%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET645+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 : 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 5 05:08:13 PM UTC 2026
% Result : Theorem 1.27s 1.72s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 45 ( 13 unt; 0 def)
% Number of atoms : 194 ( 0 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 243 ( 94 ~; 89 |; 23 &)
% ( 5 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 87 ( 6 sgn 47 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(p21,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21) ).
fof(prove_relset_1_7,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,X2))
=> ( member(ordered_pair(X3,X4),X5)
=> ( member(X3,X1)
& member(X4,X2) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_7) ).
fof(p15,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',p15) ).
fof(p10,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',p10) ).
fof(p14,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p14) ).
fof(p13,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',p13) ).
fof(p1,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',p1) ).
fof(c_0_8,plain,
! [X73,X74,X75,X76] :
( ( ~ ilf_type(X75,subset_type(cross_product(X73,X74)))
| ilf_type(X75,relation_type(X73,X74))
| ~ ilf_type(X74,set_type)
| ~ ilf_type(X73,set_type) )
& ( ~ ilf_type(X76,relation_type(X73,X74))
| ilf_type(X76,subset_type(cross_product(X73,X74)))
| ~ 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)],[p4])])])]) ).
fof(c_0_9,plain,
! [X118] : ilf_type(X118,set_type),
inference(variable_rename,[status(thm)],[p21]) ).
fof(c_0_10,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,X2))
=> ( member(ordered_pair(X3,X4),X5)
=> ( member(X3,X1)
& member(X4,X2) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_7]) ).
fof(c_0_11,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)],[p15]) ).
fof(c_0_12,plain,
! [X87,X88] :
( ( ~ ilf_type(X88,subset_type(X87))
| ilf_type(X88,member_type(power_set(X87)))
| ~ ilf_type(X88,set_type)
| ~ ilf_type(X87,set_type) )
& ( ~ ilf_type(X88,member_type(power_set(X87)))
| ilf_type(X88,subset_type(X87))
| ~ ilf_type(X88,set_type)
| ~ ilf_type(X87,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p10])])])]) ).
cnf(c_0_13,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_8]) ).
cnf(c_0_14,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_15,negated_conjecture,
( ilf_type(esk10_0,set_type)
& ilf_type(esk11_0,set_type)
& ilf_type(esk12_0,set_type)
& ilf_type(esk13_0,set_type)
& ilf_type(esk14_0,relation_type(esk10_0,esk11_0))
& member(ordered_pair(esk12_0,esk13_0),esk14_0)
& ( ~ member(esk12_0,esk10_0)
| ~ member(esk13_0,esk11_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
fof(c_0_16,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
inference(fof_simplification,[status(thm)],[p14]) ).
fof(c_0_17,plain,
! [X95,X96,X97] :
( ( ~ member(X95,power_set(X96))
| ~ ilf_type(X97,set_type)
| ~ member(X97,X95)
| member(X97,X96)
| ~ ilf_type(X96,set_type)
| ~ ilf_type(X95,set_type) )
& ( ilf_type(esk4_2(X95,X96),set_type)
| member(X95,power_set(X96))
| ~ ilf_type(X96,set_type)
| ~ ilf_type(X95,set_type) )
& ( member(esk4_2(X95,X96),X95)
| member(X95,power_set(X96))
| ~ ilf_type(X96,set_type)
| ~ ilf_type(X95,set_type) )
& ( ~ member(esk4_2(X95,X96),X96)
| member(X95,power_set(X96))
| ~ ilf_type(X96,set_type)
| ~ ilf_type(X95,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)],[p13])])])])]) ).
fof(c_0_18,plain,
! [X100,X101] :
( ( ~ ilf_type(X100,member_type(X101))
| member(X100,X101)
| empty(X101)
| ~ ilf_type(X101,set_type)
| ~ ilf_type(X100,set_type) )
& ( ~ member(X100,X101)
| ilf_type(X100,member_type(X101))
| empty(X101)
| ~ ilf_type(X101,set_type)
| ~ ilf_type(X100,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).
cnf(c_0_19,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_12]) ).
cnf(c_0_20,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_13,c_0_14]),c_0_14])]) ).
cnf(c_0_21,negated_conjecture,
ilf_type(esk14_0,relation_type(esk10_0,esk11_0)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_22,plain,
! [X99] :
( ( ~ empty(power_set(X99))
| ~ ilf_type(X99,set_type) )
& ( ilf_type(power_set(X99),set_type)
| ~ ilf_type(X99,set_type) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).
cnf(c_0_23,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_17]) ).
cnf(c_0_24,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_18]) ).
cnf(c_0_25,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_19,c_0_14]),c_0_14])]) ).
cnf(c_0_26,negated_conjecture,
ilf_type(esk14_0,subset_type(cross_product(esk10_0,esk11_0))),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,plain,
( ~ empty(power_set(X1))
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_28,plain,
! [X62,X63,X64,X65] :
( ( member(X62,X64)
| ~ member(ordered_pair(X62,X63),cross_product(X64,X65))
| ~ ilf_type(X65,set_type)
| ~ ilf_type(X64,set_type)
| ~ ilf_type(X63,set_type)
| ~ ilf_type(X62,set_type) )
& ( member(X63,X65)
| ~ member(ordered_pair(X62,X63),cross_product(X64,X65))
| ~ ilf_type(X65,set_type)
| ~ ilf_type(X64,set_type)
| ~ ilf_type(X63,set_type)
| ~ ilf_type(X62,set_type) )
& ( ~ member(X62,X64)
| ~ member(X63,X65)
| member(ordered_pair(X62,X63),cross_product(X64,X65))
| ~ ilf_type(X65,set_type)
| ~ ilf_type(X64,set_type)
| ~ ilf_type(X63,set_type)
| ~ ilf_type(X62,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_29,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_23,c_0_14]),c_0_14]),c_0_14])]) ).
cnf(c_0_30,negated_conjecture,
member(ordered_pair(esk12_0,esk13_0),esk14_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_31,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_24,c_0_14]),c_0_14])]) ).
cnf(c_0_32,negated_conjecture,
ilf_type(esk14_0,member_type(power_set(cross_product(esk10_0,esk11_0)))),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_33,plain,
~ empty(power_set(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_14])]) ).
cnf(c_0_34,plain,
( member(X1,X2)
| ~ member(ordered_pair(X1,X3),cross_product(X2,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_28]) ).
cnf(c_0_35,negated_conjecture,
( member(ordered_pair(esk12_0,esk13_0),X1)
| ~ member(esk14_0,power_set(X1)) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_36,negated_conjecture,
member(esk14_0,power_set(cross_product(esk10_0,esk11_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).
cnf(c_0_37,plain,
( member(X1,X2)
| ~ member(ordered_pair(X1,X3),cross_product(X2,X4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_14]),c_0_14]),c_0_14]),c_0_14])]) ).
cnf(c_0_38,negated_conjecture,
member(ordered_pair(esk12_0,esk13_0),cross_product(esk10_0,esk11_0)),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,plain,
( member(X1,X2)
| ~ member(ordered_pair(X3,X1),cross_product(X4,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_40,negated_conjecture,
( ~ member(esk12_0,esk10_0)
| ~ member(esk13_0,esk11_0) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_41,negated_conjecture,
member(esk12_0,esk10_0),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,plain,
( member(X1,X2)
| ~ member(ordered_pair(X3,X1),cross_product(X4,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_14]),c_0_14]),c_0_14]),c_0_14])]) ).
cnf(c_0_43,negated_conjecture,
~ member(esk13_0,esk11_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41])]) ).
cnf(c_0_44,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_38]),c_0_43]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET645+3 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n017.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 02:30:42 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.27/1.72 % Version : CSE_E---1.7
% 1.27/1.72 % Problem : theBenchmark.p
% 1.27/1.72 % SZS status Theorem for theBenchmark.p
% 1.27/1.72 % SZS output start CNFRefutation
% See solution above
% 1.27/1.72 % Total time : 1.372s
%------------------------------------------------------------------------------