TSTP Solution File: SEU187+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU187+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n028.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 16:23:10 EDT 2023
% Result : Theorem 0.19s 0.68s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 91
% Syntax : Number of formulae : 127 ( 20 unt; 81 typ; 0 def)
% Number of atoms : 120 ( 52 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 137 ( 63 ~; 53 |; 11 &)
% ( 8 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 155 ( 76 >; 79 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 73 ( 73 usr; 5 con; 0-5 aty)
% Number of variables : 85 ( 6 sgn; 45 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
proper_subset: ( $i * $i ) > $o ).
tff(decl_24,type,
empty: $i > $o ).
tff(decl_25,type,
relation: $i > $o ).
tff(decl_26,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_27,type,
set_union2: ( $i * $i ) > $i ).
tff(decl_28,type,
set_intersection2: ( $i * $i ) > $i ).
tff(decl_29,type,
subset: ( $i * $i ) > $o ).
tff(decl_30,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_31,type,
empty_set: $i ).
tff(decl_32,type,
set_meet: $i > $i ).
tff(decl_33,type,
singleton: $i > $i ).
tff(decl_34,type,
powerset: $i > $i ).
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,
relation_inverse: $i > $i ).
tff(decl_45,type,
disjoint: ( $i * $i ) > $o ).
tff(decl_46,type,
relation_composition: ( $i * $i ) > $i ).
tff(decl_47,type,
complements_of_subsets: ( $i * $i ) > $i ).
tff(decl_48,type,
union_of_subsets: ( $i * $i ) > $i ).
tff(decl_49,type,
meet_of_subsets: ( $i * $i ) > $i ).
tff(decl_50,type,
subset_difference: ( $i * $i * $i ) > $i ).
tff(decl_51,type,
are_equipotent: ( $i * $i ) > $o ).
tff(decl_52,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_53,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_54,type,
esk3_1: $i > $i ).
tff(decl_55,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_56,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_57,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_58,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_59,type,
esk8_1: $i > $i ).
tff(decl_60,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_61,type,
esk10_3: ( $i * $i * $i ) > $i ).
tff(decl_62,type,
esk11_3: ( $i * $i * $i ) > $i ).
tff(decl_63,type,
esk12_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_64,type,
esk13_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_65,type,
esk14_3: ( $i * $i * $i ) > $i ).
tff(decl_66,type,
esk15_3: ( $i * $i * $i ) > $i ).
tff(decl_67,type,
esk16_3: ( $i * $i * $i ) > $i ).
tff(decl_68,type,
esk17_2: ( $i * $i ) > $i ).
tff(decl_69,type,
esk18_3: ( $i * $i * $i ) > $i ).
tff(decl_70,type,
esk19_3: ( $i * $i * $i ) > $i ).
tff(decl_71,type,
esk20_2: ( $i * $i ) > $i ).
tff(decl_72,type,
esk21_2: ( $i * $i ) > $i ).
tff(decl_73,type,
esk22_3: ( $i * $i * $i ) > $i ).
tff(decl_74,type,
esk23_2: ( $i * $i ) > $i ).
tff(decl_75,type,
esk24_2: ( $i * $i ) > $i ).
tff(decl_76,type,
esk25_3: ( $i * $i * $i ) > $i ).
tff(decl_77,type,
esk26_3: ( $i * $i * $i ) > $i ).
tff(decl_78,type,
esk27_2: ( $i * $i ) > $i ).
tff(decl_79,type,
esk28_2: ( $i * $i ) > $i ).
tff(decl_80,type,
esk29_2: ( $i * $i ) > $i ).
tff(decl_81,type,
esk30_2: ( $i * $i ) > $i ).
tff(decl_82,type,
esk31_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_83,type,
esk32_3: ( $i * $i * $i ) > $i ).
tff(decl_84,type,
esk33_3: ( $i * $i * $i ) > $i ).
tff(decl_85,type,
esk34_3: ( $i * $i * $i ) > $i ).
tff(decl_86,type,
esk35_3: ( $i * $i * $i ) > $i ).
tff(decl_87,type,
esk36_1: $i > $i ).
tff(decl_88,type,
esk37_2: ( $i * $i ) > $i ).
tff(decl_89,type,
esk38_0: $i ).
tff(decl_90,type,
esk39_1: $i > $i ).
tff(decl_91,type,
esk40_0: $i ).
tff(decl_92,type,
esk41_0: $i ).
tff(decl_93,type,
esk42_1: $i > $i ).
tff(decl_94,type,
esk43_0: $i ).
tff(decl_95,type,
esk44_1: $i > $i ).
tff(decl_96,type,
esk45_2: ( $i * $i ) > $i ).
tff(decl_97,type,
esk46_2: ( $i * $i ) > $i ).
tff(decl_98,type,
esk47_2: ( $i * $i ) > $i ).
tff(decl_99,type,
esk48_1: $i > $i ).
tff(decl_100,type,
esk49_1: $i > $i ).
tff(decl_101,type,
esk50_1: $i > $i ).
tff(decl_102,type,
esk51_2: ( $i * $i ) > $i ).
fof(t65_zfmisc_1,lemma,
! [X1,X2] :
( set_difference(X1,singleton(X2)) = X1
<=> ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_zfmisc_1) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(t69_enumset1,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
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/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
fof(t4_boole,axiom,
! [X1] : set_difference(empty_set,X1) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
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/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
fof(fc4_relat_1,axiom,
( empty(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(t60_relat_1,conjecture,
( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_relat_1) ).
fof(c_0_10,lemma,
! [X1,X2] :
( set_difference(X1,singleton(X2)) = X1
<=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[t65_zfmisc_1]) ).
fof(c_0_11,plain,
! [X154,X155] : ordered_pair(X154,X155) = unordered_pair(unordered_pair(X154,X155),singleton(X154)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_12,lemma,
! [X414] : unordered_pair(X414,X414) = singleton(X414),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(c_0_13,lemma,
! [X412,X413] :
( ( set_difference(X412,singleton(X413)) != X412
| ~ in(X413,X412) )
& ( in(X413,X412)
| set_difference(X412,singleton(X413)) = X412 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])]) ).
fof(c_0_14,plain,
! [X111,X112,X113,X115,X116,X117,X119] :
( ( ~ in(X113,X112)
| in(ordered_pair(X113,esk19_3(X111,X112,X113)),X111)
| X112 != relation_dom(X111)
| ~ relation(X111) )
& ( ~ in(ordered_pair(X115,X116),X111)
| in(X115,X112)
| X112 != relation_dom(X111)
| ~ relation(X111) )
& ( ~ in(esk20_2(X111,X117),X117)
| ~ in(ordered_pair(esk20_2(X111,X117),X119),X111)
| X117 = relation_dom(X111)
| ~ relation(X111) )
& ( in(esk20_2(X111,X117),X117)
| in(ordered_pair(esk20_2(X111,X117),esk21_2(X111,X117)),X111)
| X117 = relation_dom(X111)
| ~ relation(X111) ) ),
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_15,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,lemma,
( set_difference(X1,singleton(X2)) != X1
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_18,plain,
! [X385] : set_difference(empty_set,X385) = empty_set,
inference(variable_rename,[status(thm)],[t4_boole]) ).
cnf(c_0_19,plain,
( in(ordered_pair(X1,esk19_3(X3,X2,X1)),X3)
| ~ in(X1,X2)
| X2 != relation_dom(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
fof(c_0_21,plain,
! [X12,X13] : unordered_pair(X12,X13) = unordered_pair(X13,X12),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(c_0_22,plain,
! [X142,X143,X144,X146,X147,X148,X150] :
( ( ~ in(X144,X143)
| in(ordered_pair(esk26_3(X142,X143,X144),X144),X142)
| X143 != relation_rng(X142)
| ~ relation(X142) )
& ( ~ in(ordered_pair(X147,X146),X142)
| in(X146,X143)
| X143 != relation_rng(X142)
| ~ relation(X142) )
& ( ~ in(esk27_2(X142,X148),X148)
| ~ in(ordered_pair(X150,esk27_2(X142,X148)),X142)
| X148 = relation_rng(X142)
| ~ relation(X142) )
& ( in(esk27_2(X142,X148),X148)
| in(ordered_pair(esk28_2(X142,X148),esk27_2(X142,X148)),X142)
| X148 = relation_rng(X142)
| ~ relation(X142) ) ),
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_23,lemma,
( set_difference(X1,unordered_pair(X2,X2)) != X1
| ~ in(X2,X1) ),
inference(rw,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_24,plain,
set_difference(empty_set,X1) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
( in(unordered_pair(unordered_pair(X1,esk19_3(X3,X2,X1)),unordered_pair(X1,X1)),X3)
| X2 != relation_dom(X3)
| ~ relation(X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,plain,
( in(ordered_pair(esk26_3(X3,X2,X1),X1),X3)
| ~ in(X1,X2)
| X2 != relation_rng(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,lemma,
~ in(X1,empty_set),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,plain,
( in(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,esk19_3(X2,X3,X1))),X2)
| X3 != relation_dom(X2)
| ~ relation(X2)
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc4_relat_1]) ).
fof(c_0_31,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
cnf(c_0_32,plain,
( in(unordered_pair(unordered_pair(esk26_3(X3,X2,X1),X1),unordered_pair(esk26_3(X3,X2,X1),esk26_3(X3,X2,X1))),X3)
| X2 != relation_rng(X3)
| ~ relation(X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_27,c_0_20]) ).
fof(c_0_33,negated_conjecture,
~ ( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ),
inference(assume_negation,[status(cth)],[t60_relat_1]) ).
cnf(c_0_34,lemma,
( X1 != relation_dom(empty_set)
| ~ in(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]) ).
fof(c_0_35,plain,
! [X48,X49,X50] :
( ( X48 != empty_set
| ~ in(X49,X48) )
& ( in(esk8_1(X50),X50)
| X50 = empty_set ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])])])]) ).
cnf(c_0_36,plain,
( in(unordered_pair(unordered_pair(X1,esk26_3(X2,X3,X1)),unordered_pair(esk26_3(X2,X3,X1),esk26_3(X2,X3,X1))),X2)
| X3 != relation_rng(X2)
| ~ relation(X2)
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[c_0_32,c_0_26]) ).
fof(c_0_37,negated_conjecture,
( relation_dom(empty_set) != empty_set
| relation_rng(empty_set) != empty_set ),
inference(fof_nnf,[status(thm)],[c_0_33]) ).
cnf(c_0_38,lemma,
~ in(X1,relation_dom(empty_set)),
inference(er,[status(thm)],[c_0_34]) ).
cnf(c_0_39,plain,
( in(esk8_1(X1),X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_40,lemma,
( X1 != relation_rng(empty_set)
| ~ in(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_36]),c_0_30])]) ).
cnf(c_0_41,negated_conjecture,
( relation_dom(empty_set) != empty_set
| relation_rng(empty_set) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_42,lemma,
relation_dom(empty_set) = empty_set,
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,lemma,
~ in(X1,relation_rng(empty_set)),
inference(er,[status(thm)],[c_0_40]) ).
cnf(c_0_44,negated_conjecture,
relation_rng(empty_set) != empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42])]) ).
cnf(c_0_45,lemma,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_39]),c_0_44]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU187+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n028.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 : Wed Aug 23 14:07:03 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 0.19/0.68 % Version : CSE_E---1.5
% 0.19/0.68 % Problem : theBenchmark.p
% 0.19/0.68 % Proof found
% 0.19/0.68 % SZS status Theorem for theBenchmark.p
% 0.19/0.68 % SZS output start Proof
% See solution above
% 0.19/0.68 % Total time : 0.107000 s
% 0.19/0.68 % SZS output end Proof
% 0.19/0.68 % Total time : 0.111000 s
%------------------------------------------------------------------------------