TSTP Solution File: SEU152+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU152+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 : n029.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 16:22:50 EDT 2023
% Result : Theorem 0.20s 0.61s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 32
% Syntax : Number of formulae : 49 ( 12 unt; 27 typ; 0 def)
% Number of atoms : 34 ( 15 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 23 ( 11 ~; 6 |; 2 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 44 ( 22 >; 22 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 5 con; 0-3 aty)
% Number of variables : 27 ( 0 sgn; 18 !; 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,
powerset: $i > $i ).
tff(decl_31,type,
set_difference: ( $i * $i ) > $i ).
tff(decl_32,type,
disjoint: ( $i * $i ) > $o ).
tff(decl_33,type,
empty: $i > $o ).
tff(decl_34,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_35,type,
esk2_1: $i > $i ).
tff(decl_36,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_37,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_38,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_39,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_40,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_41,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_42,type,
esk9_0: $i ).
tff(decl_43,type,
esk10_0: $i ).
tff(decl_44,type,
esk11_0: $i ).
tff(decl_45,type,
esk12_0: $i ).
tff(decl_46,type,
esk13_2: ( $i * $i ) > $i ).
tff(decl_47,type,
esk14_2: ( $i * $i ) > $i ).
tff(decl_48,type,
esk15_2: ( $i * $i ) > $i ).
fof(l23_zfmisc_1,conjecture,
! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l23_zfmisc_1) ).
fof(l2_zfmisc_1,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_zfmisc_1) ).
fof(t69_enumset1,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
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(t12_xboole_1,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
inference(assume_negation,[status(cth)],[l23_zfmisc_1]) ).
fof(c_0_6,lemma,
! [X91,X92] :
( ( ~ subset(singleton(X91),X92)
| in(X91,X92) )
& ( ~ in(X91,X92)
| subset(singleton(X91),X92) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l2_zfmisc_1])]) ).
fof(c_0_7,lemma,
! [X165] : unordered_pair(X165,X165) = singleton(X165),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(c_0_8,negated_conjecture,
( in(esk9_0,esk10_0)
& set_union2(singleton(esk9_0),esk10_0) != esk10_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
cnf(c_0_9,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
set_union2(singleton(esk9_0),esk10_0) != esk10_0,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,plain,
! [X11,X12] : set_union2(X11,X12) = set_union2(X12,X11),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(c_0_13,lemma,
! [X109,X110] :
( ~ subset(X109,X110)
| set_union2(X109,X110) = X110 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_xboole_1])]) ).
cnf(c_0_14,lemma,
( subset(unordered_pair(X1,X1),X2)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,negated_conjecture,
in(esk9_0,esk10_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,negated_conjecture,
set_union2(unordered_pair(esk9_0,esk9_0),esk10_0) != esk10_0,
inference(rw,[status(thm)],[c_0_11,c_0_10]) ).
cnf(c_0_17,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,lemma,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,negated_conjecture,
subset(unordered_pair(esk9_0,esk9_0),esk10_0),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,negated_conjecture,
set_union2(esk10_0,unordered_pair(esk9_0,esk9_0)) != esk10_0,
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,lemma,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_17]),c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU152+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n029.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 : Wed Aug 23 17:25:37 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 0.20/0.61 % Version : CSE_E---1.5
% 0.20/0.61 % Problem : theBenchmark.p
% 0.20/0.61 % Proof found
% 0.20/0.61 % SZS status Theorem for theBenchmark.p
% 0.20/0.61 % SZS output start Proof
% See solution above
% 0.20/0.62 % Total time : 0.023000 s
% 0.20/0.62 % SZS output end Proof
% 0.20/0.62 % Total time : 0.027000 s
%------------------------------------------------------------------------------