TSTP Solution File: SET655+3 by E-SAT---3.1
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- Process Solution
%------------------------------------------------------------------------------
% File : E-SAT---3.1
% Problem : SET655+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n011.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 19:23:16 EDT 2023
% Result : Theorem 7.27s 1.43s
% Output : CNFRefutation 7.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 79 ( 18 unt; 0 def)
% Number of atoms : 312 ( 0 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 382 ( 149 ~; 153 |; 28 &)
% ( 7 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 153 ( 3 sgn; 65 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p3,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ! [X3] :
( ilf_type(X3,subset_type(cross_product(X1,X2)))
=> ilf_type(X3,relation_type(X1,X2)) )
& ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> ilf_type(X4,subset_type(cross_product(X1,X2))) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.k4b2YMv1xW/E---3.1_31506.p',p3) ).
fof(p19,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox/tmp/tmp.k4b2YMv1xW/E---3.1_31506.p',p19) ).
fof(prove_relset_1_17,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,set_type)
=> ! [X5] :
( ilf_type(X5,relation_type(X1,X3))
=> ( ( subset(X1,X2)
& subset(X3,X4) )
=> ilf_type(X5,relation_type(X2,X4)) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.k4b2YMv1xW/E---3.1_31506.p',prove_relset_1_17) ).
fof(p12,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ( ilf_type(X1,member_type(X2))
<=> member(X1,X2) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.k4b2YMv1xW/E---3.1_31506.p',p12) ).
fof(p7,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ilf_type(X2,subset_type(X1))
<=> ilf_type(X2,member_type(power_set(X1))) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.k4b2YMv1xW/E---3.1_31506.p',p7) ).
fof(p11,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
file('/export/starexec/sandbox/tmp/tmp.k4b2YMv1xW/E---3.1_31506.p',p11) ).
fof(p2,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,set_type)
=> ( ( subset(X1,X2)
& subset(X3,X4) )
=> subset(cross_product(X1,X3),cross_product(X2,X4)) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.k4b2YMv1xW/E---3.1_31506.p',p2) ).
fof(p10,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X1,power_set(X2))
<=> ! [X3] :
( ilf_type(X3,set_type)
=> ( member(X3,X1)
=> member(X3,X2) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.k4b2YMv1xW/E---3.1_31506.p',p10) ).
fof(p5,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( subset(X1,X2)
<=> ! [X3] :
( ilf_type(X3,set_type)
=> ( member(X3,X1)
=> member(X3,X2) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.k4b2YMv1xW/E---3.1_31506.p',p5) ).
fof(p1,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.k4b2YMv1xW/E---3.1_31506.p',p1) ).
fof(p14,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.k4b2YMv1xW/E---3.1_31506.p',p14) ).
fof(c_0_11,plain,
! [X31,X32,X33,X34] :
( ( ~ ilf_type(X33,subset_type(cross_product(X31,X32)))
| ilf_type(X33,relation_type(X31,X32))
| ~ ilf_type(X32,set_type)
| ~ ilf_type(X31,set_type) )
& ( ~ ilf_type(X34,relation_type(X31,X32))
| ilf_type(X34,subset_type(cross_product(X31,X32)))
| ~ ilf_type(X32,set_type)
| ~ ilf_type(X31,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p3])])])]) ).
fof(c_0_12,plain,
! [X30] : ilf_type(X30,set_type),
inference(variable_rename,[status(thm)],[p19]) ).
fof(c_0_13,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,set_type)
=> ! [X5] :
( ilf_type(X5,relation_type(X1,X3))
=> ( ( subset(X1,X2)
& subset(X3,X4) )
=> ilf_type(X5,relation_type(X2,X4)) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_17]) ).
fof(c_0_14,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ( ilf_type(X1,member_type(X2))
<=> member(X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[p12]) ).
fof(c_0_15,plain,
! [X54,X55] :
( ( ~ ilf_type(X55,subset_type(X54))
| ilf_type(X55,member_type(power_set(X54)))
| ~ ilf_type(X55,set_type)
| ~ ilf_type(X54,set_type) )
& ( ~ ilf_type(X55,member_type(power_set(X54)))
| ilf_type(X55,subset_type(X54))
| ~ ilf_type(X55,set_type)
| ~ ilf_type(X54,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p7])])])]) ).
cnf(c_0_16,plain,
( ilf_type(X1,subset_type(cross_product(X2,X3)))
| ~ ilf_type(X1,relation_type(X2,X3))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_18,negated_conjecture,
( ilf_type(esk1_0,set_type)
& ilf_type(esk2_0,set_type)
& ilf_type(esk3_0,set_type)
& ilf_type(esk4_0,set_type)
& ilf_type(esk5_0,relation_type(esk1_0,esk3_0))
& subset(esk1_0,esk2_0)
& subset(esk3_0,esk4_0)
& ~ ilf_type(esk5_0,relation_type(esk2_0,esk4_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
fof(c_0_19,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
inference(fof_simplification,[status(thm)],[p11]) ).
fof(c_0_20,plain,
! [X14,X15,X16,X17] :
( ~ ilf_type(X14,set_type)
| ~ ilf_type(X15,set_type)
| ~ ilf_type(X16,set_type)
| ~ ilf_type(X17,set_type)
| ~ subset(X14,X15)
| ~ subset(X16,X17)
| subset(cross_product(X14,X16),cross_product(X15,X17)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p2])])]) ).
fof(c_0_21,plain,
! [X41,X42,X43] :
( ( ~ member(X41,power_set(X42))
| ~ ilf_type(X43,set_type)
| ~ member(X43,X41)
| member(X43,X42)
| ~ ilf_type(X42,set_type)
| ~ ilf_type(X41,set_type) )
& ( ilf_type(esk10_2(X41,X42),set_type)
| member(X41,power_set(X42))
| ~ ilf_type(X42,set_type)
| ~ ilf_type(X41,set_type) )
& ( member(esk10_2(X41,X42),X41)
| member(X41,power_set(X42))
| ~ ilf_type(X42,set_type)
| ~ ilf_type(X41,set_type) )
& ( ~ member(esk10_2(X41,X42),X42)
| member(X41,power_set(X42))
| ~ ilf_type(X42,set_type)
| ~ ilf_type(X41,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p10])])])])]) ).
fof(c_0_22,plain,
! [X18,X19,X20] :
( ( ~ subset(X18,X19)
| ~ ilf_type(X20,set_type)
| ~ member(X20,X18)
| member(X20,X19)
| ~ ilf_type(X19,set_type)
| ~ ilf_type(X18,set_type) )
& ( ilf_type(esk6_2(X18,X19),set_type)
| subset(X18,X19)
| ~ ilf_type(X19,set_type)
| ~ ilf_type(X18,set_type) )
& ( member(esk6_2(X18,X19),X18)
| subset(X18,X19)
| ~ ilf_type(X19,set_type)
| ~ ilf_type(X18,set_type) )
& ( ~ member(esk6_2(X18,X19),X19)
| subset(X18,X19)
| ~ ilf_type(X19,set_type)
| ~ ilf_type(X18,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p5])])])])]) ).
fof(c_0_23,plain,
! [X45,X46] :
( ( ~ ilf_type(X45,member_type(X46))
| member(X45,X46)
| empty(X46)
| ~ ilf_type(X46,set_type)
| ~ ilf_type(X45,set_type) )
& ( ~ member(X45,X46)
| ilf_type(X45,member_type(X46))
| empty(X46)
| ~ ilf_type(X46,set_type)
| ~ ilf_type(X45,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])]) ).
cnf(c_0_24,plain,
( ilf_type(X1,member_type(power_set(X2)))
| ~ ilf_type(X1,subset_type(X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_25,plain,
( ilf_type(X1,subset_type(cross_product(X2,X3)))
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17]),c_0_17])]) ).
cnf(c_0_26,negated_conjecture,
ilf_type(esk5_0,relation_type(esk1_0,esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_27,plain,
! [X56] :
( ( ~ empty(power_set(X56))
| ~ ilf_type(X56,set_type) )
& ( ilf_type(power_set(X56),set_type)
| ~ ilf_type(X56,set_type) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])]) ).
cnf(c_0_28,plain,
( subset(cross_product(X1,X3),cross_product(X2,X4))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type)
| ~ subset(X1,X2)
| ~ subset(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_29,plain,
( member(X3,X2)
| ~ member(X1,power_set(X2))
| ~ ilf_type(X3,set_type)
| ~ member(X3,X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_30,plain,
( member(esk6_2(X1,X2),X1)
| subset(X1,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_31,plain,
( member(X1,X2)
| empty(X2)
| ~ ilf_type(X1,member_type(X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_32,plain,
( ilf_type(X1,member_type(power_set(X2)))
| ~ ilf_type(X1,subset_type(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_17]),c_0_17])]) ).
cnf(c_0_33,negated_conjecture,
ilf_type(esk5_0,subset_type(cross_product(esk1_0,esk3_0))),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_34,plain,
( ~ empty(power_set(X1))
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_35,plain,
! [X11,X12,X13] :
( ~ ilf_type(X11,set_type)
| ~ ilf_type(X12,set_type)
| ~ ilf_type(X13,set_type)
| ~ subset(X11,X12)
| ~ subset(X12,X13)
| subset(X11,X13) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])]) ).
cnf(c_0_36,plain,
( subset(cross_product(X1,X2),cross_product(X3,X4))
| ~ subset(X2,X4)
| ~ subset(X1,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_17]),c_0_17]),c_0_17]),c_0_17])]) ).
cnf(c_0_37,negated_conjecture,
subset(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_38,plain,
( member(X1,X2)
| ~ member(X3,power_set(X2))
| ~ member(X1,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_17]),c_0_17]),c_0_17])]) ).
cnf(c_0_39,plain,
( member(esk6_2(X1,X2),X1)
| subset(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_17]),c_0_17])]) ).
cnf(c_0_40,plain,
( empty(X1)
| member(X2,X1)
| ~ ilf_type(X2,member_type(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_17]),c_0_17])]) ).
cnf(c_0_41,negated_conjecture,
ilf_type(esk5_0,member_type(power_set(cross_product(esk1_0,esk3_0)))),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_42,plain,
~ empty(power_set(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_17])]) ).
cnf(c_0_43,plain,
( subset(X1,X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ subset(X1,X2)
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_44,negated_conjecture,
( subset(cross_product(X1,esk3_0),cross_product(X2,esk4_0))
| ~ subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_45,negated_conjecture,
subset(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_46,plain,
( subset(X1,X2)
| ~ member(esk6_2(X1,X2),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_47,plain,
( member(esk6_2(X1,X2),X3)
| subset(X1,X2)
| ~ member(X1,power_set(X3)) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_48,negated_conjecture,
member(esk5_0,power_set(cross_product(esk1_0,esk3_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
fof(c_0_49,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[p14]) ).
cnf(c_0_50,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ ilf_type(X3,set_type)
| ~ member(X3,X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_51,plain,
( member(esk10_2(X1,X2),X1)
| member(X1,power_set(X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_52,plain,
( subset(X1,X2)
| ~ subset(X3,X2)
| ~ subset(X1,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_17]),c_0_17]),c_0_17])]) ).
cnf(c_0_53,negated_conjecture,
subset(cross_product(esk1_0,esk3_0),cross_product(esk2_0,esk4_0)),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_54,plain,
( subset(X1,X2)
| ~ member(esk6_2(X1,X2),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_17]),c_0_17])]) ).
cnf(c_0_55,negated_conjecture,
( member(esk6_2(esk5_0,X1),cross_product(esk1_0,esk3_0))
| subset(esk5_0,X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
fof(c_0_56,plain,
! [X27,X28] :
( ( ~ empty(X27)
| ~ ilf_type(X28,set_type)
| ~ member(X28,X27)
| ~ ilf_type(X27,set_type) )
& ( ilf_type(esk8_1(X27),set_type)
| empty(X27)
| ~ ilf_type(X27,set_type) )
& ( member(esk8_1(X27),X27)
| empty(X27)
| ~ ilf_type(X27,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_49])])])])]) ).
cnf(c_0_57,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ subset(X3,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_17]),c_0_17]),c_0_17])]) ).
cnf(c_0_58,plain,
( member(esk10_2(X1,X2),X1)
| member(X1,power_set(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_17]),c_0_17])]) ).
cnf(c_0_59,negated_conjecture,
( subset(X1,cross_product(esk2_0,esk4_0))
| ~ subset(X1,cross_product(esk1_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_60,negated_conjecture,
subset(esk5_0,cross_product(esk1_0,esk3_0)),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_61,plain,
( ~ empty(X1)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X1)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_62,plain,
( member(X1,power_set(X2))
| ~ member(esk10_2(X1,X2),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_63,plain,
( member(esk10_2(X1,X2),X3)
| member(X1,power_set(X2))
| ~ subset(X1,X3) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_64,negated_conjecture,
subset(esk5_0,cross_product(esk2_0,esk4_0)),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_65,plain,
( ilf_type(X1,member_type(X2))
| empty(X2)
| ~ member(X1,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_66,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_17]),c_0_17])]) ).
cnf(c_0_67,plain,
( member(X1,power_set(X2))
| ~ member(esk10_2(X1,X2),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_17]),c_0_17])]) ).
cnf(c_0_68,negated_conjecture,
( member(esk10_2(esk5_0,X1),cross_product(esk2_0,esk4_0))
| member(esk5_0,power_set(X1)) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_69,plain,
( ilf_type(X1,subset_type(X2))
| ~ ilf_type(X1,member_type(power_set(X2)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_70,plain,
( ilf_type(X1,member_type(X2))
| ~ member(X1,X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_17]),c_0_17])]),c_0_66]) ).
cnf(c_0_71,negated_conjecture,
member(esk5_0,power_set(cross_product(esk2_0,esk4_0))),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_72,plain,
( ilf_type(X1,relation_type(X2,X3))
| ~ ilf_type(X1,subset_type(cross_product(X2,X3)))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_73,plain,
( ilf_type(X1,subset_type(X2))
| ~ ilf_type(X1,member_type(power_set(X2))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_17]),c_0_17])]) ).
cnf(c_0_74,negated_conjecture,
ilf_type(esk5_0,member_type(power_set(cross_product(esk2_0,esk4_0)))),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_75,plain,
( ilf_type(X1,relation_type(X2,X3))
| ~ ilf_type(X1,subset_type(cross_product(X2,X3))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_17]),c_0_17])]) ).
cnf(c_0_76,negated_conjecture,
ilf_type(esk5_0,subset_type(cross_product(esk2_0,esk4_0))),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_77,negated_conjecture,
~ ilf_type(esk5_0,relation_type(esk2_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_78,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_77]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SET655+3 : TPTP v8.1.2. Released v2.2.0.
% 0.08/0.15 % Command : run_E %s %d THM
% 0.15/0.36 % Computer : n011.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 2400
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Mon Oct 2 16:55:23 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.22/0.51 Running first-order model finding
% 0.22/0.51 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.k4b2YMv1xW/E---3.1_31506.p
% 7.27/1.43 # Version: 3.1pre001
% 7.27/1.43 # Preprocessing class: FSMSSMSSSSSNFFN.
% 7.27/1.43 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.27/1.43 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 7.27/1.43 # Starting new_bool_3 with 300s (1) cores
% 7.27/1.43 # Starting new_bool_1 with 300s (1) cores
% 7.27/1.43 # Starting sh5l with 300s (1) cores
% 7.27/1.43 # sh5l with pid 31587 completed with status 0
% 7.27/1.43 # Result found by sh5l
% 7.27/1.43 # Preprocessing class: FSMSSMSSSSSNFFN.
% 7.27/1.43 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.27/1.43 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 7.27/1.43 # Starting new_bool_3 with 300s (1) cores
% 7.27/1.43 # Starting new_bool_1 with 300s (1) cores
% 7.27/1.43 # Starting sh5l with 300s (1) cores
% 7.27/1.43 # SinE strategy is gf500_gu_R04_F100_L20000
% 7.27/1.43 # Search class: FGHSF-FFMM21-SFFFFFNN
% 7.27/1.43 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 7.27/1.43 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2v with 163s (1) cores
% 7.27/1.43 # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2v with pid 31595 completed with status 0
% 7.27/1.43 # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2v
% 7.27/1.43 # Preprocessing class: FSMSSMSSSSSNFFN.
% 7.27/1.43 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.27/1.43 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 7.27/1.43 # Starting new_bool_3 with 300s (1) cores
% 7.27/1.43 # Starting new_bool_1 with 300s (1) cores
% 7.27/1.43 # Starting sh5l with 300s (1) cores
% 7.27/1.43 # SinE strategy is gf500_gu_R04_F100_L20000
% 7.27/1.43 # Search class: FGHSF-FFMM21-SFFFFFNN
% 7.27/1.43 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 7.27/1.43 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2v with 163s (1) cores
% 7.27/1.43 # Preprocessing time : 0.002 s
% 7.27/1.43 # Presaturation interreduction done
% 7.27/1.43
% 7.27/1.43 # Proof found!
% 7.27/1.43 # SZS status Theorem
% 7.27/1.43 # SZS output start CNFRefutation
% See solution above
% 7.27/1.43 # Parsed axioms : 20
% 7.27/1.43 # Removed by relevancy pruning/SinE : 0
% 7.27/1.43 # Initial clauses : 44
% 7.27/1.43 # Removed in clause preprocessing : 0
% 7.27/1.43 # Initial clauses in saturation : 44
% 7.27/1.43 # Processed clauses : 8175
% 7.27/1.43 # ...of these trivial : 413
% 7.27/1.43 # ...subsumed : 4541
% 7.27/1.43 # ...remaining for further processing : 3221
% 7.27/1.43 # Other redundant clauses eliminated : 0
% 7.27/1.43 # Clauses deleted for lack of memory : 0
% 7.27/1.43 # Backward-subsumed : 170
% 7.27/1.43 # Backward-rewritten : 15
% 7.27/1.43 # Generated clauses : 82456
% 7.27/1.43 # ...of the previous two non-redundant : 80589
% 7.27/1.43 # ...aggressively subsumed : 0
% 7.27/1.43 # Contextual simplify-reflections : 6
% 7.27/1.43 # Paramodulations : 82456
% 7.27/1.43 # Factorizations : 0
% 7.27/1.43 # NegExts : 0
% 7.27/1.43 # Equation resolutions : 0
% 7.27/1.43 # Total rewrite steps : 2536
% 7.27/1.43 # Propositional unsat checks : 0
% 7.27/1.43 # Propositional check models : 0
% 7.27/1.43 # Propositional check unsatisfiable : 0
% 7.27/1.43 # Propositional clauses : 0
% 7.27/1.43 # Propositional clauses after purity: 0
% 7.27/1.43 # Propositional unsat core size : 0
% 7.27/1.43 # Propositional preprocessing time : 0.000
% 7.27/1.43 # Propositional encoding time : 0.000
% 7.27/1.43 # Propositional solver time : 0.000
% 7.27/1.43 # Success case prop preproc time : 0.000
% 7.27/1.43 # Success case prop encoding time : 0.000
% 7.27/1.43 # Success case prop solver time : 0.000
% 7.27/1.43 # Current number of processed clauses : 3005
% 7.27/1.43 # Positive orientable unit clauses : 583
% 7.27/1.43 # Positive unorientable unit clauses: 0
% 7.27/1.43 # Negative unit clauses : 7
% 7.27/1.43 # Non-unit-clauses : 2415
% 7.27/1.43 # Current number of unprocessed clauses: 72390
% 7.27/1.43 # ...number of literals in the above : 141067
% 7.27/1.43 # Current number of archived formulas : 0
% 7.27/1.43 # Current number of archived clauses : 216
% 7.27/1.43 # Clause-clause subsumption calls (NU) : 568305
% 7.27/1.43 # Rec. Clause-clause subsumption calls : 470335
% 7.27/1.43 # Non-unit clause-clause subsumptions : 4202
% 7.27/1.43 # Unit Clause-clause subsumption calls : 9377
% 7.27/1.43 # Rewrite failures with RHS unbound : 0
% 7.27/1.43 # BW rewrite match attempts : 3994
% 7.27/1.43 # BW rewrite match successes : 15
% 7.27/1.43 # Condensation attempts : 0
% 7.27/1.43 # Condensation successes : 0
% 7.27/1.43 # Termbank termtop insertions : 1434550
% 7.27/1.43
% 7.27/1.43 # -------------------------------------------------
% 7.27/1.43 # User time : 0.836 s
% 7.27/1.43 # System time : 0.037 s
% 7.27/1.43 # Total time : 0.873 s
% 7.27/1.43 # Maximum resident set size: 1840 pages
% 7.27/1.43
% 7.27/1.43 # -------------------------------------------------
% 7.27/1.43 # User time : 0.839 s
% 7.27/1.43 # System time : 0.038 s
% 7.27/1.43 # Total time : 0.877 s
% 7.27/1.43 # Maximum resident set size: 1696 pages
% 7.27/1.43 % E---3.1 exiting
%------------------------------------------------------------------------------