TSTP Solution File: SET945+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET945+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n005.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 14:36:23 EDT 2023
% Result : Theorem 0.19s 0.57s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 19
% Syntax : Number of formulae : 50 ( 2 unt; 14 typ; 0 def)
% Number of atoms : 130 ( 19 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 162 ( 68 ~; 65 |; 20 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 10 >; 10 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 102 ( 5 sgn; 45 !; 3 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
set_intersection2: ( $i * $i ) > $i ).
tff(decl_24,type,
union: $i > $i ).
tff(decl_25,type,
empty: $i > $o ).
tff(decl_26,type,
disjoint: ( $i * $i ) > $o ).
tff(decl_27,type,
esk1_3: ( $i * $i * $i ) > $i ).
tff(decl_28,type,
esk2_3: ( $i * $i * $i ) > $i ).
tff(decl_29,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_30,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_31,type,
esk5_0: $i ).
tff(decl_32,type,
esk6_0: $i ).
tff(decl_33,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_34,type,
esk8_0: $i ).
tff(decl_35,type,
esk9_0: $i ).
fof(t4_xboole_0,axiom,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
& ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
& disjoint(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_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(t98_zfmisc_1,conjecture,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
=> disjoint(X3,X2) )
=> disjoint(union(X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t98_zfmisc_1) ).
fof(symmetry_r1_xboole_0,axiom,
! [X1,X2] :
( disjoint(X1,X2)
=> disjoint(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_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/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
fof(c_0_5,plain,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
& ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
& disjoint(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[t4_xboole_0]) ).
fof(c_0_6,plain,
! [X9,X10,X11,X12,X13,X14,X15,X16] :
( ( in(X12,X9)
| ~ in(X12,X11)
| X11 != set_intersection2(X9,X10) )
& ( in(X12,X10)
| ~ in(X12,X11)
| X11 != set_intersection2(X9,X10) )
& ( ~ in(X13,X9)
| ~ in(X13,X10)
| in(X13,X11)
| X11 != set_intersection2(X9,X10) )
& ( ~ in(esk1_3(X14,X15,X16),X16)
| ~ in(esk1_3(X14,X15,X16),X14)
| ~ in(esk1_3(X14,X15,X16),X15)
| X16 = set_intersection2(X14,X15) )
& ( in(esk1_3(X14,X15,X16),X14)
| in(esk1_3(X14,X15,X16),X16)
| X16 = set_intersection2(X14,X15) )
& ( in(esk1_3(X14,X15,X16),X15)
| in(esk1_3(X14,X15,X16),X16)
| X16 = set_intersection2(X14,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)],[d3_xboole_0])])])])])]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2] :
( ! [X3] :
( in(X3,X1)
=> disjoint(X3,X2) )
=> disjoint(union(X1),X2) ),
inference(assume_negation,[status(cth)],[t98_zfmisc_1]) ).
fof(c_0_8,plain,
! [X34,X35,X37,X38,X39] :
( ( disjoint(X34,X35)
| in(esk7_2(X34,X35),set_intersection2(X34,X35)) )
& ( ~ in(X39,set_intersection2(X37,X38))
| ~ disjoint(X37,X38) ) ),
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_9,plain,
( in(X1,X4)
| ~ in(X1,X2)
| ~ in(X1,X3)
| X4 != set_intersection2(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_10,plain,
! [X32,X33] :
( ~ disjoint(X32,X33)
| disjoint(X33,X32) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0])]) ).
fof(c_0_11,negated_conjecture,
! [X42] :
( ( ~ in(X42,esk8_0)
| disjoint(X42,esk9_0) )
& ~ disjoint(union(esk8_0),esk9_0) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
cnf(c_0_12,plain,
( ~ in(X1,set_intersection2(X2,X3))
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( in(X1,set_intersection2(X2,X3))
| ~ in(X1,X3)
| ~ in(X1,X2) ),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( disjoint(X2,X1)
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
( disjoint(X1,esk9_0)
| ~ in(X1,esk8_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_17,plain,
( ~ disjoint(X1,X2)
| ~ in(X3,X2)
| ~ in(X3,X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,negated_conjecture,
( disjoint(esk9_0,X1)
| ~ in(X1,esk8_0) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X3,X2)) ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_20,plain,
( disjoint(X1,X2)
| in(esk7_2(X1,X2),set_intersection2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_21,plain,
! [X18,X19,X20,X22,X23,X24,X25,X27] :
( ( in(X20,esk2_3(X18,X19,X20))
| ~ in(X20,X19)
| X19 != union(X18) )
& ( in(esk2_3(X18,X19,X20),X18)
| ~ in(X20,X19)
| X19 != union(X18) )
& ( ~ in(X22,X23)
| ~ in(X23,X18)
| in(X22,X19)
| X19 != union(X18) )
& ( ~ in(esk3_2(X24,X25),X25)
| ~ in(esk3_2(X24,X25),X27)
| ~ in(X27,X24)
| X25 = union(X24) )
& ( in(esk3_2(X24,X25),esk4_2(X24,X25))
| in(esk3_2(X24,X25),X25)
| X25 = union(X24) )
& ( in(esk4_2(X24,X25),X24)
| in(esk3_2(X24,X25),X25)
| X25 = union(X24) ) ),
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_22,negated_conjecture,
( ~ in(X1,esk9_0)
| ~ in(X2,esk8_0)
| ~ in(X1,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
( disjoint(X1,X2)
| in(esk7_2(X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
( in(X1,esk2_3(X2,X3,X1))
| ~ in(X1,X3)
| X3 != union(X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_25,negated_conjecture,
( disjoint(X1,esk9_0)
| ~ in(esk7_2(X1,esk9_0),X2)
| ~ in(X2,esk8_0) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,plain,
( in(X1,esk2_3(X2,union(X2),X1))
| ~ in(X1,union(X2)) ),
inference(er,[status(thm)],[c_0_24]) ).
cnf(c_0_27,plain,
( in(esk2_3(X1,X2,X3),X1)
| ~ in(X3,X2)
| X2 != union(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_29,negated_conjecture,
( disjoint(X1,esk9_0)
| ~ in(esk2_3(X2,union(X2),esk7_2(X1,esk9_0)),esk8_0)
| ~ in(esk7_2(X1,esk9_0),union(X2)) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,plain,
( in(esk2_3(X1,union(X1),X2),X1)
| ~ in(X2,union(X1)) ),
inference(er,[status(thm)],[c_0_27]) ).
cnf(c_0_31,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X2,X3)) ),
inference(er,[status(thm)],[c_0_28]) ).
cnf(c_0_32,negated_conjecture,
( disjoint(X1,esk9_0)
| ~ in(esk7_2(X1,esk9_0),union(esk8_0)) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,plain,
( disjoint(X1,X2)
| in(esk7_2(X1,X2),X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_20]) ).
cnf(c_0_34,negated_conjecture,
~ disjoint(union(esk8_0),esk9_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
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
% 0.00/0.12 % Problem : SET945+1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33 % Computer : n005.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Aug 26 10:07:38 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.19/0.54 start to proof: theBenchmark
% 0.19/0.57 % Version : CSE_E---1.5
% 0.19/0.57 % Problem : theBenchmark.p
% 0.19/0.57 % Proof found
% 0.19/0.57 % SZS status Theorem for theBenchmark.p
% 0.19/0.57 % SZS output start Proof
% See solution above
% 0.19/0.58 % Total time : 0.025000 s
% 0.19/0.58 % SZS output end Proof
% 0.19/0.58 % Total time : 0.028000 s
%------------------------------------------------------------------------------