TSTP Solution File: SEU107+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU107+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 : n003.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 16:22:27 EDT 2023
% Result : Theorem 0.23s 0.68s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 40
% Syntax : Number of formulae : 74 ( 18 unt; 31 typ; 0 def)
% Number of atoms : 106 ( 17 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 101 ( 38 ~; 37 |; 17 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 31 ( 25 >; 6 *; 0 +; 0 <<)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-3 aty)
% Number of variables : 59 ( 1 sgn; 35 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
empty: $i > $o ).
tff(decl_24,type,
finite: $i > $o ).
tff(decl_25,type,
preboolean: $i > $o ).
tff(decl_26,type,
cup_closed: $i > $o ).
tff(decl_27,type,
diff_closed: $i > $o ).
tff(decl_28,type,
powerset: $i > $i ).
tff(decl_29,type,
element: ( $i * $i ) > $o ).
tff(decl_30,type,
prebool_difference: ( $i * $i * $i ) > $i ).
tff(decl_31,type,
set_difference: ( $i * $i ) > $i ).
tff(decl_32,type,
empty_set: $i ).
tff(decl_33,type,
cap_closed: $i > $o ).
tff(decl_34,type,
relation: $i > $o ).
tff(decl_35,type,
function: $i > $o ).
tff(decl_36,type,
one_to_one: $i > $o ).
tff(decl_37,type,
epsilon_transitive: $i > $o ).
tff(decl_38,type,
epsilon_connected: $i > $o ).
tff(decl_39,type,
ordinal: $i > $o ).
tff(decl_40,type,
natural: $i > $o ).
tff(decl_41,type,
subset: ( $i * $i ) > $o ).
tff(decl_42,type,
esk1_1: $i > $i ).
tff(decl_43,type,
esk2_0: $i ).
tff(decl_44,type,
esk3_0: $i ).
tff(decl_45,type,
esk4_1: $i > $i ).
tff(decl_46,type,
esk5_0: $i ).
tff(decl_47,type,
esk6_1: $i > $i ).
tff(decl_48,type,
esk7_1: $i > $i ).
tff(decl_49,type,
esk8_0: $i ).
tff(decl_50,type,
esk9_1: $i > $i ).
tff(decl_51,type,
esk10_1: $i > $i ).
tff(decl_52,type,
esk11_0: $i ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(rc1_xboole_0,axiom,
? [X1] : empty(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(redefinition_k2_finsub_1,axiom,
! [X1,X2,X3] :
( ( ~ empty(X1)
& preboolean(X1)
& element(X2,X1)
& element(X3,X1) )
=> prebool_difference(X1,X2,X3) = set_difference(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_finsub_1) ).
fof(t37_xboole_1,axiom,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(dt_k2_finsub_1,axiom,
! [X1,X2,X3] :
( ( ~ empty(X1)
& preboolean(X1)
& element(X2,X1)
& element(X3,X1) )
=> element(prebool_difference(X1,X2,X3),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_finsub_1) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(t18_finsub_1,conjecture,
! [X1] :
( ( ~ empty(X1)
& preboolean(X1) )
=> in(empty_set,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_finsub_1) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(c_0_9,plain,
! [X54] :
( ~ empty(X54)
| X54 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(c_0_10,plain,
empty(esk5_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
fof(c_0_11,plain,
! [X1,X2,X3] :
( ( ~ empty(X1)
& preboolean(X1)
& element(X2,X1)
& element(X3,X1) )
=> prebool_difference(X1,X2,X3) = set_difference(X2,X3) ),
inference(fof_simplification,[status(thm)],[redefinition_k2_finsub_1]) ).
fof(c_0_12,plain,
! [X42,X43] :
( ( set_difference(X42,X43) != empty_set
| subset(X42,X43) )
& ( ~ subset(X42,X43)
| set_difference(X42,X43) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_xboole_1])]) ).
cnf(c_0_13,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
empty(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_15,plain,
! [X1,X2,X3] :
( ( ~ empty(X1)
& preboolean(X1)
& element(X2,X1)
& element(X3,X1) )
=> element(prebool_difference(X1,X2,X3),X1) ),
inference(fof_simplification,[status(thm)],[dt_k2_finsub_1]) ).
fof(c_0_16,plain,
! [X33,X34,X35] :
( empty(X33)
| ~ preboolean(X33)
| ~ element(X34,X33)
| ~ element(X35,X33)
| prebool_difference(X33,X34,X35) = set_difference(X34,X35) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])]) ).
fof(c_0_17,plain,
! [X14] : element(esk1_1(X14),X14),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
cnf(c_0_18,plain,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
empty_set = esk5_0,
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
fof(c_0_20,plain,
! [X36] : subset(X36,X36),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(c_0_21,plain,
! [X11,X12,X13] :
( empty(X11)
| ~ preboolean(X11)
| ~ element(X12,X11)
| ~ element(X13,X11)
| element(prebool_difference(X11,X12,X13),X11) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])]) ).
cnf(c_0_22,plain,
( empty(X1)
| prebool_difference(X1,X2,X3) = set_difference(X2,X3)
| ~ preboolean(X1)
| ~ element(X2,X1)
| ~ element(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
element(esk1_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
( set_difference(X1,X2) = esk5_0
| ~ subset(X1,X2) ),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_26,negated_conjecture,
~ ! [X1] :
( ( ~ empty(X1)
& preboolean(X1) )
=> in(empty_set,X1) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t18_finsub_1])]) ).
cnf(c_0_27,plain,
( empty(X1)
| element(prebool_difference(X1,X2,X3),X1)
| ~ preboolean(X1)
| ~ element(X2,X1)
| ~ element(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,plain,
( prebool_difference(X1,X2,esk1_1(X1)) = set_difference(X2,esk1_1(X1))
| empty(X1)
| ~ element(X2,X1)
| ~ preboolean(X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,plain,
set_difference(X1,X1) = esk5_0,
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
fof(c_0_30,negated_conjecture,
( ~ empty(esk11_0)
& preboolean(esk11_0)
& ~ in(empty_set,esk11_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])]) ).
cnf(c_0_31,plain,
( element(prebool_difference(X1,X2,esk1_1(X1)),X1)
| empty(X1)
| ~ element(X2,X1)
| ~ preboolean(X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_23]) ).
cnf(c_0_32,plain,
( prebool_difference(X1,esk1_1(X1),esk1_1(X1)) = esk5_0
| empty(X1)
| ~ preboolean(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_23]),c_0_29]) ).
cnf(c_0_33,negated_conjecture,
preboolean(esk11_0),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_34,negated_conjecture,
~ empty(esk11_0),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_35,plain,
! [X40,X41] :
( ~ element(X40,X41)
| empty(X41)
| in(X40,X41) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
cnf(c_0_36,plain,
( element(prebool_difference(X1,esk1_1(X1),esk1_1(X1)),X1)
| empty(X1)
| ~ preboolean(X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_23]) ).
cnf(c_0_37,negated_conjecture,
prebool_difference(esk11_0,esk1_1(esk11_0),esk1_1(esk11_0)) = esk5_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_38,negated_conjecture,
~ in(empty_set,esk11_0),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_39,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_40,negated_conjecture,
element(esk5_0,esk11_0),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_33]),c_0_37]),c_0_34]) ).
cnf(c_0_41,negated_conjecture,
~ in(esk5_0,esk11_0),
inference(rw,[status(thm)],[c_0_38,c_0_19]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_34]),c_0_41]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SEU107+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.15 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.15/0.36 % Computer : n003.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Wed Aug 23 18:17:52 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.23/0.60 start to proof: theBenchmark
% 0.23/0.68 % Version : CSE_E---1.5
% 0.23/0.68 % Problem : theBenchmark.p
% 0.23/0.68 % Proof found
% 0.23/0.68 % SZS status Theorem for theBenchmark.p
% 0.23/0.68 % SZS output start Proof
% See solution above
% 0.23/0.69 % Total time : 0.074000 s
% 0.23/0.69 % SZS output end Proof
% 0.23/0.69 % Total time : 0.077000 s
%------------------------------------------------------------------------------