TSTP Solution File: SEU143+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU143+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n032.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 16:22:44 EDT 2023
% Result : Theorem 0.15s 0.53s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 28
% Syntax : Number of formulae : 42 ( 11 unt; 24 typ; 0 def)
% Number of atoms : 48 ( 32 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 52 ( 22 ~; 20 |; 6 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 41 ( 20 >; 21 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 4 con; 0-3 aty)
% Number of variables : 33 ( 4 sgn; 23 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
proper_subset: ( $i * $i ) > $o ).
tff(decl_24,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_25,type,
set_union2: ( $i * $i ) > $i ).
tff(decl_26,type,
set_intersection2: ( $i * $i ) > $i ).
tff(decl_27,type,
subset: ( $i * $i ) > $o ).
tff(decl_28,type,
singleton: $i > $i ).
tff(decl_29,type,
empty_set: $i ).
tff(decl_30,type,
set_difference: ( $i * $i ) > $i ).
tff(decl_31,type,
disjoint: ( $i * $i ) > $o ).
tff(decl_32,type,
empty: $i > $o ).
tff(decl_33,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_34,type,
esk2_1: $i > $i ).
tff(decl_35,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_36,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_37,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_38,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_39,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_40,type,
esk8_0: $i ).
tff(decl_41,type,
esk9_0: $i ).
tff(decl_42,type,
esk10_0: $i ).
tff(decl_43,type,
esk11_2: ( $i * $i ) > $i ).
tff(decl_44,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_45,type,
esk13_2: ( $i * $i ) > $i ).
fof(l1_zfmisc_1,conjecture,
! [X1] : singleton(X1) != empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(d2_tarski,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(t69_enumset1,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(c_0_4,negated_conjecture,
~ ! [X1] : singleton(X1) != empty_set,
inference(assume_negation,[status(cth)],[l1_zfmisc_1]) ).
fof(c_0_5,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(c_0_6,plain,
! [X28,X29,X30,X31,X32,X33,X34,X35] :
( ( ~ in(X31,X30)
| X31 = X28
| X31 = X29
| X30 != unordered_pair(X28,X29) )
& ( X32 != X28
| in(X32,X30)
| X30 != unordered_pair(X28,X29) )
& ( X32 != X29
| in(X32,X30)
| X30 != unordered_pair(X28,X29) )
& ( esk3_3(X33,X34,X35) != X33
| ~ in(esk3_3(X33,X34,X35),X35)
| X35 = unordered_pair(X33,X34) )
& ( esk3_3(X33,X34,X35) != X34
| ~ in(esk3_3(X33,X34,X35),X35)
| X35 = unordered_pair(X33,X34) )
& ( in(esk3_3(X33,X34,X35),X35)
| esk3_3(X33,X34,X35) = X33
| esk3_3(X33,X34,X35) = X34
| X35 = unordered_pair(X33,X34) ) ),
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_tarski])])])])])]) ).
fof(c_0_7,negated_conjecture,
singleton(esk8_0) = empty_set,
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_8,lemma,
! [X145] : unordered_pair(X145,X145) = singleton(X145),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(c_0_9,plain,
! [X24,X25,X26] :
( ( X24 != empty_set
| ~ in(X25,X24) )
& ( in(esk2_1(X26),X26)
| X26 = 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_5])])])])]) ).
cnf(c_0_10,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,negated_conjecture,
singleton(esk8_0) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
in(X1,unordered_pair(X2,X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_10])]) ).
cnf(c_0_15,negated_conjecture,
unordered_pair(esk8_0,esk8_0) = empty_set,
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,plain,
~ in(X1,empty_set),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_17,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU143+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.11 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Thu Aug 24 01:45:11 EDT 2023
% 0.10/0.30 % CPUTime :
% 0.15/0.51 start to proof: theBenchmark
% 0.15/0.53 % Version : CSE_E---1.5
% 0.15/0.53 % Problem : theBenchmark.p
% 0.15/0.53 % Proof found
% 0.15/0.53 % SZS status Theorem for theBenchmark.p
% 0.15/0.53 % SZS output start Proof
% See solution above
% 0.15/0.53 % Total time : 0.011000 s
% 0.15/0.53 % SZS output end Proof
% 0.15/0.53 % Total time : 0.014000 s
%------------------------------------------------------------------------------