TSTP Solution File: SET807+4 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET807+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n025.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 14:35:38 EDT 2023
% Result : Theorem 54.52s 54.62s
% Output : CNFRefutation 54.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 46
% Syntax : Number of formulae : 84 ( 17 unt; 41 typ; 0 def)
% Number of atoms : 134 ( 0 equ)
% Maximal formula atoms : 46 ( 3 avg)
% Number of connectives : 131 ( 40 ~; 62 |; 21 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 75 ( 38 >; 37 *; 0 +; 0 <<)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 32 ( 32 usr; 3 con; 0-3 aty)
% Number of variables : 66 ( 0 sgn; 32 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
subset: ( $i * $i ) > $o ).
tff(decl_23,type,
member: ( $i * $i ) > $o ).
tff(decl_24,type,
equal_set: ( $i * $i ) > $o ).
tff(decl_25,type,
power_set: $i > $i ).
tff(decl_26,type,
intersection: ( $i * $i ) > $i ).
tff(decl_27,type,
union: ( $i * $i ) > $i ).
tff(decl_28,type,
empty_set: $i ).
tff(decl_29,type,
difference: ( $i * $i ) > $i ).
tff(decl_30,type,
singleton: $i > $i ).
tff(decl_31,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_32,type,
sum: $i > $i ).
tff(decl_33,type,
product: $i > $i ).
tff(decl_34,type,
disjoint: ( $i * $i ) > $o ).
tff(decl_35,type,
partition: ( $i * $i ) > $o ).
tff(decl_36,type,
equivalence: ( $i * $i ) > $o ).
tff(decl_37,type,
apply: ( $i * $i * $i ) > $o ).
tff(decl_38,type,
equivalence_class: ( $i * $i * $i ) > $i ).
tff(decl_39,type,
pre_order: ( $i * $i ) > $o ).
tff(decl_40,type,
subset_predicate: $i ).
tff(decl_41,type,
epred1_2: ( $i * $i ) > $o ).
tff(decl_42,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_43,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_44,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_45,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_46,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_47,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_48,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_49,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_50,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_51,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_52,type,
esk11_2: ( $i * $i ) > $i ).
tff(decl_53,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_54,type,
esk13_2: ( $i * $i ) > $i ).
tff(decl_55,type,
esk14_2: ( $i * $i ) > $i ).
tff(decl_56,type,
esk15_0: $i ).
tff(decl_57,type,
esk16_2: ( $i * $i ) > $i ).
tff(decl_58,type,
esk17_2: ( $i * $i ) > $i ).
tff(decl_59,type,
esk18_2: ( $i * $i ) > $i ).
tff(decl_60,type,
esk19_2: ( $i * $i ) > $i ).
tff(decl_61,type,
esk20_2: ( $i * $i ) > $i ).
tff(decl_62,type,
esk21_2: ( $i * $i ) > $i ).
fof(power_set,axiom,
! [X3,X1] :
( member(X3,power_set(X1))
<=> subset(X3,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',power_set) ).
fof(subset,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',subset) ).
fof(rel_subset,hypothesis,
! [X3,X5] :
( apply(subset_predicate,X3,X5)
<=> subset(X3,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rel_subset) ).
fof(thIV18a,conjecture,
! [X4] : pre_order(subset_predicate,power_set(X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV18a) ).
fof(pre_order,axiom,
! [X7,X4] :
( pre_order(X7,X4)
<=> ( ! [X3] :
( member(X3,X4)
=> apply(X7,X3,X3) )
& ! [X3,X5,X6] :
( ( member(X3,X4)
& member(X5,X4)
& member(X6,X4) )
=> ( ( apply(X7,X3,X5)
& apply(X7,X5,X6) )
=> apply(X7,X3,X6) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+2.ax',pre_order) ).
fof(c_0_5,plain,
! [X16,X17] :
( ( ~ member(X16,power_set(X17))
| subset(X16,X17) )
& ( ~ subset(X16,X17)
| member(X16,power_set(X17)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[power_set])]) ).
fof(c_0_6,plain,
! [X8,X9,X10,X11,X12] :
( ( ~ subset(X8,X9)
| ~ member(X10,X8)
| member(X10,X9) )
& ( member(esk1_2(X11,X12),X11)
| subset(X11,X12) )
& ( ~ member(esk1_2(X11,X12),X12)
| subset(X11,X12) ) ),
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)],[subset])])])])])]) ).
cnf(c_0_7,plain,
( member(X1,power_set(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( member(esk1_2(X1,X2),X1)
| member(X1,power_set(X2)) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
fof(c_0_11,hypothesis,
! [X85,X86] :
( ( ~ apply(subset_predicate,X85,X86)
| subset(X85,X86) )
& ( ~ subset(X85,X86)
| apply(subset_predicate,X85,X86) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[rel_subset])]) ).
cnf(c_0_12,plain,
( subset(X1,X2)
| ~ member(X1,power_set(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_13,plain,
member(X1,power_set(X1)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_7]) ).
fof(c_0_14,negated_conjecture,
~ ! [X4] : pre_order(subset_predicate,power_set(X4)),
inference(assume_negation,[status(cth)],[thIV18a]) ).
fof(c_0_15,plain,
! [X73,X74,X75,X76,X77,X78,X79,X80] :
( ( ~ member(X75,X74)
| apply(X73,X75,X75)
| ~ pre_order(X73,X74) )
& ( ~ member(X76,X74)
| ~ member(X77,X74)
| ~ member(X78,X74)
| ~ apply(X73,X76,X77)
| ~ apply(X73,X77,X78)
| apply(X73,X76,X78)
| ~ pre_order(X73,X74) )
& ( member(esk12_2(X79,X80),X80)
| member(esk11_2(X79,X80),X80)
| pre_order(X79,X80) )
& ( member(esk13_2(X79,X80),X80)
| member(esk11_2(X79,X80),X80)
| pre_order(X79,X80) )
& ( member(esk14_2(X79,X80),X80)
| member(esk11_2(X79,X80),X80)
| pre_order(X79,X80) )
& ( apply(X79,esk12_2(X79,X80),esk13_2(X79,X80))
| member(esk11_2(X79,X80),X80)
| pre_order(X79,X80) )
& ( apply(X79,esk13_2(X79,X80),esk14_2(X79,X80))
| member(esk11_2(X79,X80),X80)
| pre_order(X79,X80) )
& ( ~ apply(X79,esk12_2(X79,X80),esk14_2(X79,X80))
| member(esk11_2(X79,X80),X80)
| pre_order(X79,X80) )
& ( member(esk12_2(X79,X80),X80)
| ~ apply(X79,esk11_2(X79,X80),esk11_2(X79,X80))
| pre_order(X79,X80) )
& ( member(esk13_2(X79,X80),X80)
| ~ apply(X79,esk11_2(X79,X80),esk11_2(X79,X80))
| pre_order(X79,X80) )
& ( member(esk14_2(X79,X80),X80)
| ~ apply(X79,esk11_2(X79,X80),esk11_2(X79,X80))
| pre_order(X79,X80) )
& ( apply(X79,esk12_2(X79,X80),esk13_2(X79,X80))
| ~ apply(X79,esk11_2(X79,X80),esk11_2(X79,X80))
| pre_order(X79,X80) )
& ( apply(X79,esk13_2(X79,X80),esk14_2(X79,X80))
| ~ apply(X79,esk11_2(X79,X80),esk11_2(X79,X80))
| pre_order(X79,X80) )
& ( ~ apply(X79,esk12_2(X79,X80),esk14_2(X79,X80))
| ~ apply(X79,esk11_2(X79,X80),esk11_2(X79,X80))
| pre_order(X79,X80) ) ),
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)],[pre_order])])])])])]) ).
cnf(c_0_16,hypothesis,
( apply(subset_predicate,X1,X2)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
subset(X1,X1),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_18,negated_conjecture,
~ pre_order(subset_predicate,power_set(esk15_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
cnf(c_0_19,plain,
( apply(X1,esk12_2(X1,X2),esk13_2(X1,X2))
| pre_order(X1,X2)
| ~ apply(X1,esk11_2(X1,X2),esk11_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,hypothesis,
apply(subset_predicate,X1,X1),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,plain,
( apply(X1,esk13_2(X1,X2),esk14_2(X1,X2))
| pre_order(X1,X2)
| ~ apply(X1,esk11_2(X1,X2),esk11_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,negated_conjecture,
~ pre_order(subset_predicate,power_set(esk15_0)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,hypothesis,
( pre_order(subset_predicate,X1)
| apply(subset_predicate,esk12_2(subset_predicate,X1),esk13_2(subset_predicate,X1)) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
( pre_order(X1,X2)
| ~ apply(X1,esk12_2(X1,X2),esk14_2(X1,X2))
| ~ apply(X1,esk11_2(X1,X2),esk11_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_25,hypothesis,
( pre_order(subset_predicate,X1)
| apply(subset_predicate,esk13_2(subset_predicate,X1),esk14_2(subset_predicate,X1)) ),
inference(spm,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_26,hypothesis,
( subset(X1,X2)
| ~ apply(subset_predicate,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_27,negated_conjecture,
apply(subset_predicate,esk12_2(subset_predicate,power_set(esk15_0)),esk13_2(subset_predicate,power_set(esk15_0))),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,hypothesis,
( pre_order(subset_predicate,X1)
| ~ apply(subset_predicate,esk12_2(subset_predicate,X1),esk14_2(subset_predicate,X1)) ),
inference(spm,[status(thm)],[c_0_24,c_0_20]) ).
cnf(c_0_29,hypothesis,
( apply(subset_predicate,X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_8]) ).
cnf(c_0_30,negated_conjecture,
apply(subset_predicate,esk13_2(subset_predicate,power_set(esk15_0)),esk14_2(subset_predicate,power_set(esk15_0))),
inference(spm,[status(thm)],[c_0_22,c_0_25]) ).
cnf(c_0_31,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_32,hypothesis,
subset(esk12_2(subset_predicate,power_set(esk15_0)),esk13_2(subset_predicate,power_set(esk15_0))),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,hypothesis,
( pre_order(subset_predicate,X1)
| member(esk1_2(esk12_2(subset_predicate,X1),esk14_2(subset_predicate,X1)),esk12_2(subset_predicate,X1)) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,hypothesis,
subset(esk13_2(subset_predicate,power_set(esk15_0)),esk14_2(subset_predicate,power_set(esk15_0))),
inference(spm,[status(thm)],[c_0_26,c_0_30]) ).
cnf(c_0_35,hypothesis,
( member(X1,esk13_2(subset_predicate,power_set(esk15_0)))
| ~ member(X1,esk12_2(subset_predicate,power_set(esk15_0))) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,negated_conjecture,
member(esk1_2(esk12_2(subset_predicate,power_set(esk15_0)),esk14_2(subset_predicate,power_set(esk15_0))),esk12_2(subset_predicate,power_set(esk15_0))),
inference(spm,[status(thm)],[c_0_22,c_0_33]) ).
cnf(c_0_37,hypothesis,
( member(X1,esk14_2(subset_predicate,power_set(esk15_0)))
| ~ member(X1,esk13_2(subset_predicate,power_set(esk15_0))) ),
inference(spm,[status(thm)],[c_0_31,c_0_34]) ).
cnf(c_0_38,hypothesis,
member(esk1_2(esk12_2(subset_predicate,power_set(esk15_0)),esk14_2(subset_predicate,power_set(esk15_0))),esk13_2(subset_predicate,power_set(esk15_0))),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,hypothesis,
member(esk1_2(esk12_2(subset_predicate,power_set(esk15_0)),esk14_2(subset_predicate,power_set(esk15_0))),esk14_2(subset_predicate,power_set(esk15_0))),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_40,hypothesis,
subset(esk12_2(subset_predicate,power_set(esk15_0)),esk14_2(subset_predicate,power_set(esk15_0))),
inference(spm,[status(thm)],[c_0_9,c_0_39]) ).
cnf(c_0_41,hypothesis,
apply(subset_predicate,esk12_2(subset_predicate,power_set(esk15_0)),esk14_2(subset_predicate,power_set(esk15_0))),
inference(spm,[status(thm)],[c_0_16,c_0_40]) ).
cnf(c_0_42,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_41]),c_0_22]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET807+4 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Aug 26 16:51:08 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.54 start to proof: theBenchmark
% 54.52/54.62 % Version : CSE_E---1.5
% 54.52/54.62 % Problem : theBenchmark.p
% 54.52/54.62 % Proof found
% 54.52/54.62 % SZS status Theorem for theBenchmark.p
% 54.52/54.62 % SZS output start Proof
% See solution above
% 54.62/54.63 % Total time : 54.070000 s
% 54.62/54.63 % SZS output end Proof
% 54.62/54.63 % Total time : 54.076000 s
%------------------------------------------------------------------------------