TSTP Solution File: LCL893+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LCL893+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 : n004.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 0.21s 0.59s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 14
% Syntax : Number of formulae : 35 ( 18 unt; 7 typ; 0 def)
% Number of atoms : 43 ( 18 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 26 ( 11 ~; 8 |; 3 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 4 >; 3 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 32 ( 1 sgn; 20 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
'+': ( $i * $i ) > $i ).
tff(decl_23,type,
'0': $i ).
tff(decl_24,type,
'1': $i ).
tff(decl_25,type,
'>=': ( $i * $i ) > $o ).
tff(decl_26,type,
'==>': ( $i * $i ) > $i ).
tff(decl_27,type,
h: $i > $i ).
tff(decl_28,type,
esk1_0: $i ).
fof(sos_08,axiom,
! [X9,X10,X11] :
( '>='('+'(X9,X10),X11)
<=> '>='(X10,'==>'(X9,X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_08) ).
fof(sos_03,axiom,
! [X1] : '+'(X1,'0') = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_03) ).
fof(goals_15,conjecture,
! [X21] :
( h(X21) = X21
=> X21 = '0' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_15) ).
fof(sos_05,axiom,
! [X1] : '>='(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_05) ).
fof(sos_14,axiom,
! [X1] : h(X1) = '==>'(h(X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_14) ).
fof(sos_07,axiom,
! [X7,X8] :
( ( '>='(X7,X8)
& '>='(X8,X7) )
=> X7 = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_07) ).
fof(sos_09,axiom,
! [X1] : '>='(X1,'0'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_09) ).
fof(c_0_7,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_08])]) ).
fof(c_0_8,plain,
! [X27] : '+'(X27,'0') = X27,
inference(variable_rename,[status(thm)],[sos_03]) ).
fof(c_0_9,negated_conjecture,
~ ! [X21] :
( h(X21) = X21
=> X21 = '0' ),
inference(assume_negation,[status(cth)],[goals_15]) ).
cnf(c_0_10,plain,
( '>='(X2,'==>'(X1,X3))
| ~ '>='('+'(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
'+'(X1,'0') = X1,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,plain,
! [X29] : '>='(X29,X29),
inference(variable_rename,[status(thm)],[sos_05]) ).
fof(c_0_13,plain,
! [X50] : h(X50) = '==>'(h(X50),X50),
inference(variable_rename,[status(thm)],[sos_14]) ).
fof(c_0_14,negated_conjecture,
( h(esk1_0) = esk1_0
& esk1_0 != '0' ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
cnf(c_0_15,plain,
( '>='('0','==>'(X1,X2))
| ~ '>='(X1,X2) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,plain,
'>='(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
h(X1) = '==>'(h(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,negated_conjecture,
h(esk1_0) = esk1_0,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_19,plain,
! [X33,X34] :
( ~ '>='(X33,X34)
| ~ '>='(X34,X33)
| X33 = X34 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_07])]) ).
cnf(c_0_20,plain,
'>='('0','==>'(X1,X1)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,negated_conjecture,
'==>'(esk1_0,esk1_0) = esk1_0,
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
fof(c_0_22,plain,
! [X38] : '>='(X38,'0'),
inference(variable_rename,[status(thm)],[sos_09]) ).
cnf(c_0_23,plain,
( X1 = X2
| ~ '>='(X1,X2)
| ~ '>='(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,negated_conjecture,
'>='('0',esk1_0),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
'>='(X1,'0'),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,negated_conjecture,
esk1_0 != '0',
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]),c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL893+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
% 0.15/0.34 % Computer : n004.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu Aug 24 19:09:38 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.57 start to proof: theBenchmark
% 0.21/0.59 % Version : CSE_E---1.5
% 0.21/0.59 % Problem : theBenchmark.p
% 0.21/0.59 % Proof found
% 0.21/0.59 % SZS status Theorem for theBenchmark.p
% 0.21/0.59 % SZS output start Proof
% See solution above
% 0.21/0.60 % Total time : 0.008000 s
% 0.21/0.60 % SZS output end Proof
% 0.21/0.60 % Total time : 0.011000 s
%------------------------------------------------------------------------------