TSTP Solution File: LCL894+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LCL894+1 : TPTP v8.1.2. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n009.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 07:00:06 EDT 2023
% Result : Theorem 0.17s 0.66s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 19
% Syntax : Number of formulae : 74 ( 30 unt; 7 typ; 0 def)
% Number of atoms : 122 ( 18 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 96 ( 41 ~; 40 |; 7 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 3 >; 3 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 113 ( 9 sgn; 48 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
'+': ( $i * $i ) > $i ).
tff(decl_23,type,
'0': $i ).
tff(decl_24,type,
'>=': ( $i * $i ) > $o ).
tff(decl_25,type,
'==>': ( $i * $i ) > $i ).
tff(decl_26,type,
c: $i ).
tff(decl_27,type,
a: $i ).
tff(decl_28,type,
b: $i ).
fof(sos_03,axiom,
! [X1] : '+'(X1,'0') = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_03) ).
fof(sos_02,axiom,
! [X1,X2] : '+'(X1,X2) = '+'(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_02) ).
fof(sos_09,axiom,
! [X12,X13,X14] :
( '>='(X12,X13)
=> '>='('+'(X12,X14),'+'(X13,X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_09) ).
fof(sos_08,axiom,
! [X1] : '>='(X1,'0'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_08) ).
fof(sos_05,axiom,
! [X4,X5,X6] :
( ( '>='(X4,X5)
& '>='(X5,X6) )
=> '>='(X4,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_05) ).
fof(goals_13,conjecture,
( ( '>='(c,a)
& '>='(c,b) )
<=> '>='(c,'+'(a,'==>'(a,b))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_13) ).
fof(sos_07,axiom,
! [X9,X10,X11] :
( '>='('+'(X9,X10),X11)
<=> '>='(X10,'==>'(X9,X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_07) ).
fof(sos_04,axiom,
! [X1] : '>='(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_04) ).
fof(sos_06,axiom,
! [X7,X8] :
( ( '>='(X7,X8)
& '>='(X8,X7) )
=> X7 = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_06) ).
fof(sos_10,axiom,
! [X15,X16,X17] :
( '>='(X15,X16)
=> '>='('==>'(X16,X17),'==>'(X15,X17)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_10) ).
fof(sos_12,axiom,
! [X1,X2] : '+'(X1,'==>'(X1,X2)) = '+'(X2,'==>'(X2,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_12) ).
fof(sos_11,axiom,
! [X18,X19,X20] :
( '>='(X18,X19)
=> '>='('==>'(X20,X18),'==>'(X20,X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_11) ).
fof(c_0_12,plain,
! [X26] : '+'(X26,'0') = X26,
inference(variable_rename,[status(thm)],[sos_03]) ).
fof(c_0_13,plain,
! [X24,X25] : '+'(X24,X25) = '+'(X25,X24),
inference(variable_rename,[status(thm)],[sos_02]) ).
fof(c_0_14,plain,
! [X37,X38,X39] :
( ~ '>='(X37,X38)
| '>='('+'(X37,X39),'+'(X38,X39)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_09])]) ).
cnf(c_0_15,plain,
'+'(X1,'0') = X1,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
'+'(X1,X2) = '+'(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_17,plain,
! [X36] : '>='(X36,'0'),
inference(variable_rename,[status(thm)],[sos_08]) ).
fof(c_0_18,plain,
! [X28,X29,X30] :
( ~ '>='(X28,X29)
| ~ '>='(X29,X30)
| '>='(X28,X30) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_05])]) ).
cnf(c_0_19,plain,
( '>='('+'(X1,X3),'+'(X2,X3))
| ~ '>='(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
'+'('0',X1) = X1,
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
'>='(X1,'0'),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,plain,
( '>='(X1,X3)
| ~ '>='(X1,X2)
| ~ '>='(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
'>='('+'(X1,X2),X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).
fof(c_0_24,negated_conjecture,
~ ( ( '>='(c,a)
& '>='(c,b) )
<=> '>='(c,'+'(a,'==>'(a,b))) ),
inference(assume_negation,[status(cth)],[goals_13]) ).
cnf(c_0_25,plain,
( '>='(X1,X2)
| ~ '>='(X1,'+'(X3,X2)) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
fof(c_0_26,negated_conjecture,
( ( ~ '>='(c,a)
| ~ '>='(c,b)
| ~ '>='(c,'+'(a,'==>'(a,b))) )
& ( '>='(c,a)
| '>='(c,'+'(a,'==>'(a,b))) )
& ( '>='(c,b)
| '>='(c,'+'(a,'==>'(a,b))) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])]) ).
fof(c_0_27,plain,
! [X33,X34,X35] :
( ( ~ '>='('+'(X33,X34),X35)
| '>='(X34,'==>'(X33,X35)) )
& ( ~ '>='(X34,'==>'(X33,X35))
| '>='('+'(X33,X34),X35) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_07])]) ).
fof(c_0_28,plain,
! [X27] : '>='(X27,X27),
inference(variable_rename,[status(thm)],[sos_04]) ).
cnf(c_0_29,plain,
( '>='(X1,X2)
| ~ '>='(X1,'+'(X2,X3)) ),
inference(spm,[status(thm)],[c_0_25,c_0_16]) ).
cnf(c_0_30,negated_conjecture,
( '>='(c,a)
| '>='(c,'+'(a,'==>'(a,b))) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_31,plain,
! [X31,X32] :
( ~ '>='(X31,X32)
| ~ '>='(X32,X31)
| X31 = X32 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_06])]) ).
cnf(c_0_32,plain,
( '>='('+'(X2,X1),X3)
| ~ '>='(X1,'==>'(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,plain,
'>='(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_34,negated_conjecture,
'>='(c,a),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,plain,
( X1 = X2
| ~ '>='(X1,X2)
| ~ '>='(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_36,plain,
( '>='(X2,'==>'(X1,X3))
| ~ '>='('+'(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_37,plain,
'>='('+'(X1,'==>'(X1,X2)),X2),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,negated_conjecture,
( '>='(X1,a)
| ~ '>='(X1,c) ),
inference(spm,[status(thm)],[c_0_22,c_0_34]) ).
cnf(c_0_39,plain,
'>='('+'(X1,X2),X1),
inference(spm,[status(thm)],[c_0_23,c_0_16]) ).
fof(c_0_40,plain,
! [X40,X41,X42] :
( ~ '>='(X40,X41)
| '>='('==>'(X41,X42),'==>'(X40,X42)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_10])]) ).
cnf(c_0_41,plain,
( '==>'(X1,X2) = X3
| ~ '>='('==>'(X1,X2),X3)
| ~ '>='('+'(X1,X3),X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_42,plain,
'>='('==>'('0',X1),X1),
inference(spm,[status(thm)],[c_0_37,c_0_20]) ).
cnf(c_0_43,plain,
( '>='(X1,'==>'(X2,X3))
| ~ '>='('+'(X2,X4),X3)
| ~ '>='(X1,X4) ),
inference(spm,[status(thm)],[c_0_22,c_0_36]) ).
cnf(c_0_44,negated_conjecture,
'>='('+'(c,X1),a),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_45,plain,
( '>='('==>'(X2,X3),'==>'(X1,X3))
| ~ '>='(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_46,plain,
'==>'('0',X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_20]),c_0_33])]) ).
cnf(c_0_47,negated_conjecture,
( '>='(X1,'==>'(c,a))
| ~ '>='(X1,X2) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_48,plain,
'>='(X1,'==>'(X2,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_21])]) ).
fof(c_0_49,plain,
! [X46,X47] : '+'(X46,'==>'(X46,X47)) = '+'(X47,'==>'(X47,X46)),
inference(variable_rename,[status(thm)],[sos_12]) ).
cnf(c_0_50,plain,
( '0' = X1
| ~ '>='('0',X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_21]) ).
cnf(c_0_51,negated_conjecture,
'>='(X1,'==>'(c,a)),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_52,plain,
'+'(X1,'==>'(X1,X2)) = '+'(X2,'==>'(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_53,negated_conjecture,
'==>'(c,a) = '0',
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_54,negated_conjecture,
( ~ '>='(c,a)
| ~ '>='(c,b)
| ~ '>='(c,'+'(a,'==>'(a,b))) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_55,plain,
( '>='(X1,X2)
| ~ '>='(X1,'+'(X3,'==>'(X3,X2))) ),
inference(spm,[status(thm)],[c_0_29,c_0_52]) ).
cnf(c_0_56,negated_conjecture,
( '>='(c,b)
| '>='(c,'+'(a,'==>'(a,b))) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_57,plain,
( '>='('+'(X1,X2),'+'(X3,X1))
| ~ '>='(X2,X3) ),
inference(spm,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_58,negated_conjecture,
'+'(a,'==>'(a,c)) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_15]) ).
fof(c_0_59,plain,
! [X43,X44,X45] :
( ~ '>='(X43,X44)
| '>='('==>'(X45,X43),'==>'(X45,X44)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_11])]) ).
cnf(c_0_60,negated_conjecture,
( ~ '>='(c,'+'(a,'==>'(a,b)))
| ~ '>='(c,b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_34])]) ).
cnf(c_0_61,negated_conjecture,
'>='(c,b),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_62,negated_conjecture,
( '>='(c,'+'(X1,a))
| ~ '>='('==>'(a,c),X1) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_63,plain,
( '>='('==>'(X3,X1),'==>'(X3,X2))
| ~ '>='(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_64,negated_conjecture,
~ '>='(c,'+'(a,'==>'(a,b))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_61])]) ).
cnf(c_0_65,negated_conjecture,
( '>='(c,'+'(a,'==>'(a,X1)))
| ~ '>='(c,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_16]) ).
cnf(c_0_66,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_61])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL894+1 : TPTP v8.1.2. Released v5.5.0.
% 0.06/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.11/0.32 % Computer : n009.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Aug 25 05:04:20 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.17/0.56 start to proof: theBenchmark
% 0.17/0.66 % Version : CSE_E---1.5
% 0.17/0.66 % Problem : theBenchmark.p
% 0.17/0.66 % Proof found
% 0.17/0.66 % SZS status Theorem for theBenchmark.p
% 0.17/0.66 % SZS output start Proof
% See solution above
% 0.17/0.67 % Total time : 0.084000 s
% 0.17/0.67 % SZS output end Proof
% 0.17/0.67 % Total time : 0.086000 s
%------------------------------------------------------------------------------