TSTP Solution File: SYO633-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SYO633-1 : TPTP v8.1.2. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n023.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 : Fri Sep 1 04:12:20 EDT 2023
% Result : Unsatisfiable 0.46s 0.61s
% Output : CNFRefutation 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 13
% Syntax : Number of formulae : 28 ( 9 unt; 6 typ; 0 def)
% Number of atoms : 64 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 89 ( 47 ~; 42 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 5 >; 3 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 61 ( 59 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
f: $i > $i ).
tff(decl_23,type,
'0': $i ).
tff(decl_24,type,
s: $i > $i ).
tff(decl_25,type,
'E': ( $i * $i ) > $o ).
tff(decl_26,type,
'AP': ( $i * $i ) > $i ).
tff(decl_27,type,
'LEQ': ( $i * $i ) > $o ).
cnf(clause_1_10,axiom,
( 'E'(f(X2),s(s(s('0'))))
| ~ 'E'(f(X1),s(s(s(s('0')))))
| ~ 'E'(f(X2),s(s(s(s(s('0')))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1_10) ).
cnf(clause_6_04,axiom,
'E'(f(X1),s(s(s(s('0'))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6_04) ).
cnf(clause_8_05,axiom,
'E'(f(X1),s(s(s(s(s('0')))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_8_05) ).
cnf(clause_5_03,axiom,
( ~ 'E'(f(X1),s(s('0')))
| ~ 'E'(f(X2),s(s(s(s('0')))))
| ~ 'E'(f(X3),s(s(s('0'))))
| ~ 'E'(f(X4),s('0'))
| ~ 'E'(f(X5),'0')
| ~ 'E'(f(X6),s(s(s(s(s('0')))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5_03) ).
cnf(clause_12_09,axiom,
( 'E'(f('AP'(s(s(s(s(s(s('0')))))),X5)),s('0'))
| ~ 'E'(f(X1),s(s(s(s('0')))))
| ~ 'E'(f(X2),s(s(s(s(s('0'))))))
| ~ 'E'(f(X3),s(s(s('0'))))
| ~ 'E'(f(X4),s(s('0'))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_12_09) ).
cnf(clause_4_12,axiom,
( 'E'(f('AP'(s(s(s(s(s(s('0')))))),X4)),s(s('0')))
| ~ 'E'(f(X1),s(s(s(s('0')))))
| ~ 'E'(f(X2),s(s(s(s(s('0'))))))
| ~ 'E'(f(X3),s(s(s('0')))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4_12) ).
cnf(clause_2_07,axiom,
( 'E'(f('AP'(s(s(s(s(s(s('0')))))),X6)),'0')
| ~ 'E'(f(X1),s(s('0')))
| ~ 'E'(f(X2),s(s(s(s('0')))))
| ~ 'E'(f(X3),s(s(s('0'))))
| ~ 'E'(f(X4),s('0'))
| ~ 'E'(f(X5),s(s(s(s(s('0')))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2_07) ).
cnf(c_0_7,axiom,
( 'E'(f(X2),s(s(s('0'))))
| ~ 'E'(f(X1),s(s(s(s('0')))))
| ~ 'E'(f(X2),s(s(s(s(s('0')))))) ),
clause_1_10 ).
cnf(c_0_8,axiom,
'E'(f(X1),s(s(s(s('0'))))),
clause_6_04 ).
cnf(c_0_9,axiom,
'E'(f(X1),s(s(s(s(s('0')))))),
clause_8_05 ).
cnf(c_0_10,axiom,
( ~ 'E'(f(X1),s(s('0')))
| ~ 'E'(f(X2),s(s(s(s('0')))))
| ~ 'E'(f(X3),s(s(s('0'))))
| ~ 'E'(f(X4),s('0'))
| ~ 'E'(f(X5),'0')
| ~ 'E'(f(X6),s(s(s(s(s('0')))))) ),
clause_5_03 ).
cnf(c_0_11,plain,
'E'(f(X1),s(s(s('0')))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_8]),c_0_9])]) ).
cnf(c_0_12,axiom,
( 'E'(f('AP'(s(s(s(s(s(s('0')))))),X5)),s('0'))
| ~ 'E'(f(X1),s(s(s(s('0')))))
| ~ 'E'(f(X2),s(s(s(s(s('0'))))))
| ~ 'E'(f(X3),s(s(s('0'))))
| ~ 'E'(f(X4),s(s('0'))) ),
clause_12_09 ).
cnf(c_0_13,axiom,
( 'E'(f('AP'(s(s(s(s(s(s('0')))))),X4)),s(s('0')))
| ~ 'E'(f(X1),s(s(s(s('0')))))
| ~ 'E'(f(X2),s(s(s(s(s('0'))))))
| ~ 'E'(f(X3),s(s(s('0')))) ),
clause_4_12 ).
cnf(c_0_14,axiom,
( 'E'(f('AP'(s(s(s(s(s(s('0')))))),X6)),'0')
| ~ 'E'(f(X1),s(s('0')))
| ~ 'E'(f(X2),s(s(s(s('0')))))
| ~ 'E'(f(X3),s(s(s('0'))))
| ~ 'E'(f(X4),s('0'))
| ~ 'E'(f(X5),s(s(s(s(s('0')))))) ),
clause_2_07 ).
cnf(c_0_15,plain,
( ~ 'E'(f(X1),s(s('0')))
| ~ 'E'(f(X2),s('0'))
| ~ 'E'(f(X3),'0') ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11]),c_0_8]),c_0_9])]) ).
cnf(c_0_16,plain,
( 'E'(f('AP'(s(s(s(s(s(s('0')))))),X1)),s('0'))
| ~ 'E'(f(X2),s(s('0'))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_11]),c_0_8]),c_0_9])]) ).
cnf(c_0_17,plain,
'E'(f('AP'(s(s(s(s(s(s('0')))))),X1)),s(s('0'))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_11]),c_0_8]),c_0_9])]) ).
cnf(c_0_18,plain,
( ~ 'E'(f(X1),s(s('0')))
| ~ 'E'(f(X2),s('0')) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_11]),c_0_8]),c_0_9])]),c_0_15]) ).
cnf(c_0_19,plain,
'E'(f('AP'(s(s(s(s(s(s('0')))))),X1)),s('0')),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
~ 'E'(f(X1),s('0')),
inference(spm,[status(thm)],[c_0_18,c_0_17]) ).
cnf(c_0_21,plain,
$false,
inference(sr,[status(thm)],[c_0_19,c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYO633-1 : TPTP v8.1.2. Released v7.1.0.
% 0.04/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 23:11:56 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.46/0.60 start to proof: theBenchmark
% 0.46/0.61 % Version : CSE_E---1.5
% 0.46/0.61 % Problem : theBenchmark.p
% 0.46/0.61 % Proof found
% 0.46/0.61 % SZS status Theorem for theBenchmark.p
% 0.46/0.61 % SZS output start Proof
% See solution above
% 0.46/0.62 % Total time : 0.005000 s
% 0.46/0.62 % SZS output end Proof
% 0.46/0.62 % Total time : 0.008000 s
%------------------------------------------------------------------------------