TSTP Solution File: SET653+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET653+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 : n009.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 14:35:04 EDT 2023
% Result : Theorem 0.44s 0.61s
% Output : CNFRefutation 0.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 33
% Syntax : Number of formulae : 53 ( 8 unt; 28 typ; 0 def)
% Number of atoms : 91 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 105 ( 39 ~; 36 |; 8 &)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 33 ( 22 >; 11 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 6 con; 0-2 aty)
% Number of variables : 53 ( 3 sgn; 30 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
set_type: $i ).
tff(decl_23,type,
ilf_type: ( $i * $i ) > $o ).
tff(decl_24,type,
subset: ( $i * $i ) > $o ).
tff(decl_25,type,
relation_type: ( $i * $i ) > $i ).
tff(decl_26,type,
domain_of: $i > $i ).
tff(decl_27,type,
range_of: $i > $i ).
tff(decl_28,type,
cross_product: ( $i * $i ) > $i ).
tff(decl_29,type,
subset_type: $i > $i ).
tff(decl_30,type,
member: ( $i * $i ) > $o ).
tff(decl_31,type,
binary_relation_type: $i ).
tff(decl_32,type,
power_set: $i > $i ).
tff(decl_33,type,
member_type: $i > $i ).
tff(decl_34,type,
empty: $i > $o ).
tff(decl_35,type,
relation_like: $i > $o ).
tff(decl_36,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_37,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_38,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_39,type,
esk3_1: $i > $i ).
tff(decl_40,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_41,type,
esk5_1: $i > $i ).
tff(decl_42,type,
esk6_1: $i > $i ).
tff(decl_43,type,
esk7_2: ( $i * $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 ).
tff(decl_47,type,
esk11_0: $i ).
tff(decl_48,type,
esk12_0: $i ).
tff(decl_49,type,
esk13_0: $i ).
fof(p3,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X1,X3))
=> ( subset(domain_of(X4),X2)
=> ilf_type(X4,relation_type(X2,X3)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
fof(p22,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p22) ).
fof(prove_relset_1_15,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X1,X3))
=> ( subset(X1,X2)
=> ilf_type(X4,relation_type(X2,X3)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_15) ).
fof(p1,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(p2,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',p2) ).
fof(c_0_5,plain,
! [X11,X12,X13,X14] :
( ~ ilf_type(X11,set_type)
| ~ ilf_type(X12,set_type)
| ~ ilf_type(X13,set_type)
| ~ ilf_type(X14,relation_type(X11,X13))
| ~ subset(domain_of(X14),X12)
| ilf_type(X14,relation_type(X12,X13)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p3])])]) ).
fof(c_0_6,plain,
! [X60] : ilf_type(X60,set_type),
inference(variable_rename,[status(thm)],[p22]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X1,X3))
=> ( subset(X1,X2)
=> ilf_type(X4,relation_type(X2,X3)) ) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_15]) ).
fof(c_0_8,plain,
! [X5,X6,X7] :
( ~ ilf_type(X5,set_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X7,set_type)
| ~ subset(X5,X6)
| ~ subset(X6,X7)
| subset(X5,X7) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])]) ).
fof(c_0_9,plain,
! [X8,X9,X10] :
( ( subset(domain_of(X10),X8)
| ~ ilf_type(X10,relation_type(X8,X9))
| ~ ilf_type(X9,set_type)
| ~ ilf_type(X8,set_type) )
& ( subset(range_of(X10),X9)
| ~ ilf_type(X10,relation_type(X8,X9))
| ~ ilf_type(X9,set_type)
| ~ ilf_type(X8,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p2])])])]) ).
cnf(c_0_10,plain,
( ilf_type(X4,relation_type(X2,X3))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,relation_type(X1,X3))
| ~ subset(domain_of(X4),X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_11,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_12,negated_conjecture,
( ilf_type(esk10_0,set_type)
& ilf_type(esk11_0,set_type)
& ilf_type(esk12_0,set_type)
& ilf_type(esk13_0,relation_type(esk10_0,esk12_0))
& subset(esk10_0,esk11_0)
& ~ ilf_type(esk13_0,relation_type(esk11_0,esk12_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
cnf(c_0_13,plain,
( subset(X1,X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ subset(X1,X2)
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( subset(domain_of(X1),X2)
| ~ ilf_type(X1,relation_type(X2,X3))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( ilf_type(X1,relation_type(X2,X3))
| ~ subset(domain_of(X1),X2)
| ~ ilf_type(X1,relation_type(X4,X3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11]),c_0_11]),c_0_11])]) ).
cnf(c_0_16,negated_conjecture,
ilf_type(esk13_0,relation_type(esk10_0,esk12_0)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
( subset(X1,X2)
| ~ subset(X3,X2)
| ~ subset(X1,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_11]),c_0_11]),c_0_11])]) ).
cnf(c_0_18,negated_conjecture,
subset(esk10_0,esk11_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
( subset(domain_of(X1),X2)
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_11]),c_0_11])]) ).
cnf(c_0_20,negated_conjecture,
( ilf_type(esk13_0,relation_type(X1,esk12_0))
| ~ subset(domain_of(esk13_0),X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,negated_conjecture,
( subset(X1,esk11_0)
| ~ subset(X1,esk10_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,negated_conjecture,
subset(domain_of(esk13_0),esk10_0),
inference(spm,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_23,negated_conjecture,
~ ilf_type(esk13_0,relation_type(esk11_0,esk12_0)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_24,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]),c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET653+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 : n009.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 14:15:50 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.44/0.59 start to proof: theBenchmark
% 0.44/0.61 % Version : CSE_E---1.5
% 0.44/0.61 % Problem : theBenchmark.p
% 0.44/0.61 % Proof found
% 0.44/0.61 % SZS status Theorem for theBenchmark.p
% 0.44/0.61 % SZS output start Proof
% See solution above
% 0.44/0.62 % Total time : 0.014000 s
% 0.44/0.62 % SZS output end Proof
% 0.44/0.62 % Total time : 0.017000 s
%------------------------------------------------------------------------------