TSTP Solution File: SET984+1 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET984+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 : n020.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 14:36:31 EDT 2023
% Result : Theorem 0.21s 0.62s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 18
% Syntax : Number of formulae : 52 ( 17 unt; 11 typ; 0 def)
% Number of atoms : 102 ( 80 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 84 ( 23 ~; 48 |; 8 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 4 >; 3 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 82 ( 12 sgn; 40 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
set_intersection2: ( $i * $i ) > $i ).
tff(decl_23,type,
empty_set: $i ).
tff(decl_24,type,
empty: $i > $o ).
tff(decl_25,type,
subset: ( $i * $i ) > $o ).
tff(decl_26,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(decl_27,type,
esk1_0: $i ).
tff(decl_28,type,
esk2_0: $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 ).
fof(t138_zfmisc_1,conjecture,
! [X1,X2,X3,X4] :
( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
=> ( cartesian_product2(X1,X2) = empty_set
| ( subset(X1,X3)
& subset(X2,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t138_zfmisc_1) ).
fof(t134_zfmisc_1,axiom,
! [X1,X2,X3,X4] :
( cartesian_product2(X1,X2) = cartesian_product2(X3,X4)
=> ( X1 = empty_set
| X2 = empty_set
| ( X1 = X3
& X2 = X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t134_zfmisc_1) ).
fof(t123_zfmisc_1,axiom,
! [X1,X2,X3,X4] : cartesian_product2(set_intersection2(X1,X2),set_intersection2(X3,X4)) = set_intersection2(cartesian_product2(X1,X3),cartesian_product2(X2,X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t123_zfmisc_1) ).
fof(t28_xboole_1,axiom,
! [X1,X2] :
( subset(X1,X2)
=> set_intersection2(X1,X2) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(t17_xboole_1,axiom,
! [X1,X2] : subset(set_intersection2(X1,X2),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
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(t113_zfmisc_1,axiom,
! [X1,X2] :
( cartesian_product2(X1,X2) = empty_set
<=> ( X1 = empty_set
| X2 = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_zfmisc_1) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
=> ( cartesian_product2(X1,X2) = empty_set
| ( subset(X1,X3)
& subset(X2,X4) ) ) ),
inference(assume_negation,[status(cth)],[t138_zfmisc_1]) ).
fof(c_0_8,plain,
! [X17,X18,X19,X20] :
( ( X17 = X19
| X17 = empty_set
| X18 = empty_set
| cartesian_product2(X17,X18) != cartesian_product2(X19,X20) )
& ( X18 = X20
| X17 = empty_set
| X18 = empty_set
| cartesian_product2(X17,X18) != cartesian_product2(X19,X20) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t134_zfmisc_1])])]) ).
fof(c_0_9,plain,
! [X13,X14,X15,X16] : cartesian_product2(set_intersection2(X13,X14),set_intersection2(X15,X16)) = set_intersection2(cartesian_product2(X13,X15),cartesian_product2(X14,X16)),
inference(variable_rename,[status(thm)],[t123_zfmisc_1]) ).
fof(c_0_10,plain,
! [X27,X28] :
( ~ subset(X27,X28)
| set_intersection2(X27,X28) = X27 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t28_xboole_1])]) ).
fof(c_0_11,negated_conjecture,
( subset(cartesian_product2(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0))
& cartesian_product2(esk3_0,esk4_0) != empty_set
& ( ~ subset(esk3_0,esk5_0)
| ~ subset(esk4_0,esk6_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
cnf(c_0_12,plain,
( X1 = X2
| X3 = empty_set
| X1 = empty_set
| cartesian_product2(X3,X1) != cartesian_product2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
cartesian_product2(set_intersection2(X1,X2),set_intersection2(X3,X4)) = set_intersection2(cartesian_product2(X1,X3),cartesian_product2(X2,X4)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
subset(cartesian_product2(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_16,plain,
! [X25,X26] : subset(set_intersection2(X25,X26),X25),
inference(variable_rename,[status(thm)],[t17_xboole_1]) ).
fof(c_0_17,plain,
! [X5,X6] : set_intersection2(X5,X6) = set_intersection2(X6,X5),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
cnf(c_0_18,plain,
( X1 = set_intersection2(X2,X3)
| X1 = empty_set
| X4 = empty_set
| cartesian_product2(X4,X1) != set_intersection2(cartesian_product2(X5,X2),cartesian_product2(X6,X3)) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_19,negated_conjecture,
set_intersection2(cartesian_product2(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0)) = cartesian_product2(esk3_0,esk4_0),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,plain,
( X1 = X2
| X1 = empty_set
| X3 = empty_set
| cartesian_product2(X1,X3) != cartesian_product2(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_21,plain,
subset(set_intersection2(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,negated_conjecture,
( X1 = set_intersection2(esk4_0,esk6_0)
| X2 = empty_set
| X1 = empty_set
| cartesian_product2(X2,X1) != cartesian_product2(esk3_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
( X1 = set_intersection2(X2,X3)
| X1 = empty_set
| X4 = empty_set
| cartesian_product2(X1,X4) != set_intersection2(cartesian_product2(X2,X5),cartesian_product2(X3,X6)) ),
inference(spm,[status(thm)],[c_0_20,c_0_13]) ).
cnf(c_0_25,plain,
subset(set_intersection2(X1,X2),X2),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,negated_conjecture,
( set_intersection2(esk4_0,esk6_0) = esk4_0
| esk4_0 = empty_set
| esk3_0 = empty_set ),
inference(er,[status(thm)],[c_0_23]) ).
cnf(c_0_27,negated_conjecture,
( X1 = set_intersection2(esk3_0,esk5_0)
| X2 = empty_set
| X1 = empty_set
| cartesian_product2(X1,X2) != cartesian_product2(esk3_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_24,c_0_19]) ).
cnf(c_0_28,negated_conjecture,
( ~ subset(esk3_0,esk5_0)
| ~ subset(esk4_0,esk6_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_29,negated_conjecture,
( esk3_0 = empty_set
| esk4_0 = empty_set
| subset(esk4_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
fof(c_0_30,plain,
! [X11,X12] :
( ( cartesian_product2(X11,X12) != empty_set
| X11 = empty_set
| X12 = empty_set )
& ( X11 != empty_set
| cartesian_product2(X11,X12) = empty_set )
& ( X12 != empty_set
| cartesian_product2(X11,X12) = empty_set ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t113_zfmisc_1])])]) ).
cnf(c_0_31,negated_conjecture,
( set_intersection2(esk3_0,esk5_0) = esk3_0
| esk3_0 = empty_set
| esk4_0 = empty_set ),
inference(er,[status(thm)],[c_0_27]) ).
cnf(c_0_32,negated_conjecture,
( esk4_0 = empty_set
| esk3_0 = empty_set
| ~ subset(esk3_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,plain,
( cartesian_product2(X2,X1) = empty_set
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_34,negated_conjecture,
cartesian_product2(esk3_0,esk4_0) != empty_set,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_35,negated_conjecture,
( esk4_0 = empty_set
| esk3_0 = empty_set ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_31]),c_0_32]) ).
cnf(c_0_36,plain,
cartesian_product2(X1,empty_set) = empty_set,
inference(er,[status(thm)],[c_0_33]) ).
cnf(c_0_37,plain,
( cartesian_product2(X1,X2) = empty_set
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_38,negated_conjecture,
esk3_0 = empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).
cnf(c_0_39,plain,
cartesian_product2(empty_set,X1) = empty_set,
inference(er,[status(thm)],[c_0_37]) ).
cnf(c_0_40,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_38]),c_0_39])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET984+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n020.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 11:05:45 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.58 start to proof: theBenchmark
% 0.21/0.62 % Version : CSE_E---1.5
% 0.21/0.62 % Problem : theBenchmark.p
% 0.21/0.62 % Proof found
% 0.21/0.62 % SZS status Theorem for theBenchmark.p
% 0.21/0.62 % SZS output start Proof
% See solution above
% 0.21/0.62 % Total time : 0.025000 s
% 0.21/0.62 % SZS output end Proof
% 0.21/0.62 % Total time : 0.027000 s
%------------------------------------------------------------------------------