%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET666+3 : TPTP v9.2.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n019.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 05:08:16 PM UTC 2026
% Result : Theorem 1.35s 1.76s
% Output : CNFRefutation 1.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 51 ( 11 unt; 0 def)
% Number of atoms : 203 ( 0 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 252 ( 100 ~; 101 |; 16 &)
% ( 8 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 2 con; 0-2 aty)
% Number of variables : 94 ( 2 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p14,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/sandbox2/benchmark/theBenchmark.p',p14) ).
fof(p24,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p24) ).
fof(p3,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> subset(identity_relation_of(X1),cross_product(X1,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
fof(p22,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p22) ).
fof(p16,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/sandbox2/benchmark/theBenchmark.p',p16) ).
fof(p18,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/sandbox2/benchmark/theBenchmark.p',p18) ).
fof(p12,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/sandbox2/benchmark/theBenchmark.p',p12) ).
fof(p1,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/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(p6,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ilf_type(X2,identity_relation_of_type(X1))
<=> ilf_type(X2,relation_type(X1,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6) ).
fof(prove_relset_1_29,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ilf_type(identity_relation_of(X1),identity_relation_of_type(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_29) ).
fof(c_0_10,plain,
! [X81,X82,X83] :
( ( ~ subset(X81,X82)
| ~ ilf_type(X83,set_type)
| ~ member(X83,X81)
| member(X83,X82)
| ~ ilf_type(X82,set_type)
| ~ ilf_type(X81,set_type) )
& ( ilf_type(esk5_2(X81,X82),set_type)
| subset(X81,X82)
| ~ ilf_type(X82,set_type)
| ~ ilf_type(X81,set_type) )
& ( member(esk5_2(X81,X82),X81)
| subset(X81,X82)
| ~ ilf_type(X82,set_type)
| ~ ilf_type(X81,set_type) )
& ( ~ member(esk5_2(X81,X82),X82)
| subset(X81,X82)
| ~ ilf_type(X82,set_type)
| ~ ilf_type(X81,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)],[p14])])])])]) ).
fof(c_0_11,plain,
! [X109] : ilf_type(X109,set_type),
inference(variable_rename,[status(thm)],[p24]) ).
fof(c_0_12,plain,
! [X62] :
( ~ ilf_type(X62,set_type)
| subset(identity_relation_of(X62),cross_product(X62,X62)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p3])]) ).
fof(c_0_13,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[p22]) ).
fof(c_0_14,plain,
! [X86,X87,X88] :
( ( ~ member(X86,power_set(X87))
| ~ ilf_type(X88,set_type)
| ~ member(X88,X86)
| member(X88,X87)
| ~ ilf_type(X87,set_type)
| ~ ilf_type(X86,set_type) )
& ( ilf_type(esk6_2(X86,X87),set_type)
| member(X86,power_set(X87))
| ~ ilf_type(X87,set_type)
| ~ ilf_type(X86,set_type) )
& ( member(esk6_2(X86,X87),X86)
| member(X86,power_set(X87))
| ~ ilf_type(X87,set_type)
| ~ ilf_type(X86,set_type) )
& ( ~ member(esk6_2(X86,X87),X87)
| member(X86,power_set(X87))
| ~ ilf_type(X87,set_type)
| ~ ilf_type(X86,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)],[p16])])])])]) ).
cnf(c_0_15,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_10]) ).
cnf(c_0_16,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( subset(identity_relation_of(X1),cross_product(X1,X1))
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_18,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)],[p18]) ).
fof(c_0_19,plain,
! [X105,X106] :
( ( ~ empty(X105)
| ~ ilf_type(X106,set_type)
| ~ member(X106,X105)
| ~ ilf_type(X105,set_type) )
& ( ilf_type(esk11_1(X105),set_type)
| empty(X105)
| ~ ilf_type(X105,set_type) )
& ( member(esk11_1(X105),X105)
| empty(X105)
| ~ ilf_type(X105,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_13])])])])]) ).
cnf(c_0_20,plain,
( member(X1,power_set(X2))
| ~ member(esk6_2(X1,X2),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,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_15,c_0_16]),c_0_16]),c_0_16])]) ).
cnf(c_0_22,plain,
subset(identity_relation_of(X1),cross_product(X1,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_16])]) ).
fof(c_0_23,plain,
! [X91,X92] :
( ( ~ ilf_type(X91,member_type(X92))
| member(X91,X92)
| empty(X92)
| ~ ilf_type(X92,set_type)
| ~ ilf_type(X91,set_type) )
& ( ~ member(X91,X92)
| ilf_type(X91,member_type(X92))
| empty(X92)
| ~ ilf_type(X92,set_type)
| ~ ilf_type(X91,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])]) ).
cnf(c_0_24,plain,
( ~ empty(X1)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X1)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,plain,
( member(X1,power_set(X2))
| ~ member(esk6_2(X1,X2),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_16]),c_0_16])]) ).
cnf(c_0_26,plain,
( member(X1,cross_product(X2,X2))
| ~ member(X1,identity_relation_of(X2)) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
( member(esk6_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_14]) ).
fof(c_0_28,plain,
! [X77,X78] :
( ( ~ ilf_type(X78,subset_type(X77))
| ilf_type(X78,member_type(power_set(X77)))
| ~ ilf_type(X78,set_type)
| ~ ilf_type(X77,set_type) )
& ( ~ ilf_type(X78,member_type(power_set(X77)))
| ilf_type(X78,subset_type(X77))
| ~ ilf_type(X78,set_type)
| ~ ilf_type(X77,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p12])])])]) ).
cnf(c_0_29,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_30,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_16]),c_0_16])]) ).
cnf(c_0_31,plain,
( member(X1,power_set(cross_product(X2,X2)))
| ~ member(esk6_2(X1,cross_product(X2,X2)),identity_relation_of(X2)) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,plain,
( member(esk6_2(X1,X2),X1)
| member(X1,power_set(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_16]),c_0_16])]) ).
fof(c_0_33,plain,
! [X55,X56,X57,X58] :
( ( ~ ilf_type(X57,subset_type(cross_product(X55,X56)))
| ilf_type(X57,relation_type(X55,X56))
| ~ ilf_type(X56,set_type)
| ~ ilf_type(X55,set_type) )
& ( ~ ilf_type(X58,relation_type(X55,X56))
| ilf_type(X58,subset_type(cross_product(X55,X56)))
| ~ ilf_type(X56,set_type)
| ~ ilf_type(X55,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])])]) ).
cnf(c_0_34,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_28]) ).
cnf(c_0_35,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_29,c_0_16]),c_0_16])]),c_0_30]) ).
cnf(c_0_36,plain,
member(identity_relation_of(X1),power_set(cross_product(X1,X1))),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
fof(c_0_37,plain,
! [X67,X68] :
( ( ~ ilf_type(X68,identity_relation_of_type(X67))
| ilf_type(X68,relation_type(X67,X67))
| ~ ilf_type(X68,set_type)
| ~ ilf_type(X67,set_type) )
& ( ~ ilf_type(X68,relation_type(X67,X67))
| ilf_type(X68,identity_relation_of_type(X67))
| ~ ilf_type(X68,set_type)
| ~ ilf_type(X67,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p6])])])]) ).
cnf(c_0_38,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_33]) ).
cnf(c_0_39,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_34,c_0_16]),c_0_16])]) ).
cnf(c_0_40,plain,
ilf_type(identity_relation_of(X1),member_type(power_set(cross_product(X1,X1)))),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
fof(c_0_41,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ilf_type(identity_relation_of(X1),identity_relation_of_type(X1)) ),
inference(assume_negation,[status(cth)],[prove_relset_1_29]) ).
cnf(c_0_42,plain,
( ilf_type(X1,identity_relation_of_type(X2))
| ~ ilf_type(X1,relation_type(X2,X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_43,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_38,c_0_16]),c_0_16])]) ).
cnf(c_0_44,plain,
ilf_type(identity_relation_of(X1),subset_type(cross_product(X1,X1))),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
fof(c_0_45,negated_conjecture,
( ilf_type(esk12_0,set_type)
& ~ ilf_type(identity_relation_of(esk12_0),identity_relation_of_type(esk12_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])])]) ).
cnf(c_0_46,plain,
( ilf_type(X1,identity_relation_of_type(X2))
| ~ ilf_type(X1,relation_type(X2,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_16]),c_0_16])]) ).
cnf(c_0_47,plain,
ilf_type(identity_relation_of(X1),relation_type(X1,X1)),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_48,negated_conjecture,
~ ilf_type(identity_relation_of(esk12_0),identity_relation_of_type(esk12_0)),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_49,plain,
ilf_type(identity_relation_of(X1),identity_relation_of_type(X1)),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_50,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_49])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET666+3 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.34 % Computer : n019.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue May 5 02:30:59 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 1.35/1.76 % Version : CSE_E---1.7
% 1.35/1.76 % Problem : theBenchmark.p
% 1.35/1.76 % SZS status Theorem for theBenchmark.p
% 1.35/1.76 % SZS output start CNFRefutation
% See solution above
% 1.35/1.76 % Total time : 1.369s
%------------------------------------------------------------------------------