TSTP Solution File: SEU325+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU325+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n028.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 16:24:28 EDT 2023
% Result : Theorem 0.20s 0.63s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 47
% Syntax : Number of formulae : 92 ( 22 unt; 35 typ; 0 def)
% Number of atoms : 126 ( 23 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 118 ( 49 ~; 35 |; 20 &)
% ( 1 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 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 : 19 ( 17 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 6 con; 0-3 aty)
% Number of variables : 68 ( 11 sgn; 37 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
v1_membered: $i > $o ).
tff(decl_24,type,
element: ( $i * $i ) > $o ).
tff(decl_25,type,
v1_xcmplx_0: $i > $o ).
tff(decl_26,type,
v2_membered: $i > $o ).
tff(decl_27,type,
v1_xreal_0: $i > $o ).
tff(decl_28,type,
v3_membered: $i > $o ).
tff(decl_29,type,
v1_rat_1: $i > $o ).
tff(decl_30,type,
v4_membered: $i > $o ).
tff(decl_31,type,
v1_int_1: $i > $o ).
tff(decl_32,type,
v5_membered: $i > $o ).
tff(decl_33,type,
natural: $i > $o ).
tff(decl_34,type,
empty: $i > $o ).
tff(decl_35,type,
powerset: $i > $i ).
tff(decl_36,type,
one_sorted_str: $i > $o ).
tff(decl_37,type,
cast_as_carrier_subset: $i > $i ).
tff(decl_38,type,
the_carrier: $i > $i ).
tff(decl_39,type,
union: $i > $i ).
tff(decl_40,type,
is_a_cover_of_carrier: ( $i * $i ) > $o ).
tff(decl_41,type,
union_of_subsets: ( $i * $i ) > $i ).
tff(decl_42,type,
empty_carrier: $i > $o ).
tff(decl_43,type,
empty_set: $i ).
tff(decl_44,type,
subset: ( $i * $i ) > $o ).
tff(decl_45,type,
esk1_3: ( $i * $i * $i ) > $i ).
tff(decl_46,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_47,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_48,type,
esk4_0: $i ).
tff(decl_49,type,
esk5_1: $i > $i ).
tff(decl_50,type,
esk6_0: $i ).
tff(decl_51,type,
esk7_1: $i > $i ).
tff(decl_52,type,
esk8_1: $i > $i ).
tff(decl_53,type,
esk9_0: $i ).
tff(decl_54,type,
esk10_1: $i > $i ).
tff(decl_55,type,
esk11_0: $i ).
tff(decl_56,type,
esk12_0: $i ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(rc2_subset_1,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(redefinition_k5_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> union_of_subsets(X1,X2) = union(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
fof(t5_tops_2,conjecture,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( element(X2,powerset(powerset(the_carrier(X1))))
=> ~ ( is_a_cover_of_carrier(X1,X2)
& X2 = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_tops_2) ).
fof(d8_pre_topc,axiom,
! [X1] :
( one_sorted_str(X1)
=> ! [X2] :
( element(X2,powerset(powerset(the_carrier(X1))))
=> ( is_a_cover_of_carrier(X1,X2)
<=> cast_as_carrier_subset(X1) = union_of_subsets(the_carrier(X1),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_pre_topc) ).
fof(dt_k5_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(union_of_subsets(X1,X2),powerset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_setfam_1) ).
fof(d3_pre_topc,axiom,
! [X1] :
( one_sorted_str(X1)
=> cast_as_carrier_subset(X1) = the_carrier(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_pre_topc) ).
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(fc2_pre_topc,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(cast_as_carrier_subset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_pre_topc) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(fc6_membered,axiom,
( empty(empty_set)
& v1_membered(empty_set)
& v2_membered(empty_set)
& v3_membered(empty_set)
& v4_membered(empty_set)
& v5_membered(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_membered) ).
fof(c_0_12,plain,
! [X80] :
( ~ empty(X80)
| X80 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(c_0_13,plain,
! [X58] :
( element(esk8_1(X58),powerset(X58))
& empty(esk8_1(X58)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
cnf(c_0_14,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_15,plain,
empty(esk8_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_16,plain,
! [X63,X64] :
( ~ element(X64,powerset(powerset(X63)))
| union_of_subsets(X63,X64) = union(X64) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k5_setfam_1])]) ).
cnf(c_0_17,plain,
element(esk8_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
esk8_1(X1) = empty_set,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
fof(c_0_19,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( element(X2,powerset(powerset(the_carrier(X1))))
=> ~ ( is_a_cover_of_carrier(X1,X2)
& X2 = empty_set ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t5_tops_2])]) ).
fof(c_0_20,plain,
! [X44,X45] :
( ( ~ is_a_cover_of_carrier(X44,X45)
| cast_as_carrier_subset(X44) = union_of_subsets(the_carrier(X44),X45)
| ~ element(X45,powerset(powerset(the_carrier(X44))))
| ~ one_sorted_str(X44) )
& ( cast_as_carrier_subset(X44) != union_of_subsets(the_carrier(X44),X45)
| is_a_cover_of_carrier(X44,X45)
| ~ element(X45,powerset(powerset(the_carrier(X44))))
| ~ one_sorted_str(X44) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_pre_topc])])])]) ).
cnf(c_0_21,plain,
( union_of_subsets(X2,X1) = union(X1)
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
element(empty_set,powerset(X1)),
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
fof(c_0_23,negated_conjecture,
( ~ empty_carrier(esk11_0)
& one_sorted_str(esk11_0)
& element(esk12_0,powerset(powerset(the_carrier(esk11_0))))
& is_a_cover_of_carrier(esk11_0,esk12_0)
& esk12_0 = empty_set ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])]) ).
fof(c_0_24,plain,
! [X47,X48] :
( ~ element(X48,powerset(powerset(X47)))
| element(union_of_subsets(X47,X48),powerset(X47)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_setfam_1])]) ).
cnf(c_0_25,plain,
( cast_as_carrier_subset(X1) = union_of_subsets(the_carrier(X1),X2)
| ~ is_a_cover_of_carrier(X1,X2)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,plain,
union_of_subsets(X1,empty_set) = union(empty_set),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,negated_conjecture,
is_a_cover_of_carrier(esk11_0,esk12_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,negated_conjecture,
esk12_0 = empty_set,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
( element(union_of_subsets(X2,X1),powerset(X2))
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_30,plain,
! [X32] :
( ~ one_sorted_str(X32)
| cast_as_carrier_subset(X32) = the_carrier(X32) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_pre_topc])]) ).
cnf(c_0_31,plain,
( cast_as_carrier_subset(X1) = union(empty_set)
| ~ is_a_cover_of_carrier(X1,empty_set)
| ~ one_sorted_str(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_22]),c_0_26]) ).
cnf(c_0_32,negated_conjecture,
is_a_cover_of_carrier(esk11_0,empty_set),
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,negated_conjecture,
one_sorted_str(esk11_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_34,plain,
! [X75,X76,X77] :
( ~ in(X75,X76)
| ~ element(X76,powerset(X77))
| ~ empty(X77) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
cnf(c_0_35,plain,
element(union_of_subsets(X1,empty_set),powerset(X1)),
inference(spm,[status(thm)],[c_0_29,c_0_22]) ).
fof(c_0_36,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(cast_as_carrier_subset(X1)) ),
inference(fof_simplification,[status(thm)],[fc2_pre_topc]) ).
cnf(c_0_37,plain,
( cast_as_carrier_subset(X1) = the_carrier(X1)
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_38,negated_conjecture,
cast_as_carrier_subset(esk11_0) = union(empty_set),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]) ).
cnf(c_0_39,plain,
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_40,plain,
element(union(empty_set),powerset(X1)),
inference(rw,[status(thm)],[c_0_35,c_0_26]) ).
fof(c_0_41,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_42,plain,
! [X50] : element(esk5_1(X50),X50),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(c_0_43,plain,
! [X54] :
( empty_carrier(X54)
| ~ one_sorted_str(X54)
| ~ empty(cast_as_carrier_subset(X54)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])]) ).
cnf(c_0_44,negated_conjecture,
union(empty_set) = the_carrier(esk11_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_33])]) ).
cnf(c_0_45,plain,
( ~ empty(X1)
| ~ in(X2,union(empty_set)) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_46,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_47,plain,
element(esk5_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_48,plain,
( empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ empty(cast_as_carrier_subset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_49,negated_conjecture,
cast_as_carrier_subset(esk11_0) = the_carrier(esk11_0),
inference(rw,[status(thm)],[c_0_38,c_0_44]) ).
cnf(c_0_50,negated_conjecture,
~ empty_carrier(esk11_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_51,plain,
( ~ empty(X1)
| ~ in(X2,the_carrier(esk11_0)) ),
inference(rw,[status(thm)],[c_0_45,c_0_44]) ).
cnf(c_0_52,plain,
( empty(X1)
| in(esk5_1(X1),X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_53,negated_conjecture,
~ empty(the_carrier(esk11_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_33])]),c_0_50]) ).
cnf(c_0_54,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc6_membered]) ).
cnf(c_0_55,plain,
~ empty(X1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]) ).
cnf(c_0_56,plain,
$false,
inference(sr,[status(thm)],[c_0_54,c_0_55]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU325+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n028.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 16:10:03 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 0.20/0.63 % Version : CSE_E---1.5
% 0.20/0.63 % Problem : theBenchmark.p
% 0.20/0.63 % Proof found
% 0.20/0.63 % SZS status Theorem for theBenchmark.p
% 0.20/0.63 % SZS output start Proof
% See solution above
% 0.20/0.63 % Total time : 0.042000 s
% 0.20/0.63 % SZS output end Proof
% 0.20/0.63 % Total time : 0.045000 s
%------------------------------------------------------------------------------