TSTP Solution File: SWV488+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWV488+2 : 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 : n001.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 0.24s 0.66s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 19
% Syntax : Number of formulae : 41 ( 10 unt; 14 typ; 0 def)
% Number of atoms : 132 ( 39 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 150 ( 45 ~; 42 |; 39 &)
% ( 2 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 3 ( 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 : 54 ( 1 sgn; 40 !; 0 ?; 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(qil,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) = lu(plus(X3,X8),X3) ) )
& ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X2) )
=> a(X3,X3) = real_one )
& ! [X8] :
( ( int_less(int_zero,X8)
& X2 = plus(X1,X8) )
=> ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X1) )
=> a(X3,plus(X3,X8)) = real_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qil) ).
fof(lti,conjecture,
! [X1,X2] :
( ( int_leq(int_one,X1)
& int_leq(X1,X2)
& int_leq(X2,n) )
=> ( X1 = X2
=> a(X1,X2) != real_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lti) ).
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(real_constants,axiom,
real_zero != real_one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',real_constants) ).
fof(c_0_4,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) = lu(plus(X3,X8),X3) ) )
& ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X2) )
=> a(X3,X3) = real_one )
& ! [X8] :
( ( int_less(int_zero,X8)
& X2 = plus(X1,X8) )
=> ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X1) )
=> a(X3,plus(X3,X8)) = real_zero ) ) ) ),
introduced(definition) ).
fof(c_0_5,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) = lu(plus(X3,X8),X3) ) )
& ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X2) )
=> a(X3,X3) = real_one )
& ! [X8] :
( ( int_less(int_zero,X8)
& X2 = plus(X1,X8) )
=> ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X1) )
=> a(X3,plus(X3,X8)) = real_zero ) ) ) ),
inference(split_equiv,[status(thm)],[c_0_4]) ).
fof(c_0_6,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)],[qil,c_0_4]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2] :
( ( int_leq(int_one,X1)
& int_leq(X1,X2)
& int_leq(X2,n) )
=> ( X1 = X2
=> a(X1,X2) != real_zero ) ),
inference(assume_negation,[status(cth)],[lti]) ).
fof(c_0_8,plain,
! [X36,X37,X38,X39,X40,X41,X42] :
( ( ~ int_less(int_zero,X38)
| X37 != plus(X36,X38)
| ~ int_leq(int_one,X39)
| ~ int_leq(X39,X36)
| a(plus(X39,X38),X39) = lu(plus(X39,X38),X39)
| ~ epred1_2(X37,X36) )
& ( ~ int_leq(int_one,X40)
| ~ int_leq(X40,X36)
| a(X40,X40) = real_one
| ~ epred1_2(X37,X36) )
& ( ~ int_less(int_zero,X41)
| X36 != plus(X37,X41)
| ~ int_leq(int_one,X42)
| ~ int_leq(X42,X37)
| a(X42,plus(X42,X41)) = real_zero
| ~ 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_5])])])]) ).
fof(c_0_9,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_6])]) ).
fof(c_0_10,negated_conjecture,
( int_leq(int_one,esk2_0)
& int_leq(esk2_0,esk3_0)
& int_leq(esk3_0,n)
& esk2_0 = esk3_0
& a(esk2_0,esk3_0) = real_zero ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
cnf(c_0_11,plain,
( a(X1,X1) = real_one
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,X2)
| ~ epred1_2(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,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_9]) ).
cnf(c_0_13,negated_conjecture,
int_leq(esk3_0,n),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,negated_conjecture,
esk2_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,hypothesis,
( a(X1,X1) = real_one
| ~ int_leq(int_one,X1)
| ~ int_leq(X2,n)
| ~ int_leq(X3,n)
| ~ int_leq(int_one,X2)
| ~ int_leq(int_one,X3)
| ~ int_leq(X1,X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,negated_conjecture,
int_leq(esk2_0,n),
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,negated_conjecture,
int_leq(int_one,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_18,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])])]) ).
cnf(c_0_19,negated_conjecture,
a(esk2_0,esk3_0) = real_zero,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_20,negated_conjecture,
( a(X1,X1) = real_one
| ~ int_leq(int_one,X1)
| ~ int_leq(X2,n)
| ~ int_leq(int_one,X2)
| ~ int_leq(X1,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]) ).
cnf(c_0_21,plain,
( int_leq(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,negated_conjecture,
a(esk2_0,esk2_0) = real_zero,
inference(rw,[status(thm)],[c_0_19,c_0_14]) ).
cnf(c_0_23,negated_conjecture,
( a(X1,X1) = real_one
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_16]),c_0_17])]) ).
cnf(c_0_24,plain,
int_leq(X1,X1),
inference(er,[status(thm)],[c_0_21]) ).
cnf(c_0_25,plain,
real_zero != real_one,
inference(split_conjunct,[status(thm)],[real_constants]) ).
cnf(c_0_26,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_22,c_0_23]),c_0_17]),c_0_24])]),c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV488+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.16/0.34 % Computer : n001.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Aug 29 08:18:07 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.24/0.57 start to proof: theBenchmark
% 0.24/0.66 % Version : CSE_E---1.5
% 0.24/0.66 % Problem : theBenchmark.p
% 0.24/0.66 % Proof found
% 0.24/0.66 % SZS status Theorem for theBenchmark.p
% 0.24/0.66 % SZS output start Proof
% See solution above
% 0.24/0.66 % Total time : 0.076000 s
% 0.24/0.66 % SZS output end Proof
% 0.24/0.66 % Total time : 0.079000 s
%------------------------------------------------------------------------------