TSTP Solution File: LCL896+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LCL896+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 : n003.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 07:00:07 EDT 2023
% Result : Theorem 2.84s 2.93s
% Output : CNFRefutation 2.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 18
% Syntax : Number of formulae : 65 ( 40 unt; 6 typ; 0 def)
% Number of atoms : 83 ( 31 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 44 ( 20 ~; 17 |; 2 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 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 : 122 ( 6 sgn; 54 !; 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 ).
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_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_04,axiom,
! [X1] : '>='(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_04) ).
fof(sos_10,axiom,
! [X15,X16,X17] :
( '>='(X15,X16)
=> '>='('==>'(X16,X17),'==>'(X15,X17)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_10) ).
fof(sos_11,axiom,
! [X18,X19,X20] :
( '>='(X18,X19)
=> '>='('==>'(X20,X18),'==>'(X20,X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_11) ).
fof(sos_12,axiom,
! [X1,X2,X3] : '+'('+'(X1,'==>'(X1,X2)),'==>'('+'(X1,'==>'(X1,X2)),X3)) = '+'(X1,'==>'(X1,'+'(X2,'==>'(X2,X3)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_12) ).
fof(sos_01,axiom,
! [X1,X2,X3] : '+'('+'(X1,X2),X3) = '+'(X1,'+'(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_01) ).
fof(goals_13,conjecture,
! [X21,X22] : '+'(X21,'==>'(X21,X22)) = '+'(X22,'==>'(X22,X21)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_13) ).
fof(c_0_12,plain,
! [X28] : '+'(X28,'0') = X28,
inference(variable_rename,[status(thm)],[sos_03]) ).
fof(c_0_13,plain,
! [X26,X27] : '+'(X26,X27) = '+'(X27,X26),
inference(variable_rename,[status(thm)],[sos_02]) ).
fof(c_0_14,plain,
! [X39,X40,X41] :
( ~ '>='(X39,X40)
| '>='('+'(X39,X41),'+'(X40,X41)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_09])]) ).
fof(c_0_15,plain,
! [X38] : '>='(X38,'0'),
inference(variable_rename,[status(thm)],[sos_08]) ).
cnf(c_0_16,plain,
'+'(X1,'0') = X1,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
'+'(X1,X2) = '+'(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
( '>='('+'(X1,X3),'+'(X2,X3))
| ~ '>='(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
'>='(X1,'0'),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
'+'('0',X1) = X1,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_21,plain,
! [X35,X36,X37] :
( ( ~ '>='('+'(X35,X36),X37)
| '>='(X36,'==>'(X35,X37)) )
& ( ~ '>='(X36,'==>'(X35,X37))
| '>='('+'(X35,X36),X37) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_07])]) ).
cnf(c_0_22,plain,
'>='('+'(X1,X2),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
fof(c_0_23,plain,
! [X33,X34] :
( ~ '>='(X33,X34)
| ~ '>='(X34,X33)
| X33 = X34 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_06])]) ).
fof(c_0_24,plain,
! [X29] : '>='(X29,X29),
inference(variable_rename,[status(thm)],[sos_04]) ).
cnf(c_0_25,plain,
( '>='(X2,'==>'(X1,X3))
| ~ '>='('+'(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_26,plain,
'>='('+'(X1,X2),X1),
inference(spm,[status(thm)],[c_0_22,c_0_17]) ).
fof(c_0_27,plain,
! [X42,X43,X44] :
( ~ '>='(X42,X43)
| '>='('==>'(X43,X44),'==>'(X42,X44)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_10])]) ).
cnf(c_0_28,plain,
( X1 = X2
| ~ '>='(X1,X2)
| ~ '>='(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
'>='(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_30,plain,
! [X45,X46,X47] :
( ~ '>='(X45,X46)
| '>='('==>'(X47,X45),'==>'(X47,X46)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_11])]) ).
cnf(c_0_31,plain,
( '>='('+'(X2,X1),X3)
| ~ '>='(X1,'==>'(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_32,plain,
! [X48,X49,X50] : '+'('+'(X48,'==>'(X48,X49)),'==>'('+'(X48,'==>'(X48,X49)),X50)) = '+'(X48,'==>'(X48,'+'(X49,'==>'(X49,X50)))),
inference(variable_rename,[status(thm)],[sos_12]) ).
fof(c_0_33,plain,
! [X23,X24,X25] : '+'('+'(X23,X24),X25) = '+'(X23,'+'(X24,X25)),
inference(variable_rename,[status(thm)],[sos_01]) ).
cnf(c_0_34,plain,
'>='(X1,'==>'(X2,X2)),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_35,plain,
( '>='('==>'(X2,X3),'==>'(X1,X3))
| ~ '>='(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_36,plain,
( '0' = X1
| ~ '>='('0',X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_19]) ).
cnf(c_0_37,plain,
'>='(X1,'==>'(X2,'+'(X2,X1))),
inference(spm,[status(thm)],[c_0_25,c_0_29]) ).
cnf(c_0_38,plain,
( '>='('==>'(X3,X1),'==>'(X3,X2))
| ~ '>='(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_39,plain,
'>='('+'(X1,'==>'(X1,X2)),X2),
inference(spm,[status(thm)],[c_0_31,c_0_29]) ).
cnf(c_0_40,plain,
'+'('+'(X1,'==>'(X1,X2)),'==>'('+'(X1,'==>'(X1,X2)),X3)) = '+'(X1,'==>'(X1,'+'(X2,'==>'(X2,X3)))),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_41,plain,
'+'('+'(X1,X2),X3) = '+'(X1,'+'(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_42,plain,
( '==>'(X1,X1) = X2
| ~ '>='('==>'(X1,X1),X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_34]) ).
cnf(c_0_43,plain,
'>='('==>'(X1,X2),'==>'('+'(X1,X3),X2)),
inference(spm,[status(thm)],[c_0_35,c_0_26]) ).
cnf(c_0_44,plain,
'0' = '==>'(X1,X1),
inference(spm,[status(thm)],[c_0_36,c_0_34]) ).
cnf(c_0_45,plain,
( '==>'(X1,'+'(X1,X2)) = X2
| ~ '>='('==>'(X1,'+'(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_37]) ).
cnf(c_0_46,plain,
'>='('==>'(X1,'+'(X2,'==>'(X2,X3))),'==>'(X1,X3)),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_47,plain,
'+'(X1,'+'('==>'(X1,X2),'==>'('+'(X1,'==>'(X1,X2)),X3))) = '+'(X1,'==>'(X1,'+'(X2,'==>'(X2,X3)))),
inference(rw,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_48,plain,
'==>'('+'(X1,X2),X1) = '==>'(X1,X1),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_49,plain,
'+'(X1,'==>'(X2,X2)) = X1,
inference(spm,[status(thm)],[c_0_16,c_0_44]) ).
cnf(c_0_50,plain,
'==>'(X1,'+'(X1,'==>'(X1,X2))) = '==>'(X1,X2),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_51,plain,
'+'(X1,'==>'(X1,'+'(X2,'==>'(X2,X1)))) = '+'(X1,'==>'(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]) ).
fof(c_0_52,negated_conjecture,
~ ! [X21,X22] : '+'(X21,'==>'(X21,X22)) = '+'(X22,'==>'(X22,X21)),
inference(assume_negation,[status(cth)],[goals_13]) ).
cnf(c_0_53,plain,
'==>'(X1,'+'(X2,'==>'(X2,X1))) = '==>'(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_50]) ).
fof(c_0_54,negated_conjecture,
'+'(esk1_0,'==>'(esk1_0,esk2_0)) != '+'(esk2_0,'==>'(esk2_0,esk1_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_52])])]) ).
cnf(c_0_55,plain,
'>='('+'(X1,'==>'(X1,X2)),'+'(X2,'==>'(X2,X1))),
inference(spm,[status(thm)],[c_0_39,c_0_53]) ).
cnf(c_0_56,negated_conjecture,
'+'(esk1_0,'==>'(esk1_0,esk2_0)) != '+'(esk2_0,'==>'(esk2_0,esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_57,plain,
'+'(X1,'==>'(X1,X2)) = '+'(X2,'==>'(X2,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_55]),c_0_55])]) ).
cnf(c_0_58,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_57])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL896+1 : TPTP v8.1.2. Released v5.5.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33 % Computer : n003.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Aug 25 04:26:53 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.18/0.55 start to proof: theBenchmark
% 2.84/2.93 % Version : CSE_E---1.5
% 2.84/2.93 % Problem : theBenchmark.p
% 2.84/2.93 % Proof found
% 2.84/2.93 % SZS status Theorem for theBenchmark.p
% 2.84/2.93 % SZS output start Proof
% See solution above
% 2.84/2.94 % Total time : 2.373000 s
% 2.84/2.94 % SZS output end Proof
% 2.84/2.94 % Total time : 2.376000 s
%------------------------------------------------------------------------------