TSTP Solution File: SEU327+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU327+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 : n007.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 16:24:29 EDT 2023
% Result : Theorem 0.20s 0.61s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 38
% Syntax : Number of formulae : 61 ( 13 unt; 31 typ; 0 def)
% Number of atoms : 57 ( 27 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 48 ( 21 ~; 15 |; 3 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 37 ( 27 >; 10 *; 0 +; 0 <<)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 4 con; 0-3 aty)
% Number of variables : 40 ( 0 sgn; 26 !; 0 ?; 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,
cast_to_subset: $i > $i ).
tff(decl_37,type,
subset_complement: ( $i * $i ) > $i ).
tff(decl_38,type,
set_difference: ( $i * $i ) > $i ).
tff(decl_39,type,
union_of_subsets: ( $i * $i ) > $i ).
tff(decl_40,type,
meet_of_subsets: ( $i * $i ) > $i ).
tff(decl_41,type,
subset_difference: ( $i * $i * $i ) > $i ).
tff(decl_42,type,
complements_of_subsets: ( $i * $i ) > $i ).
tff(decl_43,type,
empty_set: $i ).
tff(decl_44,type,
union: $i > $i ).
tff(decl_45,type,
set_meet: $i > $i ).
tff(decl_46,type,
subset: ( $i * $i ) > $o ).
tff(decl_47,type,
esk1_1: $i > $i ).
tff(decl_48,type,
esk2_0: $i ).
tff(decl_49,type,
esk3_1: $i > $i ).
tff(decl_50,type,
esk4_1: $i > $i ).
tff(decl_51,type,
esk5_0: $i ).
tff(decl_52,type,
esk6_0: $i ).
fof(t47_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ( X2 != empty_set
=> subset_difference(X1,cast_to_subset(X1),union_of_subsets(X1,X2)) = meet_of_subsets(X1,complements_of_subsets(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_setfam_1) ).
fof(d4_subset_1,axiom,
! [X1] : cast_to_subset(X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_subset_1) ).
fof(t11_tops_2,conjecture,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ( X2 != empty_set
=> meet_of_subsets(X1,complements_of_subsets(X1,X2)) = subset_complement(X1,union_of_subsets(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_tops_2) ).
fof(dt_k2_subset_1,axiom,
! [X1] : element(cast_to_subset(X1),powerset(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_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/sandbox/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
fof(d5_subset_1,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,X2) = set_difference(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_subset_1) ).
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(c_0_7,plain,
! [X85,X86] :
( ~ element(X86,powerset(powerset(X85)))
| X86 = empty_set
| subset_difference(X85,cast_to_subset(X85),union_of_subsets(X85,X86)) = meet_of_subsets(X85,complements_of_subsets(X85,X86)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t47_setfam_1])]) ).
fof(c_0_8,plain,
! [X31] : cast_to_subset(X31) = X31,
inference(variable_rename,[status(thm)],[d4_subset_1]) ).
fof(c_0_9,negated_conjecture,
~ ! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ( X2 != empty_set
=> meet_of_subsets(X1,complements_of_subsets(X1,X2)) = subset_complement(X1,union_of_subsets(X1,X2)) ) ),
inference(assume_negation,[status(cth)],[t11_tops_2]) ).
cnf(c_0_10,plain,
( X1 = empty_set
| subset_difference(X2,cast_to_subset(X2),union_of_subsets(X2,X1)) = meet_of_subsets(X2,complements_of_subsets(X2,X1))
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
cast_to_subset(X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,negated_conjecture,
( element(esk6_0,powerset(powerset(esk5_0)))
& esk6_0 != empty_set
& meet_of_subsets(esk5_0,complements_of_subsets(esk5_0,esk6_0)) != subset_complement(esk5_0,union_of_subsets(esk5_0,esk6_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
fof(c_0_13,plain,
! [X34] : element(cast_to_subset(X34),powerset(X34)),
inference(variable_rename,[status(thm)],[dt_k2_subset_1]) ).
fof(c_0_14,plain,
! [X72,X73,X74] :
( ~ element(X73,powerset(X72))
| ~ element(X74,powerset(X72))
| subset_difference(X72,X73,X74) = set_difference(X73,X74) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k6_subset_1])]) ).
cnf(c_0_15,plain,
( X1 = empty_set
| subset_difference(X2,X2,union_of_subsets(X2,X1)) = meet_of_subsets(X2,complements_of_subsets(X2,X1))
| ~ element(X1,powerset(powerset(X2))) ),
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,negated_conjecture,
element(esk6_0,powerset(powerset(esk5_0))),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,negated_conjecture,
esk6_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
element(cast_to_subset(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,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_14]) ).
cnf(c_0_20,negated_conjecture,
subset_difference(esk5_0,esk5_0,union_of_subsets(esk5_0,esk6_0)) = meet_of_subsets(esk5_0,complements_of_subsets(esk5_0,esk6_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_21,plain,
element(X1,powerset(X1)),
inference(rw,[status(thm)],[c_0_18,c_0_11]) ).
fof(c_0_22,plain,
! [X32,X33] :
( ~ element(X33,powerset(X32))
| subset_complement(X32,X33) = set_difference(X32,X33) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_subset_1])]) ).
cnf(c_0_23,negated_conjecture,
meet_of_subsets(esk5_0,complements_of_subsets(esk5_0,esk6_0)) != subset_complement(esk5_0,union_of_subsets(esk5_0,esk6_0)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_24,negated_conjecture,
( meet_of_subsets(esk5_0,complements_of_subsets(esk5_0,esk6_0)) = set_difference(esk5_0,union_of_subsets(esk5_0,esk6_0))
| ~ element(union_of_subsets(esk5_0,esk6_0),powerset(esk5_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).
cnf(c_0_25,plain,
( subset_complement(X2,X1) = set_difference(X2,X1)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_26,plain,
! [X37,X38] :
( ~ element(X38,powerset(powerset(X37)))
| element(union_of_subsets(X37,X38),powerset(X37)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_setfam_1])]) ).
cnf(c_0_27,negated_conjecture,
~ element(union_of_subsets(esk5_0,esk6_0),powerset(esk5_0)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_28,plain,
( element(union_of_subsets(X2,X1),powerset(X2))
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU327+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n007.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 15:54:39 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 0.20/0.61 % Version : CSE_E---1.5
% 0.20/0.61 % Problem : theBenchmark.p
% 0.20/0.61 % Proof found
% 0.20/0.61 % SZS status Theorem for theBenchmark.p
% 0.20/0.61 % SZS output start Proof
% See solution above
% 0.20/0.62 % Total time : 0.025000 s
% 0.20/0.62 % SZS output end Proof
% 0.20/0.62 % Total time : 0.029000 s
%------------------------------------------------------------------------------