TSTP Solution File: LCL067-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LCL067-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/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 06:52:03 EDT 2023
% Result : Unsatisfiable 19.41s 19.62s
% Output : CNFRefutation 19.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 11
% Syntax : Number of formulae : 93 ( 42 unt; 6 typ; 0 def)
% Number of atoms : 147 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 123 ( 63 ~; 60 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 3 >; 1 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 194 ( 43 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
implies: ( $i * $i ) > $i ).
tff(decl_23,type,
is_a_theorem: $i > $o ).
tff(decl_24,type,
not: $i > $i ).
tff(decl_25,type,
a: $i ).
tff(decl_26,type,
b: $i ).
tff(decl_27,type,
c: $i ).
cnf(condensed_detachment,axiom,
( is_a_theorem(X2)
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condensed_detachment) ).
cnf(cn_59,axiom,
is_a_theorem(implies(implies(not(X1),X2),implies(implies(X3,X2),implies(implies(X1,X3),X2)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_59) ).
cnf(cn_37,axiom,
is_a_theorem(implies(implies(implies(X1,X2),X3),implies(not(X1),X3))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_37) ).
cnf(cn_19,axiom,
is_a_theorem(implies(implies(implies(X1,X2),X3),implies(X2,X3))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_19) ).
cnf(prove_cn_1,negated_conjecture,
~ is_a_theorem(implies(implies(a,b),implies(implies(b,c),implies(a,c)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cn_1) ).
cnf(c_0_5,axiom,
( is_a_theorem(X2)
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1) ),
condensed_detachment ).
cnf(c_0_6,axiom,
is_a_theorem(implies(implies(not(X1),X2),implies(implies(X3,X2),implies(implies(X1,X3),X2)))),
cn_59 ).
cnf(c_0_7,plain,
( is_a_theorem(implies(implies(X1,X2),implies(implies(X3,X1),X2)))
| ~ is_a_theorem(implies(not(X3),X2)) ),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_8,axiom,
is_a_theorem(implies(implies(implies(X1,X2),X3),implies(not(X1),X3))),
cn_37 ).
cnf(c_0_9,plain,
( is_a_theorem(implies(implies(X1,X2),X3))
| ~ is_a_theorem(implies(not(X1),X3))
| ~ is_a_theorem(implies(X2,X3)) ),
inference(spm,[status(thm)],[c_0_5,c_0_7]) ).
cnf(c_0_10,plain,
( is_a_theorem(implies(not(X1),X2))
| ~ is_a_theorem(implies(implies(X1,X3),X2)) ),
inference(spm,[status(thm)],[c_0_5,c_0_8]) ).
cnf(c_0_11,axiom,
is_a_theorem(implies(implies(implies(X1,X2),X3),implies(X2,X3))),
cn_19 ).
cnf(c_0_12,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(not(X2),X1))
| ~ is_a_theorem(implies(X2,X3))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(spm,[status(thm)],[c_0_5,c_0_9]) ).
cnf(c_0_13,plain,
is_a_theorem(implies(not(implies(X1,X2)),implies(X2,X3))),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(implies(X3,X1),X4))
| ~ is_a_theorem(implies(X4,implies(X1,X2))) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_15,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(implies(X3,X1),implies(X1,X2))) ),
inference(spm,[status(thm)],[c_0_14,c_0_11]) ).
cnf(c_0_16,plain,
is_a_theorem(implies(X1,X1)),
inference(spm,[status(thm)],[c_0_15,c_0_11]) ).
cnf(c_0_17,plain,
is_a_theorem(implies(not(X1),implies(X1,X2))),
inference(spm,[status(thm)],[c_0_10,c_0_16]) ).
cnf(c_0_18,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X3,implies(X1,X2)))
| ~ is_a_theorem(implies(X1,X3)) ),
inference(spm,[status(thm)],[c_0_12,c_0_17]) ).
cnf(c_0_19,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(implies(X3,X1),X2)) ),
inference(spm,[status(thm)],[c_0_5,c_0_11]) ).
cnf(c_0_20,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,implies(X1,X2))) ),
inference(spm,[status(thm)],[c_0_18,c_0_16]) ).
cnf(c_0_21,plain,
is_a_theorem(implies(X1,implies(X2,X1))),
inference(spm,[status(thm)],[c_0_19,c_0_11]) ).
cnf(c_0_22,plain,
( is_a_theorem(implies(implies(X1,X1),X1))
| ~ is_a_theorem(implies(not(X1),X1)) ),
inference(spm,[status(thm)],[c_0_20,c_0_7]) ).
cnf(c_0_23,plain,
is_a_theorem(implies(X1,implies(X2,implies(X3,X1)))),
inference(spm,[status(thm)],[c_0_19,c_0_21]) ).
cnf(c_0_24,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(not(X1),X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_22]),c_0_16])]) ).
cnf(c_0_25,plain,
( is_a_theorem(implies(X1,implies(X2,X3)))
| ~ is_a_theorem(implies(X1,X3)) ),
inference(spm,[status(thm)],[c_0_18,c_0_23]) ).
cnf(c_0_26,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(not(implies(X1,X2)),X2)) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_27,plain,
is_a_theorem(implies(not(implies(X1,X2)),implies(not(X1),X3))),
inference(spm,[status(thm)],[c_0_10,c_0_8]) ).
cnf(c_0_28,plain,
( is_a_theorem(implies(X1,not(X2)))
| ~ is_a_theorem(implies(X3,implies(X1,not(X2))))
| ~ is_a_theorem(implies(X2,X3)) ),
inference(spm,[status(thm)],[c_0_12,c_0_21]) ).
cnf(c_0_29,plain,
is_a_theorem(implies(X1,implies(not(X1),X2))),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,plain,
( is_a_theorem(implies(X1,not(X2)))
| ~ is_a_theorem(implies(X2,implies(X1,not(X2)))) ),
inference(spm,[status(thm)],[c_0_28,c_0_16]) ).
cnf(c_0_31,plain,
is_a_theorem(implies(X1,implies(not(implies(X2,X1)),X3))),
inference(spm,[status(thm)],[c_0_19,c_0_29]) ).
cnf(c_0_32,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,X3))
| ~ is_a_theorem(implies(X3,X2)) ),
inference(spm,[status(thm)],[c_0_18,c_0_25]) ).
cnf(c_0_33,plain,
is_a_theorem(implies(not(implies(X1,X2)),not(X2))),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X3,X2))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_5,c_0_25]) ).
cnf(c_0_35,plain,
( is_a_theorem(implies(not(implies(X1,X2)),X3))
| ~ is_a_theorem(implies(not(X2),X3)) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(not(X2),X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_22]),c_0_16])]) ).
cnf(c_0_37,plain,
( is_a_theorem(implies(not(X1),X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_5,c_0_29]) ).
cnf(c_0_38,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(not(X2),implies(X1,X2))) ),
inference(spm,[status(thm)],[c_0_24,c_0_35]) ).
cnf(c_0_39,plain,
( is_a_theorem(not(X1))
| ~ is_a_theorem(implies(X2,not(X1)))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_12,c_0_16]) ).
cnf(c_0_40,plain,
( is_a_theorem(implies(not(X1),X2))
| ~ is_a_theorem(implies(not(X1),X1)) ),
inference(spm,[status(thm)],[c_0_18,c_0_29]) ).
cnf(c_0_41,plain,
is_a_theorem(implies(X1,implies(X2,X2))),
inference(spm,[status(thm)],[c_0_36,c_0_13]) ).
cnf(c_0_42,plain,
( is_a_theorem(implies(X1,not(X2)))
| ~ is_a_theorem(implies(X2,not(X1))) ),
inference(spm,[status(thm)],[c_0_28,c_0_17]) ).
cnf(c_0_43,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X2,X3))
| ~ is_a_theorem(implies(X3,X1))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_12,c_0_37]) ).
cnf(c_0_44,plain,
is_a_theorem(implies(not(not(X1)),X1)),
inference(spm,[status(thm)],[c_0_38,c_0_29]) ).
cnf(c_0_45,plain,
( is_a_theorem(not(X1))
| ~ is_a_theorem(implies(X1,not(X1))) ),
inference(spm,[status(thm)],[c_0_39,c_0_16]) ).
cnf(c_0_46,plain,
is_a_theorem(implies(not(implies(X1,X1)),X2)),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_47,plain,
is_a_theorem(implies(X1,not(not(X1)))),
inference(spm,[status(thm)],[c_0_42,c_0_16]) ).
cnf(c_0_48,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(not(not(X2)))
| ~ is_a_theorem(implies(X2,X1)) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_49,plain,
is_a_theorem(not(not(implies(X1,X1)))),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_50,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(not(not(X1)),X2)) ),
inference(spm,[status(thm)],[c_0_32,c_0_47]) ).
cnf(c_0_51,plain,
is_a_theorem(implies(not(not(X1)),implies(implies(X2,X3),implies(implies(X1,X2),X3)))),
inference(spm,[status(thm)],[c_0_10,c_0_6]) ).
cnf(c_0_52,plain,
is_a_theorem(implies(not(X1),implies(not(implies(X1,X2)),X3))),
inference(spm,[status(thm)],[c_0_10,c_0_29]) ).
cnf(c_0_53,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(X2,X2),X1)) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_54,plain,
is_a_theorem(implies(X1,implies(implies(X2,X3),implies(implies(X1,X2),X3)))),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_55,plain,
( is_a_theorem(not(not(X1)))
| ~ is_a_theorem(implies(not(X1),X1)) ),
inference(spm,[status(thm)],[c_0_45,c_0_40]) ).
cnf(c_0_56,plain,
is_a_theorem(implies(X1,implies(not(implies(not(X1),X2)),X3))),
inference(spm,[status(thm)],[c_0_50,c_0_52]) ).
cnf(c_0_57,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(implies(X3,X3),X1),X2))),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_58,plain,
( is_a_theorem(not(not(implies(X1,X2))))
| ~ is_a_theorem(implies(not(implies(X1,X2)),X2)) ),
inference(spm,[status(thm)],[c_0_55,c_0_25]) ).
cnf(c_0_59,plain,
is_a_theorem(implies(not(implies(not(not(X1)),X2)),X1)),
inference(spm,[status(thm)],[c_0_38,c_0_56]) ).
cnf(c_0_60,plain,
( is_a_theorem(implies(not(not(X1)),X2))
| ~ is_a_theorem(implies(implies(implies(X3,X4),implies(implies(X1,X3),X4)),X2)) ),
inference(spm,[status(thm)],[c_0_32,c_0_51]) ).
cnf(c_0_61,plain,
is_a_theorem(implies(implies(implies(X1,X1),X2),X2)),
inference(spm,[status(thm)],[c_0_53,c_0_57]) ).
cnf(c_0_62,plain,
( is_a_theorem(implies(implies(X1,X2),implies(implies(X3,X1),X2)))
| ~ is_a_theorem(not(not(X3))) ),
inference(spm,[status(thm)],[c_0_5,c_0_51]) ).
cnf(c_0_63,plain,
( is_a_theorem(not(X1))
| ~ is_a_theorem(implies(X1,not(implies(X2,X2)))) ),
inference(spm,[status(thm)],[c_0_39,c_0_46]) ).
cnf(c_0_64,plain,
( is_a_theorem(implies(not(X1),not(X2)))
| ~ is_a_theorem(implies(X2,X1)) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_65,plain,
is_a_theorem(not(not(implies(not(not(X1)),X1)))),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_66,plain,
is_a_theorem(implies(not(not(X1)),implies(implies(X1,X2),X2))),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_67,plain,
( is_a_theorem(implies(implies(X1,X1),X1))
| ~ is_a_theorem(not(not(X1))) ),
inference(spm,[status(thm)],[c_0_20,c_0_62]) ).
cnf(c_0_68,plain,
( is_a_theorem(not(not(X1)))
| ~ is_a_theorem(implies(implies(X2,X2),X1)) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_69,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(not(not(X2)),X2),X1)) ),
inference(spm,[status(thm)],[c_0_48,c_0_65]) ).
cnf(c_0_70,plain,
is_a_theorem(implies(X1,implies(implies(X1,X2),X2))),
inference(spm,[status(thm)],[c_0_50,c_0_66]) ).
cnf(c_0_71,plain,
( is_a_theorem(not(not(not(X1))))
| ~ is_a_theorem(implies(X1,not(X1))) ),
inference(spm,[status(thm)],[c_0_55,c_0_64]) ).
cnf(c_0_72,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(not(not(X2))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_67]),c_0_16])]) ).
cnf(c_0_73,plain,
is_a_theorem(not(not(implies(X1,implies(X2,X1))))),
inference(spm,[status(thm)],[c_0_68,c_0_11]) ).
cnf(c_0_74,plain,
( is_a_theorem(implies(implies(X1,X2),X3))
| ~ is_a_theorem(implies(implies(implies(X4,X1),X2),X3))
| ~ is_a_theorem(not(not(X4))) ),
inference(spm,[status(thm)],[c_0_32,c_0_62]) ).
cnf(c_0_75,plain,
is_a_theorem(implies(implies(implies(not(not(X1)),X1),X2),X2)),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_76,plain,
( is_a_theorem(not(not(not(not(X1)))))
| ~ is_a_theorem(implies(not(X1),X1)) ),
inference(spm,[status(thm)],[c_0_71,c_0_40]) ).
cnf(c_0_77,plain,
is_a_theorem(implies(X1,implies(X2,implies(X3,X2)))),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_78,plain,
( is_a_theorem(implies(implies(X1,X2),X2))
| ~ is_a_theorem(not(not(not(not(X1))))) ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_79,plain,
is_a_theorem(not(not(not(not(implies(X1,implies(X2,X1))))))),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_80,plain,
is_a_theorem(implies(implies(implies(X1,implies(X2,X1)),X3),X3)),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_81,negated_conjecture,
~ is_a_theorem(implies(implies(a,b),implies(implies(b,c),implies(a,c)))),
prove_cn_1 ).
cnf(c_0_82,plain,
is_a_theorem(implies(not(X1),implies(X2,implies(X1,X3)))),
inference(spm,[status(thm)],[c_0_10,c_0_21]) ).
cnf(c_0_83,plain,
is_a_theorem(implies(not(not(X1)),implies(implies(X1,X2),implies(X3,X2)))),
inference(spm,[status(thm)],[c_0_60,c_0_80]) ).
cnf(c_0_84,negated_conjecture,
~ is_a_theorem(implies(b,implies(implies(b,c),implies(a,c)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_9]),c_0_82])]) ).
cnf(c_0_85,plain,
is_a_theorem(implies(X1,implies(implies(X1,X2),implies(X3,X2)))),
inference(spm,[status(thm)],[c_0_50,c_0_83]) ).
cnf(c_0_86,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_84,c_0_85])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL067-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Aug 24 18:46:35 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.56 start to proof: theBenchmark
% 19.41/19.62 % Version : CSE_E---1.5
% 19.41/19.62 % Problem : theBenchmark.p
% 19.41/19.62 % Proof found
% 19.41/19.62 % SZS status Theorem for theBenchmark.p
% 19.41/19.63 % SZS output start Proof
% See solution above
% 19.41/19.63 % Total time : 19.060000 s
% 19.41/19.63 % SZS output end Proof
% 19.41/19.63 % Total time : 19.064000 s
%------------------------------------------------------------------------------