TSTP Solution File: SEU180+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU180+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 : n003.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 16:23:07 EDT 2023
% Result : Theorem 1.20s 1.46s
% Output : CNFRefutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 81
% Syntax : Number of formulae : 118 ( 19 unt; 73 typ; 0 def)
% Number of atoms : 134 ( 35 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 149 ( 60 ~; 63 |; 14 &)
% ( 4 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 132 ( 66 >; 66 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 65 ( 65 usr; 7 con; 0-4 aty)
% Number of variables : 93 ( 6 sgn; 46 !; 1 ?; 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,
relation: $i > $o ).
tff(decl_29,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_30,type,
empty_set: $i ).
tff(decl_31,type,
set_meet: $i > $i ).
tff(decl_32,type,
singleton: $i > $i ).
tff(decl_33,type,
powerset: $i > $i ).
tff(decl_34,type,
empty: $i > $o ).
tff(decl_35,type,
element: ( $i * $i ) > $o ).
tff(decl_36,type,
cartesian_product2: ( $i * $i ) > $i ).
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,
relation_field: $i > $i ).
tff(decl_44,type,
disjoint: ( $i * $i ) > $o ).
tff(decl_45,type,
complements_of_subsets: ( $i * $i ) > $i ).
tff(decl_46,type,
union_of_subsets: ( $i * $i ) > $i ).
tff(decl_47,type,
meet_of_subsets: ( $i * $i ) > $i ).
tff(decl_48,type,
subset_difference: ( $i * $i * $i ) > $i ).
tff(decl_49,type,
are_equipotent: ( $i * $i ) > $o ).
tff(decl_50,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_51,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_52,type,
esk3_1: $i > $i ).
tff(decl_53,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_54,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_55,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_56,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_57,type,
esk8_1: $i > $i ).
tff(decl_58,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_59,type,
esk10_3: ( $i * $i * $i ) > $i ).
tff(decl_60,type,
esk11_3: ( $i * $i * $i ) > $i ).
tff(decl_61,type,
esk12_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_62,type,
esk13_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_63,type,
esk14_3: ( $i * $i * $i ) > $i ).
tff(decl_64,type,
esk15_3: ( $i * $i * $i ) > $i ).
tff(decl_65,type,
esk16_3: ( $i * $i * $i ) > $i ).
tff(decl_66,type,
esk17_2: ( $i * $i ) > $i ).
tff(decl_67,type,
esk18_3: ( $i * $i * $i ) > $i ).
tff(decl_68,type,
esk19_3: ( $i * $i * $i ) > $i ).
tff(decl_69,type,
esk20_2: ( $i * $i ) > $i ).
tff(decl_70,type,
esk21_2: ( $i * $i ) > $i ).
tff(decl_71,type,
esk22_3: ( $i * $i * $i ) > $i ).
tff(decl_72,type,
esk23_2: ( $i * $i ) > $i ).
tff(decl_73,type,
esk24_2: ( $i * $i ) > $i ).
tff(decl_74,type,
esk25_3: ( $i * $i * $i ) > $i ).
tff(decl_75,type,
esk26_3: ( $i * $i * $i ) > $i ).
tff(decl_76,type,
esk27_2: ( $i * $i ) > $i ).
tff(decl_77,type,
esk28_2: ( $i * $i ) > $i ).
tff(decl_78,type,
esk29_3: ( $i * $i * $i ) > $i ).
tff(decl_79,type,
esk30_1: $i > $i ).
tff(decl_80,type,
esk31_2: ( $i * $i ) > $i ).
tff(decl_81,type,
esk32_0: $i ).
tff(decl_82,type,
esk33_1: $i > $i ).
tff(decl_83,type,
esk34_0: $i ).
tff(decl_84,type,
esk35_1: $i > $i ).
tff(decl_85,type,
esk36_0: $i ).
tff(decl_86,type,
esk37_1: $i > $i ).
tff(decl_87,type,
esk38_2: ( $i * $i ) > $i ).
tff(decl_88,type,
esk39_0: $i ).
tff(decl_89,type,
esk40_0: $i ).
tff(decl_90,type,
esk41_0: $i ).
tff(decl_91,type,
esk42_2: ( $i * $i ) > $i ).
tff(decl_92,type,
esk43_2: ( $i * $i ) > $i ).
tff(decl_93,type,
esk44_1: $i > $i ).
tff(decl_94,type,
esk45_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(t30_relat_1,conjecture,
! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_field(X3))
& in(X2,relation_field(X3)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_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(t20_relat_1,lemma,
! [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(d2_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(d6_relat_1,axiom,
! [X1] :
( relation(X1)
=> relation_field(X1) = set_union2(relation_dom(X1),relation_rng(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_relat_1) ).
fof(c_0_8,plain,
! [X153,X154] : ordered_pair(X153,X154) = unordered_pair(unordered_pair(X153,X154),singleton(X153)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_9,lemma,
! [X373] : unordered_pair(X373,X373) = singleton(X373),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(c_0_10,negated_conjecture,
~ ! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_field(X3))
& in(X2,relation_field(X3)) ) ) ),
inference(assume_negation,[status(cth)],[t30_relat_1]) ).
fof(c_0_11,plain,
! [X141,X142,X143,X145,X146,X147,X149] :
( ( ~ in(X143,X142)
| in(ordered_pair(esk26_3(X141,X142,X143),X143),X141)
| X142 != relation_rng(X141)
| ~ relation(X141) )
& ( ~ in(ordered_pair(X146,X145),X141)
| in(X145,X142)
| X142 != relation_rng(X141)
| ~ relation(X141) )
& ( ~ in(esk27_2(X141,X147),X147)
| ~ in(ordered_pair(X149,esk27_2(X141,X147)),X141)
| X147 = relation_rng(X141)
| ~ relation(X141) )
& ( in(esk27_2(X141,X147),X147)
| in(ordered_pair(esk28_2(X141,X147),esk27_2(X141,X147)),X141)
| X147 = relation_rng(X141)
| ~ relation(X141) ) ),
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_12,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_14,negated_conjecture,
( relation(esk41_0)
& in(ordered_pair(esk39_0,esk40_0),esk41_0)
& ( ~ in(esk39_0,relation_field(esk41_0))
| ~ in(esk40_0,relation_field(esk41_0)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
cnf(c_0_15,plain,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),X3)
| X4 != relation_rng(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_17,plain,
! [X11,X12] : unordered_pair(X11,X12) = unordered_pair(X12,X11),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_18,negated_conjecture,
in(ordered_pair(esk39_0,esk40_0),esk41_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,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_15,c_0_16]) ).
cnf(c_0_20,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_21,negated_conjecture,
in(unordered_pair(unordered_pair(esk39_0,esk40_0),unordered_pair(esk39_0,esk39_0)),esk41_0),
inference(rw,[status(thm)],[c_0_18,c_0_16]) ).
fof(c_0_22,lemma,
! [X279,X280,X281] :
( ( in(X279,relation_dom(X281))
| ~ in(ordered_pair(X279,X280),X281)
| ~ relation(X281) )
& ( in(X280,relation_rng(X281))
| ~ in(ordered_pair(X279,X280),X281)
| ~ relation(X281) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t20_relat_1])])]) ).
fof(c_0_23,plain,
! [X69,X70,X71,X72,X73,X74,X75,X76] :
( ( ~ in(X72,X71)
| in(X72,X69)
| in(X72,X70)
| X71 != set_union2(X69,X70) )
& ( ~ in(X73,X69)
| in(X73,X71)
| X71 != set_union2(X69,X70) )
& ( ~ in(X73,X70)
| in(X73,X71)
| X71 != set_union2(X69,X70) )
& ( ~ in(esk11_3(X74,X75,X76),X74)
| ~ in(esk11_3(X74,X75,X76),X76)
| X76 = set_union2(X74,X75) )
& ( ~ in(esk11_3(X74,X75,X76),X75)
| ~ in(esk11_3(X74,X75,X76),X76)
| X76 = set_union2(X74,X75) )
& ( in(esk11_3(X74,X75,X76),X76)
| in(esk11_3(X74,X75,X76),X74)
| in(esk11_3(X74,X75,X76),X75)
| X76 = set_union2(X74,X75) ) ),
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)],[d2_xboole_0])])])])])]) ).
fof(c_0_24,plain,
! [X155] :
( ~ relation(X155)
| relation_field(X155) = set_union2(relation_dom(X155),relation_rng(X155)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d6_relat_1])]) ).
cnf(c_0_25,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_19,c_0_20]) ).
cnf(c_0_26,negated_conjecture,
in(unordered_pair(unordered_pair(esk39_0,esk39_0),unordered_pair(esk39_0,esk40_0)),esk41_0),
inference(rw,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_27,negated_conjecture,
relation(esk41_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_28,lemma,
( in(X1,relation_dom(X2))
| ~ in(ordered_pair(X1,X3),X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
( relation_field(X1) = set_union2(relation_dom(X1),relation_rng(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,negated_conjecture,
( in(esk40_0,X1)
| X1 != relation_rng(esk41_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
cnf(c_0_32,lemma,
( in(X1,relation_dom(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),X2) ),
inference(rw,[status(thm)],[c_0_28,c_0_16]) ).
cnf(c_0_33,plain,
( in(X1,X2)
| X2 != relation_field(X3)
| ~ relation(X3)
| ~ in(X1,relation_rng(X3)) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,negated_conjecture,
in(esk40_0,relation_rng(esk41_0)),
inference(er,[status(thm)],[c_0_31]) ).
cnf(c_0_35,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_36,lemma,
( in(X1,relation_dom(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,X3)),X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_20]) ).
cnf(c_0_37,negated_conjecture,
( in(esk40_0,X1)
| X1 != relation_field(esk41_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_27])]) ).
cnf(c_0_38,plain,
( in(X1,X2)
| X2 != relation_field(X3)
| ~ relation(X3)
| ~ in(X1,relation_dom(X3)) ),
inference(spm,[status(thm)],[c_0_35,c_0_30]) ).
cnf(c_0_39,negated_conjecture,
in(esk39_0,relation_dom(esk41_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_26]),c_0_27])]) ).
cnf(c_0_40,negated_conjecture,
( ~ in(esk39_0,relation_field(esk41_0))
| ~ in(esk40_0,relation_field(esk41_0)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_41,negated_conjecture,
in(esk40_0,relation_field(esk41_0)),
inference(er,[status(thm)],[c_0_37]) ).
cnf(c_0_42,negated_conjecture,
( in(esk39_0,X1)
| X1 != relation_field(esk41_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_27])]) ).
cnf(c_0_43,negated_conjecture,
~ in(esk39_0,relation_field(esk41_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(er,[status(thm)],[c_0_42]),c_0_43]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU180+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n003.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 23 16:59:22 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 1.20/1.46 % Version : CSE_E---1.5
% 1.20/1.46 % Problem : theBenchmark.p
% 1.20/1.46 % Proof found
% 1.20/1.46 % SZS status Theorem for theBenchmark.p
% 1.20/1.46 % SZS output start Proof
% See solution above
% 1.30/1.47 % Total time : 0.876000 s
% 1.30/1.47 % SZS output end Proof
% 1.30/1.47 % Total time : 0.882000 s
%------------------------------------------------------------------------------