TSTP Solution File: SET169+3 by E---3.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1
% Problem : SET169+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n031.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 19:18:44 EDT 2023
% Result : Theorem 1389.74s 195.01s
% Output : CNFRefutation 1389.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 7
% Syntax : Number of formulae : 103 ( 53 unt; 0 def)
% Number of atoms : 187 ( 33 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 138 ( 54 ~; 69 |; 10 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 283 ( 42 sgn; 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/tmp/tmp.GoHdp6UIbu/E---3.1_8229.p',subset_defn) ).
fof(intersection_defn,axiom,
! [X1,X2,X3] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/export/starexec/sandbox/tmp/tmp.GoHdp6UIbu/E---3.1_8229.p',intersection_defn) ).
fof(union_defn,axiom,
! [X1,X2,X3] :
( member(X3,union(X1,X2))
<=> ( member(X3,X1)
| member(X3,X2) ) ),
file('/export/starexec/sandbox/tmp/tmp.GoHdp6UIbu/E---3.1_8229.p',union_defn) ).
fof(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox/tmp/tmp.GoHdp6UIbu/E---3.1_8229.p',commutativity_of_intersection) ).
fof(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.GoHdp6UIbu/E---3.1_8229.p',equal_defn) ).
fof(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox/tmp/tmp.GoHdp6UIbu/E---3.1_8229.p',commutativity_of_union) ).
fof(prove_intersection_distributes_over_union,conjecture,
! [X1,X2,X3] : intersection(X1,union(X2,X3)) = union(intersection(X1,X2),intersection(X1,X3)),
file('/export/starexec/sandbox/tmp/tmp.GoHdp6UIbu/E---3.1_8229.p',prove_intersection_distributes_over_union) ).
fof(c_0_7,plain,
! [X16,X17,X18,X19,X20] :
( ( ~ subset(X16,X17)
| ~ member(X18,X16)
| member(X18,X17) )
& ( member(esk1_2(X19,X20),X19)
| subset(X19,X20) )
& ( ~ member(esk1_2(X19,X20),X20)
| subset(X19,X20) ) ),
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)],[subset_defn])])])])])]) ).
fof(c_0_8,plain,
! [X7,X8,X9] :
( ( member(X9,X7)
| ~ member(X9,intersection(X7,X8)) )
& ( member(X9,X8)
| ~ member(X9,intersection(X7,X8)) )
& ( ~ member(X9,X7)
| ~ member(X9,X8)
| member(X9,intersection(X7,X8)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])]) ).
cnf(c_0_9,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,plain,
( subset(X1,intersection(X2,X3))
| ~ member(esk1_2(X1,intersection(X2,X3)),X3)
| ~ member(esk1_2(X1,intersection(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_12,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_13,plain,
! [X4,X5,X6] :
( ( ~ member(X6,union(X4,X5))
| member(X6,X4)
| member(X6,X5) )
& ( ~ member(X6,X4)
| member(X6,union(X4,X5)) )
& ( ~ member(X6,X5)
| member(X6,union(X4,X5)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union_defn])])]) ).
cnf(c_0_14,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,plain,
( subset(X1,intersection(X2,X1))
| ~ member(esk1_2(X1,intersection(X2,X1)),X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,plain,
( member(X1,X2)
| ~ member(X1,intersection(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,plain,
( member(X1,union(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
( subset(intersection(X1,X2),X3)
| member(esk1_2(intersection(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_12]) ).
fof(c_0_19,plain,
! [X14,X15] : intersection(X14,X15) = intersection(X15,X14),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
cnf(c_0_20,plain,
( subset(X1,intersection(intersection(X2,X3),X1))
| ~ member(esk1_2(X1,intersection(intersection(X2,X3),X1)),X3)
| ~ member(esk1_2(X1,intersection(intersection(X2,X3),X1)),X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_10]) ).
cnf(c_0_21,plain,
( subset(intersection(X1,X2),X3)
| member(esk1_2(intersection(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_12]) ).
fof(c_0_22,plain,
! [X10,X11] :
( ( subset(X10,X11)
| X10 != X11 )
& ( subset(X11,X10)
| X10 != X11 )
& ( ~ subset(X10,X11)
| ~ subset(X11,X10)
| X10 = X11 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])]) ).
cnf(c_0_23,plain,
( subset(X1,intersection(union(X2,X3),X1))
| ~ member(esk1_2(X1,intersection(union(X2,X3),X1)),X3) ),
inference(spm,[status(thm)],[c_0_15,c_0_17]) ).
cnf(c_0_24,plain,
subset(intersection(X1,X2),X1),
inference(spm,[status(thm)],[c_0_9,c_0_18]) ).
cnf(c_0_25,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
( subset(intersection(X1,X2),intersection(intersection(X3,X1),intersection(X1,X2)))
| ~ member(esk1_2(intersection(X1,X2),intersection(intersection(X3,X1),intersection(X1,X2))),X3) ),
inference(spm,[status(thm)],[c_0_20,c_0_18]) ).
cnf(c_0_27,plain,
( subset(intersection(X1,intersection(X2,X3)),X4)
| member(esk1_2(intersection(X1,intersection(X2,X3)),X4),X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_21]) ).
cnf(c_0_28,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,plain,
subset(intersection(X1,X2),intersection(union(X3,X2),intersection(X1,X2))),
inference(spm,[status(thm)],[c_0_23,c_0_21]) ).
cnf(c_0_30,plain,
subset(intersection(X1,X2),X2),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,plain,
( subset(intersection(X1,X2),intersection(X3,X2))
| ~ member(esk1_2(intersection(X1,X2),intersection(X3,X2)),X3) ),
inference(spm,[status(thm)],[c_0_11,c_0_21]) ).
cnf(c_0_32,plain,
( subset(intersection(intersection(X1,X2),X3),X4)
| member(esk1_2(intersection(intersection(X1,X2),X3),X4),X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_18]) ).
cnf(c_0_33,plain,
subset(intersection(X1,intersection(X2,X3)),intersection(intersection(X2,X1),intersection(X1,intersection(X2,X3)))),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_34,plain,
intersection(union(X1,X2),intersection(X3,X2)) = intersection(X3,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]) ).
cnf(c_0_35,plain,
( subset(intersection(intersection(X1,X2),X3),X4)
| member(esk1_2(intersection(intersection(X1,X2),X3),X4),X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_18]) ).
cnf(c_0_36,plain,
subset(X1,intersection(X1,union(X2,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_12]),c_0_25]) ).
fof(c_0_37,plain,
! [X12,X13] : union(X12,X13) = union(X13,X12),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
cnf(c_0_38,plain,
subset(intersection(intersection(X1,X2),X3),intersection(X2,X3)),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_39,plain,
subset(intersection(X1,X2),intersection(intersection(X1,X2),intersection(X1,union(X3,X2)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_25]) ).
cnf(c_0_40,plain,
subset(intersection(intersection(X1,X2),X3),intersection(X1,X3)),
inference(spm,[status(thm)],[c_0_31,c_0_35]) ).
cnf(c_0_41,plain,
intersection(X1,union(X2,X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_36]),c_0_24])]) ).
cnf(c_0_42,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_43,plain,
( intersection(intersection(X1,X2),X3) = intersection(X2,X3)
| ~ subset(intersection(X2,X3),intersection(intersection(X1,X2),X3)) ),
inference(spm,[status(thm)],[c_0_28,c_0_38]) ).
cnf(c_0_44,plain,
intersection(intersection(X1,X2),intersection(X1,union(X3,X2))) = intersection(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_39]),c_0_24])]) ).
cnf(c_0_45,plain,
subset(intersection(X1,intersection(X2,X3)),intersection(X2,X1)),
inference(spm,[status(thm)],[c_0_40,c_0_25]) ).
cnf(c_0_46,plain,
intersection(X1,union(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_47,plain,
( subset(X1,intersection(X1,X2))
| ~ member(esk1_2(X1,intersection(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_25]) ).
cnf(c_0_48,plain,
intersection(X1,intersection(X2,union(X3,X1))) = intersection(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45])]) ).
cnf(c_0_49,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_50,plain,
subset(intersection(X1,X2),intersection(X1,union(intersection(X1,X2),X3))),
inference(spm,[status(thm)],[c_0_40,c_0_46]) ).
cnf(c_0_51,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_52,plain,
( subset(X1,intersection(X2,X1))
| ~ member(esk1_2(X1,intersection(X2,X1)),intersection(X2,union(X3,X1))) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_53,plain,
( member(X1,intersection(X2,union(intersection(X2,X3),X4)))
| ~ member(X1,intersection(X2,X3)) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_54,plain,
( subset(X1,X2)
| member(esk1_2(X1,X2),union(X3,X1)) ),
inference(spm,[status(thm)],[c_0_21,c_0_41]) ).
cnf(c_0_55,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_56,plain,
( subset(union(X1,X2),X3)
| member(esk1_2(union(X1,X2),X3),X1)
| member(esk1_2(union(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_51,c_0_12]) ).
cnf(c_0_57,plain,
( subset(X1,intersection(X2,X1))
| ~ member(esk1_2(X1,intersection(X2,X1)),intersection(X2,X3)) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_58,plain,
( subset(X1,union(X2,X3))
| ~ member(esk1_2(X1,union(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_9,c_0_17]) ).
cnf(c_0_59,plain,
subset(intersection(X1,X2),intersection(intersection(X1,X2),intersection(X1,union(X3,intersection(X1,X2))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_54]),c_0_25]),c_0_25]) ).
cnf(c_0_60,plain,
( subset(X1,intersection(union(X2,X3),X1))
| ~ member(esk1_2(X1,intersection(union(X2,X3),X1)),X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_55]) ).
cnf(c_0_61,plain,
( subset(union(X1,X2),intersection(union(X3,X1),union(X1,X2)))
| member(esk1_2(union(X1,X2),intersection(union(X3,X1),union(X1,X2))),X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_56]) ).
cnf(c_0_62,plain,
( subset(union(X1,X2),X1)
| ~ member(esk1_2(union(X1,X2),X1),intersection(X1,X3)) ),
inference(spm,[status(thm)],[c_0_57,c_0_46]) ).
cnf(c_0_63,plain,
( subset(union(X1,X2),X1)
| member(esk1_2(union(X1,X2),X1),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_56]),c_0_46]),c_0_46]) ).
cnf(c_0_64,plain,
subset(X1,union(X2,X1)),
inference(spm,[status(thm)],[c_0_58,c_0_12]) ).
cnf(c_0_65,plain,
intersection(intersection(X1,X2),intersection(X1,union(X3,intersection(X1,X2)))) = intersection(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_59]),c_0_24])]) ).
cnf(c_0_66,plain,
subset(union(X1,X2),intersection(union(X2,X1),union(X1,X2))),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_67,plain,
( subset(X1,union(X2,X3))
| ~ member(esk1_2(X1,union(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_9,c_0_55]) ).
cnf(c_0_68,plain,
subset(union(X1,intersection(X1,X2)),X1),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_69,plain,
subset(X1,union(X1,X2)),
inference(spm,[status(thm)],[c_0_64,c_0_42]) ).
cnf(c_0_70,plain,
subset(intersection(X1,X2),intersection(X2,intersection(X1,union(X3,intersection(X1,X2))))),
inference(spm,[status(thm)],[c_0_38,c_0_65]) ).
cnf(c_0_71,plain,
intersection(union(X1,X2),union(X2,X1)) = union(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_66]),c_0_30])]) ).
cnf(c_0_72,plain,
subset(intersection(intersection(X1,X2),X3),intersection(X3,X1)),
inference(spm,[status(thm)],[c_0_40,c_0_25]) ).
cnf(c_0_73,plain,
( subset(X1,union(union(X2,X3),X4))
| ~ member(esk1_2(X1,union(union(X2,X3),X4)),X3) ),
inference(spm,[status(thm)],[c_0_67,c_0_17]) ).
cnf(c_0_74,plain,
( subset(union(X1,X2),union(X3,X2))
| member(esk1_2(union(X1,X2),union(X3,X2)),X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_56]) ).
cnf(c_0_75,plain,
union(X1,intersection(X1,X2)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_68]),c_0_69])]) ).
cnf(c_0_76,plain,
intersection(X1,intersection(X2,union(X3,intersection(X2,X1)))) = intersection(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_70]),c_0_45])]) ).
cnf(c_0_77,plain,
subset(intersection(X1,union(X2,X3)),intersection(union(X3,X2),X1)),
inference(spm,[status(thm)],[c_0_45,c_0_71]) ).
cnf(c_0_78,plain,
subset(intersection(union(X1,X2),X3),intersection(X3,union(X2,X1))),
inference(spm,[status(thm)],[c_0_72,c_0_71]) ).
cnf(c_0_79,plain,
subset(union(X1,X2),union(union(X3,X1),X2)),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_80,plain,
union(X1,intersection(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_81,plain,
intersection(union(X1,X2),X3) = intersection(X3,union(X2,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_77]),c_0_78])]) ).
cnf(c_0_82,plain,
subset(union(X1,intersection(X2,union(X3,X1))),union(X3,X1)),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_83,plain,
intersection(X1,intersection(union(X1,X2),X3)) = intersection(X3,X1),
inference(spm,[status(thm)],[c_0_48,c_0_81]) ).
cnf(c_0_84,plain,
( subset(X1,union(X2,intersection(X3,X4)))
| ~ member(esk1_2(X1,union(X2,intersection(X3,X4))),X4)
| ~ member(esk1_2(X1,union(X2,intersection(X3,X4))),X3) ),
inference(spm,[status(thm)],[c_0_58,c_0_10]) ).
cnf(c_0_85,plain,
intersection(X1,intersection(union(X2,X1),X3)) = intersection(X3,X1),
inference(spm,[status(thm)],[c_0_48,c_0_25]) ).
fof(c_0_86,negated_conjecture,
~ ! [X1,X2,X3] : intersection(X1,union(X2,X3)) = union(intersection(X1,X2),intersection(X1,X3)),
inference(assume_negation,[status(cth)],[prove_intersection_distributes_over_union]) ).
cnf(c_0_87,plain,
subset(union(intersection(X1,X2),intersection(X3,X2)),X2),
inference(spm,[status(thm)],[c_0_82,c_0_80]) ).
cnf(c_0_88,plain,
intersection(X1,intersection(union(X1,X2),X3)) = intersection(X1,X3),
inference(spm,[status(thm)],[c_0_25,c_0_83]) ).
cnf(c_0_89,plain,
( subset(X1,union(intersection(X2,X3),X4))
| ~ member(esk1_2(X1,union(intersection(X2,X3),X4)),X3)
| ~ member(esk1_2(X1,union(intersection(X2,X3),X4)),X2) ),
inference(spm,[status(thm)],[c_0_67,c_0_10]) ).
cnf(c_0_90,plain,
( subset(X1,union(X2,intersection(X3,X1)))
| ~ member(esk1_2(X1,union(X2,intersection(X3,X1))),X3) ),
inference(spm,[status(thm)],[c_0_84,c_0_12]) ).
cnf(c_0_91,plain,
( subset(intersection(union(X1,X2),X3),X4)
| member(esk1_2(intersection(union(X1,X2),X3),X4),X1)
| member(esk1_2(intersection(union(X1,X2),X3),X4),X2) ),
inference(spm,[status(thm)],[c_0_51,c_0_18]) ).
cnf(c_0_92,plain,
intersection(X1,intersection(union(X2,X1),X3)) = intersection(X1,X3),
inference(spm,[status(thm)],[c_0_25,c_0_85]) ).
fof(c_0_93,negated_conjecture,
intersection(esk3_0,union(esk4_0,esk5_0)) != union(intersection(esk3_0,esk4_0),intersection(esk3_0,esk5_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_86])])]) ).
cnf(c_0_94,plain,
subset(union(intersection(X1,X2),intersection(X3,intersection(union(X1,X4),X2))),intersection(union(X1,X4),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_42]) ).
cnf(c_0_95,plain,
( subset(X1,union(intersection(X2,X1),X3))
| ~ member(esk1_2(X1,union(intersection(X2,X1),X3)),X2) ),
inference(spm,[status(thm)],[c_0_89,c_0_12]) ).
cnf(c_0_96,plain,
( subset(intersection(union(X1,X2),X3),union(X4,intersection(X2,X3)))
| member(esk1_2(intersection(union(X1,X2),X3),union(X4,intersection(X2,X3))),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_92]),c_0_92]) ).
cnf(c_0_97,negated_conjecture,
intersection(esk3_0,union(esk4_0,esk5_0)) != union(intersection(esk3_0,esk4_0),intersection(esk3_0,esk5_0)),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_98,plain,
subset(union(intersection(X1,X2),intersection(X3,X2)),intersection(union(X1,X3),X2)),
inference(spm,[status(thm)],[c_0_94,c_0_92]) ).
cnf(c_0_99,plain,
subset(intersection(union(X1,X2),X3),union(intersection(X1,X3),intersection(X2,X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_88]) ).
cnf(c_0_100,negated_conjecture,
union(intersection(esk4_0,esk3_0),intersection(esk5_0,esk3_0)) != intersection(esk3_0,union(esk4_0,esk5_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_97,c_0_25]),c_0_25]) ).
cnf(c_0_101,plain,
union(intersection(X1,X2),intersection(X3,X2)) = intersection(union(X1,X3),X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_98]),c_0_99])]) ).
cnf(c_0_102,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_100,c_0_101]),c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09 % Problem : SET169+3 : TPTP v8.1.2. Released v2.2.0.
% 0.04/0.10 % Command : run_E %s %d THM
% 0.10/0.29 % Computer : n031.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 2400
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Mon Oct 2 17:14:28 EDT 2023
% 0.10/0.30 % CPUTime :
% 0.16/0.39 Running first-order theorem proving
% 0.16/0.39 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.GoHdp6UIbu/E---3.1_8229.p
% 1389.74/195.01 # Version: 3.1pre001
% 1389.74/195.01 # Preprocessing class: FSMSSMSSSSSNFFN.
% 1389.74/195.01 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1389.74/195.01 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1389.74/195.01 # Starting new_bool_3 with 300s (1) cores
% 1389.74/195.01 # Starting new_bool_1 with 300s (1) cores
% 1389.74/195.01 # Starting sh5l with 300s (1) cores
% 1389.74/195.01 # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 8307 completed with status 0
% 1389.74/195.01 # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 1389.74/195.01 # Preprocessing class: FSMSSMSSSSSNFFN.
% 1389.74/195.01 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1389.74/195.01 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1389.74/195.01 # No SInE strategy applied
% 1389.74/195.01 # Search class: FGUSS-FFSF22-SFFFFFNN
% 1389.74/195.01 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1389.74/195.01 # Starting U----_206c_00_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 811s (1) cores
% 1389.74/195.01 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1389.74/195.01 # Starting new_bool_3 with 136s (1) cores
% 1389.74/195.01 # Starting new_bool_1 with 136s (1) cores
% 1389.74/195.01 # Starting sh5l with 136s (1) cores
% 1389.74/195.01 # sh5l with pid 8318 completed with status 7
% 1389.74/195.01 # Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 130s (1) cores
% 1389.74/195.01 # new_bool_3 with pid 8315 completed with status 7
% 1389.74/195.01 # new_bool_1 with pid 8316 completed with status 7
% 1389.74/195.01 # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 8314 completed with status 7
% 1389.74/195.01 # U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 8379 completed with status 0
% 1389.74/195.01 # Result found by U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 1389.74/195.01 # Preprocessing class: FSMSSMSSSSSNFFN.
% 1389.74/195.01 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1389.74/195.01 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1389.74/195.01 # No SInE strategy applied
% 1389.74/195.01 # Search class: FGUSS-FFSF22-SFFFFFNN
% 1389.74/195.01 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1389.74/195.01 # Starting U----_206c_00_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 811s (1) cores
% 1389.74/195.01 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1389.74/195.01 # Starting new_bool_3 with 136s (1) cores
% 1389.74/195.01 # Starting new_bool_1 with 136s (1) cores
% 1389.74/195.01 # Starting sh5l with 136s (1) cores
% 1389.74/195.01 # sh5l with pid 8318 completed with status 7
% 1389.74/195.01 # Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 130s (1) cores
% 1389.74/195.01 # Preprocessing time : 0.001 s
% 1389.74/195.01 # Presaturation interreduction done
% 1389.74/195.01
% 1389.74/195.01 # Proof found!
% 1389.74/195.01 # SZS status Theorem
% 1389.74/195.01 # SZS output start CNFRefutation
% See solution above
% 1389.74/195.01 # Parsed axioms : 9
% 1389.74/195.01 # Removed by relevancy pruning/SinE : 0
% 1389.74/195.01 # Initial clauses : 20
% 1389.74/195.01 # Removed in clause preprocessing : 2
% 1389.74/195.01 # Initial clauses in saturation : 18
% 1389.74/195.01 # Processed clauses : 129736
% 1389.74/195.01 # ...of these trivial : 23938
% 1389.74/195.01 # ...subsumed : 98289
% 1389.74/195.01 # ...remaining for further processing : 7509
% 1389.74/195.01 # Other redundant clauses eliminated : 2
% 1389.74/195.01 # Clauses deleted for lack of memory : 695594
% 1389.74/195.01 # Backward-subsumed : 162
% 1389.74/195.01 # Backward-rewritten : 1515
% 1389.74/195.01 # Generated clauses : 3518608
% 1389.74/195.01 # ...of the previous two non-redundant : 3001389
% 1389.74/195.01 # ...aggressively subsumed : 0
% 1389.74/195.01 # Contextual simplify-reflections : 36
% 1389.74/195.01 # Paramodulations : 3511174
% 1389.74/195.01 # Factorizations : 7432
% 1389.74/195.01 # NegExts : 0
% 1389.74/195.01 # Equation resolutions : 2
% 1389.74/195.01 # Total rewrite steps : 4284815
% 1389.74/195.01 # Propositional unsat checks : 0
% 1389.74/195.01 # Propositional check models : 0
% 1389.74/195.01 # Propositional check unsatisfiable : 0
% 1389.74/195.01 # Propositional clauses : 0
% 1389.74/195.01 # Propositional clauses after purity: 0
% 1389.74/195.01 # Propositional unsat core size : 0
% 1389.74/195.01 # Propositional preprocessing time : 0.000
% 1389.74/195.01 # Propositional encoding time : 0.000
% 1389.74/195.01 # Propositional solver time : 0.000
% 1389.74/195.01 # Success case prop preproc time : 0.000
% 1389.74/195.01 # Success case prop encoding time : 0.000
% 1389.74/195.01 # Success case prop solver time : 0.000
% 1389.74/195.01 # Current number of processed clauses : 5814
% 1389.74/195.01 # Positive orientable unit clauses : 1593
% 1389.74/195.01 # Positive unorientable unit clauses: 10
% 1389.74/195.01 # Negative unit clauses : 0
% 1389.74/195.01 # Non-unit-clauses : 4211
% 1389.74/195.01 # Current number of unprocessed clauses: 1764414
% 1389.74/195.01 # ...number of literals in the above : 4945798
% 1389.74/195.01 # Current number of archived formulas : 0
% 1389.74/195.01 # Current number of archived clauses : 1693
% 1389.74/195.01 # Clause-clause subsumption calls (NU) : 6092089
% 1389.74/195.01 # Rec. Clause-clause subsumption calls : 3590842
% 1389.74/195.01 # Non-unit clause-clause subsumptions : 94061
% 1389.74/195.01 # Unit Clause-clause subsumption calls : 771555
% 1389.74/195.01 # Rewrite failures with RHS unbound : 0
% 1389.74/195.01 # BW rewrite match attempts : 109865
% 1389.74/195.01 # BW rewrite match successes : 5662
% 1389.74/195.01 # Condensation attempts : 0
% 1389.74/195.01 # Condensation successes : 0
% 1389.74/195.01 # Termbank termtop insertions : 82426928
% 1389.74/195.01
% 1389.74/195.01 # -------------------------------------------------
% 1389.74/195.01 # User time : 613.080 s
% 1389.74/195.01 # System time : 3.425 s
% 1389.74/195.01 # Total time : 616.505 s
% 1389.74/195.01 # Maximum resident set size: 1736 pages
% 1389.74/195.01
% 1389.74/195.01 # -------------------------------------------------
% 1389.74/195.01 # User time : 804.526 s
% 1389.74/195.01 # System time : 5.614 s
% 1389.74/195.01 # Total time : 810.140 s
% 1389.74/195.01 # Maximum resident set size: 1676 pages
% 1389.74/195.01 % E---3.1 exiting
% 1389.74/195.01 % E---3.1 exiting
%------------------------------------------------------------------------------