TSTP Solution File: SET943+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET943+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n005.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 14:36:23 EDT 2023
% Result : Theorem 222.47s 222.70s
% Output : CNFRefutation 222.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 23
% Syntax : Number of formulae : 75 ( 17 unt; 14 typ; 0 def)
% Number of atoms : 180 ( 32 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 216 ( 97 ~; 93 |; 17 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 10 >; 10 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 121 ( 6 sgn; 57 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
set_union2: ( $i * $i ) > $i ).
tff(decl_24,type,
subset: ( $i * $i ) > $o ).
tff(decl_25,type,
union: $i > $i ).
tff(decl_26,type,
empty: $i > $o ).
tff(decl_27,type,
esk1_3: ( $i * $i * $i ) > $i ).
tff(decl_28,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_29,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_30,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_31,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_32,type,
esk6_0: $i ).
tff(decl_33,type,
esk7_0: $i ).
tff(decl_34,type,
esk8_0: $i ).
tff(decl_35,type,
esk9_0: $i ).
fof(t96_zfmisc_1,conjecture,
! [X1,X2] : union(set_union2(X1,X2)) = set_union2(union(X1),union(X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t96_zfmisc_1) ).
fof(d10_xboole_0,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
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(d4_tarski,axiom,
! [X1,X2] :
( X2 = union(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X3,X4)
& in(X4,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
fof(t8_xboole_1,axiom,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X3,X2) )
=> subset(set_union2(X1,X3),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_xboole_1) ).
fof(t7_xboole_1,axiom,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(t95_zfmisc_1,axiom,
! [X1,X2] :
( subset(X1,X2)
=> subset(union(X1),union(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t95_zfmisc_1) ).
fof(c_0_9,negated_conjecture,
~ ! [X1,X2] : union(set_union2(X1,X2)) = set_union2(union(X1),union(X2)),
inference(assume_negation,[status(cth)],[t96_zfmisc_1]) ).
fof(c_0_10,negated_conjecture,
union(set_union2(esk8_0,esk9_0)) != set_union2(union(esk8_0),union(esk9_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
fof(c_0_11,plain,
! [X9,X10] :
( ( subset(X9,X10)
| X9 != X10 )
& ( subset(X10,X9)
| X9 != X10 )
& ( ~ subset(X9,X10)
| ~ subset(X10,X9)
| X9 = X10 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])]) ).
cnf(c_0_12,negated_conjecture,
union(set_union2(esk8_0,esk9_0)) != set_union2(union(esk8_0),union(esk9_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_14,plain,
! [X20,X21,X22,X23,X24] :
( ( ~ subset(X20,X21)
| ~ in(X22,X20)
| in(X22,X21) )
& ( in(esk2_2(X23,X24),X23)
| subset(X23,X24) )
& ( ~ in(esk2_2(X23,X24),X24)
| subset(X23,X24) ) ),
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_tarski])])])])])]) ).
fof(c_0_15,plain,
! [X11,X12,X13,X14,X15,X16,X17,X18] :
( ( ~ in(X14,X13)
| in(X14,X11)
| in(X14,X12)
| X13 != set_union2(X11,X12) )
& ( ~ in(X15,X11)
| in(X15,X13)
| X13 != set_union2(X11,X12) )
& ( ~ in(X15,X12)
| in(X15,X13)
| X13 != set_union2(X11,X12) )
& ( ~ in(esk1_3(X16,X17,X18),X16)
| ~ in(esk1_3(X16,X17,X18),X18)
| X18 = set_union2(X16,X17) )
& ( ~ in(esk1_3(X16,X17,X18),X17)
| ~ in(esk1_3(X16,X17,X18),X18)
| X18 = set_union2(X16,X17) )
& ( in(esk1_3(X16,X17,X18),X18)
| in(esk1_3(X16,X17,X18),X16)
| in(esk1_3(X16,X17,X18),X17)
| X18 = set_union2(X16,X17) ) ),
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])])])])])]) ).
cnf(c_0_16,negated_conjecture,
( ~ subset(union(set_union2(esk8_0,esk9_0)),set_union2(union(esk8_0),union(esk9_0)))
| ~ subset(set_union2(union(esk8_0),union(esk9_0)),union(set_union2(esk8_0,esk9_0))) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13])]) ).
cnf(c_0_17,plain,
( subset(X1,X2)
| ~ in(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_19,plain,
! [X26,X27,X28,X30,X31,X32,X33,X35] :
( ( in(X28,esk3_3(X26,X27,X28))
| ~ in(X28,X27)
| X27 != union(X26) )
& ( in(esk3_3(X26,X27,X28),X26)
| ~ in(X28,X27)
| X27 != union(X26) )
& ( ~ in(X30,X31)
| ~ in(X31,X26)
| in(X30,X27)
| X27 != union(X26) )
& ( ~ in(esk4_2(X32,X33),X33)
| ~ in(esk4_2(X32,X33),X35)
| ~ in(X35,X32)
| X33 = union(X32) )
& ( in(esk4_2(X32,X33),esk5_2(X32,X33))
| in(esk4_2(X32,X33),X33)
| X33 = union(X32) )
& ( in(esk5_2(X32,X33),X32)
| in(esk4_2(X32,X33),X33)
| X33 = union(X32) ) ),
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_tarski])])])])])]) ).
cnf(c_0_20,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,negated_conjecture,
( ~ subset(set_union2(union(esk8_0),union(esk9_0)),union(set_union2(esk8_0,esk9_0)))
| ~ in(esk2_2(union(set_union2(esk8_0,esk9_0)),set_union2(union(esk8_0),union(esk9_0))),set_union2(union(esk8_0),union(esk9_0))) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X2) ),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
( in(X1,X4)
| ~ in(X1,X2)
| ~ in(X2,X3)
| X4 != union(X3) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,plain,
( in(esk2_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_25,plain,
! [X47,X48,X49] :
( ~ subset(X47,X48)
| ~ subset(X49,X48)
| subset(set_union2(X47,X49),X48) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_xboole_1])]) ).
fof(c_0_26,plain,
! [X45,X46] : subset(X45,set_union2(X45,X46)),
inference(variable_rename,[status(thm)],[t7_xboole_1]) ).
fof(c_0_27,plain,
! [X7,X8] : set_union2(X7,X8) = set_union2(X8,X7),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
cnf(c_0_28,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[c_0_20]) ).
cnf(c_0_29,negated_conjecture,
( ~ subset(set_union2(union(esk8_0),union(esk9_0)),union(set_union2(esk8_0,esk9_0)))
| ~ in(esk2_2(union(set_union2(esk8_0,esk9_0)),set_union2(union(esk8_0),union(esk9_0))),union(esk8_0)) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_30,plain,
( in(X1,union(X2))
| ~ in(X3,X2)
| ~ in(X1,X3) ),
inference(er,[status(thm)],[c_0_23]) ).
cnf(c_0_31,negated_conjecture,
( in(esk2_2(union(set_union2(esk8_0,esk9_0)),set_union2(union(esk8_0),union(esk9_0))),union(set_union2(esk8_0,esk9_0)))
| ~ subset(set_union2(union(esk8_0),union(esk9_0)),union(set_union2(esk8_0,esk9_0))) ),
inference(spm,[status(thm)],[c_0_16,c_0_24]) ).
cnf(c_0_32,plain,
( subset(set_union2(X1,X3),X2)
| ~ subset(X1,X2)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_33,plain,
! [X50,X51] :
( ~ subset(X50,X51)
| subset(union(X50),union(X51)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t95_zfmisc_1])]) ).
cnf(c_0_34,plain,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_35,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_36,negated_conjecture,
( ~ subset(set_union2(union(esk8_0),union(esk9_0)),union(set_union2(esk8_0,esk9_0)))
| ~ in(esk2_2(union(set_union2(esk8_0,esk9_0)),set_union2(union(esk8_0),union(esk9_0))),union(esk9_0)) ),
inference(spm,[status(thm)],[c_0_21,c_0_28]) ).
cnf(c_0_37,negated_conjecture,
( ~ subset(set_union2(union(esk8_0),union(esk9_0)),union(set_union2(esk8_0,esk9_0)))
| ~ in(esk2_2(union(set_union2(esk8_0,esk9_0)),set_union2(union(esk8_0),union(esk9_0))),X1)
| ~ in(X1,esk8_0) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_38,negated_conjecture,
( in(esk2_2(union(set_union2(esk8_0,esk9_0)),set_union2(union(esk8_0),union(esk9_0))),union(set_union2(esk8_0,esk9_0)))
| ~ subset(union(esk9_0),union(set_union2(esk8_0,esk9_0)))
| ~ subset(union(esk8_0),union(set_union2(esk8_0,esk9_0))) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_39,plain,
( subset(union(X1),union(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_40,plain,
subset(X1,set_union2(X2,X1)),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,negated_conjecture,
( ~ subset(set_union2(union(esk8_0),union(esk9_0)),union(set_union2(esk8_0,esk9_0)))
| ~ in(esk2_2(union(set_union2(esk8_0,esk9_0)),set_union2(union(esk8_0),union(esk9_0))),X1)
| ~ in(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_36,c_0_30]) ).
cnf(c_0_42,negated_conjecture,
( ~ subset(union(esk9_0),union(set_union2(esk8_0,esk9_0)))
| ~ subset(union(esk8_0),union(set_union2(esk8_0,esk9_0)))
| ~ in(esk2_2(union(set_union2(esk8_0,esk9_0)),set_union2(union(esk8_0),union(esk9_0))),X1)
| ~ in(X1,esk8_0) ),
inference(spm,[status(thm)],[c_0_37,c_0_32]) ).
cnf(c_0_43,plain,
( in(X1,esk3_3(X2,X3,X1))
| ~ in(X1,X3)
| X3 != union(X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_44,negated_conjecture,
( in(esk2_2(union(set_union2(esk8_0,esk9_0)),set_union2(union(esk8_0),union(esk9_0))),union(set_union2(esk8_0,esk9_0)))
| ~ subset(union(esk8_0),union(set_union2(esk8_0,esk9_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40])]) ).
cnf(c_0_45,negated_conjecture,
( ~ subset(union(esk9_0),union(set_union2(esk8_0,esk9_0)))
| ~ subset(union(esk8_0),union(set_union2(esk8_0,esk9_0)))
| ~ in(esk2_2(union(set_union2(esk8_0,esk9_0)),set_union2(union(esk8_0),union(esk9_0))),X1)
| ~ in(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_41,c_0_32]) ).
cnf(c_0_46,plain,
( in(esk3_3(X1,X2,X3),X1)
| ~ in(X3,X2)
| X2 != union(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_47,negated_conjecture,
( ~ subset(union(esk8_0),union(set_union2(esk8_0,esk9_0)))
| ~ in(esk2_2(union(set_union2(esk8_0,esk9_0)),set_union2(union(esk8_0),union(esk9_0))),X1)
| ~ in(X1,esk8_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_39]),c_0_40])]) ).
cnf(c_0_48,plain,
( in(X1,esk3_3(X2,union(X2),X1))
| ~ in(X1,union(X2)) ),
inference(er,[status(thm)],[c_0_43]) ).
cnf(c_0_49,negated_conjecture,
in(esk2_2(union(set_union2(esk8_0,esk9_0)),set_union2(union(esk8_0),union(esk9_0))),union(set_union2(esk8_0,esk9_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_39]),c_0_34])]) ).
cnf(c_0_50,negated_conjecture,
( ~ subset(union(esk8_0),union(set_union2(esk8_0,esk9_0)))
| ~ in(esk2_2(union(set_union2(esk8_0,esk9_0)),set_union2(union(esk8_0),union(esk9_0))),X1)
| ~ in(X1,esk9_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_39]),c_0_40])]) ).
cnf(c_0_51,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X2 != set_union2(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_52,plain,
( in(esk3_3(X1,union(X1),X2),X1)
| ~ in(X2,union(X1)) ),
inference(er,[status(thm)],[c_0_46]) ).
cnf(c_0_53,negated_conjecture,
( ~ in(esk2_2(union(set_union2(esk8_0,esk9_0)),set_union2(union(esk8_0),union(esk9_0))),X1)
| ~ in(X1,esk8_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_39]),c_0_34])]) ).
cnf(c_0_54,negated_conjecture,
in(esk2_2(union(set_union2(esk8_0,esk9_0)),set_union2(union(esk8_0),union(esk9_0))),esk3_3(set_union2(esk8_0,esk9_0),union(set_union2(esk8_0,esk9_0)),esk2_2(union(set_union2(esk8_0,esk9_0)),set_union2(union(esk8_0),union(esk9_0))))),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_55,negated_conjecture,
( ~ in(esk2_2(union(set_union2(esk8_0,esk9_0)),set_union2(union(esk8_0),union(esk9_0))),X1)
| ~ in(X1,esk9_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_39]),c_0_34])]) ).
cnf(c_0_56,plain,
( in(X1,X2)
| in(X1,X3)
| ~ in(X1,set_union2(X3,X2)) ),
inference(er,[status(thm)],[c_0_51]) ).
cnf(c_0_57,negated_conjecture,
in(esk3_3(set_union2(esk8_0,esk9_0),union(set_union2(esk8_0,esk9_0)),esk2_2(union(set_union2(esk8_0,esk9_0)),set_union2(union(esk8_0),union(esk9_0)))),set_union2(esk8_0,esk9_0)),
inference(spm,[status(thm)],[c_0_52,c_0_49]) ).
cnf(c_0_58,negated_conjecture,
~ in(esk3_3(set_union2(esk8_0,esk9_0),union(set_union2(esk8_0,esk9_0)),esk2_2(union(set_union2(esk8_0,esk9_0)),set_union2(union(esk8_0),union(esk9_0)))),esk8_0),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_59,negated_conjecture,
~ in(esk3_3(set_union2(esk8_0,esk9_0),union(set_union2(esk8_0,esk9_0)),esk2_2(union(set_union2(esk8_0,esk9_0)),set_union2(union(esk8_0),union(esk9_0)))),esk9_0),
inference(spm,[status(thm)],[c_0_55,c_0_54]) ).
cnf(c_0_60,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]),c_0_59]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SET943+1 : TPTP v8.1.2. Released v3.2.0.
% 0.10/0.11 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.11/0.32 % Computer : n005.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sat Aug 26 12:40:23 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.17/0.55 start to proof: theBenchmark
% 222.47/222.70 % Version : CSE_E---1.5
% 222.47/222.70 % Problem : theBenchmark.p
% 222.47/222.70 % Proof found
% 222.47/222.70 % SZS status Theorem for theBenchmark.p
% 222.47/222.70 % SZS output start Proof
% See solution above
% 222.47/222.71 % Total time : 221.911000 s
% 222.47/222.71 % SZS output end Proof
% 222.47/222.71 % Total time : 221.924000 s
%------------------------------------------------------------------------------