TSTP Solution File: SEU317+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU317+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/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 16:24:23 EDT 2023
% Result : Theorem 1.69s 1.75s
% Output : CNFRefutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 39
% Syntax : Number of formulae : 81 ( 17 unt; 31 typ; 0 def)
% Number of atoms : 142 ( 0 equ)
% Maximal formula atoms : 28 ( 2 avg)
% Number of connectives : 157 ( 65 ~; 65 |; 13 &)
% ( 2 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 33 ( 25 >; 8 *; 0 +; 0 <<)
% Number of predicates : 18 ( 17 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 74 ( 4 sgn; 42 !; 1 ?; 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,
subset: ( $i * $i ) > $o ).
tff(decl_37,type,
top_str: $i > $o ).
tff(decl_38,type,
the_carrier: $i > $i ).
tff(decl_39,type,
topstr_closure: ( $i * $i ) > $i ).
tff(decl_40,type,
one_sorted_str: $i > $o ).
tff(decl_41,type,
empty_set: $i ).
tff(decl_42,type,
closed_subset: ( $i * $i ) > $o ).
tff(decl_43,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_44,type,
esk2_0: $i ).
tff(decl_45,type,
esk3_0: $i ).
tff(decl_46,type,
esk4_1: $i > $i ).
tff(decl_47,type,
esk5_0: $i ).
tff(decl_48,type,
esk6_1: $i > $i ).
tff(decl_49,type,
esk7_1: $i > $i ).
tff(decl_50,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_51,type,
esk9_0: $i ).
tff(decl_52,type,
esk10_0: $i ).
fof(t48_pre_topc,conjecture,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> subset(X2,topstr_closure(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_pre_topc) ).
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(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(t4_subset,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(t45_pre_topc,axiom,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ! [X3] :
( in(X3,the_carrier(X1))
=> ( in(X3,topstr_closure(X1,X2))
<=> ! [X4] :
( element(X4,powerset(the_carrier(X1)))
=> ( ( closed_subset(X4,X1)
& subset(X2,X4) )
=> in(X3,X4) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_pre_topc) ).
fof(c_0_8,negated_conjecture,
~ ! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> subset(X2,topstr_closure(X1,X2)) ) ),
inference(assume_negation,[status(cth)],[t48_pre_topc]) ).
fof(c_0_9,negated_conjecture,
( top_str(esk9_0)
& element(esk10_0,powerset(the_carrier(esk9_0)))
& ~ subset(esk10_0,topstr_closure(esk9_0,esk10_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_10,plain,
! [X32,X33,X34,X35,X36] :
( ( ~ subset(X32,X33)
| ~ in(X34,X32)
| in(X34,X33) )
& ( in(esk1_2(X35,X36),X35)
| subset(X35,X36) )
& ( ~ in(esk1_2(X35,X36),X36)
| subset(X35,X36) ) ),
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,
! [X72,X73] :
( ~ in(X72,X73)
| ~ empty(X73) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
cnf(c_0_12,negated_conjecture,
~ subset(esk10_0,topstr_closure(esk9_0,esk10_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( in(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_14,plain,
! [X54,X55] :
( ~ element(X54,X55)
| empty(X55)
| in(X54,X55) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(c_0_15,plain,
! [X43] : element(esk4_1(X43),X43),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(c_0_16,plain,
! [X65,X66,X67] :
( ~ in(X65,X66)
| ~ element(X66,powerset(X67))
| element(X65,X67) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
cnf(c_0_17,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,negated_conjecture,
in(esk1_2(esk10_0,topstr_closure(esk9_0,esk10_0)),esk10_0),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_19,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
element(esk4_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
( element(X1,X3)
| ~ in(X1,X2)
| ~ element(X2,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
element(esk10_0,powerset(the_carrier(esk9_0))),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_23,negated_conjecture,
~ empty(esk10_0),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,plain,
( empty(X1)
| in(esk4_1(X1),X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
fof(c_0_25,plain,
! [X68,X69,X70] :
( ~ in(X68,X69)
| ~ element(X69,powerset(X70))
| ~ empty(X70) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
cnf(c_0_26,negated_conjecture,
( element(X1,the_carrier(esk9_0))
| ~ in(X1,esk10_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,negated_conjecture,
in(esk4_1(esk10_0),esk10_0),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,plain,
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_29,negated_conjecture,
element(esk4_1(esk10_0),the_carrier(esk9_0)),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,negated_conjecture,
( ~ empty(the_carrier(esk9_0))
| ~ in(X1,esk10_0) ),
inference(spm,[status(thm)],[c_0_28,c_0_22]) ).
cnf(c_0_31,negated_conjecture,
( empty(the_carrier(esk9_0))
| in(esk4_1(esk10_0),the_carrier(esk9_0)) ),
inference(spm,[status(thm)],[c_0_19,c_0_29]) ).
cnf(c_0_32,negated_conjecture,
( in(esk4_1(esk10_0),the_carrier(esk9_0))
| ~ in(X1,esk10_0) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
fof(c_0_33,plain,
! [X58,X59,X60,X61] :
( ( ~ in(X60,topstr_closure(X58,X59))
| ~ element(X61,powerset(the_carrier(X58)))
| ~ closed_subset(X61,X58)
| ~ subset(X59,X61)
| in(X60,X61)
| ~ in(X60,the_carrier(X58))
| ~ element(X59,powerset(the_carrier(X58)))
| ~ top_str(X58) )
& ( element(esk8_3(X58,X59,X60),powerset(the_carrier(X58)))
| in(X60,topstr_closure(X58,X59))
| ~ in(X60,the_carrier(X58))
| ~ element(X59,powerset(the_carrier(X58)))
| ~ top_str(X58) )
& ( closed_subset(esk8_3(X58,X59,X60),X58)
| in(X60,topstr_closure(X58,X59))
| ~ in(X60,the_carrier(X58))
| ~ element(X59,powerset(the_carrier(X58)))
| ~ top_str(X58) )
& ( subset(X59,esk8_3(X58,X59,X60))
| in(X60,topstr_closure(X58,X59))
| ~ in(X60,the_carrier(X58))
| ~ element(X59,powerset(the_carrier(X58)))
| ~ top_str(X58) )
& ( ~ in(X60,esk8_3(X58,X59,X60))
| in(X60,topstr_closure(X58,X59))
| ~ in(X60,the_carrier(X58))
| ~ element(X59,powerset(the_carrier(X58)))
| ~ top_str(X58) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t45_pre_topc])])])])]) ).
cnf(c_0_34,negated_conjecture,
element(esk1_2(esk10_0,topstr_closure(esk9_0,esk10_0)),the_carrier(esk9_0)),
inference(spm,[status(thm)],[c_0_26,c_0_18]) ).
cnf(c_0_35,negated_conjecture,
in(esk4_1(esk10_0),the_carrier(esk9_0)),
inference(spm,[status(thm)],[c_0_32,c_0_27]) ).
cnf(c_0_36,plain,
( subset(X1,esk8_3(X2,X1,X3))
| in(X3,topstr_closure(X2,X1))
| ~ in(X3,the_carrier(X2))
| ~ element(X1,powerset(the_carrier(X2)))
| ~ top_str(X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_37,negated_conjecture,
top_str(esk9_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_38,negated_conjecture,
( empty(the_carrier(esk9_0))
| in(esk1_2(esk10_0,topstr_closure(esk9_0,esk10_0)),the_carrier(esk9_0)) ),
inference(spm,[status(thm)],[c_0_19,c_0_34]) ).
cnf(c_0_39,negated_conjecture,
~ empty(the_carrier(esk9_0)),
inference(spm,[status(thm)],[c_0_17,c_0_35]) ).
cnf(c_0_40,plain,
( subset(X1,X2)
| ~ in(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_41,negated_conjecture,
( subset(esk10_0,esk8_3(esk9_0,esk10_0,X1))
| in(X1,topstr_closure(esk9_0,esk10_0))
| ~ in(X1,the_carrier(esk9_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_22]),c_0_37])]) ).
cnf(c_0_42,negated_conjecture,
in(esk1_2(esk10_0,topstr_closure(esk9_0,esk10_0)),the_carrier(esk9_0)),
inference(sr,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,negated_conjecture,
~ in(esk1_2(esk10_0,topstr_closure(esk9_0,esk10_0)),topstr_closure(esk9_0,esk10_0)),
inference(spm,[status(thm)],[c_0_12,c_0_40]) ).
cnf(c_0_44,plain,
( in(X1,topstr_closure(X2,X3))
| ~ in(X1,esk8_3(X2,X3,X1))
| ~ in(X1,the_carrier(X2))
| ~ element(X3,powerset(the_carrier(X2)))
| ~ top_str(X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_45,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_46,negated_conjecture,
subset(esk10_0,esk8_3(esk9_0,esk10_0,esk1_2(esk10_0,topstr_closure(esk9_0,esk10_0)))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]) ).
cnf(c_0_47,negated_conjecture,
( in(X1,topstr_closure(esk9_0,esk10_0))
| ~ in(X1,esk8_3(esk9_0,esk10_0,X1))
| ~ in(X1,the_carrier(esk9_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_22]),c_0_37])]) ).
cnf(c_0_48,negated_conjecture,
( in(X1,esk8_3(esk9_0,esk10_0,esk1_2(esk10_0,topstr_closure(esk9_0,esk10_0))))
| ~ in(X1,esk10_0) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_49,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_42]),c_0_18])]),c_0_43]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU317+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n028.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 23 12:29:04 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 1.69/1.75 % Version : CSE_E---1.5
% 1.69/1.75 % Problem : theBenchmark.p
% 1.69/1.75 % Proof found
% 1.69/1.75 % SZS status Theorem for theBenchmark.p
% 1.69/1.75 % SZS output start Proof
% See solution above
% 1.69/1.76 % Total time : 1.155000 s
% 1.69/1.76 % SZS output end Proof
% 1.69/1.76 % Total time : 1.158000 s
%------------------------------------------------------------------------------