%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET649+3 : TPTP v9.2.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n025.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 5 05:08:14 PM UTC 2026
% Result : Theorem 3.72s 3.13s
% Output : CNFRefutation 3.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 60 ( 14 unt; 0 def)
% Number of atoms : 250 ( 0 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 307 ( 117 ~; 120 |; 23 &)
% ( 7 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-2 aty)
% Number of variables : 115 ( 2 sgn 60 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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,set_type)
=> ( ( subset(X1,X2)
& subset(X3,X4) )
=> subset(cross_product(X1,X3),cross_product(X2,X4)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
fof(p26,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p26) ).
fof(prove_relset_1_11,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,binary_relation_type)
=> ( ( subset(domain_of(X3),X1)
& subset(range_of(X3),X2) )
=> ilf_type(X3,relation_type(X1,X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_11) ).
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/benchmark/theBenchmark.p',p1) ).
fof(p12,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/benchmark/theBenchmark.p',p12) ).
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(p2,axiom,
! [X1] :
( ilf_type(X1,binary_relation_type)
=> subset(X1,cross_product(domain_of(X1),range_of(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
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(p15,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',p15) ).
fof(p4,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',p4) ).
fof(c_0_11,plain,
! [X68,X69,X70,X71] :
( ~ ilf_type(X68,set_type)
| ~ ilf_type(X69,set_type)
| ~ ilf_type(X70,set_type)
| ~ ilf_type(X71,set_type)
| ~ subset(X68,X69)
| ~ subset(X70,X71)
| subset(cross_product(X68,X70),cross_product(X69,X71)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p3])])]) ).
fof(c_0_12,plain,
! [X127] : ilf_type(X127,set_type),
inference(variable_rename,[status(thm)],[p26]) ).
fof(c_0_13,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,binary_relation_type)
=> ( ( subset(domain_of(X3),X1)
& subset(range_of(X3),X2) )
=> ilf_type(X3,relation_type(X1,X2)) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_11]) ).
cnf(c_0_14,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_11]) ).
cnf(c_0_15,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_16,negated_conjecture,
( ilf_type(esk13_0,set_type)
& ilf_type(esk14_0,set_type)
& ilf_type(esk15_0,binary_relation_type)
& subset(domain_of(esk15_0),esk13_0)
& subset(range_of(esk15_0),esk14_0)
& ~ ilf_type(esk15_0,relation_type(esk13_0,esk14_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
fof(c_0_17,plain,
! [X64,X65,X66] :
( ~ ilf_type(X64,set_type)
| ~ ilf_type(X65,set_type)
| ~ ilf_type(X66,set_type)
| ~ subset(X64,X65)
| ~ subset(X65,X66)
| subset(X64,X66) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])]) ).
cnf(c_0_18,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_14,c_0_15]),c_0_15]),c_0_15]),c_0_15])]) ).
cnf(c_0_19,negated_conjecture,
subset(range_of(esk15_0),esk14_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_20,plain,
! [X91,X92,X93] :
( ( ~ subset(X91,X92)
| ~ ilf_type(X93,set_type)
| ~ member(X93,X91)
| member(X93,X92)
| ~ ilf_type(X92,set_type)
| ~ ilf_type(X91,set_type) )
& ( ilf_type(esk5_2(X91,X92),set_type)
| subset(X91,X92)
| ~ ilf_type(X92,set_type)
| ~ ilf_type(X91,set_type) )
& ( member(esk5_2(X91,X92),X91)
| subset(X91,X92)
| ~ ilf_type(X92,set_type)
| ~ ilf_type(X91,set_type) )
& ( ~ member(esk5_2(X91,X92),X92)
| subset(X91,X92)
| ~ ilf_type(X92,set_type)
| ~ ilf_type(X91,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)],[p12])])])])]) ).
fof(c_0_21,plain,
! [X114,X115,X116] :
( ( ~ member(X114,power_set(X115))
| ~ ilf_type(X116,set_type)
| ~ member(X116,X114)
| member(X116,X115)
| ~ ilf_type(X115,set_type)
| ~ ilf_type(X114,set_type) )
& ( ilf_type(esk10_2(X114,X115),set_type)
| member(X114,power_set(X115))
| ~ ilf_type(X115,set_type)
| ~ ilf_type(X114,set_type) )
& ( member(esk10_2(X114,X115),X114)
| member(X114,power_set(X115))
| ~ ilf_type(X115,set_type)
| ~ ilf_type(X114,set_type) )
& ( ~ member(esk10_2(X114,X115),X115)
| member(X114,power_set(X115))
| ~ ilf_type(X115,set_type)
| ~ ilf_type(X114,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)],[p20])])])])]) ).
cnf(c_0_22,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_17]) ).
cnf(c_0_23,negated_conjecture,
( subset(cross_product(X1,range_of(esk15_0)),cross_product(X2,esk14_0))
| ~ subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,negated_conjecture,
subset(domain_of(esk15_0),esk13_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_25,plain,
! [X67] :
( ~ ilf_type(X67,binary_relation_type)
| subset(X67,cross_product(domain_of(X67),range_of(X67))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p2])]) ).
fof(c_0_26,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[p24]) ).
cnf(c_0_27,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_20]) ).
cnf(c_0_28,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_29,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_22,c_0_15]),c_0_15]),c_0_15])]) ).
cnf(c_0_30,negated_conjecture,
subset(cross_product(domain_of(esk15_0),range_of(esk15_0)),cross_product(esk13_0,esk14_0)),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_31,plain,
( subset(X1,cross_product(domain_of(X1),range_of(X1)))
| ~ ilf_type(X1,binary_relation_type) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,negated_conjecture,
ilf_type(esk15_0,binary_relation_type),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_33,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_34,plain,
! [X123,X124] :
( ( ~ empty(X123)
| ~ ilf_type(X124,set_type)
| ~ member(X124,X123)
| ~ ilf_type(X123,set_type) )
& ( ilf_type(esk12_1(X123),set_type)
| empty(X123)
| ~ ilf_type(X123,set_type) )
& ( member(esk12_1(X123),X123)
| empty(X123)
| ~ ilf_type(X123,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_26])])])])]) ).
cnf(c_0_35,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_27,c_0_15]),c_0_15]),c_0_15])]) ).
cnf(c_0_36,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_28,c_0_15]),c_0_15])]) ).
cnf(c_0_37,negated_conjecture,
( subset(X1,cross_product(esk13_0,esk14_0))
| ~ subset(X1,cross_product(domain_of(esk15_0),range_of(esk15_0))) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_38,negated_conjecture,
subset(esk15_0,cross_product(domain_of(esk15_0),range_of(esk15_0))),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
fof(c_0_39,plain,
! [X119,X120] :
( ( ~ ilf_type(X119,member_type(X120))
| member(X119,X120)
| empty(X120)
| ~ ilf_type(X120,set_type)
| ~ ilf_type(X119,set_type) )
& ( ~ member(X119,X120)
| ilf_type(X119,member_type(X120))
| empty(X120)
| ~ ilf_type(X120,set_type)
| ~ ilf_type(X119,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])])])]) ).
cnf(c_0_40,plain,
( ~ empty(X1)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X1)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_41,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_42,plain,
( member(esk10_2(X1,X2),X3)
| member(X1,power_set(X2))
| ~ subset(X1,X3) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_43,negated_conjecture,
subset(esk15_0,cross_product(esk13_0,esk14_0)),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
fof(c_0_44,plain,
! [X99,X100] :
( ( ~ ilf_type(X100,subset_type(X99))
| ilf_type(X100,member_type(power_set(X99)))
| ~ ilf_type(X100,set_type)
| ~ ilf_type(X99,set_type) )
& ( ~ ilf_type(X100,member_type(power_set(X99)))
| ilf_type(X100,subset_type(X99))
| ~ ilf_type(X100,set_type)
| ~ ilf_type(X99,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p15])])])]) ).
cnf(c_0_45,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_39]) ).
cnf(c_0_46,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_15]),c_0_15])]) ).
cnf(c_0_47,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_41,c_0_15]),c_0_15])]) ).
cnf(c_0_48,negated_conjecture,
( member(esk10_2(esk15_0,X1),cross_product(esk13_0,esk14_0))
| member(esk15_0,power_set(X1)) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
fof(c_0_49,plain,
! [X72,X73,X74,X75] :
( ( ~ ilf_type(X74,subset_type(cross_product(X72,X73)))
| ilf_type(X74,relation_type(X72,X73))
| ~ ilf_type(X73,set_type)
| ~ ilf_type(X72,set_type) )
& ( ~ ilf_type(X75,relation_type(X72,X73))
| ilf_type(X75,subset_type(cross_product(X72,X73)))
| ~ ilf_type(X73,set_type)
| ~ ilf_type(X72,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p4])])])]) ).
cnf(c_0_50,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_44]) ).
cnf(c_0_51,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_45,c_0_15]),c_0_15])]),c_0_46]) ).
cnf(c_0_52,negated_conjecture,
member(esk15_0,power_set(cross_product(esk13_0,esk14_0))),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_53,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_49]) ).
cnf(c_0_54,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_50,c_0_15]),c_0_15])]) ).
cnf(c_0_55,negated_conjecture,
ilf_type(esk15_0,member_type(power_set(cross_product(esk13_0,esk14_0)))),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_56,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_53,c_0_15]),c_0_15])]) ).
cnf(c_0_57,negated_conjecture,
ilf_type(esk15_0,subset_type(cross_product(esk13_0,esk14_0))),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_58,negated_conjecture,
~ ilf_type(esk15_0,relation_type(esk13_0,esk14_0)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_59,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET649+3 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n025.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 02:31:28 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 3.72/3.13 % Version : CSE_E---1.7
% 3.72/3.13 % Problem : theBenchmark.p
% 3.72/3.13 % SZS status Theorem for theBenchmark.p
% 3.72/3.13 % SZS output start CNFRefutation
% See solution above
% 3.72/3.14 % Total time : 2.371s
%------------------------------------------------------------------------------