TSTP Solution File: LCL573+1 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LCL573+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 : n009.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 06:54:41 EDT 2023
% Result : Theorem 0.52s 0.74s
% Output : CNFRefutation 0.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 113
% Syntax : Number of formulae : 236 ( 82 unt; 83 typ; 0 def)
% Number of atoms : 281 ( 57 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 219 ( 91 ~; 93 |; 17 &)
% ( 10 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 10 >; 6 *; 0 +; 0 <<)
% Number of predicates : 37 ( 35 usr; 35 prp; 0-2 aty)
% Number of functors : 48 ( 48 usr; 39 con; 0-2 aty)
% Number of variables : 230 ( 19 sgn; 56 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
op_or: $o ).
tff(decl_23,type,
or: ( $i * $i ) > $i ).
tff(decl_24,type,
not: $i > $i ).
tff(decl_25,type,
and: ( $i * $i ) > $i ).
tff(decl_26,type,
op_and: $o ).
tff(decl_27,type,
op_implies_and: $o ).
tff(decl_28,type,
implies: ( $i * $i ) > $i ).
tff(decl_29,type,
op_implies_or: $o ).
tff(decl_30,type,
op_equiv: $o ).
tff(decl_31,type,
equiv: ( $i * $i ) > $i ).
tff(decl_32,type,
necessitation: $o ).
tff(decl_33,type,
is_a_theorem: $i > $o ).
tff(decl_34,type,
necessarily: $i > $i ).
tff(decl_35,type,
modus_ponens_strict_implies: $o ).
tff(decl_36,type,
strict_implies: ( $i * $i ) > $i ).
tff(decl_37,type,
adjunction: $o ).
tff(decl_38,type,
substitution_strict_equiv: $o ).
tff(decl_39,type,
strict_equiv: ( $i * $i ) > $i ).
tff(decl_40,type,
axiom_K: $o ).
tff(decl_41,type,
axiom_M: $o ).
tff(decl_42,type,
axiom_4: $o ).
tff(decl_43,type,
axiom_B: $o ).
tff(decl_44,type,
possibly: $i > $i ).
tff(decl_45,type,
axiom_5: $o ).
tff(decl_46,type,
axiom_s1: $o ).
tff(decl_47,type,
axiom_s2: $o ).
tff(decl_48,type,
axiom_s3: $o ).
tff(decl_49,type,
axiom_s4: $o ).
tff(decl_50,type,
axiom_m1: $o ).
tff(decl_51,type,
axiom_m2: $o ).
tff(decl_52,type,
axiom_m3: $o ).
tff(decl_53,type,
axiom_m4: $o ).
tff(decl_54,type,
axiom_m5: $o ).
tff(decl_55,type,
axiom_m6: $o ).
tff(decl_56,type,
axiom_m7: $o ).
tff(decl_57,type,
axiom_m8: $o ).
tff(decl_58,type,
axiom_m9: $o ).
tff(decl_59,type,
axiom_m10: $o ).
tff(decl_60,type,
op_possibly: $o ).
tff(decl_61,type,
op_necessarily: $o ).
tff(decl_62,type,
op_strict_implies: $o ).
tff(decl_63,type,
op_strict_equiv: $o ).
tff(decl_64,type,
op_implies: $o ).
tff(decl_65,type,
substitution_of_equivalents: $o ).
tff(decl_66,type,
esk1_0: $i ).
tff(decl_67,type,
esk2_0: $i ).
tff(decl_68,type,
esk3_0: $i ).
tff(decl_69,type,
esk4_0: $i ).
tff(decl_70,type,
esk5_0: $i ).
tff(decl_71,type,
esk6_0: $i ).
tff(decl_72,type,
esk7_0: $i ).
tff(decl_73,type,
esk8_0: $i ).
tff(decl_74,type,
esk9_0: $i ).
tff(decl_75,type,
esk10_0: $i ).
tff(decl_76,type,
esk11_0: $i ).
tff(decl_77,type,
esk12_0: $i ).
tff(decl_78,type,
esk13_0: $i ).
tff(decl_79,type,
esk14_0: $i ).
tff(decl_80,type,
esk15_0: $i ).
tff(decl_81,type,
esk16_0: $i ).
tff(decl_82,type,
esk17_0: $i ).
tff(decl_83,type,
esk18_0: $i ).
tff(decl_84,type,
esk19_0: $i ).
tff(decl_85,type,
esk20_0: $i ).
tff(decl_86,type,
esk21_0: $i ).
tff(decl_87,type,
esk22_0: $i ).
tff(decl_88,type,
esk23_0: $i ).
tff(decl_89,type,
esk24_0: $i ).
tff(decl_90,type,
esk25_0: $i ).
tff(decl_91,type,
esk26_0: $i ).
tff(decl_92,type,
esk27_0: $i ).
tff(decl_93,type,
esk28_0: $i ).
tff(decl_94,type,
esk29_0: $i ).
tff(decl_95,type,
esk30_0: $i ).
tff(decl_96,type,
esk31_0: $i ).
tff(decl_97,type,
esk32_0: $i ).
tff(decl_98,type,
esk33_0: $i ).
tff(decl_99,type,
esk34_0: $i ).
tff(decl_100,type,
esk35_0: $i ).
tff(decl_101,type,
esk36_0: $i ).
tff(decl_102,type,
esk37_0: $i ).
tff(decl_103,type,
esk38_0: $i ).
tff(decl_104,type,
esk39_0: $i ).
fof(adjunction,axiom,
( adjunction
<=> ! [X1,X2] :
( ( is_a_theorem(X1)
& is_a_theorem(X2) )
=> is_a_theorem(and(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',adjunction) ).
fof(op_strict_equiv,axiom,
( op_strict_equiv
=> ! [X1,X2] : strict_equiv(X1,X2) = and(strict_implies(X1,X2),strict_implies(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+1.ax',op_strict_equiv) ).
fof(substitution_strict_equiv,axiom,
( substitution_strict_equiv
<=> ! [X1,X2] :
( is_a_theorem(strict_equiv(X1,X2))
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',substitution_strict_equiv) ).
fof(s1_0_adjunction,axiom,
adjunction,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_adjunction) ).
fof(s1_0_op_strict_equiv,axiom,
op_strict_equiv,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_op_strict_equiv) ).
fof(s1_0_substitution_strict_equiv,axiom,
substitution_strict_equiv,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_substitution_strict_equiv) ).
fof(axiom_m1,axiom,
( axiom_m1
<=> ! [X1,X2] : is_a_theorem(strict_implies(and(X1,X2),and(X2,X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_m1) ).
fof(modus_ponens_strict_implies,axiom,
( modus_ponens_strict_implies
<=> ! [X1,X2] :
( ( is_a_theorem(X1)
& is_a_theorem(strict_implies(X1,X2)) )
=> is_a_theorem(X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',modus_ponens_strict_implies) ).
fof(axiom_m5,axiom,
( axiom_m5
<=> ! [X1,X2,X3] : is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_m5) ).
fof(op_implies_and,axiom,
( op_implies_and
=> ! [X1,X2] : implies(X1,X2) = not(and(X1,not(X2))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_implies_and) ).
fof(s1_0_axiom_m1,axiom,
axiom_m1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_axiom_m1) ).
fof(s1_0_modus_ponens_strict_implies,axiom,
modus_ponens_strict_implies,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_modus_ponens_strict_implies) ).
fof(s1_0_axiom_m5,axiom,
axiom_m5,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_axiom_m5) ).
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(op_or,axiom,
( op_or
=> ! [X1,X2] : or(X1,X2) = not(and(not(X1),not(X2))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_or) ).
fof(hilbert_op_implies_and,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
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_op_strict_implies,axiom,
op_strict_implies,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_op_strict_implies) ).
fof(s1_0_op_or,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_op_or) ).
fof(s1_0_axiom_m2,axiom,
axiom_m2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_axiom_m2) ).
fof(axiom_m4,axiom,
( axiom_m4
<=> ! [X1] : is_a_theorem(strict_implies(X1,and(X1,X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_m4) ).
fof(s1_0_axiom_m4,axiom,
axiom_m4,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_axiom_m4) ).
fof(axiom_m3,axiom,
( axiom_m3
<=> ! [X1,X2,X3] : is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_m3) ).
fof(s1_0_axiom_m3,axiom,
axiom_m3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_axiom_m3) ).
fof(op_possibly,axiom,
( op_possibly
=> ! [X1] : possibly(X1) = not(necessarily(not(X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+1.ax',op_possibly) ).
fof(s1_0_op_possibly,axiom,
op_possibly,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_op_possibly) ).
fof(axiom_m10,axiom,
( axiom_m10
<=> ! [X1] : is_a_theorem(strict_implies(possibly(X1),necessarily(possibly(X1)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_m10) ).
fof(s1_0_m10_axiom_m10,axiom,
axiom_m10,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+6.ax',s1_0_m10_axiom_m10) ).
fof(axiom_5,axiom,
( axiom_5
<=> ! [X1] : is_a_theorem(implies(possibly(X1),necessarily(possibly(X1)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_5) ).
fof(km5_axiom_5,conjecture,
axiom_5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km5_axiom_5) ).
fof(c_0_30,plain,
! [X22,X23] :
( ( ~ adjunction
| ~ is_a_theorem(X22)
| ~ is_a_theorem(X23)
| is_a_theorem(and(X22,X23)) )
& ( is_a_theorem(esk4_0)
| adjunction )
& ( is_a_theorem(esk5_0)
| adjunction )
& ( ~ is_a_theorem(and(esk4_0,esk5_0))
| adjunction ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[adjunction])])])])]) ).
fof(c_0_31,plain,
! [X98,X99] :
( ~ op_strict_equiv
| strict_equiv(X98,X99) = and(strict_implies(X98,X99),strict_implies(X99,X98)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_strict_equiv])])]) ).
fof(c_0_32,plain,
! [X26,X27] :
( ( ~ substitution_strict_equiv
| ~ is_a_theorem(strict_equiv(X26,X27))
| X26 = X27 )
& ( is_a_theorem(strict_equiv(esk6_0,esk7_0))
| substitution_strict_equiv )
& ( esk6_0 != esk7_0
| substitution_strict_equiv ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[substitution_strict_equiv])])])])]) ).
cnf(c_0_33,plain,
( is_a_theorem(and(X1,X2))
| ~ adjunction
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_34,plain,
adjunction,
inference(split_conjunct,[status(thm)],[s1_0_adjunction]) ).
cnf(c_0_35,plain,
( strict_equiv(X1,X2) = and(strict_implies(X1,X2),strict_implies(X2,X1))
| ~ op_strict_equiv ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_36,plain,
op_strict_equiv,
inference(split_conjunct,[status(thm)],[s1_0_op_strict_equiv]) ).
cnf(c_0_37,plain,
( X1 = X2
| ~ substitution_strict_equiv
| ~ is_a_theorem(strict_equiv(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_38,plain,
substitution_strict_equiv,
inference(split_conjunct,[status(thm)],[s1_0_substitution_strict_equiv]) ).
cnf(c_0_39,plain,
( is_a_theorem(and(X1,X2))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34])]) ).
cnf(c_0_40,plain,
and(strict_implies(X1,X2),strict_implies(X2,X1)) = strict_equiv(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36])]) ).
fof(c_0_41,plain,
! [X58,X59] :
( ( ~ axiom_m1
| is_a_theorem(strict_implies(and(X58,X59),and(X59,X58))) )
& ( ~ is_a_theorem(strict_implies(and(esk22_0,esk23_0),and(esk23_0,esk22_0)))
| axiom_m1 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m1])])])]) ).
fof(c_0_42,plain,
! [X18,X19] :
( ( ~ modus_ponens_strict_implies
| ~ is_a_theorem(X18)
| ~ is_a_theorem(strict_implies(X18,X19))
| is_a_theorem(X19) )
& ( is_a_theorem(esk2_0)
| modus_ponens_strict_implies )
& ( is_a_theorem(strict_implies(esk2_0,esk3_0))
| modus_ponens_strict_implies )
& ( ~ is_a_theorem(esk3_0)
| modus_ponens_strict_implies ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[modus_ponens_strict_implies])])])])]) ).
fof(c_0_43,plain,
! [X74,X75,X76] :
( ( ~ axiom_m5
| is_a_theorem(strict_implies(and(strict_implies(X74,X75),strict_implies(X75,X76)),strict_implies(X74,X76))) )
& ( ~ is_a_theorem(strict_implies(and(strict_implies(esk30_0,esk31_0),strict_implies(esk31_0,esk32_0)),strict_implies(esk30_0,esk32_0)))
| axiom_m5 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m5])])])]) ).
fof(c_0_44,plain,
! [X10,X11] :
( ~ op_implies_and
| implies(X10,X11) = not(and(X10,not(X11))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_and])])]) ).
cnf(c_0_45,plain,
( X1 = X2
| ~ is_a_theorem(strict_equiv(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]) ).
cnf(c_0_46,plain,
( is_a_theorem(strict_equiv(X1,X2))
| ~ is_a_theorem(strict_implies(X2,X1))
| ~ is_a_theorem(strict_implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_47,plain,
( is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))
| ~ axiom_m1 ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_48,plain,
axiom_m1,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m1]) ).
cnf(c_0_49,plain,
( is_a_theorem(X2)
| ~ modus_ponens_strict_implies
| ~ is_a_theorem(X1)
| ~ is_a_theorem(strict_implies(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_50,plain,
modus_ponens_strict_implies,
inference(split_conjunct,[status(thm)],[s1_0_modus_ponens_strict_implies]) ).
cnf(c_0_51,plain,
( is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3)))
| ~ axiom_m5 ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_52,plain,
axiom_m5,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m5]) ).
fof(c_0_53,plain,
! [X96,X97] :
( ~ op_strict_implies
| strict_implies(X96,X97) = necessarily(implies(X96,X97)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_strict_implies])])]) ).
fof(c_0_54,plain,
! [X6,X7] :
( ~ op_or
| or(X6,X7) = not(and(not(X6),not(X7))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_or])])]) ).
cnf(c_0_55,plain,
( implies(X1,X2) = not(and(X1,not(X2)))
| ~ op_implies_and ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_56,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[hilbert_op_implies_and]) ).
cnf(c_0_57,plain,
( X1 = X2
| ~ is_a_theorem(strict_implies(X2,X1))
| ~ is_a_theorem(strict_implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_58,plain,
is_a_theorem(strict_implies(and(X1,X2),and(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48])]) ).
cnf(c_0_59,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(strict_implies(X2,X1))
| ~ is_a_theorem(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50])]) ).
cnf(c_0_60,plain,
is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52])]) ).
fof(c_0_61,plain,
! [X62,X63] :
( ( ~ axiom_m2
| is_a_theorem(strict_implies(and(X62,X63),X62)) )
& ( ~ is_a_theorem(strict_implies(and(esk24_0,esk25_0),esk24_0))
| axiom_m2 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m2])])])]) ).
cnf(c_0_62,plain,
( strict_implies(X1,X2) = necessarily(implies(X1,X2))
| ~ op_strict_implies ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_63,plain,
op_strict_implies,
inference(split_conjunct,[status(thm)],[s1_0_op_strict_implies]) ).
cnf(c_0_64,plain,
( or(X1,X2) = not(and(not(X1),not(X2)))
| ~ op_or ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_65,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_56])]) ).
cnf(c_0_66,plain,
op_or,
inference(split_conjunct,[status(thm)],[s1_0_op_or]) ).
cnf(c_0_67,plain,
and(X1,X2) = and(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_58])]) ).
cnf(c_0_68,plain,
( is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(and(strict_implies(X1,X3),strict_implies(X3,X2))) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_69,plain,
( is_a_theorem(strict_implies(and(X1,X2),X1))
| ~ axiom_m2 ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_70,plain,
axiom_m2,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m2]) ).
cnf(c_0_71,plain,
necessarily(implies(X1,X2)) = strict_implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_63])]) ).
cnf(c_0_72,plain,
implies(not(X1),X2) = or(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_65]),c_0_66])]) ).
cnf(c_0_73,plain,
not(and(not(X1),X2)) = implies(X2,X1),
inference(spm,[status(thm)],[c_0_65,c_0_67]) ).
fof(c_0_74,plain,
! [X72] :
( ( ~ axiom_m4
| is_a_theorem(strict_implies(X72,and(X72,X72))) )
& ( ~ is_a_theorem(strict_implies(esk29_0,and(esk29_0,esk29_0)))
| axiom_m4 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m4])])])]) ).
cnf(c_0_75,plain,
( is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(strict_implies(X3,X2))
| ~ is_a_theorem(strict_implies(X1,X3)) ),
inference(spm,[status(thm)],[c_0_68,c_0_39]) ).
cnf(c_0_76,plain,
is_a_theorem(strict_implies(and(X1,X2),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_70])]) ).
cnf(c_0_77,plain,
necessarily(or(X1,X2)) = strict_implies(not(X1),X2),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_78,plain,
or(X1,X2) = or(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_73]),c_0_72]),c_0_72]) ).
cnf(c_0_79,plain,
( is_a_theorem(strict_implies(X1,and(X1,X1)))
| ~ axiom_m4 ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_80,plain,
axiom_m4,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m4]) ).
cnf(c_0_81,plain,
( is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(strict_implies(X1,and(X2,X3))) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_82,plain,
strict_implies(not(X1),X2) = strict_implies(not(X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_77]) ).
cnf(c_0_83,plain,
is_a_theorem(strict_implies(X1,and(X1,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_80])]) ).
cnf(c_0_84,plain,
( is_a_theorem(strict_implies(not(X1),X2))
| ~ is_a_theorem(strict_implies(not(and(X2,X3)),X1)) ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_85,plain,
and(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_83]),c_0_76])]) ).
cnf(c_0_86,plain,
is_a_theorem(strict_implies(not(X1),not(and(X1,X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_83]),c_0_85]),c_0_82]) ).
cnf(c_0_87,plain,
( is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(strict_implies(not(X2),X3))
| ~ is_a_theorem(strict_implies(X1,not(X3))) ),
inference(spm,[status(thm)],[c_0_75,c_0_82]) ).
cnf(c_0_88,plain,
( is_a_theorem(strict_implies(not(X1),X2))
| ~ is_a_theorem(strict_implies(not(X2),X1)) ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_89,plain,
is_a_theorem(strict_implies(not(not(X1)),implies(X2,X1))),
inference(spm,[status(thm)],[c_0_86,c_0_73]) ).
cnf(c_0_90,plain,
( X1 = not(X2)
| ~ is_a_theorem(strict_implies(not(X1),X2))
| ~ is_a_theorem(strict_implies(X1,not(X2))) ),
inference(spm,[status(thm)],[c_0_57,c_0_82]) ).
cnf(c_0_91,plain,
( is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(strict_implies(X1,not(not(X2)))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_83]),c_0_85]) ).
cnf(c_0_92,plain,
is_a_theorem(strict_implies(not(implies(X1,X2)),not(X2))),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_93,plain,
( not(not(X1)) = X1
| ~ is_a_theorem(strict_implies(X1,not(not(X1)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_83]),c_0_85]),c_0_85]) ).
cnf(c_0_94,plain,
not(not(X1)) = or(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_85]),c_0_72]) ).
cnf(c_0_95,plain,
is_a_theorem(strict_implies(not(X1),implies(X2,not(X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_82]) ).
fof(c_0_96,plain,
! [X66,X67,X68] :
( ( ~ axiom_m3
| is_a_theorem(strict_implies(and(and(X66,X67),X68),and(X66,and(X67,X68)))) )
& ( ~ is_a_theorem(strict_implies(and(and(esk26_0,esk27_0),esk28_0),and(esk26_0,and(esk27_0,esk28_0))))
| axiom_m3 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m3])])])]) ).
cnf(c_0_97,plain,
( or(X1,X1) = X1
| ~ is_a_theorem(strict_implies(X1,or(X1,X1))) ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_98,plain,
is_a_theorem(strict_implies(not(X1),or(X2,not(X1)))),
inference(spm,[status(thm)],[c_0_95,c_0_72]) ).
cnf(c_0_99,plain,
( is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3))))
| ~ axiom_m3 ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_100,plain,
axiom_m3,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m3]) ).
cnf(c_0_101,plain,
not(not(not(X1))) = not(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_94]) ).
cnf(c_0_102,plain,
is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_100])]) ).
cnf(c_0_103,plain,
implies(X1,not(not(X2))) = implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_101]),c_0_73]) ).
cnf(c_0_104,plain,
( and(and(X1,X2),X3) = and(X1,and(X2,X3))
| ~ is_a_theorem(strict_implies(and(X1,and(X2,X3)),and(and(X1,X2),X3))) ),
inference(spm,[status(thm)],[c_0_57,c_0_102]) ).
cnf(c_0_105,plain,
is_a_theorem(strict_implies(and(X1,X2),X2)),
inference(spm,[status(thm)],[c_0_76,c_0_67]) ).
cnf(c_0_106,plain,
strict_implies(X1,not(not(X2))) = strict_implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_103]),c_0_71]) ).
cnf(c_0_107,plain,
is_a_theorem(strict_implies(X1,X1)),
inference(spm,[status(thm)],[c_0_76,c_0_85]) ).
cnf(c_0_108,plain,
and(X1,and(X1,X2)) = and(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_85]),c_0_105])]) ).
cnf(c_0_109,plain,
not(not(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_106]),c_0_107])]) ).
cnf(c_0_110,plain,
and(X1,and(X2,X1)) = and(X2,X1),
inference(spm,[status(thm)],[c_0_108,c_0_67]) ).
cnf(c_0_111,plain,
not(implies(X1,X2)) = and(not(X2),X1),
inference(spm,[status(thm)],[c_0_109,c_0_73]) ).
cnf(c_0_112,plain,
implies(and(X1,not(X2)),X2) = implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_110]),c_0_65]) ).
cnf(c_0_113,plain,
and(not(X1),not(X2)) = not(or(X2,X1)),
inference(spm,[status(thm)],[c_0_111,c_0_72]) ).
cnf(c_0_114,plain,
or(not(X1),X2) = implies(X1,X2),
inference(spm,[status(thm)],[c_0_72,c_0_109]) ).
cnf(c_0_115,plain,
is_a_theorem(strict_implies(not(X1),implies(X1,X2))),
inference(spm,[status(thm)],[c_0_86,c_0_65]) ).
cnf(c_0_116,plain,
necessarily(not(not(X1))) = strict_implies(not(X1),X1),
inference(spm,[status(thm)],[c_0_77,c_0_94]) ).
cnf(c_0_117,plain,
or(X1,or(X1,X2)) = or(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_72]),c_0_72]),c_0_78]) ).
cnf(c_0_118,plain,
or(X1,not(X2)) = implies(X2,X1),
inference(spm,[status(thm)],[c_0_78,c_0_114]) ).
cnf(c_0_119,plain,
( is_a_theorem(strict_implies(X1,implies(X2,X3)))
| ~ is_a_theorem(strict_implies(X1,not(X2))) ),
inference(spm,[status(thm)],[c_0_75,c_0_115]) ).
cnf(c_0_120,plain,
strict_implies(not(X1),X1) = necessarily(X1),
inference(rw,[status(thm)],[c_0_116,c_0_109]) ).
cnf(c_0_121,plain,
implies(X1,implies(X1,X2)) = implies(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_117]),c_0_118]),c_0_114]) ).
cnf(c_0_122,plain,
( is_a_theorem(strict_implies(X1,implies(X1,X2)))
| ~ is_a_theorem(necessarily(not(X1))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_109]) ).
cnf(c_0_123,plain,
strict_implies(X1,implies(X1,X2)) = strict_implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_121]),c_0_71]) ).
fof(c_0_124,plain,
! [X94] :
( ~ op_possibly
| possibly(X94) = not(necessarily(not(X94))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_possibly])])]) ).
cnf(c_0_125,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(strict_implies(not(X1),X2))
| ~ is_a_theorem(not(X2)) ),
inference(spm,[status(thm)],[c_0_59,c_0_82]) ).
cnf(c_0_126,plain,
( is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(necessarily(not(X1))) ),
inference(rw,[status(thm)],[c_0_122,c_0_123]) ).
cnf(c_0_127,plain,
( possibly(X1) = not(necessarily(not(X1)))
| ~ op_possibly ),
inference(split_conjunct,[status(thm)],[c_0_124]) ).
cnf(c_0_128,plain,
op_possibly,
inference(split_conjunct,[status(thm)],[s1_0_op_possibly]) ).
cnf(c_0_129,plain,
( is_a_theorem(not(X1))
| ~ is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(not(X2)) ),
inference(spm,[status(thm)],[c_0_125,c_0_109]) ).
cnf(c_0_130,plain,
( is_a_theorem(strict_implies(not(X1),X2))
| ~ is_a_theorem(necessarily(X1)) ),
inference(spm,[status(thm)],[c_0_126,c_0_109]) ).
fof(c_0_131,plain,
! [X92] :
( ( ~ axiom_m10
| is_a_theorem(strict_implies(possibly(X92),necessarily(possibly(X92)))) )
& ( ~ is_a_theorem(strict_implies(possibly(esk39_0),necessarily(possibly(esk39_0))))
| axiom_m10 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m10])])])]) ).
cnf(c_0_132,plain,
not(necessarily(not(X1))) = possibly(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_127,c_0_128])]) ).
cnf(c_0_133,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(not(X2))
| ~ is_a_theorem(necessarily(X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_109]) ).
cnf(c_0_134,plain,
( is_a_theorem(strict_implies(possibly(X1),necessarily(possibly(X1))))
| ~ axiom_m10 ),
inference(split_conjunct,[status(thm)],[c_0_131]) ).
cnf(c_0_135,plain,
axiom_m10,
inference(split_conjunct,[status(thm)],[s1_0_m10_axiom_m10]) ).
cnf(c_0_136,plain,
not(and(X1,possibly(X2))) = implies(X1,necessarily(not(X2))),
inference(spm,[status(thm)],[c_0_65,c_0_132]) ).
cnf(c_0_137,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(necessarily(X1))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_133,c_0_109]) ).
cnf(c_0_138,plain,
is_a_theorem(strict_implies(possibly(X1),necessarily(possibly(X1)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_134,c_0_135])]) ).
cnf(c_0_139,plain,
possibly(and(X1,not(X2))) = not(strict_implies(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_65]),c_0_71]) ).
cnf(c_0_140,plain,
or(X1,necessarily(not(X2))) = implies(possibly(X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_73]),c_0_72]) ).
fof(c_0_141,plain,
! [X40] :
( ( ~ axiom_5
| is_a_theorem(implies(possibly(X40),necessarily(possibly(X40)))) )
& ( ~ is_a_theorem(implies(possibly(esk13_0),necessarily(possibly(esk13_0))))
| axiom_5 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_5])])])]) ).
fof(c_0_142,negated_conjecture,
~ axiom_5,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[km5_axiom_5])]) ).
cnf(c_0_143,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_137,c_0_71]) ).
cnf(c_0_144,plain,
is_a_theorem(strict_implies(not(strict_implies(X1,X2)),necessarily(not(strict_implies(X1,X2))))),
inference(spm,[status(thm)],[c_0_138,c_0_139]) ).
cnf(c_0_145,plain,
strict_implies(not(X1),necessarily(not(X2))) = strict_implies(possibly(X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_140]),c_0_71]) ).
cnf(c_0_146,plain,
( axiom_5
| ~ is_a_theorem(implies(possibly(esk13_0),necessarily(possibly(esk13_0)))) ),
inference(split_conjunct,[status(thm)],[c_0_141]) ).
cnf(c_0_147,negated_conjecture,
~ axiom_5,
inference(split_conjunct,[status(thm)],[c_0_142]) ).
cnf(c_0_148,plain,
( is_a_theorem(implies(possibly(X1),necessarily(possibly(X1))))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_143,c_0_138]) ).
cnf(c_0_149,plain,
is_a_theorem(strict_implies(possibly(strict_implies(X1,X2)),strict_implies(X1,X2))),
inference(rw,[status(thm)],[c_0_144,c_0_145]) ).
cnf(c_0_150,plain,
~ is_a_theorem(implies(possibly(esk13_0),necessarily(possibly(esk13_0)))),
inference(sr,[status(thm)],[c_0_146,c_0_147]) ).
cnf(c_0_151,plain,
is_a_theorem(implies(possibly(X1),necessarily(possibly(X1)))),
inference(spm,[status(thm)],[c_0_148,c_0_149]) ).
cnf(c_0_152,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_150,c_0_151])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL573+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n009.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 01:54:36 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 0.52/0.74 % Version : CSE_E---1.5
% 0.52/0.74 % Problem : theBenchmark.p
% 0.52/0.74 % Proof found
% 0.52/0.74 % SZS status Theorem for theBenchmark.p
% 0.52/0.74 % SZS output start Proof
% See solution above
% 0.52/0.75 % Total time : 0.173000 s
% 0.52/0.75 % SZS output end Proof
% 0.52/0.75 % Total time : 0.177000 s
%------------------------------------------------------------------------------