TSTP Solution File: PUZ008-3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : PUZ008-3 : TPTP v8.1.2. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/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 13:11:30 EDT 2023
% Result : Unsatisfiable 0.16s 0.57s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 23
% Syntax : Number of formulae : 53 ( 11 unt; 11 typ; 0 def)
% Number of atoms : 131 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 186 ( 97 ~; 89 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 8 >; 6 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 81 ( 7 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
n0: $i ).
tff(decl_23,type,
safe: ( $i * $i ) > $o ).
tff(decl_24,type,
greater_or_equal: ( $i * $i ) > $o ).
tff(decl_25,type,
s: $i > $i ).
tff(decl_26,type,
m: $i > $i ).
tff(decl_27,type,
c: $i > $i ).
tff(decl_28,type,
west: ( $i * $i ) > $i ).
tff(decl_29,type,
boatonwest: $i ).
tff(decl_30,type,
east: ( $i * $i ) > $i ).
tff(decl_31,type,
achievable: ( $i * $i * $i ) > $o ).
tff(decl_32,type,
boatoneast: $i ).
cnf(two_cannibals_west_to_east,axiom,
( achievable(west(m(X1),c(X2)),boatoneast,east(m(X3),c(s(s(X4)))))
| ~ achievable(west(m(X1),c(s(s(X2)))),boatonwest,east(m(X3),c(X4)))
| ~ safe(X1,X2)
| ~ safe(X3,s(s(X4))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',two_cannibals_west_to_east) ).
cnf(cannibal_east_to_west,axiom,
( achievable(west(m(X1),c(s(X2))),boatonwest,east(m(X3),c(X4)))
| ~ achievable(west(m(X1),c(X2)),boatoneast,east(m(X3),c(s(X4))))
| ~ safe(X1,s(X2))
| ~ safe(X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cannibal_east_to_west) ).
cnf(start_on_west_bank,hypothesis,
achievable(west(m(s(s(s(n0)))),c(s(s(s(n0))))),boatonwest,east(m(n0),c(n0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',start_on_west_bank) ).
cnf(no_missionaries_is_safe,axiom,
safe(n0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',no_missionaries_is_safe) ).
cnf(same_or_more_missionaries_is_safe,axiom,
( safe(X1,X2)
| ~ greater_or_equal(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',same_or_more_missionaries_is_safe) ).
cnf(great_eq_base,axiom,
greater_or_equal(X1,n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',great_eq_base) ).
cnf(two_missionaries_west_to_east,axiom,
( achievable(west(m(X1),c(X2)),boatoneast,east(m(s(s(X3))),c(X4)))
| ~ achievable(west(m(s(s(X1))),c(X2)),boatonwest,east(m(X3),c(X4)))
| ~ safe(X1,X2)
| ~ safe(s(s(X3)),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',two_missionaries_west_to_east) ).
cnf(missionary_and_cannibal_east_to_west,axiom,
( achievable(west(m(s(X1)),c(s(X2))),boatonwest,east(m(X3),c(X4)))
| ~ achievable(west(m(X1),c(X2)),boatoneast,east(m(s(X3)),c(s(X4))))
| ~ safe(s(X1),s(X2))
| ~ safe(X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',missionary_and_cannibal_east_to_west) ).
cnf(missionary_and_cannibal_west_to_east,axiom,
( achievable(west(m(X1),c(X2)),boatoneast,east(m(s(X3)),c(s(X4))))
| ~ achievable(west(m(s(X1)),c(s(X2))),boatonwest,east(m(X3),c(X4)))
| ~ safe(X1,X2)
| ~ safe(s(X3),s(X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',missionary_and_cannibal_west_to_east) ).
cnf(missionary_east_to_west,axiom,
( achievable(west(m(s(X1)),c(X2)),boatonwest,east(m(X3),c(X4)))
| ~ achievable(west(m(X1),c(X2)),boatoneast,east(m(s(X3)),c(X4)))
| ~ safe(s(X1),X2)
| ~ safe(X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',missionary_east_to_west) ).
cnf(prove_can_get_to_east_bank,negated_conjecture,
~ achievable(west(m(n0),c(n0)),X1,east(m(s(s(s(n0)))),c(s(s(s(n0)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_can_get_to_east_bank) ).
cnf(great_eq_recursive,axiom,
( greater_or_equal(s(X1),s(X2))
| ~ greater_or_equal(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',great_eq_recursive) ).
cnf(c_0_12,axiom,
( achievable(west(m(X1),c(X2)),boatoneast,east(m(X3),c(s(s(X4)))))
| ~ achievable(west(m(X1),c(s(s(X2)))),boatonwest,east(m(X3),c(X4)))
| ~ safe(X1,X2)
| ~ safe(X3,s(s(X4))) ),
two_cannibals_west_to_east ).
cnf(c_0_13,axiom,
( achievable(west(m(X1),c(s(X2))),boatonwest,east(m(X3),c(X4)))
| ~ achievable(west(m(X1),c(X2)),boatoneast,east(m(X3),c(s(X4))))
| ~ safe(X1,s(X2))
| ~ safe(X3,X4) ),
cannibal_east_to_west ).
cnf(c_0_14,hypothesis,
achievable(west(m(s(s(s(n0)))),c(s(s(s(n0))))),boatonwest,east(m(n0),c(n0))),
start_on_west_bank ).
cnf(c_0_15,axiom,
safe(n0,X1),
no_missionaries_is_safe ).
cnf(c_0_16,axiom,
( safe(X1,X2)
| ~ greater_or_equal(X1,X2) ),
same_or_more_missionaries_is_safe ).
cnf(c_0_17,axiom,
greater_or_equal(X1,n0),
great_eq_base ).
cnf(c_0_18,axiom,
( achievable(west(m(X1),c(X2)),boatoneast,east(m(s(s(X3))),c(X4)))
| ~ achievable(west(m(s(s(X1))),c(X2)),boatonwest,east(m(X3),c(X4)))
| ~ safe(X1,X2)
| ~ safe(s(s(X3)),X4) ),
two_missionaries_west_to_east ).
cnf(c_0_19,plain,
( achievable(west(m(X1),c(X2)),boatoneast,east(m(X3),c(s(s(X4)))))
| ~ achievable(west(m(X1),c(s(X2))),boatoneast,east(m(X3),c(s(X4))))
| ~ safe(X3,s(s(X4)))
| ~ safe(X1,s(s(X2)))
| ~ safe(X1,X2)
| ~ safe(X3,X4) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_20,hypothesis,
( achievable(west(m(s(s(s(n0)))),c(s(n0))),boatoneast,east(m(n0),c(s(s(n0)))))
| ~ safe(s(s(s(n0))),s(n0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_14]),c_0_15])]) ).
cnf(c_0_21,plain,
safe(X1,n0),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,axiom,
( achievable(west(m(s(X1)),c(s(X2))),boatonwest,east(m(X3),c(X4)))
| ~ achievable(west(m(X1),c(X2)),boatoneast,east(m(s(X3)),c(s(X4))))
| ~ safe(s(X1),s(X2))
| ~ safe(X3,X4) ),
missionary_and_cannibal_east_to_west ).
cnf(c_0_23,plain,
( achievable(west(m(X1),c(s(X2))),boatoneast,east(m(s(s(X3))),c(X4)))
| ~ achievable(west(m(s(s(X1))),c(X2)),boatoneast,east(m(X3),c(s(X4))))
| ~ safe(s(s(X1)),s(X2))
| ~ safe(s(s(X3)),X4)
| ~ safe(X1,s(X2))
| ~ safe(X3,X4) ),
inference(spm,[status(thm)],[c_0_18,c_0_13]) ).
cnf(c_0_24,hypothesis,
( achievable(west(m(s(s(s(n0)))),c(n0)),boatoneast,east(m(n0),c(s(s(s(n0))))))
| ~ safe(s(s(s(n0))),s(s(n0)))
| ~ safe(s(s(s(n0))),s(n0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_15]),c_0_21]),c_0_15])]) ).
cnf(c_0_25,plain,
( achievable(west(m(X1),c(s(X2))),boatoneast,east(m(s(s(X3))),c(X4)))
| ~ achievable(west(m(s(X1)),c(X2)),boatoneast,east(m(s(X3)),c(s(X4))))
| ~ safe(s(s(X1)),s(X2))
| ~ safe(s(s(X3)),X4)
| ~ safe(X1,s(X2))
| ~ safe(X3,X4) ),
inference(spm,[status(thm)],[c_0_18,c_0_22]) ).
cnf(c_0_26,hypothesis,
( achievable(west(m(s(n0)),c(s(n0))),boatoneast,east(m(s(s(n0))),c(s(s(n0)))))
| ~ safe(s(s(s(n0))),s(s(n0)))
| ~ safe(s(s(s(n0))),s(n0))
| ~ safe(s(s(n0)),s(s(n0)))
| ~ safe(s(n0),s(n0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_15])]) ).
cnf(c_0_27,axiom,
( achievable(west(m(X1),c(X2)),boatoneast,east(m(s(X3)),c(s(X4))))
| ~ achievable(west(m(s(X1)),c(s(X2))),boatonwest,east(m(X3),c(X4)))
| ~ safe(X1,X2)
| ~ safe(s(X3),s(X4)) ),
missionary_and_cannibal_west_to_east ).
cnf(c_0_28,axiom,
( achievable(west(m(s(X1)),c(X2)),boatonwest,east(m(X3),c(X4)))
| ~ achievable(west(m(X1),c(X2)),boatoneast,east(m(s(X3)),c(X4)))
| ~ safe(s(X1),X2)
| ~ safe(X3,X4) ),
missionary_east_to_west ).
cnf(c_0_29,hypothesis,
( achievable(west(m(n0),c(s(s(n0)))),boatoneast,east(m(s(s(s(n0)))),c(s(n0))))
| ~ safe(s(s(s(n0))),s(s(n0)))
| ~ safe(s(s(n0)),s(s(n0)))
| ~ safe(s(s(s(n0))),s(n0))
| ~ safe(s(n0),s(n0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_15])]) ).
cnf(c_0_30,plain,
( achievable(west(m(X1),c(X2)),boatoneast,east(m(s(X3)),c(s(X4))))
| ~ achievable(west(m(X1),c(s(X2))),boatoneast,east(m(s(X3)),c(X4)))
| ~ safe(s(X3),s(X4))
| ~ safe(s(X1),s(X2))
| ~ safe(X1,X2)
| ~ safe(X3,X4) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,hypothesis,
( achievable(west(m(n0),c(s(n0))),boatoneast,east(m(s(s(s(n0)))),c(s(s(n0)))))
| ~ safe(s(s(s(n0))),s(s(n0)))
| ~ safe(s(s(n0)),s(s(n0)))
| ~ safe(s(s(s(n0))),s(n0))
| ~ safe(s(n0),s(n0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_29]),c_0_15]),c_0_15]),c_0_21])]) ).
cnf(c_0_32,negated_conjecture,
~ achievable(west(m(n0),c(n0)),X1,east(m(s(s(s(n0)))),c(s(s(s(n0)))))),
prove_can_get_to_east_bank ).
cnf(c_0_33,axiom,
( greater_or_equal(s(X1),s(X2))
| ~ greater_or_equal(X1,X2) ),
great_eq_recursive ).
cnf(c_0_34,hypothesis,
( ~ safe(s(s(s(n0))),s(s(s(n0))))
| ~ safe(s(s(s(n0))),s(s(n0)))
| ~ safe(s(s(n0)),s(s(n0)))
| ~ safe(s(s(s(n0))),s(n0))
| ~ safe(s(n0),s(n0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_21])]),c_0_32]) ).
cnf(c_0_35,plain,
( safe(s(X1),s(X2))
| ~ greater_or_equal(X1,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_33]) ).
cnf(c_0_36,hypothesis,
( ~ greater_or_equal(s(s(n0)),s(s(n0)))
| ~ safe(s(s(s(n0))),s(s(n0)))
| ~ safe(s(s(s(n0))),s(n0))
| ~ safe(s(n0),s(n0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_16]) ).
cnf(c_0_37,hypothesis,
( ~ greater_or_equal(s(s(n0)),s(s(n0)))
| ~ greater_or_equal(s(s(n0)),s(n0))
| ~ safe(s(s(s(n0))),s(n0))
| ~ safe(s(n0),s(n0)) ),
inference(spm,[status(thm)],[c_0_36,c_0_35]) ).
cnf(c_0_38,hypothesis,
( ~ greater_or_equal(s(s(n0)),s(n0))
| ~ greater_or_equal(s(n0),s(n0))
| ~ safe(s(s(s(n0))),s(n0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_33]),c_0_16]) ).
cnf(c_0_39,hypothesis,
( ~ greater_or_equal(s(s(n0)),s(n0))
| ~ greater_or_equal(s(n0),s(n0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_35]),c_0_17])]) ).
cnf(c_0_40,hypothesis,
~ greater_or_equal(s(n0),s(n0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_33]),c_0_17])]) ).
cnf(c_0_41,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_33]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : PUZ008-3 : TPTP v8.1.2. Released v1.2.0.
% 0.00/0.11 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.10/0.31 % Computer : n003.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Sat Aug 26 22:37:54 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.16/0.55 start to proof: theBenchmark
% 0.16/0.57 % Version : CSE_E---1.5
% 0.16/0.57 % Problem : theBenchmark.p
% 0.16/0.57 % Proof found
% 0.16/0.57 % SZS status Theorem for theBenchmark.p
% 0.16/0.57 % SZS output start Proof
% See solution above
% 0.16/0.57 % Total time : 0.016000 s
% 0.16/0.57 % SZS output end Proof
% 0.16/0.57 % Total time : 0.018000 s
%------------------------------------------------------------------------------