TSTP Solution File: LCL903+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LCL903+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 : n013.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 07:00:09 EDT 2023
% Result : Theorem 0.16s 0.70s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 18
% Syntax : Number of formulae : 84 ( 57 unt; 6 typ; 0 def)
% Number of atoms : 104 ( 39 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 48 ( 22 ~; 19 |; 2 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 4 ( 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 129 ( 16 sgn; 44 !; 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,
'1': $i ).
tff(decl_27,type,
esk1_0: $i ).
fof(sos_12,axiom,
! [X1] : '+'(X1,'1') = '1',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_12) ).
fof(sos_02,axiom,
! [X1,X2] : '+'(X1,X2) = '+'(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_02) ).
fof(sos_07,axiom,
! [X9,X10,X11] :
( '>='('+'(X9,X10),X11)
<=> '>='(X10,'==>'(X9,X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_07) ).
fof(sos_06,axiom,
! [X7,X8] :
( ( '>='(X7,X8)
& '>='(X8,X7) )
=> X7 = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_06) ).
fof(sos_08,axiom,
! [X1] : '>='(X1,'0'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_08) ).
fof(sos_04,axiom,
! [X1] : '>='(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_04) ).
fof(sos_03,axiom,
! [X1] : '+'(X1,'0') = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_03) ).
fof(sos_09,axiom,
! [X12,X13,X14] :
( '>='(X12,X13)
=> '>='('+'(X12,X14),'+'(X13,X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_09) ).
fof(sos_13,axiom,
! [X1] : '==>'('==>'('==>'(X1,'1'),X1),X1) = '0',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_13) ).
fof(sos_11,axiom,
! [X18,X19,X20] :
( '>='(X18,X19)
=> '>='('==>'(X20,X18),'==>'(X20,X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_11) ).
fof(sos_10,axiom,
! [X15,X16,X17] :
( '>='(X15,X16)
=> '>='('==>'(X16,X17),'==>'(X15,X17)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_10) ).
fof(goals_14,conjecture,
! [X21] : '+'(X21,X21) = X21,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_14) ).
fof(c_0_12,plain,
! [X47] : '+'(X47,'1') = '1',
inference(variable_rename,[status(thm)],[sos_12]) ).
fof(c_0_13,plain,
! [X25,X26] : '+'(X25,X26) = '+'(X26,X25),
inference(variable_rename,[status(thm)],[sos_02]) ).
fof(c_0_14,plain,
! [X34,X35,X36] :
( ( ~ '>='('+'(X34,X35),X36)
| '>='(X35,'==>'(X34,X36)) )
& ( ~ '>='(X35,'==>'(X34,X36))
| '>='('+'(X34,X35),X36) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_07])]) ).
cnf(c_0_15,plain,
'+'(X1,'1') = '1',
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,
! [X32,X33] :
( ~ '>='(X32,X33)
| ~ '>='(X33,X32)
| X32 = X33 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_06])]) ).
fof(c_0_18,plain,
! [X37] : '>='(X37,'0'),
inference(variable_rename,[status(thm)],[sos_08]) ).
cnf(c_0_19,plain,
( '>='(X2,'==>'(X1,X3))
| ~ '>='('+'(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
'+'('1',X1) = '1',
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
fof(c_0_21,plain,
! [X28] : '>='(X28,X28),
inference(variable_rename,[status(thm)],[sos_04]) ).
fof(c_0_22,plain,
! [X27] : '+'(X27,'0') = X27,
inference(variable_rename,[status(thm)],[sos_03]) ).
cnf(c_0_23,plain,
( X1 = X2
| ~ '>='(X1,X2)
| ~ '>='(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
'>='(X1,'0'),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
( '>='(X1,'==>'('1',X2))
| ~ '>='('1',X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,plain,
'>='(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,plain,
'+'(X1,'0') = X1,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,plain,
( '0' = X1
| ~ '>='('0',X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,plain,
'>='(X1,'==>'('1','1')),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
fof(c_0_30,plain,
! [X38,X39,X40] :
( ~ '>='(X38,X39)
| '>='('+'(X38,X40),'+'(X39,X40)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_09])]) ).
cnf(c_0_31,plain,
'+'('0',X1) = X1,
inference(spm,[status(thm)],[c_0_27,c_0_16]) ).
cnf(c_0_32,plain,
'0' = '==>'('1','1'),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,plain,
( '>='('+'(X1,X3),'+'(X2,X3))
| ~ '>='(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_34,plain,
'+'('==>'('1','1'),X1) = X1,
inference(rw,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,plain,
( '>='(X1,'==>'(X2,X3))
| ~ '>='('+'(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_36,plain,
'>='('+'(X1,X2),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_29]),c_0_34]) ).
cnf(c_0_37,plain,
'>='(X1,'==>'(X2,X2)),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
fof(c_0_38,plain,
! [X48] : '==>'('==>'('==>'(X48,'1'),X48),X48) = '0',
inference(variable_rename,[status(thm)],[sos_13]) ).
cnf(c_0_39,plain,
( '==>'(X1,X1) = X2
| ~ '>='('==>'(X1,X1),X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_37]) ).
fof(c_0_40,plain,
! [X44,X45,X46] :
( ~ '>='(X44,X45)
| '>='('==>'(X46,X44),'==>'(X46,X45)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_11])]) ).
cnf(c_0_41,plain,
( '>='('+'(X2,X1),X3)
| ~ '>='(X1,'==>'(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_42,plain,
'==>'('==>'('==>'(X1,'1'),X1),X1) = '0',
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_43,plain,
'+'(X1,'==>'('1','1')) = X1,
inference(rw,[status(thm)],[c_0_27,c_0_32]) ).
cnf(c_0_44,plain,
'==>'(X1,X1) = '==>'(X2,X2),
inference(spm,[status(thm)],[c_0_39,c_0_37]) ).
cnf(c_0_45,plain,
( '>='('==>'(X3,X1),'==>'(X3,X2))
| ~ '>='(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_46,plain,
'>='('1',X1),
inference(spm,[status(thm)],[c_0_36,c_0_20]) ).
cnf(c_0_47,plain,
'>='('+'(X1,'==>'(X1,X2)),X2),
inference(spm,[status(thm)],[c_0_41,c_0_26]) ).
cnf(c_0_48,plain,
'==>'('==>'('==>'(X1,'1'),X1),X1) = '==>'('1','1'),
inference(rw,[status(thm)],[c_0_42,c_0_32]) ).
cnf(c_0_49,plain,
'+'(X1,'==>'(X2,X2)) = X1,
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_50,plain,
'>='('==>'(X1,'1'),'==>'(X1,X2)),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_51,plain,
'>='('==>'('==>'(X1,'1'),X1),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]) ).
cnf(c_0_52,plain,
'>='(X1,'==>'(X2,X1)),
inference(spm,[status(thm)],[c_0_19,c_0_36]) ).
cnf(c_0_53,plain,
( X1 = '1'
| ~ '>='(X1,'1') ),
inference(spm,[status(thm)],[c_0_23,c_0_46]) ).
cnf(c_0_54,plain,
'>='('+'(X1,'==>'(X1,'1')),X2),
inference(spm,[status(thm)],[c_0_41,c_0_50]) ).
cnf(c_0_55,plain,
'==>'('==>'(X1,'1'),X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_51]),c_0_52])]) ).
cnf(c_0_56,plain,
'+'(X1,'==>'(X1,'1')) = '1',
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
fof(c_0_57,plain,
! [X41,X42,X43] :
( ~ '>='(X41,X42)
| '>='('==>'(X42,X43),'==>'(X41,X43)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_10])]) ).
cnf(c_0_58,plain,
'>='('==>'('==>'(X1,'1'),'1'),X1),
inference(spm,[status(thm)],[c_0_50,c_0_55]) ).
cnf(c_0_59,plain,
'>='(X1,'==>'('==>'(X1,'1'),X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_56]),c_0_46])]) ).
cnf(c_0_60,plain,
( '>='('==>'(X2,X3),'==>'(X1,X3))
| ~ '>='(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_61,plain,
'==>'('==>'(X1,'1'),'1') = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_58]),c_0_59])]) ).
cnf(c_0_62,plain,
'>='('==>'('==>'(X1,X2),X3),'==>'('==>'(X1,'1'),X3)),
inference(spm,[status(thm)],[c_0_60,c_0_50]) ).
cnf(c_0_63,plain,
'==>'(X1,'==>'(X1,'1')) = '==>'(X1,'1'),
inference(spm,[status(thm)],[c_0_55,c_0_61]) ).
cnf(c_0_64,plain,
'>='(X1,'==>'(X2,'+'(X2,X1))),
inference(spm,[status(thm)],[c_0_19,c_0_26]) ).
cnf(c_0_65,plain,
'>='('==>'('==>'(X1,X2),X1),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_61]),c_0_61]) ).
cnf(c_0_66,plain,
'>='('==>'(X1,X2),'==>'(X1,'==>'(X3,'+'(X3,X2)))),
inference(spm,[status(thm)],[c_0_45,c_0_64]) ).
cnf(c_0_67,plain,
'==>'('==>'(X1,X2),X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_65]),c_0_52])]) ).
cnf(c_0_68,plain,
'==>'(X1,'==>'(X2,'+'(X2,X1))) = '==>'(X1,X1),
inference(spm,[status(thm)],[c_0_39,c_0_66]) ).
cnf(c_0_69,plain,
'==>'(X1,'==>'(X1,X2)) = '==>'(X1,X2),
inference(spm,[status(thm)],[c_0_67,c_0_67]) ).
fof(c_0_70,negated_conjecture,
~ ! [X21] : '+'(X21,X21) = X21,
inference(assume_negation,[status(cth)],[goals_14]) ).
cnf(c_0_71,plain,
'==>'(X1,'+'(X1,X1)) = '==>'(X1,X1),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
fof(c_0_72,negated_conjecture,
'+'(esk1_0,esk1_0) != esk1_0,
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_70])])]) ).
cnf(c_0_73,plain,
'>='(X1,'+'(X1,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_71]),c_0_49]) ).
cnf(c_0_74,plain,
'>='('+'(X1,X2),X1),
inference(spm,[status(thm)],[c_0_36,c_0_16]) ).
cnf(c_0_75,negated_conjecture,
'+'(esk1_0,esk1_0) != esk1_0,
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_76,plain,
'+'(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_73]),c_0_74])]) ).
cnf(c_0_77,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_75,c_0_76])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL903+1 : TPTP v8.1.2. Released v5.5.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.10/0.33 % Computer : n013.cluster.edu
% 0.10/0.33 % Model : x86_64 x86_64
% 0.10/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.33 % Memory : 8042.1875MB
% 0.10/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.33 % CPULimit : 300
% 0.10/0.33 % WCLimit : 300
% 0.10/0.33 % DateTime : Fri Aug 25 04:24:17 EDT 2023
% 0.10/0.33 % CPUTime :
% 0.16/0.60 start to proof: theBenchmark
% 0.16/0.70 % Version : CSE_E---1.5
% 0.16/0.70 % Problem : theBenchmark.p
% 0.16/0.70 % Proof found
% 0.16/0.70 % SZS status Theorem for theBenchmark.p
% 0.16/0.70 % SZS output start Proof
% See solution above
% 0.16/0.70 % Total time : 0.092000 s
% 0.16/0.70 % SZS output end Proof
% 0.16/0.70 % Total time : 0.094000 s
%------------------------------------------------------------------------------