TSTP Solution File: SET867+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET867+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 : 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 14:36:04 EDT 2023
% Result : Theorem 0.20s 0.59s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 13
% Syntax : Number of formulae : 25 ( 6 unt; 10 typ; 0 def)
% Number of atoms : 47 ( 17 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 55 ( 23 ~; 21 |; 7 &)
% ( 4 <=>; 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 : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 29 ( 3 sgn; 18 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
empty_set: $i ).
tff(decl_24,type,
union: $i > $i ).
tff(decl_25,type,
empty: $i > $o ).
tff(decl_26,type,
esk1_1: $i > $i ).
tff(decl_27,type,
esk2_3: ( $i * $i * $i ) > $i ).
tff(decl_28,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_29,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_30,type,
esk5_0: $i ).
tff(decl_31,type,
esk6_0: $i ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_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/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
fof(t2_zfmisc_1,conjecture,
union(empty_set) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_zfmisc_1) ).
fof(c_0_3,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(c_0_4,plain,
! [X7,X8,X9] :
( ( X7 != empty_set
| ~ in(X8,X7) )
& ( in(esk1_1(X9),X9)
| X9 = 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_3])])])])]) ).
fof(c_0_5,plain,
! [X11,X12,X13,X15,X16,X17,X18,X20] :
( ( in(X13,esk2_3(X11,X12,X13))
| ~ in(X13,X12)
| X12 != union(X11) )
& ( in(esk2_3(X11,X12,X13),X11)
| ~ in(X13,X12)
| X12 != union(X11) )
& ( ~ in(X15,X16)
| ~ in(X16,X11)
| in(X15,X12)
| X12 != union(X11) )
& ( ~ in(esk3_2(X17,X18),X18)
| ~ in(esk3_2(X17,X18),X20)
| ~ in(X20,X17)
| X18 = union(X17) )
& ( in(esk3_2(X17,X18),esk4_2(X17,X18))
| in(esk3_2(X17,X18),X18)
| X18 = union(X17) )
& ( in(esk4_2(X17,X18),X17)
| in(esk3_2(X17,X18),X18)
| X18 = union(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)],[d4_tarski])])])])])]) ).
cnf(c_0_6,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,plain,
( in(esk2_3(X1,X2,X3),X1)
| ~ in(X3,X2)
| X2 != union(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
~ in(X1,empty_set),
inference(er,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
( in(esk2_3(X1,union(X1),X2),X1)
| ~ in(X2,union(X1)) ),
inference(er,[status(thm)],[c_0_7]) ).
fof(c_0_10,negated_conjecture,
union(empty_set) != empty_set,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t2_zfmisc_1])]) ).
cnf(c_0_11,plain,
~ in(X1,union(empty_set)),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,plain,
( in(esk1_1(X1),X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_13,negated_conjecture,
union(empty_set) != empty_set,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET867+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 : 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 : Sat Aug 26 15:13:07 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 0.20/0.59 % Version : CSE_E---1.5
% 0.20/0.59 % Problem : theBenchmark.p
% 0.20/0.59 % Proof found
% 0.20/0.59 % SZS status Theorem for theBenchmark.p
% 0.20/0.59 % SZS output start Proof
% See solution above
% 0.20/0.59 % Total time : 0.007000 s
% 0.20/0.59 % SZS output end Proof
% 0.20/0.59 % Total time : 0.010000 s
%------------------------------------------------------------------------------