TSTP Solution File: SWC242+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWC242+1 : TPTP v8.1.2. Released v2.4.0.
% 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 20:21:02 EDT 2023
% Result : Theorem 0.55s 0.63s
% Output : CNFRefutation 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 81
% Syntax : Number of formulae : 102 ( 10 unt; 79 typ; 0 def)
% Number of atoms : 153 ( 40 equ)
% Maximal formula atoms : 46 ( 6 avg)
% Number of connectives : 207 ( 77 ~; 80 |; 37 &)
% ( 1 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 88 ( 69 >; 19 *; 0 +; 0 <<)
% Number of predicates : 21 ( 19 usr; 1 prp; 0-2 aty)
% Number of functors : 60 ( 60 usr; 10 con; 0-3 aty)
% Number of variables : 43 ( 0 sgn; 24 !; 8 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
ssItem: $i > $o ).
tff(decl_23,type,
neq: ( $i * $i ) > $o ).
tff(decl_24,type,
ssList: $i > $o ).
tff(decl_25,type,
memberP: ( $i * $i ) > $o ).
tff(decl_26,type,
cons: ( $i * $i ) > $i ).
tff(decl_27,type,
app: ( $i * $i ) > $i ).
tff(decl_28,type,
singletonP: $i > $o ).
tff(decl_29,type,
nil: $i ).
tff(decl_30,type,
frontsegP: ( $i * $i ) > $o ).
tff(decl_31,type,
rearsegP: ( $i * $i ) > $o ).
tff(decl_32,type,
segmentP: ( $i * $i ) > $o ).
tff(decl_33,type,
cyclefreeP: $i > $o ).
tff(decl_34,type,
leq: ( $i * $i ) > $o ).
tff(decl_35,type,
totalorderP: $i > $o ).
tff(decl_36,type,
strictorderP: $i > $o ).
tff(decl_37,type,
lt: ( $i * $i ) > $o ).
tff(decl_38,type,
totalorderedP: $i > $o ).
tff(decl_39,type,
strictorderedP: $i > $o ).
tff(decl_40,type,
duplicatefreeP: $i > $o ).
tff(decl_41,type,
equalelemsP: $i > $o ).
tff(decl_42,type,
hd: $i > $i ).
tff(decl_43,type,
tl: $i > $i ).
tff(decl_44,type,
geq: ( $i * $i ) > $o ).
tff(decl_45,type,
gt: ( $i * $i ) > $o ).
tff(decl_46,type,
esk1_0: $i ).
tff(decl_47,type,
esk2_0: $i ).
tff(decl_48,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_49,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_50,type,
esk5_1: $i > $i ).
tff(decl_51,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_52,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_53,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_54,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_55,type,
esk10_1: $i > $i ).
tff(decl_56,type,
esk11_1: $i > $i ).
tff(decl_57,type,
esk12_1: $i > $i ).
tff(decl_58,type,
esk13_1: $i > $i ).
tff(decl_59,type,
esk14_1: $i > $i ).
tff(decl_60,type,
esk15_1: $i > $i ).
tff(decl_61,type,
esk16_1: $i > $i ).
tff(decl_62,type,
esk17_1: $i > $i ).
tff(decl_63,type,
esk18_1: $i > $i ).
tff(decl_64,type,
esk19_1: $i > $i ).
tff(decl_65,type,
esk20_1: $i > $i ).
tff(decl_66,type,
esk21_1: $i > $i ).
tff(decl_67,type,
esk22_1: $i > $i ).
tff(decl_68,type,
esk23_1: $i > $i ).
tff(decl_69,type,
esk24_1: $i > $i ).
tff(decl_70,type,
esk25_1: $i > $i ).
tff(decl_71,type,
esk26_1: $i > $i ).
tff(decl_72,type,
esk27_1: $i > $i ).
tff(decl_73,type,
esk28_1: $i > $i ).
tff(decl_74,type,
esk29_1: $i > $i ).
tff(decl_75,type,
esk30_1: $i > $i ).
tff(decl_76,type,
esk31_1: $i > $i ).
tff(decl_77,type,
esk32_1: $i > $i ).
tff(decl_78,type,
esk33_1: $i > $i ).
tff(decl_79,type,
esk34_1: $i > $i ).
tff(decl_80,type,
esk35_1: $i > $i ).
tff(decl_81,type,
esk36_1: $i > $i ).
tff(decl_82,type,
esk37_1: $i > $i ).
tff(decl_83,type,
esk38_1: $i > $i ).
tff(decl_84,type,
esk39_1: $i > $i ).
tff(decl_85,type,
esk40_1: $i > $i ).
tff(decl_86,type,
esk41_1: $i > $i ).
tff(decl_87,type,
esk42_1: $i > $i ).
tff(decl_88,type,
esk43_1: $i > $i ).
tff(decl_89,type,
esk44_1: $i > $i ).
tff(decl_90,type,
esk45_1: $i > $i ).
tff(decl_91,type,
esk46_1: $i > $i ).
tff(decl_92,type,
esk47_1: $i > $i ).
tff(decl_93,type,
esk48_0: $i ).
tff(decl_94,type,
esk49_0: $i ).
tff(decl_95,type,
esk50_0: $i ).
tff(decl_96,type,
esk51_0: $i ).
tff(decl_97,type,
esk52_3: ( $i * $i * $i ) > $i ).
tff(decl_98,type,
esk53_0: $i ).
tff(decl_99,type,
esk54_0: $i ).
tff(decl_100,type,
esk55_0: $i ).
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| nil = X1
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X6,cons(X5,nil)),X7) = X1
& ! [X8] :
( ~ ssItem(X8)
| ~ memberP(X6,X8)
| ~ memberP(X7,X8)
| ~ lt(X5,X8)
| leq(X5,X8) ) ) ) )
| ( nil != X3
& ! [X9] :
( ssItem(X9)
=> ! [X10] :
( ssList(X10)
=> ! [X11] :
( ~ ssList(X11)
| app(app(X10,cons(X9,nil)),X11) != X3
| ? [X12] :
( ssItem(X12)
& ~ leq(X9,X12)
& memberP(X10,X12)
& memberP(X11,X12)
& lt(X9,X12) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax93,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( lt(X1,X2)
<=> ( X1 != X2
& leq(X1,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax93) ).
fof(c_0_2,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| nil = X1
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X6,cons(X5,nil)),X7) = X1
& ! [X8] :
( ~ ssItem(X8)
| ~ memberP(X6,X8)
| ~ memberP(X7,X8)
| ~ lt(X5,X8)
| leq(X5,X8) ) ) ) )
| ( nil != X3
& ! [X9] :
( ssItem(X9)
=> ! [X10] :
( ssList(X10)
=> ! [X11] :
( ~ ssList(X11)
| app(app(X10,cons(X9,nil)),X11) != X3
| ? [X12] :
( ssItem(X12)
& ~ leq(X9,X12)
& memberP(X10,X12)
& memberP(X11,X12)
& lt(X9,X12) ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_3,negated_conjecture,
! [X261,X262,X263,X268] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& nil != esk48_0
& ( ssItem(esk52_3(X261,X262,X263))
| ~ ssList(X263)
| app(app(X262,cons(X261,nil)),X263) != esk48_0
| ~ ssList(X262)
| ~ ssItem(X261) )
& ( memberP(X262,esk52_3(X261,X262,X263))
| ~ ssList(X263)
| app(app(X262,cons(X261,nil)),X263) != esk48_0
| ~ ssList(X262)
| ~ ssItem(X261) )
& ( memberP(X263,esk52_3(X261,X262,X263))
| ~ ssList(X263)
| app(app(X262,cons(X261,nil)),X263) != esk48_0
| ~ ssList(X262)
| ~ ssItem(X261) )
& ( lt(X261,esk52_3(X261,X262,X263))
| ~ ssList(X263)
| app(app(X262,cons(X261,nil)),X263) != esk48_0
| ~ ssList(X262)
| ~ ssItem(X261) )
& ( ~ leq(X261,esk52_3(X261,X262,X263))
| ~ ssList(X263)
| app(app(X262,cons(X261,nil)),X263) != esk48_0
| ~ ssList(X262)
| ~ ssItem(X261) )
& ( ssItem(esk53_0)
| nil = esk50_0 )
& ( ssList(esk54_0)
| nil = esk50_0 )
& ( ssList(esk55_0)
| nil = esk50_0 )
& ( app(app(esk54_0,cons(esk53_0,nil)),esk55_0) = esk50_0
| nil = esk50_0 )
& ( ~ ssItem(X268)
| leq(esk53_0,X268)
| ~ memberP(esk54_0,X268)
| ~ memberP(esk55_0,X268)
| ~ lt(esk53_0,X268)
| nil = esk50_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_4,negated_conjecture,
( app(app(esk54_0,cons(esk53_0,nil)),esk55_0) = esk50_0
| nil = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_5,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_6,negated_conjecture,
nil != esk48_0,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_7,negated_conjecture,
( ssList(esk55_0)
| nil = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_8,negated_conjecture,
( ssList(esk54_0)
| nil = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_9,negated_conjecture,
( ssItem(esk53_0)
| nil = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
fof(c_0_10,plain,
! [X250,X251] :
( ( X250 != X251
| ~ lt(X250,X251)
| ~ ssItem(X251)
| ~ ssItem(X250) )
& ( leq(X250,X251)
| ~ lt(X250,X251)
| ~ ssItem(X251)
| ~ ssItem(X250) )
& ( X250 = X251
| ~ leq(X250,X251)
| lt(X250,X251)
| ~ ssItem(X251)
| ~ ssItem(X250) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax93])])])]) ).
cnf(c_0_11,negated_conjecture,
( lt(X1,esk52_3(X1,X2,X3))
| ~ ssList(X3)
| app(app(X2,cons(X1,nil)),X3) != esk48_0
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_12,negated_conjecture,
app(app(esk54_0,cons(esk53_0,nil)),esk55_0) = esk48_0,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4,c_0_5]),c_0_5]),c_0_6]) ).
cnf(c_0_13,negated_conjecture,
ssList(esk55_0),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_5]),c_0_6]) ).
cnf(c_0_14,negated_conjecture,
ssList(esk54_0),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_5]),c_0_6]) ).
cnf(c_0_15,negated_conjecture,
ssItem(esk53_0),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_5]),c_0_6]) ).
cnf(c_0_16,negated_conjecture,
( ssItem(esk52_3(X1,X2,X3))
| ~ ssList(X3)
| app(app(X2,cons(X1,nil)),X3) != esk48_0
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_17,plain,
( leq(X1,X2)
| ~ lt(X1,X2)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,negated_conjecture,
lt(esk53_0,esk52_3(esk53_0,esk54_0,esk55_0)),
inference(cn,[status(thm)],[inference(rw,[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]),c_0_15])]) ).
cnf(c_0_19,negated_conjecture,
ssItem(esk52_3(esk53_0,esk54_0,esk55_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_12]),c_0_13]),c_0_14]),c_0_15])]) ).
cnf(c_0_20,negated_conjecture,
( ~ leq(X1,esk52_3(X1,X2,X3))
| ~ ssList(X3)
| app(app(X2,cons(X1,nil)),X3) != esk48_0
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_21,negated_conjecture,
leq(esk53_0,esk52_3(esk53_0,esk54_0,esk55_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_15])]) ).
cnf(c_0_22,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_12]),c_0_13]),c_0_14]),c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC242+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n007.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 : Mon Aug 28 15:42:13 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.18/0.56 start to proof: theBenchmark
% 0.55/0.63 % Version : CSE_E---1.5
% 0.55/0.63 % Problem : theBenchmark.p
% 0.55/0.63 % Proof found
% 0.55/0.63 % SZS status Theorem for theBenchmark.p
% 0.55/0.63 % SZS output start Proof
% See solution above
% 0.55/0.63 % Total time : 0.058000 s
% 0.55/0.63 % SZS output end Proof
% 0.55/0.63 % Total time : 0.064000 s
%------------------------------------------------------------------------------