TSTP Solution File: SEU119+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU119+2 : 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 : n001.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 16:22:31 EDT 2023
% Result : Theorem 0.17s 0.59s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 16
% Syntax : Number of formulae : 52 ( 5 unt; 12 typ; 0 def)
% Number of atoms : 131 ( 32 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 153 ( 62 ~; 63 |; 23 &)
% ( 5 <=>; 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 : 11 ( 6 >; 5 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-3 aty)
% Number of variables : 80 ( 6 sgn; 30 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
set_intersection2: ( $i * $i ) > $i ).
tff(decl_24,type,
empty_set: $i ).
tff(decl_25,type,
disjoint: ( $i * $i ) > $o ).
tff(decl_26,type,
empty: $i > $o ).
tff(decl_27,type,
esk1_1: $i > $i ).
tff(decl_28,type,
esk2_3: ( $i * $i * $i ) > $i ).
tff(decl_29,type,
esk3_0: $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(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(t3_xboole_0,conjecture,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] :
~ ( in(X3,X1)
& in(X3,X2) ) )
& ~ ( ? [X3] :
( in(X3,X1)
& in(X3,X2) )
& disjoint(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
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(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_4,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(c_0_5,plain,
! [X9,X10,X11] :
( ( X9 != empty_set
| ~ in(X10,X9) )
& ( in(esk1_1(X11),X11)
| X11 = 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_4])])])])]) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] :
~ ( in(X3,X1)
& in(X3,X2) ) )
& ~ ( ? [X3] :
( in(X3,X1)
& in(X3,X2) )
& disjoint(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t3_xboole_0])]) ).
cnf(c_0_7,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_8,plain,
! [X13,X14,X15,X16,X17,X18,X19,X20] :
( ( in(X16,X13)
| ~ in(X16,X15)
| X15 != set_intersection2(X13,X14) )
& ( in(X16,X14)
| ~ in(X16,X15)
| X15 != set_intersection2(X13,X14) )
& ( ~ in(X17,X13)
| ~ in(X17,X14)
| in(X17,X15)
| X15 != set_intersection2(X13,X14) )
& ( ~ in(esk2_3(X18,X19,X20),X20)
| ~ in(esk2_3(X18,X19,X20),X18)
| ~ in(esk2_3(X18,X19,X20),X19)
| X20 = set_intersection2(X18,X19) )
& ( in(esk2_3(X18,X19,X20),X18)
| in(esk2_3(X18,X19,X20),X20)
| X20 = set_intersection2(X18,X19) )
& ( in(esk2_3(X18,X19,X20),X19)
| in(esk2_3(X18,X19,X20),X20)
| X20 = set_intersection2(X18,X19) ) ),
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])])])])])]) ).
fof(c_0_9,negated_conjecture,
! [X31] :
( ( in(esk7_0,esk5_0)
| ~ disjoint(esk5_0,esk6_0) )
& ( in(esk7_0,esk6_0)
| ~ disjoint(esk5_0,esk6_0) )
& ( disjoint(esk5_0,esk6_0)
| ~ disjoint(esk5_0,esk6_0) )
& ( in(esk7_0,esk5_0)
| ~ in(X31,esk5_0)
| ~ in(X31,esk6_0) )
& ( in(esk7_0,esk6_0)
| ~ in(X31,esk5_0)
| ~ in(X31,esk6_0) )
& ( disjoint(esk5_0,esk6_0)
| ~ in(X31,esk5_0)
| ~ in(X31,esk6_0) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])]) ).
cnf(c_0_10,plain,
~ in(X1,empty_set),
inference(er,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( in(esk2_3(X1,X2,X3),X2)
| in(esk2_3(X1,X2,X3),X3)
| X3 = set_intersection2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
( disjoint(esk5_0,esk6_0)
| ~ in(X1,esk5_0)
| ~ in(X1,esk6_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( set_intersection2(X1,X2) = empty_set
| in(esk2_3(X1,X2,empty_set),X2) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
( in(esk2_3(X1,X2,X3),X1)
| in(esk2_3(X1,X2,X3),X3)
| X3 = set_intersection2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_16,plain,
! [X22,X23] :
( ( ~ disjoint(X22,X23)
| set_intersection2(X22,X23) = empty_set )
& ( set_intersection2(X22,X23) != empty_set
| disjoint(X22,X23) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_xboole_0])]) ).
cnf(c_0_17,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X3,X2)) ),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( in(esk1_1(X1),X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_19,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_20,plain,
( in(X1,X4)
| ~ in(X1,X2)
| ~ in(X1,X3)
| X4 != set_intersection2(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_21,negated_conjecture,
( set_intersection2(X1,esk6_0) = empty_set
| disjoint(esk5_0,esk6_0)
| ~ in(esk2_3(X1,esk6_0,empty_set),esk5_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_22,plain,
( set_intersection2(X1,X2) = empty_set
| in(esk2_3(X1,X2,empty_set),X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_15]) ).
cnf(c_0_23,plain,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,negated_conjecture,
( in(esk7_0,esk6_0)
| ~ in(X1,esk5_0)
| ~ in(X1,esk6_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_25,plain,
( set_intersection2(X1,X2) = empty_set
| in(esk1_1(set_intersection2(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_26,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X2,X3)) ),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_27,negated_conjecture,
( in(esk7_0,esk6_0)
| ~ disjoint(esk5_0,esk6_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_28,plain,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_29,negated_conjecture,
( in(esk7_0,esk5_0)
| ~ disjoint(esk5_0,esk6_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_30,plain,
( in(X1,set_intersection2(X2,X3))
| ~ in(X1,X3)
| ~ in(X1,X2) ),
inference(er,[status(thm)],[c_0_20]) ).
cnf(c_0_31,negated_conjecture,
set_intersection2(esk5_0,esk6_0) = empty_set,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_32,negated_conjecture,
( set_intersection2(X1,esk6_0) = empty_set
| in(esk7_0,esk6_0)
| ~ in(esk1_1(set_intersection2(X1,esk6_0)),esk5_0) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_33,plain,
( set_intersection2(X1,X2) = empty_set
| in(esk1_1(set_intersection2(X1,X2)),X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_18]) ).
cnf(c_0_34,negated_conjecture,
( in(esk7_0,esk6_0)
| set_intersection2(esk5_0,esk6_0) != empty_set ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_35,negated_conjecture,
( in(esk7_0,esk5_0)
| set_intersection2(esk5_0,esk6_0) != empty_set ),
inference(spm,[status(thm)],[c_0_29,c_0_28]) ).
cnf(c_0_36,negated_conjecture,
( ~ in(X1,esk6_0)
| ~ in(X1,esk5_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_10]) ).
cnf(c_0_37,negated_conjecture,
in(esk7_0,esk6_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_38,negated_conjecture,
in(esk7_0,esk5_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_31])]) ).
cnf(c_0_39,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU119+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.33 % Computer : n001.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Thu Aug 24 01:51:10 EDT 2023
% 0.17/0.33 % CPUTime :
% 0.17/0.57 start to proof: theBenchmark
% 0.17/0.59 % Version : CSE_E---1.5
% 0.17/0.59 % Problem : theBenchmark.p
% 0.17/0.59 % Proof found
% 0.17/0.59 % SZS status Theorem for theBenchmark.p
% 0.17/0.59 % SZS output start Proof
% See solution above
% 0.17/0.60 % Total time : 0.010000 s
% 0.17/0.60 % SZS output end Proof
% 0.17/0.60 % Total time : 0.012000 s
%------------------------------------------------------------------------------