TSTP Solution File: SEU321+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU321+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 16:24:25 EDT 2023
% Result : Theorem 0.20s 0.62s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 33
% Syntax : Number of formulae : 57 ( 8 unt; 28 typ; 0 def)
% Number of atoms : 89 ( 7 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 98 ( 38 ~; 26 |; 15 &)
% ( 2 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 25 ( 21 >; 4 *; 0 +; 0 <<)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn; 24 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
subset: ( $i * $i ) > $o ).
tff(decl_23,type,
empty_carrier: $i > $o ).
tff(decl_24,type,
one_sorted_str: $i > $o ).
tff(decl_25,type,
the_carrier: $i > $i ).
tff(decl_26,type,
powerset: $i > $i ).
tff(decl_27,type,
element: ( $i * $i ) > $o ).
tff(decl_28,type,
empty: $i > $o ).
tff(decl_29,type,
v5_membered: $i > $o ).
tff(decl_30,type,
v4_membered: $i > $o ).
tff(decl_31,type,
v3_membered: $i > $o ).
tff(decl_32,type,
v2_membered: $i > $o ).
tff(decl_33,type,
v1_membered: $i > $o ).
tff(decl_34,type,
v1_xcmplx_0: $i > $o ).
tff(decl_35,type,
v1_xreal_0: $i > $o ).
tff(decl_36,type,
v1_rat_1: $i > $o ).
tff(decl_37,type,
v1_int_1: $i > $o ).
tff(decl_38,type,
natural: $i > $o ).
tff(decl_39,type,
in: ( $i * $i ) > $o ).
tff(decl_40,type,
subset_complement: ( $i * $i ) > $i ).
tff(decl_41,type,
empty_set: $i ).
tff(decl_42,type,
esk1_1: $i > $i ).
tff(decl_43,type,
esk2_0: $i ).
tff(decl_44,type,
esk3_0: $i ).
tff(decl_45,type,
esk4_1: $i > $i ).
tff(decl_46,type,
esk5_0: $i ).
tff(decl_47,type,
esk6_0: $i ).
tff(decl_48,type,
esk7_0: $i ).
tff(decl_49,type,
esk8_0: $i ).
fof(t50_subset_1,axiom,
! [X1] :
( X1 != empty_set
=> ! [X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,X1)
=> ( ~ in(X3,X2)
=> in(X3,subset_complement(X1,X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_subset_1) ).
fof(l40_tops_1,conjecture,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( in(X3,subset_complement(the_carrier(X1),X2))
<=> ~ in(X3,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l40_tops_1) ).
fof(fc1_struct_0,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(the_carrier(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(t54_subset_1,axiom,
! [X1,X2,X3] :
( element(X3,powerset(X1))
=> ~ ( in(X2,subset_complement(X1,X3))
& in(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_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_5,plain,
! [X1] :
( X1 != empty_set
=> ! [X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,X1)
=> ( ~ in(X3,X2)
=> in(X3,subset_complement(X1,X2)) ) ) ) ),
inference(fof_simplification,[status(thm)],[t50_subset_1]) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( in(X3,subset_complement(the_carrier(X1),X2))
<=> ~ in(X3,X2) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[l40_tops_1])]) ).
fof(c_0_7,plain,
! [X64,X65,X66] :
( X64 = empty_set
| ~ element(X65,powerset(X64))
| ~ element(X66,X64)
| in(X66,X65)
| in(X66,subset_complement(X64,X65)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_8,negated_conjecture,
( ~ empty_carrier(esk6_0)
& one_sorted_str(esk6_0)
& element(esk7_0,powerset(the_carrier(esk6_0)))
& element(esk8_0,the_carrier(esk6_0))
& ( ~ in(esk8_0,subset_complement(the_carrier(esk6_0),esk7_0))
| in(esk8_0,esk7_0) )
& ( in(esk8_0,subset_complement(the_carrier(esk6_0),esk7_0))
| ~ in(esk8_0,esk7_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
cnf(c_0_9,plain,
( X1 = empty_set
| in(X3,X2)
| in(X3,subset_complement(X1,X2))
| ~ element(X2,powerset(X1))
| ~ element(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,negated_conjecture,
element(esk8_0,the_carrier(esk6_0)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_11,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_struct_0]) ).
cnf(c_0_12,negated_conjecture,
( the_carrier(esk6_0) = empty_set
| in(esk8_0,subset_complement(the_carrier(esk6_0),X1))
| in(esk8_0,X1)
| ~ element(X1,powerset(the_carrier(esk6_0))) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,negated_conjecture,
element(esk7_0,powerset(the_carrier(esk6_0))),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,negated_conjecture,
( in(esk8_0,subset_complement(the_carrier(esk6_0),esk7_0))
| ~ in(esk8_0,esk7_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_15,plain,
! [X67,X68,X69] :
( ~ element(X69,powerset(X67))
| ~ in(X68,subset_complement(X67,X69))
| ~ in(X68,X69) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t54_subset_1])]) ).
fof(c_0_16,plain,
! [X50] :
( empty_carrier(X50)
| ~ one_sorted_str(X50)
| ~ empty(the_carrier(X50)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])]) ).
cnf(c_0_17,negated_conjecture,
( in(esk8_0,esk7_0)
| ~ in(esk8_0,subset_complement(the_carrier(esk6_0),esk7_0)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_18,negated_conjecture,
( the_carrier(esk6_0) = empty_set
| in(esk8_0,subset_complement(the_carrier(esk6_0),esk7_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
cnf(c_0_19,plain,
( ~ element(X1,powerset(X2))
| ~ in(X3,subset_complement(X2,X1))
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
( empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ empty(the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,negated_conjecture,
( the_carrier(esk6_0) = empty_set
| in(esk8_0,esk7_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc6_membered]) ).
cnf(c_0_23,negated_conjecture,
one_sorted_str(esk6_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_24,negated_conjecture,
~ empty_carrier(esk6_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_25,negated_conjecture,
( ~ in(X1,subset_complement(the_carrier(esk6_0),esk7_0))
| ~ in(X1,esk7_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_13]) ).
cnf(c_0_26,negated_conjecture,
in(esk8_0,esk7_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_23])]),c_0_24]) ).
cnf(c_0_27,negated_conjecture,
~ in(esk8_0,subset_complement(the_carrier(esk6_0),esk7_0)),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_26])]),c_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU321+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
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 23 21:46:49 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.55 start to proof: theBenchmark
% 0.20/0.62 % Version : CSE_E---1.5
% 0.20/0.62 % Problem : theBenchmark.p
% 0.20/0.62 % Proof found
% 0.20/0.62 % SZS status Theorem for theBenchmark.p
% 0.20/0.62 % SZS output start Proof
% See solution above
% 0.20/0.63 % Total time : 0.065000 s
% 0.20/0.63 % SZS output end Proof
% 0.20/0.63 % Total time : 0.069000 s
%------------------------------------------------------------------------------