TSTP Solution File: SWV487+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWV487+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n014.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 21:41:30 EDT 2023
% Result : Theorem 0.60s 0.78s
% Output : CNFRefutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 23
% Syntax : Number of formulae : 71 ( 12 unt; 14 typ; 0 def)
% Number of atoms : 190 ( 43 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 206 ( 73 ~; 74 |; 36 &)
% ( 4 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 7 >; 7 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 102 ( 0 sgn; 59 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
int_leq: ( $i * $i ) > $o ).
tff(decl_23,type,
int_less: ( $i * $i ) > $o ).
tff(decl_24,type,
int_zero: $i ).
tff(decl_25,type,
int_one: $i ).
tff(decl_26,type,
plus: ( $i * $i ) > $i ).
tff(decl_27,type,
real_zero: $i ).
tff(decl_28,type,
real_one: $i ).
tff(decl_29,type,
n: $i ).
tff(decl_30,type,
a: ( $i * $i ) > $i ).
tff(decl_31,type,
lu: ( $i * $i ) > $i ).
tff(decl_32,type,
epred1_2: ( $i * $i ) > $o ).
tff(decl_33,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_34,type,
esk2_0: $i ).
tff(decl_35,type,
esk3_0: $i ).
fof(int_less_transitive,axiom,
! [X1,X2,X3] :
( ( int_less(X1,X2)
& int_less(X2,X3) )
=> int_less(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int_less_transitive) ).
fof(int_leq,axiom,
! [X1,X2] :
( int_leq(X1,X2)
<=> ( int_less(X1,X2)
| X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int_leq) ).
fof(ut,conjecture,
! [X1,X2] :
( ( int_leq(int_one,X2)
& int_less(X2,X1)
& int_leq(X1,n) )
=> a(X1,X2) = real_zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ut) ).
fof(int_less_irreflexive,axiom,
! [X1,X2] :
( int_less(X1,X2)
=> X1 != X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int_less_irreflexive) ).
fof(plus_and_inverse,axiom,
! [X1,X2] :
( int_less(X1,X2)
<=> ? [X3] :
( plus(X1,X3) = X2
& int_less(int_zero,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_and_inverse) ).
fof(one_successor_of_zero,axiom,
! [X1] :
( int_less(int_zero,X1)
<=> int_leq(int_one,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_successor_of_zero) ).
fof(int_less_total,axiom,
! [X1,X2] :
( int_less(X1,X2)
| int_leq(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int_less_total) ).
fof(qiu,hypothesis,
! [X1,X2] :
( ( int_leq(int_one,X1)
& int_leq(X1,n)
& int_leq(int_one,X2)
& int_leq(X2,n) )
=> ( ! [X8] :
( ( int_less(int_zero,X8)
& X1 = plus(X2,X8) )
=> ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X2) )
=> a(plus(X3,X8),X3) = real_zero ) )
& ! [X8] :
( ( int_leq(int_zero,X8)
& X2 = plus(X1,X8) )
=> ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X1) )
=> a(X3,plus(X3,X8)) = lu(X3,plus(X3,X8)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qiu) ).
fof(c_0_8,plain,
! [X2,X1] :
( epred1_2(X1,X2)
<=> ( ! [X8] :
( ( int_less(int_zero,X8)
& X1 = plus(X2,X8) )
=> ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X2) )
=> a(plus(X3,X8),X3) = real_zero ) )
& ! [X8] :
( ( int_leq(int_zero,X8)
& X2 = plus(X1,X8) )
=> ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X1) )
=> a(X3,plus(X3,X8)) = lu(X3,plus(X3,X8)) ) ) ) ),
introduced(definition) ).
fof(c_0_9,plain,
! [X2,X1] :
( epred1_2(X1,X2)
=> ( ! [X8] :
( ( int_less(int_zero,X8)
& X1 = plus(X2,X8) )
=> ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X2) )
=> a(plus(X3,X8),X3) = real_zero ) )
& ! [X8] :
( ( int_leq(int_zero,X8)
& X2 = plus(X1,X8) )
=> ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X1) )
=> a(X3,plus(X3,X8)) = lu(X3,plus(X3,X8)) ) ) ) ),
inference(split_equiv,[status(thm)],[c_0_8]) ).
fof(c_0_10,plain,
! [X11,X12,X13] :
( ~ int_less(X11,X12)
| ~ int_less(X12,X13)
| int_less(X11,X13) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[int_less_transitive])]) ).
fof(c_0_11,plain,
! [X9,X10] :
( ( ~ int_leq(X9,X10)
| int_less(X9,X10)
| X9 = X10 )
& ( ~ int_less(X9,X10)
| int_leq(X9,X10) )
& ( X9 != X10
| int_leq(X9,X10) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[int_leq])])]) ).
fof(c_0_12,negated_conjecture,
~ ! [X1,X2] :
( ( int_leq(int_one,X2)
& int_less(X2,X1)
& int_leq(X1,n) )
=> a(X1,X2) = real_zero ),
inference(assume_negation,[status(cth)],[ut]) ).
fof(c_0_13,plain,
! [X36,X37,X38,X39,X40,X41] :
( ( ~ int_less(int_zero,X38)
| X37 != plus(X36,X38)
| ~ int_leq(int_one,X39)
| ~ int_leq(X39,X36)
| a(plus(X39,X38),X39) = real_zero
| ~ epred1_2(X37,X36) )
& ( ~ int_leq(int_zero,X40)
| X36 != plus(X37,X40)
| ~ int_leq(int_one,X41)
| ~ int_leq(X41,X37)
| a(X41,plus(X41,X40)) = lu(X41,plus(X41,X40))
| ~ epred1_2(X37,X36) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).
fof(c_0_14,plain,
! [X14,X15] :
( ~ int_less(X14,X15)
| X14 != X15 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[int_less_irreflexive])]) ).
cnf(c_0_15,plain,
( int_less(X1,X3)
| ~ int_less(X1,X2)
| ~ int_less(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( int_less(X1,X2)
| X1 = X2
| ~ int_leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_17,negated_conjecture,
( int_leq(int_one,esk3_0)
& int_less(esk3_0,esk2_0)
& int_leq(esk2_0,n)
& a(esk2_0,esk3_0) != real_zero ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
cnf(c_0_18,plain,
( a(plus(X4,X1),X4) = real_zero
| ~ int_less(int_zero,X1)
| X2 != plus(X3,X1)
| ~ int_leq(int_one,X4)
| ~ int_leq(X4,X3)
| ~ epred1_2(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_19,plain,
! [X25,X26,X28,X29,X30] :
( ( plus(X25,esk1_2(X25,X26)) = X26
| ~ int_less(X25,X26) )
& ( int_less(int_zero,esk1_2(X25,X26))
| ~ int_less(X25,X26) )
& ( plus(X28,X30) != X29
| ~ int_less(int_zero,X30)
| int_less(X28,X29) ) ),
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)],[plus_and_inverse])])])])])]) ).
cnf(c_0_20,plain,
( ~ int_less(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
( X1 = X2
| int_less(X3,X2)
| ~ int_less(X3,X1)
| ~ int_leq(X1,X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,negated_conjecture,
int_leq(esk2_0,n),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,negated_conjecture,
int_less(esk3_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
( a(plus(X1,X2),X1) = real_zero
| ~ epred1_2(plus(X3,X2),X3)
| ~ int_less(int_zero,X2)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,X3) ),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
( plus(X1,esk1_2(X1,X2)) = X2
| ~ int_less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
( int_less(int_zero,esk1_2(X1,X2))
| ~ int_less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,plain,
( int_leq(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_28,plain,
! [X31] :
( ( ~ int_less(int_zero,X31)
| int_leq(int_one,X31) )
& ( ~ int_leq(int_one,X31)
| int_less(int_zero,X31) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[one_successor_of_zero])]) ).
cnf(c_0_29,plain,
~ int_less(X1,X1),
inference(er,[status(thm)],[c_0_20]) ).
cnf(c_0_30,negated_conjecture,
( n = esk2_0
| int_less(X1,n)
| ~ int_less(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_31,plain,
( int_leq(X1,X2)
| ~ int_less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_32,negated_conjecture,
( int_less(X1,esk2_0)
| ~ int_less(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_15,c_0_23]) ).
fof(c_0_33,plain,
! [X16,X17] :
( int_less(X16,X17)
| int_leq(X17,X16) ),
inference(variable_rename,[status(thm)],[int_less_total]) ).
cnf(c_0_34,plain,
( a(plus(X1,esk1_2(X2,X3)),X1) = real_zero
| ~ epred1_2(X3,X2)
| ~ int_less(X2,X3)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_35,plain,
int_leq(X1,X1),
inference(er,[status(thm)],[c_0_27]) ).
fof(c_0_36,hypothesis,
! [X1,X2] :
( ( int_leq(int_one,X1)
& int_leq(X1,n)
& int_leq(int_one,X2)
& int_leq(X2,n) )
=> epred1_2(X1,X2) ),
inference(apply_def,[status(thm)],[qiu,c_0_8]) ).
cnf(c_0_37,plain,
( int_leq(int_one,X1)
| ~ int_less(int_zero,X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_38,negated_conjecture,
( n = esk2_0
| ~ int_less(n,esk2_0) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_39,negated_conjecture,
( int_leq(X1,esk2_0)
| ~ int_less(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_40,plain,
( int_less(X1,X2)
| int_leq(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_41,negated_conjecture,
a(esk2_0,esk3_0) != real_zero,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_42,plain,
( a(X1,X2) = real_zero
| ~ epred1_2(X1,X2)
| ~ int_less(X2,X1)
| ~ int_leq(int_one,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_25]),c_0_35])]) ).
cnf(c_0_43,negated_conjecture,
int_leq(int_one,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_44,hypothesis,
! [X32,X33] :
( ~ int_leq(int_one,X32)
| ~ int_leq(X32,n)
| ~ int_leq(int_one,X33)
| ~ int_leq(X33,n)
| epred1_2(X32,X33) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])]) ).
cnf(c_0_45,negated_conjecture,
( int_leq(int_one,esk2_0)
| ~ int_less(int_zero,esk3_0) ),
inference(spm,[status(thm)],[c_0_37,c_0_32]) ).
cnf(c_0_46,plain,
( int_less(int_zero,X1)
| ~ int_leq(int_one,X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_47,negated_conjecture,
( n = esk2_0
| ~ int_leq(n,esk2_0) ),
inference(spm,[status(thm)],[c_0_38,c_0_16]) ).
cnf(c_0_48,negated_conjecture,
( int_leq(esk3_0,X1)
| int_leq(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_49,negated_conjecture,
~ epred1_2(esk2_0,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_23]),c_0_43])]) ).
cnf(c_0_50,hypothesis,
( epred1_2(X1,X2)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X2)
| ~ int_leq(X2,n) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_51,negated_conjecture,
int_leq(int_one,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_43])]) ).
cnf(c_0_52,negated_conjecture,
( n = esk2_0
| int_leq(esk3_0,n) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_53,hypothesis,
~ int_leq(esk3_0,n),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_22]),c_0_43]),c_0_51])]) ).
cnf(c_0_54,negated_conjecture,
n = esk2_0,
inference(sr,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_55,negated_conjecture,
int_leq(esk3_0,esk2_0),
inference(spm,[status(thm)],[c_0_31,c_0_23]) ).
cnf(c_0_56,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_54]),c_0_55])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWV487+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n014.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 06:02:30 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 0.60/0.78 % Version : CSE_E---1.5
% 0.60/0.78 % Problem : theBenchmark.p
% 0.60/0.78 % Proof found
% 0.60/0.78 % SZS status Theorem for theBenchmark.p
% 0.60/0.78 % SZS output start Proof
% See solution above
% 0.60/0.79 % Total time : 0.212000 s
% 0.60/0.79 % SZS output end Proof
% 0.60/0.79 % Total time : 0.215000 s
%------------------------------------------------------------------------------