TSTP Solution File: SEU154+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU154+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n010.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 16:22:51 EDT 2023
% Result : Theorem 0.17s 0.57s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 22
% Syntax : Number of formulae : 50 ( 10 unt; 14 typ; 0 def)
% Number of atoms : 110 ( 37 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 117 ( 43 ~; 48 |; 16 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 9 >; 8 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 83 ( 4 sgn; 47 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
set_intersection2: ( $i * $i ) > $i ).
tff(decl_24,type,
subset: ( $i * $i ) > $o ).
tff(decl_25,type,
singleton: $i > $i ).
tff(decl_26,type,
disjoint: ( $i * $i ) > $o ).
tff(decl_27,type,
empty_set: $i ).
tff(decl_28,type,
empty: $i > $o ).
tff(decl_29,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_30,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_31,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_32,type,
esk4_0: $i ).
tff(decl_33,type,
esk5_0: $i ).
tff(decl_34,type,
esk6_0: $i ).
tff(decl_35,type,
esk7_0: $i ).
fof(d3_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
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(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(d10_xboole_0,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(t2_xboole_1,axiom,
! [X1] : subset(empty_set,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(l28_zfmisc_1,conjecture,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l28_zfmisc_1) ).
fof(d7_xboole_0,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_intersection2(X1,X2) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(c_0_8,plain,
! [X24,X25,X26,X27,X28,X29,X30,X31] :
( ( in(X27,X24)
| ~ in(X27,X26)
| X26 != set_intersection2(X24,X25) )
& ( in(X27,X25)
| ~ in(X27,X26)
| X26 != set_intersection2(X24,X25) )
& ( ~ in(X28,X24)
| ~ in(X28,X25)
| in(X28,X26)
| X26 != set_intersection2(X24,X25) )
& ( ~ in(esk3_3(X29,X30,X31),X31)
| ~ in(esk3_3(X29,X30,X31),X29)
| ~ in(esk3_3(X29,X30,X31),X30)
| X31 = set_intersection2(X29,X30) )
& ( in(esk3_3(X29,X30,X31),X29)
| in(esk3_3(X29,X30,X31),X31)
| X31 = set_intersection2(X29,X30) )
& ( in(esk3_3(X29,X30,X31),X30)
| in(esk3_3(X29,X30,X31),X31)
| X31 = set_intersection2(X29,X30) ) ),
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)],[d3_xboole_0])])])])])]) ).
cnf(c_0_9,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_10,plain,
! [X18,X19,X20,X21,X22] :
( ( ~ subset(X18,X19)
| ~ in(X20,X18)
| in(X20,X19) )
& ( in(esk2_2(X21,X22),X21)
| subset(X21,X22) )
& ( ~ in(esk2_2(X21,X22),X22)
| subset(X21,X22) ) ),
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)],[d3_tarski])])])])])]) ).
fof(c_0_11,plain,
! [X11,X12,X13,X14,X15,X16] :
( ( ~ in(X13,X12)
| X13 = X11
| X12 != singleton(X11) )
& ( X14 != X11
| in(X14,X12)
| X12 != singleton(X11) )
& ( ~ in(esk1_2(X15,X16),X16)
| esk1_2(X15,X16) != X15
| X16 = singleton(X15) )
& ( in(esk1_2(X15,X16),X16)
| esk1_2(X15,X16) = X15
| X16 = singleton(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_tarski])])])])])]) ).
cnf(c_0_12,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X3,X2)) ),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( in(esk2_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_14,plain,
! [X7,X8] : set_intersection2(X7,X8) = set_intersection2(X8,X7),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
cnf(c_0_15,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_16,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])])]) ).
fof(c_0_17,plain,
! [X43] : subset(empty_set,X43),
inference(variable_rename,[status(thm)],[t2_xboole_1]) ).
cnf(c_0_18,plain,
( subset(set_intersection2(X1,X2),X3)
| in(esk2_2(set_intersection2(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_19,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
( X1 = X2
| ~ in(X1,singleton(X2)) ),
inference(er,[status(thm)],[c_0_15]) ).
fof(c_0_21,negated_conjecture,
~ ! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[l28_zfmisc_1])]) ).
cnf(c_0_22,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
( subset(set_intersection2(X1,X2),X3)
| in(esk2_2(set_intersection2(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,plain,
( esk2_2(set_intersection2(X1,singleton(X2)),X3) = X2
| subset(set_intersection2(X1,singleton(X2)),X3) ),
inference(spm,[status(thm)],[c_0_20,c_0_18]) ).
fof(c_0_26,negated_conjecture,
( ~ in(esk4_0,esk5_0)
& ~ disjoint(singleton(esk4_0),esk5_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])]) ).
fof(c_0_27,plain,
! [X33,X34] :
( ( ~ disjoint(X33,X34)
| set_intersection2(X33,X34) = empty_set )
& ( set_intersection2(X33,X34) != empty_set
| disjoint(X33,X34) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_xboole_0])]) ).
cnf(c_0_28,plain,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,plain,
( subset(set_intersection2(X1,singleton(X2)),X3)
| in(X2,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,negated_conjecture,
~ disjoint(singleton(esk4_0),esk5_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,plain,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_32,negated_conjecture,
~ in(esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,plain,
( set_intersection2(X1,singleton(X2)) = empty_set
| in(X2,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,negated_conjecture,
set_intersection2(esk5_0,singleton(esk4_0)) != empty_set,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_19]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU154+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.11 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.11/0.31 % Computer : n010.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Wed Aug 23 16:12:51 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.17/0.55 start to proof: theBenchmark
% 0.17/0.57 % Version : CSE_E---1.5
% 0.17/0.57 % Problem : theBenchmark.p
% 0.17/0.57 % Proof found
% 0.17/0.57 % SZS status Theorem for theBenchmark.p
% 0.17/0.57 % SZS output start Proof
% See solution above
% 0.17/0.57 % Total time : 0.011000 s
% 0.17/0.57 % SZS output end Proof
% 0.17/0.57 % Total time : 0.013000 s
%------------------------------------------------------------------------------