%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET646+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 : n004.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 05:08:13 PM UTC 2026
% Result : Theorem 1.40s 1.76s
% Output : CNFRefutation 1.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 49 ( 11 unt; 0 def)
% Number of atoms : 246 ( 15 equ)
% Maximal formula atoms : 31 ( 5 avg)
% Number of connectives : 320 ( 123 ~; 126 |; 26 &)
% ( 9 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-2 aty)
% Number of variables : 103 ( 3 sgn 56 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p5,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ( X3 = singleton(X2)
<=> ! [X4] :
( ilf_type(X4,set_type)
=> ( member(X4,X3)
<=> X4 = X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5) ).
fof(p25,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p25) ).
fof(p17,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',p17) ).
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)
=> ( member(ordered_pair(X1,X2),cross_product(X3,X4))
<=> ( member(X1,X3)
& member(X2,X4) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(prove_relset_1_8,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)
=> ( ( member(X3,X1)
& member(X4,X2) )
=> ilf_type(singleton(ordered_pair(X3,X4)),relation_type(X1,X2)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_8) ).
fof(p21,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',p21) ).
fof(p19,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',p19) ).
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(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/sandbox2/benchmark/theBenchmark.p',p3) ).
fof(c_0_9,plain,
! [X84,X85,X86,X87] :
( ( ~ member(X87,X86)
| X87 = X85
| ~ ilf_type(X87,set_type)
| X86 != singleton(X85)
| ~ ilf_type(X86,set_type)
| ~ ilf_type(X85,set_type)
| ~ ilf_type(X84,set_type) )
& ( X87 != X85
| member(X87,X86)
| ~ ilf_type(X87,set_type)
| X86 != singleton(X85)
| ~ ilf_type(X86,set_type)
| ~ ilf_type(X85,set_type)
| ~ ilf_type(X84,set_type) )
& ( ilf_type(esk2_2(X85,X86),set_type)
| X86 = singleton(X85)
| ~ ilf_type(X86,set_type)
| ~ ilf_type(X85,set_type)
| ~ ilf_type(X84,set_type) )
& ( ~ member(esk2_2(X85,X86),X86)
| esk2_2(X85,X86) != X85
| X86 = singleton(X85)
| ~ ilf_type(X86,set_type)
| ~ ilf_type(X85,set_type)
| ~ ilf_type(X84,set_type) )
& ( member(esk2_2(X85,X86),X86)
| esk2_2(X85,X86) = X85
| X86 = singleton(X85)
| ~ ilf_type(X86,set_type)
| ~ ilf_type(X85,set_type)
| ~ ilf_type(X84,set_type) ) ),
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)],[p5])])])])])]) ).
fof(c_0_10,plain,
! [X139] : ilf_type(X139,set_type),
inference(variable_rename,[status(thm)],[p25]) ).
fof(c_0_11,plain,
! [X116,X117,X118] :
( ( ~ member(X116,power_set(X117))
| ~ ilf_type(X118,set_type)
| ~ member(X118,X116)
| member(X118,X117)
| ~ ilf_type(X117,set_type)
| ~ ilf_type(X116,set_type) )
& ( ilf_type(esk6_2(X116,X117),set_type)
| member(X116,power_set(X117))
| ~ ilf_type(X117,set_type)
| ~ ilf_type(X116,set_type) )
& ( member(esk6_2(X116,X117),X116)
| member(X116,power_set(X117))
| ~ ilf_type(X117,set_type)
| ~ ilf_type(X116,set_type) )
& ( ~ member(esk6_2(X116,X117),X117)
| member(X116,power_set(X117))
| ~ ilf_type(X117,set_type)
| ~ ilf_type(X116,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)],[p17])])])])]) ).
fof(c_0_12,plain,
! [X73,X74,X75,X76] :
( ( member(X73,X75)
| ~ member(ordered_pair(X73,X74),cross_product(X75,X76))
| ~ ilf_type(X76,set_type)
| ~ ilf_type(X75,set_type)
| ~ ilf_type(X74,set_type)
| ~ ilf_type(X73,set_type) )
& ( member(X74,X76)
| ~ member(ordered_pair(X73,X74),cross_product(X75,X76))
| ~ ilf_type(X76,set_type)
| ~ ilf_type(X75,set_type)
| ~ ilf_type(X74,set_type)
| ~ ilf_type(X73,set_type) )
& ( ~ member(X73,X75)
| ~ member(X74,X76)
| member(ordered_pair(X73,X74),cross_product(X75,X76))
| ~ ilf_type(X76,set_type)
| ~ ilf_type(X75,set_type)
| ~ ilf_type(X74,set_type)
| ~ ilf_type(X73,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p2])])])]) ).
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)
=> ( ( member(X3,X1)
& member(X4,X2) )
=> ilf_type(singleton(ordered_pair(X3,X4)),relation_type(X1,X2)) ) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_8]) ).
fof(c_0_14,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[p21]) ).
cnf(c_0_15,plain,
( X1 = X3
| ~ member(X1,X2)
| ~ ilf_type(X1,set_type)
| X2 != singleton(X3)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,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_11]) ).
cnf(c_0_18,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_12]) ).
fof(c_0_19,negated_conjecture,
( ilf_type(esk12_0,set_type)
& ilf_type(esk13_0,set_type)
& ilf_type(esk14_0,set_type)
& ilf_type(esk15_0,set_type)
& member(esk14_0,esk12_0)
& member(esk15_0,esk13_0)
& ~ ilf_type(singleton(ordered_pair(esk14_0,esk15_0)),relation_type(esk12_0,esk13_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
fof(c_0_20,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)],[p19]) ).
fof(c_0_21,plain,
! [X125,X126] :
( ( ~ empty(X125)
| ~ ilf_type(X126,set_type)
| ~ member(X126,X125)
| ~ ilf_type(X125,set_type) )
& ( ilf_type(esk8_1(X125),set_type)
| empty(X125)
| ~ ilf_type(X125,set_type) )
& ( member(esk8_1(X125),X125)
| empty(X125)
| ~ ilf_type(X125,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_14])])])])]) ).
cnf(c_0_22,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_11]) ).
cnf(c_0_23,plain,
( X1 = X2
| ~ member(X1,singleton(X2)) ),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[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]),c_0_16])])]) ).
cnf(c_0_24,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_17,c_0_16]),c_0_16])]) ).
cnf(c_0_25,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_18,c_0_16]),c_0_16]),c_0_16]),c_0_16])]) ).
cnf(c_0_26,negated_conjecture,
member(esk15_0,esk13_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_27,plain,
! [X121,X122] :
( ( ~ ilf_type(X121,member_type(X122))
| member(X121,X122)
| empty(X122)
| ~ ilf_type(X122,set_type)
| ~ ilf_type(X121,set_type) )
& ( ~ member(X121,X122)
| ilf_type(X121,member_type(X122))
| empty(X122)
| ~ ilf_type(X122,set_type)
| ~ ilf_type(X121,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])]) ).
cnf(c_0_28,plain,
( ~ empty(X1)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X1)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,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_22,c_0_16]),c_0_16])]) ).
cnf(c_0_30,plain,
( esk6_2(singleton(X1),X2) = X1
| member(singleton(X1),power_set(X2)) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_31,negated_conjecture,
( member(ordered_pair(X1,esk15_0),cross_product(X2,esk13_0))
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,negated_conjecture,
member(esk14_0,esk12_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_33,plain,
! [X103,X104] :
( ( ~ ilf_type(X104,subset_type(X103))
| ilf_type(X104,member_type(power_set(X103)))
| ~ ilf_type(X104,set_type)
| ~ ilf_type(X103,set_type) )
& ( ~ ilf_type(X104,member_type(power_set(X103)))
| ilf_type(X104,subset_type(X103))
| ~ ilf_type(X104,set_type)
| ~ ilf_type(X103,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_34,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_27]) ).
cnf(c_0_35,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_16]),c_0_16])]) ).
cnf(c_0_36,plain,
( member(singleton(X1),power_set(X2))
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_37,negated_conjecture,
member(ordered_pair(esk14_0,esk15_0),cross_product(esk12_0,esk13_0)),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
fof(c_0_38,plain,
! [X77,X78,X79,X80] :
( ( ~ ilf_type(X79,subset_type(cross_product(X77,X78)))
| ilf_type(X79,relation_type(X77,X78))
| ~ ilf_type(X78,set_type)
| ~ ilf_type(X77,set_type) )
& ( ~ ilf_type(X80,relation_type(X77,X78))
| ilf_type(X80,subset_type(cross_product(X77,X78)))
| ~ 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)],[p3])])])]) ).
cnf(c_0_39,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_33]) ).
cnf(c_0_40,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_34,c_0_16]),c_0_16])]),c_0_35]) ).
cnf(c_0_41,negated_conjecture,
member(singleton(ordered_pair(esk14_0,esk15_0)),power_set(cross_product(esk12_0,esk13_0))),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,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_38]) ).
cnf(c_0_43,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_39,c_0_16]),c_0_16])]) ).
cnf(c_0_44,negated_conjecture,
ilf_type(singleton(ordered_pair(esk14_0,esk15_0)),member_type(power_set(cross_product(esk12_0,esk13_0)))),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_45,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_42,c_0_16]),c_0_16])]) ).
cnf(c_0_46,negated_conjecture,
ilf_type(singleton(ordered_pair(esk14_0,esk15_0)),subset_type(cross_product(esk12_0,esk13_0))),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_47,negated_conjecture,
~ ilf_type(singleton(ordered_pair(esk14_0,esk15_0)),relation_type(esk12_0,esk13_0)),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_48,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET646+3 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n004.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:31:18 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.40/1.76 % Version : CSE_E---1.7
% 1.40/1.76 % Problem : theBenchmark.p
% 1.40/1.76 % SZS status Theorem for theBenchmark.p
% 1.40/1.76 % SZS output start CNFRefutation
% See solution above
% 1.40/1.76 % Total time : 1.371s
%------------------------------------------------------------------------------