 630.77/80.32 # Success case prop solver time : 0.000
% 630.77/80.32 # Current number of processed clauses : 5649
% 630.77/80.32 # Positive orientable unit clauses : 1586
% 630.77/80.32 # Positive unorientable unit clauses: 2
% 630.77/80.32 # Negative unit clauses : 17
% 630.77/80.32 # Non-unit-clauses : 4044
% 630.77/80.32 # Current number of unprocessed clauses: 1640757
% 630.77/80.32 # ...number of literals in the above : 4316993
% 630.77/80.32 # Current number of archived formulas : 0
% 630.77/80.32 # Current number of archived clauses : 647
% 630.77/80.32 # Clause-clause subsumption calls (NU) : 3849429
% 630.77/80.32 # Rec. Clause-clause subsumption calls : 1999298
% 630.77/80.32 # Non-unit clause-clause subsumptions : 146803
% 630.77/80.32 # Unit Clause-clause subsumption calls : 67883
% 630.77/80.32 # Rewrite failures with RHS unbound : 0
% 630.77/80.32 # BW rewrite match attempts : 24288
% 630.77/80.32 # BW rewrite match successes : 217
% 630.77/80.32 # Condensation attempts : 0
% 630.77/80.32 # Condensation successes : 0
% 630.77/80.32 # Termbank termtop insertions : 57261403
% 630.77/80.32
% 630.77/80.32 # -------------------------------------------------
% 630.77/80.32 # User time : 76.701 s
% 630.77/80.32 # System time : 1.679 s
% 630.77/80.32 # Total time : 78.379 s
% 630.77/80.32 # Maximum resident set size: 1868 pages
% 630.77/80.32
% 630.77/80.32 # -------------------------------------------------
% 630.77/80.32 # User time : 76.703 s
% 630.77/80.32 # System time : 1.683 s
% 630.77/80.32 # Total time : 78.386 s
% 630.77/80.32 # Maximum resident set size: 1732 pages
% 630.77/80.32 % E---3.1 exiting
% 630.77/80.32 % E---3.1 exiting
%------------------------------------------------------------------------------