TSTP Solution File: SET679+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET679+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n024.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 14:35:11 EDT 2023
% Result : Theorem 0.19s 0.59s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 31
% Syntax : Number of formulae : 55 ( 10 unt; 25 typ; 0 def)
% Number of atoms : 86 ( 6 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 99 ( 43 ~; 32 |; 8 &)
% ( 4 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 30 ( 20 >; 10 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 5 con; 0-2 aty)
% Number of variables : 35 ( 3 sgn; 21 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
set_type: $i ).
tff(decl_23,type,
ilf_type: ( $i * $i ) > $o ).
tff(decl_24,type,
member: ( $i * $i ) > $o ).
tff(decl_25,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_26,type,
identity_relation_of: $i > $i ).
tff(decl_27,type,
empty_set: $i ).
tff(decl_28,type,
empty: $i > $o ).
tff(decl_29,type,
type: ( $i * $i ) > $o ).
tff(decl_30,type,
binary_relation_type: $i ).
tff(decl_31,type,
not_equal: ( $i * $i ) > $o ).
tff(decl_32,type,
relation_like: $i > $o ).
tff(decl_33,type,
cross_product: ( $i * $i ) > $i ).
tff(decl_34,type,
subset_type: $i > $i ).
tff(decl_35,type,
power_set: $i > $i ).
tff(decl_36,type,
member_type: $i > $i ).
tff(decl_37,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_38,type,
esk2_1: $i > $i ).
tff(decl_39,type,
esk3_0: $i ).
tff(decl_40,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_41,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_42,type,
esk6_1: $i > $i ).
tff(decl_43,type,
esk7_1: $i > $i ).
tff(decl_44,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_45,type,
esk9_1: $i > $i ).
tff(decl_46,type,
esk10_0: $i ).
fof(p8,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',p8) ).
fof(prove_relset_1_46,conjecture,
! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> not_equal(identity_relation_of(X1),empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_46) ).
fof(p7,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( not_equal(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7) ).
fof(p22,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p22) ).
fof(p2,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ~ member(X1,empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(p1,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X1)
<=> member(ordered_pair(X2,X2),identity_relation_of(X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(c_0_6,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[p8]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> not_equal(identity_relation_of(X1),empty_set) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[prove_relset_1_46])]) ).
fof(c_0_8,plain,
! [X16,X17] :
( ( ~ not_equal(X16,X17)
| X16 != X17
| ~ ilf_type(X17,set_type)
| ~ ilf_type(X16,set_type) )
& ( X16 = X17
| not_equal(X16,X17)
| ~ ilf_type(X17,set_type)
| ~ ilf_type(X16,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p7])])])]) ).
fof(c_0_9,plain,
! [X51] : ilf_type(X51,set_type),
inference(variable_rename,[status(thm)],[p22]) ).
fof(c_0_10,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ~ member(X1,empty_set) ),
inference(fof_simplification,[status(thm)],[p2]) ).
fof(c_0_11,plain,
! [X18,X19] :
( ( ~ empty(X18)
| ~ ilf_type(X19,set_type)
| ~ member(X19,X18)
| ~ ilf_type(X18,set_type) )
& ( ilf_type(esk2_1(X18),set_type)
| empty(X18)
| ~ ilf_type(X18,set_type) )
& ( member(esk2_1(X18),X18)
| empty(X18)
| ~ ilf_type(X18,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_6])])])])]) ).
fof(c_0_12,plain,
! [X5,X6] :
( ( ~ member(X6,X5)
| member(ordered_pair(X6,X6),identity_relation_of(X5))
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) )
& ( ~ member(ordered_pair(X6,X6),identity_relation_of(X5))
| member(X6,X5)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])])]) ).
fof(c_0_13,negated_conjecture,
( ~ empty(esk10_0)
& ilf_type(esk10_0,set_type)
& ~ not_equal(identity_relation_of(esk10_0),empty_set) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
cnf(c_0_14,plain,
( X1 = X2
| not_equal(X1,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,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,plain,
! [X7] :
( ~ ilf_type(X7,set_type)
| ~ member(X7,empty_set) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])]) ).
cnf(c_0_17,plain,
( member(esk2_1(X1),X1)
| empty(X1)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
( member(ordered_pair(X1,X1),identity_relation_of(X2))
| ~ member(X1,X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,negated_conjecture,
~ not_equal(identity_relation_of(esk10_0),empty_set),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
( X1 = X2
| not_equal(X1,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_21,plain,
( ~ ilf_type(X1,set_type)
| ~ member(X1,empty_set) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
~ empty(esk10_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_23,plain,
( empty(X1)
| member(esk2_1(X1),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_15])]) ).
cnf(c_0_24,plain,
( member(ordered_pair(X1,X1),identity_relation_of(X2))
| ~ member(X1,X2) ),
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,negated_conjecture,
identity_relation_of(esk10_0) = empty_set,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,plain,
~ member(X1,empty_set),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_15])]) ).
cnf(c_0_27,negated_conjecture,
member(esk2_1(esk10_0),esk10_0),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,negated_conjecture,
~ member(X1,esk10_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_27,c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET679+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 12:59:39 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 0.19/0.59 % Version : CSE_E---1.5
% 0.19/0.59 % Problem : theBenchmark.p
% 0.19/0.59 % Proof found
% 0.19/0.59 % SZS status Theorem for theBenchmark.p
% 0.19/0.59 % SZS output start Proof
% See solution above
% 0.19/0.59 % Total time : 0.012000 s
% 0.19/0.59 % SZS output end Proof
% 0.19/0.59 % Total time : 0.016000 s
%------------------------------------------------------------------------------