TSTP Solution File: SET664+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET664+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n011.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 : Thu Aug 31 14:35:06 EDT 2023
% Result : Theorem 0.19s 0.61s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 42
% Syntax : Number of formulae : 73 ( 11 unt; 34 typ; 0 def)
% Number of atoms : 128 ( 18 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 145 ( 56 ~; 53 |; 12 &)
% ( 1 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 45 ( 27 >; 18 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 28 ( 28 usr; 7 con; 0-3 aty)
% Number of variables : 62 ( 6 sgn; 34 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
set_type: $i ).
tff(decl_23,type,
ilf_type: ( $i * $i ) > $o ).
tff(decl_24,type,
empty_set: $i ).
tff(decl_25,type,
subset: ( $i * $i ) > $o ).
tff(decl_26,type,
binary_relation_type: $i ).
tff(decl_27,type,
domain_of: $i > $i ).
tff(decl_28,type,
range_of: $i > $i ).
tff(decl_29,type,
relation_type: ( $i * $i ) > $i ).
tff(decl_30,type,
member: ( $i * $i ) > $o ).
tff(decl_31,type,
empty: $i > $o ).
tff(decl_32,type,
type: ( $i * $i ) > $o ).
tff(decl_33,type,
cross_product: ( $i * $i ) > $i ).
tff(decl_34,type,
subset_type: $i > $i ).
tff(decl_35,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_36,type,
relation_like: $i > $o ).
tff(decl_37,type,
power_set: $i > $i ).
tff(decl_38,type,
member_type: $i > $i ).
tff(decl_39,type,
domain: ( $i * $i * $i ) > $i ).
tff(decl_40,type,
range: ( $i * $i * $i ) > $i ).
tff(decl_41,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_42,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_43,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_44,type,
esk4_0: $i ).
tff(decl_45,type,
esk5_1: $i > $i ).
tff(decl_46,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_47,type,
esk7_1: $i > $i ).
tff(decl_48,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_49,type,
esk9_1: $i > $i ).
tff(decl_50,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_51,type,
esk11_2: ( $i * $i ) > $i ).
tff(decl_52,type,
esk12_1: $i > $i ).
tff(decl_53,type,
esk13_0: $i ).
tff(decl_54,type,
esk14_0: $i ).
tff(decl_55,type,
esk15_0: $i ).
fof(p3,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ( subset(domain_of(X3),X1)
& subset(range_of(X3),X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
fof(p33,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p33) ).
fof(prove_relset_1_27,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X2,X1))
=> ( ilf_type(X3,relation_type(X2,empty_set))
=> X3 = empty_set ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_27) ).
fof(p28,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',p28) ).
fof(p6,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',p6) ).
fof(p1,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( subset(X1,empty_set)
=> X1 = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(p13,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',p13) ).
fof(p2,axiom,
! [X1] :
( ilf_type(X1,binary_relation_type)
=> ( ( domain_of(X1) = empty_set
| range_of(X1) = empty_set )
=> X1 = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
fof(c_0_8,plain,
! [X7,X8,X9] :
( ( subset(domain_of(X9),X7)
| ~ ilf_type(X9,relation_type(X7,X8))
| ~ ilf_type(X8,set_type)
| ~ ilf_type(X7,set_type) )
& ( subset(range_of(X9),X8)
| ~ ilf_type(X9,relation_type(X7,X8))
| ~ ilf_type(X8,set_type)
| ~ ilf_type(X7,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p3])])])]) ).
fof(c_0_9,plain,
! [X79] : ilf_type(X79,set_type),
inference(variable_rename,[status(thm)],[p33]) ).
fof(c_0_10,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X2,X1))
=> ( ilf_type(X3,relation_type(X2,empty_set))
=> X3 = empty_set ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_27]) ).
fof(c_0_11,plain,
! [X64,X65,X66] :
( ~ ilf_type(X64,set_type)
| ~ ilf_type(X65,set_type)
| ~ ilf_type(X66,subset_type(cross_product(X64,X65)))
| relation_like(X66) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p28])])]) ).
fof(c_0_12,plain,
! [X11,X12,X13,X14] :
( ( ~ ilf_type(X13,subset_type(cross_product(X11,X12)))
| ilf_type(X13,relation_type(X11,X12))
| ~ ilf_type(X12,set_type)
| ~ ilf_type(X11,set_type) )
& ( ~ ilf_type(X14,relation_type(X11,X12))
| ilf_type(X14,subset_type(cross_product(X11,X12)))
| ~ ilf_type(X12,set_type)
| ~ ilf_type(X11,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p6])])])]) ).
fof(c_0_13,plain,
! [X5] :
( ~ ilf_type(X5,set_type)
| ~ subset(X5,empty_set)
| X5 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])]) ).
cnf(c_0_14,plain,
( subset(range_of(X1),X2)
| ~ ilf_type(X1,relation_type(X3,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_16,negated_conjecture,
( ilf_type(esk13_0,set_type)
& ilf_type(esk14_0,set_type)
& ilf_type(esk15_0,relation_type(esk14_0,esk13_0))
& ilf_type(esk15_0,relation_type(esk14_0,empty_set))
& esk15_0 != empty_set ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
fof(c_0_17,plain,
! [X30] :
( ( relation_like(X30)
| ~ ilf_type(X30,binary_relation_type)
| ~ ilf_type(X30,set_type) )
& ( ilf_type(X30,set_type)
| ~ ilf_type(X30,binary_relation_type)
| ~ ilf_type(X30,set_type) )
& ( ~ relation_like(X30)
| ~ ilf_type(X30,set_type)
| ilf_type(X30,binary_relation_type)
| ~ ilf_type(X30,set_type) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p13])])]) ).
cnf(c_0_18,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_11]) ).
cnf(c_0_19,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_12]) ).
cnf(c_0_20,plain,
( X1 = empty_set
| ~ ilf_type(X1,set_type)
| ~ subset(X1,empty_set) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
( subset(range_of(X1),X2)
| ~ ilf_type(X1,relation_type(X3,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15]),c_0_15])]) ).
cnf(c_0_22,negated_conjecture,
ilf_type(esk15_0,relation_type(esk14_0,empty_set)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,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_17]) ).
cnf(c_0_24,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_18,c_0_15]),c_0_15])]) ).
cnf(c_0_25,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_19,c_0_15]),c_0_15])]) ).
fof(c_0_26,plain,
! [X6] :
( ( domain_of(X6) != empty_set
| X6 = empty_set
| ~ ilf_type(X6,binary_relation_type) )
& ( range_of(X6) != empty_set
| X6 = empty_set
| ~ ilf_type(X6,binary_relation_type) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p2])])]) ).
cnf(c_0_27,plain,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_15])]) ).
cnf(c_0_28,negated_conjecture,
subset(range_of(esk15_0),empty_set),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_29,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1)
| ~ ilf_type(X1,set_type) ),
inference(cn,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
( relation_like(X1)
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,negated_conjecture,
ilf_type(esk15_0,relation_type(esk14_0,esk13_0)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_32,plain,
( X1 = empty_set
| range_of(X1) != empty_set
| ~ ilf_type(X1,binary_relation_type) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,negated_conjecture,
range_of(esk15_0) = empty_set,
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,negated_conjecture,
esk15_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_35,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_15])]) ).
cnf(c_0_36,negated_conjecture,
relation_like(esk15_0),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_37,negated_conjecture,
~ ilf_type(esk15_0,binary_relation_type),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET664+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 12:00:54 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.59 start to proof: theBenchmark
% 0.19/0.61 % Version : CSE_E---1.5
% 0.19/0.61 % Problem : theBenchmark.p
% 0.19/0.61 % Proof found
% 0.19/0.61 % SZS status Theorem for theBenchmark.p
% 0.19/0.61 % SZS output start Proof
% See solution above
% 0.19/0.62 % Total time : 0.017000 s
% 0.19/0.62 % SZS output end Proof
% 0.19/0.62 % Total time : 0.021000 s
%------------------------------------------------------------------------------