TSTP Solution File: SEU109+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU109+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n027.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 16:22:28 EDT 2023
% Result : Theorem 113.50s 113.52s
% Output : CNFRefutation 113.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 43
% Syntax : Number of formulae : 99 ( 19 unt; 36 typ; 0 def)
% Number of atoms : 191 ( 14 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 212 ( 84 ~; 74 |; 43 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 37 ( 29 >; 8 *; 0 +; 0 <<)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 7 con; 0-3 aty)
% Number of variables : 84 ( 11 sgn; 34 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
empty: $i > $o ).
tff(decl_24,type,
finite: $i > $o ).
tff(decl_25,type,
preboolean: $i > $o ).
tff(decl_26,type,
cup_closed: $i > $o ).
tff(decl_27,type,
diff_closed: $i > $o ).
tff(decl_28,type,
powerset: $i > $i ).
tff(decl_29,type,
element: ( $i * $i ) > $o ).
tff(decl_30,type,
set_union2: ( $i * $i ) > $i ).
tff(decl_31,type,
set_intersection2: ( $i * $i ) > $i ).
tff(decl_32,type,
set_difference: ( $i * $i ) > $i ).
tff(decl_33,type,
empty_set: $i ).
tff(decl_34,type,
cap_closed: $i > $o ).
tff(decl_35,type,
relation: $i > $o ).
tff(decl_36,type,
function: $i > $o ).
tff(decl_37,type,
one_to_one: $i > $o ).
tff(decl_38,type,
epsilon_transitive: $i > $o ).
tff(decl_39,type,
epsilon_connected: $i > $o ).
tff(decl_40,type,
ordinal: $i > $o ).
tff(decl_41,type,
natural: $i > $o ).
tff(decl_42,type,
subset: ( $i * $i ) > $o ).
tff(decl_43,type,
esk1_3: ( $i * $i * $i ) > $i ).
tff(decl_44,type,
esk2_1: $i > $i ).
tff(decl_45,type,
esk3_0: $i ).
tff(decl_46,type,
esk4_0: $i ).
tff(decl_47,type,
esk5_1: $i > $i ).
tff(decl_48,type,
esk6_0: $i ).
tff(decl_49,type,
esk7_1: $i > $i ).
tff(decl_50,type,
esk8_1: $i > $i ).
tff(decl_51,type,
esk9_0: $i ).
tff(decl_52,type,
esk10_1: $i > $i ).
tff(decl_53,type,
esk11_1: $i > $i ).
tff(decl_54,type,
esk12_1: $i > $i ).
tff(decl_55,type,
esk13_1: $i > $i ).
tff(decl_56,type,
esk14_0: $i ).
tff(decl_57,type,
esk15_0: $i ).
fof(t21_finsub_1,conjecture,
! [X1] :
( ( ~ empty(X1)
& preboolean(X1) )
=> ! [X2] :
( ( ~ empty(X2)
& preboolean(X2) )
=> ( ~ empty(set_intersection2(X1,X2))
& preboolean(set_intersection2(X1,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_finsub_1) ).
fof(t10_finsub_1,axiom,
! [X1] :
( preboolean(X1)
<=> ! [X2,X3] :
( ( in(X2,X1)
& in(X3,X1) )
=> ( in(set_union2(X2,X3),X1)
& in(set_difference(X2,X3),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_finsub_1) ).
fof(t18_finsub_1,axiom,
! [X1] :
( ( ~ empty(X1)
& preboolean(X1) )
=> in(empty_set,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_finsub_1) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(d3_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(rc2_finset_1,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2)
& relation(X2)
& function(X2)
& one_to_one(X2)
& epsilon_transitive(X2)
& epsilon_connected(X2)
& ordinal(X2)
& natural(X2)
& finite(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_finset_1) ).
fof(c_0_7,negated_conjecture,
~ ! [X1] :
( ( ~ empty(X1)
& preboolean(X1) )
=> ! [X2] :
( ( ~ empty(X2)
& preboolean(X2) )
=> ( ~ empty(set_intersection2(X1,X2))
& preboolean(set_intersection2(X1,X2)) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t21_finsub_1])]) ).
fof(c_0_8,negated_conjecture,
( ~ empty(esk14_0)
& preboolean(esk14_0)
& ~ empty(esk15_0)
& preboolean(esk15_0)
& ( empty(set_intersection2(esk14_0,esk15_0))
| ~ preboolean(set_intersection2(esk14_0,esk15_0)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
fof(c_0_9,plain,
! [X58,X59,X60,X61] :
( ( in(set_union2(X59,X60),X58)
| ~ in(X59,X58)
| ~ in(X60,X58)
| ~ preboolean(X58) )
& ( in(set_difference(X59,X60),X58)
| ~ in(X59,X58)
| ~ in(X60,X58)
| ~ preboolean(X58) )
& ( in(esk12_1(X61),X61)
| preboolean(X61) )
& ( in(esk13_1(X61),X61)
| preboolean(X61) )
& ( ~ in(set_union2(esk12_1(X61),esk13_1(X61)),X61)
| ~ in(set_difference(esk12_1(X61),esk13_1(X61)),X61)
| preboolean(X61) ) ),
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)],[t10_finsub_1])])])])])]) ).
fof(c_0_10,plain,
! [X1] :
( ( ~ empty(X1)
& preboolean(X1) )
=> in(empty_set,X1) ),
inference(fof_simplification,[status(thm)],[t18_finsub_1]) ).
fof(c_0_11,plain,
! [X84,X85] :
( ~ in(X84,X85)
| ~ empty(X85) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
cnf(c_0_12,negated_conjecture,
( empty(set_intersection2(esk14_0,esk15_0))
| ~ preboolean(set_intersection2(esk14_0,esk15_0)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( in(esk12_1(X1),X1)
| preboolean(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_14,plain,
! [X16,X17,X18,X19,X20,X21,X22,X23] :
( ( in(X19,X16)
| ~ in(X19,X18)
| X18 != set_intersection2(X16,X17) )
& ( in(X19,X17)
| ~ in(X19,X18)
| X18 != set_intersection2(X16,X17) )
& ( ~ in(X20,X16)
| ~ in(X20,X17)
| in(X20,X18)
| X18 != set_intersection2(X16,X17) )
& ( ~ in(esk1_3(X21,X22,X23),X23)
| ~ in(esk1_3(X21,X22,X23),X21)
| ~ in(esk1_3(X21,X22,X23),X22)
| X23 = set_intersection2(X21,X22) )
& ( in(esk1_3(X21,X22,X23),X21)
| in(esk1_3(X21,X22,X23),X23)
| X23 = set_intersection2(X21,X22) )
& ( in(esk1_3(X21,X22,X23),X22)
| in(esk1_3(X21,X22,X23),X23)
| X23 = set_intersection2(X21,X22) ) ),
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)],[d3_xboole_0])])])])])]) ).
fof(c_0_15,plain,
! [X64] :
( empty(X64)
| ~ preboolean(X64)
| in(empty_set,X64) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])]) ).
fof(c_0_16,plain,
! [X83] :
( ~ empty(X83)
| X83 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(c_0_17,plain,
! [X48] :
( element(esk7_1(X48),powerset(X48))
& empty(esk7_1(X48))
& relation(esk7_1(X48))
& function(esk7_1(X48))
& one_to_one(esk7_1(X48))
& epsilon_transitive(esk7_1(X48))
& epsilon_connected(esk7_1(X48))
& ordinal(esk7_1(X48))
& natural(esk7_1(X48))
& finite(esk7_1(X48)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_finset_1])]) ).
cnf(c_0_18,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,negated_conjecture,
( empty(set_intersection2(esk14_0,esk15_0))
| in(esk12_1(set_intersection2(esk14_0,esk15_0)),set_intersection2(esk14_0,esk15_0)) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_20,plain,
( in(X1,X4)
| ~ in(X1,X2)
| ~ in(X1,X3)
| X4 != set_intersection2(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
( empty(X1)
| in(empty_set,X1)
| ~ preboolean(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,negated_conjecture,
preboolean(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_23,negated_conjecture,
~ empty(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_24,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,plain,
empty(esk7_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,negated_conjecture,
preboolean(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_27,negated_conjecture,
~ empty(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_28,plain,
( in(esk13_1(X1),X1)
| preboolean(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_29,negated_conjecture,
( in(esk12_1(set_intersection2(esk14_0,esk15_0)),set_intersection2(esk14_0,esk15_0))
| ~ in(X1,set_intersection2(esk14_0,esk15_0)) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_30,plain,
( in(X1,set_intersection2(X2,X3))
| ~ in(X1,X3)
| ~ in(X1,X2) ),
inference(er,[status(thm)],[c_0_20]) ).
cnf(c_0_31,negated_conjecture,
in(empty_set,esk15_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_32,plain,
esk7_1(X1) = empty_set,
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_33,negated_conjecture,
in(empty_set,esk14_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_26]),c_0_27]) ).
cnf(c_0_34,negated_conjecture,
( empty(set_intersection2(esk14_0,esk15_0))
| in(esk13_1(set_intersection2(esk14_0,esk15_0)),set_intersection2(esk14_0,esk15_0)) ),
inference(spm,[status(thm)],[c_0_12,c_0_28]) ).
cnf(c_0_35,negated_conjecture,
( in(esk12_1(set_intersection2(esk14_0,esk15_0)),set_intersection2(esk14_0,esk15_0))
| ~ in(X1,esk15_0)
| ~ in(X1,esk14_0) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_36,negated_conjecture,
in(esk7_1(X1),esk15_0),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,negated_conjecture,
in(esk7_1(X1),esk14_0),
inference(spm,[status(thm)],[c_0_33,c_0_32]) ).
cnf(c_0_38,plain,
( preboolean(X1)
| ~ in(set_union2(esk12_1(X1),esk13_1(X1)),X1)
| ~ in(set_difference(esk12_1(X1),esk13_1(X1)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_39,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_40,negated_conjecture,
( in(esk13_1(set_intersection2(esk14_0,esk15_0)),set_intersection2(esk14_0,esk15_0))
| ~ in(X1,set_intersection2(esk14_0,esk15_0)) ),
inference(spm,[status(thm)],[c_0_18,c_0_34]) ).
cnf(c_0_41,negated_conjecture,
in(esk12_1(set_intersection2(esk14_0,esk15_0)),set_intersection2(esk14_0,esk15_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37])]) ).
cnf(c_0_42,negated_conjecture,
( ~ in(set_union2(esk12_1(set_intersection2(esk14_0,esk15_0)),esk13_1(set_intersection2(esk14_0,esk15_0))),set_intersection2(esk14_0,esk15_0))
| ~ in(set_difference(esk12_1(set_intersection2(esk14_0,esk15_0)),esk13_1(set_intersection2(esk14_0,esk15_0))),set_intersection2(esk14_0,esk15_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_38]),c_0_18]) ).
cnf(c_0_43,plain,
( in(set_difference(X1,X2),X3)
| ~ in(X1,X3)
| ~ in(X2,X3)
| ~ preboolean(X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_44,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X3,X2)) ),
inference(er,[status(thm)],[c_0_39]) ).
cnf(c_0_45,negated_conjecture,
in(esk13_1(set_intersection2(esk14_0,esk15_0)),set_intersection2(esk14_0,esk15_0)),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_46,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_47,negated_conjecture,
( ~ in(set_union2(esk12_1(set_intersection2(esk14_0,esk15_0)),esk13_1(set_intersection2(esk14_0,esk15_0))),set_intersection2(esk14_0,esk15_0))
| ~ in(set_difference(esk12_1(set_intersection2(esk14_0,esk15_0)),esk13_1(set_intersection2(esk14_0,esk15_0))),esk15_0)
| ~ in(set_difference(esk12_1(set_intersection2(esk14_0,esk15_0)),esk13_1(set_intersection2(esk14_0,esk15_0))),esk14_0) ),
inference(spm,[status(thm)],[c_0_42,c_0_30]) ).
cnf(c_0_48,negated_conjecture,
( in(set_difference(X1,X2),esk15_0)
| ~ in(X2,esk15_0)
| ~ in(X1,esk15_0) ),
inference(spm,[status(thm)],[c_0_43,c_0_22]) ).
cnf(c_0_49,negated_conjecture,
in(esk13_1(set_intersection2(esk14_0,esk15_0)),esk15_0),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_50,negated_conjecture,
in(esk12_1(set_intersection2(esk14_0,esk15_0)),esk15_0),
inference(spm,[status(thm)],[c_0_44,c_0_41]) ).
cnf(c_0_51,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X2,X3)) ),
inference(er,[status(thm)],[c_0_46]) ).
cnf(c_0_52,negated_conjecture,
( ~ in(set_union2(esk12_1(set_intersection2(esk14_0,esk15_0)),esk13_1(set_intersection2(esk14_0,esk15_0))),set_intersection2(esk14_0,esk15_0))
| ~ in(set_difference(esk12_1(set_intersection2(esk14_0,esk15_0)),esk13_1(set_intersection2(esk14_0,esk15_0))),esk14_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]),c_0_50])]) ).
cnf(c_0_53,negated_conjecture,
( in(set_difference(X1,X2),esk14_0)
| ~ in(X2,esk14_0)
| ~ in(X1,esk14_0) ),
inference(spm,[status(thm)],[c_0_43,c_0_26]) ).
cnf(c_0_54,negated_conjecture,
in(esk13_1(set_intersection2(esk14_0,esk15_0)),esk14_0),
inference(spm,[status(thm)],[c_0_51,c_0_45]) ).
cnf(c_0_55,negated_conjecture,
in(esk12_1(set_intersection2(esk14_0,esk15_0)),esk14_0),
inference(spm,[status(thm)],[c_0_51,c_0_41]) ).
cnf(c_0_56,negated_conjecture,
~ in(set_union2(esk12_1(set_intersection2(esk14_0,esk15_0)),esk13_1(set_intersection2(esk14_0,esk15_0))),set_intersection2(esk14_0,esk15_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]),c_0_55])]) ).
cnf(c_0_57,plain,
( in(set_union2(X1,X2),X3)
| ~ in(X1,X3)
| ~ in(X2,X3)
| ~ preboolean(X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_58,negated_conjecture,
( ~ in(set_union2(esk12_1(set_intersection2(esk14_0,esk15_0)),esk13_1(set_intersection2(esk14_0,esk15_0))),esk15_0)
| ~ in(set_union2(esk12_1(set_intersection2(esk14_0,esk15_0)),esk13_1(set_intersection2(esk14_0,esk15_0))),esk14_0) ),
inference(spm,[status(thm)],[c_0_56,c_0_30]) ).
cnf(c_0_59,negated_conjecture,
( in(set_union2(X1,X2),esk15_0)
| ~ in(X2,esk15_0)
| ~ in(X1,esk15_0) ),
inference(spm,[status(thm)],[c_0_57,c_0_22]) ).
cnf(c_0_60,negated_conjecture,
~ in(set_union2(esk12_1(set_intersection2(esk14_0,esk15_0)),esk13_1(set_intersection2(esk14_0,esk15_0))),esk14_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_49]),c_0_50])]) ).
cnf(c_0_61,negated_conjecture,
( in(set_union2(X1,X2),esk14_0)
| ~ in(X2,esk14_0)
| ~ in(X1,esk14_0) ),
inference(spm,[status(thm)],[c_0_57,c_0_26]) ).
cnf(c_0_62,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_54]),c_0_55])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU109+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n027.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 12:51:31 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 113.50/113.52 % Version : CSE_E---1.5
% 113.50/113.52 % Problem : theBenchmark.p
% 113.50/113.52 % Proof found
% 113.50/113.52 % SZS status Theorem for theBenchmark.p
% 113.50/113.52 % SZS output start Proof
% See solution above
% 113.50/113.53 % Total time : 112.935000 s
% 113.50/113.53 % SZS output end Proof
% 113.50/113.53 % Total time : 112.943000 s
%------------------------------------------------------------------------------