TSTP Solution File: SET776+4 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET776+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n015.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 14:35:30 EDT 2023
% Result : Theorem 0.19s 0.68s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 48
% Syntax : Number of formulae : 71 ( 13 unt; 46 typ; 0 def)
% Number of atoms : 154 ( 0 equ)
% Maximal formula atoms : 46 ( 6 avg)
% Number of connectives : 188 ( 59 ~; 71 |; 44 &)
% ( 3 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 5 avg)
% Maximal term depth : 2 ( 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 : 37 ( 37 usr; 8 con; 0-3 aty)
% Number of variables : 49 ( 0 sgn; 34 !; 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,
epred1_2: ( $i * $i ) > $o ).
tff(decl_41,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_42,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_43,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_44,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_45,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_46,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_47,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_48,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_49,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_50,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_51,type,
esk11_2: ( $i * $i ) > $i ).
tff(decl_52,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_53,type,
esk13_2: ( $i * $i ) > $i ).
tff(decl_54,type,
esk14_2: ( $i * $i ) > $i ).
tff(decl_55,type,
esk15_0: $i ).
tff(decl_56,type,
esk16_0: $i ).
tff(decl_57,type,
esk17_0: $i ).
tff(decl_58,type,
esk18_0: $i ).
tff(decl_59,type,
esk19_0: $i ).
tff(decl_60,type,
esk20_0: $i ).
tff(decl_61,type,
esk21_0: $i ).
tff(decl_62,type,
esk22_2: ( $i * $i ) > $i ).
tff(decl_63,type,
esk23_2: ( $i * $i ) > $i ).
tff(decl_64,type,
esk24_2: ( $i * $i ) > $i ).
tff(decl_65,type,
esk25_2: ( $i * $i ) > $i ).
tff(decl_66,type,
esk26_2: ( $i * $i ) > $i ).
tff(decl_67,type,
esk27_2: ( $i * $i ) > $i ).
fof(thIII12,conjecture,
! [X4,X8,X7] :
( ( pre_order(X8,X4)
& ! [X1,X2] :
( ( member(X1,X4)
& member(X2,X4) )
=> ( apply(X7,X1,X2)
<=> ( apply(X8,X1,X2)
& apply(X8,X2,X1) ) ) ) )
=> ! [X9,X10,X11,X12] :
( ( member(X9,X4)
& member(X10,X4)
& member(X11,X4)
& member(X12,X4) )
=> ( ( apply(X7,X9,X11)
& apply(X7,X10,X12)
& apply(X8,X9,X10) )
=> apply(X8,X11,X12) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIII12) ).
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_2,negated_conjecture,
~ ! [X4,X8,X7] :
( ( pre_order(X8,X4)
& ! [X1,X2] :
( ( member(X1,X4)
& member(X2,X4) )
=> ( apply(X7,X1,X2)
<=> ( apply(X8,X1,X2)
& apply(X8,X2,X1) ) ) ) )
=> ! [X9,X10,X11,X12] :
( ( member(X9,X4)
& member(X10,X4)
& member(X11,X4)
& member(X12,X4) )
=> ( ( apply(X7,X9,X11)
& apply(X7,X10,X12)
& apply(X8,X9,X10) )
=> apply(X8,X11,X12) ) ) ),
inference(assume_negation,[status(cth)],[thIII12]) ).
fof(c_0_3,plain,
! [X78,X79,X80,X81,X82,X83,X84,X85] :
( ( ~ member(X80,X79)
| apply(X78,X80,X80)
| ~ pre_order(X78,X79) )
& ( ~ member(X81,X79)
| ~ member(X82,X79)
| ~ member(X83,X79)
| ~ apply(X78,X81,X82)
| ~ apply(X78,X82,X83)
| apply(X78,X81,X83)
| ~ pre_order(X78,X79) )
& ( member(esk12_2(X84,X85),X85)
| member(esk11_2(X84,X85),X85)
| pre_order(X84,X85) )
& ( member(esk13_2(X84,X85),X85)
| member(esk11_2(X84,X85),X85)
| pre_order(X84,X85) )
& ( member(esk14_2(X84,X85),X85)
| member(esk11_2(X84,X85),X85)
| pre_order(X84,X85) )
& ( apply(X84,esk12_2(X84,X85),esk13_2(X84,X85))
| member(esk11_2(X84,X85),X85)
| pre_order(X84,X85) )
& ( apply(X84,esk13_2(X84,X85),esk14_2(X84,X85))
| member(esk11_2(X84,X85),X85)
| pre_order(X84,X85) )
& ( ~ apply(X84,esk12_2(X84,X85),esk14_2(X84,X85))
| member(esk11_2(X84,X85),X85)
| pre_order(X84,X85) )
& ( member(esk12_2(X84,X85),X85)
| ~ apply(X84,esk11_2(X84,X85),esk11_2(X84,X85))
| pre_order(X84,X85) )
& ( member(esk13_2(X84,X85),X85)
| ~ apply(X84,esk11_2(X84,X85),esk11_2(X84,X85))
| pre_order(X84,X85) )
& ( member(esk14_2(X84,X85),X85)
| ~ apply(X84,esk11_2(X84,X85),esk11_2(X84,X85))
| pre_order(X84,X85) )
& ( apply(X84,esk12_2(X84,X85),esk13_2(X84,X85))
| ~ apply(X84,esk11_2(X84,X85),esk11_2(X84,X85))
| pre_order(X84,X85) )
& ( apply(X84,esk13_2(X84,X85),esk14_2(X84,X85))
| ~ apply(X84,esk11_2(X84,X85),esk11_2(X84,X85))
| pre_order(X84,X85) )
& ( ~ apply(X84,esk12_2(X84,X85),esk14_2(X84,X85))
| ~ apply(X84,esk11_2(X84,X85),esk11_2(X84,X85))
| pre_order(X84,X85) ) ),
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])])])])])]) ).
fof(c_0_4,negated_conjecture,
! [X93,X94] :
( pre_order(esk16_0,esk15_0)
& ( apply(esk16_0,X93,X94)
| ~ apply(esk17_0,X93,X94)
| ~ member(X93,esk15_0)
| ~ member(X94,esk15_0) )
& ( apply(esk16_0,X94,X93)
| ~ apply(esk17_0,X93,X94)
| ~ member(X93,esk15_0)
| ~ member(X94,esk15_0) )
& ( ~ apply(esk16_0,X93,X94)
| ~ apply(esk16_0,X94,X93)
| apply(esk17_0,X93,X94)
| ~ member(X93,esk15_0)
| ~ member(X94,esk15_0) )
& member(esk18_0,esk15_0)
& member(esk19_0,esk15_0)
& member(esk20_0,esk15_0)
& member(esk21_0,esk15_0)
& apply(esk17_0,esk18_0,esk20_0)
& apply(esk17_0,esk19_0,esk21_0)
& apply(esk16_0,esk18_0,esk19_0)
& ~ apply(esk16_0,esk20_0,esk21_0) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])])])]) ).
cnf(c_0_5,plain,
( apply(X5,X1,X4)
| ~ member(X1,X2)
| ~ member(X3,X2)
| ~ member(X4,X2)
| ~ apply(X5,X1,X3)
| ~ apply(X5,X3,X4)
| ~ pre_order(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_6,negated_conjecture,
apply(esk16_0,esk18_0,esk19_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,negated_conjecture,
( apply(esk16_0,X1,X2)
| ~ apply(esk17_0,X2,X1)
| ~ member(X2,esk15_0)
| ~ member(X1,esk15_0) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,negated_conjecture,
apply(esk17_0,esk18_0,esk20_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_9,negated_conjecture,
member(esk18_0,esk15_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_10,negated_conjecture,
member(esk20_0,esk15_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_11,negated_conjecture,
( apply(esk16_0,X1,X2)
| ~ apply(esk17_0,X1,X2)
| ~ member(X1,esk15_0)
| ~ member(X2,esk15_0) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_12,negated_conjecture,
apply(esk17_0,esk19_0,esk21_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_13,negated_conjecture,
member(esk21_0,esk15_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_14,negated_conjecture,
member(esk19_0,esk15_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_15,negated_conjecture,
( apply(esk16_0,X1,esk19_0)
| ~ pre_order(esk16_0,X2)
| ~ apply(esk16_0,X1,esk18_0)
| ~ member(esk19_0,X2)
| ~ member(esk18_0,X2)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_16,negated_conjecture,
apply(esk16_0,esk20_0,esk18_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9]),c_0_10])]) ).
cnf(c_0_17,negated_conjecture,
apply(esk16_0,esk19_0,esk21_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_14])]) ).
cnf(c_0_18,negated_conjecture,
( apply(esk16_0,esk20_0,esk19_0)
| ~ pre_order(esk16_0,X1)
| ~ member(esk19_0,X1)
| ~ member(esk18_0,X1)
| ~ member(esk20_0,X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,negated_conjecture,
pre_order(esk16_0,esk15_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_20,negated_conjecture,
( apply(esk16_0,X1,esk21_0)
| ~ pre_order(esk16_0,X2)
| ~ apply(esk16_0,X1,esk19_0)
| ~ member(esk21_0,X2)
| ~ member(esk19_0,X2)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_5,c_0_17]) ).
cnf(c_0_21,negated_conjecture,
apply(esk16_0,esk20_0,esk19_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_14]),c_0_9]),c_0_10])]) ).
cnf(c_0_22,negated_conjecture,
~ apply(esk16_0,esk20_0,esk21_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_23,negated_conjecture,
( ~ pre_order(esk16_0,X1)
| ~ member(esk21_0,X1)
| ~ member(esk19_0,X1)
| ~ member(esk20_0,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_24,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_19]),c_0_13]),c_0_14]),c_0_10])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET776+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n015.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 : Sat Aug 26 16:28:08 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 0.19/0.68 % Version : CSE_E---1.5
% 0.19/0.68 % Problem : theBenchmark.p
% 0.19/0.68 % Proof found
% 0.19/0.68 % SZS status Theorem for theBenchmark.p
% 0.19/0.68 % SZS output start Proof
% See solution above
% 0.19/0.69 % Total time : 0.107000 s
% 0.19/0.69 % SZS output end Proof
% 0.19/0.69 % Total time : 0.110000 s
%------------------------------------------------------------------------------