TSTP Solution File: SEU110+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU110+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 : n026.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 16:22:28 EDT 2023
% Result : Theorem 0.69s 0.84s
% Output : CNFRefutation 0.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 38
% Syntax : Number of formulae : 62 ( 6 unt; 33 typ; 0 def)
% Number of atoms : 96 ( 10 equ)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 109 ( 42 ~; 49 |; 10 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 31 ( 26 >; 5 *; 0 +; 0 <<)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 7 con; 0-2 aty)
% Number of variables : 57 ( 3 sgn; 27 !; 0 ?; 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,
finite_subsets: $i > $i ).
tff(decl_31,type,
subset: ( $i * $i ) > $o ).
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,
esk1_2: ( $i * $i ) > $i ).
tff(decl_42,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_43,type,
esk3_1: $i > $i ).
tff(decl_44,type,
esk4_0: $i ).
tff(decl_45,type,
esk5_0: $i ).
tff(decl_46,type,
esk6_1: $i > $i ).
tff(decl_47,type,
esk7_0: $i ).
tff(decl_48,type,
esk8_1: $i > $i ).
tff(decl_49,type,
esk9_1: $i > $i ).
tff(decl_50,type,
esk10_0: $i ).
tff(decl_51,type,
esk11_1: $i > $i ).
tff(decl_52,type,
esk12_1: $i > $i ).
tff(decl_53,type,
esk13_0: $i ).
tff(decl_54,type,
esk14_0: $i ).
fof(t23_finsub_1,conjecture,
! [X1,X2] :
( subset(X1,X2)
=> subset(finite_subsets(X1),finite_subsets(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_finsub_1) ).
fof(d5_finsub_1,axiom,
! [X1,X2] :
( preboolean(X2)
=> ( X2 = finite_subsets(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( subset(X3,X1)
& finite(X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_finsub_1) ).
fof(dt_k5_finsub_1,axiom,
! [X1] : preboolean(finite_subsets(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_finsub_1) ).
fof(t1_xboole_1,axiom,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
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(c_0_5,negated_conjecture,
~ ! [X1,X2] :
( subset(X1,X2)
=> subset(finite_subsets(X1),finite_subsets(X2)) ),
inference(assume_negation,[status(cth)],[t23_finsub_1]) ).
fof(c_0_6,plain,
! [X19,X20,X21,X22] :
( ( subset(X21,X19)
| ~ in(X21,X20)
| X20 != finite_subsets(X19)
| ~ preboolean(X20) )
& ( finite(X21)
| ~ in(X21,X20)
| X20 != finite_subsets(X19)
| ~ preboolean(X20) )
& ( ~ subset(X22,X19)
| ~ finite(X22)
| in(X22,X20)
| X20 != finite_subsets(X19)
| ~ preboolean(X20) )
& ( ~ in(esk2_2(X19,X20),X20)
| ~ subset(esk2_2(X19,X20),X19)
| ~ finite(esk2_2(X19,X20))
| X20 = finite_subsets(X19)
| ~ preboolean(X20) )
& ( subset(esk2_2(X19,X20),X19)
| in(esk2_2(X19,X20),X20)
| X20 = finite_subsets(X19)
| ~ preboolean(X20) )
& ( finite(esk2_2(X19,X20))
| in(esk2_2(X19,X20),X20)
| X20 = finite_subsets(X19)
| ~ preboolean(X20) ) ),
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)],[d5_finsub_1])])])])])]) ).
fof(c_0_7,plain,
! [X24] : preboolean(finite_subsets(X24)),
inference(variable_rename,[status(thm)],[dt_k5_finsub_1]) ).
fof(c_0_8,plain,
! [X47,X48,X49] :
( ~ subset(X47,X48)
| ~ subset(X48,X49)
| subset(X47,X49) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])]) ).
fof(c_0_9,negated_conjecture,
( subset(esk13_0,esk14_0)
& ~ subset(finite_subsets(esk13_0),finite_subsets(esk14_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
cnf(c_0_10,plain,
( subset(X1,X2)
| ~ in(X1,X3)
| X3 != finite_subsets(X2)
| ~ preboolean(X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
preboolean(finite_subsets(X1)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_12,plain,
! [X13,X14,X15,X16,X17] :
( ( ~ subset(X13,X14)
| ~ in(X15,X13)
| in(X15,X14) )
& ( in(esk1_2(X16,X17),X16)
| subset(X16,X17) )
& ( ~ in(esk1_2(X16,X17),X17)
| subset(X16,X17) ) ),
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])])])])])]) ).
cnf(c_0_13,plain,
( subset(X1,X3)
| ~ subset(X1,X2)
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,negated_conjecture,
subset(esk13_0,esk14_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( subset(X1,X2)
| ~ in(X1,finite_subsets(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_10]),c_0_11])]) ).
cnf(c_0_16,plain,
( in(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
( finite(X1)
| ~ in(X1,X2)
| X2 != finite_subsets(X3)
| ~ preboolean(X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_18,plain,
( in(X1,X3)
| ~ subset(X1,X2)
| ~ finite(X1)
| X3 != finite_subsets(X2)
| ~ preboolean(X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_19,negated_conjecture,
( subset(X1,esk14_0)
| ~ subset(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,plain,
( subset(esk1_2(finite_subsets(X1),X2),X1)
| subset(finite_subsets(X1),X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
( finite(X1)
| ~ in(X1,finite_subsets(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_17]),c_0_11])]) ).
cnf(c_0_22,plain,
( in(X1,finite_subsets(X2))
| ~ subset(X1,X2)
| ~ finite(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_18]),c_0_11])]) ).
cnf(c_0_23,negated_conjecture,
( subset(esk1_2(finite_subsets(esk13_0),X1),esk14_0)
| subset(finite_subsets(esk13_0),X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
( subset(finite_subsets(X1),X2)
| finite(esk1_2(finite_subsets(X1),X2)) ),
inference(spm,[status(thm)],[c_0_21,c_0_16]) ).
cnf(c_0_25,plain,
( subset(X1,X2)
| ~ in(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_26,negated_conjecture,
( subset(finite_subsets(esk13_0),X1)
| in(esk1_2(finite_subsets(esk13_0),X1),finite_subsets(esk14_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_27,negated_conjecture,
~ subset(finite_subsets(esk13_0),finite_subsets(esk14_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU110+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
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 23 18:51:16 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 0.69/0.84 % Version : CSE_E---1.5
% 0.69/0.84 % Problem : theBenchmark.p
% 0.69/0.84 % Proof found
% 0.69/0.84 % SZS status Theorem for theBenchmark.p
% 0.69/0.84 % SZS output start Proof
% See solution above
% 0.82/0.85 % Total time : 0.263000 s
% 0.82/0.85 % SZS output end Proof
% 0.82/0.85 % Total time : 0.266000 s
%------------------------------------------------------------------------------