TSTP Solution File: LCL542+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LCL542+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n032.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 06:54:34 EDT 2023
% Result : Theorem 0.14s 0.50s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 171
% Syntax : Number of formulae : 191 ( 14 unt; 163 typ; 0 def)
% Number of atoms : 53 ( 4 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 44 ( 19 ~; 16 |; 4 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 10 >; 6 *; 0 +; 0 <<)
% Number of predicates : 62 ( 60 usr; 60 prp; 0-2 aty)
% Number of functors : 103 ( 103 usr; 94 con; 0-2 aty)
% Number of variables : 26 ( 2 sgn; 14 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
modus_ponens: $o ).
tff(decl_23,type,
is_a_theorem: $i > $o ).
tff(decl_24,type,
implies: ( $i * $i ) > $i ).
tff(decl_25,type,
substitution_of_equivalents: $o ).
tff(decl_26,type,
equiv: ( $i * $i ) > $i ).
tff(decl_27,type,
modus_tollens: $o ).
tff(decl_28,type,
not: $i > $i ).
tff(decl_29,type,
implies_1: $o ).
tff(decl_30,type,
implies_2: $o ).
tff(decl_31,type,
implies_3: $o ).
tff(decl_32,type,
and_1: $o ).
tff(decl_33,type,
and: ( $i * $i ) > $i ).
tff(decl_34,type,
and_2: $o ).
tff(decl_35,type,
and_3: $o ).
tff(decl_36,type,
or_1: $o ).
tff(decl_37,type,
or: ( $i * $i ) > $i ).
tff(decl_38,type,
or_2: $o ).
tff(decl_39,type,
or_3: $o ).
tff(decl_40,type,
equivalence_1: $o ).
tff(decl_41,type,
equivalence_2: $o ).
tff(decl_42,type,
equivalence_3: $o ).
tff(decl_43,type,
kn1: $o ).
tff(decl_44,type,
kn2: $o ).
tff(decl_45,type,
kn3: $o ).
tff(decl_46,type,
cn1: $o ).
tff(decl_47,type,
cn2: $o ).
tff(decl_48,type,
cn3: $o ).
tff(decl_49,type,
r1: $o ).
tff(decl_50,type,
r2: $o ).
tff(decl_51,type,
r3: $o ).
tff(decl_52,type,
r4: $o ).
tff(decl_53,type,
r5: $o ).
tff(decl_54,type,
op_or: $o ).
tff(decl_55,type,
op_and: $o ).
tff(decl_56,type,
op_implies_and: $o ).
tff(decl_57,type,
op_implies_or: $o ).
tff(decl_58,type,
op_equiv: $o ).
tff(decl_59,type,
necessitation: $o ).
tff(decl_60,type,
necessarily: $i > $i ).
tff(decl_61,type,
modus_ponens_strict_implies: $o ).
tff(decl_62,type,
strict_implies: ( $i * $i ) > $i ).
tff(decl_63,type,
adjunction: $o ).
tff(decl_64,type,
substitution_strict_equiv: $o ).
tff(decl_65,type,
strict_equiv: ( $i * $i ) > $i ).
tff(decl_66,type,
axiom_K: $o ).
tff(decl_67,type,
axiom_M: $o ).
tff(decl_68,type,
axiom_4: $o ).
tff(decl_69,type,
axiom_B: $o ).
tff(decl_70,type,
possibly: $i > $i ).
tff(decl_71,type,
axiom_5: $o ).
tff(decl_72,type,
axiom_s1: $o ).
tff(decl_73,type,
axiom_s2: $o ).
tff(decl_74,type,
axiom_s3: $o ).
tff(decl_75,type,
axiom_s4: $o ).
tff(decl_76,type,
axiom_m1: $o ).
tff(decl_77,type,
axiom_m2: $o ).
tff(decl_78,type,
axiom_m3: $o ).
tff(decl_79,type,
axiom_m4: $o ).
tff(decl_80,type,
axiom_m5: $o ).
tff(decl_81,type,
axiom_m6: $o ).
tff(decl_82,type,
axiom_m7: $o ).
tff(decl_83,type,
axiom_m8: $o ).
tff(decl_84,type,
axiom_m9: $o ).
tff(decl_85,type,
axiom_m10: $o ).
tff(decl_86,type,
op_possibly: $o ).
tff(decl_87,type,
op_necessarily: $o ).
tff(decl_88,type,
op_strict_implies: $o ).
tff(decl_89,type,
op_strict_equiv: $o ).
tff(decl_90,type,
op_implies: $o ).
tff(decl_91,type,
esk1_0: $i ).
tff(decl_92,type,
esk2_0: $i ).
tff(decl_93,type,
esk3_0: $i ).
tff(decl_94,type,
esk4_0: $i ).
tff(decl_95,type,
esk5_0: $i ).
tff(decl_96,type,
esk6_0: $i ).
tff(decl_97,type,
esk7_0: $i ).
tff(decl_98,type,
esk8_0: $i ).
tff(decl_99,type,
esk9_0: $i ).
tff(decl_100,type,
esk10_0: $i ).
tff(decl_101,type,
esk11_0: $i ).
tff(decl_102,type,
esk12_0: $i ).
tff(decl_103,type,
esk13_0: $i ).
tff(decl_104,type,
esk14_0: $i ).
tff(decl_105,type,
esk15_0: $i ).
tff(decl_106,type,
esk16_0: $i ).
tff(decl_107,type,
esk17_0: $i ).
tff(decl_108,type,
esk18_0: $i ).
tff(decl_109,type,
esk19_0: $i ).
tff(decl_110,type,
esk20_0: $i ).
tff(decl_111,type,
esk21_0: $i ).
tff(decl_112,type,
esk22_0: $i ).
tff(decl_113,type,
esk23_0: $i ).
tff(decl_114,type,
esk24_0: $i ).
tff(decl_115,type,
esk25_0: $i ).
tff(decl_116,type,
esk26_0: $i ).
tff(decl_117,type,
esk27_0: $i ).
tff(decl_118,type,
esk28_0: $i ).
tff(decl_119,type,
esk29_0: $i ).
tff(decl_120,type,
esk30_0: $i ).
tff(decl_121,type,
esk31_0: $i ).
tff(decl_122,type,
esk32_0: $i ).
tff(decl_123,type,
esk33_0: $i ).
tff(decl_124,type,
esk34_0: $i ).
tff(decl_125,type,
esk35_0: $i ).
tff(decl_126,type,
esk36_0: $i ).
tff(decl_127,type,
esk37_0: $i ).
tff(decl_128,type,
esk38_0: $i ).
tff(decl_129,type,
esk39_0: $i ).
tff(decl_130,type,
esk40_0: $i ).
tff(decl_131,type,
esk41_0: $i ).
tff(decl_132,type,
esk42_0: $i ).
tff(decl_133,type,
esk43_0: $i ).
tff(decl_134,type,
esk44_0: $i ).
tff(decl_135,type,
esk45_0: $i ).
tff(decl_136,type,
esk46_0: $i ).
tff(decl_137,type,
esk47_0: $i ).
tff(decl_138,type,
esk48_0: $i ).
tff(decl_139,type,
esk49_0: $i ).
tff(decl_140,type,
esk50_0: $i ).
tff(decl_141,type,
esk51_0: $i ).
tff(decl_142,type,
esk52_0: $i ).
tff(decl_143,type,
esk53_0: $i ).
tff(decl_144,type,
esk54_0: $i ).
tff(decl_145,type,
esk55_0: $i ).
tff(decl_146,type,
esk56_0: $i ).
tff(decl_147,type,
esk57_0: $i ).
tff(decl_148,type,
esk58_0: $i ).
tff(decl_149,type,
esk59_0: $i ).
tff(decl_150,type,
esk60_0: $i ).
tff(decl_151,type,
esk61_0: $i ).
tff(decl_152,type,
esk62_0: $i ).
tff(decl_153,type,
esk63_0: $i ).
tff(decl_154,type,
esk64_0: $i ).
tff(decl_155,type,
esk65_0: $i ).
tff(decl_156,type,
esk66_0: $i ).
tff(decl_157,type,
esk67_0: $i ).
tff(decl_158,type,
esk68_0: $i ).
tff(decl_159,type,
esk69_0: $i ).
tff(decl_160,type,
esk70_0: $i ).
tff(decl_161,type,
esk71_0: $i ).
tff(decl_162,type,
esk72_0: $i ).
tff(decl_163,type,
esk73_0: $i ).
tff(decl_164,type,
esk74_0: $i ).
tff(decl_165,type,
esk75_0: $i ).
tff(decl_166,type,
esk76_0: $i ).
tff(decl_167,type,
esk77_0: $i ).
tff(decl_168,type,
esk78_0: $i ).
tff(decl_169,type,
esk79_0: $i ).
tff(decl_170,type,
esk80_0: $i ).
tff(decl_171,type,
esk81_0: $i ).
tff(decl_172,type,
esk82_0: $i ).
tff(decl_173,type,
esk83_0: $i ).
tff(decl_174,type,
esk84_0: $i ).
tff(decl_175,type,
esk85_0: $i ).
tff(decl_176,type,
esk86_0: $i ).
tff(decl_177,type,
esk87_0: $i ).
tff(decl_178,type,
esk88_0: $i ).
tff(decl_179,type,
esk89_0: $i ).
tff(decl_180,type,
esk90_0: $i ).
tff(decl_181,type,
esk91_0: $i ).
tff(decl_182,type,
esk92_0: $i ).
tff(decl_183,type,
esk93_0: $i ).
tff(decl_184,type,
esk94_0: $i ).
fof(necessitation,axiom,
( necessitation
<=> ! [X1] :
( is_a_theorem(X1)
=> is_a_theorem(necessarily(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',necessitation) ).
fof(op_strict_implies,axiom,
( op_strict_implies
=> ! [X1,X2] : strict_implies(X1,X2) = necessarily(implies(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+1.ax',op_strict_implies) ).
fof(axiom_m2,axiom,
( axiom_m2
<=> ! [X1,X2] : is_a_theorem(strict_implies(and(X1,X2),X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_m2) ).
fof(s1_0_axiom_m2,conjecture,
axiom_m2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_axiom_m2) ).
fof(km4b_necessitation,axiom,
necessitation,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+3.ax',km4b_necessitation) ).
fof(s1_0_op_strict_implies,axiom,
op_strict_implies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(and_1,axiom,
( and_1
<=> ! [X1,X2] : is_a_theorem(implies(and(X1,X2),X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',and_1) ).
fof(hilbert_and_1,axiom,
and_1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_and_1) ).
fof(c_0_8,plain,
! [X127] :
( ( ~ necessitation
| ~ is_a_theorem(X127)
| is_a_theorem(necessarily(X127)) )
& ( is_a_theorem(esk56_0)
| necessitation )
& ( ~ is_a_theorem(necessarily(esk56_0))
| necessitation ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[necessitation])])])])]) ).
fof(c_0_9,plain,
! [X207,X208] :
( ~ op_strict_implies
| strict_implies(X207,X208) = necessarily(implies(X207,X208)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_strict_implies])])]) ).
fof(c_0_10,plain,
! [X173,X174] :
( ( ~ axiom_m2
| is_a_theorem(strict_implies(and(X173,X174),X173)) )
& ( ~ is_a_theorem(strict_implies(and(esk79_0,esk80_0),esk79_0))
| axiom_m2 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m2])])])]) ).
fof(c_0_11,negated_conjecture,
~ axiom_m2,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[s1_0_axiom_m2])]) ).
cnf(c_0_12,plain,
( is_a_theorem(necessarily(X1))
| ~ necessitation
| ~ is_a_theorem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
necessitation,
inference(split_conjunct,[status(thm)],[km4b_necessitation]) ).
cnf(c_0_14,plain,
( strict_implies(X1,X2) = necessarily(implies(X1,X2))
| ~ op_strict_implies ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
op_strict_implies,
inference(split_conjunct,[status(thm)],[s1_0_op_strict_implies]) ).
cnf(c_0_16,plain,
( axiom_m2
| ~ is_a_theorem(strict_implies(and(esk79_0,esk80_0),esk79_0)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,negated_conjecture,
~ axiom_m2,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
( is_a_theorem(necessarily(X1))
| ~ is_a_theorem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13])]) ).
cnf(c_0_19,plain,
necessarily(implies(X1,X2)) = strict_implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15])]) ).
fof(c_0_20,plain,
! [X33,X34] :
( ( ~ and_1
| is_a_theorem(implies(and(X33,X34),X33)) )
& ( ~ is_a_theorem(implies(and(esk14_0,esk15_0),esk14_0))
| and_1 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[and_1])])])]) ).
cnf(c_0_21,plain,
~ is_a_theorem(strict_implies(and(esk79_0,esk80_0),esk79_0)),
inference(sr,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
( is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
( is_a_theorem(implies(and(X1,X2),X1))
| ~ and_1 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,plain,
and_1,
inference(split_conjunct,[status(thm)],[hilbert_and_1]) ).
cnf(c_0_25,plain,
~ is_a_theorem(implies(and(esk79_0,esk80_0),esk79_0)),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
is_a_theorem(implies(and(X1,X2),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24])]) ).
cnf(c_0_27,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : LCL542+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.10 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Thu Aug 24 17:52:42 EDT 2023
% 0.09/0.29 % CPUTime :
% 0.14/0.48 start to proof: theBenchmark
% 0.14/0.50 % Version : CSE_E---1.5
% 0.14/0.50 % Problem : theBenchmark.p
% 0.14/0.50 % Proof found
% 0.14/0.50 % SZS status Theorem for theBenchmark.p
% 0.14/0.50 % SZS output start Proof
% See solution above
% 0.14/0.50 % Total time : 0.014000 s
% 0.14/0.50 % SZS output end Proof
% 0.14/0.50 % Total time : 0.017000 s
%------------------------------------------------------------------------------