TSTP Solution File: SEU177+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU177+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n016.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 16:23:06 EDT 2023
% Result : Theorem 0.59s 0.79s
% Output : CNFRefutation 0.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 75
% Syntax : Number of formulae : 102 ( 17 unt; 69 typ; 0 def)
% Number of atoms : 99 ( 28 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 112 ( 46 ~; 46 |; 10 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 126 ( 62 >; 64 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 61 ( 61 usr; 7 con; 0-4 aty)
% Number of variables : 71 ( 4 sgn; 36 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
proper_subset: ( $i * $i ) > $o ).
tff(decl_24,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_25,type,
set_union2: ( $i * $i ) > $i ).
tff(decl_26,type,
set_intersection2: ( $i * $i ) > $i ).
tff(decl_27,type,
subset: ( $i * $i ) > $o ).
tff(decl_28,type,
empty_set: $i ).
tff(decl_29,type,
set_meet: $i > $i ).
tff(decl_30,type,
singleton: $i > $i ).
tff(decl_31,type,
powerset: $i > $i ).
tff(decl_32,type,
empty: $i > $o ).
tff(decl_33,type,
element: ( $i * $i ) > $o ).
tff(decl_34,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(decl_35,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_36,type,
relation: $i > $o ).
tff(decl_37,type,
relation_dom: $i > $i ).
tff(decl_38,type,
cast_to_subset: $i > $i ).
tff(decl_39,type,
union: $i > $i ).
tff(decl_40,type,
set_difference: ( $i * $i ) > $i ).
tff(decl_41,type,
relation_rng: $i > $i ).
tff(decl_42,type,
subset_complement: ( $i * $i ) > $i ).
tff(decl_43,type,
disjoint: ( $i * $i ) > $o ).
tff(decl_44,type,
complements_of_subsets: ( $i * $i ) > $i ).
tff(decl_45,type,
union_of_subsets: ( $i * $i ) > $i ).
tff(decl_46,type,
meet_of_subsets: ( $i * $i ) > $i ).
tff(decl_47,type,
subset_difference: ( $i * $i * $i ) > $i ).
tff(decl_48,type,
are_equipotent: ( $i * $i ) > $o ).
tff(decl_49,type,
esk1_3: ( $i * $i * $i ) > $i ).
tff(decl_50,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_51,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_52,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_53,type,
esk5_1: $i > $i ).
tff(decl_54,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_55,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_56,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_57,type,
esk9_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_58,type,
esk10_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_59,type,
esk11_3: ( $i * $i * $i ) > $i ).
tff(decl_60,type,
esk12_3: ( $i * $i * $i ) > $i ).
tff(decl_61,type,
esk13_3: ( $i * $i * $i ) > $i ).
tff(decl_62,type,
esk14_2: ( $i * $i ) > $i ).
tff(decl_63,type,
esk15_3: ( $i * $i * $i ) > $i ).
tff(decl_64,type,
esk16_3: ( $i * $i * $i ) > $i ).
tff(decl_65,type,
esk17_2: ( $i * $i ) > $i ).
tff(decl_66,type,
esk18_2: ( $i * $i ) > $i ).
tff(decl_67,type,
esk19_3: ( $i * $i * $i ) > $i ).
tff(decl_68,type,
esk20_2: ( $i * $i ) > $i ).
tff(decl_69,type,
esk21_2: ( $i * $i ) > $i ).
tff(decl_70,type,
esk22_3: ( $i * $i * $i ) > $i ).
tff(decl_71,type,
esk23_3: ( $i * $i * $i ) > $i ).
tff(decl_72,type,
esk24_2: ( $i * $i ) > $i ).
tff(decl_73,type,
esk25_2: ( $i * $i ) > $i ).
tff(decl_74,type,
esk26_3: ( $i * $i * $i ) > $i ).
tff(decl_75,type,
esk27_1: $i > $i ).
tff(decl_76,type,
esk28_2: ( $i * $i ) > $i ).
tff(decl_77,type,
esk29_0: $i ).
tff(decl_78,type,
esk30_1: $i > $i ).
tff(decl_79,type,
esk31_0: $i ).
tff(decl_80,type,
esk32_1: $i > $i ).
tff(decl_81,type,
esk33_0: $i ).
tff(decl_82,type,
esk34_1: $i > $i ).
tff(decl_83,type,
esk35_0: $i ).
tff(decl_84,type,
esk36_0: $i ).
tff(decl_85,type,
esk37_0: $i ).
tff(decl_86,type,
esk38_2: ( $i * $i ) > $i ).
tff(decl_87,type,
esk39_2: ( $i * $i ) > $i ).
tff(decl_88,type,
esk40_2: ( $i * $i ) > $i ).
tff(decl_89,type,
esk41_1: $i > $i ).
tff(decl_90,type,
esk42_2: ( $i * $i ) > $i ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(t69_enumset1,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(t20_relat_1,conjecture,
! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_dom(X3))
& in(X2,relation_rng(X3)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_relat_1) ).
fof(d5_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X4,X3),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(d4_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_dom(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X3,X4),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
fof(c_0_6,plain,
! [X145,X146] : ordered_pair(X145,X146) = unordered_pair(unordered_pair(X145,X146),singleton(X145)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_7,lemma,
! [X354] : unordered_pair(X354,X354) = singleton(X354),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(c_0_8,negated_conjecture,
~ ! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_dom(X3))
& in(X2,relation_rng(X3)) ) ) ),
inference(assume_negation,[status(cth)],[t20_relat_1]) ).
fof(c_0_9,plain,
! [X133,X134,X135,X137,X138,X139,X141] :
( ( ~ in(X135,X134)
| in(ordered_pair(esk23_3(X133,X134,X135),X135),X133)
| X134 != relation_rng(X133)
| ~ relation(X133) )
& ( ~ in(ordered_pair(X138,X137),X133)
| in(X137,X134)
| X134 != relation_rng(X133)
| ~ relation(X133) )
& ( ~ in(esk24_2(X133,X139),X139)
| ~ in(ordered_pair(X141,esk24_2(X133,X139)),X133)
| X139 = relation_rng(X133)
| ~ relation(X133) )
& ( in(esk24_2(X133,X139),X139)
| in(ordered_pair(esk25_2(X133,X139),esk24_2(X133,X139)),X133)
| X139 = relation_rng(X133)
| ~ relation(X133) ) ),
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)],[d5_relat_1])])])])])]) ).
cnf(c_0_10,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_12,negated_conjecture,
( relation(esk37_0)
& in(ordered_pair(esk35_0,esk36_0),esk37_0)
& ( ~ in(esk35_0,relation_dom(esk37_0))
| ~ in(esk36_0,relation_rng(esk37_0)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
cnf(c_0_13,plain,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),X3)
| X4 != relation_rng(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
fof(c_0_15,plain,
! [X11,X12] : unordered_pair(X11,X12) = unordered_pair(X12,X11),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_16,negated_conjecture,
in(ordered_pair(esk35_0,esk36_0),esk37_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_17,plain,
! [X102,X103,X104,X106,X107,X108,X110] :
( ( ~ in(X104,X103)
| in(ordered_pair(X104,esk16_3(X102,X103,X104)),X102)
| X103 != relation_dom(X102)
| ~ relation(X102) )
& ( ~ in(ordered_pair(X106,X107),X102)
| in(X106,X103)
| X103 != relation_dom(X102)
| ~ relation(X102) )
& ( ~ in(esk17_2(X102,X108),X108)
| ~ in(ordered_pair(esk17_2(X102,X108),X110),X102)
| X108 = relation_dom(X102)
| ~ relation(X102) )
& ( in(esk17_2(X102,X108),X108)
| in(ordered_pair(esk17_2(X102,X108),esk18_2(X102,X108)),X102)
| X108 = relation_dom(X102)
| ~ relation(X102) ) ),
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)],[d4_relat_1])])])])])]) ).
cnf(c_0_18,plain,
( in(X2,X4)
| X4 != relation_rng(X3)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,negated_conjecture,
in(unordered_pair(unordered_pair(esk35_0,esk36_0),unordered_pair(esk35_0,esk35_0)),esk37_0),
inference(rw,[status(thm)],[c_0_16,c_0_14]) ).
cnf(c_0_21,plain,
( in(X1,X4)
| ~ in(ordered_pair(X1,X2),X3)
| X4 != relation_dom(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,plain,
( in(X1,X2)
| X2 != relation_rng(X3)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,X1)),X3) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,negated_conjecture,
in(unordered_pair(unordered_pair(esk35_0,esk35_0),unordered_pair(esk35_0,esk36_0)),esk37_0),
inference(rw,[status(thm)],[c_0_20,c_0_19]) ).
cnf(c_0_24,negated_conjecture,
relation(esk37_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_25,plain,
( in(X1,X4)
| X4 != relation_dom(X3)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[c_0_21,c_0_14]) ).
cnf(c_0_26,negated_conjecture,
( in(esk36_0,X1)
| X1 != relation_rng(esk37_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).
cnf(c_0_27,plain,
( in(X1,X2)
| X2 != relation_dom(X3)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,X4)),X3) ),
inference(spm,[status(thm)],[c_0_25,c_0_19]) ).
cnf(c_0_28,negated_conjecture,
( ~ in(esk35_0,relation_dom(esk37_0))
| ~ in(esk36_0,relation_rng(esk37_0)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_29,negated_conjecture,
in(esk36_0,relation_rng(esk37_0)),
inference(er,[status(thm)],[c_0_26]) ).
cnf(c_0_30,negated_conjecture,
( in(esk35_0,X1)
| X1 != relation_dom(esk37_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_23]),c_0_24])]) ).
cnf(c_0_31,negated_conjecture,
~ in(esk35_0,relation_dom(esk37_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29])]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_30]),c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU177+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n016.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 : Thu Aug 24 02:19:08 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 0.59/0.79 % Version : CSE_E---1.5
% 0.59/0.79 % Problem : theBenchmark.p
% 0.59/0.79 % Proof found
% 0.59/0.79 % SZS status Theorem for theBenchmark.p
% 0.59/0.79 % SZS output start Proof
% See solution above
% 0.59/0.79 % Total time : 0.206000 s
% 0.59/0.79 % SZS output end Proof
% 0.59/0.79 % Total time : 0.211000 s
%------------------------------------------------------------------------------