TSTP Solution File: SET672+3 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SET672+3 : TPTP v8.2.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 02:55:15 EDT 2024
% Result : Theorem 137.41s 17.89s
% Output : CNFRefutation 137.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 16
% Syntax : Number of formulae : 94 ( 14 unt; 0 def)
% Number of atoms : 418 ( 11 equ)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 549 ( 225 ~; 224 |; 33 &)
% ( 10 <=>; 57 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 6 con; 0-4 aty)
% Number of variables : 230 ( 21 sgn 100 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p24,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p24) ).
fof(p22,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/benchmark/theBenchmark.p',p22) ).
fof(p28,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p28) ).
fof(p13,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/benchmark/theBenchmark.p',p13) ).
fof(p5,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/benchmark/theBenchmark.p',p5) ).
fof(p11,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,binary_relation_type)
<=> ( relation_like(X1)
& ilf_type(X1,set_type) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p11) ).
fof(p10,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ilf_type(restrict(X1,X2),binary_relation_type) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10) ).
fof(p19,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,subset_type(cross_product(X1,X2)))
=> relation_like(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p19) ).
fof(prove_relset_1_35,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X3,X1))
=> ilf_type(restrict4(X3,X1,X2,X4),relation_type(X3,X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_35) ).
fof(p26,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> restrict4(X1,X2,X3,X4) = restrict(X3,X4) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p26) ).
fof(p7,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)
=> ! [X5] :
( ilf_type(X5,relation_type(X1,X2))
=> ( member(ordered_pair(X3,X4),X5)
=> ( member(X3,X1)
& member(X4,X2) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7) ).
fof(p27,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> ilf_type(restrict4(X1,X2,X3,X4),relation_type(X1,X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p27) ).
fof(p20,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/benchmark/theBenchmark.p',p20) ).
fof(p18,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( relation_like(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X1)
=> ? [X3] :
( ilf_type(X3,set_type)
& ? [X4] :
( ilf_type(X4,set_type)
& X2 = ordered_pair(X3,X4) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p18) ).
fof(p3,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,binary_relation_type)
=> ( member(ordered_pair(X2,X3),restrict(X1,X4))
<=> ( member(X3,X1)
& member(ordered_pair(X2,X3),X4) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
fof(p4,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)
=> ( member(ordered_pair(X1,X2),cross_product(X3,X4))
<=> ( member(X1,X3)
& member(X2,X4) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4) ).
fof(c_0_16,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[p24]) ).
fof(c_0_17,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)],[p22]) ).
fof(c_0_18,plain,
! [X69,X70] :
( ( ~ empty(X69)
| ~ ilf_type(X70,set_type)
| ~ member(X70,X69)
| ~ ilf_type(X69,set_type) )
& ( ilf_type(esk11_1(X69),set_type)
| empty(X69)
| ~ ilf_type(X69,set_type) )
& ( member(esk11_1(X69),X69)
| empty(X69)
| ~ ilf_type(X69,set_type) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])])])]) ).
fof(c_0_19,plain,
! [X81] : ilf_type(X81,set_type),
inference(variable_rename,[status(thm)],[p28]) ).
fof(c_0_20,plain,
! [X42,X43] :
( ( ~ ilf_type(X43,subset_type(X42))
| ilf_type(X43,member_type(power_set(X42)))
| ~ ilf_type(X43,set_type)
| ~ ilf_type(X42,set_type) )
& ( ~ ilf_type(X43,member_type(power_set(X42)))
| ilf_type(X43,subset_type(X42))
| ~ ilf_type(X43,set_type)
| ~ ilf_type(X42,set_type) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p13])])])])]) ).
fof(c_0_21,plain,
! [X65,X66] :
( ( ~ ilf_type(X65,member_type(X66))
| member(X65,X66)
| empty(X66)
| ~ ilf_type(X66,set_type)
| ~ ilf_type(X65,set_type) )
& ( ~ member(X65,X66)
| ilf_type(X65,member_type(X66))
| empty(X66)
| ~ ilf_type(X66,set_type)
| ~ ilf_type(X65,set_type) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])])]) ).
cnf(c_0_22,plain,
( ~ empty(X1)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X1)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_24,plain,
! [X22,X23,X24,X25] :
( ( ~ ilf_type(X24,subset_type(cross_product(X22,X23)))
| ilf_type(X24,relation_type(X22,X23))
| ~ ilf_type(X23,set_type)
| ~ ilf_type(X22,set_type) )
& ( ~ ilf_type(X25,relation_type(X22,X23))
| ilf_type(X25,subset_type(cross_product(X22,X23)))
| ~ ilf_type(X23,set_type)
| ~ ilf_type(X22,set_type) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p5])])])])]) ).
cnf(c_0_25,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_20]) ).
cnf(c_0_26,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_21]) ).
cnf(c_0_27,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23]),c_0_23])]) ).
fof(c_0_28,plain,
! [X40] :
( ( relation_like(X40)
| ~ ilf_type(X40,binary_relation_type)
| ~ ilf_type(X40,set_type) )
& ( ilf_type(X40,set_type)
| ~ ilf_type(X40,binary_relation_type)
| ~ ilf_type(X40,set_type) )
& ( ~ relation_like(X40)
| ~ ilf_type(X40,set_type)
| ilf_type(X40,binary_relation_type)
| ~ ilf_type(X40,set_type) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p11])])])]) ).
fof(c_0_29,plain,
! [X38,X39] :
( ~ ilf_type(X38,set_type)
| ~ ilf_type(X39,binary_relation_type)
| ilf_type(restrict(X38,X39),binary_relation_type) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p10])])])]) ).
fof(c_0_30,plain,
! [X57,X58,X59] :
( ~ ilf_type(X57,set_type)
| ~ ilf_type(X58,set_type)
| ~ ilf_type(X59,subset_type(cross_product(X57,X58)))
| relation_like(X59) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p19])])])]) ).
fof(c_0_31,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X3,X1))
=> ilf_type(restrict4(X3,X1,X2,X4),relation_type(X3,X2)) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_35]) ).
cnf(c_0_32,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_24]) ).
cnf(c_0_33,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_25,c_0_23]),c_0_23])]) ).
cnf(c_0_34,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_26,c_0_23]),c_0_23])]),c_0_27]) ).
cnf(c_0_35,plain,
( relation_like(X1)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_36,plain,
( ilf_type(restrict(X1,X2),binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_37,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_38,plain,
! [X73,X74,X75,X76] :
( ~ ilf_type(X73,set_type)
| ~ ilf_type(X74,set_type)
| ~ ilf_type(X75,set_type)
| ~ ilf_type(X76,relation_type(X73,X74))
| restrict4(X73,X74,X75,X76) = restrict(X75,X76) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p26])])])]) ).
cnf(c_0_39,plain,
( relation_like(X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_40,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_24]) ).
fof(c_0_41,plain,
! [X29,X30,X31,X32,X33] :
( ( member(X31,X29)
| ~ member(ordered_pair(X31,X32),X33)
| ~ ilf_type(X33,relation_type(X29,X30))
| ~ ilf_type(X32,set_type)
| ~ ilf_type(X31,set_type)
| ~ ilf_type(X30,set_type)
| ~ ilf_type(X29,set_type) )
& ( member(X32,X30)
| ~ member(ordered_pair(X31,X32),X33)
| ~ ilf_type(X33,relation_type(X29,X30))
| ~ ilf_type(X32,set_type)
| ~ ilf_type(X31,set_type)
| ~ ilf_type(X30,set_type)
| ~ ilf_type(X29,set_type) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p7])])])])]) ).
fof(c_0_42,plain,
! [X77,X78,X79,X80] :
( ~ ilf_type(X77,set_type)
| ~ ilf_type(X78,set_type)
| ~ ilf_type(X79,set_type)
| ~ ilf_type(X80,relation_type(X77,X78))
| ilf_type(restrict4(X77,X78,X79,X80),relation_type(X77,X78)) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p27])])])]) ).
fof(c_0_43,negated_conjecture,
( ilf_type(esk12_0,set_type)
& ilf_type(esk13_0,set_type)
& ilf_type(esk14_0,set_type)
& ilf_type(esk15_0,relation_type(esk14_0,esk12_0))
& ~ ilf_type(restrict4(esk14_0,esk12_0,esk13_0,esk15_0),relation_type(esk14_0,esk13_0)) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])])]) ).
cnf(c_0_44,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_32,c_0_23]),c_0_23])]) ).
cnf(c_0_45,plain,
( ilf_type(X1,subset_type(X2))
| ~ member(X1,power_set(X2)) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
fof(c_0_46,plain,
! [X60,X61,X62] :
( ( ~ member(X60,power_set(X61))
| ~ ilf_type(X62,set_type)
| ~ member(X62,X60)
| member(X62,X61)
| ~ ilf_type(X61,set_type)
| ~ ilf_type(X60,set_type) )
& ( ilf_type(esk9_2(X60,X61),set_type)
| member(X60,power_set(X61))
| ~ ilf_type(X61,set_type)
| ~ ilf_type(X60,set_type) )
& ( member(esk9_2(X60,X61),X60)
| member(X60,power_set(X61))
| ~ ilf_type(X61,set_type)
| ~ ilf_type(X60,set_type) )
& ( ~ member(esk9_2(X60,X61),X61)
| member(X60,power_set(X61))
| ~ ilf_type(X61,set_type)
| ~ ilf_type(X60,set_type) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p20])])])])])]) ).
cnf(c_0_47,plain,
( relation_like(X1)
| ~ ilf_type(X1,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_23])]) ).
cnf(c_0_48,plain,
( ilf_type(restrict(X1,X2),binary_relation_type)
| ~ ilf_type(X2,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_23])]) ).
cnf(c_0_49,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1)
| ~ ilf_type(X1,set_type) ),
inference(cn,[status(thm)],[c_0_37]) ).
cnf(c_0_50,plain,
( restrict4(X1,X2,X3,X4) = restrict(X3,X4)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,relation_type(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_51,plain,
( relation_like(X1)
| ~ ilf_type(X1,subset_type(cross_product(X2,X3))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_23]),c_0_23])]) ).
cnf(c_0_52,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_40,c_0_23]),c_0_23])]) ).
cnf(c_0_53,plain,
( member(X1,X2)
| ~ member(ordered_pair(X1,X3),X4)
| ~ ilf_type(X4,relation_type(X2,X5))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_54,plain,
( ilf_type(restrict4(X1,X2,X3,X4),relation_type(X1,X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,relation_type(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
fof(c_0_55,plain,
! [X50,X51,X55,X56] :
( ( ilf_type(esk6_2(X50,X51),set_type)
| ~ member(X51,X50)
| ~ ilf_type(X51,set_type)
| ~ relation_like(X50)
| ~ ilf_type(X50,set_type) )
& ( ilf_type(esk7_2(X50,X51),set_type)
| ~ member(X51,X50)
| ~ ilf_type(X51,set_type)
| ~ relation_like(X50)
| ~ ilf_type(X50,set_type) )
& ( X51 = ordered_pair(esk6_2(X50,X51),esk7_2(X50,X51))
| ~ member(X51,X50)
| ~ ilf_type(X51,set_type)
| ~ relation_like(X50)
| ~ ilf_type(X50,set_type) )
& ( ilf_type(esk8_1(X50),set_type)
| relation_like(X50)
| ~ ilf_type(X50,set_type) )
& ( member(esk8_1(X50),X50)
| relation_like(X50)
| ~ ilf_type(X50,set_type) )
& ( ~ ilf_type(X55,set_type)
| ~ ilf_type(X56,set_type)
| esk8_1(X50) != ordered_pair(X55,X56)
| relation_like(X50)
| ~ ilf_type(X50,set_type) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p18])])])])])]) ).
cnf(c_0_56,negated_conjecture,
~ ilf_type(restrict4(esk14_0,esk12_0,esk13_0,esk15_0),relation_type(esk14_0,esk13_0)),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_57,plain,
( ilf_type(X1,relation_type(X2,X3))
| ~ member(X1,power_set(cross_product(X2,X3))) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_58,plain,
( member(esk9_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_46]) ).
cnf(c_0_59,plain,
( relation_like(restrict(X1,X2))
| ~ ilf_type(X2,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_60,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_23])]) ).
cnf(c_0_61,plain,
( restrict4(X1,X2,X3,X4) = restrict(X3,X4)
| ~ ilf_type(X4,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_23]),c_0_23]),c_0_23])]) ).
cnf(c_0_62,negated_conjecture,
ilf_type(esk15_0,relation_type(esk14_0,esk12_0)),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_63,plain,
( relation_like(X1)
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_64,plain,
( member(X1,X2)
| ~ member(ordered_pair(X1,X3),X4)
| ~ ilf_type(X4,relation_type(X2,X5)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_23]),c_0_23]),c_0_23]),c_0_23])]) ).
cnf(c_0_65,plain,
( ilf_type(restrict4(X1,X2,X3,X4),relation_type(X1,X2))
| ~ ilf_type(X4,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_23]),c_0_23]),c_0_23])]) ).
cnf(c_0_66,plain,
( X1 = ordered_pair(esk6_2(X2,X1),esk7_2(X2,X1))
| ~ member(X1,X2)
| ~ ilf_type(X1,set_type)
| ~ relation_like(X2)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_67,negated_conjecture,
~ member(restrict4(esk14_0,esk12_0,esk13_0,esk15_0),power_set(cross_product(esk14_0,esk13_0))),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_68,plain,
( member(esk9_2(X1,X2),X1)
| member(X1,power_set(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_23]),c_0_23])]) ).
cnf(c_0_69,plain,
( relation_like(restrict(X1,X2))
| ~ relation_like(X2) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_70,negated_conjecture,
restrict(X1,esk15_0) = restrict4(esk14_0,esk12_0,X1,esk15_0),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_71,negated_conjecture,
relation_like(esk15_0),
inference(spm,[status(thm)],[c_0_63,c_0_62]) ).
fof(c_0_72,plain,
! [X14,X15,X16,X17] :
( ( member(X16,X14)
| ~ member(ordered_pair(X15,X16),restrict(X14,X17))
| ~ ilf_type(X17,binary_relation_type)
| ~ ilf_type(X16,set_type)
| ~ ilf_type(X15,set_type)
| ~ ilf_type(X14,set_type) )
& ( member(ordered_pair(X15,X16),X17)
| ~ member(ordered_pair(X15,X16),restrict(X14,X17))
| ~ ilf_type(X17,binary_relation_type)
| ~ ilf_type(X16,set_type)
| ~ ilf_type(X15,set_type)
| ~ ilf_type(X14,set_type) )
& ( ~ member(X16,X14)
| ~ member(ordered_pair(X15,X16),X17)
| member(ordered_pair(X15,X16),restrict(X14,X17))
| ~ ilf_type(X17,binary_relation_type)
| ~ ilf_type(X16,set_type)
| ~ ilf_type(X15,set_type)
| ~ ilf_type(X14,set_type) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p3])])])])]) ).
fof(c_0_73,plain,
! [X18,X19,X20,X21] :
( ( member(X18,X20)
| ~ member(ordered_pair(X18,X19),cross_product(X20,X21))
| ~ ilf_type(X21,set_type)
| ~ ilf_type(X20,set_type)
| ~ ilf_type(X19,set_type)
| ~ ilf_type(X18,set_type) )
& ( member(X19,X21)
| ~ member(ordered_pair(X18,X19),cross_product(X20,X21))
| ~ ilf_type(X21,set_type)
| ~ ilf_type(X20,set_type)
| ~ ilf_type(X19,set_type)
| ~ ilf_type(X18,set_type) )
& ( ~ member(X18,X20)
| ~ member(X19,X21)
| member(ordered_pair(X18,X19),cross_product(X20,X21))
| ~ ilf_type(X21,set_type)
| ~ ilf_type(X20,set_type)
| ~ ilf_type(X19,set_type)
| ~ ilf_type(X18,set_type) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p4])])])])]) ).
cnf(c_0_74,plain,
( member(X1,X2)
| ~ member(ordered_pair(X1,X3),restrict4(X2,X4,X5,X6))
| ~ ilf_type(X6,relation_type(X2,X4)) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_75,plain,
( ordered_pair(esk6_2(X1,X2),esk7_2(X1,X2)) = X2
| ~ relation_like(X1)
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_23]),c_0_23])]) ).
cnf(c_0_76,negated_conjecture,
member(esk9_2(restrict4(esk14_0,esk12_0,esk13_0,esk15_0),cross_product(esk14_0,esk13_0)),restrict4(esk14_0,esk12_0,esk13_0,esk15_0)),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_77,negated_conjecture,
relation_like(restrict4(esk14_0,esk12_0,X1,esk15_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71])]) ).
cnf(c_0_78,plain,
( member(X1,X2)
| ~ member(ordered_pair(X3,X1),restrict(X2,X4))
| ~ ilf_type(X4,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_79,plain,
( member(ordered_pair(X1,X3),cross_product(X2,X4))
| ~ member(X1,X2)
| ~ member(X3,X4)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_80,negated_conjecture,
( member(X1,esk14_0)
| ~ member(ordered_pair(X1,X2),restrict4(esk14_0,esk12_0,X3,esk15_0)) ),
inference(spm,[status(thm)],[c_0_74,c_0_62]) ).
cnf(c_0_81,negated_conjecture,
ordered_pair(esk6_2(restrict4(esk14_0,esk12_0,esk13_0,esk15_0),esk9_2(restrict4(esk14_0,esk12_0,esk13_0,esk15_0),cross_product(esk14_0,esk13_0))),esk7_2(restrict4(esk14_0,esk12_0,esk13_0,esk15_0),esk9_2(restrict4(esk14_0,esk12_0,esk13_0,esk15_0),cross_product(esk14_0,esk13_0)))) = esk9_2(restrict4(esk14_0,esk12_0,esk13_0,esk15_0),cross_product(esk14_0,esk13_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_77])]) ).
cnf(c_0_82,plain,
( member(X1,X2)
| ~ member(ordered_pair(X3,X1),restrict(X2,X4))
| ~ ilf_type(X4,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_23]),c_0_23]),c_0_23])]) ).
cnf(c_0_83,plain,
( member(X1,power_set(X2))
| ~ member(esk9_2(X1,X2),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_84,plain,
( member(ordered_pair(X1,X2),cross_product(X3,X4))
| ~ member(X2,X4)
| ~ member(X1,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_23]),c_0_23]),c_0_23]),c_0_23])]) ).
cnf(c_0_85,negated_conjecture,
( member(esk6_2(restrict4(esk14_0,esk12_0,esk13_0,esk15_0),esk9_2(restrict4(esk14_0,esk12_0,esk13_0,esk15_0),cross_product(esk14_0,esk13_0))),esk14_0)
| ~ member(esk9_2(restrict4(esk14_0,esk12_0,esk13_0,esk15_0),cross_product(esk14_0,esk13_0)),restrict4(esk14_0,esk12_0,X1,esk15_0)) ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_86,plain,
( member(X1,X2)
| ~ relation_like(X3)
| ~ member(ordered_pair(X4,X1),restrict(X2,X3)) ),
inference(spm,[status(thm)],[c_0_82,c_0_60]) ).
cnf(c_0_87,plain,
( member(X1,power_set(X2))
| ~ member(esk9_2(X1,X2),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_83,c_0_23]),c_0_23])]) ).
cnf(c_0_88,negated_conjecture,
( member(esk9_2(restrict4(esk14_0,esk12_0,esk13_0,esk15_0),cross_product(esk14_0,esk13_0)),cross_product(X1,X2))
| ~ member(esk7_2(restrict4(esk14_0,esk12_0,esk13_0,esk15_0),esk9_2(restrict4(esk14_0,esk12_0,esk13_0,esk15_0),cross_product(esk14_0,esk13_0))),X2)
| ~ member(esk6_2(restrict4(esk14_0,esk12_0,esk13_0,esk15_0),esk9_2(restrict4(esk14_0,esk12_0,esk13_0,esk15_0),cross_product(esk14_0,esk13_0))),X1) ),
inference(spm,[status(thm)],[c_0_84,c_0_81]) ).
cnf(c_0_89,negated_conjecture,
member(esk6_2(restrict4(esk14_0,esk12_0,esk13_0,esk15_0),esk9_2(restrict4(esk14_0,esk12_0,esk13_0,esk15_0),cross_product(esk14_0,esk13_0))),esk14_0),
inference(spm,[status(thm)],[c_0_85,c_0_76]) ).
cnf(c_0_90,negated_conjecture,
( member(X1,X2)
| ~ member(ordered_pair(X3,X1),restrict4(esk14_0,esk12_0,X2,esk15_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_70]),c_0_71])]) ).
cnf(c_0_91,negated_conjecture,
~ member(esk7_2(restrict4(esk14_0,esk12_0,esk13_0,esk15_0),esk9_2(restrict4(esk14_0,esk12_0,esk13_0,esk15_0),cross_product(esk14_0,esk13_0))),esk13_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_89])]),c_0_67]) ).
cnf(c_0_92,negated_conjecture,
( member(esk7_2(restrict4(esk14_0,esk12_0,esk13_0,esk15_0),esk9_2(restrict4(esk14_0,esk12_0,esk13_0,esk15_0),cross_product(esk14_0,esk13_0))),X1)
| ~ member(esk9_2(restrict4(esk14_0,esk12_0,esk13_0,esk15_0),cross_product(esk14_0,esk13_0)),restrict4(esk14_0,esk12_0,X1,esk15_0)) ),
inference(spm,[status(thm)],[c_0_90,c_0_81]) ).
cnf(c_0_93,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_76])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET672+3 : TPTP v8.2.0. Released v2.2.0.
% 0.13/0.14 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n017.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon May 20 12:21:53 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.20/0.51 Running first-order theorem proving
% 0.20/0.51 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/benchmark/theBenchmark.p
% 137.41/17.89 # Version: 3.1.0
% 137.41/17.89 # Preprocessing class: FSLSSMSSSSSNFFN.
% 137.41/17.89 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 137.41/17.89 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 137.41/17.89 # Starting new_bool_3 with 300s (1) cores
% 137.41/17.89 # Starting new_bool_1 with 300s (1) cores
% 137.41/17.89 # Starting sh5l with 300s (1) cores
% 137.41/17.89 # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 21290 completed with status 0
% 137.41/17.89 # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 137.41/17.89 # Preprocessing class: FSLSSMSSSSSNFFN.
% 137.41/17.89 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 137.41/17.89 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 137.41/17.89 # No SInE strategy applied
% 137.41/17.89 # Search class: FGHSF-FFMS31-SFFFFFNN
% 137.41/17.89 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 137.41/17.89 # Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 737s (1) cores
% 137.41/17.89 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 137.41/17.89 # Starting new_bool_3 with 189s (1) cores
% 137.41/17.89 # Starting 208_C09_12_F1_SE_CS_SP_PS_S070I with 136s (1) cores
% 137.41/17.89 # Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN with 136s (1) cores
% 137.41/17.89 # 208_C09_12_F1_SE_CS_SP_PS_S070I with pid 21299 completed with status 0
% 137.41/17.89 # Result found by 208_C09_12_F1_SE_CS_SP_PS_S070I
% 137.41/17.89 # Preprocessing class: FSLSSMSSSSSNFFN.
% 137.41/17.89 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 137.41/17.89 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 137.41/17.89 # No SInE strategy applied
% 137.41/17.89 # Search class: FGHSF-FFMS31-SFFFFFNN
% 137.41/17.89 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 137.41/17.89 # Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 737s (1) cores
% 137.41/17.89 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 137.41/17.89 # Starting new_bool_3 with 189s (1) cores
% 137.41/17.89 # Starting 208_C09_12_F1_SE_CS_SP_PS_S070I with 136s (1) cores
% 137.41/17.89 # Preprocessing time : 0.002 s
% 137.41/17.89 # Presaturation interreduction done
% 137.41/17.89
% 137.41/17.89 # Proof found!
% 137.41/17.89 # SZS status Theorem
% 137.41/17.89 # SZS output start CNFRefutation
% See solution above
% 137.41/17.89 # Parsed axioms : 29
% 137.41/17.89 # Removed by relevancy pruning/SinE : 0
% 137.41/17.89 # Initial clauses : 58
% 137.41/17.89 # Removed in clause preprocessing : 3
% 137.41/17.89 # Initial clauses in saturation : 55
% 137.41/17.89 # Processed clauses : 21071
% 137.41/17.89 # ...of these trivial : 2311
% 137.41/17.89 # ...subsumed : 9420
% 137.41/17.89 # ...remaining for further processing : 9340
% 137.41/17.89 # Other redundant clauses eliminated : 0
% 137.41/17.89 # Clauses deleted for lack of memory : 0
% 137.41/17.89 # Backward-subsumed : 145
% 137.41/17.89 # Backward-rewritten : 88
% 137.41/17.89 # Generated clauses : 1223429
% 137.41/17.89 # ...of the previous two non-redundant : 1077349
% 137.41/17.89 # ...aggressively subsumed : 0
% 137.41/17.89 # Contextual simplify-reflections : 3
% 137.41/17.89 # Paramodulations : 1223367
% 137.41/17.89 # Factorizations : 62
% 137.41/17.89 # NegExts : 0
% 137.41/17.89 # Equation resolutions : 0
% 137.41/17.89 # Disequality decompositions : 0
% 137.41/17.89 # Total rewrite steps : 156935
% 137.41/17.89 # ...of those cached : 154631
% 137.41/17.89 # Propositional unsat checks : 0
% 137.41/17.89 # Propositional check models : 0
% 137.41/17.89 # Propositional check unsatisfiable : 0
% 137.41/17.89 # Propositional clauses : 0
% 137.41/17.89 # Propositional clauses after purity: 0
% 137.41/17.89 # Propositional unsat core size : 0
% 137.41/17.89 # Propositional preprocessing time : 0.000
% 137.41/17.89 # Propositional encoding time : 0.000
% 137.41/17.89 # Propositional solver time : 0.000
% 137.41/17.89 # Success case prop preproc time : 0.000
% 137.41/17.89 # Success case prop encoding time : 0.000
% 137.41/17.89 # Success case prop solver time : 0.000
% 137.41/17.89 # Current number of processed clauses : 9065
% 137.41/17.89 # Positive orientable unit clauses : 893
% 137.41/17.89 # Positive unorientable unit clauses: 8
% 137.41/17.89 # Negative unit clauses : 382
% 137.41/17.89 # Non-unit-clauses : 7782
% 137.41/17.89 # Current number of unprocessed clauses: 1055299
% 137.41/17.89 # ...number of literals in the above : 3210642
% 137.41/17.89 # Current number of archived formulas : 0
% 137.41/17.89 # Current number of archived clauses : 275
% 137.41/17.89 # Clause-clause subsumption calls (NU) : 7101956
% 137.41/17.89 # Rec. Clause-clause subsumption calls : 4570786
% 137.41/17.89 # Non-unit clause-clause subsumptions : 7400
% 137.41/17.89 # Unit Clause-clause subsumption calls : 402046
% 137.41/17.89 # Rewrite failures with RHS unbound : 0
% 137.41/17.89 # BW rewrite match attempts : 10583
% 137.41/17.89 # BW rewrite match successes : 90
% 137.41/17.89 # Condensation attempts : 0
% 137.41/17.89 # Condensation successes : 0
% 137.41/17.89 # Termbank termtop insertions : 27422662
% 137.41/17.89 # Search garbage collected termcells : 1299
% 137.41/17.89
% 137.41/17.89 # -------------------------------------------------
% 137.41/17.89 # User time : 16.635 s
% 137.41/17.89 # System time : 0.477 s
% 137.41/17.89 # Total time : 17.112 s
% 137.41/17.89 # Maximum resident set size: 1896 pages
% 137.41/17.89
% 137.41/17.89 # -------------------------------------------------
% 137.41/17.89 # User time : 83.210 s
% 137.41/17.89 # System time : 1.997 s
% 137.41/17.89 # Total time : 85.207 s
% 137.41/17.89 # Maximum resident set size: 1752 pages
% 137.41/17.89 % E---3.1 exiting
% 137.41/17.89 % E exiting
%------------------------------------------------------------------------------