TSTP Solution File: SEU108+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU108+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 16:22:28 EDT 2023
% Result : Theorem 2.35s 2.43s
% Output : CNFRefutation 2.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 48
% Syntax : Number of formulae : 98 ( 24 unt; 35 typ; 0 def)
% Number of atoms : 142 ( 16 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 135 ( 56 ~; 56 |; 13 &)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 38 ( 29 >; 9 *; 0 +; 0 <<)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 6 con; 0-3 aty)
% Number of variables : 104 ( 8 sgn; 54 !; 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,
set_union2: ( $i * $i ) > $i ).
tff(decl_31,type,
subset_union2: ( $i * $i * $i ) > $i ).
tff(decl_32,type,
subset_difference: ( $i * $i * $i ) > $i ).
tff(decl_33,type,
set_difference: ( $i * $i ) > $i ).
tff(decl_34,type,
empty_set: $i ).
tff(decl_35,type,
cap_closed: $i > $o ).
tff(decl_36,type,
relation: $i > $o ).
tff(decl_37,type,
function: $i > $o ).
tff(decl_38,type,
one_to_one: $i > $o ).
tff(decl_39,type,
epsilon_transitive: $i > $o ).
tff(decl_40,type,
epsilon_connected: $i > $o ).
tff(decl_41,type,
ordinal: $i > $o ).
tff(decl_42,type,
natural: $i > $o ).
tff(decl_43,type,
subset: ( $i * $i ) > $o ).
tff(decl_44,type,
esk1_1: $i > $i ).
tff(decl_45,type,
esk2_0: $i ).
tff(decl_46,type,
esk3_0: $i ).
tff(decl_47,type,
esk4_1: $i > $i ).
tff(decl_48,type,
esk5_0: $i ).
tff(decl_49,type,
esk6_1: $i > $i ).
tff(decl_50,type,
esk7_1: $i > $i ).
tff(decl_51,type,
esk8_0: $i ).
tff(decl_52,type,
esk9_1: $i > $i ).
tff(decl_53,type,
esk10_1: $i > $i ).
tff(decl_54,type,
esk11_1: $i > $i ).
tff(decl_55,type,
esk12_1: $i > $i ).
tff(decl_56,type,
esk13_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(fc1_subset_1,axiom,
! [X1] : ~ empty(powerset(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_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(rc2_subset_1,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(t1_subset,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(dt_k4_subset_1,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> element(subset_union2(X1,X2,X3),powerset(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_subset_1) ).
fof(idempotence_k4_subset_1,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> subset_union2(X1,X2,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k4_subset_1) ).
fof(t20_finsub_1,conjecture,
! [X1] : preboolean(powerset(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_finsub_1) ).
fof(t10_finsub_1,axiom,
! [X1] :
( preboolean(X1)
<=> ! [X2,X3] :
( ( in(X2,X1)
& in(X3,X1) )
=> ( in(set_union2(X2,X3),X1)
& in(set_difference(X2,X3),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_finsub_1) ).
fof(dt_k6_subset_1,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> element(subset_difference(X1,X2,X3),powerset(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_subset_1) ).
fof(redefinition_k6_subset_1,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> subset_difference(X1,X2,X3) = set_difference(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
fof(redefinition_k4_subset_1,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> subset_union2(X1,X2,X3) = set_union2(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_subset_1) ).
fof(c_0_13,plain,
! [X80] :
( ~ empty(X80)
| X80 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(c_0_14,plain,
empty(esk5_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
fof(c_0_15,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[fc1_subset_1]) ).
cnf(c_0_16,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,plain,
empty(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_18,plain,
! [X68,X69] :
( ~ element(X68,X69)
| empty(X69)
| in(X68,X69) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(c_0_19,plain,
! [X44] :
( element(esk7_1(X44),powerset(X44))
& empty(esk7_1(X44)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
fof(c_0_20,plain,
! [X26] : ~ empty(powerset(X26)),
inference(variable_rename,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
empty_set = esk5_0,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
element(esk7_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,plain,
( X1 = esk5_0
| ~ empty(X1) ),
inference(rw,[status(thm)],[c_0_16,c_0_21]) ).
cnf(c_0_26,plain,
empty(esk7_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_27,plain,
! [X65,X66] :
( ~ in(X65,X66)
| element(X65,X66) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
cnf(c_0_28,plain,
in(esk7_1(X1),powerset(X1)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_29,plain,
esk7_1(X1) = esk5_0,
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_31,plain,
in(esk5_0,powerset(X1)),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
fof(c_0_32,plain,
! [X16,X17,X18] :
( ~ element(X17,powerset(X16))
| ~ element(X18,powerset(X16))
| element(subset_union2(X16,X17,X18),powerset(X16)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k4_subset_1])]) ).
fof(c_0_33,plain,
! [X34,X35,X36] :
( ~ element(X35,powerset(X34))
| ~ element(X36,powerset(X34))
| subset_union2(X34,X35,X35) = X35 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[idempotence_k4_subset_1])]) ).
cnf(c_0_34,plain,
element(esk5_0,powerset(X1)),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,plain,
( element(subset_union2(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_36,plain,
( subset_union2(X2,X1,X1) = X1
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_37,plain,
element(esk7_1(X1),powerset(X2)),
inference(spm,[status(thm)],[c_0_34,c_0_29]) ).
fof(c_0_38,negated_conjecture,
~ ! [X1] : preboolean(powerset(X1)),
inference(assume_negation,[status(cth)],[t20_finsub_1]) ).
fof(c_0_39,plain,
! [X58,X59,X60,X61] :
( ( in(set_union2(X59,X60),X58)
| ~ in(X59,X58)
| ~ in(X60,X58)
| ~ preboolean(X58) )
& ( in(set_difference(X59,X60),X58)
| ~ in(X59,X58)
| ~ in(X60,X58)
| ~ preboolean(X58) )
& ( in(esk11_1(X61),X61)
| preboolean(X61) )
& ( in(esk12_1(X61),X61)
| preboolean(X61) )
& ( ~ in(set_union2(esk11_1(X61),esk12_1(X61)),X61)
| ~ in(set_difference(esk11_1(X61),esk12_1(X61)),X61)
| preboolean(X61) ) ),
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)],[t10_finsub_1])])])])])]) ).
cnf(c_0_40,plain,
( in(subset_union2(X1,X2,X3),powerset(X1))
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_35]),c_0_24]) ).
cnf(c_0_41,plain,
( subset_union2(X1,X2,X2) = X2
| ~ element(X2,powerset(X1)) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
fof(c_0_42,plain,
! [X19,X20,X21] :
( ~ element(X20,powerset(X19))
| ~ element(X21,powerset(X19))
| element(subset_difference(X19,X20,X21),powerset(X19)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k6_subset_1])]) ).
fof(c_0_43,plain,
! [X54,X55,X56] :
( ~ element(X55,powerset(X54))
| ~ element(X56,powerset(X54))
| subset_difference(X54,X55,X56) = set_difference(X55,X56) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k6_subset_1])]) ).
fof(c_0_44,plain,
! [X51,X52,X53] :
( ~ element(X52,powerset(X51))
| ~ element(X53,powerset(X51))
| subset_union2(X51,X52,X53) = set_union2(X52,X53) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k4_subset_1])]) ).
fof(c_0_45,negated_conjecture,
~ preboolean(powerset(esk13_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])])]) ).
cnf(c_0_46,plain,
( preboolean(X1)
| ~ in(set_union2(esk11_1(X1),esk12_1(X1)),X1)
| ~ in(set_difference(esk11_1(X1),esk12_1(X1)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_47,plain,
( in(X1,powerset(X2))
| ~ element(X1,powerset(X2)) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_48,plain,
( element(subset_difference(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_49,plain,
( subset_difference(X2,X1,X3) = set_difference(X1,X3)
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_50,plain,
( subset_union2(X2,X1,X3) = set_union2(X1,X3)
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_51,negated_conjecture,
~ preboolean(powerset(esk13_0)),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_52,plain,
( in(esk12_1(X1),X1)
| preboolean(X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_53,plain,
( in(esk11_1(X1),X1)
| preboolean(X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_54,plain,
( preboolean(powerset(X1))
| ~ element(set_difference(esk11_1(powerset(X1)),esk12_1(powerset(X1))),powerset(X1))
| ~ in(set_union2(esk11_1(powerset(X1)),esk12_1(powerset(X1))),powerset(X1)) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_55,plain,
( element(set_difference(X1,X2),powerset(X3))
| ~ element(X2,powerset(X3))
| ~ element(X1,powerset(X3)) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_56,plain,
( in(set_union2(X1,X2),powerset(X3))
| ~ element(X2,powerset(X3))
| ~ element(X1,powerset(X3)) ),
inference(spm,[status(thm)],[c_0_40,c_0_50]) ).
cnf(c_0_57,negated_conjecture,
in(esk12_1(powerset(esk13_0)),powerset(esk13_0)),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_58,negated_conjecture,
in(esk11_1(powerset(esk13_0)),powerset(esk13_0)),
inference(spm,[status(thm)],[c_0_51,c_0_53]) ).
cnf(c_0_59,plain,
( preboolean(powerset(X1))
| ~ element(esk12_1(powerset(X1)),powerset(X1))
| ~ element(esk11_1(powerset(X1)),powerset(X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]) ).
cnf(c_0_60,negated_conjecture,
element(esk12_1(powerset(esk13_0)),powerset(esk13_0)),
inference(spm,[status(thm)],[c_0_30,c_0_57]) ).
cnf(c_0_61,negated_conjecture,
element(esk11_1(powerset(esk13_0)),powerset(esk13_0)),
inference(spm,[status(thm)],[c_0_30,c_0_58]) ).
cnf(c_0_62,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_59]),c_0_60]),c_0_61])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU108+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.36 % Computer : n005.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Aug 23 15:22:24 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.22/0.59 start to proof: theBenchmark
% 2.35/2.43 % Version : CSE_E---1.5
% 2.35/2.43 % Problem : theBenchmark.p
% 2.35/2.43 % Proof found
% 2.35/2.43 % SZS status Theorem for theBenchmark.p
% 2.35/2.43 % SZS output start Proof
% See solution above
% 2.35/2.44 % Total time : 1.831000 s
% 2.35/2.44 % SZS output end Proof
% 2.35/2.44 % Total time : 1.834000 s
%------------------------------------------------------------------------------