TSTP Solution File: LCL889+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LCL889+1 : TPTP v8.1.2. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n028.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 07:00:05 EDT 2023
% Result : Theorem 5.28s 5.34s
% Output : CNFRefutation 5.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 18
% Syntax : Number of formulae : 83 ( 54 unt; 7 typ; 0 def)
% Number of atoms : 109 ( 34 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 55 ( 22 ~; 19 |; 7 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 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 : 130 ( 21 sgn; 52 !; 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,
esk1_0: $i ).
tff(decl_27,type,
esk2_0: $i ).
tff(decl_28,type,
esk3_0: $i ).
fof(sos_03,axiom,
! [X1] : '+'(X1,'0') = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_03) ).
fof(sos_02,axiom,
! [X1,X2] : '+'(X1,X2) = '+'(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_02) ).
fof(sos_06,axiom,
! [X7,X8] :
( ( '>='(X7,X8)
& '>='(X8,X7) )
=> X7 = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_06) ).
fof(sos_08,axiom,
! [X1] : '>='(X1,'0'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_08) ).
fof(sos_07,axiom,
! [X9,X10,X11] :
( '>='('+'(X9,X10),X11)
<=> '>='(X10,'==>'(X9,X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_07) ).
fof(sos_10,axiom,
! [X15,X16,X17] :
( '>='(X15,X16)
=> '>='('==>'(X16,X17),'==>'(X15,X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_10) ).
fof(goals_13,conjecture,
! [X21,X22,X23] :
( ( '>='(X21,'==>'(X21,X22))
& X23 = '==>'(X23,X22) )
=> '>='(X21,X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_13) ).
fof(sos_12,axiom,
! [X1,X2] : '+'(X1,'==>'(X1,X2)) = '+'(X2,'==>'(X2,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_12) ).
fof(sos_09,axiom,
! [X12,X13,X14] :
( '>='(X12,X13)
=> '>='('+'(X12,X14),'+'(X13,X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_09) ).
fof(sos_01,axiom,
! [X1,X2,X3] : '+'('+'(X1,X2),X3) = '+'(X1,'+'(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_01) ).
fof(sos_05,axiom,
! [X4,X5,X6] :
( ( '>='(X4,X5)
& '>='(X5,X6) )
=> '>='(X4,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_05) ).
fof(c_0_11,plain,
! [X29] : '+'(X29,'0') = X29,
inference(variable_rename,[status(thm)],[sos_03]) ).
fof(c_0_12,plain,
! [X27,X28] : '+'(X27,X28) = '+'(X28,X27),
inference(variable_rename,[status(thm)],[sos_02]) ).
fof(c_0_13,plain,
! [X34,X35] :
( ~ '>='(X34,X35)
| ~ '>='(X35,X34)
| X34 = X35 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_06])]) ).
fof(c_0_14,plain,
! [X39] : '>='(X39,'0'),
inference(variable_rename,[status(thm)],[sos_08]) ).
fof(c_0_15,plain,
! [X36,X37,X38] :
( ( ~ '>='('+'(X36,X37),X38)
| '>='(X37,'==>'(X36,X38)) )
& ( ~ '>='(X37,'==>'(X36,X38))
| '>='('+'(X36,X37),X38) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_07])]) ).
fof(c_0_16,plain,
! [X43,X44,X45] :
( ~ '>='(X43,X44)
| '>='('==>'(X44,X45),'==>'(X43,X45)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_10])]) ).
fof(c_0_17,negated_conjecture,
~ ! [X21,X22,X23] :
( ( '>='(X21,'==>'(X21,X22))
& X23 = '==>'(X23,X22) )
=> '>='(X21,X23) ),
inference(assume_negation,[status(cth)],[goals_13]) ).
cnf(c_0_18,plain,
'+'(X1,'0') = X1,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,plain,
'+'(X1,X2) = '+'(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_20,plain,
! [X49,X50] : '+'(X49,'==>'(X49,X50)) = '+'(X50,'==>'(X50,X49)),
inference(variable_rename,[status(thm)],[sos_12]) ).
cnf(c_0_21,plain,
( X1 = X2
| ~ '>='(X1,X2)
| ~ '>='(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,plain,
'>='(X1,'0'),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,plain,
( '>='(X2,'==>'(X1,X3))
| ~ '>='('+'(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,plain,
( '>='('==>'(X2,X3),'==>'(X1,X3))
| ~ '>='(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_25,negated_conjecture,
( '>='(esk1_0,'==>'(esk1_0,esk2_0))
& esk3_0 = '==>'(esk3_0,esk2_0)
& ~ '>='(esk1_0,esk3_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])]) ).
cnf(c_0_26,plain,
'+'('0',X1) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_27,plain,
'+'(X1,'==>'(X1,X2)) = '+'(X2,'==>'(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,plain,
( '0' = X1
| ~ '>='('0',X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_29,plain,
'>='(X1,'==>'(X2,'0')),
inference(spm,[status(thm)],[c_0_23,c_0_22]) ).
fof(c_0_30,plain,
! [X40,X41,X42] :
( ~ '>='(X40,X41)
| '>='('+'(X40,X42),'+'(X41,X42)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_09])]) ).
cnf(c_0_31,plain,
'>='('==>'('0',X1),'==>'(X2,X1)),
inference(spm,[status(thm)],[c_0_24,c_0_22]) ).
cnf(c_0_32,negated_conjecture,
esk3_0 = '==>'(esk3_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_33,plain,
'+'(X1,'==>'(X1,'0')) = '==>'('0',X1),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_34,plain,
'==>'(X1,'0') = '0',
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_35,plain,
( '>='('+'(X1,X3),'+'(X2,X3))
| ~ '>='(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_36,plain,
! [X24,X25,X26] : '+'('+'(X24,X25),X26) = '+'(X24,'+'(X25,X26)),
inference(variable_rename,[status(thm)],[sos_01]) ).
fof(c_0_37,plain,
! [X31,X32,X33] :
( ~ '>='(X31,X32)
| ~ '>='(X32,X33)
| '>='(X31,X33) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_05])]) ).
cnf(c_0_38,negated_conjecture,
'>='('==>'('0',esk2_0),esk3_0),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_39,plain,
'==>'('0',X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34]),c_0_18]) ).
cnf(c_0_40,plain,
'>='('+'(X1,X2),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_22]),c_0_26]) ).
cnf(c_0_41,plain,
'+'('+'(X1,X2),X3) = '+'(X1,'+'(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_42,plain,
( '>='(X1,X3)
| ~ '>='(X1,X2)
| ~ '>='(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_43,negated_conjecture,
'>='(esk1_0,'==>'(esk1_0,esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_44,negated_conjecture,
'>='(esk2_0,esk3_0),
inference(rw,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_45,plain,
'>='('+'(X1,X2),X1),
inference(spm,[status(thm)],[c_0_40,c_0_19]) ).
cnf(c_0_46,plain,
'+'(X1,'+'('==>'(X1,'0'),X2)) = '+'('==>'('0',X1),X2),
inference(spm,[status(thm)],[c_0_41,c_0_33]) ).
cnf(c_0_47,negated_conjecture,
( '>='(X1,'==>'(esk1_0,esk2_0))
| ~ '>='(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_48,negated_conjecture,
( '>='(X1,esk3_0)
| ~ '>='(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_42,c_0_44]) ).
cnf(c_0_49,plain,
'>='('+'('==>'('0',X1),X2),X1),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_50,plain,
( '>='('+'(X2,X1),X3)
| ~ '>='(X1,'==>'(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_51,negated_conjecture,
'>='('+'(X1,esk1_0),'==>'(esk1_0,esk2_0)),
inference(spm,[status(thm)],[c_0_47,c_0_40]) ).
cnf(c_0_52,negated_conjecture,
'>='('+'(esk2_0,X1),esk3_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_39]) ).
cnf(c_0_53,negated_conjecture,
'>='('+'(esk1_0,'+'(X1,esk1_0)),esk2_0),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_54,plain,
'+'(X1,'+'('==>'(X1,X2),X3)) = '+'(X2,'+'('==>'(X2,X1),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_27]),c_0_41]) ).
cnf(c_0_55,negated_conjecture,
'>='(X1,'==>'(esk2_0,esk3_0)),
inference(spm,[status(thm)],[c_0_23,c_0_52]) ).
cnf(c_0_56,negated_conjecture,
'>='('+'(X1,'+'(esk1_0,'==>'(X1,esk1_0))),esk2_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_19]) ).
cnf(c_0_57,negated_conjecture,
'==>'(esk2_0,esk3_0) = '0',
inference(spm,[status(thm)],[c_0_28,c_0_55]) ).
cnf(c_0_58,plain,
'>='('+'(X1,'+'(X2,X3)),X3),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_59,negated_conjecture,
'>='('+'(esk1_0,'==>'(X1,esk1_0)),'==>'(X1,esk2_0)),
inference(spm,[status(thm)],[c_0_23,c_0_56]) ).
cnf(c_0_60,negated_conjecture,
'+'(esk3_0,esk3_0) = esk2_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_57]),c_0_18]),c_0_32]) ).
cnf(c_0_61,plain,
'>='('+'(X1,'+'(X2,X3)),X2),
inference(spm,[status(thm)],[c_0_58,c_0_19]) ).
cnf(c_0_62,negated_conjecture,
'>='('+'(esk1_0,'==>'(esk3_0,esk1_0)),esk3_0),
inference(spm,[status(thm)],[c_0_59,c_0_32]) ).
cnf(c_0_63,negated_conjecture,
'+'(esk3_0,'+'(esk3_0,X1)) = '+'(esk2_0,X1),
inference(spm,[status(thm)],[c_0_41,c_0_60]) ).
cnf(c_0_64,plain,
'>='('+'(X1,X2),'==>'(X3,X1)),
inference(spm,[status(thm)],[c_0_23,c_0_61]) ).
cnf(c_0_65,negated_conjecture,
'>='('==>'(esk3_0,esk1_0),'==>'(esk1_0,esk3_0)),
inference(spm,[status(thm)],[c_0_23,c_0_62]) ).
cnf(c_0_66,negated_conjecture,
'+'(esk3_0,'+'(X1,esk3_0)) = '+'(esk2_0,X1),
inference(spm,[status(thm)],[c_0_63,c_0_19]) ).
cnf(c_0_67,plain,
'>='(X1,'==>'(X2,'==>'(X3,X2))),
inference(spm,[status(thm)],[c_0_23,c_0_64]) ).
cnf(c_0_68,negated_conjecture,
'>='('+'('==>'(esk3_0,esk1_0),X1),'+'('==>'(esk1_0,esk3_0),X1)),
inference(spm,[status(thm)],[c_0_35,c_0_65]) ).
cnf(c_0_69,negated_conjecture,
'+'(X1,'+'(esk3_0,'==>'(X1,esk3_0))) = '+'(esk2_0,'==>'(esk3_0,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_54]),c_0_19]) ).
cnf(c_0_70,plain,
'==>'(X1,'==>'(X2,X1)) = '0',
inference(spm,[status(thm)],[c_0_28,c_0_67]) ).
cnf(c_0_71,plain,
'+'(X1,'+'(X2,X3)) = '+'(X2,'+'(X3,X1)),
inference(spm,[status(thm)],[c_0_41,c_0_19]) ).
cnf(c_0_72,plain,
'+'(X1,'+'('==>'(X1,X2),'==>'('==>'(X2,X1),X3))) = '+'(X2,'+'(X3,'==>'(X3,'==>'(X2,X1)))),
inference(spm,[status(thm)],[c_0_54,c_0_27]) ).
cnf(c_0_73,negated_conjecture,
'>='('+'(esk3_0,esk1_0),esk2_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70]),c_0_18]),c_0_71]),c_0_19]),c_0_72]),c_0_70]),c_0_18]),c_0_19]) ).
cnf(c_0_74,negated_conjecture,
~ '>='(esk1_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_75,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_73]),c_0_32]),c_0_74]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL889+1 : TPTP v8.1.2. Released v5.5.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n028.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Aug 24 18:34:35 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.55 start to proof: theBenchmark
% 5.28/5.34 % Version : CSE_E---1.5
% 5.28/5.34 % Problem : theBenchmark.p
% 5.28/5.34 % Proof found
% 5.28/5.34 % SZS status Theorem for theBenchmark.p
% 5.28/5.34 % SZS output start Proof
% See solution above
% 5.28/5.34 % Total time : 4.778000 s
% 5.28/5.34 % SZS output end Proof
% 5.28/5.34 % Total time : 4.781000 s
%------------------------------------------------------------------------------