TSTP Solution File: SET804+4 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET804+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 : 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 14:35:37 EDT 2023
% Result : Theorem 0.20s 0.61s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 37
% Syntax : Number of formulae : 58 ( 9 unt; 34 typ; 0 def)
% Number of atoms : 80 ( 11 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 90 ( 34 ~; 30 |; 18 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 79 ( 29 >; 50 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-4 aty)
% Number of functors : 21 ( 21 usr; 5 con; 0-4 aty)
% Number of variables : 50 ( 2 sgn; 30 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
order: ( $i * $i ) > $o ).
tff(decl_23,type,
member: ( $i * $i ) > $o ).
tff(decl_24,type,
apply: ( $i * $i * $i ) > $o ).
tff(decl_25,type,
total_order: ( $i * $i ) > $o ).
tff(decl_26,type,
upper_bound: ( $i * $i * $i ) > $o ).
tff(decl_27,type,
lower_bound: ( $i * $i * $i ) > $o ).
tff(decl_28,type,
greatest: ( $i * $i * $i ) > $o ).
tff(decl_29,type,
least: ( $i * $i * $i ) > $o ).
tff(decl_30,type,
max: ( $i * $i * $i ) > $o ).
tff(decl_31,type,
min: ( $i * $i * $i ) > $o ).
tff(decl_32,type,
least_upper_bound: ( $i * $i * $i * $i ) > $o ).
tff(decl_33,type,
greatest_lower_bound: ( $i * $i * $i * $i ) > $o ).
tff(decl_34,type,
epred1_2: ( $i * $i ) > $o ).
tff(decl_35,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_36,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_37,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_38,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_39,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_40,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_41,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_42,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_43,type,
esk9_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_44,type,
esk10_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_45,type,
esk11_0: $i ).
tff(decl_46,type,
esk12_0: $i ).
tff(decl_47,type,
esk13_0: $i ).
tff(decl_48,type,
esk14_0: $i ).
tff(decl_49,type,
esk15_0: $i ).
tff(decl_50,type,
esk16_2: ( $i * $i ) > $i ).
tff(decl_51,type,
esk17_2: ( $i * $i ) > $i ).
tff(decl_52,type,
esk18_2: ( $i * $i ) > $i ).
tff(decl_53,type,
esk19_2: ( $i * $i ) > $i ).
tff(decl_54,type,
esk20_2: ( $i * $i ) > $i ).
tff(decl_55,type,
esk21_2: ( $i * $i ) > $i ).
fof(thIV16,conjecture,
! [X1,X2] :
( order(X1,X2)
=> ! [X8,X9] :
( ( min(X8,X1,X2)
& min(X9,X1,X2)
& X8 != X9 )
=> ~ ? [X6] : least(X6,X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV16) ).
fof(min,axiom,
! [X1,X2,X6] :
( min(X6,X1,X2)
<=> ( member(X6,X2)
& ! [X3] :
( ( member(X3,X2)
& apply(X1,X3,X6) )
=> X6 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+3.ax',min) ).
fof(least,axiom,
! [X1,X2,X6] :
( least(X6,X1,X2)
<=> ( member(X6,X2)
& ! [X3] :
( member(X3,X2)
=> apply(X1,X6,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+3.ax',least) ).
fof(c_0_3,negated_conjecture,
~ ! [X1,X2] :
( order(X1,X2)
=> ! [X8,X9] :
( ( min(X8,X1,X2)
& min(X9,X1,X2)
& X8 != X9 )
=> ~ ? [X6] : least(X6,X1,X2) ) ),
inference(assume_negation,[status(cth)],[thIV16]) ).
fof(c_0_4,plain,
! [X60,X61,X62,X63,X64,X65,X66] :
( ( member(X62,X61)
| ~ min(X62,X60,X61) )
& ( ~ member(X63,X61)
| ~ apply(X60,X63,X62)
| X62 = X63
| ~ min(X62,X60,X61) )
& ( member(esk8_3(X64,X65,X66),X65)
| ~ member(X66,X65)
| min(X66,X64,X65) )
& ( apply(X64,esk8_3(X64,X65,X66),X66)
| ~ member(X66,X65)
| min(X66,X64,X65) )
& ( X66 != esk8_3(X64,X65,X66)
| ~ member(X66,X65)
| min(X66,X64,X65) ) ),
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)],[min])])])])])]) ).
fof(c_0_5,negated_conjecture,
( order(esk11_0,esk12_0)
& min(esk13_0,esk11_0,esk12_0)
& min(esk14_0,esk11_0,esk12_0)
& esk13_0 != esk14_0
& least(esk15_0,esk11_0,esk12_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
fof(c_0_6,plain,
! [X44,X45,X46,X47,X48,X49,X50] :
( ( member(X46,X45)
| ~ least(X46,X44,X45) )
& ( ~ member(X47,X45)
| apply(X44,X46,X47)
| ~ least(X46,X44,X45) )
& ( member(esk6_3(X48,X49,X50),X49)
| ~ member(X50,X49)
| least(X50,X48,X49) )
& ( ~ apply(X48,X50,esk6_3(X48,X49,X50))
| ~ member(X50,X49)
| least(X50,X48,X49) ) ),
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)],[least])])])])])]) ).
cnf(c_0_7,plain,
( X4 = X1
| ~ member(X1,X2)
| ~ apply(X3,X1,X4)
| ~ min(X4,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,negated_conjecture,
min(esk14_0,esk11_0,esk12_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( apply(X3,X4,X1)
| ~ member(X1,X2)
| ~ least(X4,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
least(esk15_0,esk11_0,esk12_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_11,plain,
( member(X1,X2)
| ~ least(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
( member(X1,X2)
| ~ min(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_13,negated_conjecture,
( X1 = esk14_0
| ~ apply(esk11_0,X1,esk14_0)
| ~ member(X1,esk12_0) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_14,negated_conjecture,
( apply(esk11_0,esk15_0,X1)
| ~ member(X1,esk12_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,negated_conjecture,
member(esk15_0,esk12_0),
inference(spm,[status(thm)],[c_0_11,c_0_10]) ).
cnf(c_0_16,negated_conjecture,
member(esk14_0,esk12_0),
inference(spm,[status(thm)],[c_0_12,c_0_8]) ).
cnf(c_0_17,negated_conjecture,
min(esk13_0,esk11_0,esk12_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_18,negated_conjecture,
esk15_0 = esk14_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_16])]) ).
cnf(c_0_19,negated_conjecture,
( X1 = esk13_0
| ~ apply(esk11_0,X1,esk13_0)
| ~ member(X1,esk12_0) ),
inference(spm,[status(thm)],[c_0_7,c_0_17]) ).
cnf(c_0_20,negated_conjecture,
( apply(esk11_0,esk14_0,X1)
| ~ member(X1,esk12_0) ),
inference(rw,[status(thm)],[c_0_14,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
member(esk13_0,esk12_0),
inference(spm,[status(thm)],[c_0_12,c_0_17]) ).
cnf(c_0_22,negated_conjecture,
esk13_0 != esk14_0,
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_23,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_19,c_0_20]),c_0_16]),c_0_21])]),c_0_22]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET804+4 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n007.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 12:09:11 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.59 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 : 0.019000 s
% 0.20/0.62 % SZS output end Proof
% 0.20/0.62 % Total time : 0.022000 s
%------------------------------------------------------------------------------