TSTP Solution File: SET935+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET935+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 : n025.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 14:36:21 EDT 2023
% Result : Theorem 0.18s 0.58s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 20
% Syntax : Number of formulae : 55 ( 16 unt; 12 typ; 0 def)
% Number of atoms : 120 ( 31 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 120 ( 43 ~; 55 |; 14 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 8 >; 7 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 76 ( 3 sgn; 44 !; 0 ?; 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,
powerset: $i > $i ).
tff(decl_26,type,
inclusion_comparable: ( $i * $i ) > $o ).
tff(decl_27,type,
empty: $i > $o ).
tff(decl_28,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_29,type,
esk2_3: ( $i * $i * $i ) > $i ).
tff(decl_30,type,
esk3_0: $i ).
tff(decl_31,type,
esk4_0: $i ).
tff(decl_32,type,
esk5_0: $i ).
tff(decl_33,type,
esk6_0: $i ).
fof(d1_zfmisc_1,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(t82_zfmisc_1,conjecture,
! [X1,X2] :
( set_union2(powerset(X1),powerset(X2)) = powerset(set_union2(X1,X2))
=> inclusion_comparable(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_zfmisc_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/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(t7_xboole_1,axiom,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(d10_xboole_0,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(d9_xboole_0,axiom,
! [X1,X2] :
( inclusion_comparable(X1,X2)
<=> ( subset(X1,X2)
| subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_xboole_0) ).
fof(c_0_8,plain,
! [X11,X12,X13,X14,X15,X16] :
( ( ~ in(X13,X12)
| subset(X13,X11)
| X12 != powerset(X11) )
& ( ~ subset(X14,X11)
| in(X14,X12)
| X12 != powerset(X11) )
& ( ~ in(esk1_2(X15,X16),X16)
| ~ subset(esk1_2(X15,X16),X15)
| X16 = powerset(X15) )
& ( in(esk1_2(X15,X16),X16)
| subset(esk1_2(X15,X16),X15)
| X16 = powerset(X15) ) ),
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)],[d1_zfmisc_1])])])])])]) ).
fof(c_0_9,negated_conjecture,
~ ! [X1,X2] :
( set_union2(powerset(X1),powerset(X2)) = powerset(set_union2(X1,X2))
=> inclusion_comparable(X1,X2) ),
inference(assume_negation,[status(cth)],[t82_zfmisc_1]) ).
fof(c_0_10,plain,
! [X18,X19,X20,X21,X22,X23,X24,X25] :
( ( ~ in(X21,X20)
| in(X21,X18)
| in(X21,X19)
| X20 != set_union2(X18,X19) )
& ( ~ in(X22,X18)
| in(X22,X20)
| X20 != set_union2(X18,X19) )
& ( ~ in(X22,X19)
| in(X22,X20)
| X20 != set_union2(X18,X19) )
& ( ~ in(esk2_3(X23,X24,X25),X23)
| ~ in(esk2_3(X23,X24,X25),X25)
| X25 = set_union2(X23,X24) )
& ( ~ in(esk2_3(X23,X24,X25),X24)
| ~ in(esk2_3(X23,X24,X25),X25)
| X25 = set_union2(X23,X24) )
& ( in(esk2_3(X23,X24,X25),X25)
| in(esk2_3(X23,X24,X25),X23)
| in(esk2_3(X23,X24,X25),X24)
| X25 = set_union2(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)],[d2_xboole_0])])])])])]) ).
cnf(c_0_11,plain,
( in(X1,X3)
| ~ subset(X1,X2)
| X3 != powerset(X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,negated_conjecture,
( set_union2(powerset(esk5_0),powerset(esk6_0)) = powerset(set_union2(esk5_0,esk6_0))
& ~ inclusion_comparable(esk5_0,esk6_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
cnf(c_0_13,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X2 != set_union2(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( in(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(er,[status(thm)],[c_0_11]) ).
cnf(c_0_15,negated_conjecture,
set_union2(powerset(esk5_0),powerset(esk6_0)) = powerset(set_union2(esk5_0,esk6_0)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( in(X1,X2)
| in(X1,X3)
| ~ in(X1,set_union2(X3,X2)) ),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_17,negated_conjecture,
( in(X1,set_union2(powerset(esk5_0),powerset(esk6_0)))
| ~ subset(X1,set_union2(esk5_0,esk6_0)) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
fof(c_0_18,plain,
! [X36] : subset(X36,X36),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_19,plain,
( subset(X1,X3)
| ~ in(X1,X2)
| X2 != powerset(X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_20,negated_conjecture,
( in(X1,powerset(esk5_0))
| in(X1,powerset(esk6_0))
| ~ subset(X1,set_union2(esk5_0,esk6_0)) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,plain,
( subset(X1,X2)
| ~ in(X1,powerset(X2)) ),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_23,negated_conjecture,
( in(set_union2(esk5_0,esk6_0),powerset(esk6_0))
| in(set_union2(esk5_0,esk6_0),powerset(esk5_0)) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
fof(c_0_24,plain,
! [X40,X41] : subset(X40,set_union2(X40,X41)),
inference(variable_rename,[status(thm)],[t7_xboole_1]) ).
fof(c_0_25,plain,
! [X7,X8] : set_union2(X7,X8) = set_union2(X8,X7),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(c_0_26,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_27,negated_conjecture,
( subset(set_union2(esk5_0,esk6_0),esk6_0)
| in(set_union2(esk5_0,esk6_0),powerset(esk5_0)) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,plain,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_30,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,negated_conjecture,
( subset(set_union2(esk5_0,esk6_0),esk6_0)
| subset(set_union2(esk5_0,esk6_0),esk5_0) ),
inference(spm,[status(thm)],[c_0_22,c_0_27]) ).
cnf(c_0_32,plain,
subset(X1,set_union2(X2,X1)),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
fof(c_0_33,plain,
! [X27,X28] :
( ( ~ inclusion_comparable(X27,X28)
| subset(X27,X28)
| subset(X28,X27) )
& ( ~ subset(X27,X28)
| inclusion_comparable(X27,X28) )
& ( ~ subset(X28,X27)
| inclusion_comparable(X27,X28) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d9_xboole_0])])]) ).
cnf(c_0_34,negated_conjecture,
( set_union2(esk5_0,esk6_0) = esk6_0
| subset(set_union2(esk5_0,esk6_0),esk5_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]) ).
cnf(c_0_35,negated_conjecture,
~ inclusion_comparable(esk5_0,esk6_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_36,plain,
( inclusion_comparable(X1,X2)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_37,negated_conjecture,
( set_union2(esk5_0,esk6_0) = esk6_0
| set_union2(esk5_0,esk6_0) = esk5_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_34]),c_0_28])]) ).
cnf(c_0_38,negated_conjecture,
~ subset(esk5_0,esk6_0),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,plain,
( inclusion_comparable(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_40,negated_conjecture,
set_union2(esk5_0,esk6_0) = esk5_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_37]),c_0_38]) ).
cnf(c_0_41,negated_conjecture,
~ subset(esk6_0,esk5_0),
inference(spm,[status(thm)],[c_0_35,c_0_39]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_40]),c_0_41]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET935+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Aug 26 09:54:07 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.18/0.56 start to proof: theBenchmark
% 0.18/0.58 % Version : CSE_E---1.5
% 0.18/0.58 % Problem : theBenchmark.p
% 0.18/0.58 % Proof found
% 0.18/0.58 % SZS status Theorem for theBenchmark.p
% 0.18/0.58 % SZS output start Proof
% See solution above
% 0.18/0.59 % Total time : 0.016000 s
% 0.18/0.59 % SZS output end Proof
% 0.18/0.59 % Total time : 0.019000 s
%------------------------------------------------------------------------------