TSTP Solution File: SET908+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET908+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 : 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 14:36:13 EDT 2023
% Result : Theorem 0.20s 0.58s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 17
% Syntax : Number of formulae : 35 ( 12 unt; 12 typ; 0 def)
% Number of atoms : 69 ( 33 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 78 ( 32 ~; 31 |; 9 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 7 >; 5 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 53 ( 5 sgn; 36 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
set_union2: ( $i * $i ) > $i ).
tff(decl_24,type,
singleton: $i > $i ).
tff(decl_25,type,
empty_set: $i ).
tff(decl_26,type,
empty: $i > $o ).
tff(decl_27,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_28,type,
esk2_1: $i > $i ).
tff(decl_29,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_30,type,
esk4_0: $i ).
tff(decl_31,type,
esk5_0: $i ).
tff(decl_32,type,
esk6_0: $i ).
tff(decl_33,type,
esk7_0: $i ).
fof(t49_zfmisc_1,conjecture,
! [X1,X2] : set_union2(singleton(X1),X2) != empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_zfmisc_1) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
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(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(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2] : set_union2(singleton(X1),X2) != empty_set,
inference(assume_negation,[status(cth)],[t49_zfmisc_1]) ).
fof(c_0_6,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(c_0_7,plain,
! [X20,X21,X22,X23,X24,X25,X26,X27] :
( ( ~ in(X23,X22)
| in(X23,X20)
| in(X23,X21)
| X22 != set_union2(X20,X21) )
& ( ~ in(X24,X20)
| in(X24,X22)
| X22 != set_union2(X20,X21) )
& ( ~ in(X24,X21)
| in(X24,X22)
| X22 != set_union2(X20,X21) )
& ( ~ in(esk3_3(X25,X26,X27),X25)
| ~ in(esk3_3(X25,X26,X27),X27)
| X27 = set_union2(X25,X26) )
& ( ~ in(esk3_3(X25,X26,X27),X26)
| ~ in(esk3_3(X25,X26,X27),X27)
| X27 = set_union2(X25,X26) )
& ( in(esk3_3(X25,X26,X27),X27)
| in(esk3_3(X25,X26,X27),X25)
| in(esk3_3(X25,X26,X27),X26)
| X27 = set_union2(X25,X26) ) ),
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_8,negated_conjecture,
set_union2(singleton(esk6_0),esk7_0) = empty_set,
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_9,plain,
! [X7,X8] : set_union2(X7,X8) = set_union2(X8,X7),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(c_0_10,plain,
! [X16,X17,X18] :
( ( X16 != empty_set
| ~ in(X17,X16) )
& ( in(esk2_1(X18),X18)
| X18 = 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_6])])])])]) ).
cnf(c_0_11,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
set_union2(singleton(esk6_0),esk7_0) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_15,plain,
! [X9,X10,X11,X12,X13,X14] :
( ( ~ in(X11,X10)
| X11 = X9
| X10 != singleton(X9) )
& ( X12 != X9
| in(X12,X10)
| X10 != singleton(X9) )
& ( ~ in(esk1_2(X13,X14),X14)
| esk1_2(X13,X14) != X13
| X14 = singleton(X13) )
& ( in(esk1_2(X13,X14),X14)
| esk1_2(X13,X14) = X13
| X14 = singleton(X13) ) ),
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_tarski])])])])])]) ).
cnf(c_0_16,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
set_union2(esk7_0,singleton(esk6_0)) = empty_set,
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,plain,
~ in(X1,empty_set),
inference(er,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
( in(X1,X3)
| X1 != X2
| X3 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,negated_conjecture,
~ in(X1,singleton(esk6_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
cnf(c_0_21,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_19])]) ).
cnf(c_0_22,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_20,c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET908+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n027.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 : Sat Aug 26 13:58:05 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 0.20/0.58 % Version : CSE_E---1.5
% 0.20/0.58 % Problem : theBenchmark.p
% 0.20/0.58 % Proof found
% 0.20/0.58 % SZS status Theorem for theBenchmark.p
% 0.20/0.58 % SZS output start Proof
% See solution above
% 0.20/0.58 % Total time : 0.007000 s
% 0.20/0.58 % SZS output end Proof
% 0.20/0.58 % Total time : 0.009000 s
%------------------------------------------------------------------------------