TSTP Solution File: SEU114+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU114+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n002.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 16:22:29 EDT 2023
% Result : Theorem 2.60s 2.76s
% Output : CNFRefutation 2.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 41
% Syntax : Number of formulae : 71 ( 10 unt; 32 typ; 0 def)
% Number of atoms : 119 ( 17 equ)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 126 ( 46 ~; 55 |; 13 &)
% ( 5 <=>; 7 =>; 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 : 16 ( 16 usr; 6 con; 0-2 aty)
% Number of variables : 66 ( 1 sgn; 37 !; 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 ).
fof(t1_subset,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
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/sandbox/benchmark/theBenchmark.p',d5_finsub_1) ).
fof(dt_k5_finsub_1,axiom,
! [X1] : preboolean(finite_subsets(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_finsub_1) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(cc2_finset_1,axiom,
! [X1] :
( finite(X1)
=> ! [X2] :
( element(X2,powerset(X1))
=> finite(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finset_1) ).
fof(t27_finsub_1,conjecture,
! [X1] :
( finite(X1)
=> finite_subsets(X1) = powerset(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_finsub_1) ).
fof(d10_xboole_0,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(t26_finsub_1,axiom,
! [X1] : subset(finite_subsets(X1),powerset(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_finsub_1) ).
fof(c_0_9,plain,
! [X49,X50] :
( ~ in(X49,X50)
| element(X49,X50) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
fof(c_0_10,plain,
! [X15,X16,X17,X18,X19] :
( ( ~ subset(X15,X16)
| ~ in(X17,X15)
| in(X17,X16) )
& ( in(esk1_2(X18,X19),X18)
| subset(X18,X19) )
& ( ~ in(esk1_2(X18,X19),X19)
| subset(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_tarski])])])])])]) ).
fof(c_0_11,plain,
! [X21,X22,X23,X24] :
( ( subset(X23,X21)
| ~ in(X23,X22)
| X22 != finite_subsets(X21)
| ~ preboolean(X22) )
& ( finite(X23)
| ~ in(X23,X22)
| X22 != finite_subsets(X21)
| ~ preboolean(X22) )
& ( ~ subset(X24,X21)
| ~ finite(X24)
| in(X24,X22)
| X22 != finite_subsets(X21)
| ~ preboolean(X22) )
& ( ~ in(esk2_2(X21,X22),X22)
| ~ subset(esk2_2(X21,X22),X21)
| ~ finite(esk2_2(X21,X22))
| X22 = finite_subsets(X21)
| ~ preboolean(X22) )
& ( subset(esk2_2(X21,X22),X21)
| in(esk2_2(X21,X22),X22)
| X22 = finite_subsets(X21)
| ~ preboolean(X22) )
& ( finite(esk2_2(X21,X22))
| in(esk2_2(X21,X22),X22)
| X22 = finite_subsets(X21)
| ~ preboolean(X22) ) ),
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_12,plain,
! [X26] : preboolean(finite_subsets(X26)),
inference(variable_rename,[status(thm)],[dt_k5_finsub_1]) ).
fof(c_0_13,plain,
! [X55,X56] :
( ( ~ element(X55,powerset(X56))
| subset(X55,X56) )
& ( ~ subset(X55,X56)
| element(X55,powerset(X56)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
cnf(c_0_14,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( in(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_16,plain,
! [X8,X9] :
( ~ finite(X8)
| ~ element(X9,powerset(X8))
| finite(X9) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_finset_1])])]) ).
fof(c_0_17,negated_conjecture,
~ ! [X1] :
( finite(X1)
=> finite_subsets(X1) = powerset(X1) ),
inference(assume_negation,[status(cth)],[t27_finsub_1]) ).
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_11]) ).
cnf(c_0_19,plain,
preboolean(finite_subsets(X1)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
( subset(X1,X2)
| element(esk1_2(X1,X2),X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_22,plain,
( finite(X2)
| ~ finite(X1)
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_23,negated_conjecture,
( finite(esk13_0)
& finite_subsets(esk13_0) != powerset(esk13_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])]) ).
cnf(c_0_24,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_19])]) ).
cnf(c_0_25,plain,
( subset(esk1_2(powerset(X1),X2),X1)
| subset(powerset(X1),X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
( subset(powerset(X1),X2)
| finite(esk1_2(powerset(X1),X2))
| ~ finite(X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_27,negated_conjecture,
finite(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,plain,
( subset(powerset(X1),X2)
| in(esk1_2(powerset(X1),X2),finite_subsets(X1))
| ~ finite(esk1_2(powerset(X1),X2)) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,negated_conjecture,
( subset(powerset(esk13_0),X1)
| finite(esk1_2(powerset(esk13_0),X1)) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
fof(c_0_30,plain,
! [X13,X14] :
( ( subset(X13,X14)
| X13 != X14 )
& ( subset(X14,X13)
| X13 != X14 )
& ( ~ subset(X13,X14)
| ~ subset(X14,X13)
| X13 = X14 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])]) ).
cnf(c_0_31,plain,
( subset(X1,X2)
| ~ in(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_32,negated_conjecture,
( subset(powerset(esk13_0),X1)
| in(esk1_2(powerset(esk13_0),X1),finite_subsets(esk13_0)) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
fof(c_0_33,plain,
! [X51] : subset(finite_subsets(X51),powerset(X51)),
inference(variable_rename,[status(thm)],[t26_finsub_1]) ).
cnf(c_0_34,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_35,negated_conjecture,
subset(powerset(esk13_0),finite_subsets(esk13_0)),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,plain,
subset(finite_subsets(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_37,negated_conjecture,
finite_subsets(esk13_0) != powerset(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]),c_0_37]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU114+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n002.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 : Wed Aug 23 22:22:01 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.57 start to proof: theBenchmark
% 2.60/2.76 % Version : CSE_E---1.5
% 2.60/2.76 % Problem : theBenchmark.p
% 2.60/2.76 % Proof found
% 2.60/2.76 % SZS status Theorem for theBenchmark.p
% 2.60/2.76 % SZS output start Proof
% See solution above
% 2.60/2.77 % Total time : 2.183000 s
% 2.60/2.77 % SZS output end Proof
% 2.60/2.77 % Total time : 2.186000 s
%------------------------------------------------------------------------------